Bulletin 2017–2018

Home , Columbia Water Center

• VISUALIZ ING ATI G ON A IM LTHY • • A M E O G H S D N E I E 2018 S C L I N U N – E R G S E E • • L S

E B I M C

A U N

L E N I

2017

C T

A O

T FOR N

S A

•

S HUMANITY COLUMBIA

T R

I ENGINEERING

T I

B E

•

C E N

R •

C V

I E E D

• C

E BULLETIN BULLETIN

Columbia | Engineering 2017 –2018 500 West 120th Street 120th West 500 NY 10027 York, New Academic Calendar 2017–2018 The following Academic Calendar was correct and complete when compiled; however, the University reserves the right to revise or amend it, in whole or in part, at any time. Information on the current Academic Calendar may be obtained in the Student Service Center, 205 Kent, 212-854-4330, or visit registrar.columbia.edu.

FALL TERM 2017 SPRING TERM 2018

August January 18–31 Graduate orientation and graduate 3–5, 8–12 Registration by appointment for all classes. department orientations. 8–12 Graduate orientation. 29–Sept. 4 New student orientation program. 9–12 Registration by appointment (graduate). 20–24, Sept. 2 Registration by appointment 15 Birthday of Martin Luther King Jr. (undergraduate). University holiday. 29–31 Registration by appointment (graduate). 16 First day of classes. 16–19, Change of program by appointment. UNDERGRADUATE ADMISSIONS Need more information? September 22–26 Office of Undergraduate Admissions You can find the contact information 1 Last Day to apply for October degrees. 26 Last day to (1) register for academic credit, 212 Hamilton Hall, Mail Code 2807 for the people who know in the 4 Labor Day. University holiday. (2) change course programs, (3) submit written notice of withdrawal from the 1130 Amsterdam Avenue Columbia University Resource List 5 First day of classes. 5–8, 11–15 Change of program by appointment. spring term to the Dean of Student Affairs New York, NY 10027 on pages 256–259 or visit the Columbia Engineering 15 Last day to (1) register for academic credit, for full refund of tuition and special fees. Phone: 212-854-2522 website, engineering.columbia.edu. (2) change course programs, (3) submit No adjustment of fees for individual Fax: 212-854-3393 written notice of withdrawal from the fall courses dropped after this date. Last day For the most current information, visit our online Email: [email protected] term to the Dean of Student Affairs for to confirm, update, or request a waiver bulletin at bulletin.engineering.columbia.edu. undergrad.admissions.columbia.edu full refund of tuition and special fees. No from the Student Medical Insurance Plan. adjustment of fees for individual courses dropped after this date. February GRADUATE ADMISSIONS Photography: 30 Last day to confirm, update, or equestr 4 February degrees conferred. Graduate Admissions, Financial Aid, and Student Affairs New technology developed at Columbia Engineering a waiver from the Student Medical 530 S. W. Mudd, Mail Code 4708 is providing 3D views of the living brain. (Image Insurance Plan. March 500 West 120th Street courtesy of Elizabeth Hillman) 5 Midterm date. New York, NY 10027 October 12–16 Spring holiday. Phone: 212-854-6438 Superimposed over this image is the emblem of 18 October degrees conferred. 22 Last day to drop Engineering courses 19 Midterm date. without academic penalty. Last day Fax: 212-854-5900 the School’s new vision, Columbia Engineering for to change grading option. Email: [email protected] Humanity. November gradengineering.columbia.edu 1 Last day to apply for February degrees. April 6 Academic holiday. 18–20 Registration by appointment for fall 2018. FINANCIAL AID 7 Election Day. University holiday. 30 Last day of classes. Office of Financial Aid and Educational Financing 16–17 Registration by appointment for spring 2018. 20–22 Registration by appointment (graduate). May Office: 618 Lerner Hall 16 Last day to drop Engineering courses 1 Last day for continuing students to apply Mailing: 100 Hamilton Hall, Mail Code 2802 without academic penalty. Last day to for financial aid for the 2018–2019 1130 Amsterdam Avenue change a grading option. academic year. New York, NY 10027 23–24 Thanksgiving holiday. 1–3 Study days. Phone: 212-854-3711 4–11 Final examinations. Fax: 212-854-5353 December 13 Baccalaureate Service. Email: [email protected] 1 Last day to apply for May degrees. 14 Engineering Class Day. cc-seas.financialaid.columbia.edu 11 Last day of classes. 16 2018 University Commencement. 12–14 Study days. 15–22 Final examinations. 23–Jan. 15 Winter holiday. BULLETIN 2017 – 2018 Mission The mission of The Fu Foundation School of Engineering and Applied Science is to expand knowledge and advance technology through research, while educating students to become leaders informed by an engineering foundation. Enriched with the intellectual resources of a global university in the City of New York, we push forward disciplinary frontiers, confront complex issues, and engineer innovative solutions to address the grand challenges of our time. We create a collaborative environment that embraces interdisciplinary thought, integrates entrepreneurship, cultural awareness, and social responsibility, and fosters the translation of ideas into practical innovations.

Our mission can be encapsulated as "Transcending Disciplines, Education Leaders, Transforming Lives."

ENGINEERING 2017–2018 A MESSAGE FROM THE DEAN

elcome to Columbia University’s This vision highlights the innovative and Fu Foundation School of interdisciplinary work that our faculty and W Engineering and Applied Science students are engaged in to create a more (SEAS). As students here, you are among the sustainable, healthy, secure, connected, and very best and brightest of your generation. creative world. Together with a talented group of students This work is conducted in collaboration from around the world, you are embarking with our world-class sister schools in on a course of study that will enable you medicine, public health, architecture, to become the next generation of leaders. science, business, policy, the social Engineering today is a foundational degree sciences, social work, journalism, even the that prepares you for a wealth of pursuits, arts and humanities. We also benefit from the and your education here will serve you not resources of leading institutes such as the only in fields of engineering and applied Zuckerman Mind Brain Behavior Institute, the science, but in other disciplines as well. Data Science Institute, The Earth Institute, You are joining a vibrant and intellectually the Precision Medicine Initiative, and the challenging community, with a long history of Columbia Nano Initiative. scientific and engineering breakthroughs that Columbia Engineering is an exciting and have impacted our world. From the School’s stimulating community. I encourage you beginning in 1864 through today, the work to take full advantage of the exceptional of faculty, alumni, and students of Columbia opportunities for learning and advancement Engineering has pushed disciplinary frontiers that await you here. to create, invent, and innovate devices, materials, and processes to make life better. With best wishes for the academic year, Our first dean, Charles Frederick Chandler, served as president of New York City’s Metropolitan Board of Health. In this role, he crusaded to ensure the purity of food and drugs, the safety of milk, the availability of clean water in the city, and the introduction of building codes. Today, our faculty and Mary C. Boyce students continue to develop innovative Dean of Engineering solutions to the world’s most challenging Morris A. and Alma Schapiro Professor problems, and with entrepreneurial energy, translate their ideas into real-world solutions at an ever faster pace. You are coming to Columbia Engineering at an extraordinary moment. In the spring, we unveiled a new strategic vision for the School—Columbia Engineering for Humanity.

ENGINEERING 2017–2018 TABLE OF CONTENTS

About the School and 1 Faculty and Administration 35 Campus and Student Life 213 University CAMPUS LIFE 214 HISTORY OF THE SCHOOL 2 Departments and Academic 47 STUDENT SERVICES 219 RESOURCES AND FACILITIES 5 Programs KEY TO COURSE LISTINGS 48 Scholarships, Fellowships, 223 Undergraduate Studies 9 APPLIED PHYSICS AND 50 Awards, and Prizes THE UNDERGRADUATE 10 APPLIED MATHEMATICS Endowed Scholarships and Grants 224 PROGRAMS Endowed Fellowships 229 Policy on Degree Requirements 10 BIOMEDICAL ENGINEERING 64 Outside Fellowship 232 The First-Year/Sophomore Program 10 CHEMICAL ENGINEERING 77 Medals and Prizes 232 Study Abroad 13 Residence Hall Scholarships 236 Combined Plan Programs 15 CIVIL ENGINEERING AND 87 The Junior-Senior Programs 16 ENGINEERING MECHANICS University and School 237 Programs in Preparation for 17 Policies, Procedures, and Other Professions COMPUTER ENGINEERING 100 Regulations Joint Programs 18 PROGRAM Undergraduate Admissions 19 ACADEMIC PROCEDURES 238 COMPUTER SCIENCE 105 AND STANDARDS UNDERGRADUATE TUITION, 20 EARTH AND ENVIRONMENTAL 119 FEES, AND PAYMENTS ACADEMIC STANDING 242 ENGINEERING FINANCIAL AID FOR 22 POLICY ON CONDUCT AND 245 ELECTRICAL ENGINEERING 133 UNDERGRADUATE STUDY DISCIPLINE INDUSTRIAL ENGINEERING 153 ESSENTIAL POLICIES FOR THE Graduate Studies 23 AND OPERATIONS RESEARCH COLUMBIA COMMUNITY 248 THE GRADUATE PROGRAMS 24 MATERIALS SCIENCE AND 171 OFFICIAL UNIVERSITY The Master of Science Degree 24 ENGINEERING PROGRAM Doctoral Degrees: Eng.Sc.D. 25 REGULATIONS 249 and Ph.D. MECHANICAL ENGINEERING 181 STUDENT GRIEVANCES, 252 Nondegree Students 26 ACADEMIC CONCERNS, AND Undergraduate Minors 197 COLUMBIA VIDEO NETWORK 27 COMPLAINTS

GRADUATE ADMISSIONS 28 Interdisciplinary Courses 203 Directory of University 255 and Courses in Other GRADUATE TUITION, FEES, 30 Resources Divisions of the University AND PAYMENTS COLUMBIA UNIVERSITY 256 INTERDISCIPLINARY 204 RESOURCE LIST FINANCIAL AID FOR GRADUATE 32 ENGINEERING COURSES STUDY MAPS 260 Financing Graduate Education 32 COURSES IN OTHER DIVISIONS 205 INDEX 262 Instructions for Financial Aid 32 OF THE UNIVERSITY Applicants Biological Sciences 205 Academic Calendar (see inside Graduate School Departmental 32 Business 205 back cover) Funding Chemistry 205 Alternative Funding Sources 33 Earth and Environmental Sciences 207 Other Financial Aid—Federal 33 Humanities and Social Sciences 208 and Private Programs Mathematics 209 Veteran's Benefits 33 Physics 209 Employment 33 Statistics 211 Contact Information 34 About the School and University 2 HISTORY OF THE SCHOOL

A COLONIAL CHARTER mark both at home and abroad. surface chemistry led to a Nobel Prize Since its founding in 1754, as King’s Working around the globe, William in chemistry in 1932. College, Columbia University has Barclay Parsons, Class of 1882, was But early work on radio vacuum always been an institution both of and an engineer on the Chinese railway tubes was not restricted to private for the City of New York. And it has and the Cape Cod and Panama industry. Working with Pupin, an always been an institution of and for Canals. Most importantly for New York, engineering student named Edwin engineers. In its original charter, the he was chief engineer of the city’s first Howard Armstrong was conducting college stated that it would teach, subway. Opened in 1904, the subway’s experiments with the Audion tube among other things, “the arts of electric cars took passengers from in the basement of Philosophy Hall Number and Measuring, of Surveying City Hall to Brooklyn, the Bronx, and when he discovered how to amplify and Navigation, . . . the knowledge the newly renamed and relocated radio signals through regenerative of . . . Meteors, Stones, Mines and Columbia University in Morningside circuits. Armstrong, Class of 1913, Minerals, Plants and Animals, and Heights. was stationed in France during the everything useful for the Comfort, the First World War, where he invented the superheterodyne circuit to tune Convenience and Elegance of Life.” A MODERN SCHOOL in and detect the frequencies of FOR MODERN TIMES enemy aircraft ignition systems. After EARLY ENGINEERS The School of Mines became the the war, Armstrong improved his School of Mines, Engineering, and An early and influential graduate from method of frequency modulation (FM), Chemistry in 1896, and its professors— the School was John Stevens, Class of and by 1931, had both eliminated now called the Faculty of Engineering 1768. Instrumental in the establishment the static and improved the fidelity and Applied Science—included of U.S. patent law, Stevens procured of radio broadcasting forever. The Michael Idvorsky Pupin, a graduate many patents in early steamboat historic significance of Armstrong’s of the Columbia College Class of technology, operated the first steam contributions was recognized by the 1883. As a professor at Columbia, ferry between New York and New U.S. government when the Philosophy Pupin did pioneering work in carrier- Jersey, received the first railroad charter Hall laboratory was designated a wave detection and current analysis, in the U.S., built a pioneer locomotive, National Historic Landmark in 2003. with important applications in radio and amassed a fortune, which allowed As the United States evolved into a broadcasting. He is perhaps most his sons to found the Stevens Institute major twentieth-century political power, famous for having invented the “Pupin of Technology. the University continued to build onto coil,” which extended the range of long- its undergraduate curriculum the distance telephones. THE GILDED AGE broad range of influential graduate An early student of Pupin’s was and professional schools that define it As the city grew, so did the School. Irving Langmuir. Langmuir, Class of today. Renamed once again in 1926, King’s College was rechartered 1903, enjoyed a long career at the the School of Engineering prepared as Columbia College in 1784, and General Electric research laboratory. students for careers not only as relocated from the Wall Street area to There he invented a gas-filled tungsten engineers of nuclear-age technology, what is now Midtown in 1857. Students lamp, contributed to the development but as leaders engaged with the far- began entering the new School of of the radio vacuum tube, and reaching political implications of that Mines in 1864. Trained in mining, extended Gilbert Lewis’s work on technology as well. mineralogy, and engineering, Columbia electron bonding and atomic structure. After receiving a master’s degree graduates continued to make their His research in monolayering and from the School in 1929, Admiral

ENGINEERING 22017–2018013–2014 3

Hyman George Rickover served during among and between other schools NEW RESEARCH FRONTIERS the Second World War as head of the and departments within the University. Columbia’s technology transfer office, electrical section of the Navy’s Bureau The School’s newest department, Columbia Technology Ventures, of Ships. A proponent of nuclear sea Biomedical Engineering, with close works with faculty inventors to power, Rickover directed the planning ties to the Medical School, is but one commercialize ideas and brings in and construction of the world’s first example. Interdisciplinary centers millions in licensing revenue annually. nuclear submarine, the 300-foot-long are the norm, with cross-disciplinary Columbia Engineering faculty have Nautilus, launched in 1954. research going on in biomedical been instrumental in developing some imaging, environmental chemistry, of the most successful inventions materials science, nanotechnology, TECHNOLOGY AND BEYOND in consumer electronics, as well digital, and new media technologies. as establishing many of the widely Today, The Fu Foundation School of The School and its departments accepted global standards for storage Engineering and Applied Science, have links to the Departments of and transmission of high-quality audio as it was named in 1997, continues Physics, Chemistry, Earth Science, and video data. Columbia is the to provide leadership for scientific and Mathematics, as well as the only university actively participating and educational advances. Even College of Physicians and Surgeons, in a broad range of standards- Joseph Engelberger, Class of 1946, the Graduate School of Journalism, based patent pools, including AVC the father of modern robotics, could Lamont-Doherty Earth Observatory, (Advanced Video Coding), the world not have anticipated the revolutionary The Earth Institute, Teachers College, standard for audio/video compression speed with which cumbersome and Columbia Business School, and the that is now one of the most commonly expensive “big science” computers Graduate School of Architecture, used HD formats and most commonly would shrink to the size of a wallet. Planning and Preservation. The used in streaming media; and ATSC, a No one could have imagined transforming gift of The Fu Foundation standard developed by the Advanced the explosive growth of technology has catapulted the School into the Television Systems Committee for and its interdisciplinary impact. The forefront of collaborative research and digital television transmission. It is now Engineering School is in a unique teaching and has given students the the U.S. standard for recording and position to take advantage of the opportunity to work with prize-winning retrieval of data and HD audio-visual research facilities and talents housed academicians, including Nobel media. In addition to the standards, at Columbia to form relationships laureates, from many disciplines. Columbia Engineering faculty have

ENGINEERING 2017–2018 4 patents in areas as diverse as modular Competition, Design Challenges, A FORWARD-LOOKING cameras, waste management, a Hackathons, and the Ignition Grants TRADITION search engine that matches facial program, which funds ventures started But, for all its change, there is still features, and even methods to combat by current students. a continuous educational thread virtual reality sickness. The School's Translational Fellows that remains the same. Columbia Increasingly, the inventions Program (TFP) supports 20 percent Engineering still remains an emerging from Columbia Engineering of the salary of selected SEAS institution of manageable size within are developed in collaboration with postdoctoral researchers and research a great university. Committed to the biomedical and other researchers, scientists for one year, providing educational philosophy that a broad, expanding the potential applications them with the opportunity to pursue rigorous exposure to the liberal arts for their important work. Programs commercialization of a technology that provides the surest chart with which such as the Columbia-Coulter originated in their research work here an engineer can navigate the future, Translational Research Partnership, at the Engineering School. Another all undergraduates must complete a PowerBridgeNY, the NYC Media exciting way the School fosters modified but equally rigorous version Lab Combine program, and the entrepreneurship is with its Coulter of Columbia College’s celebrated Integrated Photonics Manufacturing Program. A major goal of the program Core Curriculum. It is these selected Innovation Hub in Rochester, NY, are is to educate researchers, clinicians, courses in contemporary civilization in strengthening interdisciplinary capacity and students about the many aspects the West and other global cultures that and fostering an entrepreneurial and involved in commercializing biomedical best prepare a student for advanced inventive energy within the School. innovation. coursework; a wide range of eventual Some of these programs have helped Entrepreneurship remains an professions; and a continuing, life-long prepare ideas for commercialization, important central educational theme pursuit of knowledge, understanding, including personalized robotics for at Columbia Engineering. The School and social perspective. It is also use in physical rehabilitation and an offers a range of programs and a these Core courses that most closely implantable device that acts as a 15-credit, interdisciplinary minor in tie today’s student to the alumni of minimally-invasive glucose sensor for entrepreneurship made up of both centuries past. Through a shared diabetic patients. Engineering and Business School exposure to the nontechnical areas, courses. The School also provides a all Columbia Engineering students— four-year entrepreneurship experience ENTREPRENEURSHIP past, present, and future—gain the for all interested Columbia Engineering humanistic tools needed to build lives Another exciting area at Columbia students, regardless of major. not solely as technical innovators, but Engineering is entrepreneurship. In And for alumni, entrepreneurial as social and political ones as well. 2016, the School’s faculty and students support continues. The Columbia generated 120 inventions, almost 40 Startup Lab, a co-working facility licenses and options, and four startup located in SoHo, provides subsidized companies in all kinds of fields, from space for 71 Columbia alumni biomedical to cleantech to high-tech. entrepreneurs to house and nurture Throughout the academic year, their fledgling ventures. The Lab is the the School hosts many activities result of a unique partnership between and networking events to support its the deans of Columbia College and the active startup community, including Schools of Business, Engineering, Law, the Columbia Engineering Fast Pitch and International and Public Affairs. Competition, Columbia Venture

ENGINEERING 2017–2018 RESOURCES AND FACILITIES 5

A COLLEGE WITHIN THE Broadway; food from around the world; THE UNIVERSITY AT LARGE UNIVERSITY and every sport imaginable, New York Columbia University occupies A unique educational opportunity, The is the crossroads of the world. three major campuses, as well as Fu Foundation School of Engineering New York is a major player in high- additional special-purpose facilities and Applied Science at Columbia tech research and development, where throughout the area. Besides the University offers programs to both Fortune 500 companies traded on Wall main campus located on the Upper undergraduate and graduate students Street seek partnerships with high- West Side in Morningside Heights is who undertake a course of study tech startups in Tribeca and Brooklyn. Manhattanville, the newest addition to leading to the bachelor’s, master’s, As part of the research community Columbia University. This open and or doctoral degree in engineering themselves, Columbia students have environmentally sustainable campus and applied science. Combining exceptional opportunities for contact will grow over the next decade to the advantages of a small college with industry both on and off campus. encompass more than 17 acres. with the extensive resources of a Senior representatives of these Further uptown in Washington Heights major research university, students at companies often visit Columbia to is the Columbia University Medical Columbia Engineering pursue their lecture as adjunct faculty members or Center (CUMC), which includes academic interests under the guidance as guest speakers, and undergraduate Columbia’s College of Physicians of outstanding senior faculty members and graduate students frequently and Surgeons, the Mailman School who teach both undergraduate and undertake research or internships of Public Health, the New York graduate level courses. Encouraged with these and other companies, State Psychiatric Institute, College by the faculty to undertake research oftentimes leading to offers of full-time of Dental Medicine, and School of at all levels, students at the School employment after graduation. Nursing. Columbia Medical Center receive the kind of personal attention In addition to its ties to private is the world’s first academic medical that only Columbia’s exceptionally high industry, Columbia also has a center, and opened in 1928 when faculty-student ratio affords. historically close relationship with the Columbia’s health-related schools and public sector of New York, stretching Presbyterian Hospital (now NewYork- back to the eighteenth century. No Presbyterian Hospital) moved to the THE NEW YORK ADVANTAGE other city in the world offers as many Washington Heights location. Columbia Besides the faculty, the single greatest impressive examples of the built Engineering’s Biomedical Engineering facility at a Columbia student’s disposal environment—the world’s most famous Department has offices on both the is without doubt the City of New York. collection of skyscrapers, long-span Morningside campus and CUMC. Within easy reach by walking, bus, bridges, road and railroad tunnels, Beyond its schools and programs, subway, or taxi, New York’s broad and one of the world’s largest subway the measure of Columbia’s true range of social, cultural, and business and water supply systems. Involved breadth and depth must take into communities offer an unparalleled in all aspects of the city’s growth account its seventy-odd internationally opportunity for students to expand their and capital improvements over the recognized centers and institutions for horizons or deepen their understanding years, Columbia engineers have been specialized research. These centers of almost any human endeavor responsible for the design, analysis, study everything from human rights to imaginable. With art from small Chelsea and maintenance of New York’s molecular recognition and hold close galleries to major museums; music from enormous infrastructure of municipal affiliations with Teachers College, Harlem jazz clubs to the Metropolitan services and communications links, Barnard College, the Juilliard School, Opera; theater from performance as well as its great buildings, bridges, and both the Jewish and Union art in the East Village to musicals on tunnels, and monuments.

ENGINEERING 2017–2018 6 Theological Seminaries. Columbia also members and will serve as a thriving to support nano research at the maintains major off-campus facilities hub where faculty and students from Engineering School include a state- such as the Lamont-Doherty Earth across Columbia, scholars from of-the-art clean room in the Schapiro Observatory in Palisades, NY, and around the world, and members of Center for Engineering and Physical the Nevis Laboratories in Irvington, the local community come together Science Research (CEPSR) and a NY. Involved in many cooperative in the search for new insights about Transmission Electron Microscope ventures, Columbia also conducts ourselves, exploring the complexities (TEM) Laboratory on the first floor of ongoing research at such facilities as of the human mind and brain. The Havemeyer. Brookhaven National Laboratory in Institute will also house a community Among this group of advanced Upton, NY, and the NASA Goddard wellness center and an education research opportunities is the Columbia Institute for Space Studies located just lab to give hands-on experience in Data Science Institute. Founded in off the Morningside campus. science to local students. 2012 by Columbia Engineering, the Data Science Institute is a University- wide resource that spans nine schools, THE MORNINGSIDE HEIGHTS THE FU FOUNDATION SCHOOL including Journalism, the Graduate CAMPUS OF ENGINEERING AND APPLIED School of Arts and Sciences, and The Fu Foundation School of SCIENCE Columbia University Medical Center. Engineering and Applied Science is The Fu Foundation School of The mission of the Data Science located on Columbia’s Morningside Engineering and Applied Science Institute is to train data science campus. One of the handsomest urban occupies four laboratory and innovators and develop ideas for the institutions in the country, the 13.1 classroom buildings at the north end of social good. million gross square feet (gsf) of the the campus, including the Northwest Details about specific programs’ Morningside campus comprise more Corner Science and Engineering laboratories and equipment can be than 200 buildings of housing; off- Building, an interdisciplinary found in the sections describing those campus apartments and commercial teaching and research building on programs. buildings; recreation and research the Morningside campus. It was facilities; centers for the humanities designed by the world-renowned Columbia Engineering Computing and social and pure sciences; and architect Jose Rafael Moneo to serve Facilities professional schools in architecture, as a physical and intellectual bridge, The Botwinick Multimedia Learning business, the fine arts, journalism, law, linking laboratories and maximizing Laboratory at Columbia University and many other fields. the ready sharing and exchange of has redefined the way engineers are ideas, resources, and information. educated here. The building enables researchers MANHATTANVILLE CAMPUS Designed with both education and across the University to work together From Broadway and 125th Street interaction in mind, the lab provides to create new areas of knowledge, West to a revitalized Hudson River students and instructors with: in fields where the biological, waterfront, Columbia's 17-acre physical, and digital worlds fuse. This Manhattanville campus will be a • 48 desktops pandisciplinary frontier is the nexus welcoming environment of publicly • A full set of professional-grade at which our advances will provide accessible open space, tree-lined engineering software tools innovative solutions to some of modern streets, neighborhood-friendly retail, • A collaborative classroom society’s most challenging problems in and innovative academic buildings learning environment to help a wide range of sectors, from health to that invite community engagement. students engage in real-world cybersecurity, from smart infrastructure The Jerome L. Greene Science interactions with community clients, to the environment. Center, home to Columbia's Mortimer Engineering faculty, and professional Supporting multiple programs B. Zuckerman Mind Brain Behavior practitioners. of study, the School's facilities are Institute, and the Lenfest Center specifically designed and equipped for the Arts opened in spring 2017 The lab is utilized in some of the to meet the laboratory and research and will be joined by the University School’s introductory first-year needs of both undergraduate and Forum, a venue for hosting academic engineering projects, as well as graduate students. The School is also conferences, meetings, and symposia; advanced classes in modeling and the site of an almost overwhelming and Columbia Business School by animation, technology and society, and array of basic and advanced research 2021. These spaces will house cutting- entrepreneurship. installations, such as the Columbia edge research and teaching in brain Genome Center and the Columbia science, an art gallery, screening Nano Initiative, established to serve The Makerspace room, and performance spaces, as the hub for multidisciplinary and Columbia Engineering’s Makerspace and space for active community collaborative research programs in provides students with a dedicated engagement. The Zuckerman Mind nanoscale science and engineering. place to collaborate, learn, explore, Brain Behavior Institute includes Shared facilities and equipment experiment, and create prototypes. several Columbia Engineering faculty Students can utilize the space to work

ENGINEERING 2017–2018 on a variety of innovative projects, of technical support services via the speed, high-volume printers are 7 including independent or group design CUIT Helpdesk. located in CUIT computer labs, projects, product development, and CUIT services include the following: libraries, residence halls, and other new venture plans. Located on the computer clusters and electronic twelfth floor of the Mudd Building, • Email accounts: CUIT provides a classrooms. this facility fosters student creativity web-based program for accessing • Computer security is extremely by bringing together the workspace Columbia email. It provides a secure important at Columbia and CUIT and tools for computer-aided design, and convenient way to send and provides several resources online, physical prototyping, fabric arts, receive mail from anywhere, using including links to download antivirus woodworking, electronics, and any web browser. and anti-spyware software. The site software. The School has plans under • Computer account IDs provide also provides information on how way to expand the Makerspace in the access to Columbia’s secure online to protect your system, data, and near future. information resources, campus privacy when working online. computer labs, and printing on CUIT • Digital Social Science Center, run Carleton Commons printers. All Columbia students, jointly by CUIT and the Libraries, Located on the fourth floor (campus faculty, and staff are assigned an ID provides computing support for level) of the Mudd Building, Carleton account (called University Network researchers with data-intensive Commons and Blue Java Café ID or UNI). applications, including statistical comprise 3,200 square feet with seating • Columbia’s website provides software, and finding and selecting for 160 and areas for casual meetings, access to hundreds of online appropriate data. individual and group work, and quiet services and resources, including • Telephone and cable TV service study. Carleton Commons gives extensive academic, scholarly, and is available to students living in students a dedicated and comfortable administrative resources, myriad University residence halls. space to gather, relax between classes, library catalogs and references, the Directory of Classes, registration or meet and work with one another COLUMBIA UNIVERSITY information, campus publications, on problem sets or projects. The LIBRARIES new design also enables flexible and and events listings. Phone: 212-851-2950 reconfigurable use of the space for • Technical support is available through Email: [email protected] larger gatherings and special events. the CUIT Help Desk, which provides library.columbia.edu technical assistance to students on the Morningside campus online, by Columbia University Libraries (CUL) is CENTRAL COMPUTING phone, or in person. (See beginning one of the top five academic research RESOURCES of this section for hours and contact library systems in North America. Columbia University Information information.) The collections include 11.9 million Technology (CUIT) • Canvas is the University course volumes, 168,000 current serial Help Desk Support Center management system. It allows subscriptions, as well as extensive 202 Philosophy Hall instructors to easily develop and electronic resources, manuscripts, rare Monday–Friday: 10:00 a.m.–6:00 p.m. maintain course websites, distribute books, microforms, maps, graphic and class materials, link to online audio-visual materials. The services Phone: 212-854-1919 reserves, administer quizzes and and collections are organized into Monday–Thursday: 8:00 a.m.–11:00 tests, communicate with students, 19 libraries and various academic p.m. and promote online discussions. technology centers. The Libraries Friday: 8:00 a.m.–7:00 p.m. • Electronic classrooms are equipped employ more than 550 professional Saturday: 10:00 a.m.–6:00 p.m. with multimedia capabilities such as and support staff. The website of the Sunday: 3:00 p.m.–11:00 p.m. computer and projection systems, Libraries is the gateway to its services Email: [email protected] DVD and CD-ROM players, VCRs, and resources. cuit.columbia.edu/support and audio systems. The Science and Engineering • Public computer kiosks are available Library, located in 401 Northwest CUIT provides Columbia University in various locations around the Corner Building, focuses on research students, faculty, and staff with Morningside campus for accessing support for the fields of astronomy, myriad central computing and Columbia’s web resources and email. biology, chemistry, engineering, communications services, including • Computer labs and clusters provide physics, and psychology, as well as Columbia’s wireless and high-speed students, faculty, and researchers providing a collaborative environment campus Ethernet network, available with access to a range of software. supporting rapidly expanding to all students in residence hall Some locations have consultants to interdisciplinary science and rooms. CUIT also manages an array provide lab help. engineering research. The Science of computer labs, terminal clusters, • Printing facilities are available and Engineering Library is home to the ColumbiaNet kiosk stations, electronic throughout the Morningside campus Digital Science Center, where high-end classrooms, and provides a variety and Barnard College. These high-

ENGINEERING 2017–2018 8 computers are especially equipped CCE provides career development at East Campus or via our website with software and hardware to opportunities for students beginning at careereducation.columbia.edu to support teaching, learning, research, in their first year at Columbia, offering learn more about our programs and and innovation in the science and externships, internships, résumé and resources. engineering disciplines. Group interviewing preparation, site visits to study, individual carrels, and staff employers, career fairs, alumni-student INTERNATIONAL STUDENTS AND consultation spaces along with printing networking events, and individual SCHOLARS OFFICE (ISSO) and scanning facilities are included in counseling. International House North this library, which offers spectacular Highlights among career fairs 524 Riverside Drive, Ground Floor views of the Columbia campus and include the Engineering Career Fair Morningside Heights. in the fall and the Startup Career Phone: 212-854-3587 Online, CUL provides access to Fair in the spring. Additionally, CCE Email: [email protected] extensive collections of electronic partners with Columbia Engineering isso.columbia.edu journals, ebooks, handbooks, on specialized networking events, standards, patents, and society employer information sessions, and Columbia University, continuing publications. Databases such as workshops tailored to department and its tradition as a preeminent world Compendex, INSPEC, Scopus, and student club needs. center of learning, welcomes more Web of Science help patrons to CCE also developed formal than 15,000 students, postgraduate pinpoint relevant engineering and externship and internship and interns, researchers, professors and science research. professional development programs accompanying family members from in partnership with alumni and more than 160 countries. employers, including the Science CENTER FOR CAREER The ISSO serves the immigration Technology Engineering Program, the EDUCATION and documentation related needs of Virtual Internship Program, the Startup East Campus, Lower Level students and scholars at Columbia. Internship Program, Columbia Arts Mailing: 2960 Broadway, MC 5727 They issue Certificates of Eligibility Experience, and the Kenneth Cole Delivery: 70–74 Morningside Drive (form I-20/DS-2019) that admitted Community Action Program. Through New York, NY 10027 students need to apply for F and J our Columbia Experience Overseas student visas. program, we offer summer internships Phone: 212-854-5609 After students arrive on campus, in London, Hong Kong, Beijing, Fax: 212-854-5640 ISSO advisers take part in their Shanghai, Singapore, Mumbai, Seoul, Email: [email protected] school or department’s new student and Amman. Alumni mentors are careereducation.columbia.edu orientation program by providing an assigned to all students participating immigration information session. in these formal internship programs. The Columbia University Center Throughout the year, the ISSO CCE also administers the Work for Career Education (CCE) helps monitors federal regulations relevant to Exemption Program, the Columbia students and alumni develop the international students and broadcasts Engineering Internship Fund, and key competencies to make informed timely alerts and updates through the Startup Internship Fund. Some decisions and take the necessary the ISSO website and ISSOnews of these programs are open to all steps to achieve their career goals. messages sent to students' Columbia students while others are open only CCE establishes connections email addresses. to undergraduate students. Connect and facilitates interaction among The ISSO provides: with the CCE to learn about eligibility undergraduate students, graduate • travel signatures on I-20s for requirements. students, alumni, and employers students who will travel and return CCE also maintains a dossier to generate opportunities that help from a trip abroad during their service, managed by Interfolio, for students pursue their personal and program graduate students and alumni. A professional career objectives. • employment-related workshops and dossier is typically used in applying CCE encourages students and webinars for teaching positions at either the alumni to (1) visit us at the Career • documentation needed for Social secondary school or the college Center; (2) create a profile in Security number applications level and for graduate/ professional LionSHARE, CCE's job and internship • information sessions by nationally school and fellowship applications. database; and (3) review our website recognized immigration attorneys Undergraduate students or alumni to access a wide range of services on employment-based visas after with undergraduate degrees from and resources. CCE develops student status Columbia Engineering work with the relationships with employers to • tax workshops (February–April) James H. and Christine Turk Berick connect students with internships, full- • tax preparation software for Center for Student Advising for dossier time, part-time, and temporary on- and international students who are management. off-campus employment opportunities nonresidents for federal tax purposes We welcome your visit to the throughout the year. In addition, Center for Career Education in person

ENGINEERING 2017–2018 Undergraduate Studies 10 THE UNDERGRADUATE PROGRAMS

he undergraduate programs at While pursuing their own interests, Requirements for the major or minor Columbia Engineering not only undergraduate students are are in accordance with the bulletin T are academically exciting and encouraged to participate in a broad during the year in which the student technically innovative but also lead range of ongoing faculty research declares the major or minor. into a wide range of career paths for projects encompassed by the Student the educated citizen of the twenty-first Research Program. Students can THE FIRST-YEAR/SOPHOMORE century. Whether you want to become a apply for available research positions PROGRAM professional engineer, work in industry or in Columbia Labs through the website Students entering Columbia government, or plan to pursue a career at studentresearch.engineering. Engineering are encouraged to in the physical and social sciences, columbia.edu. consider the wide range of possibilities medicine, law, business, or education, In addition to in-depth exploration open to them, both academically and Columbia Engineering will provide you of engineering and applied science, professionally. To this end, the first with an unparalleled education. Columbia Engineering undergraduates and second years of the four-year The School firmly believes explore the humanities and social undergraduate program comprise that students gain the most when sciences with Columbia College approximately 66 semester points of engineering is brought up front, early students through intellectually credit that expose students to a cross- in the four-year curriculum. Therefore, challenging Core Curriculum courses fertilization of ideas from different each first-year student takes the Art taught by the Faculty of Arts and disciplines within the University. The of Engineering, which addresses the Sciences. These courses in art, sequence of study proceeds from fundamental concepts of math and literature, music, major cultures, and an engagement with engineering science in an engineering context, economics, among others, provide and scientific fundamentals, along as well as nontechnical issues in students with a broad, intellectually with humanities and social sciences, professional engineering practice such disciplined, cultural perspective on the toward an increasingly focused as ethics and project management. times they live in and the work they do. training in the third and fourth years Students in the Art of Engineering designed to give students mastery of choose a half-semester, hands-on POLICY ON DEGREE certain principles and arts central to project in one of the School’s nine REQUIREMENTS engineering and applied science. undergraduate engineering disciplines, The Committee on Instruction and followed by a half-semester general faculty of The Fu Foundation School project that changes each year. Liberal Arts Core for of Engineering and Applied Science Depending on the project chosen, Columbia Engineering Students: review degree requirements and students will solder, 3D print, laser 27-Point Nontechnical Requirement curricula matters each year, and cut, simulate, design websites, and This requirement provides a broad the bulletin reflects these faculty much more. These skills are further liberal arts component that enhances recommendations and curricular developed as students progress the Engineering professional curriculum changes in its yearly reprinting. School toward their senior year projects. Since to help students meet the challenges policy requires students to fulfill all the fall of 2014, Columbia Engineering of the twenty-first century. Our general degree requirements as stated students have been able to utilize students are destined to be leaders in the bulletin of the first year of their the School’s brand new Makerspace, in their professions and will require matriculation into the School. Students a collaborative environment where sophisticated communication, planning, declare their major during the first students can learn, explore, and management skills. The Committee semester of their sophomore year. experiment, and create prototypes. on Instruction established the School’s

ENGINEERING 2017–2018 nontechnical requirement so that may not take BC1003: Introduction to EARTH AND ENVIRONMENTAL SCIENCES: 11 students would learn perspectives and economic reasoning as a substitute for No courses principles of the humanities and social ECON UN1105. (4 points) EAST ASIAN LANGUAGES AND CULTURE: sciences as part of a well-rounded and All courses multiperspective education. Through B. Elective Nontechnical Courses discussion, debate, and writing, (9–11 points of credit) ECOLOGY, EVOLUTION, AND students improve their abilities to The following course listing by ENVIRONMENTAL BIOLOGY: No courses engage in ethical, analytic, discursive, department specifies the Columbia except EEEB GU4321 or GU4700 and imaginative thinking that will prove College, Barnard, or Columbia ECONOMICS: All courses except indispensable later in life. Engineering courses that either fulfill or do not fulfill the nontechnical UN3025 Financial economics • Engineering students must take 16 requirement. UN3211 Intermediate microeconomics to 18 points of credit of required (Professional, workshop, lab, UN3213 Intermediate macroeconomics courses in list A and 9 to 11 elective project, scientific, studio, music UN3412 Introduction to econometrics GU4020 Economics of uncertainty and points chosen from the approved instruction, and master’s-level information courses in list B. The total combined professional courses do not satisfy the GU4211 Advanced microeconomics number of nontechnical points (from 27-point nontechnical requirement.) lists A and B, below) must add GU4213 Advanced macroeconomics up to at least 27. Neither list can AFRICAN-AMERICAN STUDIES: All courses GU4251 Industrial organization GU4280 Corporate finance be modified by advising deans or AMERICAN STUDIES: All courses faculty advisers. GU4412 Advanced econometrics • Advanced Placement (AP) credit in ANCIENT STUDIES: All courses GU4415 Game theory GU4911 Seminar in microeconomics appropriate subject areas can be ANTHROPOLOGY: All courses in sociocul- GU4913 Seminar in macroeconomics applied toward the 9-point elective tural anthropology GU4918 Seminar in econometrics nontechnical requirement. All courses in archaeology except field work BC1003 Introduction to economic reasoning No courses in biological/physical anthropol- A. Required Nontechnical Courses (equivalent to ECON UN1105) ogy [UN1010, UN1011, UN3204, UN3940, (16–18 points of credit) BC1007 Mathematical methods for econom- GU4147-GU4148, GU4200, GU4700] These courses must be taken at ics Columbia. ARCHITECTURE: No courses BC2411 Statistics for economics BC3014 Entrepreneurship 1. ENGL UN1010: University writing (3 ART HISTORY AND ARCHEOLOGY: BC3018 Econometrics points) All courses BC3033 Intermediate macroeconomic theory 2. One of the following two-semester ASIAN AMERICAN STUDIES: All courses BC3035 Intermediate microeconomic theory sequences: HUMA CC1001-CC1002: BC3038 International money and finance Masterpieces of Western literature and ASTRONOMY: No courses EDUCATION: All courses philosophy (All students registering for BIOLOGICAL SCIENCES: No courses this course should be prepared to dis- ENGINEERING: Only BUSINESS: No courses cuss books 1–12 of the Iliad on the first BMEN E4010 Ethics for biomedical engineers day of class) or CHEMISTRY: No courses EEHS E3900 History of telecommunications COCI CC1101-CC1102: Introduction to contemporary civilization in the West or CLASSICS: All courses ENGLISH AND COMPARATIVE LITERATURE: All courses Global Core: Any 2 courses from COLLOQUIA: All courses approved list (6–8 points) FILM STUDIES: All courses except lab COMPARATIVE ETHNIC STUDIES: All If electing Global Core, students courses, and courses must take two courses from the UN3920 Senior seminar in screenwriting List of Approved Courses (college. COMPARATIVE LITERATURE AND UN2400 The film medium: script analysis columbia.edu/sites/default/files/glob- SOCIETY: All courses al_core.pdf) for a letter grade. FRENCH AND ROMANCE PHILOLOGY: COMPUTER SCIENCE: No courses All courses 3. One of the following two courses: HUMA UN1121: Masterpieces of CREATIVE WRITING: All courses GERMANIC LANGUAGES: All courses (This is an exception to the workshop rule.) Western art, or HUMA UN1123: GREEK: All courses Masterpieces of Western music (3 DANCE: All courses except performance points) HISTORY: All courses classes 4. ECON UN1105: Principles of HISTORY AND PHILOSOPHY OF SCIENCE: DRAMA AND THEATRE ARTS: All courses All courses economics. (This course can be except workshops, rehearsal, or performance satisfied through Advanced Placement; classes, THTR BC2120 Technical produc- HUMAN RIGHTS: All courses see the Advanced Placement chart on tion, THTR BC3135 Set design, and THTR ITALIAN: All courses page 14.) Note: Engineering students BC3134 Lighting design

ENGINEERING 2017–2018 12 JAZZ STUDIES: All courses UN2640 Introduction to social cognition how their high school science and UN2680 Social and personality development math knowledge can be applied in LATIN: All courses UN3615 Children at risk an engineering context to solve real- LATINO STUDIES: All courses UN3630 Seminar in social cognition world problems through classroom presentations and participation LINGUISTICS: All courses except CLLN RELIGION: All courses GU4202 in an in-depth, hands-on project. SLAVIC LANGUAGES: All courses Along the way, guest lecturers MATHEMATICS: No courses discuss social implications of SOCIOLOGY: All courses except technology, entrepreneurship, project MEDIEVAL AND RENAISSANCE STUDIES: SOCI UN3020 Social Statistics All courses management, and other important SPANISH AND PORTUGUESE: All courses nontechnical issues affecting the MIDDLE EASTERN AND ASIAN LANGUAGE practicing engineer. SPEECH: No courses AND CULTURES: All courses While students need not officially MUSIC: All courses except performance STATISTICS: No courses commit to a particular branch of engineering until the third semester, courses, instrument instruction courses, and SUSTAINABLE DEVELOPMENT: No courses workshops most programs recommend, and URBAN STUDIES: All courses in some cases may require, that PHILOSOPHY: All courses except particular courses be taken earlier UN1401 Introduction to logic VISUAL ARTS: No more than one course, for maximum efficiency in program UN3411 Symbolic logic which must be at the 3000-level or higher planning. For information concerning GU4137 Nonclassical logics (This is an exception to the workshop rule.) these requirements, students should GU4431 Introduction to set theory WOMEN AND GENDER STUDIES: All turn to the individual program sections GU4424 Modal logic courses in this bulletin. CSPH GU4801 Mathematical logic I CSPH GU4802 Incompleteness results in Music Instruction Courses logic Professional-Level Courses Music instruction and performance Courses in logic The courses listed below may courses do not count toward the 128 be taken by first- and second-year PHYSICAL EDUCATION: No courses points of credit required for a B.S. students. Some departments require degree. Please note that this includes PHYSICS: No courses one of these courses; please consult courses taken at Teachers College, with departmental charts for more POLITICAL SCIENCE: All courses except Columbia College, and the School of information. UN3220 Logic of collective choice the Arts. The courses stipulate minimal UN3704 Data analysis and statistics for politi- prerequisites. Each course serves as cal science research Visual Arts Courses an introduction to the area of study in UN3720 Scope and methods Students are allowed to take courses addition to teaching the subject matter. GU4730 Game theory and political theory in the Visual Arts Department for Each course is taught by regular GU4732 Research topics in game theory general credit to be applied toward the department faculty and thus provides GU4791 Advanced topics in quantitative B.S. degree. However, no more than research a double introduction to both subject one visual arts course, which must be area and faculty. GU4792 Advanced topics in quantitative taken at the 3000 level or higher, may research The courses are: count toward the nontechnical elective GU4700 Math methods for political science requirement. This 3000 course is an BMEN E1001x Engineering in medicine GU4765 Design and analysis of sample exception to the rule that no workshop Not offered in 2017–2018. surveys The present and historical role of engineering in classes can fulfill the nontech elective GU4768 Experimental research: design, medicine and health care delivery. Engineering requirement. analysis and interpretation approaches to understanding organismic and GU4710 Principles of quantitative political cellular function in living systems. Engineering in research Technical Course Requirements the diagnosis and treatment of disease. Medical GU4711 Analysis of political data The prescribed First Year–Sophomore imaging, medical devices: diagnostic and surgical GU4712 Multivariate political analysis Program curriculum requires students instruments, drug delivery systems, prostheses, to complete a program of technical artificial organs. Medical informatics and PSYCHOLOGY: Only coursework introducing them to five organization of the health care system. Current UN1001 The science of psychology trends in biomedical engineering research. major areas of technical inquiry: UN2235 Thinking and decision making engineering, mathematics, physics, CHEN E2100x Introduction to chemical UN2240 Human communication chemistry, and computer science. engineering UN2280 Introduction to developmental All first-year Engineering This course serves as an introduction to the psychology undergraduate students take ENGI chemical engineering profession. Students are UN2610 Introduction to personality E1102: The art of engineering (4 exposed to concepts used in the analysis of UN2620 Abnormal behavior points). In this course, students see chemical engineering problems. Rigorous analysis UN2630 Social psychology of material and energy balances on open and

ENGINEERING 2017–2018 closed systems is emphasized. An introduction students. No more than 4 points of science. The benefit of advanced 13 to important processes in the chemical and physical education courses may placement is acceleration through biochemical industries is provided. be counted toward the degree. certain First Year–Sophomore Program CIEN E3000y The art of structural design One point of the physical education requirements and thus the opportunity of Basic scientific and engineering principles used requirement can be fulfilled with a taking specialized courses earlier. for the design of buildings, bridges, and other Barnard physical education course or Each year the school reviews the parts of the built infrastructure. Application of a Barnard dance technique course. A CEEB advanced placement curriculum these principles to the analysis and design student who intends to participate in and makes determinations as to of a number of actual large-scale structures. an intercollegiate sport should register appropriate placements, credit, and/or History of major structural design innovations for the appropriate section of UN1005: exemption. Please see the Advanced and the engineers who introduced them. Critical Intercollegiate athletics. Intercollegiate Placement Credit Chart. examination of the unique aesthetic/artistic athletes who attend regularly receive perspectives inherent in structural design. 1 point of credit up to the maximum of International Baccalaureate (IB) Management, socioeconomic, and ethical issues 4. Those who are advised to follow a involved in the design and construction of Entering students may be granted 6 large-scale structures. Recent developments in restricted or adapted activity program points of credit for each score of 6 sustainable engineering, including green building should contact the Department of or 7 on IB Higher Level Examinations design and adaptable structural systems. Intercollegiate Athletics and Physical if taken in disciplines offered as Education. The physical education undergraduate programs at Columbia. EAEE E2100x A better planet by design program offers a variety of activities in Introduction to design for a sustainable planet. Students should consult their adviser the areas of aquatics, fitness, martial Scientific understanding of the challenges. Innovative at the James H. and Christine Turk arts, individual and dual lifetime sports, technologies for water, energy, food, materials Berick Center for Student Advising for provision. Multiscale modeling and conceptual team sports, and outdoor education. further clarification. framework for understanding environmental, Most activities are designed for the resource, human ecological, and economic impacts beginner/intermediate levels. Advanced British Advanced Level Examinations courses are indicated on the schedule. and design performance, evaluation. Focus on Pending review by the appropriate linkages between planetary, regional, and urban The majority of the activities are offered department at Columbia, students with waste, energy, mineral, food, climate, economic, and in ten time preferences. However, grades of A or B on British Advanced ecological cycles. Solution strategies for developed there are early-morning conditioning Level examinations may be granted and developing country settings. activities, Friday-only classes at Baker 6 points of credit if the examinations Athletics Complex, and special courses ELEN E1201x and y Introduction to electrical were taken in disciplines offered as that utilize off-campus facilities during engineering undergraduate programs at Columbia weekends and vacation periods. The Basic concepts of electrical engineering. University. The appropriate transcript Exploration of selected topics and their courses offered by the department for should be submitted to the James H. application. Electrical variables, circuit laws, each term are included in the online and Christine Turk Berick Center for nonlinear and linear elements, ideal and real Directory of Classes, and a description Student Advising, 403 Lerner. sources, transducers, operational amplifiers in of the scheduled activities for each time simple circuits, external behavior of diodes and preference is posted on the www.perec. Other National Systems transistors, first order RC and RL circuits. Digital columbia.edu website. Students may representation of a signal, digital logic gates, flip- Pending review by the appropriate register for only one section of physical flops. A lab is an integral part of the course. department at Columbia, students education each term. whose secondary school work was MECE E1001x Mechanical engineering: in other national systems, such as micro-machines to jumbo jets Advanced Placement the French Baccalauréat, may be Not offered in 2017–2018. Prior to entering Columbia, students The role of mechanical engineering in developing granted credit in certain disciplines for may have taken Advanced Placement many of the fundamental technological advances sufficiently high scores. The appropriate on which today’s society depends. Topics examinations through the College transcript should be submitted to the include airplanes, automobiles, robots, and Entrance Examination Board (CEEB) James H. and Christine Turk Berick modern manufacturing methods, as well as the in a number of technical and Center for Student Advising, 403 Lerner. emerging fields of micro-electro-mechanical nontechnical areas. A maximum of 16 machines (MEMS) and nanotechnology. The points may be applied. Students may STUDY ABROAD physical concepts that govern the operation of be assigned to an advanced level Engineering today is a global profession. these technologies will be developed from basic course in mathematics or physics Engineers are increasingly being called principles and then applied in simple design based on their AP scores. upon to work with other engineers from problems. Students will also be exposed to state- In the required pure science areas, across the world, or they may even find of-the art innovations in each case study. the number of advanced placement themselves living abroad on an overseas academic credits awarded to students assignment. Learning problem-solving Physical Education of engineering and applied science skills in a foreign context will help Two terms of physical education varies from the levels awarded for liberal engineering students to expand their (UN1001-UN1002) are a degree arts programs, notably in mathematics, horizons, and their adaptability to cross- requirement for Columbia Engineering physics, chemistry, and computer

ENGINEERING 2017–2018 14 Advanced Placement Credit Chart In order to receive AP credit, students must be in possession of appropriate transcripts or scores. AP AP Subject Score Credit Requirements or Status Art history 5 3 No exemption from HUMA UN1121 Biology 5 3 No exemption Chemistry 4 or 5 3 Requires completion of CHEM UN1604 with grade of C or better 4 or 5 6 Requires completion of CHEM UN2045-UN2046 with grade of C or better Computer science A or AB 4 or 5 3 Exemption from COMS W1004 English Language and composition 5 3 No exemption Literature and composition 5 3 No exemption Economics Micro & macro 5 and 4 4* Exemption from ECON UN1105 (Test must be in both with a score of 5 in one and at least 4 in the other) French Language 4 or 5 3 Literature 4 or 5 3 German Language 4 or 5 3 Government and politics United States 4 or 5 3* Requires completion of 3000 level or higher course in the American politics subfield with a C or higher Comparative 4 or 5 3* Requires completion of 3000 level or higher course in the Comparative politics subfield with a C or higher. Students may be given an exemption, based on AP scores, from only one undergraduate introduction political science class, either POLS UN1201 or POLS UN1501 History European 5 3 United States 5 3 Italian language 4 or 5 3 Latin literature 5 3 Mathematics Calculus AB 4 or 5 3 Requires completion of APMA E2000 with a grade of C or higher Calculus BC 4 3 Requires completion of APMA E2000 with a grade of C or higher Calculus BC 5 6 Requires completion of APMA E2000 with a grade of C or higher Physics C-E&M 4 or 5 3 Requires beginning with PHYS UN2801 and earning grade of C or better C-MECH 4 or 5 3 Requires beginning with PHYS UN2801 and earning grade of C or better Physics 1 and 2 4 or 5 3 No exemption Spanish Language 4 or 5 3 Literature 4 or 5 3 *AP credits may be applied toward minor requirements. cultural communication will make them a Columbia Engineering interest and their major. The Associate valuable addition to a team of engineers. undergraduate students can study Dean for Undergraduate Student Affairs Study abroad allows engineering abroad for either a semester (fall, and departmental advisers will help students to discover the field through spring, or summer) or, exceptionally, students with their course equivalencies the perspective of engineers working for a full academic year. Students from for approved programs so they can in a different language and culture, every engineering major have studied graduate on time. Students can take enabling them to learn the relationship of abroad. Most do so in the spring nontechnical electives overseas, or with culture to science and develop the range semester of their sophomore year or in departmental permission, they may of transferable skills that employers their junior year. choose technical electives or courses in are seeking today. Study abroad will The Office for Undergraduate Student their major. help students develop intellectually, Affairs will help students identify the It is essential that students begin emotionally, culturally, and socially. appropriate choice for their country of planning as early as possible—ideally

ENGINEERING 2017–2018 this would be during their first year. in Columbia-approved programs pay experience and exposure. 15 Students are encouraged to meet housing costs directly to their host Non-credit-bearing internships, with the Office of Global Programs to or sponsoring institution. Students including the CEO program in London, review possible overseas destinations receiving financial aid at Columbia will Hong Kong, Singapore, Shanghai, and to decide on an appropriate remain eligible for financial aid when Beijing, and Amman, are coordinated abroad experience. The SEAS Office they study abroad with Columbia’s by the Center for Career Education. of Undergraduate Student Affairs will approval. Students who wish to be Please visit the Center’s website for explain all Columbia Engineering study considered for financial aid while more information. abroad formalities and requirements. studying abroad should consult the In addition, the Summer Ecosystems Students must obtain approval from Office of Financial Aid and Educational Experience for Undergraduate their departmental advisers to ensure Financing, 618 Lerner. Education through the Center that their work abroad meets the for Environmental Research and requirements of their majors, as well as Program Information Conservation (CERC) provides clearance from their Advising Dean in Choosing the right university abroad is opportunities for engineering students the James H. and Christine Turk Berick an important step in planning to study in Brazil, Puerto Rico, the Dominican Center for Student Advising. abroad. Study-abroad options vary Republic, and Jordan. Other internship widely in size, geographical location, options may be possible through Eligibility Requirements academic philosophy, language Columbia Engineering international In order to participate in a semester- requirements, living arrangements, partner institutions. long or yearlong study-abroad program, and opportunities for research and students must: internships. Students must establish Academic Credit a set of goals for the study-abroad Students in Columbia-sponsored • Have at least a 3.0 GPA experience, taking into account their programs receive direct Columbia • Be making good progress toward foreign-language skills and adaptability credit, and the courses and grades finishing the first and second year to new environments, as well as their appear on students’ academic requirements research objectives and professional transcripts. These include Reid Hall, • Although knowledge of the language aspirations. Paris; the Berlin Consortium for German of the study abroad country is not a Students must visit the Office of Studies; the Kyoto Center for Japanese requirement, students are encouraged Global Programs’ website to review the Studies; the Columbia University to have some foreign language skills various lists of program options and Summer Arabic Language Program in order to enhance their cultural then consult with the SEAS Associate in Amman, Jordan, and the Tsinghua competency and their overall study Dean for Undergraduate Student University program in Beijing. abroad experience. Affairs for specific information or help Credit from approved programs that in choosing an institution that offers the are not Columbia sponsored is certified NOTE: For programs in countries best courses in their engineering major. as transfer credit toward the Columbia where the language of instruction is Early planning is crucial so that study degree upon successful completion not English, students must take all abroad plans can be integrated into the of the program verifiable by academic coursework in the local language and student’s curriculum plan. transcript. Students must earn a grade will have to show proficiency in that Summer study-abroad programs of C or better in order for credits to language prior to departure. allow students to earn credits for transfer. Course titles and grades for approved programs do not appear on Students’ study-abroad plans must language instruction and nontechnical the Columbia transcript, and the grades be approved by the Office of Global electives. Students can either are not factored into students’ GPAs. Programs by October 1 for spring participate in Columbia-approved Faculty from the Columbia programs and March 1 for summer, summer programs for transfer credit or Engineering academic departments fall and academic-year programs. A on Columbia-sponsored programs for have the responsibility to assess all review of each student’s academic direct credit. The Columbia-sponsored work completed abroad and make and disciplinary records is conducted summer programs include the Chinese decisions about how these courses fit as part of this process. Students on Language Program in Beijing, the Business Chinese and Internship into major requirements. It is imperative academic or disciplinary probation are that students gain course-by-course not permitted to study abroad during Program in Shanghai, the Italian Cultural Studies Program in Venice, the approval from their department prior to the term of their probation. Students departure on a study-abroad program. must then register for their study abroad Columbia University Summer Arabic with the Office of Global Programs Language Program in Amman, Jordan, by November 15 for spring programs and the Columbia University Programs COMBINED PLAN PROGRAMS and March 15 for summer, fall, and in Paris at Reid Hall. Office of Undergraduate Admissions academic year programs. Students who wish to have an 212 Hamilton Hall, MC 2807 Study-abroad students remain international experience but are unable 1130 Amsterdam Avenue to study abroad are encouraged to enrolled at Columbia, and tuition is paid New York, NY 10027 consider the following options as viable to Columbia. Students participating Phone: 212-854-2522 alternatives to gaining such global

ENGINEERING 2017–2018 16 Fax: 212-854-1209 receive guidance about completing with an adviser and the respective Email: [email protected] program requirements. Applicants from departments to find alternative courses undergrad.admissions.columbia.edu/ nonaffiliated schools are welcome to for duplicate requirements. apply/combined-plan apply through our competitive review 3-2 students are not eligible to have process. a second major due to the time con- Columbia Engineering maintains Visit the Office of Undergraduate straints of their program. cooperative program relationships with Admissions website for a complete list institutions nationwide and with other of affiliated schools, admission applica- Tau Beta Pi Columbia University undergraduate tion instructions, information on financial Tau Beta Pi is the nation’s second- divisions. The Combined Plan programs aid, and curriculum requirements for oldest honor society, founded at (3-2 and 4-2) allow students to receive Combined Plan program admission. Lehigh University in 1885. With the a degree both in the liberal arts and in Please note that no change of major is creed “Integrity and excellence in engineering. Combined Plan students allowed after an admission decision has engineering,” it is the only engineering been rendered. complete the requirements for the honor society representing the entire See page 25 for information on the liberal arts degree along with required engineering profession. Columbia’s 4-2 Master of Science Program, which prerequisite coursework for their studies chapter, New York Alpha, is the ninth is administered through the Office of in engineering during the three or four oldest and was founded in 1902. Many Graduate Student Affairs. years at their liberal arts college before Columbia buildings have been named entering the School of Engineering for some of the more prominent chapter and Applied Science. They then must THE JUNIOR-SENIOR PROGRAMS alumni: Charles Fredrick Chandler, complete all the requirements for the Students may review degree progress Michael Idvorsky Pupin, Augustus B.S. degree within four consecutive via DARS (Degree Audit Reporting Schermerhorn, and, of course, Harvey semesters. System) as presented on Student Seeley Mudd. Services Online. Required courses Undergraduate students whose The Combined Plan Program within that are not completed are detailed as scholarship places them in the top Columbia University deficiencies and must be completed eighth of their class in their next-to-last Under this plan, the pre-engineering during summer session or carried as year or in the top fifth of their class student studies in Columbia College, overload courses in later semesters. in their last college year are eligible Barnard College, or the School of Having chosen their program major for membership consideration. These General Studies for three or four years, in the second semester of their sopho- scholastically eligible students are then attends The Fu Foundation School more year, students are assigned to further considered on the basis of of Engineering and Applied Science for a faculty adviser in the department in personal integrity, breadth of interest two years, and is awarded the Bachelor which the program is offered. In addi- both inside and outside engineering, of Arts degree and the Bachelor of tion to the courses required by their adaptability, and unselfish activity. Science degree in engineering upon program, students must continue to Benefits of membership include completion of the fifth or sixth year. satisfy certain distributive requirements, exclusive scholarships and fellowships. This program is optional at Columbia, choosing elective courses that provide Many networking opportunities for jobs but the School recommends it to all sufficient content in engineering sci- and internships are also available, with students who wish greater enrichment ences and engineering design. The 230 collegiate chapters and more than in the liberal arts and pure sciences. order and distribution of the prescribed 500,000 members in Tau Beta Pi. coursework may be changed with The Combined Plan with Other the adviser’s approval. Specific ques- Taking Graduate Courses as an Affiliated Colleges tions concerning course requirements Undergraduate There are more than one hundred should be addressed to the appropriate With the faculty adviser’s approval, a affiliated liberal arts colleges, including department or division. The Vice Dean’s student may take graduate courses while still an undergraduate in the School. those at Columbia, in which a student concurrent approval is required for all Such work may be credited toward can enroll in a Combined Plan program waivers and substitutions. one of the graduate degrees offered by leading to two degrees. Each college the Engineering Faculty, subject to the requires the completion of a specified Double Major following conditions: (1) the course must curriculum, including major and Students who wish to apply for a second be accepted as part of an approved degree requirements, to qualify for major must consult their advising dean graduate program of study; (2) the the baccalaureate from that institution. about next steps. A proposal to double course must not have been used to fulfill Every affiliated school has a liaison major must be approved by both a requirement for the B.S. degree and officer who coordinates the program departments and then forwarded to the must be so certified by the Dean; and at his or her home institution. Students Vice Dean for Undergraduate Programs (3) the amount of graduate credit earned interested in this program should inform for a final decision. by an undergraduate cannot exceed 15 the liaison officer as early as possible, Courses cannot be cross-counted points. Undergraduates may not take preferably in the first year, in order to between dual majors. Please consult CVN courses.

ENGINEERING 2017–2018 The Bachelor of Science Degree Minors preparatory work that may be required 17 Students who complete a four-year Columbia Engineering undergraduates for admission into highly specialized sequence of prescribed study are may choose to add minors to their programs such as medicine. awarded the Bachelor of Science programs. This choice should be made degree. The general requirement for in the fall of their sophomore year, when Premed the Bachelor of Science degree is they also decide on a major. Medical, dental, and other health the completion of a minimum of 128 In considering a minor, students must professional schools prefer that academic credits with a minimum understand that all minors are not, and undergraduates complete a four-year cumulative grade-point average (GPA) cannot, be available to all students. In program of study toward the bachelor's of 2.0 (C) at the time of graduation. addition, the School cannot guarantee degree. All health professional schools The program requirements, specified that a selected minor can be completed require prerequisite coursework, but elsewhere in this bulletin, include the first- within the usual residence period needed they do not prefer one type of major or year–sophomore course requirements, for a major. Indeed, students choos- scholarly concentration. Students with the major departmental requirements, ing minors should expect to encounter all types of engineering backgrounds and technical and nontechnical elective scheduling difficulties. The potential for are highly valued. requirements. Students who wish to the successful completion of a minor It is important to note, however, transfer points of credit may count no depends on the student’s major and that each medical school in the more than 68 transfer points toward the the minor chosen, as well as the course United States and Canada individually degree and must satisfy the University’s schedules and availability, which may determines its own entrance residence requirements by taking at least change from year to year. The list of requirements, including prerequisite 60 points of credit while enrolled in The minors, as well as their requirements, coursework and/or competencies. Fu Foundation School of Engineering appear on pages 198–202. Each medical school also sets its own and Applied Science. Courses may not rules regarding acceptable courses be repeated for credit unless it is stated or course equivalents. It is therefore PROGRAMS IN PREPARATION FOR otherwise in the course description. essential that students plan early and OTHER PROFESSIONS The bachelor’s degree in engineering confirm the premedical requirements and applied science earned at Columbia for those schools to which they intend James H. and Christine Turk Berick University prepares students to enter to apply. The Engineering curriculum Center for Student Advising a wide range of professions. Students covers many of the prerequisite 403 Lerner Hall, MC 1201 are, however, encouraged to consider courses required by medical schools, Phone: 212-854-6378 graduate work, at least to the master’s however, in addition to completing the degree level, which is increasingly Email: [email protected] mathematics, chemistry, and physics considered necessary for many cc-seas.columbia.edu/preprofessional/ courses required by the First Year– professional careers. Sophomore Program, most schools ask The Engineering Accreditation The Fu Foundation School of Engineering for a full year of organic chemistry, a full Commission (EAC) of ABET, an and Applied Science prepares its year of biology, a full year of English, a organization formed by the major students to enter any number of semester of statistics, and a semester engineering professional societies, graduate programs and professions of biochemistry. Advanced Placement accredits university engineering outside of what is generally thought of as credit is accepted in fulfillment of these programs on a nationwide basis. the engineering field. In an increasingly requirements by some schools but Completion of an accredited program technological society, where the line not all. Students are responsible for of study is usually the first step toward between humanities and technology monitoring the requirements of each a professional engineering license. is becoming blurred, individuals with school to which they intend to apply. Advanced study in engineering a thorough grounding in applied Generally, students with Advanced at a graduate school sometimes mathematics and the physical and Placement credit are strongly advised presupposes the completion of an engineering sciences find themselves to take further courses in the field in accredited program of undergraduate highly sought after as professionals in which they have received such credit. study. practically all fields of endeavor. In addition to medical school The following undergraduate Engineering students interested in requirements, all medical schools programs are accredited by the EAC pursuing graduate work in such areas currently require applicants to sit for of ABET: biomedical engineering, as architecture, business, education, the Medical College Admissions Test chemical engineering, civil engineering, journalism, or law will find themselves (MCAT). A new format of this exam Earth and environmental engineering, well prepared to meet the generally was introduced in the spring of 2015, electrical engineering, and mechanical flexible admissions requirements of most for which recommended minimum engineering. professional schools. Undergraduate preparation is: students should, however, make careful inquiry into the kinds of specific

ENGINEERING 2017–2018 18 • One year of general chemistry and www.cc-seas.columbia.edu/ recommendation, is the first Monday in general chemistry lab preprofessional/health/ March of the student’s sophomore year. • One year of organic chemistry and This allows program faculty to support organic chemistry lab Prelaw students through program planning • One year of introductory biology and Students fulfilling the School of to ensure that students can meet the biology lab Engineering and Applied Science’s requirements for certification. However, • One semester of biochemistry curriculum are well prepared to apply when space allows, applications will • One year of general physics and to and enter professional schools of be considered through the fall of the physics lab law, which generally do not require any junior year. Applications from juniors • One semester of introductory psy- specific prelaw coursework. Schools of are due no later than the first Monday chology law encourage undergraduate students in October. Students who plan to to complete a curriculum characterized study abroad during the spring of their As you prepare for this path, you by rigorous intellectual training involving junior year should apply during the should consult regularly with both relational, syntactical, and abstract fall semester of their sophomore year. your assigned adviser and one of the thinking. While selecting courses, keep Students should decide on their interest premedical advisers in the James H. in mind the need to hone your writing in teacher certification by the end of the Christine Turk Berick Center for Student skills, your communication skills, and first year in order to start coursework in Advising. These individuals will help your capacity for logical analysis. the sophomore year. to guide you in your course selection While engineering students may find and planning, and introduce you to interests in many areas of the law, for JOINT PROGRAMS extracurricular and research opportuni- intellectual property and patent law, a ties related to your interests in health science and technology background will The 4-1 Program at Columbia and medicine. Preprofessional Advising be greatly valued if not essential. College maintains an online list of many different clinical volunteer and research Students who are admitted as Urban Teaching: New York State first-year students to the School of opportunities across New York City and Initial Certification in Adolescence Engineering and Applied Science and beyond. Exploration of the career and Education Grades 7–12 for Teachers subsequently complete the four-year sustained interactions with patients is of Mathematics and the Sciences or program for the Bachelor of Science viewed by many medical schools as in Elementary Education Grades 1–6 essential preparation and therefore degree have the opportunity to apply for admission to either Columbia students are strongly encouraged to Barnard College Education Program spend time volunteering/working in clin- College or Barnard College and, after 335-336 Milbank Hall one additional year of study, receive ical and research environments before 3009 Broadway the Bachelor of Arts degree. applying to medical school. New York, NY 10027 The program will be selective, Students must apply for admission Phone: 212-854-7072 and admission will be based on the to health professional schools more education.barnard.edu than one year in advance of the entry following factors: granting of the B.S. at Columbia Engineering at the end of date. Students who are interested in The Barnard Education Program the fourth year; fulfillment of the College going directly on to health professional provides courses leading to certification Core requirements by the end of the schools following graduation should to teach in New York State (with fourth year at the School; a minimum complete all prerequisite courses reciprocal agreements with 41 other GPA of 3.0 in the College Core and required for the MCAT by the end of states) at either the elementary other courses; and the successful the junior year. It is entirely acceptable or secondary level. Students gain completion of any prerequisites for (and most common) for students to experience and develop skills in the College major or concentration. take time between undergraduate and urban school classrooms. Required To be admitted to the program, a plan health professional school and thus coursework includes psychology and needs to be in place for the student to delay application to these schools for education, a practicum, and student complete the major or concentration by one or more years. Students planning teaching, totaling 23–26 points of credit the end of their fifth year. to apply to medical or dental school depending on the level of certification Interested students should should be evaluated by the Premedical sought. contact their advising dean for further Advisory Committee prior to applica- Certification to teach mathematics information. tion. A Premedical Advisory Committee requires 36 points in mathematics. application is made available each Pure science courses required are: year in December. For more informa- 36 points in the sciences, of which 18 School of International and Public tion regarding this process and other must be in the area of the certification Affairs premedical-related questions, please sought: chemistry, biology, physics, or The Fu Foundation School of consult with a premedical adviser in Earth science. Engineering and Applied Science and the Berick Center for Student Advising Deadline for application, which the School of International and Public or peruse their website: https:// includes an essay and letters of Affairs offer a joint program enabling a

ENGINEERING 2017–2018 small number of students to complete information, please contact your Phone: 212-854-2522 19 the requirements for the degrees of advising dean. Fax: 212-854-3393 Bachelor of Science and Master of Email: [email protected] International Affairs in five years instead undergrad.admissions.columbia.edu UNDERGRADUATE ADMISSIONS of six. Not only an excellent academic record but also maturity, fluency in an Office of Undergraduate Admissions For information about undergraduate appropriate foreign language, and 212 Hamilton Hall, MC 2807 admissions, please visit the Office of pertinent experience will determine 1130 Amsterdam Avenue Undergraduate Admissions website or admission to this program. For more New York, NY 10027 contact the office by phone or email.

ENGINEERING 2017–2018 20 UNDERGRADUATE TUITION, FEES, AND PAYMENTS

he 2017–2018 tuition and fees TUITION Comprehensive levels of coverage. are estimated. Tuition and fees Undergraduate students enrolled Full-time students are automatically T are prescribed by statute and in The Fu Foundation School of enrolled in the Basic level of the Plan are subject to change at the discretion Engineering and Applied Science and billed for the insurance premium in of the Trustees. pay a flat tuition charge of $27,252 addition to the Health Service fee. Visit University charges such as tuition, per term, regardless of the number of the Columbia Health website at health. fees, and residence hall and meal course credits taken. columbia.edu for detailed information plans are billed in the first Student about medical insurance coverage Account Statement of the term, which options and directions for making MANDATORY FEES is sent out in July and December of confirmation, enrollment, or waiver each year for the upcoming term. This Orientation fee: $450 (one-time charge requests. account is payable and due in full in the first term of registration) on or before the payment due date Student Life fee: $811 per term PERSONAL EXPENSES announced in the Statement, typically Health and Related Services fee: $541 Students should expect to incur at the end of August or early January per term miscellaneous personal expenses before the beginning of the billed term. International Services charge: $80 per for such items as clothing, linen, Any student who does not receive term (international students only) laundry, dry cleaning, and so forth. the first Student Account Statement is Document fee: $105 (one-time charge) Students should also add to the above expected to pay at registration. expenses the cost of two round trips If the University does not receive OTHER FEES between home and the University to the full amount due for the term on or Application and late fees: cover travel during the summer and before the payment due date of the the month-long, midyear break. first Statement, a late payment charge • Application for undergraduate The University advises students to of $150 will be assessed. An additional admission: $85 open a local bank account upon arrival charge of 1.5 percent per billing cycle • Application for undergraduate in New York City. Since it often takes may be imposed on any amount past transfer admission: $85 as long as three weeks for the first due thereafter. • Late registration fee during late deposit to clear, students should plan Students with an overdue account registration: $50; to cover immediate expenses using balance may be prohibited from after late registration: $100 either a credit card, traveler’s checks, registering, changing programs, or or cash draft drawn on a local bank. obtaining a diploma or transcripts. In Books and course materials: Depends Students are urged not to arrive in New the case of persistently delinquent upon course York without sufficient start-up funds. accounts, the University may utilize the services of an attorney and/or Laboratory fees: See course listings collection agent to collect any amount LABORATORY CHARGES Room and board (estimated): $13,618 past due. If a student’s account is Students may need to add another referred for collection, the student $100 to $300 for drafting materials may be charged an additional HEALTH INSURANCE or laboratory fees in certain courses. amount equal to the cost of collection, Columbia University offers the Each student taking laboratory including reasonable attorney’s Student Medical Insurance Plan, courses must furnish, at his or her own fees and expenses incurred by the which provides both Basic and expense, the necessary notebooks, University.

ENGINEERING 2017–2018 blank forms, and similar supplies. The amount of the charge will be For students receiving federal student 21 In some laboratory courses, a fee stated at that time or as soon as it can aid, refunds will be made to the federal is charged to cover expendable be determined. aid programs in accordance with materials and equipment maintenance. Department of Education regulations. Students engaged in special tests, Refunds will be credited in the TUITION AND FEE REFUNDS investigations, theses, or research following order: Students who make a complete work are required to meet the costs Federal Unsubsidized Stafford Loans withdrawal from a term are assessed of expendable materials as may Federal Stafford Loans a withdrawal fee of $75. Late fees, be necessary for this work and in Federal Perkins Loans application fees, withdrawal fees, accordance with such arrangements Federal PLUS Loans (when disbursed tuition deposits, special fees, computer as may be made between the student through the University) fees, special examination fees, and and the department immediately Federal Pell Grants transcript fees are not refundable. concerned. Federal Supplemental Educational The Health Service Fee, Health Opportunity Grants Insurance Premium, University facilities Other Title IV funds DAMAGES fees, and student activity fees are not All students will be charged for refundable after the change of program Withdrawing students should be damage to instruments or apparatus period. aware that they will not be entitled to caused by their carelessness. The Students who withdraw within the any portion of a refund until all Title amount of the charge will be the actual first 60 percent of the academic period IV programs are credited and all cost of repair, and, if the damage are subject to a refund calculation, outstanding charges have been paid. results in total loss of the apparatus, which refunds a portion of tuition adjustment will be made in the charge based on the percentage of the term for age or condition. To ensure that remaining after the time of withdrawal. there may be no question as to the This calculation is made from the liability for damage, students should date the student’s written notice of note whether the apparatus is in good withdrawal is received by the Dean’s condition before use and, in case Office. of difficulty, request instruction in its proper operation. Where there is Percentage Refund for Withdrawal danger of costly damage, an instructor during First Nine Weeks of Term should be requested to inspect the Prorated for calendars of a different apparatus. Liability for breakage will duration: be decided by the instructor in charge 1st week 100% of the course. 2nd week 100% When the laboratory work is done 3rd week 90% by a group, charges for breakage will 4th week 80% be divided among the members of 5th week 70% the group. The students responsible 6th week 60% for any damage will be notified that a 7th week 50% charge is being made against them. 8th week 40% 9th week and after 0%

ENGINEERING 2017–2018 22 FINANCIAL AID FOR UNDERGRADUATE STUDY

Office of Financial Aid and All applicants who are citizens or Satisfactory Academic Progress Educational Financing permanent residents of the United Columbia University complies with 618 Lerner Hall States, who are granted refugee visas federal SAP regulations. To be eligible 2920 Broadway by the United States, or who are for Federal Student Aid (Federal Pell Mailing: 100 Hamilton Hall, MC 2802 undocumented students in the United Grant, Federal SEOG, Federal Work- 1130 Amsterdam Avenue States are considered for admission in Study, Federal Perkins Loan, Federal New York, NY 10027 a need-blind manner. Direct/PLUS loan), an otherwise Monday–Friday: 9:00 a.m.–5:00 p.m. International students who did eligible student must meet or exceed not apply for financial aid in their the SAP standards set by his or her Phone: 212-854-3711 first year are not eligible to apply for school or program at the time SAP Fax: 212-854-5353 financial aid in any subsequent years. is assessed. The SAP policy may be Email: [email protected] Foreign transfer candidates applying found online at sfs.columbia.edu/ cc-seas.financialaid.columbia.edu for aid must understand that such aid central-sap-policy. is awarded on an extremely limited Columbia is committed to meeting the basis. Columbia does not give any full demonstrated financial need for scholarships for academic, athletic, or all applicants admitted as first-year artistic merit. students or transfer students pursuing Please visit the Financial Aid their first degree. Financial aid is website at cc-seas.financialaid. available for all four undergraduate columbia.edu/ for more information on years, provided that students continue financial aid, including requirements to demonstrate financial need. and application instructions.

ENGINEERING 2017–2018 Graduate Studies 24 THE GRADUATE PROGRAMS

raduate programs of study for at least 15 points while registered in THE MASTER OF SCIENCE DEGREE in The Fu Foundation School the School. For residence requirements The Master of Science degree is G of Engineering and Applied for students registered in the Graduate offered in many fields of engineering Science are not formally prescribed, but School of Arts and Sciences or those and applied science upon the are planned to meet the particular needs wishing to change from the Eng.Sc.D. satisfactory completion of a minimum and interests of each individual student. degree to the Ph.D. degree, see the of 30 points of credit of approved Departmental requirements for each bulletin of the Graduate School of Arts graduate study extending over at degree, which supplement the general and Sciences. least one academic year. requirements given below, appear in the Students admitted to graduate study While a suitable Master of Science sections on individual graduate programs. are expected to enter upon and continue program will necessarily emphasize Applicants for a graduate program their studies in each succeeding regular some specialization, the program should are required to have completed an term of the academic year. Any such be well balanced, including basic undergraduate degree and to furnish student who fails to register for the subjects of broad importance as well as an official transcript as part of the following term will be assumed to have theory and applications. The history of admissions application. Ordinarily the withdrawn unless a leave of absence has modern economic, social, and political candidate for a graduate degree will have been granted by the Office of Graduate institutions is important in engineering, completed an undergraduate course in Student Affairs. and this is recognized in the prescribed the same field of engineering in which While many candidates study on a undergraduate program of the School. he or she seeks a graduate degree. full-time basis, it is usually possible to If the candidate’s undergraduate However, if the student’s interests have obtain all or a substantial part of the credit education has been largely confined to changed, it may be necessary to make requirement for the master’s or Eng.Sc.D. pure science and technology, a program up such basic undergraduate courses as degrees through part-time study. of general studies, totaling from 6 to 8 are essential to graduate study in his or Under special conditions, and with points, may be required. Supplementary her new field of interest. the prior approval of the department statements covering these special No more than one term of graduate- of his or her major interest and of the requirements are issued by the School’s level coursework or, in the case of part- Assistant Dean, a student may be separate departments. An applicant time students, no more than 15 points permitted to take a required subject at who lacks essential training will be of credit of graduate-level coursework, another school. However, credit for such required to strengthen or supplement completed before the program is courses will not reduce the 30-point the undergraduate work by taking or approved, may be counted toward minimum that must be taken. repeating certain undergraduate courses the degree. Students registered in the For graduation, a candidate for before proceeding to graduate study. School have a minimum requirement any degree except a doctoral degree No graduate credit (that is, credit toward for each Columbia degree of 30 points must file an Application for Degree or the minimum 30-point requirement for of credit of coursework completed at Certificate on the date specified in the the Master of Science degree) will be Columbia University. The student must Academic Calendar. Candidates for a allowed for such subjects. Accordingly, enroll for at least 15 of these points while doctoral degree must apply for the final Master of Science programs may include registered as a matriculating student in examination. If the degree is not earned from 35 to 45 points and may require a degree program in the Engineering by the next regular time for the issuance three terms for completion. Doctoral School. (See also the section Nondegree of diplomas subsequent to the date of research credits cannot be used toward Students and the chapter Columbia filing, the application must be renewed. M.S. degree requirements. Video Network.) Students wishing to Degrees are awarded three times a All degree requirements must be change from the Ph.D. degree to the year—in October, February, and May. completed within five years of the Eng.Sc.D. degree must therefore enroll

ENGINEERING 2017–2018 beginning of graduate study. Under require supplementary preparation Medical Center, the Mailman School 25 extraordinary circumstances, a written in some specific area, or who has of Public Health, and the Law School. request for an extension of this time been out of school for a considerable The Institute offers a master’s degree limit may be submitted to the student’s period, will have to carry a heavier program allowing students to select department for approval by the than normal course load or extend the an elective concentration of study department chair and the Assistant program beyond two years. incorporating one of the six centers: Dean. A minimum grade-point average Graduates of the 4-2 Master Cybersecurity, Financial and Business of 2.5 is required for the M.S. degree. of Science program may not be Analytics, Foundations of Data A student who, at the end of any eligible to take the Fundamentals Science, Health Analytics, New Media, term, has not attained the grade-point of Engineering (FE) exam if their and Smart Cities. Students can also average required for the degree may undergraduate degree is not in pursue an Entrepreneurship track. be asked to withdraw. engineering or a related field. Students After the first semester of enrollment, should also check with individual Master of Science Program in an M.S. student may submit an state boards to determine eligibility Management Science and Engineering application to apply and transfer to requirements for employment. In collaboration with the Graduate another academic program. If the Please contact the Office of Graduate School of Business, the Industrial student is not successful with the Student Affairs, The Fu Foundation Engineering and Operations Research application process, then he or she must School of Engineering and Applied department offers a unique master’s make sure requirements for the original Science, 530 S. W. Mudd, MC 4718, degree program in which students take academic program are completed. 500 West 120th Street, New York, NY business and engineering courses. 10027; you should also contact your (See Industrial Engineering and The 4-2 Master of Science Program home institution’s Combined Plan Operations Research.) The 4-2 Master of Science Program liaison for program information. You may, in addition, email questions to provides the opportunity for students DOCTORAL DEGREES: [email protected]. holding bachelor’s degrees from ENG.SC.D. AND PH.D. affiliated liberal arts colleges (see Two doctoral degrees in engineering Dual Degree Program with the School the listing under the heading The are offered by the University: the of Journalism in Computer Science Combined Plan Program with Other Doctor of Engineering Science, Affiliate Colleges) with majors in The Graduate School of Journalism administered by The Fu Foundation mathematics, physics, chemistry, or and the Engineering School offer a dual School of Engineering and Applied certain other physical sciences to degree program leading to the degrees Science and the Doctor of Philosophy, receive the M.S. degree after two of Master of Science in Journalism and administered by the Graduate School years of study at Columbia in the the Master of Science in Computer of Arts and Sciences. Both doctoral Science. (See Computer Science.) following fields of engineering and programs are subject to review by applied science: biomedical, chemical, the Committee on Instruction of the civil, computer science, Earth and Joint Program with the School of School. Doctoral students may submit Business in Industrial Engineering environmental, electrical, industrial, a petition to the Office of Graduate and mechanical engineering; applied The Graduate School of Business Student Affairs to change from the physics; applied mathematics; and the Engineering School offer a Eng.Sc.D. degree to the Ph.D. degree engineering mechanics; operations joint program leading to the degrees or from the Ph.D. degree to the Eng. research; and materials science. of Master of Business Administration Sc.D. degree. The petition must be Each applicant must produce and Master of Science in Industrial submitted within the first year of evidence of an outstanding Engineering. (See Industrial Engineering enrollment in the doctoral program. undergraduate record, including and Operations Research.) Any petitions submitted after this superior performance in physics period will not be considered. Doctoral and mathematics through differential Master of Science Program in Data degree status can be changed only equations. The program of study will Science once; students, therefore, must be individually designed in consultation The Data Science Institute is housed determine which doctoral degree with a faculty adviser and will integrate in the Engineering School and program is most appropriate for undergraduate work with the field of encompasses the interdisciplinary their academic and professional engineering or applied science the expertise of nine schools within endeavours. student chooses to follow. During the first Columbia University, including the Departmental requirements may year, the program will consist primarily Engineering School, the Graduate include comprehensive written and oral of basic undergraduate courses; during School of Arts and Sciences, the qualifying examinations. A student must the second year, of graduate courses Journalism School, the Graduate have a satisfactory grade-point average in the selected field. The student must School of Business, the Graduate to be admitted to the doctoral qualifying complete at least 30 credits of graduate School of Architecture, Planning examination. Thereafter, the student study to qualify for the degree. and Preservation, the School of must write a dissertation embodying A student whose background may International and Public Affairs, the original research under the sponsorship

ENGINEERING 2017–2018 26 of a member of his or her department the bachelor’s degree. Eng.Sc.D. period begins at the time of enrollment and submit it to the department. If candidates will be required to complete and extends to the date on which the the department recommends the not less than 30 additional points of dissertation defense is held. dissertation for defense, the student credit in residence beyond the M.S. Extension of the time allowed applies for final examination, which is for a letter grade. A master’s degree for completion of the degree may held before an examining committee from an accredited institution may be be granted on recommendation approved by the appropriate Dean’s accepted in the form of advanced of the student’s sponsor and the Office. This application must be made standing as the equivalent of 30 points department chair to the Dean when at least three weeks before the date of of credit. Candidates for the Eng.Sc.D. special circumstances warrant. Such the final examination. degree must, in addition to the 60-point extensions are initiated by submitting The defense of the dissertation requirement, accumulate 12 points a statement of work in progress and a constitutes the final test of the of credit in the departmental course schedule for completion together with candidate’s qualifications. It must be E9800: Doctoral research instruction (see the sponsor’s recommendation to the demonstrated that the candidate has below). The candidate for the degree department chair. made a contribution to knowledge in a of Doctor of Engineering Science Please contact the Office of chosen area. In content the dissertation must submit evidence that his or her Graduate Student Affairs for more should, therefore, be a distinctly original dissertation has been filed in compliance information. contribution in the selected field of study. with requirements set by the faculty of In form it must show the mastery of Engineering and Applied Science. NONDEGREE STUDENTS written English, which is expected of a Qualified persons who are not university graduate. Doctoral Research Instruction interested in a degree program but An Eng.Sc.D. candidate is required who wish only to take certain courses For the Ph.D. Degree to complete 12 credits in the may be permitted to register as departmental course E9800: Doctoral A student must obtain the master’s nondegree students, provided facilities research instruction in accordance with degree (M.S.) before enrolling as are available. the following guidelines: a candidate for the Ph.D. degree. Many graduate courses in The Fu Application for admission as a doctoral Foundation School of Engineering and 1. After obtaining a master’s degree candidate may be made while a Applied Science are offered in the or advanced standing, at which student is enrolled as a master’s degree late afternoon and evening in order time the student begins doctoral candidate. Candidates for the Ph.D. to make them available to working research, the student is eligible to degree must register full time and individuals who wish to further their register for E9800 (3, 6, 9, or 12 complete six Residence Units. The knowledge in the areas of engineering points of credit). minimum requirement in coursework and applied science. Individuals who 2. Registration for E9800 at a time for the doctoral degree is 60 points of find it difficult or impossible to attend other than that prescribed above is credit beyond the bachelor’s degree. classes on the Columbia campus not permitted, except by written A master’s degree from an accredited may be able to receive instruction permission of the Dean. institution may be accepted in the form from the School through the Columbia 3. The 12 points of E9800 required of advanced standing as the equivalent Video Network without leaving their for the Eng.Sc.D. degree do not of one year of residence (30 points of work sites. Individuals interested in count toward the minimum resi- credit and two Residence Units). An this program should read the section dence requirements, e.g., 30 points application for advanced standing must describing the distance learning beyond the master’s degree or be completed during the first semester of Columbia Video Network (CVN), which 60 points beyond the bachelor’s study. Ph.D. candidates will be required follows in this bulletin. degree. to complete not less than 30 additional Nondegree students receive 4. If a student is required to take points of credit in residence for a letter grades and must maintain satisfactory coursework beyond the minimum grade beyond the M.S. attendance and performance in classes residence requirements, the 12 Ph.D. candidates should obtain a or laboratories and will be subject to points of doctoral research instruc- copy of the bulletin of the Graduate the same rules as degree candidates. tion must still be taken in addition to School of Arts and Sciences, in which Should a nondegree student decide the required coursework. are printed the requirements of the to pursue a degree program, work 5. A student must register continu- department of major interest. completed as a nondegree student ously through the fall and the spring may be considered for advanced terms. This requirement does not For the Eng.Sc.D. Degree standing, but no more than 15 points of include the summer session. A student must obtain the master’s coursework completed as a nondegree degree (M.S.) before enrolling student may be counted toward a as a candidate for the Eng.Sc.D. Completion of Requirements graduate degree. degree. The minimum requirement The requirements for the Eng.Sc.D. For additional information and in coursework for the doctoral degree must be completed in no more regulations pertaining to nondegree degree is 60 points of credit beyond than seven years. The seven-year time students, see Graduate Admissions.

ENGINEERING 2017–2018 COLUMBIA VIDEO NETWORK 27

Columbia Video Network continuing students around the world. be counted toward a degree when 540 S. W. Mudd, MC 4719 During the summer semester (and applying through CVN, subject to the 500 West 120th Street on request in the autumn and spring approval of the student’s departmental New York, NY 10027 terms), CVN makes prerecorded adviser. Earning credit as a nondegree courses available. SEAS currently student does not guarantee Phone: 212-854-6447 offers M.S. degrees in the following acceptance into a degree program. Email: [email protected] disciplines through CVN: Only CVN students may transfer cvn.columbia.edu up to 6 credits from another university • Applied physics toward an M.S., subject to the BACKGROUND • Applied math approval of the student’s adviser and Continuing a long-standing tradition of • Biomedical engineering the department. academic excellence and innovation, • Chemical engineering Columbia University students Columbia University’s Fu Foundation • Civil engineering admitted to an on-campus program School of Engineering and Applied • Computer science are not eligible to take CVN courses. Science established the Columbia • Earth and environmental engineering Video Network (CVN) in 1986 to meet • Electrical engineering a growing need within the engineering • Industrial engineering—Systems PROGRAM BENEFITS community for a graduate distance engineering The CVN program allows working education program. Classes and • Materials science and engineering professionals to enroll in courses and degrees offered through CVN are fully • Mechanical engineering earn graduate engineering degrees accredited; the degrees are granted • Operations research without leaving their communities, by Columbia University. • Operations research—Methods in their families, or their jobs. The key Classes available through CVN finance component of CVN is flexibility without are taught on campus by Columbia compromise to the high-caliber University faculty in electronic In addition, students admitted to teaching, resources, and standards classrooms. Faculty and students the Doctor of Engineering Science can inherent in The Fu Foundation meet in classrooms equipped with complete the coursework component School of Engineering and Applied cameras and electronic writing of the program via CVN. Science. CVN students are a part of tablets. The recorded lectures are the Columbia community and may fully downloadable for study at home, STUDENT REGISTRATION take classes on campus. To further office, or on the road. enhance the sense of community, Students who have earned an CVN students take the same CVN uses the Canvas Learning undergraduate degree in engineering, classes, have the same homework Management System to provide a mathematics, or related field can assignments, take the same exams, place where CVN students and faculty apply to take classes for credit or and earn the same degrees as can communicate. Homework and audit without first enrolling in a degree on-campus students in Master of exams are submitted and graded program at the University or taking the Science (M.S.) programs. there, and course notes and other GRE or TOEFL exams by registering reference materials are available for as nondegree students. CVN also downloading. COURSE OFFERINGS AND offers Certification of Professional Professors and teaching assistants DEGREE PROGRAMS Achievement programs in various are available via email, phone, or online CVN makes select SEAS graduate fields, which may lead to study in a office hours to address academic courses available to off-campus related M.S. program. questions. CVN’s administrative staff students in autumn (September– Although you need not be admitted is available to assist with registration December), spring (January–May), to a degree program to begin taking procedures, technical queries, and and summer (June–August) terms. classes through CVN, you should academic advising, so working CVN administrators work closely with apply as soon as possible if you would professionals can devote their energies faculty representatives from each like to earn a degree from Columbia to their studies, their families, and their department to select the classes University; up to 6 credits taken careers. that best fit the needs of new and as a CVN nondegree student may

ENGINEERING 2017–2018 28 GRADUATE ADMISSIONS

Office of Graduate Student Affairs APPLICATION REQUIREMENTS and Applied Science. Regardless 530 S. W. Mudd, MC 4708 Applicants can only apply to one of TOEFL, IELTS, or PTE scores 500 West 120th Street degree program per admission submitted for admission, students New York, NY 10027 term. Applicants must submit an should continue to work on maintaining online application and required adequate verbal and/or written abilities Phone: 212-854-6438 supplemental materials, as described for successful integration within Fax: 212-854-5900 below. An official transcript from each their classes and future professional Email: [email protected] postsecondary institution attended, endeavors. Students are highly gradengineering.columbia.edu personal statement, and resume or encouraged to be proactive about curriculum vitae must be submitted. addressing their English proficiency by The basic requirement for admission Consideration for admission will be utilizing the many resources available as a graduate student is a bachelor’s based not only on the completion of an within Columbia University and degree received from an institution of earlier course of study, but also upon throughout New York City. acceptable standing. Ordinarily, the the quality of the record presented Students have the option of applicant will have majored in the field and upon such evidence as can be enrolling in courses offered through the in which graduate study is intended, obtained concerning the applicant’s American Language Program (ALP) at but in certain programs, preparation personal fitness to pursue professional Columbia University. However, course in a related field of engineering work. credits earned through ALP do not or science is acceptable. The Additionally, applicants must provide count toward the minimum engineering applicant will be admitted only if the three letters of recommendation and the academic coursework requirements. undergraduate record shows promise results of required standardized exams. Enrollment in ALP courses is solely the of productive and effective graduate The Graduate Record Examination financial responsibility of the student. work. (general) is required for all candidates. As a rule, ISSO will not permit students Students who hold an appropriate Applicants to the doctoral program to drop courses or fall below full-time degree in engineering may apply in applied physics are also required registration for language proficiency for admission to study for the Ph.D. to submit official GRE Physics Test deficiencies. degree. However, students are scores. GRE general and subject test required to obtain the master’s degree scores are valid for five years from the APPLICATION FEE first. Students currently enrolled test administration date according to The nonrefundable application fee for in the School's M.S. program may the Educational Testing Service (ETS). all graduate degree and nondegree apply for admission to the doctoral English language test scores are programs is $85. program after completing 15 points of required of all applicants who received coursework. Completion of a relevant their bachelor's degree in a country master's degree is required prior to in which English is not the official and GRADUATE ADMISSION entry into the Ph.D. program. widely spoken language. The Test of CALENDAR Students may be admitted in one English as a Foreign Language (TOEFL), Applicants are admitted twice yearly, of the following five classifications: International English Language Testing for the fall and spring semesters. candidate for the M.S. degree, System (IELTS), or Pearson Test of candidate for the M.S. degree leading English (PTE) scores satisfy the test • Fall admission application deadlines: to the Ph.D. degree, candidate for requirement and are valid for two years December 15 for Ph.D., Eng.Sc.D., the Doctor of Engineering Science according to the test organizations. and M.S. leading to Ph.D. programs degree, candidate for the Doctor of and February 15 for most M.S. only Philosophy degree (see also the bulletin and nondegree applicants. Please ENGLISH PROFICIENCY of the Graduate School of Arts and visit the Office of Graduate Student The Office of Graduate Student Sciences), or nondegree student (not Affairs website for specific M.S. only Affairs no longer requires students a degree candidate). Note: Not more program deadlines. to demonstrate English proficiency than 15 points of credit completed as • Spring admission application as a graduation requirement at The a nondegree student may be counted deadline: October 1 for all Fu Foundation School of Engineering toward a degree. departments and degree levels.

ENGINEERING 2017–2018 Applicants who wish to be considered the application process for graduate taking classes the following term or to 29 for scholarships, fellowships, and study. Contact your academic become a degree candidate, a formal assistantships should file complete department or the Office of Graduate application must be made through the applications for fall admission. Student Affairs for further details. Office of Graduate Student Affairs.

EXPRESS APPLICATION ONE-TERM NONDEGREE TRANSFER APPLICANTS Columbia Engineering, Columbia STUDENT STATUS Master's degree students are not College, General Studies, and Individuals who meet the eligibility eligible for transfer credits. Barnard seniors as well as alumni requirements, who are U.S. citizens, Students admitted to the doctoral from the same schools, who have U.S. permanent residents, or hold program who have been conferred graduated within three years, may an appropriate visa, and who wish an appropriate M.S. degree may be be eligible to apply to a master's to take courses for enrichment, may awarded two residence units toward program using the express application secure faculty approval to take up to their Ph.D., as well as 30 points of process. A minimum cumulative GPA two graduate-level courses for one advanced standing toward their Ph.D. of 3.50 in an approved undergraduate term only as a one-term nondegree or Eng.Sc.D. with approval from the program is required to be eligible to student. This option is also appropriate academic department and the Office submit an M.S.0 Express application. for individuals who missed application of Graduate Student Affairs. For more information about eligibility, deadlines. Applications for the one- visit the Office of Graduate Student term nondegree student status are Affairs website. available at the Office of Graduate The M.S. Express online Student Affairs and must be submitted application, which waives the during the first week of the fall or submission of GRE scores, letters spring semester. of recommendation, and official If a one-term nondegree student transcripts, streamlines and simplifies subsequently wishes either to continue

ENGINEERING 2017–2018 30 GRADUATE TUITION, FEES, AND PAYMENTS

he 2017–2018 tuition and fees TUITION Health and Related Services fee: are estimated. Tuition and fees Graduate students enrolled in M.S. $541 per term are prescribed by statute and and Eng.Sc.D. programs pay $1,936 T International Services charge: are subject to change at the discretion per credit, except when a special fee $80 per term (international students of the Trustees. is fixed. Graduate tuition for Ph.D. only) University charges such as tuition, students is $22,432 per Residence fees, and residence hall and meal plans Unit. The Residence Unit, full-time Document fee: $105 (one-time charge) are billed in the first Student Account registration for one semester rather Statement of the term, which is sent than for individual courses (whether out in July and December of each year or not the student is taking courses), OTHER FEES for the upcoming term. This account provides the basis for tuition charges. Activities fees for master's programs: is payable and due in full on or before Ph.D. students should consult the • First-year full-time student (12 or more the payment due date announced in bulletin for the Graduate School of Arts credits): $150 the Statement, typically at the end of and Sciences. • Continuing full-time students (12 or August or early January before the more credits): $100 beginning of the billed term. Any student COMPREHENSIVE FEE/ • First-year part-time students (less who does not receive the first Student than 12 credits): $75 MATRICULATION AND Account Statement is expected to pay at • Continuing part-time students (less FACILITIES registration. than 12 credits): $50 If the University does not receive Eng.Sc.D. candidates engaged only in research, and who have completed the full amount due for the term on or All full-time and part-time M.S.-Ph.D. their twelve (12) credits of Doctoral before the payment due date of the track and Ph.D. students shall be Research Instruction (see “The first Statement, a late payment charge charged, per term, a student activities Graduate Programs” in this bulletin), of $150 will be assessed. An additional fee of $25. are assessed a Comprehensive Fee of charge of 1.5 percent per billing cycle $2,146 per term by The Fu Foundation may be imposed on any amount past Application and late fees: School of Engineering and Applied due thereafter. • Application for graduate admission: Science. Students with an overdue account $85 Ph.D. candidates engaged only balance may be prohibited from • Late registration fee: in research are assessed $2,146 per registering, changing programs, or - during late registration: $50 term for Matriculation and Facilities obtaining a diploma or transcripts. In - after late registration: $100 the case of persistently delinquent by the Graduate School of Arts and accounts, the University may utilize Sciences. Books and course materials: the services of an attorney and/or Depends upon course collection agent to collect any amount MANDATORY FEES Laboratory fees: See course listings past due. If a student’s account is University facilities fee: referred for collection, the student IEOR master’s program fee: may be charged an additional • Full-time master’s programs: • Full-time master’s program: $1,000 amount equal to the cost of collection, $518 per term • Part-time master’s program: $500 including reasonable attorney’s • All other full-time programs: fees and expenses incurred by the $480 per term University.

ENGINEERING 2017–2018 HEALTH INSURANCE DAMAGES 31 Columbia University offers the All students will be charged for 1st week 100% Student Medical Insurance Plan, damage to instruments or apparatus 2nd week 100% which provides both Basic and caused by their carelessness. The 3rd week 90% Comprehensive levels of coverage. amount of the charge will be the actual 4th week 80% Full-time students are automatically cost of repair, and, if the damage 5th week 70% enrolled in the Basic level of the Plan results in total loss of the apparatus, 6th week 60% and billed for the insurance premium in adjustment will be made in the charge 7th week 50% addition to the Health Service fee. Visit for age or condition. To ensure that 8th week 40% the Columbia Health website at health. there may be no question as to the 9th week and after 0% columbia.edu for detailed information liability for damage, students should about medical insurance coverage note whether the apparatus is in good Refund Policy When Dropping options and directions for making condition before use and, in case Individual Courses confirmation, enrollment, or waiver of difficulty, request instruction in Tuition for courses dropped by the requests. its proper operation. Where there is last day of the Change-of-Program danger of costly damage, an instructor period is refunded in full. There is should be requested to inspect the PERSONAL EXPENSES no refund of tuition for individual apparatus. Liability for breakage will courses dropped after the last day of Students should expect to incur be decided by the instructor in charge the Change-of-Program period. The miscellaneous personal expenses for of the course. Change-of-Program period is usually such items as food, clothing, linen, When the laboratory work is done by the first two weeks of the fall or spring laundry, dry cleaning, and so forth. a group, charges for breakage will semesters (please note that the first The University advises students to be divided among the members of week of the semester usually begins open a local bank account upon arrival the group. The students responsible on a Tuesday). in New York City. Since it often takes for any damage will be notified that a Please note: The prorated schedule as long as three weeks for the first charge is being made against them. above does not pertain to individual deposit to clear, students should plan The amount of the charge will be classes dropped (unless your entire to cover immediate expenses using stated at that time or as soon as it can schedule consists of only one class). either a credit card, traveler’s checks, be determined. The prorated schedule pertains to or cash draft drawn on a local bank. withdrawals. Withdrawal is defined as Students are urged not to arrive in New dropping one’s entire program. York without sufficient start-up funds. TUITION AND FEE REFUNDS For students receiving federal Students who make a complete student aid, refunds will be made withdrawal from a term are assessed LABORATORY CHARGES to the federal aid programs in a withdrawal fee of $75. Late fees, Students may need to add another accordance with Department of application fees, withdrawal fees, $100 to $300 for drafting materials Education regulations. Refunds will be tuition deposits, special fees, computer or laboratory fees in certain courses. credited in the following order: fees, special examination fees, and Each student taking laboratory transcript fees are not refundable. courses must furnish, at his or her own Federal Unsubsidized Stafford Loans The Health Service Fee, Health expense, the necessary notebooks, Federal Stafford Loans Insurance Premium, University facilities blank forms, and similar supplies. Federal Perkins Loans fees, and student activity fees are In some laboratory courses, a fee Federal PLUS Loans (when disbursed not refundable after the change of is charged to cover expendable through the University) program period. materials and equipment maintenance; Federal Pell Grants Students who withdraw within the amount of the fee is shown with Federal Supplemental Educational the first 60 percent of the academic the descriptions in the course listings. Opportunity Grants period are subject to a pro rata refund Students engaged in special tests, Other Title IV funds calculation, which refunds a portion investigations, theses, or research of tuition based on the percentage of Withdrawing students should be work are required to meet the costs the term remaining after the time of aware that they will not be entitled to of expendable materials as may withdrawal. This calculation is made any portion of a refund until all Title be necessary for this work and in from the date the student’s written IV programs are credited and all accordance with such arrangements notice of withdrawal is received by the outstanding charges have been paid. as may be made between the student Office of Graduate Student Affairs. and the department immediately concerned. Percentage Refund for Withdrawal during First Nine Weeks of Term Prorated for calendars of a different duration, if the entire program is dropped:

ENGINEERING 2017–2018 32 FINANCIAL AID FOR GRADUATE STUDY

FINANCING GRADUATE INSTRUCTIONS FOR prospective and continuing graduate EDUCATION FINANCIAL AID APPLICANTS students must complete their FAFSA The academic departments of in order to be considered for all Columbia Engineering and the Office Deadlines forms of graduate financing (both of Financial Aid and Educational Apply for financial aid at the same departmentally-administered and Financing seek to ensure that all time that you apply for admission. financial aid–administered funds). The academically qualified students have Your admissions application must application for admission to Columbia enough financial support to enable be received by the December 15 Engineering graduate programs is them to work toward their degree. deadline to be eligible for The Fu also used to apply for departmental Possible forms of support for tuition, Foundation School of Engineering and funding. Outside scholarships for fees, books, and living expenses Applied Science departmental funding which you qualify must be reported are: institutional grants, fellowships, (institutional grants, fellowships, and to your department and the Office teaching and research assistantships, teaching and research assistantships). of Financial Aid and Educational on- or off-campus employment, and Spring admissions applicants will Financing. The School reserves the student loans. The Office of Financial not be considered for departmental right to adjust your institutional award Aid and Educational Financing assists funding. if you hold an outside scholarship, students with developing financing Incoming applicants and continuing fellowship, or other outside funding. plans for completing a degree. students should complete the FAFSA Columbia University graduate by May 5 for fall enrollment. Institutional Grants funds are administered by two Guidelines for continuing students Institutional grants are awarded to separate branches of the University, are available from departmental graduate students on the basis of and the application materials advisers in advance of the established academic merit. Recipients must required by the two branches differ. deadline. All continuing supported maintain satisfactory academic Institutional grants, fellowships, students must preregister for classes standing. and teaching and research during the preregistration period. assistantships are all departmentally- Fellowships Fellowships are financial and administered funds. Questions GRADUATE SCHOOL intellectual awards for academic merit regarding these awards should DEPARTMENTAL FUNDING that provide stipends to be used by be directed to your academic The graduate departments of fellows to further their research. If department. Federal Student Loans Columbia Engineering offer an you are awarded a fellowship, you (Unsubsidized, Graduate PLUS, extensive array of funding. Funding are expected to devote time to your and Perkins) and private student decisions, based solely on merit, and own work, and you are not required loans are administered by the Office contingent upon making satisfactory to render any service to the University of Financial Aid and Educational academic progress, are made by or donor. You may publish research Financing. Questions about loans the departments. All applicants for produced by your fellowship work. should be directed to the financial admission and continuing students As a fellow, you may not engage in aid office. maintaining satisfactory academic remunerative employment without standing will be considered for consent of the Dean. Applicants departmental funds. Applicants should should contact the department directly contact their department directly for for information. See the complete information. Columbia Engineering listing of fellowships on pages 228–230.

ENGINEERING 2017–2018 Assistantships to a Columbia Engineering doctoral Detailed information and 33 Teaching and research program are automatically considered application instructions for student assistantships, available to doctoral for departmental funding (institutional loans may be found at the Office students in all departments, grants, fellowships, and teaching of Financial Aid and Educational provide tuition exemption and a and research assistantships, upon Financing website at cc-seas. living stipend. Duties may include completion of the required financial financialaid.columbia.edu/content/ teaching, laboratory supervision, aid forms referred to above. Spring graduate-engineering-aid. participation in faculty research, and admissions applicants will not be Determination of your eligibility other related activities. Teaching and considered for departmental funding. for financial aid is based in part on research assistantships require up to Continuing international students must the number of courses for which you twenty hours of work per week. If you preregister for classes during the register. If you enroll in fewer courses are participating in faculty research preregistration period and complete than you initially reported on the loan that fulfills degree requirements, an enrollment status form to be request form, your loan eligibility may you may apply for a research considered for departmental funding. be reduced. assistantship. Assistantships are Most private student loan programs The FAFSA and the online loan awarded on the basis of academic are restricted to U.S. citizens and request form must be completed each merit. permanent residents. However, academic year, and you must maintain international students may be eligible satisfactory academic progress as ALTERNATIVE FUNDING to apply for these domestic loan defined in “The Graduate Programs” SOURCES programs with a creditworthy cosigner section in order to remain eligible for who is a citizen or permanent resident federal student loans. External Awards in the United States. Depending on the loan program, you may need a valid VETERAN’S BENEFITS Because it is not possible to offer full U.S. Social Security number. grant and fellowship support to all Various Department of Veterans Students who study at Columbia graduate students and because of the Affairs programs provide educational Engineering on temporary visas prestige inherent in holding an award benefits for sons, daughters, and should fully understand the regulations through open competition, applicants spouses of deceased or permanently concerning possible employment under are encouraged to consider major disabled veterans as well as for those visas. Before making plans for national and international fellowship veterans and in-service personnel employment in the United States, opportunities. It is important that who served on active duty in the U.S. international students should consult prospective graduate students explore Armed Forces after January 1, 1955. with the International Students and every available source of funding for In these programs the amount of Scholars Office (ISSO), located at 524 graduate study. benefits varies. Under most programs Riverside Drive, Suite 200; 212-854- In researching outside funding the student pays tuition and fees at 3587. Its website is columbia.edu/cu/ you may look to faculty advisers, the time of registration but receives isso. career services offices, deans of a monthly allowance from Veterans students, and offices of financial Affairs. OTHER FINANCIAL AID— aid where frequently you may find Since interpretation of regulations FEDERAL AND PRIVATE resource materials, books, and grant governing veterans’ benefits is applications for a wide variety of PROGRAMS subject to change, veterans and their funding sources. You must notify both U.S. citizens and permanent dependents should keep in touch with your Columbia Engineering academic residents enrolled at least half-time the Department of Veterans Affairs. For department and the Office of Financial in a degree-granting program are additional information and assistance Aid and Educational Financing of eligible to apply in completing the necessary forms, any outside awards that you will be for federal student loans. To apply contact 1-800-827-1000, or consult receiving. for federal student loans, students their website (www.va.gov). should complete the Free Application Detailed information regarding Funding for International Students for Federal Student Aid (FAFSA) the veteran population at Columbia using Columbia University’s school and policies including the Veteran’s To secure a visa, international students code 002707 by May 5 for fall Readmission Provision may be found must demonstrate that they have enrollment on the Veterans Affairs website sufficient funding to complete the Several private student loan (veteranaffairs.columbia.edu). degree. Many international students programs are available to both U.S. obtain support for their educational citizens and international students. EMPLOYMENT expenses from their government, a These loans require that you have a foundation, or a private agency. Students on fellowship support must good credit standing. International International students who apply obtain the permission of the Dean students may be eligible for a private to doctoral programs of study by the before accepting remunerative loan with a creditworthy U.S. citizen December 15 deadline and are admitted employment. or permanent resident cosigner.

ENGINEERING 2017–2018 34

Students who study at Columbia Off-Campus Employment in Campus, Lower Level, 212-854-5609, Engineering on temporary visas New York City careereducation.columbia.edu. should fully understand the regulations One of the nation’s largest urban For questions about student loans, concerning possible employment areas, the city offers a wide variety contact: under those visas. Before making of opportunities for part-time work. Office of Financial Aid and plans for employment in the United Many students gain significant Educational Financing States, international students should experience in fields related to their 618 Lerner Hall consult with the International Students research and study while they Mailing: 100 Hamilton Hall, MC 2802 and Scholars Office (ISSO) located at meet a portion of their educational 1130 Amsterdam Avenue 524 Riverside Drive, Suite 200; 212- expenses. New York, NY 10027 854-3587. Its website is columbia.edu/ cu/isso. Phone: 212-854-3711 CONTACT INFORMATION Fax: 212-854-5353 On-Campus Employment For questions about institutional Email: [email protected] grants, fellowships, and teaching and The Center for Career Education cc-seas.financialaid.columbia.edu/ research assistantships, contact your maintains an extensive listing of student content/graduate-engineering-aid. academic department. employment opportunities. The Center For questions about on- or for Career Education (CCE) is located off-campus non-need-based at East Campus, Lower Level, 212-854- employment, contact the Center for 5609, careereducation.columbia.edu. Career Education, located at East

ENGINEERING 2017–2018 Faculty and Administration 36 FACULTY AND ADMINISTRATION

OFFICERS William E. Bailey Allison Breton Bishop Lee C. Bollinger, J.D. Associate Professor of Materials Assistant Professor of Computer Science President of the University Science (Henry Krumb School of Mines) A.B., Princeton, 2006; Ph.D., Texas and of Applied Physics and Applied (Austin), 2012 John H. Coatsworth, Ph.D. Mathematics Provost of the University B.A., B.S., Brown, 1993; Kyle J. M. Bishop M.S., Stanford, 1995; Ph.D., 1999 Associate Professor of Chemical Mary C. Boyce, Ph.D. Engineering Dean Scott A. Banta B.S., University of Virginia, 2003; Ph.D., Professor of Chemical Engineering Northwestern, 2009 Andrew Laine, D.Sc. B.S., Maryland (Baltimore), 1997; M.S., Secretary Rutgers, 2000; Ph.D., 2002 Paul Blaer Lecturer in Computer Science Katayun Barmak Vaziri B.A., Columbia, 2000; M.S., 2002; FACULTY Philips Electronics Professor of Applied Ph.D., 2008 Shipra Agrawa Physics and Applied Mathematics Assistant Professor of Industrial B.A., University of Cambridge (England), Jose H. Blanchet Mancilla Engineering and Operations Research 1983; M.A., 1987; S.M., MIT, 1985; Associate Professor of Industrial B.E., M.B.M., Engineering College Ph.D., 1989 Engineering and Operations Research (India), 2002; M.E., Indian Institute of and of Statistics (Arts and Sciences) Science (India), 2004; Ph.D., Stanford, Daniel Bauer B.S., Instituto Tecnológico Autónomo de 2011 Lecturer in Computer Science México (Mexico), 2000; M.S., Stanford, B.S., University of Osnabrück 2001; Ph.D., 2004 Sunil Agrawal (Germany), 2007; M.S., Saarland Professor of Mechanical Engineering University (Germany), 2009; Ph.D., David M. Blei B.S., Indian Institute of Technology Columbia, 2017 Professor of Computer Science and of (India), 1984; M.S., Ohio State, 1986; Statistics (Arts and Sciences) Ph.D., Stanford, 1990 Peter N. Belhumeur B.Sc., Brown, 1997; Ph.D., California Professor of Computer Science (Berkeley), 2004 Alfre V. Aho B.S., Brown, 1985; M.S., Harvard, Lawrence Gussman Professor of 1991; Ph.D., 1993 Allen H. Boozer Computer Science Professor of Applied Physics B.A.Sc., University of Toronto (Canada), Steven M. Bellovin B.A., Virginia, 1966; Ph.D., Cornell, 1970 1963; M.A., Princeton, 1965; Ph.D., Professor of Computer Science Mary C. Boyce 1967 B.A., Columbia, 1972; M.S., North Carolina (Chapel Hill), 1977; Ph.D., 1987 Morris A. and Alma Schapiro Professor Peter K. Allen and Professor of Mechanical Engineering Professor of Computer Science Keren Bergman S.B., Virginia Polytechnic Institute and B.A., Brown, 1971; M.S., Oregon, 1976; Charles Batchelor Professor of Electrical State University, 1981; S.M., MIT, 1983; Ph.D., Pennsylvania, 1985 Engineering Ph.D., MIT, 1987 B.S., Bucknell University, 1988; Dimitris Anastassiou M.S., MIT, 1991; Ph.D., 1994 Robert G. Bozic Charles Batchelor Professor of Electrical Lecturer in Chemical Engineering Engineering Raimondo Betti B.S., United States Military Academy, Dipl., National Technical University of Professor of Civil Engineering and 1989; M.E., Florida, 1999; Ph.D., Athens (Greece), 1974; M.S., California Engineering Mechanics Columbia, 2008 (Berkeley), 1975; Ph.D., 1979 B.S., Rome La Sapienza (Italy), 1985; M.S., Southern California, 1988; Ph.D., 1991 Michael P. Burke Alexandr Andoni Assistant Professor of Mechanical Associate Professor of Computer Science Daniel Bienstock Engineering B.S., Politehnica University of Bucharest Professor of Industrial Engineering and B.S., Pennsylvania State, 2005; Ph.D., (Romania), 2004; M.S., MIT, 2005; Operations Research and of Applied Princeton, 2011 Ph.D., 2009 Physics and Applied Mathematics B.S., Brandeis, 1982; Ph.D., MIT, 1985 Mark A. Cane Gerard H. A. Ateshian G. Unger Vetlesen Professor of Earth Andrew Walz Professor of Mechanical Simon J. L. Billinge and Environmental Sciences and Engineering and Professor of Biomedical Professor of Materials Science and of Professor of Applied Physics and Engineering Applied Physics and Applied Mathematics Applied Mathematics B.S., Columbia, 1986; M.S., 1987; B.A., University of Oxford (England), B.A., Harvard, 1965; M.A., 1966; M.Phil., 1990; Ph.D., 1991 1986; Ph.D., Pennsylvania, 1992 Ph.D., MIT, 1975

ENGINEERING 2017–2018 37

Adam Cannon Xi Chen Emanuel Derman Senior Lecturer in Machine Learning Associate Professor of Computer Professor of Professional Practice of (Computer Science) Science Industrial Engineering and Operations B.S., California (Los Angeles), 1991; B.S., Tsinghua University (P.R. China), Research M.S., 1994; M.A., Johns Hopkins, 1997; 2003; Ph.D., 2007 B.Sc., University of Cape Town (South Ph.D., 2000 Africa), 1965; M.A., Columbia, 1968; Xi Chen Ph.D., 1973 Agostino Capponi Associate Professor of Earth and Assistant Professor of Industrial Environmental Engineering (Henry Xuan Sharon Di Engineering and Operations Research Krumb School of Mines) Assistant Professor of Civil Engineering B.S., University of Rome (Italy), 2001; B.E., Xi’an Jiaotong University (P.R. and Engineering Mechanics M.S., Caltech, 2006; Ph.D., 2009 China), 1994; M.E., Tsinghua University B.S., Tongji University (China), 2005; (P.R. China), 1997; S.M., Harvard, M.A., 2008; Ph.D., Minnesota (Twin Luca Carloni 1998; Ph.D., 2001 Cities), 2014 Associate Professor of Computer Science B.S., University of Bologna (Italy), 1995; M.S., Matei T. Ciocarlie Antonius Dieker California (Berkeley), 1997; Ph.D., 2004 Assistant Professor of Mechanical Associate Professor of Industrial Engineering Engineering and Operations Research Augustin Chaintreau B.S., Polytechnic University of Bucharest M.Sc., Vrije Universiteit (Netherlands), Assistant Professor of Computer Science (Romania), 2003; M.S., Columbia, 2005; 2002; Ph.D., University of Amsterdam Magistère, École Normale Supérieure Ph.D., 2010 (Netherlands), 2006 (France), 2001; D.E.A., Université Pierre et Marie Curie (France), 2002; Ph.D., INRIA- Andrew J. Cole Eleni Drinea École Normale Supérieure (France), 2006 Assistant Professor of Applied Physics Lecturer in the Data Science Institute and Applied Mathematics and in Computer Science Siu-Wai Chan B.A., Oregon, 2000; Ph.D., Texas B.S./M.S., University of Patras Professor of Materials Science (Henry (Austin), 2006 (Greece), 1999; M.Sc., Harvard, 2005; Krumb School of Mines) and of Applied Ph.D., 2005 Physics and Applied Mathematics Michael J. Collins B.S., Columbia, 1980; Sc.D., MIT, 1985 Vikram S. Pandit Professor of Qiang Du Computer Science The Fu Foundation Professor of Applied Kartik Chandran B.A., University of Cambridge Mathematics Professor of Earth and Environmental (England), 1992; M.Phil., 1993; Ph.D., B.S., University of Science and Engineering (Henry Krumb School of Pennsylvania, 1999 Technology of China, 1983; Ph.D., Mines) Carnegie Mellon, 1988 B.S., Indian Institute of Technology Patricia J. Culligan (India), 1995; Ph.D., Connecticut, 1999 Professor of Civil Engineering and Paul F. Duby Engineering Mechanics Professor of Mineral Engineering (Earth Julius Chang B.Sc., University of Leeds (England), and Environmental Engineering, Henry Lecturer in Civil Engineering and 1982; M.Phil., University of Cambridge Krumb School of Mines) Engineering Mechanics Ing. Civil M.E., University of Brussels B.S., Columbia, 1986; M.S., 1989; M.S., (England), 1985; Ph.D., 1989 Penn, 1991; Mastère, Institut Français (Belgium), 1956; Eng.Sc.D., du Petrole (France), 1991; Eng.Sc.D., Tal Danino Columbia, 1962 Columbia, 2007 Assistant Professor of Biomedical Engineering Christopher J. Durning Shih-Fu Chang B.S., California (Los Angeles), 2005; Professor of Chemical Engineering The Richard Dicker Professor of Ph.D., 2011 B.S., Columbia, 1978; M.A., Princeton, Telecommunications (Electrical 1979; Ph.D., 1982 Engineering) and Professor of Computer Gautam Dasgupta Science Professor of Civil Engineering and Stephen A. Edwards B.S., National Taiwan University Engineering Mechanics Associate Professor of Computer Science (Taiwan), 1985; M.S., California B.Engr., University of Calcutta (India), B.S., Caltech, 1992; M.S., California (Berkeley), 1991; Ph.D., 1993 1967; M.Engr., 1969; Ph.D., California (Berkeley), 1994; Ph.D., 1997 (Berkeley), 1974 Jingguang G. Chen Adam Elmachtoub Thayer Lindsley Professor of Engineering George Deodatis Assistant Professor of Industrial (Chemical Engineering) The Santiago and Robertina Calatrava Engineering and Operations Research B.S., Nanjing University (P.R. China), Family Professor of Civil Engineering B.S., Cornell, 2009; Ph.D., MIT, 2014 1982; Ph.D., Pittsburgh, 1988 B.S., National Technical University of Athens (Greece), 1982; M.S., Columbia, 1984; Ph.D., 1987

ENGINEERING 2017–2018 38 Yaniv Erlich Javad Ghaderi Dehkordi Elizabeth M. C. Hillman Assistant Professor of Computer Science Assistant Professor of Electrical Associate Professor of Biomedical B.S., Tel-Aviv University (Israel), 2006; Engineering Engineering and of Radiology Ph.D., 2010 B.Sc., University of Tehran, 2006; (Health Sciences) M.A.Sc., University of Waterloo, 2008; M.Sci., University College London Daniel Esposito Ph.D., Illinois (Urbana-Champaign), (England), 1998; Ph.D., 2002 Assistant Professor of Chemical Engineering 2013 B.S., Lehigh, 2006; Ph.D., Julia B. Hirschberg Delaware, 2012 Donald Goldfarb Percy K. and Vida L. W. Hudson Alexander and Hermine Avanessians Professor of Computer Science Yuri Faenza Professor of Industrial Engineering and B.A., Eckert College, 1968; Ph.D., Assistant Professor of Industrial Operations Research Michigan, 1976; M.S.E.E., Pennsylvania, Engineering and Operations Research B.Ch.E., Cornell, 1963; M.A., Princeton, 1982; Ph.D., 1985 B.S., Università di Roma Tor Vergata 1965; Ph.D., 1966 (Italy), 2004; M.S., 2006; Ph.D., James C. Hone Sapienza Università di Roma (Italy), 2010 Vineet Goyal Wang Fong-Jen Professor of Mechanical Associate Professor of Industrial Engineering Robert J. Farrauto Engineering and Operations Research B.S., Yale, 1990; Ph.D., California Professor of Professional Practice of B.Tech., Indian Institute of Technology (Berkeley), 1998 Earth and Environmental Engineering (India), 2003; M.S., Carnegie Mellon, B.S., Manhattan College, 1964; Ph.D., 2005; Ph.D., 2008 Daniel J. Hsu Rensselaer Polytechnic Institute, 1968 Assistant Professor of Computer Science Luis Gravano B.S., California (Berkeley), 2004; M.S., Steven K. Feiner Professor of Computer Science California (San Diego), 2007; Ph.D., 2010 Professor of Computer Science B.S., Escuela Superior Latinoamericana A.B., Brown, 1973; Ph.D., 1985 de Informática (Argentina), 1990; Clark T. Hung M.S., Stanford, 1994; Ph.D., 1997 Professor of Biomedical Engineering Maria Q. Feng Sc.B., Brown, 1990; M.S.E., Renwich Professor of Civil Engineering Eitan Grinspun Pennsylvania, 1992; Ph.D., 1995 and Engineering Mechanics Associate Professor of Computer Science B.S., Nanjing Institute of Technology B.A., University of Toronto (Canada), James S. Im (P.R. China), 1982; M.S., University of 1997; M.S., Caltech, 2000; Ph.D., 2003 Professor of Materials Science (Henry Tokyo (Japan), 1987; Ph.D., 1992 Krumb School of Mines) and of Applied X. Edward Guo Physics and Applied Mathematics Jacob Fish Professor of Biomedical Engineering B.S., Cornell, 1984; Ph.D., MIT, 1989 Robert A. W. and Christine S. Carleton B.S., Peking University (P.R. China), Professor of Civil Engineering 1984; M.S., Harvard-MIT, 1990; Garud N. Iyengar B.S., Technion (Israel), 1982; M.S., 1985; Ph.D., 1994 Professor of Industrial Engineering and Ph.D., Northwestern, 1989 Operations Research Christine P. Hendon B. Tech., Indian Institute of Technology Alexander Gaeta Assistant Professor of Electrical (India), 1993; M.S., Stanford, 1995; David M. Rickey Professor of Applied Engineering Ph.D., 1998 Physics and of Materials Science B.S., MIT, 2004; M.S., Case Western B.S., Rochester, 1983; M.S., 1985; Reserve, 2007; Ph.D., 2010 Christopher R. Jacobs Ph.D., 1991 Professor of Biomedical Engineering Irving P. Herman B.S., Washington (St. Louis), 1988; Oleg Gang Professor of Applied Physics M.S., Stanford, 1989; Ph.D., 1994 Professor of Chemical Engineering S.B., MIT, 1972; Ph.D., 1977 M.S., Bar-llan University (Israel), 1994; Joshua Jacobs Ph.D., 2000 Henry S. Hess Assistant Professor of Biomedical Associate Professor of Biomedical Engineering Roxana Geambasu Engineering B.S., MIT, 2001; M.Eng., 2002; Ph.D., Associate Professor of Computer Science B.S., Technical University Clausthal Pennsylvania, 2008 B.S., Polytechnic University of Bucharest (Germany), 1993; M.Sc., Technical Suman Jana (Romania), 2005; M.S., Washington University Berlin (Germany), 1996; Ph.D., Assistant Professor of Computer (Seattle), 2007; Ph.D., 2011 Free University Berlin (Germany), 1999 Science B.E., Jadavpur University, 2003; M.S., Pierre Gentine Andreas H. Hielscher Utah, 2009; Ph.D., Texas (Austin), 2014 Associate Professor of Earth and Professor of Biomedical Engineering Environmental Engineering (Henry and of Electrical Engineering and of Tony Jebara Krumb School of Mines) Radiology (Health Sciences) Associate Professor of Computer Science B.Sc., Supaéro (France), 2002; M.S., B.S., University of Hannover (Germany), B.Eng., McGill University (Canada), MIT, 2006; M.S., Sorbonne (France), 1987; M.S., 1991; Ph.D., Rice, 1995 1996; M.S., MIT, 1998; Ph.D., 2002 2009; Ph.D., MIT, 2009

ENGINEERING 2017–2018 Predrag R. Jelenkovic John R. Kender Aaron M. Kyle 39 Professor of Electrical Engineering Professor of Computer Science Senior Lecturer in Biomedical Engineering Dipl.Ing., Belgrade University (Serbia), B.S., Detroit, 1970; M.S., Michigan, Design 1991; M.S., Columbia, 1993; M. Phil., 1972; Ph.D., Carnegie Mellon, 1980 B.S., Kettering University, 2002; 1995; Ph.D., 1996 Ph.D., Purdue, 2007 Angelos D. Keromytis Xiaofan Fred Jiang Associate Professor of Computer Science Ioannis Kymissis Assistant Professor of Electrical B.Sc., University of Crete (Greece), 1996; Associate Professor of Electrical Engineering M.S., Pennsylvania, 1997; Ph.D., 2001 Engineering B.S., California (Berkeley), 2004; M.S., S.B., MIT, 1998; M.Eng., 1999; 2007, Ph.D., 2010 Martha A. Kim Ph.D., 2003 Associate Professor of Computer Hardeep V. Johar Science Jeffrey W. Kysar Lecturer in Industrial Engineering and B.A., Harvard, 2002; M.E., University Professor of Mechanical Engineering Operations Research of Lugano (Switzerland), 2003; M.S., B.S., Kansas State, 1987; M.S., 1992; M.A., Birla Institute of Technology and Washington (Seattle), 2005; Ph.D., 2008 S.M., Harvard, 1993; Ph.D., 1998 Science (India), 1980; Ph.D., NYU, 1994 Peter R. Kinget Andrew F. Laine Jingyue Ju Professor of Electrical Engineering Percy K. and Vida L. W. Hudson Samuel Ruben–Peter G. Viele Professor Ph.D., Katholieke Universiteit Leuven Professor of Biomedical Engineering of Engineering (Chemical Engineering) (Belgium), 1996 and Professor of Radiology (Health B.S., Inner Mongolia University (P.R. Sciences) China), 1985; M.S., Chinese Academy Jeffrey T. Koberstein B.S., Cornell, 1977; M.S., Connecticut, of Sciences (P.R. China), 1988; Ph.D., Percy K. and Vida L. W. Hudson 1980; M.S., Washington (St. Louis), Southern California, 1993 Professor of Chemical Engineering 1983; D.Sc., 1989 B.S., Wisconsin, 1974; Ph.D., Christoph W. Juchem Massachusetts, 1979 Upmanu Lall Associate Professor of Biomedical Alan and Carol Silberstein Professor of Engineering Elisa E. Konofagou Earth and Environmental Engineering Ph.D., University of Tübingen (Germany), Professor of Biomedical Engineering and (Henry Krumb School of Mines) and 2006 of Radiology (Health Sciences) of Civil Engineering and Engineering B.S., Université de Paris VI (France), Mechanics Soulaymane Kachani 1992; M.S., University of London B.Tech., Indian Institute of Technology Professor of Professional Practice of (England), 1993; Ph.D., Houston, 1999 (India), 1976; M.S., Texas, 1980; Industrial Engineering and Operations Ph.D., 1981 Research Zoran Kostic Diplôme, École Centrale Paris (France), Associate Professor of Professional Aurel A. Lazar 1998; M.S., MIT, 1999; Ph.D., 2002 Practice in Electrical Engineering Professor of Electrical Engineering Dipl.Ing., University of Novi Sad B.S., Bucharest Polytechnical Institute Gail E. Kaiser (Yugoslavia), 1987; M.S., Rochester, (Romania), 1971; M.S., Darmstadt Institute Professor of Computer Science 1988; Ph.D., 1991 of Technology (Germany), 1976; Sc.B., MIT, 1979; M.S., Carnegie Ph.D., Princeton, 1980 Mellon, 1980; Ph.D., 1985 Ioannis A. Kougioumtzoglou Assistant Professor of Civil Engineering Jae Woo Lee Lance C. Kam and Engineering Mechanics Senior Lecturer in Computer Science Associate Professor of Biomedical B.S., National Technical University of B.A., Columbia, 1994; M.S., 2006; Engineering Athens (Greece), 2007; M.S., Rice, Ph.D., 2012 B.S., Washington (St. Louis), 1991; M.S., 2009; Ph.D., 2011 Hawaii, 1994; Ph.D., RPI, 1999 Edward F. Leonard Harish Krishnaswamy Professor of Chemical Engineering Karen Kasza Associate Professor of Electrical B.S., MIT, 1953; M.S., Pennsylvania, Assistant Professor of Mechanical Engineering 1955; Ph.D., 1960 Engineering B.Tech., Indian Institute of Technology B.A., B.S., Chicago, 2003; Ph.D., (India), 2001; M.S., Southern California, Kam Leong Harvard, 2009 2003; Ph.D., 2009 Samuel Y. Sheng Professor of Biomedical Engineering Shiho Kawashima Sanat K. Kumar B.S., California (Santa Barbara), 1977; Assistant Professor of Civil Engineering Bykhovsky Professor of Chemical Ph.D., Pennsylvania, 1987 and Engineering Mechanics Engineering B.S., Columbia, 2007; M.S., B.Tech., Indian Institute of Technology Qiao Lin Northwestern, 2009; Ph.D., 2012 (India), 1981; S.M., MIT, 1984; Sc.D., 1987 Associate Professor of Mechanical Engineering B.S., Tsinghua University (P.R. China), 1985; M.S., 1988; Ph.D., Caltech, 1993

ENGINEERING 2017–2018 40 Hoe I. Ling V. Faye McNeill Gerald A. Navratil Professor of Civil Engineering and Associate Professor of Chemical Thomas Alva Edison Professor Engineering Mechanics Engineering of Applied Physics B.S., Kyoto University (Japan), 1988; M.S., B.S., Caltech, 1999; M.S., MIT, 2001; Ph.D., B.S., Caltech, 1973; M.S., Wisconsin, University of Tokyo (Japan), 1990; Ph.D., 1993 2005 1974; Ph.D., 1976

Hod Lipson Nima Mesgarani Shree K. Nayar Professor of Mechanical Engineering Associate Professor of Electrical T. C. Chang Professor of Computer B.Sc., Technion (Israel), 1989; Ph.D., 1998 Engineering Science B.Sc., Sharif University of Technology B.S., Birla Institute of Technology (India), Michal Lipson (Iran) 1999; M.Sc., Maryland, 2005; Ph.D., 1984; M.S., North Carolina State, 1986; Professor of Electrical Engineering 2008 Ph.D., Carnegie Mellon, 1990 B.Sc., Technion (Israel), 1992; M.S., 1994; Ph.D., 1998 Vishal Misra Jason Nieh Professor of Computer Science Professor of Computer Science Richard W. Longman B.Tech., Indian Institute of Technology B.S., MIT, 1989; M.S., Stanford, 1990; Professor of Mechanical Engineering (India), 1992; M.S., Massachusetts Ph.D., 1999 and of Civil Engineering and Engineering (Amherst), 1996; Ph.D., 2000 Mechanics Steven M. Nowick B.S., California (Riverside), 1965; Debasis Mitra Professor of Computer Science and M.S., California (San Diego), 1967; Professor of Electrical Engineering Electrical Engineering Ph.D., 1968, M.A., 1969 B.Sc., London University (England), B.A., Yale, 1976; M.A., Columbia, 1979; 1964; Ph.D., 1967 Ph.D., Stanford, 1993 Helen H. Lu Professor of Biomedical Engineering Vijay Modi Ismail Cevdet Noyan B.S., Pennsylvania, 1992; M.S., 1997; Professor of Mechanical Engineering Professor of Materials Science (Henry Ph.D., 1998 B.Tech., Indian Institute of Technology Krumb School of Mines) and of Applied (India), 1978; Ph.D., Cornell, 1984 Physics and Applied Mathematics Tal Malkin B.S., Middle East Technical University Associate Professor of Computer Science Barclay Morrison III (Turkey), 1978; Ph.D., Northwestern, B.S., Bar-Ilan University (Israel), 1993; Professor of Biomedical Engineering 1984 M.S., Weizmann Institute of Science B.S., Johns Hopkins, 1992; M.S.E., (Israel), 1995; Ph.D., MIT, 2000 Pennsylvania, 1994; Ph.D., 1999 Allie C. Obermeyer Assistant Professor of Chemical Kyle Mandli Van C. Mow Engineering Assistant Professor of Applied Stanley Dicker Professor of Biomedical B.S., Rice; Ph.D., California (Berkeley), Mathematics Engineering in the Faculty of Engineering 2013 B.S., Wisconsin, 2004; M.Sc., and Applied Science and Professor of Washington, 2005; Ph.D., 2011 Orthopedic Engineering (Orthopedic Ibrahim S. Odeh Surgery) Lecturer in Civil Engineering and Chris A. Marianetti B.A.E., RPI, 1962; Ph.D., 1966 Engineering Mechanics Associate Professor of Materials B.S., Jordan University of Science Science (Henry Krumb School of Mines) Andreas Christian Mueller and Technology, 2000; M.B.A., St. and of Applied Physics and Applied Lecturer in Data Science (Computer Thomas, 2004; Ph.D., Illinois (Urbana– Mathematics Science) Champaign), 2010 B.S., Ohio State, 1997; M.S., 1998; B.S., University of Bonn (Germany), Ph.D., MIT, 2004 2009; Ph.D., 2014 Elizabeth S. Olson Associate Professor of Biomedical Mike Massimino Kristin M. Myers Engineering and Auditory Biophysics (in Professor of Professional Practice of Associate Professor of Mechanical Otolaryngology/Head and Neck Surgery) Mechanical Engineering Engineering B.A., Barnard, 1981; Ph.D., MIT, 1988 B.S., Columbia, 1984; M.S., MIT, 1988; B.S., Michigan, 2002; M.S., MIT, 2005; Ph.D., 1992 Ph.D., 2008 Mariana Olvera-Cravioto Associate Professor of Industrial Arvind Narayanaswamy Engineering and Operations Research Michael E. Mauel Associate Professor of Mechanical B.S., Instituto Technológico Autónomo Professor of Applied Physics Engineering de México (Mexico), 2000; B.S., MIT, 1978; M.S., 1979; Sc.D., 1983 B.Tech., Indian Institute of Technology M.S., Stanford, 2004; Ph.D., 2006 (India), 1997; M.S., Delaware, 1999; Kathleen McKeown Vanessa Ortiz Henry and Gertrude Rothschild Ph.D., MIT, 2007 Assistant Professor of Chemical Professor of Computer Science Engineering A.B., Brown, 1976; M.S., Pennsylvania, B.S.E., University of Puerto Rico, 2002; 1979; Ph.D., 1982 Ph.D., Pennsylvania, 2007

ENGINEERING 2017–2018 41

Ben O’Shaughnessy Feniosky Peña-Mora Katherine E. Reuther Professor of Chemical Engineering Edwin Howard Armstrong Professor Lecturer in Biomedical Engineering B.Sc., University of Bristol (England), of Civil Engineering and Engineering B.S.E., The College of New Jersey, 1977; Ph.D., University of Cambridge Mechanics and Professor of Earth 2009; Ph.D., Pennsylvania, 2014 (England), 1984 and Environmental Engineering and of Computer Science Kenneth A. Ross John Paisley B.S., Universidad Nacional Pedro Professor of Computer Science Assistant Professor of Electrical Henríquez Ureña (Dominican Republic), B.Sc., University of Melbourne Engineering 1987; S.M., MIT, 1991; Sc.D., 1994 (Australia), 1986; Ph.D., Stanford, 1991 B.S.E., Duke, 2004; M.S., 2007; Ph.D., 2010 Aron Pinczuk Dan Rubenstein Professor of Applied Physics and of Associate Professor of Computer Science Thomas Panayotidi Physics (Arts and Sciences) B.S., MIT, 1992; M.A., California (Los Lecturer in Civil Engineering and Licenciado, Buenos Aires (Argentina), Angeles), 1994; Ph.D., Massachusetts Engineering Mechanics 1962; Ph.D., Pennsylvania, 1969 (Amherst), 2000 B.S., Columbia, 1981; M.S., 1983; Ph.D., 1986 Lorenzo M. Polvani Paul Sajda Professor of Applied Mathematics and Professor of Biomedical Engineering Ah-Hyung Alissa Park of Earth and Environmental Sciences and of Electrical Engineering and of Lenfest Earth Institute Associate (Arts and Sciences) Radiology (Health Sciences) Professor in Climate Change (Earth and B.Sc., McGill University (Canada), 1981; B.S., MIT, 1989; M.S., Pennsylvania, Environmental Engineering) M.Sc., 1982; Ph.D., MIT, 1988 1992; Ph.D., 1994 B.S., University of British Columbia (Canada), 1998; M.S., 2000; Ph.D., Ohio Matthias Preindl Ansaf Salleb-Aouissi State, 2005 Assistant Professor of Electrical Lecturer in Computer Science Engineering Ph.D., University of Orléans (France), Itsik Pe’er B.Sc., University of Padua (Italy), 2008; 2003 Associate Professor of Computer Science M.Sc., ETH Zurich (Switzerland), 2010; B.S., Tel Aviv University (Israel), 1990; Ph.D., University of Padua (Italy), 2014 M.S., 1995; Ph.D., 2002

ENGINEERING 2017–2018 42 Peter Schlosser Samuel K. Sia WaiChing Steve Sun Maurice Ewing and J. Lamar Worzel Professor of Biomedical Engineering Assistant Professor of Civil Engineering Professor of Geophysics (Earth and B.Sc., University of Alberta (Canada), and Engineering Mechanics Environmental Engineering) and 1997; Ph.D., Harvard, 2002 B.S., California (Davis), 2005; M.S. Professor of Earth and Environmental Stanford, 2007; M.A., Princeton, 2008; Sciences (Arts and Sciences) Karl Sigman Ph.D., Northwestern, 2011 B.S./M.S., University of Heidelberg Professor of Industrial Engineering and (Germany), 1981; Ph.D., 1985 Operations Research James Teherani B.A., California (Santa Cruz), 1980; Assistant Professor of Electrical Henning G. Schulzrinne M.A., California (Berkeley), 1983; Engineering Julian Clarence Levi Professor of M.S., 1984; Ph.D., 1986 B.S., Texas (Austin), 2008; M.S., MIT, Mathematical Methods and Computer 2010, Ph.D., 2015 Science and Professor of Electrical Andrew W. Smyth Engineering Professor of Civil Engineering and Michael K. Tippett B.S., Technical University of Darmstadt Engineering Mechanics Associate Professor of Applied Physics (Germany), 1984; M.S., Cincinnati, B.A., B.Sc., Brown, 1992; M.S., Rice, and Applied Mathematics 1987; Ph.D., Massachusetts (Amherst), 1994; M.S., Southern California, 1997; B.S., North Carolina State, 1987; 1992 Ph.D., 1998 M.S., New York University, 1990; Ph.D., 1992 Mingoo Seok Adam H. Sobel Assistant Professor of Electrical Professor of Applied Physics and Applied Van-Anh Truong Engineering Mathematics and of Environmental Assistant Professor of Industrial B.S., Seoul National University (South Sciences (Arts and Sciences) Engineering and Operations Research Korea), 2005; M.S., Michigan, 2007; B.A., Wesleyan, 1989; Ph.D., MIT, 1998 B.S., University of Waterloo (Canada); Ph.D., 2011 Ph.D., Cornell, 2007 Ponisseril Somasundaran Rocco A. Servedio LaVon Duddleson Krumb Professor Yannis P. Tsividis Professor of Computer Science of Mineral Engineering (Earth and Edwin Howard Armstrong Professor of A.B., Harvard, 1993; M.S., 1997; Environmental Engineering) Electrical Engineering Ph.D., 2001 B.Sc., Kerala University (India), 1958; B.E., Minnesota, 1972; M.S., California B.E., Indian Institute of Science (India), (Berkeley), 1973; Ph.D., 1976 Simha Sethumadhavan 1961; M.S., California (Berkeley), 1962; Associate Professor of Computer Ph.D., 1964 David G. Vallancourt Science Senior Lecturer in Circuits and Systems B.S.E., University of Madras (India), Marc W. Spiegelman (Electrical Engineering) 2000; M.S., Texas, 2005; Ph.D., 2007 Arthur D. Storke Memorial Professor of B.S., Columbia, 1981; M.S., 1984; Earth and Environmental Sciences (Arts Ph.D., 1987 Jay Sethuraman and Sciences) and Professor of Applied Professor of Industrial Engineering and Physics and Applied Mathematics John T. Vaughan Operations Research B.A. Harvard, 1985; Ph.D., University of Professor of Biomedical Engineering in B.E., Birla Institute of Technology and Cambridge (England), 1989 the Mortimer B. Zuckerman Mind Brain Science (India), 1991; M.S., Indian Clifford Stein Behavior Institute Institute of Science (India), 1994; Professor of Industrial Engineering and B.S., Auburn, 1982; Ph.D., Alabama at Ph.D., MIT, 1999 Operations Research and of Computer Birmingham, 1993 Science Michael P. Sheetz B.S.E., Princeton, 1987; Latha Venkataraman William R. Kenan Jr. Professor of Cell M.S., MIT, 1989; Ph.D., 1992 Associate Professor of Applied Physics Biology and Professor of Biomedical B.S., MIT, 1993; M.S., Harvard, 1997; Engineering Milan N. Stojanovic Ph.D., 1999 B.A., Albion, 1968; Ph.D., Caltech, 1972 Associate Professor of Biomedical Engineering and of Medical Science Venkat Venkatasubramanian Kenneth L. Shepard Ph.D., Harvard, 1995 Samuel Ruben–Peter G. Viele Lau Family Professor of Electrical Professor of Engineering (Chemical Engineering and Professor of Biomedical Fred R. Stolfi Engineering) Engineering Senior Lecturer in Mechanical B.Tech., University of Madras (India), B.S.E., Princeton, 1987; Engineering 1977; M.S., Vanderbilt, 1979; Ph.D., M.S., Stanford, 1988; Ph.D., 1992 B.S., Fordham, 1972; M.S., RPI, 1976; Cornell, 1984 Ph.D., 2001 Masanobu Shinozuka Francesco A. Volpe Professor of Civil Engineering and Salvatore J. Stolfo Associate Professor of Applied Physics Engineering Mechanics Professor of Computer Science Laurea, University of Pisa (Italy), B.S., Kyoto University (Japan), 1953; B.S., Brooklyn, 1974; M.S., New York 1998; Ph.D., University of Greifswald M.S., 1955; Ph.D., Columbia, 1960 University, 1976; Ph.D., 1979 (Germany), 2003

ENGINEERING 2017–2018 Sinisa Vukelic Renata Maria Mattosinho David Da-Wei Yao 43 Lecturer in Mechanical Engineering Wentzcovitch Piyasombatkul Family Professor of Dipl.Ing., University of Belgrade, Professor of Materials Science and Industrial Engineering and Operations 2004; M.S., Columbia, 2005; Applied Physics, and Earth and Research Ph.D., 2009 Environmental Science M.A.Sc., University of Toronto (Canada), B.A., University of São Paulo (Brazil), 1981; Ph.D., 1983 Gordana Vunjak-Novakovic 1980; M.S., 1982; Ph.D., California The Mikati Foundation Professor of (Berkley), 1988 Y. Lawrence Yao Biomedical Engineering and Professor of Professor of Mechanical Engineering Medical Sciences (Medicine) Alan C. West B.E., Shanghai Jiao Tong University B.S., University of Belgrade (Serbia), Samuel Ruben-Peter G. Viele Professor (P.R. China), 1982; M.S., Wisconsin 1972; S.M., 1975; Ph.D., 1980 of Electrochemistry (Chemical Engineering) (Madison), 1984; Ph.D., 1988 B.S., Case Western Reserve, 1985; Haim Waisman Ph.D., California (Berkeley), 1989 Huiming Yin Associate Professor of Civil Engineering Associate Professor of Civil Engineering and Engineering Mechanics Ward Whitt and Engineering Mechanics B.S., Technion (Israel), 1999; M.S., Wai T. Chang Professor of Industrial B.S.E., Hohai University (P.R. China), 2002; Ph.D., RPI, 2005 Engineering and Operations Research 1995; M.S., Peking University (P.R. China), A.B., Dartmouth, 1964; 1998; Ph.D., Iowa, 2004 Qi Wang Ph.D., Cornell, 1969 Assistant Professor of Biomedical Ngai Yin Yip Engineering Chris H. Wiggins Assistant Professor of Earth and B.S., North China University of Electric Associate Professor of Applied Mathematics Environmental Engineering Power (P.R. China), 1992; M.S., Harbin B.A., Columbia, 1993; B.E., Nanyang Technological University Institute of Technology (P.R. China), Ph.D., Princeton, 1998 (Singapore), 2004; M.S., Yale, 2011; 1995; Ph.D., 1999; Ph.D., McGill Ph.D., 2015 University (Canada), 2006 John Wright Associate Professor of Electrical Nanfang Yu Wen I. Wang Engineering Assistant Professor of Applied Physics Thayer Lindsley Professor in the Faculty B.S., Illinois (Urbana-Champaign), 2004; B.S., Peking University (China), 2004; of Engineering and Applied Science M.S., 2007; Ph.D., 2009 Ph.D., Harvard, 2009 (Electrical Engineering) and Professor of Applied Physics Eugene Wu Changxi Zheng B.S., National Taiwan University (Taiwan), Assistant Professor of Computer Science Assistant Professor of Computer Science 1975; M.E.E., Cornell, 1979; Ph.D., 1981 B.S., California (Berkeley), 2007; M.S., B.Eng., Shanghai Jiao Tong University MIT, 2010; Ph.D., 2014 (P.R. China), 2005; Ph.D., Cornell, 2012 Xiaodong Wang Professor of Electrical Engineering Cheng-Shie Wuu Xunyu Zhou B.S., Shanghai Jiao Tong University (P.R. Professor of Clinical Radiation Oncology, Liu Family Professor of Industrial China), 1992; M.S., Purdue, 1995; and of Environmental Health Sciences, Engineering and Operations Research Ph.D., Princeton, 1998 and of Applied Physics B.S., Fudan University (China), 1984; B.S., National Tsing Hua University Ph.D., 1989 Anthony C. Webster (Taiwan), 1979; M.S., 1982; Ph.D., Lecturer in Finance in the Department Kansas, 1985 Charles Zukowski of Industrial Engineering and Operations Professor of Electrical Engineering Research Junfeng Yang B.S., MIT, 1982; M.S., 1982; B.S., Rutgers, 1980; M.S., Columbia, Associate Professor of Computer Science Ph.D., 1985 1983; M.B.A., 1999 B.S., Tsinghua University (P.R. China), 2000; M.S., Stanford, 2002; Gil Zussman Michael I. Weinstein Ph.D., 2007 Associate Professor of Electrical Professor of Applied Mathematics Engineering B.S., Union College, 1977; M.S., Yuan Yang B.A., B.Sc., Technion (Israel), 1995; Courant Institute–NYU, 1979; Ph.D., Assistant Professor of Applied Physics M.Sc., 1999; Ph.D., 2004 1982 and Applied Mathematics B.S., Peking University (China), 2007; Omri Weinstein Ph.D., Stanford, 2012 FACULTY MEMBERS-AT-LARGE Assistant Professor of Computer Carlos J. Alonso Science Mihalis Yannakakis Dean, Graduate School of Arts and B.S., Tel Aviv University (Israel), 2010; Percy K. and Vida L. W. Hudson Sciences Ph.D., Princeton, 2015 Professor of Computer Science Dipl., National Technical University of Peter B. Kelemen Athens (Greece), 1975; Chair, Department of Earth and Ph.D., Princeton, 1979 Environmental Sciences

ENGINEERING 2017–2018 44 Liang Tong Jonathan L. Gross Thomas E. Stern Chair, Department of Biological Sciences Professor Emeritus of Computer Science Dicker Professor Emeritus of Electrical Engineering R. Glenn Hubbard Robert A. Gross Dean, Columbia Business School Percy K. and Vida L. W. Hudson Robert D. Stoll Professor Emeritus of Applied Physics Professor Emeritus of Civil Engineering James L. Leighton and Dean Emeritus Chair, Department of Chemistry Horst Stormer John T. F. Kuo I. I. Rabi Professor Emeritus of Physics Henry Pinkham Maurice Ewing and J. Lamar Worzel (Arts and Sciences) and Professor Chair, Department of Mathematics Professor Emeritus of Geophysics Emeritus of Applied Physics

James J. Valentini W. Michael Lai Malvin Carl Teich Dean, Columbia College Professor Emeritus of Mechanical Professor Emeritus of Engineering Engineering and of Orthopedic Science Philip Tuts Bioengineering (Orthopedic Surgery) Chair, Department of Physics Rene B. Testa Leon Lidofsky Professor Emeritus of Civil Engineering Professor Emeritus of Applied Physics and Engineering Mechanics EMERITI AND RETIRED and Nuclear Engineering OFFICERS (NOT IN RESIDENCE) Nickolas J. Themelis Daniel N. Beshers Eugene S. Machlin Professor Emeritus of Earth and Professor Emeritus of Metallurgy (Earth Henry Marion Howe Professor Emeritus Environmental Engineering and Environmental Engineering) of Metallurgy Stephen H. Unger Huk Yuk Cheh Thomas C. Marshall Professor Emeritus of Computer Science Samuel Ruben-Peter G. Viele Professor Professor Emeritus of Applied Physics and of Electrical Engineering Emeritus of Electrochemistry Henry E. Meadows Jr. Rimas Vaicaitis Rene Chevray Professor Emeritus of Electrical Engineering Renwick Professor Emeritus of Civil Professor Emeritus of Mechanical Engineering Engineering Christian Meyer C. K. Chu Professor Emeritus of Civil Engineering Omar Wing Fu Foundation Professor Emeritus and Engineering Mechanics Professor Emeritus of Electrical of Applied Physics in the Faculty of Engineering Engineering and Applied Science Richard M. Osgood Jr. Higgins Professor Emeritus of Electrical Henryk Wozniakowski Edward G. Coffman Engineering and Professor Emeritus Professor Emeritus of Computer Science Professor Emeritus of Electrical Engineering of Applied Physics and Applied and of Computer Science Mathematics Edward S. Yang Professor Emeritus of Electrical Engineering Paul Diament Glenn K. Rightmire Professor Emeritus of Electrical Engineering Associate Emeritus in Mechanical Tuncel M. Yegulalp Engineering Professor Emeritus of Mining (Earth Frank L. DiMaggio and Environmental Engineering, Henry Robert A. W. and Christine S. Carleton Enders Robinson Krumb School of Mines) Professor Emeritus of Civil Engineering Maurice Ewing and J. Lamar Worzel Professor Emeritus of Applied Yechiam Yemini George W. Flynn Geophysics (Earth and Environmental Professor Emeritus of Computer Science Higgins Professor Emeritus of Chemistry Engineering) and Professor Emeritus of Chemical Engineering Mischa Schwartz ADMINISTRATIVE OFFICERS Charles Batchelor Professor Emeritus AND STAFF Zvi Galil of Electrical Engineering Mary C. Boyce Julian Clarence Leu Professor Emeritus Dean of Mathematical Methods and of Amiya K. Sen Computer Science and Dean Emeritus Professor Emeritus of Electrical Daniel P. Alicea Engineering and of Applied Physics Associate Director of Finance and Atle Gjelsvik Grants Management, Data Science Professor Emeritus of Civil Engineering Jordan L. Spencer Institute Professor Emeritus of Chemical Fletcher H. Griffis Engineering Rumana Ashraf Professor Emeritus of Civil Engineering Manager, Grants and Contracts

ENGINEERING 2017–2018 Leslie Barna Jaime Flores-Vivero Kiley Kula 45 Assistant Director of Operations, Data Production Manager, Columbia Video Human Resources Manager Science Institute Network Jackson Lau Ellie Bastani Emily Ford System Administrator Assistant Dean of Graduate Student Director of Outreach Programs and Services and Postdoctoral Affairs Special Projects Christina Liu Reunion Coordinator Rene Baston Kathleen Gay Executive Director, NE Big Data Hub, Student Services Officer, Graduate Elizabeth Manchester Data Science Institute Student Affairs Assistant Director, Alumni Relations

David Meir Blei Mark A. Habana Jessica L. Marinaccio Director of Graduate Programs, Data Associate Director of Research and Dean of Undergraduate Admissions and Science Institute Grants Development, Data Science Financial Aid Institute Kimberly Bregenzer Betty Matias Chief Financial Officer Jill Galas Hickey CUCSSA Student Affairs Officer Director of Annual Giving Leora Brovman Neil McClure Associate Dean of Undergraduate Katherine B. Hickey Associate Dean of Faculty Affairs and Student Affairs and Academic Financial Support Specialist, Center for Human Resources Administration Computational Learning Systems Theresa A. McKenzie Shih-Fu Chang Michael Holve Director of Budget and Finance Senior Executive Vice Dean Assistant Director of Information Technology, Data Science Institute Kathleen McKeown Rachel Fuld Cohen Director, Data Science Institute Assistant Director of Student Services Zachary Howell and Career Development, Data Science Director of Major Gifts, Alumni Relations Alexis Moore Institute Manager of Academic Administration Shu-Yi Hsu Brianne Cortese Instructional Technologist, Columbia Jocelyn Morales Assistant Director of Admissions and Video Network Associate Director, Graduate Student Academic Affairs, Data Science Institute Services Margaret Hughes Ralph Cruz Stewardship Officer Thomas Morgan Manager of Purchasing and Accounts Media Producer, Columbia Video Payable Joanne M. Hvala Network Senior Director, Communications Patricia Culligan Barclay Morrison Associate Director, Data Science Idrija Ibrahimagic Vice Dean of Undergraduate Programs Institute Manager of Finance and Grants, Data Science Institute Kathryn E. Naum Julianne Del Gatto Program Coordinator, Data Science Human Resources Coordinator Eileen Irizarry Institute Financial Coordinator, Data Science Allison Elliott Institute Sharnice Neale-Ottley Communications Writer Program Coordinator, Data Science Jessie Jones Institute Holly Evarts Administrative Assistant, Graduate Director, Strategic Communications Student Affairs Jane Nisselson and Media Relations Associate Director, Multimedia Soulaymane Kachani Communications Jennifer Feierman Senior Vice Dean Major Gifts Officer Martin Nolan Leander Keizer Project Engineer Rachel Fitzgerald Video Editor, Columbia Video Network Facilities Coordinator Quy O Christian Kmetz Associate Director of Technology Genevieve Fleming Assistant Production Manager, Columbia Services Special Projects Manager Video Network

ENGINEERING 2017–2018 46 Timothy J. O'Neill Ivy Schultz Laura G. Tejeda Associate Director of Web Associate Director of Entrepreneurship Manager of Grants and Contracts Communication Programs Jeffrey Urstadt Lourdes Pineiro Esther Schwartz Manager of Payroll and Financial Aid Development Assistant Executive Assistant to the Dean Dario Vasquez Axinia Radeva Alexis Seeley I-Corps Program Coordinator Systems Administrator Executive Director of CVN and Associate Dean of Online Learning Tania Velimirovici Jack Reilly Academic Programs and Special Assistant Director, Alumni Relations Tiffany M. Simon Projects Manager Associate Dean of Graduate Student Israel Rodriguez Affairs Woodrow David Webb Facilities Manager Associate Director of Executive David Simpson Education Programs Alvaro Rojas-Caamano Administrative Assistant Assistant Director of Graduate Student Sofia Yagaeva Services Sharon Sputz Assistant Director, Columbia Video Director of Strategic Programs, Data Network Stan Sakry Science Institute Director of Facilities and Space Planning William Yandolino Jonathan R. Stark Executive Director of Finance and Paolo Santonocito Director of Operations, Data Science Operations Assistant Director, Engineering Fund Institute Marina Zamalin Starling Sawyer Michelle R. Stevenson Associate Director of Online Learning, Executive Director of Alumni Relations Coordinator, Columbia Video Network Columbia Video Network

Anthony Schmitt Maura Swisher Manager, Grants and Contracts Financial Coordinator

ENGINEERING 2017–2018 Departments and Academic Programs 48 KEY TO COURSE LISTINGS

his section contains a descrip- BMCH Biomedical and Chemical Engineering CSOR Computer Science and Operations Research tion of the curriculum of each BMEB Biomedical Engineering, Electrical T department in the School, along Engineering, and Biology DNCE Dance with information regarding undergraduate and graduate degree requirements, BMEE Biomedical Engineering and DRAN Decision, Risk, and Operations Electrical Engineering elective courses, and suggestions about DROM Decision, Risk, and Operations courses and programs in related fields. BMEN Biomedical Engineering Management All courses are listed, whether or not BMME Biomedical Engineering and EACE Earth and Environmental Engineering they are being offered during the current Mechanical Engineering and Chemical Engineering year; if a course is not being given, that is indicated. Included as well are cours- BUSI Business EAEE Earth and Environmental Engineering es cross-listed with other departments CBMF Computer Science, Biomedical EAIA Earth and Environmental Engineering and undergraduate divisions within the Engineering and Medical Informatics and International and Public Affairs University. CEOR Civil Engineering and Operations ECBM Electrical Engineering, Computer Research Science and Biomedical Engineering DESIGNATORS CHAP Chemical Engineering and ECIA Earth and Environmental and Civil Each course is preceded by a four-letter Applied Physics and Applied Math Engineering and International and Public designator, which indicates the department Affairs or departments presenting the course. CHBM Chemical Engineering and Biomedical Engineering ECIE Economics and Industrial Engineering CHCB Chemistry, Biology and ECON Economics Course Designator Department Subject Computer Science EEBM Electrical Engineering and AHIS Art History CHEE Chemical Engineering and Biomedical Engineering AMCS Applied Math and Computer Science Earth and Environmental Engineering EECS Electrical Engineering and AMST American Studies CHEM Chemistry Computer Science APAM Applied Physics and Applied Math CHEN Chemical Engineering EEHS Electrical Engineering and History APBM Applied Physics and CIEE Civil Engineering and EEME Electrical Engineering and Biomedical Engineering Earth and Environmental Engineering Mechanical Engineering APCH Applied Physics and CIEN Civil Engineering EEOR Electrical Engineering and Chemical Engineering Operations Research CMBS Cellular, Molecular, and APMA Applied Mathematics Biophysical Studies EESC Earth and Environmental Sciences APPH Applied Physics COCI Contemporary Civilization EHSC Environmental Health Sciences ARCH Architecture COMS Computer Science ELEN Electrical Engineering ASCE Asian Civilization: East Asian COSA Computer Science, Industrial ENGI Engineering Engineering and Operations Research, ASCM Asian Civilization: Middle East ENGL English Statistics, and Applied Physics and Applied ASTR Astronomy Mathematics EMME Engineering Mechanics and Mechanical Engineering BIOC Biology and Chemistry CSEE Computer Science and Electrical Engineering ENME Engineering Mechanics BIOL Biology CSEN Computer Science and FINC Finance BIST Biostatistics English

ENGINEERING 2017–2018 49

FREN French PSYC Psychology 1 Undergraduate course GERM German RELI Religion 2 Undergraduate course, intermediate GRAP Graphics SCNC Science 3 Undergraduate course, advanced HIST History SIEO Statistics and Industrial Engineering 4 Graduate course that is open to qualified and Operations Research undergraduates HSAM History and Applied Mathematics SOCI Sociology 6 Graduate course HUMA Humanities SPAN Spanish 8 Graduate course, advanced IEME Industrial Engineering and Mechanical Engineering STAT Statistics 9 Graduate research course or seminar IEOR Industrial Engineering and STCS Statistics and Computer Science Operations Research An x following the course number URBS Urban Studies means that the course meets in the fall INAF International Affairs VIAR Visual Arts semester; y indicates the spring semester. INTA Earth and Environmental Engineering, Civil Engineering, and HOW COURSES ARE NUMBERED DIRECTORY OF CLASSES International and Public Affairs The course number that follows each Room assignments, days and hours, MATH Mathematics designator consists of one or two capital and course changes for all courses are MEBM Mechanical Engineering and letters followed by four digits. The capital available online at columbia.edu/cu/ Biomedical Engineering letter indicates the University division or bulletin/uwb. The School reserves the right to MECE Mechanical Engineering affiliate offering the course: withdraw or modify the courses of MECH Mechanical Engineering and B Business instruction or to change the instructors Chemical Engineering E Engineering and Applied Science at any time. MECS Mechanical Engineering and P Mailman School of Public Health Computer Science S Summer Session MEEM Mechanical Engineering and Engineering Mechanics U International and Public Affairs MEIE Mechanical Engineering and W Interfaculty course Industrial Engineering Z American Language Program MSAE Materials Science and Engineering Arts and Sciences MSIE Management Science and Industrial Engineering and Operations Research CC Columbia College MUSI Music UN Undergraduate PHED Physical Education GU Undergraduate, Graduate PHIL Philosophy GR Graduate Only PHYS Physics The first digit indicates the level of the PLAN Planning course, as follows: POLS Political Science 0 Course that cannot be credited PSLG Physiology toward any degree

ENGINEERING 2017–2018 50 APPLIED PHYSICS AND APPLIED MATHEMATICS 200 S. W. Mudd, MC 4701 Phone: 212-854-4457 Applied Physics and Applied Mathematics: apam.columbia.edu/ Materials Science and Engineering: seas.columbia.edu/matsci

CHAIR Engineering Timothy M. Hall Igor Geogdzhayev Qian Cheng Ismail C. Noyan Adam Sobel David E. Keyes Catherine Naud Insung Choi 208 S. W. Mudd Marc W. Spiegelman Jerome Meli Yoshitomo Okawachi Colton Conroy Latha Venkataraman Ron L. Miller Anastasia Romanou Lingjie Du DEPARTMENT Wen I. Wang, Electrical Thomas Morgan Alessandro Farsi ADMINISTRATOR Engineering Stephen L. Ostrow ADJUNCT RESEARCH Ren Gu Stella M. Lau Michael I. Weinstein Thomas S. Pedersen SCIENTISTS Michael Inkpen Renata M. Wentzcovitch Lawrence N. Rothenberg Darrien T. Garnier Jae Kyung Jang PROFESSORS Cheng-Shie Wuu, Stephen A. Sabbagh Mark Holzer Yanzheng Jiang Katayun Barmak Radiation Oncology George Tselioudis Conal C. Murray Alexander Klenner Daniel Bienstock, Shalom J. Wind Emmanuel Yashchin Tae Kyung Lee Industrial Engineering ASSOCIATE Pat Zanzonico Guozhan Liang and Operations PROFESSORS ASSOCIATE RESEARCH Giacomo Lovat Research William E. Bailey ADJUNCT ASSOCIATE SCIENTISTS Cassier Maxence Simon J. L. Billinge Eitan Grinspun, PROFESSOR Mikhail Alexandrov Hadrien Montelli Allen H. Boozer Computer Science Brian Cairns Michael Bauer Aditi Sheshadri Mark A. Cane, Earth Chris A. Marianetti Anna Rozenshtein Yonghua Chen Inigo Urteaga and Environmental Michael K. Tippett Gabriel Chiodo Chongzhao Wu Sciences Francesco A. Volpe ADJUNCT ASSISTANT Robert Field Shangmin Xiong Siu-Wai Chan Chris H. Wiggins PROFESSOR Jeremy Hanson Yaping Zang Qiang Du Jacob Hofman Seung Yub Lee Alexander Gaeta ASSISTANT Seung Yub Lee Jeffrey Levesque SPECIAL LECTURERS Oleg Gang, Chemical PROFESSORS Cassier Maxence Li Liu Daniel N. Beshers Engineering Andrew J. Cole Young Seouk Park C. K. Chu Irving P. Herman Kyle Mandli SENIOR RESEARCH Francesca Turco Monique C. Katz James S. Im Donsub Rim SCIENTISTS Shuguang Wang Michal Lipson, Electrical Yuan Yang John Berkery Jingbo Wu SPECIAL RESEARCH Engineering Nanfang Yu James Bialek SCIENTISTS Michael E. Mauel Rainer Bleck ADJUNCT ASSOCIATE Leonard Druyan Gerald A. Navratil SENIOR LECTURER Steven A. Sabbagh RESEARCH SCIENTISTS Qiancheng Ma Ismail C. Noyan Marco Zaider Emmanouil Thomas C. Marshall Richard M. Osgood Jr., ADJUNCT SENIOR Antonogiannakis Shalom J. Wind Professor Emeritus, LECTURER IN RESEARCH SCIENTISTS Chris Hansen Electrical Engineering DISCIPLINE C. Julian Chen Denis Potapenko Aron Pinczuk Drew Youngren Yigal Komem Lorenzo M. Polvani John Marshall POSTDOCTORAL RESEARCH SCIENTISTS Malvin A. Ruderman, ADJUNCT Patricia Mooney Jae Heon Ahn Physics PROFESSORS RESEARCH Antara Banerjee Christopher H. Scholz, Vittorio M. Canuto SCIENTISTS Gregory Vincent Cesana Earth and Environmental Barbara E. Carlson Jacek Chowdhary Rei Chemke Sciences C. Julian Chen Jerry I. Dadap Jia Chen Amiya K. Sen, Electrical Anthony Del Genio

he Department of Applied Physics Current Research Activities in new plasma measurement techniques. and Applied Mathematics Applied Physics and Applied The results from our fusion science Tincludes undergraduate and Mathematics experiments are used as a basis graduate studies in the fields of Plasma physics and fusion energy. for collaboration with large national applied physics, applied mathematics, In experimental plasma physics, research and international experiments. For and materials science and engineering. is being conducted on (1) equilibrium, example, methods of active feedback The graduate program in applied stability, and transport in fusion control of plasma instability developed physics includes plasma physics and plasmas: high-beta tokamaks, spherical at Columbia University are guiding controlled fusion; solid-state physics; tokamaks, and levitated dipoles; (2) research on NSTX at the Princeton optical and laser physics; medical magnetospheric physics: trapped Plasma Physics Laboratory, on the physics; atmospheric, oceanic, particle instabilities and stochastic DIII-D tokamak at General Atomics, and and earth physics; and applied particle motion; (3) confinement for the design of the next generation mathematics. The graduate programs of toroidal nonneutral plasmas; (4) burning plasma experiment, ITER. In in materials science and engineering plasma source operation and heating theoretical plasma physics, research are described on pages 175–177. techniques; and (5) the development of is conducted in the theory of plasma

ENGINEERING 2017–2018 equilibrium and stability, active control modeling, including collaborations with with laboratory magnetospheres 51 of MHD instabilities, the kinetic theory Columbia’s Data Science Institute (DSI), and advanced models for space of turbulence and transport, and the the Department of Systems Biology, and weather and radiation belt dynamics. development of techniques based on the Department of Statistics. Extensive The stellarator known as Columbia the theory of general coordinates and collaborations exist with national climate Nonneutral Torus (CNT) conducts dynamical systems. The work is applied research centers (the Geophysical Fluid research on the magnetohydrodynamic to magnetic fusion, nonneutral and Dynamics Laboratory and the National stability, microwave heating, and space plasmas. Center for Atmospheric Research) and microwave diagnostics of neutral with national laboratories of the U.S. stellarator plasmas. Two smaller Optical and laser physics. Active Department of Energy, custodians of the devices investigate respectively an areas of research include inelastic light nation’s most powerful supercomputers. innovative tokamak-stellarator hybrid scattering in nanomaterials, optical plasma confinement concept and the diagnostics of film processing, new Atmospheric, oceanic, and earth use of toroidal electron-heated plasmas laser systems, nonlinear optics, ultrafast physics. Current research focuses on as sources of ions for accelerators. optoelectronics, photonic switching, the dynamics of the atmosphere and the The Columbia Linear Machine (CLM) is optical physics of surfaces, laser- ocean, climate modeling, cloud physics, a continuously operating, linear mirror induced crystallization, and photon radiation transfer, remote sensing, device for the study of collisionless integrated circuits. geophysical/geological fluid dynamics, plasma instabilities, plasma, transport, geochemistry. The department engages and feedback stabilization. Columbia’s Solid-state physics. Research in in ongoing research with the NASA Collisionless Terrella Experiment solid-state physics covers nanoscience Goddard Institute for Space Studies and investigates plasma transport in and nanoparticles, electronic transport the Lamont-Doherty Earth Observatory. magnetospheric geometry and the and inelastic light scattering in low- Six faculty members share appointments generation of strong plasma flow from dimensional correlated electron with the Department of Earth and nonlinear electrostatic potentials. systems, fractional quantum Hall Environmental Sciences. Experimental research in solid- effect, heterostructure physics and In addition to the faculty and state physics and laser physics is applications, molecular beam epitaxy, graduate students, many others conducted within the department and grain boundaries and interfaces, participate in these projects, including also in association with the Columbia nucleation in thin films, molecular full-time research faculty, faculty and Nano Initiative. Facilities include electronics, nanostructure analysis, students from other departments, and laser processing and spectroscopic and electronic structure calculations. visiting scientists. apparatus, ultrahigh vacuum chambers Research opportunities also exist within for surface analysis, picosecond and the Columbia Nano Initiative (CNI), Laboratory and Computation femtosecond lasers, a molecular beam including the NSF Nanoscale Science Facilities in Applied Physics and epitaxy machine, and a clean room that and Engineering Center, which focuses Applied Mathematics includes photo-lithography and thin film on electron transport in molecular fabrication systems. Within this field, The Plasma Physics Laboratory, nanostructures; and the DOE Energy the Laser Diagnostics and Solid-State founded in 1961, is one of the leading Frontier Research Center, which focuses Physics Laboratory conducts studies university laboratories for the study of on conversion of sunlight into electricity in laser spectroscopy of nanomaterials plasma physics in the United States. in nanometer-sized thin films. and semiconductor thin films, and laser There are four experimental facilities. diagnostics of thin film processing. The Columbia High-Beta Tokamak Applied mathematics. Current research The Laser Lab focuses on the study (HBT-EP) supports the national program encompasses analytical and numerical of materials under high pressure, laser to develop controlled fusion energy. analysis of deterministic and stochastic surface chemical processing, and new It utilizes high voltage, pulsed power partial differential equations, large-scale semiconductor structures. Research systems, and laser and magnetic scientific computation, fluid dynamics, is also conducted in the shared diagnostics to study the properties dynamical systems and chaos, as characterization laboratories and clean of high-beta plasmas and the use well as applications to various fields of room operated by the NSF Nanoscale of feedback stabilization to increase physics and biology. The applications Science and Engineering Center. the achievable beta. A collaborative to physics include quantum and The department maintains an program with the Princeton Plasma condensed-matter physics, materials extensive network of computing Physics Laboratory and the DIII-D science, electromagnets and optics, clusters and desktop computers. tokamak group at General Atomics is plasma physics, medical imaging, and The research of the Plasma Lab studying the properties of high-beta is supported by a dedicated data the earth sciences, notably atmospheric, plasmas in order to maximize fusion acquisition/data analysis system, and oceanic, and climate science, and power production in these large, neutral the applied math group has access to a solid earth geophysics (see below). beam-heated tokamaks and spherical Beowulf cluster. Materials Science and The applications to biology include tori. The plasma physics group Applied Physics built an intel-based machine learning and biophysical and MIT conduct joint experiments 600 core computing cluster that is

ENGINEERING 2017–2018 52 APPLIED PHYSICS PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

APMA E2000 (4)3 MATHEMATICS1 MATH UN1101 (3) MATH UN1102 (3) and ODE (3)2

PHYSICS UN1401 (3) UN1402 (3) UN1403 (3) Lab UN1494 (3) (three tracks, UN1601 (3.5) UN1602 (3.5) UN2601 (3.5) Lab UN2699 (3) choose one) UN2801 (4.5) UN2802 (4.5) Lab UN3081 (2)

CHEMISTRY/ CHEM UN1403 (3), or higher or BIOLOGY (choose one course) BIOL UN2001 (4) or BIOL UN2005 (4), or higher

UNIVERSITY UN1010 (3) either semester WRITING

HUMA CC1001, HUMA CC1002, COCI CC1101, COCI CC1102, REQUIRED or Global Core (3–4) or Global Core (3–4) NONTECHNICAL ELECTIVES HUMA UN1121 or ECON UN1105 (4) and UN1123 (3) UN1155 recitation (0)

REQUIRED (3) Student’s choice TECH ELECTIVES

COMPUTER ENGI E1006 (3) any semester SCIENCE

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 With the permission of the faculty adviser, students with advanced standing may start the calculus sequence at a higher level. 2 Applied physics majors should satisfy their ODE requirement with the Mathematics Department (ordinarily MATH UN2030). Students who take APMA E2101 prior to declaring their major in applied physics may use this course to satisfy their ODE requirement with the permission of the faculty adviser. 3 Effective Class of 2021.

dedicated to performing first-principles Current Research Activities and sophistication are important. Using the large computations of materials. Researchers Laboratory Facilities in Materials number of electives in these programs, in the department are additionally using Science and Engineering students can tailor their programs to fit supercomputing facilities at the National See page 172. their personal and career interests. By Center for Atmospheric Research; focusing their technical electives, students the San Diego Supercomputing can obtain a strong base of knowledge Center; the National Energy Research UNDERGRADUATE PROGRAMS in a specialized area. In addition to formal Supercomputer Center in Berkeley, The Department of Applied Physics minors, some areas of specialization that California; the National Leadership and Applied Mathematics offers three are available are described on pages Class Facility at Oak Ridge, Tennessee; undergraduate programs: applied phys- 55–56. All technical electives are normally various allocations via XSEDE; and ics, applied mathematics, and materials at the 3000 level or above. others. The Amazon Elastic Compute science. The materials science program Cloud (EC2) is also utilized to is described on pages 172–175. UNDERGRADUATE PROGRAM supplement computing resources in The applied physics and applied IN APPLIED PHYSICS times of high demand. mathematics programs provide an excellent preparation for graduate study or for careers The applied physics program stresses in which mathematical and technical the basic physics that underlies most

ENGINEERING 2017–2018 53 APPLIED PHYSICS: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

APPH E3200 (3) APPH E4300 (3) APPH E3100 (3) Mechanics Applied electrodynamics Intro. to quantum mechanics MSAE E3111 (3) APPH E4100 (3) Course in second Thermodynamics Quantum physics AP area (3) REQUIRED APPH E3300 (3) COURSES Applied electromagnetism APMA E3101 (3) Course in first APPH E4018 (2) Linear algebra AP area (3) Laboratory APMA E3102 (3) Partial differential APPH E4901 (1) APPH E4903 (2) equations Seminar Seminar

TECH1 3 points 3 points 2 points 9 points

NONTECH 3 points 3 points 3 points 3 points OR TECH ELECTIVES

TOTAL POINTS 16 15 16 17

1 They must include at least 2 points of laboratory courses. If PHYS UN3081 is taken as part of the first two years of the program, these technical electives need not include laboratory courses. Technical electives must be at the 3000 level or above unless prior approval is obtained.

developments in engineering and the member. Opportunities also exist for In addition to these courses, courses mathematical tools that are important undergraduate students in the applied listed in the Specialty Areas in Applied to both physicists and engineers. Since physics program to participate in this Physics can be used to satisfy this the advances in most branches of research through part-time employment requirement with preapproval of the technology lead to rapid changes in during the academic year and full-time applied physics adviser. state-of-the-art techniques, the applied employment during the summer, either All students must take 30 points of physics program provides the student at Columbia or as part of the NSF REU electives in the third and fourth years, with a broad base of fundamental program nationwide. Practical research of which 17 points must be technical science and mathematics while retaining experience is a valuable supplement to courses approved by the adviser. The 17 the opportunity for specialization through the formal course of instruction. Applied points include 2 points of an advanced technical electives. physics students participate in an informal laboratory in addition to APPH E4018. The applied physics curriculum offers undergraduate seminar to study current Technical electives must be at the 3000 students the skills, experience, and and practical problems in applied physics, level or above unless prior approval is preparation necessary for several career and obtain hands-on experience in at least obtained from the department. A number options, including opportunities to minor two advanced laboratory courses. of approved technical electives are in economics and to take business- Majors are introduced to two areas of listed in the section on specialty areas. related courses. In recent years, applied application of applied physics (AP) by a The remaining points of electives are physics graduates have entered graduate course in each of two areas. Approved intended primarily as an opportunity to programs in many areas of applied areas and courses are complete the absolutely mandatory four- physics or physics, enrolled in medical year, 27-point nontechnical requirement school, or been employed in various DYNAMICAL SYSTEMS: for the B.S. degree, but if this 27-point technical or financial areas immediately APMA E4101 or PHYS GU4003 nontechnical requirement has been met after receiving the B.S. degree. OPTICAL OR LASER PHYSICS: already, then any type of coursework can Opportunities for undergraduate APPH E4110 or E4112 satisfy these elective points. research exist in the many research NUCLEAR SCIENCE: APPH E4010 programs in applied physics. These PLASMA PHYSICS: APPH E4301 UNDERGRADUATE PROGRAM include fusion and space plasma physics, IN APPLIED MATHEMATICS optical and laser physics, and condensed PHYSICS OF FLUIDS: APPH E4200 The applied mathematics program is matter physics. Undergraduate students SOLID STATE/CONDENSED MATTER flexible and intensive. A student must can receive course credit for research PHYSICS: PHYS GU4018 take the required courses listed below, or an independent project with a faculty BIOPHYSICAL MODELING: APMA E4400

ENGINEERING 2017–2018 54 APPLIED MATHEMATICS PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

APMA E2000 (4)3 MATHEMATICS1 MATH UN1101 (3) MATH UN1102 (3) and ODE (3)2

PHYSICS UN1401 (3) UN1402 (3) UN1403 (3)4 Lab UN1494 (3)5 (three tracks, UN1601 (3.5) UN1602 (3.5) UN2601 (3.5) Lab UN2699 (3)5 choose one) UN2801 (4.5) UN2802 (4.5) Lab UN3081 (2)5

CHEMISTRY/ CHEM UN1403 (3), or higher or BIOL UN2001 (4) BIOLOGY (choose one course) or BIOL UN2005 (4), or higher

UNIVERSITY UN1010 (3) either semester WRITING

HUMA CC1001, HUMA CC1002, COCI CC1101, COCI CC1102, REQUIRED or Global Core (3–4) or Global Core (3–4) NONTECHNICAL ELECTIVES HUMA UN1121 or ECON UN1105 (4) and UN1123 (3) UN1155 recitation (0)

REQUIRED (3) Student’s choice TECH ELECTIVES

COMPUTER ENGI E1006 (3) any semester SCIENCE

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF E1102 (4) either semester ENGINEERING

1 With the permission of the faculty adviser, students with advanced standing may start the calculus sequence at a higher level. 2 Applied mathematics majors should satisfy their ODE requirement with the Mathematics Department (ordinarily MATH UN2030). Students who take APMA E2101 prior to declaring their major in applied mathematics may use this course to satisfy their ODE requirement with the permission of the faculty adviser. 3 Effective Class of 2021. 4 Transfer students who have not fulfilled the physics requirement prior to enrolling at Columbia may substitute this course with PHYS BC3001. 5 Or a lab course in Astronomy, Astrophysics, Biology, or Chemistry.

or prove equivalent standing, and While it is common for students can satisfy these elective points. then may elect the other courses from in the program to go on to graduate Transfers into the applied mathematics, computer science, physics, school, many graduating seniors will mathematics program from other majors Earth and environmental sciences, find employment directly in industry, require a GPA of 3.0 or above, and the biophysics, economics, business and government, education, or other fields. approval of the applied mathematics finance, or other application fields. Each Of the 27 points of elective content program chair. student tailors his or her own program in in the third and fourth years, at least 15 close collaboration with an adviser. He points of technical courses approved UNDERGRADUATE DOUBLE or she must also register for the applied by the adviser must be taken. The MAJOR IN APPLIED PHYSICS mathematics seminar during both the remaining points of electives are AND APPLIED MATHEMATICS junior and senior years. During the junior intended primarily as an opportunity to Students satisfy all requirements for year, the student attends the seminar complete the absolutely mandatory four- both majors, except for the seminar lectures for 0 points; during the senior year, 27-point nontechnical requirement requirements. They are required to take year, he or she attends the seminar for the B.S. degree, but if this 27-point both senior seminars, APMA E4903 and lectures as well as tutorial problem nontechnical requirement has been met APPH E4903 (taking one in the junior sessions for 3 or 4 points. already, then any type of coursework year and one in the senior year, due

ENGINEERING 2017–2018 55 APPLIED MATHEMATICS: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

APMA E3101 (3)1 Linear algebra (Applied math, I) MATH GU4061 (3)1 APMA E3102 (3)1 Modern analysis Partial differential APMA E4204 (3)1 equations APMA E3900 (3)3 Complex variables APMA E4101 (3) (Applied math, II) Research REQUIRED Introduction to COURSES APMA E4300 (3) dynamical systems Course from Group A2 Courses designated Introduction to numerical (Applied math, III) MATH, APMA, or STAT (3) methods (Computational Course from Group B2 math, I) APMA E4903 (3 or 4) Seminar APMA E4901 (0) Seminar

TECH4 3 points 3 points 3 points 6 points

NONTECH 3 points 3 points 3 points 3 points ELECTIVES

TOTAL POINTS 15 15 16 15

1 MATH UN2010 may be substituted for APMA E3101; MATH UN3028 may be substituted for APMA E3102; MATH UN3007 may be substituted for APMA E4204; MATH UN2500 may be substituted for MATH GU4061. 2 One course from Group A and one course from Group B required for graduation. Group A: IEOR E3658: Probability for engineers; STAT GU4105: Probability; SIEO W3600: Introduction to probability and statistics; STAT GU4001: Introduction to probability and statistics; STAT UN3105: Introduction to probability; MATH W4155: Probability theory. Group B: STAT UN3107: Statistical inference; STAT GU4107: Statistical inference; STAT GU4109: Probability and statistical inference; SIEO GU4606: Elementary stochastic processes; IEOR E3106: Stochastic systems and applications; IEOR E4106: Stochastic models; IEOR E4703: Monte Carlo simulation; COMS W4771: Machine learning. 3 With an adviser’s permission, an approved technical elective may be substituted. 4 Any course in science or engineering at the 3000 level or above qualifies as a technical elective, except for required or elective courses in the minor in entrepreneurship and innovation which do not count as technical electives unless authorized by an adviser. 3 Other elective courses may be chosen from other departments in SEAS and Arts and Sciences, e.g., the Departments of Mechanical Engineering, Electrical Engineering, Mathematics, and Statistics. to timing conflicts), but not the junior There is no requirement to focus elec- PHYS GU4018y: Solid-state physics seminars, APMA E4901 and APPH tives, so students may take as many or APMA E4101x: Intro to dynamical systems E4901. A single foundational course may as few of the recommended courses APPH E4110y: Modern optics APPH E4112x: Laser physics be used to fulfill a requirement in both in a specialty area as is appropriate to APPH E4200x: Physics of fluids majors. Students must maintain a GPA their schedules and interests. Some APPH E4301y: Intro to plasma physics at or above 3.75, and must graduate specialties are given below, but this with at least 143 points, 15 above the is not an exclusive list and others can • Earth and Atmospheric Sciences regular 128-point requirement. These be worked out in coordination with the The Earth sciences provide a wide extra 15 points should be technical student’s adviser. The courses that are range of problems of interest to electives appropriate for one or both often taken, or in some cases need to physicists and mathematicians ranging majors. be taken, in the junior year are denoted from the dynamics of the Earth’s To apply, a student first obtains with a “J.” climate to earthquake physics to the approval of both the general dynamics of Earth’s deep interior. The undergraduate AP adviser and the Technical Electives Lamont-Doherty Earth Observatory, general undergraduate AM adviser, and • Applications of Physics which is part of Columbia University, then the approval of the Dean. Courses that will give a student a broad provides enormous resources for background in applications of physics: students interested in this area. SPECIALTY AREAS IN APAM ELEN E3000x: Circuits, systems, and ATMOSPHERE, OCEANS, AND CLIMATE electronics (J) Both applied physics and applied math- EESC GU4008x: Intro to atmospheric science MSAE E3010x: Introduction to materials ematics students can focus their tech- APPH E4200x: Physics of fluids science, I nical electives and develop a strong APPH E4210y: Geophysical fluid dynamics APPH E4010x: Intro to nuclear science base of knowledge in a specialty area.

ENGINEERING 2017–2018 56 EESC GU4925x: Principles of physical APMA E4001y: Principles of applied mathematics CBMF W4761y: Computational genomics oceanography APMA E4101x: Intro to dynamical systems EESC GU4930y: Earth’s oceans and APMA E4301y: Numerical methods for partial NEUROBIOLOGY atmosphere differential equations BIOL UN3004x: Neurobiology , I (J) APMA E4302x: Methods in computational BIOL UN3005y: Neurobiology, II (J) SOLID EARTH GEOPHYSICS science ELEN E4011x: Computational neuroscience EESC GU4001x: Advanced general geology PHYS GU4019y: Mathematical methods of physics EESC GU4113x: Intro to mineralogy The second term of biology will be APPH E4200x: Physics of fluids • Fundamental Mathematics in Applied considered a technical elective if a EESC GU4701y: Intro to igneous petrology Mathematics student has credits from at least two EESC GU4941y: Principles of geophysics This specialization is intended for EESC GU4950x: Mathematical methods in the other of the recommended courses in students who desire a more solid Earth sciences quantitative biology at the 3000 level foundation in the mathematical (See also courses listed under or above. methods and underlying theory. For Scientific Computation and Computer example, this specialization could be Science on page 56.) • Scientific Computation and followed by students with an interest in Computer Science graduate work in applied mathematics. • Basic Physics and Astrophysics Advanced computation has become Fundamental physics and astrophysics MATH UN3386x: Differential geometry a core tool in science, engineering, can be emphasized. Not only is APMA E4101x: Intro to dynamical systems and mathematics and provides astrophysics providing a deeper APMA E4150x: Applied functional analysis challenges for both physicists understanding of the universe, but it is MATH GU4032x: Fourier analysis and mathematicians. Courses also testing the fundamental principles MATH GU4062y: Modern analysis, II that build on both practical and of physics. STAT GU4001x, y: Intro to probability and theoretical aspects of computing and statistics (J) computation include: PHYS UN3002y: From quarks to the cosmos: PHYS GU4386x-GU4387y: Geometrical applications of modern concepts in physics MATH UN3020x: Number theory and cryptog- physics raphy (J) ASTR UN3601x: General relativity, black holes, • Quantitative Biology COMS W3137x,y: Data structures and and cosmology (J) Traditionally biology was considered a algorithms (or COMS W3139y: ASTR UN3602y: Physical cosmology (J) descriptive science in contrast to the Honors data structures and ASTR GU4001y: Astrophysics, I quantitative sciences that are based algorithms) (J) APMA E4101x: Intro to dynamical systems COMS W3157x,y: Advanced programming (J) on mathematics, such as physics. This COMS W3203x,y: Discrete mathematics: intro • Business and Finance view no longer coincides with reality. to combinatorics and graph The knowledge of physics and math- Researchers from biology as well as theory (J) ematics that is gained in the applied from the physical sciences, applied COMS W4203y: Graph theory APMA E4300x: Intro to numerical methods physics and applied mathematics mathematics, and computer science are rapidly building a quantitative base APMA E4301y: Numerical methods for partial programs is a strong base for a career differential equations of biological knowledge. Students can in business or finance. APMA E4302x: Methods in computational acquire a strong base of knowledge in science ECONOMICS quantitative biology, both biophysics COMS W4701x,y: Artificial intelligence ECON UN3211x,y: Intermed microeconomics (J) and computational biology, while COMS W4771y: Machine learning ECON UN3213x,y: Intermed completing the applied physics or macroeconomics(J) applied mathematics programs. • Solid-State Physics Much of modern technology is based INDUSTRIAL ENGINEERING RECOMMENDED: AND OPERATIONS RESEARCH on solid-state physics, the study of BIOL UN2005x-UN2006y: Intro biology, I and II solids and liquids. Courses that will IEOR E4003x: Industrial economics APPH E3400y: Physics of the human body build a strong base for a career in this IEOR E4201x: The eng of management, I APMA E4400y: Intro to biophysical modeling IEOR E4202y: The eng of management, II area are OTHER TECHNICAL ELECTIVES (A COURSE FINANCE PHYS UN3083y: Electronics laboratory (J) IN AT LEAST TWO AREAS RECOMMENDED): MATH GU4071x: Mathematics of finance MSAE E3110x: Introduction to materials IEOR E4106y: Intro to operations research: BIOLOGICAL MATERIALS science, I stochastic models (J) BIOL GU4070x: The biology and physics of ELEN E3106x: Solid-state devices and STAT GU4001x,y: Probability and statistics (J) single molecules materials (J) ECIE GU4280: Corporate finance CHEN E4650x: Biopolymers MSAE E4100x: Crystallography IEOR E4700x: Intro to financial engineering PHYS GU4018y: Solid-state physics BIOMECHANICS MSAE E4206x: Electronic and magnetic • Mathematics Applicable to Physics BMEN E3320y: Fluid biomechanics (J) properties of solids Applied physics students can specialize BMEN E4300y: Solid biomechanics (J) in the mathematics that is applicable UNDERGRADUATE PROGRAM GENOMICS AND BIOINFORMATICS to physics. This specialization is IN MATERIALS SCIENCE particularly useful for students BIOL UN3037y: Whole genome bioinformatics (J) See page 172. interested in theoretical physics. ECBM E3060x: Intro to genomic information MATH UN3386x: Differential geometry science and technology (J)

ENGINEERING 2017–2018 GRADUATE PROGRAMS APMA E4301: Numerical methods for partial toward certification by the American 57 Financial aid is available for students differential equations Board of Radiology. The program pursuing a doctorate. Fellowships, APMA E6301: Analytic methods for partial consists of a core curriculum of medical differential equations scholarships, teaching assistantships, and nuclear physics courses, anatomy, APMA E6302: Numerical analysis for partial lab, seminar, a tutorial, one elective, and graduate research assistantships differential equations are awarded on a competitive basis. The and two practicums. Specific course Aptitude Test of the Graduate Record requirements are APPH E4010, E4330, Examination is required of candidates Students must also take a required E4710, E4500, E4501, E4550, E4600, for admission to the department and Research Seminar course, APMA E6100 E6319, E6330, E6335, and APBM for financial aid; the Advanced Tests are x or y E4650. Approved electives include recommended. APPH E4711, APPH E6336, APAM A student must select five elective E6650, and a third practicum. Up to M.S. Program in Applied Physics courses from those listed below (or any 6 points of this 36-point program may be waived based on prior equivalent The program of study leading to the of those not used to satisfy the core academic work. A student who enters degree of Master of Science, while requirements from the list above) for the 36-point M.S. Program in Medical emphasizing continued work in basic a total of 15 points of graduate credit. Physics having satisfactorily completed, physics, permits many options in Additional courses not listed below prior to beginning the Program, a several applied physics specialties. The can be applied toward the elective course determined by the faculty to program may be considered simply as requirements, subject to the approval of be equivalent in content to a required additional education in areas beyond the faculty adviser. Computer science course within the Program may be the bachelor’s level, or as preparatory to elective courses include: considered to have satisfied that doctoral studies in the applied physics CSOR W4231: Analysis of algorithms, I content requirement, may be allowed fields of plasma physics, laser physics, COMS W4236: Intro to computational complexity to have that requirement waived, and or solid-state physics. Specific course COMS W4241: Numerical algorithms and may be permitted to graduate from requirements for the master’s degree complexity COMS W4252: Computational learning theory the M.S. Program in Medical Physics are determined in consultation with the with fewer than 36 points, but not program adviser, but must include four Industrial engineering/operations fewer than the 30-point minimum of the six core courses listed below. research elective courses include: required by the School of Engineering The core courses provide a and Applied Science. Evaluation of student with a solid foundation in the IEOR E4003: Industrial economics prior coursework may include review fundamentals of applied physics, but IEOR E4004: Intro to operations research: of syllabi, comparison of textbooks, with the approval of the faculty adviser, deterministic models consultation with instructors, and/or other graduate-level courses with APPH IEOR E4007: Optimization: models and methods written or oral examination administered designators not listed below may also IEOR E4106: Stochastic models by Program faculty. A passing grade on count as core courses. STAT GU4001: Intro to probability and statistics IEOR E4403: Advanced engineering and corporate a comprehensive examination is required APPH E4100: Quantum physics of matter economics for graduation. This examination, on APPH E4110: Modern optics IEOR E4407: Game theoretic models of operations subjects covered in the curriculum, is APPH E4112: Laser physics STAT GU5207: Elementary stochastic processes taken after two terms of study. APPH E4200: Physics of fluids IEOR E4700: Intro to financial engineering APPH E4300: Applied electrodynamics Certification of Professional APPH E4301: Introduction to plasma physics Other elective courses may be cho- Achievement in Medical Physics sen from other departments in SEAS This graduate program of instruction M.S. Program in Applied Physics/ and Arts and Sciences, e.g., the leads to the Certification of Professional Concentration in Applied Departments of Mechanical Engineering, Achievement and requires satisfactory Mathematics Electrical Engineering, Mathematics, and completion of six of the following This 30-point program leads to an M.S. Statistics. courses: degree. Students must complete five APPH E4330: Radiobiology core courses and five electives. The M.S. Program in Materials Science APPH E4500: Health physics core courses provide a student with and Engineering APPH E4600: Dosimetry APBM E4650: Anatomy for physicists and engineers a foundation in the fundamentals of See page 175. applied mathematics and contribute APPH E6319: Clinical nuclear medicine physics or APPH E6330: Diagnostic radiology physics 15 points of graduate credit toward the M.S. Program in Medical Physics APPH E6335: Radiation therapy physics degree. Students must complete five of This CAMPEP-approved 36-point or APPH E6336: Advanced topics in radiation the following seven courses: program in medical physics leads to the therapy APMA E4001: Principles of applied mathematics M.S. degree. It is administered by faculty APMA E4101: Intro to dynamical systems from the School of Engineering and This is a part-time nondegree program. APMA E4150: Applied functional analysis Applied Science in collaboration with Students are admitted to the department APMA E4200: Partial differential equations faculty from the College of Physicians as certificate-track students. APMA E4204: Functions of a complex variable and Surgeons and the Mailman School APMA E4300: Intro to numerical methods of Public Health. It provides preparation

ENGINEERING 2017–2018 58 PH.D. AND ENG.SC.D. PROGRAMS and has remained a field of fascination ultrahigh vacuum systems, lasers, After completing the M.S. program and excitement for active minds. equipment for the study of optical in applied physics, doctoral students properties and transport on the specialize in one applied physics field. Materials Science nanoscale, and the instruments in Some specializations have specific and Engineering Program the shared facilities overseen by the course requirements for the doctorate; See page 171. Columbia Nano Initiative (CNI). There elective courses are determined in are also significant resources for consultation with the program adviser. Plasma Physics electrical and optical experimentation Successful completion of an approved at low temperatures and high magnetic This graduate specialty is designed to 30-point program of study is required in fields. Specific course requirements emphasize preparation for professional addition to successful completion of a for the solid-state physics doctoral careers in plasma research, controlled written qualifying examination taken after specialization are set with the academic fusion, and space research. This two semesters of graduate study. An oral adviser, in consultation with the includes basic training in relevant areas examination, taken within one year after Committee on Materials Science and of applied physics, with emphasis the written qualifying examination, and a Engineering/Solid-State Science and on plasma physics and related areas thesis proposal examination, taken within Engineering. two years after the written qualifying leading to extensive experimental and examination, are required of all doctoral theoretical research in the Columbia University Plasma Physics Laboratory. candidates. COURSES IN APPLIED PHYSICS Specific course requirements for the plasma physics doctoral program are APPH E3100y Introduction to quantum Applied Mathematics mechanics APPH E4018, E4200, E4300, E6101, This graduate specialty, for students 3 pts. Lect: 3. Professor Herman. E6102, and E9142 or E9143, or registered in the Department of Applied Prerequisites: PHYS UN1403 or equivalent, and equivalents taken at another university. Physics and Applied Mathematics, differential and integral calculus. Corequisites: emphasizes applied mathematics APMA E3101 or equivalent. Basic concepts and research in nonlinear dynamics, fluid Optical and Laser Physics assumptions of quantum mechanics, Schrodinger’s mechanics, and scientific computation, This graduate specialty involves a basic equation, solutions for one-dimensional problems, including square wells, barriers, and the harmonic with a current emphasis on geophysical, training in relevant areas of applied oscillator, introduction to the hydrogen atom, biophysical, and plasma physics physics with emphasis in quantum atomic physics and X-rays, electron spin. applications. mechanics, quantum electronics, and Applied mathematics deals with related areas of specialization. Some APPH E3200x Mechanics: fundamentals and the use of mathematical concepts active areas of research in which the applications and techniques in various fields of student may concentrate are laser 3 pts. Lect: 3. Professor Cole. Prerequisites: PHYS UN1402, MATH UN2030, science and engineering. Historically, modification of surfaces, optical or equivalent. Basic non-Euclidean coordinate mathematics was first applied with great diagnostics of film processing, inelastic systems, Newtonian mechanics, oscillations, success in astronomy and mechanics. light scattering in nanomaterials, nonlinear Green’s functions, Newtonian gravitation, Then it developed into a main tool of optics, ultrafast optoelectronics photonic Lagrangian mechanics, central force motion, physics, other physical sciences, and switching, optical physics of surfaces, two-body collisions, noninertial reference frames, engineering. It is now important in and photon integrated circuits. Specific rigid body dynamics. Applications, including GPS and feedback control systems, are emphasized the biological, geological, and social course requirements for the optical and sciences. With the coming of age of throughout. laser physics doctoral specialization are the computer, applied mathematics has set with the academic adviser. APPH E3300y Applied electromagnetism transcended its traditional style and now 3 pts. Lect: 3. Professor Navratil. assumes an even greater importance Corequisite: APMA E3102. Vector analysis, and a new vitality. Solid-State Physics electrostatic fields, Laplace’s equation, multipole Compared with the pure mathematician, This graduate specialty encompasses expansions, electric fields in matter: dielectrics, the applied mathematician is more the study of the electrical, optical, magnetostatic fields, magnetic materials, and magnetic, thermal, high-pressure, and superconductors. Applications of electromagnetism interested in problems coming from to devices and research areas in applied physics. other fields. Compared with the engineer ultrafast dynamical properties of solids, and the physical scientist, he or she is with an aim to understanding them APPH E3400y Physics of the human body more concerned with the formulation of in terms of the atomic and electronic 3 pts. Lect: 3. Not offered in 2017–2018. Prerequisites: PHYS UN1201 or UN1401, problems and the nature of solutions. structure. The field emphasizes the and Calculus I. Corequisites: PHYS UN1202 formation, processing, and properties of Compared with the computer scientist, or UN1402, and Calculus II. This introductory he or she is more concerned with the thin films, low-dimensional structures— course analyzes the human body from the basic accuracy of approximations and the such as one- and two-dimensional principles of physics. Topics covered include interpretation of results. Needless to say, electron gases, nanocrystals, surfaces the energy balance in the body, the mechanics even in this age of specialization, the of electronic and optoelectronic of motion, fluid dynamics of the heart and work of mathematicians, scientists, and interest, and molecules. Facilities circulation, vibrations in speaking and hearing, engineers frequently overlaps. Applied include a microelectronics laboratory, muscle mechanics, gas exchange and transport in the lungs, vision, structural properties and mathematics, by its very nature, has high-pressure diamond anvil cells, limits, electrical properties and the development occupied a central position in this interplay a molecular beam epitaxy machine, and sensing of magnetic fields, and basics of

ENGINEERING 2017–2018 equilibrium and regulatory control. In each case, Introduces fundamental ideas, concepts, and hypothesis and its restatement in terms of Helmholtz 59 a simple model of the body organ, property, or approaches in soft condensed matter with and Gibbs free energies and for open systems. function will be derived and then applied. emphasis on biomolecular systems. Covers the Correlation times and lengths. Exploration of phase broad range of molecular, nanoscale and colloidal space and observation time scale. Correlation APPH E3900x and y Undergraduate research phenomena with revealing their mechanisms and functions. Fermi-Dirac and Bose-Einstein statistics. in applied physics 0–4 pts. Members of the faculty. physical foundations. The relationship between Fluctuation-response theory. Applications to ideal Prerequisite: Written permission from instructor molecular architecture and interactions and gases, interfaces, liquid crystals, microemulsions and approval from adviser. This course may be macroscopic behavior are discussed for the broad and other complex fluids, polymers, Coulomb gas, repeated for credit, but no more than 6 points of range of soft and biological matter systems, interactions between charged polymers and charged this course may be counted toward the satisfaction from surfactants and liquid crystals to polymers, interfaces, ordering transitions. nanoparticles, and biomolecules. Modern of the B.S. degree requirements. Candidates for APPH E4130x Physics of solar energy characterization methods for soft materials, the B.S. degree may conduct an investigation in 3 pts. Lect: 3. Professor Chen. including X-ray scattering, molecular force probing, applied physics or carry out a special project under Prerequisites: General physics (PHYS UN1403 and electron microcopy are reviewed. Example the supervision of the staff. Credit for course is or UN1602) and mathematics, including ordinary contingent upon the submission of an acceptable problems, drawn from the recent scientific differential equations and complex numbers (such thesis or final report. literature, link the studied materials to the actively as MATH UN1202 or UN2030) or instructor’s developed research areas. Course grade based APAM E3999x, y or s Undergraduate fieldwork permission. The physics of solar energy including on midterm and final exams, weekly homework 1–2 pts. Members of the faculty. solar radiation, the analemma, atmospheric efforts, assignments, and final individual/team project. Prerequisite(s): Obtained internship and approval thermodynamics of solar energy, physics of solar from adviser. Restricted to ENAPMA, ENAPPH, APPH E4090y Nanotechnology cells, energy storage and transmission, and ENMSAE. May be repeated for credit, but no 3 pts. Lect: 3. Professor Wind. physics and economics in the solar era. more than 3 total points may be used toward the Prerequisites: APPH E3100 and MSAE E3010 APPH E4200x Physics of fluids 128-credit degree requirement. Only for APAM or their equivalents with instructor’s permission. 3 pts. Lect: 3. Professor Volpe. undergraduate students who include relevant The science and engineering of creating Prerequisites: APMA E3102 or equivalent; PHYS off-campus work experience as part of their materials, functional structures and devices on the UN1401 or UN1601 or equivalent. An introduction approved program of study. Final report and letter nanometer scale. Carbon nanotubes, nanocrystals, to the physical behavior of fluids for science and of evaluation required. Fieldwork credits may not quantum dots, size dependent properties, self- engineering students. Derivation of basic equations count toward any major core, technical, elective, assembly, nanostructured materials. Devices of fluid dynamics: conservation of mass, momentum, and nontechnical requirements. May not be taken and applications, nanofabrication. Molecular and energy. Dimensional analysis. Vorticity. for pass/fail credit or audited. engineering, bionanotechnology. Imaging and Laminar boundary layers. Potential flow. Effects of manipulating at the atomic scale. Nanotechnology APPH E4008x Introduction to atmospheric compressibility, stratification, and rotation. Waves on in society and industry. science a free surface; shallow water equations. Turbulence. 3 pts. Lect: 3. Professor Polvani. APPH E4100x Quantum physics of matter APPH E4210y Geophysical fluid dynamics Prerequisites: Advanced calculus and general 3 pts. Lect: 3. Professor Venkataraman. 3 pts. Lect: 3. Professor Abernathey. physics, or instructor’s permission. Basic physical Prerequisite: APPH E3100. Corequisite: APMA Prerequisites: APMA E3101, E3102 (or processes controlling atmospheric structure: E3102 or equivalent. Basic theory of quantum equivalents) and APPH E4200 (or equivalent), or thermodynamics; radiation physics and radiative mechanics, well and barrier problems, the permission from instructor. Fundamental concepts transfer; principles of atmospheric dynamics; cloud harmonic oscillator, angular momentum identical in the dynamics of rotating, stratified flows. processes; applications to Earth’s atmospheric particles, quantum statistics, perturbation theory Geostrophic and hydrostatic balances, potential general circulation, climatic variations, and the and applications to the quantum physics of atoms, vorticity, f and beta plane approximations, gravity atmospheres of the other planets. molecules, and solids. and Rossby waves, geostrophic adjustment APPH E4010x Introduction to nuclear science APPH E4110y Modern optics and quasigeostrophy, baroclinic and barotropic 3 pts. Lect: 3. Professor Ostrow. 3 pts. Lect: 3. Professor Yu. instabilities, Sverdrup balance, boundary Prerequisites: MATH UN1202 and UN2030 and Prerequisite: APPH E3300. Ray optics, matrix currents, Ekman layers. PHYS UN1403 or equivalents. Introductory formulation, wave effects, interference, Gaussian course for individuals with an interest in medical APPH E4300x Applied electrodynamics beams, Fourier optics, diffraction, image formation, physics and other branches of radiation science. 3 pts. Lect: 3. Professor Gaeta. Topics include basic concepts, nuclear models, electromagnetic theory of light, polarization and Prerequisite: APPH E3300. Overview of properties semiempirical mass formula, interaction of crystal optics, coherence, guided wave and fiber and interactions of static electric and magnetic radiation with matter, nuclear detectors, nuclear optics, optical elements, photons, selected topics fields. Study of phenomena of time dependent structure and instability, radioactive decay process in nonlinear optics. electric and magnetic fields including induction, and radiation, particle accelerators, and fission and APPH E4112x Laser physics waves, and radiation as well as special relativity. fusion processes and technologies. 3 pts. Lect: 3. Professor Yu. Applications are emphasized. APPH E4018y Applied physics laboratory Recommended but not required: APPH E3100 APPH E4301y Introduction to plasma physics 2 pts. Lab: 4. Professor Cole. and E3300 or their equivalents. Optical resonators, 3 pts. Lect: 3. Professor Volpe. Prerequisite: APPH E3300 or ELEN E3401 interaction of radiation and atomic systems, Prerequisite: PHYS UN3008 or APPH E3300. or equivalent. Typical experiments are in the theory of laser oscillation, specific laser systems, Definition of a plasma. Plasmas in laboratories areas of plasma physics, microwaves, laser rate processes, modulation, detection, harmonic and nature, plasma production. Motion of charged applications, optical spectroscopy physics, and generation, and applications. particles in electric and magnetic fields, adiabatic superconductivity. CHAP E4120y Statistical mechanics invariants. Heuristic treatment of collisions, diffusion, transport, and resistivity. Plasma as a APCH E4080 Soft condensed matter 3 pts. Lect: 3. Professor O’Shaughnessy. conducting fluid. Electrostatic and magnetostatic 3 pts. Lect: 3. Professor Gang. Prerequisite: CHEN E3210 or equivalent equilibria of plasmas. Waves in cold plasmas. Prerequisite(s): MSAE E3111, CHEE E3010, or thermodynamics course, or instructor’s permission. Demonstration of laboratory plasma behavior, CHEN E3120 or equivalent. Course is aimed at Fundamental principles and underlying assumptions measurement of plasma properties. Illustrative senior undergraduate and graduate students. of statistical mechanics. Boltzmann’s entropy

ENGINEERING 2017–2018 60 problems in fusion, space, and nonneutral or beam APBM E4650x Anatomy for physicists and experience as part of their program of study. Final plasmas. engineers report required. This course may not be taken for 3 pts. Lect: 3. Professors Rozenshtein and Katz. pass/fail or audited. APPH E4330y Radiobiology for medical Prerequisite: Engineering or physics background. physicists APPH E6081x Solid state physics, I Systemic approach to the study of the human body 3 pts. Lect: 3. Professor Zaider. 3 pts. Lect: 3. Professor Pinczuk. from a medical imaging point of view: skeletal, Prerequisite: APPH E4010 or equivalent or Prerequisites: APPH E3100 or the equivalent. respiratory, cardiovascular, digestive, and urinary Corequisite: APPH E4010. Interface between Knowledge of statistical physics on the level systems, breast and women’s issues, head and clinical practice and quantitative radiation of MSAE E3111 or PHYS GU4023 strongly neck, and central nervous system. Lectures are biology. Microdosimetry, dose-rate effects recommended. Crystal structure, reciprocal reinforced by examples from clinical two- and and biological effectiveness thereof; radiation lattices, classification of solids, lattice dynamics, three-dimensional and functional imaging (CT, MRI, biology data, radiation action at the cellular anharmonic effects in crystals, classical electron PET, SPECT, U/S, etc.). and tissue level; radiation effects on human models of metals, electron band structure, and populations, carcinogenesis, genetic effects; APPH E4710x Radiation instrumentation and low-dimensional electron structures. radiation protection; tumor control, normal- measurement laboratory, I APPH E6082y Solid state physics, II tissue complication probabilities; treatment plan 3 pts. Lect: 1. Lab: 4. Professor Ostrow. 3 pts. Lect: 3. Professor Altshuler. optimization. Prerequisite or corequisite: APPH E4010. Lab Prerequisite: APPH E6081 or instructor’s fee: $50. Theory and use of alpha, beta, gamma, APPH E4500x Health physics permission. Semiclassical and quantum mechanical and X-ray detectors and associated electronics 3 pts. Lect: 3. Professor Morgan. electron dynamics and conduction, dielectric for counting, energy spectroscopy, and dosimetry; Prerequisite: APPH E4600 or Corequisite: APPH properties of insulators, semiconductors, defects, radiation safety; counting statistics and error E4600. Fundamental principles and objectives of magnetism, superconductivity, low-dimensional propagation; mechanisms of radiation emission health physics (radiation protection), quantities of structures, and soft matter. and interaction. (Topic coverage may be revised.) radiation dosimetry (the absorbed dose, equivalent APPH E6085x Computing the electronic dose, and effective dose) used to evaluate human APPH E4711x or y Radiation instrumentation structure of complex materials radiation risks, elementary shielding calculations and measurement laboratory, II 3 pts. Lect: 3. Professor Wentzcovitch. and protection measures for clinical environments, 3 pts. Lect: 1. Lab: 4. Not offered in 2017–2018. Prerequisite: APPH E3100 or equivalent. Basics of characterization and proper use of health physics Prerequisite: APPH E4710. Lab fee: $50. Additional density functional theory (DFT) and its application instrumentation, and regulatory and administrative detector types; applications and systems including to complex materials. Computation of electronics coincidence, low-level, and liquid scintillation requirements of health physics programs in and mechanical properties of materials. Group counting; neutron activation; TLD dosimetry, general and as applied to clinical activities. theory, numerical methods, basis sets, computing, gamma camera imaging. (Topic coverage may be and running open source DFT codes. Problem sets APPH E4501y Medical health physics tutorial revised.) 0 pts. Professor Morgan. and a small project. APPH E4901x Seminar: problems in applied Prerequisite: Permission of the course coordinator. APPH E6091y Magnetism and magnetic physics Required for, and limited to, M.S. degree candidates materials 1 pt. Lect: 1. Professor Herman. in the Medical Physics Program. Course addresses 3 pts. Lect. 3. Not offered in 2017–2018. This course is required for, and can be taken procedures for personnel and area monitoring, Prerequisites: MSAE E4206, APPH E6081, or only by, all applied physics majors and minors radiation and contamination surveys, instrument equivalent. Types of magnetism. Band theory in the junior year. Discussion of specific and calibration, radioactive waste disposal, radiation of ferromagnetism. Magnetic metals, insulators, self-contained problems in areas such as applied safety compliance, licensure requirements, and semiconductors. Magnetic nanostructures: electrodynamics, physics of solids, and plasma and other matters contributing to professional ultrathin films, superlattices, and particles. Surface physics. Topics change yearly. competence in the field of medical health physics. magnetism and spectroscopies. High speed Course includes lectures, seminars, tours, and APPH E4903x Seminar: problems in applied magnetization dynamics. Spin electronics. hands-on experience. This two-week tutorial is physics APPH E6101x Plasma physics, I offered immediately following spring semester final 2 pts. Lect: 1. Tutorial: 1. Professor Herman. 3 pts. Lect: 3. Professor Navratil. examinations and is taken for Pass/fail only. This course is required for, and can be taken only Prerequisite: APPH E4300. Debye screening. by, all applied physics majors in the senior year. APPH E4550y Medical physics seminar Motion of charged particles in space- and Discussion of specific and self-contained problems 0 pts. Lect: 1. Professor Wuu. time-varying electromagnetic fields. Two-fluid in areas such as applied electrodynamics, physics Required for all graduate students in the Medical description of plasmas. Linear electrostatic and of solids, and plasma physics. Formal presentation Physics Program. Practicing professionals and electromagnetic waves in unmagnetized and of a term paper required. Topics change yearly. faculty in the field present selected topics in magnetized plasmas. The magnetohydrodynamic medical physics. APPH E4990x and y Special topics in applied (MHD) model, including MHD equilibrium, stability, physics and MHD waves in simple geometries. APPH E4600x Fundamentals of radiological 1–3 pts. Instructor to be announced. APPH E6102y Plasma physics, II physics and radiation dosimetry Prerequisite: Instructor’s permission. This 3 pts. Lect: 3. Professor Mauel. 3 pts. Lect: 3. Professor Meli. course may be repeated for credit. Topics and Prerequisite: APPH E6101. Magnetic coordinates. Prerequisite: APPH E4010 or equivalent or instructors change from year to year. For advanced Equilibrium, stability, and transport of toroidal Corequisite: APPH E4010. Basic radiation physics: undergraduate students and graduate students in plasmas. Ballooning and tearing instabilities. radioactive decay, radiation producing devices, engineering, physical sciences, and other fields. characteristics of the different types of radiation Kinetic theory, including Vlasov equation, Fokker- (photons, charged and uncharged particles) and APAM E4999x and y–S4999 Supervised Planck equation, Landau damping, kinetic transport mechanisms of their interactions with materials. internship theory. Drift instabilities. Essentials of the determination, by measurement 1–3 pts. Members of the faculty. APPH E6110x Laser interactions with matter and calculation, of absorbed doses from ionizing Prerequisite: Obtained internship and approval 3 pts. Lect: 3. Not offered in 2017–2018. radiation sources used in medical physics (clinical) from adviser. Only for master’s students in the Prerequisites: APPH E4112 or equivalent, and situations and for health physics purposes. Department of Applied Physics and Applied Mathematics who may need relevant work quantum mechanics. Principles and applications

ENGINEERING 2017–2018 of laser-matter coupling, nonlinear optics, three- stereotactic, and hypofractionated radiation repeated for credit. A special investigation of a 61 and four-wave mixing, harmonic generation, therapy. Emphasis on advanced technological, problem in nuclear engineering, medical physics, laser processing of surfaces, laser probing of engineering, clinical and quality assurance issues applied mathematics, applied physics, and/or materials, spontaneous and stimulated light associated with high-technology radiation therapy plasma physics consisting of independent work on scattering, saturation spectroscopy, multiphoton and the special role of the medical physicist in the part of the student and embodied in a formal excitation, laser isotope separation, transient the safe clinical application of these tools. report. optical effects. APPH E6340x or y Diagnostic radiology APPH E9142x-E9143y Applied physics seminar APPH E6319y Clinical nuclear medicine practicum 3 pts. Sem: 3. Not offered in 2017–2018. physics 3 pts. Lab: 6. Members of the faculty. These courses may be repeated for credit. 3 pts. Lect: 3. Professor Zanzonico. Prerequisites: Grade of B+ or better in APPH Selected topics in applied physics. Topics and Prerequisite: APPH E4010 or equivalent E6330 and instructor’s permission. Practical instructors change from year to year. recommended. Introduction to the applications of diagnostic radiology for various APAM E9301x and y–S9301 Doctoral research instrumentation and physics used in clinical measurements and equipment assessments. 0–15 pts. Members of the faculty. nuclear medicine and PET with an emphasis Instruction and supervised practice in radiation Prerequisite: Qualifying examination for the on detector systems, tomography and quality safety procedures, image quality assessments, doctorate. Required of doctoral candidates. control. Problem sets, papers, and term project. regulatory compliance, radiation dose evaluations and calibration of equipment. Students participate APAM E9800x and y–S9800 Doctoral APPH E6330y Diagnostic radiology physics in clinical QC of the following imaging equipment: research instruction 3 pts. Lect: 3. Professors Jambalwalikar and radiologic units (mobile and fixed), fluoroscopy 3, 6, 9, or 12 pts. Members of the faculty. Liang. units (mobile and fixed), angiography units, A candidate for the Eng.Sc.D. degree must register Prerequisite: APPH E4600. Physics of medical mammography units, CT scanners, MRI units and for 12 points of doctoral research instruction. imaging. Imaging techniques: radiography, ultrasound units. The objective is familiarization Registration for APAM E9800 may not be used fluoroscopy, computed tomography, in routine operation of test instrumentation to satisfy the minimum residence requirement for mammography, ultrasound, magnetic resonance. and QC measurements utilized in diagnostic the degree. Includes conceptual, mathematical/theoretical, and medical physics. Students are required to submit practical clinical physics aspects. APAM E9900x and y–S9900 Doctoral QC forms with data on three different types of dissertation APPH E6333x or y Radiation therapy physics radiology imaging equipment. 0 pts. Members of the faculty. practicum APPH E6365x or y Nuclear medicine A candidate for the doctorate may be required 3 pts. Lab: 6. Professor Wuu. practicum to register for this course every term after the Prerequisites: Grade of B+ or better in APPH 3 pts. Lab: 6. Members of the faculty. coursework has been completed, and until the E6335 and instructor’s permission. Students Prerequisites: Grade of B+ or better in APPH dissertation has been accepted. spend two to four days per week studying the E6319 and instructor’s permission. Practical clinical aspects of radiation therapy physics. applications of nuclear medicine theory and Projects on the application of medical physics application for processing and analysis of COURSES IN APPLIED in cancer therapy within a hospital environment clinical images and radiation safety and quality MATHEMATICS are assigned; each entails one or two weeks of assurance programs. Topics may include work and requires a laboratory report. Two areas tomography, instrumentation, and functional APMA E2000x and y Multivariable calculus for are emphasized: 1. computer-assisted treatment imaging. Reports. engineers and applied scientists planning (design of typical treatment plans for 4 pts. Lect: 3. Professor Youngren. various treatment sites including prostate, breast, APPH E6380x or y Health physics practicum Differential and integral calculus of multiple head and neck, lung, brain, esophagus, and 3 pts. Lab: 6. Members of the faculty. variables. Topics include partial differentiation; cervix) and 2. clinical dosimetry and calibrations Prerequisites: Grade of B+ or better in APPH optimization of functions of several variables; (radiation measurements for both photon and E4500 and instructor’s permission or Corequisite: line, area, volume, and surface integrals; vector electron beams, as well as daily, monthly, and APPH E4500 and permission of the instructor. functions and vector calculus; theorems of Green, part of annual QA). Radiation protection practices and procedures for Gauss, and Stokes; applications to selected clinical and biomedical research environments. problems in engineering and applied science. APPH E6335y Radiation therapy physics Includes design, radiation safety surveys of 3 pts. Lect: 3. Professor Wuu. APMA E2101y Introduction to applied diagnostic and therapeutic machine source Prerequisites: APPH E4600; APPH E4330 mathematics facilities, the design and radiation protection recommended. Review of X-ray production and 3 pts. Lect: 3. Professor Tippett. protocols for facilities using unsealed sources of fundamentals of nuclear physics and radioactivity. Prerequisite: Calculus III. A unified, single- radioactivity—nuclear medicine suites and sealed Detailed analysis of radiation absorption and semester introduction to differential equations and sources—brachytherapy suites. Also includes interactions in biological materials as specifically linear algebra with emphases on (1) elementary radiation protection procedures for biomedical related to radiation therapy and radiation therapy analytical and numerical technique and (2) research facilities and the administration dosimetry. Surveys of use of teletherapy isotopes discovering the analogs on the continuous and of programs for compliance to professional and X-ray generators in radiation therapy plus discrete sides of the mathematics of linear health physics standards and federal and state the clinical use of interstitial and intracavitary operators: superposition, diagonalization, regulatory requirements for the possession and isotopes. Principles of radiation therapy treatment fundamental solutions. Concepts are illustrated use of radioactive materials and machine sources planning and isodose calculations. Problem sets with applications using the language of of ionizing and nonionizing radiations in clinical taken from actual clinical examples are assigned. engineering, the natural sciences, and the social situations. Individual topics are decided by the sciences. Students execute scripts in Mathematica APPH E6336x Advanced topics in radiation student and the collaborating Clinical Radiation and MATLAB (or the like) to illustrate and visualize therapy Safety Officer. course concepts (programming not required). 3 pts. Lect: 3. Professors Wuu and Amols. APAM E6650x and y–S6650 Research project Prerequisite: APPH E6335. Advanced technology HSAM W2901y Data: past, present and future 1–6 pts. Members of the faculty. applications in radiation therapy physics, 3 pts. Lect: 1.5. Lab: 1.5. Professors Wiggins Prerequisite: Written permission from instructor including intensity modulated, image guided, and Jones. and approval from adviser. This course may be

ENGINEERING 2017–2018 62 Prerequisites: Instructor's permission. Critical product spaces, projection operators, orthogonal APMA E4300x Computational math: thinking and practice regarding the past, present, bases, Gram-Schmidt orthogonalization. Least introduction to numerical methods and future of data. Readings covering how squares method, pseudo-inverses, singular value 3 pts. Lect: 3. Professor Mandli. students, scholars, and citizens can make sense decomposition. Adjoint operators, Hermitian and Prerequisites: MATH UN1201, UN2030, and APMA of data in science, public policy, and our personal unitary operators, Fredholm Alternative Theorem. E3101 and ENGI E1006 or their equivalents. lives. Labs covering descriptive, predictive, and Fourier series and eigenfunction expansions. Programming experience in Python extremely prescriptive modeling of data. Introduction to the theory of distributions and the useful. Introduction to fundamental algorithms and Fourier Integral Transform. Green’s functions. analysis of numerical methods commonly used APMA E3101x Linear algebra Application to Partial Differential Equations. by scientists, mathematicians, and engineers. 3 pts. Lect: 3. Professor Tippett. Designed to give a fundamental understanding of APMA E4101x Introduction to dynamical Matrix algebra, elementary matrices, inverses, the building blocks of scientific computing that will systems rank, determinants. Computational aspects of be used in more advanced courses in scientific 3 pts. Lect: 3. Professor Spigelman. solving systems of linear equations: existence- computing and numerical methods for PDEs (e.g., Prerequisites: APMA E2101 (or MATH UN1201) uniqueness of solutions, Gaussian elimination, APMA E4301, APMA E4302). Topics include and APMA E3101 or their equivalents, or scaling, ill-conditioned systems, iterative numerical solutions of algebraic systems, linear instructor’s permission. An introduction to the techniques. Vector spaces, bases, dimension. least-squares, eigenvalue problems, solution of analytic and geometric theory of dynamical Eigenvalue problems, diagonalization, inner nonlinear systems, optimization, interpolation, systems; basic existence, uniqueness and products, unitary matrices. numerical integration and differentiation, initial parameter dependence of solutions to ordinary value problems, and boundary value problems for APMA E3102y Partial differential equations differential equations; constant coefficient and systems of ODE’s. All programming exercises will 3 pts. Lect: 3. Professor Rim. parametrically forced systems; Fundamental be in Python. Prerequisite: MATH UN2030 or equivalent. solutions; resonance; limit points, limit cycles Introduction to partial differential equations; and classification of flows in the plane (Poincare- APMA E4301y Numerical methods for partial integral theorems of vector calculus. Partial Bendixson Theorem); conservative and dissipative differential equations differential equations of engineering in rectangular, systems; linear and nonlinear stability analysis 3 pts. Lect: 3. Professor Mandli. cylindrical, and spherical coordinates. Separation of equilibria and periodic solutions; stable and Prerequisites: APMA E4300 and APMA E3102 of the variables. Characteristic-value problems. unstable manifolds; bifurcations, e.g., Andronov- or APMA E4200 or equivalents. Numerical Bessel functions, Legendre polynomials, other Hopf; sensitive dependence and chaotic dynamics; solution of differential equations, in particular orthogonal functions; their use in boundary value selected applications. partial differential equations arising in various problems. Illustrative examples from the fields fields of application. Presentation emphasizes of electromagnetic theory, vibrations, heat flow, APMA E4150x Applied functional analysis finite difference approaches to present theory on and fluid mechanics. 3 pts. Lect: 3. Professor Weinstein. stability, accuracy, and convergence with minimal Prerequisites: Advanced calculus and course coverage of alternate approaches (left for other APAM E3105x Programming methods for in basic analysis, or instructor’s permission. courses). Method coverage includes explicit and scientists and engineers Introduction to modern tools in functional analysis implicit time-stepping methods, direct and iterative 3 pts. Lect: 2.5. Lab: 1. Not offered in 2017–2018. that are used in the analysis of deterministic and solvers for boundary-value problems. Introduction to modern techniques of computer stochastic partial differential equations and in programming for the numerical solutions to the analysis of numerical methods: metric and APMA E4302x Methods in computational familiarity with basic and advanced concepts normed spaces, Banach space of continuous science of modern numerical programming and acquire functions, measurable spaces, the contraction 3 pts. Lect: 3. Professor Du. practical experience solving representative mapping theorem, Banach and Hilbert spaces Prerequisites: APMA E4300, application and problems in math and physics. bounded linear operators on Hilbert spaces and knowledge in C, Fortran or similar compiled their spectral decomposition, and time permitting language. Introduction to the key concepts and APMA E3900x and y Undergraduate research issues in computational science aimed at getting in applied mathematics distributions and Fourier transforms. students to a basic level of understanding where 0–4 pts. Members of the faculty. APMA E4200x Partial differential equations they can run simulations on machines aimed at Prerequisite: Written permission from instructor 3 pts. Lect: 3. Professor Rim. a range of applications and sizes from a single and approval from adviser. This course may be Prerequisite: Course in ordinary differential workstation to modern super-computer hardware. repeated for credit, but no more than 6 points of equations. Techniques of solution of partial Topics include but are not limited to basic this course may be counted toward the satisfaction differential equations. Separation of the variables. knowledge of unix shells, version control systems, of the B.S. degree requirements. Candidates for Orthogonality and characteristic functions, reproducibility, OpenMP, MPI, and many-core the B.S. degree may conduct an investigation in nonhomogeneous boundary value problems. technologies. Applications will be used throughout applied mathematics or carry out a special project Solutions in orthogonal curvilinear coordinate to demonstrate the various use cases and pitfalls under the supervision of the staff. Credit for the systems. Applications of Fourier integrals, Fourier of using the latest computing hardware. course is contingent upon the submission of an and Laplace transforms. Problems from the fields acceptable thesis or final report. of vibrations, heat conduction, electricity, fluid APMA E4400y Introduction to biophysical modeling APMA E4001y Principles of applied dynamics, and wave propagation are considered. 3 pts. Lect: 3. Not offered in 2017–2018. mathematics APMA E4204x Functions of a complex Prerequisites: PHYS UN1401 or equivalent, and 3 pts. Lect: 3. Professor Spiegelman. variable APMA E2101 or MATH UN2030 or equivalent. Prerequisites: Introductory Linear Algebra required. 3 pts. Lect. 3. Instructor to be announced. Introduction to physical and mathematical models Ordinary Differential Equations recommended. Prerequisite: MATH UN1202 or equivalent. Complex of cellular and molecular biology. Physics at the Review of finite-dimensional vector spaces and numbers, functions of a complex variable, cellular scale (viscosity, heat, diffusion, statistical elementary matrix theory. Linear transformations, differentiation and integration in the complex plane. mechanics). RNA transcription and regulation change of basis, eigenspaces. Matrix representation Analytic functions, Cauchy integral theorem and of genetic expression. Genetic and biochemical of linear operators and diagonalization. formula, Taylor and Laurent series, poles and networks. Bioinformatics as applied to reverse- Applications to difference equations, Markov residues, branch points, evaluation of contour engineering of naturally-occurring networks and processes, ordinary differential equations, and integrals. Conformal mapping. Schwarz-Christoffel to forward-engineering of synthetic biological stability of nonlinear dynamical systems. Inner transformation. Applications to physical problems.

ENGINEERING 2017–2018 networks. Mathematical and physical aspects of operators in normed and metric spaces, fixed point differential equations in problems arising in applied 63 functional genomics. theorems and their applications. mathematics. Asymptotic series. Asymptotic evaluation of integrals. Expansion of solutions of APMA E4901x Seminar: problems in applied APMA E6301y Analytic methods for partial ordinary differential equations: connection problem mathematics differential equations and turning points. Stoke’s phenomenon. Differential 0 pts. Lect: 1. Professor Wiggins. 3 pts. Lect: 2. Professor Weinstein. equations with a parameter: “boundary layer” This course is required for, and can be taken only Prerequisites: Advanced calculus, basic concepts phenomenon. Application to partial differential by, all applied mathematics majors in the junior in analysis, APMA E3101 or E4200 or their equations: problems from fluid dynamics, wave year. Prerequisites or corequisites: APMA E4200 equivalents, or instructor’s permission. Introduction propagation theory, electromagnetic theory. and E4204 or their equivalents. Introductory to analytic theory of PDEs of fundamental and seminars on problems and techniques in applied applied science; wave (hyperbolic), Laplace and APMA E9101x-E9102y Research mathematics. Typical topics are nonlinear Poisson equations (elliptic), heat (parabolic) and 1–4 pts. Members of the faculty. dynamics, scientific computation, economics, Schroedinger (dispersive) equations; fundamental Prerequisite: Permission of the supervising faculty operations research, etc. solutions, Green’s functions, weak/distribution member. This course may be repeated. Advanced solutions, maximum principle, energy estimates, study in a special area. APMA E4903x Seminar: problems in applied variational methods, method of characteristics; mathematics APMA E9810x or y SEAS colloquium in elementary functional analysis and applications 3–4 pts. Lect: 1. Tutorial: 2. Professor Wiggins. climate science to PDEs; introduction to nonlinear PDEs, shocks; This course is required for all applied mathematics 0 pts. Lect: 1. Professors Polvani and Sobel. selected applications. majors in the senior year. Prerequisites or Prerequisite: Instructor’s permission. Current corequisites: APMA E4200 and E4204 or their APMA E6302x Numerical analysis of partial research in problems at the interface between equivalents. For 4 pts. Credit, term paper required. differential equations applied mathematics and earth and environmental Examples of problem areas are nonlinear dynamics, 3 pts. Lect: 2. Professor Du. sciences. asymptotics, approximation theory, numerical Prerequisite: APMA E3102 or E4200. Numerical APMA E9815x or y Geophysical fluid methods, etc. Approximately three problem areas analysis of initial and boundary value problems dynamics seminar are studied per term. for partial differential equations. Convergence 1–3 pts. May be repeated for up to 10 points of and stability of the finite difference method, the APMA E4990x and y Special topics in applied credit. Not offered in 2017–2018. spectral method, the finite element method and mathematics Prerequisite: Instructor’s permission. Problems in applications to elliptic, parabolic, and hyperbolic 1–3 pts. Lect: 3. Instructor to be announced. the dynamics of geophysical fluid flows. equations. Prerequisites: Advanced calculus and junior year applied mathematics, or their equivalents. APMA E6304y Integral transforms This course may be repeated for credit. Topics 3 pts. Lect: 2. Not offered in 2017–2018. COURSES IN MATERIALS and instructors from the Applied Mathematics Prerequisites: APMA E4204 and MATH UN2030, SCIENCE AND ENGINEERING Committee and the staff change from year to or their equivalents. Laplace, Fourier, Hankel, and See page 177. year. For advanced undergraduate students Mellin transforms. Selection of suitable transform and graduate students in engineering, physical for a given partial differential equation boundary sciences, biological sciences, and other fields. value problem. Operational properties of transforms. Inversion theorems. Approximate evaluation of APMA E6100 x or y Research Seminar inversion integrals for small and large values of 0 pts. Lect: 3. Members of the faculty. parameter. Application to the solution of integral Prerequisites: MATH UN3027 or APMA E4101, equations. MATH UN3028 or APMA E4200, MATH UN2010 or APMA E3101 or their equivalents. This course APMA E6901x and y–E6901y Special topics in is an M.S. degree requirement. Students attend applied mathematics at least three Applied Mathematics research 3 pts. Lect: 3. Members of the faculty. seminars within the Department of Applied Prerequisites: Advanced calculus and junior Physics and Applied Mathematics and submit year applied mathematics, or their equivalents. reports on each. This course may be repeated for credit. Topics and instructors from the Applied Mathematics APMA E6209x Approximation theory Committee and the staff change from year to year. 3 pts. Lect: 2. Not offered in 2017–2018. For students in engineering, physical sciences, Prerequisite: MATH GU4061 or some knowledge biological sciences, and other fields. of modern analysis. Theory and application of approximate methods of analysis from the APMA E8308y Asymptotic methods in applied viewpoint of functional analysis. Approximate mathematics numerical and analytical treatment of linear and 3 pts. Lect: 2. Not offered in 2017–2018. nonlinear algebraic, differential, and integral Prerequisite: APMA E4204 or equivalent. equations. Topics include function spaces, Asymptotic treatment of ordinary and partial

ENGINEERING 2017–2018 64 BIOMEDICAL ENGINEERING 351 Engineering Terrace, MC 8904 Phone: 212-854-4460 E-mail: [email protected] bme.columbia.edu

CHAIR ADMINISTRATIVE Andrew F. Laine, ASSOCIATE ADJUNCT Andrew F. Laine, ASSISTANT Percy K. and Vida PROFESSORS PROFESSORS Percy K. and Vida Zachary Corter L. W. Hudson Christoph Juchem Nicolas W. Chbat L. W. Hudson Professor of Lance C. Kam David Elad Professor of FINANCIAL ASSISTANT Biomedical Ernest Feleppa Biomedical Michelle Cintron Engineering ASSISTANT Mark Gelfand Engineering Helen H. Lu PROFESSORS Howard Levin ADMINISTRATIVE Kam W. Leong, Tal Danino VICE CHAIR ASSISTANT FOR Samuel Y. Sheng Josh Jacobs ADJUNCT ASSOCIATE X. Edward Guo DEPARTMENTAL Professor of Nandan Nerurkar PROFESSOR AFFAIRS Biomedical Qi Wang Alayar Kangarlu DEPARTMENT Paulette Louissaint Engineering ADMINISTRATOR Barclay Morrison III SENIOR LECTURER AFFILIATES Shila Maghji CHAIR OF Van C. Mow, Aaron M. Kyle Peter K. Allen UNDERGRADUATE Stanley Dicker Dimitris Anastassiou, BUSINESS MANAGER STUDIES Professor of LECTURER Charles Batchelor Kidest Shenkoru Clark T. Hung Biomedical Katherine Reuther Professor of Electrical Engineering Engineering STUDENT AFFAIRS CHAIR OF GRADUATE Paul Sajda JOINT FACULTY George H. Humphrey II MANAGER STUDIES Samuel K. Sia Gerard H. A. Ateshian, Kung-Ming Jan James Ihn Elisa E. Konofagou J. Thomas Vaughan, Andrew Walz Lawrence Schwartz, Professor of Professor of James Picker LABORATORY PROFESSORS Biomedical Mechanical Professor of Radiology MANAGER X. Edward Guo Engineering and Engineering Scott A. Small, Arthur Autz Henry Hess Radiology in Mind Shunichi Homma Bob and Rose Katz Andreas H. Hielscher Brain Behavior Edward F. Leonard Professor of Neurology COMPUTER SYSTEMS Elizabeth M. C. Hillman Institute Elizabeth S. Olson (in the Taub Institute, ADMINISTRATOR Clark T. Hung Gordana Vunjak- Michael P. Sheetz, Sergievsky Center and Ian Brown Christopher R. Jacobs Novakovic, University William R. Kenan Jr. in Radiology) Elisa E. Konofagou, Professor and the Professor of Cell Henry M. Spotnitz, EXTERNAL RELATIONS Robert and Margaret Mikati Foundation Biology Professor of Surgery AND EVENTS MANAGER Hariri Professor Professor of Kenneth L. Shepard, Binsheng Zhao Natalie Chee of Biomedical Biomedical Lau Family Professor Engineering and Engineering of Electrical GRANTS ANALYST Radiology Engineering Wendy Goldberg Milan N. Stojanovic

iomedical engineering is an sophisticated approaches to of other Engineering departments, evolving discipline in engineering measurement, data acquisition and and faculty from other University Bthat draws on collaboration analysis, simulation, and systems divisions who have strong interests and among engineers, physicians, and identification. These approaches involvement in biomedical engineering. scientists to provide interdisciplinary are useful in the study of individual Several of the faculty hold joint insight into medical and biological cells, organs, entire organisms, appointments in Biomedical Engineering problems. The field has developed its and populations of organisms. The and other University departments. own knowledge base and principles increasing value of mathematical Courses offered by the Department that are the foundation for the academic models in the analysis of living systems of Biomedical Engineering are programs designed by the Department is an important sign of the success of complemented by courses offered by of Biomedical Engineering at Columbia. contemporary activity. The programs other departments in The Fu Foundation The programs in biomedical offered in the Department of Biomedical School of Engineering and Applied engineering at Columbia (B.S., Engineering seek to emphasize the Science and by many departments in M.S., Ph.D., Eng.Sc.D., and M.D./ confluence of basic engineering the Faculty of Medicine, the College Ph.D.) prepare students to apply science and applied engineering with of Dental Medicine, and the Mailman engineering and applied science to the physical and biological sciences, School of Public Health, as well as problems in biology, medicine, and particularly in the areas of biomechanics, the science departments within the the understanding of living systems cell and tissue engineering, and Graduate School of Arts and Sciences. and their behavior, and to develop biosignals and biomedical imaging. The availability of these courses in a biomedical systems and devices. Programs in biomedical engineering university that contains a large medical Modern engineering encompasses are taught by its own faculty, members center and enjoys a basic commitment

ENGINEERING 2017–2018 to interdisciplinary research is important practices in biomedical engineering and 1. Professional employment in 65 to the quality and strength of the related sciences. areas such as the medical device program. Research facilities of the Biomedical industry, engineering consulting, and Educational programs at all Engineering faculty include the Synthetic biotechnology; levels are based on engineering and Biological Systems Laboratory (Professor 2. Graduate studies in biomedical biological fundamentals. From this Danino), the Liu Ping Laboratory for engineering or related fields; basis, the program branches into Functional Tissue Engineering (Professor 3. Attendance at medical, dental, or other concentrations of contemporary Mow), the Heffner Biomedical Imaging professional schools. biomedical engineering fields. Laboratory (Professor Laine), the The intrinsic breadth of these Laboratory for Intelligent Imaging and The undergraduate program in concentrations, and a substantial Neural Computing (Professor Sajda), biomedical engineering will prepare elective content, prepare bachelor’s the Biophotonics and Optical Radiology graduates who will have: and master’s students to commence Laboratory (Professor Hielscher), professional activity in any area of the Bone Bioengineering Laboratory (a) an ability to apply knowledge biomedical engineering or to go on (Professor Guo), the Cellular Engineering of mathematics, science, and to graduate school for further studies Laboratory (Professor Hung), the engineering in related fields. The program also Biomaterial and Interface Tissue (b) an ability to design and conduct provides excellent preparation for Engineering Laboratory (Professor Lu), experiments, as well as to analyze the health sciences and the study of the Neurotrauma and Repair Laboratory and interpret data medicine. Graduates of the doctoral (Professor Morrison), the Laboratory (c) an ability to design a system, program are prepared for research for Stem Cells and Tissue Engineering component, or process to meet activities at the highest level. (Professor Vunjak-Novakovic), the desired needs within realistic Areas of particular interest to Ultrasound and Elasticity Imaging constraints such as economic, Columbia faculty include biomechanics Laboratory (Professor Konofagou), environmental, social, political, (Professors Ateshian, Guo, Hess, the MR Science Laboratory (Professor ethical, health and safety, Jacobs, Morrison, and Mow), cellular Juchem), the Microscale Biocomplexity manufacturability, and sustainability and tissue engineering and artificial Laboratory (Professor Kam), the (d) an ability to function on organs (Professors Danino, Hung, Kam, Molecular and Microscale Bioengineering multidisciplinary teams (e) an ability to identify, formulate, and Leonard, Leong, Lu, Morrison, Sia, and Laboratory (Professor Sia), the solve engineering problems Vunjak-Novakovic), auditory biophysics Laboratory for Functional Optical (f) an understanding of professional and (Professor Olson), and biosignals and Imaging (Professor Hillman), the Cell ethical responsibility biomedical imaging (Professors Guo, and Molecular Biomechanics Laboratory (g) an ability to communicate effectively Hielscher, Hillman, Jacobs, Juchem, (Professor C. Jacobs), the Cognitive (h) the broad education necessary to Konofagou, Laine, Sajda, Vaughan, and Electrophysiology Laboratory (Professor understand the impact of engineering Wang). J. Jacobs), the Nanobiotechnology solutions in a global, economic, and Synthetic Biology Laboratory environmental, and societal context (Professor Hess), the Raymond and Facilities (i) a recognition of the need for, and an The Department of Biomedical Beverly Sackler Laboratory for Neural ability to engage in life-long learning Engineering has been supported by Engineering and Control (Professor (j) a knowledge of contemporary issues grants obtained from NIH, NSF, DoT, Wang), the Morphogenesis and (k) an ability to use the techniques, DoD, New York State, numerous Developmental Biomechanics Lab skills, and modern engineering tools research foundations, and University (Professor Nerurkar), and the Laboratory necessary for engineering practice funding. The extensive new facilities for Nanomedicine and Regenerative (l) an understanding of biology and that have recently been added both at Medicine (Professor Leong). These physiology the Medical Center and Morningside laboratories are supplemented with (m) the capability to apply advanced campus include teaching and research core facilities, including a tissue mathematics (including differential laboratories that provide students culture facility, a histology facility, a equations and statistics), science, with unusual access to contemporary confocal microscope, an atomic force and engineering, to solve the research equipment specially selected microscope, a 2-photon microscope, problems at the interface of for its relevance to biomedical epifluorescence microscopes, a engineering and biology engineering. Another addition is an freezer room, biomechanics facilities, (n) the ability to make measurements undergraduate wet laboratory devoted a machine shop, and a specimen on and interpret data from living to biomechanics and cell and tissue preparation room. systems, addressing the problems engineering, together with a biosignals associated with the interaction between living and nonliving materials and biomedical imaging and data UNDERGRADUATE PROGRAM processing laboratory. Each laboratory and systems. The objectives of the undergraduate incorporates equipment normally program in biomedical engineering are reserved for advanced research and The undergraduate curriculum is as follows: provides exceptional access to current designed to provide broad knowledge

ENGINEERING 2017–2018 66 of the physical and engineering requirements for most U.S. medical sequence (BMEN E4001-E4002), which sciences and their application to the schools. is taught by biomedical engineering solution of biological and medical All biomedical engineering students faculty and emphasizes quantitative problems. Students are strongly are expected to register for nontechnical applications of engineering principles encouraged to take courses in the electives, both those specifically required in understanding biological systems order specified in the course tables; by the School of Engineering and and phenomena from molecular to implications of deviations must Applied Science and those needed to organ system levels. In the fields of be discussed with a departmental meet the 27-point total of nontechnical biomedical engineering, experimental adviser before registration. The electives required for graduation. techniques and principles are first two years provides a strong fundamental skills that good biomedical grounding in the physical and chemical First and Second Years engineers must master. Beginning in junior year, all students take the sciences, engineering fundamentals, As outlined in this bulletin, in the first two-semester sequence Biomedical mathematics, and modern biology. This two years, all engineering students engineering laboratory, I & II (BMEN background is used to provide a unique are expected to complete a sequence E3810, E3820). In this two-semester physical approach to the study of of courses in mathematics, physics, series, students learn through hands- biological systems. The last two years chemistry, computer science, on experience the principles and of the undergraduate program provide engineering, modern biology, English methods of biomedical engineering substantial exposure to fundamentals in composition, and physical education, as experimentation, measurement biomedical engineering with emphasis well as nontechnical electives including techniques, quantitative theories of on the integration of principles of the humanities. For most of these biomedical engineering, data analysis, biomedical engineering, quantitative sequences, the students may choose and independent design of biomedical analysis of physiology, and experimental from two or more tracks. If there is a engineering experiments, in parallel to quantification and measurements of question regarding the acceptability of a the Biomedical engineering I & II and biomedical systems. course as a nontechnical elective, please Quantitative physiology I & II courses. In The common core biomedical consult the approved listing of courses addition, all students must take BMEN engineering curriculum provides a beginning on page 11 or contact your E4110: Biostatistics for engineers. In broad yet solid foundation in biomedical advising dean for clarification. the senior year, students are required engineering. The flexible choice of Please see the charts in this to take a two-semester capstone technical electives in the Department section for a specific description of design course, Biomedical engineering of Biomedical Engineering, other course requirements. design (BMEN E3910 and E3920), in departments in the Engineering School, For students who are interested which students work within a team to as well as in other departments in the in the biomedical engineering major, tackle an open-ended design project in arts and sciences allows students to they must take E1201: Introduction to biomedical engineering. The underlying broaden their biomedical engineering electrical engineering. For the computer philosophy of these core requirements education to their individualized science requirement, students must is to provide our biomedical engineering interests for a personalized curriculum. take ENGI W1006. They must take students with a broad knowledge and These qualities allow the faculty to the two-semester BIOL UN2005 and understanding of topics in the field of prepare students for activity in all UN2006: Introduction to Biology I & II in biomedical engineering. contemporary areas of biomedical the second year, which gives students Parallel to these studies in core cours- engineering. Graduates of the program a comprehensive overview of modern es, students are required to take flexible are equipped for employment in the biology from molecular to organ system technical elective courses (21 points) to large industrial sector devoted to health levels. In addition, all students must take obtain an in-depth understanding of their care, which includes pharmaceuticals, APMA E2101: Introduction to applied chosen interests. A technical elective is medical devices, artificial organs, mathematics in their second year. defined as a 3000-level or above course prosthetics and sensory aids, taught in SEAS or 3000-level or above diagnostics, medical instrumentation, Third and Fourth Years courses in biology, chemistry, biochemis- and medical imaging. Graduates The biomedical engineering programs try, or biotechnology. Exceptions include also accept employment in oversight at Columbia are based on engineering organic chemistry lecture courses and organizations (FDA, NIH, OSHA, and biological fundamentals. This is laboratory (which are 2000-level courses). and others), medical centers, and emphasized in our core requirements. At least 15 points (five courses) of these research institutes. They are prepared All students must take the two- technical electives must have engineer- for graduate study in biomedical semester introduction to biomedical ing content, while at least two of the five engineering and several related engineering courses, BMEN E3010 courses have to be from the Department areas of engineering and the health and E3020: Biomedical engineering of Biomedical Engineering. The cur- sciences. Students can meet entrance I & II, which provide a broad yet riculum prepares students who wish to requirements for graduate training in solid foundation in the biomedical pursue careers in medicine by satisfying the various allied health professions. engineering discipline. In parallel, most requirements in the premedical No more than three additional courses all students take the two-semester programs with no more than three addi- are required to satisfy entrance Quantitative physiology, I and II tional courses. Some of these additional

ENGINEERING 2017–2018 courses may also be counted as nonen- E4131, E4132, E4133, E4134, core requirements while providing 67 gineering technical electives. Please see E4135, E4136, E4138, and E4140 flexibility to meet the individualized the course tables for schedules leading f. All 3000-level or higher courses interests of the students. The following to a bachelor’s degree in biomedical in the Earth and Environmental are suggested sample courses for engineering. Engineering program various topic areas that students may It is strongly advised that students 2. Courses from the following consider. Note that students are not take required courses during the specific departments are not allowed to limited to these choices. All students term that they are designated in the count toward the required 48 units of are encouraged to design their own course tables, as scheduling conflicts engineering courses: educational paths through flexible may arise if courses are taken out of technical electives while meeting the sequence. a. Department of Applied Physics and following requirements: (1) courses Applied Mathematics must be at the 3000-level or above; (2) Technical Elective Requirements b. Department of Computer Science five of the seven electives must meet Students are required to take at least c. Department of Industrial the above criteria to be considered 48 points of engineering content Engineering and Operations engineering content; and (3) two of the coursework toward their degree. The Research seven electives must be biomedical 48-point requirement is a criterion d. Program of Materials Science and engineering courses. To help students established by ABET. Taking into Engineering choose their electives, the following consideration the number of engineering suggested sample curricula in various content points conferred by the required Once 48 points of engineering interest fields in biomedical engineering courses of the BME curriculum, a content are satisfied, students may are provided. Students do not need to portion of technical electives must be choose any course above the 3000 follow them rigidly and may substitute clearly engineering in nature (Engineering level in Columbia Engineering as well other courses, provided they meet the Content Technical Electives), specifically as biology, chemistry, biochemistry, and requirements above. as defined below: biotechnology as technical electives. If the 3000-level course is greater CELL AND TISSUE ENGINEERING 1. Technical elective courses with than or equal to the course cross sufficient engineering content that listed, its eligibility as an engineering CHEM UN2443: Organic chemistry I (3.5) CHEM UN2444: Organics chemistry II (3.5) can count toward the 48 units of content technical elective is determined BMCH E4500: Biological transport and rate engineering courses required for by the call letters of the first (owning) ABET accreditation: process (3) department in the course name BMEN E4510: Tissue engineering (3) designation. The department owning the BMEN E4590: BioMems: cellular and molecular a. All 3000-level or higher courses course must be ABET accredited to be applications (3) in the Department of Biomedical considered engineering. Engineering, except BMEN E4010, For example, APBM E4560 Anatomy BMEN E4210: Thermodynamics of biological E4103, E4104, E4105, E4106, for physicists & engineers does not systems (3) E4107, and E4108. (Note that only BMEN E4550: Micro- and nanostructures in count as engineering content technical 3 points of BMEN E3998 may be cellular engineering (3) elective, since the course is owned counted toward technical elective by Applied Physics (and cross-listed BIOMECHANICS degree requirements.) MECE E3100: Introduction to mechanics of fluids (3) b. All 3000-level or higher courses with Biomedical Engineering). BMCH EMEN E3105: Mechanics (4) in the Department of Mechanical E4810 Artificial organs is counted as an engineering content technical elective, MECE E3113: Mechanics of solids (3) Engineering, except MECE MECE E3301: Thermodynamics (3) as the course is owned by Biomedical E4007: Creative engineering and BMEN E4310: Solid biomechanics (3) entrepreneurship Engineering (and cross listed with BMEN E4320: Fluid biomechanics (3) c. All 3000-level or higher courses Chemical Engineering). BMEN E4340: Biomechanics of cells (3) in the Department of Chemical Based on the above for Engineering Engineering, except CHEN E4020: Technical Electives, a cross-listed course BIOSIGNALS AND BIOMEDICAL IMAGING Safeguarding intellectual and that is greater than or equal to 3000 ELEN E3810: Signals and systems (3.5) business property level and with BMEN as its starting call BMEN E4410: Ultrasound imaging (3) letters will qualify as a BME Engineering d. All 3000-level or higher BMEN E4420: Biosignal process and modeling (3) courses in the Department of Technical Elective. BMEN E4430: Principles of MRI (3) Electrical Engineering, except The accompanying charts describe the ELEN E4810: Digital signal processing (3) EEHS E3900: History of eight-semester degree program schedule BMEN E4894: Biomedical imaging (3) telecommunications: from the of courses leading to the bachelor’s BMEN E4898: Biophotonics (3) telegraph to the Internet degree in biomedical engineering. e. All 3000-level or higher courses The undergraduate Biomedical NEURAL ENGINEERING in the Civil Engineering and Engineering program is designed ELEN E3810: Signals and systems (3.5) Engineering Mechanics program, to provide a solid biomedical BMEB W4020: Computational neuroscience: except CIEN E4128, E4129, E4130, engineering curriculum through its circuits in the brain (3)

ENGINEERING 2017–2018 68 BMEE E4030: Neural control engineering (3) ROBOTICS AND CONTROL OF BIOLOGICAL Test only) is required of all applicants. BMEN E4420: Biosignal process and modeling (3) SYSTEMS Students whose bachelor’s degree was BMEN E4430: Principles of MRI (3) MECE E3100: Introduction to mechanics of not earned in a country where English ELEN E4810: Digital signal processing (3) fluids (3) is the dominant spoken language are BMEN E4894: Biomedical imaging (3) EMEN E3105: Mechanics (4) required to take the TOEFL test. In MECE E3113: Mechanics of solids (3) addition, for the doctoral program, the BMEE E4030: Neural control engineering (3) GENOMICS AND SYSTEMS BIOLOGY individual tracks require applicants to MEBM E4439: Modeling and identification of ECBN E4060: Introduction to genomic information have taken the following foundation dynamic systems (3) science and technology (3) MECE E4602: Introduction to robotics (3) courses: BMEN E4150: The cell as a machine (3) BMEE E4740: Bioinstrumentation (3) CHBM E4321: The genome and the cell (3) • Biomechanics: One year of biology BMEN E4420: Biosignal process and modeling (3) and/or physiology, solid mechanics, CHEN E4700: Principles of genomic technologies PREMED AND PRE-HEALTH PROFESSIONAL (3) statics and dynamics, fluid mechanics, MECE E3100: Introduction to mechanics of ordinary differential equations. CHEN E4760: Genomics sequence laboratory (3) fluids (3) • Cell and Tissue Engineering: One CHEN E4800: Protein engineering (3) EMEN E3105: Mechanics (4) year of biology and/or physiology, MECE E3113: Mechanics of solids (3) one year of organic chemistry or QUANTITATIVE BIOLOGY CHEM UN2443: Organic chemistry I (3.5) biochemistry with laboratory, fluid BMEB W4020: Computational neuroscience: CHEM UN2444: Organic chemistry II (3.5) mechanics, rate processes, ordinary circuits in the brain (3) BMEN E4310: Solid biomechanics (3) ECBN E4060: Introduction to genomic information BMEN E4320: Fluid biomechanics (3) differential equations. science and technology (3) • Biosignals and Biomedical Imaging: BIOL GU4070: The biology and physics of single To meet entrance requirements One year of biology and/or physiology molecules (3.5) of most U.S. medical schools, stu- and/or biochemistry. Linear algebra, BMEN E4310: Solid biomechanics (3) dents will need to take BIOC UN3501 ordinary differential equations, Fourier BMEN E4320: Fluid biomechanics (3) Biochemistry: Structure and metabolism analysis, digital signal processing. APMA E4400: Introduction to biological modeling (4), CHEM UN2545 Organic chem- (3) istry laboratory (3), PHYS UN1493: Applicants lacking some of these CHEN E4650: Biopolymers (3) Introduction to experimental physics (3), courses may be considered for and PSYC UN1001: The science of psy- admission with stipulated deficiencies BIOINDUCTIVE AND BIOMIMETIC MATERIALS chology (3) as well. that must be satisfied in addition to the CHEM UN2443: Organic chemistry I (3.5) requirements of the degree program. BMCH E4500: Biological transport process (3) Columbia Engineering does not admit GRADUATE PROGRAMS BMEN E4510: Tissue engineering (3) students holding the bachelor’s degree The graduate curriculum in biomedical BMEN E4590: BioMems: cellular and molecular directly to doctoral studies; admission applications (3) engineering is track-free at the master’s is offered either to the M.S. program or CHEN E4620: Introduction to polymers and soft level while at the doctoral level, it to the M.S. program/doctoral track. The materials (3) consists of three tracks: biomechanics, Department of Biomedical Engineering CHEN E4640: Polymer surface and interface (3) cell and tissue engineering, and CHEN E4800: Protein engineering (3) also admits students into the 4-2 biosignals and biomedical imaging. Initial program, which provides the opportunity graduate study in biomedical engineering for students holding a bachelor’s degree BIOMATERIALS is designed to expand the student’s from certain physical sciences to receive CHEM UN2443: Organic chemistry I (3.5) undergraduate preparation in the the M.S. degree after two years of study BMCH E3000: Biological transport process (3) direction of the concentration of interest. at Columbia. BMEN E4301: Structure, mechanics, and In addition, sufficient knowledge is adaptation of bone (3) acquired in other areas to facilitate broad BMEN E4310: Solid biomechanics (3) appreciation of problems and effective CURRICULUM AND EXAM BMEN E4510: Tissue engineering (3) REQUIREMENTS BMEN E4590: BioMems: cellular and molecular collaboration with specialists from other applications (3) scientific, medical, and engineering ELEN E4944: Principles of device disciplines. The Department of Master’s Degree microfabrication (3) Biomedical Engineering offers a graduate In consultation with an appointed faculty program leading to the Master of Science BIOMEMS AND NANOTECHNOLOGY adviser, M.S. students should select degree (M.S.), the Doctor of Philosophy MECE E3100: Introduction to mechanics of fluids (3) a program of 30 points of credit of degree (Ph.D.), and the Doctor of EMEN E3105: Mechanics (4) graduate courses (4000 level or above) MECE E3113: Mechanics of solids (3) Engineering Science degree (Eng.Sc.D.). appropriate to their career goals. This MSAE E4090: Nanotechnology (3) Applicants who have a Master of Science program must include the course in MECE E4212: Microelectromechanical systems (3) degree or equivalent may apply directly computational modeling of physiological BMEN E4550: Micro- and nanostructures in to the doctoral degree program. All systems (BMEN E6003); two semesters cellular engineering (3) applicants are expected to have earned of BMEN E9700: Biomedical engineering BMEN E4590: BioMems: cellular and molecular the bachelor’s degree in engineering seminar; at least four other biomedical applications (3) or in a cognate scientific program. The engineering courses; and at least one Graduate Record Examination (General

ENGINEERING 2017–2018 69 BIOMEDICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

MATHEMATICS MATH UN1102 (3) APMA E2000 (4)3

PHYSICS UN1401 (3) UN1402 (3) UN1403 (3) (three tracks, UN1601 (3.5) UN1602 (3.5) UN2601 (3.5) choose one) UN2801 (4.5) UN2802 (4.5)

UN1403 (3.5) UN1404 (3.5) CHEMISTRY UN1500 (3) (or semester 1) (three tracks, choose one) UN1604 (3.5) UN1507 (3) UN2045 (3.5) UN2046 (3.5), UN1507 (3)

UNIVERSITY UN1010 (3) either semester WRITING

COMPUTER ENGI W1006 (3) SCIENCE (or semester II)

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION1

THE ART OF ENGI E1102 (4) ENGINEERING1 (or in semester I)

HUMA CC1002, COCI CC1102, HUMA CC1001, HUMA UN1121 (3) or Global Core (3–4) NONTECHNICAL COCI CC1101, REQUIREMENTS1 or UN1123 (3) or Global Core (3–4) ECON UN1105 (4) and UN1155 recitation (0)

ELEN E1201 APMA E2101 (3) Intro. to EE (3.5) Intro. to applied math TECHNICAL REQUIREMENTS BIOL UN2005 BIOL UN2006 (4) Intro. to Biology, I (4) Intro to Biology, II

TOTAL POINTS 19.52 17.52 17.52 152

1 Students can mix these requirements according to what is available. 2 Estimations 3 Effective Class of 2021. graduate-level mathematics course for BMEN E9100 Master’s Research and Biostatistics course). If BMEN E6003 or (excluding statistics). Up to 6 credits of consult with their BME faculty adviser. a graduate-level mathematics course Master’s Research BMEN E9100 may has already been taken for the master’s be taken to fulfill degree requirements. Doctoral Degree degree, a technical elective can be Students with deficiency in physiology Doctoral students must complete used to complete the core course coursework are required to take the a program of 30 points of credit requirements. Students must register for BMEN E4001-E4002 sequence before beyond the M.S. degree. The core BMEN E9700: Biomedical engineering taking BMEN E6003. Candidates must course requirements (9 credits) for the seminar and for research credits during achieve a minimum grade-point average doctoral program include the course in the first two semesters of doctoral study. of 2.5. A thesis based on experimental, computational modeling of physiological Remaining courses should be selected computational, or analytical research is systems (BMEN E6003), plus at least in consultation with the student’s faculty optional. Students wishing to pursue the two graduate mathematics courses adviser to prepare for the doctoral Master’s Thesis option should register (one of these can be a graduate-level qualifying examination and to develop

ENGINEERING 2017–2018 70 BIOMEDICAL ENGINEERING: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

BMEN E3010 (3) BMEN E3020 (3) Biomedical eng., I Biomedical eng., II BMEN E3910 (4) BMEN E3920 (4) BME design, I BME design, II BMEN E3810 (3) BMEN E3820 (3) BME laboratory, I REQUIRED BME laboratory, II Technical elective (3)1 Technical elective (3)1 COURSES BMEN E4001 (3) BMEN E4002 (3) Technical elective (3)1 Technical elective (3)1 Quantitative physiol., I Quantitative physiol., II Technical elective (3)1 Technical elective (3)1 BMEN E4110 (4) Technical elective (3)1 Biostat. for engineers

NONTECH 3 points 3 points 3 points ELECTIVES

TOTAL POINTS 16 15 16 13

1 Five of seven technical electives must have engineering content, and two of them must be from the Biomedical Engineering Department.

expertise in a clearly identified area of the oral exam. A minimum cumulative COURSES IN BIOMEDICAL biomedical engineering. grade-point average of 3.2 is required to ENGINEERING All graduate students admitted to register for this examination. the doctoral degree program must BMEN E1001x Engineering in medicine 3 pts. Lect: 3. Not offered in 2017–2018. satisfy the equivalent of two semesters’ Doctoral Committee and Thesis The present and historical role of engineering experience in teaching (one semester Students who pass the qualifying in medicine and health care delivery. for M.D./Ph.D. students). This may examination choose a faculty member Engineering approaches to understanding include supervising and assisting to serve as their research adviser. organismic and cellular function in living undergraduate students in laboratory Each student is expected to submit systems. Engineering in the diagnosis and treatment of disease. Medical imaging, medical experiments, grading, and preparing a research proposal and present it lecture materials to support the teaching devices: diagnostic and surgical instruments, to a committee that consists of three mission of the department. The drug delivery systems, prostheses, artificial BME faculty members. The committee Department of Biomedical Engineering organs. Medical informatics and organization considers the scope of the proposed of the health care system. Current trends in is the only engineering department research, its suitability for doctoral biomedical engineering research. that offers Ph.D. training to M.D./ research and the appropriateness Ph.D. students. These candidates BMEN E3010x Biomedical engineering, I of the research plan. The committee are expected to complete their Ph.D. 3 pts. Lect: 3. Professor Lu. may approve the proposal without program within 3.5 years, with otherwise Prerequisites: BIOL UN2005 and UN2006, or reservation or may recommend instructor’s permission. Corequisites: BMEN the same requirements as those outlined modifications. In general, the student E4001, BMEN E3810. Various concepts within for the Doctoral Degree program. is expected to submit his/her research the field of biomedical engineering, foundational proposal after five semesters of knowledge of engineering methodology applied Doctoral Qualifying Examination doctoral studies. In accordance with to biological and/or medical problems through modules in biomechanics, biomaterials, and cell Doctoral candidates are required to regulations of the Graduate School and tissue engineering. pass a qualifying examination. This of Arts and Sciences, each student examination is given once a year, and is expected to submit a thesis and BMEN E3020y Biomedical engineering, II it should be taken after the student has defend it before a committee of five 3 pts. Lect: 3. Professor Hung. completed 30 points of graduate study. faculty, one of whom holds primary Prerequisites: BIOL UN2005 and UN2006, or The qualifying examination consists of appointment in another department instructor’s permission. Corequisites: BMEN E4002, BMEN E3820. Various concepts within an oral exam during which the student or school or university. Every doctoral the field of biomedical engineering, foundational presents an analysis of assigned candidate is required to have had knowledge of engineering methodology applied scientific papers, as well as answers accepted at least one first-author to questions in topics covering applied to biological and/or medical problems through full-length paper for publication in modules in biomechanics, bioinstrumentation, and mathematics, quantitative biology and a peer-reviewed journal prior to biomedical imaging. physiology, and track-specific material. A recommendation for award of the written analysis of the assigned scientific degree. ECBM E3060x Introduction to genomic papers must be submitted prior to information science and technology 3 pts. Lect: 3. Professor Varadan.

ENGINEERING 2017–2018 Introduction to the information system paradigm of BMEN E3999x, y or s Fieldwork feedback, population time encoding machines. 71 molecular biology. Representation, organization, 1–2 pts. Members of the faculty. Dendritic computation: elements of spike processing structure, function and manipulation of the Prerequisites: Obtained internship and approval and neural computation, synaptic plasticity and biomolecular sequences of nucleic acids and from faculty adviser. BMEN undergraduate learning algorithms, unsupervised learning and proteins. The role of enzymes and gene regulatory students only. May be used toward the spike time-dependent plasticity, basic dendritic elements in natural biological functions as well 128-credit degree requirement. Only for BMEN integration. Projects in MATLAB. as in biotechnology and genetic engineering. undergraduate students who include relevant BMEE E4030x Neural control engineering Recombination and other macromolecular off-campus work experience as part of their 3 pts. Lect: 3. Professor Wang. processes viewed as mathematical operations with approved program of study. Final report and letter Prerequisites: ELEN E3801. Topics include simulation and visualization using simple computer of evaluation required. Fieldwork credits may not count toward any major core, technical, elective, basic cell biophysics, active conductance and programming. This course shares lectures with the Hodgkin-Huxley model, simple neuron ECBM E4060, but the work requirements differ and nontechnical requirements. May not be taken for pass/fail credit or audited. models, ion channel models and synaptic somewhat. models, statistical models of spike generation, BMEN E3810x Biomedical engineering BMEN E4000x Special topics Wilson-Cowan model of cortex, large-scale laboratory, I 3 pts. Lect: 3. Professor Leong. electrophysiological recording methods, 3 pts. Lab: 4. Professor Kyle. Additional current topics in biomedical sensorimotor integration and optimal state Fundamental considerations of wave mechanics; engineering taught by regular or visiting estimation, operant conditioning of neural design philosophies; reliability and risk concepts; faculty. The same subject matter is not usually activity, nonlinear modeling of neural systems, basics of fluid mechanics; design of structures considered in different years. sensory systems: visual pathway and somatosensory pathway, neural encoding subjected to blast; elements of seismic design; BMEN E4001x Quantitative physiology, I: model: spike triggered average (STA) and spike elements of fire design; flood considerations; cells and molecules advanced analysis in support of structural design. 3 pts Lect: 3. Professor Kam. triggered covariance (STC) analysis, neuronal response to electrical micro-stimulation, DBS BMEN E3820y Biomedical engineering Prerequisites: BIOL UN2005 and UN2006. Corequisites: BMEN E3010 and E3810. for Parkinson’s disease treatment, motor neural laboratory, II prostheses, and sensory neural prostheses. 3 pts. Lab: 4. Professor Kyle. Physiological systems at the cellular and Biomedical experimental design and hypothesis molecular level are examined in a highly BMEN E4050x or y Electrophysiology of testing. Statistical analysis of experimental quantitative context. Topics include chemical human memory and navigation measurements. Analysis of variance, post hoc kinetics, molecular binding and enzymatic 3 pts. Lect: 3. Professor Jacobs. testing. Fluid shear and cell adhesion, neuro- processes, molecular motors, biological mem- Prerequisites: Instructor's permission. Human electrophysiology, soft tissue biomechanics, branes, and muscles. memory, including working, episodic, and biomedical imaging and ultrasound, BMEN E4002y Quantitative physiology, II: procedural memory. Electrophysiology of cognition, characterization of excitable tissues, microfluidics. organ systems noninvasive and invasive recordings. Neural basis of spatial navigation, with links to spatial BMEN E3910x-E3920y Biomedical 3 pts. Lect: 3. Professor Morrison. Prerequisites: BIOL UN2005 and UN2006. and episodic memory. Computational models of engineering design, I and II memory, brain stimulation, lesion studies. 4 pts. Lect: 1. Lab: 3. Professor Kyle. Corequisites: BMEN E3020, E3820. Students are A two-semester design sequence to be taken in introduced to a quantitative, engineering approach ECBM E4060x Introduction to genomic the senior year. Elements of the design process, to cellular biology and mammalian physiology. information with specific applications to biomedical engineering: Beginning with biological issues related to the cell, 3 pts. Lect: 3. Professor Anastassiou. concept formulation, systems synthesis, design the course progresses to considerations of the Prerequisites: None. Introduction to the analysis, optimization, biocompatibility, impact major physiological systems of the human body information system paradigm of molecular biology. on patient health and comfort, health care costs, (nervous, circulatory, respiratory, renal). Representation, organization, structure, function regulatory issues, and medical ethics. Selection BMEN E4010y Ethics for biomedical engineers and manipulation of the biomolecular sequence of and execution of a project involving the design 2 pts. Lect: 2. Not offered in 2017–2018. nucleic acids and proteins. The role of enzymes of an actual engineering device or system. Prerequisite: senior status in biomedical and gene regulatory elements in natural biological Introduction to entrepreneurship, biomedical start- engineering or the instructor’s permission. functions as well as in biotechnology and ups, and venture capital. Semester I: statistical Covers a wide range of ethical issues expected to genetic engineering. Recombination and other analysis of detection/classification systems confront graduates as they enter the biotechnology macromolecular processes viewed as mathematical (receiver operation characteristic analysis, logistic industry, research, or medical careers. Topics vary operations with simulation and visualization using regression), development of design prototype, and incorporate guest speakers from Physicians simple computer programming. need, approach, benefits and competition analysis. and Surgeons, Columbia Law School, Columbia Semester II: spiral develop process and testing, College, and local industry. ECBM E4090x or y Brain computer interfaces iteration and refinement of the initial design/ (BCI) laboratory prototype, and business plan development. A lab BMEB W4020x Computational neuroscience: 3 pts. Lect: 2. Lab: 3. Professor Mesgarani. fee of $100 each is collected. circuits in the brain Prerequisite: ELEN E3801. Hands-on experience 3 pts. Lect: 3. Professor Lazar. with basic neural interface technologies. BMEN E3998x or y Projects in biomedical Prerequisite: ELEN E3801 or BIOL UN3004. The Recording EEG (electroencephalogram) signals engineering biophysics of computation: modeling biological using data acquisition systems (noninvasive 1–3 pts. Hours to be arranged. Members of the neurons, the Hodgkin-Huxley neuron, modeling scalp recordings). Real-time analysis and faculty. channel conductances and synapses as monitoring of brain responses. Analysis of Independent projects involving experimental, memristive systems, bursting neurons and central intention and perception of external visual and theoretical, computational, or engineering design pattern generators, I/O equivalence and spiking audio signals. work. May be repeated, but no more than 3 points neuron models. Information representation and of this or any other projects or research course may neural encoding: stimulus representation with BMEN E4103x Anatomy of the thorax and be counted toward the technical elective degree time encoding machines, the geometry of time abdomen requirements as engineering technical electives. encoding, encoding with neural circuits with 2 pts. Lect: 2. Professor April.

ENGINEERING 2017–2018 72 Prerequisite: Graduate standing in Biomedical hydrophobicity), energy transduction (motors, examined. The establishment of basic governing Engineering. This course is designed for the transporters, chaperones, synthesis complexes), mechanical principles and constitutive relations for Biomedical Engineering graduate student basic cell functions. Biophysical principles, each tissue. Experimental determination of various interested in acquiring in-depth knowledge of feedback controls for robust cell function, tissue properties. Medical and clinical implications anatomy relevant to his/her doctoral research. adaptation to environmental perturbations. of tissue mechanical behavior. Lectures and tutorial sessions may be taken BMEN E4210y Thermodynamics of biological BMEN E4320x or y Fluid biomechanics with or without the associated laboratory (BMEN systems 3 pts. Lect: 3. Professor Guo. E4104). 4 pts. Lect: 4. Professor Sia. Prerequisites: APMA E2101, ENME E3105, BMEN E4104x Anatomy laboratory: thorax Prerequisites: CHEM UN1404 and MATH and MECE E4100. The principles of continuum and abdomen UN1202. Corequisite: BIOL UN2005 or equivalent. mechanics as applied to biological fluid flows 2 pts. Lect: 2. Professor April. Introduction to the thermodynamics of biological and transport. Continuum formulations of basic Prerequisites: Graduate standing in Biomedical systems, with a focus on connection microscopic conservation laws, Navier-Stokes equations, Engineering. Corequisites: BMEN E4103. molecular properties to macroscopic states. Both mechanics of arterial and venous blood flow, blood classical and statistical thermodynamics are rheology and non-Newtonian properties, flow and BMEN E4105x Anatomy of the extremities applied to biological systems; phase equilibria, transport in the microcirculation, oxygen diffusion, 2 pts. Lect: 2. Professor April. chemical reactions, and colligative properties. capillary filtration. Prerequisite: Graduate standing in Biomedical Topics in modern biology, macromolecular behavior Engineering. This course is designed for the in solutions and interfaces, protein-ligand binding, CHBM E4321y The genome and the cell Biomedical Engineering graduate student and the hydrophobic effect. 3 pts. Lect: 3. Not offered in 2017–2018. interested in acquiring in-depth knowledge of Prerequisites: BIOL UN2005 and MATH UN2030. anatomy relevant to his/her doctoral research. BMEN E4301x Structure, mechanics, and The utility of genomic information lies in its Lectures and tutorial sessions may be taken adaptation of bone capacity to predict the behavior of living cells in with or without the associated laboratory (BMEN 3 pts. Lect: 3. Not offered in 2017–2018. physiological, developmental, and pathological E4106). Introduction to structure, physiology, and situations. The effect of variations in genome biomechanics of bone. Structure, function, structure between individuals within a species, BMEN E4106x Anatomy laboratory: and physiology of skeletal bones; linear elastic including those deemed healthy or diseased, extremities properties of cortical and trabecular bone; and among species, can be inferred statistically 2 pts. Lab: 2. Professor April. anisotropy and constitutive models of bone tissue; by comparisons of sequences with behaviors Prerequisites: Graduate standing in Biomedical failure and damage mechanics of bone; bone and mechanistically, by studying the action of Engineering. Corequisites: BMEN E4105. adaptation and fracture healing; experimental molecules whose structure is encoded within determination of bone properties; and morphological BMEN E4107x Anatomy of the head and neck the genome. This course examines known analysis of bone microstructure. 2 pts. Lect: 2. Professor April. mechanisms that elucidate the combined effect Prerequisite: Graduate standing in Biomedical BMEN E4302x Biomechanics of of environmental stimulation and genetic makeup on the behavior of cells in homeostasis, disease Engineering. This course is designed for the musculoskeletal soft tissues states, and during development, and includes Biomedical Engineering graduate student 3 pts. Lect: 3. Professors Reuther and assessments of the probable effect of these interested in acquiring in-depth knowledge of Thompopoulos. behaviors on the whole organism. Quantitative anatomy relevant to his/her doctoral research. Prerequisite: ENME E3113 or equivalent. models of gene translation and intracellular Lectures and tutorial sessions may be taken with or Restricted to seniors and graduate students. signal transduction will be used to illustrate without the associated laboratory (BMEN E4108). Biomechanics of orthopaedic soft tissues switching of intracellular processes, transient and (cartilage, tendon, ligament, meniscus, etc.). BMEN E4108x Anatomy laboratory: head permanent gene activation, and cell commitment, Basic and advanced viscoelasticity applied to and neck development, and death. 2 pts. Lab: 2. Professor April. the musculoskeletal system. Topics include BMEN E4340x Biomechanics of cells Prerequisites: Graduate standing in Biomedical mechanical properties, applied viscoelasticity 3 pts. Lect: 3. Professor Jacobs. Engineering. Corequisites: BMEN E4107. theory, and biology of orthopaedic soft tissues. Prerequisites: BMEN E3320 and BMEN E4300 or BMEN E4110x Biostatistics for engineers BMEN E4305y Cardiac mechanics equivalents. Survey of experiments and theoretical 4 pts. Lect: 4. Professor Jacobs. 3 pts. Lect: 3. Not offered in 2017–2018. analyses of the mechanical behavior of individual Prerequisites: MATH UN1202 and APMA Prerequisites: BMEN E4310 and BMEN E4320 or living nonmuscle cells. Emphasis on quantitative E2101. Fundamental concepts of probability equivalents. Cardiac anatomy, passive myocardial analytic description using continuum mechanics and statistics applied to biology and medicine. constitutive properties, electrical activation, and molecular level theory from the standpoint Probability distributions, hypothesis testing and ventricular pump function, ventricular-vascular of statistical mechanics and mechanical models. inference, summarizing data and testing for coupling, invasive and noninvasive measures of Mechanics of erythrocytes, leukocytes, endothelial trends. Signal detection theory and the receiver regional and global function, models for predicting cells, and fibroblasts; models of aggregation, operator characteristic. Lectures accompanied by ventricular wall stress. Alterations in muscle adhesion, locomotion, amoeba motility, cell division data analysis assignments using MATLAB and properties and ventricular function resulting and morphogenesis; molecular level models of R as well as discussion of bioethics and case from myocardial infarction, heart failure, and left actin, myosin, microtubules, and intermediate studies in biomedicine. ventricular assist. filaments and relation to mechanical properties of cells and cytoskeleton. Alternative models of BMEN E4150x The cell as a machine BMEN E4310x or y Solid biomechanics cytoskeletal mechanics, foam theory, tensegrity. 3 pts. Lect: 3. Professors Sheetz and Kam. 3 pts. Lect: 3. Professor Guo. Analysis of experimental techniques including Prerequisite: MATH UN1101 or equivalent. Prerequisites: ENME-MECE E3105 and ENME micropipette studies, optical and magnetic Corequisites: One semester of BIOL UN2005 E3113. Applications of continuum mechanics to cytometry, and nanoindentation. or BIOC UN3501, and one semester of PHYS the understanding of various biological tissues UN1401 or equivalent. Cells as complex micron- properties. The structure, function, and mechanical BMEE E4400x Wavelet applications in sized machines, basic physical aspects of cell properties of various tissues in biological systems, biomedical image and signal processing components (diffusion, mechanics, electrostatics, such as blood vessels, muscle, skin, brain tissue, 3 pts. Lect: 3. Not offered in 2017–2018. bone, tendon, cartilage, ligaments, etc., are

ENGINEERING 2017–2018 Prerequisite: APMA E2101 or E3101 or equivalent. Kalman Filter. Parameter estimation via prediction- and fundamental bioengineering design criteria 73 An introduction to methods of wavelet analysis error and subspace approaches. Iterative and behind the development of cell-based tissue and processing techniques for the quantification bootstrap methods. Fit criteria. Wide applicability: substitutes. Topics include biocompatibility, of biomedical images and signals. Topics include medical, energy, others. MATLAB and Simulink biological grafts, gene therapy-transfer, and frames and overcomplete representations, environments. bioreactors. multiresolution algorithms for denoising and image restoration, multiscale texture segmentation BMEN E4440y Physiological control systems BMEN E4520x Synthetic biology: principles of and classification methods for computer aided 3 pts. Lect: 3. Professor Chbat. genetic circuits diagnosis. Prerequisites: MEBM E4439 and APMA E2101, 3 pts. Lect: 3. Professor Danino. or instructor’s permission. Fundamentals of Basic principles of synthetic biology and survey BMEN E4410y Ultrasound in diagnostic time and frequency domains analyses and of the field. Fundamentals of biological circuits, imaging stability. Frequency domain controller design. including circuit design, modern techniques for 3 pts. Lect: 3. Professor Konofagou. Cardiovascular and respiratory systems DNA assembly, quantitative characterization of Prerequisites: MATH UN1202 or equivalent. simulation. Endogenous control systems: genetic circuits, and ODE modeling of biological Fourier analysis. Physics of diagnostic baroreflex, chemoreflex, thermoregulation, circuits with MATLAB. Knowledge of biology, ultrasound and principles of ultrasound imaging pupillary light reflex. Open and closed loop ordinary differential equations, and MATLAB will be instrumentation. Propagation of plane waves physiological systems. Exogenous control assumed. Intended for advanced undergraduate in lossless medium; ultrasound propagation systems: ventilators, infusion pumps. Nonlinear and graduate students. through biological tissues; single-element actuators and delayed feedback systems. Acute and array transducer design; pulse-echo and disease simulation and clinical decision support BMEN E4540y Bioelectrochemistry Doppler ultrasound instrumentation, performance in the intensive care unit. MATLAB and Simulink 3 pts. Lect: 3. Not offered in 2017–2018. evaluation of ultrasound imaging systems using environments utilized. Prerequisites: CHEM UN3079 and UN2443 or tissue-mimicking phantoms, ultrasound tissue equivalent. Application of electrochemical kinetics BMEN E4450y Dental and craniofacial tissue characterization; ultrasound nonlinearity and to interfacial processes occurring in biomedical bubble activity; harmonic imaging; acoustic engineering systems. Basics of electrochemistry, electrochemical output of ultrasound systems; biological effects of 3 pts. Lect: 3. Not offered in 2017–2018. instrumentation, and relevant cell and electrophysiology ultrasound. Prerequisites: MSAE E3103, BMEN E4210, E4501, reviewed. Applications to interpretation of excitable or equivalent. Principles of dental and craniofacial and nonexcitable membrane phenomena, with BMEN E4420y Biomedical signal processing bioengineering, periodontal tissue engineering: emphasis on heterogeneous mechanistic steps. and signal modeling beyond guided tissue regeneration, craniofacial Examples of therapeutic devices created as a 3 pts. Lect: 3. Professor Sajda. regeneration by stem cells and engineered result of bioelectrochemical studies. Prerequisites: ELEN E3801 and either APMA scaffolds, biomaterials: Engineering approaches in E2101 or E3101 or instructor’s permission. tissue regeneration, bone biology and development: BMEN E4550y Micro- and nanostructures in Fundamental concepts of signal processing instructive cues for tissue engineers. cellular engineering in linear systems and stochastic processes. BMCH E4500x or y Biological transport and 3 pts. Lect: 3. Professor Kam. Estimation, detection, and filtering methods applied rate processes Prerequisites: BIOL UN2005 and UN2006 or to biomedical signals. Harmonic analysis, auto- equivalent. Design, fabrication, and application of regressive model, Wiener and Matched filters, 3 pts. Lect: 3. Not offered in 2017–2018. Prerequisites: CHEM UN2443, APMA E2101. micro-/nanostructured systems for cell engineering. linear discriminants, and independent components. Recognition and response of cells to spatial Methods are developed to answer concrete Corequisites: BIOL UN2005. Convective and diffusive movement and reaction of molecules aspects of their extracellular environment. Focus questions on specific data sets in modalities on neural, cardiac, coculture, and stem cell such as ECG, EEG, MEG, ultrasound. Lectures in biological systems. Kinetics of homogeneous systems. Molecular complexes at the nanoscale. accompanied by data analysis assignments using and heterogeneous reactions in biological environments. Mechanisms and models of MATLAB. BMEN E4560y Dynamics of biological membranes transport across membranes. Convective diffusion 3 pts. Lect: 3. Not offered in 2017–2018. BMEN E4430x Principles of magnetic with and without chemical reaction. Diffusion in Prerequisites: BIOL UN2005, BMEN E4001, resonance imaging restricted spaces. Irreversible thermodynamic or equivalent. The structure and dynamics of 3 pts. Lect: 3. Professor Kangarlu. approaches to transport and reaction in biological biological (cellular) membranes are discussed, Prerequisites: PHYS UN1403 and APMA E2101, systems. with an emphasis on biophysical properties. Topics or instructor’s permission. Fundamental principles BMEN E4501 Biomaterials of Magnetic Resonance Imaging (MRI), including include membrane composition, fluidity, lipid 3 pts. Lect: 3. Not offered in 2017–2018. the underlying spin physics and mathematics asymmetry, lipid-protein interactions, membrane Prerequisites: BIOL UN2005, UN2006, BMEN of image formation with an emphasis on the turnover, membrane fusion, transport, lipid phase E4001, and E4002. An introduction to the application of MRI to neuroimaging, both behavior. In the second half of the semester, strategies and fundamental bioengineering design anatomical and functional. The course examines students will lead discussions of recent journal criteria in the development of biomaterials and both theory and experimental design techniques. articles. tissue engineered grafts. Materials structural- MEBM E4439x Modeling and identification of functional relationships, biocompatibility in BMEN E4570x Science and engineering of dynamic systems terms of material and host responses. Through body fluids 3 pts. Lect: 3. Professor Chbat. discussions, readings, and a group design project, 3 pts. Lect: 3. Not offered in 2017–2018. Prerequisites: APMA E2101, ELEN E3801 students acquire an understanding of cell-material Prerequisites: General chemistry, organic or corequisite EEME E3601, or instructor’s interactions and identify the parameters critical chemistry, and basic calculus. Body fluids as a permission. Generalized dynamic system modeling in the design and selection of biomaterials for dilute solution of polyelectrolyte molecules in and simulation. Fluid, thermal, mechanical, diffusive, biomedical applications. water. Study of physical behavior as affected electrical, and hybrid systems are considered. by the presence of ions in surrounding BMEN E4510x or y Tissue engineering Nonlinear and high order systems. System environments. The physics of covalent, ionic, 3 pts. Lect: 3. Professor Hung. identification problem and Linear Least Squares and hydrogen bonds are reviewed, in relation Prerequisites: BIOL UN2005, UN2006, BMEN method. State-space and noise representation. to the structure/properties of the body fluid. E4001, E4002. An introduction to the strategies

ENGINEERING 2017–2018 74 Selected physiological processes are examined in FRET, optical traps, AFM, and superresolution BMEN E4750y Sound and hearing physical-chemical terms for polymers. imaging,for understanding molecular mechanics 3 pts. Lect: 3. Professor Olson. and dynamics. Prerequisites: PHYS UN1401 and MATH UN1105- BMEN E4590x BioMems: cellular and MATH UN1106. Introductory acoustics, basics molecular applications MEBM E4710x or y Morphogenesis: shape of waves and discrete mechanical systems. The 3 pts. Lect: 3. Professor Sia. and structure in biological materials mechanics of hearing—how sound is transmitted Prerequisites: Chemistry, CHEM UN3443, or 3 pts. Lect: 2.5. Professor Kasza through the external and middle ear to the inner CHEM UN3545 or equivalent, MATH UN1201, Prerequisites: Courses in mechanics, ear, and the mechanical processing of sound within BIOL UN2005, and UN2006. Topics include thermodynamics, and ordinary differential the inner ear. biomicroelectromechanical, microfluidic, and lab- equations at the undergraduate level or instructor's on-a-chip systems in biomedical engineering, with permission. Introduction to how shape and CBMF W4761y Computational genomics a focus on cellular and molecular applications. structure are generated in biological materials 3 pts. Lect: 3. Professor Pe’er. Microfabrication techniques, biocompatibility, using engineering approach emphasizing Prerequisites: Working knowledge of at least one miniaturization of analytical and diagnostic application of fundamental physical concepts to a programming language, and some background in devices, high-throughput cellular studies, diverse set of problems. Mechanisms of pattern probability and statistics. Computational techniques microfabrication for tissue engineering, and in formation, self-assembly, and self-organization for analyzing and understanding genomic data, vivo devices. in biological materials, including intracellular including DNA, RNA, protein and gene expression structures, cells, tissues, and developing embryos. data. Basic concepts in molecular biology relevant BMEN E4601y Cellular electricity Structure, mechanical properties, and dynamic to these analyses. Emphasis on techniques from 3 pts. Lect: 2. Lab: 1. Not offered in behavior of these materials. Discussion of artificial intelligence and machine learning. String- 2017–2018. experimental approaches and modeling. Course matching algorithms, dynamic programming, Bioelectricity of the cell membrane. Basis of cell uses textbook materials as well as collection of hidden Markov models, expectation-maximization, resting voltage, voltage changes that lead to the research papers. neural networks, clustering algorithms, support action potential and electrical oscillations used BMEN E4737x Computer control of medical vector machines. Students with life sciences in sensing systems. Laboratory includes building instrumentation backgrounds who satisfy the prerequisites are electronic circuits to measure capacitance of 3 pts. Lect: 2. Lab: 1. Not offered in 2017–2018. encouraged to enroll. artificial membranes and ion pumping in frog skin. Prerequisite: Basic knowledge of the C programming Lab required. BMCH E4810y Artificial organs language. Acquisition and presentation of data 3 pts. Lect: 3. Professor Leonard. APBM E4650x Anatomy for physicists and for medical interpretation. Operating principles of Analysis and design of replacements for the heart, engineers medical devices: technology of medical sensors, kidneys, and lungs. Specification and realization of 3 pts. Lect: 3. Professors Katz and Rozenshtein. algorithms for signal analysis, computer interfacing structures for artificial organ systems. Prerequisite: Engineering or physics background. and programming, interface design. Laboratory A systemic approach to the study of the human assignments cover basic measurement technology, BMEN E4840y Functional imaging for the brain body from a medical imaging point of view: interfacing techniques, use of Labview software 3 pts. Lect: 3. Lab: 1. Professor Razlighi. skeletal, respiratory, cardiovascular, digestive, and instrument interrogation and control, automated ECG Prerequisites: APMA E2101, APMA E4200, ELEN urinary systems, breast and women’s issues, head analysis, ultrasonic measurements, image processing E3801, or instructor’s permission. Fundamentals and neck, and central nervous system. Lectures applied to X-ray images and CAT scans. of modern medical functional imaging. In-depth are reinforced by examples from clinical two- and exploration of functional magnetic resonance BMEN E4738y Transduction and acquisition three-dimensional and functional imaging (CT, MRI, imaging (fMRI), arterial spin labeling (ASL), of biomedical data PET, SPECT, U/S, etc.). and positron emission tomography (PET). 3 pts. Lect: 2. Lab: 1. Not offered in 2017–2018. Human brain anatomy, physiology, and BMME E4702x Advanced musculoskeletal Data transduction and acquisition systems used in neurophysiological bases underlying each biomechanics biomedicine. Assembly of biotransducers and the functional imaging. Statistical and digital signal 3 pts. Lect: 2.5. Lab: 0.5. Not offered in analog/digital circuitry for acquiring electrocardiogram, processing methods specific for functional image 2017–2018. electromyogram, and blood pressure signals. Each analysis. Final cumulative project requiring Advanced analysis and modeling of the small group will develop and construct a working coding in MATLAB, Python, R, or C. musculoskeletal system. Topics include data acquisition board, which will be interfaced advanced concepts of 3D segmental kinematics, with a signal generator to elucidate the dynamics BMEN E4894x Biomedical imaging musculoskeletal dynamics, experimental of timing constraints during retrieval of biodata. 3 pts. Lect: 3. Professor Hielscher. measurements of joint kinematics and anatomy, Lab required. This course covers image formation, methods of modeling of muscles and locomotion, multibody analysis, and representation of digital images. BMEE E4740y Bioinstrumentation joint modeling, introduction to musculoskeletal Measures of qualitative performance in the context 3 pts. Lect: 1. Lab: 3. Professor Kyle. surgical simulations. of clinical imaging. Algorithms fundamental to Prerequisites: ELEN E1201, COMS W1005. the construction of medical images via methods MEBM E4703y Molecular mechanics in Hands-on experience designing, building, and of computed tomography, magnetic resonance, biology testing the various components of a benchtop and ultrasound. Algorithms and methods for 3 pts. Lect: 3. Professor Chbat. cardiac pacemaker. Design instrumentation the enhancement and quantification of specific Prerequisites: ENME E3105, APMA E2101, or to measure biomedical signals as well as to features of clinical importance in each of these instructor’s permission. Mechanical understanding actuate living tissues. Transducers, signal modalities. of biological structures including proteins, DNA conditioning electronics, data acquisition boards, and RNA in cells and tissues. Force response the Arduino microprocessor, and data acquisition BMEN E4895x or y Analysis and of proteins and DNA, mechanics of membranes, and processing using MATLAB will be covered. quantification of medical images biophysics of molecular motors, mechanics Various devices will be discussed throughout the 3 pts. Lect: 3. Professor Laine. of protein-protein interactions. Introduction to course, with laboratory work focusing on building Prerequisite: BMEN E4894. Corequisite: BMEN modeling and simulation techniques, and modern an emulated version of a cardiac pacemaker. E4894. Novel methods of mathematical analysis biophysical techniques such as single molecule applied to problems in medical imaging. Design

ENGINEERING 2017–2018 requirements for screening protocols, treatment 3 pts. Lect: 3. Professor Reuther and Nye. 3 pts. Lect: 3. Professor Jacobs. 75 therapies, and surgical planning. Sensitivity and Introduction to and application of Prerequisite: MECE E6422, or ENME E6315, specificity in screening mammography and chest commercialization of biomedical innovations. or equivalent. Structure-function relations and radiographs, computer-aided diagnosis systems, Topics include needs clarification, stakeholder linear/nonlinear constitutive models of biological surgical planning in orthopaedics, quantitative analysis, market analysis, value proposition, tissues: anisotropic elasticity, viscoelasticity, analysis of cardiac performance, functional business models, intellectual property, regulatory, porous media theories, mechano-electrochemical magnetic resonance imaging, positron emission and reimbursement. Development of path-to- models, infinitesimal and large deformations. tomography, and echocardiography data. market strategy and pitch techniques. Emphasis on the application and implementation of constitutive models for biological tissues BMEN E4898y Biophotonics EEBM E6020y Methods of computational into existing finite element software packages. 3 pts. Lect: 3. Professor Hielscher. neuroscience Model generation from biomedical images by Prerequisites: BMEN E4894 Biomedical imaging, 4.5 pts. Lect: 3. Not offered in 2017–2018. extraction of tissue geometry, inhomogeneity and PHYS UN1403 Classical and quantum waves, Prerequisite: BMEB W4020. Formal methods in anisotropy. Element-by-element finite element or instructor’s permission. This course provides computational neuroscience including methods solver for large-scale image based models a broad-based introduction into the field of of signal processing, communications theory, of trabecular bone. Implementation of tissue Biophotonics. Fundamental concepts of optical, information theory, systems and control, system remodeling simulations in finite element models. thermal, and chemical aspects of the light-tissue identification and machine learning. Molecular interactions will be presented. The application models of transduction pathways. Robust adaptation MEBM E6310x-E6311y Mixture theories for of these concepts for medical therapy and and integral feedback. Stimulus representation biological tissues, I and II diagnostics will be discussed. The course and groups. Stochastic and dynamical systems 3 pts. Lect: 3. Not offered in 2017–2018. includes theoretical modeling of light-tissue models of spike generation. Neural diversity and Prerequisites: MECE E6422 and APMA E4200, or interactions as well as optical medical instrument ensemble encoding. Time encoding machines and equivalent Development of governing equations for design and methods of clinical data interpretation. neural codes. Stimulus recovery with time decoding mixtures with solid matrix, interstitial fluid, and ion BMEN E6000x and y Graduate special topic machines. MIMO models of neural computation. constituents. Formulation of constitutive models for 3 pts. Lect: 3. Members of faculty. Synaptic plasticity and learning algorithms. Major biological tissues. Linear and nonlinear models of Current topics in biomedical engineering. project(s) in MATLAB. fibrillar and viscoelastic porous matrices. Solutions to special problems, such as confined and Subject matter will vary by year. Instructors may BMEE E6030x Neural modeling and unconfined compression, permeation, indentation impose prerequisites depending on the topic. neuroengineering and contact, and swelling experiments. BMEN E6003x Computational modeling of 3 pts. Lect: 3. Not offered in 2017–2018. physiological systems Prerequisites: ELEN E3801, and either APMA BMEN E6400x Analysis and quantification of 3 pts. Lect: 3. Professor Reuther. E2101 or E3101, or equivalent, or instructor’s medical images Prerequisites: BMEN E4001 and E4002 or permission. Engineering perspective on the study 3 pts. Lect: 3. Professor Laine. equivalent, and APMA E4200 or equivalent. of multiple levels of brain organization, from Novel methods of mathematical analysis Advanced computational modeling and single neurons to cortical modules and systems. applied to problems in medical imaging. Design quantitative analysis of selected physiological Mathematical models of spiking neurons, neural requirements for screening protocols, treatment systems from molecules to organs. Selected dynamics, neural coding, and biologically-based therapies, and surgical planning. Sensitivity and systems are analyzed in depth with an emphasis computational learning. Architectures and learning specificity in screening mammography and chest on modeling methods and quantitative analysis. principles underlying both artificial and biological radiographs, computer aided diagnosis systems, Topics may include cell signaling, molecular neural networks. Computational models of cortical surgical planning in orthopaedics, quantitative transport, excitable membranes, respiratory processing, with an emphasis on the visual analysis of cardiac performance, functional physiology, nerve transmission, circulatory system. Applications of principles in neuroengineering; magnetic resonance imaging, positron emission control, auditory signal processing, muscle neural prostheses, neuromorphic systems and tomography, and echocardiography data. biomimetics. Course includes a computer simulation physiology, data collection and analysis. BMEN E6500x Tissue and molecular laboratory. Lab required. BMEN E6005x Biomedical design I engineering laboratory 3 pts. Lect: 3. Professor Reuther. ECBM E6070-6079x or y Topics in 4 pts. Lect: 1. Lab: 3. Professor Reuther. Master's students only. Project-based design neuroscience and deep learning Prerequisites: Biology BIOL UN2005 and BIOL 3 pts. Lect: 2. Members of the faculty. experience for graduate students. Elements of UN2006 or permission of instructor. Hands-on Prerequisites: the instructor's permission. Selected design process, including need identification, experiments in molecular and cellular techniques, advanced topics in neuroscience and deep learn- concept generation, concept selection, and including fabrication of living engineered tissues. ing. Content varies from year to year, and different implementation. Development of design prototype Covers sterile technique, culture of mammalian topics rotate through the course numbers 6070 and introduction to entrepreneurship and cells, microscopy, basic subcloning and gel to 6079. implementation strategies. Real-world training in electrophoresis, creation of cell-seeded scaffolds, biomedical design and innovation. EEBM E6090-6099x or y Topics in and the effects of mechanical loading on the computational neuroscience and metabolism of living cells or tissues. Theory, BMEN E6006y Biomedical design II neuroengineering background, and practical demonstration for each 3 pts. Lect 3. Professor Reuther. 3 pts. Lect: 2. Professor Sajda. technique will be presented. Lab required. Second semester of project-based design Prerequisite: Instructor’s permission. Selected experience for graduate students. Elements of BMEN E6505x Advanced scaffold design and advanced topics in computational neuroscience design process, with focus on skills development, engineering complex tissues and neuroengineering. Content varies from year to prototype development and testing, and business 3 pts. Lect: 2.5. Lab: 0.5. Professor Lu. year, and different topics rotate through the course planning. Real-world training in biomedical Prerequisites: BMEN E4501 or equivalent. numbers 6090-6099. design, innovation, and entrepreneurship. Corequisites: BMEN E4001 or E4002. Advanced BMEN E6301y Modeling of biological tissues biomaterial selection and biomimetic scaffold BMEN E6007y Lab-to-market: commercializing with finite elements design for tissue engineering and regenerative biomedical innovations medicine. Formulation of bio-inspired design

ENGINEERING 2017–2018 76 criteria, scaffold characterization and testing, an investigation of some problem in biomedical engineering must register for 12 points of doctoral and applications on forming complex tissues or engineering culminating in a thesis describing the research instruction. Registration may not be used organogenesis. Laboratory component includes results of their work. No more than 6 points in this to satisfy the minimum residence requirement for basic scaffold fabrication, characterization and in course may be counted for graduate credit, and the degree. vitro evaluation of biocompatibility. Group projects this credit is contingent upon the submission of an BMEN E9900x or y Doctoral dissertation target the design of scaffolds for select tissue acceptable thesis. 0 pts. Members of the faculty. engineering applications. BMEN E9500x or y Doctoral research A candidate for the doctorate in biomedical BMEN E8001y Current topics in 1–6 pts. Members of the faculty. engineering or applied biology may be required nanobiotechnology and synthetic biology Doctoral candidates are required to make an to register for this course in every term after the 3 pts. Lect: 3. Professor Hess. original investigation of a problem in biomedical student’s coursework has been completed and Targeted toward graduate students; undergraduate engineering, the results of which are presented in until the dissertation has been accepted. student may participate with permission of the the dissertation. instructor. Review and critical discussion of recent BMEN E9700x or y Biomedical engineering literature in nanobiotechnology and synthetic seminar biology. Experimental and theoretical techniques, 0 pts. Sem: 1. Professors Wang and Olson. critical advances. Quality judgments of scientific All matriculated graduate students are required impact and technical accuracy. Styles of written and to attend the seminar as long as they are in graphical communication, the peer review process. residence. No degree credit is granted. The EEBM E9070y Massively parallel neural seminar is the principal medium of communication computation among those with biomedical engineering interests 3 pts. Lect: 3. Professor Mesgarani. within the University. Guest speakers from other Prerequisites: BMEB W4020 or permission of institutions, Columbia faculty, and students within instructor. Drosophila connectomics. Detailed the department who are advanced in their studies description of the fruit fly’s olfactory and vision frequently offer sessions. systems. Parallel processing on GPSs. BMEN E9800x or y Doctoral research BMEN E9100x or y Master’s research instruction 1–6 pts. Members of the faculty. 3–12 pts. Members of the faculty. Candidates for the M.S. degree may conduct A candidate for the Eng.Sc.D. degree in biomedical

ENGINEERING 2017–2018 CHEMICAL ENGINEERING 7777 801 S. W. Mudd, MC 4721 Phone: 212-854-2965 cheme.columbia.edu

CHAIR Christopher J. Durning Edward F. Leonard ASSOCIATE ADJUNCT Alan C. West George W. Flynn, Ben O’Shaughnessy PROFESSORS PROFESSORS Higgins Professor of Venkat Kyle Bishop Elias Mattas DIRECTOR OF Chemistry Venkatasubramanian, V. Faye McNeill Kenneth Spall FINANCE AND Oleg Gang Samuel Ruben–Peter Alissa Park OPERATIONS Jingyue Ju, G. Viele Professor of ADJUNCT ASSOCIATE Kathy Marte Samuel Ruben–Peter Engineering ASSISTANT PROFESSORS G. Viele Professor of Alan C. West, Samuel PROFESSORS Aghavni Bedrossian- Engineering Ruben–Peter G. Christopher Boyce Omer PROFESSORS Sanat K. Kumar, Viele Professor of Daniel Esposito Hartoun Hartounian Gregory Hounsell Scott A. Banta Bykhovsky Professor Electrochemistry Allie Obermeyer Kevin Joback Jingguang G. Chen, of Chemical Thayer Lindsley Engineering LECTURER Professor of Chemical Robert Bozic Engineering

hemical engineering is a biotechnologies of major medical with applications in gene expression highly interdisciplinary field importance employing DNA- or protein- and drug discovery; the physics and C concerned with materials and based chemical sensors, controlled- chemistry of nanoparticle-polymer processes at the heart of a broad range release drugs, new agricultural composites with novel electronic and of technologies. Practicing chemical products, nanoparticle-based materials, photonic properties; programmable engineers are the experts in charge bio-nanoparticle conjugates, and many assembly of nanoparticle systems; of the development and production of others. DNA-guided assembly of inorganic and diverse products in traditional chemical Driven by this diversity of biological nanoscale objects. Many industries as well as many emerging applications, chemical engineering experimental techniques are employed, new technologies. The chemical is perhaps the broadest of all from neutron scattering to fluorescence engineer guides the passage of the engineering disciplines: chemistry, microscopy, and the theoretical work product from the laboratory to the physics, mathematics, biology, and involves both analytical mathematical marketplace, from ideas and prototypes computing are all deeply involved. The physics and numerical computational to functioning articles and processes, research of the faculty of Columbia’s analysis. from theory to reality. This requires Chemical Engineering Department is Students enrolling in the Ph.D. a remarkable depth and breadth correspondingly broad. Some of the program will have the opportunity of understanding of physical and areas under active investigation are the to conduct research in these and chemical aspects of materials and their fundamental physics, chemistry, and other areas. Students with degrees production. engineering of polymers and other soft in chemical engineering and other The expertise of chemical engineers materials; the electrochemistry of fuel engineering disciplines, in chemistry, is essential to production, marketing, cells and other interfacial engineering in physics, in biochemistry, and in and application in such areas as phenomena; the bioengineering of other related disciplines are all natural pharmaceuticals, high-performance artificial organs and immune cell participants in the Ph.D. program materials in the aerospace and activation; the engineering and and are encouraged to apply. The automotive industries, biotechnologies, biochemistry of sequencing the human Department of Chemical Engineering at semiconductors in the electronics genome; the chemistry and physics Columbia is committed to a leadership industry, paints and plastics, petroleum of surface-polymer interactions; the role in research and education in frontier refining, synthetic fibers, artificial organs, biophysics of cellular processes in areas of research and technology biocompatible implants and prosthetics living organisms; the physics of thin where progress derives from the and numerous others. Increasingly, polymer films; the chemistry of smart conjunction of many different traditional chemical engineers are involved in new polymer materials with environment- research disciplines. Increasingly, technologies employing highly novel sensitive surfaces; biosensors with new technologies and fundamental materials whose unusual response at tissue engineering applications; the research questions demand this type of the molecular level endows them with physics and chemistry of DNA-DNA interdisciplinary approach. unique properties. Examples include hybridization and melting; the chemistry The undergraduate program environmental technologies, emerging and physics of DNA microarrays provides a chemical engineering degree

ENGINEERING 2017–2018 78 that is a passport to many careers in scattering experiments. A digital image MHz, and two 300 MHz instruments that directly related industries as diverse as analysis system for the characterization are operated by students and postdocs biochemical engineering, environmental of sessile and pendant drop shapes after training. The mass spectrometry management, and pharmaceuticals. The is also available for the purpose of facility is run by students for routine degree is also used by many students polymer surface and interfacial tension samples and by a professional mass as a springboard from which to launch measurements as well as contact angle spectrometrist for more difficult careers in medicine, law, management, analysis. An X-ray reflectometer that can samples. The Chemistry Department banking and finance, politics, and perform X-ray standing wave–induced also provides access to the services of so on. For those interested in the fluorescence measurements is also a glass blower and machine shop and fundamentals, a career of research and housed in the new shared equipment to photochemical and spectroscopic teaching is a natural continuation of laboratory, along with instrumentation facilities. These facilities consist of (1) their undergraduate studies. Whichever for characterizing the friction and wear two nanosecond laser flash photolysis path the student may choose after properties of polymeric surfaces. The instruments equipped with UV-VIS, graduation, the program offers a deep laboratory also houses an infrared infrared, EPR, and NMR detection; understanding of the physical and spectrometer (Nicolet Magna 560, (2) three EPR spectrometers; (3) two chemical nature of things and provides MCT detector) with a variable angle fluorescence spectrometers; (4) a single an insight into an exploding variety grazing incidence, temperature- photon counter for analysis of the of new technologies that are rapidly controlled attenuated-total-reflectance, lifetimes and polarization of fluorescence reshaping the society we live in. transmission, and liquid cell accessories. and phosphorescence; and (5) a high- These facilities are suitable for mid-IR, performance liquid chromatographic Facilities for Teaching and spectroscopic investigations of bulk instrument for analysis of polymer materials as well as thin films. Research molecular weight and dispersity. The laboratory also has a UV-Vis The Department of Chemical Engineering spectrometer (a Cary 50), an SLM is continually striving to provide access to Columbia Genome Center. Because of Aminco 8000 spectrofluorimeter, state-of-the-art research instrumentation its affiliation with the Columbia Genome and a high-purity water system Center (CGC), the Department of and computational facilities for its (Millipore Biocel) used for preparation Chemical Engineering also has access undergraduate and graduate students, of biological buffers and solutions. to more than 3,000 sq. ft. of space postdoctoral associates, and faculty. Facilities are available for cell tissue equipped with a high-throughput DNA Departmental equipment is considered to culture and for experiments involving sequencer (Amersham Pharmacia be in most cases shared, which means biocompatibilization of materials or Biotech Mega-Bace 1000), a nucleic that equipment access is usually open to cellular engineering. In addition, gel acid synthesizer (PE Biosystems 8909 all qualified individuals with a need to use electrophoresis apparatus is available for Expedite Nucleic Acid/Peptide Synthesis particular instrumentation. the molecular weight characterization of System), an UV/VIS spectrophotometer The most extensive collection of nucleic acids. A total-internal-reflection- (Perkin-Elmer Lambda 40), a instrumentation in the department fluorescence (TIRF) instrument with fluorescence spectrophotometer (Jobin is associated with the polymer and an automated, temperature-controlled Yvon, Inc. Fluorolog-3), Waters HPLC, soft matter research faculty. Faculty flow cell has been built for dedicated and a sequencing gel electrophoresis banded together to create a unique investigations of surface processes apparatus (Life Technologies Model shared-facilities laboratory, completed involving fluorescently tagged biological S2), as well as the facilities required at the end of 2001. The shared facilities and synthetic molecules. The instrument for state-of-the-art synthetic chemistry. include a fully equipped polymer can operate at different excitation synthesis lab with four fumes hoods, wavelengths (typically HeNe laser, The division of DNA sequencing and a 10'x16' soft wall clean room, metal 633 nm, using Cy5 labeled nucleic chemical biology at the Columbia evaporator system, a Milligen 9050 acids). Fluorescence is collected by Genome Center consists of 6,000 sq. peptide synthesizer, and polymer a highly sensitive photomultiplier tube ft. of laboratory space and equipment thin film preparation and substrate and logged to a personal computer. necessary for carrying out the state-of- cleaning stations. Also installed are new, Because fluorescence is only excited the-art DNA analysis. The laboratory computer-controlled thermal analysis, in the evanescent wave region near an has one Amersham Pharmacia Biotech rheometric, and light-scattering setups. interface, signals from surface-bound MegaBace 1000 sequencer, three ABI Specialized instrumentation for surface fluorescent species can be determined 377 sequencers with complete 96 land analysis includes an optical/laser system with minimal background interference upgrades, a Qiagen 9600 Biorobot, a dedicated to characterization of polymer from fluorophores in bulk solution. Hydra 96 microdispenser robot, and surface dynamics by Fluorescence standard molecular biology equipment. Recovery after Photobleaching and Chemistry Department. Access to a PHI 5500 X-ray photoelectron NMR and mass spectrometry facilities is UNDERGRADUATE PROGRAM spectrophotometer with monochromator possible through interactions with faculty that is capable of angle-dependent members who also hold appointments Chemical Engineering depth profiling and XPS imaging. The in the Chemistry Department. The NMR The undergraduate program in chemical system can also perform SIMS and ion facility consists of a 500 MHz, a 400

ENGINEERING 2017–2018 engineering at Columbia has five formal environmental management, and electives are courses that are not 79 educational objectives: pharmaceuticals. Because the deep quantitative, such as those taught in and broad-ranging nature of the degree the humanities and social sciences. 1. Prepare students for careers in has earned it a high reputation across These provide an opportunity to pursue industries that require technical society, the chemical engineering interests in areas other than engineering. expertise in chemical engineering. degree is also a natural platform from A crucial part of the junior-senior which to launch careers in medicine, 2. Prepare students to assume program is the 21-point (7 courses) law, management, banking and finance, leadership positions in industries technical elective requirement. Technical politics, and so on. Many students that require technical expertise in electives are science and/or technology choose it for this purpose, to have a chemical engineering. based and feature quantitative analysis. firm and respected basis for a range Generally, technical electives must be 3. Enable students to pursue of possible future careers. For those 3000 level or above but there are a graduate-level studies in chemical interested in the fundamentals, a career few exceptions: PHYS UN1403, PHYS engineering and related technical or of research and teaching is a natural UN2601, BIOL UN2005, BIOL UN2006, scientific fields (e.g., biomedical or continuation of undergraduate studies. BIOL UN2501, and CHEM UN2444. The environmental engineering, materials The first and sophomore years technical electives are subject to the science). of study introduce general principles following constraints: of science and engineering and 4. Provide a strong foundation for include a broad range of subjects in • Two technical electives must be within students to pursue alternative career the humanities and social sciences. chemical engineering (e.g., with the paths, especially careers in business, Although the program for all engineering designator BMCH, CHEN, CHEE, or management, finance, law, medicine, students in these first two years is to CHAP). or education. some extent similar, there are a few • One technical elective must be within important differences for chemical 5. Establish in students a commitment SEAS but taken outside of chemical engineering majors. Those wishing to life-long learning and service engineering (that is, a course with a to learn about, or major in, chemical within their chosen profession and designator other than BMCH, CHEN, engineering should take the professional society. CHEE, or CHAP). elective CHEN E2100 Introduction The expertise of chemical engineers to chemical engineering in term III, • Two technical electives must be within is essential to production, marketing, taught by the Chemical Engineering SEAS (may or may not be within and application in such areas as Department. This course is a chemical engineering). pharmaceuticals, high performance requirement for the chemical engineering • Two technical electives must contain materials as in the automotive and major. It can also possibly serve as a “advanced science” coursework, aerospace industries, semiconductors technical elective for other engineering which can include chemistry, physics, in the electronics industry, paints and majors. Those wishing to major in biology, and certain engineering plastics, consumer products such as chemical engineering should also take courses. Qualifying engineering food and cosmetics, petroleum refining, ENGI E1006 Introduction to computing courses are determined by Chemical industrial chemicals, synthetic fibers, for engineering and applied scientists Engineering Department advisers. and just about every bioengineering and in term II. Chemical engineering majors At least one of these classes must biotechnology area from artificial organs receive additional instruction in their be taken outside of SEAS (e.g., in a to biosensors. Increasingly, chemical junior year on the use of computational science department at Columbia; see engineers are involved in exciting new methods to solve chemical engineering listing of possible courses above). technologies employing highly novel problems. In the junior-senior sequence one materials, whose unusual response at • At most, only two computer science specializes in the chemical engineering the molecular level endows them with (COMS) or industrial engineering and major. The table on page 81 spells unique properties. Examples include operations research (IEOR) classes out the core course requirements, controlled release drugs, materials can be counted toward the technical which are split between courses with designed interaction with in vivo elective requirement. environments, “nanomaterials” for emphasizing engineering science and electronic and optical applications, those emphasizing practical and/or The junior-senior technical electives agricultural products, and a host of professional aspects of the discipline. provide the opportunity to explore others. This requires a depth and Throughout, skills required of practicing new, interesting areas beyond the core breadth of understanding of physical engineers are developed (e.g., writing requirements of the degree. Often, and chemical aspects of materials and and presentation skills, competency with students satisfy the technical electives their production that is without parallel. computers). by taking courses from another SEAS The chemical engineering degree The table also shows that a department in order to obtain a minor also serves as a passport to exciting significant fraction of the junior-senior from that department. Alternately, you careers in directly related industries as program is reserved for electives, both may wish to take courses in several diverse as biochemical engineering, technical and nontechnical. Nontechnical new areas, or perhaps to explore

ENGINEERING 2017–2018 80 familiar subjects in greater depth, or you (CHAP E4120); and (2) 18 points of engineering problems. Pure systems are treated, may wish to gain experience in actual 4000- or 6000-level courses, approved followed by an introduction to mixtures and phase laboratory research. Up to 6 points of by the graduate coordinator or research equilibrium. CHEN E3900: Undergraduate research adviser, of which up to 6 may be Master’s CHEN E3020x Analysis of chemical project may be counted toward the research (CHEN 9400). Students with engineering problems technical elective content. (Note that undergraduate preparation in physics, 3 pts. Lect: 1.5. Lab: 1.5. Professor West. if more than 3 points of research are chemistry, biochemistry, pharmacy, and Prerequisites: Vector calculus, ordinary pursued, an undergraduate thesis is related fields may take advantage of a differential equations. Corequisites: CHEE E3010, CHEN E3110. Computational required.) special program leading directly to the solutions of chemical engineering problems in The program details discussed master’s degree in chemical engineering. thermodynamics, transport phenomena, and above apply to undergraduates who This program enables such students to reaction design. are enrolled at Columbia as first-years avoid having to take all undergraduate CHEN E3110x Transport phenomena, I and declare the chemical engineering courses in the bachelor’s degree program. 3 pts. Lect: 3. Professor McNeill. major in the sophomore year. Prerequisites: mechanics, vector calculus, ordinary However, the chemical engineering Doctoral Degrees differential equations. Corequisite: CHEN E3020. program is designed to be readily The Ph.D. and D.E.S. degrees have Analysis of momentum and energy transport accessible to participants in any of essentially the same requirements. processes at molecular, continuum, and system scales for systems of simple fluids (gases and low- Columbia’s Combined Plans and to All students in a doctoral program transfer students. In such cases, the molecular-weight liquids). Molecular-level origins of must (1) earn satisfactory grades fluid viscosity, continuum fluid mechanics analysis guidance of one of the departmental in the three core courses (CHEN of laminar flows, and the resulting dimensionless advisers in planning your program is E4010, E4110, E4330, E4130/CHAP correlations of kinematic and mechanical required (contact information for the E4120); (2) pass a qualifying exam; characteristics of a system needed for engineering departmental UG advisers is listed (3) defend a proposal of research design (e.g., friction factor vs. Reynolds number on the department’s website: within 12 months of passing the correlations). Molecular origins of fluid conductivity, cheme.columbia.edu). qualifying exam; (4) defend their thesis; continuum heat transfer analysis, and the resulting correlations of a system’s thermal characteristics Columbia’s program in chemical and (5) satisfy course requirements useful in engineering design (e.g., Nusselt engineering leading to the B.S. degree beyond the three core courses. For number correlations). Examples are reviewed is fully accredited by the Engineering detailed requirements, please consult of analyses typical in chemical engineering Accreditation Commission of ABET. the departmental office or graduate technologies. Essential mathematical methods are coordinator. Students with degrees reviewed or introduced in context. Requirements for a Minor in in related fields such as physics, CHEN E3120y Transport phenomena, II Chemical Engineering chemistry, biochemistry, and others 3 pts. Lect: 3. Professor Durning. See page 199. are encouraged to apply to this highly Prerequisite: CHEN E3110. Corequisite: CHEN interdisciplinary program. E3220. Developments in Transport I are extended to handle turbulence. Topics include: Turbulent GRADUATE PROGRAMS energy cascade, wall-bounded turbulent shear The graduate program in chemical COURSES IN CHEMICAL flow, time-averaging of the equations of change, engineering, with its large proportion ENGINEERING Prandtl’s mixing length hypothesis for the Reynolds of elective courses and independent Note: Check the department website stress, the Reynolds analogy, continuum modeling of turbulent flows and heat transfer processes, research, offers experience in any for the most current course offerings friction factor, and Nusselt number correlations for of the fields of departmental activity and descriptions. turbulent conditions. Then, macroscopic (system- mentioned in previous sections. For CHEN E2100x Introduction to chemical level) mass, momentum, and energy balances for both chemical engineers and those engineering one-component systems are developed and applied with undergraduate educations in other 3 pts. Lect: 3. Professor Banta. to complex flows and heat exchange processes. related fields such as physics, chemistry, Prerequisites: First year chemistry and physics, or The final part focuses on mass transport in mixtures and biochemistry, the Ph.D. program equivalent. This course serves as an introduction of simple fluids: Molecular-level origins of diffusion provides the opportunity to become to the chemical engineering profession. Students phenomena, Fick’s law and its multi-component generalizations, continuum-level framework for expert in research fields central to are exposed to concepts used in the analysis of chemical engineering problems. Rigorous analysis mixtures and its application to diffusion dominated modern technology and science. of material and energy balances on open and processes, diffusion with chemical reaction, and closed systems is emphasized. An introduction forced/free convection mass transport. M.S. Degree to important processes in the chemical and CHEN E3210y Chemical engineering The requirements are (1) the core biochemical industries is provided. thermodynamics courses: Chemical process analysis CHEE E3010x Principles of chemical 3 pts. Lect: 3. Professor Obermeyer. (CHEN E4010)/Partial differential equations engineering thermodynamics Prerequisites: CHEE E3010 and CHEN E2100. (APMA E4200), Transport phenomena, 3 pts. Lect: 3. Professor Kumar. Corequisite: CHEN E3220. This course deals with III (CHEN E4110), Advanced chemical Prerequisite: CHEM UN1403. Corequisite: fundamental and applied thermodynamic principles that form the basis of chemical engineering kinetics (CHEN E4130), and Advanced CHEN E3020. Introduction to thermodynamics. practice. Topics include phase equilibria, methods chemical engineering thermodynamics Fundamentals are emphasized: the laws of thermodynamics are derived and their meaning to treat ideal and nonideal mixtures, and estimation (CHEN E4130)/Statistical mechanics explained and elucidated by applications to of properties using computer-based methods.

ENGINEERING 2017–2018 81 CHEMICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

APMA E2000 (4)4 either semester

MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) MATH UN2030 (3) ODE MATH elective (3)5 or APMA E2101 (3)

PHYSICS UN1401 (3) UN1402 (3) Lab UN1493 (3) (three tracks, UN1601 (3.5) UN1602 (3.5) choose one) UN2801 (4.5) UN2802 (4.5) Lab UN3081 (2)

UN1403 (4) and UN1404 (4) UN2443 (4) CHEMISTRY Lab UN1500 (3) UN1507 (3) (three tracks, choose one) UN1604 (4) UN2046 (4) and UN2045 (4) Lab UN1507 (3)

UNIVERSITY UN1010 (3) either semester WRITING

REQUIRED One core humanities Three core humanities NONTECHNICAL 1 1 ELECTIVES elective (3–4 points) electives (11 points)

CHEN E2100 (3)2 CHEM. ENG. Intro to chemical REQUIREMENT engineering

COMPUTER ENGI E1006 (3) SCIENCE

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

TOTAL POINTS3 17 18 16.5 18

1 Four core humanities electives should be taken as follows: In Semester III, HUMA CC1001, CC1101 (4), or any initial course in one of the Global Core sequences offered by the College (3–4); in Semester IV, HUMA CC1002, CC1102 (4), or the second course in the Global Core sequence elected in Semester III (3–4); also in Semester IV, ECON UN1105 (4) with UN1105 recitation (0) and either HUMA UN1121 or UN1123 (3). 2 Should be taken in Semester III, but may be moved upon adviser’s approval to Semester V if CHEM UN2543: Organic chemistry lab is taken in Semester III. This course fulfills the SEAS professional engineering elective requirement. 3 Taking the first track in each row and E1102 in Semester II. 4 Effective Class of 2021. 5 Elective options include APMA E3101, MATH UN2010, APMA E3102, APMA E4001, APMA E4150, APMA E4300, STAT GU 4001, or another course approved by the major adviser.

CHEN E3230y Reaction kinetics and reactor 3 pts. Lect: 3. Not offered in 2017–2018. CHEN E3810y Chemical engineering design Prerequisites: CHEM UN2443 and MATH UN2030. laboratory 3 pts. Lect: 3. Professor Chen. Corequisite: BIOL UN2005. Convective and 3 pts. Lab: 3. Professors Ju and Bedrossian. Prerequisite: CHEE E3010. Reaction kinetics, diffusive movement and reaction of molecules in Prerequisites: Completion of core chemical applications to the design of batch and continuous biological systems. Kinetics of homogeneous and engineering curricula through the fall semester reactors. Multiple reactions, nonisothermal heterogeneous reactions in biological environments. of senior year (includes: CHEN E3110, E3120, reactors. Analysis and modeling of reactor Mechanisms arid models of transport across E4230, E2100, E3210, E4140, E4500, CHEE behavior. Recitation section required. membranes. Convective diffusion with and without E3010), or instructor’s permission. The course chemical reaction. Diffusion in restricted spaces. emphasizes active, experiment-based resolution of BMCH E3500y Transport in biological Irreversible thermodynamic approaches to transport open-ended problems involving use, design, and systems and reaction in biological systems. optimization of equipment, products, or materials.

ENGINEERING 2017–2018 82 CHEMICAL ENGINEERING: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

CHEN E3110 (3) CHEN E3120 (3) Transp. phenomena, I Transp. phenomena, II CHEN E4500 (4) Process and product CHEE E3010 (3) CHEN E3210 (3) design, I REQUIRED Principles of chem. Chem. eng. COURSES eng. thermodynamics thermodynamics CHEE E4140 (3) Eng. separations CHEN E3020 (3) CHEN E4230 (3) processes Analysis of Reaction kinetics and chem. eng. problems, I reactor design

CHEM UN2495 (1.5)1 CHEM UN2496 (1.5)1 CHEN E4300 (3) CHEN E3810 (3) REQUIRED LABS Org. chem. lab Org. chem. lab Chem. eng. control Chem. eng. lab

NONTECH 3 points 3 points 3 points

TECH2 3 points 3 points 3 points 12 points REQUIRED ELECTIVES

TOTAL POINTS (normal track) 16.5 16.5 16 15

1 May be taken in Semester III and IV with adviser’s permission. Additional option is that Intensive organic chemistry lab course UN2545 (3) can count in place of UN2495 and UN2496. 2 The total of 21 points (7 courses) of required technical electives must include five engineering courses, two of which must be in chemical engineering and one must be outside chemical engineering, and 6 points (2 courses) of "advanced science" (i.e., courses in chemistry, physics, biology, and certain engineering courses, one of which must be outside engineering).

Under faculty guidance students formulate, carry engineering in relevant intern or fieldwork CHEN E4002x Essentials of chemical out, validate, and refine experimental procedures, experience as part of their program of study as engineering—B and present results in oral and written form. The determined by the instructor. Written application 3 pts. Lect: 3. Professor Banta. course develops analytical, communications, and must be made prior to registration outlining Prerequisites: First-year chemistry and physics, cooperative problem-solving skills in the context proposed internship/study program. A written report vector calculus, ordinary differential equations, of problems that span from traditional, large describing the experience and how it relates to the and the instructor’s permission. Part of an scale separations and processing operations to chemical engineering core curriculum is required. accelerated consideration of the essential molecular level design of materials or products. Employer feedback on student performance chemical engineering principles from the Sample projects include: scale up of apparatus, and the quality of the report are the basis of the undergraduate program, including topics from process control, chemical separations, microfluidics, grade. This course may not be taken for pass/ Chemical Engineering Thermodynamics, I and surface engineering, molecular sensing, and fail or audited. May not be used as a technical or II, Chemical and Biochemical Separations. alternative energy sources. Safety awareness is nontechnical elective. May be repeated for credit, Reaction Kinetics and Reactor Design. While integrated throughout the course. but no more than 3 points total of CHEN E3999 required for all M.S. students with Scientist to may be used for degree credit. Engineer status, the credits from this course CHEN E3900x and y Undergraduate research may not be applied toward any chemical project CHEN E4001x Essentials of chemical engineering degree. 1–6 pts. Members of the faculty. engineering—A Candidates for the B.S. degree may conduct 3 pts. Lect: 3. Professor Banta. CHEN E4010y Mathematical methods an investigation of some problem in chemical Prerequisites: First-year chemistry and physics, in chemical engineering engineering or applied chemistry or carry out a special vector calculus, ordinary differential equations, 3 pts. Lect: 3. Professor Bozic. project under the supervision of the staff. Credit for and the instructor’s permission. Part of an Prerequisites: CHEN E3120 and E4230, or the course is contingent upon the submission of accelerated consideration of the essential chemical equivalent, or instructor’s permission. Mathematical an acceptable thesis or final report. No more than engineering principles from the undergraduate description of chemical engineering problems 6 points in this course may be counted toward the program, including topics from Reaction Kinetics and the application of selected methods for their satisfaction of the B.S. degree requirements. and Reactor Design, Chemical Engineering solution. General modeling principles, including Thermodynamics, I and II, and Chemical and model hierarchies. Linear and nonlinear ordinary CHEN E3999x, y, or s Undergraduate Biochemical Separations. While required for all differential equations and their systems, including fieldwork M.S. students with Scientist to Engineer status, the those with variable coefficients. Partial differential 1–2 pts. Members of the faculty. credits from this course may not be applied toward equations in Cartesian and curvilinear coordinates Prerequisites: Obtained internship and approval any chemical engineering degree. for the solution of chemical engineering problems. from adviser. Restricted to CHEN undergraduate students. Provides work experience on chemical

ENGINEERING 2017–2018 CHEN E4020y Protection of industrial and for junior/senior level undergraduates and graduate fuels. Applications include solar fuels technology 83 intellectual property students in engineering and the physical sciences. for grid-scale energy storage, chemical industry, 3 pts. Lect: 3. Professor Spall. manufacturing, environmental remediation. CHAP E4120y Statistical mechanics To expose engineers, scientists and technology 3 pts. Lect: 3. Professor O’Shaughnessy. CHEN E4235 Surface reactions and kinetics managers to areas of the law they are most likely Prerequisites: CHEE E3010 or equivalent 3 pts. Lect: 3. Professor Chen. to be in contact with during their career. Principles thermodynamics course, or instructor’s permission. are illustrated with various case studies together Fundamental concepts and techniques to Fundamental principles and underlying with active student participation. describe electronic, structural, chemical, assumptions of statistical mechanics. Boltzmann’s and catalytic properties of surfaces. Kinetics CHEE E4050y Principles of industrial entropy hypothesis and its restatement in terms and thermodynamics in adsorption, reaction, electrochemistry of Helmholtz and Gibbs free energies and for desorption, and diffusion processes on surfaces. 3 pts. Lect: 3. Not offered in 2017–2018. open systems. Correlation times and lengths. Effects of transport in modifying surface reaction Prerequisites: CHEE E3010 or equivalent. A Exploration of phase space and observation kinetics. Applies basic concepts in the chemical presentation of the basic principle underlying timescale. Correlation functions. Fermi-Dirac and engineering curriculum (mathematical modeling, electrochemical processes. Thermodynamics, Bose-Einstein statistics. Fluctuation-response reaction kinetics, thermodynamics, transport) to electrode kinetics, and ionic mass transport. theory. Applications to ideal gases, interfaces, surface reactions. Examples of industrial and environmental liquid crystals, microemulsions and other complex applications illustrated by means of laboratory fluids, polymers, Coulomb gas, interactions CHEE E4252x Introduction to surface and experiments: electroplating, refining, and winning in between charged polymers and charged interfaces, colloid chemistry aqueous solutions and in molten salts; electrolytic ordering transitions. 3 pts. Lect: 3. Professor Somasundaran. treatment of wastes; primary, secondary, and fuel Prerequisites: Elementary physical chemistry. CHEN E4130x Advanced chemical cells. Thermodynamics of surfaces, properties of engineering thermodynamics surfactant solutions and surface films, electrostatic APCH E4080 Soft condensed matter 3 pts. Lect: 3. Professor O'Shaughnessy. and electrokinetic phenomena at interfaces, 3 pts. Lect: 3. Professor Gang. Prerequisite: Successful completion of an adsorption; interfacial mass transfer and modern Prerequisites: MSAE E3111, CHEE E3010, or undergraduate thermodynamics course. The course experimental techniques. CHEN E3120 or equivalent. Course is aimed at provides a rigorous and advanced foundation in senior undergraduate and graduate students. chemical engineering thermodynamics suitable for CHEN E4300x Chemical process control and Introduces fundamental ideas, concepts, and chemical engineering Ph.D. students expected to process safety approaches in soft condensed matter with undertake diverse research projects. Topics include 3 pts. Lect: 1. Lab: 2. Professor emphasis on biomolecular systems. Covers the intermolecular interactions, nonideal systems, Venkatasubramanian. broad range of molecular, nanoscale, and colloidal mixtures, phase equilibria and phase transitions Prerequisites: Material and energy balances. phenomena with revealing their mechanisms and and interfacial thermodynamics. Ordinary differential equations including Laplace physical foundations. The relationship between transforms. Reactor Design. An introduction to molecular architecture and interactions and CHEN E4140x Engineering separations process control applied to chemical engineering macroscopic behavior are discussed for the broad processes through lecture and laboratory. Concepts include range of soft and biological matter systems, 3 pts. Lect: 3. Professor Durning. the dynamic behavior of chemical engineering from surfactants and liquid crystals to polymers, Prerequisites: CHEN E2100, E3120, and E3210 systems, feedback control, controller tuning, and nanoparticles, and biomolecules. Modern or permission of instructor. Design and analysis of process stability. Introduction to the fundamentals characterization methods for soft materials, unit operations employed in chemical engineering of process safety and hazard analysis. including X-ray scattering, molecular force probing, separations. Fundamental aspects of single and CHEN E4320y Molecular phenomena in and electron microcopy are reviewed. Example multistaged operations using both equilibrium and chemical engineering problems, drawn from the recent scientific rate-based methods. Examples include distillation, 3 pts. Lect: 3. Not offered in 2017–2018. literature, link the studied materials to the actively absorption and stripping, extraction, membranes, Prerequisites: CHEN E3120 or instructor’s developed research areas. Course grade based crystallization, bioseparations, and environmental permission. This course introduces a molecular- on midterm and final exams, weekly homework applications. level understanding of topics in modern chemical assignments, and final individual/team project. CHEN E4201x Engineering applications of engineering. It builds upon and validates the concepts CHEN E4110y Transport phenomena, III electrochemistry presented in the rest of the chemical engineering 3 pts. Lect: 3. Professor Durning. 3 pts. Lect: 3. Professor West. curriculum via a molecular perspective. Prerequisite: CHEN E3120. Tensor analysis; Prerequisites: Physical chemistry and a course CHBM E4321x The genome and the cell kinematics of continua; balance of laws for one- in transport phenomena. Engineering analysis of 3 pts. Lect: 3. Not offered in 2017–2018. component media; constitutive laws for free energy electrochemical systems, including electrode kinetics, Prerequisites: BIOL UN2005, MATH UN2030. The and stress in one-component media; exact and transport phenomena, mathematical modeling, utility of genomic information lies in its capacity to asymptotic solutions to dynamic problems in fluids and thermodynamics. Common experimental predict the behavior of living cells in physiological, and solids; balance laws for mixtures; constitutive methods are discussed. Examples from common developmental, and pathological situations. The laws for free energy, stress and diffusion fluxes applications in energy conversion and metallization effect of variations in genome structure between in mixtures; solutions to dynamic problems in are presented. individuals within a species, including those mixtures. CHEN E4231x Solar fuels deemed healthy or diseased, and among species, CHEN E4115y Topics in transport phenomena 3 pts. Lect: 3. Professors Esposito and West. can be inferred statistically by comparisons of 3 pts. Instructor to be announced. Prerequisite: Graduate standing or CHEN sequences with behaviors, and mechanistically, by Prerequisites: Undergraduate fluid mechanics, or E4230. Fundamentals and applications of solar studying the action of molecules whose structure transport phenomena, or instructor’s permission. energy conversion, especially technologies for is encoded within the genome. This course Self-contained treatments of selected topics conversion of sunlight into storable chemical examines known mechanisms that elucidate the in transport phenomena (e.g., rheology, energy or solar fuels. Topics include fundamentals combined effect of environmental stimulation nonequilibrium thermodynamics, molecular-level of photoelectrochemistry, kinetics of solar fuels and genetic makeup on the behavior of cells aspects of transport turbulence). Topics and production, solar harvesting technologies, solar in homeostasis, disease states, and during instructor may change from year to year. Intended reactors, and solar thermal production of solar development, and includes assessments of the

ENGINEERING 2017–2018 84 probable effect of these behaviors on the whole assessment, inherently safer design, hazard illustrative experimental studies are discussed organism. Quantitative models of gene translation operability analysis, and engineering ethics. along with basic theoretical treatments. High and intracellular signal transduction will be used Application of safety to full spectrum of chemical molecular weight organic polymers are discussed to illustrate switching of intracellular processes, engineering operations. first (basic notions, synthesis, properties of single transient and permanent gene activation, and cell polymer molecules, polymer solution and blend CHEN E4510y Process and product design, II commitment, development, and death. thermodynamics, rubber and gels). Colloidal 4 pts. Lect: 4. Professors Joback and systems are treated next (dominant forces in CHEN E4330y Advanced chemical kinetics Venkatasubramanian. colloidal systems, flocculation, preparation and 3 pts. Lect: 3. Professor Esposito. Prerequisite: CHEN E4500. Students carry out a manipulation of colloidal systems) followed by a Prerequisite: CHEN E4230 or instructor’s semester long process or product design course discussion of self-organizing surfactant systems permission. Complex reactive systems, molecular with significant industrial involvement. The project (architecture of surfactants, micelles and view of reaction kinetics, reactions in liquid, culminates with a formal written design report and surfactant membranes, phase behavior). reactions at surfaces, diffusion-reaction systems. a public presentation. Recitation section required. Applications to the design of batch and continuous CHEN E4630y Topics in soft materials CHEE E4530y Corrosion of metals reactors. 3 pts. Instructor to be announced. 3 pts. Lect: 3. Prerequisite: Physical chemistry or instructor’s CHEN E4400x Chemical process development Prerequisite: CHEE E3010 or equivalent. The 3 pts. Lect: 3. Professor Mattas. theory of electrochemical corrosion, corrosion permission. Self-contained treatments of Prerequisites: CHEM UN2443 or equivalent or tendency, rates, and passivity. Application to selected topics in soft materials (e.g., polymers, instructor’s permission. Process development various environments. Cathodic protection and colloids, amphiphiles, liquid crystals, glasses, for new compounds, including fine and specialty coatings. Corrosion testing. powders). Topics and instructor may change chemicals, pharmaceuticals, biologicals, and from year to year. Intended for junior/senior agrochemicals. Experimental strategy and methods CHEN E4540y Energy and process integration level undergraduates and graduate students in for process scale-up from bench to pilot plant. 3 pts. Lect: 3. Not offered in 2017–2018. engineering and the physical sciences. Evaluation of process economics. Hazard and risk Prerequisite: CHEN E4500 or equivalent. Energy CHEN E4640x Polymer surfaces and evaluation for environmental and industrial hygiene optimization of chemical processes through interfaces safety. Capture and use of process know-how for identification of thermodynamically attainable 3 pts. Lect: 3. Not offered in 2017–2018. process and plant design, regulatory approvals, minimum energy targets. Energy cascade Prerequisite: CHEN E4620 or instructor's and technology transfer to first manufacture. diagrams. Composite curves. Identification of energy saving opportunities. Maximum energy permission. A fundamental treatment of the CHEN E4410x Environmental control recovery networks. Euler’s Principle. Capital cost thermodynamics and properties relating to polymer technology targeting. Introduction to combined heat and power surfaces and interfaces. Topics include the 3 pts. Lect: 3. Not offered in 2017–2018. site integration. characterization of interfaces, theoretical modeling Prerequisites: CHEN E3010 or the equivalent. of interfacial thermodynamics and structure, and Causes of pollution and effect on life. Legal CHEN E4600x Atmospheric aerosols practical means for surface modification. aspects, OSHA and EPA rules. Pollution at home 3 pts. Lect: 3. Not offered in 2017–2018. and at work; radon, fumes, and dust; ventilation, Prerequisite: CHEN E3120 or instructor’s permission. CHEN E4645x Inorganic polymers, hybrid dust collection, carbon adsorption. Fuel and Atmospheric aerosols and their effects on materials and gels acid gases, smog and dispersion. Treatment atmospheric composition and climate. Major topics 3 pts. Lect: 3. Not offered in 2017–2018. of ground, saline, and wastewater. Primary are aerosol sources and properties, field and Prerequisite: Organic chemistry. The focus of the and secondary (biological) treatment. Tertiary laboratory techniques for characterization, gas- first part of the course, taught by Prof. Mark, is on water treatment with membranes, ion exchange, aerosol interactions, secondary organic aerosols, the preparation, characterization, and applications carbon, and sieves. Solid hazardous waste. Visit aerosol direct and indirect effects on climate. of inorganic polymers, with a heavy emphasis on those based on main-group elements. Main New York City wastewater treatment plant. CHEN E4610y Chemical product design topics are characterization methods, polysiloxanes, 3 pts. Lect: 3. Professor Joback. CHEN E4500x Process and product design, I polysilanes, polyphosphazenes, ferrocene-based Prerequisite: CHEN E3210 and CHEM UN2443 or 4 pts. Lect: 4. Professor Bozic. polymers, other phosphorous-containing equivalent, or instructor’s permission. Application Prerequisites: CHEN E2100, CHEN E4140. The polymers, boron-containing polymers, preceramic of chemical and engineering knowledge to the practical application of chemical engineering inorganic polymers, and inorganic-organic hybrid principles for the design and economic evaluation design of new chemical products. Relationships between composition and physical properties. composites. The focus of the second part of the of chemical processes and plants. Use of ASPEN course, taught by Prof. Koberstein, is on gels, Plus for complex material and energy balances Strategies for achieving desired volumetric, rheological, phase equilibrium, thermal, and both physical and chemical. Topics will include of real processes. Students are expected to gel chemistry, including epoxies, polyurethanes, build on previous coursework to identify creative environmental behavior. Case studies, including polyester, vinyl esters and hydrogels, as well as solutions to two design projects of increasing separation solvents, blood substitutes, theoretical methods used to characterize the gel complexity. Each design project culminates in an refrigerants, and aircraft deicing fluids. point and gel properties. oral presentation, and in the case of the second CHEN E4620y Introduction to polymers and project, a written report. soft materials CHEN E4650y Polymer physics 3 pts. Lect.: 3. Professor Kumar. CHEN E4501y Chemical engineering process 3 pts. Lect: 3. Not offered in 2017–2018. Prerequisites: CHEN E3110, CHEN E3120 and safety Prerequisite: An elementary course in physical E4620. Senior undergraduate/first-year graduate 3 pts. Lect.: 3. Professor Bozic. chemistry or thermodynamics. Organic chemistry, course on the physics of polymer systems. Topics Aimed at seniors and graduate students. Provides statistics, calculus and mechanics are helpful, but include scaling behavior of chains under different classroom experience on chemical engineering not essential. An introduction to the chemistry and conditions, mixing thermodynamics, networks and process safety as well as Safety in Chemical physics of soft material systems (polymers, colloids, geation, polymer dynamics, including reptation and Engineering certification. Process safety and organized surfactant systems and others), entanglements. Special topics: nanocomposites. process control emphasized. Application of basic emphasizing the connection between microscopic structure and macroscopic physical properties. chemical engineering concepts to chemical CHEN E4660x Biochemical engineering To develop an understanding of each system, reactivity hazards, industrial hygiene, risk 3 pts. Lect.: 3. Professor Obermeyer.

ENGINEERING 2017–2018 Prerequisite: CHEN E4320 or instructor’s high-throughput DNA sequencer development. on different protein functions with specific 8585 permission. Engineering of biochemical and Construction of gene chip and micro array for emphasis on enzymatic catalysis. Case studies microbiological reaction systems. Kinetics, reactor gene expression analysis. Technology and reinforce concepts covered, and demonstrate analysis, and design of batch and continuous biochemical approach for functional genomics the wide impact of protein engineering research. fermentation and enzyme processes. Recovery and analysis. Gene discovery and genetics database Application of basic concepts in the chemical separations in biochemical engineering systems. search method. The application of genetic engineering curriculum (reaction kinetics, database for new therapeutics discovery. mathematical modeling, thermodynamics) to CHEN E4670 Chemical engineering data specific approaches utilized in protein engineering. analysis CHEN E4740x Biological transport and rate 3 pts. Lect: 3. Professor Bishop. phenomena, II BMCH E4810y Artificial organs Prerequisites: CHEN E4230, CHEN E3120, and 3 pts. Lect: 3. Not offered in 2017–2018. 3 pts. Lect: 3. Professor Leonard. CHEN E3210 or equivalents. Course is aimed Prerequisites: Any two of the following: CHEN Analysis and design of replacements for the heart, at senior undergraduate and graduate students. E3110; BIOL UN2005; CHEN E3210 or BMCH kidneys, and lungs. Specification and realization of Introduces fundamental concepts of Bayesian E3500. Analysis of transport and rate phenomena structures for artificial organ systems. data analysis as applied to chemical engineering in biological systems and in the design of biomimetic CHEN E4850x or y Contaminated site cleanup problems. Covers basic elements of probability transport-reaction systems for technological and 3 pts. Lect: 3. Professor Tsiamis. theory, parameter estimation, model selection, and therapeutic applications. Modeling of homogeneous Course is aimed at senior undergraduate and experimental design. Advanced topics such as and heterogeneous biochemical reactions. The graduate students. Introduces the science nonparametric estimation and Markov chain Monte Bases of biological transport: roles of convection, fundamentals and the policies and regulations Carlo (MEME) techniques are introduced. Example ordinary diffusion, forced diffusion. Systems that govern the cleanup of sites contaminated problems and case studies drawn from chemical where reaction and transport interact strongly. with hazardous materials and discusses engineering practice are used to highlight the Applications to natural and artificial tissue beds, the processes used for their treatment and practical relevance of the material. Theory reduced tumor modeling, controlled release, natural and safe disposal. Covers the methods used to to practice through programming in Mathematica. artificial organ function. Course grade based on midterm and final exams, investigate the extent of contamination in soil and groundwater and to quantify the impacts on biweekly homework assignments, and final team CHEN E4760y Genomics sequencing human health and the environment. Uses case project. laboratory studies from current projects to illustrate the 3 pts. Lect: 1. Lab: 2. Not offered in 2017–2018. CHEN E4680x Soft materials laboratory application of state-of-the-art technologies used Prerequisites: Undergraduate level biology, 3 pts. Lect/lab: 3. Not offered in 2017–2018. to address different categories of contaminants organic chemistry, and instructor’s permission. Prerequisites: Two years of undergraduate (metals, volatile organics, semivolatiles) in order The chemical, biological and engineering principles science courses and the instructor’s permission. to reinforce the concepts covered. Applies basic involved in the genomics sequencing process will Limited to 15 students. Covers modern concepts in the chemical engineering curriculum be illustrated throughout the course for engineering characterization methods for soft materials (such as material balances, thermodynamics, students to develop the hands-on skills in conducting (polymers, complex fluids, biomaterials). transport phenomena, unit operations, applied genomics research. Techniques include differential scanning calorimetry, chemistry, engineering economics) to specific dynamic light scattering, gel permeation CHEN E4780x or y Quantitative methods in approaches utilized in characterizing the fate chromatography, rheology, and spectroscopic cell biology and transport of contaminants and for designing methods. Team-taught by several faculty and 3 pts. Lect: 3. Professor O’Shaughnessy. the engineering processes utilized for their open to graduate and advanced undergraduate Prerequisites: Elementary calculus, physics and treatment. students. Lab required. biology, or instructor’s permission. Quantitative CHEN E4890 Biopharmaceuticals, statistical analysis and mathematical modeling CHOR E4690y Managing systemic risk in entrepreneurship, and chemical engineering in cell biology for an audience with diverse complex systems 3 pts. Lect: 3. Professor Hartounian. backgrounds. The course presents quantitative 3 pts. Lect: 3. Professor Venkatasubramanian. This course is aimed at graduate students of methods needed to analyze complex cell biological Chemical Engineering. The class will examine Prerequisites: Senior or graduate standing in experimental data and to interpret the analysis the application of Chemical Engineering SEAS or instructor's permission. Course will in terms of the underlying cellular mechanisms. fundamentals and entrepreneurship in starting introduce systems engineering concepts and Optical and electrical experimental methods to up a biopharmaceutical company and in tools such as digraphs, fault trees, probabilistic study cells and basic image analysis techniques developing a biopharmaceutical product. This risk assessment, HAZOP, FMEA, etc., for are described. Methods of statistical analysis of modeling enterprise-wide risk in complex experimental data and techniques to test and course will serve as a description of the major systems. Important industrial accidents will be compare mathematical models against measured stages of developing a biopharmaceutical discussed as case studies. statistical properties will be introduced. Concepts product. Topics presented in this course will and techniques of mathematical modeling will be include drug discovery, preclinical and clinical CHEN E4700x Principles of genomic illustrated by applications to mechanosensing in development, IP, manufacturing, and regulatory technologies cells, the mechanics of cytokinesis during cell process. In addition, implementation of the lean 3 pts. Lect: 3. Professor Ju. division and synaptic transmission in the nervous startup methodology, business valuation, and Prerequisites: Undergraduate-level biology, system. Image analysis, statistical analysis, and financial considerations for a biopharmaceutical organic chemistry, and instructor’s permission. model assessment will be illustrated for these startup will be offered. Basic topics in the Chemical and physical aspects of genome systems. chemical engineering curriculum (reaction structure and organization, genetic information kinetics, mathematical modeling, unit operations, flow from DNA to RNA to protein. Nucleic acid CHEN E4800x Protein engineering thermodynamics), as well as specific topics in hybridization and sequence complexity of DNA 3 pts. Lect: 3. Professor Banta. developing biopharmaceuticals will be discussed and RNA. Genome mapping and sequencing Prerequisite: CHEN E4230, may be taken in this course. methods. The engineering of DNA polymerase concurrently, or the instructor’s permission. for DNA sequencing and polymerase chain Fundamental tools and techniques currently CHEN E4900x or y Topics in chemical reaction. Fluorescent DNA sequencing and used to engineer protein molecules. Methods engineering used to analyze the impact of these alterations 3 pts. Members of the faculty.

ENGINEERING 2017–2018 86 Prerequisite: Instructor's permission. Additional CHEN E6620y Physical chemistry of in chemical engineering are required to make an current topics in chemical engineering taught by macromolecules original investigation of a problem in chemical regular or visiting faculty. Special topics arranged 3 pts. Lect: 3. Not offered in 2017–2018. engineering or applied chemistry, the results of as the need and availability arise. Topics usually Prerequisite: CHEN E4620 or the instructor’s which are presented in their dissertations. No more offered on a one-time basis. Since the content of permission. Modern studies of static and dynamic than 15 points of credit toward the degree may be this course changes each time it is offered, it may behavior in macromolecular systems. Topics granted when the dissertation is accepted by the be repeated for credit. include single-chain behavior adsorption, solution department. thermodynamics, the glass transition, diffusion, and CHEN E4999x and y Fieldwork CHEN E9600x and y Advanced research viscoelastic behavior. The molecular understanding 1.5–3 pts. Lect: 3. Members of the faculty. problems of experimentally observed phenomena is 2–10 pts. Members of the faculty. Prerequisite: M.S. student. Course intended only stressed. for M.S. students. Provides work experience Prerequisites: Recommendation of the professor on chemical engineering in relevant intern or CHEN E8100y Topics in biology concerned and approval of the master’s research fieldwork experience as part of their program 3 pts. Lect: 3. Professor O’Shaughnessy. department. For postdoctoral students and other of study as determined by the instructor. A Prerequisites: Instructor’s permission. This qualified special students who wish to pursue written report describing their experience and research seminar introduces topics at the research under the guidance of members of the how it relates to the chemical engineering core forefront of biological research in a format and department. Not open to undergraduates or to curriculum is required. Employer feedback on language accessible to quantitative scientists and candidates for the degrees of Ch.E., M.S., Ph.D., student performance and the quality of the report engineers lacking biological training. Conceptual or Eng.Sc.D. and technical frameworks from both biological are the basis of the grade. This course may not CHEN E9800x and y Doctoral research and physical science disciplines are utilized. be taken for pass/fail credit or audited. Only 3 instruction points of CHEN E4999 can be credited toward The objective is to reveal to graduate students where potential lies to apply techniques from 3, 6, 9 or 12 pts. Members of the faculty. the M.S. degree. Furthermore, students who A candidate for the Eng.Sc.D. degree in take CHEN E4999 can use a only maximum of 3 their own disciplines to address pertinent biological questions in their research. Classes chemical engineering must register for 12 points of CHEN E 9400 in fulfillment of the M.S. points of doctoral research instruction. degree. entail reading, criticism and group discussion of research papers and textbook materials providing Registration in CHEN E9800 may not be used to CHEN E6050x Advanced electrochemistry overviews to various biological areas including: satisfy the minimum residence requirement for 3 pts. Lect: 3. Not offered in 2017–2018. evolution, immune system, development and the degree. Prerequisite: Instructor’s permission. An advanced cell specialization, the cytoskeleton and cell CHEN E9900x and y–S9900 Doctoral overview of the fundamentals of electrochemistry, motility, DNA transcription in gene circuits, protein dissertation with examples taken from modern applications. networks, recombinant DNA technology, aging, and 0 pts. Members of the faculty. An emphasis is placed on mass transfer and gene therapy. Open only to certified doctoral candidates. scaling phenomena. Principles are reinforced A candidate for the doctorate in chemical through the development of mathematical models CHEN E9000x and y Chemical engineering colloquium engineering may be required to register for of electrochemical systems. Course projects this course in every term after the student’s will require computer simulations. The course 0 pts. Col: 1. Professor Esposito. Graduate students on the Ph.D. track are required coursework has been completed, and until the is intended for advanced graduate students, dissertation has been accepted. conducting research involving electrochemical to attend the department colloquium as long as technologies. they are in residence. No degree credit is granted. CHEE E6220y Equilibria and kinetics in CHEN E9001x M.S. Chemical engineering hydrometallurgical systems colloquium 3 pts. Lect: 3. Not offered in 2017–2018. 0 pts. Lect.: 1. Professor Bozic. Prerequisite: Instructor’s permission. An advanced Required for all M.S. students in residence in overview of the fundamentals of electrochemistry, their first semester. Topics related to professional with examples taken from modern applications. development and the practice of chemical An emphasis is placed on mass transfer and engineering. No degree credits granted. Intended scaling phenomena. Principles are reinforced for M.S. students only. through the development of mathematical models CHEN E9400x and y Master’s research of electrochemical systems. Course projects 1–6 pts. Members of the faculty. will require computer simulations. The course Prescribed for M.S. and Ch.E. candidates; is intended for advanced graduate students, elective for others with the approval of the conducting research involving electrochemical Department. Degree candidates are required technologies. to conduct an investigation of some problem in CHEE E6252y Applied surface and colloid chemical engineering or applied chemistry and chemistry to submit a thesis describing the results of their 3 pts. Lect: 2. Lab: 3. Professors Somasundaran work. No more than 6 points in this course may and Farinato. be counted for graduate credit, and this credit is Prerequisites: CHEE E4252. Applications of contingent upon the submission of an acceptable surface chemistry principles to wetting, flocculation, thesis. The concentration in pharmaceutical flotation, separation techniques, catalysis, mass engineering requires a 2-point thesis internship. transfer, emulsions, foams, aerosols, membranes, CHEN E9500x and y–S9500 Doctoral research biological surfactant systems, microbial surfaces, 1–15 pts. Members of the faculty. enhanced oil recovery, and pollution problems. Prerequisites: The qualifying examinations for the Appropriate individual experiments and projects. doctorate. Open only to certified candidates for the Lab required. Ph.D. and Eng.Sc.D. degrees. Doctoral candidates

ENGINEERING 2017–2018 CIVIL ENGINEERING AND ENGINEERING MECHANICS 8787 610 S. W. Mudd, MC 4709 Phone: 212-854-3143 civil.columbia.edu

CHAIR ADMINISTRATIVE ASSISTANT Eli B. Gottlieb Pawel Woelke George Deodatis ASSISTANT PROFESSORS Paul Haining Bojidar Yanev Nathalie Rodriguez Sharon (Xuan) Di William M. Hart Theodore P. Zoli DEPARTMENT Marco Giometto Hauke Jungjohann ADMINISTRATOR PROFESSORS Shiho Kawashima Ark Latt DIRECTOR OF Alma Levin Raimondo Betti Ioannis Kougioumtzoglou Christopher LaTuso RESEARCH, CARLETON Patricia J. Culligan WaiChing Sun George Leventis LABORATORY GRADUATE Gautam Dasgupta Elisabeth Malsch Andrew Smyth LECTURERS IN ADMISSIONS AND George Deodatis Nasri Munfakh DISCIPLINE STUDENT AFFAIRS Maria Q. Feng Robert D. Mutch MANAGER, CARLETON Julius Chang OFFICER Jacob Fish Mysore Nagaraja LABORATORY Ibrahim Odeh Scott Kelly Upmanu Lall, Earth Daniel Peterson Adrian Brügger Thomas Panayotidi and Environmental Alan Poeppel CAREER PLACEMENT Engineering Bettina Quintas ASSOCIATE ADJUNCT FACULTY OFFICER Hoe I. Ling Robert Ratay MANAGER, CARLETON Emily-Anne McCormack Richard W. Longman, Amr Aly LABORATORY Ali Ashrafi Robert A. Rubin Mechanical Engineering Gregory Sauter Brannon Blake FINANCIAL ANALYST William Becker Feniosky Peña-Mora Matthew Sisul Laura Lichtblau Andrew Smyth Gabriel Calatrava Richard F. Carbonaro Lixun Sun Vincent Tirolo SYSTEM ASSOCIATE Raymond Daddazio Richard L. Tomasetti ADMINISTRATOR PROFESSORS Jonathan David Mario Valenti Michael Smith Haim Waisman Rudolph Frizzi Philip White Huiming Yin Marc Gallagher

he Department of Civil Engineering Current Research Activities and safety of structural systems, and Engineering Mechanics Current research activities in the computational stochastic mechanics, Tfocuses on two broad areas of Department of Civil Engineering and stochastic finite element and boundary instruction and research. The first, the Engineering Mechanics are centered element techniques, Monte Carlo classical field of civil engineering, deals in the areas outlined below. A number simulation techniques, random with the planning, design, construction, of these activities impact directly on micromechanics. and maintenance of the built problems of societal importance, such environment. This includes buildings, as rehabilitation of the infrastructure, Structural control and health foundations, bridges, transportation mitigation of natural or man-made monitoring: topics of research in this facilities, nuclear and conventional disasters, and environmental concerns. highly cross-disciplinary field include the power plants, hydraulic structures, and development of “smart” systems for the other facilities essential to society. The Solid mechanics: mechanical properties mitigation and reduction of structural second is the science of mechanics and of new and exotic materials, constitutive vibrations, assessment of the health its applications to various engineering equations for geologic materials, failure of structural systems based on their disciplines. Frequently referred to as of materials and components, properties vibration response signatures, and the applied mechanics, it includes the study of fiber-reinforced cement composites, modeling of nonlinear systems based of the mechanical and other properties damage mechanics. on measured dynamic behavior. of materials, stress analysis of stationary and movable structures, the dynamics Multihazard risk assessment and Fluid mechanics: numerical simulation and vibrations of complex structures, mitigation: integrated risk studies of the of flow and transport processes, aero- and hydrodynamics, and the civil infrastructure form a multihazard turbulence and turbulent mixing, urban mechanics of biological systems. perspective including earthquake, canopy flow and transport processes, wind, flooding, fire, blast, and terrorism. natural and mixed mode ventilation, wind loading, solid-laden turbulent flows, MISSION The engineering, social, financial, and decision-making perspectives of the porous surface turbulence, flow through The department aims to provide problem are examined in an integrated porous media, flow and transport in students with a technical foundation manner. fractured rock. anchored in theory together with the breadth needed to follow diverse career Probabilistic mechanics: random Environmental engineering/water paths, whether in the profession via processes and fields to model uncertain resources: modeling of flow and advanced study or apprenticeship, or as loads and material/soil properties, pollutant transport in surface and a base for other pursuits. nonlinear random vibrations, reliability subsurface waters, unsaturated

ENGINEERING 2017–2018 88 zone hydrology, geoenvironmental (e.g., homogenization and multigrid users to communicate with centers containment systems, analysis of methods); multiphysics modeling; throughout the world. All faculty and watershed flows including reservoir material and geometric nonlinearities; student offices and department labora- simulation. strong and weak discontinuities (e.g., tories are hardwired to the computing cracks and inclusions); discretization facility, which is also accessible remotely Structures: dynamics, stability, and techniques (e.g., extended finite element to users. Numerous personal computers design of structures, structural failure methods and mixed formulations); and graphics terminals exist throughout and damage detection, fluid and soil verification and validation (e.g., error the department, and a PC lab is avail- structure interaction, ocean structures analysis); software development and able to students in the department in subjected to wind-induced waves, parallel computing. addition to the larger school-wide facility. inelastic dynamic response of reinforced concrete structures, earthquake- Multiscale mechanics: solving Laboratories resistant design of structures. various engineering problems that have important features at multiple Robert A. W. Carleton Strength of Geotechnical engineering: soil spatial and temporal scales, such as Materials Laboratory behavior, constitutive modeling, predicting material properties or system The Carleton Laboratory serves as the reinforced soil structures, geotechnical behavior based on information from finer central laboratory for all experimental earthquake engineering, liquefaction scales; focus on information reduction work performed in the Department and numerical analysis of geotechnical methods that provide balance between of Civil Engineering and Engineering systems. computational feasibility and accuracy. Mechanics. It is the largest laboratory at Columbia University’s Morningside Structural materials: cement-based Construction engineering and campus and is equipped for teaching materials, micro- and macromodels of management: contracting strategies; and research in all types of engineer- fiber-reinforced cement composites, alternative project delivery systems; ing materials and structural elements, utilization of industrial by-products minimizing project delays and disputes; as well as damage detection, fatigue, and waste materials, beneficiation of advanced technologies to enhance vibrations, and sensor networks. The dredged material. productivity and efficiency; strategic Laboratory has a full-time staff who decisions in global engineering and provide assistance in teaching and Earthquake engineering: response of construction markets; industry trends research. The Laboratory is equipped structures to seismic loading, seismic and challenges. with a strong floor that allows for the risk analysis, active and passive control testing of full-scale structural compo- of structures subject to earthquake Infrastructure delivery and nents such as bridge decks, beams, and excitation, seismic analysis of long-span management: decision support systems columns. Furthermore, it is equipped cable-supported bridges. for infrastructure asset management; with universal testing machines ranging assessing and managing infrastructure in capacity from 150 kN (30,000 lbs.) Flight structures: composite materials, assets and systems; capital budgeting to 3 MN (600,000 lbs.). The seamless smart and multifunctional structures, processes and decisions; innovative integration of both research and teach- multiscale and failure analysis, vibration financing methods; procurement ing in the same shared space allows civil control, computational mechanics and strategies and processes; data engineering students of all degree tracks finite element analysis, fluid-structure management practices and systems; to gain a unique appreciation of modern interaction, aeroelasticity, optimal design, indicators of infrastructure performance experimental approaches to material sci- and environmental degradation of and service; market analysis. ence and engineering mechanics. structures. The Carleton Laboratory serves as the hub of instruction for classes offered FACILITIES Advanced materials: multifunctional by the Department of Civil Engineering The offices and laboratories of the engineering materials, advanced and Engineering Mechanics, most department are in the S. W. Mudd energy materials, durable infrastructure prominently ENME E3114 Experimental Building and the Engineering Terrace. materials, new concretes/composites Mechanics of Materials, ENME E3106 using nanotubes, nanoparticles, and Dynamics and Vibrations, and CIEN other additives with alternative binders, Computing E3141 Soil Mechanics. The Laboratory sustainable manufacturing technologies, The department manages a substantial also hosts and advises the AISC Steel rheological characterization for computing facility of its own in addition Bridge Team in the design, fabrication, advanced cement/concrete placement to being networked to all the systems and construction phases of their bridge, processes. operated by the University. The depart- which goes to regional and national ment facility enables its users to perform competition annually. Computational mechanics: aimed at symbolic and numeric computation, Additionally, the Carleton Laboratory understanding and solving problems in three-dimensional graphics, and expert has a fully outfitted machine shop science and engineering, topics include systems development. Connections to capable of machining parts, fittings, and multiscale methods in space and time wide-area networks allow the facility’s testing enclosures in steel, nonferrous

ENGINEERING 2017–2018 metals, acrylic, and wood. The Carleton serves as a state-of-the-art medium scale engineering workforce either with a 8989 Machine Shop’s machine tool pool is non-destructive structural health monitoring B.S. to develop specialized expertise state-of-the-art, either of the latest gen- facility, allowing the conduct of research in by way of apprenticeship or through eration or recently rebuilt and modern- the assessment of our nation’s degrading the increasingly common path of a ized. The machine shop is open for use civil infrastructure. specialized M.S. by undergraduate students performing independent research and is supported The Institute of Flight Structures 2. Graduates with a firm foundation in the basic math, science, and by the Lab’s senior lab technician. The Institute of Flight Structures was engineering science which underlie established within the department The Donald M. Burmister Soil all technological development will be through a grant by the Daniel and Mechanics Laboratory well equipped to adapt to changing Florence Guggenheim Foundation. It The Burmister Laboratory contains technology in the profession. provides a base for graduate training equipment and workspace to carry out in aerospace and aeronautical related all basic soil mechanics testing for our 3. Graduates equipped with a broad applications of structural analysis and undergraduate and graduate programs. technical background will be able to design. Several unique apparatuses have been follow other technical or nontechnical acquired or fabricated for advanced soil career paths. Center for Infrastructure Studies testing and research: automated plain The Center was established in the 4. Graduates will practice their strain/triaxial apparatus for stress path department to provide a professional profession with effective writing testing at both drained and undrained environment for faculty and students from and communication skills, with conditions, direct sheer device for mini- a variety of disciplines to join with industry professional ethics, as well as with mum compliance, and a unique sand and government to develop and apply awareness of societal issues. hopper which prepares foundations and the technological tools and knowledge slopes for small scale model testing. The bases needed to deal with the massive Engineering Mechanics Laboratory has established a link and problems of the city, state, and regional The prerequisites for this program are cooperation for large-scale testing for infrastructure. The Center is active in the courses listed in the First Year– earthquake and geosynthetic applica- major infrastructure projects through a Sophomore Program (page 95) or their tions with NRIAE, the centrifuge facilities consortium of universities and agencies. equivalents, with the provision that at the Rensselaer Polytechnic Institute ENME E3105: Mechanics be taken in and the Tokyo Institute of Technology. the sophomore year and that the student UNDERGRADUATE PROGRAMS The Heffner Hydrologic Research have obtained a grade of B or better. The Department of Civil Engineering Laboratory and Engineering Mechanics focuses The Heffner Laboratory is a facility for Civil Engineering on two broad areas of instruction and both undergraduate instruction and The prerequisites for this program research. The first, the classical field research in aspects of fluid mechanics, are the courses listed in the First of civil engineering, deals with the environmental applications, and water Year–Sophomore Program (page planning, design, construction, and resources. The Heffner Laboratory hous- 93) or their equivalents. The civil maintenance of structures and the es the facilities for teaching the laborato- engineering program offers three areas infrastructure. These include buildings, ry component of the ENME E3161 Fluid of concentration: civil engineering and foundations, bridges, transportation Mechanics course and includes multiple construction management, geotechnical facilities, nuclear and conventional hydraulic benches with a full array of engineering or structural engineering, power plants, hydraulic structures, and experimental modules. and water resources/environmental other facilities essential to society. The engineering. In the junior and senior second is the science of mechanics and The Eugene Mindlin Laboratory for years, 15 credits of technical electives its applications to various engineering Structural Deterioration Research are allocated. The Mindlin Laboratory has been devel- disciplines. Frequently referred to as oped for teaching and research dedicated applied mechanics, it includes the Minor in Architecture to all facets of the assessment of struc- study of the mechanical properties of Civil engineering program students may tures, deterioration of structural perfor- materials, stress analysis of stationary want to consider a minor in architecture mance and surface coatings, dynamic test- and movable structures, the dynamics ing for earthquakes, and other applications. and vibrations of complex structures, (see page 198). The commissioning of a state-of-the-art aero- and hydrodynamics, micro- and 150 kN Instron universal testing machine, a nanomechanics, and the mechanics of GRADUATE PROGRAMS biological and energy systems. QUV ultraviolet salt spray corrosion system, The Department of Civil Engineering a freeze-thaw tester, a Keyence optical and Engineering Mechanics offers microscope and surface analyzer have Program Objectives graduate programs leading to the further expanded the Mindlin Laboratory’s 1. Graduates with a broad and degree of Master of Science (M.S.) and capabilities in material testing and char- fundamental technical base will be the degrees of Doctor of Engineering acterization. The Mindlin Laboratory also able to enter the professional civil

ENGINEERING 2017–2018 9090 CIVIL ENGINEERING PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

APMA E2101 (3) MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) APMA E2000 (4)1 Intro. to applied math.

UN1401 (3) UN1402 (3) Lab UN1493 (3) PHYSICS or chem. lab (three tracks, choose one) UN1601 (3.5) UN1602 (3.5) UN2801 (4.5) UN2802 (4.5) Lab UN3081 (2)

one-semester lecture (3–4): UN1403 or UN1404 or UN2045 or UN1604 CHEMISTRY Chem lab UN1500 (3) either semester or physics lab

GEOLOGY EESC UN1011 (4)

MECHANICS ENME-MECE E3105 (4) either semester

CIEN E3004 (3) CIVIL ENGINEERING CIEN E3000 (3) (recommended but not required) Urban infra. systems

UNIVERSITY UN1010 (3) either semester WRITING

HUMA CC1001, HUMA CC1C002, COCI CC1101, COCI CC1102, REQUIRED or Global Core (3–4) or Global Core (3–4) NONTECHNICAL ELECTIVES HUMA UN1121 or ECON UN1105 (4) and UN1123 (3) UN1155 recitation (0)

COMPUTER Computer Language: W1005 (3) (any semester) SCIENCE

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 Effective Class of 2021. Science (Eng.Sc.D.) and Doctor of Civil Engineering industry law, construction techniques, Philosophy (Ph.D.). These programs are By selecting technical electives, students managing civil infrastructure systems, flexible and may involve concentrations may focus on one of several areas of civil engineering and construction in structures, construction engineering, concentration or prepare for future entrepreneurship reliability and random processes, endeavors such as architecture. Some • Environmental engineering and soil mechanics, fluid mechanics, typical concentrations are: water resources: transport of hydrogeology, continuum mechanics, • Structural engineering: applications water-borne substances, hydrology, finite element methods, computational to steel and concrete buildings, sediment transport, hydrogeology, mechanics, experimental mechanics, bridges, and other structures and geoenvironmental design of vibrations and dynamics, earthquake • Geotechnical engineering: soil containment systems engineering, forensic structural mechanics, foundation engineering, engineering, or any combination thereof, tunneling, and geodisasters Engineering Mechanics such as fluid-structure interaction. • Construction engineering and Programs in engineering mechanics offer The Graduate Record Examination management: capital facility planning comprehensive training in the principles (GRE) is required for admission to the and financing, strategic management, of applied mathematics and continuum department. managing engineering and mechanics and in the application of construction processes, construction these principles to the solution of

ENGINEERING 2017–2018 9191 CIVIL ENGINEERING: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

CIEN E3125 (3) Structural design CIEN E3111 (3.5) ENME E3113 (3) Uncertainty and risk in Mech. of solids CIEN E3126 (1) civil infrastructure systems CORE CIEN E3128 (4) REQUIRED Computer-aided Design projects COURSES ENME E3161 (4) struct. design CIEN E3129 (3) Fluid mech. Proj. mgmt. for CIEN E3141 (4) construction Soil mech.

ENME E3332 (3) ENME E3106 (3) A first course in finite Dynamics and vibrations elements GEOTECH ENG. (GE) ENME E3114 (4) CIEN E3127 (3) OR STRUCT. Exper. mech. of materials Struct. design projects ENG. (SE) (SE) CIEN E3121 (3) or Struct. anal. CIEN E4241 (3) Geotech. eng. fund. (GE)

TECH 3 points 3 points 9 points ELECTIVES

CIEN E4133 (3) ENME E3114 (4) Capital facility planning Exper. mech. of materials and financing CIVIL ENG. CIEN E3121 (3) CIEN E4131 (3) AND CIEN E3127 (3) CONSTR. Struct. anal. Princ. of constr. tech. Struct. design projects MGMT. or or CIEE E3250 (3) CIEN E4241 (3) Hydrosystems eng. Geotech. eng. fund.) CONCENTRATIONS

TECH 6 points 3 points 6 points ELECTIVES

CIEE E3255 (3) CIEE E4163 (3) Environ. control / pollution Environ. eng. wastewater EAEE E4006 (3) WATER RES./ CIEE E3250 (3) ENVIRON. Field methods for Hydrosystems eng. ENG. CIEE E4257 (3) environ. eng. contam. transport CIEN E3303 (1) in subsurface sys. Independent studies

TECH 6 points 3 points 6 points ELECTIVES

NONTECH 3 points 3 points 3 points ELECTIVES

TOTAL POINTS 13 21 18.5 13

engineering problems. The emphasis is analysis, and in fields as diverse as and inelastic behavior, and damage on basic principles, enabling students transportation, environmental, structural, mechanics to choose from among a wide range nuclear, and aerospace engineering. • Vibrations: nonlinear and random of technical areas. Students may work Program areas include: vibrations; dynamics of continuous on problems in such disciplines as media, of structures and rigid bodies, Continuum mechanics: solid and systems analysis, acoustics, and stress and of combined systems, such as fluid mechanics, theories of elastic

ENGINEERING 2017–2018 92 ENGINEERING MECHANICS PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

APMA E2101 (3) MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) APMA E2000 (4)1 Intro. to applied math.

UN1401 (3) UN1402 (3) Lab UN1493 (3) PHYSICS or chem. lab (three tracks, choose one) UN1601 (3.5) UN1602 (3.5) UN2801 (4.5) UN2802 (4.5) Lab UN3081 (2)

one-semester lecture (3–4): UN1403 or UN1404 or UN2045 or UN1604 CHEMISTRY Chem lab UN1500 (3) either semester or physics lab

MECHANICS ENME-MECE E3105 (4) any semester

UNIVERSITY UN1010 (3) either semester WRITING

HUMA CC1001, HUMA CC1002, COCI CC1101, COCI CC1102 REQUIRED or Global Core (3–4) or Global Core (3–4) NONTECHNICAL ELECTIVES HUMA UN1121 or ECON UN1105 (4) and UN1123 (3) UN1155 recitation (0)

REQUIRED (3) Student’s choice, see list of first- and second-year technical electives TECH ELECTIVES

COMPUTER Computer Language: W1005 (3) (any semester) SCIENCE

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 Effective Class of 2021.

fluid-structure interaction; active, • Computational mechanics: finite COURSES IN CIVIL passive, and hybrid control systems element and boundary element ENGINEERING for structures under seismic loading; techniques, symbolic computation, See also Courses in Engineering dynamic soil-structure interaction and bioengineering applications. Mechanics at the end of this section. effects on the seismic response of CIEN E3000y The art of structural design structures A flight structures program is 3 pts. Lect: 3. Professor Deodatis. • Random processes and reliability: designed to meet the needs of industry Basic scientific and engineering principles for the problems in design against failure in the fields of high-speed and space design of buildings, bridges, and other parts of under earthquake, wind, and wave flight. The emphasis is on mechanics, the built infrastructure. Application of principles loadings; noise, and turbulent flows; mathematics, fluid dynamics, flight to analysis and design of actual large-scale analysis of structures with random structures, and control. The program structures. Coverage of the history of major properties is a part of the Guggenheim Institute structural design innovations and of the engineers • Fluid mechanics: turbulent flows, of Flight Structures in the department. who introduced them. Critical examination of the two-phase flows, fluid-structure Specific information regarding degree unique aesthetic/artistic perspectives inherent in structural design. Consideration of management, interaction, fluid-soil interaction, flow in requirements is available in the socioeconomic, and ethical issues involved in porous media, computational methods department office. design and construction of large-scale structures. for flow and transport processes, and Introduction to recent developments in sustainable flow and transport in fractured rock engineering, including green building design and under mechanical loading adaptable structural systems.

ENGINEERING 2017–2018 9393 ENGINEERING MECHANICS: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

APMA E3102 (3) ENME E3113 (3) Applied math., II ENME E3332 (3) Mech. of solids A first course in finite ENME E3106 (3) elements ENME E3161 (4) Dynamics and vibrations CORE ENME E4202 (3) REQUIRED Fluid mechanics ENME E4113 (3) Advanced mech. COURSES ENME E3114 (4) Advanced solids APMA E3101 (3) Experimental mech. Applied math., I ENME E4215 (3) CIEN E3121 (3) Theory of vibrations Structural analysis

TECH 3 points 6 points 6 points 9 points

NONTECH 3 points 3 points ELECTIVES

TOTAL POINTS 13 19 18 15

CIEN E3004y Urban infrastructure systems CIEN E3125y Structural design skills are stressed. Outside lecturers will address 3 pts. Lect: 3. Professor Odeh. 3 pts. Lect: 3. Professor Panayotidi. important current issues in engineering practice. Introduction to: (a) the infrastructure systems Prerequisite: ENME E3113. Design criteria for Every student in the course will be exposed with that support urban socioeconomic activities, and varied structural applications, including buildings equal emphasis to issues related to geotechnical (b) fundamental system design and analysis and bridges; design of elements using steel, engineering, water resources/environmental methods. Coverage of water resources, vertical, concrete, masonry, wood, and other materials. engineering, structural engineering, and transportation, communications and energy construction engineering and management. CIEN E3126y Computer-aided structural infrastructure. Emphasis upon the purposes that CIEN E3129x Project management for these systems serve, the factors that influence design their performance, the basic mechanisms that 1 pt. Lect: 1. Lab: 1. Professor Deodatis. construction govern their design and operation, and the impacts Corequisite: CIEN E3125. Introduction to software 3 pts. Lect: 3. Professor Chang. that they have regionally and globally. Student for structural analysis and design with lab. Prerequisite: Senior standing in Civil Engineering teams complete a semester-long design/analysis Applications to the design of structural elements or instructor’s permission. Introduction to project with equal emphasis given to water and connections. Lab required. Project Management for design and construction processes. Elements of planning, estimating, resources / environmental engineering, geotechnical CIEN E3127x Structural design projects scheduling, bidding, and contractual relationships. engineering and construction engineering and 3 pts. Lect: 3. Professor Panayotidi. Computer scheduling and cost control. Critical path management topics. Prerequisites: CIEN E3125 and E3126 or the method. Design and construction activities. Field instructor’s permission. Design of steel members in CIEN E3111x Uncertainty and risk in civil supervision. accordance with AISC 360: moment redistribution infrastructure systems in beams; plastic analysis; bearing plates; beam- CIEN E3141y Soil mechanics 3.5 pts. Lect: 3. Professor Deodatis. columns: exact and approximate second-order 4 pts. Lect: 3. Lab 3. Professor W. Sun. Prerequisite: Working knowledge of calculus. analysis; design by the Effective Length method Prerequisite: ENME E3113. Index properties Introduction to basic probability; hazard and the Direct Analysis method. Design of and classification; compaction; permeability and function; reliability function; stochastic models concrete members in accordance with ACI 318: bar seepage; effective stress and stress distribution; of natural and technological hazards; extreme anchorage and development length, bar splices, shear strength of soil; consolidation; slope stability. value distributions; statistical inference design for shear, short columns, slender columns. methods; Monte Carlo simulation techniques; CIEE E3250y Hydrosystems engineering AISC/ASCE NSSBC design project: design fundamentals of integrated risk assessment 3 pts. Lect: 3. Instructor to be announced. of a steel bridge in accordance with National and risk management; topics in risk-based Prerequisites: CHEN E3110 or ENME E3161 or Student Steel Bridge Competition rules; computer insurance; case studies involving civil equivalent, SIEO W3600 or equivalent, or the simulation and design by using SAP2000. infrastructure systems, environmental systems, instructor’s permission. A quantitative introduction mechanical and aerospace systems, construction CIEN E3128y Design projects to hydrologic and hydraulic systems, with a management. 4 pts. Lect: 4. Professor Panayotidi. focus on integrated modeling and analysis of the Prerequisites: CIEN E3125 and E3126. water cycle and associated mass transport for CIEN E3121y Structural analysis Capstone design project in civil engineering. water resources and environmental engineering. 3 pts. Lect: 3. Professor Panayotidi. This project integrates structural, geotechnical Coverage of unit hydrologic processes such Methods of structural analysis. Trusses, arches, and environmental/water resources design as precipitation, evaporation, infiltration, cables, frames; influence lines; deflections; problems with construction management tasks runoff generation, open channel and pipe flow, force method; displacement method; computer and sustainability, legal and other social issues. subsurface flow and well hydraulics in the context applications. Project is completed in teams, and communication of example watersheds and specific integrative

ENGINEERING 2017–2018 9494 problems such as risk-based design for flood CEOR E4011x Infrastructure systems systems, construction management. Not open to control, provision of water, and assessment of optimization undergraduate students. environmental impact or potential for nonpoint 3 pts. Lect: 3. Professor Di. source pollution. Spatial hydrologic analysis using Prerequisites: Basic linear algebra. Basic CIEN E4128y Civil engineering management GIS and watershed models. Note: This course probability and statistics. Engineering economic 3 pts. Not offered in 2017–2018. is to be joint listed with CIEN and replaces the concepts. Basic spreadsheet analysis and Principles of engineering management with a previous CIEN 3250. programming skills. Subject to instructor's strong emphasis on planning of infrastructure permission. Infrastructure design and systems systems. The course stresses leadership, creativity, CIEE E3255y Environmental control and concepts, analysis, and design under competing/ and management analysis. Program planning with pollution reduction systems conflicting objectives, transportation network optimization under financial and environmental 3 pts. Lect: 3. Professor Farrauto. models, traffic assignments, optimization, and the constraints; project planning and scheduling using Prerequisite: EAEE E3200 or ENME E3161 or simplex algorithm. deterministic and stochastic network theories; MECE E3100. Review of engineered systems for production rate development and control using prevention and control of pollution. Fundamentals CIEN E4011y Traffic engineering statistical, heuristic, simulation, and queuing of material and energy balances and reaction 3 pts. Lect: 3. Professor Di. theory approaches. Students prepare and formally kinetics. Analysis of engineered systems to Prerequisite: ENME E3105 or instructor's present term projects. address environmental problems, including solid permission. Introduction to analysis and design of and hazardous waste, and air, water, soil and fundamental transportation system components, CIEN E4129x and y Managing engineering and noise pollution. Life cycle assessments and including individual vehicle motion, basic elements construction processes emerging technologies. of geometric design, vehicle flow and elementary 3 pts. Lect: 3. Professors Odeh and Nagaraja. traffic flow relations, capacity analysis, and traffic Prerequisite: Graduate standing in Civil CIEE E3260y Engineering for developing forecasting. Engineering, or instructor’s permission. communities Introduction to the principles, methods and tools CIEN E4021x Elastic and plastic analysis of 3 pts. Lect: 3. Professor Sisul. necessary to manage design and construction structures Introduction to engineering problems faced processes. Elements of planning, estimating, by developing communities and exploration of 3 pts. Lect: 3. Professor Kawashima. scheduling, bidding and contractual relationships. design solutions in the context of a real project Prerequisite: CIEN E3121 or the equivalent. Valuation of project cash flows. Critical path with a community client. Emphasis is on the Overview of classical indeterminate structural method. Survey of construction procedures. Cost design of sustainable solutions that take account analysis methods (force and displacement methods), control and effectiveness. Field supervision. of social, economical, and governance issues, approximate methods of analysis, plastic analysis and that can be implemented now or in the near methods, collapse analysis, shakedown theorem, CIEN E4130x Design of construction systems future. The course is open to all undergraduate structural optimization. 3 pts. Lect: 3. Professor Tirolo. engineering students. Multidisciplinary teamwork Prerequisite: CIEN E3125 or the equivalent, or the CIEN E4022y Bridge design and management and approaches are stressed. Outside instructor’s permission. Introduction to the design 3 pts. Lect: 3. Professor Yanev. lecturers are used to address issues specific of systems that support construction activities Prerequisite: CIEN E3125 or the equivalent. Bridge to developing communities and the particular and operations. Determination of design loads design history, methods of analysis, loads: static, project under consideration. during construction. Design of excavation support live, dynamic. Design: allowable stress, ultimate systems, earth retaining systems, temporary CIEN E3303x and y Independent studies in strength, load resistance factor, supply/demand. supports and underpinning, concrete formwork civil engineering for juniors Steel and concrete superstructures: suspension, and shoring systems. Cranes and erection 1–3 pts. By conference. Members of the faculty. cable stayed, prestressed, arches. Management systems. Tunneling systems. Instrumentation and A project on civil engineering subjects approved of the assets, life-cycle cost, expected useful life, monitoring. Students prepare and present term by the chairman of the department. inspection, maintenance, repair, reconstruction. projects. Bridge inventories, condition assessments, data CIEN E3304x and y Independent studies in acquisition and analysis, forecasts. Selected case CIEN E4131x and y Principles of construction civil engineering for seniors histories and field visits. techniques 1–3 pts. By conference. Members of the faculty. 3 pts. Lect: 3. Professors Hart and Odeh. A project on civil engineering subjects approved by CIEN E4100y Earthquake and wind Prerequisite: CIEN E4129 or equivalent. Current engineering the chairman of the department. methods of construction, cost-effective designs, 3 pts. Lect: 3. Professor Ashrafi. maintenance, safe work environment. Design Prerequisite: ENME E3106 or the equivalent. Basic CIEN E3999x, y or s Fieldwork functions, constructability, site and environmental concepts of seismology. Earthquake characteristics, 1–2 pts. Professor Deodatis. issues. Prerequisites: Obtained internship and approval magnitude, response spectrum, dynamic response from faculty adviser. CEEM undergraduate of structures to ground motion. Base isolation CIEN E4132x Prevention and resolution of students only. Written application must be made and earthquake-resistant design. Wind loads and construction disputes prior to registration outlining proposed internship/ aeroelastic instabilities. Extreme winds. Wind 3 pts. Lect: 3. Professor White. study program. Final reports required. This course effects on structures and gust factors. Prerequisite: CIEN E4129 or equivalent. may not be taken for pass/fail credit or audited. Contractual relationships in the engineering and CIEN E4111x Uncertainty and risk in International students must also consult with the construction industry and the actions that result infrastructure systems International Students and Scholars Office. in disputes. Emphasis on procedures required to 3 pts. Lect: 3. Professor Smyth. prevent disputes and resolve them quickly and Introduction to basic probability, hazard function, CIEN E4010y Transportation engineering cost-effectively. Case studies requiring oral and reliability function, stochastic models of natural 3 pts. Lect: 3. Professor Peterson. written presentations. and technological hazards, extreme value An overview of the planning, design, operation, distributions, Monte Carlo simulation techniques, CIEN E4133x Capital facility planning and and construction of urban highways and mass fundamentals of integrated risk assessment and financing transportation systems. Transportation planning risk management, topics in risk-based insurance, 3 pts. Lect: 3. Professor Chang. and traffic studies; traffic and highway engineering; Prerequisite: CIEN E4129 or equivalent. Planning rapid transit and railroad engineering. case studies involving civil infrastructure systems, environmental systems, mechanical and aerospace and financing of capital facilities with a strong

ENGINEERING 2017–2018 emphasis upon civil infrastructure systems. estate and infrastructure projects are covered. CIEN E4210x Forensic structural engineering 9595 Project feasibility and evaluation. Design of Basics of real-estate accounting and finance, 3 pts. Lect: 3. Professor Ratay. project delivery systems to encourage best followed by in-depth studies of private, public, Prerequisites: Working knowledge of structural value, innovation and private sector participation. and public/private-partnership projects and their analysis and design; graduate student standing Fundamentals of engineering economy and financial structures. Focused on U.S.-based or instructor’s permission. Review of significant project finance. Elements of life cycle cost financing, with some international practices failures, civil/structural engineering design and estimation and decision analysis. Environmental, introduced and explored. Financial risks and construction practices, ethical standards and institutional, social and political factors. Case rewards, and pertinent capital markets and the legal positions as necessary background to studies from transportation, water supply and their financing roles. Impacts and incentives of forensic engineering. Discussion of standard- wastewater treatment. various government programs, such as LEED of-care. Study of the process of engineering certification and solar power tax credits. Case CIEN E4134y Construction industry law evaluation of structural defects and failures studies provide opportunity to compare U.S. 3 pts. Lect: 3. Professors Quintas and Rubin. in construction and in service. Examination practices to several international methods. Prerequisite: Graduate standing or the instructor’s of the roles, activities, conduct and ethics of permission. Practical focus upon legal concepts CIEN E4139y Theory and practice of virtual the forensic consultant and expert witness. applicable to the construction industry. Provides design and construction Students are assigned projects of actual cases sufficient understanding to manage legal aspects, 3 pts. Lect: 3. Professor David. of nonperformance or failure of steel, concrete, instead of being managed by them. Topics include Prerequisites: CIEN E4129 or instructor’s masonry, geotechnical, and temporary structures, contractual relationships, contract performance, permission. History and development of Building in order to perform, discuss, and report their own contract flexibility and change orders, liability and Information Modeling (BIM), its uses in design and investigations under the guidance of the instructor. negligence, dispute avoidance/resolution, surety construction, and introduction to the importance CIEN E4212y Structural failures: cases, bonds, insurance and site safety. of planning in BIM implementation. Role of visual causes, lessons learned design and construction concepts and methodologies, CIEN E4135y Strategic management global 3 pts. Lect: 3. Professor Ratay. including integrated project delivery form in design and construction Prerequisites: A course each in engineering architecture, engineering, and construction 3 pts. Lect: 3. Professor LaTuso. materials, structural analysis, concrete design, industries from project design, cost estimating, Core concepts of strategic planning, management steel design, soil mechanics and foundations, scheduling, coordination, fabrication, installation, and analysis within the construction industry. and construction; graduate student standing or and financing. Industry analysis, strategic planning models instructor's permission. The nature and causes and industry trends. Strategies for information CIEN E4140x Environmental, health, and of structural failures and the lessons learned technology, emerging markets and globalization. safety concepts in construction processes from them; insight into failure investigation in the Case studies to demonstrate key concepts in real- 3 pts. Lect: 3. Professor Haining. practice of forensic structural engineering. Case world environments. Prerequisite: Graduate standing in Civil histories of actual failures of real-life structures Engineering and Engineering Mechanics. A during construction and in service are introduced, CIEN E4136y Global entrepreneurship in civil definitive review of and comprehensive introduction examined, analyzed, and discussed. Students engineering to construction industry best practices and are assigned documented cases of failures of 3 pts. Lect: 3. Professors Odeh and Sauter. fundamental concepts of environmental health structures of various types and materials to Capstone practicum where teams develop and safety management systems (EH&S) for the review, discuss, and, in some cases, to conduct strategies and business plans for a new enterprise investigations of the causes and responsibilities. in the engineering and construction industry. construction management field. How modern Students are required to prepare written reports Identification of attractive market segments and EH&S management system techniques and locations; development of an entry strategy; theories not only result in improved safe work and make oral presentations of selected cases. environments but ultimately enhance operational acquisition of financing, bonding and insurance; CIEN E4213x Elastic and inelastic buckling of processes and performance in construction organizational design; plans for recruiting and structures projects. retaining personnel; personnel compensation/ 3 pts. Lect: 3. Professor Valenti. incentives. Invited industry speakers. CIEN E4141x or y Public-private partnerships Stability of framed structures in the elastic and CIEN E4137y Managing civil infrastructure in global infrastructure development inelastic ranges. Lateral buckling of beams. systems 3 pts. Professor Chang. Torsional buckling of compression members. 3 pts. Lect: 3. Professor Chang. Graduate students only. Delivery of infrastructure Buckling of plates of plate-stiffener combinations. Prerequisites: IEOR E4003, CIEN E4133, or assets through Public-Private Partnerships (PPP). Linear stability analysis of cylindrical shells and equivalent. Examination of the fundamentals of Value for Money analysis. Project organization. discussion of its limitations. Discussion of the infrastructure planning and management, with a Infrastructure sector characterization. Risk semiempirical nature of the elastoplastic relations focus on the application of rational methods that analysis, allocation, and mitigation. Monte Carlo used in the case of plates and shells. methods and Real Options. Project finance support infrastructure decision-making. Institutional CIEN E4226y Advanced design of steel environment and issues. Decision-making under and financing instruments. Case studies from transportation, water supply, and energy sectors. structures certainty and uncertainty. Capital budgeting and 3 pts. Lect: 3. Professors Aly and Woelke. financing. Group decision processes. Elements of CIEE E4163x Sustainable water treatment Prerequisite: CIEN E3125 or equivalent. Review of decision and finance theory. and reuse loads and structural design approaches. Material CIEN E4138y Real-estate finance for 3 pts. Lect: 3. Professor Becker. considerations in structural steel design. Behavior construction management Prerequisites: Introductory chemistry (with and design of rolled steel, welded, cold-formed 3 pts. Lect: 3. Professor Latt. laboratory) and fluid mechanics. Fundamentals light-gauge, and composite concrete/steel members. Prerequisites: IEOR E2261, CIEN E3129 or of water pollution and wastewater characteristics. Design of multistory buildings and space structures. Chemistry, microbiology, and reaction kinetics. permission of instructor. Introduction to financial CIEN E4232x Advanced design of concrete Design of primary, secondary, and advanced mechanics of public and private real-estate structures treatment systems. Small community and development and management. Working from 3 pts. Lect: 3. Professor Panayotidi. residential systems. perspectives of developers, investors and Prerequisite: CIEN E3125 or equivalent. Design taxpayers, financing of several types of real-

ENGINEERING 2017–2018 9696

of concrete beams for combined torsion, shear Topics include overview of major projects, project CIEN E4237x or y Architectural design, and flexure; moment-curvature relation; bar cut-off criteria and interface with architecture, design computation, and method locations; design of two-way slabs; strut-and-tie of foundations and structural systems, design 3 pts. Lect: 1.5. Lab: 1.5. Professor Calatrava. method for the design of deep beams and corbels; challenges in the post 9/11 environment, and roles, Prerequisites: CIEN E3121 or equivalent. CIEN gravity and shear wall design; retaining wall responsibilities, and legal issues. E3125 or equivalent. Integrated methods of design design. and structural analysis between engineering and CIEN E4235x Multihazard design of architecture. Lectures on historical precedents CIEN E4233x Design of large-scale bridges structures on material use, structural inventiveness, and 3 pts. Lect: 3. Professor Zoli. 3 pts. Lect: 3. Professor Daddazio. social importance. Labs on drafting and modeling Prerequisites: CIEN E3121 or equivalent, and Prerequisite: CIEN E3125 or E4232 or instructor’s software; physical modeling techniques and virtual CIEN E3127 or equivalent. Design of large-scale permission. Fundamental considerations of wave reality visualization. and complex bridges with emphasis on cable- mechanics; design philosophies; reliability and supported structures. Static and dynamic loads, risk concepts; basics of fluid mechanics; design CIEN E4241x Geotechnical engineering component design of towers, superstructures of structures subjected to blast; elements of fundamentals and cables; conceptual design of major bridge seismic design; elements of fire design; flood 3 pts. Lect: 3. Professor Ling. types including arches, cable stayed bridges and considerations; advanced analysis in support of Prerequisite: CIEN E3141 or instructor’s permission. suspension bridges. structural design. Bearing capacity and settlement of shallow and deep foundations; earth pressure theories; CIEN E4234y Design of large-scale building CIEN E4236y Design of prestressed concrete retaining walls and reinforced soil retaining walls; structures structures sheet pile walls; braced excavation; slope stability. 3 pts. Lect: 3. Professor Tomasetti. 3 pts. Lect: 3. Professor Panayotidi. Prerequisites: CIEN E3121 and E3127. Modern Prerequisite: CIEN E4232 or instructor's CIEN E4242y Geotechnical earthquake challenges in the design of large-scale building permission. Properties of materials used in engineering structures will be studied. Tall buildings, large prestressed concrete; pretensioning versus 3 pts. Lect: 3. Not offered in 2017–2018. convention centers, and major sports stadiums posttensioning; loss of prestress due to elastic Prerequisite: CIEN E3141 or equivalent. Seismicity, present major opportunities for creative solutions shortening, friction, anchorage slip, shrinkage, earthquake intensity, propagation of seismic and leadership on the part of engineers. This creep and relaxation; full versus partial waves, design of earthquake motion, seismic site course is designed to expose the students to this prestressing; design of beams for flexure, shear, response analysis, in situ and laboratory evaluation environment by having them undertake the complete and torsion; method of load balancing; anchorage of dynamic soil properties, seismic performance of design of a large structure from initial design zone design; calculation of deflection by the underground structures, seismic performance of concepts on through all the major design decisions. lump-sum and incremental time-step methods; port and harbor facilities, evaluation and mitigation The students work as members of a design team to continuous beams; composite construction; of soil liquefaction and its consequences. Seismic overcome the challenges inherent in major projects. prestressed slabs and columns. earth pressures, slopes stability, safety of dams

ENGINEERING 2017–2018 and embankments, seismic code provisions and aspects of problems involving human interaction collaborative work in global projects. Information 9797 practice. To alternate with E4244. with the natural environment. Review of technologies for design, visualization, project fundamentals principles that underlie the discipline management, and collaboration in globally CIEN E4243x Foundation engineering of environmental engineering, i.e., constituent distributed networks of design, fabrication, and 3 pts. Lect: 3. Professor L. Sun. transport and transformation processes in construction organizations, including web-based, Prerequisite: CIEN E3141 or equivalent. environmental media such as water, air and parametric computer-aided modeling, project Conventional types of foundations and foundation ecosystems. Engineering applications for organizational simulation, and other emerging problems: subsurface exploration and testing. addressing environmental problems such as water applications. Global team project with students at Performance of shallow and deep foundations and quality and treatment, air pollutant emissions, collaborating universities abroad. evaluation by field measurements. Case histories and hazardous waste remediation. Presented to illustrate typical design and construction CIEN E6133y Advanced construction and in the context of current issues facing practicing problems. To alternate with CIEN E4246. engineers and government agencies, including infrastructure risk management using real options CIEN E4244y Geosynthetics and waste legal and regulatory framework, environmental 3 pts. Lect: 3. Not offered in 2017–2018. containment impact assessments, and natural resource Prerequisite: CIEN E6131. Advanced concepts 3 pts. Lect: 3. Professor Ling. management. of risk analysis and management applied to civil Prerequisite: CIEN E4241 or the equivalent. CIEN E4253x Finite elements and plasticity in engineering systems. Identifying and valuing Properties of geosynthetics. Geosynthetic design geotechnical engineering flexibility in construction and operation. Tools for soil reinforcement. Geosynthetic applications in 3 pts. Lect: 3. Professor Sun. to perform risk analysis in flexible civil solid waste containment system. To alternate with Prerequisites: CIEN E3141 and ENME E4332. infrastructure systems. Valuation methods for real CIEN E4242. State-of-the-art computer solutions in geotechnical options. Risk flexibility analysis; integrating real CIEN E4245x Tunnel design and construction engineering; 3D consolidation, seepage flows, options analysis with quantitative risk analysis. 3 pts. Lect: 3. Professor Munfakh. and soil-structure interaction; element and mesh Applications to case studies on construction Engineering design and construction of different instabilities. management, life-cycle cost analysis for types of tunnel, including cut and cover tunnel, infrastructure assets, public-private partnerships CIEE E4257x Groundwater contaminant rock tunnel, soft ground tunnel, immersed tub projects, real estate developments, and renewable transport and remediation tunnel, and jacked tunnel. The design for the liner, energy infrastructure projects. 3 pts. Lect: 3. Professor Mutch. excavation, and instrumentation are also covered. ENME E3161 and CIEE E3250 or instructor's CIEN E6232x Advanced topics in concrete A field trip will be arranged to visit the tunneling permission. Sources and types of groundwater engineering site. contamination. Groundwater hydrology. 3 pts. Lect: 3. Not offered in 2017–2018. CIEN E4246y Earth retaining structures Groundwater contaminant fate and transport. Prerequisite: CIEN E3125 or the equivalent. 3 pts. Lect: 3. Not offered in 2017–2018. Flow and transport in the unsaturated zone. Behavior of concrete under general states of Prerequisite: CIEN E3141. Retaining structures, Nonaqueous phase liquids and multiphase flow. stress, numerical modeling of steel and concrete, bulkheads, cellular cofferdams, and braced Physical and numerical models for contaminant finite element analysis of reinforced concrete, excavations. Construction dewatering and transport. Characterization and assessments of design of slabs and their shell concrete structures. underpinning. Instrumentation to monitor actual contaminated sites. Groundwater remediation CIEN E6246y Advanced soil mechanics performances. Ground improvement techniques, alternatives. Regulations. 3 pts. Lect: 2.5. Professor Ling. including earth reinforcement, geotextiles, and CIEN E4260x Urban ecology studio Prerequisite: CIEN E3141. Stress-dilatancy of grouting. To alternate with CIEN E4243. 3 pts. Lect: 3. Professor Culligan. sand; failure criteria; critical state soil mechanics; CIEN E4247y Design of large-scale deep Prerequisites: Senior undergraduate or graduate limit analysis; finite element method and case foundation systems student standing and instructor’s permission. histories of consolidation analysis. Conjoint studio run with the Graduate School of 3 pts. Lect.: 3. Professors Leventis and Frizzi. CIEN E6248x Experimental soil mechanics Prerequisite: CIEN E3141. Focus on deep Architecture, Planning and Preservation (GSAPP) that explores solutions to problems of urban 3 pts. Lect: 2.5. Not offered in 2017–2018. foundations in difficult conditions and constraints Prerequisite: CIEN E3141. Advanced soil testing, of designing foundations. Design process density. Engineering and GSAPP students will engage in a joint project that address habitability including triaxial and plane strain compression from the start of field investigations through tests; small-strain measurement. Model testing; construction and the application of deep and sustainability issues in an urban environment, and also provides community service. Emphasis application (of test results) to design. foundations. will be on the integration of science, engineering CIEN E9101x and y–S9101 Civil engineering CIEN E4250y Waste containment design and and design within a social context. Interdisciplinary research practice approaches and communication will be stressed. 1–4 pts. Members of the faculty. 3 pts. Lect: 3. Not offered in 2017–2018. CIEN E4999x and y Fieldwork Advanced study in a specialized field under the Prerequisites: ENME E3161 and CIEN E3141, 1 pt. Professor Deodatis. supervision of a member of the department staff. or equivalents. Strategies for the containment Prerequisite: Instructor’s written approval. Before registering, the student must submit an of buried wastes. Municipal and hazardous Written application must be made prior to outline of the proposed work for approval of the waste landfill design; bioreactor landfills; vertical registration outlining proposed study program. supervisor and the department chair. barriers, evapotranspiration barriers and capillary Final reports required. May not be taken barriers; hydraulic containment; in situ stabilization CIEN E9120x and y–S9120 Independent for pass/fail credit or audited. International and solidification techniques; site investigation; studies in flight sciences students must consult with the International monitoring and stewardship of buried wastes; 3 pts. Not offered in 2017–2018. Students and Scholars Office. options for land reuse/redevelopment. Prerequisite: Instructor’s permission. This course CIEN E6132y Advanced systems and is geared toward students interested in flight CIEE E4252x Environmental engineering technologies for global project collaboration sciences and flight structures. Topics related to 3 pts. Lect: 3. Professor Chandran. 3 pts. Lect: 3. Not offered in 2017–2018. aerodynamics, propulsion, noise, structural dynamics, Prerequisites: CHEM UN1403 or equivalent; Prerequisite: CIEN E4129 or the equivalent. aeroelasticity, and structures may be selected for ENME E3161 or the equivalent. Engineering Systems and technologies that support supervised study. A term paper is required.

ENGINEERING 2017–2018 98 CIEN E9130x and y–S9130 Independent Prerequisite: MATH UN1201. Corequisite: ENME Prerequisite: ENME E4113 or instructor’s studies in construction E3105. Kinematics of rigid bodies; momentum and approval. An introduction to the constitutive 3 pts. Not offered in 2017–2018. energy methods; vibrations of discrete and continuous modeling of composite materials: Green’s Prerequisites: Permission by department chair systems; eigenvalue problems, natural frequencies functions in heterogenous media, Eshelby’s and instructor. Independent study of engineering and modes. Basics of computer simulation of equivalent inclusion methods, eigenstrains, and construction industry problems. Topics dynamics problems using MATLAB. spherical and ellipsoidal inclusions, dislocations, related to capital planning and financing, project homogenization of elastic fields, elastic, ENME E3113x Mechanics of solids management, contracting strategies and risk viscoelastic and elastoplastic constitutive modeling, 3 pts. Lect: 3. Professor Betti. allocation, dispute mitigation and resolution, and micromechanics-based models. Pre- or corequisite: ENME E3105 or equivalent. infrastructure assessment and management may Stress and strain. Mechanical properties of ENME E4202y Advanced mechanics be selected for supervised study. A term paper materials. Axial load, bending, shear, and torsion. 3 pts. Lect: 3. Professor Smyth. is required. Stress transformation. Deflection of beams. Buckling Prerequisite: ENME E3105 or equivalent. CIEN E9165x and y–S9165 Independent of columns. Combined loadings. Thermal stresses. Differentiation of vector functions. Review of studies in environmental engineering kinematics. Generalized coordinates and constraint ENME E3114y Experimental mechanics of 4 pts. Not offered in 2017–2018. equations. Generalized forces. Lagrange’s materials Prerequisite: CIEE E4252 or the equivalent. equations. Impulsive forces. Collisions. 4 pts. Lect: 2. Lab: 3. Professor Kawashima. Emphasizes a one-on-one study approach to Hamiltonian. Hamilton’s principle. Prerequisite: ENME E3113. Material behavior specific environmental engineering problems. and constitutive relations. Mechanical properties ENME E4214y Theory of plates and shells Students develop papers or work on design of metals and cement composites. Structural 3 pts. Lect: 3. Professor Dasgupta. problems pertaining to the treatment of solid materials. Modern construction materials. Prerequisite: ENME E3113. Static flexural and liquid waste, contaminant migration, Experimental investigation of material properties response of thin, elastic, rectangular, and circular and monitoring and sampling programs for and behavior of structural elements including plates. Exact (series) and approximate (Ritz) remediation design. fracture, fatigue, bending, torsion, buckling. solutions. Circular cylindrical shells. Axisymmetric CIEN E9201x and y–S9201 Civil engineering and nonaxisymmetric membrane theory. Shells of ENME E3161x Fluid mechanics reports arbitrary shape. 4 pts. Lect: 3. Lab: 3. Instructor to be announced. 1–4 pts. Not offered in 2017–2018. Prerequisites: ENME E3105 and ordinary differential ENME E4215x Theory of vibrations A project on some civil engineering subject equations. Fluid statics. Fundamental principles 3 pts. Lect: 3. Professor Betti. approved by department chair. and concepts of flow analysis. Differential and Frequencies and modes of discrete and continuous CIEN E9500x and y Departmental seminar finite control volume approach to flow analysis. elastic systems. Forced vibrations-steady-state 0 pts. Professor Ling. Dimensional analysis. Application of flow analysis: and transient motion. Effect of damping. Exact and All doctoral students are required to attend flow in pipes, external flow, flow in open channels. approximate methods. Applications. the department seminar as long as they are in ENME E3332x A first course in finite elements ENME E4332x Finite element analysis, I residence. No degree credit is granted. 3 pts. Lect: 3. Professor Fish. 3 pts. Lect: 3. Professor Waisman. CIEN E9800x and y–S9800 Doctoral research Prerequisite: Senior standing or instructor’s permission. Prerequisites: Mechanics of solids, structural instruction Recommended corequisite: differential equations. analysis, elementary computer programming 3–12 pts. May be taken for 3, 6, 9, or 12 points, Focus on formulation and application of the finite (MATLAB) is recommended, linear algebra dependent on instructor’s permission. element to engineering problems such as stress and ordinary differential equations. Direct A candidate for the Eng.Sc.D. degree in civil analysis, heat transfer, fluid flow, and electromagnetics. stiffness approach for trusses. Strong and engineering must register for 12 points of doctoral Topics include finite element formulation for one- weak forms for one-dimensional problems. research instruction. Registration in CIEN E9800 dimensional problems, such as trusses, electrical Galerkin finite element formulation, shape may not be used to satisfy the minimum residence and hydraulic systems; scalar field problems in two functions, Gauss quadrature, convergence. requirement for the degree. dimensions, such as heat transfer; and vector field Multidimensional scalar field problems (heat problems, such as elasticity and finally usage of the conduction), triangular and rectangular elements, CIEN E9900x and y–S9900 Doctoral dissertation commercial finite element program. Students taking Isoparametric formulation. Multidimensional 0 pts. Members of the faculty. ENME E3332 cannot take ENME E4332. vector field problems (linear elasticity). Practical A candidate for the doctorate may be required FE modeling with commercial software (ABAQUS). to register for this course every term after the ENME E4113x Advanced mechanics of solids Computer implementation of the finite element student’s coursework has been completed and 3 pts. Lect: 3. Professor Yin. method. Advanced topics. Not open to until the dissertation has been accepted. Stress and deformation formulation in two-and three- undergraduate students. dimensional solids; viscoelastic and plastic material in one and two dimension energy methods. ENME E4363y Multiscale computational COURSES IN ENGINEERING science and engineering MECHANICS ENME E4114y Mechanics of fracture 3 pts. Lect: 3. Professor Fish. and fatigue Prerequisites: ENME E4332, elementary See also Courses in Civil Engineering at 3 pts. Lect: 3. Not offered in 2017–2018. computer programming, linear algebra. the beginning of this section. Prerequisite: Undergraduate mechanics of solids Introduction to multiscale analysis. Information- course. Elastic stresses at a crack; energy and ENME E3105x and y Mechanics passing bridging techniques: among them, stress intensity criteria for crack growth; effect generalized mathematical homogenization 4 pts. Lect: 4. Professors Hone and of plastic zone at the crack; fracture testing theory, the heterogeneous multiscale method, Kougioumtzoglou. applications. Fatigue characterization by stress-life variational multiscale method, the discontinuous Prerequisites: PHYS UN1401 and MATH UN1101, and strain-life; damage index; crack propagation; Galerkin method and the kinetic Monte UN1102, and UN1201. Elements of statics; fail safe and safe life analysis. Carlo–based methods. Concurrent multiscale dynamics of a particle and systems of particles. techniques: domain bridging, local enrichment, EMME E4115y Micromechanics of composite ENME E3106y Dynamics and vibrations and multigrid-based concurrent multiscale materials 3 pts. Lect: 2. Professor Smyth. methods. Analysis of multiscale systems. 3 pts. Lect: 3. Professor Yin.

ENGINEERING 2017–2018 ENME E6215y Principles and applications of swelling, fracture, or liquefaction. These students with instructor’s permission. Review of 99 sensors for structural health monitoring coupling phenomena are important for numerous continuum mechanics in Cartesian coordinates; 3 pts. Lect: 2.5. Lab: 0.5. Professor Feng. disciplines, including geophysics, biomechanics, tensor calculus and the calculus of variation; large Prerequisite: ENME E4215. Concepts, principles, and material sciences. Fundamental principles of deformations in curvilinear coordinates; electricity and applications of various sensors for sensing poromechanics essential for engineering practice problems and applications. structural parameters and nondestructive and advanced study on porous media. Topics evaluation techniques for subsurface inspection, include balance principles, Biot’s poroelasticity, ENME E8320x Viscoelasticity and plasticity data acquisition, and signal processing mixture theory, constitutive modeling of path 4 pts. Lect: 3. Professor Dasgupta. techniques. Lectures, demonstrations, and independent and dependent multiphase Prerequisite: ENME E6315 or equivalent, or hands-on laboratory experiments. materials, numerical methods for parabolic and instructor’s permission. Constitutive equations hyperbolic systems, inf-sup conditions, and of viscoelastic and plastic bodies. Formulation ENME E6216y Structural health monitoring common stabilization procedures for mixed and methods of solution of the boundary value, 3 pts. Lect: 3. Professor Betti. finite element models, explicit and implicit time problems of viscoelasticity and plasticity. Prerequisites: ENME E4215 and ENME integrators, and operator splitting techniques for E4332. Principles of traditional and emerging ENME E8323y Nonlinear vibrations poromechanics problems. sensors, data acquisition and signal processing 3 pts. Lect: 2.5. Not offered in 2017–2018. techniques, experimental modal analysis (input- ENME E6333y Finite element analysis, II Prerequisite: ENME E4215 or equivalent. Free output), operational modal analysis (output- 3 pts. Lect: 3. Professor Waisman. and forced motion of simple oscillators with only), model-based diagnostics of structural Prerequisite: ENME E4332. FE formulation nonlinear damping and stiffness. Exact, perturbation, integrity, long-term monitoring and intelligence for beams and plates. Generalized eigenvalue iteration, and graphical methods of solution. maintenance. Lectures and demonstrations, problems (vibrations and buckling). FE Stability of motion. Chaotic vibrations. hands-on laboratory experiments. formulation for time-dependent parabolic and hyperbolic problems. Nonlinear problems, ENME E6220y Random processes in linearization, and solution algorithms. Geometric COURSES IN GRAPHICS mechanics and material nonlinearities. Introduction to 3 pts. Lect: 3. Professor Kougioumtzoglou. GRAP E2005y Computer-aided engineering continuum mechanics. Total and updated Prerequisites: CIEN E4111 and ENME E4215 (or graphics Lagrangian formulations. Hyperelasticity and equivalent). Review of random variables. Random 3 pts. Lect: 1.5. Lab: 2.5. Not offered in 2017–2018. plasticity. Special topics: fracture and damage process theory: stationary and ergodic processes, Prerequisite: MATH UN1101. Basic concepts mechanics, extended finite element method. correlation functions, power spectra. Nonstationary needed to prepare and understand engineering and non-Gaussian processes. Linear random ENME E6364x Nonlinear computational drawings and computer-aided representations: vibration theory. Crossing rates, peak distributions, mechanics preparation of sketches and drawings, and response analysis of nonlinear structures to 3 pts. Lect: 3. Not offered in 2017–2018. preparation and transmission of graphic random loading. Major emphasis on simulation of Prerequisites: ENME E4332 or equivalent, information. Lectures and demonstrations, hands- various types of random processes. Monte Carlo elementary computer programming, linear on computer-aided graphics laboratory work. Term simulation. algebra. The formulations and solution strategies project. for finite element analysis of nonlinear problems ENME E6315x Theory of elasticity are developed. Topics include the sources of GRAP E4005x Computer graphics in 3 pts. Lect: 2.5. Not offered in 2017–2018. nonlinear behavior (geometric, constitutive, engineering Foundations of continuum mechanics. General boundary condition), derivation of the governing 3 pts. Lect: 3. Professor Dasgupta. theorems of elasticity. Application to stress analysis discrete equations for nonlinear systems such Prerequisites: Any programming language and and wave propagation. as large displacement, nonlinear elasticity, rate linear algebra. Numerical and symbolic (algebraic) ENME E6320x Computational poromechanics independent and dependent plasticity and other problem solving with Mathematica. Formulation 3 pts. Lect: 3. Not offered in 2017–2018. nonlinear constitutive laws, solution strategies for graphics application in civil, mechanical, and Prerequisite: ENME E3332 or instructor’s for nonlinear problems (e.g., incrementation, bioengineering. Example of two-and three-dimen- permission. A fluid infiltrating porous solid is a iteration), and computational procedures for large sional curve and surface objects in C++ multiphase material whose mechanical behavior systems of nonlinear algebraic equations. and Mathematica; special projects of interest to is significantly influenced by the pore fluid. electrical and computer science. ENME E8310y Advanced continuum Diffusion, advection, capillarity, heating, cooling, mechanics and freezing of pore fluid, buildup of pore 3 pts. Lect: 3. Professor Dasgupta. pressure, and mass exchanges among solid and Prerequisites: MECE E6422 and E6423. This fluid constituents all influence the stability and course is open to Ph.D. students and to M.S. integrity of the solid skeleton, causing shrinkage,

ENGINEERING 2017–2018 100 COMPUTER ENGINEERING PROGRAM Administered by both the Electrical Engineering and Computer Science Departments through a joint Computer Engineering Committee. Student records are kept in the Electrical Engineering Department.

1300 S. W. Mudd, MC 4712 450 Computer Sciences Phone: 212-854-3105 compeng.columbia.edu

IN CHARGE Martha A. Kim, Simha Sethumadhavan, Charles A. Zukowski Associate Professor of Computer Science Associate Professor of Computer Science 1026 CEPSR Vishal Misra, Kenneth L. Shepard, Professor of Computer Science Professor of Electrical Engineering and COMPUTER ENGINEERING COMMITTEE Steven M. Nowick, Biomedical Engineering Luca Carloni, Professor of Computer Science Stephen H. Unger, Associate Professor of Computer Science Daniel Rubenstein, Professor Emeritus of Computer Science Stephen A. Edwards, Associate Professor of Computer Science and Electrical Engineering Associate Professor of Computer Science Mingoo Seok, Charles A. Zukowski, Xiaofang Fred Jiang, Assistant Professor of Electrical Professor of Electrical Engineering Assistant Professor of Electrical Engineering Gil Zussman, Engineering Associate Professor of Electrical Engineering

he computer engineering embedded system (CSEE W4840) as the Computer Science Department’s program is run jointly by the (including both software and hardware advanced programming course. T Computer Science and Electrical components), or providing hands-on Detailed lists of requirements can be Engineering departments. It offers both experience in designing and using a found at compeng.columbia.edu. B.S. and M.S. degrees. computer network (CSEE W4140). Students will be prepared to work The program covers some of Students in the programs have two on all aspects of the design of digital engineering’s most active, exciting, “home” departments. The Electrical hardware, as well as on the associated and critical areas, which lie at the Engineering Department maintains software that is now often an integral interface between CS and EE. The student records and coordinates part of computer architecture. They will focus of the major is on computer advising appointments. also be well equipped to work in the systems involving both digital growing field of telecommunications. hardware and software. UNDERGRADUATE PROGRAM Students will have the prerequisites to Some of the key topics covered delve more deeply into either hardware This undergraduate program are computer design (i.e., computer or software areas, and enter graduate incorporates most of the core curricula architecture); embedded systems (i.e., programs in computer science, in both electrical engineering and the design of dedicated hardware/ electrical engineering, or computer computer science so that students software for cell phones, automobiles, engineering. For example, they could will be well prepared to work in the robots, games, and aerospace); digital take more advanced courses in VLSI, area of computer engineering, which and VLSI circuit design; computer communications theory, computer substantially overlaps both fields. Both networks; design automation (i.e., architecture, electronic circuit theory, hardware and software aspects of CAD); and parallel and distributed software engineering, or digital design. computer science are included, and, systems (including architectures, Minors in electrical engineering and in electrical engineering, students programming, and compilers). computer science are not open to receive a solid grounding in circuit The undergraduate major includes computer engineering majors, due to theory and in electronic circuits. The one substantial senior design excessive overlap. program includes several electrical course, either designing an entire engineering laboratory courses as well microprocessor (EECS E4340), or an

ENGINEERING 2017–2018 101 COMPUTER ENGINEERING PROGRAM: FIRST AND SECOND YEARS EARLY-STARTING STUDENTS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

APMA E2000 (4)3 MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) APMA E2101 (3)1

UN1401 (3) UN1402 (3) Lab UN1493 (3) or chem. lab UN1500 (3)

PHYSICS UN1601 (3.5) UN1602 (3.5) Lab UN1493 (3) or (three tracks, choose one) chem. lab UN1500 (3) UN2801 (4.5) UN2802 (4.5) Lab UN3081 (2) or chem. lab UN1500 (3)

one-semester lecture (3–4) UN1403 or UN1404 or UN2045 or UN1604 CHEMISTRY Lab UN1500 (3) either semester or physics lab UN1493 (3)

COMS W3134 (3) or W3137 (4) CORE REQUIRED ELEN E1201 (3.5) ELEN E3801 (3.5) Data structures COURSES Intro. to elec. eng. (either semester) Signals and systems CSEE W3827 (3) Fund. of computer sys.

ELEN E3084 (1) ELEN E3082 (1) REQUIRED LABS Signals and systems lab Digital systems lab

UNIVERSITY UN1010 (3) either semester WRITING

HUMA CC1001, HUMA CC1002, COCI CC1101, COCI CC1102, REQUIRED or Global Core (3–4) or Global Core (3–4) NONTECHNICAL ELECTIVES2 HUMA UN1121 or ECON UN1105 (4) and UN1123 (3) UN1155 recitation (0)

COMS W1004 (3) or COMS W3203 (3) COMPUTER ENGI E1006 (3) SCIENCE W1007 (3) Discrete math.

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 APMA E2101 may be replaced by MATH UN2030 (formerly MATH E1210) and either APMA E3101, or MATH UN2010, or COMS W3251. 2 Some of these courses can be postponed to the junior or senior year to make room for taking the required core computer engineering courses. 3 Effective Class of 2021.

ENGINEERING 2017–2018 102 COMPUTER ENGINEERING: THIRD AND FOURTH YEARS EARLY-STARTING STUDENTS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

ELEN E3331 (3) Electronic circuits COMS W4118 (3) Operating systems IEOR E3658 (3) or Probability COMS W3261 (3) COMS W4115 (3) Programming lang. Computer sci. theory CORE REQUIRED COMS W3157 (4) COURSES Advanced programming (Choose 3 of 6)2 ELEN E3201 (3.5) CSEE W4119 (3) Computer networks, EECS E4321 (3) Digital VLSI circuits, CSEE Circuit analysis W4823 (3) Advanced logic design, CSEE W4824 (3) Computer architecture, CSEE W4840 (3) Embedded systems, CSEE W4868 (3) System-on-chip platforms

ELEN E3081 (1) ELEN E3083 (1) REQUIRED LABS Circuit analysis lab Electronic circuits lab

TECH 15 points required; see details below

Complete 27-point requirement; see page 10 or seas.columbia.edu for details NONTECH (administered by the advising dean) ELECTIVES

TOTAL POINTS1 17.5 17 15 15

For a discussion about programming languages used in the program, please see compeng.columbia.edu. Check the late-starting student chart for footnotes about various courses. 1 “Total points” assumes that 20 points of nontechnical electives and other courses are included. 2 Class of 2017 and 2018 students can follow new requirements or continue following requirements outlined in their entry year.

Technical Electives Starting Early prepared to work (or study further) in The Computer Engineering Program Students are strongly encouraged to such fields as digital computer design, includes 15 points of technical begin taking core computer engineering digital communications, and the design electives. Any 3000-level or higher courses as sophomores. They start of embedded computer systems. courses listed in the Computer with ELEN E1201: Introduction to Applicants are generally expected to Science or Electrical Engineering electrical engineering in the second have a bachelor’s degree in computer sections of this bulletin can be used semester of their first year and may engineering, computer science, or for this requirement with the following continue with other core courses electrical engineering with at least a 3.2 exceptions: COMS W3101, W3251, one semester after that. For sample GPA in technical courses. The Graduate courses used for other computer “early-starting” and “late-starting” Record Examination (GRE), General Test engineering requirements and courses programs, see the degree track charts. only, is required of all applicants. that have significant overlap with It must be emphasized that these Students must take at least 30 points other required or elective courses charts present examples only; actual of courses at Columbia University at or (e.g., COMS W3134 and W3137), and schedules may be customized in above the 4000 level. These must include courses with significant amounts of consultation with academic advisers. at least 15 points from the courses nontechnical content such as EEHS listed below that are deemed core to E3900. Courses at the 3000 level or computer engineering. Other courses GRADUATE PROGRAM higher in other areas of engineering, may be chosen with the prior approval The Computer Engineering Program math, and science can be considered of a faculty adviser in the Computer offers a course of study leading to the for approval, as long as they do not Engineering Program. degree of Master of Science (M.S.). significantly overlap with other required The basic courses in the M.S. program or elective courses. Economics come from the Electrical Engineering courses cannot be used as technical and Computer Science Departments. electives. Students completing the program are

ENGINEERING 2017–2018 103 COMPUTER ENGINEERING PROGRAM: FIRST AND SECOND YEARS LATE-STARTING STUDENTS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

APMA E2000 (4)3 MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) APMA E2101 (3)1

UN1401 (3) UN1402 (3) Lab UN1493 (3) or chem. lab UN1500 (3)

PHYSICS UN1601 (3.5) UN1602 (3.5) Lab UN1493 (3) or (three tracks, choose one) chem. lab UN1500 (3) UN2801 (4.5) UN2802 (4.5) Lab UN3081 (2) or chem. lab UN1500 (3)

one-semester lecture (3–4) UN1403 or UN1404 or UN2045 or UN1604 CHEMISTRY Lab UN1500 (3) either semester or physics lab UN1493 (3)

CORE REQUIRED ELEN E1201 (3.5)2 COURSES Intro. to elec. eng. (either semester)

UNIVERSITY UN1010 (3) either semester WRITING

HUMA CC1001, HUMA CC1002, COCI CC1101, COCI CC1102, REQUIRED or Global Core (3–4) or Global Core (3–4) NONTECHNICAL ELECTIVES HUMA UN1121 or ECON UN1105 (4) and UN1123 (3) UN1155 recitation (0)

COMS W1004 (3) or W3203 (3) COMPUTER ENGI E1006 (3) SCIENCE W1007 (3) Discrete math.

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 APMA E2101 may be replaced by MATH UN2030 (formerly MATH E1210) and either APMA E3101, or MATH UN2010, or COMS W3251. 2 Transfer and combined-plan students are expected to have completed the equivalent of the first- and second-year program listed above before starting their junior year. Note that this includes some background in discrete math (see COMS W3203) and electronic circuits (see ELEN E1201). Transfer and combined-plan students are also expected to be familiar with Java before they start their junior year. If students must take the one-point Java course (COMS W3101-03) junior year, prerequisite constraints make it difficult to complete the remaining computer engineering program by the end of the senior year. 3 Effective Class of 2021.

ENGINEERING 2017–2018 104 COMPUTER ENGINEERING: THIRD AND FOURTH YEARS LATE-STARTING STUDENTS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

COMS W4118 (3) Operating systems IEOR E3658 (3)1 COMS W3157 (4) or Probability Advanced programming COMS W4115 (3) Programming lang. COMS W3134 (3) or ELEN E3331 (3) W3137 (4) Electronic circuits Data structures CORE REQUIRED (Choose 3 of 6)6 COURSES COMS W3261 (3)2 CSEE W4119 (3) Computer networks, EECS E4321 ELEN E3201 (3.5) Models of comp. (3) Digital VLSI circuits, CSEE W4823 (3) Advanced Circuit analysis logic design, CSEE W4824 (3) Computer architecture, CSEE W3827 (3) CSEE W4840 (3) Embedded systems, CSEE W4868 ELEN E3801 (3.5) Fund. of computer (3) System-on-chip platforms Signals and systems systems

ELEN E3081 (1)3 ELEN E3083 (1)3 Circuit analysis lab Electronic circuits lab REQUIRED LABS ELEN E3084 (1)3 ELEN E3082 (1)3 Signals and systems lab Digital systems lab

TECH 15 points required; see details on page 103

Complete 27-point requirement; see page 10 or seas.columbia.edu for details NONTECH (administered by the advising dean) ELECTIVES

TOTAL POINTS5 15 18 15 18

For a discussion about programming languages used in the program, please see compeng.columbia.edu. 1 SIEO W3600, STAT GU4203, and STAT GU4001 can be used instead of IEOR E3658, but W3600 and GU4001 may not provide enough probability background for elective courses such as ELEN E3701. Students completing an economics minor who want such a background can take IEOR E3658 and augment it with IEOR E4307. 2 COMS W3261 can be taken one semester later than pictured. 3 If possible, ELEN E3081 and ELEN E3084 should be taken along with ELEN E3201 and ELEN 3801 respectively, and ELEN E3083 and ELEN E3082 taken with ELEN E3331 and CSEE W3827 respectively. 4 The total points of technical electives is reduced to 12 if APMA E2101 has been replaced by MATH UN2030 (formerly MATH E1210) and either APMA E3101 or MATH UN2010, or COMS W3251. 5 Assuming technical electives taken Semesters VII and VIII, and 9 points of nontechnical electives taken Semesters VI, VII, and VIII. 6 Class of 2017 and 2018 students can follow new requirements or continue following requirements outlined in their entry year.

Core Computer Engineering Courses EECS E6765: Internet of things—sys. & physical The overall program must include at CSEE W4119: Computer networks data analytics least 12 points of 6000-level ELEN, CSEE W4140: Networking laboratory CSEE E6824: Parallel computer architecture EECS, CSEE, or COMS courses CSEE E6861: CAD of digital systems EECS E4321: Digital VLSI circuits (exclusive of seminars). No more than 9 CSEE E6863: Formal verification of hardware/ EECS E4750: Hybrid comp. for sig. & data proc. points of research project may be taken EECS E4764: Iot—intelligent & connected sys. software systems for credit. No more than 3 points of a CSEE W4823: Advanced logic design CSEE E6868: Embedded scalable platforms CSEE W4824: Computer architecture nontechnical elective (at or above the CSEE W4840: Embedded systems 4000 level and with adviser approval) CSEE W4868: Systems-on-chip platforms may be included. A minimum GPA of EECS E4951: Wireless networks & systems at least 2.7 must be maintained, and all EECS E6180: Modeling & performance eval degree requirements must be completed EECS E6321: Adv. digital electronic circuits within five years of the beginning of the EECS E6322: VLSI hard. arch. for sig. proc. & ml first course credited toward the degree.

ENGINEERING 2017–2018 COMPUTER SCIENCE 105 450 Computer Science, MC 0401 Phone: 212-939-7000 cs.columbia.edu

CHAIR PROFESSORS ASSOCIATE Carl Vondrick Henryk Wozniakowski** Julia B. Hirschberg Alfred V. Aho PROFESSORS Omri Weinstein Yechiam Yemini** 450 Computer Science Peter K. Allen Alexandr Andoni Eugene Wu 212-939-7004 Peter N. Belhumeur Luca Carloni Changxi Zheng Steven M. Bellovin Xi Chen SPECIAL RESEARCH VICE CHAIR David Blei Stephen A. Edwards SENIOR LECTURER IN SCIENTIST Rocco A. Servedio Michael J. Collins Roxana Geambasu DISCIPLINE Henryk Wozniakowski** 512 Computer Science Steven K. Feiner Eitan Grinspun Adam Cannon 212-939-7065 Luis Gravano Tony Jebara Jae Woo Lee SENIOR RESEARCH Julia B. Hirschberg Angelos D. Keromytis SCIENTIST DIRECTOR OF Gail E. Kaiser Martha Allen Kim LECTURER IN DISCIPLINE Moti Yung UNDERGRADUATE John R. Kender Tal Malkin Ansaf Salleb-Aouissi STUDIES Kathleen R. McKeown Itsik Pe’er Daniel Bauer RESEARCH SCIENTIST Paul Blaer Vishal Misra Daniel S. Rubenstein Paul Blaer Smaranda Muresan* 703 CEPSR Shree Kumar Nayar Simha Sethumadhavan Nakul Verma Owen Rambow* 212-939-7034 Jason Nieh Junfeng Yang Steven M. Nowick ASSOCIATED FACULTY ASSOCIATE RESEARCH DIRECTOR OF Christos Papadimitriou ASSISTANT Shih-Fu Chang SCIENTISTS FINANCE AND Kenneth A. Ross PROFESSORS Matei Ciocarlie Giuseppe Di Guglielmo ADMINISTRATION Henning G. Schulzrinne Allison Breton Bishop Eleni Drinea Hiroshi Sasaki Maria Joanta Rocco A. Servedio Augustin Chaintreau Edward G. Coffman Jr.** Eran Tromer Salvatore J. Stolfo Lydia Chilton Jonathan L. Gross** Jeannette Wing Yaniv Erlich Andreas Mueller Mihalis Yannakakis Ronghui Gu Clifford Stein *Data Science Institute Daniel Hsu Steven H. Unger** **Professor Emeritus Suman Jana Vladimir Vapnik

he function and influence of computational complexity and the and business process servers, a large the computer is pervasive analysis of algorithms, combinatorial Linux computer cluster and a number T in contemporary society. methods, computer architecture, of computing facilities for individual Today’s computers process the daily computer-aided digital design, research labs. In addition, the data transactions of international banks, the computer communications, databases, center houses a computer cluster data from communications satellites, the mathematical models for computation, consisting of a Linux cloud with more images in video games, and even the optimization, and software systems. than 20 servers each with 12 cores and fuel and ignition systems of automobiles. 128GB memory. This cloud can support Computer software is as Laboratory Facilities thousands of VMware instances. commonplace in education and The department has well-equipped lab The labs for research in image recreation as it is in science and areas for research in computer graphics, processing, vision, graphics, and business. There is virtually no field or computer-aided digital design, computer robotics contain specialized equipment profession that does not rely upon vision, databases and digital libraries, such as Baxter Research Robot, PR2 computer science for the problem- data mining and knowledge discovery, mobile robot manipulator, Staubli solving skills and the production distributed systems, mobile and RX-60L Robot arm, Kinova, MICO expertise required in the efficient wearable computing, natural-language arm, custom-built overhead XYZ gantry processing of information. Computer processing, networking, operating robot, Toshiba FMA manipulator, Barrett scientists, therefore, function in a wide systems, programming systems, Technology robotic hand, 2 RWI Pioneer variety of roles, ranging from pure robotics, user interfaces, real-time mobile robots, 1 Evolution ER-1 robot, theory and design to programming and multimedia, and speech research. 1 RWI ATRV-2 mobile robot with RTK marketing. The computer facilities include GPS, Leica HDS-500 and HDS-3000 The computer science curriculum a shared infrastructure of Linux 100 meter range scanners, and real- at Columbia places equal emphasis multiprocessor servers, NetApp file time Imaging boards; a networking on theoretical computer science and servers providing more than 300 testbed with Cisco backbone routers, mathematics and on experimental terabytes of storage space, several traffic generators; an IDS testbed computer technology. A broad range high-end graphics workstations for with secured LAN, Cisco routers, of upper-level courses is available in teaching and research purposes, a load EMC storage, and Linux servers; a such areas as artificial intelligence, balanced web cluster with 8 servers simulation testbed with several Linux

ENGINEERING 2017–2018 106 COMPUTER SCIENCE PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) APMA E2000 (4)1

PHYSICS UN1401 (3) UN1402 (3) (three tracks, UN1601 (3.5) UN1602 (3.5) Chemistry or physics lab: choose one) UN2801 (4.5) UN2802 (4.5) PHYS UN1493 (3) or PHYS UN3081 (2) or CHEM UN1500 (3) or CHEMISTRY/ CHEM UN1403 (3) or higher or CHEM UN1507 (3) or BIOLOGY EEEB UN2001 (4) or UN2005 (4) or higher CHEM UN3085 (4) (choose one course) either semester

UNIVERSITY UN1010 (3) either semester WRITING

ECON UN1105 (4) and UN1105 recitation (0) any semester

HUMA CC1002 or REQUIRED COCI CC1102 or NONTECHNICAL ELECTIVES HUMA CC1001 or Major Cultures (3–4) COCI CC1101 or Major Cultures (3–4) HUMA UN1121 or UN1123 (3)

REQUIRED ENGI E1006 Computing for EAS (3) either semester TECH ELECTIVES

COMS W1004 (3) COMS W3134 (3) or COMS W3157 (4) Intro. to computer science COMS W3137 (4) Adv. programming COMPUTER or Data structures and SCIENCE COMS W1007 (3) and CSEE W3827 (3) Object-oriented programming COMS W3203 (3) Fund. of computer either semester Discrete math systems

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 Effective Class of 2021.

servers and Cisco Catalyst routers. UNDERGRADUATE PROGRAM program. Undergraduate students The department uses a SIP IP phone Computer science majors at Columbia are often involved in advanced faculty system. The protocol was developed in study an integrated curriculum, research projects using state-of-the-art the department. partially in areas with an immediate computing facilities. Qualified majors The department’s computers are relationship to the computer, such as sometimes serve as consultants connected via a switched 1 Gb/s programming languages, operating at Columbia University Information Ethernet network, which has direct systems, and computer architecture, Technology (CUIT), which operates connectivity to the campus OC-3 and partially in theoretical computer several computer labs at convenient Internet and Internet2 gateways. The science and mathematics. Thus, locations on the campus. campus has 802.11b/g wireless LAN students obtain the background Upper-level students in computer coverage. to pursue their interests both in science may assist faculty members The research facility is supported by applications and in theoretical with research projects, particularly a full-time staff of professional system developments. in the development of software. administrators and programmers. Practical experience is an essential Ongoing faculty projects include component of the computer science algorithmic analysis, computational

ENGINEERING 2017–2018 107 COMPUTER SCIENCE: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

APMA E2101 (3) or MATH UN2010 (3) and COMS W3261 (3) REQUIRED Computer sci. theory COURSES and STAT GU4001 (3) or IEOR E4150 (3) Prob. and stat.

NONTECH 3 points 6 points 3 points

TECH 6 points 12 points 9 points 9 points ELECTIVES

TOTAL POINTS 15–16 15 15 12

The primary programming languages for the undergraduate major are Python, C, and Java, and students are expected to learn all three at an early stage. The language for COMS W1004-W3134 and COMS W1007-3137 is Java. COMS W1004 may be waived for students who have scored 4 or 5 on the AP computer science A exam. complexity, software tool design, (cs.columbia.edu/education/undergrad) 3000 level or above and in mathematics, distributed computation, modeling and and the Quick Guide (cs.columbia.edu science, engineering or closely related performance evaluation, computer /education/undergrad/seasguide). disciplines. networks, computer architecture, CAD Students who pass the Computer for digital systems, computer graphics, Technical Electives Science Advanced Placement (AP) Exam programming environments, expert Students are encouraged to select with a 4 or 5 will receive 3 points of credit systems, natural language processing, one of the following six preapproved and exemption from COMS W1004. computer vision, robotics, computational groupings of electives called “tracks.” Note: A maximum of one course biology, computer security, An advanced version of each track worth no more than 4 points passed multicomputer design, user interfaces, is available by invitation for qualified with a grade of D may be counted VLSI applications, artificial intelligence, students who wish an extra opportunity toward the major or minor. combinatorial modeling, virtual for advanced learning. environments, and microprocessor An additional 15 points of adviser- Track 1: Foundations of CS Track applications. Students are strongly approved technical elective points The foundations track is suitable encouraged to arrange for participation beyond those used to satisfy the track for students who are interested in by consulting individual faculty members requirements are also required. algorithms, computational complexity, and by attending the Computer Science The following courses are required and other areas of theoretical Computer Research Fair held at the beginning of as a preparation for all tracks: COMS Science. Register for track course each semester. W1004 or W1007, W3134 or W3137, COMS E0001. Most graduates of the computer W3157, W3203, W3261, MATH REQUIRED: 6 points science program at Columbia step UN2010 or UN2020 or APMA E2101 directly into career positions in computer CSOR W4231: Analysis of algorithms or E3101, CSEE W3827, and STAT COMS W4236: Introduction to computational science with industry or government, GU4001 (IEOR E4150 is an acceptable complexity or continue their education in graduate substitute for GU4001). Collectively ELECTIVES: 15 points from the following list: degree programs. Many choose to these courses are called the CS Core MATH UN3020: Number theory and cryptography combine computer science with a Curriculum. In addition, all students second career interest by taking MATH UN3025: Making, breaking codes are required to take ENGI E1006 COMS W3902: Undergraduate thesis* additional programs in business Introduction to computing for engineers COMS W3998: Projects in Computer Science* administration, medicine, or other and applied scientists in their first year. COMS W4203: Graph theory professional studies. All technical electives except those MATH GU4032: Fourier analysis For further information on the noted in each track must be approved MATH GU4041: Introduction to modern algebra I undergraduate computer science by the faculty adviser. Technical electives MATH GU4042: Introduction to modern algebra II MATH GU4061: Introduction to modern analysis I program, please see the home page not noted in the track must be at the

ENGINEERING 2017–2018 108 MATH GU4155: Probability theory * With adviser approval, may be repeated for credit COMS W4170: User interface design COMS W4252: Computational learning theory Note: No more than 6 units of project/thesis courses ELECTIVES: 15 points from the following list: COMS W4261: Introduction to cryptography (COMS W3902, W3998, W4901) can count toward APMA E4300: Numerical methods COMS W3902: Undergraduate thesis* the track. IEOR E4407: Game theoretic models of operation COMS W3998: Undergraduate projects in computer PHIL GU4431: Set theory science* CSPH GU4801: Mathematical logic I Track 3: Intelligent Systems Track Any COMS W41xx course CSPH GU4802: Mathematical logic II: The intelligent systems track is for Any COMS W47xx course COMS W4901: Projects in computer science* incompleteness students interested in machine learning, COMS W4995-W4996: Special topics in computer COMS W4901: Projects in computer science* robots, and systems capable of COMS W4995: Special topics in computer science, I* science, I and II (with adviser exhibiting “human-like” intelligence. A COMS E6232: Analysis of algorithms, II approval) MATH GR6238: Enumerative combinatorics total of seven required breadth and Any COMS E69xx course (with adviser approval) COMS E6253: Advanced topics in computational elective courses are to be chosen from * With adviser approval, may be repeated for credit learning theory the following schedule. Register for track COMS E6261: Advanced cryptography course COMS E0003. Note: No more than 6 units of project/thesis IEOR E6400: Scheduling: deterministic models courses (COMS W3902, W3998, W4901) can IEOR E6603: Combinatorial optimization REQUIRED: 9 Points from: count toward the track. IEOR E6606: Advanced topics in network flows COMS W4701: Artificial intelligence IEOR E6608: Integer programming COMS W4705: Natural language processing Track 5: Vision, Interaction, Graphics, IEOR E6610: Approximation algorithms COMS W4706: Spoken language processing and Robotics Track EEOR E6616: Convex optimization COMS W4731: Computer vision The vision, interaction, graphics, and IEOR E6613: Optimization I (4.5) COMS W4733: Computational aspects of robotics IEOR E6614: Optimization II (4.5) COMS W4771: Machine learning robotics track exposes students to IEOR E6711: Stochastic models I interesting new fields and focuses on ELECTIVES: 12 points required IEOR E6712: Stochastic models II visual information with topics in vision, Up to 12 points from the following list: ELEN E6717: Information theory graphics, human-computer interaction, ELEN E6718: Algebraic coding theory Any COMS W40xx course with adviser approval COMS W4165: Pixel processing robotics, modeling, and learning. ELEN E6970: Resource allocation and networking Students learn about fundamental ways games COMS W4252: Computational learning theory in which visual information is captured, COMS E6998: Topics in computer science* Any COMS W47xx course if not used as a required course manipulated, and experienced. Register * With adviser approval, may be repeated for credit COMS W4995: Special topics, I* for track course COMS E0005. COMS W4996: Special topics, II* Note: No more than 6 units of project/thesis REQUIRED: 6 points from: courses (COMS W3902, W3998, W4901) can Any COMS W67xx course COMS W4160: Computer graphics count toward the track. COMS E6998: Topics in computer science, I (with adviser approval) COMS W4731: Computer vision Students who declared their Computer Science COMS E6999: Topics in computer science, II (with COMS W4167: Computer animation major prior to Fall 2016 may also count COMS adviser approval) W4241, W4205, W4281, W4444, W4771, and ELECTIVES: 15 points from the following list: W4772 as elective courses. Up to 6 points from the following list: COMS W3902: Undergraduate thesis* COMS W3902: Undergraduate thesis* COMS W3998: Undergraduate projects in COMS W3998: Undergraduate projects in computer computer science* Track 2: Software Systems Track science* COMS W4162: Advanced computer graphics The software systems track is for COMS W4901: Projects in computer science* COMS W4165: Pixel processing students interested in networks, COMS W4167: Computer animation Up to 3 points from the following list: programming languages, operating COMS W4170: User interface design systems, and software systems. COMS W4111: Database systems COMS W4172: 3D user interface design COMS W4160: Computer graphics Register for track course COMS E0002. COMS W4701: Artificial intelligence COMS W4170: User interface design COMS W4733: Computational aspects of robotics REQUIRED: 9 points COMS W4999: Computing and the humanities COMS W4735: Visual interfaces to computers COMS W4115: Programming languages and * With adviser approval, may be repeated for credit COMS W4771: Machine learning translators COMS W4901: Projects in computer science* COMS W4118: Operating systems Note: No more than 6 units of project/thesis COMS W4995: Video game technology and design CSEE W4119: Networking courses (COMS W3902, W3998, W4901) can COMS W4995-W4996: Special topics in computer count toward the track. science, I and II (with adviser ELECTIVES: 12 points from the following list: approval) COMS W3902: Undergraduate thesis* Track 4: Applications Track Any COMS E691x course (with adviser approval) COMS W3998: Undergraduate projects in computer The applications track is for students science* * With adviser approval, may be repeated for credit Any COMS W41xx course interested in the implementation of Note: No more than 6 units of project/thesis COMS W4444: Programming and problem solving interactive multimedia applications for courses (COMS W3902, W3998, W4901) can Any COMS W48xx course the Internet and wireless networks. count toward the track. COMS W4901: Projects in computer science* Register for track course COMS E0004. COMS W4995-W4996: Special topics in computer Track 6: Digital Systems Track science REQUIRED: 6 points Any COMS E61xx or E68xx course (with adviser COMS W4115: Programming languages and The digital systems track is for students approval) translators interested in working at the interface of

ENGINEERING 2017–2018 hardware and software. Subjects include majors in course performance in computer science DUAL DEGREE PROGRAM IN 109 digital design, computer architecture courses will be considered for invitation during the JOURNALISM AND COMPUTER junior year. (A student in the advanced track who (both sequential and parallel) and SCIENCE does not maintain this status may be required to embedded systems. Register for track return to his or her previously selected track area.) The Graduate School of Journalism course COMS E0006. and the School of Engineering and Applied Science offer a dual REQUIRED: 3 points GRADUATE PROGRAMS CSEE W4824: Computer architecture degree program leading to the M.S. The Department of Computer Science degree from the Graduate School of Plus 3 points from: offers graduate programs leading to Journalism and the M.S. degree in EECS E4340: Computer hardware design the degree of Master of Science and Computer Science from the School of CSEE W4823: Advanced logic design the degree of Doctor of Philosophy. Engineering and Applied Science. CSEE W4840: Embedded systems The Graduate Record Examination Admitted students will enroll for Plus 3 points from: (GRE) is required for admission to a total of four semesters consisting COMS W4115: Programming languages and the department’s graduate programs. of 27 points of Computer Science translators Applicants for September admission coursework in addition to the COMS W4118: Operating systems should take the GREs by October of the Journalism requirements. In addition COMS W4130: Parallel programming preceding year. Applicants for January to taking classes already offered at the ELECTIVES: 12 points from the following list: admission should take these exams by journalism and engineering schools, COMS W3902: Undergraduate thesis April of the preceding year. students will attend a seminar and COMS E3998: Undergraduate projects in computer The course requirements in all workshop designed specifically for science programs are flexible, and each student the joint program. The seminar will Any COMS/CSEE W41xx course is urged to design his or her own teach students about the impact of Any COMS/CSEE W48xx course COMS E4901: Projects in computer science program under the guidance of a faculty digital techniques on journalism; the CSEE E6824: Parallel computer architecture* adviser. The student’s program should emerging role of citizens in the news CSEE E6827: Distributed embedded systems* focus on a particular field of computer process; the influence of social media; CSEE E6861: CAD of digital systems* science. Among the fields of graduate and the changing business models CSEE E6868: System-on-chip platforms study in computer science are analysis that will support newsgathering. In the * With adviser approval, may be repeated for credit of algorithms, artificial intelligence, workshop, students will use a hands- on approach to delve deeply into Note: No more than 6 units of project/thesis expert systems, natural language courses (COMS W3902, W3998, W4901) can understanding, computer vision, information design, focusing on how count toward the track. multicomputer design, VLSI applications, to build a site, section, or application combinatorial modeling, combinatorial from concept to development, Track 7: Advanced optimization, computational complexity, ensuring the editorial goals are kept The advanced track of the B.S. in computer architecture and design, uppermost in mind. Computer Science provides extra computer communications networks, opportunity for advanced learning. computer graphics, database machines COURSES IN COMPUTER It comprises accelerated versions of and systems, microprocessors, SCIENCE parallel computation, programming the other six tracks. Entry is only by In the listing below, the designator environments, programming languages, collective faculty invitation, extended to COMS (Computer Science) is robotics, user interfaces, software students who have already completed understood to precede all course design, computational biology, computer the core courses and the required numbers for which no designator is security, and machine learning. courses for one of those tracks. indicated. NOTE: Students may receive Graduate students are encouraged REQUIRED TRACK COURSES credit for only one of the following two actively to pursue research. Faculty A student designates one of the six other track courses: COMS W1004 and W1005. members of the Department of areas and completes the set of required track Likewise, students may receive credit for courses for that track, prior to entry into the Computer Science are engaged in only one of the following three courses: Advanced Track. There are two or three courses, experimental and theoretical research COMS W3134, W3136, or W3137. depending on the designated area. in most of the fields in which courses are offered. The degree of doctor of COMS W1001x or y Introduction to ELECTIVES information science philosophy requires a dissertation based At least 6 points of 4000-level lecture courses 3 pts. Lect: 3. Instructor to be announced. on the candidate’s original research, from the menu for the designated track, plus 6 Basic Introduction to concepts and skills points of 6000-level courses in the designated which is supervised by a faculty member. in Information Sciences: human-computer track area. For information on the M.S. interfaces, representing information digitally, THESIS program, please see cs.columbia.edu/ organizing and searching information on the There is a required 6-point senior thesis. education/MS and for information on World Wide Web, principles of algorithmic the Ph.D. program, see cs.columbia. problem solving, introduction to database INVITATION edu/education/phd. concepts, introduction to programming in Only the top 20 percent of computer science Python.

ENGINEERING 2017–2018 110 COMS W1002x Computing in context undergraduates considering a major in computer programming in UNIX environment, object-oriented 4 pts. Lect: 4. Professor Cannon. science. Pass/fail only. programming in C++, trees, graphs, generic Introduction to elementary computing concepts programming, hash tables. Due to significant ECBM E3060x Introduction to genomic and Python programming with domain-specific overlap, students may only receive credit for either information science and technology applications. Shared CS concepts and Python COMS W3134, W3136, or W3137. 3 pts. Lect: 3. Professor Anastassiou. programming lectures with track-specific Introduction to the information system paradigm of COMS W3137y Honors data structures and sections. Track themes will vary but may include molecular biology. Representation, organization, algorithms computing for the social sciences, computing for structure, function and manipulation of the 4 pts. Lect: 3. Professor Blaer. economics and finance, digital humanities, and biomolecular sequences of nucleic acids and Prerequisite: COMS W1004 or W1007. more. Intended for nonmajors. Students may proteins. The role of enzymes and gene regulatory Corequisite: COMS W3203. An honors introduction receive credit for only one of the following two elements in natural biological functions as well to data types and structures: arrays, stacks, singly courses: ENGI E1006 and COMS W1002. as in biotechnology and genetic engineering. and doubly linked lists, queues, trees, sets, and COMS W1004x and y Introduction to Recombination and other macromolecular graphs. Programming techniques for processing computer science and programming in Java processes viewed as mathematical operations with such structures: sorting and searching, hashing, 3 pts. Lect: 3. Professor Cannon. simulation and visualization using simple computer garbage collection. Storage management. Design A general introduction to computer science for programming. This course shares lectures with and analysis of algorithms. Taught in Java. Note: science and engineering students interested in ECBM E4060, but the work requirements differ Due to significant overlap, students may receive majoring in computer science or engineering. somewhat. credit for only one of the following three courses: COMS W3134, W3136, or W3137. Covers fundamental concepts of computer science, COMS W3101x and y Programming languages algorithmic problem-solving capabilities, and 1 pt. Lect: 1. Members of the faculty. COMS W3157x and y Advanced programming introductory Java programming skills. Assumes Prerequisite: Fluency in at least one programming 4 pts. Lect: 4. Professor Lee. no prior programming background. Columbia language. Introduction to a programming language. Prerequisite: Two terms of programming University students may receive credit for only one Each section is devoted to a specific language. experience. COMS W3134/3137. Recommended: of the following two courses: 1004 and 1005. Intended only for those who are already fluent in Data Structures. C programming language COMS W1005x or y Introduction to computer at least one programming language. Sections may and Unix systems programming. Also covers science and programming in MATLAB meet for one hour per week for the whole term, for Git, Make, TCP/IP networking basics, C++ 3 pts. Lect: 3. Professor Blaer. three hours per week for the first third of the term, fundamentals. or for two hours per week for the first six weeks. A general introduction to computer science COMS W3203x and y Discrete mathematics: May be repeated for credit if different languages concepts, algorithmic problem-solving capabilities, introduction to combinatorics and graph are involved. and programming skills in MATLAB. Assumes theory no prior programming background. Columbia COMS W3102x and y Development 3 pts. Lect: 3. Professors Salleb-Aouissi and University students may receive credit for only one technologies Ouyang. of the following two courses: 1004 and 1005. 1–2 pts. Lect: 2. Lab: 0-2. Members of the Prerequisite: Any introductory course in computer ENGI E1006x and y Introduction to computing faculty. programming. Logic and formal proofs, sequences for engineers and applied scientists Prerequisite: Fluency in at least one and summation, mathematical induction, binomial 3 pts. Lect: 3. Professor Salleb-Aouissi. programming language. Introduction to software coefficients, elements of finite probability, An interdisciplinary course in computing development tools and environments. Each recurrence relations, equivalence relations and intended for first year SEAS students. Introduces section devoted to a specific tool or environment. partial orderings, and topics in graph theory computational thinking, algorithmic problem One-point sections meet for two hours each (including isomorphism, traversability, planarity, solving and Python programming with applications week for half a semester, and two-point sections and colorings). include an additional two-hour lab. in science and engineering. Assumes no prior COMS W3210x or y Scientific computation programming background. COMS W3134x and y Data structures in Java 3 pts. Lect: 3. Instructor to be announced. COMS W1007x Honors introduction to 3 pts. Lect: 3. Professor Blaer. Prerequisites: Two terms of calculus. Introduction computer science Prerequisite: COMS W1004 or knowledge of to computation on digital computers. Design 3 pts. Lect: 3. Professor Kender. Java. Data types and structures: arrays, stacks, and analysis of numerical algorithms. Numerical Prerequisite: AP Computer Science with a grade singly and doubly linked lists, queues, trees, solution of equations, integration, recurrences, of 4 or 5 or similar experience. An honors-level sets, and graphs. Programming techniques chaos, differential equations. Introduction to introduction to computer science, intended for processing such structures: sorting and Monte Carlo methods. Properties of floating point primarily for students considering a major in searching, hashing, garbage collection. Storage arithmetic. Applications to weather prediction, computer science. Computer science as a science management. Rudiments of the analysis of computational finance, computational science, of abstraction. Creating models for reasoning algorithms. Taught in Java. Note: Due to and computational engineering. significant overlap, students may receive credit about and solving problems. The basic elements of COMS W3251x Computational linear algebra for only one of the following three courses: computers and computer programs. Implementing 3 pts. Lect: 3. Professor Papageorgiou. COMS W3134, W3136, or W3137. abstractions using data structures and algorithms. Prerequisites: Two terms of calculus. Taught in Java. COMS W3136y Data structures with C/C++ Computational linear algebra, solution of linear COMS W1404x and y Emerging scholars 4 pts. Lect: 3. Professor Lee. systems, sparse linear systems, least squares, program seminar Prerequisite: COMS W1004, W1005, W1007, eigenvalue problems, and numerical solution of 1 pt. Sem: 1. Professor Cannon. or ENGI E1006. A second programming course other multivariate problems as time permits. intended for nonmajors with at least one semester Corequisite: COMS W1004/1007 or ENGI E1006. COMS W3261x and y Computer science theory of introductory programming experience. Basic Enrollment with instructor permission only. Peer-led 3 pts. Lect: 3. Professor Aho. elements of programming in C and C++, array- weekly seminar intended for first- and second-year Prerequisite: COMS W3203. Corequisites: COMS based data structures, heaps, linked lists, C

ENGINEERING 2017–2018 W3134, W3136, or W3137. Regular languages: SEAS computer science undergraduate students tolerance, distributed transactions, agreement 111 deterministic and nondeterministic finite automata, who include relevant off-campus work experience and commitment, Paxos-based consensus, regular expressions. Context-free languages: as part of their approved program of study. Final MapReduce infrastructures, scalable distributed context-free grammars, push-down automata. report and letter of evaluation may be required. databases. Combines concepts and algorithms Turing machines, the Chomsky hierarchy, and the May not be used as a technical or nontechnical with descriptions of real-world implementations Church-Turing thesis. Introduction to complexity elective. May not be taken for pass/fail credit or at Google, Facebook, Yahoo, Microsoft, theory and NP-completeness. audited. Linkedin, etc. COMS W3410y Computers and society ECBM E4060x Introduction to genomic COMS W4115x and y Programming languages 3 pts. Lect: 3. Professor Bellovin. information and translators Broader impact of computers. Social networks 3 pts. Lect: 3. Professor Anastassiou. 3 pts. Lect: 3. Professor Edwards. Introduction to the information system paradigm of and privacy. Employment, intellectual property, Prerequisites: COMS W3134, W3136, or W3137 molecular biology. Representation, organization, and the media. Science and engineering ethics. (or equivalent), W3261, and CSEE W3827, or structure, function, and manipulation of the Suitable for nonmajors. instructor’s permission. Modern programming biomolecular sequences of nucleic acids and CSEE W3827x and y Fundamentals of proteins. The role of enzymes and gene regulatory languages and compiler design. Imperative, object- computer systems elements in natural biological functions as well oriented, declarative, functional, and scripting 3 pts. Lect: 3. Professors Kim. as in biotechnology and genetic engineering. languages. Language syntax, control structures, Prerequisite: An introductory programming course. Recombination and other macromolecular data types, procedures and parameters, binding, Fundamentals of computer organization and digital processes viewed as mathematical operations with scope, run-time organization, and exception logic. Boolean algebra, Karnaugh maps, basic gates simulation and visualization using simple computer handling. Implementation of language translation and components, flip-flops and latches, counters programming. This course shares lectures with tools including compilers and interpreters. Lexical, and state machines, basics of combinational and ECBM E3060, but the work requirements differ syntactic, and semantic analysis; code generation; sequential digital design. Assembly language, somewhat. introduction to code optimization. Teams implement instruction sets, ALUs, single-cycle and multi- a language and its compiler. cycle processor design, introduction to pipelined COMS W4111x and y Introduction to databases processors, caches, and virtual memory. 3 pts. Lect: 3. Professors Biliris and Wu. COMS W4117x or y Compilers and interpreters Prerequisites: COMS W3134, W3136, or W3137, 3 pts. Lect: 3. Professor Aho. COMS W3902x and y Undergraduate thesis fluency in Java; or instructor’s permission. The Prerequisite: COMS W4115 or instructor’s 1–6 pts. Members of the faculty. fundamentals of database design and application permission. Continuation of COMS W4115, Prerequisite: Agreement by faculty member to development using databases: entity-relationship with broader and deeper investigation into the serve as thesis adviser. An independent theoretical modeling, logical design of relational databases, design and implementation of contemporary or experimental investigation by an undergraduate relational data definition and manipulation language translators, be they compilers or major of an appropriate problem in computer languages, SQL, XML, query processing, physical interpreters. Topics include parsing, semantic science carried out under the supervision of database tuning, transaction processing, security. analysis, code generation and optimization, run- a faculty member. A formal written report is Programming projects are required. time environments, and compiler-compilers. A mandatory and an oral presentation may also programming project is required. be required. May be taken over more than one COMS W4112y Database system term, in which case the grade is deferred until implementation COMS W4118x and y Operating systems, I all 6 points have been completed. Consult the 3 pts. Lect: 2.5. Professor Ross. 3 pts. Lect: 3. Professor Nieh. department for section assignment. Prerequisites: COMS W4111; fluency in Java Prerequisites: CSEE W3827 and knowledge of or C++. CSEE W3827 is recommended. The C and programming tools as covered in W3136, COMS W3995x or y Special topics in principles and practice of building large-scale W3157, or W3101, or instructor’s permission. computer science database management systems. Storage methods 3 pts. Lect: 3. and indexing, query processing and optimization, Design and implementation of operating systems. Prerequisite: Instructor’s permission. Consult the materialized views, transaction processing and Topics include process management, process department for section assignment. Special topics recovery, object-relational databases, parallel and synchronization and interprocess communication, arranged as the need and availability arise. Topics distributed databases, performance considerations. memory management, virtual memory, interrupt are usually offered on a one-time basis. Since Programming projects are required. handling, processor scheduling, device the content of this course changes each time it is management, I/O, and file systems. Case study of COMS W4113x Fundamentals of large-scale offered, it may be repeated for credit. the UNIX operating system. A programming project distributed systems is required. COMS W3998x and y Undergraduate projects 3 pts. Lect: 3. Professor Geambasu. in computer science Prerequisites: COMS W3134, W3136, or CSEE W4119x and y Computer networks 1–3 pts. Members of the faculty. W3137. COMS W3157 or good working 3 pts. Lect: 3. Professor Schulzrinne or Prerequisite: Approval by a faculty member who knowledge of C and C++. COMS W4118 or Rubenstein. agrees to supervise the work. Independent project CSEE W4119. Design and implementation Corequisite: IEOR E4150 or IEOR E3658 or involving laboratory work, computer programming, of large-scale distributed and cloud systems. equivalent. Introduction to computer networks and analytical investigation, or engineering design. Abstractions, design, and implementation the technical foundations of the Internet, including May be repeated for credit, but not for a total of techniques that enable the building of fast, applications, protocols, local area networks, more than 3 points of degree credit. Consult the algorithms for routing and congestion control, department for section assignment. scalable, fault-tolerant distributed systems. Topics include distributed communication security, elementary performance evaluation. COMS E3999x, y or s Fieldwork models (e.g., sockets, remote procedure Several written and programming assignments 1–2 pts. Members of the faculty. calls, distributed shared memory), distributed required. Prerequisites: Obtained internship and approval synchronization (clock synchronization, logical COMS W4130x Principles and practice of from a faculty adviser. May be repeated for credit, clocks, distributed mutex), distributed file parallel programming but no more than 3 total points may be used systems, replication, consistency models, fault 3 pts. Lect: 2.5. Professor Kim. toward the 128-credit degree requirement. Only for

ENGINEERING 2017–2018 112 Prerequisites: Experience in Java, basic geometric modeling with meshes, advanced COMS W4187x or y Security architecture and understanding of analysis of algorithms. COMS image synthesis including ray tracing and global engineering W3134, W3136, or W3137 (or equivalent). illumination, and other topics as time permits. 3 pts. Lect: 3. Professor Bellovin. Principles of parallel software design. Topics Emphasis will be placed both on implementation Prerequisite: COMS W4118; W4180 and/or W4119 include task and data decomposition, load- of systems and important mathematical and recommended. Secure programming. Cryptographic balancing, reasoning about correctness, geometric concepts such as Fourier analysis, engineering and key handling. Access controls. determinacy, safety, and deadlock-freedom. mesh algorithms and subdivision, and Monte Trade-offs in security design. Design for security. Carlo sampling for rendering. Note: Course will Application of techniques through semester-long COMS W4203y Graph theory be taught every two years. design project implementing performant, parallel 3 pts. Lect: 3. Instructor to be announced. application in a modern parallel programming COMS W4167x or y Computer animation Prerequisite: COMS W3203. General introduction language. 3 pts. Lect: 3. Professor Grinspun. to graph theory. Isomorphism testing, algebraic Prerequisite: Multivariable calculus, linear algebra, specification, symmetries, spanning trees, CSEE W4140x or y Networking laboratory C++ programming proficiency. COMS W4156 traversability, planarity, drawings on higher-order 3 pts. Lect: 3. Professor Zussman. recommended. Theory and practice of physics- surfaces, colorings, extremal graphs, random Prerequisite: CSEE W4119 or equivalent. In this based animation algorithms, including animated graphs, graphical measurement, directed graphs, course, students will learn how to put “principles into practice,” in a hands-on networking lab clothing, hair, smoke, water, collisions, impact, Burnside-Polya counting, voltage graph theory. and kitchen sinks. Topics covered: integration course. The course will cover the technologies COMS W4205x Combinatorial theory of ordinary differential equations, formulation and protocols of the Internet using equipment 3 pts. Lect: 3. Professor Gross. of physical models, treatment of discontinuities currently available to large Internet service Prerequisites: COMS W3203 and course in including collisions/contact, animation control, providers such as CISCO routers and end calculus. Sequences and recursions, calculus of constrained Lagrangian Mechanics, friction/ systems. A set of laboratory experiments provides finite differences and sums, elementary number dissipation, continuum mechanics, finite elements, hands-on experience with engineering wide- theory, permutation group structures, binomial area networks and will familiarize students with rigid bodies, thin shells, discretization of Navier- coefficients, Stilling numbers, harmonic numbers, the Internet Protocol (IP), Address Resolution Stokes equations. General education requirement: generating functions. Protocol (ARP), Internet Control Message quantitative and deductive reasoning (QUA). Protocol (ICMP), User Datagram Protocol (UDP) CSOR W4231x Analysis of algorithms, I COMS W4170x User interface design and Transmission Control Protocol (TCP), the 3 pts. Lect: 3. Professor Yannakakis, Breton 3 pts. Lect: 3. Professor Feiner. Domain Name System (DNS), routing protocols Bishop, Drinea, or Andoni. Prerequisite: COMS W3134, W3136, or W3137. (RIP, OSPF, BGP), network management Prerequisites: COMS W3134, W3136 or W3137, Introduction to the theory and practice of computer protocols (SNMP, and application-level protocols and W3203. Introduction to the design and user interface design, emphasizing the software (FTP, TELNET, SMTP). analysis of efficient algorithms. Topics include design of graphical user interfaces. Topics include models of computation, efficient sorting and COMS W4156x Advanced software engineering basic interaction devices and techniques, human searching, algorithms for algebraic problems, 3 pts. Lect: 3. Professor Kaiser. factors, interaction styles, dialogue design, and graph algorithms, dynamic programming, Prerequisite: COMS W3157 or equivalent. software infrastructure. Design and programming probabilistic methods, approximation algorithms, Software lifecycle from the viewpoint of designing projects are required. and implementing N-tier applications (typically and NP-completeness. COMS W4172y 3D user interfaces and utilizing web browser, web server, application COMS W4236y Introduction to computational augmented reality server, database). Major emphasis on quality complexity 3 pts. Lect: 3. Professor Feiner. assurance (code inspection, unit and integration 3 pts. Lect: 3. Professor Chen. testing, security and stress testing). Centers on Prerequisite: COMS W4160 or W4170 or Prerequisite: COMS W3261. Develops a a student-designed team project that leverages instructor’s permission. Design, development, quantitative theory of the computational component services (e.g., transactions, resource and evaluation of 3D user interfaces. Interaction difficulty of problems in terms of the resources pooling, publish/subscribe) for an interactive techniques and metaphors, from desktop to (e.g., time, space) needed to solve them. multi-user application such as a simple game. immersive. Selection and manipulation. Travel Classification of problems into complexity and navigation. Symbolic, menu, gestural, and COMS W4160y Computer graphics classes, reductions and completeness. Power multimodal interaction. Dialogue design. 3D 3 pts. Lect: 3. Professor Reed. and limitations of different modes of computation software support. 3D interaction devices and Prerequisite: COMS W3134, W3136, or W3137; such as nondeterminism, randomization, displays. Virtual and augmented reality. Tangible W4156 is recommended. Strong programming interaction and parallelism. user interfaces. Review of relevant 3D math. background and some mathematical familiarity COMS W4241y Numerical algorithms and including linear algebra is required. Introduction COMS W4180x or y Network security complexity to computer graphics. Topics include 3D viewing 3 pts. Lect: 3. Professor Cook. 3 pts. Lect: 3. Instructor to be announced. and projections, geometric modeling using spline Prerequisites: COMS W3134, W3136, or W3137, Prerequisite: Knowledge of a programming curves, graphics systems such as OpenGL, and W4119, or instructor’s permission. Introduction language. Some knowledge of scientific computation lighting and shading, and global illumination. to network security concepts and mechanisms. is desirable. Modern theory and practice of Significant implementation is required: the final Foundations of network security and an in-depth computation on digital computers. Introduction to project involves writing an interactive 3D video review of commonly used security mechanisms concepts of computational complexity. Design and game in OpenGL. and techniques, security threats and network- analysis of numerical algorithms. Applications to based attacks, applications of cryptography, COMS W4162x or y Advanced computer computational finance, computational science, and authentication, access control, intrusion detection graphics computational engineering. 3 pts. Lect: 3. Professor Zheng. and response, security protocols (IPsec, SSL, Prerequisite: COMS W4160 or equivalent, or Kerberos), denial of service, viruses and worms, STCS W4242x or y Introduction to data instructor’s permission. A second course in software vulnerabilities, web security, wireless science computer graphics covering more advanced security, and privacy. 3 pts. Lect: 3. Professor Salleb-Aouissi. topics including image and signal processing, Practical techniques for working with large-scale

ENGINEERING 2017–2018 data. Topics include statistical modeling and computational hardness, identification and zero Emphasis on creativity, cooperation, and 113 machine learning, data pipelines, programming knowledge protocols. collaboration. Projects spanning a variety languages, “big data” tools, and real-world of areas within computer science, typically COMS W4281x or y Introduction to quantum topics and case studies. Statistical and data requiring the development of computer programs. computing manipulation software required. Intended for Generalization of solutions to broader problems, 3 pts. Lect: 3. Instructor to be announced. nonquantitative graduate-level disciplines. and specialization of complex problems to make Prerequisite: Knowledge of linear algebra. them manageable. Team-oriented projects, student Prior knowledge of quantum mechanics is COMS W4252x or y Introduction to presentations, and in-class participation required. computational learning theory not required although helpful. Introduction to 3 pts. Lect: 3. Professor Servedio. quantum computing. Shor’s factoring algorithm, COMS W4460y Principles of innovation and Prerequisites: CSOR W4231 or COMS W4236 Grover’s database search algorithm, the quantum entrepreneurship or W3203 and instructor’s permission or summation algorithm. Relationship between 3 pts. Lect: 3. Professor Yemini. COMS W3261 and instructor’s permission. classical and quantum computing. Potential power Prerequisites: COMS W3134, W3136, or W3137 Possibilities and limitations of performing of quantum computers. (or equivalent), or instructor’s permission. Team learning by computational agents. Topics include project-centered course focused on principles EECS E4340x Computer hardware design computational models of learning, polynomial time of planning, creating, and growing a technology 3 pts. Lect: 2. Lab: 3. Professor Sethumadhavan. learnability, learning from examples and learning venture. Topics include identifying and analyzing Prerequisites: ELEN E3331 and CSEE W3827. from queries to oracles. Computational and opportunities created by technology paradigm Practical aspects of computer hardware design statistical limitations of learning. Applications to shifts, designing innovative products, protecting through the implementation, simulation, and Boolean functions, geometric functions, automata. intellectual property, engineering innovative prototyping of a PDP-8 processor. High-level business models. COMS W4261x or y Introduction to and assembly languages, I/O, interrupts, cryptography datapath and control design, pipelining, MECS E4510x Evolutionary computation and 3 pts. Lect: 2.5. Professor Malkin. busses, memory architecture. Programmable design automation Prerequisites: Comfort with basic discrete math logic and hardware prototyping with FPGAs. 3 pts. Lect: 3. Professor Lipson. and probability. Recommended: COMS W3261 Fundamentals of VHDL for register-transfer Prerequisite: Basic programming experience in or CSOR W4231. An introduction to modern level design. Testing and validation of hardware. any language. Fundamental and advanced topics cryptography, focusing on the complexity- Hands-on use of industry CAD tools for in evolutionary algorithms and their application to open-ended optimization and computational theoretic foundations of secure computation and simulation and synthesis. communication in adversarial environments; a design. Covers genetic algorithms, genetic rigorous approach, based on precise definitions COMS W4444x Programming and problem programming, and evolutionary strategies, as and provably secure protocols. Topics include solving well as governing dynamic of coevolution and private and public key encryption schemes, 3 pts. Lect: 3. Professor Ross. symbiosis. Includes discussions of problem representations and applications to design digital signatures, authentication, pseudorandom Prerequisites: COMS W3134, W3136, or W3137, problems in a variety of domains including generators and functions, one-way functions, and CSEE W3827. Hands-on introduction to software, electronics, and mechanics. trapdoor functions, number theory and solving open-ended computational problems.

ENGINEERING 2017–2018 114 COMS W4560x Introduction to computer machine translation, dialogue systems, and 3 pts. Lect: 3. Professor Kender. applications in health care and biomedicine emotional speech. Particular attention is Prerequisite: COMS W3134, W3136, or W3137. 3 pts. Lect: 3. given to robust techniques that can handle Visual input as data and for control of computer Prerequisites: Experience with computers and understanding and generation for the large systems. Survey and analysis of architecture, a passing familiarity with medicine and biology. amounts of text on the web or in other large algorithms, and underlying assumptions Undergraduates in their senior or junior years corpora. Programming exercises in several of of commercial and research systems that may take this course only if they have adequate these areas. recognize and interpret human gestures, background in mathematics and receive permission analyze imagery such as fingerprint or iris COMS W4706y Spoken language processing from the instructor. An overview of the field of patterns, generate natural language descriptions 3 pts. Lect: 3. Professor Hirschberg. biomedical informatics, combining perspectives of medical or map imagery. Explores foundations Prerequisite: COMS W3134, W3136, or W3137 from medicine, computer science, and social in human psychophysics, cognitive science, and (or equivalent), or instructor’s permission. science. Use of computers and information in artificial intelligence. Computational approaches to speech health care and the biomedical sciences, covering generation and understanding. Topics include COMS W4737x or y Biometrics specific applications and general methods, current speech recognition and understanding, speech 3 pts. Lect: 3. Professor Belhumeur. issues, capabilities and limitations of biomedical analysis for computational linguistics research, Prerequisite: A background at the sophomore informatics. Biomedical Informatics studies the and speech synthesis. Speech applications level in computer science, engineering, or like organization of medical information, the effective including dialogue systems, data mining, discipline. In this course we will explore the latest management of information using computer advances in biometrics as well as the machine summarization, and translation. Exercises technology, and the impact of such technology learning techniques behind them. Students will involve data analysis and building a small text- on medical research, education, and patient learn how these technologies work and how they to-speech system. care. The field explores techniques for assessing are sometimes defeated. Grading will be based on current information practices, determining the COMS W4725x or y Knowledge representation homework assignments and a final project. There information needs of health care providers and and reasoning will be no midterm or final exam. This course patients, developing interventions using computer 3 pts. Lect: 3. shares lectures with COMS E6737. Students technology, and evaluating the impact of those Prerequisite: COMS W4701. General aspects taking COMS E6737 are required to complete interventions. of knowledge representation (KR). The two additional homework problems and undertake a fundamental paradigms (semantic networks and more rigorous final project. Students will only be MECS E4603x Applied robotics: algorithms frames) and illustrative systems. Topics include allowed to earn credit for COMS W4737 or COMS and software hybrid systems, time, action/plans, defaults, E6737 but not both. 3 pts. Lect: 3. Professor Ciocarlie. abduction, and case-based reasoning. Throughout Prerequisites: Fundamental programming skills EECS E4750x or y Heterogeneous computing (e.g., COMS W1002, W1004, W1005, ENGI E1006, the course particular attention is paid to design for signal and data processing or equivalent). Science and systems aspects of trade-offs between language expressiveness and 3 pts. Lect: 2. Professor Marianetti. Robotics from applied perspective, focusing on reasoning complexity, and issues relating to the Prerequisites: ELEN E3801 and COMS algorithms and software tools. Spatial reasoning; use of KR systems in larger applications. W3134 or similar, recommended. Methods for tools for manipulating and visualizing spatial COMS W4731x or y Computer vision deploying signal and data processing algorithms relationships. Analysis of robotic manipulators; 3 pts. Lect: 3. Professor Nayar. on contemporary general purpose graphics numerical methods for kinematic analysis. Motion Prerequisites: The fundamentals of calculus, linear processing units (GPGPUs) and heterogeneous planning, search-based and stochastic approaches. algebra, and C programming. Students without any computing infrastructures. Using programming Applications for force and impedance control. of these prerequisites are advised to contact the languages such as OpenCL and CUDA for Grading based on combination of exams and instructor prior to taking the course. Introductory computational speedup in audio, image, and projects implemented using Robot Operating course in computer vision. Topics include image video processing and computational data System (ROS) software framework and executed formation and optics, image sensing, binary analysis. Significant design project. on real and simulated robotic manipulators. images, image processing and filtering, edge CBMF W4761x or y Computational genomics COMS W4701x or y Artificial intelligence extraction and boundary detection, region growing 3 pts. Lect: 3. Professor Pe’er. 3 pts. Lect: 3. Professor Salleb-Aouissi. and segmentation, pattern classification methods, Prerequisites: Introductory probability and Prerequisite: COMS W3134, W3136, or W3137 brightness and reflectance, shape from shading statistics and basic programming skills. Provides and any course on probability. Recommended: and photometric stereo, texture, binocular stereo, comprehensive introduction to computational Prior knowledge of Python. Overview of Artificial optical flow and motion, 2D and 3D object techniques for analyzing genomic data including Intelligence (AI) covering Search, Problem Solving, representation, object recognition, vision systems DNA, RNA and protein structures; microarrays; Game Playing, Knowledge Representation, and applications. transcription and regulation; regulatory, metabolic Propositional logic, Predicate Calculus (first order COMS W4733x or y Computational aspects and protein interaction networks. The course logic), Reasoning under uncertainty, Machine of robotics covers sequence analysis algorithms, dynamic Learning, and other topics in AI (including vision, 3 pts. Lect: 3. Professor Allen. programming, hidden Markov models, phylogenetic natural language processing, and robotics) as time analysis, Bayesian network techniques, neural Prerequisite: COMS W3134, W3136, or W3137. permits. networks, clustering algorithms, support vector Introduction to robotics from a computer science machines, Boolean models of regulatory networks, COMS W4705x Natural language processing perspective. Topics include coordinate frames and flux based analysis of metabolic networks and 3 pts. Lect: 3. Professor Radev. kinematics, computer architectures for robotics, scale-free network models. The course provides Prerequisite: COMS W3134, W3136, or W3137 integration and use of sensors, world modeling self-contained introduction to relevant biological (or equivalent), or instructor’s permission. systems, design and use of robotic programming mechanisms and methods. Computational approaches to natural language languages, and applications of artificial intelligence generation and understanding. Recommended for planning, assembly, and manipulation. COMS W4771y Machine learning preparation: Some previous or concurrent COMS W4735x or y Visual interfaces to 3 pts. Lect: 3. Professor Kale or Hsu. Prerequisites: Any introductory course in linear exposure to AI or machine learning. Topics computers include information extraction, summarization, algebra and any introductory course in statistics

ENGINEERING 2017–2018 are both required. Highly recommended: COMS CSEE W4824x Computer architecture COMS E6111y Advanced database systems 115 W4701 or knowledge of artificial intelligence. 3 pts. Lect: 3. Professor Sethumadhavan. 3 pts. Lect: 2. Professor Gravano. Topics from generative and discriminative Prerequisite: CSEE W3827 or equivalent. Focuses Prerequisites: COMS W4111 and knowledge machine learning including least squares on advanced topics in computer architecture, of Java or instructor’s permission. Continuation methods, support vector machines, kernel illustrated by case studies from classic and of COMS W4111, covers latest trends in both methods, neural networks, Gaussian distributions, modern processors. Fundamentals of quantitative database research and industry: information linear classification, linear regression, maximum analysis. Pipelining. Memory hierarchy design. retrieval, web search, data mining, data likelihood, exponential family distributions, Instruction-level and thread-level parallelism. Data- warehousing, OLAP, decision support, multimedia Bayesian networks, Bayesian inference, mixture level parallelism and graphics processing units. databases, and XML and databases. Programming models, the EM algorithm, graphical models and Multiprocessors. Cache coherence. Interconnection projects required. networks. Multi-core processors and systems-on- hidden Markov models. Algorithms implemented COMS E6113y Topics In database systems in MATLAB. chip. Platform architectures for embedded, mobile, and cloud computing. 3 pts. Lect: 2. COMS W4772x Advanced machine learning Prerequisite: COMS W4111. Concentration on 3 pts. Lect: 3. Professor Hsu. CSEE W4840y Embedded systems some database paradigm, such as deductive, Prerequisites: COMS W4771 or instructor’s 3 pts. Lect: 3. Professor Edwards. heterogeneous, or object-oriented, and/or permission; knowledge of linear algebra and Prerequisite: CSEE W4823. Embedded system some database issue, such as data modeling, introductory probability or statistics is required. design and implementation combining hardware distribution, query processing, semantics, or and software. I/O, interfacing, and peripherals. transaction management. A substantial project is An exploration of advanced machine learning Weekly laboratory sessions and term project on typically required. May be repeated for credit with tools for perception and behavior learning. design of a microprocessor-based embedded instructor’s permission. How can machines perceive, learn from, and system including at least one custom peripheral. classify human activity computationally? Topics COMS E6117x or y Topics in programming Knowledge of C programming and digital logic include appearance-based models, principal and required. Lab required. languages and translators independent components analysis, dimensionality 3 pts. Lect: 2. Professor Aho. reduction, kernel methods, manifold learning, CSEE E4868x or y System-on-chip platforms Prerequisite: COMS W4115 or instructor’s latent models, regression, classification, Bayesian 3 pts. Lect: 3. Professor Carloni. permission. Concentration on the design and methods, maximum entropy methods, real-time Prerequisites: COMS W3157 and CSEE W3827 implementation of programming languages, and tracking, extended Kalman filters, time series Design and programming of System-on-Chip tools focused on advanced applications in new prediction, hidden Markov models, factorial (SoC) platforms. Topics include overview of areas in software verification, distributed systems, HMMs, input-output HMMs, Markov random fields, technology and economic trends, methodologies programming in the large, and web computing. variational methods, dynamic Bayesian networks, and supporting CAD tools for system-level A substantial project is typically required. May be and Gaussian/Dirichlet processes. Links to design; models of computation, the SystemC repeated for credit. cognitive science. language, transaction-level modeling, hardware- software partitioning, high-level synthesis, system COMS E6118y Operating systems, II COMS W4776x Machine learning for data programming, on-chip communication, memory 3 pts. Lect: 2. Professor Nieh. science organization, power management and optimization, Prerequisite: COMS W4118. Corequisite: CSEE 3 pts. Lect: 3. Professor Jebara. integration of programmable processor cores and W4119. Continuation of COMS W4118, with Prerequisites: IEOR E4150 or STAT GU4001 specialized accelerators. Case studies of modern emphasis on distributed operating systems. Topics or equivalent, COMS W3251 or equivalent. SoC platforms for various classes of applications. include interfaces to network protocols, distributed Introduction to machine learning, emphasis on run-time binding, advanced virtual memory issues, COMS W4901x and y Projects in computer data science. Topics include least square methods, advanced means of interprocess communication, science file system design, design for extensibility, security Gaussian distributions, linear classification, linear 1–3 pts. Members of the faculty. in a distributed environment. Investigation is regression, maximum likelihood, exponential Prerequisite: Approval by a faculty member who deeper and more hands-on than in COMS W4118. family distributions, Bayesian networks, Bayesian agrees to supervise the work. A second-level A programming project is required. inference, mixture models, the EM algorithm, independent project involving laboratory work, graphical models, hidden Markov models, support COMS E6121x Reliable software computer programming, analytical investigation, vector machines kernel methods. Emphasizes or engineering design. May be repeated for 3 pts. Lect: 3. Professor Yang. methods and problems relevant to big data. credit, but not for a total of more than 3 points of Prerequisite: at least one of COMS W4118, Students may not receive credit for both COMS degree credit. Consult the department for section W4115, or W4117, or significant software W4771 and W4776. assignment. development experiences. Topics include automated debugging, automated software CSEE W4823x or y Advanced logic design COMS W4995x or y Special topics in 3 pts. Lect: 3. Professor Nowick. repair, concurrent software reliability, software computer science, I error detection, and more. Prerequisite: CSEE W3827, or a half-semester 3 pts. Lect: 3. Members of the faculty. introduction to digital logic, or equivalent. An Prerequisite: Instructor’s permission. Special topics COMS E6123x or y Programming introduction to modern digital system design. arranged as the need and availability arises. Topics environments and software tools (PEST) Advanced topics in digital logic: controller are usually offered on a one-time basis. Since 3 pts. Lect: 2. Professor Kaiser. synthesis (Mealy and Moore machines); the content of this course changes each time it is Prerequisite: COMS W4156 or equivalent. adders and multipliers; structured logic offered, it may be repeated for credit. Consult the Software methodologies and technologies blocks (PLDs, PALs, ROMs); iterative circuits. department for section assignment. concerned with development and operation of Modern design methodology: register transfer today’s software systems. Reliability, security, level modeling (RTL); algorithmic state COMS W4996x or y Special topics in systems management and societal issues. machines (ASMs); introduction to hardware computer science, II Emerging software architectures such as description languages (VHDL or Verilog); 3 pts. Lect: 3. enterprise and grid computing. Term paper and system-level modeling and simulation; design Prerequisite: Instructor’s permission. A continuation programming project. Seminar focus changes of COMS W4995 when the special topic extends examples. frequently to remain timely. over two terms.

ENGINEERING 2017–2018 116 COMS E6125y Web-enhanced information Collaboration with other users. Display, COMS E6204x or y Topics in graph theory management (WHIM) interaction, and communication technologies. 3 pts. Lect: 2. Professor Gross. 3 pts. Lect: 2. Professor Kaiser. Sensors for tracking position, orientation, motion, Prerequisite: COMS W4203 or instructor’s Prerequisites: At least one COMS W41xx or COMS environmental context, and personal context. permission. Content varies from year to year. This E61xx course and/or COMS W4444, or instructor’s Applications and social consequences. course may be repeated for credit. Concentration permission. Strongly recommended: COMS on some aspect of graph theory, such as CSEE E6180x or y Modeling and performance W4111. History of hypertext, markup languages, topological graph theory, algebraic graph theory, 3 pts. Lect: 2. Professor Misra. groupware and the web. Evolving web protocols, Prerequisites: COMS W4118 and STAT GU4001. enumerative graph theory, graphical optimization formats and computation paradigms such as Introduction to queuing analysis and simulation problems, or matroids. HTTP, XML and Web Services. Novel application techniques. Evaluation of time-sharing and domains enabled by the web and societal issues. COMS E6206x or y Topics in combinatorial multiprocessor systems. Topics include priority Term paper and programming project. Seminar theory queuing, buffer storage, and disk access, focus changes frequently to remain timely. 3 pts. Lect: 2. Professor Gross. interference and bus contention problems, and Prerequisite: COMS W4203 or W4205, or COMS E6156y Topics in software engineering modeling of program behaviors. instructor’s permission. Concentration on some 3 pts. Lect: 2. Professor Kaiser. COMS E6181x or y Advanced Internet aspect of combinatorial theory. Content varies Topics in software engineering arranged as the services from year to year. This course may be repeated need and availability arises. Topics are usually 3 pts. Lect: 2. Professor Schulzrinne. for credit. offered on a one-time basis. Since the content In-depth survey of protocols and algorithms of this course changes, it may be repeated COMS E6232x or y Analysis of algorithms, II needed to transport multimedia information across for credit with adviser approval. Consult the 3 pts. Lect: 2. the Internet, including audio and video encoding, department for section assignment. Note: Prerequisites: CSOR W4231. Continuation of multicast, quality-of-service, voice-over IP, streaming Example of a past course that would fit into CSOR W4231. media and peer-to-peer multimedia systems. this: Programming environments and software Includes a semester-long programming project. COMS E6253y Advanced topics in tools. Description: Software methodologies computational learning theory and technologies concerned with development COMS E6183x or y Advanced topics in 3 pts. Lect: 3. and operation of today’s software systems. network security Prerequisite: CSOR W4231 or equivalent; COMS Reliability, security, systems management, and 3 pts. Lect: 3. Professor Jana. W4252 or W4236 helpful but not required. societal issues. Emerging software architectures Prerequisites: COMS W4180, CSEE W4119 In-depth study of inherent abilities and limitations such as enterprise and grid computing. Term and COMS W4261 recommended. Review of computationally efficient learning algorithms. paper and programming project. the fundamental aspects of security, including Algorithms for learning rich Boolean function authentication, authorization, access control, COMS E6160x or y Topics in computer classes in online, Probably Approximately confidentiality, privacy, integrity, and availability. graphics Correct, and exact learning models. Connections Review security techniques and tools, and their 3 pts. Lect: 2. Professor Belhumeur. with computational complexity theory applications in various problem areas. Study the Prerequisite: COMS W4160 or instructor’s emphasized. Substantial course project or term state of the art in research. A programming project permission. An advanced graduate course, paper required. is required. involving study of an advanced research topic COMS E6261x or y Advanced cryptography in Computer Graphics. Content varies between COMS E6184y Seminar on anonymity and 3 pts. Lect: 3. Professor Malkin or Breton Bishop. offerings, and the course may be repeated for privacy Prerequisite: COMS W4261. A study of advanced credit. Recent offerings have included appearance 3 pts. Lect: 3. cryptographic research topics such as: secure models in graphics, and high quality real-time Prerequisite: COMS W4261 or W4180 or computation, zero knowledge, privacy, anonymity, rendering. CSEE W4119 or instructor’s permission. This cryptographic protocols. Concentration on COMS E6174y Interaction design: a course covers the following topics: Legal and theoretical foundations, rigorous approach, perceptual approach social framework for privacy. Data mining and and provable security. Content varies between 3 pts. Lect: 3. databases. Anonymous commerce and Internet offerings. May be repeated for credit. Prerequisite: COMS W4170 or instructor’s usage. Traffic analysis. Policy and national permission. Design methodology for special- security considerations. Classes are seminars COMS E6291x or y Theoretical topics in purpose user interfaces. Emphasis on how with students presenting papers and discussing computer science psychology and perception inform good design. them. Seminar focus changes frequently to 3 pts. Lect: 3. Interviewing and task modeling, participatory remain timely. Prerequisite: Instructor’s permission. Concentration design, and low-fidelity prototyping. Applications of on some theoretical aspect of computer science. COMS E6185x or y Intrusion and anomaly brain research, graphic design and art to develop Content varies from year to year. May be repeated detection systems custom user interfaces components, screen for credit. 2 pts. Lect: 2. Professor Stolfo. layouts, and interaction techniques for application- Pre- or corequisite: COMS W4180 Network EECS E6321y Advanced digital electronic specific systems. security. The state of threats against computers, circuits COMS E6176x or y User interfaces for mobile and networked systems. An overview of computer 3 pts. Lect: 2. Professor Seok. and wearable computing security solutions and why they fail. Provides a Prerequisite: EECS E4321. Advanced topics in 3 pts. Lect: 2. Professor Feiner. detailed treatment for network and host-based the design of digital integrated circuits. Clocked Prerequisite: COMS W4170 or instructor’s intrusion detection and intrusion prevention and nonclocked combinational logic styles. permission. Introduction to research on user systems. Considerable depth is provided on Timing circuits: latches and flip-flops, phase- interfaces for mobile and wearable computing anomaly detection systems to detect new attacks. locked loops, delay-locked loops. SRAM and through lectures, invited talks, student-led Covers issues and problems in e-mail (spam, and DRAM memory circuits. Modeling and analysis discussions of important papers, and programming viruses) and insider attacks (masquerading and of on-chip interconnect. Power distribution projects. Designing and authoring for mobility impersonation). and power-supply noise. Clocking, timing, and and wearability. Ubiquitous/pervasive computing.

ENGINEERING 2017–2018 synchronization issues. Circuits for chip-to-chip camera lens arrays, programmable lighting, face domain-specific applications including on-chip 117 electrical communication. Advanced technology detection, single and multiview geometry, and micro-networks, multiprocessor systems, fault- issues that affect circuit design. The class may more. tolerant architectures, and robust deployment of include a team circuit design project. embedded software. Research challenges such COMS E6735y Visual databases as design complexity, reliability, scalability, safety, EECS E6690-6699x or y Topics in data driven 3 pts. Lect: 3. Professor Kender. and security. The course requires substantial analysis and computation Prerequisite: COMS W3134, W3136, or W3137 (or reading, class participation and a research 3 pts. Lect: 2. Members of the faculty. equivalent). COMS W4731 and W4735 helpful but project. Prerequisite: the instructor's permission. Selected not required. Contact instructor if uncertain. The advanced topics in data-driven analysis and analysis and retrieval of large collections of image CSEE E6861y Computer-aided design of computation. Content varies from year to year, and and video data, with emphasis on visual semantics, digital systems different topics rotate through the course numbers human psychology, and user interfaces. Low-level 3 pts. Lect: 2. Professor Nowick. 6690 to 6699. processing: features and similarity measures; shot Prerequisites: (i) one semester of advanced detection; key frame selection; machine learning digital logic (CSEE W4823 or equivalent, or COMS E6731y Humanoid robots methods for classification. Middle-level processing: instructor’s permission); and (ii) a basic course 3 pts. Lect: 2. Professor Allen. organizational rules for videos, including unedited in data structures and algorithms COMS Prerequisite: A course in at least one of the (home, educational), semiedited (sports, talk W3134, W3136, W3137, W3157, or equivalent, following: AI, robotics, computer graphics, or shows), edited (news, drama); human memory and familiarity with programming. Introduction computer vision. Seminar on humanoid robots. limits; progressive refinement; visualization to modern digital CAD synthesis and Analysis of existing hardware and software techniques; incorporation of audio and text. High- optimization techniques. Topics include modern platforms. Programming of multi-degree-of- level processing: extraction of thematic structures; digital system design (high-level synthesis, freedom robots. Understanding sensor feedback ontologies, semantic filters, and learning; register-transfer level modeling, algorithmic in perceive-act-sense control paradigms. Task- personalization of summaries and interfaces; state machines, optimal scheduling algorithms, level planning and reasoning. Final project detection of pacing and emotions. Examples and resource allocation and binding, retiming), includes implementing a humanoid robot task on demonstrations from commercial and research controller synthesis and optimization, exact either a simulated or physical robot. systems throughout. Substantial course project or and heuristic two-level logic minimization, term paper required. advanced multilevel logic optimization, optimal COMS E6732x or y Computational imaging technology mapping to library cells (for delay, COMS E6737x or y Biometrics 3 pts. Lect: 3. Professor Nayar. power and area minimization), advanced Prerequisite: COMS W4731 or instructor’s 3 pts. Lect: 3. Professor Belhumeur. data structures (binary decision diagrams), permission. Computational imaging uses a Prerequisite: Background at the sophomore level SAT solvers and their applications, static combination of novel imaging optics and a in computer science, engineering, or like discipline. timing analysis, and introduction to testability. computational module to produce new forms of Corequisites: None In this course we will explore Includes hands-on small design projects using visual information. Survey of the state-of-the- the latest advances in biometrics as well as and creating CAD tools. art in computational imaging. Review of recent the machine learning techniques behind them. papers on omnidirectional and panoramic imaging, Students will learn how these technologies work CSEE E6863 Formal verification of hardware catadioptric imaging, high dynamic range imaging, and how they are sometimes defeated. Grading and software systems mosaicing and superresolution. Classes are will be based on homework assignments and a 3 pts. Lect: 2. Professors Theobald and Ivancic. seminars with the instructor, guest speakers, and final project. There will be no midterm or final Prerequisite: COMS W3134, W3136, or W3137 students presenting papers and discussing them. exam. This course shares lectures with COMS and COMS W3261. Introduction to the theory W4737. Students taking COMS E6737 are required and practice of formal methods for the design COMS E6733x or y 3D photography to complete additional homework problems and and analysis of correct (i.e., bug-free) concurrent 3 pts. Lect: 2. Professor Allen. undertake a more rigorous final project. Students and embedded hardware/software systems. Prerequisite: Experience with at least one of the will only be allowed to earn credit for COMS Topics include temporal logics; model checking; following topics: Computer graphics, computer W4737 or COMS E6737 but not both. deadlock and liveness issues; fairness; vision, pixel processing, robotics or computer-aided satisfiability (SAT) checkers; binary decision design, or permission of instructor. Programming CSEE E6824y Parallel computer architecture diagrams (BDDs); abstraction techniques; proficiency in C, C++, or JAVA. 3D Photography— 3 pts. Lect: 2. Professor Sethumadhavan. introduction to commercial formal verification the process of automatically creating 3D, Prerequisite: CSEE W4824. Parallel computer texture-mapped models of objects in detail. principles, machine organization and design of tools. Industrial state-of-the-art, case studies, Applications include robotics, medicine, graphics, parallel systems including parallelism detection and experiences: software analysis (C/C++/ virtual reality, entertainment and digital movies methods, synchronization, data coherence and Java), hardware verification (RTL). etc. Topics include 3D data acquisition devices, interconnection networks. Performance analysis CSEE E6868x or y Embedded scalable 3D modeling systems and algorithms to acquire, and special purpose parallel machines. platforms create, augment, manipulate, render, animate and CSEE E6847y Distributed embedded systems 3 pts. Lect: 2. Professor Carloni. physically build such models. 3 pts. Lect: 2. Prerequisites: CSEE W4868 or instructor's COMS E6734y Computational photography Prerequisite: Any COMS W411X, CSEE permission. Interdisciplinary graduate-level 3 pts. Lect: 3. Professor Belhumeur. W48XX, or ELEN E43XX course, or instructor’s seminar on design and programming of Prerequisites: COMS W4160, W4731, or a working permission. An interdisciplinary graduate-level embedded scalable platforms. Content varies knowledge of photography are recommended. seminar on the design of distributed embedded between offerings to cover timely relevant issues Students should have knowledge in any of three systems. System robustness in the presence and latest advances in system-on-chip design, core areas: computer vision, computer graphics, of highly variable communication delays and embedded software programming, and electronic or photography. Computational techniques are heterogeneous component behaviors. The design automation. Requires substantial reading used to produce a new level of images and visual study of the enabling technologies (VLSI of research papers, class participation, and representations. Topics include HDR imaging, circuits, communication protocols, embedded semester-long project. feature matching using RANSAC, image mosaics, processors, RTOSs), models of computation, EECS E6870x or y Speech recognition image-based rendering, motion magnification, and design methods. The analysis of modern 3 pts. Lect: 3. Members of the faculty.

ENGINEERING 2017–2018 118 Prerequisites: Basic probability and statistics. No more than 9 points of COMS E6902 may research for approval by faculty member who Theory and practice of contemporary automatic be taken. Consult the department for section will supervise. The department must approve the speech recognition. Gaussian mixture distributions, assignment. number of points. May be repeated for credit. This hidden Markov models, pronunciation modeling, course is only for Eng.Sc.D. candidates. COMS E6910x and y Fieldwork decision trees, finite-state transducers, and 1 pt. Members of the faculty. COMS E9910x and y Graduate research, I language modeling. Selected advanced topics will Prerequisites: Obtained internship and approval be covered in more depth. 1–6 pts. Members of the faculty. from faculty adviser. Only for M.S. students in the Prerequisites: Submission of an outline of the COMS E6900x and y Tutorial in computer Computer Science Department who need relevant proposed research for approval by the faculty science work experience as part of their program of study. member who will supervise. The department must 1–3 pts. Members of the faculty. Final report required. This course may not be taken approve the number of credits. May be repeated Prerequisite: Instructor’s permission. A reading for pass/fail credit or audited. for credit. This course is only for M.S. candidates course in an advanced topic for a small number of holding GRA or TA appointments. Note: It is NOT COMS E6915y Technical writing for computer students, under faculty supervision. required that a student take Graduate research, I scientists and engineers prior to taking Graduate research, II. Consult the COMS E6901x Projects in computer science 3 pts. Members of the faculty. department for section assignment. 1–12 pts. Members of the faculty. Available to M.S. or Ph.D. candidates in CS/ Prerequisite: Instructor’s permission. Software or CE. Topics to help CS/CE graduate students’ COMS E9911x and y Graduate research, II hardware projects in computer science. Before communication skills. Emphasis on writing, 1-15 pts. Members of the faculty. registering, the student must submit a written presenting clear, concise proposals, journal Prerequisites: Submission of an outline of the proposal to the instructor for review. The proposal articles, conference papers, theses, and technical proposed research for approval by the faculty should give a brief outline of the project, estimated presentations. May be repeated for credit. Credit member who will supervise. The department must schedule of completion, and computer resources may not be used to satisfy degree requirements. approve the number of points. May be repeated needed. Oral and written reports are required. for credit. This course is only for M.S./Ph.D. track COMS E6998x and y Topics in computer May be taken over more than one semester, in and Ph.D. students. Note: It is NOT required that science which case the grade will be deferred until all 12 a student take Graduate research, I prior to taking points have been completed. No more than 12 3 pts. Members of the faculty. Graduate research, II. Consult the department for points of COMS E6901 may be taken. Consult the Prerequisite: Instructor’s permission. Selected section assignment. department for section assignment. topics in computer science. Content varies from year to year. May be repeated for credit. COMS E6902x and y Thesis COMS E6999x and y Topics in computer 1–9 pts. Members of the faculty. Available to M.S. and CSE candidates. An science, II independent investigation of an appropriate 3 pts. problem in computer science carried out under the Prerequisite: COMS E6998. Continuation of supervision of a faculty member. A formal written COMS E6998. report is essential and an oral presentation may COMS E9800x and y Directed research in also be required. May be taken over more than computer science one semester, in which case the grade will be 1–15 pts. Members of the faculty. deferred until all 9 points have been completed. Prerequisites: Submission of outline of proposed

ENGINEERING 2017–2018 EARTH AND ENVIRONMENTAL ENGINEERING 119 Henry Krumb School of Mines OUR MISSION Earth and Environmental Engineering at the Henry Krumb 918 S. W. Mudd, MC 4711 School of Mines fosters excellence in education and research Phone: 212-854-2905 for the development and application of science and technology eee.columbia.edu to maximize the quality of life for all, through the sustainable use and responsible management of Earth’s resources.

DEPARTMENT CHAIR ADJUNCT PROFESSORS SPECIAL RESEARCH Peter Schlosser PROFESSOR OF William Becker SCIENTIST PROFESSIONAL Athanasios Bourtsalas Nickolas J. Themelis DEPARTMENT PRACTICE Raymond S. Farinato ADMINISTRATOR Robert Farrauto Vasilis M. Fthenakis SENIOR RESEARCH Jackeline Paulino D. R. Nagaraj SCIENTIST ASSOCIATE Vasilis M. Fthenakis PROFESSORS PROFESSORS ADJUNCT ASSISTANT Kartik Chandran Pierre Gentine PROFESSORS ASSOCIATE RESEARCH Xi Chen Ah-Hyung (Alissa) Park Yuri Gorokhovich SCIENTISTS Paul F. Duby Christoph Meinrenken Joon Ho Ahn Upmanu Lall ASSISTANT Srinivasan Rangarajan Irina Chernyshova Ismail C. Noyan PROFESSORS Seungbu Park Peter Schlosser Ngai Yin Yip LAMONT ASSOCIATE Partha Patra Ponisseril Somasundaran RESEARCH PROFESSOR Xiaozhou Zhou Wade McGillis

EARTH RESOURCES AND THE mining and metallurgy, including the first EARTH AND ENVIRONMENTAL ENVIRONMENT mining (Peele) and mineral processing ENGINEERING (EEE) The Earth and Environmental (Taggart) handbooks, flotation, chemical Starting in 1996, the educational Engineering program fosters education thermodynamics and kinetics, surface programs of Columbia University in and research in the development and colloid chemistry, and materials mining and mineral engineering were and application of technology for science. transformed into the present program the sustainable development, use, Nearly 100 years after its formation, in Earth and Environmental Engineering and integrated management of the School of Mines was renamed (EEE). This program is concerned with Earth’s resources. Resources are Henry Krumb School of Mines (HKSM) the environmentally sound extraction identified as minerals, energy, water, in honor of the generous Columbia and processing of primary materials air, and land, as well as the physical, benefactor of the same name. The (minerals, fuels, water), the management chemical, and biological components Henry Krumb School of Mines supports and development of land and water of the environment. There is close three components: resources, and the recycling or disposal collaboration with other engineering of used materials. EEE offers the disciplines, the Lamont-Doherty Earth • The Department of Earth and Bachelor of Science (B.S.) in Earth and Observatory, the International Research Environmental Engineering Environmental Engineering, the Master of Institute for Climate Prediction, the (eee.columbia.edu) (EEE), one Science (M.S.) in Earth and Environmental Center for Environmental Research and of Columbia Engineering’s nine Engineering, and the doctorate degrees Conservation, and other Columbia Earth departments. (Ph.D., Eng.Sc.D.) in EEE. Institute units. • Columbia’s interdepartmental The EEE program welcomes program in Materials Science and Combined Plan students. An EEE minor Engineering (matsci.columbia.edu) is offered to all Columbia engineering THE HENRY KRUMB SCHOOL students who want to enrich their (MSE). This program, administered OF MINES AT COLUMBIA academic record by concentrating by the Department of Applied UNIVERSITY some of their technical electives on Physics and Applied Mathematics, is The School of Mines of Columbia Earth/Environment subjects. There is described on page 175. University was established in 1864 and close collaboration between EEE and • The Earth Engineering Center was the first mining and metallurgy the Departments of Civil Engineering (seas.columbia.edu/earth). The department in the U.S. It became the and Earth and Environmental Sciences, current research areas include energy, foundation for Columbia’s School of including several joint appointments. materials, and water resources. Engineering and Applied Sciences and has been a pioneer in many areas of

ENGINEERING 2017–2018 120 RESEARCH CENTERS of and investment in the replacement The CLCA, together with the ASSOCIATED WITH EARTH of aging infrastructure; pricing and Brookhaven National Laboratory are AND ENVIRONMENTAL allocating water, given changing values developing technologies for optimizing ENGINEERING and climate; the management of the recycling of various elements from Columbia Water Center. The Center total urban water cycle through new end-of-life photovoltaic systems and was established in 2008 to address technologies and network topologies; infrastructures for their collection. issues of Global Water Security. It groundwater depletion and national • Life-cycle environmental and currently has 3 major initiatives: food and economic futures; and novel environmental health and safety The Global Water Sustainability opportunities for flood risk management (EH&S) risk assessment: Risk- and Initiative is focused on an assessment and non-point-source pollution LCA-based comparisons of solar of global water scarcity and risk, and mitigation. electric and conventional energy innovations across scales, from farmer’s In addition, the department has active technologies in collaboration with field to reservoir optimization to national research on improving the efficiency of Brookhaven National Laboratory and policy modifications to international water use, reclamation and recycling in several European, South American, trade, to develop real world solutions natural resource processing industries, and Asian institutions. to an impending global water crisis. and on the use of environmental microbiology for wastewater treatment This includes the development of For more information: clca.columbia and energy conversion. State-of-the- new agro-water and chemical sensor .edu; e-mail: [email protected]. systems to improve water use efficiency art methods from molecular genomics and reduce non-point-source pollution are being developed and used to Earth Engineering Center (EEC). as well as field studies on how to get address nitrification and denitrification EEC was formed in 1995 with the farmers to use them; comprehensive in wastewater treatment and energy original mission to direct engineering modeling and optimization of regional production. research at Columbia on processes and crop and energy facility siting to improve products that balance the increasing Center for Life Cycle Analysis (LCA). water sustainability and income; field use of materials by humanity with the The Center for Life Cycle Analysis experiments of water/energy pricing need for clean air, water, and soil. EEC (CLCA) of Columbia University was policy changes; participatory reservoir introduced the teaching of industrial formed in the spring of 2006 with the management using climate scenarios, ecology, was the first engineering objective of conducting comprehensive elicited stakeholder values, option unit of Columbia’s Earth Institute, life cycle analyses of energy systems. contracts and insurance; and models and co-organized the 1997 Global LCA provides a framework for for replicable community-managed rural Warming International Conference quantifying the potential environmental drinking water systems. Active field (GW8) at Columbia University. As impacts of material and energy inputs research projects are in India, China, of 1998, EEC has concentrated on and outputs of a process or product Brazil, and Peru. advancing the goals of sustainable from “cradle to grave.” The mission The Global Flood Initiative recognizes waste management in the U.S. and of the Center is to guide technology that of all natural hazards, floods are globally. Economic development has and energy policy decisions with data- responsible for the largest average resulted in the generation of billions based, well-balanced, and transparent annual loss of property and life. They of tons of used materials that can be descriptions of the environmental profiles are also a significant contributor to a considerable resource, but when pollutant loading and environmental of energy generation and storage not managed properly, constitute a impact in water bodies. In a globalized systems in current and future electricity major environmental problem both in society the disruption of food, energy, grids. Current research thrusts include: developed and developing nations. In and manufactured goods supply chains 2003, in collaboration with the Energy by floods has also emerged as an issue. • Solar energy grid integration: Recovery Council of the U.S., EEC The initiative is developing state-of-the- The CLCA is engaged in model founded the Waste to Energy Research art climate analyses for global flood development and technical and and Technology Council (WTERT). As of risk projection, its mapping onto supply environmental systems analyses of 2013, the Global WTERT Council chains, and risk management using renewable energy integration into (www.wtert.org) has sister organizations novel structural and financial tools. electricity grids. It is developing in 14 countries including Canada, America’s Water is the third models for evaluating and optimizing China, Germany, Greece, India, major initiative. It is driven by the energy storage units for ramping Italy, Mexico, and the U.K. Over the goal of developing sustainable water rate control in photovoltaic power years, WTERT research at Columbia management and infrastructure plants, optimizing penetration of st has engaged many M.S. and Ph.D. design paradigms for the 21 century, solar and wind resources, and students on all aspects of waste recognizing the linkages between urban unit commitment and economic management (see www.wtert.org, functioning, food, water, energy, and dispatch of conventional generators Publications, Theses). EEC conducts a climate. It seeks to pull together a to compensate for solar and wind biannual survey of waste management comprehensive understanding of the variability in large-scale penetrations. in the 50 states of the Union. issues facing water infrastructure in • Resource assessment and recycling the USA. These include the financing of critical energy materials variability:

ENGINEERING 2017–2018 Environmental Tracer Group (ETG). their performance, promote the use of destabilize Earth’s natural systems. 121 The Environmental Tracer Group uses environmentally benign surfactants in a The mission of the Lenfest Center natural and anthropogenic (frequently wide array of technological processes, is shaped by two global challenges. transient) tracers, as well as deliberately and build a resource center to perform First, the Center seeks to reduce the released tracers, to investigate the and provide state-of-the-art facilities emission of carbon dioxide into the physics and chemistry of transport in for characterization of surface-active atmosphere and to forestall a disruption environmental systems. The tracers reagents: columbia.edu/cu/iucrc. of global climate systems that would include natural or anthropogenically impose negative consequences for produced isotopes (e.g., tritium or International Research Institute for human welfare. Second, the Center radioactive hydrogen, helium and oxygen Climate Prediction (IRI). The IRI is seeks to create energy options that will isotopes, or radiocarbon), as well as the world’s leading institute for the meet the legitimate energy demands noble gases and chemical compounds development and application of seasonal of a larger and increasingly wealthy (e.g., CFCs and SF6). The ETG analytical to interannual climate forecasts. The world population. In order to meet these facilities include four mass spectrometric mission of the IRI is to enhance society’s two challenges, the Center seeks to systems that can be used in the analysis capability to understand, anticipate, and develop new sources, technologies, and of tritium and noble gases in water, manage the impacts of seasonal climate infrastructures. sediments, and rocks. In addition to the fluctuations, in order to improve human The Lenfest Center focuses primarily mass spectrometric systems, there are welfare and the environment, especially on the technological and institutional several gas chromatographic systems in developing countries. This mission development of the three energy equipped with electron capture detectors is to be conducted through strategic resources sufficient to support the world’s and applied research, education and that are used for measurements of SF6 projected population in 2100 without capacity building, and provision of in continental waters and CFCs and SF6 increased carbon emissions: solar, forecast and information products, with in the atmosphere. GC/MS capability is nuclear, and fossil fuels combined with an emphasis on practical and verifiable being added to the spectrum of analytical carbon capture and storage. Although utility and partnerships. capabilities. each of these options can, in theory, be developed on a scale to satisfy global Industry/University Cooperative Langmuir Center for Colloids demand, they each face a combination of Research Center for Particulate and and Interfaces (LCCI). This Center technological and institutional obstacles Surfactant Systems (CPaSS). CPaSS brings together experts from mineral that demand research and development was established in 1998 by the Henry engineering, applied chemistry, chemical before they can be deployed. Krumb School of Mines, Department of engineering, biological sciences, and The Center’s main activities are Chemical Engineering, and Department chemistry to probe complex interactions based within the range of natural of Chemistry at Columbia University. The of colloids and interfaces with science and engineering disciplines. Center encompasses detailed structure- surfactants and macromolecules. LCCI At the same time, it integrates property assessment of several classes activities involve significant interaction technological research with analysis of surface-active molecules, including with industrial sponsors and adopt of the institutional, economic, and oligomeric, polymeric, and biomolecules. an interdisciplinary approach toward political context within which energy The aim of CPaSS is to develop and state-of-the-art research on interfacial technologies are commercialized and characterize novel surfactants for phenomena. Major areas of research deployed. For more information: energy industrial applications such as coatings, at LCCI are thin films, surfactant and .columbia.edu. dispersions, deposition, gas hydrate polymer adsorption, environmental control, personal care products, soil problems, enhanced oil recovery, decontamination, waste treatment, computer tomography, corrosion and SCHOLARSHIPS, FELLOWSHIPS, corrosion prevention, flotation, and catalysis mechanisms, membrane AND INTERNSHIPS controlled chemical reactions. The technology, novel separations of The department arranges for proposed research thus focuses on the minerals, biocolloids, microbial surfaces, undergraduate summer internships design and development of specialty and interfacial spectroscopy. after the sophomore and junior years. surfactants, characterization of their Undergraduates can also participate in Lenfest Center for Sustainable Energy. solution and interfacial behavior, and graduate research projects under the The mission of the Lenfest Center identification of suitable industrial work-study program. Graduate research for Sustainable Energy is to develop application for these materials. and teaching assistantships, as well as technologies and institutions to ensure The goals of CPaSS are to perform fellowships funded by the Department, a sufficient supply of environmentally industrially relevant research to are available to qualified graduate sustainable energy for all humanity. To address the technological needs in students. GRE scores are required of all meet this goal, the Center supports commercial surfactant and polymer applicants for graduate studies. research programs in energy science, systems, develop new and more engineering, and policy across Columbia efficient surface-active reagents for University to develop technical and policy specific applications in the industry solutions that will satisfy the world’s future and methodologies for optimizing energy needs without threatening to

ENGINEERING 2017–2018 122 UNDERGRADUATE PROGRAM processes for remediation, recycling, courses listed in the section “Courses in The Bachelor of Science (B.S.) degree and disposal of used materials. Other Divisions” in this bulletin. However, in Earth and Environmental Engineering 4. Graduates will practice their at least four of the six junior/senior prepares students for careers in the profession with excellent written electives must consist of engineering public and private sector concerned with and communication skills and topics. Alternatives for sophomore-year primary materials (minerals, fuels, water) with professional ethics and science courses are shown in the EEE and the environment. Graduates are responsibilities. program table. also prepared to continue with further A student may also choose to studies in Earth/Environmental sciences The Curriculum develop an individual concentration and engineering, business, public policy, The first two years of the EEE program conforming to his/her specific interests, international studies, law, and medicine. are similar to those of other engineering provided that it satisfies ABET The EEE program is accredited as an programs. Students are provided with engineering accreditation criteria. environmental engineering program a strong foundation in basic sciences Therefore, this must be developed in by the Engineering Accreditation and mathematics, as well as the liberal close consultation with and approved by Commission of ABET. arts core. Specific to the EEE program a faculty adviser. is an early and sustained introduction What Is Earth and Environmental to Earth science and environmental Water Resources and Climate Risks Engineering? engineering, and options for a number Concentration It is now recognized by the U.S. and of science courses to meet the specific Preapproved course sequence: other nations that continuing economic interests of each student. The junior PHYS UN1403: Introduction to classical and quantum waves (SEM III) development must be accompanied by and senior years of the program consist of a group of required courses EESC UN2100: Climate system (SEM III) intelligent use of Earth’s resources and EAEE E4006: Field methods for environmental in engineering science and a broad that engineers can contribute much engineering (SEM VI) to the global efforts for sustainable selection of technical electives organized EAEE E4009: GIS for resource, environmental, development. The technologies that have into three distinct concentrations, and infrastructure management been developed for identifying, extracting, representing major areas of focus within (SEM VII) and processing primary materials are the department. EAEE E4350: Planning and management of urban also being applied to the twenty-first- Several Columbia departments, hydrologic systems (SEM VII) EAEE E4257: Environmental data analysis and century problems of resource recovery such as Civil Engineering, Mechanical Engineering, and Earth and modeling (SEM VIII) from used materials, pollution prevention, ECIA W4100: Management and development of Environmental Sciences (Lamont- and environmental remediation. The EEE water systems (SEM VIII) undergraduate program encompasses Doherty Earth Observatory), as well as CIEE E4257: Groundwater contaminant transport these technologies. the Mailman School of Public Health, and remediation contribute courses to the EEE program. Undergraduate Program Objectives EEE students are strongly encouraged Alternatives for junior/senior electives: to work as summer interns in industry EAEE E4001: Industrial ecology of Earth resources 1. Graduates equipped with the or agencies on projects related to Earth EESC GU4008: Introduction to atmospheric necessary tools (mathematics, and Environmental Engineering. The science chemistry, physics, Earth sciences, CIEE E4163: Environmental engineering: wastewater department helps students get summer and engineering science) will APPH E4200: Physics of fluids internships. understand and implement the CIEN E4250: Waste containment design and practice underlying principles used in the CIEN E4255: Flow in porous media engineering of processes and systems. Technical Elective Concentrations EESC GU4401: Quantitative models of climate- sensitive natural and human 2. Graduates will be able to pursue Students majoring in Earth and Environmental Engineering select one systems careers in industry, government EESC GU4404: Regional dynamics, climate and of the following three preapproved agencies, and other organizations climate impacts concerned with the environment technical elective concentrations. Note that the eight-course sequence for each and the provision of primary and Sustainable Energy and Materials preapproved concentration includes two secondary materials and energy, Concentration as well as continue their education science courses during sophomore year Preapproved course sequence: (fall semester) and six technical elective as graduate students in related CHEM UN2443: Organic chemistry (SEM III) disciplines. courses during junior and senior years. EESC UN2200: Solid earth system (SEM III) 3. Graduates will possess the basic skills Any deviations from a preapproved EESC GU4001: Advanced general geology (SEM III) needed for the practice of Earth and concentration must be approved by MECE E3311: Heat transfer (SEM VI) Environmental Engineering, including an undergraduate faculty adviser. EAEE E4001: Industrial ecology of Earth resources (SEM VII) measurement and control of material Alternatives for junior/senior electives

within each concentration are listed, and EAEE E4361: Economics of Earth resource flows through the environment; industries (SEM VII) assessment of environmental impact others may be considered among 3000- EAEE E4190: Photovoltaic systems engineering of past, present, and future industrial to 4000-level courses of any Columbia and sustainability (SEM VII) activities; and analysis and design of Engineering department, as well as MECE E4302: Advanced thermodynamics (SEM VIII)

ENGINEERING 2017–2018 123 EARTH AND ENVIRONMENTAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

MATH UN1101 (3) MATH UN1102 (3) APMA E2000 (4)1 APMA E2101 (3) MATHEMATICS or MATH UN1207 (4) MATH UN1208 (4) MATH UN2030 (3) ODE

UN1401 (3) UN1402 (3)

PHYSICS or UN1601 (3.5) UN1602 (3.5) CHEM UN2443 (3.5) or UN2801 (4.5) UN2802 (4.5) or PHYS UN1403 (3) or UN1403 (3.5) UN1404 (3.5) PHYS UN2601 (3.5) or and Lab UN1500 (3) either semester BIOL UN2005 (4) CHEMISTRY or UN1604 (3.5) UN1507 (3)

or UN2045 (3.5) UN2046 (3.5) and Lab UN1507 (3)

HUMA CC1002, COCI CC1102, or Global Core (3–4)

REQUIRED UN1010 (3) HUMA CC1001, NONTECHNICAL UN1010 (3) COCI CC1101, ECON UN1105 (4) and ELECTIVES or Global Core (3–4) UN1155 recitation (0)

HUMA UN1121 or UN1123 (3)

EESC GU4001 (4) or EESC UN2100 (4.5) REQUIRED or EESC UN2200 (4.5) SIEO W3600 (4) PROFESSIONAL Introduction to AND TECHNICAL ELECTIVES probability and statistics EEAE E2100 (3) A better planet by design

COMPUTER ENGI E1006 (3) any semester SCIENCE

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 Effective Class of 2021.

EESC UN3015: The Earth’s carbon cycle (SEM CHEN E3120: Transport phenomena, II Environmental Health Engineering VIII) EESC GU4008: Introduction to atmospheric science Concentration MECE E4211: Energy: sources and conversion EAEE E4210: Thermal treatment of waste and Preapproved course sequence: (SEM VIII) biomass materials CHEM UN2443: Organic chemistry (SEM III) CHEE E4140: Engineering separations processes CHEM GU4230: Statistical thermodynamics EESC UN2100: Climate system (SEM III) EAEE E4550: Catalysis for emissions control Alternatives for junior/senior electives: EAEE E4006: Field methods for environmental EACE E4560: Particle technology CHEM UN3071: Introduction to inorganic chemistry engineering (SEM VI) MSAE E3103: Elements of materials science EAEE E4009: GIS for resource, environmental and CHEN E3110: Transport phenomena, I infrastructure management (SEM VII)

ENGINEERING 2017–2018 124 EARTH AND ENVIRONMENTAL ENGINEERING: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

CIEE E3255 (3) EAEE E3103 (3) EAEE E3998 (2) EAEE E3999 (2) Environmental control and Energy, minerals, and Undergraduate Undergraduate pollution reduction material systems design project design project systems

CIEE E4252 (3) CIEE E3250 (3) EAEE E4003 (3) Environmental engineering Hydrosystems engineering Aquatic chemistry

EAEE E3200 (3) EAEE E4160 (3) EAEE E3801 (2) Applied transport REQUIRED Solid and hazardous Earth and environmental and chemical rate COURSES waste management engineering lab, II phenomena

EAEE E3800 (2) Earth and environmental CHEE E3010 (3) engineering lab, I Principles of chemical engineering thermodynamics EAEE E3901 (3) Environmental microbiology

TECHNICAL 3 points 6 points 9 points ELECTIVES

NONTECHNICAL 3 points 3 points 6 points ELECTIVES

TOTAL POINTS 15 17 16 17

EHSC P6300: Environmental health sciences for engineers and scientists who plan U.S. environmental industry comprises (SEM VII) to pursue, or are already engaged in, nearly 30,000 big and small businesses EAEE E4257: Environmental data analysis and environmental management/development with total revenues of more than $150 modeling (SEM VIII) billion. Sustainable development and EAEE E4150: Air pollution prevention and control careers. The focus of the program is (SEM VIII) the environmentally sound mining and environmental quality has become a top EHSC P6309: Biochemistry basic to environmental processing of primary materials (minerals, priority of government and industry in the health (SEM VIII) energy, and water) and the recycling or United States and many other nations. Alternatives for junior/senior electives: proper disposal of used materials. The This M.S. program is offered in EAEE E4001: Industrial ecology of Earth resources program also includes technologies for collaboration with the Departments CIEE E4163: Environmental engineering: assessment and remediation of past of Civil Engineering and Earth and wastewater damage to the environment. Students Environmental Sciences. Many of CIEE E4257: Groundwater contaminant transport can choose a pace that allows them to the teaching faculty are affiliated with and remediation Columbia’s Earth Engineering Center. EAEE E4900: Applied transport and chemical rate complete the M.S.-EEE requirements For students with a B.S. in phenomena while being employed. EAEE E4950: Environmental biochemical M.S.-EEE graduates are specially engineering, at least 30 points (ten processes qualified to work for engineering, courses) are required. For students financial, and operating companies with a nonengineering B.S. or a B.A., preferably with a science major, up to 48 engaged in mineral processing ventures, GRADUATE PROGRAMS points (total of sixteen courses) may be the environmental industry, environmental required for makeup courses. Students groups in all industries, and for city, state, M.S. in Earth and Environmental may carry out a research project and and federal agencies responsible for Engineering (M.S.-EEE) write a thesis worth 3–6 points. A the environment and energy/resource number of areas of study are available The M.S.-EEE program is designed conservation. At the present time, the

ENGINEERING 2017–2018 for the M.S.-EEE, and students may • Numerical and statistical modeling of and technologies for addressing the 125 choose courses that match their interest global and regional climate systems environmental concerns over the use of and career plans. The areas of study and attendant uncertainties fossil fuels and nuclear energy. Classes include: • Methods for forecasting seasonal to on climate change, air quality, and health interannual climate variations and their impacts focus on the consequences of • Alternative energy and carbon sectoral impacts energy use. Policy and its interactions management • Models for design and operation of with environmental sciences and energy • Climate risk assessment and water resource systems, considering engineering will be another aspect of the management climate and other uncertainties concentration. Additional specialization • Environmental health engineering • Integrated risk assessment and may consider region-specific energy • Sustainable waste management management across water resources development. • Natural and mineral resource and related sectors development and management Sustainable Waste Management • Novel technologies: surfacial and Sustainable Energy Humanity generates nearly 2 billion tons colloidal chemistry and Building and shaping the energy of municipal solid wastes (MSW) annually. nanotechnology infrastructure of the twenty-first century Traditionally, these wastes have been • Urban environments and spatial analysis is one of the central tasks for modern discarded in landfills that have a finite Additionally, there are three optional engineering. The purpose of the lifetime and then must be replaced by concentrations in the program, in each sustainable energy concentration is converting more greenfields to landfills. of which there are a number of required to expose students to modern energy This method is not sustainable because specific core courses and electives. The technologies and infrastructures and to it wastes land and valuable resources. concentrations are described briefly the associated environmental, health, Also, it is a major source of greenhouse below; details and the lists of specific and resource limitations. Emphasis gases and of various contaminants of courses for each track are available from will be on energy generation and use air and water. In addition to MSW, the the department. technologies that aim to overcome the U.S. alone generates billions of tons of limits to growth that are experienced industrial and extraction wastes. Also, Water Resources and Climate Risks today. Energy and economic well-being the by-product of water purification is a Climate-induced risk is a significant are tightly coupled. Fossil fuel resources sludge or cake that must be disposed component of decision making for the are still plentiful, but access to energy is in some way. The IWM concentration planning, design, and operation of water limited by environmental and economic prepares engineers to deal with the resource systems, and related sectors constraints. A future world population major problem of waste generation such as energy, health, agriculture, of 10 billion people trying to approach by exposing them to environmentally ecological resources, and natural the standard of living of the developed better means for dealing with wastes: hazards control. Climatic uncertainties nations cannot rely on today’s energy waste reduction, recycling, composting, can be broadly classified into two areas: technologies and infrastructures without and waste-to-energy via combustion, (1) those related to anthropogenic severe environmental impacts. Concerns anaerobic digestion, or gasification. climate change; (2) those related to over climate change and changes in Students are exposed not only to the seasonal- to century-scale natural ocean chemistry require reductions in technical aspects of integrated waste variations. The climate change issues carbon dioxide emissions, but most management but also to the associated impact the design of physical, social, alternatives to conventional fossil economic, policy, and urban planning and financial infrastructure systems to fuels, including nuclear energy, are too issues. support the sectors listed above. The expensive to fill the gap. Yet access Since the initiation of the Earth and climate variability and predictability to clean, cheap energy is critical for environmental engineering program in issues impact systems operation, and providing minimal resources: water, 1996, there have been several graduate hence design. The goal of the M.S. food, housing, and transportation. research projects and theses that concentration in water resources and Concentration-specific classes will exemplify the engineering problems that climate risks is to provide (1) a capacity sketch out the availability of resources, will be encompassed in this concentration: for understanding and quantifying the their geographic distribution, the projections for climate change and economic and environmental cost of • Design of an automated materials variability in the context of decisions resource extraction, and avenues for recovery facility for water resources and related sectors increasing energy utilization efficiency, • Analysis of the bioreactor landfill of impact; and (2) skills for integrated such as cogeneration, district heating, • Generation of methane by anaerobic risk assessment and management and distributed generation of energy. digestion of organic materials for operations and design, as well Classes will discuss technologies for • Design of corrosion inhibitors as for regional policy analysis and efficiency improvement in the generation • Flocculation modeling management. Specific areas of interest and consumption sector; energy • Analysis of formation of dioxins in high- include: recovery from solid wastes; alternatives temperature processes to fossil fuels, including solar and wind • Combination of waste-to-energy and energy, and nuclear fission and fusion; anaerobic digestion

ENGINEERING 2017–2018 126 • Application of GIS in siting new WTE All graduate students are expected energy markets. Comparison of conventional and facilities to have a background equivalent to unconventional, renewable and nonrenewable • Corrosion phenomena in WTE the required core of our undergraduate energy resources and analysis of the consequences of various technological choices • Combustion chambers program. They have, of course, an and constraints. Economic considerations, energy • Mathematical modeling of transport opportunity to make up for any deficiency availability, and the environmental consequences phenomena in a combustion chamber in their master’s program. In order to be of large-scale, widespread use of each particular • Effect of oxygen enrichment on prepared for the exam, students can take technology. Introduction to carbon dioxide capture combustion of paper and other types of at least one course in each core area and carbon dioxide disposal as a means of solid wastes during their first two semesters at Columbia sustaining the fossil fuel option. • Feasibility study and design of WTE (see website for up-to-date course listing). EAEE E2100x A better planet by design facilities In case the student declares an explicit 3 pts. Lect: 3. Professors Lall and Yip. minor in another department, the qualifying Introduction to design for a sustainable planet. Doctoral Programs exam requirements will be modified in Scientific understanding of the challenges. Innovative technologies for water, energy, EEE offers two doctoral degrees: consultation with the graduate committee. The minor has to be approved by both food, materials provision. Multiscale modeling (1) the Eng.Sc.D. degree, administered by and conceptual framework for understanding departments. Columbia Engineering; and (2) the Ph.D. environmental, resource, human, ecological, degree, administered by the Graduate The engineering objectives of EEE and economic impacts and design performance School of Arts and Sciences. research and education include: evaluation. Focus on the linkages between planetary, regional, and urban water, energy, Doctoral Qualifying Examination and • Provision and disposal of materials: mineral, food, climate, economic, and ecological cycles. Solution strategies for developed and Research Proposal environmentally sustainable extraction and processing of primary developing country settings. Before the end of the first semester in materials; manufacturing of derivative the doctoral program, the student and CHEE E3010x Principles of chemical products; recycling of used materials; engineering thermodynamics her/his adviser will set up an advisory management of industrial residues 3 pts. Lect: 3. Professor Kumar. committee of two or three faculty and used products; materials-related Prerequisite: CHEM UN1403. Corequisite: CHEN members. This committee will meet application of industrial ecology. E3030. Introduction to thermodynamics. at least once a semester to assess Fundamentals are emphasized: the laws of • Management of water resources: academic and research progress of the thermodynamics are derived and their meaning understanding, prediction, and student and to recommend corrective explained and elucidated by applications to management of the processes that action in case of emerging or existing engineering problems. Pure systems are treated, govern the quantity and quality of deficiencies. with an emphasis on phase equilibrium. water resources, including the role Doctoral students are required to EAEE E3101y Earth resource production of climate; development/operation of pass a qualifying exam within their systems water resource facilities; management of first year into the program. They will 3 pts. Lect: 3. Not offered in 2017–2018. water-related hazards. submit and defend their research Technologies and equipment common to a wide • Energy resources and carbon range of surface and subsurface engineering proposal approximately one year after management: mitigation of activities: mine reclamation, hazardous waste successful completion of the qualifying environmental impacts of energy remediation, discovering and operating surface exam. Submission of the dissertation production; energy recovery from waste and underground mines, detection and removal and thesis defense will follow general of hidden underground objects, waste disposal, materials; advancement of energy University rules. dredging and harbor rehabilitation, and tunneling efficient systems; new energy sources; The qualifying examination will be for transportation or water distribution systems. development of carbon sequestration an oral exam administered by three These methods and equipment are examined strategies. as they apply across the spectrum from mining faculty members. The adviser of the • Sensing and remediation: to environmental engineering projects. The aim student will be a member of the exam understanding of transport processes at is to provide a broad background for earth and committee but may not be the chair. different scales and in different media; environmental engineers in careers involving The students will be examined in their minerals and industrial, large-scale environmental containment systems; modeling flow understanding of fundamentals as they projects. and transport in surface and subsurface apply in the areas of research of the systems; soil/water decontamination EAEE E3103x Energy, minerals, and materials department: water resources, materials and bioremediation. systems processing, energy, and chemical and 3 pts. Lect: 3. Not offered in 2017–2018. biochemical processes. It is expected Prerequisites: MSAE E3111 or MECE E3301 that each question period will last about COURSES IN EARTH and ENME E3161 or MECE E3100 or equivalent 20 minutes, of which 15 minutes will AND ENVIRONMENTAL Corequisites: MSAE E3111 or MECE E3301 and be led by the faculty member from the ENGINEERING ENME E3161 or MECE E3100 or equivalent. Overview of energy resources, resource area and the remaining 5 minutes will be EAEE E2002x Alternative energy resources management from extraction and processing to open for questions by all faculty present 3 pts. Lect: 3. Instructor to be announced. recycling and final disposal of wastes. Resources at the exam. There will be a final period Unconventional, alternative energy resources. availability and resource processing in the context of 20 minutes for general questions. Technological options and their role in the world of the global natural and anthropogenic material

ENGINEERING 2017–2018 cycles; thermodynamic and chemical conditions Examination of geophysical case studies for emphasis on the principles underlying water 127 including nonequilibrium effects that shape the engineering and environmental purposes. analysis for inorganic, organic, and bacterial resource base; extractive technologies and their contaminants. Lab required. CIEE E3250y Hydrosystems engineering impact on the environment and the biogeochemical EAEE E3900x and y–S3900 Undergraduate cycles; chemical extraction from mineral ores, and 3 pts. Lect: 3. Professor Gentine. metallurgical processes for extraction of metals. Prerequisites: CHEN E3110 or ENME E3161 research in Earth and environmental In analogy to metallurgical processing, power or equivalent, SIEO W3600 or equivalent, engineering generation and the refining of fuels are treated as or instructor’s permission. A quantitative 0–3 pts. Directed study. Members of the faculty. extraction and refining processes. Large scale of introduction to hydrologic and hydraulic This course may be repeated for credit, but power generation and a discussion of its impact on systems, with a focus on integrated no more than 3 points of this course may be the global biogeochemical cycles. modeling and analysis of the water cycle counted toward the satisfaction of the B.S. and associated mass transport for water degree requirements. Candidates for the B.S. EAEE E3112y Introduction to rock mechanics resources and environmental engineering. degree may conduct an investigation in Earth 3 pts. Lect: 3. Not offered in 2017–2018. Coverage of unit hydrologic processes such and Environmental Engineering, or carry out a Prerequisites: EAEE E3101 and ENME 3111, or as precipitation, evaporation, infiltration, special project under the supervision of EAEE their equivalents. Rock as an engineering material, faculty. Credit for the course is contingent on runoff generation, open channel and pipe flow, geometry and strength of rock joints, geotechnical the submission of an acceptable thesis or final subsurface flow and well hydraulics in the classification of rock masses, strength and failure report. This course cannot substitute for the context of example watersheds and specific of rock, field investigations prior to excavation in Undergraduate design project (EAEE E3999 or rock, rock reinforcement, analysis and support of integrative problems such as risk-based EAEE E3999). rock slopes and tunnels, and case histories. design for flood control, provision of water, and assessment of environmental impact EAEE E3901y Environmental microbiology MSAE E3141y Processing of metals and or potential for non-point source pollution. 3 pts. Lect: 3. Professor Chandran. semiconductors Spatial hydrologic analysis using GIS and Prerequisite: CHEM UN1404 or equivalent. 3 pts. Lect: 3. Instructor to be announced. watershed models. Fundamentals of microbiology, genetics and Prerequisite: MSAE E3103 or equivalent. molecular biology, principles of microbial nutrition, Synthesis and production of metals and CIEE E3255y Environmental control and energetics and kinetics, application of novel and semiconductors with engineered microstructures pollution reduction systems state-of-the-art techniques in monitoring the for desired properties. Includes high-temperature, 3 pts. Lect: 3. Professor Farrauto. structure and function of microbial communities aqueous, and electrochemical processing; thermal Prerequisite: EAEE E3200 or ENME E3161 in the environment, engineered processes for and mechanical processing of metals and alloys; or MECE E3100. Sources of solid/gaseous air biochemical waste treatment and bioremediation, casting and solidification; diffusion, microstructural pollution and the technologies used for modern microorganisms and public health, global microbial evolution, and phase transformations; modification methods of abatement. Air pollution and its elemental cycles. and processing of surfaces and interfaces; abatement from combustion of coal, oil, and deposition and removal of thin films. Processing of natural gas and the thermodynamics of heat EAEE E3998x-E3999y Undergraduate design Si and other materials for elemental and compound engines in power generation. Catalytic emission project semiconductor-based electronic, magnetic, and control is contrasted to thermal processes for 2 pts. (each semester). Lect: 1. Lab: 2. optical devices. abating carbon monoxide, hydrocarbons, oxides Professor Farrauto. of nitrogen and sulfur from vehicles and stationary Prerequisite: senior standing. Students must enroll EAEE E3185y Summer fieldwork for Earth and sources. Processing of petroleum for generating for both 3998x and 3999y during their senior environmental engineers fuels. Technological challenges of controlling year. Selection of an actual problem in Earth and 0.5 pt. Not offered in 2017–2018. greenhouse gas emissions. Biomass and the environmental engineering, and design of an Undergraduates in Earth and environmental hydrogen economy coupled with fuel cells as future engineering solution including technical, economic, engineering may spend up to 3 weeks in the field sources of energy. environmental, ethical, health and safety, social under staff direction. The course consists of mine, issues. Use of software for design, visualization, landfill, plant, and major excavation site visits and EAEE E3800y Earth and environmental economic analysis, and report preparation. brief instruction of surveying methods. A final report engineering laboratory, I Students may work in teams. Presentation of is required. 2 pts. Lect: 1. Lab: 3. Professor Farrauto and results in a formal report and public presentation. Bourtsalas. EAEE E3200x Applied transport and chemical Prerequisite: CHEE E3010. Corequisite: CIEE EAEE E4001x Industrial ecology of earth rate phenomena E3255. Experiments on fundamental aspects resources 3 pts. Lect: 3. Not offered in 2017–2018. of Earth and environmental engineering with 3 pts. Lect: 3. Instructor to be announced. Prerequisite: APMA E2101. Fluid statics. Basics emphasis on the applications of chemistry, Industrial ecology examines how to reconfigure of flow analysis. Dimensional analysis. Pipe flow. biology and thermodynamics to environmental industrial activities so as to minimize the adverse Fluid dynamics, heat and mass transfer. Effects of processes: energy generation, analysis and environmental and material resource effects on the velocity, temperature, and concentration gradients purification of water, environmental biology, and planet. Engineering applications of methodology and material properties on fluid flow, heat and biochemical treatment of wastes. Students will of industrial ecology in the analysis of current mass transfer. Applications to environmental learn the laboratory procedures and use analytical processes and products and the selection or engineering problems. equipment firsthand, hence demonstrating design of environmentally superior alternatives. Home assignments of illustrative quantitative EAEE E3221x Environmental geophysics experimentally the theoretical concepts learned problems. 3 pts. Lect: 3. Not offered in 2017–2018. in class. Introduction to applied and environmental EAEE E3801x Earth and environmental EAEE E4003x Introduction to aquatic chemistry geophysics methods. Overview of principles of engineering laboratory, II 3 pts. Lect: 3. Professor Yip. geophysics, geophysical methods and techniques 2 pts. Lect: 1. Lab: 3. Professor Farrauto and Prerequisite: CHEE E3010. Principles of physical (seismic, ground penetrating radar, resistivity, Bourtsalas. chemistry applied to equilibria and kinetics of frequency em, and magnetics), and theory and Prerequisite: EAEE E3800. Corequisite: EAEE aqueous solutions in contact with minerals and practical aspects of data processing and inversion. E4003. A continuation of EAEE E3800, with anthropogenic residues. The scientific background

ENGINEERING 2017–2018 128 for addressing problems of aqueous pollution, justifiable model of the subsurface. Geophysical electrode kinetics, and ionic mass transport. water treatment, and sustainable production of methods include GPR (Ground Penetrating Examples of industrial and environmental materials with minimum environmental impact. Radar), conductivity, and magnetic and seismic applications illustrated by means of laboratory Hydrolysis, oxidation-reduction, complex formation, methods. Field applications include infrastructure/ experiments: electroplating, refining, and dissolution and precipitation, predominance environmental assessment, archeological studies, winning in aqueous solutions and in molten diagrams; examples of natural water systems, and high resolution geology. salts; electrolytic treatment of wastes; primary, processes for water treatment and for the secondary, and fuel cells. EAEE E4009x Geographic information production of inorganic materials from minerals. systems (GIS) for resource, environmental ECIA W4100y Management and development EAEE E4004x Physical processing and and infrastructure management of water systems recovery of solids 3 pts. Lect: 3. Professor Gorokhovich. 3 pts. Lect: 3. Professors Gentine and Lall. 3 pts. Lect: 3. Not offered in 2017–2018. Prerequisite: Permission of the instructor. Basic Decision analytic framework for operating, Generalized treatment of processes for solids concepts of geomatics, spatial data representation managing, and planning water systems, separation. Applications to materials processing and organization, and analytical tools that considering changing climate, values and needs. and handling; mining; solid waste, recycling, and comprise GIS are introduced and applied to a Public and private sector models explored through resource recovery; construction materials and variety of problems including watershed protection, U.S.-international case studies on topics ranging debris; scrap materials, yard and park wastes. environmental risk assessment, material mass from integrated watershed management to the Economic considerations and context. Relevant balance, flooding, asset management, and analysis of specific projects for flood mitigation, materials properties and bulk materials analyses. emergency response to natural or man-made water and wastewater treatment, or distribution Process system flow-sheets and analysis. Solid/ hazards. Technical content includes geography and system evaluation and improvement. solid, solid/liquid, and solid/gas separation map projections, spatial statistics, database design CHEE E4140x Engineering separations process. Liberation, concentration, and auxiliary and use, interpolation and visualization of spatial processes processes. Design of separation machines: types surfaces and volumes from irregularly spaced data, 3 pts. Lect: 3. Not offered in 2017–2018. and intensities of force involved; scaling-up factors. and decision analysis in an applied setting. Taught Laboratory demonstrations and a field trip will be in a laboratory setting using ArcGIS. Access to Prerequisites: CHEN E3100, E3120, and included. New York City and other standard databases. Term E3210 or permission of instructor. Design projects emphasize information synthesis toward and analysis of unit operations employed in EAEE E4005x Near-surface engineering the solution of a specific problem. chemical engineering separations. Fundamental geophysics aspects of single and multistaged operations 3 pts. Lect: 3. Not offered in 2017–2018. EAEE E4010y Remote sensing and using both equilibrium and rate-based methods. Geophysical methods as applicable to environmental change Examples include distillation, absorption and engineering problems. Principles of geophysics 3 pts. Lect: 3. Not offered in 2017–2018. stripping, extraction, membranes, crystallization, and noninvasive imaging techniques (inversion Prerequisite: EAEE E4009 or EESC GU4050 or bioseparations, and environmental applications. technology) and benefits and pitfalls of geophysics instructor’s permission. Practical and theoretical vs. direct imaging methods. Discussion of theory foundations for the application of remote sensing EAEE E4150y Air pollution prevention and of each method. Discussion of data acquisition, techniques to identification and monitoring of control processing and interpretation for each method. environmental change. Designing and applying 3 pts. Lect: 3. Professor Fthenakis. Treatment of several case studies. Class-wide spectral indices for assessment and monitoring, Adverse effects of air pollution, sources and planning and execution of small-scale geophysical time series analysis of remote sensing data for transport media, monitoring and modeling of survey. analyzing environmental problems. Discussions air quality, collection and treatment techniques, of published literature relevant to the central topic pollution prevention through waste minimalization EAEE E4006y Field methods for covered in class. Analysis of remote sensing data and clean technologies, laws, regulations, environmental engineering using IRI data library. standards, and guidelines. 3 pts. Lect: 1.5. Lab: 2. Professor McGillis. Prerequisite: ENME E3161 or equivalent or EAEE E4011y Industrial ecology for EAEE E4160y Solid and hazardous waste instructor’s permission Principles and methods for manufacturing management designing, building and testing systems to sense 3 pts. Lect: 3. Professor Bourtsalas. 3 pts. Lect: 3. Professor Somasundaran. the environment. Monitoring the atmosphere, water Prerequisite: EAEE E4001 or instructor's Generation, composition, collection, transport, bodies and boundary interfaces between the two. permission. Application of industrial ecology to storage and disposal of solid and hazardous Sensor systems for monitoring heat and mass Design for Environment (DFE) of processes and waste. Impact on the environment and public flows, chemicals, and biota. Measurements of products using environmental indices of resources health. Government regulations. Recycling and velocity, temperature, flux and concentration in the consumption and pollution loads. Introduction of resource recovery. field. The class will involve planning and execution methodology for Life Cycle Assessment (LCA) of of a study to sense a local environmental system. manufactured products. Analysis of several DFE CIEE E4163x Sustainable water treatment and LCA case studies. Term project required on and reuse EAEE E4007y Environmental geophysics field use of DFE/LCA on a specific product/process: 3 pts. Lect: 3. Professor Becker. studies (a) product design complete with materials and Prerequisites: Introductory chemistry (with lab) 3 pts. Lect: 3. Not offered in 2017–2018. process selection, energy consumption, and and fluid mechanics, or the equivalent. Theory and Application of geophysical methods to noninvasive waste loadings; (b) LCA of an existing industrial application of the physical and chemical processes assessment of the near surface. First part consists or consumer product using a commercially for treating potable water and reusing wastewater. of series of two-hour lectures of physics and established method. Disinfection/oxidation, coagulation and flocculation, math involved in instrumental methods and data clarification, filtration, ion exchange, adsorption, acquisition and processing. The field (nine field CHEE E4050x Industrial and environmental membrane processes, advanced oxidation days) students plan surveys; collect and analyze electrochemistry processes, activated sludge, and anaerobic sludge geophysical data in teams; learn how to integrate 3 pts. Lect: 3. Not offered in 2017–2018. digestion. geophysical data with invasive data, hydrological, Prerequisite: CHEN E3010 or equivalent. A geological, engineering, and contaminant transport presentation of the basic principle underlying EAEE E4190x Photovoltaic systems models; and develop a comprehensive and electrochemical processes. Thermodynamics, engineering and sustainability 3 pts. Lect: 3. Professor Fthenakis.

ENGINEERING 2017–2018 Prerequisite: Senior standing or instructor’s Analysis and design of transportation systems estuaries and sea level fluctuations at the river- 129 permission. A systems approach for intermittent for bulk solids in tunnels, mines, and large estuary boundary. renewable energy involving the study of resources, excavations. Design of hoisting, cable transport, CIEE E4257y Groundwater contaminant generation, demand, storage, transmission, rail and trackless haulage systems, conveyor economics and politics. Study of current and belts, selection of loaders, excavators, off-highway transport and remediation emerging photovoltaic technologies, with focus on trucks, and draglines for large excavations. 3 pts. Lect: 3. Not offered in 2017–2018. basic sustainability metrics (e.g., cost, resource Prerequisite: CIEE E3250 or equivalent. Sources CIEE E4250y Hydrosystems engineering availability, and life-cycle environmental impacts). and types of groundwater contamination. The status and potential of first- and second- 3 pts. Lect: 2.5. Professors Lall and Gentine. Groundwater hydrology. Groundwater contaminant generation photovoltaic technologies (e.g., Prerequisites: CHEN E3110 or ENME E3161 or rate and transport. Flow and transport in the crystalline and amorphous Si, CdTe, CIGS) and equivalent, SIEO W3600 or equivalent, or the unsaturated zone. Nonaqueous phase liquids and emerging third-generation ones. Storage options instructor’s permission. A quantitative introduction multiphase flow. Physical and numerical models to overcome the intermittency constraint. Large to hydrologic and hydraulic systems, with a for contaminant transport. Characterization and scales of renewable energy technologies and focus on integrated modeling and analysis of the assessment of contaminated sites. Groundwater plug-in hybrid electric cars. water cycle and associated mass transport for remediation alternatives. Regulations. water resources and environmental engineering. EAEE E4200y Production of inorganic materials Coverage of unit hydrologic processes such as EAEE E4257y Environmental data analysis and 3 pts. Lect: 3. Not offered in 2017–2018. precipitation, evaporation, infiltration, runoff modeling Prerequisite: CHEE E3010 or equivalent. generation, open channel and pipe flow, 3 pts. Lect: 3. Professor Lall. Production and recycling of inorganic materials in subsurface flow and well hydraulics in the context Prerequisite: SIEO W3600 or GU4250 or aqueous and high temperature systems. Industrial of example watersheds and specific integrative equivalent. Statistical methods for the analysis and environmental applications of hydrometallurgy, problems such as risk-based design for flood of the space and time structure in environmental pyrometallurgy, and electrometallurgy. Reactor control, provision of water, and assessment of data. Application to problems of climate variation systems for, e.g., leaching, precipitation, and environmental impact or potential for non-point and change; hydrology; air, water and soil pollution solvent extraction, bath and flash smelting source pollution. Spatial hydrologic analysis using dynamics; disease propagation; ecological reactors, rotary kilns, and fluid bed reactors. GIS and watershed models. change; and resource assessment. Applications Thermodynamic and kinetic factors and are developed using the ArcView Geographical CHEE E4252x Introduction to surface and materials/energy balances involved in the design Information System (GIS), integrated with currently and performance of such reactors in typical colloid chemistry available statistical packages. Team projects applications. 3 pts. Lect: 3. Professor Somasundaran. that lead to publication-quality analyses of data Prerequisite: Elementary physical chemistry. in various environmental fields of interest. An EAIA W4200y Alternative energy resources Thermodynamics of surfaces, properties of interdisciplinary perspective is emphasized in this 3 pts. Lect: 3. Instructor to be announced. surfactant solutions and surface films, electrostatic applications-oriented class. Unconventional, alternative energy resources. and electrokinetic phenomena at interfaces, Technological options and their role in the world adsorption; interfacial mass transfer and modern EAEE E4300x or y Introduction to carbon energy markets. Comparison of conventional and experimental techniques. management unconventional, renewable and nonrenewable, 3 pts. Lect: 3. Professor Schlosser. energy resources and analysis of the CIEE E4252y Environmental engineering Prerequisites: Undergraduate level mathematics consequences of various technological choices 3 pts. Lect: 3. Professor Chandran. and science, or instructor’s permission. and constraints. Economic considerations, energy Prerequisites: CHEM UN1403, or equivalent; Introduction to natural and anthropogenic carbon availability, and the environmental consequences ENME E3161 or equivalent. Engineering aspects cycle, and carbon and climate. Rationale and need of large-scale, widespread use of each particular of problems involving human interaction with to manage carbon and tools with which to do so technology. Introduction to carbon dioxide disposal the natural environment. Review of fundamental (basic science, psychology, economics and policy as a means of sustaining the fossil fuel option. principles that underlie the discipline of background, negotiations and society; emphasis Recitation section required. environmental engineering, i.e., constituent on interdisciplinary and inter-dependent approach). transport and transformation processes in Simple carbon emission model to estimate the EAEE E4210x Thermal treatment of waste and environmental media such as water, air, and impacts of a specific intervention with regard to biomass materials ecosystems. Engineering applications for national, per capita, and global emissions. Student- 3 pts. Lect: 3. Professor Bourtsalas. addressing environmental problems such as water led case studies (e.g., reforestation, biofuels, Prerequisite: CHEE E3010 or the equivalent quality and treatment, air pollution emissions, CCS, efficiency, alternative energy) to illustrate or instructor’s permission. Origins, quantities and hazardous waste remediation. Presented in necessary systems approach required to tackle generated, and characterization of solid wastes. the context of current issues facing the practicing global challenges. Chemical and physical phenomena in the engineers and government agencies, including combustion or gasification of wastes. Application legal and regulatory framework, environmental EAEE E4301y Carbon storage of thermal conversion technologies, ranging impact assessments, and natural resource 3 pts. Lect: 3. Not offered in 2017–2018. from combustion to gasification and pyrolysis. management. Prerequisites: Undergraduate level mathematics Quantitative description of the dominant waste and science, or instructor’s permission. Major EAEE E4255x River and coastal to energy processes used worldwide, including technologies to capture carbon dioxide via new or feedstock preparation, moving grate and fluid bed hyrdrodynamics retrofitted power plant designs, during industrial combustion, heat transfer from combustion gases 3 pts. Lect: 3. Not offered in 2017–2018. processes, and from ambient air. In addition to steam, mitigation of high-temperature corrosion, Prerequisites: CHEN E3110 or ENME E3161 or the to basic science and engineering challenges electricity generation, district heating, metal equivalent. Dynamics of flow and waves in rivers of each technology, full spectrum of economic, recovery, emission control, and beneficial use of and coastal settings, with applications to flooding environmental, regulatory, and political/policy ash residues. and mixing of saline and fresh waters, sediment aspects, and their implication for regional and transport. Integrative hydrodynamics modeling global carbon management strategies of the EAEE E4241x Solids handling and transport experience using numerical and analytical tools future. Combination of lectures, class debates systems applied to complex real world setting, including and breakout groups, student presentations, and 3 pts. Lect: 3. Not offered in 2017–2018. concerns of anthropogenic change in rivers and independent final projects.

ENGINEERING 2017–2018 130 EAEE E4302x or y Carbon capture and reactor design will be discussed using processes involving particulates and powders. 3 pts. Lect: 3. Professor Park. technological examples such as enhanced oil The fundamentals of particle characterization, Prerequisites: Undergraduate level math recovery, shale fracking, photo and electrochemical multiphase flow behavior, particle formation,

and science or instructor’s permission. Major conversion of CO2 to chemical and fuels, and processing and utilization of particles in various technologies to store carbon dioxide, geological, formation of solid carbonates and their various engineering applications with examples in ocean, and in the carbon chemical pool. Carbon uses. Life cycle analyses of potential products energy and environment related technologies. dioxide transport technologies also covered. and utilization schemes will also be discussed, Engineering of functionalized particles and

In addition to basic science and engineering as well as the use of renewable energy for CO2 design of multiphase reactors and processing challenges of each technology, full spectrum of conversion. units with emphasis on fluidization technology. economic, environmental, regulatory, and political/ Particle technology is an interdisciplinary field. EAEE E4350x Planning and management of policy aspects, and their implication for regional Due to the complexity of particulate systems, urban hydrologic systems and global carbon management strategies of the particle technology is often treated as art rather 3 pts. Lect: 3. Professor Rangarajan. future. Combination of lectures, class debates than science. In this course, the fundamental Prerequisite: ENME E3161 or equivalent. and breakout groups, student presentations, and principles governing the key aspects of particle Introduction to runoff and drainage systems in an independent final projects. science and technology are introduced along with urban setting, including hydrologic and hydraulic various industrial examples. EAEE E4303x or y Carbon measurement and analyses, flow and water quality monitoring, monitoring common regulatory issues, and mathematical EAEE E4901y Environmental microbiology 3 pts. Lect: 3. Professor Meinrenken. modeling. Applications to problems of climate 3 pts. Lect: 3. Professor Chandran. Prerequisites: Undergraduate level math and variation, land use changes, infrastructure Basic microbiological principles; microbial science or instructor permission. Sources of operation and receiving water quality, developed metabolism; identification and interactions various GHGs (whether fossil/industrial or using statistical packages, public-domain models, of microbial populations responsible for the biogenic), their chemical behavior, interactions, and Geographical Information Systems (GIS). biotransformation of pollutants; mathematical and global warming potential once airborne; Team projects that can lead to publication quality modeling of microbially mediated processes; available measurement, monitoring, and detection analyses in relevant fields of interest. Emphasis on biotechnology and engineering applications using technologies to track gas emissions, including the unique technical, regulatory, fiscal, policy, and microbial systems for pollution control. other interdisciplinary issues that pose a challenge leakage from storage sites. Carbon accounting EAEE E4950x Environmental biochemical to effective planning and management of urban and reporting methodologies such as life cycle hydrologic systems. processes analysis, and corporate carbon footprinting. 3 pts. Lect: 3. Professor Chandran. In addition to basic science and engineering EAEE E4361y Economics of Earth resource Prerequisite: EAEE E4901, E4003, CIEE E4252, or challenges of each technology, full spectrum of industries instructor’s approval. Qualitative and quantitative economic, environmental, regulatory, and political/ 3 pts. Lect: 3. Not offered in 2017–2018. considerations in engineered environmental policy aspects, and their implication for regional Prerequisite: EAEE E3103 or instructor’s biochemical processes. Characterization of and global carbon management strategies of the permission. Definition of terms. Survey of multiple microbial reactions in a community and future. Combination of lectures, class debates Earth resource industries: resources, reserves, techniques for determining associated kinetic and and breakout groups, student presentations, and production, global trade, consumption of mineral stoichiometric parameters. Engineering design independent final projects. commodities and fuels. Economics of recycling of several bioreactor configurations employed and substitution. Methods of project evaluation: for biochemical waste treatment. Mathematical EAEE E4304x Closing the carbon cycle estimation of operating costs and capital modeling of engineered biological reactors using 3 pts. Lect: 3. Professor Eisenberger. requirements, project feasibility, risk assessment, state-of-the-art simulation packages. Prerequisites: Calculus, basic inorganic chemistry, and environmental compliance. Cost estimation EAEE E4951x Engineering systems for water and basic physics, including thermodynamics, or for reclamation/remediation projects. Financing of instructor’s permission. Introduction to complex reclamation costs at abandoned mine sites and treatment and reuse systems, their impact on our understanding waste-disposal postclosure liability. 3 pts. Lect: 3. Not offered in 2017–2018. and predictability of the carbon cycle, the use Prerequisites: CIEE E4163 and EAEE E3901, of systems analysis and modeling tools, as well CHEE E4530y Corrosion of metals or the instructor’s permission. Application of as Bayesian statistics and decision theory for 3 pts. Lect: 3. Instructor to be announced. fundamental principles to designing water evaluating various solutions to close the carbon Prerequisite: CHEN E3010 or equivalent. The treatment and reuse plants. Development of cycle, a detailed examination of the geochemical theory of electrochemical corrosion, corrosion process designs for a potable water treatment carbon cycle, major conceptual models that tendency, rates, and passivity. Application to plant, a biological wastewater treatment plant, or couple its changes to climate change, analysis of various environments. Cathodic protection and a water reclamation and reuse facility by students the anthropogenic carbon sources and sinks and coatings. Corrosion testing. working in teams. Student work in evaluation role of carbon in energy production, closing the of water quality and pilot plant data, screening EAEE E4550x Catalysis for emissions control carbon cycle impacts on energy security, economic process alternatives, conducting regulatory reviews 3 pts. Lect: 3. Professor Farrauto. development and climate change protection, and recommending a process for implementation, Prerequisite: One year of general college analysis of solutions to close the carbon cycle. supported by engineering drawings and capital chemistry. Fundamentals of heterogeneous operating costs. Periodic oral progress reports EAEE E4305y Carbon utilization and catalysis including modern catalytic preparation and a full engineering report are required. conversion techniques. Analysis and design of catalytic Presentations by practicing engineers, utility 3 pts. Lect: 3. Professor Park. emissions control systems. Introduction to current personnel, and regulators; and field trips to water, Prerequisites: Undergraduate level industrial catalytic solutions for controlling gaseous wastewater, and water reuse facilities. thermodynamics or instructor's permission. emissions. Introduction to future catalytically enabled control technologies. EAEE E4980 Urban environmental technology Introduction to various CO2 utilization and and policy conversion technologies that can reduce the EACE E4560y Particle technology overall carbon footprint of commodity chemicals 3 pts. Lect: 3. Not offered in 2017–2018. 3 pts. Lect: 3. Professor Park. and materials. Fundamentals of thermodynamics, Progress of urban pollution engineering via Prerequisites: ENME E3161 and MSAE E3111 fluid mechanics, reaction kinetics, catalysis contaminant abatement technology, government or equivalent. Introduction to engineering

ENGINEERING 2017–2018 policy, and public action in urban pollution. profiling. Radon transform and Fourier migration. measurements of risk, and their use in public 131 Pollutant impact on modern urban environmental Multidimensional geological interpretation. policy and regulation. quality, natural resources, and government, EAEE E6200y Theory and applications of EAEE E6212y Carbon sequestration municipal, and social planning and management programs. Strong emphasis on current and extreme value statistics in engineering and 3 pts. Lect: 3. Professor Park. twentieth-century waste management in New earth sciences Prerequisite: EAEE E3200 or equivalent or York City. 3 pts. Lect: 3. Not offered in 2017–2018. instructor’s permission. New technologies for Prerequisite: STAT GR5204 or equivalent capturing carbon dioxide and disposing of it away EAEE E4999x and y Fieldwork background in probability and statistical inference, from the atmosphere. Detailed discussion of the 1 pt. Members of faculty. or instructor’s permission. Introduction of extent of the human modifications to the natural Prerequisite: Instructor’s written permission. Only fundamental concepts in extreme value statistics. carbon cycle, the motivation and scope of future EAEE graduate students who need relevant off- The exact and asymptotic theory of extremes. carbon management strategies and the role of campus work experience as part of their program Development of statistical methodology for carbon sequestration. Introduction of several of study as determined by the instructor. Written estimating the parameters of asymptotic extremal carbon sequestration technologies that allow for application must be made prior to registration distributions from experimental data. Examples of the capture and permanent disposal of carbon outlining proposed study program. Final reports applications of extreme value statistics to regional dioxide. Engineering issues in their implementation, required. This course may not be taken for pass/ and global earthquake forecasting, laboratory economic impacts, and the environmental issues fail credit or audited. International students must testing of rocks and metals, fatigue failure, floods, raised by the various methods. also consult with the International Students and droughts, extreme wind velocities, and rainfalls. Scholars Office. CHEE E6220y Equilibria and kinetics in EAIA W6201x or y Complexity science hydrometallurgical systems EAEE E6132y Numerical methods in 4 pts. Lect: 4. Professors Castner, Dumas, Lall, 3 pts. Lect: 3. Instructor to be announced. geomechanics Mutter, and Rising. Prerequisite: CHEE E4050 or EAEE E4003. 3 pts. Lect: 3. Instructor to be announced. Prerequisites: Graduate standing and instructor’s Detailed examination of chemical equilibria Prerequisites: EAEE E3112 and CIEN E4241 permission. Survey of techniques, applications, and in hydrometallurgical systems. Kinetics and or instructor’s permission. A detailed survey implications of complexity science and complex mechanisms of homogeneous and heterogeneous of numerical methods used in geomechanics, systems. Topics include systems dynamics, chaos, reactions in aqueous solutions. emphasizing the Finite Element Method (FEM). scaling, fat-tailed distributions, fractals, information EAEE E6220x Remedial and corrective action Review of the behavior of geological materials. theory, emergence, criticality, agent-based models, 3 pts. Lect: 3. Not offered in 2017–2018. Water and heat flow problems. FEM techniques graph theory, and social networks. Applications Prerequisite: EAEE E4160 or equivalent. Integrates for solving nonlinear problems, and simulating will cover climate science, ecology, conflict, the engineering aspects of cleanup of hazardous incremental excavation and loading on the surface hydrology, geomorphology, physics, social theory, materials in the environment. Site assessment/ and underground. epidemiology, and governance. investigation. Site closure, containment, and EAEE E6140y Environmental physicochemical EAEE E6208y Combustion chemistry and control techniques and technologies. Techniques processes processes used to treat hazardous materials in the 3 pts. Lect: 2.5. Professor Yip. 3 pts. Lect: 3. Not offered in 2017–2018. environment, in situ and removal for treatment, Prerequisites: CIEE E4252 and CIEE E4163 or Prerequisite: EAEE E3200 or equivalent or focusing on those aspects that are unique to the the equivalent, or the instructor's permission. instructor’s permission. The fundamentals application of those technologies in an uncontrolled Fundamentals and applications of key of combustion phenomena and the intrinsic natural environment. Management, safety, and physicochemical processes relevant to water chemistry of combustion processes. The theory training issues. quality engineering (such as water treatment, of the essential combustion processes such as EAEE E6228y Theory of flotation waste water treatment/reuse/recycling, ignition, sustained reaction, stability and flame 3 pts. Lect: 3. Not offered in 2017–2018. desalination) and the natural environment (e.g., quenching. Processes that govern reactant Prerequisite: CHEE E4252 or instructor’s lakes, rivers, groundwater). consumption and product formation, in particular permission. A detailed study of the by-products that are formed that result in pollutant EAEE E6150y Industrial catalysis physicochemical principles of the flotation process. emissions, and the impacts and implications 3 pts. Lect: 3. Professor Farrauto. that combustion has locally and globally on the Prerequisite: EAEE E4550 or equivalent, or EAEE E6240x or y Physical hydrology environment. Detailed examination of the entire instructor’s permission. Fundamental principles 3 pts. Lect: 3. Professor Gentine. range of combustion systems from diffusion flame of kinetics, characterization and preparation of Prerequisite: Engineering hydrology or equivalent. processes to current developing technologies catalysts for production of petroleum products Spatial/temporal dynamics of the hydrologic cycle including millisecond catalytic combustion for conventional transportation fuels, specialty and its interactions with landforms and vegetation. processes, noncarbon fueled combustion, fuel chemicals, polymers, food products, hydrogen Hydroclimatology at regional to planetary scales, cells, and plasma combustion. and fuel cells and the application of catalysis focusing on mechanisms of organization and in biomass conversion to fuel. Update of the EAEE E6210x Quantitative environmental risk variation of water fluxes as a function of season, location, reservoir (ocean, atmosphere, land), and ever changing demands and challenges in analysis time scale. Land-atmosphere interaction and the environmental applications, focusing on advanced 3 pts. Lect: 3. Not offered in 2017–2018. role of vegetation and soil moisture. Topography catalytic applications as described in modern Prerequisite: EAEE E3101, STAT GU4001, or as an organizing principle for land water fluxes. literature and patents. equivalent. Comprises the tools necessary for Geomorphology and the evolution of river technical professionals to produce meaningful EAEE E6151y Applied geophysics networks. Sedimentation, erosion and hill slope risk analyses. Review of relevant probability and 3 pts. Lect: 3. Not offered in 2017–2018. hydrology. Dynamics of water movement over land, statistics; incorporation of probability in facility Potential field data, prospecting, wave equations. in rivers and in the subsurface, with an emphasis failure analysis. Availability, assessment, and Huygens’ principle, Green’s functions, Kirchoff on modeling interfaces. Integrated models and the incorporation of risk-related data. Contaminant equation, WKB approximation, ray tracing. Wave scale problem. Emphasis on data-based spatial/ transport to exposed individuals; uptake, morbidity, propagation, parameters. Computer applications. temporal modeling and exploration of outstanding and mortality. Computational tools necessary to Wavelet processing, filters and seismic data. theoretical challenges. risk modeling. Use and applicability of resulting Stratified Earth model, seismic processing and

ENGINEERING 2017–2018 132 CHEE E6252y Advanced surface and colloid 3 pts. Lect: 3. Instructor to be announced. EAEE E9281x Prospects for nuclear energy– chemistry Prerequisites: EAEE E4003 and CHEE earth and environmental engineering seminar 3 pts. Lect: 2. Lab: 3. Professors Somasundaran E4050, or instructor’s permission. Review of 0–1 pt. Lect: 1.5. Not offered in 2017–2018. and Farinato. current research and literature in the field of This seminar course examines the prospects for Prerequisite: CHEE E4252. Applications of surface hydrometallurgy, electrometallurgy, and corrosion. nuclear energy as a source of safe, secure, and chemistry principles to wetting, flocculation, Topics will be selected by the instructor to environmentally sustainable energy both in the flotation, separation techniques, catalysis, mass illustrate the application of thermodynamics and U.S. and internationally. In particular, it analyzes transfer, emulsions, foams, aerosols, membranes, rate phenomena to the design and control of the four key issues that limit the expansion biological surfactant systems, microbial surfaces, electrochemical engineering processes. of nuclear energy: cost, safety, proliferation enhanced oil recovery, and pollution problems. EAEE E8233x and y Research topics in concerns, and long-term disposal of radioactive Appropriate individual experiments and projects. particle processing wastes. Through readings, research, and class Lab required. 0 pts. Professor Somasundaran. discussions, it engages students to critically EAEE E6255x-E6256y Methods and Emergent findings in the interactions of particles evaluate arguments both for and against nuclear applications of analytical decision making in with reagents and solutions, especially inorganics, power. The course builds basic literacy in nuclear mineral industries surfactants, and polymers in solution, and technology and is open to students with technical, 3 pts. Lect: 3. Not offered in 2017–2018. their role in grinding, flotation, agglomeration, policy, or economic backgrounds. filtration, enhanced oil recovery, and other mineral Prerequisites: Instructor’s permission. Advanced EAEE E9302x and y Mining engineering processing operations. study of decision-making problems with critical research survey and applications of quantitative decision- EAEE E8273x-E8274y Mining engineering 0–4 pts. Not offered in 2017–2018. making techniques in mineral industries. reports Graduate research directed toward solution of Systematic development of methods of the 0–4 pts. Not offered in 2017–2018. technicoscientific problems in mining. formulation, analysis, and resolution of these May substitute for formal thesis, EAEE E9271, problems. EAEE E9305x and y–S9305 Earth and upon recommendation of the student’s adviser. environmental engineering research EAEE P6329 Water, sanitation, and human EAEE E9271x and y–S9271 Earth and 0–12 pts. Members of the faculty. health environmental engineering thesis Graduate research directed toward solution of 3 pts. Lect: 3. Professor Shaman. 0–6 pts. Members of the faculty. a problem in mineral processing or chemical Prerequisite: Instructor’s permission. In-depth Research work culminating in a creditable metallurgy. analysis of issues relating to water, sanitation, and dissertation on a problem of a fundamental hygiene in both the developed and developing EAEE E9800x and y–S9800 Doctoral research nature selected in conference between student worlds. Hydrologic cycle, major causes of enteric instruction and adviser. Wide latitude is permitted in choice morbidity and mortality, and design, financing and 3, 6, 9, or 12 pts. Members of the faculty. of a subject, but independent work of distinctly implementation of sanitation systems. For both A candidate for the Eng.Sc.D. degree in mineral graduate character is required in its handling. engineering and public health students; intended to engineering must register for 12 points of doctoral foster dialog between the two communities. EAEE E9273x-E9274y Earth and research instruction. Registration in EAEE E9800 may not be used to satisfy the minimum residence EAEE E8229x Selected topics in processing environmental engineering reports requirement for the degree. minerals and wastes 0–4 pts. May substitute for the formal master’s thesis, 3 pts. Lect: 2. Lab: 3. Not offered in 2017–2018. EAEE E9900x and y–S9900 Doctoral EAEE E9271, upon recommendation of the Prerequisite: CHEE E4252 or instructor’s dissertation department. permission. Critical discussion of current research 0 pts. Members of the faculty. topics and publications in the area of flotation, EAEE E9280x and y Earth and environmental A candidate for the doctorate may be required flocculation, and other mineral processing engineering colloquium to register for this course every term after the student’s coursework has been completed, and techniques, particularly mechanisms of adsorption, 0 pts. Lect: 1.5. Professor Yip. until the dissertation has been accepted. interactions of particles in solution, thinning of All graduate students are required to attend the liquid films, and optimization techniques. departmental colloquium as long as they are in residence. Advanced doctoral students may be EAEE E8231y Selected topics in hydro- and excused after three years of residence. No degree electrometallurgy credit is granted.

ENGINEERING 2017–2018 ELECTRICAL ENGINEERING 133 1300 S. W. Mudd, MC 4712 Phone: 212-854-3105 ee.columbia.edu

CHAIR Debasis Mitra Mingoo Seok Timothy Dickson Peter Kinget Steven Nowick, James Teherani Meikang Qiu Robert Laibowitz 1305 S. W. Mudd Computer Science John Wright Yi Sun Reuven Opher Henning G. Schulzrinne, Jacob Trevino VICE CHAIR Computer Science ASSOCIATE George Tulevski ASSOCIATE RESEARCH SCIENTISTS Charles A. Zukowski Amiya K. Sen PROFESSOR OF Deepak Turaga Svebor Alan Marin 1026 CEPSR Kenneth L. Shepard PROFESSIONAL Karaman Thomas N. Theis PRACTICE ADJUNCT ASSISTANT Mohammad Amin DIRECTOR OF Yannis P. Tsividis Zoran Kostic PROFESSORS Tadayon FINANCE AND Wen I. Wang Liangliang Cao Erik F. Young ADMINISTRATION Xiaodang Wang SENIOR LECTURER Jinfeng Du To be announced Charles A. Zukowski David Vallancourt Chong Li 1303 S. W. Mudd Vasanthan Raghavab ADJUNCT POSTDOCTORAL ASSOCIATE Brian Souhan PROFESSORS RESEARCH PROFESSORS PROFESSORS Michael S. Wang Yves Baeyens SCIENTISTS Dimitris Anastassiou Ethan Katz-Bassett Doru Calin SENIOR RESEARCH Marco R. Cavallari Keren Bergman Harish Krishnaswamy Xiaodong Cui SCIENTISTS You Chia Chang Shih-Fu Chang Ioannis (John) Kymissis Mark Feuer Qixiang Cheng Dan Ellis Nima Mesgarani Irving Kalet Cheng-Yun Chou Alexander Gaeta, Gil Zussman Applied Physics and Ching-Yun Lin Utsav Deepak Dave Truong-Thao Nguyen Yu Gu Applied Mathematics ASSISTANT Andreas Hartel Andreas H. Hielscher, PROFESSORS Krishan Sabnani Krishna Jayant Biomedical Engineering Javad Ghaderi Anwar Walid Kukjoo Kim Predrag Jelenkovic Christine Hendon Thomas Woo Changhyuk Lee Peter Kinget Xiaofan Fred Jiang Sheryl Woodward Yoonhee Lee Aurel A. Lazar Dion Khodagholy ADJUNCT ASSOCIATE Tiago Miguel Lopes Michal Lipson John Paisley PROFESSORS Marta da Costa Nicholas Maxemchuk Matthias Preindl Alexei Ashikhmin James A. O'Sullivan

ontemporary electrical handling systems of the future. Previous learn firsthand about current research engineering is a broad discipline innovations in electrical engineering have activities by participating in a program Cthat encompasses a wide range had a dramatic impact on the way in of undergraduate research projects with of activities. A common theme is the which we work and live: the transistor, the faculty. use of electrical and electromagnetic integrated circuits, computers, radio and A master’s level program in electrical signals for the generation, transmission, television, satellite transmission systems, engineering permits the graduate processing, storage, conversion, and lasers, fiber optic transmission systems, student to further specialize her/his control of information and energy. An and medical electronics. knowledge and skills within a wide equally important aspect is the human The faculty of the Electrical range of disciplines. For those who interface and the role of individuals as Engineering Department at Columbia are interested in pursuing a career in the sources and recipients of information. University is dedicated to the teaching or research, our Ph.D. program The rates at which information is continued development of further offers the opportunity to conduct transmitted today range from megabits innovations through its program of research under faculty super-vision at per second to gigabits per second and academic instruction and research. the leading edge of technology and in some cases, as high as terabits per Our undergraduate academic program applied science. Research seminars second. The range of frequencies over in electrical engineering is designed are offered in a wide range of areas, which these processes are studied to prepare the student for a career in including telecommunications, very large extends from direct current (i.e., zero industry or business by providing her scale integrated circuits, photonics, and frequency), to microwave and optical or him with a thorough foundation microelectronics. frequencies. of the fundamental concepts and The Electrical Engineering The need for increasingly faster and analytical tools of contemporary Department, along with the Computer more sophisticated methods of handling electrical engineering. A wide range of Science Department, also offers B.S. information poses a major challenge to elective courses permits the student to and M.S. programs in computer the electrical engineer. New materials, emphasize specific disciplines such as engineering. Details on those programs devices, systems, and network concepts telecommunications, microelectronics, can be found in the Computer are needed to build the advanced digital systems, or photonics. Engineering section in this bulletin. communications and information Undergraduates have an opportunity to

ENGINEERING 2017–2018 134 Research Activities conductors, pin diodes, avalanche Lightwave Communications Laboratory, The research interests of the faculty photodiodes, optical interconnects, and Photonics Laboratory, Plasma Physics encompass a number of rapidly growing quantum optics. A major effort is the Laboratory (in conjunction with the areas, vital to the development of future picosecond optoelectronics program, Department of Applied Physics). technology, that will affect almost every focusing on the development of new Laboratory instruction is provided in a aspect of society: communications devices and their applications to high- suite of newly-renovated facilities on the and information processing; solid-state speed optoelectronic measurement twelfth floor of the S. W. Mudd Building. devices; ultrafast optics and photonics; systems, photonic switching, and optical These teaching laboratories are used for microelectronic circuits, integrated logic. In addition, research is being circuit prototyping, device measurement, systems and computer-aided design; performed in detection techniques for VLSI design, embedded systems systems biology; and electromagnetics optical communications and radar. design, and IoT experiments. and plasmas. Details on all of Members of the photonics group play a leading role in a multi-university these areas can be found at UNDERGRADUATE PROGRAM ee.columbia.edu/research. consortium: The National Center for The educational objective of the Communications research focuses Integrated Photonics Technology. Electrical Engineering program, in on wireless communication, multimedia Integrated systems research involves support of the mission of the School, is networking, real-time Internet, the analysis and design of analog, digital, to prepare graduates to achieve success lightwave (fiber optic) communication and mixed-signal microelectronic circuits in one or more of the following within a networks, optical signal processing and systems. These include novel signal few years after graduation: and switching, service architectures, processors and related systems, data network management and control, converters, radio frequency circuits, A. Graduate or professional studies—as the processing of image and video low noise and low power circuits, and evidenced by admission to a top-tier information, and media engineering. fully integrated analog filters that share program, attainment of advanced Current studies include wireless and the same chip with digital logic. VLSI degrees, research contributions, or mobile computing environments, architectures for parallel computation, professional recognition. broadband kernels, object-oriented packet switching, and signal processing B. Engineering practice—as evidenced network management, real-time are also under investigation. Computer- by entrepreneurship; employment in monitoring and control, lightwave aided design research involves the industry, government, academia, or network architectures, lightweight development of techniques for the nonprofit organizations in engineering; protocol design, resource allocation and analysis and design of large-scale patents; or professional recognition. networking games, real-time Internet integrated circuits and systems. C. Careers outside of engineering that services, future all-digital HDTV systems, Electromagnetics research ranges take advantage of an engineering coding and modulation. from the classical domains of microwave education—as evidenced by Solid-state device research generation and transmission and contributions appropriate to the is conducted in the Columbia wave propagation in various media to chosen field. Microelectronics Sciences Laboratories. modern applications involving lasers, This is an interdisciplinary facility, optical fibers, plasmas, and solid-state The B.S. program in electrical involving aspects of electrical devices. Problems relevant to controlled engineering at Columbia University seeks engineering and applied physics. It thermonuclear fusion are under to provide a broad and solid foundation investigation. includes the study of semiconductor in the current theory and practice of physics and devices, optical electronics, electrical engineering, including familiarity Laboratory Facilities and quantum optics. The emphasis is with basic tools of math and science, on laser processing and diagnostics Current research activities are fully an ability to communicate ideas, and for submicron electronics, fabrication supported by more than a dozen well- a humanities background sufficient to of compound semiconductor equipped research laboratories run by understand the social implications of optoelectronic devices by molecular the department. Specifically, laboratory engineering practice. Graduates should beam epitaxy, physics of superlattices research is conducted in the following be qualified to enter the profession and quantum wells, and interface laboratories: Multimedia Networking of engineering, to continue toward a devices such as Schottky barriers, Laboratory, Lightwave Communications career in engineering research, or to MOS transistors, heterojunctions, and Laboratory, Systems Laboratory, Image enter other fields in which engineering bipolar transistors. Another area of and Advanced Television Laboratory, knowledge is essential. Required activity is the physics and chemistry of Laser Processing Laboratory, Molecular nontechnical courses cover civilization microelectronics packaging. Beam Epitaxy Laboratory, Surface and culture, philosophy, economics, Research in photonics includes Analysis Laboratory, Microelectronics and a number of additional electives. development of semi conductor light Fabrication Laboratory, Device English communication skills are an sources such as LEDs and injection Measurement Laboratory, Ultrafast important aspect of these courses. lasers, fabrication and analysis of Optoelectronics Laboratory, Columbia Required science courses cover basic quantum confined structures, photo Integrated Systems Laboratory (CISL), chemistry and physics, whereas math

ENGINEERING 2017–2018 135 ELECTRICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS EARLY-STARTING STUDENTS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

APMA E2000 (4)4 MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) and APMA E2101 (3)1

PHYSICS UN1401 (3) UN1402 (3) (three tracks, UN1601 (3.5) UN1602 (3.5) choose one) UN2801 (4.5) UN2802 (4.5)

one-semester lecture (3–4) CHEMISTRY UN1403 or UN1404 or UN2045 or UN1604

ELEN E3201 (3.5) ELEN E3331 (3) ELEN E1201 (3.5) Circuit analysis Electronic circuts CORE REQUIRED Introduction to electrical engineering COURSES (either semester) ELEN E3801 (3.5) CSEE E3827 (3) Signals and systems Fund. of computer sys.

ELEN E3081 (1)2 ELEN E3083 (1)2 Circuit analysis lab Electronic circuits lab REQUIRED LABS ELEN E3084 (1)2 ELEN E3082 (1)2 Signals and systems lab Digital systems lab

UNIVERSITY UN1010 (3) either semester WRITING

REQUIRED HUMA CC1001, COCI CC1101, or Global Core (3–4); HUMA UN1121 or UN1123 (3); HUMA CC1002, COCI NONTECHNICAL CC1102, or Global Core (3–4); ECON UN1105 (4) and UN1155 recitation (0); some of these courses can be ELECTIVES postponed to the junior or senior year, to make room for taking the above electrical engineering courses.

COMPUTER ENGI E1006 (3) either semester3 SCIENCE

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 APMA E2101 may be replaced by MATH UN2030 (formerly MATH E1210) and either APMA E3101 or MATH UN2010. 2 If possible, these labs should be taken along with their corresponding lecture courses. 3 ENGI E1006 may not be offered every semester. See ee.columbia.edu for more discussion about the Computer Science sequences. 4 Effective Class of 2021. requirements cover calculus, differential Topics include a sequence of two on experience early and to motivate equations, probability, and linear algebra. courses on circuit theory and electronic theoretical work. Simple creative design Basic computer knowledge is also circuits, one course on semiconductor experiences start immediately in this included, with an introductory course on devices, one on electromagnetics, one first-year course. Following this is a using engineering workstations and two on signals and systems, one on digital sequence of lab courses that parallel rigorous introductory computer science systems, and one on communications the core lecture courses. Opportunities courses. Core electrical engineering or networking. Engineering practice is for exploring design can be found courses cover the main components developed further through a sequence both within these lab courses and of modern electrical engineering and of laboratory courses, starting with a in the parallel lecture courses, often illustrate basic engineering principles. first-year course to introduce hands- coupled with experimentation and

ENGINEERING 2017–2018 136 ELECTRICAL ENGINEERING: THIRD AND FOURTH YEARS EARLY-STARTING STUDENTS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

UN1403 (3) Lab UN1494 (3)1 PHYSICS (tracks continued) UN2601 (3.5) Lab UN2699 (3) Lab W3081 (2)

ELEN E3401 (4) Electromagnetics

EE CORE ELEN E3106 (3.5) ELEN E3701 (3)2 REQUIRED Solid-state devices and Intro. to COURSES materials communication systems or CSEE W4119 (3)2 Computer networks

ELEN E3043 (3) Solid state, microwave, ELEN E3390 (3)3 and fiber optics lab EE REQUIRED LABS Capstone design course ELEN E3399 (1) EE practice

IEOR E3658 or STAT GU42034; and COMS W3136 (or W3134 or W3137)5 OTHER REQUIRED (Some of these courses are not offered both semesters. Students with an adequate COURSES background can take some of these courses in the sophomore year)

At least two technical electives in one depth area. The four depth areas are EE DEPTH (a) photonics, solid-state devices, and electromagnetics; (b) circuits and electronics; TECH (c) signals and systems; and (d) communications and networking (For details, see ee.columbia.edu)

(at least 6 points total) BREADTH At least two technical electives outside the chosen depth area; must be courses with significant TECH engineering content (see ee.columbia.edu) ELECTIVES OTHER Additional technical electives (consisting of more depth or breadth courses, or further options listed at TECH ee.columbia.edu/ee-undergraduate-program) as required to bring the total points of technical electives to 186

Complete 27-point requirement; see page 10 or seas.columbia.edu for details NONTECH (administered by the advising dean)

TOTAL POINTS7 16.5 17 16 18

1 Chemistry lab (CHEM UN1500) may be substituted for physics lab, although this is not generally recommended. 2 These courses can be taken in the sophomore year if the prerequisites/corequisites are satisfied. 3 The capstone design course provides ELEN majors with a “culminating design experience.” As such, it should be taken near the end of the program and involve a project that draws on material from a range of courses. If special arrangements are made in ELEN E3399, it is possible to use courses such as ELEN E3998, E4350, E4998, EECS E4340, or CSEE W4840 in place of ELEN E3390. 4 SIEO W3600 and STAT GU4001 cannot generally be used to replace IEOR E3658 or STAT GU4203. 5 Students who plan to minor in Computer Science should choose COMS W3134 or W3137. 6 The total points of technical electives is reduced to 15 if APMA E2101 has been replaced by MATH UN2030 (formerly MATH E1210) and either APMA E3101 or MATH UN2010. 7 “Total points” assumes that 20 points of nontechnical electives and other courses are included.

ENGINEERING 2017–2018 137 ELECTRICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS LATE-STARTING STUDENTS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

APMA E2000 (4)5 MATHEMATICS MATH UN1101(3) MATH UN1102 (3) and APMA E2101 (3)1

PHYSICS UN1401 (3) UN1402 (3) UN1403 (3) Lab UN1494 (3)2 (three tracks, UN1601 (3.5) UN1602 (3.5) UN2601 (3.5) Lab UN2699 (3) choose one) UN2801 (4.5) UN2802 (4.5) Lab UN3081 (2)

one-semester lecture (3–4) CHEMISTRY UN1403 or UN1404 or UN2045 or UN1604

ELECTRICAL ELEN E1201 (3.5) either semester3 ENGINEERING

UNIVERSITY UN1010 (3) either semester WRITING

HUMA CC1001, HUMA CC1002, COCI CC1101, COCI CC1102, REQUIRED or Global Core (3–4) or Global Core (3–4) NONTECHNICAL ELECTIVES HUMA UN1121 or ECON UN1105 (4) and UN1123 (3) UN1155 recitation (0)

COMPUTER ENGI E1006 (3) any semester4 SCIENCE

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 APMA E2101 may be replaced by MATH UN2030 (formerly MATH E1210) and either APMA E3101 or MATH UN2010. 2 Chemistry lab (CHEM UN1500) may be substituted for physics lab, although this is not generally recommended. 3 Transfer students and 3-2 Combined Plan students who have not taken ELEN E1201 prior to the junior year are expected to have taken a roughly equivalent course when they start ELEN E3201. 4 ENGI E1006 may not be offered every semester. See ee.columbia.edu for more discussion about the Computer Science sequences. 5 Effective Class of 2021.

computer simulation, respectively. The specific area of interest. More detailed EE Core Curriculum culmination of the laboratory sequence program objectives and outcomes are All electrical engineering (EE) students and the design experiences introduced posted at ee.columbia.edu. must take a set of core courses, which throughout earlier courses is a senior The program in electrical engineering collectively provide the student with design course (capstone design leading to the B.S. degree is accredited fundamental skills, expose him/her course), which includes a significant by the Engineering Accreditation to the breadth of EE, and serve as a design project that ties together the Commission of ABET. springboard for more advanced work, or core program, encourages creativity, There is a strong interaction between for work in areas not covered in the core. explores practical aspects of engineering the Department of Electrical Engineering These courses are shown on the charts practice, and provides additional and the Departments of Computer in Undergraduate Degree Tracks. A full experience with communication skills in Science, Applied Physics and Applied curriculum checklist is also posted at an engineering context. Finally, several Mathematics, Industrial Engineering ee.columbia.edu. technical electives are required, chosen and Operations Research, Physics, and to provide both breadth and depth in a Chemistry.

ENGINEERING 2017–2018 138 ELECTRICAL ENGINEERING: THIRD AND FOURTH YEARS LATE-STARTING STUDENTS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

CSEE W3827(3) Fund. of computer sys.

ELEN E3106 (3.5) ELEN E3331 (3) Solid-state devices and Electronic circuits materials EE CORE ELEN E3401 (4) REQUIRED ELEN E3201 (3.5) Electromagnetics COURSES Circuit analysis ELEN E3701 (3) ELEN E3801 (3.5) Intro. to Signals and systems communication systems or CSEE W4119 (3) Computer networks

ELEN E3043 (3) ELEN E3081 (1)1 ELEN E3083 (1)1 Solid state, microwave, Circuit analysis lab Electronic circuits lab ELEN E3390 (3)2 and fiber optics lab EE REQUIRED LABS Capstone design ELEN E3084 (1)1 ELEN E3082 (1)1 course ELEN E3399 (1) Signals and systems lab Digital systems lab EE practice

OTHER REQUIRED IEOR E3658 or STAT GU42033; and COMS W3136 (or W3134 or W3137)4 COURSES (Some of these courses are not offered both semesters)

At least two technical electives in one depth area. The four depth areas are EE DEPTH (a) photonics, solid-state devices, and electromagnetics; (b) circuits and TECH electronics; (c) signals and systems; and (d) communications and networking. (For details, see ee.columbia.edu.)

(at least 6 points total) BREADTH At least two technical electives outside the chosen depth area; must be courses with significant engineering TECH content (see ee.columbia.edu) ELECTIVES OTHER Additional technical electives (consisting of more depth or breadth courses, or further options listed at TECH ee.columbia.edu/ee-undergraduate-program) as required to bring the total points of technical electives to 185

Complete 27-point requirement; see page 10 or seas.columbia.edu for details NONTECH (administered by the advising dean)

TOTAL POINTS6 15.5 18 16 18

Note: This chart shows one possible schedule for a student who takes most of his or her major program in the final two years. Please refer to the previous chart for a recommended earlier start. 1 If possible, these labs should be taken along with their corresponding lecture courses. 2 The capstone design course provides ELEN majors with a “culminating design experience.” As such, it should be taken near the end of the program and involve a project that draws on material from a range of courses. If special arrangements are made in ELEN E3399, it is possible to use courses such as ELEN E3998, E4350, E4998, EECS E4340, or CSEE W4840 in place of ELEN E3390. 3 SIEO W3600 and STAT GU4001 cannot generally be used to replace IEOR E3658 or STAT GU4203. 4 Students who plan to minor in Computer Science should choose COMS W3134 or W3137. 5 The total points of technical electives is reduced to 15 if APMA E2101 has been replaced by MATH UN2030 (formerly MATH E1210) and either APMA E3101 or MATH UN2010. 6 “Total points” assumes that 9 points of nontechnical electives are included.

ENGINEERING 2017–2018 Technical Electives in a chosen depth area, or gives them of Science degrees in an integrated 139 The 18-point technical elective more time to explore before choosing fashion. Up to 6 points may be credited requirement for the electrical engineering a depth area. Students can start with to both degrees, and some graduate program consists of three components: ELEN E1201: Introduction to electrical classes taken in the senior year depth, breadth, and other. A general engineering in the second semester of may count toward the M.S. degree. outline is provided here, and more their first year, and can continue with Interested students can find further specific course restrictions can be found other core courses one semester after information at ee.columbia.edu and can at ee.columbia.edu. For any course not that, as shown in the “early-starting discuss options directly with their faculty clearly listed there, adviser approval is students” chart. It is emphasized that adviser. Students must be admitted prior necessary. both the early- and late-starting sample to the start of their seventh semester The depth component must consist of programs shown in the charts are at Columbia Engineering. Students in at least 6 points of electrical engineering examples only; schedules may vary the 3-2 Combined Plan undergraduate courses in one of four defined areas: depending on student preparation and program are not eligible for admission to (a) photonics, solid-state devices, interests. this program. and electromagnetics; (b) circuits and electronics; (c) signals and systems; and Transfer Students GRADUATE PROGRAMS (d) communications and networking. Transfer students coming to The Department of Electrical Engineering The depth requirement provides an Columbia as juniors with sufficient offers graduate programs leading to the opportunity to pursue particular interests general background can complete all degree of Master of Science (M.S.) and and exposure to the process of exploring requirements for the B.S. degree in the degrees of Doctor of Engineering a discipline in depth—an essential electrical engineering. Such students fall Science (Eng.Sc.D.) and Doctor of process that can be applied later to other into one of two categories: Philosophy (Ph.D.). The Graduate disciplines, if desired. Record Examination (General Test only) The breadth component must consist Plan 1: Students coming to Columbia is required of all applicants except of at least 6 additional points of courses without having taken the equivalent of special students. An undergraduate that are outside of the chosen depth ELEN E1201 must take this course in grade-point average equivalent to B or area and have significant engineering their junior year. This requires postponing better from an institution comparable to content. These courses can be from the core courses in circuits and electronics until the senior year, and thus Columbia is expected. other departments within the School. does not allow taking electives in that Applicants who, for good reasons, The breadth requirement precludes area; thus, such students cannot choose are unable to submit GRE test results overspecialization. Breadth is particularly circuits and electronics as a depth area. by the deadline date but whose important today, as innovation requires undergraduate record is clearly superior more and more of an interdisciplinary Plan 2: This plan is for students who may file an application without the GRE approach, and exposure to other have taken a course equivalent to ELEN scores. An explanatory note should be fields is known to help one’s creativity E1201 at their school of origin, including added to ensure that the application will in one’s own main field. Breadth also a laboratory component. See the bulletin be processed even while incomplete. If reduces the chance of obsolescence as for a description of this course. Many the candidate’s admissibility is clear, the technology changes. pre-engineering programs and physics decision may be made without the GRE Any remaining technical elective departments at four-year colleges offer scores; otherwise, it may be deferred courses, beyond the minimum 12 points such courses. Such students can start until the scores are received. of depth and breadth, do not have to be taking circuits at Columbia immediately, There are no prescribed course engineering courses (except for students and thus can choose circuits and requirements in any of the regular without ELEN E1201 or approved transfer electronics as a depth area. graduate degree programs. Students, in credit for ELEN E1201) but must be It is stressed that ELEN E1201 or consultation with their faculty advisers, technical. Generally, math and science its equivalent is a key part of the EE design their own programs, focusing on courses that do not overlap with courses curriculum. The preparation provided by particular fields of electrical engineering. used to fill other requirements are allowed. this course is essential for a number of Among the fields of graduate study are other core courses. microelectronics, communications and Starting Early Sample programs for both Plan 1 signal processing, integrated circuit The EE curriculum is designed to allow and Plan 2 transfer students can be and system analysis and synthesis, students to start their study of EE in their found at ee.columbia.edu. photonics, electromagnetic theory first year. This motivates students early and applications, plasma physics, and and allows them to spread nontechnical B.S./M.S. Program quantum electronics. requirements more evenly. It also makes The B.S./M.S. degree program is open Graduate course charts for evident the need for advanced math and to a select group of undergraduate several focus areas can be found at physics concepts, and motivates the students. This double degree program ee.columbia.edu. study of such concepts. Finally, it allows makes possible the earning of both more time for students to take classes the Bachelor of Science and Master

ENGINEERING 2017–2018 140 Master of Science Degree Doctoral candidates must obtain With an adviser’s approval, any of the Candidates for the M.S. degree in a minimum of 60 points of formal courses above can be replaced by the electrical engineering must complete 30 course credit beyond the bachelor’s following closely related subjects: CSEE points of credit beyond the bachelor’s degree. A master’s degree from an E4140: Networking laboratory; CSEE degree. A minimum of 15 points of credit accredited institution may be accepted W4119: Computer networks; COMS must be at the 6000 level or higher. No as equivalent to 30 points. A minimum W4180: Network security; ELEN E6762: credit will be allowed for undergraduate of 30 points beyond the master’s degree Computer communication networks, courses (3000 or lower). At least 15 must be earned while in residence in the II; ELEN E6850: Visual information points must be in electrical engineering, doctoral program. systems; ELEN E6951: Wireless and defined as including all courses with an More detailed information regarding mobile networking, II. ELEN designator or a joint designator the requirements for the doctoral degree containing electrical engineering as a may be obtained in the department Concentration in Telecommunications member, e.g., EECS, CSEE, EEME, office and at ee.columbia.edu. Engineering ECBM, etc. And it is expected that at Advisers: Professors Henning least 12 of the first 24 points taken will be Optional M.S. Concentrations Schulzrinne, Pedrag Jelenkovic, in electrical engineering. Students in the electrical engineering Ed Coffman, Gil Zussman Not all technical courses can be M.S. program often choose to use applied toward the M.S. degree, and some of their electives to focus on 1. Satisfy M.S. degree requirements. some have restrictions. Also, no more a particular field. Students may pick 2. One basic hardware or software than 6 points of research (such as one of a number of optional, formal course such as: EECS E4321: ELEN E4998, ELEN E6001, and ELEN concentration templates or design their Digital VLSI circuits; ELEN E4411: E6002) can be used, and no more than own M.S. program in consultation with Fundamentals of photonics; COMS 3 points of approved courses that do an adviser. These concentrations are not W4118: Operating systems, I; COMS not contain primarily engineering, math, degree requirements. They represent W4111: Database systems. or science content can be used. Any suggestions from the faculty as to how 3. One basic systems course such course that is not on the list of standard one might fill one’s programs so as to as: ELEN E4702: Communication courses specified at ee.columbia.edu/ focus on a particular area of interest. theory; ELEN E4703: Wireless masters-program requires prior written Students may wish to follow these communications; CSEE W4119: department approval, including during suggestions, but they need not. The Computer networks; ELEN E6761: the summer session. degree requirements are quite flexible Computer communication networks, I. The general school requirements and are listed in the Master of Science 4. At least two approved courses from listed earlier in this bulletin, such as Degree section, above. All students, a focus area such as Signal/Image minimum GPA, must also be satisfied. whether following a formal concentration Processing and Telecommunications/ All degree requirements must be template or not, are expected to include Multimedia Networks. completed within five years of the breadth in their program. Not all of the beginning of the first course credited elective courses listed here are offered Concentration in Lightwave toward the degree. every year. For the latest information (Photonics) Engineering More details and a requirements on available courses, visit the Electrical Advisers: Professors Keren Bergman, checklist for approvals can be found at Engineering home page at Ioannis (John) Kymissis, Michael Lipson ee.columbia.edu/masters-program. ee.columbia.edu. 1. Satisfy M.S. degree requirements. Doctoral Degree Concentration in Multimedia 2. Take both ELEN E4411: The requirements for the Ph.D. and Eng. Networking Fundamentals of photonics and ELEN Sc.D. degrees are identical. Both require Advisers: Professors Henning E6412: Lightware devices (or an a dissertation based on the candidate’s Schulzrinne, Predrag Jelenkovic E&M course, such as APPH E4300: original research, conducted under the Applied electrodynamics or PHYS supervision of a faculty member. The 1. Satisfy M.S. degree requirements. GR6092: Electromagnetic theory). work may be theoretical or experimental 2. Both ELEN E6761: Computer 3. One more device/circuits/photonics or both. communication networks, I and course such as: ELEN E6413: Students who wish to become ELEN E6950: Wireless and mobile Lightwave systems; ELEN E6414: candidates for the doctoral degree in networking, I. Photonic integrated circuits; ELEN electrical engineering have the option of 3. Either COMS W4118: Operating E4314: Communication circuits; applying for admission to the Eng.Sc.D. systems or COMS W4111: Database ELEN E4488: Optical systems; ELEN program or the Ph.D. program. Students systems. E6488: Optical interconnects and who elect the Eng.Sc.D. degree register 4. COMS E6181: Advanced Internet interconnection networks; ELEN in the School of Engineering and Applied services or ELEN E6776: Topic: E4193: Modern display science and Science; those who elect the Ph.D. content distribution networks. technology. degree register in the Graduate School 4. At least two additional approved of Arts and Sciences. courses in photonics or a related

ENGINEERING 2017–2018 area. Options also include courses Concentration in Integrated Circuits as APPH E4090: Nanotechnology; 141 outside EE such as APPH E4090: and Systems APPH E4100: Quantum physics of Nanotechnology; APPH E4100: Advisers: Professors Peter Kinget, matter; APPH E4110: Modern optics; Quantum physics of matter; APPH Harish Krishnaswamy, Mingoo Seok, CHAP E4120: Statistical mechanics; E4110: Modern optics; CHAP E4120: Kenneth Shepard, Yannis Tsividis, APPH E4112: Laser physics; APPH Statistical mechanics; APPH E4112: Charles Zukowski E4130: Physics of solar energy; Laser physics; APPH E4130: Physics APPH E6081: Solid state physics, of solar energy; APPH E6081: Solid 1. Satisfy M.S. degree requirements. I; APPH E6082: Solid state physics, state physics, I; APPH E6082: Solid 2. One digital course from: EECS E4321: II; APPH E6091: Magnetism and state physics, II; APPH E6091: Digital VLSI circuits or EECS E6321: magnetic materials; APPH E6110: Magnetism and magnetic materials; Advanced digital electronic circuits. Laser interactions with matter; APPH E6110: Laser interactions 3. One analog course from ELEN E4312: MSAE E4202: Thermodynamics and with matter; MSAE E4202: Analog electronic circuits; ELEN reactions in solids; MSAE E4206: Thermodynamics and reactions in E6312: Advanced analog integrated Electronic and magnetic properties solids; MSAE E4206: Electronic circuits; ELEN E6316: Analog circuits of solids; MSAE E4207: Lattice and magnetic properties of solids; and systems in VLSI; ELEN E4314: vibrations and crystal defects; MSAE E4207: Lattice vibrations Communication circuits; ELEN E6314: MSAE E6120: Grain boundaries and and crystal defects; MSAE E6120: Advanced communication circuits; interfaces; MSAE E6220: Crystal Grain boundaries and interfaces; ELEN E6320: Millimeter-wave IC physics; MSAE E6229: Energy and MSAE E6220: Crystal physics; design. particle beam processing of materials; MSAE E6229: Energy and particle 4. Two additional courses such as other MSAE E6225: Techniques in X-ray beam processing of materials; MSAE courses from no. 2 and 3; ELEN and neutron diffraction. E6225: Techniques in X-ray and E6350: VLSI design laboratory; ELEN neutron diffraction. E6304: Topics in electronic circuits; Concentration in Systems Biology ELEN E6318: Microwave circuit and Neuroengineering Concentration in Wireless and Mobile design; ELEN E9303: Seminar in Advisers: Professors Dimitris Communications electronic circuits. Anastassiou, Christine Hendon, Pedrag Adviser: Professors Gil Zussman, 5. At least one additional approved Jelenkovic, Aurel A. Lazar, Nima Predrag Jelenkovic, Xiaodong Wang course in integrated circuits and Mesgarani, Kenneth Shepard, Xiaodong systems or a related area. Wang 1. Satisfy M.S. degree requirements. 2. One basic circuits course such as: Concentration in Microelectronic 1. Satisfy M.S. degree requirements. ELEN E4312: Analog electric circuits; Devices 2. Take both ECBM E4060: Introduction ELEN E4314: Communication Advisers: Professors Wen Wang, Ioannis to genomic information science circuits; ELEN E6314: Advanced (John) Kymissis and technology and BMEB W4020: communication circuits; ELEN E6312: Computational neuroscience, circuits Advanced analog ICs. 1. Satisfy M.S. degree requirements. in the brain 3. Two communications or networking 2. One basic course such as: ELEN 3. Take at least one course from courses such as: CSEE W4119: E4301: Introduction to semiconductor BMEE E4030: Neural control Computer networks; ELEN E4702: devices or ELEN E4411: engineering; ECBM E4040: Neural Digital communications; ELEN Fundamentals of photonics. networks and deep learning; ECBM E4703: Wireless communications; 3. One advanced course such as: ELEN E4090: Brain computer interfaces ELEN E6711: Stochastic signals E4193: Modern display science (BCI) laboratory; CBMF W4761: and noise; ELEN E4810: Digital and technology; ELEN E4944: Computational genomics; ELEN signal processing; ELEN E6950: Principles of device microfabrication; E6010: Systems biology: design Wireless and mobile networking, ELEN E4503: Sensors, actuators, principles for biological circuits; EEBM I; ELEN E6951: Wireless and and electromechanical systems; E6020: Methods in computational mobile networking, II; ELEN E6761: ELEN E6151: Surface physics and neuroscience; BMEE E6030: Neural Computer communication networks, analysis of electronic materials; ELEN modeling and neuroengineering. I; ELEN E6712: Communication E6331: Principles of semiconductor 4. Take at least one course from ECBM theory; ELEN E6713: Topics in physics, I; ELEN E6332: Principles E6040: Neural networks and deep communications; ELEN E6717: of semiconductor physics, II; ELEN learning research; ECBM E607x: Information theory; ELEN E677x: E6333: Semiconductor device Topics in neuroscience and deep Topics in telecommunication physics; ELEN E6945: Nanoscale learning; ELEN E608x: Topics in networks. fabrication and devices. systems biology; EEBM E609x: 4. At least two additional approved 4. At least two other approved courses Topics in computational neuroscience courses in wireless communications or in devices or a related area. Options and neuroengineering; ELEN E6261: a related area. also include courses outside EE such Computational methods of circuit analysis ELEN E6717: Information

ENGINEERING 2017–2018 142 theory; ELEN E6860: Advanced digital ELEN E1201x and y Introduction to electrical function; forced response. The lab generally signal processing. engineering meets on alternate weeks. 3.5 pts. Lect: 3. Lab:1. Professor Vallancourt. ELEN E3106x Solid-state devices and materials Prerequisite: MATH UN1101. Basic concepts of Concentration in Data-Driven Analysis 3.5 pts. Lect: 3. Recit: 1. Professor Kymissis. electrical engineering. Exploration of selected and Computation Prerequisite: MATH UN1201 or equivalent. topics and their application. Electrical variables, Corequisite: PHYS UN1403 or PHYS UN2601 Advisers: Professors Dimitris circuit laws, nonlinear and linear elements, or equivalent. Crystal structure and energy Anastassiou, Shih-Fu Chang, Pedrag ideal and real sources, transducers, operational band theory of solids. Carrier concentration Jelenkovic, Zoran Kostic, Aurel A. Lazar, amplifiers in simple circuits, external behavior and transport in semiconductors. P-n junction Nima Mesgarani, John Paisley, John of diodes and transistors, first order RC and RL and junction transistors. Semiconductor surface Wright, Xiaofan (Fred) Jiang circuits. Digital representation of a signal, digital and MOS transistors. Optical effects and logic gates, flip-flops. A lab is an integral part of optoelectronic devices. 1. Satisfy M.S. degree requirements. the course. Required of electrical engineering 2. Take at least two courses from ECBM and computer engineering majors. ELEN E3201x Circuit analysis 3.5 pts. Lect: 3. Recit: 1. Professor Zukowski. E4040: Neural networks and deep ELEN E3043x Solid state, microwave, and Prerequisite: ELEN E1201 or equivalent. learning; EECS E4764: Internet of fiber optics laboratory Corequisite: MATH UN1201. A course on things—intelligent and connected 3 pts. Lect: 1. Lab: 6. Professor W. Wang. analysis of linear and nonlinear circuits and their systems; ELEN E4810: Digital signal Prerequisites: ELEN E3106 and ELEN E3401. applications. Formulation of circuit equations. Optical electronics and communications. processing; ELEN E4903: Topic: Network theorems. Transient response of first and Microwave circuits. Physical electronics. machine learning (or equivalent); second order circuits. Sinusoidal steady state- EEOR E6616: Convex optimization; ELEN E3081x Circuit analysis laboratory analysis. Frequency response of linear circuits. EECS E6893: Topic: big data 1 pt. Lab: 3. Professor Zukowski. Poles and zeros. Bode plots. Two-port networks. analytics. Prerequisite: ELEN E1201 or equivalent. ELEN E3331y Electronic circuits 3. Take at least one courses from Corequisite: ELEN E3201. Companion lab course 3 pts. Lect: 3. Professor Kostic. for ELEN E3201. Experiments cover such topics ECBM E6040: Neural networks Prerequisites: ELEN E3201. Operational as: use of measurement instruments; HSPICE and deep learning research; EECS amplifier circuits. Diodes and diode circuits. simulation; basic network theorems; linearization of E6720: Bayesian models for machine MOS and bipolar junction transistors. Biasing nonlinear circuits using negative feedback; op-amp learning; EECS E6765: Internet of techniques. Small-signal models. Single-stage circuits; integrators; second order RLC circuits. things—systems and physical data transistor amplifiers. Analysis and design of The lab generally meets on alternate weeks. analytics; EECS E6895: Topic: CMOS logic gates. A/D and D/A converters. ELEN E3082y Digital systems laboratory advanced big data analytics. ELEN E3390y Electronic circuit design 1 pt. Lab: 3. Professor Shepard. 4. Take a second course from #3 or laboratory Corequisite: CSEE W3827. Recommended one course from ECBM E4060: 3 pts. Lab: 6. Professor Vallancourt. preparation: ELEN E1201 or equivalent. Introduction to genomic information Prerequisites: ELEN E3082, E3083, E3331, Companion lab course for CSEE W3827. science and technology; ECBM: E3401, E3801. Advanced circuit design Experiments cover such topics as logic gates; 6070: Topics in neuroscience and flip-flops; shift registers; counters; combinational laboratory. Students work in teams to specify, deep learning; ELEN E6690: Topics in logic circuits; sequential logic circuits; design, implement and test an engineering data-driven analysis and computation; programmable logic devices. The lab generally prototype. The work involves technical as ELEN E6886: Sparse representation meets on alternate weeks. well as non-technical considerations, such as and high-dimensional geometry; manufacturability, impact on the environment, ELEN E3083y Electronic circuits laboratory ELEN E9601: Seminar in data-driven and economics. The projects may change from 1 pt. Lab: 3. Professor Kostic. analysis and computation. year to year. Prerequisite: ELEN E3081. Corequisite: ELEN E3331. Companion lab course for ELEN ELEN E3399x Electrical engineering practice COURSES IN ELECTRICAL E3331. Experiments cover such topics as 1 pt. Professor Vallancourt. ENGINEERING macromodeling of nonidealities of opamps Design project planning, written and oral using SPICE; Schmitt triggers and astable technical communication, practical aspects of ELEN E1101x or y The digital information age multivibrations using opamps and diodes; logic engineering as a profession, such as career 3 pts. Lect: 3. Professor Vallancourt. inverters and amplifiers using bipolar junction development and societal and environmental An introduction to information transmission and transistors; logic inverters and ring oscillators impact. Generally taken senior year. storage, including technological issues. Binary using MOSFETs; filter design using opamps. The ELEN E3401y Electromagnetics numbers; elementary computer logic; digital lab generally meets on alternate weeks. speech and image coding; basics of compact 4 pts. Lect: 3. Professor Kash. ELEN E3084x Signals and systems laboratory disks, telephones, modems, faxes, UPC bar Prerequisite: MATH UN1201, PHYS UN1402 1 pt. Lab: 3. Professor X. Wang. codes, and the World Wide Web. Projects or PHYS UN1602, or equivalents. Basic Corequisite: ELEN E3801. Companion lab include implementing simple digital logic systems field concepts. Interaction of time-varying course for ELEN E3801. Experiments cover and Web pages. Intended primarily for students electromagnetic fields. Field calculation of topics such as: introduction and use of MATLAB outside the School of Engineering and Applied lumped circuit parameters. Transition from for numerical and symbolic calculations; Science. The only prerequisite is a working electrostatic to quasistatic and electromagnetic linearity and time invariance; continuous-time knowledge of elementary algebra. regimes. Transmission lines. Energy transfer, convolution; Fourier-series expansion and signal dissipation, and storage. Waveguides. Radiation. reconstruction; impulse response and transfer

ENGINEERING 2017–2018 EEME E3601x Classical control systems member who agrees to supervise the work. Introduction to the information system 143 3 pts. Lect: 3. Professor Longman. May be repeated for credit, but no more than paradigm of molecular biology. Representation, Prerequisite: MATH UN2030. Analysis and 3 total points may be used for degree credit. organization, structure, function and manipulation design of feedback control systems. Transfer Independent project involving laboratory work, of the biomolecular sequences of nucleic functions; block diagrams; proportional, rate, and computer programming, analytical investigation, acids and proteins. The role of enzymes and integral controllers; hardware; implementation. or engineering design. gene regulatory elements in natural biological functions as well as in biotechnology and Routh stability criterion, root locus, Bode and BMEB W4020x Computational neuroscience: genetic engineering. Recombination and Nyquist plots, compensation techniques. circuits in the brain other macromolecular processes viewed as 3 pts. Lect: 3. Professor Lazar. ELEN E3701y Introduction to communication mathematical operations with simulation and Prerequisite: ELEN E3801 or BIOL UN3004. systems visualization using simple computer programming. The biophysics of computation: modeling 3 pts. Lect: 3. Professor Kalet. This course shares lectures with ECBM E3060, biological neurons, the Hodgkin-Huxley neuron, Prerequisite: ELEN E3801. Corequisite: IEOR but the work requirements differ somewhat. E3658. A basic course in communication theory, modeling channel conductances and synapses stressing modern digital communication systems. as memristive systems, bursting neurons and ECBM E4090x or y Brain computer interfaces (BCI) laboratory Nyquist sampling, PAM and PCM/DPCM systems, central pattern generators, I/O equivalence and spiking neuron models. Information representation 3 pts. Lect: 2. Lab: 3. Professor Mesgarani. time division multiplexing, high frequency digital and neural encoding: stimulus representation Prerequisites: ELEN E3801. Hands-on (ASK, OOK, FSK, PSK) systems, and AM and with time encoding machines, the geometry of experience with basic neural interface FM systems. An introduction to noise processes, time encoding, encoding with neural circuits with technologies. Recording EEG detecting signals in the presence of noise, feedback, population time encoding machines. (electroencephalogram) signals using data Shannon’s theorem on channel capacity, and Dendritic computation: elements of spike acquisition systems (noninvasive, scalp elements of coding theory. processing and neural computation, synaptic recordings). Real-time analysis and monitoring ELEN E3801x Signals and systems plasticity and learning algorithms, unsupervised of brain responses. Analysis of intention and 3.5 pts. Lect: 3. Professor X. Wang. learning and spike time-dependent plasticity, basic perception of external visual and audio signals. Corequisite: MATH UN1201. Modeling, description, dendritic integration. Projects in MATLAB. CSEE W4119x and y Computer networks and classification of signals and systems. BMEE E4030 y Neural control engineering 3 pts. Lect: 3. Professor Rubenstein. Continuous-time systems. Time domain analysis, 3 pts. Lect: 3. Professor Wong. Corequisite: IEOR E3658 or SIEO W3600 or convolution. Frequency domain analysis, transfer Prerequisite: ELEN E3801. Topics include equivalents. Introduction to computer networks functions. Fourier series. Fourier and Laplace Basic cell biophysics, active conductance and and the technical foundations of the Internet, transforms. Discrete-time systems and the Z the Hodgkin-Huxley model, simple neuron including applications, protocols, local area transform. models, ion channel models and synaptic networks, algorithms for routing and congestion CSEE W3827x and y Fundamentals of models, statistical models of spike generation, control, security, elementary performance computer systems Wilson-Cowan model of cortex, large-scale evaluation. Several written and programming 3 pts. Lect: 3. Professor Kim. electrophysiological recording methods, assignments required. Prerequisites: An introductory programming sensorimotor integration and optimal state CSEE W4140x or y Networking laboratory course. Fundamentals of computer organization estimation, operant conditioning of neural activity, 3 pts. Lect: 3. Professor Zussman. and digital logic. Boolean algebra, Karnaugh nonlinear modeling of neural systems, sensory Prerequisite: CSEE W4119 or equivalent. In this maps, basic gates and components, flip-flops systems: visual pathway and somatosensory course, students learn how to put “principles and latches, counters and state machines, basics pathway, neural encoding model: spike triggered into practice,” in a hands-on-networking lab of combinational and sequential digital design. average (STA) and spike triggered covariance course. The technologies and protocols of the Assembly language, instruction sets, ALUs, (STC) analysis, neuronal response to electrical Internet are covered, using equipment currently single-cycle and multicycle processor design, micro-stimulation, DBS for Parkinson’s disease available to large Internet service providers introduction to pipelined processors, caches, and treatment, motor neural prostheses, and sensory such as CISCO routers and end-systems. A set virtual memory. neural prostheses. of laboratory experiments provides hands-on ELEN E3990x, y or s Fieldwork ECBM E4040x or y Neural networks and deep experience with engineering wide-area networks 1–2 pts. Members of the faculty. learning and familiarizes students with the Internet Prerequisites: Obtained internship and approval 3 pts. Lect: 3. Professor Kostic. Protocol (IP), Address Resolution Protocol from a faculty adviser. May be repeated for credit, Prerequisites: BMEB W4020 or BMEE E4030 (ARP), Internet Control Message Protocol but no more than 3 total points may be used for or ECBM E4090 or ELEN E4750 or COMS (ICMP), User Datagram Protocol (UDP) and degree credit. Only for Electrical Engineering and W4771 or an equivalent. Developing features Transmission Control Protocol (TCP), the Computer Engineering undergraduate students and internal representations of the world, Domain Name System (DNS), routing protocols who include relevant off-campus work experience artificial neural networks, classifying handwritten (RIP, OSPF, BGP), network management as part of their approved program of study. Final digits with logistics regression, feedforward protocols (SNMP), and application-level protocols report and letter of evaluation required. May not deep networks, back propagation in multilayer (FTP, TELNET, SMTP). be used as technical or nontechnical electives perceptrons, regularization of deep or distributed ELEN E4193x or y Modern display science or to satisfy any other Electrical Engineering or models, optimization for training deep models, and technology Computer Engineering major requirements. May convolutional neural networks, recurrent and 3 pts. Lect: 3. Professor Kymissis. not be taken for pass/fail credit or audited. recursive neural networks, deep learning in speech, and object recognition. Prerequisites: Linear algebra, differential ELEN E3998x and y Projects in electrical equations, and basic semiconductor physics. engineering ECBM E4060x Introduction to genomic Introduction to modern display systems in 0 to 3 pts. Members of faculty. information science and technology an engineering context. The basis for visual Prerequisite: Requires approval by a faculty 3 pts. Lect: 3. Professor Anastassiou. perception, image representation, color

ENGINEERING 2017–2018 144 space, metrics of illumination. Physics of logic and hardware prototyping with FPGAs. homojunction and heterojunction laser diodes. luminescence, propagation and manipulation Fundamentals of VHDL for register-transfer Semiconductor photon detectors: p-n, p-i-n, of light in anisotropic media, emissive displays, level design. Testing and validation of hardware. and heterostructure photo diodes; avalanche and spatial light modulators. Fundamentals Hands-on use of industry CAD tools for photodiodes. of display addressing, the Alt-Pleshko simulation and synthesis. ELEN E4488x Optical systems theorem, multiple line addressing. Large area ELEN E4361x or y Power electronics electronics, fabrication, and device integration of 3 pts. Lect: 3. Professor Hendon. 3 pts. Lect: 3. Professor Preindl. commercially important display types. A series of Prerequisite: ELEN E3401 or equivalent. Prerequisites: ELEN E3801 and E3331. short laboratories will reinforce material from the Introduction to optical systems based on physical Introduction to power electronics; power lectures. Enrollment may be limited. design and engineering principles. Fundamental semiconductor devices: power diodes, thyristors, geometrical and wave optics with specific commutation techniques, power transistors, ELEN E4301y Introduction to semiconductor emphasis on developing analytical and numerical power MOSFETs, Triac, IGBTs, etc., and switch devices tools used in optical engineering design. Focus selection; nonsinusoidal power definitions and 3 pts. Lect: 3. Professor Laibowitz or Teherani. on applications that employ optical systems and computations, modeling, and simulation; half- Prerequisite: ELEN E3106 or equivalent. networks, including examples in holographic Semiconductor physics. Carrier injection and wave rectifiers; single-phase, full-wave rectifiers; three-phase rectifiers; AC voltage controllers; imaging, tomography, Fourier imaging, confocal recombination. P-n junction and diodes: Schottky microscopy, optical signal processing, fiber optic barrier and heterojunctions, solar cells and light- DC/DC buck, boost, and buck-boost converters; communication systems, optical interconnects emitting diodes. Junction and MOS field-effect discontinuous conduction mode of operation; DC power supplies: flyback, forward converter; and networks. transistors, bipolar transistors. Tunneling and DC/AC inverters, PWM techniques; three-phase charge-transfer devices. ELEN E4510x or y Solar energy and smart inverters. grid power systems ELEN E4312x Analog electronic circuits BMEE E4400x Wavelet applications in 3 pts. Lect: 3. Professors Kymissis and Schwartz. 3 pts. Lect: 3. Professor Dickson. biomedical image and signal processing Prerequisite: Background in circuits. Inorganic Prerequisites: ELEN E3331 and E3801. 3 pts. Lect: 3. solar cell semiconductor physics. Single and Differential and multistage amplifiers; small- Prerequisites: APMA E2101 or E3101 or tandem junction design. Measures of spectral signal analysis; biasing techniques; frequency equivalent. An introduction to methods of and energy efficiency. Introduction to organic response; negative feedback; stability criteria; wavelet analysis and processing techniques solar cells and thin film inorganic cells. frequency compensation techniques. Analog for the quantification of biomedical images and layout techniques. An extensive design project is Batteries and other energy storage systems. signals. Topics include frames and overcomplete an integral part of the course. Introduction to legacy power networks: Single representations, multiresolution algorithms for phase equivalents to three-phase networks. ELEN E4314y Communication circuits denoising and image restoration, multiscale Reactive and real power. Equivalent circuits 3 pts. Lect: 3. Professor Tsividis. texture segmentation and classification methods of synchronous machines, transformers, and Prerequisite: ELEN E4312. Principles of for computer-aided diagnosis. transmission lines. Smart grid technology: electronic circuits used in the generation, ELEN E4401x Wave transmission and fiber Control and management of distributed solar transmission, and reception of signal waveforms, optics energy and other intermittent renewable power as used in analog and digital communication 3 pts. Lect: 3. Professor Diament. sources connected to legacy power networks. systems. Nonlinearity and distortion; power Microgrid concept. “Small world” networks and amplifiers; tuned amplifiers; oscillators; Prerequisite: ELEN E3401 or equivalent. Waves and Maxwell’s equations. Field energetics, fault management. Communication over power multipliers and mixers; modulators and lines. Smart metering. demodulators; phase-locked loops. An extensive dispersion, complex power. Waves in dielectrics design project is an integral part of the course. and in conductors. Reflection and refraction. ELEN E4511x or y Power systems analysis Oblique incidence and total internal reflection. and control EECS E4321x Digital VLSI circuits Transmission lines and conducting waveguides. 3 pts. Lect: 3. 3 pts. Lect: 3. Professor Shepard. Planar and circular dielectric waveguides; Prerequisites: ELEN E3201 and E3401, or Recommended preparation: ELEN E3106, integrated optics and optical fibers. Hybrid and equivalents, or instructor’s permission. Modeling E3331, and CSEE W3827. Design and analysis LP modes. Graded-index fibers. Mode coupling; of power networks, steady-state and transient of high speed logic and memory. Digital CMOS wave launching. behaviors, control and optimization, electricity and BiCMOS device modeling. Integrated circuit market, and smart grid. fabrication and layout. Interconnect and parasitic ELEN E4411x Fundamentals of photonics elements. Static and dynamic techniques. 3 pts. Lect: 3. Professor Lipson. EEME E4601y Digital control systems Worst-case design. Heat removal and I/O. Yield Prerequisite: ELEN E3401 or equivalent. Planar 3 pts. Lect: 3. Professor Longman. and circuit reliability. Logic gates, pass logic, resonators. Photons and photon streams. Prerequisite: ELEN E3801 or EEME E3601, latches, PLAs, ROMs, RAMs, receivers, drivers, Photons and atoms: energy levels and band or equivalent. Real-time control using digital repeaters, sense amplifiers. structure; interactions of photons with matter; computers. Solving scalar and state-space absorption, stimulated and spontaneous EECS E4340x Computer hardware design difference equations. Discrete equivalents of emission; thermal light, luminescence light. 3 pts. Lect: 2. Lab: 3. Professor Sethumadhavan. continuous systems fed by holds. Z-transfer Laser amplifiers: gain, saturation, and phase Prerequisites: ELEN E3331 and CSEE W3827. functions. Creating closed-loop difference shift; rate equations; pumping. Lasers: theory of Practical aspects of computer hardware design equation models by Z-transform and state oscillation; laser output characteristics. Photons through the implementation, simulation, and variable approaches. The Nyquist frequency in semiconductors: generation, recombination, prototyping of a PDP-8 processor. High-level and sample rate selection. Classical- and and assembly languages, I/O, interrupts, and injection; heterostructures; absorption modern-based digital control laws. Digital system datapath and control design, pipelining, and gain coefficients. Semiconductor photon identification. busses, memory architecture. Programmable sources: LEDs; semiconductor optical amplifiers;

ENGINEERING 2017–2018 EEOR E4650x or y Convex optimization for and Internet of Things. Various sensors and CSEE W4824x or y Computer architecture 145 electrical engineering actuators, communication with devices through 3 pts. Lect: 3. Professor Sethumadhavan. 3 pts. Lect: 3. serial protocols and buses, embedded hardware, Prerequisite: CSEE W3827 or equivalent. Prerequisite: ELEN E3801 or instructor’s wired and wireless networks, embedded platforms Focuses on advanced topics in modern permission. Theory of convex optimization; such as Arduino and smartphones, web services computer architecture, illustrated by recent numerical algorithms; applications in circuits, on end devices and in the cloud, visualization case studies. Fundamentals of quantitative communications, control, signal processing and and analytics on sensor data, end-to-end IoT analysis. Pipelined, out-of-order, and power systems. applications. Group projects to create working speculative execution. Superscalar, VLIW and CPS/IoT system. vector processors. Embedded processors. ELEN E4702x or y Digital communications Memory hierarchy design. Multiprocessors and 3 pts. Lect: 3. Professor Raghavan. EECS E4766 Internet of things—engineering thread-level parallelism. Synchronization and Prerequisite: ELEN E3701 or equivalent. Digital innovations and commercialization 3 pts. Lect: 3. Professor Kostic. communications for both point-to-point and cache coherence protocols. Interconnection Prerequisites: Basic programming and switched applications is further developed. networks. instructor’s permission. Deep dive into a couple Optimum receiver structures and transmitter of selected topics/use-cases from the area of ELEN E4830y Digital image processing signal shaping for both binary and M-ary signal Internet of Things. Coverage of the topic from 3 pts. Lect: 3. Professor Hendon. transmission. An introduction to block codes and device to the cloud, with focus on practical Introduction to the mathematical tools and convolutional codes, with application to space aspects. Innovative product definition, product algorithmic implementation for representation communications. development, marketing, commercialization, and processing of digital pictures, videos, and ELEN E4703y Wireless communications and monetization. Cross-disciplinary coverage: visual sensory data. Image representation, 3 pts. Lect: 3. Professor Samardzia. EE, MechE, CS, Bioengineering, marketing, filtering, transform, quality enhancement, Prerequisite: ELEN E3701 or equivalent. business, design. Building products and startups restoration, feature extraction, object Wireless communication systems. System design in the IoT domain. Collaboration between the segmentation, motion analysis, classification, fundamentals. Trunking theory. Mobile radio Engineering School, Business School, industry and coding for data compression. A series of propagation. Reflection of radio waves. Fading experts, and engagement in IoT activities in NYC. programming assignments reinforces material and multipath. Modulation techniques; signal Collaborative project by groups of students from from the lectures. different disciplines. This course shares lectures space; probability of error, spread spectrum. with E6766, but the expected project complexity ELEN E4835 Introduction to adaptive signal Diversity. Multiple access. is lower. representations BMEE E4740y Bioinstrumentation 3 pts. Lect: 2. Professor Wright. ELEN E4810x Digital signal processing 3 pts. Lect: 1. Lab: 3. Professor Kyle. Prerequisites: Linear algebra (APMA E3101, MATH 3 pts. Lect: 3. Professor Wright. Prerequisites: COMS W1005, ELEN E1201. UN2010, or equivalent), probability (IEOR E3658 Prerequisite: ELEN E3801. Digital filtering in Hands-on experience designing, building, and or equivalent), and signals and systems (ELEN time and frequency domain, including properties testing the various components of a benchtop E3801), or instructor’s permission. Introduces of discrete-time signals and systems, sampling cardiac pacemaker. Design instrumentation to numerical tools for adaptive processing of signals. theory, transform analysis, system structures, measure biomedical signals as well as to actuate IIR and FIR filter design techniques, the discrete Signal representations, sparsity in overcomplete living tissues. Transducers, signal conditioning Fourier transform, fast Fourier transforms. bases. Techniques for sparse recovery, electronics, data acquisition boards, the Arduino applications to inpainting and denoising. Adaptive microprocessor, and data acquisition and processing ELEN E4815y Random signals and noise representations: principal component analysis, using MATLAB will be covered. Various devices will 3 pts. Lect: 3. Professor Kalet. clustering and vector quantization, dictionary be discussed throughout the course, with laboratory Prerequisite: IEOR E3658 or equivalent. learning. Source separation: independent work focusing on building an emulated version of a Characterization of stochastic processes as component analysis and matrix factorizations. cardiac pacemaker. Lab required. models of signals and noise; stationarity, ergodicity, Signal classification: support vector machines EECS E4750x or y Heterogeneous computing correlation functions, and power spectra. and boosting, learning with invariances. Hashing for signal and data processing Gaussian processes as models of noise in linear and signal retrieval. Case studies from image 3 pts. Lect: 2. Professor Marianetti. and nonlinear systems; linear and nonlinear processing, audio, multimedia. transformations of random processes; orthogonal Prerequisites: ELEN E3801 and COMS CSEE W4840y Embedded systems series representations. Applications to circuits and W3134 or similar, recommended. Methods for 3 pts. Lect: 3. Professor Edwards. devices, to communication, control, filtering, and deploying signal and data processing algorithms Prerequisite: CSEE W4823 or equivalent. on contemporary general purpose graphics prediction. Embedded system design and implementation processing units (GPGPUs) and heterogeneous CSEE W4823x or y Advanced logic design combining hardware and software. I/O, computing infrastructures. Using programming 3 pts. Lect: 3. Professor Nowick. interfacing, and peripherals. Weekly laboratory languages such as OpenCL and CUDA for Prerequisite: CSEE W3827 or equivalent. An sessions and term project on design of a computational speedup in audio, image, and introduction to modern digital system design. microprocessor-based embedded system video processing and computational data Advanced topics in digital logic: controller including at least one custom peripheral. analysis. Significant design project. synthesis (Mealy and Moore machines); adders Knowledge of C programming and digital logic EECS E4764 Internet of things—intelligent and multipliers; structured logic blocks (PLDs, required. and connected systems PALs, ROMs); iterative circuits. Modern design CSEE E4868x or y System-on-chip platforms 3 pts. Lect 3. Professor Jiang. methodology: register transfer level modeling 3 pts. Lect: 3. Professor Carloni. Prerequisite: Knowledge of programming (RTL); algorithmic state machines (ASMs); Prerequisites: COMS W3157 and CSEE W3827 or instructor's permission. Recommended: introduction to hardware description languages Design and programming of System-on-Chip ELEN E4703, CSEE W4119, CSEE W4840, (VHDL or Verilog); system-level modeling and (SoC) platforms. Topics include overview of or related courses. Cyber-physical systems simulation; design examples. technology and economic trends, methodologies

ENGINEERING 2017–2018 146 and supporting CAD tools for system-level points may be used for degree credit. Substantial study of multiple levels of brain organization, design; models of computation, the SystemC independent project involving laboratory work, from single neurons to cortical modules and language, transaction-level modeling, hardware- computer programming, analytical investigation, systems. Mathematical models of spiking software partitioning, high-level synthesis, system or engineering design. neurons, neural dynamics, neural coding, programming, on-chip communication, memory and biologically based computational learning. ELEN E6001x-E6002y Advanced projects in organization, power management and optimization, Architectures and learning principles underlying integration of programmable processor cores and electrical engineering both artificial and biological neural networks. specialized accelerators. Case studies of modern 1–4 pts. Members of the faculty. Computational models of cortical processing, SoC platforms for various classes of applications. Prerequisite: Requires approval by a faculty with an emphasis on the visual system. member who agrees to supervise the work. ELEN E4896y Music signal processing Applications of principles in neuroengineering; May be repeated for up to 6 points of credit. 3 pts. Lect: 3. Professor Ellis. neural prostheses, neuromorphic systems and Graduate-level projects in various areas of Prerequisite: ELEN E3801, E4810, or the biomimetics. Course will include a computer electrical engineering and computer science. equivalent. An investigation of the applications simulation laboratory. In consultation with an instructor, each student of signal processing to music audio, spanning designs his or her project depending on the ECBM E6040y Neural networks and deep the synthesis of musical sounds (including student’s previous training and experience. learning research. frequency modulation [FM], additive sinusoidal Students should consult with a professor in their 3 pts. Lect: 3. Professor Lazar. synthesis, and linear predictive coding Prerequisite: ECBM E4040 or the equivalent. [LPC]), the modification of real and synthetic area for detailed arrangements no later than the last day of registration. Regularized autoencoders, sparse coding and sounds (including reverberation and time/ predictive sparse decomposition, denoising pitch scaling), and the analysis of music ELEN E6010y Systems biology: design autoencoders, representation learning, manifold audio to extract musical information (including principles for biological circuits perspective on representation learning, pitch tracking, chord transcription, and music 4.5 pts. Lect: 3. Professor Jelenkovic. structured probabilistic models for deep learning, matching). Emphasis on practical, hands-on Prerequisite: ECBM E4060 or instructor’s Monte Carlo methods, training and evaluating experimentation, with a wide range of software permission. Beyond bioinformatics, cells as models with intractable partition functions, implementations introduced and modified within systems. Metabolic networks, transcription restricted Boltzmann machines, approximate the class. regulatory networks, signaling networks. inference, deep belief networks, deep learning in ELEN E4900-4909x or y Topics in electrical Deterministic and stochastic kinetics. speech, and object recognition. Mathematical representation of reconstructed and computer engineering ECBM E6070-6079x or y Topics in networks. Network motifs. Signal transduction 3 pts. Lect: 2. Members of the faculty. neuroscience and deep learning and neuronal networks. Robustness. Prerequisite: Instructor’s permission. Selected 3 pts. Lect: 2. Members of the faculty. topics in electrical and computer engineering. Bacterial chemotaxis and patterning in fruit fly Prerequisites: the instructor's permission. Selected Content varies from year to year, and different development. Kinetic proofreading. Optimal advanced topics in neuroscience and deep topics rotate through the course numbers 4900 gene circuit design. Rules for gene regulation. learning. Content varies from year to year, and to 4909. Random networks and multiple time scales. different topics rotate through the course numbers Biological information processing. Numerical 6070 to 6079. ELEN E4944x or y Principles of device and simulation techniques. Major project(s) in ELEN E6080–6089x or y Topics in systems microfabrication MATLAB. 3 pts. Lect: 3. Professor Trevino. biology Science and technology of conventional and EEBM E6020y Methods of computational 3 pts. Lect: 2. Members of the faculty. advanced microfabrication techniques for neuroscience Prerequisite: Instructor’s permission. Selected electronics, integrated and discrete components. 4.5 pts. Lect: 3. advanced topics in systems biology. Content Topics include diffusion; ion implantation, Prerequisite: BMEB W4020 or instructor’s varies from year to year, and different topics thin-film growth including oxides and metals, permission. Formal methods in computational rotate through the course numbers 6080 to molecular beam and liquid-phase epitaxy; neuroscience including methods of signal 6089. optical and advanced lithography; and plasma processing, communications theory, information EEBM E6090–6099x or y Topics in computational and wet etching. theory, systems and control, system identification neuroscience and neuroengineering and machine learning. Molecular models of EECS E4951y Wireless networks and systems 3 pts. Lect: 2. Members of the faculty. transduction pathways. Robust adaptation and 3 pts. Lect: 3. Professor Zussman. Prerequisite: Instructor’s permission. Selected integral feedback. Stimulus representation and Prerequisite: CSEE W4119 or instructor’s advanced topics in computational neuroscience groups. Stochastic and dynamical systems permission. Various topics in the area of and neuroengineering. Content varies from year models of spike generation. Neural diversity and wireless and mobile networks and systems. to year, and different topics rotate through the ensemble encoding. Time encoding machines Functionalities in the layers above the physical course numbers 6090 to 6099. and neural codes. Stimulus recovery with time layer. The latest wireless networking design CSEE E6180x or y Modeling and performance decoding machines. MIMO models of neural challenges, protocols, proposed algorithms, evaluation computation. Synaptic plasticity and learning and applications. Includes several hands-on 3 pts. Lect: 2. Professor Misra. algorithms. Major project(s) in MATLAB. experiments as well as a final project. Prerequisites: COMS W4118 and STAT GU4001 or permission of the instructor. Introduction to queuing ELEN E4998x or y Intermediate projects in BMEE E6030x Neural modeling and analysis and simulation techniques. Evaluation of electrical engineering neuroengineering 3 pts. Lect: 3. Professor Sajda. time-sharing and multiprocessor systems. Topics 0–3 pts. Members of the faculty. include priority queuing, buffer storage, and disk Prerequisites: ELEN E3801 and either APMA Prerequisite: Requires approval by a faculty access, interference and bus contention problems, E2101 or E3101, or equivalent, or instructor’s member who agrees to supervise the work. May and modeling of program behaviors. be repeated for credit, but no more than 3 total permission. Engineering perspective on the

ENGINEERING 2017–2018 ELEN E6201x Linear system theory ELEN E6318x or y Microwave circuit design approximations, the k.p. method, quantitative 147 3 pts. Lect: 3. Professor Sun. 3 pts. Lect: 3. Professor Baeyens. calculation of band structures and their Prerequisites: ELEN E3801 and APMA E3101, Prerequisites: ELEN E3331 and E3401, applications to quantum structure transistors, or equivalents. Abstract objects, the concepts of or equivalents. Introduction to microwave photodetectors, and lasers; semiconductor state. Definition and properties of linear systems. engineering and microwave circuit design. Review statistics, Boltzmann transport equation, Characterization of linear continuous-time and of transmission lines. Smith chart, S-parameters, scattering processes, quantum effect in transport discrete-time, fixed, and time-varying systems. microwave impedance matching, transformation phenomena, properties of heterostructures. State-space description; fundamental matrix, and power combining networks, active and Quantum mechanical treatment throughout. calculation by computer and matrix methods. passive microwave devices, S-parameter- ELEN E6332y Principles of semiconductor Modes in linear systems. Adjoint systems. based design of RF and microwave amplifiers. physics, II Controllability and observability. Canonical A microwave circuit design project (using 3 pts. Lect: 2. forms and decompositions. State estimators. microwave CAD) is an integral part of the course. Prerequisites: ELEN E3106 or ELEN E6331. Lyapunov’s method and stability. ELEN E6320x or y Millimeter-wave IC design Optical properties including absorption ELEN E6302x or y MOS transistors 3 pts. Lect: 3. Professor Krishnaswamy. and emission of radiation, electron-phonon 3 pts. Lect: 2. Professor Tsividis. Prerequisites: ELEN E3401 or equivalent, interactions, radiative and phonon-mediated Prerequisite: ELEN E3106 or equivalent. ELEN E4314 and E6312. Principles behind the processes, excitons, plasmons, polaritons, carrier Operation and modeling of MOS transistors. implementation of millimeter-wave (30GHz- recombination and generation, and related optical MOS two- and three-terminal structures. The 300GHz) wireless circuits and systems in devices, tunneling phenomena, superconductivity. MOS transistor as a four-terminal device; general silicon-based technologies. Silicon-based Quantum mechanical treatment throughout, heavy charge-sheet modeling; strong, moderate, and active and passive devices for millimeter- use of perturbation theory. weak inversion models; short-and-narrow- wave operation, millimeter-wave low-noise ELEN E6333y Semiconductor device physics channel effects; ion-implanted devices; scaling amplifiers, power amplifiers, oscillators and 3 pts. Lect: 2. considerations in VLSI; charge modeling; large- VCOs, oscillator phase noise theory, mixers and Prerequisites: ELEN E3106 or ELEN E4301 signal transient and small-signal modeling for frequency dividers for PLLs. A design project is or equivalent. Physics and properties of quasistatic and nonquasistatic operation. an integral part of the course. semiconductors. Transport and recombination ELEN E6312y Advanced analog integrated EECS E6321y Advanced digital electronic of excess carriers. Schottky, P-N, MOS, circuits circuits and heterojunction diodes. Field effect and 3 pts. Lect: 2. Professor Krishnaswamy. 3 pts. Lect: 2. Professor Seok. bipolar junction transistors. Dielectric and Prerequisite: ELEN E4312. Integrated circuit Prerequisite: EECS E4321. Advanced topics in optical properties. Optical devices including device characteristics and models; temperature- the design of digital integrated circuits. Clocked semiconductor lamps, lasers, and detectors. and supply-independent biasing; IC operational and non-clocked combinational logic styles. ELEN E6350y VLSI design laboratory amplifier analysis and design and their Timing circuits: latches and flip-flops, phase- 3 pts. Lab: 3. Professor Kinget. applications; feedback amplifiers, stability and locked loops, delay-locked loops. SRAM and Prerequisites: ELEN E4321 and E4312, or frequency compensation techniques; noise in DRAM memory circuits. Modeling and analysis instructor’s permission. Design of a CMOS mixed- circuits and low-noise design; mismatch in circuits of on-chip interconnect. Power distribution signal integrated circuit. The class divides up into and low-offset design. Computer-aided analysis and power-supply noise. Clocking, timing, and teams to work on mixed-signal integrated circuit techniques are used in homework or a design synchronization issues. Circuits for chip-to-chip designs. The chips are fabricated to be tested the project. electrical communication. Advanced technology following term. Lectures cover use of computer- issues that affect circuit design. The class may ELEN E6314x Advanced communication aided design tools, design issues specific to the include a team circuit design project. circuits projects, and chip integration issues. This course 3 pts. Lect: 2. EECS E6322x VLSI Hardware architecture for shares lectures with E4350, but the complexity Prerequisites: ELEN E4314 and E6312. signal processing and machine learning requirements of integrated circuits are higher. Overview of communication systems, modulation 3 pts. Lect: 3. Professor Seok. ELEN E6412y Lightwave devices and detection schemes. Receiver and transmitter Prerequisites: CSEE W3827 and ELEN E3801. 3 pts. Lect: 2. Professor Woodward. architectures. Noise, sensitivity, and dynamic Recommended: ELEN E4810. Design of Prerequisites: ELEN E4411. Electro-optics: range. Nonlinearity and distortion. Low-noise digital VLSI hardware for various digital signal principles; electro-optics of liquid crystals and RF amplifiers, mixers, and oscillators. Phase- processing and machine learning algorithms. photo-refractive materials. Nonlinear optics: locked loops and frequency synthesizers. Data flow graphs, iteration bounds, pipelining, second-order nonlinear optics; third-order Typical applications discussed include wireless parallel architectures, retiming, unfolding/ nonlinear optics; pulse propagation and solitons. RF transceivers or data links. Computer-aided folding, systolic architectures, bit-level Acousto-optics: interaction of light and sound; analysis techniques are used in homework(s) or arithmetic, numerical and algorithmic strength acousto-optic devices. Photonic switching a design project. reductions, CORDIC, distributed arithmetic, FFT, neural network hardware, vector processors, and computing: photonic switches; all-optical ELEN E6316y Analog systems in VLSI subwordparallel architecture, and SIMD. May switches; bistable optical devices. Introduction 3 pts. Lect: 3. Professor Dickson. include a team circuit design project. to fiber-optic communications: components of Prerequisite: ELEN E4312. Analog-digital the fiber-optic link; modulation, multiplexing ELEN E6331y Principles of semiconductor interfaces in very large scale integrated circuits. and coupling; system performance; receiver physics, I Precision sampling; A/D and D/A converter sensitivity; coherent optical communications. 3 pts. Lect: 2. Professor Wang. architectures; continuous-time and switched Prerequisite: ELEN E4301. Designed for ELEN E6413y Lightwave systems capacitor filters; system considerations. A design students interested in research in semiconductor 3 pts. Lect: 2. Professor Feuer. project is an integral part of this course. materials and devices. Topics include energy Prerequisites: ELEN E4411. Recommended bands: nearly free electron and tight-binding preparation: ELEN E6412. Fiber optics. Guiding,

ENGINEERING 2017–2018 148 dispersion, attenuation, and nonlinear properties diagram manipulations, closed-loop response. ELEN E6713y Topics in communications of fibers. Optical modulation schemes. Photonic Proportional, rate, and integral controllers, 3 pts. Lect: 3. components, optical amplifiers. Semiconductor and compensators. Design by root locus and Prerequisite: ELEN E6712 or E4702 or E4703 or laser transmitters. Receiver design. Fiber optic frequency response. Controllability, observability. equivalent, or instructor’s permission. Advanced telecommunication links. Nonregenerative Luenberger observers, pole placement, and topics in communications, such as turbo codes, transmission using erbium-doped fiber amplifier linear-quadratic cost controllers. LDPC codes, multiuser communications, network chains. Coherent detection. Local area networks. coding, cross-layer optimization, cognitive radio. Advanced topics in light wave networks. EEME E6602y Modern control theory Content may vary from year to year to reflect the 3 pts. Lect: 3. latest development in the field. ELEN E6414y Photonic integrated circuits Prerequisite: EEME E6601 or E4601 or ELEN 3 pts. Lect: 3. E6201, or instructor’s permission. Singular value ELEN E6717x Information theory Photonic integrated circuits are important decomposition. ARX model and state-space model 3 pts. Lect: 2. Professor Wang. subsystem components for telecommunications, system identification. Recursive least squares Prerequisite: IEOR E3658 or a course in stochastic processes. Corequisite: ELEN E4815. Mutual optically controlled radar, optical signal filters and Kalman filters. LQR, H, linear robust information and entropy. The source coding processing, and photonic local area networks. control, predictive control. Learning control, An introduction to the devices and the design of theorem. The capacity of discrete memoryless repetitive control, adaptive control. Liapunov these circuits. Principle and modeling of dielectic channels and the noisy channel coding theorem. and Popov stability. Nonlinear adaptive control, waveguides (including silica on silicon and InP The rate distortion function. Discrete memoryless nonlinear robust control, sliding mode control. based materials), waveguide devices (simple and sources and single-letter distortion measures. star couplers), and surface diffractive elements. EEOR E6616x or y Convex optimization Bhattacharya bounds, convolutional codes, and the Discussion of numerical techniques for modeling 3 pts. Lect: 2.5. Professor Iyengar. Viterbi algorithm. circuits, including beam propagation and finite Prerequisites: IEOR E6613 and EEOR E4650. ELEN E6718y Error correcting codes: difference codes, and design of other devices: Convex sets and functions, and operations classical and modern optical isolators, demultiplexers. preserving convexity. Convex optimization 3 pts. Lect: 2. Professor Ashikhmin. problems. Convex duality. Applications of convex ELEN E6430x or y Applied quantum optics Prerequisite: IEOR E3658. Main concepts 3 pts. Lect: 2. optimization problems ranging from signal of error control codes. Linear block codes. Prerequisites: Background in electromagnetism processing and information theory to revenue Elements of algebra: Galois fields. BCH and (ELEN E3401, E4401, E4411, or PHYS GR6092) management. Convex optimization in Banach Reed Solomon codes. Convolutional Codes. and quantum mechanics (APPH E3100, spaces. Algorithms for solving constrained convex Modern, capacity-achieving codes: Low Density E4100, or PHYS GU402x). An introduction to optimization problems. Parity Check codes, TURBO codes, and Polar codes. EXIT Charts analysis. fundamental concepts of quantum optics and EECS E6690-6699x or y Topics in data-driven quantum electrodynamics with an emphasis analysis and computation EECS E6720 Bayesian models for machine on applications in nanophotonic devices. 3 pts. Lect: 2. Members of the faculty. learning The quantization of the electromagnetic Prerequisite: the instructor's permission. Selected 3 pts. Lect: 3. Professor Paisley. field; coherent and squeezed states of light; advanced topics in data-driven analysis and Prerequisites: Basic calculus, linear algebra, interaction between light and electrons in the computation. Content varies from year to year, and probability, and programming. Basic statistics language of quantum electrodynamics (QED); different topics rotate through the course numbers and machine learning strongly recommended. optical resonators and cavity QED; low-threshold 6690 to 6699. Bayesian approaches to machine learning. Topics lasers; and entangled states of light. ELEN E6711x Stochastic models in include mixed-membership models, latent factor ELEN E6488y Optical interconnects and information systems models, Bayesian nonparametric methods, probit interconnection networks 4.5 pts. Lect: 3. Professor Baryshnikov. classification, hidden Markov models, Gaussian mixture models, model learning with mean-field 3 pts. Lect: 2. Professor Bergman. Prerequisite: IEOR E3658. Foundations: variational inference, scalable inference for Big Prerequisite: ELEN E4411 or E4488 or an probability review, Poisson processes, discrete- Data. Applications include image processing, equivalent photonics course. Introduction time Markov models, continuous-time Markov topic modeling, collaborative filtering, and to optical interconnects and interconnection models, stationarity, and ergodicity. The course recommendation systems. networks for digital systems. Fundamental presents a sample-path (time domain) treatment optical interconnects technologies, optical of stochastic models arising in information ELEN E6761x Computer communication interconnection network design, characterization, systems, including at least one of the following networks I and performance evaluation. Enabling photonic areas: communications networks (queueing 3 pts. Lect: 3. Professor Ghaderi. technologies including free-space structures, systems), biological networks (hidden Markov Prerequisites: IEOR E3658 and CSEE W4119 hybrid and monolithic integration platforms for models), Bayesian restoration of images (Gibbs or equivalent, or instructor’s permission. Focus photonic on-chip, chip-to-chip, backplane, and fields), and electric networks (random walks). on architecture protocols and performance node-to-node interconnects, as well as photonic evaluation of geographically distributed and networks on-chip. ELEN E6712x Communication theory local area data networks. Emphasis on layered 3 pts. Lect: 3. EEME E6601x Introduction to control theory protocols. Data link layer. Network layer: flow Prerequisite: ELEN E4815, or equivalent, or 3 pts. Lect: 3. Professor Longman. and congestion control routing. Transport layer. instructor’s permission. Representation of Prerequisite: MATH UN2030. A graduate-level Typical Local and Metropolitan Area Network bandlimited signals and systems. Coherent introduction to classical and modern feedback standards: Ethernet, DQDB, FDDI. Introduction and incoherent communications over control that does not presume an undergraduate to Internetting. Review of relevant aspects Gaussian channels. Basic digital modulation background in control. Scalar and matrix of queueing theory to provide the necessary schemes. Intersymbol inference channels. differential equation models, and solutions in analytical background. Fading multipath channels. Carrier and clock terms of state transition matrices. Transfer synchronization. functions and transfer function matrices, block

ENGINEERING 2017–2018 EECS E6765 Internet of things—systems and 3 pts. Lect: 2. Professor Mesgarani. digital signal processing. Topics include multirate 149 physical data analytics Prerequisite: ELEN E4810 or instructor’s signal processing, multidimensional signal 3 pts. Lect: 3. Professor Kostic. permission. Fundamentals of digital speech processing, short-time Fourier transform, signal Prerequisites: Knowledge of programming; ELEN processing and audio signals. Acoustic and expansion in discrete and continuous time, filter E4703 or related; or CSEE W4119; or instructor's perceptual basics of audio. Short-time Fourier banks, multiresolution analysis, wavelets, and permission. Internet of Things from the point analysis. Analysis and filter bank models. Speech their applications to image compression and of view of data. Methods for data analytics to and audio coding, compression, and reconstruction. understanding. Other topics may be included to understand trade-offs and partitioning between Acoustic feature extraction and classification. reflect developments in the field. cloud-based data-analytics and physical-device Recognition techniques for speech and other data analytics. Two-way interaction between CSEE E6861y Computer-aided design of sounds, including hidden Markov models. data and physical devices to support a truly digital systems ubiquitous, networked, and autonomous cyber- CSEE E6824y Parallel computer architecture 3 pts. Lect: 2. Professor Nowick. physical ecosystem. System-focused design of 3 pts. Lect: 2. Prerequisites: (i) one semester of advanced architectures, algorithms, networks, protocols, Prerequisite: CSEE W4824. Parallel computer digital logic (CSEE W4823 or equivalent, or communications, power, security, and standards. principles, machine organization and design of instructor’s permission); and (ii) a basic course Focus on a significant design project. parallel systems including parallelism detection in data structures and algorithms (COMS EECS E6766 Internet of things—engineering methods, synchronization, data coherence and W3133, W3134, W3137, W3139 or W3157, or innovations and commercialization interconnection networks. Performance analysis equivalent, and familiarity with programming. 3 pts. Lect: 3. Professor Kostic. and special purpose parallel machines. Introduction to modern digital CAD synthesis and optimization techniques. Topics include Prerequisites: Basic programming and instructor’s CSEE E6847y Distributed embedded systems modern digital system design (high-level permission. Deep dive into a couple of selected 3 pts. Lect: 2. topics/use-cases from the area of Internet of synthesis, register-transfer level modeling, Prerequisite: Any COMS W411X, CSEE Things. Coverage of the topic from device algorithmic state machines, optimal scheduling W48XX, or ELEN E43XX course, or instructor’s to the cloud, with focus on practical aspects. algorithms, resource allocation and binding, permission. An interdisciplinary graduate-level Innovative product definition, product development, retiming), controller synthesis and optimization, marketing, commercialization, and monetization. seminar on the design of distributed embedded exact and heuristic two-level logic minimization, Cross-disciplinary coverage: EE, MechE, CS, systems. System robustness in the presence advanced multi-level logic optimization, optimal Bioengineering, marketing, business, design. of highly variable communication delays and technology mapping to library cells (for delay, Building products and start-ups in the IoT heterogeneous component behaviors. The power and area minimization), advanced data domain. Collaboration between the Engineering study of the enabling technologies (VLSI structures (binary decision diagrams), SAT School, Business School, industry experts, and circuits, communication protocols, embedded solvers and their applications, static timing engagement in IoT activities in NYC. Collaborative processors, RTOSs), models of computation, analysis, and introduction to testability. Includes project by groups of students from different and design methods. The analysis of modern hands-on small design projects using and disciplines. This course shares lectures with domain-specific applications including on-chip creating CAD tools. E4766, but a more complex project is expected. micro-networks, multiprocessor systems, fault- CSEE E6863 Formal verification of hardware tolerant architectures, and robust deployment of ELEN E6767x or y Internet economics, and software systems engineering, and the implications for society embedded software. Research challenges such 3 pts. Lect: 2. Professor Theobald and Ivancic. 3 pts. Lect: 2. Professor Mitra. as design complexity, reliability, scalability, safety, Prerequisite: COMS W3134, W3136, or W3137 Prerequisites: CSEE W4119 or ELEN E6761 and security. The course requires substantial and COMS W3261. Introduction to the theory recommended, and ability to comprehend and reading, class participation and a research and practice of formal methods for the design track development of sophisticated models. project. and analysis of correct (i.e., bug-free) concurrent Mathematical models, analyses of economics and embedded hardware/software systems. ELEN E6850x Visual information systems and networking interdependencies in the Internet. Topics include temporal logics; model checking; 3 pts. Lect: 2. Topics include microeconomics of pricing and deadlock and liveness issues; fairness; Prerequisite: ELEN E4830 or instructor’s regulations in communications industry, game satisfiability (SAT) checkers; binary decision permission. Introduction to critical image theory in revenue allocations, ISP settlements, diagrams (BDDs); abstraction techniques; technologies in advanced visual information network externalities, two-sided markets. introduction to commercial formal verification systems, such as content-based image Economic principles in networking and network tools. Industrial state-of-the-art, case studies and databases, video servers, and desktop video design, decentralized vs. centralized resource experiences: software analysis (C/C++/Java), allocation, “price of anarchy,” congestion control. editors. Intended for graduate students. hardware verification (RTL). Topics include visual data representation and Case studies of topical Internet issues. Societal CSEE E6868x or y Embedded scalable compression, content-based visual indexing and and industry implications of Internet evolution. platforms retrieval, storage system design (data placement, 3 pts. Lect: 2. Professor Carloni. ELEN E6770–6779x or y Topics in networking scheduling, and admission control), compressed 3 pts. Lect: 2. Members of the faculty. Prerequisites: CSEE W4868 or instructor's video editing, and synchronization issues of permission. Inter-disciplinary graduate-level Further study of areas such as communication stored video/audio signals. Programming projects seminar on design and programming of protocols and architectures, flow and congestion and final presentations are required. embedded scalable platforms. Content varies control in data networks, performance evaluation ELEN E6860y Advanced digital signal between offerings to cover timely relevant issues in integrated networks. Content varies from year and latest advances in system-on-chip design, to year, and different topics rotate through the processing 3 pts. Lect: 2. Professor Nguyen. embedded software programming and electronic course numbers 6770 to 6779. design automation. Requires substantial reading Prerequisite: ELEN E4810. This course is of research papers, class participation, and ELEN E6820y Speech and audio processing designed as an extension to ELEN E4810, with semester-long project. and recognition emphasis on emerging techniques in the area of

ENGINEERING 2017–2018 150 EECS E6870x or y Speech recognition photon, electron, ion and atom, scanning probe, ELEN E9900x and y–9900 Doctoral dissertation 3 pts. Lect: 2. soft lithography, and nanoimprinting; pattern 0 pts. Members of the faculty. Prerequisites: Basic probability and statistics. transfer; self-assembly; process integration; and A candidate for the doctorate may be required Theory and practice of contemporary applications. to register for this course every term after the automatic speech recognition. Gaussian student’s coursework has been completed, and ELEN E6950x Wireless and mobile networking, I mixture distributions, hidden Markov models, until the dissertation has been accepted. 4.5 pts. Lect: 2. Lab: 1. Professor Jelenkovic. pronunciation modeling, decision trees, finite- Corequisite: ELEN E6761 or instructor’s state transducers, and language modeling. permission. Overview of mobile and wireless Selected advanced topics will be covered in COURSES IN ELECTRICAL networking. Fundamental concepts in mobile more depth. ENGINEERING OFFERED wireless systems: propagation and fading, OCCASIONALLY ELEN E6873x or y Detection and estimation cellular systems, channel assignment, power theory control, handoff. Examples of second-generation ECBM E3060x Introduction to genomic 3 pts. Lect: 2. circuits-switched systems and standards. information science and technology Prerequisite: ELEN E4815. Introduction to Quantitative homework assignments may require 3 pts. Lect: 3. Professor Anastassiou. the fundamental principles of statistical signal use of a mathematical software package. Introduction to the information system paradigm of processing related to detection and estimation. molecular biology. Representation, organization, ELEN E6999 Fieldwork Hypothesis testing, signal detection, parameter structure, function, and manipulation of the 0.5–1.5 pts. Members of the faculty. estimation, signal estimation, and selected biomolecular sequences of nucleic acids and Prerequisites: Obtained internship and approval advanced topics. Suitable for students doing proteins. The role of enzymes and gene regulatory from a faculty adviser. May be repeated for research in communications, control, signal elements in natural biological functions as well credit, but no more than 3 total points may processing, and related areas. as in biotechnology and genetic engineering. be used for degree credit. Only for electrical Recombination and other macromolecular ELEN E6880-6889x or y Topics in signal engineering and computer engineering graduate processes viewed as mathematical operations with processing students who include relevant off-campus work simulation and visualization using simple computer 3 pts. Lect: 2. Members of the faculty. experience as part of their approved program of programming. This course shares lectures with Prerequisite: ELEN E4810. Advanced topics study. Final report required. May not be taken for ECBM E4060, but the work requirements differ in signal processing, such as multidimensional pass/fail credit or audited. somewhat. signal processing, image feature extraction, EEME E8601y Advanced topics in control image/video editing and indexing, advanced EEHS E3900y History of telecommunications: theory digital filter design, multirate signal processing, from the telegraph to the Internet 3 pts. Lect: 3. Members of the faculty. adaptive signal processing, and wave-form 3 pts. Lect: 3. See entry under “Courses in Mechanical coding of signals. Content varies from year to Historical development of telecommunications from Engineering” for description. year, and different topics rotate through the the telegraphy of the mid-1800s to the Internet course numbers 6880 to 6889. ELEN E9001x and y–E9002 Research at present. Included are the technologies of 0–6 pts. Members of the faculty. telephony, radio, and computer communications. EECS E6890-6899x or y Topics in information Prerequisite: Requires approval by a faculty The coverage includes both the technologies processing member who agrees to supervise the work. themselves and the historical events that shaped, 3 pts. Lect: 2. Members of the faculty. Points of credit to be approved by the and in turn were shaped by, the technologies. Advanced topics spanning electrical department. Requires submission of an outline of The historical development, both the general engineering and computer science such as the proposed research for approval by the faculty context and the particular events concerning speech processing and recognition, image and member who is to supervise the work of the communications, is presented chronologically. The multimedia content analysis, and other areas student. The research facilities of the department social needs that elicited new technologies and drawing on signal processing, information theory, are available to qualified students interested in the consequences of their adoption are examined. machine learning, pattern recognition, and advanced study. Throughout the course, relevant scientific and related topics. Content varies from year to year, engineering principles are explained as needed. and different topics rotate through the course ELEN E9011x and y–E9012 Doctoral research These include, among others, the concept and numbers 6890 to 6899. 0–6 pts. Members of the faculty. effective use of spectrum, multiplexing to improve Prerequisite: Requires approval by a faculty ELEN E6900–6909x or y Topics in electrical capacity, digital coding, and networking principles. member who agrees to supervise the work. and computer engineering There are no prerequisites, and no prior scientific Points of credit to be approved by the 3 pts. Lect: 2. Members of the faculty. or engineering knowledge is required. Engineering department. Open only to doctoral students Prerequisite: Instructor’s permission. Selected students may not count this course as a technical who have passed the qualifying examinations. topics in electrical and computer engineering. elective. The course shares lectures with EEHS Requires submission of an outline of the Content varies from year to year, and different E4900, but the work requirements differ somewhat. proposed research for the approval of the faculty topics rotate through the course numbers 6900 member who is to supervise the work of the ELEN E3999x or y Electrical engineering to 6909. student. design challenge ELEN E6945x or y Device nanofabrication 1 pt. ELEN E9800x and y Doctoral research 3 pts. Lect: 3. Prerequisite: Approval by a faculty member who instruction Prerequisites: ELEN E3106 and E3401, or agrees to supervise the work. May be repeated 3, 6, 9 or 12 pts. Professor Kinget. equivalents. Recommended: ELEN E4944. for credit, but no more than 3 total points may be A candidate for the Eng.Sc.D. degree in This course provides an understanding of used for degree credit. Short-term design project electrical engineering must register for 12 points the methods used for structuring matter on organized as a faculty-led team competition. of doctoral research instruction. Registration the nanometer length: thin-film technology; Particular design targets are set that vary by in ELEN E9800 may not be used to satisfy the lithographic patterning and technologies including semester. A set of hardware and software minimum residence requirement for the degree.

ENGINEERING 2017–2018 constraints is specified. The project takes place magnetic circuits. Electric and magnetic energy ELEN E6304x or y Topics in electronic circuits 151 over an advertised subset of the semester, storage, loss, and transfer. Circuit behavior of 3 pts. Lect: 3. beginning around the third week. energy storage and transfer devices. Field theory Prerequisite: Instructor’s permission. State-of- of moving bodies. Dynamical equations of an the-art techniques in integrated circuits. Topics ELEN E4215y Analog filter synthesis and electromechanical system. Electromechanical may change from year to year. design and thermo-electric sensors and actuators. 3 pts. Lect: 3. EEME E6610x Optimal control theory Prerequisites: ELEN E3201 and ELEN E3801, Rotating electric energy converters. 3 pts. Lect: 3. or equivalent. Approximation techniques for Superconductivity and applications. Prerequisite: ELEN E6201 or EEME E6601. magnitude, phase, and delay specifications, ELEN E4503x Sensors, actuators, and Objectives of optimal control. Continuous and transfer function realization sensitivity, passive LC electromechanical systems discrete control problems. Calculus of variations: filters, active RC filters, MOSFET-C filters, Gm-C 3 pts. Lect: 3. Mayer and Bolza; Pontryagin’s maximum principle. filters, switched-capacitor filters, automatic tuning Prerequisites: ELEN E3201 and E3401, Bang-bang and singular controls. Existence techniques for integrated filters. Filter noise. A or equivalents. Electromagnetic energy of optimal control. Hamilton-Jacobi theory and design project is an integral part of the course. storage, loss, and transfer. Dynamics of dynamic programming. Numerical methods. Optimal feedback control regulatory problems. ELEN E4302x or y Magnetic sensors and electromechanical systems. Linearization Linear-quadratic-Gaussian estimation. Applications. instruments for medical imaging of nonlinear coupled dynamical equations 3 pts. Lect: 2.5, Lab: 0.5. and equivalent circuits. Electromechanical ELEN E6762y Computer communication Prerequisite: ELEN E3106, ELEN E3401, or actuators: acoustic, IC-processed networks, II instructor’s permission. Physics of nuclear micromachines. Electromechanical sensors: 3 pts. Lect: 2. magnetic resonance (NMR) and superconducting acoustic, pressure, and acceleration. Thermal Prerequisite: ELEN E6761. Broadband quantum interference device (SQUID). Design sensors: polysilicon thermopiles and bipolar ISDN, services and protocols; ATM. Traffic and operation of superconducting DC magnet, transistor temperature sensors. Electro-optic characterization and modeling: Markov- RF receiver, Josephson junction, and integrated sensors: visible light, infrared, and X-ray. modulated Poisson and Fluid Flow processes; SQUID. Principles of biomedical sensoring systems application to voice, video, and images. Traffic ELEN E6151y Surface physics and analysis of including Magnetic Resonance Imaging (MRI), Management in ATM networks: admission electronic materials SQUID magnetometer, and NMR spectroscopy. and access control, flow control. ATM switch 3 pts. Lect: 2. Medical image formation and processing. architectures; input/output queueing. Quality of Prerequisite: Instructor’s permission. Basic service (QoS) concepts. ELEN E4350y VLSI design laboratory physical principles of methods of surface 3 pts. Lab: 3. analysis, surfaces of electronic materials ELEN E6781y Topics in modeling and Prerequisites: EECS E4321 and ELEN E4312, including structure and optical properties (auger analysis of random phenomena or instructor’s permission. Design of a CMOS electron spectroscopy, X-ray photoemission, 3 pts. Lect: 3. mixed-signal integrated circuit. The class divides ultraviolet photoelectron spectroscopy, Prerequisite: ELEN E6711. Recommended up into teams to work on mixed-signal integrated electron energy loss spectroscopy, inverse preparation: a course on real analysis circuit designs. The chips are fabricated to be photoemission, photo stimulated desorption, and advanced probability theory. Current tested the following term. Lectures cover use and low energy electron diffraction), physical methodology in research in stochastic processes of computer-aided design tools, design issues principles of each approach. applied to communication, control, and signal specific to the projects, and chip integration processing. Topics vary from year to year to ELEN E6211x or y Circuit theory issues. This course shares lectures with E6350, reflect student interest and current developments 3 pts. Lect: 3. but the complexity requirements of integrated in the field. Prerequisites: ELEN E3331 and ELEN E3801. circuits are lower. An axiomatic development of circuit theory. ELEN E6920x or y Topics in VLSI systems ELEN E4420x Topics in electromagnetics Circuit theorems, circuit topology, general design 3 pts. Lect: 3. methods of circuit analysis. Normal form 3 pts. Lect: 2. Prerequisites: Undergraduate electromagnetic characterizations. Scattering characterization Prerequisite: ELEN E4321. Design automation: theory. Selected topics in the theory and practice and sensitivity function. Basic network synthesis layout, placement, and routing. Circuit simulation of electromagnetics, varying from year to year. methods: immittance and transfer function algorithms and optimization of performance Topic for current term will be available in the realization, multiport realization, approximation and area. Multiprocessor computing systems. department office one month before registration. techniques. Verification of testing. Topics may change from This course may be taken more than once when year to year. ELEN E6261y Computational methods of topics are different. Possible topics: microwave circuit analysis ELEN E9060x or y Seminar in systems biology theory and design (generalized waveguides, 3 pts. Lect: 3. 3 pts. Lect: 2. excitation and coupling of waveguides, junctions, Prerequisites: ELEN E3331 and APMA E3101. Open to doctoral candidates, and to qualified microwave networks, periodic structures, optical Computational algorithms for DC, transient, M.S. candidates with instructor’s permission. fibers); antennas (filamentary antennas, arrays, and frequency analysis of linear and nonlinear Study of recent developments in the field of aperture radiation, system properties, pattern circuits. Formulation of equations: state systems biology. synthesis); electrodynamics (special relativity, equations, hybrid equations, sparse tableaux. radiation by charged particles, relativistic beams, EEBM E9070x or y Seminar in computational Solution techniques: iterative methods to solve free electron lasers). neuroscience and neuroengineering nonlinear algebraic equations; piecewise linear 3 pts. Lect: 2. Professor Mesgarani. methods; sparse matrix techniques; numerical ELEN E4501x Electromagnetic devices and Open to doctoral candidates and qualified integration of stiff, nonlinear differential energy conversion M.S. candidates with instructor’s permission. equations, companion network models; waveform 3 pts. Lect: 3. Professor Sen. Study of recent developments in computational relaxation. Prerequisite: ELEN E3401. Linear and nonlinear neuroscience and neuroengineering.

ENGINEERING 2017–2018 152 ELEN E9101x or y Seminar in physical M.S. candidates with instructor’s permission. EECS E9601x or y Seminar in data-driven electronics Recent experimental and theoretical analysis and computation 3 pts. Lect: 2. developments in various areas of quantum 3 pts. Lect: 2. Instructor to be announced. Prerequisites: Quantum electronics and ELEN electronics research. Examples of topics that Prerequisite: Open to doctoral candidates and E4944, or instructor’s permission. Advanced may be treated include novel nonlinear optics, qualified M.S. candidates with the instructor's topics in classical and quantum phenomena lasers, transient phenomena, and detectors. permission. Advanced topics and recent that are based on ion and electron beams, developments in mathematical techniques ELEN E9403x or y Seminar in photonics gas discharges, and related excitation and computational tools for data science and 3 pts. Lect: 2. sources. Application to new laser sources and engineering problems. Prerequisite: ELEN E4411. Open to doctoral microelectronic fabrication. candidates, and to qualified M.S. candidates with ELEN E9701x or y Seminar in information and communication theories ELEN E9201x or y Seminar in circuit theory instructor’s permission. Recent experimental 3 pts. Lect: 2. 3 pts. Lect: 2. and theoretical developments in various areas of Open to doctoral candidates, and to qualified Open to doctoral candidates, and to qualified photonics research. Examples of topics that may M.S. candidates with instructor’s permission. M.S. candidates with instructor’s permission. be treated include squeezed-light generation, Recent developments in telecommunication Study of recent developments in linear, quantum optics, photon detection, nonlinear networks, information and communication nonlinear, and distributed circuit theory and optical effects, and ultrafast optics. analysis techniques important to the design of theories, and related topics. ELEN E9404x or y Seminar in lightwave very large scale integrated circuits. communications ELEN E9801x or y Seminar in signal processing ELEN E9301x or y Seminar in electronic 3 pts. Lect: 2. 3 pts. Lect: 2. devices Open to doctoral candidates, and to qualified Open to doctoral candidates, and to qualified 3 pts. Lect: 2. Professor Kymissis. M.S. candidates with instructor’s approval. M.S. candidates with instructor’s approval. Open to doctoral candidates, and to qualified Recent theoretical and experimental Recent developments in theory and applications M.S. candidates with instructor’s permission. developments in light wave communications of signal processing, machine learning, content Theoretical and experimental studies of research. Examples of topics that may be analysis, and related topics. semiconductor physics, devices, and technology. treated include information capacity of light wave channels, photonic switching, novel light ELEN E9303x or y Seminar in electronic wave network architectures, and optical neural circuits networks. 3 pts. Lect: 2. Open to doctoral candidates, and to qualified ELEN E9501x or y Seminar in electrical power M.S. candidates with instructor’s permission. networks Study of recent developments in electronic 3 pts. Lect: 2. circuits. Prerequisites: Open to doctoral candidates, and to qualified M.S. candidates with the instructor’s ELEN E9402x or y Seminar in quantum permission. Recent developments in control & electronics optimization for power systems, design of smart 3 pts. Lect: 2. grid, and related topics. Open to doctoral candidates, and to qualified

ENGINEERING 2017–2018 INDUSTRIAL ENGINEERING AND OPERATIONS RESEARCH 153 315 S. W. Mudd, MC 4704 Phone: 212-854-2941 ieor.columbia.edu

CHAIR DIRECTOR: PROFESSORS PROFESSORS OF ADJUNCT FACULTY Garud Iyengar UNDERGRADUATE Daniel Bienstock PROFESSIONAL Yair Avgav 326 S. W. Mudd PROGRAMS Jose Blanchet PRACTICE Aaron Brown Karl Sigman Mark Broadie, Emanuel Derman Krzysztof Choromanski VICE CHAIR Business School Soulaymane Kachani Siddhartha Dastidar Jay Sethuraman DIRECTOR: FINANCIAL Awi Federgruen, Kosrow Dehnad 314 S. W. Mudd ENGINEERING Business School ASSOCIATE David DeRosa Emanuel Derman Paul Glasserman, PROFESSORS Tony Effik EXECUTIVE DIRECTOR Business School Ton Dieker Robert Farrokhnia Jenny S. Mak DIRECTOR: DOCTORAL Donald Goldfarb Vineet Goyal Soumyadip Ghosh PROGRAMS 324 S. W. Mudd Garud Iyengar Henry Lam Leon S. Gold Jay Sethuraman Jay Sethuraman David Gulley Karl Sigman ASSISTANT Mark Herman DIRECTOR: Clifford Stein PROFESSORS Ali Hirsa EXECUTIVE Shipra Agrawal Garrett van Ryzin, Ebad Jahangir EDUCATION Agostino Capponi Business School Iraj Kani Soulaymane Kachani Adam Elmachtoub Michael D. Lipkin Ward Whitt Yuri Faenza Paul Logston David D. Yao Daniel Lacker Allan Malz Xunyu Zhou Dylan Possamaï Gerard Neumann Van Anh Truong Moshe Rosenwein Sacha Stanton LECTURER IN Maya Waisman DISCIPLINE Sheldon Weinig Hardeep Johar

ndustrial engineering is the branch Operations research is concerned decision making and managing risks in of the engineering profession that with quantitative decision problems, complex systems. Iis concerned with the design, generally involving the allocation and Financial engineering is a analysis, and control of production control of limited resources. Such multidisciplinary field integrating financial and service systems. Originally, problems arise, for example, in the theory with economics, methods of an industrial engineer worked in a operations of industrial firms, financial engineering, tools of mathematics, manufacturing plant and was involved institutions, health care organizations, and practice of programming. The only with the operating efficiency transportation systems, and government. field provides training in the application of workers and machines. Today, The operations research analyst of engineering methodologies and industrial engineers are more broadly develops and uses mathematical and quantitative methods to finance. concerned with productivity and all of statistical models to help solve these the technical problems of production decision problems. Like engineers, they Current Research Activities management and control. They may are problem formulators and solvers. In industrial engineering, research is be found in every kind of organization: Their work requires the formation of conducted in the area of logistics, manufacturing, distribution, a mathematical model of a system routing, scheduling, production and transportation, mercantile, and service. and the analysis and prediction of the supply chain management, inventory Their responsibilities range from the consequences of alternate modes of control, revenue management, and design of unit operations to that of operating the system. The analysis quality control. controlling complete production and may involve mathematical optimization In operations research, new service systems. Their jobs involve the techniques, probabilistic and statistical developments are being explored in integration of the physical, financial, methods, experiments, and computer mathematical programming, combinatorial economic, computer, and human simulations. optimization, stochastic modeling, components of such systems to attain Management Science and Engineering computational and mathematical finance, specified goals. Industrial engineering (also known as Engineering Management queueing theory, reliability, simulation, and includes activities such as production Systems) is a multidisciplinary field both deterministic and stochastic network planning and control; quality control; integrating industrial engineering, flows. inventory, equipment, warehouse, and operations research, contemporary In engineering and management materials management; plant layout; technology, business, economics, and systems, research is conducted in and workstation design. management. It provides a foundation for

ENGINEERING 2017–2018 154 the areas of logistics, supply chain wide variety of industrial and commercial 2. To prepare students for the workplace optimization, and revenue and risk applications. by fostering their ability to participate management. The FDT Center for Intelligent in teams, understand and practice In financial engineering, research Asset Management is led by interpersonal and organizational is being carried out in portfolio Professor Xunyu Zhou at Columbia behaviors, and communicate their management; option pricing, including University. The Center will focus solutions and recommendations exotic and real options; computational on the exploration of theoretical effectively through written, oral, and finance, such as Monte Carlo simulation underpinnings and modeling strategies electronic presentations; and numerical methods; as well as data for financial portfolio management 3. To familiarize students with the mining and risk management. through the introduction of big data historical development of industrial Projects are sponsored and analytical techniques. The Center's engineering tools and techniques and supported by leading private firms research will combine modern portfolio with the contemporary state of the and government agencies. In addition, theory, behavioral finance, machine art, and to instill the need for lifelong our students and faculty are involved learning, and data science to study learning within their profession; and in the work of four research and core problems including optimal asset 4. To instill in our students an educational centers: the Center for allocation and risk management; and understanding of ethical issues Applied Probability (CAP), the Center the research of the Center sits at the and professional and managerial for Financial Engineering (CFE), the crossroads of financial engineering, responsibilities. Computational and Optimization computer science, statistics, and Research Center (CORC), and the finance, aiming at providing innovative Operations Research FDT Center for Intelligent Asset and intelligent investment solutions. The operations research program Management. is one of several applied science The Center for Applied Probability BACHELOR OF SCIENCE programs offered at the School. At (CAP) is a cooperative center involving PROGRAMS the undergraduate level, it offers the School of Engineering and Applied basic courses in probability, statistics, Science, several departments in the applied mathematics, simulation, Industrial Engineering Graduate School of Arts and Sciences, and optimization as well as more The undergraduate program is and the Graduate School of Business. professionally oriented operations designed to develop the technical Its interests are in four applied areas: research courses. The curriculum is well skills and intellectual discipline needed mathematical and computational finance, suited for students with an aptitude for by our graduates to become leaders stochastic networks, logistics and mathematics applications. in industrial engineering and related distribution, and population dynamics. It prepares graduates for professional professions. The program is distinctive The Center for Financial Engineering employment as operations research in its emphasis on quantitative, (CFE) at Columbia University encourages analysts, e.g., with management economic, computer-aided approaches interdisciplinary research in financial consultant and financial service to production and service management engineering and mathematical modeling organizations, as well as for graduate problems. It is focused on providing in finance and promoting collaboration studies in operations research or an experimental and mathematical between Columbia faculty and financial business. It is flexible enough to be problem-formulating and problem- institutions, through the organization adapted to the needs of future medical solving framework for industrial of research seminars, workshops, and and law students. the dissemination of research done by engineering work. The curriculum provides a broad foundation in the members of the Center. Operations Research: Engineering current ideas, models, and methods of The Computational Optimization Management Systems Research Center (CORC) at Columbia industrial engineering. It also includes a This operations research option is University is an interdisciplinary group substantial component in the humanities designed to provide students with of researchers from a variety of and social sciences to help students an understanding of contemporary departments on the Columbia campus. understand the societal implications of technology and management. It is Its permanent members are Professors their work. for students who are interested in a Daniel Bienstock, Don Goldfarb, Garud The industrial engineering program technical-management background Iyengar, Jay Sethuraman, and Cliff objectives are: rather than one in a traditional Stein, from the Industrial Engineering engineering field. It consists of required and Operations Research Department, 1. To provide students with the requisite courses in industrial engineering and and Professor David Bayer, from analytical and computational skills operations research, economics, the Department of Mathematics at to assess practical situations and business, and computer science, Barnard College. Researchers at academic problems, formulate intended to provide a foundation CORC specialize in the design and models of the problems represented for dealing with engineering and implementation of state-of-the-art or embedded therein, design management systems problems. algorithms for the solution of large-scale potential solutions, and evaluate their Elective courses are generally intended optimization problems arising from a impact;

ENGINEERING 2017–2018 155 INDUSTRIAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) APMA E2000 (4)2 Linear algebra (3)1

Chemistry or physics lab: PHYS UN1493 (3) or UN1401 (3) UN1402 (3) PHYSICS PHYS UN3081 (2) or (three tracks, UN1601 (3.5) UN1602 (3.5) CHEM UN1500 (3) or choose one) UN2801 (4.5) UN2802 (4.5) CHEM UN1507 (3) or CHEM UN3085 (4) or

CHEMISTRY UN1403 (3) or UN1404 (3) or (choose one course) UN1604 (3.5) or UN2045 (3.5)

UNIVERSITY UN1010 (3) either semester WRITING

HUMA CC1001, HUMA CC1002, COCI CC1101, COCI CC1102, or Global core (3–4) or Global core (3–4) REQUIRED ECON UN1105 (4) and UN1155 recitation (0) NONTECHNICAL ELECTIVES either semester HUMA UN1121 or UN1123 (3) either semester

FIRST- AND IEOR E2261 (3) SECOND-YEAR IEOR E4307 (3) DEPT. IEOR E3658 (3) REQUIREMENTS

COMPUTER 1. COMS W1004 (3) and COMS W3134 (3) SCIENCE or (two tracks, 3 choose one) 2. ENGI E1006 (3) and COMS W3136 (3)

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 The linear algebra requirement may be filled by either MATH UN2010 or APMA E3101. 2 Effective Class of 2021. 3 The department encourages students to select sequence 1 or 2. COMS W1007 (3) and COMS W3137 (4) may be substituted in place of sequence 1 or 2.

INDUSTRIAL ENGINEERING: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

IEOR E3402 (4) Production & inventory MATH UN2030 (3) IEOR E4003 (3) IEOR E4405 (3) planning Ordinary diff. equations Corporate finance for eng. Scheduling IEOR E3404 (4) IEOR E3106 (3) IEOR E4207 (3) IEOR E4510 (3) Simulation Stochastic systems and Human factors Project management applications IEOR E3609 (3)2 REQUIRED Advanced optimization COURSES1 IEOR E3608 (3)2 Foundations of IEOR E4412 (3) optimization Quality control and management Choose One: IEOR E4505 (3) or IEOR E4211 (3) OR in public policy Applied consulting COMS W4111(3) Database systems either semester

NONTECH Complete 27-point requirement. See page 10 or engineering.columbia.edu for details. ELECTIVES

INDUSTRIAL ENGINEERING Choose three (9 pts.): Please consult the list on the departmental website: ieor.columbia.edu ELECTIVES

1 Taking required courses later than the prescribed semester is not permitted. 2 IEOR E3609 will be offered beginning in Spring 2018, relevant to Class of 2019 and beyond.

ENGINEERING 2017–2018 156 OPERATIONS RESEARCH PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) APMA E2000 (4)2 Linear algebra (3)1

CHEMISTRY UN1403 (3) or UN1404 (3) or (choose one course) UN1604 (3.5) or UN2045 (3.5)

UNIVERSITY UN1010 (3) either semester WRITING

HUMA CC1001, HUMA CC1002, COCI CC1101, COCI CC1102, or Global Core (3–4) or Global Core (3–4) REQUIRED ECON UN1105 (4) and UN1155 recitation (0) NONTECHNICAL ELECTIVES either semester HUMA UN1121 or UN1123 (3) either semester

FIRST- AND IEOR E2261 (3) SECOND- IEOR E4307 (3) YEAR DEPT. IEOR E3658 (3) REQUIREMENTS

COMPUTER 1. COMS W1004 (3) and COMS W3134 (3) SCIENCE or (two tracks, 3 choose one) 2. ENGI E1006 (3) and COMS W3136 (3)

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

OPERATIONS RESEARCH: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

MATH UN2030 (3) IEOR E3402 (4) Ordinary diff. equations Production & inventory IEOR E4003 (3) planning Corporate finance for eng. IEOR E3106 (3) IEOR E4405 (3) Stochastic systems and IEOR E3404 (4) IEOR E4407 (3) Scheduling applications Simulation Game theoretic models of operations REQUIRED IEOR E3608 (3)2 IEOR E3609 (3)2 COURSES1 Foundation of optimization Advanced optimization

Choose one: IEOR E4505 Operations research for public policy COMS W4111(3) Database systems either semester IEOR E4507 Healthcare operations management IEOR E4650 Business analytics IEOR E4700 Introduction to FE

OPERATIONS Choose four OR electives (12 pts. total):3 RESEARCH ELECTIVES Please consult the list on the departmental website: ieor.columbia.edu

NONTECH Complete 27-point requirement. See page 10 or engineering.columbia.edu for details. ELECTIVES

1 Taking required courses later than the prescribed semester is not permitted. 2 IEOR E3609 will be offered beginning in Spring 2018, relevant to Class of 2019 and beyond. 3 6 pts. need to be taken within the IEOR Department.

ENGINEERING 2017–2018 157 OPERATIONS RESEARCH: ENGINEERING MANAGEMENT SYSTEMS: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) APMA E2000 (4)2 Linear algebra (3)1

CHEMISTRY UN1403 (3) or UN1404 (3) or (choose one course) UN1604 (3.5) or UN2045 (3.5)

UNIVERSITY UN1010 (3) either semester WRITING

FIRST- AND IEOR E2261 (3) SECOND- IEOR E4307 (3) YEAR DEPT. IEOR E3658 (3) REQUIREMENTS

COMPUTER 1. COMS W1004 (3) and COMS W3134 (3) SCIENCE or (two tracks, 3 choose one) 2. ENGI E1006 (3) and COMS W3136 (3)

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

OPERATIONS RESEARCH: ENGINEERING MANAGEMENT SYSTEMS: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

MATH UN2030 (3) ECON 3213 (3) Ordinary diff. equations Macroeconomics IEOR E3106 (3) IEOR E3402 (4) Choose one: Stochastic systems and Production & inventory IEOR E4003 (3) IEOR E4211 (3) Applied applications planning Corporate finance for eng. consulting ECON UN3211 (3) REQUIRED IEOR E3404 (4) IEOR E4510 (3) 1 Microeconomics COURSES Simulation Project management IEOR E3608 (3)3 IEOR E3609 (3)3 Foundations of Advanced optimization optimization

Choose one: COMS W4111(3) Database systems either semester IEOR E4550 Entrepreneurial business creation IEOR E4998 Managing technological innovations

TECH Technical electives (12 pts. total)2

Management electives (9 pts. total): MANAGEMENT Please consult lists posted on IEOR website: ieor.columbia.edu ELECTIVES NONTECH Complete 27-point requirement; see page 10 or engineering.columbia.edu for details.

1 Taking required courses later than the prescribed semester is not permitted. 2 At least two technical electives must be chosen from IEOR; the complete list is available at ieor.columbia.edu. ENGINEERING 2017–2018 3 IEOR E3609 will be offered beginning in Spring 2018, relevant to Class of 2019 and beyond. 158 OPERATIONS RESEARCH: FINANCIAL ENGINEERING: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

Linear algebra (3)1 MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) APMA E2000 (4)3 and ODE (3)

Physics or chemistry lab: PHYS UN1493 (3) or UN1401 (3) UN1402 (3) PHYSICS PHYS UN3081 (2) or (three tracks, UN1601 (3.5) UN1602 (3.5) CHEM UN1500 (3) or choose one) UN2801 (4.5) UN2802 (4.5) CHEM UN1507 (3) or CHEM UN3085 (4) or

CHEMISTRY UN1403 (3.5) or UN1404 (3.5) or (choose one course) UN1604 (3.5) or UN2045 (3.5)

UNIVERSITY UN1010 (3) either semester WRITING

FIRST- AND IEOR E2261 (4) SECOND-YEAR DEPT. REQUIREMENTS IEOR E3658 (3) IEOR E4307 (3)2

COMPUTER 1. COMS W1004 (3) and COMS W3134 (3) SCIENCE or (two tracks, 3 choose one) 2. ENGI E1006 (3) and COMS W3136 (3)

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 The linear algebra requirement may be filled by either MATH UN2010 or APMA E3101. 2 Students may also take STAT UN3107 or GU4107; however, the department strongly recommends IEOR E4307 in the spring term. 3 Effective Class of 2021. 4 The department encourages students to select sequence 1 or 2. COMS W1007 (3) and COMS W3137 (4) may be substituted in place of sequence 1 or 2.

OPERATIONS RESEARCH: FINANCIAL ENGINEERING: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

ECON UN3211 (3) Microeconomics IEOR E3106 (3) Stochastic systems and IEOR E3402 (4) IEOR E4407 (3) applications Production & inventory Game theoretic models planning of operations ECON UN3213 (3) Macroeconomics IEOR E4630 (3) IEOR E3404 (4) IEOR E4500 (3) Asset allocation REQUIRED Simulation Applications prog. for FE IEOR E3608 (3)1 COURSES1 Foundations of optimization IEOR E3609 (3)1 IEOR E4620 (3) Advanced optimization Pricing models for FE IEOR E4003 (3) Corporate finance for eng. IEOR E4700 (3) Intro. to FE

COMS W4111(3) Database systems either semester ECON E3412 (3) Intro. to econometrics either semester

FINANCIAL ENGINEERING Choose three (9 pts.): Please consult the list on the departmental website: ieor.columbia.edu

NONTECH Complete 27-point requirement; see page 10 or engineering.columbia.edu for details ELECTIVES

1 Taking required courses later than the prescribed semester is not permitted. 2 IEOR E3609 will be offered beginning in Spring 2018, relevant to Class of 2019 and beyond. ENGINEERING 2017–2018 to provide a substantive core in at least apply to the track upon the completion A minimum grade-point average of 3.0 159 one technology area and at least one of their sophomore year. Advanced (B) or its equivalent in an undergraduate management area. track students are required to take engineering program is required for Due to the flexibility of this option, it higher-level IEOR courses, including the admission to the M.S. programs. At a can incorporate the varied educational following: minimum, students are expected, on needs of preprofessional students entry, to have completed courses in IEOR E4004 instead of IEOR E3608 interested in law, medicine, business, ordinary differential equations, linear IEOR E4106 instead of IEOR E3106 and finance. In addition, most students algebra, probability, and a programming IEOR E4403 instead of IEOR E4003 are encouraged to add a minor in language such as C, Java, or Python. IEOR E4404 instead of IEOR E3404 economics or computer science to their The Department requires that M.S. and MATH UN2500 standard course schedules. students achieve grades of B– or Students successfully completing higher in each of the fundamental Operations Research: Financial the requirements of the undergraduate core courses in the discipline of study. Engineering advanced track will receive recognition Poor performance in core courses is The operations research concentration on their academic record. indicative of inadequate preparation and in financial engineering is designed to is very likely to lead to serious problems provide students with an understanding Minors in completing the program. As a result, of the application of engineering A number of minors are available for students failing to meet this criterion methodologies and quantitative students wishing to add them to their may be asked to withdraw. methods to finance. Financial programs. These minors are described Courses taken at the School of engineering is a multidisciplinary starting on page 198 of this bulletin. Professional Studies will not be counted field integrating financial theory with IEOR program students may want toward the M.S. degree in the IEOR economics, methods of engineering, to consider minors in economics Department (e.g., courses with the tools of mathematics, and practice of or computer science. In addition, following prefixes: ACTU, BUSI, COPR, programming. Students graduating with operations research and engineering IKNS, SUMA, FUND, and more). Please this concentration are prepared to enter and management systems majors may consult with your academic adviser careers in securities, banking, financial elect to minor in industrial engineering, regarding electives offered in other management, and consulting industries, and industrial engineering majors may departments and schools, prior to and fill quantitative roles in corporate elect to minor in operations research. registration. treasury and finance departments of The department does not offer a general manufacturing and service firms. minor in engineering management Financial Engineering Students who are interested in systems or financial engineering. The M.S. program in Financial pursuing the rigorous concentration in Engineering is offered on a full time basis only. Financial Engineering is financial engineering must demonstrate MASTER OF SCIENCE intended to provide a unique technical proficiency in calculus, computer PROGRAMS programming, linear algebra, ordinary background for students interested in The Department of Industrial differential equations, probability, pursuing career opportunities in financial Engineering and Operations Research and statistics. Applications to the analysis and risk management. In offers courses and M.S. programs in concentration are accepted during addition to the basic requirements for (1) financial engineering on a full-time the fall and spring semesters of the graduate study, students are expected, basis only; (2) management science sophomore year, and students will be on entry, to have attained a high and engineering on a full-time basis notified of the departmental decision level of mathematical and computer only; (3) industrial engineering on by the end of that spring semester. The programming skills, particularly in either a full- or part-time basis; and (4) department is seeking students who probability, statistics, linear algebra, and operations research on either a full- or demonstrate strength and consistency the use of a programming language part-time basis. The Department’s M.S. in all the above-mentioned areas. such as C, Python or JAVA. Previous program in Management Science and Application to this concentration is professional experience is highly Engineering is offered in conjunction available online: ieor.columbia.edu desirable but not required. with the Columbia Graduate School of /bs-financial-engineering. Graduate studies in Financial Business. Lastly, the Department and Engineering consists of 36 points (12 the Graduate School of Business offer a courses), starting the fall semester. Undergraduate Advanced Track combined M.S./M.B.A. degree program Students may complete the program The undergraduate advanced in industrial engineering. in May, August, or December of the track is designed for advanced All degree program applicants are following year. The requirements include undergraduate students with the desire required to take the Aptitude Tests six required core courses and additional to pursue further higher education of the Graduate Record Examination elective courses chosen from a variety after graduation. Students with a (GRE). M.S./M.B.A. candidates are of departments or schools at Columbia. minimum cumulative GPA of 3.4 and also required to take the Graduate The six required core courses for faculty approval have the opportunity Management Admissions Test (GMAT). to participate. Students are invited to Financial Engineering are IEOR E4007,

ENGINEERING 2017–2018 160 E4701, E4703, E4706, E4707, and E4709. In addition, students are required Financial Engineering—June or December 2018 Completion (36 points)1 to attend the Financial Engineering Seminar Series and submit learning Fall Semester Spring Semester Summer and/or Fall Semester journals. (9 points)2 (9 points)2 (For remaining credits)2 Financial Engineering has five concentrations: (1) Computation Required core courses: Required core courses: IEOR E4715 Commodity and Programming; (2) Finance and derivatives (1.5) Economics; (3) Derivatives; (4) Asset IEOR E4007 Optimization IEOR E4703 Monte Carlo Management; and (5) Computational models and methods simulation IEOR E4718 Beyond Black- Scholes: the implied volatility Finance and Trading Systems. A sample IEOR E4701 Stochastic models IEOR E4707 Continuous time smile schedule is available in the Department finance IEOR E4706 Foundations of office and on the IEOR website: ieor. IEOR E4725 Big data in finance financial engineering IEOR E4709 Statistical analysis columbia.edu. Students select electives and time series IEOR E4731 Credit risk and from a group of specialized offerings credit derivatives in both the fall and spring terms. They Plus Financial Engineering IEOR E4732 Computational may select from a variety of approved 3 electives, 3–6 points Plus Financial Engineering methods in derivative pricing electives from the department, the electives, 3–6 points 3 School of Business, and the Graduate IEOR E4733 Algorithmic trading School of Arts and Sciences. IEOR E4734 Foreign exchange and related derivatives Management Science and instruments (1.5) Engineering IEOR E4735 Introduction to Management Science and Engineering structured and hybrid products (MS&E), offered by the IEOR Department in conjunction with Columbia Business IEOR E4736 Event driven finance School, is the first such program between Columbia Engineering Additional Financial Engineering and Columbia Business School. It electives will be offered 3 reflects the next logical step in the

long-standing close collaboration 1 Students may conclude the program in June, August, or December 2018. Please visit the departmental between the IEOR Department at the website (ieor.columbia.edu/ms-financial-engineering) for more information.

Engineering School and the Decision, 2 All courses listed are for 3 points, unless stated otherwise. Risk, and Operations (DRO) Division 3 The list of semi-core electives can be found at ieor.columbia.edu/ms-financial-engineering. at the Business School. Coursework emphasize both management and semesters. Students enter in the fall term these electives are available in the engineering perspectives in solving and can either finish their coursework Departmental office and on the MS&E problems, making decisions, and at the end of the following August, or website: mse.ieor.columbia.edu. managing risks in complex systems. alternatively, have the option to take the Students pursuing this specialization are summer term off (e.g., for an internship) Industrial Engineering provided with a rigorous exposure to and complete their coursework by the optimization and stochastic modeling, Graduate studies in Industrial Engineering end of the following fall term. Students and a deep coverage of applications in enable students with industrial are required to take the equivalent of 12 the areas of operations engineering and engineering bachelor’s degrees to 3-point courses (36 points). management. enhance their undergraduate training Students must take at least six Graduates of this program are with studies in special fields such as courses (18 points) within the IEOR expected to assume positions as production planning, inventory control, Department, three to six courses at the analysts and associates in consulting scheduling, and industrial economics. Business School, and the remaining firms, business analysts in logistics, However, the department also offers a courses (if any) within the School of broader master’s program for engineers supply chain, operations, or revenue Engineering, the School of International management departments of large whose undergraduate training is not in and Public Affairs, the Law School, industrial engineering. Students may corporations, and as financial or the Departments of Economics, analysts in various functions (e.g., risk complete the studies on a full-time (12 Mathematics, and Statistics. Students points per term) or part-time basis. management) of investment banks, in residence during the summer hedge funds, credit-card companies, Industrial Engineers are required term can take two to four Business to satisfy a core program of graduate and insurance firms. School courses in the third (summer) Management Science and courses in production management, semester in order to complete their probability theory, statistics, simulation, Engineering (36 points) can be completed program. Additional details regarding in a single calendar year, in three and operations research. Students with

ENGINEERING 2017–2018 B.S. degrees in industrial engineering will 161 usually have satisfied this core in their Management Science and Engineering (36 points) undergraduate programs. All students must take at least 18 points of graduate Required Core IEOR E4004 Optimization models and methods (first fall semester) work in industrial engineering and at Courses (12 points) IEOR E4101 Probability models (first fall semester) least 30 points of graduate studies at IEOR E4102 Stochastic models (spring semester) Columbia. Industrial Engineering may IEOR E4111 Operations consulting (starts first fall semester, all-year course) include concentrations in: (1) industrial regulation studies and (2) systems Plus Semi-Core Courses (DRO, Analaysis, and Management Electives (18) engineering. Additional details regarding these concentrations and electives are Decision, Risk, and IEOR E4650 Business analysis (fall and spring semester) Operations Electives available in the Departmental office and DROM B8106-060 Operations strategy (1.5) (summer—second half) (9 points) on IEOR website: ieor.columbia.edu. DROM B8107-060 Service operations (fall semester) DROM B8108-060 Supply chain management (spring semester) DROM B8116-060 Risk management (fall semester) Operations Research DROM B8122-060 MSE game-theoretic business strategy (fall semester) Graduate studies in Operations Research DROM B8127-060 Immersion seminar in big data (1.5) (fall semester) enables students to concentrate their DROM B8131-060 Sports analytics (fall semester) studies in methodological areas such as DROM B8510-060 Managerial negotiations (with game theoretical analysis) mathematical programming, stochastic (fall semester) models, and simulation. Students may MRKT B8617-001 Marketing research (summer) complete the studies on a full time (12 DROM B9106-001 Applied multivariate statistics (summer) points per term) or part time basis. DROM B9122-001 Computing for business research Operations Research has five areas of concentrations including: (1) applied Analysis and Management Electives (9 points minimum) probability; (2) business analytics; (3) financial and managerial applications ECON GU4280 Corporate finance (by application, fall and spring semester) Management Group of operations research; (4) logistics IEME E4310 The manufacturing enterprise (fall semester) At least one of the IEOR E4412 Quality control and management (spring semester) and supply chain management and (5) following: optimization. Students may select from IEOR E4505 Operations research in public policy (spring semester) a variety of approved electives from the IEOR E4510 Project management (spring semester) Department, the School of Business, IEOR E4550 Entrepreneurial business creation for engineers (fall or spring and the Graduate School of Arts and semester) Sciences. Additional details regarding IEOR E4555 Design and Agile Project Management Engineerng Lab (fall semester) these concentrations and electives are IEOR E4560 Lean LaunchPad (weeklong course in mid-January, by available in the Departmental office and application only) on IEOR website: ieor.columbia.edu. IEOR E4575 Designing digital operating models (fall and spring semester) IEOR E4711 Global capital markets (fall semester) IEOR E4998 Managing technological innovation and entrepreneurship (fall or spring semester) FINC B8307 Advanced corporate finance (spring semester)

Analysis Group IEOR E4000 Operations management (fall semester) At least one of the IEOR E4403 Quantitative corp. finance (fall semester) following: IEOR E4405 Scheduling (spring semester) IEOR E4407 Game theoretic models of operations (fall semester) IEOR E4418 Transportation analytics and logistics (spring semester) IEOR E4507 Healthcare operations management (spring semester) IEOR E4522 Python for operations research (1.5) (fall and spring semester) IEOR E4523 Data analytics for operations research (fall or spring semester) IEOR E4570 Data mining (fall semester) IEOR E4601 Dynamic pricing and revenue optimization (spring semester)

Breadth Electives: The breadth electives can be selected from the Business School, the School of Engineering, the School of International and Public Affairs, the Law School, or the Departments of Economics, Mathematics, and Statistics.

ENGINEERING 2017–2018 162 Operations Research (30 points)

Required Core Courses IEOR E4150 Intro to probability and statistics (or STAT GU4001 for spring intake only)1 (12 points) IEOR E4004 Optimization models and methods IEOR E4106 Stochastic models IEOR E4404 Simulation

ELECTIVES FOR CONCENTRATION

Applied Probability IEOR E4000 Operations management IEOR E4210 Supply chain management The department IEOR E4407 Game theoretic models of operation IEOR E4601 Dynamic pricing and revenue management recommends taking at IEOR E4602 Quantitative risk management IEOR E4700 Intro to financial engineering least three of the following elective courses: DROM B8108 Supply chain management DROM B8123 Demand and supply analytics

Business Analytics Technical Courses Management Courses The department recommends taking: IEOR E4525 Machine learning for OR and FE IEOR E4650 Business analytics

At least two of: IEOR E4000 Operations management At least two of: IEOR E4500 Applications programming for financial engineering IEOR E4510 Project management IEOR E4521 Systems engineering tools and methods IEOR E4550 Entrepreneurial business creation for engineers IEOR E4522 Python for operations research (1.5) IEOR E4560 The Lean Launchpad IEOR E4523 Data analytics for operations research IEOR E4561 Dynamic pricing and revenue management IEOR E4524 Industry projects in analytics2 IEOR E4998 Managing technological innovation and IEOR E4570 Data mining entrepreneurship IEOR E4574 Cloud Computing IEOR E4736 Event driven finance DROM B8123 Demand and supply analytics DROM B8127 Immersion seminar in big data DROM B8131 Sports analytics DROM B9122 Computing for business research

Entrepreneurship and IEOR E4403 Quantitative corporate finance Innovation IEOR E4550 Entrepreneurial business creation for engineers The department IEOR E4998 Managing technological innovation and entrepreneurship recommends taking: At least two of: DROM B8858 Data-driven entrepreneurship IEME E4310 The manufacturing enterprise IEOR E4418 Transportation analytics and logistics IEOR E4560 Lean launchpad2 IEOR E4573 Design and agile project management engineering lab2 IEOR E4601 Dynamic pricing and revenue management COMS W4460 Principles of innovation and entrepreneurship

Financial and Managerial Corporate Finance Courses Derivatives Pricing Courses Management Courses Applications IEOR E4403 Quantitative corporate finance IEOR E4700 Intro to financial engineering The department At least one of: recommends taking: And at least one of: IEOR E4505 OR in public policy IEOR E4711 Global capital market And at least one of: IEOR E4507 Healthcare operations FINC B8307 Advanced corporate finance IEOR E4602 Quantitative risk management management ECON GU4280 Corporate finance IEOR E4620 Pricing models IEOR E4510 Project management or INAF GR6022 Economics of finance IEOR E4630 Asset allocation IEOR E4550 Entrepreneurial business creation for engineers IEOR E4734 Foreign exchange and related IEOR E4731 Credit risk modeling and derivatives instruments derivatives IEOR E4998 Managing technological innovation IEOR E4735 Introduction to structured and DROM B8112 Quantitative finance: models hybrid products and computation

1 STAT GU4001 will not count towards the 18 IEOR point requirement. 2 Courses require application process for registration.

ENGINEERING 2017–2018 163 Operations Research (30 points)

Logistics and Supply Technical Courses Management Courses Chain Management At least three of: At least two of: The department recommends taking: IEOR E4000 Operations management IEME E4310 The manufacturing enterprise IEOR E4403 Quantitative corporate finance IEOR E4412 Quality control IEOR E4405 Production scheduling IEOR E4510 Project management IEOR E4418 Transportation analytics and logistics IEOR E4520 Applied systems engineering IEOR E4505 OR in public policy IEOR E4550 Entrepreneurial business creation for engineers IEOR E4507 Healthcare operations management IEOR E4998 Managing technological innovation IEOR E4525 Machine learning for OR and FE IEOR E4601 Dynamic pricing and revenue management IEOR E4602 Quantitative risk management DROM B8107 Service operations management DROM B8108 Supply chain management DROM B8123 Demand and supply analytics

Optimization IEOR E4000 Operations management IEOR E4510 Project management The department IEOR E4405 Scheduling IEOR E4630 Asset allocation recommends taking at IEOR E4418 Transportation analytics and logistics DROM B8107 Service operations management least three of the following IEOR E4505 Operations research in public policy DROM B8108 Supply chain management elective courses: IEOR E4507 Healthcare operations management

JOINT M.S. AND M.B.A. and (2) Operations Research. The Ph.D. committee is not satisfied with a The department and the Graduate requirements for the Ph.D. in industrial student's performance in components School of Business offer a joint engineering and operations research (2) and (3), they may be asked to M.S. master's program in Industrial are identical. Both programs require withdraw from the program at the end Engineering. Prospective students for this the student to complete the qualifying of the second year. special program must submit separate procedure and submit and defend a Doctoral students are also required applications to Columbia Engineering and dissertation based on the candidate's to select a concentration for their the Graduate School of Business and be original research, conducted under studies and complete a certain amount admitted to both schools for entrance the supervision of the faculty. The of coursework in one of the following into the joint program. dissertation work may be theoretical or fields: applied probability, mathematical Admissions requirements are the computational or both. programming, financial engineering, same as those for the regular M.S. The qualifying procedure consists or supply chain management and program in Industrial Engineering and of three components, including: (1) logistics. Doctoral candidates must for the M.B.A. This joint program is complete the four Ph.D. core courses obtain a minimum of 60 points of formal coordinated so that both degrees can during the first year with at most one course credit beyond the bachelor’s be obtained after five terms of full-time grade of (B+) or better; (2) conduct degree. A master’s degree from an study (30 points in two terms while research during the first summer, and accredited institution may be accepted registered in Columbia Engineering and give a talk based on this research at as equivalent to 30 points. A minimum 45 points in three terms while registered the beginning of the third semester; and of 30 points beyond the master’s degree in the Graduate School of Business). (3) submit a research paper at the end must be earned while in residence in the Students in the joint program must of the third semester. Students in the doctoral program. Detailed information complete certain courses by the end of doctoral programs are reviewed by the regarding the requirements for the their first year of study. If a substantial Ph.D. committee after each of the three doctoral degree may be obtained in the equivalent has been completed during components. A student who fails to Department office and on IEOR website: undergraduate studies, students should complete component (1) may be asked ieor.columbia.edu. consult with a faculty adviser in order to to withdraw from the Ph.D. program at the end of the first year. A student obtain exemption from a required course. COURSES IN INDUSTRIAL who successfully completes component ENGINEERING AND (1) will typically move on to conduct Ph.D. Program OPERATIONS RESEARCH research during the first summer under The IEOR Department offers two Ph.D. For up-to-date course offerings, please the advisement by a faculty member in programs in (1) Industrial Engineering; visit ieor.columbia.edu. the Department. In the rare instance the

ENGINEERING 2017–2018 164 IEOR E2261x and y Accounting and finance when analytical or numerical techniques do not convex optimization, and optimization under 3 pts. Lect: 3. Professor Webster. suffice. The course focuses on discrete-event uncertainty ,with a strong focus on modeling, Prerequisite: ECON UN1105 Principles of simulation, a general technique used to analyze formulations, and applications. economics. For undergraduates only. This course a model over time and determine the relevant IEOR E3900x and y Undergraduate research is required for all undergraduate students majoring quantities of interest. Topics covered in the course or project in IE, OR:EMS, OR:FE, and OR. This course include the generation of random numbers, 1–3 pts. Members of the faculty. examines the fundamental concepts of financial sampling from given distributions, simulation of Prerequisite: Approval by a faculty member who accounting and finance, from the perspective discrete-event systems, output analysis, variance agrees to supervise the work. Independent work of both managers and investors. Key topics reduction techniques, goodness of fit tests, and involving experiments, computer programming, covered include principles of accrual accounting; the selection of input distributions. The first half analytical investigation, or engineering design. recognizing and recording accounting transactions; of the course is oriented toward the design and preparation and analysis of financial statements; implementation of algorithms, while the second IEOR E3999x, y or s Fieldwork ratio analysis; pro-forma projections; time value of half is more theoretical in nature and relies heavily 1–2 pts. Professor Sigman. money (present values, future values and interest/ on material covered in prior probability courses. Prerequisites: Obtained internship and approval discount rates); inflation; discounted-cash-flow The teaching methodology consists of lectures, from faculty adviser. Only for IEOR undergraduate (DCF) project evaluation methods; deterministic recitations, weekly homework, and both in-class students who need relevant work experience as and probabilistic measures of risk; capital and take-home exams. Homework almost always part of their program of study. Final reports are budgeting. includes a programming component for which required. This course may not be taken for pass/ students are encouraged to work in teams. IEOR E3106x Stochastic systems and fail credit or audited. applications SIEO W3600y Introduction to probability IEOR E4000x Operations management 3 pts. Lect: 3. Professor Possamaï. and statistics 3 pts. Lect: 3. Professor Truong. Prerequisite: SIEO W3600. For undergraduates 4 pts. Lect: 3. Recit: 1. Prerequisites or Corequisite: Probability theory only. This course is required for all undergraduate Prerequisite: Calculus. For undergraduates only. and linear programming. Required course for students majoring in IE, OR:EMS, OR:FE, and OR. This course is required for undergraduate students MSIE. An introduction to production management This class must be taken during (or before) the majoring in IE, OR:EMS, and OR. This class must for students not having an industrial engineering fifth semester. Some of the main stochastic models be taken during the fourth semester. Fundamentals bachelor’s degree. Topics include deterministic used in engineering and operations research of probability and statistics used in engineering inventory models, aggregate production planning, applications: discrete-time Markov chains, Poisson and applied science. Probability: random variables, material requirements planning, forecasting, processes, birth and death processes and other useful distributions, expectations, law of large stochastic inventory models and supply chain continuous Markov chains, renewal reward numbers, central limit theorem. Statistics: point and management. Emphasis is on modeling and its processes. Applications: queueing, reliability, confidence interval estimation, hypothesis tests, implications for managerial decisions. inventory, and finance. IEOR E3106 must be linear regression. SIEO W3600 must be completed IEOR E4001y Design and management of completed by the fifth term. Only students with by the fourth term. Only students with special production and service systems special academic circumstances may be allowed to academic circumstances may be allowed to take 3 pts. Lect: 3. Not offered in 2017–2018. take these courses in alternative semesters with the these courses in alternative semesters with the Prerequisite: IEOR E4000 or E3402. This course consultation of CSA and Departmental advisers. consultation of CSA and Departmental advisers. is required for undergraduate students majoring in Recitation section required. IEOR E3402x or y Production and inventory OR:EMS. Design and management problems in planning IEOR E3608x Foundations of optimization production and service systems: process design 4 pts. Lect: 3. Recit: 1. Professor Truong. (Class of 2019 and beyond) and capacity management, inventory system Prerequisites: SIEO W3600 Probability and 3 pts. Lect: 3. Professor Sethuraman. design and management, aggregate planning, staff Statistics and IEOR E3608 Foundations to Prerequisite: MATH UN2010. Corequisite: Data scheduling, and quality control system design. optimization. For undergraduates only. This course structures. This first course in optimization IEOR E4003x Corporate finance for engineers is required for all undergraduate students majoring focuses on theory and applications of linear 3 pts. Lect: 3. Professor Waisman. in IE, OR:EMS, OR:FE, and OR. This class must optimization, network optimization, and dynamic Prerequisites or corequisites: Probability theory be taken during (or before) the sixth semester. programming. Inventory management and production planning. and linear programming. This course is required Continuous and periodic review models: optimal IEOR E3609y Advanced optimization (Class of for all undergraduate students majoring in IE, policies and heuristic solutions, deterministic and 2019 and beyond) OR:EMS, OR:FE, and OR. Introduction to the probabilistic demands. Material requirements 3 pts. Lect: 3. Professor Stein. economic evaluation of industrial projects. Economic planning. Aggregate planning of production, Prerequisite: IEOR E3608. For undergraduates equivalence and criteria. Deterministic approaches to inventory, and work force. Multi-echelon integrated only. This course is required for all undergraduate economic analysis. Multiple projects and constraints. production-inventory systems. Production students majoring in IE, OR:EMS, OR:FE, and Analysis and choice under risk and uncertainty. OR. This course is a follow-up to IEOR E3608 scheduling. Term project. Recitation section IEOR E4004x and y Optimization models and required. and will cover advanced topics in optimization, including integer optimization, convex optimization, methods IEOR E3404y Simulation modeling and analysis and optimization under uncertainty, with a strong 3 pts. Lect: 3. Professors Agrawal, Bienstock, and 4 pts. Lect: 4. Members of the faculty. focus on modeling, formulations, and applications. Faenza. Prerequisites: SIEO W3600 or STAT GU4001, and This graduate course is only for MS&E, IE, and knowledge of a programming language such as IEOR E3658x Probability for engineers OR students. This is also required for students in Python, C, C++ or Matlab. It is strongly advised 3 pts. Lect: 3. Professor Dieker. the Undergraduate Advanced Track. For students that Stochastic modeling (IEOR E3106 or IEOR Prerequisite: Calculus. For undergraduates who have not studied linear programming. E4106) be taken before this course. This is an only. This course is required for the OR:FE Some of the main methods used in IEOR introductory course to simulation, a statistical concentration. This course is a follow-up to applications involving deterministic models: linear sampling technique that uses the power of IEOR E3608 and will cover advanced topics programming, the simplex method, nonlinear, computers to study complex stochastic systems in optimization including integer optimization, integer and dynamic programming.

ENGINEERING 2017–2018 IEOR E4007x Optimization models and and continuous random variable, law of large IEOR E4150x or y Introduction to Probability 165 methods for financial engineering numbers, central limit theorem, and stochastic and Statistics 3 pts. Lect: 3. Professor Iyengar. simulation, basic statistics, including point and 3 pts. Lect: 3. Professor Dieker. Prerequisite: Linear algebra. This graduate course interval estimation, hypothesis testing, and Prerequisite: Calculus, including multiple is only for M.S. Program in Financial Engineering regression; examples from business applications integration. Course covers the following students. Linear, quadratic, nonlinear, dynamic, such as inventory management, medical treatments, topics: fundamentals of probability theory and and stochastic programming. Some discrete and finance. This course is a specialized version of statistical inference used in engineering and optimization techniques will also be introduced. IEOR E4150 for MSE students. applied science; Probabilistic models, random The theory underlying the various optimization variables, useful distributions, expectations, methods is covered. The emphasis is on modeling IEOR E4102y Stochastic models for MSE law of large numbers, central limit theorem; and the choice of appropriate optimization 3 pts. Lect: 2.5. Statistical inference: pint and confidence interval methods. Applications from financial engineering Prerequisite: IEOR E4101. Introduction to sto- estimation, hypothesis tests, linear regression. are discussed. chastic processes and models, with emphasis For IEOR graduate students. on applications to engineering and management; IEOR E4009x or y Nonlinear optimization random walks, gambler’s ruin problem, Markov IEME E4200x or y Introduction to human- 3 pts. Lect: 2.5. Professor Goldfarb. chains in both discrete and continuous time, centered design Prerequisites: A course on optimization models Poisson processes, renewal processes, stopping 1.5 pts. Lect: 4.5. Professor West. and methods (at the level of IEOR E4004) and a times, Wald’s equation, binomial lattice model Prerequisite: Application to instructor for approval. course on linear algebra. Unconstrained and con- for pricing risky assets, simple option pricing; Open to SEAS graduate and advanced under- strained nonlinear optimization involving continu- graduate students, Business School, and GSAPP. simulation of simple stochastic processes, ous functions. Additionally, fundamental concepts Students from other schools may apply. Fast- Brownian motion, and geometric Brownian such as optimality conditions and convergence, paced introduction to human-centered design. motion. This course is a specialized version of principle focus on practical optimization methods. Students learn the vocabulary of design methods, IEOR E4106 for MSE students. understanding of design process. Small group CSOR E4010y Graph theory: a combinatorial view IEOR E4106x or y Stochastic models projects to create prototypes. Design of simple 3 pts. Lect: 3. Not offered in 2017–2018. 3 pts. Lect: 3. Professor Yao. product, more complex systems of products and Prerequisites: Linear algebra, or instructor’s Prerequisites: STAT GU4001 or probability theory. services, and design of business. permission. An introductory course in graph theory This graduate course is only for MS&E, IE, and with emphasis on its combinatorial aspects. Basic IEOR E4205x and y Studies in operations OR students. This is also required for students in definitions, and some fundamental topics in graph research the Undergraduate Advanced Track. Some of the theory and its applications. Topics include trees 3 pts. Lect: 3. Not offered in 2017–2018. main stochastic models used in engineering and and forests graph coloring, connectivity, matching Prerequisites: IEOR E3608 or E4004, and IEOR operations research applications: discrete-time theory and others. E3106 or E4106, or instructor’s permission. Markov chains, Poisson processes, birth and death Applications of operations research models CEOR E4011x Infrastructure systems processes and other continuous Markov chains, in practice; examples of successful projects; optimization renewal reward processes. Applications: queueing, discussion of difficulties in applying operations 3 pts. Lect: 3. Professor Di. reliability, inventory, and finance. research techniques in practice; understanding the Prerequisites: Basic linear algebra. Basic prob- factors leading to successful applications. Students ability and statistics. Engineering economic IEOR E4111x and y Operations consulting will be required to do a project that may involve concepts. Basic spreadsheet analysis and 3 pts. Lect: 3. Professor Kachani. the following: project management and budgeting, programming skills. Subject to instructor's Prerequisites: Probability and statistics at the contract preparation, change-order negotiations, permission. Infrastructure design and systems level of SIEO W3600 or STAT GU4001, and concepts, analysis and design under competing/ Deterministic Models at the level of IEOR progress reporting, organizational and personal conflicting objectives, transportation network E3608 or IEOR E4004, or instructor permission. dynamics, client communications and relationships, models, traffic assignments, optimization, and This course is for MS-MS&E students only. and presentation skills. the simplex algorithm. This course aims to develop and harness the IEOR E4207x Human factors: performance modeling, analytical, and managerial skills IEOR E4100x Probability models for MSE 3 pts. Lect: 3. Professor Gold. of engineering students and apply them to 1.5 pts. Lect: 2.5. Professor Lam. This course is required for undergraduate improve the operations of both service and Prerequisites: Understanding of single- and multi- students majoring in IE. Sensory and cognitive manufacturing firms. This course is structured (brain) processing considerations in the design, variable calculus. Basic probability theory, includ- as a hands-on laboratory in which students ing independence and conditioning, discrete and development, and operations of systems, products, "learn by doing" on real-world consulting and tools. User or operator limits and potential in continuous random variable, law of large numbers, projects (October to May). The student teams central limit theorem, and stochastic simulation, sensing, perceiving decision making, movement focus on identifying, modeling, and testing coordination, memory, and motivation. basic statistics, including point and interval estima- (and sometimes implementing) operational tion, hypothesis testing, and regression; examples improvements and innovations with high IEOR E4208y Seminar in human factors design from business applications such as inventory potential to enhance the profitability and/or 3 pts. Lect: 3. Professor Gold. management, medical treatments, and finance. This achieve sustainable competitive advantage for Prerequisite: IEOR E4207 or instructor’s course is a specialized version of IEOR E4150 for their sponsor companies. The course is targeted permission. This course is an elective for MSE students who are exempt from the first half of toward students planning careers in technical undergraduate students majoring in IE. An in-depth IEOR E4101. consulting (including operations consulting) exploration of the application potential of human factor principles for the design of products and IEOR E4101x Probability models for MSE and management consulting, or pursuing positions as business analysts in operations, processes. Applications to industrial products, 3 pts. Lect: 3. Professor Lam. logistics, supply chain and revenue management tools, layouts, workplaces, and computer displays. Prerequisites: Understanding of single- and functions, positions in general management, and Consideration to environmental factors, training multivariable calculus. Basic probability theory, future entrepreneurs. and documentation. Term project. including independence and conditioning, discrete

ENGINEERING 2017–2018 166 DROM B8108y Supply chain management assess the financial performance of a firm in networks; equitable resource allocation with 3 pts. Lect: 3. Professor Federgruen. and perform the economic evaluation of discrete decision variables. Prerequisite: IEOR E3402, E4000, or industrial projects. Deterministic mathematical permission of instructor. This is a IE elective for programming models for capital budgeting. IEOR E4412y Quality control and management undergraduate students majoring in IE. Major Concepts in utility theory, game theory and 3 pts. Lect: 3. Members of the faculty. issues in supply chain management, including, real options analysis. Prerequisite: SIEO W3600 or STAT GU4001. This definition of a supply chain; role of inventory; course is required for undergraduate students IEOR E4404x and y Simulation supply contracts; bullwhip effect and information majoring in IE. Statistical methods for quality 4 pts. Lect: 3. Recit: 1. Professor Ghosh. sharing; vendor-managed inventories and control and improvement: graphical methods, Prerequisites: SIEO W3600 or STAT GU4001, other distribution strategies; third-party logistics introduction to experimental design and reliability computer programming. Corequisite: IEOR providers; managing product variety; information engineering and the relationships between quality E3106 or IEOR E4106. This course is required technology and supply chain management; and productivity. Contemporary methods used by international issues. Emphasis on quantitative for all undergraduate students majoring in IE, manufacturing and service organizations in product models and analysis. OR:EMS, OR:FE, and OR. This course is also and process design, production and delivery of required for MSIE and MSOR. Generation of products and services. IEOR E4211y Applied consulting random numbers from given distributions; variance IEOR E4418x or y Transportation analytics 3 pts. Lect: 2.5. Professor Herman. reduction; statistical output analysis; introduction and logistics Prerequisites: Probability at the level of SIEO to simulation languages; application to financial, 3 pts. Lect: 3. Professor Elmachtaub. W3600 or STAT GU4001, familiarity with R or telecommunications, computer, and production Prerequisite: IEOR E3608 or E4404 or permission SAS. Basic and advanced techniques in com- systems. Graduate students must register for 3 of instructor. Introduces quantitative techniques mercial and government consulting. Case stud- points. Undergraduate students must register for and state-of-the-art practice of operations research ies supported by lectures focused on collecting 4 points. NOTE: Students who have taken IEOR relevant to the design and both the tactical and analyzing skills, client/market data, client E4703 Monte Carlo simulation may not register for and strategic management of logistical and interview techniques, and application of quanti- this course for credit. Recitation section required. transportation systems. Discusses a wide variety of tative and qualitative methodologies. Exposure IEOR E4405x or y Scheduling passenger and freight systems, including air, urban to critical skills on workplan development, inter- 3 pts. Lect: 3. Professor Stein. and highway traffic, rail, and maritime systems. view techniques, presentation deck preparation, Prerequisites: SIEO W3600, IEOR E3608, Explores the practice of revenue management and costing, and application of analytic techniques to computer programming. This course is required dynamic pricing. Through case studies, analyzes solve complex problems. for undergraduate students majoring in IE and successes and failures in third-party logistics, DROM B8123y Demand and supply analytics OR. Job shop scheduling: parallel machines, postal, truck and rail pickup and delivery systems. 3 pts. Lect: 3. Members of the faculty. machines in series; arbitrary job shops. Algorithms, Investigates large-scale integrated logistics and Prerequisites: IEOR E4004 (or E3608), IEOR complexity, and worst-case analysis. Effects transportation systems and studies the underlying E4106 (or E3608). Tools to efficiently manage of randomness: machine breakdowns, random principles governing transportation planning, supply and demand networks. Topics include processing time. Term project. investment and operations. service and inventory trade-offs, stock allocation, IEOR E4407x Game theoretic models of IEOR E4500x Applications programming for pricing, markdown management and contracts, operations financial engineering timely product distribution to market while avoiding 3 pts. Lect: 3. Professor Goyal. 3 pts. Lect: 3. Professor Bienstock. excess inventory, allocating adequate resources to Prerequisites: IEOR E4004 (or E3608), IEOR Prerequisite: Computer programming or the most profitable products and selling the right E4106 (or E3106), familiarity with differential instructor’s approval. This course is required for product to the right customer at the right price and equations and computer programming; undergraduate students majoring in OR:FE. In at the right time. or instructor’s permission. This course is this course we will take a hands-on approach to IEOR E4307x or y Statistics and data analysis required for undergraduate students majoring developing computer applications for Financial 3 pts. Lect: 3. Professor Dieker. in OR:FE and OR. A mathematically rigorous Engineering. Special focus will be placed on Prerequisites: probability, linear algebra. study of game theory and auctions, and high-performance numerical applications that Descriptive statistics, central limit theorem, their application to operations management. interact with a graphical interface. In the course parameter estimation, sufficient statistics, Topics include introductory game theory, of developing such applications we will learn how hypothesis testing, regression, logistic regression, private value auction, revenue equivalence, to create DLLs, how to integrate VBA with C/ goodness-of-fit tests, applications to operations mechanism design, optimal auction, multiple- C++ programs, and how to write multithreaded research models. unit auctions, combinatorial auctions, programs. Examples of problems settings that incentives, and supply chain coordination with we consider include simulation of stock price IEME E4310x The manufacturing enterprise contracts. No previous knowledge of game evolution, tracking, evaluation and optimization of 3 pts. Lect: 3. Professor Weinig. theory is required. a stock portfolio; optimal trade execution. In the The strategies and technologies of global course of developing these applications, we review manufacturing and service enterprises. IEOR E4408x Resource allocation: models, topics of interest to OR:FE in a holistic fashion. Connections between the needs of a global algorithms, and applications enterprise, the technology and methodology 3 pts. Lect: 3. Not offered in 2017–2018. IEOR E4505y Operations research in public needed for manufacturing and product Prerequisites: Linear programming (IEOR E3608 or policy development, and strategic planning as currently E4004), basic knowledge of nonlinear and integer 3 pts. Lect: 3. Professor Sethuraman. practiced in industry. programming. Overview of resource allocation Prerequisites: IEOR E3608 or IEOR E4004, IEOR E3106 or IEOR E4106. This course aims IEOR E4403x Quantitative corporate finance models. Single resource allocation with concave to give the student a broad overview of the role 3 pts. Lect: 3. Professor Sunada-Wong. returns; equitable resource allocation; lexicographic of Operations Research in public policy. The Prerequisites: Probability theory and linear minmax/maxmin optimization; extensions to specific areas covered include voting theory, programming This course is required for substitutable resources; multi-period resource apportionment, deployment of emergency units, students in the Undergraduate Advanced allocation; equitable allocation in multicommodity location of hazardous facilities, health care, organ Track. Key measures and analytical tools to network flow models; equitable content distribution allocation, management of natural resources,

ENGINEERING 2017–2018 energy policy, and aviation security. The course will IEOR E4522x and y Python for operations Introduces the basic concepts and methodologies 167 draw on a variety techniques such as linear and research that are used by the nonengineering part of the integer programming, statistical and probabilistic 1.5 pts. Lect: 1.5 Professor Logston. world in creating, funding, investing in, relating to, methods, decision analysis, risk analysis, and IEOR students only; priority to MSOR students. and operating entrepreneurial ventures. The first analysis and control of dynamic systems. Introduction to programming in Python, providing a half of the course focuses on the underpinning working knowledge of how to use Python to extract principles and skills required in recognizing, IEOR E4507y Healthcare operations knowledge and information from data. Overview analyzing, evaluating, and nurturing a business management of Python libraries for data analysis. Fundamental idea. The second half focuses on basic legal 3 pts. Lect: 3. Not offered in 2017–2018. course for MSOR students in order to engage in knowledge necessary in creating a business entity, Prerequisite(s): for senior undergraduate higher level analytics course. defending your business assets, and in promoting Engineering students: SIEO W3600 and IEOR effective interaction with other individuals and E3608; for Engineering graduate students (M.S. IEOR E4523x and y Data analytics for organizations. or Ph.D.): Probability and statistics at the level operations research of IEOR E4150, and deterministic models at the 3 pts. Lect: 3. Professors Johar and Avgar. IEOR E4555x or y Design and agile project level of IEOR E4004; for health care management Corequisite: IEOR E4522. IEOR students only; management engineering lab students: P8529 Analytical methods for health priority to MSOR students. Survey tools available 3 pts. Lect: 3. Professor Farrokhnia. services management. Develops modeling, in Python for getting, cleaning, and analyzing data. Intensive, team-, and project-based seminar analytical, and managerial skills of engineering Obtain data from files (csv, html, json, xml) and covering multidisciplinary approach to evidence- and health care management students. Enables databases (Mysql, PostgreSQL, NoSQL), cover based product design; agile project planning and students to master an array of fundamental the rudiments of data cleaning, and examine data execution; rapid MVP prototyping; and launch operations management tools adapted to the analysis, machine learning, and data visualization strategy formulation and implementation. Focuses management of health care systems. Through real- packages (numpy, Pandas, Scikitlern, bokeh) avail- on practical use of design thinking, design stu- world business cases, students learn to identify, able in Python. Brief overview of natural language dio, and iterative design sprint methodologies. model, and analyze operational improvements and processing, network analysis, and big data tools Systematic approaches to Lean User Research, innovations in a range of health care contexts. available in Python. Contains a group project com- User Experience (UX), and User Interface (UI) ponent that will require students to gather, store, design and deployment are integral components IEOR E4510y Project management and analyze a data set of their choosing. of course curriculum. Mix of startup and enterprise 3 pts. Lect: 3. Professor Rosenwein. projects, including application drive, data-driven, Prerequisites: IEOR E4004 (or IEOR E3608). IEOR E4524x and y Industry projects in or combination of both. Teams are fully supported Management of complex projects and the tools analytics in devising prototypes and actualizing proposed that are available to assist managers with 3 pts. Lect: 3. Professor Johar. solutions. such projects. Topics include project selection, Prerequisites: IEOR E4522 or equivalent and project teams and organizational issues, project concurrent registration in either Data Mining or IEOR E4561x or y Launch your startup monitoring and control, project risk management, Machine Learning. MSOR students only. Groups of 3 pts. Lect: 3. Professor Davis project resource management, and managing students will work on real world projects in analyt- Tools and knowledge to develop a comprehensive multiple projects. ics, focusing on three aspects: identifying client new venture that is scalable, repeatable, and capi- analytical requirements; assembling, cleaning, tal efficient. Covers customer discovery, market IEOR E4520y Applied systems engineering and organizing data; identifying and implement- sizing, pricing, competition, distribution, funding, 3 pts. Lect: 3. Professor Johangir. ing analytical techniques (statistics, OR, machine developing a minimal viable product, and other fac- Prerequisites: B.S. in engineering or applied learning); and delivering results in a client-friendly ets of creating new ventures. A company blueprint sciences; professional experience recommended; format. Each project has a well-defined goal, and final investor pitch are deliverables. calculus, probability and statistics, linear algebra. comes with sources of data preidentified, and has Introduction to fundamental methods used in IEOR E4577x or y Intellectual property for been structured so that it can be completed in systems engineering. Rigorous process that entrepreneurs and managers one semester. Client-facing class with numerous translates customer needs into a structured set 0 pts. Lect: 3. Professors Orin and Sears. on-site client visits; students should keep Fridays of specific requirements; synthesizes a system An overview of commercial opportunities in clear for this purpose. architecture that satisfies those requirements and intellectual property, with a focus on technology allocates them in a physical system, meeting cost, IEOR E4540x or y Data mining for engineers patents for the business or tech entrepreneur. schedule, and performance objectives throughout 3 pts. Lect: 2.5. Professor Choromanski. IEOR E4601y Dynamic pricing and revenue the product life-cycle. Sophisticated modeling of Prerequisites: Linear Algebra, Calculus, Probability, management requirements optimization and dependencies, risk and some basic programming. Course covers major 3 pts. Lect: 3. Professor Truong. management, probabilistic scenario scheduling, statistical learning methods for data mining under Prerequisites: STAT GU4001 and IEOR E4004. verification matrices, and systems-of-systems both supervised and unsupervised settings. Topics Focus on capacity allocation, dynamic pricing and constructs are synthesized to define the meta- covered include linear regression and classification, revenue management. Perishable and/or limited workflow at the top of every major engineering model selection and regularization, tree-based product and pricing implications. Applications to project. methods, support vector machines, and unsuper- various industries including service, airlines, hotel, vised learning. Students learn about principles IEOR E4521x or y Systems engineering tools resource rentals, etc. underlying each method, how to determine which and methods methods are most suited to applied settings, con- IEOR E4602y Quantitative risk management 3 pts. Lect: 2.5. Professor Johangir. cepts behind model fitting and parameter tuning, 3 pts. Lect: 3. Not offered in 2017–2018. Prerequisites: B.S. in engineering or applied and how to apply methods in practice and assess Prerequisites: STAT GU4001 and IEOR E4106. sciences; probability and statistics, optimization, their performance. Emphasizes roles of statistical Risk management models and tools; measure risk linear algebra, and basic economics. Applications modeling and optimization in data mining. using statistical and stochastic methods, hedging of SE tools and methods in various settings. and diversification. Examples include insurance Encompasses modern complex system IEOR E4550x and y Entrepreneurial business risk, financial risk, and operational risk. Topics development environments, including aerospace and creation for engineers 3 pts. Lect: 3. Professor Gulley. covered include VaR, estimating rare events, defense, transportation, energy, communications, extreme value analysis, time series estimation of and modern software-intensive systems. Prerequisite: IEOR E2261. This course is required for undergraduate students majoring in OR:EMS. extremal events; axioms of risk measures, hedging

ENGINEERING 2017–2018 168 using financial options, credit risk modeling, and tools to support operations, risk management, Prerequisites: IEOR E4701. This graduate course various insurance risk models. and response to disruptions. Analysis is done is only for MS program in FE students. Modeling, by targeting economic and financial decisions in analysis, and computation of derivative securities. IEOR E4611y Decision models and complex systems that involve multiple partners. Applications of stochastic calculus and stochastic applications Topics include probability, statistics, hypothesis differential equations. Numerical techniques: finite- 3 pts. Lect: 3. Not offered in 2017–2018. testing, experimentation, and forecasting. difference, binomial method, and Monte Carlo. Prerequisites: For undergraduates: SIEO W3600/ STAT GU4001 or equivalent and IEOR E3608/ IEOR E4700x and y Introduction to financial IEOR E4708y Seminar on important papers in IEOR E4004 or equivalent. For graduate students: engineering financial engineering Instructor’s permission required. Corequisite: IEOR 3 pts. Lect: 3. Professors Derman and Yao. 3 pts. Lect: 3. Not offered in 2017–2018. E4404 or equivalent. Introduction to deterministic Prerequisite: IEOR E4106 or E3106. This course Prerequisites: IEOR E4703, E4706, probability and stochastic decision tools used by leading is required for undergraduate students majoring and statistics. Selected topics of special interest to corporations and applied researchers. Real-world in OR:FE. Introduction to investment and financial M.S. students in financial engineering. If topics are problems in engineering and finance are discussed. instruments via portfolio theory and derivative different then this course can be taken more than once for credit. IEOR E4615y Service engineering securities, using basic operations research/ 3 pts. Lect: 3. Not offered in 2017–2018. engineering methodology. Portfolio theory, IEOR E4709x or y Statistical analysis and Prerequisites: Introductory courses in probability arbitrage; Markowitz model, market equilibrium, time series and statistics such as SIEO W3600, and and the capital asset pricing model. General 3 pts. Lect: 3. Members of the faculty. introductory courses in stochastic processes such models for asset price fluctuations in discrete Prerequisites: Probability and IEOR E4702. as IEOR E3106 or IEOR E4106. Focus on service and continuous time. Elementary introduction to Corequisites: IEOR E4706, E4707. This graduate systems viewed as stochastic networks, exploiting Brownian motion and geometric Brownian motion. course is only for M.S. Program in Financial the theoretical framework of queueing theory. Option theory; Black-Scholes equation and call Engineering students. Empirical analysis of asset Includes multidisciplinary perspectives involving option formula. Computational methods such as prices: heavy tails, test of the predictability of stock Statistics, Psychology, and Marketing. Significant Monte Carlo simulation. returns. Financial time series: ARMA, stochastic emphasis on data analysis, exploiting data from volatility, and GARCH models. Regression models: IEOR E4701x or y Stochastic models for banks, hospitals, and call centers to demonstrate linear regression and test of CAPM, nonlinear the use of decision support tools. Analytical financial engineering regression and fitting of term structures. models, flow models of service networks, Little’s 3 pts. Lect: 3. Professor Lacker. IEOR E4710x or y Fixed income and term law, measuring methods in face-to-face and Prerequisite: STAT GU4001. This graduate course structure modeling computerized systems, forecasting methods, is only for M.S. Program in Financial Engineering 3 pts. Lect: 3. Not offered in 2017–2018. stability of service systems, operational quality students, offered during the summer session. Prerequisites: IEOR E4706, E4707, and computer of service, economies of scale, staffing, complex Review of elements of probability theory, Poisson programming. Interest rate models and numerical service networks, skill-based routing. processes, exponential distribution, renewal theory, Wald’s equation. Introduction to discrete-time techniques for pricing and hedging interest rate IEOR E4620x Pricing models for financial Markov chains and applications to queueing theory, contracts and fixed income securities. engineering inventory models, branching processes. IEOR E4711x Global capital markets 3 pts. Lect: 3. Professor DeRosa. 3 pts. Lect: 3. Professor Dastidar. Prerequisite: IEOR E4700. This course is IEOR E4703y Monte Carlo simulation Prerequisites: Refer to course syllabus. An required for undergraduate students majoring in 3 pts. Lect: 3. Members of the faculty. introduction to capital markets and investments OR:FE. Characteristics of commodities or credit Prerequisite: IEOR E4701. This graduate course providing an overview of financial markets and derivatives. Case study and pricing of structures is only for M.S. Program in Financial Engineering students. Multivariate random number generation, tools for asset valuation. Topics covered include and products. Topics covered include swaps, the pricing of fixed-income securities (treasury credit derivatives, single tranche CDO, hedging, bootstrapping, Monte Carlo simulation, efficiency improvement techniques. Simulation output analysis, markets, interest rate swaps futures, etc.), convertible arbitrage, FX, leverage leases, debt discussions on topics in credit, foreign exchange, markets, and commodities. Markov-chain Monte Carlo. Applications to financial engineering. Introduction to financial engineering sovereign ad securitized markets—private equity IEOR E4630y Asset allocation simulation software and exposure to modeling with and hedge funds, etc. 3 pts. Lect: 3. Professor Alonso. real financial data. NOTE: Students who have taken IEOR E4712x Behavioral finance Prerequisite: IEOR E4700. Models for pricing IEOR E4404 Simulation may not register for this 1.5 pts. Lect: 3. Not offered in 2017–2018. and hedging equity, fixed-income, credit- course for credit. Prerequisite: IEOR E4700. Behavioral finance derivative securities, standard tools for hedging IEOR E4706 Foundations of financial is the application of behavioral psychology to and risk management, models and theoretical engineering financial decision making. Focuses on the portfolio foundations for pricing equity options (standard 3 pts. Lect: 3. Professor Possamaï. aspect of behavioral finance and briefly touches European, American equity options, Asian Prerequisites: IEOR E4701, E4702, and linear on other aspects. Compared with classical theory options), standard Black-Scholes model (with algebra. This graduate course is only for M.S. of portfolio choice, behavioral portfolio choice multiasset extension), asset allocation, portfolio Program in Financial Engineering students, offered features human being’s psychological biases. It optimization, investments over longtime during the summer session. Discrete-time models builds both on behavioral preference structures horizons, and pricing of fixed-income derivatives of equity, bond, credit, and foreign-exchange different from mean variance theory and expected (Ho-Lee, Black-Derman-Toy, Heath-Jarrow- markets. Introduction to derivative markets. Pricing utility theory and on systematic biases against Morton interest rate model). and hedging of derivative securities. Complete rational beliefs such as Bayesian rule. IEOR E4650x or y Business analytics and incomplete markets. Introduction to portfolio IEOR E4714x Risk management, financial 3 pts. Lect 3. Recit: 1. Professors Elmachtoub optimization and the capital asset pricing model. system and financial crisis and Leshno. IEOR E4707y Financial engineering: 1.5 pts. Professor Malz. Prerequisite: STAT GU4001 or IEOR E4150. This continuous-time asset pricing Risk-taking and risk management are at course prepares students to gather, describe, 3 pts. Lect: 3. Professor Capponi. the heart of the financial system, and of the and analyze data, using advanced statistical current financial crisis. An introduction to risk

ENGINEERING 2017–2018 management both from an individual financial IEOR E4731x Credit risk modeling and familiarizing the student with the nature of the 169 firm’s and from a public policy viewpoint. derivatives foreign exchange market and those factors that Overview of the contemporary financial 3 pts. Lect: 3. Professor Capponi. make it special among financial markets, enabling system, focusing on innovations of the past Prerequisites: IEOR E4701 and E4707. the student to gain a deeper understanding of the few decades that have changed how financial Introduction to quantitative modeling of credit risk, related market for derivatives on foreign exchange. risk is generated and distributed among with a focus on the pricing of credit derivatives. IEOR E4735y Structured and hybrid products market participants, such as the growth Focus on the pricing of single-name credit 3 pts. Lect: 3. Professor Kani. of non-bank financial intermediaries, the derivatives (credit default swaps) and collateralized Prerequisite: IEOR E4700. Conceptual and increased prevalence of leverage and liquidity debt obligations (CDOs). Detail topics include practical understanding of structured and hybrid risk, and the development of structured credit default and credit risk, multiname default barrier products from the standpoint of relevant risk products. Introduction to the basic quantitative models and multiname reduced form models. factors, design goals and characteristics, pricing, tools used in market, credit, and liquidity risk hedging, and risk management. Detailed analysis management. The two strands of the course IEOR E4732x Computational methods in of the underlying cash-flows, embedded derivative are brought together to help understand how derivatives pricing instruments, and various structural features the financial crisis arose and is playing out, 3 pts. Professor Hirsa. of these transactions, both from the investor examining the mechanics of runs and the Prerequisite: IEOR E4700. Introduction and and issuer perspectives, and analysis of the behavior of asset prices during crises. Attempt application of various computational techniques impact of the prevailing market conditions and to understand the emergency programs in pricing derivatives and risk management. parameters on their pricing and risk characteristics. deployed by central bankers and other policy Transform techniques, numerical solutions of Numerical methods for valuing and managing makers to address crises historically and today. partial differential equations (PDEs) and partial integro-differential equations (PIDEs) via finite risk of structured/hybrid products and their IEOR E4715x, s Commodity derivatives differences, Monte-Carlo simulation techniques, embedded derivatives and their application to 1.5 pts. Professor Higgins. calibration techniques, and parameter estimation equity, interest rates, commodities and currencies, Commodities markets have been much in the and filtering techniques. The computational inflation, and credit-related products. Conceptual public eye recently as volatility has increased and platform will be Java/C++. The primary application and mathematical principles underlying these they changed from markets dominated by physical focus will be pricing of financial derivatives and techniques, and practical issues that arise in participants to ones which have a significant calibration. These techniques are useful for various their implementations in the Microsoft Excel/VBA investor component. The largest banks either other problems in financial modeling and practical and other programming environments. Special already have profitable commodities franchises or implementations from the theory of mathematical contractual provisions encountered in structured are actively building them, and money managers finance. and hybrid transactions, and incorporation of and funds are increasingly including these assets yield curves, volatility smile, and other features in their portfolio mix. The end result is a dramatic IEOR E4733x Algorithmic trading of the underlying processes into pricing and increase in focus on these markets from all 3 pts. Professor Kani. implementation framework for these products. aspects of the financial markets, including the Prerequisite: IEOR E4700. Large and amorphous IEOR E4736x and y Event-driven finance quantitative end. collection of subjects ranging from the study of market microstructure, to the analysis of 3 pts. Lect: 2.5. Professors Lipkin and Stanton. IEOR E4718x or y Beyond Black-Scholes: the optimal trading strategies, to the development of Prerequisites: IEOR E4706, IEOR E4707, and implied volatility smile computerized, high-frequency trading strategies. familiarity with simple Black-Scholes pricing. 3 pts. Lect: 3. Professor Derman. Analysis of these subjects, the scientific and Examines actual behavior of real stocks and Prerequisites: IEOR E4706, knowledge of practical issues they involve, and the extensive options in presence of commonplace, but derivatives valuation models. During the past body of academic literature they have spawned. singular, events, such as earning take-overs, 15 years the behavior of market options prices Attempt to understand and uncover the economic hard-to-borrowness, expirations, etc. Propose have shown systematic deviations from the and financial mechanisms that drive and ultimately trading schema (tests via IVY options/stock classic Black-Scholes model. The course relate them. database and carry out tests efficiently and examines the empirical behavior of implied accurately). Differences between model-based IEOR E4734y Foreign exchange and related volatilities, in particular the volatility smile that (static, thermodynamic/SDE model solutions) derivatives instruments now characterizes most markets, the mathematics behavior predicted for stocks and options and 1.5 pts. Lect: 1.5. Professor DeRosa. and intuition behind new models that can account their real behavior. Students become familiar with Prerequisite: IEOR E4700. Foreign exchange for the smile, and their consequences for hedging computational techniques for modeling and testing market and its related derivative instruments—the proposals for trading strategies. and valuation. latter being forward contracts, futures, options, IEOR E4720x and y–E4729 Topics in and exotic options. What is unusual about foreign IEOR E4738x Programming for FE 1: tools for quantitative finance exchange is that although it can rightfully claim to building financial data and risk systems 1.5–3 pts. Lect: 2–2.5. Members of the faculty. be the largest of all financial markets, it remains 3 pts. Lect: 2.5. Professor Hirsa. Prerequisites: IEOR E4700; additional an area where very few have any meaningful Prerequisite: Familiarity with object-oriented prerequisites will be announced depending on experience. Virtually everyone has traded stocks, programming. Object-oriented programming and offering. Selected topics of interest in the area bonds, and mutual funds. Comparatively few database development for building financial data of quantitative finance. Offerings vary each individuals have ever traded foreign exchange. and risk systems; Python and Python's scientific year; some topics include energy derivatives, In part that is because foreign exchange is an libraries; basic database theory, querying and experimental finance, foreign exchange interbank market. Ironically the foreign exchange constructing databases; basic risk management and related derivative instruments, inflation markets may be the best place to trade derivatives and design of risk systems. and to invent new derivatives—given the massive derivatives, hedge fund management, modeling two-way flow of trading that goes through bank IEOR E4739y Programming for FE 2: equity derivatives in Java, mortgage-backed dealing rooms virtually twenty-four hours a day. implementing high-performance financial securities, numerical solutions of partial differential And most of that is transacted at razor-thin systems equations, quantitative portfolio management, risk margins, at least comparatively speaking, a fact 3 pts. Lect: 2.5. Professor Bienstock. management, trade and technology in financial that makes the foreign exchange market an ideal markets. Prerequisites: IEOR E4738 and instructor’s platform for derivatives. The emphasis is on permission. Developing effective software

ENGINEERING 2017–2018 170 implementations in C programming language; of (s, S) policies. Multiproduct and multiechelon Jump diffusion models. Applications, including modeling of portfolio optimization; modeling systems. Computational methods. pricing of real and electricity options and hedging of price impact trading models; review of of real options. IEOR E6602y Nonlinear programming synchronization of programs using the file 3 pts. Lect: 3. Members of the faculty. IEOR E6711x Stochastic models, I system; review of synchronization of programs Prerequisite: Ph.D.-level linear programming. 4.5 pts. Lect: 3. Professor Sigman. using threads; review of synchronization of Convex sets and functions, convex duality and Prerequisite: STAT GU4001 or equivalent. programs using sockets; implementation of high- optimality conditions. Computational methods: Advanced treatment of stochastic modeling in the performance simulations in finance. steepest descent, Newton and quasi-newton context of queueing, reliability, manufacturing, IEOR E4900s, x and y Master’s research or methods for unconstrained problems, active set, insurance risk, financial engineering and other project penalty set, interior point, augmented Lagrangian engineering applications. Review of elements of 1–3 pts. Members of the faculty. and sequential quadratic programming methods probability theory; exponential distribution; renewal Prerequisite: Approval by a faculty member who for constrained problems. Introduction to theory; Wald’s equation; Poisson processes. agrees to supervise the work. Independent work nondifferentiable optimization and bundle methods. Introduction to both discrete and continuous-time involving experiments, computer programming, Markov chains; introduction to Brownian motion. IEOR E6613x Optimization, I analytical investigation, or engineering design. 4.5 pts. Lect: 3. Professor Goldfarb. IEOR E6712y Stochastic models, II IEOR E4998x and y Managing technological Prerequisite: Linear algebra. Theory and geometry 4.5 pts. Lect: 3. Professor Yao. innovation and entrepreneurship of linear programming. The simplex method. Prerequisite: IEOR E6711 or equivalent. 3 pts. Lect: 3. Professor Neumann. Duality theory, sensitivity analysis, column Continuation of IEOR E6711, covering further This is a required course for undergraduate generation and decomposition. Interior point topics in stochastic modeling in the context of students majoring in OR:EMS. Focus on the methods. Introduction to nonlinear optimization: queueing, reliability, manufacturing, insurance management and consequences of technology- convexity, optimality conditions, steepest descent, risk, financial engineering, and other engineering based innovation. Explores how new industries and Newton’s method, active set, and barrier applications. Topics from among generalized are created, how existing industries can be methods. semi-Markov processes; processes with a transformed by new technologies, the linkages nondiscrete state space; point processes; IEOR E6614y Optimization, II between technological development and the stochastic comparisons; martingales; introduction 4.5 pts. Lect: 3. Professor Stein. creation of wealth and the management challenges to stochastic calculus. of pursuing strategic innovation. Prerequisite: Linear algebra. An introduction to combinatorial optimization, network flows and IEOR E8100x and y Advanced topics in IEOR IEOR E4999s, x and y Fieldwork discrete algorithms. Shortest path problems, 1–3 pts. Members of the faculty. 1–3 pts. Professor Derman and Mak. maximum flow problems. Matching problems, Prerequisite: Faculty adviser’s permission. Prerequisites: Obtained internship and approval bipartite and cardinality nonbipartite. Introduction Selected topics of current research interest. May from faculty adviser. Only for IEOR graduate to discrete algorithms and complexity theory: be taken more than once for credit. students who need relevant work experience NP-completeness and approximation algorithms. IEOR E9101s, x and y Research as part of their program of study. Final reports 1–6 pts. Members of the faculty. required. This course may not be taken for pass/ IEOR E6703y Advanced financial engineering Before registering, the student must submit an fail credit or audited. 3 pts. Lect: 2. Not offered in 2017–2018. Prerequisites: Probability theory and advanced outline of the proposed work for approval by MSIE W6408y Inventory theory stochastic models at the SIEO GR6501 level. the supervisor and the chair of the Department. 3 pts. Lect: 3. Not offered in 2017–2018. Review of basic mathematics, including renewal Advanced study in a specialized field under the Prerequisites: Probability theory, dynamic theory and stochastic calculus. Martingale supervision of a member of the department staff. programming. Construction and analysis of approach to Black-Scholes formula. Optimal This course may be repeated for credit. mathematical models used in the design and stopping and American options. Pricing of analysis of inventory systems. Deterministic and continuous and discrete exotic options. Term stochastic demands and lead times. Optimality structure models and pricing of bond options.

ENGINEERING 2017–2018 MATERIALS SCIENCE AND ENGINEERING PROGRAM 171 Program in the Department of Applied Physics and Applied Mathematics, sharing teaching and research with the faculty of the Henry Krumb School of Mines.

200 S. W. Mudd, MC 4701 Phone: 212-854-4457 apam.columbia.edu seas.columbia.edu/matsci

IN CHARGE OF MATERIALS Katayun Barmak Oleg Gang Ismail C. Noyan Wen I. Wang SCIENCE AND ENGINEERING Professor of Materials Professor of Chemical Professor of Materials Professor of Electrical Professor Katayun Barmak Science Engineering and Applied Science and Engineering Engineering 1137 S. W. Mudd Simon J. Billinge Physics and Materials Ben O'Shaughnessy Renata Wentzcovitch Professor of Materials Science Professor of Chemical Professor of Materials IN CHARGE OF SOLID- Science Irving P. Herman Engineering Science and Applied STATE SCIENCE AND Louis E. Brus Professor of Applied Physics Richard M. Osgood Jr. Physics, and Earth and ENGINEERING Professor of Chemistry James C. Hone Professor Emeritus of Environmental Science Professor Irving P. Herman Siu-Wai Chan Professor of Mechanical Electrical Engineering Yuan Yang 905 CEPSR Professor of Materials Engineering Aron Pinczuk Assistant Professor of Science James S. Im Professor of Applied Physics Materials Science and COMMITTEE ON Christopher J. Durning Professor of Materials and Physics Engineering MATERIALS SCIENCE AND Professor of Science Ponisseril Somasundaran Nanfang Yu ENGINEERING/SOLID-STATE Chemical Engineering Michal Lipson Professor of Mineral Assistant Professor of SCIENCE AND ENGINEERING Engineering Applied Physics William E. Bailey Alexander Gaeta Professor of Electrical Yasutomo Uemura Associate Professor of Professor of Applied Physics Engineering Professor of Physics Materials Science Chris A. Marianetti Associate Professor of Latha Venkataraman Materials Science Professor of Applied Physics

aterials Science and Students interested in materials macroscopic scale—details essential to Engineering (MSE) focuses on science and engineering enroll in the understanding the relationship between M understanding, designing, and materials science and engineering materials synthesis and processing producing technology-enabling materials program in the Department of Applied and materials properties, including by analyzing the relationships among the Physics and Applied Mathematics. electronic, magnetic, mechanical, synthesis and processing of materials, Those interested in the solid-state optical, and thermal properties. These their properties, and their detailed science and engineering specialty enroll studies also give insight into problems structure. This includes a wide range in the doctoral program within Applied of the deterioration of materials in of materials such as metals, polymers, Physics and Applied Mathematics or service, enabling designers to prolong ceramics, and semiconductors. Solid- Electrical Engineering. the useful life of their products. Materials state science and engineering focuses The faculty in the interdepartmental science and engineering also focuses on understanding and modifying the committee constitute but a small on new ways to synthesize and process properties of solids from the viewpoint fraction of those participating in this materials, from bulk samples to ultrathin of the fundamental physics of the program, who include Professors Bailey, films to epitaxial heterostructures to atomic and electronic structure. Barmak, Billinge, Chan, Gaeta, Gang, nanocrystals. This involves techniques The undergraduate and graduate Herman, Im, Marianetti, Noyan, Pinczuk, such as UHV sputtering; molecular programs in materials science Venkataraman, Wentzcovitch, Yang, and beam epitaxy; plasma etching; laser and engineering are coordinated Yu from Applied Physics and Applied ablation, chemistry, and recrystallization; through the MSE Program in the Mathematics; Brus, Durning, Flynn, and other nonequilibrium processes. Department of Applied Physics and Koberstein, and O’Shaughnessy from The widespread use of new materials Applied Mathematics. This program Chemical Engineering; Somasundaran and the new uses of existing materials promotes the interdepartmental and Themelis from Earth and in electronics, communications, nature of the discipline and involves Environmental Engineering; Lipson, and computers have intensified the the Departments of Applied Physics Osgood, and Wang from Electrical demand for a systematic approach and Applied Mathematics, Chemical Engineering; and Hone from Mechanical to the problem of relating properties Engineering and Applied Chemistry, Engineering. to structure and necessitates a Electrical Engineering, and Earth and Materials science and engineering multidisciplinary approach. Environmental Engineering in the Henry uses optical, electron, and scanning Solid-state science and engineering Krumb School of Mines (HKSM) with probe microscopy and diffraction uses techniques such as transport advisory input from the Departments of techniques to reveal details of structure, measurements, X-ray photoelectron Chemistry and Physics. ranging from the atomic to the spectroscopy, inelastic light scattering,

ENGINEERING 2017–2018 172 luminescence, and nonlinear optics clean room, shared materials character- and fuel cells; electrodeposition and to understand electrical, optical, and ization laboratories, and electron micros- corrosion of metals; and the analysis magnetic properties on a quantum copy facility (SEM, S/TEM). and design of high-temperature mechanical level. Such methods are reactors and first principles calculations. used to investigate exciting new types Through involvement with our research UNDERGRADUATE PROGRAM of structures, such as two-dimensional groups, students gain valuable hands- IN MATERIALS SCIENCE electron gases in semiconductor on experience and are often engaged heterostructures, superconductors, The objectives of the undergraduate in joint projects with industrial and and semiconductor surfaces and program in the Materials Science government laboratories. nanocrystals. Program of the Department of Applied Students are strongly encouraged Physics and Applied Mathematics are as to take courses in the order specified follows: in the course tables; implications of Current Research Activities 1. Professional employment in industry, deviations should be discussed with a Current research activities in the materials including materials production, auto- departmental adviser before registration. science and engineering program motive, aerospace, microelectronics, The first two years provide a strong at Columbia focus on thin films and information storage, medical devices, grounding in the physical and chemical electronic materials that enable significant energy production, storage and con- sciences, materials fundamentals, and advances in information technologies. version, and in engineering consulting mathematics. This background is used Specific topics under investigation firms; to provide a unique physical approach include interfaces, stresses, and grain 2. Graduate studies in materials science to the study of materials. The last two boundaries in thin films; lattice defects and engineering or related fields; years of the undergraduate program and electrical properties of metals and provide substantial exposure to modern semiconductors; laser processing and The undergraduate curriculum materials science and include courses ultrarapid solidification of thin films; is designed to provide the basis in processing, structure and properties nucleation in condensed systems; for developing, improving, and of materials that extend the work of optical and electrical properties of understanding materials and processes the first two years. Graduates of the semiconductors and metals; synthesis of for application in engineered systems. program are equipped for employment nanocrystals, two-dimensional materials, It draws from physics, chemistry and in the large industrial sector that includes and nanotechnology-related materials; other disciplines to provide a coherent materials production, automotive, deposition, in-situ characterization, background for immediate application in aerospace, microelectronics, information electronic testing, and ultrafast engineering or for subsequent advanced storage, medical devices, and energy spectroscopy of magnetoelectronic study. The emphasis is on fundamentals production, storage and conversion. ultrathin films and heterostructures. In relating atomic-to-microscopic-scale Graduates are prepared for graduate addition, there is research in surface phenomena to materials properties study in materials science and and colloid chemistry involving both and processing, including design and engineering and related fields. inorganic and organic materials such control of industrially important materials as surfactants, polymers, and latexes, processes. Core courses and electives Required Materials Science Courses with emphasis on materials/environment combine rigor with flexibility and provide Students are required to take 14 interactions. opportunities for focusing on such areas Materials Science courses for a total The research activities in solid-state as nanomaterials, materials for green of 40 points. The required courses are science and engineering are described energy, materials for infrastructure and MSAE E3010, E3011, E3012, E3013, later in this section. manufacturing, materials for health and E4100, E4102, E4200, E4201, E4250, biotechnology, and materials for next E3156, E4206, E3157, E4202, and generation electronics. LABORATORY FACILITIES E4215. The unifying theme of understanding Facilities and research opportunities and interrelating materials synthesis, also exist within the interdepartmental Technical Elective Requirements processing, structure, and properties Columbia Nanotechnology Initiative forms the basis of our program and is Students are required to take eight (CNI). Modern clean room facilities with evident in the undergraduate curriculum technical electives (24 points) from the optical and e-beam lithography, thin film and in faculty research activities. These list given below, which offers significant deposition, and surface analytical probes activities include work on polycrystalline flexibility in allowing students to tailor (STM, SPM, XPS) are available. More silicon for flat panel displays; high- their degree program to their interests. specialized equipment exists in individual temperature superconductors for research groups in solid state engineer- power transmission and sensors; a. All 3000-level or higher courses in ing and materials science and engineer- semiconductors for lasers and solar cell the Materials Science program of the ing. The research facilities in solid-state applications, magnetic heterostructures Department of Applied Physics and science and engineering are listed in for information storage and novel Applied Mathematics, except those the sections for each host department. computation architectures; electronic MSAE courses that are required. Facilities, and research opportunities, ceramics for batteries, gas sensors b. All 3000-level or higher courses also exist within the interdepartmental

ENGINEERING 2017–2018 173 MATERIALS SCIENCE PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

APMA E2000 (4)1 MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) and APMA E2101 (3)

UN1401 (3) UN1402 (3) PHYSICS UN1403 (3) (three tracks, UN1601 (3.5) UN1602 (3.5) UN2601 (3.5) choose one) UN2801 (4.5) UN2802 (4.5)

UN1403 (4) or UN1404 (4) or UN2045 (4) CHEMISTRY or UN1604 (4)

PHYS UN1493 (3) or UN3081 (2) or REQUIRED LABS CHEM UN1500 (3) or UN1507 (3) or UN3085 (4)

UNIVERSITY UN1010 (3) either semester WRITING

HUMA CC1002, COCI CC1102, HUMA CC1001, HUMA UN1121 (3) or Global Core (3–4) NONTECHNICAL COCI CC1101, REQUIREMENTS or UN1123 (3) or Global Core (3–4) ECON UN1105 (4) and UN1155 recitation (0)

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

COMPUTER ENGI E1006 (3) any semester SCIENCE

TECHNICAL MSAE E3010 (3) MSAE E3011 (3) REQUIREMENTS Intro to mat. sci. I Intro to mat. sci. II

1 Effective Class of 2021. in Applied Physics or Applied courses that require graduate ELEN E4193x: Modern display technology Math Programs of the Department standing. MECE E4212x or y: Microelectromechanical of Applied Physics and Applied d. Courses in the Department of systems BMEN E4550y: Micro- and nanostructures in Mathematics. Chemistry listed in the Focus Areas cellular engineering c. All 3000-level or higher courses below. ELEN E4944x: Principles of device in the Department of Biomedical microfabrication Engineering Civil Engineering and Focus Areas for technical electives Engineering Mechanics program, are listed below. Students may choose MATERIALS FOR NEXT GENERATION Department of Chemical Engineering, from any one area if they so choose. ELECTRONICS Department of Computer Science, They are not required to do so. APPH E3100y: Intro to quantum mechanics Earth and Environmental Engineering ELEN E3106x: Solid state devices-materials APPH E4100x: Quantum physics of matter program, Department of Electrical NANOMATERIALS ELEN E4301y: Intro to semiconductor devices APPH E3100y: Intro to quantum mechanics Engineering, Department of Industrial ELEN E4944x: Principles of device CHEM GU4071x: Inorganic chemistry Engineering and Operations microfabrication MSAE E4090y: Nanotechnology Research, and Department of APPH E4100x: Quantum physics of matter MATERIALS FOR GREEN ENERGY Mechanical Engineering, except for CHEM GU4168x: Materials chemistry, I EAEE E3103x: Energy, minerals, materials systems

ENGINEERING 2017–2018 174 MATERIALS SCIENCE PROGRAM: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

MSAE E3157 (2) MSAE E3012 (3)1 MSAE E3013 (3)1 MSAE E3156 (2) Design project Laboratory in mat. sci. I Laboratory in mat. sci. II Design project MSAE E4202 (3) MSAE E4100 (3) MSAE E4201 (3) MSAE E4200 (3) Kinetics of transformations Crystallography Materials thermodynamics Theory of crystalline in materials REQUIRED and phase diagrams materials COURSES MSAE E4102 (3) MSAE E4206 (3) MSAE E4215 (3) Synthesis and processing MSAE E4250 (3) Electronic and magnetic Mechanical behavior of materials Ceramics and composites properties of solids of materials Technical Electives (6) Technical Electives (6) Technical Electives (6) Technical Electives (6)

NONTECHNICAL 3 points 3 points 4 points 3 points ELECTIVES

TOTAL POINTS 18 18 18 17

1Motivated students are highly encouraged to take the materials science laboratory I and II courses in the sophomore year to obtain practical understanding of material covered in the junior and senior years.

MATERIALS SCIENCE PROGRAM: THIRD AND FOURTH YEARS (TRANSFER STUDENTS)

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

MSAE E3156 (2) MSAE E3011 (3) MSAE E3010 (3) Design project Introduction to materials Introduction to materials MSAE E3157 (2) science, II science, I MSAE E4100 (3) Design project Crystallography MSAE E3013 (3) MSAE E3012 (3) MSAE E4202 (3) Laboratory in materials Laboratory in materials MSAE E4200 (3) Kinetics of transformations science, II REQUIRED science, I Theory of crystalline in materials COURSES materials MSAE E4201 (3) MSAE E4215 (3) Materials thermodynamics MSAE E4102 (3) MSAE E4206 (3) Mechanical behavior of and phase diagrams Synthesis and processing Electronic and magnetic materials of materials properties of solids MSAE E4250 (3) Technical Elective (3) Ceramics and composites Technical Elective (3) Technical Elective (3)

NONTECHNICAL 3 points 3 points 4 points 3 points ELECTIVES

TOTAL POINTS 15 15 18 14

1Students following this chart will need four additional technical electives in order to complete the requirements for the degree and should consult the guidelines for technical electives detailed on pp. 173 and 175.

ENGINEERING 2017–2018 EAEE E4004x: Physical processing and recovery Engineering and Applied Science and The remaining 12 points will be 175 of solids those needed to meet the 27-point chosen from elective courses, 6 points CHEE E4050x: Industrial and environmental total of nontechnical electives required of which must be Type I and 6 points of electrochemistry which may be Type I or Type II: CHEM GU4071x: Inorganic chemistry for graduation. APPH E4130: Physics of solar energy • Type I Electives: EAEE E4190x: Photovoltaic systems engineering Transfer Students and sustainability MSAE E4090: Nanotechnology 3-2/Transfer students and students MSAE E4101: Structural analysis of materials EAIA E4200y: Alternative energy resources transferring from another SEAS MSAE E4102: Synthesis and processing of MECE E4210x: Energy infrastructure planning department into the Materials Science materials MECE E4211y: Energy: sources and conversion MSAE E4132: Fundamentals of polymers and EAEE E4550x: Catalysis for emissions control Program in the junior year (upon approval of the Materials Science ceramics MSAE E4250: Ceramics and composites MATERIALS FOR 21ST CENTURY Undergraduate Transfer Committee) MSAE E4260: Electrochemical materials and INFRASTRUCTURE AND MANUFACTURING will take the following courses to devices: from structure to performance CIEE E3255y: Environmental control and pollution satisfy the degree requirements: The MSAE E4301: Materials science laboratory reduction systems required courses are MSAE E3010, MSAE E4990: Special topics in materials science CIEE E3260y: Engineering for developing E3011, E3012, E3013, E4100, E4102, and engineering communities MSAE E6085: Computing the electronic structure ENME E3114y: Experimental mechanics of E4200, E4201, E4250, E3156, E4206, of complex materials materials E3157, E4202, and E4215. MSAE E6091: Magnetism and magnetic materials MECE E3610y: Materials and processes in 3-2/Transfer Students will be MSAE E6225: Techniques in X-ray and neutron manufacturing guided by their academic advisers to diffraction ENME E4113x: Advanced mechanics of solids avoid duplication of courses previously MSAE E6229: Energy and particle beam ENME E4114y: Mechanics of fracture and fatigue taken. The course tables describe processing of materials ENME E4115y: Micromechanics of composite the four-semester program schedule MSAE E6230: Kinetics of phase transformations materials of courses leading to the bachelor’s MSAE E6251: Thin films and layers CIEN E4226y: Advanced design of steel structures MSAE E6273: Materials science reports CHEE E4530x: Corrosion of metals degree in the Materials Science Program of the Department of Applied MSAE E8235: Selected topics in materials science MSAE E4000-, 6000- or 8000-level courses not MATERIALS FOR HEALTH AND Physics and Applied Mathematics. listed here BIOTECHNOLOGY CHEM UN2443x-UN2444y: Organic chemistry • Type II Electives: APPH E3400y: Physics of the human body GRADUATE PROGRAMS IN CHEM GU4168: Materials chemistry, I MATERIALS SCIENCE AND BMEN E4300: Solid biomechanics BMEN E4300: Solid biomechanics ENGINEERING BMEN E4301: Structure, mechanics, and BMEN E4301x: Structure, mechanics, and adaptation of bone adaptation of bone BMEN E4501: Tissue engineering, I BMEN E4450y: Dental and craniofacial tissue Master of Science Degree APPH E4100: Quantum physics of matter engineering Candidates for the Master of Science APPH E4110: Modern optics BMEN E4501x: Tissue engineering, I: biomaterials degree in Materials Science and APPH E4130: Physics of solar energy APPH E6081: Solid state physics, I and scaffold design Engineering will follow a program of APPH E6082: Solid state physics, II CHEE E4530: Corrosion of metals study formulated in consultation with BMEN E4550x: Micro- and nanostructures in ELEN E4301: Intro to semiconductor devices and approved by a faculty adviser. cellular engineering ELEN E4411: Fundamentals of photonics Thirty points of credit are required at a ELEN E4944: Principles of device microfabrication * BMEN E4210y: Thermodynamics of biological minimum. EAEE E4001: Industrial ecology of earth resources systems accepted as substitute for MSAE E3111 The following six courses (18 points) EAEE E4160: Solid and hazardous waste in this track. are required for the degree: management ENME E4113: Advanced mechanics of solids ** Note that BIOL UN2005x: Introductory biology, ENME E4114: Mechanics of fracture and fatigue 18 points: ENME E4608: Manufacturing processes I and BIOL UN2006y: Introductory biology, II are MSAE E4100: Crystallography prerequisites for a number courses in this track. CHEE E4252: Intro to surface and colloid MSAE E4200: Theory of crystalline materials chemistry MSAE E4201: Materials thermodynamics and CHEE E4530: Corrosion of metals MATERIALS CHEMISTRY/SOFT MATERIALS phase diagrams CHEM UN2443x-UN2444y: Organic chemistry CHEN E4620: Intro to polymers and soft materials MSAE E4202: Kinetics of transformations in CHEN E4640: Polymer surfaces and interfaces CHEN E4201: Applications of electrochemistry materials CHEE E4252: Intro surface & colloid chemistry CHEM GU4168: Materials chemistry MSAE E4206: Electronic and magnetic properties MECE E4211: Energy sources and conversion CHEN E4620: Intro polymers / soft materials of solids CHEN E4640: Polymer surfaces and interfaces APMA E4101: Intro to dynamical systems MSAE E4215: Mechanical behavior of structural APMA E4200: Partial differential equations materials APMA E4300: Intro to numerical methods Nontechnical Elective Requirements If a candidate has already taken one APMA E4400: Intro to biophysical modeling All materials science students or more of these courses at Columbia Columbia Video Network (CVN) are also expected to register for University, substitutions from the Type I students may have their programs nontechnical electives, both those Elective list may be approved. approved by faculty. Special reports (3 specifically required by the School of

ENGINEERING 2017–2018 176 points) are required of CVN students. processing, ceramic nanocomposites, begin an association with a research All degree requirements must be electrodeposition and corrosion group, individual laboratory work, and completed within five years. A candidate processes, structure, properties, and participation in graduate seminars during is required to maintain at least a 2.5 transmission electron microscopy and their first year. GPA. Applicants for admission are crystal orientation mapping, magnetic required to take the Graduate Record thin films for giant and colossal GRADUATE SPECIALTY IN Examinations. magnetoresistance, chemical synthesis SOLID-STATE SCIENCE AND of nanoscale materials, nanocrystals, ENGINEERING Doctoral Program carbon nanotubes, nanostructure Solid-state science and engineering At the end of the first year of graduate analysis using X-ray and neutron is an interdepartmental graduate study in the doctoral program, diffraction techniques, and electronic specialty that provides coverage of an candidates are required to take a structure calculation of materials using important area of modern technology comprehensive written qualifying density functional and dynamical that no single department can provide. It examination, which is designed to test mean-field theories. Application targets encompasses the study of the full range the ability of the candidate to apply for polycrystalline silicon are thin film of properties of solid materials, with coursework in problem solving and transistors for active matrix displays special emphasis on electrical, magnetic, creative thinking. The standard is first- and silicon-on-insulator structures for optical, and thermal properties. The year graduate level. There are two ULSI devices. Novel applications are science of solids is concerned with four-hour examinations over a two-day being developed for oxide thin films, understanding these properties in period. including uncooled IR focal plane arrays terms of the atomic and electronic Candidates in the program must and integrated fuel cells for portable structure of the materials in question. take an oral examination within one year equipment. Long-range applications Insulators (dielectrics), semiconductors, of taking the qualifying examination. of high-temperature superconductors ceramics, and metallic materials are all Within two years of taking the qualifying include efficient power transmission and studied from this viewpoint. Quantum examination, candidates must submit highly sensitive magnetic field sensors. and statistical mechanics are key a written proposal and defend it orally Thin film synthesis and processing background subjects. The engineering before a Thesis Proposal Defense in this program include evaporation, aspects deal with the design of materials Committee consisting of three sputtering, electrodeposition, and to achieve desired properties and the members of the faculty, including the plasma and laser processing. For assembling of materials into systems to adviser. Doctoral candidates must analyzing materials structures and produce devices of interest to modern submit a thesis to be defended before properties, faculty and students employ technology, e.g., for computers and for a Dissertation Defense Committee electron microscopy, scanning probe energy production and utilization. consisting of five faculty members, microscopy, cathodoluminescence including two professors from outside and electron beam–induced current Areas of Research the doctoral program. Requirements imaging, photoluminescence, dielectric The graduate specialty in solid-state for the Eng.Sc.D. (administered by the and anelastic relaxation techniques, science and engineering includes School of Engineering and Applied ultrasonic methods, magnetotransport research programs in semiconductor Science) and the Ph.D. (administered measurements, and X-ray diffraction nanocrystals (Professor Brus, Chemistry/ by the Graduate School of Arts and techniques. Faculty members have Chemical Engineering); optics of Sciences) are listed elsewhere in this research collaborations with Lucent, semiconductors and nanomaterials bulletin. Exxon, IBM, and other New York area research and manufacturing centers, (Professor Herman, Applied Physics and Applied Mathematics); chemical Areas of Research as well as major international research physics of surfaces and photoemission Materials science and engineering is centers. Scientists and engineers from (Professor Osgood, Electrical concerned with synthesis, processing, these institutions also serve as adjunct Engineering/Applied Physics and structure, and properties of metals, faculty members at Columbia. The Applied Mathematics); molecular beam ceramics, polymers, and other materials, National Synchrotron Light Source at epitaxy leading to semi-conductor with emphasis on understanding Brookhaven National Laboratory is used devices (Professor Wang, Electrical and exploiting relationships among for high-resolution X-ray diffraction and Engineering/Applied Physics and structure, properties, and applications absorption measurements. Applied Mathematics); metamaterials requirements. Our graduate research Entering students typically have and infrared optoelectronic devices programs encompass projects in areas undergraduate degrees in materials (Professor Yu, Applied Physics and as diverse as polycrystalline silicon, science, metallurgy, physics, chemistry, Applied Mathematics); and inelastic electronic ceramics grain boundaries or other science and engineering light scattering in low-dimensional and interfaces, microstructure and disciplines. First-year graduate courses electron gases within semiconductors stresses in microelectronics thin films, provide a common base of knowledge (Professor Pinczuk, Applied Physics oxide thin films for novel sensors and and technical skills for more advanced and Applied Mathematics/Physics); fuel cells, optical diagnostics of thin-film courses and for research. In addition to coursework, students usually large-area electronics and thin-film

ENGINEERING 2017–2018 transistors (Professor Im, Henry Krumb ELEN E6403: Classical electromagnetic theory MSAE E3111x Thermodynamics, kinetic 177 theory and statistical mechanics School of Mines/Applied Physics or 3 pts. Lect: 3. Professor Herman. and Applied Mathematics); structural PHYS GR6092: Electromagnetic theory, I analysis and high Tc superconductors MSAE E4100: Crystallography An introduction to the basic thermodynamics (Professor Chan, Henry Krumb School MSAE E4206: Electronic and magnetic properties of systems, including concepts of equilibrium, entropy, thermodynamic functions, and phase of Mines/Applied Physics and Applied of solids changes. Basic kinetic theory and statistical Mathematics); X-ray microdiffraction MSAE E6240: Impurities and defects in semiconductor materials mechanics, including diffusion processes, concept and stresses (Professor Noyan, Henry PHYS GR6018: Physics of the solid state of phase space, classical and quantum statistics, Krumb School of Mines/Applied Physics PHYS GR6037: Quantum mechanics and applications thereof. and Applied Mathematics); electronic and magnetic metal thin films (Professor MSAE E3141y Processing of metals and semiconductors Barmak, Applied Physics and Applied COURSES IN MATERIALS 3 pts. Lect: 3. Instructor to be announced. Mathematics); magnetic properties of SCIENCE AND ENGINEERING Prerequisite: MSAE E3011 or equivalent. Synthesis For related courses, see also Applied thin films (Professor Bailey, Applied and production of metals and semiconductors Physics and Applied Mathematics); the Physics and Applied Mathematics, with engineered microstructures for desired structure of nanomaterials (Professor Chemical Engineering, Earth and properties. Includes high-temperature, aqueous, Billinge, Applied Physics and Applied Environmental Engineering, and and electrochemical processing; thermal and Mathematics); and electronic structure Electrical Engineering. mechanical processing of metals and alloys; calculations of materials (Professor casting and solidification; diffusion, microstructural MSAE E3010x Introduction to materials evolution, and phase transformations; modification Marianetti, Applied Physics and Applied science, I and processing of surfaces and interfaces; Mathematics). 3 pts. Lect: 3. Professor Noyan. deposition and removal of thin films. Processing of Introduction to quantum mechanics: atoms, electron Si and other materials for elemental and compound Program of Study shells, bands, bonding; introduction to group theory: semiconductor-based electronic, magnetic, and crystal structures, symmetry, crystallography; The applicant for the graduate specialty optical devices. introduction to materials classes: metals, ceramics, must be admitted to one of the polymers, liquid crystals, nanomaterials; properties MSAE E3142y Processing of ceramics and participating programs: applied physics of single crystals: optical properties, electrical polymers and applied mathematics, or electrical properties, magnetic properties, thermal properties, 3 pts. Lect: 3. Not offered in 2017–2018. engineering. A strong undergraduate mechanical properties. Prerequisite: MSAE E3011 or equivalent. background in physics or chemistry and MSAE E3011y Introduction to materials Established and novel methods involved in in mathematics is important. science, II the processing of polymers and ceramics. The doctoral student must meet the 3 pts. Lect: 3. Professor Noyan. The fundamental aspects of the structure and formal requirements for the Eng.Sc.D. or Prerequisite: MSAE E3010. Introduction to properties of polymers and ceramic materials; Ph.D. degree set by the department in polycrystals and disordered materials; noncrystalline strategy in the preparatory, synthesis, and which he or she is registered. However, and amorphous structures; grain boundary processing methods for obtaining them. the bulk of the program for the specialty structures, diffusion; phase transformations; Topics include polymer synthesis, elastomers, will be arranged in consultation with phase diagrams, time-temperature-transformation thermoplastics, thermoset materials, design and molding processes. Ceramics: inorganic a member of the interdepartmental diagrams; properties of polycrystalline and glasses and composites, materials production Committee on Materials Science and amorphous materials: mechanical properties and failure, the Drude model of electrical properties, and principle inorganic chemistry. Processing Engineering/ Solid-State Science and thermal properties; corrosion; materials selection for methodology, conditioning, drying, forming, Engineering. At the end of the first year engineering design. sintering, and microstructure development. of graduate study, doctoral candidates Relevant aspects of transport phenomena, colloid MSAE E3012x Laboratory in materials science, I are required to take a comprehensive and sol-gel science, contemporary issues in 3 pts. Lect: 3. Professors Noyan and Lee. written examination concentrating on modern polymer and ceramic processing. Prerequisite: MSAE E3010. Measurement of solid-state science and engineering. electrical, thermal, and magnetic properties of MSAE E3156x-E3157y Design project The following are regarded as core single crystals. Single crystal diffraction analysis, 2 pts (each semester). Lect.: 3. Professor Im. courses of the specialty: polarized light microscopy, and infrared microscopy Prerequisite: Senior standing. Written permission in Si single crystals, written and oral reports. from instructor and approval from adviser. E3156: A APPH E4100: Quantum physics of matter design problem in materials science or metallurgical MSAE E3013y Laboratory in materials science, II APPH E4110: Modern optics engineering selected jointly by the student and a APPH E4112: Laser physics 3 pts. Lect: 3. Professors Noyan and Lee. professor in the department. The project requires Pre/Corequisite: MSAE E3011. Metallographic research by the student, directed reading, and APPH-MSAE E6081-E6082: Solid state physics, sample preparation, optical microscopy, regular conferences with the professor in charge. I and II quantitative metallography, hardness and tensile E3157: Completion of the research, directed CHEM GU4230: Statistical thermodynamics testing, plastic deformation, annealing, phase diagrams, brittle fracture of glass, temperature and reading, and conferences, culminating in a written or strain-rate dependent deformation of polymers; report and an oral presentation to the department. CHAP E4120: Statistical mechanics written and oral reports. This is the second of ELEN E4301: Intro to semiconductor devices MSAE E3900x and y Undergraduate research a two-semester sequence materials laboratory ELEN E4944: Principles of device microfabrication in materials science course. ELEN E6331-E6332: Principles of semiconductor 0–4 pts. Members of the faculty. physics Prerequisite: Written permission from instructor

ENGINEERING 2017–2018 178

and approval from adviser. This course may be MSAE E4101x Structural analysis of materials Electrical, mechanical, thermal and optical repeated for credit, but no more than 6 points 3 pts. Lect: 3. Not offered in 2017–2018. properties. Common and advanced technological of this course may be counted toward the Prerequisites or corequisite: MSAE E3011 or applications, electrical/optical devices, catalytic and satisfaction of the B.S. degree requirements. instructor’s permission. Geometry of crystals, basic environmental applications. Candidates for the B.S. degree may conduct an diffraction theory. X-ray diffraction. Techniques MSAE E4200x Theory of crystalline materials investigation in materials science or carry out and theory of electron microscopy. Analysis of 3 pts. Lect: 3. Professor Billinge. a special project under the supervision of the crystal structures and orientations. Microstructure Pre/Corequisite: MSAE E4100 or instructor’s staff. Credit for the course is contingent upon the characterization and analysis of crystalline defects. permission. Electronic and vibrational properties submission of an acceptable thesis or final report. MSAE E4102x Synthesis and processing of of crystalline materials from the atomic scale using MSAE E4090y Nanotechnology materials classical and quantum mechanics. Introduction to 3 pts. Lect: 3. Professor Wind. 3 pts. Lect: 3. Professor Chan. the theory of groups: irreducible representations, Prerequisites: APPH E3100 and MSAE E3011 Prerequisite: MSAE E3011 or equivalent or Great Orthogonality Theorem, Character or their equivalents with instructor’s permission. instructor’s permission. A course on synthesis and tables, degeneration, and product groups. Use The science and engineering of creating processing of engineering materials. Established of translational and point symmetry to block materials, functional structures and devices on the and novel methods to produce all types of diagonalize the Hamiltonian, including Bloch’s nanometer scale. Carbon nanotubes, nanocrystals, materials (including metals, semiconductors, Theorem. Covers band structures and the concept quantum dots, size dependent properties, self- ceramics, polymers, and composites). of band gap formation. Derive elastic constants assembly, nanostructured materials. Devices Fundamental and applied topics relevant to from vibrational spectra. Tight binding and nearly and applications, nanofabrication. Molecular optimizing the microstructure of the materials with free electron limits. Survey of electronic and engineering, bionanotechnology. Imaging and desired properties. Synthesis and processing phonon band structures in real materials. manipulating at the atomic scale. Nanotechnology of bulk, thin-film, and nano materials for various MSAE E4201y Materials thermodynamics and in society and industry. Offered in alternate years. mechanical and electronic applications. phase diagrams MSAE E4100x Crystallography MSAE E4132y Fundamentals of polymers and 3 pts. Lect: 3. Professor Im. 3 pts. Lect: 3. Professor Barmak. ceramics Prerequisite: MSAE E3011 or equivalent or Prerequisites: CHEM UN1403, PHYS UN1403, 3 pts. Lect: 3. Not offered in 2017–2018. instructor’s permission. Review of laws of APMA E2101, or equivalent. A first course on Prerequisite: MSAE E3011 or instructor’s thermodynamics, thermodynamic variables crystallography. Crystal symmetry, Bravais lattices, permission. The science and engineering of and relations, free energies and equilibrium point groups, space groups. Diffraction and polymer, ceramic and composite inorganic in thermodynamic systems, statistical diffracted intensities. Exposition of typical crystal materials. Fundamental aspects of structure, thermodynamics. Unary, binary, and ternary structures in engineering materials, including processing and properties. Polymers: classification, phase diagrams, compounds and intermediate metals, ceramics, and semiconductors. Crystalline synthesis, elastomers, thermoplastics, thermosets; phases, solid solutions and Hume-Rothery anisotropy. ceramics: Crystal structure, morphology, rules, relationship between phase diagrams and classification, oxides, nitrides, carbides, silicates. metastability, defects in crystals. Thermodynamics

ENGINEERING 2017–2018 of surfaces and interfaces, effect of particle size thermodynamics of materials, diffusion in materials, defects; magnetism; superconductivity; low- 179 on phase equilibria, adsorption isotherms, grain and crystal structures of materials. dimensional structures; and soft matter. boundaries, surface energy, electrochemistry. MSAE E4260x Electrochemical materials and MSAE E6085y Computing the electronic MSAE E4202y Kinetics of transformation in devices: from structure to performance structure of complex materials materials 3 pts. Lect: 3. Professor Yang. 3 pts. Lect: 3. Professor Wentzcovitch. 3 pts. Lect: 3. Professor Im. Prerequisites: CHEM UN1403, MSAE E3011, Prerequisite: APPH E3100 or equivalent. Basics Pre/Corequisite: MSAE E4201. Review of equivalents, or instructor's permission. Overview of density functional theory (DFT) and its thermodynamics, irreversible thermodynamics, of electrochemical processes and applications application to complex materials. Computation diffusion in crystals and noncrystalline materials, from perspectives of materials and devices. of electronics and mechanical properties of materials. Group theory, numerical methods, phase transformations via nucleation and Thermodynamics and principles of electrochem- basis sets, computing, and running open source growth, overall transformation analysis and time- istry, methods to characterize electrochemical DFT codes. Problem sets and a small project. temperature-transformation (TTT) diagrams, processes, application of electrochemical materials precipitation, grain growth, solidification, spinodal and devices, including batteries, supercapacitors, MSAE E6091y Magnetism and magnetic fuel cells, electrochemical sensor, focus on link and order-disorder transformations, martensitic materials between material structure, composition, and prop- transformation. 3 pts. Lect. 3. Not offered in 2017–2018. erties with electrochemical performance. Prerequisite: MSAE E4206, APPH E6081, or MSAE E4206x Electronic and magnetic MSAE E4301x Materials science laboratory equivalent. Types of magnetism. Band theory of properties of solids 3 pts. Professor Yang. ferromagnetism. Magnetic metals, insulators, and 3 pts. Lect: 3. Professor Bailey. Prerequisites: Introductory materials course or semiconductors. Magnetic nanostructures: ultrathin Prerequisite: PHYS UN1401-3 or equivalent. A equivalent and instructor’s permission. General films, superlattices, and particles. Surface magnetism survey course on the electronic and magnetic experimental techniques in materials science, and spectroscopies. High speed magnetization properties of materials, oriented toward materials including X-ray diffraction, scanning electron dynamics. Spin electronics. Offered in alternate years. for solid state devices. Dielectric and magnetic microscopies, atomic force microscopy, materials properties, ferroelectrics and ferromagnets. MSAE E6100y Transmission electron synthesis and thermodynamics, characterization of Conductivity and superconductivity. Electronic microscopy material properties (mechanical, electrochemical, band theory of solids: classification of metals, 3 pts. Lect: 3. Not offered in 2017–2018. magnetic, electronic). Additional experiments at insulators, and semiconductors. Materials in Prerequisite: permission of the instructor. Theory discretion of instruction. devices: examples from semiconductor lasers, and practice of transmission electron microscopy cellular telephones, integrated circuits, and MSAE E4990x and y Special topics in (TEM): principles of electron scattering, diffraction, magnetic storage devices. Topics from physics materials science and engineering and microscopy; analytical techniques used to are introduced as necessary. 1–3 pts. Members of the faculty. determine local chemistry; introduction to sample Prerequisite: Instructor’s permission. This preparation; laboratory and in-class remote MSAE E4215y Mechanical behavior of course may be repeated for credit. Topics and access demonstrations, several hours of hands-on structural materials instructors change from year to year. For advanced laboratory operation of the microscope; the use of 3 pts. Lect: 3. Professor Bailey. undergraduate students and graduate students in simulation and analysis software; guest lectures Prerequisite: MSAE E3011. Recommended engineering, physical sciences, and other fields. on cryomicroscopy for life sciences and high preparation: A course in mechanics of materials. resolution transmission electron microscopy for Review of states of stress and strain and MSAE E4999x or y–S4999 Supervised physical sciences; and, time permitting, a visit to their relations in elastic, plastic, and viscous internship the electron microscopy facility in the Center for materials. Dislocation and elastic-plastic concepts 1 pt. Members of the faculty. Functional Nanomaterials (CFN) at the Brookhaven introduced to explain work hardening, various Prerequisite: Internship and approval from adviser National Laboratory (BNL). materials-strengthening mechanisms, ductility, must be obtained in advance. Only for master’s and toughness. Macroscopic and microstructural students in the Department of Applied Physics and MSAE E6120x Grain boundaries and interfaces aspects of brittle and ductile fracture mechanics, Applied Mathematics who may need relevant work 3 pts. Lect: 2. Not offered in 2017–2018. creep and fatigue phenomena. Case studies experience as part of their program of study. Final Prerequisites: the instructor’s permission. used throughout, including flow and fracture of report required. This course may not be taken for Suggested background: basic knowledge of structural alloys, polymers, hybrid materials, pass/fail or audited. materials science, dislocations and point defects. composite materials, ceramics, and electronic The course gives an overview of the classic MSAE E6081x Solid state physics, I materials devices. Materials reliability and fracture approaches in studying grain boundaries. Topics 3 pts. Lect: 3. Professor Pinczuk. prevention emphasized. include boundary geometry and structure, Prerequisite: APPH E3100 or equivalent. boundary interactions with crystal defects, Knowledge of statistical physics on the level MSAE E4250y Ceramics and composites boundaries as short-circuit diffusion paths, of MSAE E3111 or PHYS GU4023 strongly 3 pts. Lect: 3. Professor Chan. applications of boundary concepts to interfaces, recommended. Crystal structure; reciprocal Prerequisites or corequisites: MSAE E3142 and and roles of grain boundaries in material properties lattices; classification of solids; lattice dynamics; E3013, or instructor’s permission. The course and in kinetic phenomena in polycrystalline anharmonic effects in crystals; stress and strain; will cover some of the fundamental processes materials. of atomic diffusion, sintering and microstructural classical electron models of metals; and periodic, evolution, defect chemistry, ionic transport, and nearly periodic, and more advanced analysis of MSAE E6221x Introduction to dislocation electrical properties of ceramic materials. Following electron band structure. theory this, we will examine applications of ceramic MSAE E6082y Solid state physics, II 3 pts. Lect: 3. Not offered in 2017–2018. materials, specifically, ceramic thick and thin film 3 pts. Lect: 3. Instructor to be announced. Prerequisite: MSAE E4215 or course in theory of materials in the areas of sensors and energy Prerequisite: MSAE E6081 or instructor’s elasticity, or instructor’s permission. Point and line conversion/storage devices such as fuel cells, and permission. Semiclassical and quantum imperfections. Theory of dislocations. Relation batteries. The coursework level assumes that the mechanical electron dynamics and conduction; between imperfections and structure-sensitive student has already taken basic courses in the dielectric properties of insulators; semiconductors; properties.

ENGINEERING 2017–2018 MSAE E6225y Techniques in X-ray and and growth, epitaxy, critical thickness, defects 180 Required of doctoral candidates. neutron diffraction properties, effect of deposition procedure, MSAE E9309x and y–S9309 Proposal of 3 pts. Lect: 3. Not offered in 2017–2018. mechanical properties, adhesion, interconnects, Research for the Doctorate Prerequisite: MSAE E4101. Crystal symmetry, and electromigration. 0–3 pts. Members of the faculty. diffraction, reciprocal space and Ewald sphere MSAE E6273x and y–S6273 Materials science A written report prepared by the prospective construction, radiation sources, analytical doctoral candidate defining the proposed research representation of diffraction peaks, diffraction reports for the dissertation, and oral defense of the line broadening, Fourier analysis of peak shape, 0 to 6 pts. Members of the faculty. texture analysis, diffraction analysis of stress Prerequisite: Written permission from instructor proposal at the time of the qualifying examinations. and approval from adviser. Formal written reports and strain, diffraction analysis of order-disorder MSAE E9800x and y–S9800 Doctoral research and conferences with the appropriate member thermal diffuse scattering, small angle scattering, instruction instrumentation in diffraction experiments, error of the faculty on a subject of special interest to 3, 6, 9, or 12 pts. Members of the faculty. analysis. the student but not covered in the other course A candidate for the Eng.Sc.D. degree must register offerings. MSAE E6229x Energy and particle beam for 12 points of doctoral research instruction. processing of materials MSAE E8235x and y Selected topics in Registration in MSAE E9800 may not be used to 3 pts. Lect: 3. Not offered in 2017–2018. materials science satisfy the minimum residence requirement for the degree. Prerequisites: MSAE E4202 or instructor’s 3 pts. Lect: 3. Professor Noyan. permission. Laser-, electron-, and ion-beam This course may be repeated for credit. Selected MSAE E9900x and y–S9900 Doctoral modification of materials to achieve unique topics in materials science. Topics and instructors dissertation microstructures and metastable phases change from year to year. For students in 0 pts. Members of the faculty. for electronic and structural applications. engineering, physical sciences, biological sciences, A candidate for the doctorate may be required Fundamentals of energy deposition and heat and related fields. to register for this course every term after the flow during laser- and electron-beam irradiation. coursework has been completed and until the MSAE E9000x and y Materials science and Atomic displacement processes in ion-irradiated dissertation has been accepted. engineering colloquium materials. Beam-induced microstructural evolution, 0 pts. Professor Yang. crystallization, surface alloying, rapid solidification, Speakers from industry are invited to speak on the and metastable phase formation. Review of current recent impact of materials science and engineering industrial applications. innovations. MSAE E6230y Kinetics of phase transformations MSAE E9259x-E9260y Research topics 3 pts. Lect: 3. Not offered in 2017–2018. in materials science and metallurgical Prerequisite: MSAE E4202 or instructor’s engineering permission. Principles of nonequilibrium 1 pt. Lect: 1. Members of the faculty. thermodynamics; stochastic equations; nucleation, Discussion of a group of technical papers related growth, and coarsening reactions in solids; to a topic of current research interest. spinodal decomposition; eutectic and eutectoid transformations. MSAE E6251y Thin films and layers MSAE E9301x-S9301 Doctoral research 3 pts. Lect: 3. Professor Chan. 0–15 pts. Members of the faculty. Vacuum basics, deposition methods, nucleation Prerequisite: Qualifying examination for doctorate.

ENGINEERING 2017–2018 MECHANICAL ENGINEERING 181 220 S. W. Mudd, MC 4703 Phone: 212-854-0661 me.columbia.edu

CHAIR PROFESSORS ASSOCIATE PROFESSOR OF ADJUNCT FACULTY Jeffrey W. Kysar Sunil Agrawal PROFESSORS PROFESSIONAL Sean Bradshaw 248 S. W. Mudd Gerard A. Ateshian Qiao Lin PRACTICE Joshua Browne Mary C. Boyce Arvind Narayanaswamy Michael J. Massimino Nicholas Chbat DEPARTMENT James Hone P. James Schuck Adam Hurst ADMINISTRATOR Jeffrey W. Kysar SENIOR LECTURER Peter LeVoci ASSISTANT Sandra Morris Hod Lipson Fred Stolfi Mohammad H. N. PROFESSORS 220 S. W. Mudd Richard W. Longman Naraghi Michael P. Burke Vijay Modi LECTURER IN Graham Walker Y. Lawrence Yao Matei Ciocarlie DISCIPLINE Karen Kasza Sinisa Vukelic MANAGER OF Kristin Myers INSTRUCTIONAL LABORATORIES Robert G. Stark

echanical engineering is a pharmaceutical industries); computers a variety of career options beyond diverse subject that derives and electronics (disk drives, printers, some of the industries listed above. Mits breadth from the need to cooling systems, semiconductor tools); Regardless of the particular future design and manufacture everything from microelectromechanical systems, or path they envision for themselves small individual parts/devices (e.g., micro- MEMS (sensors, actuators, micro after they graduate, their education scale sensors, inkjet printer nozzles) power generation); energy conversion would have provided them with the to large systems (e.g., spacecraft and (gas turbines, wind turbines, solar creative thinking that allows them to machine tools). The role of a mechanical energy, fuel cells); environmental design an exciting product or system, engineer is to take a product from an control (HVAC, air-conditioning, the analytical tools to achieve their idea to the marketplace. In order to refrigeration, compressors); automation design goals, the ability to meet several accomplish this, a broad range of skills (robots, data/image acquisition, sometimes conflicting constraints, and are needed. The particular skills in which recognition, and control); manufacturing the teamwork needed to design, market, the mechanical engineer acquires deeper (machining, machine tools, prototyping, and produce a system. These skills also knowledge are the ability to understand microfabrication). prove to be valuable in other endeavors the forces and the thermal environment To put it simply, mechanical and can launch a career in medicine, that a product, its parts, or its engineering deals with anything law, consulting, management, banking, subsystems will encounter; design them that moves. Mechanical engineers finance, and so on. for functionality, aesthetics, and the ability learn about materials, solid and fluid For those interested in applied to withstand the forces and the thermal mechanics, thermodynamics, heat scientific and mathematical aspects environment they will be subjected to; transfer, control, instrumentation, of the discipline, graduate study in determine the best way to manufacture design, and manufacturing to realize/ mechanical engineering can lead to a them and ensure they will operate without understand mechanical systems. career of research and teaching. failure. Perhaps the one skill that is the Specialized mechanical engineering mechanical engineer’s exclusive domain is subjects include biomechanics, Current Research Activities the ability to analyze and design objects cartilage tissue engineering, energy Current research activities in the and systems with motion. conversion, laser-assisted materials Department of Mechanical Engineering Since these skills are required processing, combustion, MEMS, are in the areas of controls and for virtually everything that is made, microfluidic devices, fracture mechanics, robotics, energy and micropower mechanical engineering is perhaps nanomechanics, mechanisms, generation, fluid mechanics, heat/ the broadest and most diverse micropower generation, tribology mass transfer, mechanics of materials, of engineering disciplines. Hence (friction and wear), and vibrations. manufacturing, material processing, mechanical engineers play a central role The American Society of Mechanical MEMS, nanotechnology, and orthopedic in such industries as automotive (from Engineers (ASME) currently lists thirty- biomechanics. the car chassis to its every subsystem— six technical divisions, from advanced engine, transmission, sensors); energy systems and aerospace Biomechanics and Mechanics aerospace (airplanes, aircraft engines, engineering to solid waste engineering of Materials. Some of the current control systems for airplanes and and textile engineering. research in biomechanics is concerned spacecraft); biotechnology (implants, The breadth of the mechanical with the application of continuum prosthetic devices, fluidic systems for engineering discipline allows students theories of mixtures to problems of

ENGINEERING 2017–2018 182 electromechanical behavior of soft creates controllers that learn from At the Creative Machines Lab biological tissues, contact mechanics, previous experience performing a (CreativeMachines.org) we are interested lubrication of diarthrodial joints, and specific command, such as robots in robots that create and robots that cartilage tissue engineering. (Ateshian) on an assembly line, aiming for high- are themselves creative. We develop The Kysar group studies the precision mechanical motions. RC learns novel autonomous systems that can mechanics and mechanical properties to cancel repetitive disturbances, such design and make other machines— of small-scale structures and materials. as precision motion through gearing, automatically. We are working on a Examples of material systems include machining, satellite precision pointing, self-replicating robots, self-aware robots, two-dimensional materials such as particle accelerators, etc. Time optimal robots that improve themselves over graphene, nanoporous metal thin films, control of robots is being studied for time, and robots that compete and metallic and polymeric composites increased productivity on assembly cooperate with other robots. We build containing nanoscale strengthening lines through dynamic motion planning. robots that paint art, cook food, build agents, single crystal metals, and the Research is also being conducted on bridges and fabricate other robots. ear's round Window Membrane, among improved system identification, making Our work is inspired from biology, several others. The work is experimental, mathematical models from input-output as we seek new biological concepts theoretical, and computational in nature. data. The results can be the starting for engineering and new engineering The ultimate goal is to understand and point for designing controllers, but they insights into biology. (Lipson) predict the mechanical behavior based are also studied as a means of assessing In the area of advanced on fundamental physics and chemistry damage in civil engineering structures manufacturing processes and systems, through the development of multiple from earthquake data. (Longman) current research concentrates on laser length scale models. Robotics research focuses on materials processing. Investigations The Kasza group studies the physical design of novel rehabilitation machines are being carried out in laser principles underlying the mechanics and and training algorithms for functional micromachining; laser forming of sheet self-organization of biological materials rehabilitation of neural impaired adults metal; microscale laser shock-peening, by combining quantitative approaches and children. The research also aims material processing using improved from engineering, biology, and physics. to design intelligent machines using laser-beam quality. Both numerical and The group builds tools to measure and nonlinear system theoretic principles, experimental work is conducted using manipulate the behaviors of protein, computational algorithms for planning, state-of-the-art equipment, instruments, cells, and tissues in order to uncover the and optimization. and computing facilities. Close ties mechanisms by which living multicellular Robotic Systems Engineering (ROSE) with industry have been established for tissues change shape, move, and grow Lab develops technology capable collaborative efforts. (Yao) to build functional tissues and organs. of solving difficult design problems, For example, the group is currently using such as cable-actuated systems, Energy, Fluid Mechanics, and Heat/ the Drosophila (fruit fly) embryo as a under-actuated systems, and others. Mass Transfer. In the area of energy, model system for understanding how Robotics and Rehabilitation (ROAR) one effort addresses the design of mechanical forces shape tissues during Lab focuses on developing new and flow/mass transport systems for the embryonic development. These studies innovative technologies to improve the extraction of carbon dioxide from combine confocal microscopy, genetics, quality of care and patient outcomes. air. Another effort addresses the and biomechanical measurements. The lab designs novel exoskeletons development of distributed sensors Other areas of biomechanics for upper and lower limbs training of for use in micrositing and performance include characterizing the structure- stroke patients, and mobile platforms evaluation of energy and environmental function behavior of the cervix during to improve socialization in physically systems. The design and testing the remodeling events of pregnancy impaired infants (Agrawal). of components and systems for and characterizing the mechanical The Robotic Manipulation and micropower generation is part of the properties of the eye-wall in relation to Mobility (ROAM) Lab focuses on thermofluids effort as well as part of the glaucoma. Research in our lab includes versatile manipulation and mobility in MEMS effort. (Modi) the mechanical testing of biological robotics, aiming for robotic applications In the area of fluid mechanics, study soft tissues, the biochemical analysis pervasive in everyday life. Research of low-Reynolds-number chaotic flows of tissue microstructure, and material areas include manipulation and is being conducted both experimentally modeling based on structure-mechanical grasping, interactive or Human-in-the- and numerically, and the interactions property relationships. In collaboration Loop robotics, dynamic simulators and with molecular diffusion and inertia are with clinicians, our goal is to understand virtual environments, machine perception presently being investigated. Other the etiologies of tissue pathology and and modeling, and many more. We are areas of investigation include the fluid disease. (Myers) interested in application domains such mechanics of inkjet printing, drop on as versatile automation in manufacturing demand, the suppression of satellite Control, Robotics, Design, and and logistics, assistive and rehabilitation droplets, shock wave propagation, and Manufacturing. Control research robotics in health care, space robotics, remediation in high-frequency printing emphasizes iterative learning control and mobile manipulation in unstructured systems. (Modi) (ILC) and repetitive control (RC). ILC environments. (Ciocarlie) In the area of nanoscale thermal

ENGINEERING 2017–2018 transport, our research efforts center on Research in the area of nanotechnology mechanics; and mixture theory for 183 the enhancement of thermal radiation focuses on nanomaterials such as biological tissues with experiments and transport across interfaces separated by nanotubes and nanowires and computational analysis (Ateshian). a nanoscale gap. The scaling behavior their applications, especially in The Hone group is involved in a of nanoscale radiation transport is nanoelectromechanical systems (NEMS). number of projects that employ the measured using a novel heat transfer A laboratory is available for the synthesis tools of micro- and nanofabrication measurement technique based on of graphene and other two-dimensional toward the study of biological the deflection of a bimaterial atomic materials using chemical vapor systems. With collaborators in biology force microscope cantilever. Numerical deposition (CVD) techniques and to build and applied physics, the group has simulations are also performed to devices using electron-beam lithography developed techniques to fabricate confirm these measurements. The and various etching techniques. This metal patterns on the molecular scale measurements are also used to infer effort will seek to optimize the fabrication, (below 10 nanometers) and attach extremely small variations of van der readout, and sensitivity of these devices biomolecules to create biofunctionalized Waals forces with temperature. This for numerous applications, such as nanoarrays. The group is currently enhancement of radiative transfer will sensitive detection of mass, charge, and using these arrays to study molecular ultimately be used to improve the power magnetic resonance. (Hone, Kysar, Modi) recognition, cell spreading, and protein density of thermophotovoltaic energy Research in BioMEMS aims to crystallization. The project seeks to conversion devices. (Narayanaswamy) design and create MEMS and micro/ understand and modify at the nanoscale Also in the area of energy, research nanofluidic systems to control the force- and geometry-sensing pathways is being performed to improve the motion and measure the dynamic in health and disease. The Hone group thermochemical models used in behavior of biomolecules in solution. fabricates many of the tools used by the accelerating development of cleaner, Current efforts involve modeling and researchers to measure and apply force more fuel-efficient engines through understanding the physics of micro/ on a cellular level. (Hone) computational design. In particular, nanofluidic devices and systems, Microelectromechanical systems data-driven approaches to creating exploiting polymer structures to (MEMS) are being exploited to enable high-accuracy, uncertainty-quantified enable micro/nanofluidic manipulation, and facilitate the characterization and thermochemicals models are being and integrating MEMS sensors with manipulation of biomolecules. MEMS developed that utilize both theoretical microfluidics for measuring physical technology allows biomolecules to and experimental data. Special properties of biomolecules. (Lin) be studied in well-controlled micro/ emphasis is placed on the generation The Schuck group aims to nanoenvironments of miniaturized, and analysis of data across the full characterize, understand, and control integrated devices, and may enable range of relevant scales—from the nanoscale light-matter interactions, novel biomedical investigations not small-scale electronic behavior that with a primary focus on sensing, attainable by conventional techniques. governs molecular reactivity to the large- engineering, and exploiting novel The research interests center on the scale turbulent, reactive phenomena that optoelectronic phenomena emerging development of MEMS devices and govern engine performance. (Burke) from nanostructures and interfaces. This systems for label-free manipulation offers unprecedented opportunities for and interrogation of biomolecules. MEMS and Nanotechnology. In these developing innovative devices that rely Current research efforts primarily involve areas, research activities focus on power on the dynamic manipulation of single microfluidic devices that exploit specific generation systems, nanostructures for photons and charge carriers. We are and reversible, stimulus-dependent photonics, fuel cells and photovoltaics, continuously developing new multimodal binding between biomolecules and and microfabricated adaptive cooling and multidimensional spectroscopic receptor molecules to enable selective skin and sensors for flow, shear, and methods that provide unique access purification, concentration, and wind speed. Basic research in fluid to optical, electrical, and structural label-free detection of nucleic acid, dynamics and heat/mass transfer properties at relevant length scales in protein, and small molecule analytes; phenomena at small scales also support real environments encountered in energy miniaturized instruments for label-free these activities. (Hone, Kysar, Lin, Modi, and biological applications. (Schuck) characterization of thermodynamic Narayanaswamy) and other physical properties of We study the dynamics of Biological Engineering and biomolecules; and subcutaneously microcantilevers and atomic force Biotechnology. Active areas of research implantable MEMS affinity biosensors for microscope cantilevers to use them in the musculoskeletal biomechanics continuous monitoring of glucose and as microscale thermal sensors based laboratory include theoretical and other metabolites. (Kysar, Lin) on the resonance frequency shifts experimental analysis of articular The Kysar group has an NIH- of vibration modes of the cantilever. cartilage mechanics; theoretical and funded project to design and develop a Bimaterial microcantilever-based experimental analysis of cartilage method to deliver therapeutics into the sensors are used to determine the lubrication, cartilage tissue engineering, inner ear through the Round Window thermophysical properties of thin films. and bioreactor design; growth and Membrane (RWM) that serves as a (Narayanaswamy) remodeling of biological tissues; cell portal for acoustic energy between the

ENGINEERING 2017–2018 184 middle ear and inner ear. This involves individual cells selected on the as standard vertical milling machines, the design and fabrication of arrays of basis of optically detectable multiple engine and bench lathes, programmable microneedles, the measurements of features at critical time points in surface grinder, band saw, drill press, diffusive flux of chemical species across dynamic processes can be rapidly tool grinders, and a power hacksaw. The a perforated RWM, and the design, and robotically micromanipulated into shop also has a tig welder. delivery, and testing of surgical tools, reaction chambers to permit amplified A mechatronics laboratory affords all in close collaboration with Anil K. DNA synthesis and subsequent array the opportunity for hands-on experience Lalwani, M.D., at Columbia University analysis. Customized image processing with microcomputer-embedded control Medical Center. (Kysar) and pattern recognition techniques of electromechanical systems. Facilities The Schuck group is involved in are developed, including Fisher’s for the construction and testing of engineering novel near-infrared (NIR) linear discriminant preprocessing with analog and digital electronic circuits upconverting nanoparticles (UCNPs) and neural net, a support vector machine aid the students in learning the basic UCNP-based microdevices for large- with improved training, multiclass cell components of the microcomputer scale sensing applications, including detection with error correcting output architecture. The laboratory is divided deployment in projects aimed at coding, and kernel principal component into work centers for two-person deep-tissue imaging and the control of analysis. (Yao) student laboratory teams. Each work neural function deep within brain tissue. center is equipped with several power UCNPs have the potential to overcome Facilities for Teaching and Research supplies (for low-power electronics nearly all limitations of current optical The undergraduate laboratories, and higher power control), a function probes and sensors, which have run into occupying an area of approximately generator, a multimeter, a protoboard fundamental chemical and photophysical 6,000 square feet of floor space, are for building circuits, a microcomputer incompatibilities with living systems. the site of experiments ranging in circuit board (which includes the (Schuck) complexity from basic instrumentation microcomputer and peripheral Mass radiological triage is critical and fundamental exercises to advanced components), a microcomputer after a large-scale radiological event experiments in such diverse areas as programmer, and a personal computer because of the need to identify automatic controls, heat transfer, fluid that contains a data acquisition board. those individuals who will benefit mechanics, stress analysis, vibrations, The data acquisition system serves from medical intervention as soon as microcomputer-based data acquisition, as an oscilloscope, additional function possible. The goal of the ongoing NIH- and control of mechanical systems. generator, and spectrum analyzer for funded research project is to design Equipment includes microcomputers the student team. The computer also a prototype of a fully automated, ultra and microprocessors, analog-to-digital contains a complete microcomputer high throughput biodosimetry. This and digital-to-analog converters, software development system, including prototype is supposed to accommodate lasers and optics for holography editor, assembler, simulator, debugger, multiple assay preparation protocols and interferometry, a laser-Doppler and C compiler. The laboratory that allow the determination of the velocimetry system, a Schlieren is also equipped with a portable levels of radiation exposure that a system, dynamic strain indicators, a oscilloscope, an EPROM eraser (to patient received. The input to this fully servohydraulic and servoelectric material erase microcomputer programs from the autonomous system is a large number testing machines, a photoelastic and erasable chips), a logic probe, and an of capillaries filled with blood of patients servoelectric testing machine, Digital analog filter bank that the student teams collected using finger sticks. These Image Correlation (DIC) capabilities, share, as well as a stock of analog and capillaries are processed by the system a dynamometer, subsonic and digital electronic components. to distill the micronucleus assay in supersonic wind tunnels, a cryogenic The department maintains a modern lymphocytes, with all the assays being apparatus, computer numerically computer-aided design laboratory carried out in situ in multiwell plates. controlled vertical machine centers equipped with thirty computer work The research effort on this project (VMC), a coordinate measurement stations with state-of-the-art design involves the automation system design machine (CMM), and three-dimensional software. The research facilities are and integration including hierarchical printers as well as a laser cutter. A located within individual or group control algorithms, design and control CNC wire electrical discharge machine research laboratories in the department, of custom built robotic devices, and (EDM) is also available for the use of and these facilities are being continually automated image acquisition and specialized projects for students with upgraded. To view the current research processing for sample preparation and prior arrangement. The undergraduate capabilities please visit the various analysis. (Yao) laboratory also houses experimental laboratories within the research section A technology that couples the setups for the understanding and of the department website. The students power of multidimensional microscopy performance evaluation of a complete and staff of the department can, by (three spatial dimensions, time, and small steam power generation system, a prior arrangement, use much of the multiple wavelengths) with that of heat exchanger, a solar cell system, a fuel equipment in these research facilities. DNA array technology is investigated cell system, and a compressor. Part of Through their participation in the NSF- in an NIH-funded project. Specifically, the undergraduate laboratory is a staffed MRSEC center, the faculty also have a system is developed in which machine shop with machining tools such access to shared instrumentation and

ENGINEERING 2017–2018 185 MECHANICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS STANDARD TRACK

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

APMA E2000 (4)6

MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) APMA E2101 (3)1 or Linear Algebra (3)2 and ODE (3)3

PHYSICS UN1401 (3) UN1402 (3) UN1403 (3)4 (three tracks, UN1601 (3.5) UN1602 (3.5) UN2601 (3.5)4 choose one) UN2801 (4.5) UN2802 (4.5)

one semester lecture (3–4) CHEMISTRY UN1403 or UN1404 or Lab UN1500 (3)5 UN2045 or UN1604

UNIVERSITY UN1010 (3) either semester WRITING

HUMA CC1001, HUMA CC1002, COCI CC1101, COCI CC1102, REQUIRED or Global Core (3–4) or Global Core (3–4) NONTECHNICAL COURSES HUMA UN1121 or ECON UN1105 (4) and UN1123 (3) UN1155 recitation (0)

REQUIRED TECHNICAL (3) Student’s choice of technical electives ENME E3105 (4) COURSES

COMPUTER Computer language: COMS W1004 or COMS W1005 (3) or ENGI E1006 (3) (in semester I or III) SCIENCE

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 Students who take APMA E2101 must complete an additional 3 point course in math or basic science with the following course designators: MATH, PHYS, CHEM, BIOL, STAT, APMA, or EEEB. One technical elective may be substituted for this purpose. 2 Linear algebra may be fulfilled by either APMA E3101 or MATH UN2010. 3 Ordinary differential equations may be fulfilled by either MATH UN2030 or MATH UN3027. 4 May substitute EEEB UN2001, BIOL UN2005, or higher. 5 May substitute Physics Lab UN1493 (3), UN1494 (3), or UN3081 (2). 6 Effective Class of 2021. the clean room located in the Schapiro UNDERGRADUATE PROGRAM 2. Pursue advanced education, research Center for Engineering and Physical The objectives of the undergraduate and development, and other creative Science Research. Columbia University’s program in mechanical engineering are and innovative efforts in science, extensive library system has superb as follows: engineering, and technology, as well scientific and technical collections. The Mechanical Engineering as other professional careers Email and computing services are Department at Columbia University is 3. Conduct themselves in a responsible, maintained by Columbia University dedicated to graduating mechanical professional, and ethical manner Information Technology (CUIT) engineers who: 4. Participate as leaders in their fields of (columbia.edu/cuit). expertise and in activities that support 1. Practice mechanical engineering in a service and economic development broad range of industries nationally and throughout the world

ENGINEERING 2017–2018 186 MECHANICAL ENGINEERING: THIRD AND FOURTH YEARS STANDARD TRACK

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

MECE E3028 (3) MECE E3018 (3) Lab II Lab I ENME E3106 (3) MECE E3100 (3) Dynamics and Vibrations Fluids I MECE E3409 (3) MECE E3311 (3) Machine design MECE E3301 (3) Heat transfer Thermodynamics MECE E3420 (1) MECE E3430 (3) REQUIRED MECE E3610 (3) Engineering design: Engineering design: COURSES MECE E3408 (3)1 Materials and processes concept creation Graphics and design in manufacturing EEME E3601 (3) ENME E3113 (3) ELEN E1201 (3.5)1 Classical control sys. Mechanics of solids Intro. elec. eng.

MECE E1008 (1) Intro to machining (either semester)

TECHNICAL 6 points 6 points ELECTIVES2

NONTECH 3 points 6 points ELECTIVES

TOTAL POINTS3 15–16 16.5–17.5 16 15

1 Strongly recommended to be taken in Semester III or IV. 2 If APMA E2101 is taken instead of Linear algebra and ODE, students must complete an additional 3-point course in math or basic science with the following course designators: MATH, PHYS, CHEM, BIOL, STAT, APMA, or EEEB. One technical elective may be substituted for this purpose. 3 Students must complete 128 points to graduate.

Highly qualified students are Track. Students who declare in their Undergraduate students who permitted to pursue an honors course second year should follow the Standard intend to pursue graduate studies in consisting of independent study under Track. Students who wish to declare engineering are strongly encouraged to the guidance of a member of the faculty. during or after the fall semester of their take the combination of a stand-alone Upon graduation the student may junior year must first obtain approval from course in linear algebra (either APMA wish to enter employment in industry the Mechanical Engineering Department. E3101 or MATH UN2010) and a stand- or government, or continue with Of the 21 points of elective content alone course in ordinary differential graduate study. Alternatively, training in in the third and fourth years, at least equations (either MATH UN2030 or mechanical engineering may be viewed 12 points of technical elective courses, UN3027), instead of the combined as a basis for a career in business, including at least 6 points from the topics course APMA E2101. In addition, patent law, medicine, or management. Department of Mechanical Engineering, such students are encouraged to take Thus, the department’s undergraduate must be taken. A technical elective can a course in partial differential equations program provides a sound foundation be any engineering course offered in the (APMA E3102 or E4200) as well as a for a variety of professional endeavors. SEAS bulletin that is 3000 level or above. course in numerical methods (APAM The program in mechanical Those prior remaining points of electives E3105 or APMA E4300) as technical engineering leading to the B.S. degree are intended primarily as an opportunity electives. Ideally, planning for these is accredited by the Engineering to complete the four-year, 27-point courses should start at the beginning of Accreditation Commission of ABET. nontechnical requirement. Consistent the sophomore year. Undergraduates who wish to declare with professional accreditation standards, mechanical engineering as their major courses in engineering science and Fundamentals of Engineering (FE) should do so prior to the start of their courses in design must have a combined Exam junior year. Students who declare in their credit of 48 points. Students should see The FE exam is a state licensing exam first year should follow the Early Decision their advisers for details. and the first step toward becoming

ENGINEERING 2017–2018 187 MECHANICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS EARLY DECISION TRACK

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

APMA E2000 (4)6

MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) APMA E2101 (3)1 or Linear Algebra (3)2 and ODE (3)3

PHYSICS UN1401 (3) UN1402 (3) UN1403 (3)4 (three tracks, UN1601 (3.5) UN1602 (3.5) UN2601 (3.5)4 choose one) UN2801 (4.5) UN2802 (4.5)

one semester lecture (3–4) CHEMISTRY UN1403 or UN1404 or Lab UN1500 (3)5 UN2045 or UN1604

UNIVERSITY UN1010 (3) either semester WRITING

REQUIRED HUMA CC1001, HUMA CC1002, NONTECHNICAL COCI CC1101, COCI CC1102, COURSES or Global Core (3–4) or Global Core (3–4)

ELEN E1201 (3.5) Intro. to elec. eng. REQUIRED (3) Student’s choice of ENME E3105 (4) ENME E3113 (3) TECHNICAL technical electives Mechanics Mechanics of solids COURSES MECE E3408 (3) Graphics and design

COMPUTER Computer language: COMS W1004 or COMS W1005 (3) or ENGI E1006 (3) (in semester I and III) SCIENCE

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 Students who take APMA E2101 must complete an additional 3 point course in math or basic science with the following course designators: MATH, PHYS, CHEM, BIOL, STAT, APMA, or EEEB. One technical elective may be substituted for this purpose. 2 Linear algebra may be fulfilled by either APMA E3101 or MATH UN2010. 3 Ordinary differential equations may be fulfilled by either MATH UN2030 or MATH UN3027. 4 May substitute EEEB UN2001, BIOL UN2005, or higher. 5 May substitute Physics Lab UN1493 (3), UN1494 (3), or UN3081 (2). 6 Effective Class of 2021. a Professional Engineer (P.E.). P.E. the student’s mind. In addition to the FE review course covering material relevant licensure is important for engineers exam, achieving P.E. licensure requires to the exam, including a practice exam to obtain—it shows a demonstrated some years of experience and a second to simulate the testing experience. The commitment to professionalism and examination, which tests knowledge FE exam is given in the fall and spring of an established record of abilities that gained in engineering practice. For more each year. The review course is offered will help a job candidate stand out in information, please see http://ncees.org in the spring semester, concluding the field. Ideally, the FE exam should /exams/fe-exam/. before the spring exam. be taken in the senior year while the The Mechanical Engineering technical material learned while pursuing Department strongly encourages all Integrated B.S./M.S. Program the undergraduate degree is still fresh in seniors to take this exam and offers a The Integrated B.S./M.S. degree

ENGINEERING 2017–2018 188 MECHANICAL ENGINEERING: THIRD AND FOURTH YEARS EARLY DECISION TRACK

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

MECE E3038 (3) Lab III MECE E3028 (3) MECE E3018 (3) Lab II Lab I MECE E3409 (3) Machine design MECE E3311 (3) MECE E3430 (3) REQUIRED MECE E3100 (3) Heat transfer Engineering design: COURSES Fluids I MECE E3420 (1) creation Engineering design: MECE E3610 (3) MECE E3301 (3) concept Materials and processes Thermodynamics in manufacturing EEME E3601 (3) Classical control sys

REQUIRED HUMA UN1121 or ECON UN1105 (4) and NONTECHNICAL COURSES UN1123 (3) UN1155 recitation (0)

TECHNICAL 3 points 3 points 6 points ELECTIVES1

NONTECH 3 points 6 points ELECTIVES

TOTAL POINTS2 12 16 16 15

1 If APMA E2101 is taken instead of Linear Algebra and ODE, students must complete an additional 3-point course in math or basic science with the following course designators: MATH, PHYS, CHEM, BIOL, STAT, APMA, or EEEB. One technical elective may be substituted for this purpose. 2 Students must complete a minimum of 128 points to graduate.

program is open to a qualified group of to an application form, please visit engineering requires a student to take Columbia juniors and makes possible me.columbia.edu/integrated-bsms a sequence of courses that shows the earning of both the B.S. and M.S. -program. a “clearly discernible specialization.” degree in an integrated fashion. Benefits In consultation with his/her adviser of this program include optimal matching an M.S. student can develop a focus GRADUATE PROGRAMS of graduate courses with corresponding specifically tailored to his/her interests undergraduate prerequisites, greater and objectives, and we refer to this ability to plan ahead for most Master of Science Degree Program as the standard track. Alternatively, advantageous course planning, The program leading to the Master M.S. students can pick from a set of opportunities to do research for credit of Science degree in mechanical predefined elective specializations. during the summer after senior year, and engineering requires completion of a Typical choices in the standard track up to 6 points of 4000-level technical minimum of 30 points of approved include such subjects as mechanics of electives from the B.S. requirement coursework consisting of no fewer solids and fluids, thermodynamics, heat may count toward the fulfillment of the than ten courses. A thesis based on transfer, manufacturing engineering, point requirement of the M.S. degree. either experimental, computational, or robotics, kinematics, dynamics and Additional benefits include simplified analytical research is optional and may vibrations, controls, and power application process, no GRE is required, be counted in lieu of up to 6 points of generation. Nevertheless, the following and no reference letters are required. coursework. In general, attainment of guidelines must be adhered to: To qualify for this program, students the degree requires one academic year must have a cumulative GPA of at of full-time study, although it may also 1. The sequence of courses selected least 3.5 and strong recommendations be undertaken on a part-time basis must show a clearly discernible from within the Department. Students over a correspondingly longer period. A specialty. should apply for the program by minimum grade-point average of 2.5 is 2. All courses must be at the graduate April 30 in their junior year. For more required for graduation. level, i.e., numbered 4000 or higher, information on requirements and access The M.S. degree in mechanical with at least two 6000-level courses,

ENGINEERING 2017–2018 chosen in consultation with an MECE E4210: Energy infrastructure planning Matei Ciocarlie, Hod Lipson, Richard 189 adviser. MECE E4211: Energy: sources and conversion Longman, and Fred Stolfi 3. Every program must contain at least MECE E4302: Advanced thermodynamics MECE E4304: Turbomachinery The field of robotics is seeing one course in mathematics (APMA, MECE E4305: Mechanics and thermodynamics unprecedented growth, in areas as MATH, STAT course designations) propulsion diverse as manufacturing, logistics, covering material beyond what the MECE E4312: Solar thermal engineering transportation, health care, space student has taken previously. It is MECE E4314: Energy dynamics of green buildings exploration, and more. This program recommended to be taken early in the MECH E4320: Intro to combustion prepares students for a career in sequence, in order to serve as a basis MECE E4330: Thermofluid systems design robotics and its many applications in for the technical coursework. MECE E6100: Advanced mechanics of fluids society. Students perform in-depth study 4. Out-of-department study is MECE E6104: Case studies in computational fluid dynamics of topics such as robotic manipulation, encouraged, but at least five courses MECE E6313: Advanced heat transfer navigation, perception, human must be in mechanical engineering. EAEE E6126: Carbon sequestration interaction, medical robotics, assistance Rather than selecting the standard and rehabilitation. This specialization *One 3-point research course can be option, students can select an elective is a suitable preparation for joining counted toward the specialization if the specialization in either energy systems, established companies, information-age research is approved by the student's micro/nanoscale engineering, or robot- dominant players investing heavily in adviser and is energy related. ics and control. The requirements for a this field, or the new wave of robotics specialization are identical to those of start-ups aiming to provide disruptive M.S. in Mechanical Engineering with the standard track, with one exception: innovations. Many of the acquired skills Specialization in Micro/Nanoscale students must take at least 15 points can be applied in other fields as diverse from a list determined by an adviser in Engineering as automation, manufacturing, computer consultation with an advisory committee. Advisers: Professors James Hone and graphics or machine vision. This The currently available elective special- Jeffrey Kysar program can also be a foundation for a izations are listed below. The elective specialization in micro/ research career in robotics and related nanoscale engineering provides the areas, in both academia and industry. M.S. in Mechanical Engineering with M.S. candidate with an understanding Candidates for the M.S. with Specialization in Energy Systems of engineering challenges and specialization in Robotics and Control Advisers: Professors Vijay Modi and opportunities in micro- and nanoscale should simultaneously satisfy these two Arvind Narayanaswamy systems. The curriculum addresses sets of requirements: fundamental issues of mechanics, fluid Take at least five courses from the list The specialization in energy systems mechanics, optics, heat transfer, and below during their M.S. (courses taken provides the M.S. candidate with a manufacturing at small-size scales. during undergraduate studies do not global understanding of current energy Application areas include MEMS, bio- count): challenges. Advanced thermofluidic MEMS, microfluidics, thermal systems, knowledge is provided to design Courses in the Mechanical Engineering and carbon nanostructures. and optimize energy systems, with Department Requirements: While satisfying a strong emphasis on renewable MECE E4058: Mechanics and embedded the general mechanical engineering energies. Courses related to energy and microcomputer control requirements, take at least five courses MECE E4601: Digital control systems environmental policy, two strong areas from: MECE E4602: Intro to robotics of Columbia as a global university, can MECE E6400: Advanced machine dynamics be integrated into the course sequence. MECE E4212: Microelectromechanical systems MECE E6601: Intro to control theory This specialization is a suitable MECE E4213: BioMEMS MECE E6602: Modern control theory preparation for careers in energy MECE E6105: Transport phenomena in the MECE E6610: Optimal control theory production and energy consultation. presence of interfaces MECE E6614: Advanced topics in robotics and MECE E6700: Carbon nanotubes mechanism synthesis MECE E4606: Digital manufacturing Requirements: 30 points of MECE E6710: Nanofabrication laboratory MECE E6720: Nano/microscale thermal transport graduate level coursework, i.e., courses processes Courses in the other Departments in the School numbered 4000-level or higher, at least MECE E8990: Small scale mechanical behavior of Engineering and Applied Science two of which must be a 6000-level, ELEN E4503: Sensors, actuators, and ELEN E4501: Sensors, actuators and chosen in consultation with an adviser electromechanical systems electromechanical systems (MECE E6100 Advanced mechanics of ELEN E6945: Device nanofabrication BMME E4702: Advanced musculoskeletal fluids and MECE E6313 Advanced heat BMEN E4590: BioMEMS: cellular and molecular biomechanics COMS W4731: Computer vision transfer are strongly recommended). applications MSAE E4090: Nanotechnology COMS W4733: Computational aspects of robotics Furthermore, students must take one ELEN E4810: Digital signal processing course in statistics (STAT designations) COMS E6733: 3D photography and at least five courses from the M.S. in Mechanical Engineering with Specialization in Robotics and Control following list*: Examples of suitable APMA courses Advisers: Professors Sunil Agrawal, are: APMA E4001y Principles of

ENGINEERING 2017–2018 190 applied mathematics; APMA E4300y, year in May, it is usually taken after the Introduction to the manual machine operation, CNC Introduction to numerical methods; student has spent two semesters in fabrication and usage of basic hand tools, band/ APMA E4301x Numerical methods for the graduate program as a M.S./Ph.D. hack saws, drill presses, grinders and sanders. partial differential equations; and APMA or Ph.D. student. The exam consists MECE E1304x or y Naval ship systems, I E4204x Functions for complex variables. of a written exam covering several 3 pts. Lect: 3. Instructor to be announced. areas of Mechanical Engineering. A Students are strongly advised to consult with the Express M.S. Application candidate who fails the examination ME Department prior to registering for this course. The Express M.S. Application is may be permitted to repeat it once in A study of ship characteristics and types including ship design, hydrodynamic forces, stability, offered to current seniors, including the following year, at the discretion of 3-2 students, who are enrolled in the compartmentation, propulsion, electrical and the faculty. auxiliary systems, interior communications, ship BS program. In the Express M.S. After passing the qualifying control, and damage control; theory and design Application, a master’s degree can be examination, the student chooses a of steam, gas turbine, and nuclear propulsion; earned seamlessly. Graduate classes faculty member in the pertinent area shipboard safety and firefighting. This course is are available for seniors to apply toward of specialization who then serves as part of the Naval ROTC program at Columbia but their M.S. degree and the advanced the research adviser. This adviser will be taught at SUNY Maritime. Enrollment may be limited; priority is given to students participating courses that will be taken have been helps select a research problem and designed to have the exact prerequisites in Naval ROTC. This course will not count as a supervises the research, writing, and technical elective. Students should see a faculty completed as an undergraduate. Other defense of the dissertation. Once a adviser as well as Columbia NROTC staff (nrotc@ advantages include the opportunity for specific problem has been identified columbia.edu) for more information. better course planning and creating and a tentative plan for the research a streamlined set of courses more MECE E3018x Mechanical engineering prepared, the student submits a research laboratory, I possible. Additional benefits include proposal and presents it to a faculty 3 pts. Lect: 3. Professor Kysar. simplified application process, no committee. The committee considers Experiments in instrumentation and measurement: GRE is required and no reference whether the proposed problem is optical, pressure, fluid flow, temperature, stress, letters are required. To qualify for this suitable for doctoral research, whether and electricity; viscometry, cantilever beam, digital program, your cumulative GPA should the plan of attack is well formulated and data acquisition. Probability theory: distribution, functions of random variables, tests of significance, be at least 3.5. For more information appropriate to the problem, and whether on requirements and access to an correlation, ANOVA, linear regression. A lab fee of the student is adequately prepared. $50.00 is collected. application, please visit me.columbia. It may approve the plan without edu/ms-express-application-1. reservation, or it may recommend MECE E3028y Mechanical engineering modifications or additions. This is the last laboratory, II 3 pts. Lect: 3. Professor Lin. Doctoral Degree Program formal requirement until the dissertation Experiments in engineering and physical When a student becomes a prospective is submitted for approval. phenomena: aerofoil lift and drag in wind tunnels, candidate for either the Doctor of All doctoral students are required to laser Doppler anemometry in immersed fluidic Engineering Science (Eng.Sc.D.) or successfully complete four semesters channels, supersonic flow and shock waves, Doctor of Philosophy (Ph.D.) degree, a of the mechanical engineering seminar Rankine thermodynamical cycle for power faculty adviser is assigned whose task MECE E9500. generation, and structural truss mechanics and is to help choose a program of courses, analysis. A lab fee of $50.00 is collected. provide general advice on academic MECE E3038x Mechanical engineering COURSES IN MECHANICAL matters, and monitor academic laboratory, III ENGINEERING performance. 3 pts. Lect: 3. Not offered in 2017–2018. The doctoral candidate is expected MECE E1001x Mechanical engineering: Mechatronic control of mechanical and to attain a level of mastery in some micromachines to jumbo jets electromechanical systems. Control of various thermodynamic cycles, including internal area of mechanical engineering, and 3 pts. Lect: 3. Not offered in 2017–2018. combustion engine (Otto cycle). Reverse must therefore choose a field and Corequisite: MATH UN1101 Calculus I. This introductory course explores the role of Mechanical engineering of an electromechanical product. A lab concentrate in it by taking the most Engineering in developing many of the fundamental fee of $50.00 is collected. advanced courses offered. This choice technological advances on which today’s society MECE E3100x Introduction to mechanics of specialty is normally made by the time depends. Students will be exposed to several of fluids the student has completed 30 points of mature and emerging technologies through a 3 pts. Lect: 3. Professor Myers credit beyond the bachelor’s degree, at series of case studies. Topics include airplanes, Prerequisite: ENME E3105. Basic continuum which time a complete course program automobiles, robots, modern manufacturing concepts. Liquids and gases in static equilibrium. is prepared and submitted to the methods as well as the emerging fields of Continuity equation. Two-dimensional kinematics. microelectromechanical machines (MEMS) and departmental doctoral committee for Equation of motion. Bernoulli’s equation and nanotechnology. The physical concepts that govern approval. The student must maintain a applications. Equations of energy and angular the operation of these technologies will be developed momentum. Dimensional analysis. Two- grade-point average of 3.2 or better in from basic principles and then applied in simple dimensional laminar flow. Pipe flow, laminar, and graduate courses. design problems. Students will also be exposed to turbulent. Elements of compressible flow. The department requires the state-of-the art innovations in each case study. prospective candidate to pass a ENME E3105x and y Mechanics MECE E1008x or y Introduction to machining 4 pts. Lect: 4. Professor Hone. qualifying examination. Given once a 1 pt. Instructor to be announced. Prerequisites: PHYS UN1401 and MATH UN1101,

ENGINEERING 2017–2018 UN1102, and UN1201. Elements of statics, thermodynamics, heat transfer, materials and 3 pts. Lect: 3. Members of the faculty. 191 dynamics of a particle, and systems of particles. processing, control, and mechanical design and Prerequisite: 3.2 or higher GPA. Individual study; analysis. Review of additional topics, including may be selected after the first term of the junior ENME E3113x Mechanics of solids engineering economics and ethics in engineering. year by students maintaining a 3.2 grade-point 3 pts. Lect: 3. Professor Deodatis. The course culminates with a comprehensive average. Normally not to be taken in a student's Pre- or corequisite: ENME E3105 or equivalent. examination, similar to the Fundamentals of final semester. Course format may vary from Stress and strain. Mechanical properties of Engineering examination. This course meets the individual tutorial to laboratory work to seminar materials. Axial load, bending, shear, and first 4.5 weeks only. instruction under faculty supervision. Written torsion. Stress transformation. Deflection of application must be made prior to registration beams. Buckling of columns. Combined loadings. outlining proposed study program. Projects MECE E3420x Engineering concept and Thermal stresses. requiring machine-shop use must be approved design by the laboratory supervisor. Students may count MECE E3301x Thermodynamics 1 pt. Lect: 1. Professor Stolfi. up to 6 points toward degree requirements. 3 pts. Lect: 3. Professor Narayanaswamy. Prerequisite: Senior standing. Corequisite: MECE Students must submit both a project outline prior to Classical thermodynamics. Basic properties and E3409. A preliminary design for an original project registration and a final project write up at the end concepts, thermodynamic properties of pure is a prerequisite for the capstone design course. of the semester. substances, equation of state, work, heat, the first This course will focus on the steps required for and second laws for flow and nonflow processes, generating a preliminary design concept. Included MECE E3998x and y Projects in mechanical energy equations, entropy, and irreversibility. will be a brainstorming concept generation phase, engineering Introduction to power and refrigeration cycles. a literature search, and the production of a layout 1–3 pts. Members of the faculty. drawing of the proposed capstone design project in Prerequisite: Approval by faculty member who MECE E3311y Heat transfer a Computer Aided Design (CAD) software package agrees to supervise the work. Normally not to be 3 pts. Lect: 3. Professor Narayanaswamy. (i.e., ProEngineer). taken in a student’s final semester. Independent Steady and unsteady heat conduction. Radiative project involving theoretical, computational, heat transfer. Internal and external forced and free MECE E3430y Engineering design experimental, or engineering design work. May convective heat transfer. Change of phase. Heat 3 pts. Lect: 2. Lab: 4. Professor Stolfi. be repeated, but no more than 3 points may be exchangers. Prerequisite: MECE E3420. Building on the counted toward degree requirements. Projects preliminary design concept, the detailed elements MECE E3401x Mechanics of machines requiring machine-shop use must be approved by of the design process are completed: systems 3 pts. Lect: 3. Professor Lipson. the laboratory supervisor. Students must submit synthesis, design analysis optimization, and Prerequisites: ENME E3105 and MECE E3408. both a project outline prior to registration and a Computer Aided Design (CAD) component part Introduction to mechanisms and machines, final project write-up at the end of the semester. drawings. Execution of a project involving the analytical and graphical synthesis of mechanism, design, fabrication, and performance testing of an MECE E3999x, y or s Fieldwork displacement analysis, velocity analysis, actual engineering device or system. A laboratory 1–2 pts. Instructor to be announced. acceleration analysis of linkages, dynamics of fee of $125 is collected. Prerequisites: Obtained internship and approval mechanism, cam design, gear and gear trains, and from a faculty adviser. May be repeated for credit, computer-aided mechanism design. MECE E3450x or y Computer-aided design but no more than 3 total points may be used 3 pts. Lect: 3. Professor Ateshian. MECE E3408x or y Computer graphics and toward the 128-credit degree requirement. Only for Prerequisites: ENME E3105, E3113, MECE design MECE undergraduate students who include rel- E3408, E3311. Introduction to numerical methods 3 pts. Lect: 3. Professor Stolfi. evant on-campus and off-campus work experience and their applications to rigid body mechanics for Introduction to drafting, engineering graphics, as part of their approved program of study. Final mechanisms and linkages. Introduction to finite computer graphics, solid modeling, and mechanical report and letter of evaluation required. Fieldwork element stress analysis for deformable bodies. engineering design. Interactive computer graphics credits may not count toward any major core, tech- Computer-aided mechanical engineering design and numerical methods applied to the solution nical, elective, and nontechnical requirements. May using established software tools and verifications of mechanical engineering design problems. A not be taken for pass/fail credit or audited. against analytical and finite difference solutions. laboratory fee of $175 is collected. MECE E4058y Mechatronics and embedded EEME E3601x Classical control systems MECE E3409x Machine design microcomputer control 3 pts. Lect: 3. Professor Longman. 3 pts. Lect: 3. Professor Lipson. 3 pts. Lect: 3. Instructor to be announced. Prerequisite: MATH UN2030. Analysis and design Prerequisite: MECE E3408. Computer-aided Prerequisite: ELEN E1201. Recommended: of feedback control systems. Transfer functions; analysis of general loading states and deformation ELEN E3000. Enrollment limited to 12 students. block diagrams; proportional, rate, and integral of machine components using singularity functions Mechatronics is the application of electronics and controllers; hardware, implementation. Routh and energy methods. Theoretical introduction to microcomputers to control mechanical systems. stability criterion, root locus, Bode and Nyquist static failure theories, fracture mechanics, and Systems explored include on/off systems, plots, compensation techniques. fatigue failure theories. Introduction to conceptual solenoids, stepper motors, DC motors, thermal design and design optimization problems. Design MECE 3610y Materials and processes in systems, magnetic levitation. Use of analog and of machine components such as springs, shafts, manufacturing digital electronics and various sensors for control. fasteners, lead screws, rivets, welds. Modeling, 3 pts. Lect: 3. Professor Yao. Programming microcomputers in Assembly and C. analysis, and testing of machine assemblies for Prerequisites: ENME E3113 or the equivalent. A lab fee of $75.00 is collected. Lab required. prescribed design problems. Problems will be Introduction to microstructures and properties drawn from statics, kinematics, dynamics, solid of metals, polymers, ceramics and composites; MECE E4100y Mechanics of fluids modeling, stress analysis, and design optimization. typical manufacturing processes: material removal, 3 pts. Lect: 3. Professor Kasza. shaping, joining, and property alteration; behavior Prerequisite: MECE E3100 or equivalent. Fluid MECE E3411y Fundamentals of engineering of engineering materials in the manufacturing dynamics and analyses for mechanical engineering 1 pt. Lect: 3. Professor Vukelic. processes. and aerospace applications: boundary layers Prerequisite: Senior standing. Review of core and lubrication, stability and turbulence, and courses in mechanical engineering, including MECE E3900x-E3901y Honors tutorial in compressible flow. Turbomachinery as well as mechanics, strength of materials, fluid mechanics, mechanical engineering additional selected topics.

ENGINEERING 2017–2018 192 IEME E4200x or y Introduction to human- separation and detection; sample preparation; Prerequisite: MECE E3311 (Heat transfer). centered design micro bioreactors and temperature control; Fundamentals of solar energy transport: 1.5 pts. Lect: 4.5. Professor West. implantable MEMS, including sensors, actuators radiation heat transfer, convention, conduction Prerequisite: Application to instructor for approval. and drug delivery devices. and phase change processes. Heat exchangers Open to SEAS graduate and advanced under- and solar collectors: basic methods of thermal MECE E4302y Advanced thermodynamics graduate students, Business School, and GSAPP. design, flow arrangements, effects of variable 3 pts. Lect: 3. Professors Burke and Vukelic. Students from other schools may apply. Fast- conditions, rating procedures. Solar energy Prerequisite: MECE E3301. Advanced classical paced introduction to human-centered design. concentration. Piping Systems: series and thermodynamics. Availability, irreversibility, Students learn the vocabulary of design methods, parallel arrangements, fluid movers. Thermal generalized behavior, equations of state for understanding of design process. Small group response and management of photovoltaic nonideal gases, mixtures and solutions, phase and projects to create prototypes. Design of simple energy conversion. Solar energy storage. Solar chemical behavior, combustion. Thermodynamic product, more complex systems of products and cooling, solar thermal power and cogeneration. properties of ideal gases. Applications to services, and design of business. Applications to the design of solar thermal automotive and aircraft engines, refrigeration and engineering systems. MECE E4210x or y Energy infrastructure air conditioning, and biological systems. planning MECE E4314y Energy dynamics of green MECE E4304x Turbomachinery 3 pts. Lect: 3. Professor Modi. buildings 3 pts. Lect: 3. Professor Leylegian. Prerequisites: One year each of college level 3 pts. Lect: 3. Professor Naraghi. This course will introduce you to the basics physics, chemistry, and mathematics. Energy Prerequisites: MECE E3301 and E3311. of theory, design, selection and applications infrastructure planning with specific focus on Introduction to analysis and design of heating, of turbomachinery. Turbomachines are widely countries with rapidly growing infrastructure ventilating and air-conditioning systems. Heating used in many engineering applications such as needs. Spatiotemporal characteristics, scale, and and cooling loads. Humidity control. Solar gain and energy conversion, power plants, air-conditioning, environmental footprints of energy resources, passive solar design. Global energy implications. pumping, refrigeration and vehicle engines, power generation and storage, modeling as there are pumps, blowers, compressors, Green buildings. Building-integrated photovoltaics. demand growth, technology choices and learning gas turbines, jet engines, wind turbines, etc. Roof-mounted gardens and greenhouses. Financial for planning. Computer-assisted decision Applications are drawn from energy conversion assessment tools and case studies. Open to support and network design/optimization tools. technologies, HVAC and propulsion. The course Mechanical Engineering graduate students only. Similarities, differences and interactions among provides a basic understanding of the different electricity, gas, information, transportation and MECH E4320x Introduction to combustion kinds of turbomachines. water distribution networks. Penetration of 3 pts. Lect: 3. Professor Burke. renewable and/or decentralized technologies MECE E4305y Mechanics and Prerequisites: Introductory thermodynamics, fluid into existing or new infrastructure. Special guest thermodynamics of propulsion dynamics, and heat transfer at the undergraduate lectures on infrastructure finance, regulation and 3 pts. Lect: 3. Professor Leylegian. level or instructor’s permission. Thermodynamics public-private partnerships. Prerequisites: MECE E3301x Thermodynamics and kinetics of reacting flows; chemical kinetic and MECE E3311y Heat transfer; MECE mechanisms for fuel oxidation and pollutant MECE E4211x or y Energy: sources and E4304x Turbomachinery (or instructor approval). formation; transport phenomena; conservation conversion Principles of propulsion. Thermodynamic cycles equations for reacting flows; laminar nonpremixed 3 pts. Lect: 3. Professor Modi. of air breathing propulsion systems including flames (including droplet vaporization and burning); Prerequisite: MECE E3301. Energy sources such ramjet, scramjet, turbojet, and turbofan engine laminar premixed flames; flame stabilization, as oil, gas, coal, gas hydrates, hydrogen, solar, and rocket propulsion system concepts. Turbine quenching, ignition, extinction, and other limit and wind. Energy conversion systems for electrical engine and rocket performance characteristics. phenomena; detonations; flame aerodynamics and power generation, automobiles, propulsion and Component and cycle analysis of jet engines and turbulent flames. refrigeration. Engines, steam and gas turbines, turbomachinery. Advanced propulsion systems. MECE E4330x Thermofluid systems design wind turbines; devices such as fuel cells, Columbia Engineering interdisciplinary course. thermoelectric converters, and photovoltaic cells. 3 pts. Lect: 3. Professor Bradshaw. Specialized topics may include carbon-dioxide MECE E4306x or y Introduction to Prerequisites: MECE E3100, E3301, E3311. sequestration, cogeneration, hybrid vehicles and aerodynamics Theoretical and practical considerations, and design principles, for modern thermofluids systems. Topics energy storage devices. 3 pts. Lect: 3. Professor LeVoci. Principles of flight, incompressible flows, include boiling, condensation, phase change heat MECE E4212x or y Microelectromechanical compressible regimes. Inviscid compressible transfer, multimode heat transfer, heat exchangers, systems aerodynamics in nozzles (wind tunnels, jet and modeling of thermal transport systems. 3 pts. Lect: 1.5. Lab: 3. engines), around wings (aircraft, space shuttle) Emphasis on applications of thermodynamics, heat MEMS markets and applications; scaling laws; and around blunt bodies (rockets, reentry transfer, and fluid mechanics to modeling actual silicon as a mechanical material; Sensors and vehicles). Physics of normal shock waves, oblique physical systems. Term project on conceptual design actuators; micromechanical analysis and design; shock waves, and explosion waves. and presentation of a thermofluid system that meets substrate (bulk) and surface micromachining; specified criteria. IEME E4310x The manufacturing enterprise computer aided design; packaging; testing and 3 pts. Lect: 3. Professor Weinig. MECE E4400x and y Computer laboratory access characterization; microfluidics. The strategies and technologies of global 0 pts. Professor Kysar. MECE E4213x or y Biomicroelectromechanical manufacturing and service enterprises. Sign up for this class to obtain a computer account systems (BioMEMS): design, fabrication, and Connections between the needs of a global and access to the Department of Mechanical analysis enterprise, the technology and methodology Engineering Computer Laboratory. 3 pts. Lect: 3. Professor Lin. needed for manufacturing and product MECE E4404x or y Tribology: friction, Prerequisites: MECE E3100 and E3311, course in development, and strategic planning as currently lubrication, and wear transport phenomena, or instructor’s permission. practiced in industry. 3 pts. Lect: 3. Not offered in 2017–2018. Silicon and polymer micro/nanofabrication MECE E4312x Solar thermal engineering Prerequisites: MECE E3100, E3311, and ENME techniques; hydrodynamic microfluidic control; 3 pts. Lect: 3. Professor Narayanaswamy. E3113, or permission of the instructor. Friction, electrokinetic microfluidic control; microfluidic

ENGINEERING 2017–2018 lubrication, and wear between sliding surfaces. satellite attitude dynamics, gravity gradient and associated data structures; applications of 193 Surface metrology, contact mechanics, and sliding stabilization of satellites, spin-stabilized satellites, geometrical modeling in vision and robotics. friction. Deformation, wear, and temperature rise of dual-spin satellites, satellite attitude control, MECE E4502x Computational geometry for nonlubricated, liquid-lubricated, and solid-lubricated modeling, dynamics, and control of large flexible CAD/CAM rolling and sliding materials. The theories of spacecraft. 3 pts. Lect: 3. Professor Rajan. boundary, elastohydrodynamic, hydrodynamic, MEBM E4439x Modeling and identification of Prerequisite: COMS W1005 FORTRAN or hydrostatic, and solid-phase lubrication. Lubricant dynamic systems PASCAL. Analysis of geometric problems and flow and load-carrying capacity in bearings. Special 3 pts. Lect: 3. Professor Chbat. the design of efficient methodologies to obtain applications such as geartrains, cam/tappets, and Prerequisite: APMA E2101, ELEN E3801, or solutions to these problems. Algorithms to be micro- and nanoscale tribological interfaces. corequisite EEME E3601, or permission of studied include geometric searching, convex hulls, MECE E4430y Automotive dynamics instructor. Generalized dynamic system modeling triangulations, Voronoi diagrams, intersections, 3 pts. Lect: 3. Instructor to be announced. and simulation. Fluid, thermal, mechanical, hidden surfaces. Emphasis will be on practical Prerequisite: ENME 3105 or equivalent; diffusive, electrical, and hybrid systems are aspects of these algorithms, and on applications of recommended: ENME 3106 or equivalent. considered. Nonlinear and high order systems. the solutions in computer-aided product design and Automobile dynamic behavior is divided into System identification problem and Linear manufacturing. Least Squares method. State-space and noise three subjects: vehicle subsystems, ride, and MECS E4510x Evolutionary computation and representation. Kalman filter. Parameter estimation handling. Vehicle subsystems include tire, steering, design automation mechanisms, suspensions, gearbox, engine, via prediction-error and subspace approaches. Iterative and bootstrap methods. Fit criteria. Wide 3 pts. Lect: 3. Professor Lipson. clutch, etc. Regarding ride, vibrations and ride Prerequisite: Basic programming experience in comfort are analyzed, and suspension optimization applicability: medical, energy, others. MATLAB and Simulink environments. any language. Fundamental and advanced topics of a quarter car model is treated. Regarding in evolutionary algorithms and their application handling, vehicle dynamic behavior on the road is MECE E4501y Geometrical modeling to open-ended optimization and computational analyzed, with emphasis on numerical simulations 3 pts. Lect: 3. Professor Rajan. design. Covers genetic algorithms, genetic pro- using planar as well as roll models. Prerequisite: COMS W1005. Relationship between gramming, and evolutionary strategies, as well as 3D geometry and CAD/CAM; representations MECE E4431x or y Space vehicle dynamics governing dynamic of coevolution and symbiosis. of solids; geometry as the basis of analysis, Includes discussions of problem representations and control design, and manufacturing; constructive solid and applications to design problems in a variety 3 pts. Lect: 3. Professor Longman. geometry and the CSG tree; octree representation of domains including software, electronics, and Prerequisite: ENME-MECE E3105; ENME E4202 and applications; surface representations and mechanics. recommended. Space vehicle dynamics and intersections; boundary representation and control, rocket equations, satellite orbits, initial boundary evaluation; applied computational EEME E4601y Digital control systems trajectory designs from earth to other planets, geometry; analysis of geometrical algorithms 3 pts. Lect: 3. Professor Longman.

ENGINEERING 2017–2018 194 Prerequisite: EEME E3601 or ELEN E3201. Real- tooling and fixturing, computer numeric control, knowledge of MATLAB or equivalent. Introduction time control using digital computers. Solving scalar rapid prototyping, process engineering, fixed and to human spaceflight from a systems engineering and state-space difference equations. Discrete programmable automation, industrial robotics. perspective. Historical and current space programs equivalents of continuous systems fed by holds. and spacecraft. Motivation, cost, and rationale MECE E4610x Advanced manufacturing Z-transer functions. Creating closed-loop difference for human space exploration. Overview of space processes equation models by Z-transform and state variable environment needed to sustain human life and 3 pts. Lect: 3. Professor Vukelic. approaches. The Nyquist frequency and sample health, including physiological and psychological Prerequisites: Introductory course on rate selection. Classical and modern based digital concerns in space habitat. Astronaut selection and manufacturing processes, and heat transfer, control laws. Digital system identification. training processes, spacewalking, robotics, mission knowledge of engineering materials, or operations, and future program directions. Systems MECE E4602x Introduction to robotics instructor’s permission. Principles of nontraditional integration for successful operation of a spacecraft. 3 pts. Lect: 3. Professor Agrawal. manufacturing, nontraditional transport and media. Highlights from current events and space research, Overview of robot applications and capabilities. Emphasis on laser assisted materials processing, Space Shuttle, Hubble Space Telescope, and Linear algebra, kinematics, statics, and laser material interactions with applications to International Space Station (ISS). Includes a dynamics of robot manipulators. Survey of laser material removal, forming, and surface design project to assist International Space Station sensor technology: force, proximity, vision, modification. Introduction to electrochemical astronauts. compliant manipulators. Motion planning and machining, electrical discharge machining and artificial intelligence; manipulator programming abrasive water jet machining. MECE E4990x or y Special topics in requirements and languages. mechanical engineering BMME E4702x Advanced musculoskeletal 3 pts. Lect: 3. Instructor to be announced. MECS E4603x Applied robotics: algorithms biomechanics Prerequisites: Permission of the instructor. Topics and software 3 pts. Lect: 3. Professor Guo. and Instructors change from year to year. For 3 pts. Lect: 3. Professor Ciocarlie. Advanced analysis and modeling of the advanced undergraduate students and graduate Prerequisites: Fundamental programming skills musculoskeletal system. Topics include students in engineering, physical sciences, and (e.g., COMS W1002, W1004, W1005, ENGI advanced concepts of 3D segmental kinematics, other fields. E1006, or equivalent). Science and systems musculoskeletal dynamics, experimental aspects of Robotics from applied perspective, measurements of joints kinematics and anatomy, MECE E4999x and y Curricular practical training focusing on algorithms and software tools. Spatial modeling of muscles and locomotion, multibody 1 pt. Professor Kysar. reasoning; tools for manipulating and visualizing joint modeling, introduction to musculoskeletal Prerequisite: Instructor’s written permission. Only spatial relationships. Analysis of robotic manipula- surgical simulations. for ME graduate students who need relevant off- tors; numerical methods for kinematic analysis. campus work experience as part of their program Motion planning, search-based and stochastic MEBM E4703x Molecular mechanics in biology of study as determined by the instructor. Written approaches. Applications for force and impedance 3 pts. Lect: 3. Not offered in 2017–2018. application must be made prior to registration control. Grading based on combination of exams Prerequisite: ENME E3105, APMA E2101, or outlining proposed study program. Final reports and projects implemented using Robot Operating instructor’s permission. Mechanical understanding required. May not be taken for pass/fail credit or System (ROS) software framework and executed of biological structures including proteins, DNA audited. International students must consult with on real and simulated robotic manipulators. and RNA in cells and tissues. Force response the International Students and Scholars Office. of proteins and DNA, mechanics of membranes, MECE E4604x Product design for biophysics of molecular motors, mechanics MECE E6100x Advanced mechanics of fluids manufacturability 3 pts. Lect: 3. Professor Walker. of protein-protein interactions. Introduction to 3 pts. Lect: 3. Professor Ateshian. Prerequisites: Manufacturing process, computer modeling and simulation techniques, and modern Prerequisites: MATH UN2030 and MECE E3100. graphics, engineering design, mechanical design. biophysical techniques such as single molecule Eulerian and Lagrangian descriptions of motion. General review of product development process; FRET, optical traps, AFM, and superresolution Stress and strain rate tensors, vorticity, integral market analysis and product system design; imaging, for understanding molecular mechanics and differential equations of mass, momentum, principles of design for manufacturing; strategy and dynamics. and energy conservation. Potential flow. for material selection and manufacturing process MEBM E4710x or y Morphogenesis: shape MECE E6102y Computational heat transfer choice; component design for machining; casting; and structure in biological materials and fluid flow molding; sheet metal working and inspection; 3 pts. Lect: 2.5. Professor Kasza 3 pts. Lect: 3. Not offered in 2017–2018. general assembly processes; product design Prerequisites: Courses in mechanics, thermody- Prerequisites: MECE E3100 and E3311; COMS for manual assembly; design for robotic and namics, and ordinary differential equations at the W1005 FORTRAN. Mathematical description of automatic assembly; case studies of product undergraduate level or instructor's permission. pertinent physical phenomena. Basics of finite- design and improvement. Introduction to how shape and structure are gen- difference methods of discretization, explicit MECE E4606y Digital manufacturing erated in biological materials using engineering and implicit schemes, grid sizes, stability, and 3 pts. Lect: 3. Professor Lipson. approach emphasizing application of fundamental convergence. Solution of algebraic equations, Prerequisite: Basic programming in any language. physical concepts to a diverse set of problems. relaxation. Heat conduction. Incompressible Additive manufacturing processes, CNC, Sheet Mechanisms of pattern formation, self-assembly, fluid flow, stream function-vorticity formulation. cutting processes, Numerical control, Generative and self-organization in biological materials, Forced and natural convection. Use of primitive and algorithmic design. Social, economic, legal, including intracellular structures, cells, tissues, variables, turbulence modeling, and coordinate and business implications. Course involves both and developing embryos. Structure, mechanical transformations. theoretical exercises and a hands-on project. properties, and dynamic behavior of these materials. Discussion of experimental approaches and MECE E6103x Compressible flow MECE E4609y Computer-aided manufacturing modeling. Course uses textbook materials as well 3 pts. Lect: 3. Not offered in 2017–2018. 3 pts. Lect: 3. Professor Walker. as collection of research papers. Prerequisites: APMA E4200, MECE E3100 and Prerequisites: Introductory course on manufacturing E3301. Fundamental analysis of compressible processes and knowledge of computer-aided design, MEIE E4810y Introduction to human spaceflight flows and its applications for various sonic/ and mechanical design or instructor’s permission. 3 pts. Lect: 3. Professor Massimino. supersonic elements including supersonic airfoils/ Computer-aided design, free-form surface modeling, Prerequisites: Department permission and projectiles, nozzles, and shock tubes. Steady

ENGINEERING 2017–2018 and unsteady shock/expansion waves, oblique solution of multidimensional steady and transient and transfer function matrices, block diagram 195 shock waves. Shock reflections, methods of problems in heat conduction and convection. manipulations, closed loop response. Proportional, characteristic. Lumped, integral, and differential formulations. rate, and integral controllers, and compensators. Topics include use of sources and sinks, laminar/ Design by root locus and frequency response. MECE E6104x or y Case studies in turbulent forced convection, and natural convection Controllability and observability. Luenberger computational fluid dynamics in internal and external geometries. observers, pole placement, and linear-quadratic 3 pts. Lect: 3. Professor Henry. cost controllers. Prerequisites: APAM E4200 and MECE E6100. MECE E6400y Advanced machine dynamics Corequisites: APAM E4300 and MECE E4400. 3 pts. Lect: 3. Professor Chbat. EEME E6602y Modern control theory Hands-on case studies in computational fluid Prerequisite: MECE E3401. Review of classical 3 pts. Lect: 3. Not offered in 2017–2018. dynamics, including steady and transient dynamics, including Lagrange’s equations. Analysis Prerequisite: EEME E6601 or E4601 or ELEN flows, heat and mass transfer, turbulence, of dynamic response of high-speed machine E6201, or instructor’s permission. Singular value compressible flow and multiphase flow. elements and systems, including mass-spring decomposition. ARX model and state space Identifying assumptions, computational domain systems, cam-follower systems, and gearing; model system identification. Recursive least selection, model creation and setup, boundary shock isolation; introduction to gyrodynamics. squares filters and Kalman filters. LQR, Hlinear robust control, predictive control, adaptive conditions, choice of convergence criteria, MECE E6422x–E6423y Introduction to the control. Liapunov and Popov stability. Nonlinear visualization and interpretation of computed theory of elasticity, I and II adaptive control, nonlinear robust control, sliding results. Taught in the Mechanical Engineering 3 pts. Lect: 3. Professors Ateshian and Kysar. mode control. Computer Laboratory with Computational Fluid Corequisite: APMA E4200. Analysis of stress Dynamics software. and strain. Formulation of the problem of elastic EEME E6610y Optimal control theory MECE E6105y Transport phenomena in the equilibrium. Torsion and flexure of prismatic bars. 3 pts. Lect: 3. Not offered in 2017–2018. presence of interfaces Problems in stress concentration, rotating disks, Prerequisite: EEME E6601 or E4601 or instructor’s 3 pts. Lect: 3. Not offered in 2017–2018. shrink fits, and curved beams; pressure vessels, permission. Covers topics in calculus of variations, contact and impact of elastic bodies, thermal Prerequisites: MECE E3301 Thermodynamics Pontryagin maximum principle, quadratic cost stresses, propagation of elastic waves. optimal control, predictive control, dynamic and MECE E3311 Heat transfer; MECE E4100 programming for optimal control, Kalman filtering, Mechanics of fluids, or equivalent or instructor’s MECE E6424x Vibrations in machines, I numerical methods for solution. Some applications permission; CHEE E4252 Introduction to surface 3 pts. Lect: 3. Instructor to be announced. discussed include minimum energy subway and colloid chemistry, or the equivalent, or the Prerequisite: MECE E3401. Review of vibration operation (our solution saved 11% in tests on the instructor’s permission. Surface energy and analysis of systems and mechanisms with one Flushing Line, and the method was adopted by the capillary phenomena. Wetting and spreading degree of freedom. Natural frequencies. Forced transit authority, saving many millions of dollars per of liquids, wetting line pinning and hysteresis, vibrations. Effects of dry and viscous friction. year), minimum time robot optimal control allowing dynamics of wetting. Surfactants. Bubbles: Energy methods of Rayleigh and Ritz. Suppression one to run assembly lines faster for increased nucleation, stability, dynamics, microstreaming. and elimination of vibration. Vibration isolation. productivity. Jets and Drops: generation, dynamics, stability and Measuring instruments. Critical speeds in machinery. impact with surfaces. Measurement of transport Synchronous whirl. Half-frequency whirl. Influence of MECE E6614x or y Advanced topics in phenomena involving interfaces. Interfacial bearing characteristics on critical speeds. Effect of robotics and mechanism synthesis transport phenomena involving thermal, chemical gyroscopic moments. Systems with multiple degrees 3 pts. Lect: 3. Professor Agrawal. or electrical gradients. Applications in microfluidic of freedom. Dynamic vibration absorbers. Self-tuning Prerequisites: APMA E2101, E3101, MECE E4602 systems. absorbers of pendulum and roller types. Lagrangian (or COMS W4733). Recommended: MECE E3401 equations of motion as applied to vibrating systems. or instructor’s permission. Kinematic modeling MECE E6200y Turbulence General equations for transverse critical speeds of methods for serial, parallel, redundant, wire- 3 pts. Lect: 3. Not offered in 2017–2018. shafts. Surging of helical springs. actuated robots and multifingered hands with Prerequisite: MECE E6100. Introductory concepts discussion of open research problems. Introduction MEEM E6432y Small-scale mechanical and statistical description. Kinematics of random to screw theory and line geometry tools for behavior velocity fields, dynamics of vorticity, and scalar kinematics. Applications of homotopy continuation 3 pts. Lect: 3. Professor Kysar. quantities. Transport processes in a turbulent methods and symbolic-numerical methods for Prerequisites: ENME E3113 or equivalent; APMA medium. Turbulent shear flows: deterministic and direct kinematics of parallel robots and synthesis E4200 or equivalent. Mechanics of small-scale random structures. Experimental techniques, of mechanisms. Course uses textbook materials as materials and structures require nonlinear kinematics prediction methods, and simulation. well as a collection of recent research papers. and/or nonlinear stress vs. strain constitutive MEBM E6310x-E6311y Mixture theories for relations to predict mechanical behavior. Topics MECE E6615x or y Robotic manipulation: biological tissues, I and II include variational calculus, deformation and vibration sensing, planning, design, and execution 3 pts. Lect: 3. Not offered in 2017–2018. of beam, strings, plates, and membranes; fracture, 3 pts. Lect: 3. Professor Ciocarlie. Prerequisites: MECE E6422 and APMA E4200 or delamination, bulging, buckling of thin films, among Prerequisite: MECE E4602 or COMS W4733. equivalent. Development of governing equations others. Thermodynamics of solids will be reviewed Theory and mechanisms of robotic manipulation, for mixtures with solid matrix, interstitial fluid, to provide the basis for a detailed discussion of from sensor data, reasoning, and planning to and ion constituents. Formulation of constitutive nonlinear elastic behavior as well as the study of the implementation and execution. Grasp quality models for biological tissues. Linear and nonlinear equilibrium and stability of surfaces. measures and optimization; planning and models of fibrillar and viscoelastic porous matrices. execution for manipulation primitives; sensor Solutions to special problems, such as confined EEME E6601x Introduction to control theory 3 pts. Lect: 3. Professor Longman. modalities: vision, touch, and proprioception; and unconfined compression, permeation, simulation for manipulation planning; design indentation and contact, and swelling experiments. Prerequisite: MATH UN2030. A graduate-level introduction to classical and modern feedback of robot manipulators. Grading based on a MECE E6313x Advanced heat transfer control that does not presume an undergraduate combination of class presentations of novel 3 pts. Lect: 3. Professor Narayanaswamy. background in control. Scalar and matrix research results in the field, participation in Prerequisites: MECE E3311. Corequisites: MECE differential equation models and solutions in terms discussions, and course projects combining E6100. Application of analytical techniques to the of state transition matrices. Transfer functions simulation, processing of sensor data, planning

ENGINEERING 2017–2018 for manipulation, design, and implementation on Kinetic theory of gases. Boltzmann transport 196 EEME E8601y Advanced topics in control theory real robot hands. equation (BTE), classical and quantum size 3 pts. Lect: 3. Not offered in 2017–2018. effects. Landauer formalism for transport Prerequisites: EEME E6601 and E4601 or MECE E6620x or y Applied signal recognition via nanostructures. Macroscopic constitutive instructor’s permission This course may be taken and classification equations from BTE. Application to electronics more than once, since the content changes from 3 pts. Lect: 3. Not offered in 2017–2018. cooling, thermoelectric and thermophotovoltaic year to year, electing different topics from control Prerequisites: MATH UN2030, APMA E3101, devices, and energy conversion. theory such as learning and repetitive control, knowledge of a programming language, or adaptive control, system identification, Kalman MECE E8020x or E8021y Master’s thesis permission of instructor. Applied recognition filtering, etc. and classification of signals using a selection 3–6 pts. Members of the faculty. of tools borrowed from different disciplines. Research in an area of mechanical engineering MECE E8990x and y Special topics in Applications include human biometrics, imaging, culminating in a verbal presentation and a written mechanical engineering geophysics, machinery, electronics, networking, thesis document approved by the thesis adviser. 3 pts. Lect: 3. Instructor to be announced. languages, communications, and finance. Must obtain permission from a thesis adviser to Prerequisite: Instructor’s permission. This course Practical algorithms are covered in signal enroll. Recommended enrollment for two terms, may be taken for credit more than once. The instruc- generation, modeling, feature extraction, metrics one of which can be the summer. A maximum tor from the Mechanical Engineering Department for comparison and classification, parameter of 6 points of master’s thesis may count toward and the topics covered in the course will vary from estimation, supervised, unsupervised and an M.S. degree, and additional research points year to year. This course is intended for students hierarchical clustering and learning, optimization, cannot be counted. On completion of all master’s with graduate standing in Mechanical Engineering scaling and alignment, signals as codes emitted thesis credits, the thesis adviser will assign a and other engineering and applied sciences. from natural sources, information, and extremely single grade. Students must use a department- MECE E9000x-E9001y and E9002s Graduate large-scale search techniques. recommended format for thesis writing. research and study MECE E6700x Carbon nanotube science and MECE E8100y Advanced topics in fluid 1–3 pts. Members of the faculty. technology mechanics Theoretical or experimental study or research in 3 pts. Lect: 3. Not offered in 2017–2018. 3 pts. Lect: 3. Not offered in 2017–2018. graduate areas in mechanical engineering and Prerequisite: Knowledge of introductory solid Prerequisite: MECE E6100. This course may engineering science. Undergraduate Minors state physics (e.g., PHYS GU4018, APPH E6081, be taken more than once, since its content has MECE E9500x and y Graduate seminar or MSAE E3103) or instructor’s permission. minimal overlap between consecutive years. 0 pts. Pass/fail only. Professor Ciocarlie. Basic science of solid state systems. Crystal Selected topics from viscous flow, turbulence, All doctoral students are required to complete structure, electronic and phonon band structures compressible flow, rarefied gas dynamics, successfully four semesters of the mechanical of nanotubes. Synthesis of nanotubes and other computational methods, and dynamical systems engineering seminar MECE E9500. nanomaterials. Experimental determination theory, non-Newtonian fluids, etc. of nanotube structures and techniques for MECE E8501y Advanced continuum MECE E9800x and y Doctoral research nanoscale imaging. Theory and measurement of biomechanics instruction mechanical, thermal, and electronic properties of 3, 6, 9, or 12 pts. Members of the faculty. 3 pts. Lect: 2. Professor Myers. nanotubes and nanomaterials. Nanofabrication and A candidate for the Eng.Sc.D. degree in Prerequisite: Instructor’s permission. The nanoelectronic devices. Applications of nanotubes. mechanical engineering must register for 12 points essentials of finite deformation theory of solids and of doctoral research instruction. Registration in MECE E6710y Nanofabrication laboratory fluids needed to describe mechanical behavior of MECE E9800 may not be used to satisfy the 3 pts. Lect: 3. Instructor to be announced. biological tissue: kinematics of finite deformations, minimum residence requirement for the degree. Prerequisite: ELEN E6945 or instructor’s balance laws, principle of material objectivity, permission. Laboratory in techniques for theory of constitutive equations, concept of simple MECE E9900x and y Doctoral dissertation fabrication at the nanometer scale. Electron- solids and simple fluids, approximate constitutive 0 pts. Members of the faculty. beam lithography. Plasma etching and 3D equations, some boundary-value problems. Topics A candidate for the doctorate may be required nanofabrication. Thin film deposition. Self- include one- and two-point tensor components to register for this course every term after his/ assembly and “bottom up” nanofabrication. with respect to generalized coordinates; finite her coursework has been completed and until the Fabrication of and testing of complete deformation tensors, such as right and left Cauchy- dissertation has been accepted. nanodevices. A lab fee of $300 is required. Green tensors; rate of deformation tensors, such as Rivlin-Ericksen tensors; various forms of MECE E6720x Nano/microscale thermal objective time derivatives, such as corotational and transport process convected derivatives of tensors; viscometric flows 3 pts. Lect: 3. Not offered in 2017–2018. of simple fluids; examples of rate and integral type Nano- and microscale origins of thermal of constitutive equations. transport phenomena by molecules, electrons, phonons, and photons. Quantum mechanics and statistical physics. Density of states. Undergraduate Minors 198 UNDERGRADUATE MINORS

ndergraduate minors are Associate Dean of Undergraduate or any other course designated APMA, MATH, designed to allow engineering Student Affairs. STAT, IEOR, or COMS that is approved by the U and applied science students applied mathematics program adviser. to study, to a limited extent, a discipline MINOR IN ANTHROPOLOGY other than their major. Besides MINOR IN APPLIED PHYSICS engineering minors offered by Columbia 1. ANTH UN1002: The interpretation of culture (3) Prospective students should consult the Engineering departments, liberal arts or ANTH UN1008: The rise of civilization (3) first- and second-year requirements for minors are also available. Note: UN1002 serves as a preview to applied physics majors to ensure that A minor requires at least 15 points of sociocultural anthropology, while UN1008 prerequisites for the applied physics credit, and no more than one course can serves as a preview to archaeology. minor are satisfied in the first two years. be taken outside of Columbia or met 2–5. Any four courses in the Anthropology Coursework counting toward the through AP or IB credit. This includes department, in ethnomusicology, or taught applied physics minor may not include courses taken through study abroad. by an Anthropology instructor, regardless of advanced placement credits. In Engineering departments with more department. No distribution requirement. 1. APPH E4901: Problems in applied physics (1) than one major program, a minor in the 2. APPH E3200: Mechanics (3) second program may be permitted, if MINOR IN APPLIED 3. APPH E3100: Intro to quantum mechanics (3) approved by the department. MATHEMATICS No substitutions or changes of any Prospective students should consult 4. APPH E3300: Applied electromagnetism (3) kind from the approved minors are the first- and second-year requirements 5. MSAE E3111: Thermodynamics, kinetic theory, permitted (see lists below). No appeal for for applied mathematics majors to and statistical mechanics (3) changes will be granted. Please note that ensure that prerequisites for the applied the same courses may not be used to 6. Two of the following courses mathematics minor are satisfied in the APPH E4010: Intro to nuclear science (3) satisfy the requirements of more than one first two years. APPH E4100: Quantum physics of matter (3) minor. No courses taken for pass/fail may Coursework counting toward the APPH E4110: Modern optics (3) be counted for a minor. Minimum GPA for applied mathematics minor may not APPH E4112: Laser physics (3) the minor is 2.0. Departments outside the APPH E4300: Applied electrodynamics (3) include advanced placement credits. Engineering School have no responsibility APPH E4301: Intro to plasma physics (3) Any substitutions for the courses listed for nonengineering minors offered by below require the approval of the applied Engineering. mathematics program adviser. MINOR IN ARCHITECTURE For a student to receive credit for a course taken while studying abroad, 1. APMA E3101: Linear algebra (3) 1. Studio: One of the following courses the department offering the minor must or MATH UN2010: Linear algebra (3) ARCH UN1020: Intro to architectural design and visual culture (3) approve the course in writing, ahead of 2. APMA E3102: Partial differential equations (3) ARCH UN3101: Abstraction (4) or MATH UN3028: Partial differential equations the student’s study abroad. ARCH UN3103: Perception (4) Students must expect a course load (3) 2–4. History/theory courses (see Note below) that is heavier than usual. In addition, 3–5. Three of the following courses: unforeseen course scheduling changes, APMA E4300: Intro to numerical methods (3) 5. Elective: must be either an approved second problems, and conflicts may occur. The APMA E4204: Func of complex variable (3) design studio or an additional history/theory School cannot guarantee a satisfactory APMA E4101: Intro to dynamical systems (3) course MATH UN2500: Analysis and optimization (3) completion of the minor. STAT GU4001: Intro to probability and statistics (3) Note: A list of the approved history/theory Students interested in establishing STAT GR5204: Statistical inference (3) courses is available at the departmental a new minor should consult with the office each semester.

ENGINEERING 2017–2018 MINOR IN ART HISTORY MSAE E3103: Elements of mat sci (3) performance/choreography courses 199 MSAE E3142: Ceramics and polymers (3) below count toward the nontech 1–7. Seven courses in art history, covering requirement for Engineering students. four of the following areas: (a) ancient Mediterranean, (b) medieval Europe, MINOR IN CIVIL 1–2. History/criticism: Two of the following: (c) Renaissance and baroque, (d) 18th, ENGINEERING DNCE BC2565: World dance history (3) 19th, and 20th century, and (e) non- DNCE BC2570: Dance in New York City (3) 1. CIEN E3121: Structural analysis (3) DNCE BC2575: Choreography for the Western or ENME E3161: Fluid mechanics (4) American musical (3) or MECE E3100: Intro to mech of fluids (3) DNCE BC3000: From the page to the MINOR IN BIOMEDICAL 2. ENME E3105: Mechanics (4) dance stage (3) ENGINEERING DNCE BC3001: Western theatrical dance 3. ENME E3113: Mechanics of solids (3) The Biomedical Engineering program from the Renaissance to the 1960s (3) 4–6. Electives: Three of the following courses: DNCE BC3200: Dance in film (3) offers a minor that consists of the CIEN E1201: Design of buildings, bridges, and DNCE BC3567: Dance of India (3) following six courses. Participation in the spacecraft (3) DNCE BC3570: Latin American and minor is subject to the approval of the ENME E3161: Fluid mechanics (4) Caribbean dance (3) major program adviser. ENME E3114: Exp mechanics of materials (4) DNCE BC3576: Dance criticism (3) ENME E3332: A first course in finite elements (3) DNCE BC3577: Performing the political (3) MECE E3414: Adv strength of materials (3) DNCE BC3578: Traditions of African- 1. BIOL UN2005: Introduction to biology, I (3) CIEN E3125: Structural design (3) American dance (3) 2. BIOL UN2006: Introduction to biology, II (3) CIEN E4241: Geotech eng fundamentals (3) 3–4. Performance/choreography: Two of the CIEE E3250: Hydrosystems engineering (3) 3. BMEN E3010: Biomedical engineering, I (3) following: CIEE E4163: Environ eng: wastewater (3) DNCE BC2563: Dance composition: form (3) 4. BMEN E3020: Biomedical engineering, II (3) CIEN E3129: Project mgmt for construction (3) DNCE BC2564: Dance composition: content (3) CIEN E4131: Prin of construction tech (3) 5. BMEN E4001: Quantitative physiology, I (3) DNCE BC2567: Music for dance (3) DNCE BC2580: Tap as an American art 6. BMEN E4002: Quantitative physiology, II (3) MINOR IN COMPUTER SCIENCE form (3) Students who pass the Computer DNCE BC3565: Composition: collaboration and the creative process (3) MINOR IN CHEMICAL Science Advanced Placement Exam A DNCE BC3601-3604: Rehearsal and ENGINEERING with a 4 or 5 will receive 3 points and performance in dance (1–3) Of the six courses required, at least exemption from COMS W1004. Taking 5. One elective three must have the CHEN, CHEE, or COMS W1007 is recommended but CHAP designator: not required for those students exempt MINOR IN EARTH AND from COMS W1004. Participation in 1. CHEN E2100: Intro to chemical engineering (3) the minor is subject to the approval of ENVIRONMENTAL 2. CHEE E3010: Prin of chemical engineering the major program adviser. For further ENGINEERING thermodynamics (3) information, please see the QuickGuide 1–3. Three of the following courses: or MSAE E3111: Thermodynamics, kinetic EAEE E3103: Energy, minerals, and mat syst (3) theory, and statistical mechanics (3) at cs.columbia.edu/education/undergrad/ CIEE E3255: Environmental control and or MECE E3301: Thermodynamics (3) seasguide. pollution reduction systems (3) or BMEN E4210: Thermodynamics of biological 1. COMS W1004: Intro to computer science and EAEE E4001: Industrial ecology of Earth res (3) systems (3) programming in Java (3) EAEE E4003: Intro to aquatic chemistry (3) 3. CHEN E3110: Transport phenomena, I (3) or COMS W1007: Honors intro to comp sci (3) EAEE E4004: Physical processing and recovery or EAEE E4900: Applied transport and 2. COMS W3134: Data structures in Java (3) of solids (3) chemical rate phenomena (3) or COMS W3137: Honors data structures and EAEE E4006: Field methods for environ eng (3) or MECE E3100: Intro to mech of fluids (3) algorithms (4) EAEE E4009: GIS for resource, environment, or ENME E3161: Fluid mechanics (4) and infrastructure management (3) or BMEN E3220: Fluid biomechanics (4) 3. COMS W3157: Advanced programming (4) EAEE E4150: Air pollution prevention and control (3) 4. CHEN E4230: Reaction kinetics and 4. COMS W3203: Discrete mathematics (3) EAEE E4160: Solids and hazardous waste reactor design (3) 5. COMS W3261: Comp science theory (3) management (3) 5–6. Two of the following courses: 6. CSEE W3827: Fund of computer systems (3) EAEE E4200: Prod of inorganic materials (3) Any 3000-level or higher BMCH, CHEN, CHAP, or a 4000-level COMS technical elective EAEE E4257: Environ data analysis and or CHEE course modeling (3) APMA E3101: Linear algebra (3) 7. APMA E2101 (or E3101): Intro to applied EAEE E4361: Econ of Earth res industries (3) APMA E3102: Partial differential equations (3) mathematics (Applied math I: linear algebra) (3) EACE E4560: Particle technology (3) BMEN E3320: Fluid biomechanics (3) or MATH UN2010 (or E2020): Linear BMEN E4001: Quantitative physiology, I (3) algebra (3) 4–6. Three of the following courses: BMEN E4002: Quantitative physiology, II (3) or STAT GU4001( or SIEO W3600): Intro to CHEE E3010: Prin of chemical engineering ELEN E3201: Circuit analysis (3.5) probability and statistics (3) thermodynamics (3) ELEN E3331: Electronic circuits (3) CHEE E3110: Transport phenomena, I (3) CIEN E3141: Soil mechanics (3) SIEO W3600: Intro to probability and statistics (4) MINOR IN DANCE CIEE E3250: Hydrosystems engineering (3) IEOR W4105: Probability (3) The dance minor consists of five IEOR W4106: Stochastic models (3) SIEO W3600: Intro to probability and statistics (4) 3-point courses. Please note that no

ENGINEERING 2017–2018 200 ECIA W4100: Mgmt and dev of water systems (3) ECON GU4457: Industrial organization of art, 3. CSEE W3827: Fund of computer systems (3) CIEE E4163: Environ eng: wastewater (3) entertainment and communications (3) 4. ELEN E3081 and ELEN E3082: EAEE E4190: Photovoltaic systems eng (3) ECON GU4465: Public economics (3) Electrical engineering labs (2) MECE E4211: Energy: sources and conv (3) ECON GU4480: Gender and applied CIEN E4250: Waste contain design and prac (3) economics (3) 5. ELEN E3801: Signals and systems (3.5) CHEE E4252: Intro to surface and colloid chem ECON GU4490: Economics of the Internet (3) 6. ELEN E3106: Solid-state dev and mat (3.5) (3) ECON GU4500: International trade (3) CIEE E4252: Environmental engineering (3) ECON GU4505: Int’l macroeconomics (3) or ELEN E3401: Electromagnetics (4) CIEE E4257: Groundwater contaminant ECON GU4615: Law and economics (3) Note: Not available to computer transport and remediation (3) ECON GU4625: Economics of the engineering majors CHEN E4410: Environmental control technology (3) environment (3) ECON GU4750: Globalization and its risks (3) MINOR IN ENGINEERING MINOR IN EAST ASIAN STUDIES Note: Electives may be taken only after the MECHANICS 1–5. Any two of the survey courses on completion of both UN3211 and UN3213, Chinese, Japanese, Korean, or Tibetan with the exception of UN2257, which may 1. ENME E3105: Mechanics (4) civilization (ASCE UN1359, UN1361, be taken after completion of UN1105. 2. ENME E3113: Mechanics of solids (3) UN1363, UN1365), plus three elective Some of the elective courses listed above courses dealing with East Asia. The have additional prerequisites. Courses 3. ENME E3161: Fluid mechanics (4) elective courses may be taken in may be taken only after the completion of or MECE E3100: Intro to mech of fluids (3) departments outside of East Asian all prerequisites. Please see the Columbia 4–6. Electives: Three of the following: Languages and Cultures. The minor does College bulletin for course descriptions and ENME E3106: Dynamics and vibrations (3) not include a language requirement. complete lists of prerequisites. However, one semester of an East Asian ENME E3114: Exp mechanics of materials (4) language class may be used to fulfill one or MECE E3414: Adv strength of materials (3) 7. Statistics: One of the following three of the three electives, as long as at least CIEN E3121: Structural analysis (3) probability and statistics options (course two semesters of that language have ENME E4202: Advanced mechanics (3) or sequence): been taken. Placement exams may not ENME E4113: Advanced mechanics of solids (3) a. SIEO W3600 (or STAT GU4001): Intro to be used in place of these courses. ENME E4114: Mech of fracture and fatigue (3) probability and statistics ENME E4214: Theory of plates and shells (3) b. IEOR E3658: Probablity and ENME E4215: Theory of vibrations (3) MINOR IN ECONOMICS E4307: Applied statistical models MECE E3301: Thermodynamics (3) c. STAT UN3203 (or GR5203): Probability 1. ECON UN1105: Principles of economics (4) theory and STAT UN3204 (or GR5204): 2. ECON UN3211: Intermediate microeconomics (3) Statistical inference MINOR IN ENGLISH AND COMPARATIVE LITERATURE 3. ECON UN3213: Intermediate macroeconomics Notes: (3) • The statistics course must be finished 1–5. Any five courses in the English before taking UN3412, and it is 4. ECON UN3412:Introduction to econometrics (3) Department with no distribution recommended that students take requirement. No speech courses, only one Note: UN1105 is a prerequisite for UN3211, UN3412 in the semester following the writing course as above and excluding statistics course. UN3213, and UN3412. Students must ENGL UN1010, may be taken; total 15 • Some courses done as part of the have completed Calculus I before taking points. UN3213, Calculus III before taking UN3211, economics minor may count toward and one of the introductory statistics fulfilling the School’s nontechnical MINOR IN ENTREPRENEURSHIP courses (see list) before taking UN3412. requirements. However, other courses, such as UN3412: Intro to econometrics, AND INNOVATION 5–6. Electives: Two of the following courses: may not be applied toward satisfaction Minimum: 15 points ECON UN2257: Global economy (3) of the nontechnical course requirements. 1–2. Required courses: ECON UN3025: Financial economics (3) To determine which economic class IEOR E2261: Accounting and finance (3) ECON UN3265: Econ of money and banking (3) can count toward the nontech elective and IEOR E4998: Managing technological ECON GU4020: Econ of uncertainty and info requirement, please consult the nontech innovation and entrepreneurship (3) (3) elective section of this bulletin for further ECON GU4211: Advanced microeconomics (3) details. 3–5. Electives: Three of the following courses: ECON GU4213: Advanced macroeconomics (3) • Students with AP credit for economics BIOT GU4180: Entrepreneurship in biotech (3) ECON GU4228: Urban economics (3) and an exemption for UN1105 may use BMEN E3998: Projects in biomedical eng (3) ECON GU4235: Historical foundations of the credit toward the minor. BUSI W3021: Marketing management (3) modern economics (3) • Transfer or study abroad credits may not CHEN E4020: Protection of industrial and ECON GU4251: Industrial organization (3) be applied to fulfill the requirements of intellectual property (3) ECON GU4280: Corporate finance (3) the economics minor. CIEN E4136: Global entrepreneurship in civil ECON GU4301: Economic growth engineering (3) and develop (3) MINOR IN ELECTRICAL COMS W4444: Program and problem solving (3) ECON GU4321: Economic development (3) COMS W4460: Principles of innovation in ENGINEERING ECON GU4370: Political economy (3) biotechnology (3) ECON GU4400: Labor economics (3) 1. ELEN E1201: Intro to electrical eng (3.5) ECON E4280: Corporate finance (3) ECON GU4412: Advanced econometrics (3) (May be replaced by a similar course or roughly IEOR E4003: Corporate finance for engineers (3) ECON GU4415: Game theory (3) equivalent experience) IEOR E4510: Project management (3) ECON GU4438: Economics of race in the IEOR E4550: Entrepreneurial business U.S. (3) 2. ELEN E3201: Circuit analysis (3.5) creation for engineers (3)

ENGINEERING 2017–2018 IEOR E4573: Design and agile project MINOR IN HISTORY 5–6. Electives: Two additional mechanical 201 management (3) engineering courses from either the above (Fall semester by application only) 1–5. Minimum 5 courses in the History list or the following (not all courses in this IEOR E4560: Lean LaunchPad (3) Department with no distribution or seminar list are given every year): (by application only with adviser approval) requirements. Transfer or study-abroad MECE E3401: Mechanics of machines (3) IEME E4310: The manufacturing enterprise (3) credits may not be applied. MECE E4058: Mechatronics and embedded microcomputer control (3) MINOR IN INDUSTRIAL MECE E4100: Mechanics of fluids (3) MINOR IN FRENCH ENGINEERING MECE E4211: Energy: sources and conversion (3) MECE E4212: Microelectromechanical sys (3) 1–2. FREN UN3333: Intro to literary study I (3) 1. IEOR E3658: Probability for engineers1 (4) MECE E4302: Advanced thermodynamics (3) and UN3334: Intro to literary study II (3) or STAT GU4001: Intro to probability and MECE E4404: Tribology (3) 3–5. Three additional courses in French statistics (3) MECE E4501: Geometrical modeling (3) beyond satisfaction of the language MECE E4502: Comp geometry for CAD/CAM (3) 2. IEOR E3608: Foundations of optimization (3) requirement EEME E4601: Digital control systems (3) 3. IEOR E3402: Production inventory planning MECE E4602: Intro to robotics (3) MINOR IN FRENCH AND and control (4) MECE E4604: Product design for manufact (3) MECE E4609: Computer-aided manufacturing (3) FRANCOPHONE STUDIES 4. IEOR E4003: Corporate finance for engineers (3) MECE E4610: Adv manufacturing processes (3) Required: 15 points beyond second-year French 5–6. Electives: Two IEOR courses of interest Note: Equivalent substitution courses and approved by a faculty adviser 1–2. FREN UN3420 and UN3421: Intro to French require the approval of the Mechanical and francophone studies, I and II (3, 3) Note: In addition to the required courses, Engineering Program Adviser. 3–5. Three additional courses in French students majoring in operations research beyond satisfaction of the language and its concentrations (EMS or FE) requirement minoring in industrial engineering must take MINOR IN MIDDLE EASTERN, three industrial engineering courses that SOUTH ASIAN, AND AFRICAN are not used to satisfy the requirements of MINOR IN GERMAN STUDIES their major. Required: 15 points beyond second-year German 1–5. Five courses, to be chosen with the approval 1 Preferred course. Class of 2018, 2019, and 2020 1. GERM UN3001 or 3002: Adv German, I or II (3) of the MESAAS Director of Undergraduate can take SIEO W3600 in place of IEOR E3658. 2. GERM UN3333: Intro to German literature (3) Studies; no elementary or intermediate language courses may be counted. 3. One of the period survey courses in MINOR IN MATERIALS SCIENCE German literature and culture, GERM AND ENGINEERING UN3442, UN3443, UN3444, UN3445 MINOR IN MUSIC 1–5. Any five MSAE E3000 or MSAE E4000- 1. MUSI UN2318-2319: Music theory, I and II (3, 3) 4–5. Two courses taken from any 3000/4000- level courses, excluding MSAE E3900 level German or CompLit-German courses (Undergraduate research), and excluding 2. MUSI UN1312-1313: Intro ear training (1) taught in German or English MSAE E3156, E3157 (Design project), and 3. MUSI UN2314: Ear training, I (1) excluding MSAE E4301 (Materials science MINOR IN GREEK OR LATIN laboratory). 4. One of the following courses: MUSI UN3128: History of Western music, I (3) 1–4. A minimum of 13 points in the chosen MUSI UN3129: History of Western music, II (3) language at the 1200 level or higher MINOR IN MECHANICAL 5–6. Any two electives at the 3000 or 4000 ENGINEERING 5. 3 points in ancient history of the level. See also the Engineering-approved appropriate civilization 1–4. Four of the following courses: nontechnical electives in music (page 12). MECE E3100: Intro to mechanics of fluids (3) Notes: MINOR IN HISPANIC STUDIES or ENME E3161: Fluid mechanics (4) • Students must successfully place out of or CHEN E3110: Transport phenomena, I (3) 1. SPAN UN3300: Adv language through content (3) MUSI UN1002: Fundamentals of music or EAEE E4900: App transport and (3.0 points). 2. SPAN UN3330: Intro to the study of Hispanic chemical rate phenomena (3) • Steps 4 and 5 must be completed cultures (3) ENME E3105: Mechanics (4) to fulfill the nontechnical elective MECE E3301: Thermodynamics (3) 3–4. SPAN UN3349 and UN3350: Hispanic requirement for graduation. or CHEE E3010: Principles of chemical cultures, I and II (3, 3) • Students are strongly encouraged to engineering thermodynamics (3) take HUMA UN1123: Masterpieces of 5. One additional 3000-level elective course or MSAE E3111: Thermodynamics, kinetic Western music (3.0 points) from the list theory, and statistical mechanics (3) in the Department of Latin American and of nontechnical electives. Iberian Cultures ENME E3113: Mechanics of solids (3) MECE E3408: Comp graphics and design (3) Note: Please see the director of MECE E3311: Heat transfer (3) MINOR IN OPERATIONS undergraduate studies in the Department MECE E3610: Materials and processes in RESEARCH of Latin American and Iberian Cultures for manufacturing (3) 1 more information and to declare the minor. MECE E3409: Machine design (3) 1. IEOR E3658: Probability for engineers (4) EEME E3601: Classical control systems (3) or STAT GU4001: Intro to probability and statistics (3)

ENGINEERING 2017–2018 202 2. IEOR E3106: Stochastic systems and I. PERCEPTION AND COGNITION • Students may, with permission of the applications (3) Courses numbered in the 2200s, 3200s, Director of Undergraduate Studies or 4200s. Also PSYC UN1420, UN1480, or in Statistics, substitute for courses. 3. IEOR E3608: Intro to math programming (4) UN1490 Students may count up to two courses 4. IEOR E3404: Simulation modeling and analysis toward both the Statistics minor and (4) another Engineering major. II. PSYCHOBIOLOGY AND NEUROSCIENCE 5–6. Electives: Two IEOR courses (6 pts) of MINOR IN SUSTAINABLE PSYC UN1010: Mind, brain, and behavior (3) interest and approved by a faculty adviser. ENGINEERING Courses numbered in the 2400s, 3400s, or IEOR E3402: Production-inventory planning 4400s; also PSYC UN1440 and control (3) is strongly recommended. Total of six courses from the following III. SOCIAL, PERSONALITY, AND ABNORMAL lists required with no substitutions Note In addition to the required courses, : Courses numbered in the 2600s, 3600s, or allowed: students majoring in industrial engineering 4600s; also PSYC UN1450 or UN1455 must take three operations research 1–4. Four of the following courses: courses that are not used to satisfy the EAEE E2002: Alternative energy sources (3) requirements of their major. MINOR IN RELIGION EAEE E2100: Better planet by design (3) CIEE E3260: Eng for developing comm (3) 1 1–5. Five courses (total 15 points), one of Preferred course. Class of 2018, 2019, and 2020 EAEE E3901: Environmental microbiology (3) can take SIEO W3600 in place of IEOR E3658. which must be at the 2000 level EAEE E4001: Industrial ecology (3) ECIA W4100: Mgmt and dev of water systems (3) MINOR IN SOCIOLOGY APPH E4130: Physics of solar energy (3) MINOR IN PHILOSOPHY EAEE E4190: Photovoltaic systems eng and 1–5. Any five courses in the Philosophy 1. SOCI UN1000: The social world (3) sustainability (3) MECE E4211: Energy sources and conversion (3) Department with no distribution 2. SOCI UN3000: Social theory (3) requirement; total 15 points. See also MECE E4312: Solar thermal engineering (3) the list of exceptions under Elective 3–5. Any two 2000-, 3000-, or 4000-level MECE E4314: Dynamics of green buildings (3) courses offered by the Department of EESC GU4404: Regional climate and climate Nontechnical Courses. Sociology; total 6 points impacts (3) Note: Please be aware that some 5. One of the following courses: philosophy courses may not count as MINOR IN STATISTICS ECON UN2257: Global economy (3) nontechnical electives. PLAN A4151: Found of urban economic 1. STAT UN1001: Intro to statistical reason (3) analysis (3) or UN1101: Intro to statistics (w/o calculus) (3) MINOR IN POLITICAL SCIENCE PLAN A4304: Intro to housing (3) or UN1201: Intro to statistics (w/calculus) (3) ECON UN4321: Economic development (3) 1–2. Two of the following courses: 2. STAT UN2102: App statistical computing (3) ECON GU4527: Econ org and develop of POLS UN1201: Intro to American govt and China (3) politics (3) 3. STAT UN2104: App categorical data anal. (3) PLAN A4579: Intro to environmental POLS UN1501: Intro to comparative politics (3) 4. STAT UN3105: Appl. statistical methods (3) planning (3) POLS UN1601: International politics (3) ECON GU4625: Economics of the 5. STAT UN3106: Applied data mining (3) 3–5. Any three courses in the Political Science environment (3) Department with no distribution requirement; 6. Any Statistics Department offering numbered 6. One of the following courses: total 9 points 5291 or above. POLS UN3212: Environmental politics (3) POLS UN3213: American urban politics (3) Notes: SOCI UN3235: Social movements (3) MINOR IN PSYCHOLOGY • The curriculum is designed for students SOCI UN3324: Global urbanism (3) seeking practical training in applied Minimum: 15 points statistics; students seeking a foundation 1. PSYC UN1001: The science of psychology (3) for advanced work in probability and statistics should consider substituting 2–5. Any four courses from, at a minimum, two UN3203, UN3204, UN3205, and of the three groups below: GR5207.

ENGINEERING 2017–2018 Interdisciplinary Courses and Courses in Other Divisions of the University 204 INTERDISCIPLINARY ENGINEERING COURSES

f the following courses, ENGI E4000x and y Professional development doctoral fieldwork for their corporate sponsor). The some may be requirements and leadership for engineers and applied doctoral student must be registered for this course during the same term as the fieldwork experience. for degree programs, and scientists O 0 pts. Professor Mak. others may be taken as electives. See Master of Science in Data Science PDL course aims to enhance and expand Candidates for the Master of Science in Data your departmental program of study Columbia Engineering graduate students' interper- Science are required to complete a minimum of or consult with an adviser for more sonal, professional, and leadership skills, through 30 graduate-level credits, which includes seven information. six modules, including (1) professional portfolio; required courses: Algorithms for data science, (2) communication skills; (3) business etiquette ENGI E1102x and y The art of engineering Machine learning for data science, Exploratory and networking; (4) leadership, followership, and 4 pts. Lect: 4. Professor Vallancourt. data analysis and visualization, Probability theory, teamwork; (5) life management; and (6) ethics Core requirement for all entering SEAS students. Statistical inference & modeling, Computer and integrity. Students build upon and enhance This course is a bridge between the science- systems for data science, and Capstone & ethics. interpersonal and intrapersonal skills to further dis- oriented, high school way of thinking and the A minimum of three elective courses are chosen tinguish themselves in classroom and career. engineering point of view. Fundamental concepts in consultation with the student's adviser should of math and science are reviewed and re-framed in ENGI W4100y Research to revenue be a technical nature, 4000-graduate level course an engineering context, with numerous examples 3 pts. Lect: 3. Professors Sia and Toubia. or higher that expands the student's expertise in of each concept drawn from all disciplines of An interschool course with Columbia Business data science. engineering represented at Columbia. Non- School that trains engineering and business Certification of Professional Achievement in technical issues of importance in professional students to identify and pursue innovation Data Sciences engineering practice such as ethics, engineering opportunities that rely on intellectual Graduate: Online delivery. project management, and societal impact are property coming out of academic research. Candidate for the Certification of Professional addressed. Lab fee: $350. Idea generation, market research, product Achievement in Data Sciences, a nondegree part- EEHS E3900y History of telecommunications: development, and financing. Teams develop time program, are required to complete a minimum from the telegraph to the internet and present business model for a technological of 12 credits, including four required courses: 3 pts. Lect: 3. invention. This course has limited enrollment Algorithms for data science, Probability and Historical development of telecommunications from by application and is open to advanced statistics, Machine learning for data science, and the telegraphy of the mid-1800s to the Internet undergraduate students and graduate students. Exploratory data analysis and visualization. at present. Included are the technologies of Consult with department for questions on telephony, radio, and computer communications. fulfillment of technical elective requirement. COSA E9800x and y Data Science Doctoral The coverage includes both the technologies ENGI E8000 Doctoral fieldwork Seminar themselves and the historical events that shaped, 1 pts. Professor Kachani and Associate Dean 1 pts. Professor Blei. and in turn were shaped by, the technologies. Simon. Prerequisite and Corequisite: Faculty approval. The historical development, both the general Fieldwork is integral to the academic preparation Course required for all Data Science Doctoral context and the particular events concerning and professional development of doctoral students. students. Others by faculty approval. The Data communications, is presented chronologically. The This course provides the academic framework for Science Doctoral Seminar is a 1-credit course social needs that elicited new technologies and fieldwork experience required for the student’s the consequences of their adoption are examined. that meets weekly. The purpose is to expose program of study. Fieldwork documentation the doctoral students to a breadth of ideas in Throughout the course, relevant scientific and and faculty advisor approval is required prior engineering principles are explained as needed. data science across disciplinary domains. The to registration. A final written report must be syllabus combines guest lectures from academic These include, among others, the concept and submitted. This course will count toward the effective use of spectrum, multiplexing to improve data scientists in the greater NYC area and degree program and cannot be taken for pass/ faculty at Columbia, along with a selection of capacity, digital coding, and networking principles. fail credit or audited. With approval from the related readings chosen by the guest lecturers. There are no prerequisites, and no prior scientific department chair or the doctoral program director, As part of this seminar, students will be expected or engineering knowledge is required. Engineering doctoral students can register for this course at to engage in active open discussion about the students may not count this course as a technical most twice. In rare situations, exceptions may be topics and readings covered in class, as well elective. granted by the Dean's Office to register for the as discuss how such topics apply to their own course more than twice (e.g., doctoral students respective research areas. funded by industrial grants who wish to perform

ENGINEERING 2017–2018 COURSES IN OTHER DIVISIONS OF THE UNIVERSITY 205

his listing of courses has been and recitation. Recommended as the introductory focuses on mechanistic organic chemistry selected with specific engineering biology course for biology and related majors, and involved in metabolic pathways. for premedical students. Fundamental principles of program requirements in mind. T biochemistry, molecular biology, and genetics. For information on these courses BUSINESS and additional courses offered by BIOL UN2006y Introductory biology, II: cell BUSI UN3021x and y Marketing management these departments, please consult biology, development, and physiology 4 pts. Professor Mowshowitz. 3 pts. Lect: 3. Professor Amano. the bulletins of Columbia College, the Prerequisite: EEEB W2001 or BIOL UN2005, or Designed to provide students with an School of Continuing Education, the the instructor’s permission. Lecture and recitation. understanding of the fundamental marketing School of General Studies, and the Recommended second term of biology for majors concepts and their application by business Graduate School of Arts and Sciences. in biology and related majors, and for premedical and non-business organizations. The goal students. Cellular biology and development; is to expose students to these concepts as physiology of cells and organisms. they are used in a wide variety of settings, APPLIED SCIENCE AND including consumer goods firms, manufacturing BIOL UN2501x or y Contemporary biology APPLIED MATHEMATICS and service industries, and small and large laboratory businesses. The course gives an overview 3 pts. Professor Hazen. Undergraduates are required to take of marketing strategy issues, elements of a Strongly recommended prerequisite or corequisite: APMA E2000 instead of MATH UN1201 market (company, customers, and competition), BIOL UN2005 or UN2401. Experiments focus on and UN1202 for major programs in the genetics and molecular biology, with an emphasis as well as the fundamental elements of the four-year course of study in the School on data analysis and experimental techniques. marketing mix (product, price, placement/ of Engineering and Applied Science. The class also includes a study of mammalian distribution, and promotion). Students in the Class of 2018, 2019, anatomy and histology. Each section is limited to and 2020 are allowed to count MATH 28 students. Lab fee: $150. CHEMISTRY UN1201 and UN1202 instead of APMA BIOC UN3501 Biochemistry: structure and Placement Exam E2000. Students in the Class of 2021 metabolism and beyond must participate in APMA 4 pts. Professor Stockwell. All students must take the placement E2000 to satisfy a portion of their basic Prerequisites: BIOL UN2005 or UN2006 exam during Orientation week. The mathematics and degree requirements. and one year of organic chemistry. Lecture, results of the placement exam are recitation, and discussion. Students wishing used to advise students which track to APMA E2000x and y Multivariable calculus for to cover the full range of modern biochemistry pursue. engineers and applied scientists should take both BIOC UN3501 and UN3512. 4 pts. Lect: 3. Professor Youngren. UN3501 covers subject matters in modern Differential and integral calculus of multiple Courses of Instruction biochemistry, including chemical biology and variables. Topics include partial differentiation; structural biology, discussing the structure and Pre-engineering students should optimization of functions of several variables; function of both proteins and small molecules refer to the First Year–Sophomore line, area, volume, and surface integrals; vector in biological systems. Proteins are the primary Program to determine the chemistry functions and vector calculus; theorems of Green, class of biological macromolecules and serve to Gauss, and Stokes; applications to selected requirements for admission to particular carry out most cellular functions. Small organic problems in engineering and applied science. Junior-Senior Programs. Special Offered through Columbia Engineering. molecules function in energy production and attention should be given to the creating building blocks for the components requirements for admission to chemical of cells and can also be used to perturb the engineering, biomedical engineering, BIOLOGICAL SCIENCES functions of proteins directly. The first half of the course covers protein structure, enzyme kinetics materials science and metallurgical BIOL UN2005x Introductory biology, I: and enzyme mechanism. The second half of the engineering, and other related fields. biochemistry, genetics, and molecular biology course explores how small molecules are used 4 pts. Professors Price and Mowshowitz. endogenously by living systems in metabolic Laboratory Fee Prerequisite: one year of college chemistry, or a and catabolic pathways; this part of the course strong high school chemistry background. Lecture The laboratory fee covers the cost of

ENGINEERING 2017–2018 206 nonreturnable items, chemicals, and theory of gases); binary collision model for and trains students in the execution and evaluation reasonable breakage. In addition, chemical reactions; chemical kinetics; acid-base of scientific data. The technique experiments in students may be charged for lab equilibria; thermochemistry (Thermodynamics the first half of the course (CHEM UN2495) teach I); spontaneous processes (Thermodynamics students to develop and master the required handouts and excessive breakage, for II); chemical bonding in polyatomic molecules. experimental skills to perform the challenging cleaning of equipment returned dirty, Recitation section required. synthesis experiments in the second semester. The and for checking out late. learning outcomes for this lab are the knowledge CHEM UN2045x-UN2046y Intensive organic and experimental skills associated with the most CHEM UN1403x-UN1404y General chemistry chemistry I and II (lecture) I and II important synthetic routes widely used in industrial 4 pts. Professors Breslow and Ng. and research environments. Attendance at the first 4 pts. Lect: 3.5. Members of the faculty. Prerequisites: A grade of 5 on the Chemistry Prerequisites: Concurrent registration in MATH lab lecture and laboratory session is mandatory. Advanced Placement exam and an acceptable Please note that CHEM UN2494 is the second part UN1101; for UN1404: CHEM UN1403. Preparation grade on the Department placement exam or equivalent to one year of high school chemistry is of a full year organic chemistry laboratory course. CHEM UN1604. Corequisite: CHEM UN1507. Students must register for the lab lecture section assumed, and concurrent registration in Calculus Premedical students may take CHEM UN2045, I. Students lacking such preparation should plan (CHEM UN2495), which corresponds to their lab UN2046, and UN2545 to meet the minimum section. Students must attend one lab lecture and independent study of chemistry over the summer requirements for admission to medical school. one lab section every other week. or take CHEM UN0001 before taking UN1403. This course covers the same material as UN1403: topics include stoichiometry, states of CHEM UN2443-UN2444 but is intended for CHEM UN2545x Intensive organic chemistry matter, nuclear properties, electronic structures students who have learned the principles laboratory of atoms, periodic properties, chemical bonding, of general chemistry in high school or have 3 pts. Lab: 3. Professor Ng. molecular geometry, introduction to quantum completed CHEM UN1604 in their first year Prerequisites: CHEM UN2045 and UN2046 mechanics and atomic theory, introduction to at Columbia. First year students enrolled and UN1507. Lab fee: $125. Intended for those organic and biological chemistry, solid state in CHEM UN2045-UN2046 are expected to students who have taken Intensive Organic and materials science, polymer science and enroll concurrently in CHEM UN1507. Although Chemistry for First-Year Students, CHEM UN2045- macromolecular structures and coordination CHEM UN 2045 and UN 2046 are separate UN2046 and who intend to major in Chemistry, chemistry. UN1404: topics include gases, courses, students are expected to take both Biochemistry, Chemical Physics, Environmental kinetic theory of gases, states of matter—liquids terms sequentially. Recitation section required. Chemistry. and solids, chemical equilibria, applications of equilibria, acids and bases, chemical CHEM UN2443x-UN2444y Organic chemistry I CHEM UN3079x-UN3080y Physical chemistry, thermodynamics, energy, enthalpy, entropy, free and II (lecture) I and II energy, periodic properties, chemical kinetics, 4 pts. Professors Campos, Cornish, Doubleday, 4 pts. Professor Kaufman. and electrochemistry. Although UN1403 and and Nuckolls. Prerequisites: PHYS UN1201-UN1202 is UN1404 are separate courses, students are Prerequisites: CHEM UN1403 or UN1404 or acceptable, PHYS UN1401-UN1402 is highly expected to take both terms sequentially. The UN1604, and UN1500. The principles of organic recommended, or the equivalent. Corequisite: order of presentation of topics may differ from chemistry. The structure and reactivity of organic CHEM UN3085-UN3086. Elementary but the order presented here, and from year to year. molecules are examined from the standpoint comprehensive treatment of the fundamental laws Corresponding recitation section required. of modern theories of chemistry. Topics include governing the behavior of individual atoms and stereochemistry, reactions of organic molecules, molecules and collections of them. UN3079: The CHEM UN1500x or y General chemistry mechanisms of organic reactions, syntheses and thermodynamics of chemical systems at equilibrium laboratory degradations of organic molecules, and techniques and the chemical kinetics of nonequilibrium systems. 3 pts. Lab: 3. Professors Hansen and Ulichny. of structure determination. Although UN2443 UN3080: The quantum mechanics of atoms and Corequisite: CHEM UN1403 or UN1404. Lab and UN2444 are separate courses, students molecules, the quantum statistical mechanics fee: $140. An introduction to basic techniques are expected to take both terms sequentially. of chemical systems, and the connection of of modern experimental chemistry, including Corresponding recitation section required. statistical mechanics to thermodynamics. Although quantitative procedures and chemical analysis. A CHEM UN3079 and UN 3080 are separate CHEM UN2493 Organic chemistry laboratory lab lecture section is also required for this course courses, students are expected to take both terms I (techniques) (UN1501). sequentially. Recitation section required. 1.5 pts. CHEM UN1507x or y Intensive general Corequisite: CHEM UN2495. Lab fee: $63. CHEM UN3085x-UN3086y Physical and chemistry laboratory Techniques of experimental organic chemistry, with analytical chemistry laboratory I and II 3 pts. Lab: 3. Professor Avila. emphasis on understanding fundamental principles 4 pts. Lab: 4. Professor Avila. Pre/corequisites: CHEM UN1604, UN2045, or underlying the experiments in methodology of Prerequisite: CHEM UN3085 is prerequisite UN2046. Lab fee: $140. An introduction to theory solving laboratory problems involving organic for UN3086. Corequisites: CHEM UN3079 for and practice of modern experimental chemistry in a modlecules. Attendance at the first lab lecture CHEM UN3085 and UN3080 for UN3080. Fee: contextual, student-centered collaborative learning and laboratory session is mandatory. Please note $125 per term. Techniques of experimental environment. This course differs from CHEM that CHEM UN2493 is the first part of a full year physical chemistry and instrumental analysis, UN1500 in its pedagogy and its emphasis on organic chemistry laboratory course. Students including vibrational, electronic, and laser instrumentation and methods. Students must also must register for the lab lecture section (CHEM spectrophotometry, electroanalytical methods, attend the compulsory mentoring session. Please UN2495), which corresponds to their lab section. calorimetry, reaction kinetics, hydrodynamic check the Directory of Classes for details. Students must attend one lab lecture and one lab methods, scanning probe microscopy, and CHEM UN1604x Intensive general chemistry section every other week. applications of computers to reduce experimental data, and computational chemistry. Students must (lecture) CHEM UN2494 Organic chemistry laboratory also attend compulsory mentoring session. 4 pts. Professor Brus. I (synthesis) Prerequisite: A grade of “B” or better in CHEM 1.5 pts. CHEM UN3098x or y Supervised independent UN1403 or UN1404 or acceptable performance Corequisite: CHEM UN2496. Must complete CHEM research on the Department placement exam. Corequisite: UN2493 before registering for UN2494. Lab fee: 4 pts. Lab: 4. Professor Gasperov. Calculus II. Topics include gases (kinetic $62. Introduces students to experimental design Prerequisite: Instructor's permission for entrance

ENGINEERING 2017–2018 and permission of the departmental representative the basic physical principles controlling the Enrollment limited to 20 students. General 207 for aggregate points in excess of 12 or less than 4. hazardous phenomena and develops simple introduction to fundamentals of remote sensing, Laboratory fee: $105 per term. This course may be quantitative methods for making scientifically electromagnetic radiation, sensors, interpretation, repeated for credit (see major and concentration reasoned assessments of the threats (to health quantitative image analysis and modeling. Example requirements). Individual research under the and wealth) posed by various events, processes, applications in the Earth and environmental sciences supervision of a member of the staff. Research and exposures. Discusses methods of risk are explored through the analysis of remote sensing areas include organic, physical, inorganic, mitigation and sociological, psychological, and imagery in a state-of-the-art visualization laboratory. analytical, and biological chemistry. economic aspects of risk control and management. Lab required. Discussion section required. CHEM UN3546y Advanced organic chemistry EESC GU4076y Geologic mapping laboratory EESC UN1600x Earth resources and 3 pts. Lect: 3. Professor Anders. 3 pts. Lab: 3. Professor Ng. sustainable development Prerequisite: Permission of instructor. Fieldwork Prerequisite: CHEM UN2545. Corequisite: CHEM 3 pts. Lect: 3. Professor Kelemen. on weekends in April and two weeks in mid-May, UN2444. Lab fee: $125. A project laboratory with Prerequisites: none. High school chemistry immediately following the end of examinations. emphasis on complex synthesis and advanced recommended. Survey of the origin and extent Enrollment limited. Estimated expense: $250. The techniques including qualitative organic analysis of mineral resources, fossil fuels, and industrial principles and practices of deciphering geologic and instrumentation. materials, that are nonrenewable, finite history through the observation of rocks in the resources, and the environmental consequences field, mapmaking, construction of geological cross- sections, and short written reports. Please be EARTH AND ENVIRONMENTAL of their extraction and use, using the textbook Earth Resources and the Environment, by James advised: graduating undergraduate seniors may SCIENCES Craig, David Vaughan and Brian Skinner. This have to miss graduation. Undergraduates in the four-year course course provides an overview but includes focus EESC GU4085x Geodynamics of study in the School of Engineering on topics of current societal relevance, including 3 pts. Lect: 3. Offered in alternate years. and Applied Science may take courses estimated reserves and extraction costs for Prerequisites: calculus, differential equations, numbered up to 4999 but may enter fossil fuels, geological storage of CO2, sources introductory physics. An introduction to how the courses of higher numbers only if and disposal methods for nuclear energy fuels, Earth and planets work. The focus is on physical sources and future for luxury goods such as gold processes that control plate tectonics and the and diamonds, and special, rare materials used in evolution of planetary interiors and surfaces; (1) the course is expressly included in consumer electronics (e.g., “Coltan,” mostly from analytical descriptions of these processes; weekly the prescribed curriculum or Congo) and in newly emerging technologies such physical model demonstrations. (2) special permission is obtained as superconducting magnets and rechargeable EESC GU4113x Introduction to mineralogy from the Department of Earth and batteries (e.g., heavy rare earth elements, mostly 4 pts. Professor Class Environmental Sciences. from China). Guest lectures from economists, Prerequisites: introductory geology or the commodity traders and resource geologists will equivalent, elementary college physics and provide “real world” input. Discussion session chemistry, or the instructor’s permission. EESC UN1011x Earth: origin, evolution, required. processes, future Elementary crystallography and crystal structures, 4 pts. Lect: 3. Lab: 1. Professor Maenza-Gmelch. EESC GU4001x Advanced general geology optical properties of minerals, mineral associations, Students who wish to take only the lectures should 4 pts. Lect: 3. Lab: 1. Professor Scholz. economic minerals. Laboratory: identification register for UN1411. What is the nature of our Prerequisites: one term of college-level calculus, of minerals in hand specimens and use of the planet and how did it form? From geochemical physics, and chemistry. A concentrated introduction petrographic microscope. Lab required. and geophysical perspectives we explore to the solid Earth, its interior, and near-surface EESC GU4230y Crustal deformation Earth’s internal structure, its dynamical character geology. Intended for students with good 3 pts. Lect: 3. Professor Holtzman. expressed in plate tectonics, and ask if its future backgrounds in the physical sciences but none in Prerequisites: introductory geology and one year of behavior can be known. Students who wish to take geology. Laboratory and field trips. calculus. Recommended preparation: higher levels only the lectures should register for UN1411. EESC GU4008x Introduction to atmospheric of mathematics. Introduction to the deformation EESC UN1030x Oceanography science processes in the Earth’s crust. Fundamental 3 pts. Lect: 3. Professor Hoenisch. 3 pts. Lect: 3. Professor Polvani. theories of stress and strain; rock behavior Explore the geology of the sea floor, understand Prerequisites: advanced calculus and general in both brittle and ductile fields; earthquake what drives ocean currents and how ocean physics, or the instructor’s permission. Basic processes; ductile deformation; large-scale crustal ecosystems operate. Case studies and discussions physical processes controlling atmospheric contractional and extensional events. centered on ocean-related issues facing society. structure: thermodynamics; radiation physics EESC GU4300x The Earth’s deep interior and radiative transfer; principles of atmospheric EESC UN1201y Environmental risks and 3 pts. Lect: 3. Offered in alternate years. dynamics; cloud processes; applications to Earth’s disasters Prerequisites: calculus, differential equations, atmospheric general circulation, climatic variations, 3 pts. Lect: 3. Offered in alternate years. one year of college physics, and EESC GU4950 and the atmospheres of the other planets. Prerequisites: high school science and math. or its equivalent. An introduction to properties First-years and sophomores will have priority. EESC GU4009x Chemical geology of the Earth’s mantle, fluid outer core, and solid An introduction to risks and hazards in the 4 pts. Offered in alternate years. inner core. Current knowledge of these features is environment. Different types of hazards are Prerequisite: physical chemistry or the instructor’s explored, using observations of seismology, heat analyzed and compared: natural disasters, such permission. Thermodynamics as applied to earth flow, gravity, and geomagnetism, plus information as tornados, earthquakes, and meteorite impacts; systems. on the Earth’s bulk composition. acute and chronic health effects caused by EESC GU4050x Global assessment and EESC GU4600x Earth resources and exposure to radiation and toxic substances such sustainable development as radon, asbestos, and arsenic; long-term societal monitoring using remote sensing 3 pts. Professor Small. 3 pts. Lect: 3. Professor Kelemen. effects due to environmental change, such as Prerequisite: Calculus I and Physics I and II. Prerequisites: none. High school chemistry sea level rise and global warming. Emphasizes

ENGINEERING 2017–2018 208 recommended. Survey of the origin and extent in mathematics, physics, and chemistry. Physical Preservation; the Graduate School of of mineral resources, fossil fuels, and industrial properties of seawater, water masses and their Business; and the Graduate School of materials, that are nonrenewable, finite resources, distribution, sea-air interaction influence on the ocean Arts and Sciences. and the environmental consequences of their structure, basic ocean circulation pattern, relation of extraction and use, using the textbook Earth diffusion and advection with respect to distribution COCI CC1101x-CC1102y Introduction to Resources and the Environment, by James Craig, of ocean properties, ocean tides and waves, contemporary civilization in the West David Vaughan and Brian Skinner. This course turbulence, and introduction to ocean dynamics. 4 pts. Lect: 4. Members of the faculty. provides an overview, but includes focus on topics Taught by members of the Departments of EESC GU4926y Principles of chemical of current societal relevance, including estimated Anthropology, Classics, English and Comparative oceanography reserves and extraction costs for fossil fuels, Literature, French, German, History, Middle East 3 pts. Lect: 3. Professor Anderson. geological storage of CO , sources and disposal and Asian Languages and Cultures, Philosophy, 2 Prerequisites: Instructor’s permission for students methods for nuclear energy fuels, sources and future Political Science, Religion, Slavic Languages, for luxury goods such as gold and diamonds, and without one year of chemistry. Course open to undergraduates with one year of chemistry. and Sociology; and members of the Society of special, rare materials used in consumer electronics Fellows. A study in their historical context of major (e.g., “Coltan,” mostly from Congo) and in newly Recommended preparation: a solid background in mathematics, physics, and chemistry. Factors contributions to the intellectual traditions that emerging technologies such as superconducting underpin contemporary civilization. Emphasis is magnets and rechargeable batteries (e.g., heavy rare controlling the concentration and distribution of dissolved chemical species within the sea. on the history of political, social, and philosophical earth elements, mostly from China). Guest lectures thought. Students are expected to write at least from economists, commodity traders and resource Application of tracer and natural radioisotope methods to large-scale mixing of the ocean, the three papers to complete two examinations, and to geologists will provide “real world” input. Required participate actively in class discussions. discussion and recitation sessions. geological record preserved in marine sediments, the role of ocean processes in the global carbon ECON UN1105x and y Principles of EESC GU4701y Introduction to igneous cycle, and biogeochemical processes influencing economics petrology the distribution and fate of elements in the ocean. 4 pts. Professors Gulati, O’Flaherty, Musatti, 4 pts. Offered in alternate years EESC GU4930y Earth’s oceans and Miller, and Vergate. Prerequisite: introductory geology or the Corequisites: ECON UN1155 recitation section equivalent. Recommended preparation: atmosphere with the same instructor. How a market economy EESC GU4113 and knowledge of chemistry. 3 pts. Lect: 3. Professor Gordon. determines the relative prices of goods, factors of Compositional characteristics of igneous and Recommended preparation: a good background production, and the allocation of resources and metamorphic rocks and how they can be used as in the physical sciences. Physical properties of the circumstances under which it does it efficiently. tools to investigate earth processes. Development water and air. Overview of the stratification and Why such an economy has fluctuations and how of igneous and metamorphic rocks in a plate- circulation of Earth’s oceans and atmosphere and they may be controlled. Recitation section required. tectonic framework. their governing processes; ocean-atmosphere interaction; resultant climate system; natural and ENGL CC1010x or y University writing EESC GU4885y The chemistry of continental anthropogenic forced climate change. 3 pts. Members of the faculty. waters EESC GU4947y Plate tectonics 3 pts. Lect: 3. Offered in alternate years. University Writing helps undergraduates engage 3 pts. Lect: 3. Professor Gaberly. Recommended preparation: a solid background in in the conversations that form our intellectual Prerequisite: A course in solid earth geology or basic chemistry. Introduction to geochemical cycles community. By reading and writing about scholarly geophysics. Prepares students for research and oral involving the atmosphere, land, and biosphere; and popular essays, students learn that writing is exams with cross-disciplinary analysis of the plate- chemistry of precipitation, weathering reactions, a process of continual refinement of ideas. Rather tectonic cycle. Driving forces and mantle convection, rivers, lakes, estuaries, and groundwaters; than approaching writing as an innate talent, this plate kinematics, magmatism, structure, thermal students are introduced to the use of major and course teaches writing as a learned skill. We give and chemical evolution of mid-ocean ridges and minor ions as tracers of chemical reactions and special attention to textual analysis, research, and subduction zones, continental rifts and collisions, biological processes that regulate the chemical revision practices. It offers themed sections, all of and hot spots. Includes literature readings of great composition of continental waters. which welcome students with no prior experience debates, and emphasizes integration of geophysical, studying the theme. Students interested in a EESC GU4924y Introduction to atmospheric geological and geochemical observations and particular theme should register for the section chemistry processes. within the specified range of section numbers. 3 pts. Lect: 3. Professor Fiore. EESC GU4949x Introduction to seismology Prerequisites: PHYS UN1201, CHEM UN1403, Global Core 3 pts. Lect: 3. Offered in alternate years. Calculus III, or equivalent or instructor’s The Global Core requirement asks students to Prerequisites: Solid Earth dynamics (UN3201 or permission. EESC UN2100 preferred. Physical engage directly with the variety of civilizations and equivalent), differential equations (APMA E3102, and chemical processes determining atmospheric the diversity of traditions that, along with the West, E4200, or equivalent). Methods and underpinnings composition and the implications for climate and have formed the world and continue to interact of seismology including seismogram analysis, regional air pollution. Atmospheric evolution and in it today. Courses in the Global Core typically elastic wafe propogation theory, earthquake sourde human influence; basics of greenhouse effect, explore the cultures of Africa, Asia, the Americas, characterization, instrumentation, inversion of photolysis, reaction kinetics; atmospheric transport and the Middle East in an historical context. These seismic data to infer Earth structure. of trace species; stratospheric ozone chemistry; courses are organized around a set of primary tropospheric hydrocarbon chemistry; oxidizing materials produced in these traditions and may power, nitrogen, oxygen, sulfur, carbon, mercury HUMANITIES AND SOCIAL draw from texts or other forms of media, as well cycles; chemistry-climate-biosphere interactions; SCIENCES as from oral sources or performance. Global Core aerosols, smog, acid rain. courses fall into two categories and can be, on For listings of additional courses of occasion, a hybrid of the two types: those with a EESC GU4925x Principles of physical interest to engineering students, consult comparative, multidisciplinary, or interdisciplinary oceanography the bulletins of Columbia College; the focus on specific cultures or civilizations, tracing 3 pts. Lect: 3. Professors Abernathey and Gordon. School of General Studies; the Graduate their existence across a significant span of time Recommended preparation: a solid background School of Architecture, Planning, and and may include Europe and the U.S.; and those

ENGINEERING 2017–2018 that address a common theme or set of analytic their level, not changing their program. of order one, systems of linear equations, second- 209 questions comparatively (and may include Europe They must, however, obtain the approval order equations, series solutions at regular and and the U.S.). The Global Core requirement of the new instructor and the Center for singular points, boundary value problems, selected applications. consists of courses that examine areas not the Student Advising before reporting to the primary focus of Literature, Humanities and Registrar. MATH UN3028y Partial differential equations Contemporary Civilization and that, like other Core 3 pts. Lect: 3. Professor Brendle. courses, are broadly introductory, interdisciplinary, MATH UN1101x or y Calculus, I Prerequisite: MATH UN3027 and UN2010 or and temporarily and/or spatially expansive. 3pts. Lect: 3. equivalent. Introduction to partial differential Prerequisite: Functions, limits, derivatives, HUMA CC1001x-CC1002y Masterpieces of equations. First-order equations. Linear second- introduction to integrals, or an understanding of Western literature and philosophy order equations, separation of variables, solution precalculus will be assumed. 4 pts. Lect: 4. Members of faculty. by series expansions. Boundary value problems. Taught by members of the Departments of MATH UN1102x or y Calculus, II MATH GU4032x Fourier analysis Classics, English and Comparative Literature, 3 pts. Lect: 3. 3 pts. Lect: 3. Professor Woit. French, German, Italian, Middle East and Asian Prerequisite: MATH UN1101 or equivalent. Prerequisites: three terms of calculus and linear Languages and Cultures, Philosophy, Religion, Methods of integration, applications of integral, algebra or four terms of calculus. Fourier series Slavic Languages, and Spanish; and members of Taylor’s theorem, infinite series. and integrals, discrete analogues, inversion the Society of Fellows in the Humanities. Major MATH UN1207x-UN1208y Honors math A-B and Poisson summation, formulae, convolution, works by over twenty authors, ranging in time, 4 pts. Lect and recit. Professors Gallagher, Heisenberg uncertainty principle. Stress on the theme, and genre from Homer to Virginia Woolf. Thaddeus, and Hansen. application of Fourier analysis to a wide range of Students are expected to write at least two papers, Prerequisite: Score of 5 on the Advanced disciplines. to complete two examinations each semester, and Placement BC calculus exam. The second term MATH GU4041x-GU4042y Introduction to to participate actively in class discussions. of this course may not be taken without the first. modern algebra I and II Multivariable calculus and linear algebra from a HUMA UN1121x or y Masterpieces of 3 pts. Lect: 3. Professors Friedman, Gallagher, rigorous point of view. Western art Harris, Khovanov, and Thaddeus. 3 pts. Lect: 3. Members of faculty. MATH UN2010 x or y Linear algebra The second term of this course may not be Discussion and analysis of the artistic qualities 3 pts. Lect: 3. Professors Bayer, Stein, and taken without the first. Prerequisites: MATH and significance of selected works of painting, Pinkham. UN1102-UN1202 and UN2010 or equivalent. sculpture, and architecture from the Parthenon in Prerequisite: MATH UN1201 or equivalent. Groups, homomorphisms, rings, ideals, fields, Athens to works of the 20th century. Matrices, vector spaces, linear transformations, polynominals, and field extensions, Galois theory. eigenvalues and eigenvectors, canonical forms, HUMA UN1123x or y Masterpieces of MATH GU4061x-GU4062y Introduction to applications. Western music modern analysis I and II 3 pts. Lect: 3. Members of faculty. MATH UN2030x or y Ordinary differential 3 pts. Lect: 3. Professors De Silva, Guo, Zhang, Popularly known as “Music Hum,” this course aims equations and Chang-Lora. to instill in students a basic comprehension of the 3 pts. Lect: 3. Professors Chang-Lara, Wang, and The second term of this course may not be taken many forms of the Western musical imagination. Barraquand. without the first. Prerequisite: MATH UN1202 or The course involves students actively in the Prerequisite: MATH UN1102-UN1201 or the equivalent and UN2010. Real numbers, metric process of critical listening, both in the classroom equivalent. Special differential equations of order spaces, elements of general topology. Continuous and in concerts. Although not a history of Western one. Linear differential equations with constant and and differentiable functions. Implicit functions. music, the course is taught in chronological variable coefficients. Systems of such equations. Integration, change of variables. Function spaces. format and includes masterpieces by Josquin Transform and series solution techniques. MATH GU4065x Honors complex variables Emphasis on applications. des Prez, Monteverdi, Bach, Handel, Mozart, 3 pts. Lect: 3. Professor Dubedat or Urban. Haydn, Beethoven, Verdi, Wagner, Schoenberg, MATH UN2500x or y Analysis and optimization Prerequisite: MATH UN1207 and UN1208, or Stravinsky, Louis Armstrong, Duke Ellington, and 3 pts. Lect: 3. Professors Halpern-Leistne and GU4061. A theoretical introduction to analytic Charles Parker, among others. Makisumi. functions. Holomorphic functions, harmonic Prerequisites: MATH UN1102-UN1201 or equivalent, functions, power series, Cauchy-Riemann MATHEMATICS and UN2010. Mathematical methods for economics. equations, Cauchy’s integral formula, poles, Quadratic forms, Hessian, implicit functions. Convex Laurent series, residue theorem. Other topics as Courses for First-Year Students sets, convex functions. Optimization, constrained time permits: elliptic functions, the gamma and Depending on the program, completion optimization, Kuhn-Tucker conditions. Elements of zeta functions, the Riemann mapping theorem, of APMA E2000 satisfies the basic the calculus of variations and optimal control. Riemann surfaces, Nevanlinna theory. mathematics requirement. Normally MATH UN3007y Complex variables students who have taken an AP Calculus 3 pts. Lect: 3. Professor Gallagher. PHYSICS course begin with either Calculus II or Prerequisite: MATH UN1202. An elementary The general four-term preengineering APMA E2000. Refer to the AP guidelines course in functions of a complex variable. physics sequence consists of PHYS on page 14 for placement information. Fundamental properties of the complex numbers, UN1401, UN1402, UN1403, and The sequence ends with MATH UN2030: differentiability, Cauchy-Riemann equations, UN1494 (laboratory); or PHYS UN1601, Ordinary differential equations. Cauchy integral theorem, Taylor and Laurent series, poles, and essential singularities. Residue UN1602, UN2601, and UN2699 Students who wish to transfer theorem and conformal mapping. (laboratory). from one calculus course to another are allowed to do so beyond the date MATH UN3027x Ordinary differential equations PHYS UN1018y Weapons of mass destruction specified on the Academic Calendar. 3 pts. Lect: 3. Professor Chang-Lara. 3 pts. Lect: 3. Professor Marka. Prerequisite: MATH UN1102-UN1201 or Prerequisites: high school science and math. They are considered to be adjusting equivalent. Corequisite: MATH UN2010. Equations A review of the history and environmental

ENGINEERING 2017–2018 210 consequences of nuclear, chemical, and biological Fundamental laws of mechanics, kinematics and energy physics, astrophysics, and cosmology. The weapons of mass destruction (WMD), of how dynamics, work and energy, rotational dynamics, ongoing Columbia research programs in these these weapons work, what they cost, how they oscillations, gravitation, fluids, introduction to fields are used as practical examples. The course have spread, how they might be used, how they special relativity and relativistic kinematics. The is preparatory for advanced work in physics and are currently controlled by international treaties course is preparatory for advanced work in physics related fields. and domestic legislation, and what issues of policy and related fields. and technology arise in current debates on WMD. PHYS UN3003x Mechanics What aspects of the manufacture of WMD are PHYS UN1602y Physics, II: thermodynamics, 3 pts. Lect: 2.5. Professor Parsons. easily addressed, and what aspects are technically electricity, and magnetism Prerequisites: General physics; differential challenging? It may be expected that current 3.5 pts. Lect: 2.5. Professor Humensky. and integral calculus. Newtonian mechanics, events/headlines will be discussed in class. Prerequisite: PHYS UN1601. Corequisite: oscillations and resonance, conservative forces MATH UN1201 or equivalent. Temperature and potential energy, central forces, noninertial PHYS UN1401x Introduction to mechanics and heat, gas laws, the first and second laws frames of reference, rigid body motion, an and thermodynamics of thermodynamics, kinetic theory of gases, introduction to Lagrange’s formulation of 3 pts. Lect: 2.5. Professors Zajc and Zelevinsky. electric fields, direct currents, magnetic fields, mechanics, coupled oscillators, and normal modes. Corequisite: MATH UN1101 or equivalent. alternating currents, electromagnetic waves. PHYS UN3007y Electricity and magnetism Fundamental laws of mechanics, kinematics and The course Is preparatory for advanced work in 3 pts. Lect: 2.5. Professor Pasupathy. dynamics, work and energy, rotational dynamics, physics and related fields. oscillations, gravitation, fluids, temperature Prerequisite: General physics; differential and and heat, gas laws, first and second laws of PHYS UN2601x Physics, III: classical and integral calculus. Electrostatics and magnetostatics, thermodynamics. quantum waves Laplace’s equation and boundary-value problems, 3.5 pts. Lect: 2.5. Professor Dodd. multipole expansions, dielectric and magnetic PHYS UN1402y Introduction to electricity, Prerequisite: PHYS UN1602 or UN1402. materials, Faraday’s law, AC circuits, Maxwell’s magnetism, and optics Corequisite: MATH UN1202 or equivalent. equations, Lorentz covariance, and special relativity. 3 pts. Lect: 2.5. Professors Dodd, Hughes, and Classical waves and the wave equation, Zelevinsky. PHYS UN3008x Electromagnetic waves and geometrical optics, interference and diffraction, Prerequisite: PHYS UN1401. Corequisite: MATH optics Fourier series and integrals, normal modes, UN1102 or equivalent. Electric fields, direct 3 pts. Lect: 2.5. Professor Johnson. wave-particle duality, the uncertainty principle, currents, magnetic fields, alternating currents, Prerequisite: PHYS UN3007. Maxwell’s equations basic principles of quantum mechanics, energy electromagnetic waves, polarization, geometrical and electromagnetic potentials, the wave levels, reflection and transmission coefficients, optics, interference and diffraction. equation, propagation of plane waves, reflection the harmonic oscillator. The course is preparatory and refraction, geometrical optics, transmission PHYS UN1403x Introduction to classical and for advanced work in physics and related fields. quantum waves lines, wave guides, resonant cavities, radiation, 3 pts. Lect: 2.5. Professor Rosen. PHYS UN2699y Experiments in classical and interference of waves, and diffraction. modern physics Prerequisite: PHYS UN1402. Corequisite: MATH PHYS UN3081x or y Intermediate laboratory 3 pts. Lab: 3. Professor Clark. UN1201 or equivalent. Classical waves and the work Prerequisites: PHYS UN1601 (or UN1401), wave equation, Fourier series and integrals, normal 2 pts. Lab: 2. Members of the faculty. UN1602 (or UN1402), and UN2601. Laboratory modes, wave-particle duality, the uncertainty Prerequisite: PHYS UN2601 or UN2802. Primarily work associated with the three prerequisite principle, basic principles of quantum mechanics, for junior and senior physics majors. Other lecture courses. Experiments in mechanics, energy levels, reflection and transmission majors require the instructor’s permission. May coefficients, applications to atomic physics. thermodynamics, electricity, magnetism, optics, be repeated for credit by performing different wave motion, atomic and nuclear physics. PHYS UN1493x Introduction to experimental experiments. The laboratory has 15 individual physics PHYS UN2801x-UN2802y Accelerated physics, experiments available, of which two are required 3 pts. Lab: 3. Members of the faculty. I and II per 2 points. Each experiment is chosen by Prerequisites: PHYS UN1401 and UN1402. 4.5 pts. Lect: 3.5. Rec: 1 hour weekly to be the student in consultation with the instructor. Laboratory work associated with the two arranged. Professors Mawhinney and Cole. Each section meets one afternoon per week, prerequisite lecture courses. Experiments Prerequisite: Advanced placement in physics with registration in each section limited by the in mechanics, thermodynamics, electricity, and mathematics, or equivalent, and instructor’s laboratory capacity. Experiments (classical and magnetism, optics, wave motion, atomic and permission. (A special placement meeting is held modern) cover topics in electricity, magnetism, nuclear physics. (Students cannot receive credit for during Orientation.) This accelerated two-semester optics, atomic physics, and nuclear physics. both PHYS UN1493 and UN1494.) sequence covers the subject matter of PHYS PHYS UN3083y Electronics laboratory UN1601, UN1602, and UN2601 and is intended PHYS UN1494y Introduction to experimental 3 pts. Lab: 3. Professor Parsons. for students who have an exceptionally strong physics Registration is limited to the capacity of the background in both physics and mathematics. The 3 pts. Lab: 3. Members of the faculty. laboratory. Corequisite or prerequisite: PHYS course is preparatory for advanced work in physics Prerequisites: PHYS UN1401 and UN1402. UN3003 or UN3007. A sequence of experiments in Laboratory work associated with the two and related fields. There is no accompanying solid-state electronics, with introductory lectures. prerequisite lecture courses. Experiments laboratory; however, students are encouraged to in mechanics, thermodynamics, electricity, take the intermediate laboratory, PHYS UN3081, in PHYS GU4003y Advanced mechanics magnetism, optics, wave motion, atomic and the following year. 3 pts. Lect: 2.5. Professor Cole. Prerequisites: Differential and integral calculus, nuclear physics. (Students cannot receive credit for PHYS UN3002y From quarks to the cosmos: differential equations, and PHYS UN3003 or both PHYS UN1493 and UN1494.) applications of modern physics equivalent. Lagrange’s formulation of mechanics, PHYS UN1601x Physics, I: mechanics and 3.5 pts. Lect: 3.5. Not offered in 2017–2018. calculus of variations and the Action Principle, relativity Prerequisite: PHYS UN2601 or UN2802. This Hamilton’s formulation of mechanics, rigid body 3.5 pts. Lect: 2.5. Professor Humensky. course reinforces basic ideas of modern physics motion, Euler angles, continuum mechanics, Corequisite: MATH UN1102 or equivalent. through applications to nuclear physics, high- Introduction to chaotic dynamics.

ENGINEERING 2017–2018 PHYS GU4018y Solid-state physics STATISTICS theory causality, sample survey design, multilevel 211 3 pts. Lect: 2.5. Professors Pinczuk and Uemura. Engineering students interested in models, generalized linear regression, generalized Prerequisites: PHYS GU4021 and GU4023, or estimating equations and overdispersion, survival advancing their studies in Statistics should equivalent. Introduction to solid-state physics: analysis including the Kaplan-Meier estimator, log- crystal structures, properties of periodic lattices, consult with a departmental adviser to rank statistics, and the Cox proportional hazards electrons in metals, band structure, transport determine the most appropriate courses regression model. Power calculations and proposal properties, semiconductors, magnetism, and for their interests. and report writing will be discussed. superconductivity. STAT UN2103x Applied linear regression STAT UN3106y Applied data mining PHYS GU4019x Mathematical methods of analysis 3 pts. Professor Young. physics 3 pts. Professor Young. Prerequisite: STAT UN2103. Students without 3 pts. Lect: 3. Professor Metzger. Prerequisite: An introductory course in statistics programming experience in R might find STAT Prerequisites: Differential and integral calculus; (STAT UN1101 is recommended). Students without UN2102 very helpful. Data mining is a dynamic linear algebra; PHYS UN3003 and UN3007 or programming experience in R might find STAT and fast growing field at the interface of Statistics instructor’s permission. Presents a wide variety UN2102 very helpful. Develops critical thinking and Computer Science. The emergence of massive of mathematical ideas and techniques used in and data analysis skills for regression analysis in datasets containing millions or even billions of the study of physical systems. Topics include science and policy settings. Simple and multiple observations provides the primary impetus for the ordinary and partial differential equations, linear regression, nonlinear and logistic models, field. Such datasets arise, for instance, in large- generalized functions, integral transforms, random-effects models, penalized regression scale retailing, telecommunications, astronomy, Green’s functions, nonlinear equations, methods. Implementation in a statistical package. computational and statistical challenges. This chaos and solitons, Hilbert space and linear Optional computer-lab sessions. Emphasis on course will provide an overview of current practice operators, Feynman path integrals, Riemannian real-world examples and on planning, proposing, in data mining. Specific topics covered include manifolds, tensor analysis, probability and implementing, and reporting. databases and data warehousing, exploratory data statistics. Discussion of applications to classical analysis and visualization, descriptive modeling, mechanics, fluid dynamics, electromagnetism, STAT UN2105x Statistical applications and predictive modeling, pattern and rule discovery, plasma physics, quantum mechanics, and case studies text mining, Bayesian data mining, and causal general relativity. 3 pts. Instructor to be announced. inference. The use of statistical software will be Prerequisite: STAT UN2104. A sample of topics emphasized. PHYS GU4021x-GU4022y Quantum and application areas in applied statistics. mechanics, I and II Topic areas may include Markov processes and STAT GU4001x and y Introduction to 3 pts. Lect: 2.5. Professor Hughes. queuing theory; meta-analysis of clinical trial probability and statistics Prerequisite: PHYS UN2601 or UN2802, or research; receiver-operator curves in medical 3 pts. Members of the faculty. equivalent. Formulation of quantum mechanics diagnosis; spatial statistics with applications in Prerequisites: MATH UN1101 and UN1102 in terms of state vectors and linear operators, geology, astronomy, and epidemiology; multiple or equivalent. A calculus-based tour of the three-dimensional spherically symmetric comparisons in bioinformatics; causal modeling fundamentals of probability theory and statistical potentials, theory of angular momentum and with missing data; statistical methods in genetic inference. Probabilistic models, random variables, spin, time-independent and time-dependent epidemiology; stochastic analysis of neural spike useful distributions, conditioning, expectations, perturbation theory, scattering theory, and identical train data; graphical models for computer and laws of large numbers, central limit theorem, point particles and the exclusion principle. Methods social network data. and confidence interval estimation, hypothesis of approximation. Multielectron atoms. Selected tests, linear regression. This course replaces SIEO phenomena from atomic physics, nuclear physics, STAT UN3103x Mathematical methods for W4150. and elementary particle physics are described statistics STAT GU4203x and y Probability theory and then interpreted using quantum mechanical 6 pts. Professor Hannah. 3 pts. Professors Lo and Wang. models. Prerequisite: MATH UN1101 or instructor’s permission. A fast-paced coverage of those aspects Prerequisites: MATH UN1101 and UN1102 or PHYS GU4023x Thermal and statistical of the differential and integral calculus of one equivalent. An introductory course (STAT UN1201) physics and several variables and of the linear algebra is strongly recommended. A calculus-based 3 pts. Lect: 2.5. Professor Denef. required for the core courses in the Statistics major. introduction to probability theory. A quick review of Pre/Corequisite: PHYS GU4021 or equivalent. The mathematical topics are integrated with an multivariate calculus is provided. Topics covered Thermodynamics, kinetic theory, and methods introduction to computing. Students seeking more include random variables, conditional probability, of statistical mechanics; energy and entropy; comprehensive background should replace this expectation, independence, Bayes’ rule, important Boltzmann, Fermi, and Bose distributions; ideal course with MATH UN1102 and UN2010, and any distributions, joint distributions, moment generating and real gases; blackbody radiation; chemical COMS course numbered from W1003 to W1009. functions, central limit theorem, laws of large equilibrium; phase transitions; ferromagnetism. numbers and Markov’s inequality. STAT UN3105y Applied statistical methods PHYS GU4040x Introduction to general 3 pts. Professors Landwehr and Whalen. STAT GU4204x and y Statistical inference relativity Prerequisite: At least one, and preferably both, 3 pts. Professors Sobel and Young. 3 pts. Lect: 2.5. of STAT UN2103 and UN2104 are strongly Prerequisite: STAT GU4203. At least one semester Prerequisites: PHYS UN3003 and UN3007, or recommended. Students without programming of Calculus is required; two or three semesters equivalent. Tensor algebra, tensor analysis, experience in R might find STAT UN2102 very are strongly recommended. Calculus-based introduction to Riemann geometry. Motion of helpful. Intended to give students practical introduction to the theory of statistics. Useful particles, fluid, and fields in curved spacetime. experience with statistical methods beyond distributions, law of large numbers and central Einstein equation. Schwarzschild solution; test- linear regression and categorical data analysis. limit theorem, point estimation, hypothesis testing, particle orbits and light bending. Introduction to The focus will be on understanding the uses confidence intervals maximum likelihood, likelihood black holes, gravitational waves, and cosmologi- and limitations of models, not the mathematical ratio tests, nonparametric procedures, theory of cal models. foundations for the methods. Topics that may be least squares, and analysis of variance. covered include random and mixed-effects models, STAT GU4205x Linear regression models classical nonparametric techniques, the statistical 3 pts. Professors Neath, Wu, Liu, and Polak.

ENGINEERING 2017–2018 212 Prerequisites: STAT GU4204 or equivalent and STAT GU4234x Sample surveys Prerequisite: STAT GU4205. At least one Statistics a course in linear algebra. Theory and practice 3 pts. Professor Neath. course between GU4221 and GU4261. This of regression analysis. Simple and multiple Prerequisite: STAT GU4204 of the equivalent. is a course on getting the most out of data. regression, testing, estimation, prediction, and Introductory course on the design and analysis The emphasis will be on hands-on experience, confidence procedures, modeling, regression of sample surveys. How sample surveys are involving case studies with real data and using diagnostics and plots, polynomial regression, conducted, why the designs are used, how to common statistical packages. The course covers, colinearity and confounding, model selection, analyze survey results, and how to derive from at a very high level, exploratory data analysis, geometry of least squares. Extensive use of the first principles the standard results and their model formulation, goodness of fit testing, and computer to analyze data. generalizations. Examples from public health, other standard and nonstandard statistical social work, opinion polling, and other topics of procedures, including linear regression, analysis of STAT GU4207x and y Elementary stochastic interest. variance, nonlinear regression, generalized linear processes models, survival analysis, time series analysis, 3 pts. Professors Brown and Wang. STAT GU4261y Statistical methods in finance and modern regression methods. Students will be Prerequisite: STAT GU4203 and two, preferably 3 pts. Professors ElBarmi, Wang, and Ying. expected to propose a data set of their choice for three, semesters of calculus. Review of elements Prerequisite: STAT GU4204 or the equivalent. A use as case study material. of probability theory. Poisson processes. Renewal fast-paced introduction to statistical methods used theory. Wald’s equation. Introduction to discrete in quantitative finance. Financial applications and STAT GR5242x Data mining and continuous time Markov chains. Applications statistical methodologies are intertwined in all 3 pts. Professors Mazumder, Motta, and to queueing theory, inventory models, branching lectures. Topics include regression analysis and Rabinowitz. processes. applications to the Capital Asset Pricing Model and Prerequisite: COMS W1003, W1004, W1005, multifactor pricing models, principal components W1007, or the equivalent. Corequisites: Either STAT GU4221x and y Time series analysis and multivariate analysis, smoothing techniques STAT UN3203 or GR5203, and either STAT 3 pts. Professors Safikhani, Wu, and Wang. and estimation of yield curves statistical methods UN3204 or GR5204. Data Mining is a dynamic and Prerequisite: STAT GU4205 or equivalent. Least for financial time series, value at risk, term fast growing field at the interface of Statistics and squares smoothing and prediction, linear systems, structure models and fixed income research, and Computer Science. The emergence of massive Fourier analysis, and spectral estimation. Impulse estimation and modeling of volatilities. Hands-on datasets containing millions or even billions of response and transfer function. Fourier series, the experience with financial data. observations provides the primary impetus for the fast Fourier transform, autocorrelation function, and field. Such datasets arise, for instance, in large- spectral density. Univariate Box-Jenkins modeling STAT GU4262y Stochastic processes for scale retailing, telecommunications, astronomy, and forecasting. Emphasis on applications. finance computational and statistical challenges. This Examples from the physical sciences, social 3 pts. Professor Rios. course will provide an overview of current sciences, and business. Computing is an integral Prerequisite: STAT GU4203. STAT GU4207 is research in data mining and will be suitable for part of the course. recommended. A careful review of the concept graduate students from many disciplines. Specific of stochastic process as a model of random STAT GU4222y Nonparametric statistics topics covered with include databases and data phenomena evolving through time and of 3 pts. Professor Polak. warehousing, exploratory data analysis and conditional expectation, basic Markov process Prerequisite: STAT UN3204 or the equivalent. visualization, descriptive modeling, predictive theory, and the exponential distribution. Marked Statistical inference without parametric model modeling, pattern and rule discovery, text mining, point processes and their compensators, beginning assumption. Hypothesis testing using ranks, Bayesian data mining, and causal inference. with Poisson processes, and proceeding through permutations, and order statistics. Nonparametric general marked point processes. The use of STAT GR5703x Statistical inference and analogs of analysis of variance. Nonparametric compensators will be justified by the Doob- modeling regression, smoothing and model selection. Meyer decomposition theorem, and as such it 3 pts. Professors Hannah. STAT GU4231y Survival analysis will connect the theory to martingales. Markov Prerequisites: Working knowledge of calculus and 3 pts. Professor Shnaidman. processes will enter to provide a description of linear algebra (vectors and matrics), and STAT Prerequisite: STAT GU4205 or the equivalent. sufficient conditions for the compensators to have GR5203 or equivalent. Fundamentals of statistical Survival distributions, types of censored absolutely continuous paths (and as such, have inference and testing, and introduction of statistical data, estimation for various survival models, "hazard rates"). Applications to survival analysis modeling. Focuses on inference and testing, nonparametric estimation of survival distributions, and, especially, to mathematical finance, including covering topics such as maximum likelihood the proportional hazard and accelerated lifetime default and bankruptcy models. Cox process estimates, hypothesis testing, likelihood ratio test, models for regression analysis with failure-time construction. Bayesian inference, etc. Introduction to statistical data. Extensive use of the computer. modeling via introductory lectures on linear STAT GU4281x Theory of interest regression models, generalized linear regression 3 pts. Professor Zhang. STAT GU4232y Generalized linear models models, nonparametric regression, and statistical Prerequisite: MATH UN1101 or equivalent. 3 pts. Professor Sobel. computing. Real-data examples used in lecture Introduction to the mathematical theory of interest Prerequisite: STAT GU4205 of the equivalent. discussion and homework problems. Provides as well as the elements of economic and financial Statistical methods for rates and proportions, foundation for other courses in machine learning, theory of interest. Topics include rates of interest ordered and nominal categorical responses, data mining, and visualization. contingency tables, odds-ratios, exact inference, and discount; simple, compound, real, nominal, logistic regression, Poisson regression, generalized effective, dollar (time)-weighted; present, current, linear models. future value; discount function; annuities; stocks and other instruments; definitions of key terms STAT GU4233x Multilevel models of modern financial analysis; yield curves; spot 3 pts. Not offered in 2017-2018. (forward) rates; duration; immunization; and short Prerequisites: STAT GU4205. Theory and sales. The course will cover determining equivalent practice, including model-checking, for random measures of interest, discounting, accumulating, and mixed-effects models (also called hierarchical, determining yield rates, and amortization. multilevel models). Extensive use of the computer to analyze data. STAT GU4291x and y Advanced data analysis 3 pts. Professors Alemayehu and Liu.

ENGINEERING 2017–2018 Campus and Student Life 214 CAMPUS LIFE

he Fu Foundation School JAMES H. AND CHRISTINE Every undergraduate is assigned of Engineering and Applied TURK BERICK CENTER FOR an adviser from the Berick Center for T Science attracts and admits an STUDENT ADVISING Student Advising for the duration of exceptionally interesting, diverse, and 403 Lerner Hall, MC 1201 his or her undergraduate career. Each multicultural group of students, and Phone: 212-854-6378 matriculating student is assigned to it takes steps to provide a campus Email: [email protected] an advising dean, who is a liaison to environment that promotes the cc-seas.columbia.edu/csa the department the student indicated continued expansion of each student’s as his or her first interest on the ideas and perspectives. The James H. and Christine Turk Berick Columbia application. When a student This begins within the residence Center for Student Advising (CSA) declares a major, a faculty member is halls, in which nearly all first-year reflects the mission of the University also appointed to advise him or her undergraduate students live. The in striving to support and challenge for the next two years. Depending on University assigns rooms to both the intellectual and personal growth their chosen major, students may be Engineering and Columbia College of its undergraduate students and by assigned to a new advising dean who undergraduate students, ensuring that creating a developmental, diverse, and is a CSA liaison to their department. all students will live either with or near open learning environment. Individually Advising deans regularly refer students a student attending the other program. and collaboratively, each advising dean: to their academic departments to Once students have moved into their receive expert advice about their • provides individual and group new campus home, they will find engineering course selections. academic advisement, exploration, themselves part of a residential system and counseling that offers undergraduates a network Preprofessional Advising • provides information on of social and academic support (more Preprofessional Advising is a specialized preprofessional studies, major information about the residence halls advising unit within the James H. and declaration and completion, as well as can be found in the chapter “Housing Christine Turk Berick Center for Student various leadership, career, graduate and Residence Life” in this bulletin). Advising. It is dedicated to providing school, and research opportunities In addition to robust residential information and guidance to students • designs and facilitates programming offerings, a blend of academic, who plan a career in law or the health to meet the unique developmental educational, social, and cocurricular professions, through individual advising, needs of each class and to enhance activities enhances the Columbia workshops, and other events related community among students, faculty, experience through integrated efforts to professions of law and health. and administrators of numerous units including the Preprofessional advisers work closely • interprets and disseminates Berick Center for Student Advising, with other CSA advisers to support information regarding University Undergraduate Student Life, Parent students during their undergraduate polices, procedures, resources, and and Family Programs, and the Office program of study. They also provide programs of Student Conduct and Community extensive individualized support to • educates and empowers students to Standards. students and alumni through their take responsibility in making informed While the School is large enough to application process to professional decisions support a wide variety of programs, it is schools. • refers students to additional campus also small enough to promote the close resources interaction among students, faculty, and administration that has created a strong sense of community on campus.

ENGINEERING 2017–2018 UNDERGRADUATE STUDENT sophomores, juniors, and seniors to students may visit cc-seas.columbia. 215 LIFE live together clustered in the Living edu/orientation for additional information The Student Life team works to foster a Learning Center (LLC) housed in on NSOP. vibrant and welcoming undergraduate Hartley and Wallach Halls. This initiative community through organizational seeks to bridge the academic and Student Organizations advising, leadership development, cocurricular experience for students and Programs and activities at Columbia advocacy, diversity education, encourages and supports engineers are shaped primarily by students civic engagement, and community with entrepreneurial ideas. Mentorship who assume leadership and programming. The team includes between students, connection among volunteer positions in hundreds of Multicultural Affairs, Residential Life, the class years, and alumni interaction organizations across the campus. The and Student Engagement. A wide array are the foundations for the success of Engineering Student Council (ESC) of student organizations addresses the program. and its associated class councils both student interests and professional are the elected representative body concerns, including the arts, politics, Student Engagement of undergraduates at Columbia identity, culture, and religion. Joining Student Engagement is committed Engineering. ESC represents student such groups offers an exciting and to building a strong sense of campus interests on committees and projects dynamic opportunity to develop community by helping students addressing a wide range of issues facing leadership skills that will serve students enhance their leadership skills, engage the Columbia community and help well throughout their lives. in their communities, and explore the shape the quality of life for Columbia cocurricular opportunities available at students. Multicultural Affairs Columbia University. Working in conjunction with the Multicultural Affairs is devoted to This unit supports many of the Student Council, the Activities Board promoting a just society and explores student organizations on campus and at Columbia (ABC), Student Governing issues of interculturalism and diversity aids them in meeting the objectives Board (SGB), InterGreek Council (IGC), within and beyond the Columbia of their student group or organization. Community Impact (CI), Club Sports, community. By promoting forums that Staff will assist students who are and Interschool Governing Board address diversity issues, self-discovery looking for advisement on running an (IGB) oversee the management and takes place along with a greater organization, planning an event, sorting funding of more than 500 student awareness and appreciation of cultural their organization’s financial records, organizations. history within and between communities or starting a student group. They The ABC provides governance on campus. Multicultural Affairs are there to guide students through for recognized student organizations, endeavors to empower students, faculty, formal University processes, help them including cultural organizations, and staff with the tools to be able to navigate Columbia’s resources, or simply performance-based and theatrical successfully navigate their environments brainstorm new ideas with students. groups, media and publications and thus be able to positively change groups, competition and special and impact the community at large. Undergraduate Orientation interests groups and preprofessional All new students are required to organizations and societies. The Residential Life participate in an orientation program preprofessional organizations and Residential Life strives to cultivate an that is designed to acquaint them with societies are of special interest to atmosphere of learning and development the University and its traditions, the engineering students. These societies that extends beyond the classroom. administration and faculty of The Fu reflect the range of academic The residential life staff actively works Foundation School of Engineering and disciplines and interests to be found with students to shape a residential Applied Science, upperclass students, among students and include the community that supports individual and New York City. The New Student National Society of Black Engineers, expression and collective responsibility. Orientation Program (NSOP) for new the Society of Women Engineers, Working alongside a team of professional undergraduate students begins the the American Institute of Aeronautics and graduate staff, undergraduate week prior to the start of the fall and Astronautics, and the Biomedical Resident Advisers (RAs) live on the semester. Engineering Society, just to name a few. floor of every residence hall and serve NSOP assists all new students The SGB provides governance as role models and mentors for their with the transition to college life, both for recognized student organizations residents. RAs serve as the front line of academically and socially. Scheduled that are faith-based, spiritual, political, a layered on-call system and are trained into the program are information activist, and humanitarian and to respond to the variety of issues that sessions and opportunities to meet with that encourage open interreligious emerge in community life. Fraternity academic advisers. Through large group and political dialogue at Columbia and Sorority Life is recognized within programs and small group activities, University’s Morningside campus. The Residential Life. students will be introduced to faculty IGB recognizes student organizations Begun in fall 2006, Res. Inc. allows members, deans, resident advisers, whose membership spans across the Engineering and College first-years, and other students. Undergraduate various undergraduate and graduate schools.

ENGINEERING 2017–2018 216 For more information on any religious, cultural, academic, athletic, Chaplain also fosters learning through programs within Undergraduate political, literary, professional, public spiritual, ethical, religious, political, Student Life, refer to our website: service, and other organizations. At and cultural exchanges and hosts https://www.cc-seas.columbia.edu/ SEAS, graduate students are encour- programs on matters of justice, faith, studentlife aged to become active members of the and spirituality. Through these and Engineering Graduate Student Council other means, the Office of the University (EGSC). The EGSC is a recognized Chaplain cultivates interfaith and OFFICE OF GRADUATE group that consists of representatives intercultural awareness. STUDENT AFFAIRS from each of the nine academic depart- The University Chaplain is available The Office of Graduate Student ments at SEAS. The objectives of the for confidential pastoral counseling to Affairs at The Fu Foundation School EGSC are to foster interaction among individuals, couples, and families in the of Engineering and Applied Science graduate engineering students, to serve Columbia University community. The is integral to the School’s teaching, as a voice for graduate engineering stu- Office of the University Chaplain may research, and service mission and works dents, and to sponsor social and educa- also assist with private ceremonies such to enhance the educational opportuni- tional events of interest to the graduate as weddings, christenings, and memorial ties available to students. This office engineering community. services. We warmly welcome your provides leadership for the integration interest, questions, and participation. of educational programs and services Graduate Judicial Affairs For more information, please call that enhance recruitment, retention, and The Office of Graduate Student Affairs the Earl Hall Center at 212-854-1474 or quality of campus life for graduate stu- is responsible for assisting graduate 212-854-6242 or visit columbia.edu dents at Columbia Engineering. It strives students with upholding academic /cu/earl. to demonstrate sensitivity and concern and community standards. The office in addressing the needs of the School’s provides mandatory academic integrity population. The office is dedicated to THE OFFICE OF UNIVERSITY training for graduate students and is providing service to prospective, new, LIFE responsible for the Dean’s Discipline and continuing students pursuing a The mission of the Office of University process. graduate education in engineering or Life is to further the academic and applied science. community experience of students, STUDENT CONDUCT AND faculty, and staff at Columbia. Graduate Orientation COMMUNITY STANDARDS Throughout the academic year, this All new graduate students participate in Student Conduct and Community office in collaboration with other the New Graduate Student Orientation Standards strives to effect change Columbia student life offices and program. During this weeklong program, and promote integrity, accountability, academic departments will sponsor new graduate students learn about vari- and respect in the Columbia University programming and other required ous School and University resources, community. Working with students, initiatives to achieve this mission. policies and procedures, and other faculty, and other community partners, All Columbia students are essential information to assist them with SCCS thoroughly investigates and encouraged to participate in required their transition to the graduate program. resolves incidents of academic, Office of University Life initiatives. Orientation for new graduate students behavioral, and gender-based However, new students must participate begins in late August. misconduct through a collaborative, in and complete the Sexual Respect In addition to providing information educational, and relfective process and Community Citizenship Initiative and on university resources and policies, guided by established values: Integrity; the pre-arrival or postorientation tutorial. students engage in cultural, social, Accountability; Education; and Respect. For more information, visit universitylife. and professional networking activities. columbia.edu. Through these activities graduate OFFICE OF THE students are encouraged to connect UNIVERSITY CHAPLAIN LERNER HALL with their peers, acclimate to the Lerner Hall is dedicated to student campus and New York City as well as Columbia is home to a community life at Columbia University. A develop their professional portfolios. of scholars, students, and staff from 225,000-square-foot facility located The Office of Graduate Student Affairs many different religious backgrounds. on the southwest corner of campus, strongly believes that orientation serves The Office of the University Chaplain Lerner Hall was designed by Bernard as a vehicle in onboarding our graduate ministers to their individual faiths and Tschumi, the former Dean of Columbia’s students into an active and engaging supports individual spirituality, while Graduate School of Architecture, student life experience at Columbia. promoting interreligious understanding. The University Chaplain oversees Planning and Preservation. The building features a glass facade and ramps to Graduate Student Organizations the work of the United Campus Ministries—a fellowship of more than offer those within Lerner scenic views Columbia University graduate students twenty religious life advisers representing of campus and to allow those on can participate in and enjoy hundreds specific faith traditions. The University campus to clearly view the activities of diverse, University-affiliated social, within the building.

ENGINEERING 2017–2018 Opened in 1999, Lerner Hall contains Columbia’s commitment to success 217 an auditorium that seats up to 1,100, a in intercollegiate athletics competition • Be a candidate for a bachelor’s fully operational cinema, a party space, has been matched by the determination degree plus a diverse offering of meeting, of alumni and administrators to upgrade • Be registered for at least 12 points of rehearsal, and performance spaces, the University’s athletic facilities. The credit computer labs and kiosks, and 7,000 Baker Field Athletics Complex, a few • Make appropriate progress student mailboxes. miles up the Hudson River on the toward the degree as defined by The building also features the northern tip of Manhattan, has been the NCAA, the Ivy League, and University Bookstore, two dining completely rebuilt and expanded. Columbia University. These criteria facilities, a banking center and ATM, The complex features Robert K. Kraft are monitored by the Director of Package Center, and the Ticket and Field at Lawrence A. Wien Stadium, Compliance and certified by the Information Center. Lerner Hall is home a 17,000-seat football and lacrosse Office of the Registrar. to many critical University resources facility; Robertson Field at Satow • Have attended the University for not such as Undergraduate Student Life, Stadium, home of the baseball program; more than eight terms the James H. and Christine Turk Berik softball and field hockey venues; and • Not have completed the requirements Center for Student Advising, University an Olympic-quality synthetic track. At for the bachelor’s degree Chaplain, University Event Management, Columbia’s Dick Savitt Tennis Center at Questions about athletic eligibility and Health Services. the Baker Athletics Complex there are should be referred to the appropriate Lerner Hall is much more than a six cushioned hard tennis courts, all of academic adviser or the Associate building for performances and events— which are covered by a state-of-the-art Athletics Director for Compliance in the it is the center of student and campus air dome for winter use. The Remmer Department of Intercollegiate Athletics activity at Columbia. and 1929 Boathouse includes a three- and Physical Education. For more information, visit bay shell house, complete with an upper lernerhall.columbia.edu. level that includes an erg and weight Recreational Programs room. The Campbell Sports Center, the newest athletics building at the Baker In addition to the required physical INTERCOLLEGIATE ATHLETICS Athletics Complex, features coaches, education courses (see page 13), PROGRAM offices, a strength and conditioning the Department of Intercollegiate Columbia has a long tradition of success center, a theatre-style meeting room, Athletics and Physical Education in intercollegiate athletics, and The Fu as well as a student-athlete lounge and offers a comprehensive Intramural Foundation School of Engineering and study space. and Club Sports Program. Through Applied Science has always been an Columbia’s Dodge Physical Fitness intramurals, students have the active participant in these programs. Center draws thousands of students opportunity to participate in both While Columbia’s intercollegiate athletics each day for recreation, physical individual and team sports. Individual program is governed by Ivy League education classes, intramural play, club activities function through tournaments, regulations, Columbia is also a member competition, and varsity sport contests while team activities feature both of the National Collegiate Athletic and practices. The Center houses league and tournament competition. Association. Columbia sponsors men’s most indoor sports and is available to Club sports are designed to allow varsity teams in baseball, basketball, all registered students. Major athletic groups of individuals who share a cross-country, fencing, football, golf, facilities on campus include two full-size common athletics interest to organize rowing (heavyweight and lightweight), gymnasiums for basketball, volleyball, and collectively pursue this activity. soccer, squash, swimming and diving, and badminton; eight squash and Clubs are organized on recreational, tennis, track and field (indoor and handball courts; the eight-lane Uris instructional, and competitive levels. outdoor), and wrestling. pool with three diving boards; a fully Activities range from organized Women in all undergraduate divisions equipped three-level exercise and weight instruction to intercollegiate and of Columbia and in Barnard College room facility; two aerobic dance/martial tournament competition. A list of the compete together as members of arts rooms; a fencing room; a wrestling intramural activities and sports clubs University-wide athletic teams. The room; an indoor running track; and two as well as all information regarding the arrangement, called a consortium under fully equipped saunas. program can be obtained in the Office NCAA rules, is one of only three in the of Intramurals and Club Sports, 331 nation and the only one on a Division Dodge Fitness Center or on the website Eligibility for Intercollegiate Athletics I level. Currently, there are women’s at perec.columbia.edu. Any student in the Engineering School varsity teams in archery, basketball, who is pursuing the undergraduate cross-country, fencing, field hockey, program or an approved combined CAMPUS SAFETY golf, lacrosse, rowing, soccer, softball, program toward a first degree is eligible AND SECURITY squash, swimming and diving, tennis, for intercollegiate athletics. To be eligible track and field (indoor and outdoor), and Columbia University prepares an annual for athletic activities, the student must: volleyball. security report, which is available to

ENGINEERING 2017–2018 218 all current and prospective employees accessible from, the campus. The columbia.edu/cu/publicsafety and students. The report includes report also includes institutional policies /SecurityReport.pdf. statistics for the three previous concerning campus security, such as years concerning reported crimes policies concerning sexual assault, that occurred on campus, in certain and other matters. You can obtain a off campus buildings or property copy of this report by contacting the owned or controlled by Columbia Director of Administration and Planning, University, and on public property Public Safety at 212-854-3815 or within, or immediately adjacent to and by accessing the following website:

ENGINEERING 2017–2018 STUDENT SERVICES 219

UNIVERSITY HOUSING John Jay and Carman have kitchens (OCHA). UAH operates Columbia-owned on each floor. Carleton, East Campus, apartments and dormitory-style suites in Undergraduate Housing 47 Claremont, Hartley (which, together the Morningside Heights and Manhattan The residence halls are an important with Wallach, comprises the Living- Valley areas within walking distance of focal point of campus life outside Learning Center), Hogan, River, Ruggles, the campus, as well as in Riverdale, in the classroom, with the University 600 West 113th Street, Watt, and the Bronx. For further information, see housing more than 95 percent of the Woodbridge offer suite-style living, and UAH’s website at columbia.edu undergraduate population in residence all have kitchens. All residence hall /uah. International House, a privately halls on or near the campus. A trained rooms are either single or double. Both owned student residence near the Residential Life staff lives with the single and double rooms are available in campus, has accommodations for about students in the halls. They work to all halls except Carman, which has only five hundred graduate students, both create an atmosphere conducive doubles, and Hogan, which is all singles. international and American, who attend to educational pursuits and the The residence halls are also various area colleges and universities. development of community among the home to a variety of Special Interest It provides a supportive and cross- diverse student body. Throughout the Communities. These communities cultural environment with many activities year the Residential Life staff presents provide an opportunity for students and resources, and it is conveniently programs in the residence halls and with a common interest to live together located two blocks from the Engineering off campus that are both social and and develop programs in their area of building. For more information, write or educational. interest. The themes may vary from call: International House, 500 Riverside Columbia guarantees housing for year to year. First-year students are Drive, New York, NY 10027; 212-316- all undergraduate students (except not eligible to live in Special Interest 8400; or check their website at www Combined Plan students and visiting Communities but are welcome to attend .ihouse-nyc.org. students) who have filed their intent events. There are also a number of to reside on campus by the stated Upperclass Columbia students also resources available to search for deadline and who have continuously have the option of living in brownstones, off-campus housing opportunities. registered as full-time students. Each a limited number of fraternity and Columbia’s Off-Campus Housing spring, continuing students participate sorority organizations, and certain Assistance (OCHA) office assists in a room selection process to select Barnard College halls. These rooms are Columbia students and affiliates their accommodations for the next also chosen through a room selection in their search for rental housing academic year. Students who take process, which takes place each spring. in the metropolitan area. OCHA an unauthorized leave of absence are For more information, please manages a database known as the placed on the nonguaranteed wait list visit the Housing website at housing. Housing Registry at ocha.facilities. upon their return and are on the wait list columbia.edu. columbia.edu that contains listings for each subsequent year. of available rooms and apartments A variety of residence hall Graduate Housing in non-Columbia-owned buildings accommodations are available to Graduate students have a number of in NYC. The Registry also contains Columbia students. Carman, John housing opportunities in the Morningside listings of sublets of rooms and Jay, Wallach, Wien, Furnald, McBain, Heights neighborhood. The three main apartments in Columbia-managed Schapiro, Harmony and Broadway sources are University Apartment housing. Prospective roommates Residence Halls are traditional corridor- Housing (UAH), International House, can post and search profiles on the style residence halls. Of these, all but and Off-Campus Housing Assistance Roommates section of the Registry. OCHA offers one-on-one counseling

ENGINEERING 2017–2018 220

and is supported in these efforts by 2 students (those who live between can be used at the 12 dining locations a cooperative relationship with two 50 and 250 miles from campus). All on campus. Plan 3 is the only first-year New York City real estate/relocation continuing students and applications plan that also includes Off Campus Flex. agencies, CitiHabitats and Douglas from Zone 3 areas (within 50 miles) Elliman, which also offer a discounted are automatically placed on a waiting First-Year Dining Plans broker fee. Only students/affiliates list. Depending on availability, students with a UNI or admission acceptance placed on the UAH waitlist receive 1. 19 meals per week and 75 Dining letter are permitted to use the housing assignments between late Dollars per term, plus 15 floating Registry. Office hours and instructions December and January for the spring meals and 6 faculty meals are posted on the website at columbia term, and between early August and late 2. 15 meals per week and 125 Dining .edu/ocha. September for the fall term. Dollars per term, plus 10 floating UAH application information is sent UAH-approved students can begin meals and 6 faculty meals along with acceptance packets from moving in during the last week of August 3. 19 meals per week, $50 Flex and the Office of Graduate Student Affairs. for the fall term, and early January for the 25 Dining Dollars per term, plus 15 Information on applying for housing is spring term. Students will be properly floating meals and 6 faculty meals also available in the Office of Graduate notified of Graduate Orientation and The dining plans are transacted through Student Affairs and the UAH Office. You Registration, which are generally held the the University ID Card, which serves as can also seek additional information on week before the first day of class. If a a convenient way to enjoy dining all over the Columbia Students Page: columbia. student needs to move in earlier, proper campus without carrying cash. edu/cu/students. documentation from the department in Due to the growing demand for support of the request is necessary. housing, graduate housing is no Meals longer guaranteed, but every effort The meals portion of the dining plan COLUMBIA DINING is made to accommodate you. It is enables students to help themselves critical that you follow the instructions to unlimited servings of food served in your acceptance packet. Housing First-Year Students in John Jay Dining Hall, Ferris Booth applications received after the set All first-year students in residence are Commons, or JJ’s Place. The hours dates are not guaranteed housing. required to enroll in one of three dining of operations for these locations offer The order of priority for selection is: plans, each of which is comprised of a dining options for breakfast, lunch, graduate fellowship recipients, Zone 1 varying number of meals served in John dinner, and late-night, with continuous students (those who live further than Jay Dining Hall, Ferris Booth Commons, dining. 250 miles from campus), and then Zone or JJ’s Place, and Dining Dollars, which

ENGINEERING 2017–2018 Dining Dollars EZ3. 19 meals per week and 25 Dining Columbia Health is an integrated 221 In addition to meals, Dining Dollars Dollars, plus $50 Flex, 6 guest meals, program that provides extensive on- and comprise the other portion of the first- and 15 floating meals off-campus health care and services year dining plan. Each Dining Dollar is for you while you are enrolled at the equal to one dollar and operates as a Kosher Dining Plan University. The Columbia Health Program declining balance account, much like a All students who participate in a dining and an accepted medical insurance plan debit card. plan, including first-year, upperclass, work together to meet your health care Columbia Dining maintains 10 dining General Studies, or graduate students, needs. Columbia requires all full-time facilities conveniently located on campus. are eligible for the Columbia Kosher students to enroll in both. To meet the Each of the locations accepts Dining Dining Plan. Signing up for this dining insurance requirement, you must either Dollars, an alternative to cash payment plan allows access to a restricted confirm your enrollment in the Columbia that is accessed by the University ID kosher area within John Jay Dining Student Health Insurance Plan (Columbia Card. Hall as well as Express Meals to go. Plan) or provide proof of alternate With Dining Dollars, students will CU kosher meals can also, for an coverage that meets the established enjoy the ease and flexibility of cashless additional charge, be exchanged for criteria listed on the Columbia Health transactions as well as the savings of a kosher meal at Barnard’s Hewitt website. International students are sales tax on all food purchases. Dining Hall (kosher to kosher only). To sign required to enroll in the Columbia Dollars will roll over from year to year up, the student selects a plan from Student Health Insurance Plan. Part-time until graduation. either the First Year Dining Plan or students may also enroll in the Columbia the Upperclass Dining Plan options, Health Program and Columbia Plan. Upperclass and Graduate Students according to the student’s status, then Many upperclass and graduate students elects to enroll in the Kosher Dining Benefits and Services of the who dine on campus open a Dining Plan. For more details, a dining plan Columbia Health Program Dollars account; however, some choose comparison, and additional tools, visit The Columbia Health Program to enroll in an upperclass/graduate the Columbia Dining website at dining. compromises five departments and a student dining plan. columbia.edu. diverse group of highly-trained clinicians Columbia Dining offers ten plans—all to meet your health needs on campus. are accessed by the University ID Card Locations/Menus/Hours Medical Services and can be used for meals in John Jay Locations, menus, and hours of all John Jay Hall, 4th Floor Dining Hall, Ferris Booth Commons, or campus dining facilities can be found at Phone: 212-854-7426 JJ’s Place. The hours of operations for dining.columbia.edu. You can also view health.columbia.edu/medical-services these locations offers dining options for photos and take a virtual tour of some of breakfast, lunch, dinner, and late-night, our facilities. Menus and hours are also Medical Services provides routine and with continuous dining. available on the Dine@CU iPhone app. urgent medical care, travel medicine, and immunizations, as well as sexual Upperclass, GS, and Graduate Dining Nutrition, Food Allergies, and health services, reproductive and Plans Special Diets gynecological services, LGBTQ health Registered Dietitian Christina Lee care, and confidential HIV testing. A Weekly. 14 meals per week and 200 is available on site as well as online Students can make appointments Dining dollars per term, plus 15 to address individual questions and online with their health care provider floating meals and 6 guest meals concerns related to food allergies, and are encouraged to do so (bios and A Term. 210 meals per term and 200 intolerances, and dietary preferences. photos are available online). Students Dining dollars per term Christina can be contacted via email are encouraged to make appointments A Meal Only. 210 meals only at [email protected] or by phone online: health.columbia.edu. B Dining Dollars. 175 meals per term at 212-854-3353 with questions, to and 200 Dining Dollars per term, plus Counseling and Psychological Services schedule a consultation, or to discuss 6 guest meals Lerner Hall, 8th Floor personal meal planning. For more B Flex. 175 meals and 200 Flex per Phone: 212-854-2878 information and a nutrition calculator, term, plus 6 guest meals health.columbia.edu/cps visit the Columbia Dining website. C. 100 meals and 125 Dining Dollars Nutrition data can also be accessed on Counseling and Psychological per term, plus 4 guest meals the Dine@CU iPhone app. Services offers short-term individual D. 75 meals and 75 Dining Dollars per counseling, referrals for longer-term term, plus 2 guest meals therapy, consultations for couples, EZ1. 19 meals per week and 75 Dining COLUMBIA HEALTH student-life support groups, medication Dollars per term, plus 6 guest meals Phone: 212-854-2284 consultation, and emergency and 15 floating meals After-hours Urgent Health consultation. Students are welcome to EZ2. 15 meals per week and 125 Dining Concerns: 212-854-7426 select a mental-health clinician (bios and Dollars, plus 6 guest meals and 10 Email: [email protected] photos are available online). floating meals health.columbia.edu

ENGINEERING 2017–2018 222 Disability Services Student Health Insurance Meningococcal Meningitis Vaccination Wien Hall, 1st Floor John Jay, 3rd Floor New York State public health law Phone: 212-854-2388 Phone: 212-854-3286 requires that students receive health.columbia.edu/ods health.columbia.edu/insurance-and- information from their institutions about meningococcal meningitis and the Disability Services facilitates equal immunization-compliance-offices vaccine that protects against most access for students with disabilities strains of the disease that can occur on by coordinating accommodations and All full-time students are automatically university campuses. Columbia students support services, including assistive enrolled in the Basic level of the must make an informed decision about technology, networking groups, Columbia Plan. To request a waiver being vaccinated and certify their academic skills workshops, and learning from automatic enrollment, you must decision online. Full instructions are specialists. Disability documentation submit a request at health.columbia.edu given at health.columbia.edu and the and registration guidelines are available before September 30 (February 15 for process takes two to three minutes to online. new spring term enrollment or for newly arrived full-time summer students). All complete. You must formally indicate Alice! Health Promotion waiver requests are considered but your decision about being vaccinated John Jay, 3rd Floor approval is not guaranteed. before you will be permitted to register Phone: 212-854-5453 Navigating the U.S. health care for classes. health.columbia.edu/alice system can be complex. To help ensure Deadline: Decisions must be recorded online before classes begin. Alice! Health Promotion connects that international students have access Students will not be permitted to register individuals and groups with information to the highest quality of care on- and until a decision is recorded. and resources, cultivates healthy off-campus, Columbia University attitudes and behaviors, promotes requires all international students to Documentation of Immunity to Measles, health-supporting policy, and fosters enroll in the Columbia Student Health Mumps, and Rubella (MMR) a culture that values and supports Insurance Plan. Confirm your enrollment New York State public health law individual and community health. in the Columbia Student Health requires all students to document their Insurance Gold Plan; upgrade your immunity to measles, mumps, and Sexual Violence Response selection to the Platinum Plan online. rubella. Instructions and the Columbia Lerner Hall, 7th Floor For more up-to-date information, visit University MMR Form are available at Phone: 212-854-HELP (4357) the Columbia Health website at health. health.columbia.edu. health.columbia.edu/sexual-violence- columbia.edu. Deadline: Completed forms must response be mailed or faxed 30 days before Immunization Compliance registering for classes. Sexual Violence Response works to John Jay, 3rd Floor promote behaviors that support positive, Please visit us at health.columbia Phone: 212-854-7210 healthy, and consensual relationships, .edu or contact us for questions. and supports survivors and co-survivors There are two immunization requirements of violence through advocacy, that all new students must meet before connection to resources, community arrival on campus: education, training, and engagement.

ENGINEERING 2017–2018 Scholarships, Fellowships, Awards, and Prizes 224 SCHOLARSHIPS, FELLOWSHIPS, AWARDS, AND PRIZES

ENDOWED SCHOLARSHIPS given to students who have graduated Engineering (1985) AND GRANTS from Stuyvesant High School in New Gift of Edwin W. ’42 and Mary Elizabeth All endowed scholarships are awarded York City. Bright to support students studying annually to undergraduate students as mechanical engineering. part of Columbia’s financial aid program. Frank and Harriet Ayer Scholarship We are unable to accept applications (1977) Lewis G. Burnell Memorial for these awards independent of this Bequest of Frank A. Ayer. Graduates Scholarship (2001) process. of Deerfield Academy are given first Gift of Roger W. Burnell in memory of preference. his father, Lewis G. Burnell ’32. Leslie Abbot Scholarship For an undergraduate student Cesare Barbieri Scholarship (1953) Burns and Roe, Arthur J. Fiehn pursuing course of study in mechanical Gift of Cesare Barbieri Fund. Scholarship (1989) engineering. Gifts from various donors in memory of William S. Barstow Scholarship (1935) Arthur J. Fiehn ’46. Cvi Abel Memorial Scholarship (2003) Gift of William S. Barstow. Gift of Jack Abel ’71. Samuel J. Clarke Scholarship (1960) Edwin D. Becker Scholarship Fund Bequest of Agnes Robertson Clarke. Aigrain Family Scholarship (2008) (1993) Gift of Jacques and Nicolleta Aigrain Gift of Edwin D. Becker ’56. Preference Class of 1885 (1910) P’08. Preference is given to international is given to students from the Rocky Gift of the Class of 1885 School of students studying civil or mechanical Mountain states. Mines in commemoration of the twenty- engineering. fifth anniversary of their graduation. John E. Bertram Memorial Walter H. Aldridge (1936) Scholarship (1990) Class of 1889 (1939) Gift of Walter H. Aldridge. Gift of Mrs. Lucy Bertram and friends Gift of the Class of 1889 College and in honor of John E. Bertram. Awarded Engineering. M. Alenda and John F. Crymble to students in electrical engineering or Scholarship (2011) computer science. Class of 1900 (1940) Gift of John F. '38CC, '39, '40 and Gift of the Class of 1900 College and Alenda Crymble for the benefit of Jerry and Evelyn Bishop Scholarship Engineering. students who enroll in the College and (1984) Class of 1902 (1952) later transfer to Columbia Engineering, Gift of Jerry ’42 and Evelyn Bishop Gift of the Class of 1902 College and whether or not they earn a dual degree. for students in the Combined Plan Program. Preference is given to students Engineering. Alvey-Ferguson Company in the program who attended Columbia Class of 1906 (1940) Scholarship (1948) College. Gift of the Class of 1906 in honor of Gift of the Alvey-Ferguson Company. Paul H. Blaustein Scholarship (1994) Frank D. Fackenthal 1906. Erwin H. Amick Memorial Scholarship Gift of Barbara Blaustein, Stacey Class of 1907 (1937) (1970) Blaustein Divack, and Joshua Divack. Gift of the Class of 1907. Preference is Gift of various donors for students given to sons and descendants of class in chemical engineering and applied Philip P. Bonanno Scholarship (1999) members. chemistry. Donated by Philip P. Bonanno ’55. Class of 1909 (1959) Nathaniel Arbiter Scholarship (1985) Cecil Ane and Tullio J. Borri Family Gift of the Class of 1909 in honor of Gift of various donors in honor of Scholarship John J. Ryan. Professor Nathaniel Arbiter for students Gift of Tullio J. ’51 and Cecil Ane in the following specializations in order of Borri. Preference for students who are Class of 1913 (1963) preference: mineral beneficiation, mines, majoring in or studying civil engineering. Gift of the Class of 1913 in and physical metallurgy. Cornelius A. Boyle Scholarship (1962) commemoration of the fiftieth anniversary of their graduation. Attardo Scholarship (1999) Bequest of Cornelius A. Boyle. Gift of Michael J. Attardo ’63. Lauren Breakiron Scholarships (1999) Class of 1914 (1937) Gift of the Class of 1914 College and Jee Yin and Choi Heung Au Gift of Lauren P. Breakiron ’56. Engineering for a pre-engineering or pre- Scholarship Fund (2002) Edwin W. and Mary Elizabeth architecture student. Gift of Michael M. Au ’90. Preference is Bright Scholarship in Mechanical

ENGINEERING 2017–2018 225

Class of 1945 50th Reunion Gift of Dr. Stanley Dicker ’61 in honor of Z. Y. Fu Scholarship (1993) Scholarship the hundredth anniversary of his mother’s Gift of The Fu Foundation for Gift of the Class of 1945. birth (March 5, 1900). Preference is given undergraduate scholarship support. to juniors and seniors in the Department Class of 1950 Endowed Scholarship of Biomedical Engineering. Jewell M. Garrelts Scholarship (2000) Gift of Jewell Garrelts; preference for a Gift of members of the Class of 1950 Jack Dicker Endowed Scholarship junior or senior in the Department of Civil in commemoration of the fiftieth (2003) Engineering and Engineering Mechanics. anniversary of their graduation. Gift of Dr. Stanley Dicker ’61 in honor of his father. Preference is given to Gavaudan Family Scholarship (2014) Class of 1951 Endowed Scholarship juniors and seniors in the Department of Gift of Francesca and Emmanuel (2001) Biomedical Engineering. Gavaudan P'17, P'20. Gift of members of the Class of 1951 in commemoration of the fiftieth James and Donna Down Scholarship General Motors Scholarship anniversary of their graduation. (1997) Designated for minorities and women. Gift of James ’73 and Donna Down Preference is given to General Motors Class of 1952 Endowed Scholarship to support a deserving minority employees, their spouses, or children. (2002) undergraduate who has demonstrated Established by Alexander Feiner ’52. academic achievement. Ben and Ethelyn Geschwind Endowed Scholarship (2004) Class of 1964 Scholarship (2014) Stancliffe Bazen Downes Scholarship Gift of Benjamin and Ethelyn ’84 Gift of members of the Class of 1964 in (1945) Geschwind. honor of their 50th class reunion. Bequest of Bezena Treat Downes Merriman in honor of her brother, for a Alger C. Gildersleeve Scholarship Hugo Cohn Scholarship (1984) student in civil engineering. (1955) Gift of Hugo Cohn 1909. Preference is Bequest of Josephine M. Gildersleeve, in given to electrical engineering students. Brooke Lynn Elzweig Scholarship honor of Alger G. Gildersleeve 1889. (2002) Herbert J. Cooper Scholarship (1999) Gift of Gary Elzweig ’77. Preference is Frederick A. Goetze Scholarship (1960) Gift of Mrs. Deborah Cooper and the given to students with high financial need. Gift of William A. Baum, in honor of the Estate of Herbert J. Cooper ’46. former Dean of Columbia Engineering. John L. Erikson Memorial Scholarship Milton L. Cornell Scholarship (1958) Gift from Betty Erikson in memory of her Sarah E. Grant Memorial Scholarship Gift of various donors in memory of husband, John L. Erikson ’50. (1997) Milton L. Cornell. Gift of Geoffrey T. ’82 and Annette M. Jeffrey and Lina Franklin Scholarship Grant in memory of their daughter, Paul and Lillian Costallat Scholarship (2014) Sarah. Designated to support students (1972) Gift of Jeffrey M. '68 and Linda Franklin. who have demonstrated academic Gift of Paul and Lillian Costallat. Preference is given to students who achievement and are student athletes. attended high school in New York City, Frederick Van Dyke Cruser served in an organizational leadership Adam R. Greenbaum Memorial Scholarship (1980) role while in high school, and excelled Scholarship Fund Bequest of Maude Adelaide Cruser on the SAT. Established in memory of Adam R. to support students in chemical Greenbaum by his parents, relatives, engineering with financial need. Jack B. Freeman Scholarship (1994) and friends following his death in Gift of Jack B. Freeman ’55. Designated February 2001, when he was a Cytryn Family Scholarship (2002) to support students who are members sophomore. The scholarship is given to Gift from Allan ’72, ’79 and Carol Cytryn. of the varsity baseball team. a SEAS sophomore who was named to the Dean’s List as a first-year, as Adam Peter del Valle Scholarship (2015) Pier-Luigi Focardi Scholarship (1964) was, with a preference to students from Established by Peter del Valle ’54CC, Bequest of Clara G. Focardi. New Jersey and New York. ’55, ’56. Ford/EEOC Scholarship Luther E. Gregory Scholarship (1963) Frank W. Demuth Scholarship (1965) Designated for minorities and women. Bequest of Luther E. Gregory 1893. Bequest of Frank W. Demuth 1914. Preference is given to Ford employees, their spouses, or children. Robert Gross Fund (1999) Freda Imber Dicker Endowed Gifts of friends of Robert Gross to Scholarship Fund (2000) support a student in applied physics.

ENGINEERING 2017–2018 226 Wallace K. Grubman-Graham Albert M. Hall Scholarship Edward Gurnee Hewitt Scholarship Scholarship (1998) Preference for students in metallurgy or (1980) Gift of Wallace Grubman ’50 and materials science. Bequest of Mary Louise Cromwell. the Grubman Graham Foundation to support a student in chemical The Hamann Scholarship (1970) Prentice Hiam Memorial Scholarship engineering. Bequest of Adolf M. Hamann 1910. (2007) Gift of Atul Khanna ’83. Preference for Gu Scholarship (2012) Alfred M. and Cornelia H. Haring residents of India or students who have Gift of David '86 and Janice Gu P'18CC Scholarship (1965) lived for a period of time in India. to support students studying computer Gift of the Aeroflex. science. James T. Horn Scholarship (1938) H. Field Haviland Scholarship Fund Gift of Sarah L. and Mary T. Horn, in Lawrence A. Gussman Scholarship (1988) memory of their brother, James T. Horn (1987) Bequest of Henry F. Haviland 1902. 1884. Gift of Lawrence Gussman ’38. Awarded Scholarships are awarded equally annually to students studying computer between Columbia Engineering and Richard and Janet Hunter Scholarship science. Columbia College. (2000) Gift of Richard ’67 and Janet Hunter. Haight Family Scholarship (2004) Harold T. Helmer Scholarship (1965) Scholarship awarded to 3-2 program Gift of Deborah E. Haight ’00. Bequest of Harold T. Helmer. participants entering Columbia Engineering with preference given to Ralph W. Haines Scholarship (2002) David Bendel Hertz College/ graduates of Whitman College. Gift of Ralph W. Haines ’69 for needy Engineering Interschool Scholarship and deserving students in Columbia (1989) Hurr Scholarship (2014) Engineering. Gift of David B. Hertz ’39. Awarded in Gift of Larry and Stephanie Ho P'16, alternate years to the College and to the P'18. A. A. Halden Scholarship (1962) Engineering School to a student electing Established by bequests from Dorothy to receive a B.A. from Columbia College Isaacs-Jonas Memorial Scholarship C. Halden and Barbara Schwartz in and a B.S. from Columbia Engineering. (2001) memory of Alfred A. Halden. This scholarship was endowed in 2001

ENGINEERING 2017–2018 by Gary F. Jonas ’66 and Jonathan L. Gift of Kulite Semiconductor Products, the 3-2 Combined Plan Program and who 227 Isaacs ’66 as the Future Entrepreneurs Inc., and Kulite Tungsten, for have a commitment to community service. Scholarship to acknowledge the thirty- undergraduates, preferably studying in fifth anniversary of their graduation from the fields of metallurgy or solid-state Bruce and Doris Lister Endowed Columbia Engineering. On April 30, 2003, physics. In memory of Jacob Kurtz Scholarship (2000) Mr. Isaacs died at the young age of fifty- 1917. Gift of Bruce A. Lister ’43, ’47 to seven, and the scholarship was then support a needy and deserving renamed in his memory by Gary F. Jonas, Ronald A. Kurtz Scholarship Fund undergraduate student. with the support of Jon’s wife, Charlotte (1990) Isaacs. Following the passing of Mr. Gift of Kulite Tungsten. Lu Lo Family Scholarship Jonas on Sept 26, 2014, the scholarship Gift of Lu Lo. Established to provide was again renamed to honor the legacy Lahey Scholarship (1932) scholarships to undergraduate students, of both Mr. Isaacs and Mr. Jonas. Bequest of Richard Lahey. with a preference for students from China. Note: this was previously listed as Jonathan Lewis Isaacs Memorial Charles and Sarah Lapple Anna Kazanjian and Guy Longobardo Scholarship. Scholarship (2004) Scholarship (2007) Bequest from the Estate of Charles E. Gift of Anna Kazanjian ’49, ’52 and Sheldon E. Isakoff Endowed Lapple and Sarah V. Lapple to be used Guy Longobardo ’49, ’50, ’62. Scholarship Fund (2000) to provide scholarships to deserving Preference given to students studying Gift of Sheldon E. ’45, '47, '52 and Anita undergraduate students. mechanical engineering who have Isakoff to support chemical engineering demonstrated academic excellence. student. Frank H. Lee Memorial Scholarships (1986) Donald D. MacLaren Scholarship Alfred L. Jaros Memorial Scholarship Awarded to a student in the Combined (1995) (1967) Plan Program in honor of Professor Established by Donald D. MacLaren ’45 Gift of various donors, in memory of Frank H. Lee. to support a student who is studying Alfred L. Jaros 1911. biochemical engineering. Samuel and Minerva K. Lee and Cavalier Hargrave Jouet Scholarship David A. Lee Scholarship (2005) Manelski Family Scholarship (2004) (1941) Bequest of the Estate of Samuel Lee to Gift of Darren E. Manelski ’91. Bequest of Belinda Hearn Jouet, in support students pursuing a degree in memory of C. H. Jouet 1882. chemical engineering studies. Mango Family Scholarship (2016) Gift of Donald and Patricia Mango P'16 Alfred E. Kadell Scholarship (1995) Leung Endowed Scholarship (2006) to support high need students who Bequest of the Estate of Alfred E. Kadell Gift of Lawrence Leung P’10, P’15. attended high school in New York City, 1921. with preference for members of an James F. Levens Scholarship (1973) athletic team. Wayne Kao Scholarship (1988) Bequest of Ola Levens Poole for Gift of Mabel C. Kao in memory of students in chemical engineering and Ernest Marquardt Scholarship (1968) Wayne Kao ’49. applied chemistry. Bequest of Ernest Marquardt 1912.

Ruth Katzman Scholarship (2011) George J. Lewin Scholarship (1965) Louis F. Massa Scholarship (1952) Bequest from Ruth Katzman in loving Gift of George J. Lewin 1917 and family. Bequest of Louis F. Massa 1890. memory of her parents, Max and Lilian Preference given to hearing-impaired Katzman. students. Ralph Edward Mayer Scholarship (1924) Stanley A. and Minna Kroll Alvin and Richard H. Lewis Contributed by friends in memory of Scholarship for Engineering and Scholarship Professor Ralph Edward Mayer. Computer Science (1987) Gift of Alvin and Helen S. Lewis in Gift of Stanley A. Kroll ’28 to support memory of their son, Richard Lewis ’63. Lilavati Mehta Scholarship (2015) students who are studying electrical Gift of Asheet Mehta. Preference given engineering or computer science. James M. and Elizabeth S. Li to students who promote diversity of the Endowed Scholarship (2006) student body. Henry Krumb Scholarship (1945) Gift of James ’68, ’70, ’76 and Elizabeth Gift of Henry Krumb for annual Li. Awarded to students majoring in Henry Michel Scholarship (2005) scholarships in mining engineering, industrial engineering and operations. Gift of Mrs. Mary-Elizabeth Michel in metallurgy, and ore dressing. memory of Henry Michel ’49 to support Robert D. Lilley Memorial Scholarship civil engineering majors. Jacob Kurtz Memorial Scholarship (1988) (1982) For students who are in their final year of

ENGINEERING 2017–2018 228 Stuart Miller Endowed Scholarship in Brainerd F. Phillipson Scholarship Edgar Lewisohn Rossin Scholarship Engineering (2003) (1936) (1949) Gift of Stuart Miller. Gift of an anonymous donor in memory Bequest of Edgar L. Rossin, to provide of Brainerd F. Phillipson. a scholarship for students in mining John K. Mladinov Scholarship (1994) engineering. Gift of Barbara P. Mladinov in honor of Andre Planiol Scholarship (1967) her husband, John K. Mladinov ’43. Bequest of Andre Planiol for a student Harry B. Ryker (1947) Awarded to a deserving undergraduate from France. Bequest of Miss Helen L. Ryker in with a minor in liberal arts. memory of her brother, Harry Benson Roy Howard Pollack Scholarship Ryker 1900. Frank C. Mock and Family (1998) Scholarship (1987) Bequest of Roy Howard Pollack to be Walter H. Sammis Scholarship (1999) Bequest of Frank C. Mock 1913. For used for scholarships for junior or senior Bequest of Mignon Wright. students in electrical engineering with students. financial need. Thomas J. Sands Endowed Polychrome-Gregory Halpern Scholarship Fund (2001) New Hope Foundation Scholarship Scholarship Gift of Thomas J. Sands ’86. (2006) For students in chemical engineering Gift of Lee and Margaret Lau P’09, and applied chemistry. Peter K. Scaturro Scholarship Fund P’10CC. Preference is given to students (1997) from Ontario, Canada, or mainland China. Rodman K. Reef Scholarship (1999) Gift of Peter K. Scaturro ’82, ’85 Gift of Rodman Reef ’69, ’78. to support students at Columbia A. Peers Montgomery Memorial Engineering or Columbia College, with Scholarship (1990) Professor William H. Reinmuth preference given to scholar-athletes from Gift of the family of A. Peers Scholarship (1988) Archbishop Molloy H.S. in Briarwood, Montgomery ’26. Gift of Curtis Instruments, Inc., awarded Queens, NY. in alternate years to Columbia College John J. Morch Scholarship (1963) and Columbia Engineering. Preference Norman A. Schefer Scholarship (1999) Bequest of John J. Morch. will be given to college students studying Gift of Norman A. Schefer ’50 and Fay chemistry and to engineering students J. Lindner Foundation. Seeley W. Mudd Scholarship (1958) studying electrochemistry. Established in Gift of the Seeley W. Mudd Foundation. honor of Professor William H. Reinmuth. Mark Schlowsky-Fischer Scholarship (2005) Mary Y. Nee and Douglas Ng Family Patricia Remmer Scholarship (2004) Gift of George Schlowsky ’65 in memory Scholarship (2008) Bequest of Patricia Cady Remmer of Mark Schlowsky-Fischer ’97 to Gift of Mary Yuet-So Nee ’84, '91BU, ’45BC. support students studying computer P'15CC. science. Note: this was previously listed as Mary Brenda and Dave Rickey Endowed Y. Nee Endowed Scholarship. Scholarship Fund (2008) Ralph J. Schwarz Scholarship (1993) Gift of David ’79 and Brenda Rickey Gift of the Class of 1943 and other Frederick Noel Nye Scholarship P’08 to benefit undergraduate students donors in memory of Ralph J. Schwarz (1971) from California. ’43. To be awarded to academically Bequest of Frederick Noel Nye ’27. outstanding students who require Kevin T. Roach Endowed Scholarship financial aid. David Novick Scholarship (2011) (2003) Bequest of David Novick ’48, ’54 to Gift of Kevin T. Roach ’77. David C. and Gilbert M. Serber support civil engineering students. Memorial Scholarship (1950) The Frederick Roeser Fund for Gift of the Serber family in honor of Parker Family Endowed Scholarship Student Aid (1934) David Serber 1896. Designated to (2001) An annual loan to help pay educational support a student in civil engineering. Gift of Peter D. Parker ’72, ’74. expenses, which is awarded to students chosen by the Committee on Varsha H. Shah Scholarship (2003) Robert I. Pearlman Scholarship (1989) Scholarships. The amount is individually Gift of Hemant and Varsha Shah to Gift of Robert I. Pearlman ’55. determined and is to be repaid only if support undergraduate female minority Preference is given to students from and when the student can do so without students. single-parent households. personal sacrifice. Repayments go into the Frederick Roeser Research Fund for Jared K. Shaper Scholarship Robert Peele Scholarship (1925) research in physics and chemistry. For deserving and qualified candidates Gift of E. E. Olcott 1874. for degrees in engineering.

ENGINEERING 2017–2018 Samuel Y. Sheng Scholarship (2007) and the Community Foundation of New Robert H. and Margaret H. Wyld 229 Gift of Samuel Y. Sheng ’51, Lauren Jersey. Preference is given to Greek- Scholarship Wong Sheng ’76, Kent Sheng, and American students. Gift of Robert H. 1904 and Margaret H. Jean Sheng. Awarded to students who Wyld. demonstrate academic excellence. Upton Scholarship For the children of employees of D. Max Yablick Memorial Scholarship Edith Shih Interschool Scholarship C. Heath and Company of Lexington, (1986) Fund (2008) Massachusetts. Bequest of Max Yablick 1914. Gift of Edith Shih, Esq. ’77TC, ’78TC. Preference is given to graduates of Preference is given to international Valeiras Family Scholarship (2009) Hebrew day schools and to students students. Gift of Horacio and Amy Valeiras P’09 in the Combined Plan Program with and Peter Valeiras ’09. Yeshiva University. Silent Hoist and Crane Company (1950) Kenneth Valentine Memorial Theresa Ann Yeager Memorial Gift of the Silent Hoist and Crane Scholarship (1986) Scholarship (1983) Company. Bequest of Julia H. Valentine, in memory Gift of the family of Theresa Ann Yeager of Kenneth Valentine 1914. Preference ’81 to support a woman who is enrolled David W. Smyth Scholarship (1957) is given to students in chemical Columbia Engineering. Bequest of Mrs. Millicent W. Smyth, engineering. in memory of her husband, David W. Yu Family Scholarship Smyth 1902. Frank Vanderpoel Scholarship (1936) Gift of Richard ’82 and Jean Yu. Bequest of Frank Vanderpoel. Fritz and Emma Spengler Memorial Bong and May Yu Engineering Scholarship (2005) William E. Verplanck Scholarship Scholarship (2016) Gift of Manfred Spengler ’56, ’55CC (1957) Gift of Bong and May Yu P'89CC, to support student athletes in the 3-2 Gift of Mrs. T. Bache Bleecker and P'90 to support students enrolled in Combined Plan Program. Edward F. Verplanck 1912 in memory of the Department of Civil Engineering their father, William E. Verplanck 1876. and Engineering Mechanics who have Gene F. Straube Fund (2007) exceptional academic achievement and Gift of Gene F. Straube ’50, ’49 CC. Arnold Von Schrenk Scholarship demonstrated financial need. Preference is given to students who (1943) graduated from a high school or prep Bequest of Mrs. Helen von Schrenk in ENDOWED FELLOWSHIPS school in northern California, and memory of her husband, Arnold von who are pursing studies in electrical Schrenk. All endowed fellowships are awarded engineering, computer engineering, or annually to graduate students. computer science. George Wascheck Scholarship Preference is given to students who Bequest of George Wascheck ’26. serve as teaching assistants. Graduate Steve Tai and Kin-Ching Wu Endowed students who qualify for these awards Scholarship Fund (2001) J. Watumull Scholarship (1989) will be contacted directly for application Gift of Steve Tai ’80. For students in the Graduate School materials. of Arts and Sciences and in the Tai Family Scholarship (2003) Engineering School who are of East James Albaugh Fellowship (2013) Gift of Timothy Tai P’06 to be used to Indian ancestry. Gift of James F. Albaugh '74. support Asian students demonstrating financial need and outstanding academic Wells and Greene Scholarship H. Dean Baker Fellowship (1982) potential, with preference given to Hong Bequest of Josephine Wells Greene. Awarded to support deserving graduate Kong, Taiwanese, mainland Chinese, students in mechanical engineering. and Chinese-American applicants for Herbert A. Wheeler Scholarship (1923) Boris A. Bakhmeteff Research admission. A T. Tai Family Scholar will Gift of Herbert A. Wheeler. Fellowship in Fluid Mechanics be named in a first-year class, and with Frederick C. Winter Scholarship Provides a stipend for the academic suitable academic achievement and (1966) year with tuition exemption to be continuing need, would retain that honor Gift of various donors in memory of arranged by the recipient’s department, until graduation. Frederick C. Winter ’43. to a candidate for a doctoral degree in Grace C. Townsend Scholarship (1941) any department at Columbia University William F. Wurster Scholarship (1974) Bequest of Miss Grace C. Townsend. whose research is in fluid mechanics. Gifts of William F. Wurster 1913. Theodosios and Ekaterine Typaldos Awarded to a student of chemical Quincy Ward Boese Fellowships Endowed Scholarship Fund (2000) engineering and applied chemistry. Pre-doctoral fellowships for students Gift of Andreas ’69 and Renee Typaldos studying under the Faculty of Engineering and Applied Science.

ENGINEERING 2017–2018 230 Roy S. Bonsib Memorial Fellowship Michael Frydman Endowed Professor Emeritus Hassialis. Previously (1957) Fellowship (2000) awarded to students of the Henry Awarded to worthy students for Established in 2000, a generous gift Krumb School of Mines. Now supports advanced study or research in of a SEAS alumnus, Michael Frydman. students in the Department of Earth engineering. Fellowship is designed to support and Environmental Engineering, with a academically gifted graduate students in preference for those in the field of Earth Arthur Brant Fellowship (1997) the Department of Industrial Engineering resources economics and management. Gift of Arthur Brant. Awarded to and Operations Research, particularly students of the Henry Krumb School of in the Management Science program. Higgins Fellowships Mines in the field of applied geophysics. Students are awarded a certificate and Designated to support first-year monetary prize. graduate students. Samuel Willard Bridgham-William Petit Trowbridge Fellowship Robert F. Gartland Fellowship Leta Stetter Hollingworth Fellowship A combined fellowship awarded annually Gift of Robert Gartland, an IEOR Gift of Harry L. Hollingworth in memory for research. alumnus. The fellowship is designated of his wife to support women who are to support students who completed the graduates of the University of Nebraska, Byron Fellowship (1980) B.S. and M.S. degrees from Columbia with preference given to those who were Bequest of Verna and Oscar Byron 1914. Engineering, who have demonstrated born in Nebraska or received their earlier academic excellence and professional education there. William Campbell Fellowships for promise. Students are awarded a Encouraging Scientific Research certificate and monetary prize. Edward J. Ignall Research Fellowship Four or five fellowships for research in Gift of family, friends, and former students the general field of metals. GEM Fellowship in memory of Professor Edward J. Ignall. The GEM fellowship provides African- Awarded to encourage and help support Robert A. W. and Christine S. Carleton Americans, Hispanic Americans, and the research activities of a graduate Fellowships in Civil Engineering Native Americans access to graduate student in the Department of Industrial Fellowships awarded to students in the education. The fellowship includes Engineering and Operations Research. Department of Civil Engineering and tuition, fees, a stipend, and a paid Engineering Mechanics. summer internship. Applicants for George M. Jaffin Fellowship this fellowship must be engineering or Awarded for graduate study and Chiang Chen Fellowship (2004) applied science majors. research leading to the Ph.D. degree Gift of the Chiang Chen Industrial Charity in orthopedic biomechanics by the Foundation. Awarded to students in Governor’s Committee on Scholarship Department of Bioengineering of the mechanical engineering. Achievement Hospital for Joint Diseases, Orthopedic One year awards based on financial Institute, and the Department of Professor Bergen Davis Fellowship need. Renewal is based on academic Mechanical Engineering. Gift of Dr. Samuel Ruben. To be progress, financial need, and availability awarded to a student in chemical of funds. The student applies directly to Herbert H. Kellogg Fellowship (1988) engineering and applied chemistry the GCSA; the awards are matched by Funded by former students and friends upon the recommendation of the senior the School and are not in supplement to of Professor Emeritus H. H. Kellogg and professor in chemical engineering active initial School awards. the generous contribution of Professor in electrochemistry research. Kellogg. Awarded to students of mineral Carl Gryte Fellowship (2007) engineering and chemical metallurgy. George W. Ellis Fellowships Gift from friends of Professor Carl Awarded annually for graduate study in Campbell Gryte. Awarded to students Otto Kress Fellowship (1990) any division of the University. Open to who are studying chemical engineering. Bequest of Mrs. Florence T. Kress in students who are residents of the state memory of her husband, Otto Kress. of Vermont or who have been graduated Daniel and Florence Guggenheim Awarded to postgraduate students. from a Vermont college or university. Fellowships Two Ph.D. fellowships for the study of Henry Krumb Fellowships Erbilgin Family Fellowship (2011) engineering mechanics in the Institute Annual fellowships in mining engineering, Gift of Vural Erbilgin P'09. Awarded to of Flight Structures in the Department metallurgy, and ore dressing. graduate students enrolled in the Civil of Civil Engineering and Engineering Engineering and Engineering Mechanics Mechanics. U.S. citizenship or John F. T. Kuo Fellowship (1992) Department, with a preference for permanent residence required. Established by Dr. I. J. Won and other students studying concrete technology students of Professor Emeritus Kuo and concrete structures in the future. M. D. Hassialis Memorial Fellowship for the support of graduate students in (2002) applied geophysics. Herbert French Fellowship (2010) Gift of former students of the late Krumb Bequest of Ralph S. French ’42CC.

ENGINEERING 2017–2018 231

Charles and Sarah Lapple Fellowship industry regulatory policy, procurement Bernard R. Queneau Fellowship (2004) procedures and trade regulations. Gift of Bernard R. Queneau ’32CC, ’33. Bequest of Charles ’36, ’37 and Sarah Awarded to a student in the Department Lapple. Awarded to support deserving Nickolaus Fellowship of Earth and Environmental Engineering. students in the Department of Chemical Gift of Nicholas Nickolaus ’50. Engineering. David M. Rickey Endowed Fellowship Yunni and Maxine Pao Memorial (2000) Kuo and Grace Li Memorial Fellowship (2015) Gift of David M. Rickey ’79. Awarded to Fellowship (1993) Gift of Frank and Eleanor Pao in honor students studying electrical engineering Gift from the Li Foundation Inc. Awarded of the memory of their parents. Provides under the holder of the David M. Rickey to students interested in mining, mineral fellowships to doctoral students enrolled Professorship. resources, metallurgy, and materials in the Department of Civil Engineering science. and Engineering Mechanics. Lydia C. Roberts Graduate Fellowships Ralph H. McKee Fellowship (1979) Anthony Pesco Fellowship (2006) Open to persons born in Iowa who have Bequest of Ralph H. Mckee to support Gift of Dr. Anthony Pesco ’82, ’83, ’87 been graduated from an Iowa college or fellowships in the fields of mathematics to support students in the Chemical university. In addition to the stipend, the or chemical engineering. Engineering Department who wish to fellow is reimbursed the cost of traveling pursue careers in academia. once from Iowa to New York City and Walter Mielziner Fellowship (2011) back. Special provisions: holders may Bequest of Walter Mielziner ‘49 to Presidential Distinguished not concentrate their studies in law, support fellowships for students Fellowships medicine, dentistry, veterinary medicine, studying computer science, automatic These fellowships are awarded annually or theology, and each holder must, controls or communications. to selected incoming Ph.D., Eng.Sc.D., when accepting the award, state that it and master’s/Ph.D. students. Fellowships is his or her purpose to return to Iowa Benjamin Miller Memorial Fellowship include tuition plus an annual stipend of for at least two years after completing Awarded to a student in the Department $24,000 for up to four years, including studies at Columbia; holders are eligible of Industrial Engineering and Operations three months of summer research. All for reappointment. Research. Preference is given to students applications for admission are considered concerned with work in government- for these new fellowships.

ENGINEERING 2017–2018 232 Samuel N. Rubinstein Endowed MEDALS AND PRIZES The Charles F. Bonilla Medal Fellowship (2005) The Bonilla Medal is an award for Bequest of Leo Rubinstein ’63 and gift American Society of Civil Engineers— outstanding academic merit. It is of Frederick Rubinstein. Awarded to The Robert Ridgway Award presented annually to that student in students studying applied mathematics Awarded to the senior showing the most the graduating class in the Department or industrial design. promise for a professional career in civil of Chemical Engineering who best engineering. exemplifies the qualities of Professor Frank E. Stinchfield Fellowship in Charles F. Bonilla. Orthopedic Biomechanics American Society of Civil Engineers— Awarded for graduate study and Student Chapter Service Award The Tullio J. Borri ’51 Award in Civil research in the Department of Established in 2008 to reward one Engineering Mechanical Engineering through the or more students who have been A certificate and cash prize presented Orthopedic Research Laboratory of particularly active in the Student Steel annually by the Department of Civil the Department of Orthopedic Surgery, Bridge Competition. Engineering and Engineering Mechanics College of Physicians and Surgeons, it to a senior for outstanding promise of carries tuition exemption and a twelve- American Society of Civil Engineers— scholarly and professional achievement month stipend of up to $15,000. Younger Member Forum Award in civil engineering. This award has Awarded annually to members of the been made possible by gifts from the Tarmy Summer Scholars Fund (2014) graduating class in civil engineering who stockholder/employees and the board Gift of Barry L. Tarmy '54, '56 to have been the most active in promoting of directors of the Damon G. Douglas provide stipends to potential Chemical the aims of the Society. Company, a New Jersey-based general Engineering doctorial applicants who are contractor, in appreciation of Mr. Borri’s conducting research under the direction American Society of Mechanical many years of dedicated service and of the faculty in the Department of Engineers visionary leadership as chairman and Chemical Engineering. In recognition of outstanding efforts president. and accomplishments on behalf of the Nickolas and Liliana Themelis American Society of Mechanical Engineers Computer Engineering Award of Fellowship in Earth and Student Section at Columbia University. Excellence Environmental Engineering (2000) Awarded each year by vote of the Gift of Nickolas and Liliana Themelis to Applied Mathematics Faculty Award Computer Engineering faculty to an support students in the Department of Presented to an outstanding graduating outstanding senior in the computer Earth and Environmental Engineering. senior in the applied mathematics engineering program. program. Joseph F. Traub Graduate Fellowship Computer Science Scholarship Award Fund (2017) Applied Physics Faculty Award of Excellence Gift from alumni and friends in memory Presented to an outstanding graduating A cash prize to a graduating student of Professor Joseph F. Traub. senior in the applied physics program. who has demonstrated outstanding ability in the field of computer science. Erwin S. and Rose F. Wolfson Memorial The Edwin Howard Armstrong Engineering Fellowship (1979) Memorial Award The Edward A. Darling Prize in Gift of Erwin S. and Rose F. Wolfson. Awarded by the faculty of Electrical Industrial Engineering and Operations Engineering to one outstanding Research graduating senior and one outstanding Established in 1903 by a gift from OUTSIDE FELLOWSHIP candidate for the M.S. degree to honor the late Edward A. Darling, formerly the late Edwin Howard Armstrong, superintendent of Buildings and Wei Family Private Foundation professor of electrical engineering Grounds; a certificate and prize Fellowship and noted inventor of wideband awarded annually to the most faithful The Wei Family Private Foundation FM broadcasting, the regenerative and deserving student of the graduating is a 501(c)(3) nonprofit organization circuit, and other basic circuits of class in industrial engineering and established to honor the memory of Dr. communications and electronics. operations research. Chung Kwai Lui Wei and Mr. Hsin Hsu Wei. The purpose of the foundation is The Theodore R. Bashkow Award The Edward A. Darling Prize in to award scholarship grants to students A cash award presented to a computer Mechanical Engineering of Chinese heritage with high academic science senior who has excelled in Established in 1903 by a gift from credentials who are pursuing a graduate independent projects. This is awarded in the late Edward A. Darling, formerly degree in Electrical Engineering. Visit honor of Professor Theodore R. Bashkow, superintendent of Buildings and www.wfpf888.org for more information. whose contributions as a researcher, Grounds; a certificate and cash prize teacher, and consultant have significantly awarded annually to the most faithful advanced the art of computer science. and deserving student of the graduating class in mechanical engineering.

ENGINEERING 2017–2018 The Adam J. Derman Memorial Award of Professor Garrelts and from the honor the grandfathers of Professor 233 Established in 1989 by family and Garrelts family in honor of an outstanding Clark T. Hung in the Department of friends in memory of Adam J. Derman engineer, educator, and administrator. Biomedical Engineering. His paternal ’89 and graduate student in the grandfather,Yuen-huo Hung, was a Department of Industrial Engineering The Carl Gryte Prize surgeon in Taipei who was renowned and Operations Research. A certificate Awarded annually to an undergraduate for his practice of medicine and for his and cash prize awarded annually by the student for service to the Department of compassion toward patients. Professor Department of Industrial Engineering Chemical Engineering. Hung’s maternal grandfather, Chao- and Operations Research to a member chin Huang, was a famous politician of the graduating class who has The Jonathan L. Gross Award for in Taiwan who dedicated his life to the demonstrated exceptional ability to Academic Excellence citizens of his country, serving as mayor make computer-oriented contributions This award was established in 2017 of Taipei, speaker of the Taiwan Provincial to the fields of industrial engineering and in honor of the much loved Professor Assembly, and consul general to the operations research. Emeritus Jonathan Gross. Each United States. This award is given to year a cash gift is awarded to one a graduating doctoral student in the Electrical Engineering Department graduating master's student and to one Department of Biomedical Engineering Research Award graduating senior from each of the four who embodies the collective attributes Awarded by the faculty of Electrical undergraduate schools served by the of these distinguished individuals. Engineering to one outstanding Department of Computer Science. This student will have demonstrated graduating senior who has great potential for making significant demonstrated outstanding passion and The Stephen D. Guarino Memorial contributions to the fields of biomedical accomplishment in research. Award in Industrial Engineering and engineering and public health, and for Operations Research serving as an ambassador of biomedical A certificate and cash prize established Electrical Engineering Department engineering. Service Award by a gift from Roger Guarino (1951) in Awarded by the faculty of Electrical memory of his son. To be awarded to The Illig Medal Engineering to one outstanding one outstanding senior in the Industrial Established in 1898 by a bequest graduating senior who has made Engineering and Operations Research from William C. Illig, E.M., 1882, and significant contributions to the Department who, in the opinion of awarded by the faculty to a member of department and community at large. the faculty and Board of Managers the graduating class for commendable of the Columbia Engineering School proficiency in his or her regular studies. Morton B. Friedman Memorial Prize Alumni Association, has been active for Excellence in undergraduate activities and has Industrial Engineering and Operations Morton B. Friedman was a visionary in displayed leadership, school spirit, and Research Academic Excellence the vanguard of engineering education scholarship achievement. Award through his lifelong service as professor, Given to exceptional students who department chair, and senior vice The William A. Hadley Award in completed both B.S. and M.S. in dean. Awarded periodically to an Mechanical Engineering the IEOR Department consecutively. undergraduate or graduate student Established in 1973 by Lucy Hadley in Students are awarded a certificate and who best exhibits Dean's Friedman's memory of her husband. The award is monetary prize. characteristics of academic excellence, made annually in the form of a certificate visionary leadership, and outstanding and prize to students in the graduating Industrial Engineering and Operations promise for the future. class in mechanical engineering who Research Graduate Fellowship have best exemplified the ideals of Gift from the IEOR Department, Zvi Galil Award for Improvement in character, scholarship, and service of nominated by the faculty. This fellowship Engineering Student Life Professor William A. Hadley. is designated to support graduate Given annually to the student group that students pursuing degrees in operations most improves engineering student life The Thomas “Pop” Harrington Medal research or industrial engineering. during the academic year. Established Presented annually to the student Recipients have demonstrated academic in honor of Zvi Galil, Dean of the School who best exemplifies the qualities of excellence and professional promise from 1995 to 2007. character that Professor Harrington in the fields. Students are awarded a exhibited during his forty years of certificate and monetary prize. The Jewell M. Garrelts Award teaching. The medal is made possible Awarded to the outstanding graduating by Dr. Myron A. Coler. Industrial Engineering and Operations senior(s) who will pursue graduate study Research Academic Outstanding in the department that was so long and The Yuen-huo Hung and Chao-chin Service Award successfully shepherded by Professor Huang Award in Biomedical In recognition of significant contributions Jewell M. Garrelts. This award is made Engineering to the IEOR Department, this award possible by gifts from alumni and friends This award has been endowed to goes to graduate students who have

ENGINEERING 2017–2018 234 represented the department with grace Charles Kandel Award outstanding promise for a career in and intelligence through their work as Medal and cash prize presented annually research and academia. ambassadors, student leaders, etc. by the Columbia Engineering School Students are awarded a certificate and Alumni Association to that member The Sebastian B. Littauer Award monetary prize. of the graduating class who has best Established in 1979 in honor of Professor promoted the interests of the School Littauer, a certificate and cash prize The Bernard Jaffe Prize for the through participation in extracurricular presented annually by the Department Encouragement of Inventiveness in activities and student-alumni affairs. of Industrial Engineering and Operations Engineering Research to a senior for outstanding Gift of Fern Jaffe in honor of her late Andrew P. Kosoresow Memorial promise of scholarly and professional husband, Bernard Jaffe ’38, ’39. Award for Excellence in Teaching, achievement in operations research. Given annually to an undergraduate TA-ing, and Service and graduate engineering and Awarded each year by the Department Robert D. Lilley Award for Socially applied science student who exhibits of Computer Science to up to three Responsible Engineering exceptional qualities of curiosity computer science students for Established in 2013 by a gift from toward the engineered world and a outstanding contributions to teaching in Helen M. Lilley, this award supports the predisposition toward inventiveness and the department and exemplary service activities of student clubs at the School novel problem solving in both theoretical to the department and its mission. that have as their primary focus socially and physical contexts. Preference is responsible engineering. given to students whose endeavors are Dongju Lee '03 Memorial Award directed toward the betterment of the Established in 2005 by family and Mechanical Engineering Certificate human condition. friends in memory of Dongju Lee (DJ), of Merit graduate student in the Department In recognition of excellence in Eliahu I. Jury Award of Civil Engineering and Engineering undergraduate studies. Established 1991 for outstanding Mechanics, 1999–2003. A certificate achievement by a graduate student or and cash prize awarded annually Mechanical Engineering Excellence in recent graduate in the areas of systems, by the department to a doctoral Undergraduate Research communications, signal processing, or student specializing in geotechnical/ Established in 2017, the Mechanical circuits. geoenvironmental engineering and of Engineering Department makes the

ENGINEERING 2017–2018 award to a student of the graduating C. Mills, a Ph.D. candidate in computer The Claire S. and Robert E. Reiss 235 class in mechanical engineering for science who exemplified academic Prize in Biomedical Engineering participation in, and contributions to, excellence by his boundless energy and This award is given by Robert E. Reiss, research. intellectual curiosity. B.S.’66, and his wife, Claire S., to the graduating senior(s) in biomedical Mechanical Engineering Faculty The Mindlin Scholar in Civil engineering judged by faculty of the Award in Leadership, Service, and Engineering and Engineering program as most likely to contribute Scholarly Work Mechanics substantially to the field. Established in 2017, awarded by the This award is presented to graduate Mechanical Engineering Faculty annually students in the Department of The Robert Edward Reiss Award in to a student of the graduating class in Civil Engineering and Engineering Chemical Engineering mechanical engineering for dedication Mechanics in recognition of outstanding Awarded annually to the student in the and contributions to leadership service promise of a creative career in research Department of Chemical Engineering and scholarly work. and/or practice. This award is made who shows the greatest promise of possible by gifts of friends, colleagues, success in applying the discipline The Henry L. Michel Award in Civil and former students of Professor of chemical engineering to the Engineering Raymond D. Mindlin, and, above all, improvement of biological products and Established by the Columbia Engineering by the Mindlin family. It is intended to medical devices. School Alumni Association in memory honor the Mindlin brothers, Raymond, of Henry M. Michel ’49, C.E., who built Eugene, and Rowland, who excelled The Francis B. F. Rhodes Prize Parsons Brinkerhoff into one of the in their respective scientific fields of Established in 1926 by Eben Erskine world’s leading engineering companies. engineering research, engineering Olcott, 1874, in memory of his A certificate and a cash prize are practice, and medical practice. classmate, Francis Bell Forsyth Rhodes, presented annually by the Department School of Mines, 1874, and awarded of Civil Engineering and Engineering The Moles’ Student Award in Civil from time to time to the member of the Mechanics to a student or group Engineering graduating class in materials science of students in the Civil Engineering Awarded to the student in engineering and metallurgical engineering who has Department who demonstrate whose academic achievement and shown the greatest proficiency in his or outstanding promise of leadership and enthusiastic application show outstanding her course of study. professional achievement in civil and promise of personal development leading construction engineering. The award is to a career in construction engineering School of Engineering and Applied in support of a project with emphasis on and management. Science Scholar Athlete Award the construction industry in which the Presented from time to time by the students participate. The James F. Parker Memorial Award Office of the Dean to that graduating (Mechanical Engineering Design Award) student who has distinguished himself or Paul Michelman Award for Exemplary James F. Parker served and represented herself as a varsity athlete and scholar. Service to the Computer Science Columbia engineering students as Department their Dean from 1975 to 1984. He also School of Engineering and Applied This award is given to a Ph.D. distinguished himself in the pursuit Science Student Activities Award student in computer science who and analysis of two-dimensional art. In This award is presented to an has performed exemplary service to recognition of his special combination undergraduate degree candidate in the department, devoting time and of talents and their integration, the Columbia Engineering who by virtue effort beyond the call to further the School of Engineering and Applied of his or her willingness, energy, and department’s goals. It is given in Science salutes the graduate student leadership has significantly contributed memory of Dr. Paul Michelman ’93, who has distinguished her- or himself to the cocurricular life of the School. who devoted himself to improving as a designer. A person of creative our department through service while and innovative inclination receives the Robert Simon Memorial Prize excelling as a researcher. James Parker Medal, as evidenced by The Robert Simon Memorial Prize was outstanding performance in courses established in 2001 to honor Robert Millman Award integrating engineering analysis and Simon, a Columbia alumnus who spent A certificate and prize, in honor of Jacob design. a lifetime making valuable contributions Millman, awarded to two of the most to computational and mathematical outstanding teaching assistants for the The Robert Peele Prize sciences, and is awarded annually by academic year. A cash prize awarded from time to time the Department of Applied Physics and to that member of the graduating class Applied Mathematics to the doctoral The Russell C. Mills Award in mining engineering who has shown student who has completed the most Presented to one or more computer the greatest proficiency in his or her outstanding dissertation. Should no science majors for excellence in course of studies. dissertation qualify in a given year, the computer science in memory of Russell prize may be awarded to either the most

ENGINEERING 2017–2018 236 outstanding student who has completed Student Excellence Award in Trustees, and CAA co-founder. Special a Master of Science degree in the Information and Systems consideration will be given to student department or to the most outstanding Awarded by the faculty of Electrical leaders who have demonstrated a graduating senior in the department. Engineering to one outstanding willingness and ability to work across graduating senior who has schools or organizations. The Richard Skalak Memorial Prize demonstrated outstanding passion and The Richard Skalak Memorial Prize accomplishment in information and RESIDENCE HALL SCHOLARSHIPS was founded in recognition of the systems. pioneering contributions of Richard Class of 1887 Mines Residence Skalak to the development of the Professor Rene B. Testa Award Scholarship biomedical engineering program at A prize that will be given to graduate Awarded annually to a third-year degree Columbia University. Dr. Skalak was and undergraduate students who have candidate, with preference given to an inspirational teacher and scholar achieved excellence in their academic descendants of members of the Class of who taught students and colleagues program and have actively participated 1887 Mines. to appreciate the value of broad in the research and testing mission of interactions between engineering and the Carleton Laboratory. Class of 1896 Arts and Mines medicine, particularly in the fields Scholarship of cardiovascular mechanics, tissue The George Vincent Wendell Awarded annually to a degree candidate engineering, and orthopedics. The Memorial Medal in Columbia College, Columbia Richard Skalak Memorial Prize is Established in 1924 by the friends in the Engineering, or the Graduate School awarded annually to a senior biomedical alumni and faculty of the late Professor of Architecture and Planning, with engineering student who exemplifies George Vincent Wendell to honor and preference given to descendants of the qualities of outstanding engineering perpetuate his memory; a certificate members of the Class of 1896 Arts and scholarship and breadth of scientific and medal awarded annually by choice Mines. curiosity that form the basis for lifelong of the class and the faculty to that member of the graduating class who learning and discovery. Class of 1916 College and best exemplifies his ideals of character, Engineering Fund Student Excellence Award in scholarship, and service. Gift of the Class of 1916 College and Electronics, Circuits, and Physics Engineering. Awarded by the faculty of Electrical Bill Campbell Award Engineering to one outstanding Presented by the CAA to a graduating graduating senior who has student at each school who shows demonstrated outstanding passion and exceptional leadership and Columbia accomplishment in electronics, circuits, spirit as exemplified by Bill Campbell, and physics. '62CC, '64TC, Chair Emeritus, University

ENGINEERING 2017–2018 University and School Policies, Procedures, and Regulations 238 ACADEMIC PROCEDURES AND STANDARDS

REGISTRATION AND are to be sent to a third party for completion of all requirements is ENROLLMENT payment. Students who are not citizens obligatory for each degree. Students Registration is the process that reserves of the United States and who need are exempted from the requirement to seats in particular classes for eligible authorization for special billing of tuition register continuously only when granted students. It is accomplished by following and/or fees to foreign institutions, a voluntary or medical leave of absence the procedures announced in advance agencies, or sponsors should go by their Committee on Academic of each term’s registration period. to the International Students and Standing (for undergraduate students) Enrollment is the completion of the Scholars Office with two copies of the or the Office of Graduate Student Affairs registration process and affords the full sponsorship letter. (for graduate students). rights and privileges of student status. Enrollment is accomplished by the University Regulations Registration Instructions payment or other satisfaction of tuition Each person whose enrollment has Registration instructions are announced and fees and by the satisfaction of other been completed is considered a student in advance of each registration obligations to the University. of the University during the term for period. Students should consult Registration alone does not which he or she is enrolled unless his these instructions for the exact dates guarantee enrollment; nor does or her connection with the University and times of registration activities. registration alone guarantee the right is officially severed by being withdrawn Students must be sure to obtain all to participate in class. In some cases, or for other reasons. No student necessary written course approvals and students will need to obtain the approval enrolled in any school or college of the advisers’ signatures before registering. of the instructor or of a representative University shall at the same time be Undergraduate students who have not of the department that offers a course. enrolled in any other school or college, registered for a full-time course load by Students should check this bulletin, their either of Columbia University or of any the end of the change of program period registration instructions, the Directory of other institution, without the specific will be withdrawn, as will graduate Classes, and also with an adviser for all authorization of the dean or director of students who have not registered for approvals that may be required. the school or college of the University in any coursework by the end of the To comply with current and which he or she is first enrolled. change of program period. International anticipated Internal Revenue Service The privileges of the University students enrolled in graduate degree mandates, the University requires are not available to any student until programs must maintain full-time status all students who will be receiving enrollment has been completed. until degree completion. financial aid or payment through the Students are not permitted to attend any University payroll system to report University course for which they are not DEGREE REQUIREMENTS AND their Social Security number at the officially enrolled or for which they have SATISFACTORY PROGRESS time of admission. Newly admitted not officially filed a program unless they students who do not have a Social have been granted auditing privileges. Security number should obtain one The University reserves the right to Undergraduate well in advance of their first registration. withhold the privileges of registration Undergraduate students are International students should consult and enrollment or any other University required to complete the School’s the International Students and Scholars privilege from any person who has degree requirements and graduate Office, located at 524 Riverside Drive outstanding financial, academic, in eight academic terms. Full-time (212-854-3587), for further information. or administrative obligations to the undergraduate registration is defined Special billing authorization is University. as at least 12 semester credits per required of all students whose bills Continuous registration until term. However, in order to complete the

ENGINEERING 2017–2018 degree, students must be averaging or she has earned a cumulative GPA Transfer Credits 239 16 points per term. Students may not of 2.5 or minimum GPA required by Undergraduate students may obtain register for point loads greater than 21 the academic department, whichever academic credit toward the B.S. points per term without approval from is higher. Candidates in the Doctor of degree by completing coursework at the Committee on Academic Standing. Engineering Science (Eng.Sc.D.) program other accredited four-year institutions. To be eligible to receive the Bachelor are expected to achieve a 3.0 grade- Normally, this credit is earned during of Science degree, a student must point average or minimum GPA required the summer. To count as credit toward complete the courses prescribed in a by the academic department, whichever the degree, a course taken elsewhere faculty-approved major/program (or is higher. must have an equivalent at Columbia faculty-authorized substitutions) and Graduate students (on-campus University and the student must achieve achieve a minimum cumulative grade- and online students) who do not meet a grade of at least B. An exception to point average (GPA) of 2.0. Although the minimum cumulative GPA of the this policy is made for students enrolled the minimum number of academic school and the department by the end in an approved study abroad program. credits is 128 for the B.S. degree, some of their first semester will be placed Students in an approved study abroad programs of the School require a greater on academic probation. During the program will receive transfer credit if they number of credits in order to complete probation period students must meet earn a grade of C or higher. To transfer all the requirements. Undergraduate with their department to discuss and credit, a student must obtain prior engineering degrees are awarded only to develop an academic plan to improve approval from his or her CSA adviser students who have completed at least their overall GPA. If the student does and the department before taking such 60 points of coursework at Columbia. not meet the academic benchmarks courses. A course description and No credit is earned for duplicate courses, required by their department after the syllabus should be furnished as a part including courses that are taken pass/fail term in which they have been placed on of the approval process. Courses taken and the final grade is a P. probation, then they may be asked to before the receipt of the high school Undergraduates in the programs leave the School permanently. Degree diploma may not be credited toward the accredited by the Engineering requirements for master’s degrees B.S. degree. A maximum of 6 credits Accreditation Commission of ABET must be completed within five years; may be applied toward the degree for (biomedical engineering, chemical those for the doctoral degrees must college courses taken following the engineering, civil engineering, Earth be completed within seven years. receipt of a high school diploma and and environmental engineering, A minimum cumulative grade-point initial enrollment at Columbia University. electrical engineering, and mechanical average of 2.5 (in all courses taken as Master degree students are not engineering) satisfy ABET requirements a degree candidate) is required for the eligible for transfer credits. by taking the courses in prescribed M.S. degree; a minimum GPA of 3.0 is Students possessing a conferred programs, which have been designed required for the Doctor of Engineering M.S. degree may be awarded 2 by the departments so as to meet the Science (Eng.Sc.D.) degree. The residence units toward their Ph.D., as ABET criteria. minimum residence requirement for well as 30 points of advanced standing each Columbia degree is 30 points of toward their Ph.D. or Eng.Sc.D. with Attendance coursework completed at Columbia. departmental approval. Students are expected to attend their classes and laboratory periods. Changes in Registration Examinations Instructors may consider attendance in A student who wishes to drop or add Midterm examinations: Instructors assessing a student’s performance and courses or to make other changes in generally schedule these in late October may require a certain level of attendance his or her program of study after the and mid-March. for passing a course. change of program period must obtain Final examinations: These are given the approval of his or her CSA adviser. at the end of each term. The Master Graduate A student who wishes to drop or add a University Examination Schedule is Graduate students are required course in his or her major must obtain available online and is confirmed by to complete the School’s degree department approval. The deadline for November 1 for the fall term and April requirements as outlined on page 26 (The making program changes in each term 1 for the spring term. This schedule is Graduate Programs). Full-time graduate is shown in the Academic Calendar. sent to all academic departments and registration is defined as at least 12 After this date, undergraduate students is available for viewing on the Columbia credits per term. M.S. students may not must petition their Committee on website. Students should consult with register for point loads greater than 15 Academic Standing; graduate students their instructors for any changes to the credits per term or 9 credits for the last must petition the Office of Graduate exam schedule. Examinations will not term. Student Affairs. For courses dropped be rescheduled to accommodate A graduate student who has after these dates, no adjustment of fees travel plans. matriculated in an M.S. program or will be made. Failure to attend a class Note: If a student has three final is a nondegree student is considered without officially dropping the class will examinations scheduled during one to be making normal progress if he result in a grade indicating permanent calendar day, as certified by the unofficial withdrawal (UW).

ENGINEERING 2017–2018 240 Registrar, an arrangement may be made be given only to those students who regularly extend beyond the end of with one of the student’s instructors indicate, upon registration and to the the term. Upon completion, a final to take that examination at another, instructor, their intention to take the qualitative grade is then assigned and mutually convenient time during the course for R, or who, with the approval credit allowed. The mark of CP implies final examination period. This refers of the instructor, file written notice of satisfactory progress. to a calendar day, not a 24-hour time change of intention with the registrar The mark of MU (make-up period. Undergraduate students unable not later than the last day for change of examination): given to a student who to make suitable arrangements on their program. Students wishing to change has failed the final examination in a own should contact their CSA adviser. to R credit after this date are required course but who has been granted the Graduate students should contact the to submit written approval from the privilege of taking a second examination Office of Graduate Student Affairs. Office of Graduate Student Affairs and in an effort to improve his or her final the course instructor to the registrar. grade. The privilege is granted only Transcripts and Certifications The request to change to R credit must when there is a wide discrepancy For information on the Federal Family be made by the last day to change a between the quality of the student’s Education Rights and Privacy Act course grading option. A course that work during the term and his or her (FERPA) of 1974, please visit http:// has been taken for R credit may not performance on the final examination, facets.columbia.edu—Essential Policies be repeated later for examination credit and when, in the instructor’s judgment, for the Columbia Community. Information and cannot be uncovered under any the reasons justify a make-up on obtaining University transcripts and circumstances. The mark of R does not examination. A student may be granted certifications will be found as a subhead count toward degree requirements for the mark of MU in only two courses in under Essential Resources. graduate students. The mark of R is one term, or, alternatively, in three or automatically given in Doctoral Research more courses in one term if their total Report of Grades Instruction courses. point value is not more than 7 credits. The mark of UW (unofficial The student must remove MU by taking Grades can be viewed by using the withdrawal): given to students who a special examination administered as Student Services Online feature located discontinue attendance in a course but soon as the instructor can schedule it. on the Student Services home page at are still officially registered for it, or who The mark of P/F (pass/fail): columbia.edu/students. If you need an fail to take a final examination without an Undergraduate students may take up to official printed report, you must request authorized excuse. two courses of the 9-11 nontechnical a transcript (please see Transcripts and The mark of IN (incomplete): granted elective credit on a P/F basis. These Certifications above). only in the case of incapacitating illness courses must be at the 3000-level or All graduate students must have a as certified by the Health Services at higher and must be courses that can current mailing address on file with the Columbia, serious family emergency, or be taken P/F by students attending Registrar’s Office. circumstances of comparable gravity. Columbia College (e.g., instruction Undergraduate students request an IN classes in foreign language and core Transcript Notations by filling out the Incomplete Request curriculum classes are not eligible). The grading system is as follows: A, Form with their CSA adviser prior to the These courses may not count toward excellent; B, good; C, satisfactory; final exam for the course in the semester the minor, and cannot be uncovered D, poor but passing; F, failure (a final of enrollment. Students requesting an under any circumstances. Students may grade not subject to re-examination). IN must gain permission from both the take only one class P/F per semester Occasionally, P (Pass) is the only Committee on Academic Standing (CAS) to count toward the 128 points, passing option available. The grade- and the instructor. Graduate students exclusive of physical education credit point average is computed on the basis should contact their instructor. If granted and any other course that is taught of the following index: A=4, B=3, C=2, an IN, students must complete the only on a P/F basis. Please note that D=1, F=0. Designations of + or – (used required work within a period of time physical education classes are the only only with A, B, C) are equivalent to 0.33 stipulated by the instructor but not to courses taught solely on a P/F basis (i.e., B+=3.33; B–=2.67). Grades of P, exceed one year. After a year, the IN will that may apply toward the 128 credits INC, UW, and MU will not be included be automatically changed into an F or for the degree. The P/F option does in the computation of the grade-point the contingency grade. not count toward degree requirements average. The mark of YC (year course): a mark for graduate students and cannot be The mark of R (registration credit; no given at the end of the first term of a uncovered under any circumstances. qualitative grade earned): not accepted course in which the full year of work The mark of W (official withdrawal): a for degree credit in any program. R must be completed before a qualitative mark given to students who are granted credit is not available to undergraduate grade is assigned. The grade given at a leave of absence after the drop students for academic classes. In some the end of the second term is the grade deadline for the semester. The grade divisions of the University, the instructor for the entire course. of W, meaning “official withdrawal,” will may stipulate conditions for the grade The mark of CP (credit pending): be recorded as the official grade for and report a failure if those conditions given only in graduate research courses the course in lieu of a letter grade. The are not satisfied. The R notation will in which student research projects grade of W will zero out the credits for

ENGINEERING 2017–2018 the class so the student’s GPA will not their application for the degree with Diplomas 241 be affected. the Diploma Division, 210 Kent Hall, There is no charge for the preparation or through the registrar’s website: and conferral of an original diploma. Name Changes registrar.columbia.edu/registrar-forms/ If your diploma is lost or damaged, Students may change their name of application-degree-or-certificate. there will be a charge of $100 for record by submitting a name change Candidates for doctoral and Master of a replacement diploma. Note that affidavit to the Student Service Center. Philosophy degrees should inquire at replacement diplomas carry the Affidavits are available from this office or their departments but must also follow signatures of current University online at registrar.columbia.edu. the instructions of the Dissertation officials. Applications for replacement Office, 107 Low Library. diplomas are available on our website: General deadlines for applying for registrar.columbia.edu/registrar-forms/ GRADUATION graduation are November 1 for February, application-replacement-diploma. Columbia University awards degrees December 1 for May, and August 1 for Any questions regarding graduation three times during the year: in February, October. (When a deadline falls on a or diploma processing should be May, and October. There is one weekend or holiday, the deadline moves addressed to [email protected]. commencement ceremony in May. to the next business day.) Doctoral students must deposit their dissertations Application or Renewal of two days before the above conferral Application for the Degree dates in order to graduate. In general, students pick up and file an Students who fail to earn the degree application for a degree at their schools by the conferral date for which they or departments, but there are several applied must file another application for exceptions. Candidates for Master of a later conferral date. Science degrees may pick up and file

ENGINEERING 2017–2018 242 ACADEMIC STANDING

ACADEMIC HONORS and determine when circumstances • Continued Probation: Students who warrant exceptions to them. are already on probation and fail to Dean’s List Academic performance is reviewed meet the minimum requirements as To be eligible for Dean’s List honors, an by advisers at the end of each semester. stated in their sanction letter undergraduate student must achieve a The Undergraduate Committee on • Strict Probation: Students who are grade-point average of 3.5 or better and Academic Standing, in consultation already on probation, fail to meet the complete at least 15 graded credits with with the departments, meets to review minimum requirements as stated in no unauthorized incompletes, UWs, or undergraduate grades and progress their sanction letter, and are far below grades lower than C. toward the degree. Indicators of minimum expectations. This action is academic well-being are grades that typically made when there are signs of average above 2.0 each term, in a severe academic difficulty. Honors Awarded with the Degree coordinated program of study, with no • Suspension and Dismissal: Students At the end of the academic year, a incomplete grades. who have been placed on academic select portion of the candidates for Possible academic sanctions include: probation and who fail to be restored the Bachelor of Science degree who to good academic standing in the have achieved the highest academic • Warning: C– or below in any core following semester can be considered cumulative grade-point average are science course or in a required course either for suspension or dismissal by accorded Latin honors. Latin honors are for their major; low points toward the Undergraduate Committee on awarded in three categories (cum laude, degree completion Academic Standing. The decision to magna cum laude, and summa cum • Academic Probation: Students will be suspend or dismiss a student will be laude) to no more than 25 percent of the placed on academic probation if they made by the Committee on Academic graduating class, with no more than 5 meet any of the conditions below: Standing in the Berick Center for percent summa cum laude, 10 percent – fall below a 2.0 GPA in a given Student Advising and the Dean’s magna cum laude, and 10 percent semester Office in close consultation with the cum laude. Honors are awarded on – have not completed 12 points student’s departmental adviser when the overall record of graduating seniors successfully in a given semester the student has declared a major. who have completed a minimum of four – have not completed chemistry, In cases of suspension, the student semesters at Columbia. Students may physics, University Writing, The Art will be required to make up the not apply for honors. of Engineering, and calculus during deficiencies in their academic record the first year by taking appropriate courses at a ACADEMIC MONITORING – receive a D, F, UW, or unauthorized four-year accredited institution in North The Undergraduate Committee on Incomplete in any first-year/ America. Students must be able to Academic Standing determines sophomore required courses complete their degree requirements in academic policies and regulations – receive a D, F, UW, or unauthorized their eighth semester at Columbia after for the School except in certain Incomplete in any course required readmission. If this is not achievable, instances when decisions are for the major then students should be considered for made by the faculty as a whole. – receive straight C’s in the core dismissal instead. The Undergraduate Committee on science courses (chemistry, Academic Standing is expected to calculus, physics) The courses that the student uphold the policies and regulations – not making significant progress must take will be determined by of the Committee on Instruction toward the degree the Undergraduate Committee of

ENGINEERING 2017–2018 Academic Standing and by the deadline. If after the drop deadline, the should consult the Office of Graduate 243 student’s departmental adviser when course grades will normally be W (official Student Affairs. the student has declared a major. All withdrawal) in all courses. In certain proposed courses will be reviewed circumstances a student may qualify VOLUNTARY LEAVE by the appropriate faculty who teach for an incomplete, which would have to OF ABSENCE the equivalent classes at Columbia be completed by the first week of the A voluntary leave of absence (VLOA) University. All courses that are being semester in which the student returns may be granted by the Committee on taken to fulfill a major requirement or as to Columbia. If the Incomplete is not Academic Standing to undergraduate a technical elective must be approved completed by that time, a W will be students who request a temporary by the student’s departmental adviser. inserted. withdrawal from Columbia Engineering Courses being taken to count as a In exceptional cases, an for a nonmedical reason. Students nontech elective or to count as general undergraduate student may apply considering a voluntary leave must credit would only require the approval for readmission following a one-term discuss this option in advance with of the Undergraduate Committee medical leave of absence. In addition their CSA adviser. Voluntary leaves are on Academic Standing. The existing to providing a personal statement and granted for a period of one academic procedures for the approval of outside supporting medical documentation year only; VLOAs will ordinarily not credit will be followed in these cases. for the medical leave readmission be granted for one semester, or for Students must receive a grade of B or committee to review, the student will more than one year. Students must better for the credit to be transferred. also need to provide a well-developed be in good academic standing at the The Office of Graduate Student academic plan that has been approved time of the leave and must be able to Affairs monitors the academic progress by the departmental adviser and the complete their major and degree in eight of graduate students in consultation with Berick Center for Student Advising as semesters. the departments. part of the readmission process. This A voluntary leave of absence for plan must demonstrate that his or her a graduate student is granted by the return to Columbia Engineering following MEDICAL LEAVE OF ABSENCE Office of Graduate Student Affairs. A a one-semester leave of absence will A medical leave of absence for an graduate student may request to return allow the student to properly follow the undergraduate student is granted by from a voluntary leave of absence for sequence of courses as required for the the James H. and Christine Turk Berick the fall, spring, or summer semester. A major and to meet all other graduation Center for Student Advising to a student request to return must be made before requirements by their eighth semester. whose health prevents him or her from the semester starts. Please contact the The final decision regarding whether successfully pursuing full-time study. Office of Graduate Student Affairs for or not a student will be allowed to be Undergraduates who take a medical leave more information. readmitted after a one-semester leave of absence are guaranteed housing upon When a voluntary leave of absence will be made by the Medical Leave their return. is granted during the course of the Readmission Committee. The deadlines A medical leave of absence for a semester, the semester will be deleted for petitioning a readmission are June graduate student is granted by the if the leave begins prior to the drop 1 for the fall semester and November 1 Office of Graduate Student Affairs, so deadline. If after the drop deadline, for the spring semester. The deadlines please consult with this office for more the course grades will normally be a for petitioning a return from a medical information. W (official withdrawal) in all courses. In leave for graduate students after Documentation from a physician or certain circumstances a student may one semester are July 15 for the fall counselor must be provided before such qualify for an incomplete, which would semester and December 15 for the a leave is granted. In order to apply for have to be completed by the first week spring. Students are not eligible to return readmission following a medical leave, a of the semester in which the student from a medical leave during the summer. student must submit proof of recovery returns to Columbia. If the Incomplete is A return from a medical leave request from a physician or counselor. Graduate not completed by that time, a W will be must be made before the start of the fall students may also be required to meet inserted. or spring semester. Graduate students with a medical provider at Columbia. A In exceptional cases, an should contact the Office of Graduate medical leave is for a minimum of one undergraduate may apply for Student Affairs for more information year and cannot be longer than two readmission following a one-term about petitioning to return after a one- years. If the student does not return within voluntary leave of absence. The student semester medical leave. the two-year time frame, he or she will be will need to provide to the Committee During the course of the leave, permanently withdrawn from the School. on Academic Standing a well-developed students are not permitted to take any Students may only return in the fall or academic plan that has been approved courses for the purpose of transferring spring term, not in summer sessions. by the departmental adviser and the credit and are not permitted to be on When a medical leave of absence Berick Center for Student Advising as campus. For more information about the is granted during the course of the part of the admission process. This medical leave of absence policy, consult semester, the semester will be deleted plan must demonstrate that his or her your CSA adviser; graduate students if the leave begins prior to the drop return to Columbia Engineering following

ENGINEERING 2017–2018 244 a one-semester leave of absence will of the semester, the semester will be the Columbia Community allow the student to properly follow the deleted if the leave begins prior to the (facets.columbia.edu) for recent sequence of courses as required for the drop deadline. If after the drop deadline, updates regarding leave for military duty. major and to meet all other graduation the course grades will normally be W requirements by their eighth semester. (official withdrawal) in all courses. In INVOLUNTARY LEAVE The Committee on Academic Standing certain circumstances, a student may OF ABSENCE POLICY will review the student’s academic qualify for an incomplete, which would Please refer to Involuntary Leave of plan and request for readmission. The have to be completed by the first week Absence Policy in Essential Policies deadlines for petitioning for readmission of the semester in which the student for the Columbia Community are June 1 for the fall semester and returns to Columbia. If the Incomplete is facets.columbia.edu). November 1 for the spring semester. not completed by that time, a W will be The deadlines for petitioning a return inserted. from a voluntary leave for graduate To return, students must notify the REQUIRED MEDICAL LEAVE students after one semester are July 15 Berick Center for Student Advising as FOR STUDENTS WITH for the fall semester and December 15 soon as possible, ideally by November EATING DISORDERS for the spring. 1 for the spring semester and June 1 Please refer to Required Medical Leave Students may not take courses for for the fall semester. Students must for Students with Eating Disorders in transferable credit while on leave. Finally, request readmission in writing and Essential Policies for the Columbia students who choose to take voluntary submit a statement describing their Community (facets.columbia.edu). leaves are not guaranteed housing upon readiness to return. Once readmission return to the University. International is granted, housing will be guaranteed. students should contact the International SEAS students may request permission READMISSION Students and Scholars Office to ensure to return after one semester as long Students seeking readmission must that a leave will not jeopardize their as they can demonstrate that they submit evidence that they have ability to return to Columbia Engineering. can remain on sequence with their achieved the purposes for which they coursework and have the prior approval left. Consequently, specific readmission of the departmental adviser. procedures are determined by the UNDERGRADUATE EMERGENCY Students who decide not to return reasons for the withdrawal. Further FAMILY LEAVE OF ABSENCE must notify the James H. and Christine information for undergraduate students Students who must leave the University Turk Berick Center for Student Advising is available in the Berick Center for for urgent family reasons that neces- of their decision. The date of separation Student Advising. Graduate students sitate a semester-long absence (e.g., for the leave of absence will be the date should see the Office of Graduate family death or serious illness in the of separation for withdrawal. Leaves Student Affairs. family) may request an emergency family may not extend beyond four semesters. Students applying for readmission leave of absence. Documentation of the Students who do not notify the Berick should complete all parts of the serious nature of the emergency must Center for Student Advising of their appropriate readmission procedures be provided. Students must request an intentions by the end of the two-year by June 1 for the autumn term or emergency family leave of absence from period will be permanently withdrawn. November 1 for the spring term. their advising dean in the James H. and Christine Turk Berick Center for Student Advising. LEAVE FOR MILITARY DUTY When an emergency family leave of Please refer to Military Leave of absence is granted during the course Absence Policy in Essential Policies for

ENGINEERING 2017–2018 POLICY ON CONDUCT AND DISCIPLINE 245

LIFE IN THE student in the School will act in an • Falsification ACADEMIC COMMUNITY honest way and will respect the rights • Federal, State, or Local laws, Violation The Fu Foundation School of of others. Freedom of expression is an of Engineering and Applied Science within essential part of University life, but it • Fire Safety Policies, Violation of Columbia University is a community. does not include intimidation, threats of • Illegal Drugs Policy, Violation of Admitted students, faculty, and violence, or the inducement of others to • Hazing administrators come together and engage in violence or in conduct which • Information Technologies Policies, work through committees and other harasses others. We state emphatically Violation of representative bodies to pursue and to that conduct which threatens or • Physical Endangerment, Threats, and promote learning, scholarly inquiry, and harasses others because of their race, Harassment free discourse. As in any community, sex, religion, disability, sexual orientation, • Retaliation principles of civility and reasoned or for any other reason is unacceptable • Smoking Policy, Violation of University interaction must be maintained. Thus, and will be dealt with severely. If each • Theft methods for addressing social as well as of us at Columbia can live up to these • Vandalism academic behaviors exist. standards, we can be confident that • Weapons all in our community will benefit fully from the diversity to be found here. Any STANDARDS AND DISCIPLINE RULES OF UNIVERSITY undergraduate student who believes he CONDUCT As members of the Columbia University or she has been victimized should speak • Guide to Living community, all students are expected with an adviser in the James H. and • Gender-Based Misconduct Policy for to uphold the highest standards of Christine Turk Berick Center for Student Students respect, integrity, and civility. These Advising, a member of the Residential • Columbia University Information core values are key components of the Life staff, or a member of Student Technology (CUIT) policies and Columbia University experience and Conduct and Community Standards; procedures reflect the community's expectations of graduate students should speak with an • Undergraduate Student Travel Policy Columbia University students. Students officer in the Office of Graduate Student are therefore expected to conduct Affairs. themselves in an honest, civil, and While every subtlety of proper ACADEMIC INTEGRITY respectful manner in all aspects of their behavior cannot be detailed here, Academic integrity defines a university lives. Students who violate standards examples of other actions subject to and is essential to the mission of of behavior related to academic or discipline are: education. At Columbia students are behavioral conduct interfere with their expected to participate in an academic ability, and the ability of others, to take • Access, Unauthorized community that honors intellectual work advantage of the full complement of • Alcohol, Prohibited use of and respects its origins. In particular, University life, and will thus be subject to • Collusion the abilities to synthesize information Dean's Discipline. • Columbia University Identification and produce original work are key Undergraduate Community members Card, Unauthorized use of components in the learning process. As may find a full description of University • Columbia Identity (or affiliated such, a violation of academic integrity policies at: http://studentconduct. organizations), Unauthorized use of is one of the most serious offenses a columbia.edu/. • Disruptive Behavior student can commit at Columbia and We expect that in and out of the • Failure to Comply can result in dismissal. classroom, on and off campus, each • Entry/Egress, Unauthorized

ENGINEERING 2017–2018 246 Students rarely set out with the laboratory reports, and analytic essays make sound decisions regarding intent of engaging in violations of of different lengths. These papers play academics, extracurricular activities, academic integrity. But classes are a major role in course performance, but and personal issues. If you don’t know challenging at Columbia, and students more important, they play a major role where to go, see your advising dean. will often find themselves pressed for in intellectual development. Plagiarism, time, unprepared for an assignment or the use of words, phrases, or ideas Academic Integrity Policies and exam, or feeling that the risk of earning belonging to another, without properly Expectations a poor grade outweighs the need to citing or acknowledging the source, Violations of policy may be intentional be thorough. Such circumstances is considered one of the most serious or unintentional and may include lead some students to behave in violations of academic integrity and dishonesty in academic assignments a manner that compromises the is a growing problem on university or in dealing with University officials, integrity of the academic community, campuses. including faculty and staff members. disrespects their instructors and One of the most prevalent forms Moreover, dishonesty during the Dean’s classmates, and deprives them of an of plagiarism involves students using Discipline hearing process may result in opportunity to learn. In short, they information from the Internet without more serious consequences. cheat. Students who find themselves in proper citation. While the Internet Types of academic integrity violations: such circumstances should immediately can provide a wealth of information, contact their instructor and adviser for sources obtained from the web must • Academic Dishonesty, Facilitation of: advice. be properly cited just like any other assisting another student in a violation The easiest way to avoid the source. If you are uncertain how to of academic integrity is prohibited. temptation to cheat in the first place properly cite a source of information This may include but is not limited to is to prepare yourself as best you can. that is not your own, whether from the selling and/or providing notes, exams, Here are some basic suggestions to Internet or elsewhere, it is critical that and papers. help you along the way: you do not hand in your work until • Assistance, Unauthorized Giving: you have learned the proper way to unauthorized assistance to another • Understand instructor expectations use in-text references, footnotes, and student or receiving unauthorized aid and policies. bibliographies. Faculty members are from another person on tests, quizzes, • Clarify any questions or concerns available to help as questions arise assignments, or examinations without about assignments with instructors as about proper citations, references, the instructor's express permission is early as possible. and the appropriateness of group prohibited. • Develop a timeline for drafts and work on assignments. You can also • Bribery: offering or giving any favor final edits of assignments and begin check with the Undergraduate Writing or thing of value for the purpose of preparation in advance. Program. Ignorance of proper citation improperly influencing a grade or other • Avoid plagiarism: acknowledge methods does not exonerate one from evaluation of a student in an academic people’s opinions and theories by responsibility. program is prohibited. carefully citing their words and always • Cheating: wrongfully using or indicating sources. Personal Responsibility, Finding attempting to use unauthorized • Utilize the campus’s resources, Support, and More Information materials, information, study aids, such as the advising centers and A student’s education at Columbia or the ideas or work of another in Counseling and Psychological University is comprised of two order to gain an unfair advantage is Services, if feeling overwhelmed, complementary components: a prohibited. Cheating includes, but burdened, or pressured. mastery over intellectual material is not limited to, using or consulting • Assume that collaboration in the within a discipline and the overall unauthorized materials or using completion of assignments is development of moral character unauthorized equipment or devices prohibited unless specified by the and personal ethics. Participating on tests, quizzes, assignments, instructor. in forms of academic dishonesty or examinations, working on any Students found responsible for an violates the standards of our examination, text, quiz, or assignment academic integrity violation may be community at Columbia and severely outside the time constraints imposed, disqualified from receiving Latin Honors. inhibits a student’s chance to grow the unauthorized use of prescription academically, professionally, and medication to enhance academic Plagiarism and socially. As such, Columbia’s approach performance, and /or submitting an Acknowledgment of Sources to academic integrity is informed by altered examination or assignment to Columbia has always believed that its explicit belief that students must an instructor for regrading. writing effectively is one of the most take full responsibility for their actions, • Collaboration, Unauthorized: important goals a college student can meaning you will need to make collaborating on academic work achieve. Students will be asked to do informed choices inside and outside without the instructor's permission is a great deal of written work while at the classroom. Columbia offers a prohibited. This includes, but is not Columbia: term papers, seminar and wealth of resources to help students limited to, unauthorized collaboration

ENGINEERING 2017–2018 on tests, quizzes, assignments, labs, conditions, to intentionally or Standards is responsible for 247 and projects. unintentionally create access to an administering the Dean's Discipline • Dishonesty: falsification, forgery, or unfair advantage for oneself or others disciplinary process for all disciplinary misrepresentation of information is prohibited. affairs concerning students that are not to any University official in order to reserved to some other body. gain an unfair academic advantage Students are expected to familiarize DISCIPLINARY PROCEDURES in coursework or lab work, on any themselves with the Standards Many policy violations that occur in application, petition, or documents and Discipline handbook and the the Residence Halls or within fraternity submitted to this University is comprehensive list of policies and and sorority housing are handled by prohibited. This includes, but is not expectations available on the Students Residential Life. Some serious offenses limited to, falsifying information on a Conduct and Community Standards are referred directly to Student Conduct resume, fabrication of credentials or website (studentconduct.columbia.edu). and Community Standards. Violations academic records, misrepresenting For more information about the in University Apartment Housing are one's own research, providing false or discipline process for graduate students, handled by building managers and misleading information in order to be please visit the Office of Graduate housing officials. Some incidents are excused from classes or assignments, Student Affairs website (engineering. referred directly to the School’s housing and/or intentionally underperforming columbia.edu/graduate-student-affairs). liaison in the Office of Graduate Student on a placement exam. Affairs. • Ethics, Honor Codes, and Professional Confidentiality In matters involving rallies, picketing, Standards, Violation of: any violation and other mass demonstrations, the Privacy and Reporting: Disciplinary proof published institutional policies Rules of University Conduct outlines ceedings conducted by the University related to ethics, honor codes, or procedures. are subject to the Family Education professional standards of a student's Student Conduct and Community Rights and Privacy Act ("FERPA," also respective school is prohibited. Standards is responsible for all called "The Buckley Amendment"). • Failing to Safeguard Work: failure to disciplinary affairs concerning There are several important exceptions take precautions to safeguard one's undergraduate students that are not to FERPA that will allow the University own work is prohibited. reserved to some other body. The to release information to third parties • Giving or Taking Academic Materials, Office of Graduate Student Affairs is without a student's consent. For exam- Unauthorized: unauthorized circulation responsible for all disciplinary affairs ple, the release of student disciplinary or sharing of past or present course concerning graduate students that are records is permitted without prior stu- material(s) without the instructor's not reserved to some other body. dent consent to University officials with express permission is prohibited. a legitimate educational interest such This includes, but is not limited to, as a student's academic adviser and to Dean’s Discipline Process for assignments, exams, lab reports, Columbia Athletics if the student is an Undergraduate and Graduate notebooks, and papers. athlete. The University will also release Students • Obtaining Advanced Knowledge: information when a student gives written It is expected that all students act in an unauthorized advanced access to permission for information to be shared. honest way and respect the rights of exams or other assignments without To obtain a FERPA waiver, please visit: others at all times. Dean's Discipline is an instructor's express permission is http://www.columbia.edu/cu/student- the process utilized to investigate and prohibited. conduct/documents/FerpaRelease. respond to allegations of behavioral • Plagiarism: the use of words, phrases, pdf. To read more about the exceptions or academic misconduct. The Dean's or ideas belonging to another without that apply to the disclosure of student Discipline process is not meant to be properly citing or acknowledging records information, please visit: http:// an adversarial or legal process, but the source is prohibited. This may www.essentialpolicies.columbia.edu/ instead aims to educate students about include, but is not limited to, copying policy-access-student-recordferpa. the impact their behavior may have on computer programs for the purposes Students found responsible for their own lives as well as on the greater of completing assignments for reportable violations of conduct, community and, as a result, is not meant submission. including academic integrity violations, to be an adversarial or legal process. • Sabotage: inappropriately and may face reports of such offenses The process is initiated when an deliberately harming someone else's on future recommendations for law, allegation is reported that a student academic performance is prohibited. medical, or graduate school. Students may have violated University policies. • Self-Plagiarism: using any material found responsible for any violations Students may be subject to Dean's portion of an assignment to fulfill the of conduct may be disqualifited Discipline for any activity that occurs requirements of more than one course from receiving Latin Honors or other on or off campus that impinges on the without the instructor's express awards. The parents or guardians of rights of other students and community permission is prohibited. undergraduate students may also be members. This also includes violations • Test Conditions: violations of notified. compromising a testing environment of local, state, or federal laws. or violating specified testing Student Conduct and Community

ENGINEERING 2017–2018 248 ESSENTIAL POLICIES FOR THE COLUMBIA COMMUNITY

his bulletin is intended for the Policies on this website pertain to • Protection of Minors guidance of persons applying campus safety (including harassment • University Event Policies Tfor or considering application for and discrimination), the confidentiality of • Policy on Partisan Political Activity admission to Columbia University and for student records, drug and alcohol use, • Campus Safety and Security the guidance of Columbia students and student leaves, and political activity, as • Crime Definitions in Accordance with faculty. The bulletin sets forth in general the well as others. This is a useful reference the Federal Bureau of Investigation’s manner in which the University intends to to several important polices the Columbia Uniform Crime Reporting Program proceed with respect to the matters set University maintains including the following: • Morningside Campus: Required forth herein, but the University reserves Medical Leave for Students with the right to depart without notice from the • Student Email Communication Policy Eating Disorders terms of this bulletin. The bulletin is not • Information Technology Policies • Voluntary Leave of Absence Policy intended to be and should not be regarded • Social Security Number Reporting • Involuntary Leave of Absence Policy as a contract between the University and • Policy on Access to Student Records • Military Leave of Absence Policy any student or other person. (FERPA) • Central Administration of the Valuable information to help students, • University Regulations (including Rules University’s Academic Programs faculty, and staff understand some of the of University Conduct) • Non-Retaliation Policy policies and regulations of the University • Policies on Alcohol and Drugs • Essential Resources can be found in Essential Policies for • Columbia University Non- • Student Consumer Information the Columbia Community at facets Discrimination Statement and Policy • Additional Policy Sources .columbia.edu. • Gender-Based Misconduct Policy and • Directory Procedures for Students

ENGINEERING 2017–2018 OFFICIAL UNIVERSITY REGULATIONS 249

RESERVATION OF UNIVERSITY academic activities or essential individual merit and not on bias or RIGHTS services are expected to avoid conflict stereotypes. This bulletin is intended for the with religious holidays as much as The Office of Equal Opportunity and guidance of persons applying for or possible. If a suitable arrangement Affirmative Action (EOAA) has overall considering application for admission cannot be worked out between the responsibility for the management of to Columbia University and for the student and the instructor involved, the University’s Student Policies and guidance of Columbia students they should consult the appropriate Procedures on Discrimination and and faculty. The bulletin sets forth dean or director. If an additional appeal Harassment and the Employment in general the manner in which the is needed, it may be taken to the Policies and Procedures and local University intends to proceed with Provost. laws and has been designated as respect to the matters set forth the University’s Compliance Office for the Title IX, Section 504 of the herein, but the University reserves the ACADEMIC DISCIPLINE right to depart without notice from the Rehabilitation Act, and other equal See Policy on Conduct and Discipline. terms of this bulletin. The bulletin is opportunity, nondiscrimination, and not intended to be, and should not be affirmative action laws. Students, regarded as, a contract between the THE FEDERAL FAMILY faculty, and staff may contact the University and any student or other EDUCATIONAL RIGHTS AND EOAA to inquire about their rights person. PRIVACY ACT (FERPA) under University policies, request See Transcripts and Certifications. assistance, seek information about filing a complaint, or report conduct ATTENDANCE or behavior that may violate these COLUMBIA UNIVERSITY Students are held accountable for policies. absences incurred owing to late OMBUDS OFFICE All students and applicants enrollment. The Ombuds Office is a neutral and for admission are protected from confidential resource for informal coercion, intimidation, interference, RELIGIOUS HOLIDAYS conflict resolution, serving the entire or retaliation for filing a complaint or Columbia University community— It is the policy of the University to assisting in an investigation under any students, faculty, and employees. respect its members’ religious beliefs. of the applicable policies and laws. As an institution, Columbia In compliance with New York State University is committed to the law, each student who is absent from principles of equity and excellence. COLUMBIA UNIVERSITY NON- school because of his or her religious It is actively pursues both, adhering DISCRIMINATION STATEMENT beliefs will be given an equivalent to the belief that equity is the partner AND POLICY opportunity to register for classes or of excellence. Columbia University’s Columbia University is committed make-up any examination, study, or goal is a workforce and student body to providing a learning, living, and work requirements that he or she may that reflects the diversity and talent of working environment free from unlawful have missed because of such absence New York City, the larger metropolitan discrimination and to foster a nurturing due to religious beliefs, and alternative area, and the nation. In furtherance of and vibrant community founded upon means will be sought for satisfying the this goal, Columbia has implemented the fundamental dignity and worth of academic requirements involved. policies and programs which seek all its members. Consistent with this Officers of administration and of to ensure that its employment and commitment, and with all applicable instruction responsible for scheduling educational decisions are based on laws, it is the policy of the University

ENGINEERING 2017–2018 250 not to tolerate unlawful discrimination The Staff-Student Relationship For more information about the in any form and to provide persons Policy states that no staff member Dean's Discipline process, please visit who feel that they are victims of at Columbia should participate in the Student Conduct and Community discrimination with mechanisms for supervision, employment actions, Standards or the Office of Graduate seeking redress. evaluation, advising, or mentoring Student Affairs in order to speak with a Columbia University prohibits any of any Columbia University student staff member. form of discrimination against any with whom that staff member has or person on the basis of race, color, has had a consensual romantic or Procedure for Complaints Against a sex, gender, pregnancy, religion, sexual relationship, except in unusual Student Organization creed, marital status, partnership circumstances, where explicit advance Students who wish to file a complaint status, age, sexual orientation, national authorization has been obtained. of discrimination or harassment against origin, disability, military status, or For additional information on these a student organization should do so any other legally protected status in issues, policies and resources, please in consultation with the Dean of their the administration of its educational visit the Sexual Respect website at own school; the Dean will identify the policies, admissions policies, titleix.columbia.edu. appropriate procedure and channels employment, scholarship and loan and assist the student in pursuing the programs, and athletic and other DISABILITY ACCOMMODATION complaint. University-administered programs. Students seeking access, Nothing in this policy shall accommodations or support services Procedure for Complaint Against a abridge academic freedom or the for a disability should contact Disability Member of the Faculty or Staff University’s educational mission. Services at 212-854-2388. Information Prohibitions against discrimination Office of Equal Opportunity and on the services provided by Disability and discriminatory harassment do Services may be found online at Affirmative Action not extend to statements or written health.columbia.edu/docs/services/ Complaints against employees and materials that are relevant and ods/index.html. third parties affiliated with the University appropriately related to the subject for discrimination and harassment matter of courses. are processed in accord with the This policy governs the conduct FORMAL COMPLAINT Columbia University Employee Policies of all Columbia University students, PROCEDURES and Procedures on Discrimination, faculty, staff, and visitors that occurs Harassment, Sexual Assault, Domestic on the University's campuses or in Procedure for Complaint Against Violence, Dating Violence, and Stalking. connection with University-sponsored Another Student The use of the term “discrimination and programs. This policy also governs harassment” includes discrimination, dis- conduct by Columbia University Gender-Based Misconduct Policy and criminatory harassment, gender-based students, faculty, staff, and visitors that Procedures for Students harassment, stalking, intimate partner creates, contributes to, or continues Complaints against students for gender- violence, sexual harassment, and sexual a hostile work, educational, or living based misconduct are processed assault. environment for a member or members in accord with the Gender-Based Violations of the University’s of the University community. Misconduct Policy and Procedures Employment Policies and Procedures for Students by Student Conduct and on Discrimination and Harassment and CONSENSUAL ROMANTIC AND Community Standards. Students who the Student Policies and Procedures SEXUAL RELATIONSHIPS attend Teachers College as well as on Discrimination and Harassment are Columbia University are covered by Columbia University maintains policies prohibited. Appropriate disciplinary these policies. The use of the term regarding consensual romantic and action may be taken against any “gender-based misconduct” includes sexual relationships between faculty employee or student who violates these sexual assault, sexual harassment, and students, and staff and students. policies. gender-based harassment, stalking, The Faculty-Student Relationship Columbia also offers a number dating violence, and domestic violence. Policy states that no faculty member of confidential resources to students shall exercise academic or professional who believe they were subjected to authority over any student with whom Columbia University Non- discrimination, harassment, or gender- he or she has or previously has had Discrimination Statement and Policy based or sexual misconduct and who a consensual romantic or sexual Dean's Discipline procedures will be do not wish to report to the University. relationship. This policy covers all used to investigate and respond to officers of instruction, research, and allegations that a student has engaged Counseling Services the libraries, including student officers in discrimination or discriminatory Columbia Morningside: 212-854-2878 of instruction, research, and teaching harassment as set out in the Columbia CUMC: 212-496-8491 assistants. University Non-Discrimination Statement.

ENGINEERING 2017–2018 Rape Crisis/Anti-Violence Support *Medical providers are considered 251 Center confidential resources in the context of Phone: 212-854-HELP providing medical treatment of a patient.

Health Services* Grievance Procedures Columbia Morningside: 212-854-2284 Students should consult SEAS policies Columbia Morningside Clinician On-Call: on Student Grievances, Academic 212-854-9797 Concerns and Complaints for the CUMC: 212-305-3400 appropriate procedure to complain CUMC Clinician On-Call: 212-305-3400 about a faculty member’s conduct in an instructional setting.

ENGINEERING 2017–2018 252 STUDENT GRIEVANCES, ACADEMIC CONCERNS, AND COMPLAINTS

he following procedures are part dishonesty, or issues of behavioral procedure below also applies to of a process to ensure that concerns as they relate to student complaints against instructional and Tstudent concerns about experi- conduct (see item B). They also should administrative staff): ences in the classroom or with faculty not be used when students believe that Students are encouraged to are addressed in an informed and they have been the victim of sexual seek a resolution to their complaints appropriate manner. harassment or discrimination (see item about faculty misconduct by talking Due to the size and diverse nature C) or that faculty have engaged in directly with the faculty member. If of our scholarly community, each scholarly or scientific misconduct (see they feel uncomfortable handling the school maintains its own processes for item D). situation in this manner, they may ask addressing issues raised by students, We welcome students’ thoughts for help from a departmental faculty including their concerns about on ways to clarify or enhance these mediator, who will assist students with experiences in the classroom or with procedures. If you are an Engineering complaints about faculty members, faculty at their school. Experience has student, please email seasdean@ other academic personnel, or shown that most student concerns are columbia.edu. administrators. best resolved in a collaborative way at The name of the faculty mediator the school level. Columbia Engineering is posted in the department COMPLAINTS ABOUT FACULTY offers several informal paths for office and on the departmental AND STAFF ACADEMIC students to use, as described in this website. Students may also ask the MISCONDUCT statement. department chair or administrator to In fulfilling their instructional If a student’s concerns are not direct them to the faculty mediator. responsibilities, faculty are expected satisfied through this process, The faculty mediator tries to resolve to treat their students with civility or if the student believes that a any issue by informal meetings with and respect. They “should promote direct complaint to the Dean is the student and others, including an atmosphere of mutual tolerance, more appropriate, formal grievance faculty as seems appropriate. respect, and civility. They should allow procedures are available through Students who are dissatisfied the free expression of opinions within the Vice Dean of the School. with the outcome may request a the classroom that may be different These procedures should be used meeting with the department chair. from their own and should not permit for complaints about Engineering The chair will review the mediator’s any such differences to influence faculty. For those faculty who are not recommendation and seek informally their evaluation of their students’ members of Columbia Engineering, to resolve the student’s complaint. performance. They should confine the student should consult the their classes to the subject matter • Students may bring their concerns to procedures of the school in which covered by their courses and not use the University’s Ombuds Officer, who they serve. them to advocate any political or social serves as an informal, confidential For academic complaints relating cause” (2008 Faculty Handbook). resource for assisting members of the to Engineering faculty, these A fuller description of faculty rights University with conflict resolution. The procedures, like those of other and obligations may be found in the Ombuds Officer provides information, schools, provide for a final appeal Faculty Handbook (columbia.edu/ counseling, and referrals to to the University Provost. cu/vpaa/handbook). Students who appropriate University offices and will The procedures under item A do feel that members of the Engineering also mediate conflicts if both parties not take the place of the grievance faculty have not met those obligations agree. The Ombuds Officer does procedures already established to may take the following steps (the not have the authority to adjudicate address disputes over grades, academic

ENGINEERING 2017–2018 disputes and does not participate (undergraduate students), who acts member are all subject to appeal. A 253 in any formal University grievance as chair; a faculty member chosen by written appeal must be submitted to the proceedings. Further information on the Vice Dean; and a student chosen Provost within 15 working days of the the Ombuds Office may be found at by one of the student councils (an date of the letter informing them of the columbia.edu/cu/ombuds. undergraduate or a graduate student Dean’s decision. • Students may seek a grievance to correspond to the status of the Normally, the Provost will take hearing if informal mediation fails. The student grieving). no longer than 30 working days to grievance procedures students should The faculty member is given the evaluate an appeal. The Provost usually follow will depend upon the school student’s letter of complaint and confines his or her review to the written within which the faculty member invited to submit a written response. record but reserves the right to collect is appointed and the nature of the The Committee reviews both information in any manner that will help alleged misconduct. statements and is given access to any to make his or her decision on the other written documents relevant to appeal. If the faculty member holds an the complaint. It will normally interview The Provost will inform both the appointment in Columbia Engineering, both the grievant and the faculty student and the faculty member of his the student may use the procedures member and may, at its discretion, or her decision in writing. If the Provost described below to address the issues ask others to provide testimony. The decides that the faculty member listed below. If the faculty member merits of the grievance are evaluated should be dismissed for cause, the belongs to another school, students within the context of University and case is subject to further review must use the procedure of that school. Engineering school policy. according to the procedures in Section They may, however, ask for help from The investigative committee serves 75 of the University Statutes, as noted the departmental faculty mediator, chair, in an advisory capacity to the Dean of above. Otherwise the decision of the and the School’s deans in identifying the School. It is expected to complete Provost is final and not subject to and understanding the appropriate its investigation in a timely manner and further appeal. procedures. submit a written report to the Dean, All aspects of an investigation of a Conduct that is subject to formal who may accept or modify its findings student grievance are confidential. The grievance procedure includes: and any recommendations it may proceedings of the grievance committee • failure to show appropriate respect in have made to remedy the student’s are not open to the public. Only the an instructional setting for the rights of complaint. The Dean will inform both student grievant and the faculty member others to hold opinions differing from the student and the faculty member of accused of misconduct receive copies their own; his decision in writing. of the decisions of the Dean and the • misuse of faculty authority in an The committee ordinarily convenes Provost. Everyone who is involved instructional setting to pressure within 10 working days of receiving with the investigation of a grievance is students to support a political or the complaint from the Vice Dean and expected to respect the confidentiality of social cause; and ordinarily completes its investigation the process. • conduct in the classroom or another and sends the Dean its report within instructional setting that adversely 30 working days of convening. The DISPUTES OVER GRADES OR affects the learning environment. Dean normally issues his or her decision OTHER ACADEMIC EVALUATIONS within 30 working days of receiving the The awarding of grades and all other Formal grievance procedure at committee’s report. academic evaluations rests entirely Columbia Engineering The Dean may discipline faculty with the faculty. If students have If the informal mediation mentioned members who are found to have a concern relating to a particular above failed, the student should committed professional misconduct. Any grade or other assessment of their compose and submit to the Vice Dean sanctions will be imposed in a manner academic work, the student first of the School a written statement that is consistent with the University’s should speak with the instructor of documenting the grievance and should policies and procedures on faculty the class to understand how the also include a description of the remedy discipline. In particular, if the Dean grade or other evaluation was derived sought. This should be done no later believes that the offense is sufficiently and to address the student’s specific than 30 working days after the end of serious to merit dismissal, he or she can concern. the semester in which the grievance initiate the procedures in Section 75 of If the students do not feel occurred. the University Statutes for terminating comfortable speaking with the class The Vice Dean will review the tenured appointments, and nontenured instructor about the matter, they should complaint to determine if a grievance appointments before the end of their then bring the issue to the attention hearing is warranted. If so, the stated term, for cause. of their class dean (undergraduate Vice Dean will convene an ad hoc Either the student or the faculty students) or department chair (graduate committee consisting of the Associate member may appeal the decision of students). Dean for Graduate Student Affairs the Dean to the Provost. Findings If the students are unable thus to (graduate students) or the Senior of fact, remedies given the student, resolve the matter to their satisfaction Associate Dean of Student Affairs and penalties imposed on the faculty

ENGINEERING 2017–2018 254 and believe that a procedural issue is that there is no need for further action, SCIENTIFIC OR involved, they should bring the matter to the student will be informed and the SCHOLARLY MISCONDUCT the attention of the Vice Dean. The Vice decision will be final. Complaints against the School’s Dean will work with the student and the faculty that allege scientific or scholarly faculty to determine whether there has DISCRIMINATION, misconduct are evaluated using other been a procedural breach and if so, take HARASSMENT, AND GENDER- procedures. These are contained in the immediate steps to remedy the matter. If BASED MISCONDUCT Columbia University Institutional Policy the Vice Dean, together with appropriate on Misconduct in Research. See Formal Complaint Procedures. faculty other than the instructor, decides

ENGINEERING 2017–2018 Directory of University Resources 256 COLUMBIA UNIVERSITY RESOURCE LIST

UNDERGRADUATE ADMISSIONS Cristen Kromm, [email protected] COLUMBIA COLLEGE Dean of Undergraduate Student Life 208 Hamilton, MC 2805 Undergraduate Admissions 212-854-2441 212 Hamilton, MC 2807 Jesse Adamo Grimes, ja3180@ columbia.edu 212-854-2522 James J. Valentini Director of Administration and Planning undergrad.admissions.columbia.edu Dean of Columbia College [email protected] Lauren Iannia, [email protected] Lisa Hollibaugh Senior Associate Director, Student Jessica Marinaccio Dean of Academic Planning and Financial Advising Dean of Undergraduate Admissions and Administration Financial Aid Multicultural Affairs 510 Lerner, MC 2607 CORE CURRICULUM PROGRAM Joanna May, [email protected] 212-854-0720 Associate Dean and Director of Center for the Core Curriculum Undergraduate Admissions Melinda Aquino, [email protected] 202 Hamilton, MC 2811 Associate Dean of Multicultural Affairs Meaghan McCarthy, [email protected] 212-854-2453 Chia-Ying Sophia Pan, cp2804@ Director of Programming and Outreach Roosevelt Montás, [email protected] columbia.edu Director of the Center for the Core David Buckwald, [email protected] Director of Education, Outreach, and Curriculum Director of International Admissions and International Student Support Strategic Initiatives Art Humanities Diane McKoy, [email protected] Intercultural Resource Center (IRC) 826 Schermerhorn, MC 5517 Senior Associate Director 552 West 114th Street, MC 5755 212-854-4505 212-854-7461 Dana Pavarini, [email protected] Branden Joseph, [email protected] Associate Director, Director of Director of Undergraduate Studies Residential Life Engineering Recruitment 515 Lerner, MC 4205 Music Humanities 212-854-6805 621 Dodge, MC 1813 UNDERGRADUATE ADVISING 212-854-3825 Tara Hanna, [email protected] James H. and Christine Turk Berick Director of Residential Life Susan Boynton, [email protected] Center for Student Advising Director of Undergraduate Studies 403 Lerner Hall, MC 1201 Student Engagement Contemporary Civilization 212-854-6378 515 Lerner, MC 2601 514 Fayerweather, MC 2811 cc-seas.columbia.edu/csa 212-854-3611 212-854-5682 [email protected] Josh Lucas, [email protected] James Zetzel, [email protected] Andrew Plaa, [email protected] Director of Student Engagement Director of Undergraduate Studies Dean of Advising Philip Masciantonio, pm2811@ Angie Carrillo, [email protected] columbia.edu Literature Humanities Associate Dean Director of Broadcasting and 202 Hamilton, 212-854-2453 Operations, WKCR 89.9FM Mail Code 2811 A. Alex España, [email protected] All inquiries concerning Lit Hum should Associate Dean Peter Cerneka, [email protected] be directed to the Center for the Core Associate Director of Student Megan Rigney, [email protected] Curriculum (listed above) Engagement Associate Dean Aaron Gomes, [email protected] Undergraduate Writing Program Cheryl de Moose, [email protected] Associate Director of Student 310 Philosophy, MC 4995 Director Engagement 212-854-3886 [email protected] UNDERGRADUATE STUDENT LIFE Kyrena Wright, [email protected] Associate Director of Student Nicole Wallack, Director 510–515 Lerner, MC 2601 Engagement 212-854-3612

ENGINEERING 2017–2018 257

GRADUATE STUDENT AFFAIRS THE EARL HALL CENTER Marjorie Ortiz, [email protected] Senior Assistant Director Graduate Student Affairs University Chaplain 530 S. W. Mudd, MC 4708 Office: W710 Lerner Institutional Financial Aid 212-854-6438 Mailing: 202 Earl Hall, MC 2008 (Grants, Fellowships, Assistantships) 212-854-6242, 212-854-1493 Office of Graduate Student Affairs Tiffany M. Simon, [email protected] 530 S. W. Mudd, MC 4708 Associate Dean of Graduate Student Jewelnel Davis, [email protected] 212-854-6438 Affairs University Chaplain

Ellie Bastani, [email protected] HEALTH SERVICES Assistant Dean of Graduate Student EQUAL OPPORTUNITY AND General Info: 212-854-2284 Services and Postdoctoral Affairs AFFIRMATIVE ACTION After-hours Urgent Health Concerns: 103 Low Library, MC 4333 212-854-7426 Graduate Admissions 212-854-5511 health.columbia.edu 530 S. W. Mudd, MC 4708 Heather Parlier, [email protected] 212-854-6438 Associate Provost CU-EMS (Ambulance) Jocelyn Morales, [email protected] 212-854-5555 or 4-5555 from a campus Associate Director phone Durelle Hill, [email protected] Kathleen Gay, [email protected] Interim Assistant Director Insurance and Immunization Student Services Officer Compliance Student Services for Gender-Based John Jay, 3rd Floor, MC 2605 Graduate Student Life and Sexual Misconduct Insurance Office: 212-854-3286 530 S. W. Mudd, MC 4708 Wien Hall, Suite 108C Immunization Compliance Office: 212-854-6438 212-854-1717 212-854-7210 Alvaro Rojas-Caamano Rosalie Siler, [email protected] Assistant Director of Graduate Student Assistant Director Student Medical Insurance Plan Services Administrators Aetna Student Health FINANCIAL AID (UNDERGRADUATE) 1-800-859-8471 COLUMBIA VIDEO NETWORK www.aetnastudenthealth.com/ Undergraduate Financial Aid and columbiadirect.html 540 S. W. Mudd, MC 4719 Educational Financing 212-854-6447 Office: 618 Lerner Alice! Health Promotion cvn.columbia.edu Mailing: 100 Hamilton, MC 2802 John Jay, 3rd Floor, MC 2605 [email protected] 212-854-3711 212-854-5453 [email protected] health.columbia.edu/alice Alexis Seeley, [email protected] Executive Director of and Associate Michael Hall, [email protected] Counseling and Psychological Dean of Online Education Executive Director of Financial Aid and Services Enrollment Operations Lerner, 8th floor, MC 2606 212-854-2878 CENTER FOR CAREER EDUCATION Pamela Mason, pamela.mason@ East Campus, Lower Level, MC 5727 columbia.edu Disability Services 212-854-5609 Director of Financial Aid Administration 108A Wien Hall, MC 3711 Leah Soman, [email protected] Voice/TTY: 212-854-2388 careereducation.columbia.edu Financial Aid Specialist Medical Services [email protected] John Jay Hall, 3rd and 4th Floors FINANCIAL AID (GRADUATE) 212-854-7426 (Appointments) COMPUTING SUPPORT CENTER 212-854-6655 (Gay Health Advocacy Federal Financial Aid (Loans, Work Study) Project) Client Services Help Desk Financial Aid and Educational Financing 202 Philosophy, MC 4926 615 Lerner, MC 2802 212-854-1919 212-854-3711 [email protected]

ENGINEERING 2017–2018 258 Sexual Violence Response Deborah Mowshowitz, dbm2@ Joan C. Waters Rape Crisis/Anti-Violence Support columbia.edu Ombuds Officer Center Director of Undergraduate Programs Lerner, 7th floor PUBLIC SAFETY 212-854-HELP (4357) Chemistry 344 Havemeyer, MC 3178 111 Low Library, MC 4301 212-854-2202 212-854-2797 (24 hours a day) HOUSING AND DINING [email protected] Vesna Gasperov, [email protected] Columbia Housing Undergraduate Program Coordinator Campus Emergencies: 118 Hartley, MC 3003 212-854-5555 (4-5555) 212-854-2946 Earth and Environmental Sciences [email protected] 106 Geoscience, Lamont-Doherty Escort Service: Earth Observatory, 845-365-8550 212-854-SAFE (4-7233) Columbia Dining Sidney Hemming, sidney@ 125 Wallach, MC 3003 ldeo.columbia.edu James F. McShane 212-854-4076 Codirector of Undergraduate Studies Vice President for Public Safety [email protected]

Walter C. Pitman, pitman@ REGISTRAR INTERCOLLEGIATE ATHLETICS ldeo.columbia.edu 210 Kent, MC 9202 AND PHYSICAL EDUCATION Codirector of Undergraduate Studies Barry Kane, [email protected] Dodge Physical Fitness Center Terry Plank, [email protected] Associate Vice President and University 212-854-3439 Codirector of Undergraduate Studies Registrar

Jessica De Palo, [email protected] Mathematics Monica Avitsur, [email protected] 410 Mathematics, MC 4426 Associate Athletics Director for Deputy University Registrar 212-854-2432 Enrichment Services Jennifer Love, [email protected] Panagiota Daskalopoulos, Associate Director, Student Service and [email protected] INTERNATIONAL STUDENTS ID Centers AND SCHOLARS (ISSO) Director of Undergraduate Studies Jennifer Caplan, [email protected] Office: 524 Riverside Drive, Ground Floor Physics Associate Registrar Mailing: 2960 Broadway, MC 5724 704 Pupin, Mail Code 5255 Sheila Serrano, [email protected] 212-854-3587 212-854-3348 Associate Registrar [email protected] Jeremy Dodd, [email protected] isso.columbia.edu Director of Undergraduate Studies Kristabelle Munson, km2137@columbia. David Austell, david.austell@ edu Statistics columbia.edu Associate Registrar and Director of 1255 Amsterdam Avenue Associate Provost and Director Client Services Room 1005 SSW, MC 4690 212-851-2132 Austin Wanta, [email protected] LIBRARIES Assistant Registrar for IT Daniel Rabinowitz, [email protected] Butler Library Information Director of Undergraduate Studies James Cunha, [email protected] 535 W. 114th Street Assistant Registrar 212-854-7309 OMBUDS OFFICE Angelica Borrero, ab4370@columbia. 660 Schermerhorn Ext., MC 5558 edu Science & Engineering Library 212-854-1234 Assistant Registrar 401 Northwest Corner [email protected] Jeanelle Folkes, [email protected] 212-851-2950 columbia.edu/cu/ombuds Operations and Systems Support Specialist

MATH/SCIENCE DEPARTMENTS On Wednesdays the Ombuds Officer is Bill Santin, [email protected] at the Columbia Medical Center office: Registrar Services Associate Biological Sciences 101 Bard Hall Michael Lam, [email protected] 600 Fairchild, MC 2402 50 Haven Avenue Reporting Specialist 212-854-4581 212-304-7026

ENGINEERING 2017–2018 Justin Merced, [email protected] Jeri Henry, [email protected] UNIVERSITY LIFE 259 Scheduling Analyst Associate Vice President for Student 212-854-0411 Conduct and Community Standards [email protected]

STUDENT CONDUCT AND Suzanne Goldberg, sgoldberg@ STUDENT SERVICE CENTER COMMUNITY STANDARDS columbia.edu 205 Kent, MC 9202 Executive Vice President for 800 Watson Hall 212-854-4400 University Life 612 West 115 Street, MC 2611 212-854-6872

ENGINEERING 2017–2018 260 COLUMBIA UNIVERSITY THE MORNINGSIDE CAMPUS & ENVIRONS

ENGINEERING 2017–2018 COLUMBIA UNIVERSITY THE MORNINGSIDE HEIGHTS AREA OF NEW YORK CITY 261 THE MORNINGSIDE CAMPUS & ENVIRONS

ENGINEERING 2017–2018 262 INDEX

A applications Biomedical Engineering, Department for degrees, 241 of, 64–76 academic advising. See James H. and Christine Turk Berick Center for graduate, 28–29 graduate programs, 68–70 Student Advising undergraduate, 19 undergraduate program, 65–68 academic calendar, inside back cover applied chemistry. See Chemical Bookstore, Columbia University, 217 academic community, conduct Engineering, Department of Botwinick Multimedia Learning expected in, 245 applied mathematics Laboratory, 6 academic concerns, grievances, and courses in, 61–63 Business, Graduate School of complaints, student, 252–254 minor in, 198 courses for engineering students, academic discipline, 245–247 applied physics 205 academic dishonesty, 245-247 courses in, 58–61 joint programs with, 25, 159–161 academic honors, 242 minor in, 198 Butler Library, 258 academic integrity, 245–247 Applied Physics and Applied Mathematics, Department of, 50–63 academic monitoring, 242 C academic procedures and standards, current research activities, 50–51 238–241 graduate programs, 57–58 cable TV service, 7 academic progress, satisfactory, 22, laboratory facilities, 51–52 calendar 238–240 specialty areas, 55–56 academic, inside back cover academic standing, 242–244 undergraduate programs, 52–56 for graduate admissions, 28 ABET, 17, 67, 80, 122, 137, 186, 239 architecture, minor in, 90, 198 campus life, 214–218 addresses of Columbia University art history, minor in, 199 campus safety and security, 217–218 departments and resources, 256–259 assistantships, 33 Canvas, 7 administrative officers, lists of, 36, athletic programs, 13, 217 career counseling, 8 45–46 attendance, 239, 249 Carleton Commons, 7 admissions Center for Applied Probability (CAP), 154 graduate, 28–29, 257. See also B Graduate Student Affairs Center for Career Education (CCE), 8, undergraduate, 19, 256 Bachelor of Science degree (B.S.), 17 15, 34, 257 advanced placement, 11, 13, 14 Baker Field Athletics Complex, 217 Center for Financial Engineering, 154 advanced standing, of transfer Barnard Education Program, 18 Center for Infrastructure Studies, 89 students, 29 bioinductive and biomimetic materials, Center for Life Cycle Analysis (LCA), advising centers. See James H. and program in, 68 120 Christine Turk Berick Center for Biological Sciences, Department of, 258 Chaplain, University, Office of the, 216, Student Advising courses for engineering students, 205 258 Alice! Columbia University’s Health biomedical engineering chemical engineering Promotion program, 222, 257 courses in, 70–76 courses in, 80–86 American Language Program (ALP), 28 minor in, 199 minor in, 80, 199 anthropology, minor in, 198

ENGINEERING 2017–2018 Chemical Engineering, Department of, Combined Plan programs, 15–16 D 263 77–86 commencement ceremony, 241 damages, payment for, 21, 31 facilities and laboratories, 78 Committee on Academic Standing, dance, minor in, 199 graduate programs, 80 239, 240, 242 Data-Driven Analysis, concentration undergraduate program, 78–80 Committee on Instruction, 10, 25, 242 in, 142 Chemistry, Department of, 258 complaints, academic concerns, and Dean’s discipline, 247 courses for engineering students, grievances, student, 250, 252–254 Dean’s List, 242 205–207 Computational and Optimization Degree Audit Reporting System civil engineering Research Center (CORC), 154 (DARS), 16 courses in, 92–98 computer accounts, obtaining, 7 degrees minor in, 199 Computer Engineering Program, 100–104 application for, 241 Civil Engineering and Engineering graduate program, 102–104 doctoral, requirements, 26, 239 Mechanics, Department of, undergraduate program, 100–102 See also individual degrees 87–99 computer kiosks, public, 7 Digital Social Science Center, 7 current research activities, 87–88 computer labs and clusters, 7 Dining Dollars, 220–221 facilities and laboratories, 88–89 computer science dining facilities, locations, 221 graduate programs, 89–92 courses in, 110–118 diplomas, 241 undergraduate programs, 89 minor in, 199 Disability Services, University Office of, classes Computer Science, Department of, 222, 250, 257 attendance at, 239 105–118 discipline, academic, 245–247 registration and enrollment in, 238 dual degree program, with School Dean’s, 247 classrooms, electronic, 7 of Journalism, 25, 109 procedures for administering, Club Sports, 217 laboratory facilities, 105–106 245–247 colleges and universities in Combined graduate programs, 109 discrimination Plan program, 15–16 undergraduate program, 106–107 and harassment, and gender-based Columbia College, 256 computer security resources, 7 misconduct policy and procedure, Columbia Dining, 220–221, 258 computing resources, University, 7 249–250, 254 Columbia Dining Dollars, 220–221 Computing Support Center, 257 dishonesty, academic, 245–247 Columbia Genome Center (CGC), 78 conduct disputes over grades or other Columbia Health, 221–222, 257 expected in the academic academic evaluations, 253–254 Columbia Housing, 211–220, 258 community, 245 distance education. See Columbia Columbia Microelectronic Sciences unacceptable, subject to discipline, Video Network Laboratories, 134 245–247 Doctor of Engineering Science (Eng. Columbia University Core Curriculum of Columbia Sc.D.), 25–26 campuses, schools, affiliations, and program offices, 256 Doctor of Philosophy (Ph.D.), 25–26 resources and facilities, 5–8 Counseling and Psychological Services Dodge Physical Fitness Center, 217, email addresses, list of, 256–259 (CPS), 221, 257 256 history of, 2–4 courses dual degree maps of campus, 260–261 for professions other than with the School of Journalism, in policy, procedures, and regulations, engineering, 17–18 computer science, 25, 109 237–254 interdisciplinary engineering, 204 See also joint programs reservation of rights, 249 key to listings, 48–49 resources, phone numbers, and in other divisions of the University, website, 7 of interest to engineering students, E Columbia University Bookstore, 217 205–212 Earl Hall Center, 216, 257 Columbia University Information in Engineering School departments. Earth and environmental engineering Technology (CUIT), 7 See individual departments courses in, 126–132 Columbia University Libraries, 7–8 credit, points of, required for degree minor in, 199–200 Columbia University’s Health Promotion graduate, 25–26, 239 Earth and Environmental Engineering, Program (Alice!), 222, 257 undergraduate, 10–14, 238–239 Department of, 119–132 Columbia Video Network (CVN), 27, 257 graduate programs, 124–126 application to, 27 research centers, 120–121 Columbia Water Center, 120

ENGINEERING 2017–2018 264 scholarships, fellowships, and Engineering, School of how to apply for, 22 internships, 121 courses. See individual departments private programs, 33 undergraduate program, 122–124 department and course codes, to undergraduate students, 22, 257 See also Henry Krumb School of 48–49 departments and programs, Financial Aid and Educational Mines 50–196 Financing, Office of, 22, 32, 34, 257 Earth and Environmental Engineering faculty and administration, 36–46 financial engineering (EEE) program, 119 history of, 2–4 graduate program in, 159–160 Earth and Environmental Sciences, resources and facilities, 5–8 First Year–Sophomore Program course Department of (Columbia College), engineering students requirements 258 and campus life, 214–218 nontechnical, 10–12 courses for engineering students, courses for, offered by other professional-level, 12–13 207–208 University divisions, 205–212 technical, 12 Earth Engineering Center, 120 interdisciplinary courses for, 204 4-1 Combined Plan B.S. program, 18 East Asian studies, See also students 4-2 Combined Plan M.S. program, 25 minor in, 200 Engineering Student Council, 215 fraternities and sororities, 215, 219 economics English and comparative literature, Free Application for Federal Student minor in, 200 minor in, 200 Aid (FAFSA), 33 electrical engineering English proficiency requirement, 28 French courses in, 142–152 enrollment, 238 and francophone studies, minor in, minor in, 200 entrepreneurship and innovation, minor 201 Electrical Engineering, Department of, in, 200–201 minor in, 201 133–152 environmental health engineering, Fu Foundation School of Engineering B.S./M.S. program, 139 concentration in, 123–124 and Applied Science, The. See concentration options in the M.S. Environmental Tracer Group, 121 Engineering, School of program, 140–142 Equal Opportunity and Affirmative Fundamentals of Engineering (FE) graduate programs, 139–140 Action, Office of, 249–250, 257 exam, 25, 186 laboratory facilities, 134 Equal Opportunity and research activities, 134 Nondiscrimination Policies, 249–250 G undergraduate program, 134–139 examinations, midterm and final, electronic classrooms, 7 239–240 German, minor in, 201 email grade-point average (GPA), 239–240 addresses of Columbia University F grades, report of, 240 resources and staff, 256–259 grading system, explained, 240 as service of CUIT, 7 faculty graduate courses, taking as an emeriti and retired officers, list of, 44 and staff academic misconduct, undergraduate, 16 employment, student, 33–34 complaints about, 252–254 graduate programs, 24–26 endowed fellowships, list of, 229–232 lists of, 36–44 admission to, 28–29 endowed scholarships and grants, members-at-large, list of, 45 applying to, 28–29 list of, 224–229 Family Educational Rights and Privacy requirements, 24–26 Engineering Accreditation Commission Act (FERPA), 240, 247, 248, 249 See also individual programs (EAC), 17 federal financial aid, 22, 33, 257 Graduate Record Examination (GRE), 28 engineering courses, interdisciplinary, fees Graduate Student Affairs, Office of, 204 graduate, 30–31 28, 257 Engineering Graduate Student Council refunds of, 21, 31 graduate students (EGSC), 216 undergraduate, 20–21 degree requirements for, 239 Engineering Library, 7–8, 258 See also payments discipline process for, 245–247 engineering mechanics fellowships, 33 financial aid for, 32–34, 257 courses in, 98–99 endowed, list of, 229–232 housing, 219–221 graduate program in, 89–92 outside, 232 tuition and fees, 30–31 minor in, 200 financial aid graduation, 241 undergraduate program in, 89 eligibility for, 22 grants and scholarships See also Civil Engineering and employment and, 33–34 endowed, list of, 224–229 Engineering Mechanics, federal, 33 graphics, courses in, 99 Department of to graduate students, 32–34, 257 Greek or Latin, minor in, 201

ENGINEERING 2017–2018 grievance procedures, 251, 252–254 interdisciplinary engineering courses, M 265 grievances, academic concerns, and 204 Makerspace, 6–7 complaints, student, 252–254 International and Public Affairs, School management science and engineering, of, joint programs with, 18 graduate program in, 160 International English Language Testing H maps of Columbia Morningside Heights System (IELTS), 28 campus, 260–261 harassing or threatening behavior, 254 International Students and Scholars marks. See grading system harassment Office (ISSO), 8, 258 Master of Science degree (M.S.), discriminatory, 254 Internet access, 7 24–25 gender-based misconduct, 250, 254 Interschool Governing Board, 215 materials chemistry/soft materials, 175 health insurance, 20, 30, 222 internships, 121 materials for green energy, 173 health service. See Columbia Health Intramural and Club Sports Program, materials for health and biotechnology, Henry Krumb School of Mines (HKSM), 217 175 119 materials for next generation See also Earth and Environmental J electronics, 173 Engineering, Department of materials science and engineering Hispanic studies, minor in, 201 James H. and Christine Turk Berick courses in, 177–180 history, minor in, 201 Center for Student Advising, 214, minor in, 201 honors, academic, 242, 246 256 Materials Science and Engineering housing, University and off-campus, John Jay Dining Hall, 220, 221 program (MSE), 57, 119, 171 219–221 joint programs current research activities, 172 See also residence halls with Data Science Institute, 25 graduate programs, 175–177 Humanities and Social Sciences, with the Graduate School of graduate specialty in solid-state Department of, Business, in industrial engineering, science and engineering, 176–177 courses for engineering students, 25, 161 interdepartmental committee and, 171 208–209 with the School of International and laboratory facilities, 172 Public Affairs, 18 undergraduate program, 172–175 with School of Journalism, 25 I Mathematics, Department of, 258 See also dual degree courses for engineering students, 209 immunization requirements, 222 judicial Affairs, 216 meal plans. See dining plans industrial engineering Junior-Senior programs, 16–17 mechanical engineering courses in, 163–170 courses in, 190–196 minor in, 201 L minor in, 201 Industrial Engineering and Operations Mechanical Engineering, Department Research, Department of, 153–170 laboratory charges, 20–21, 31 of, 181–196 current research activities, 153–154 Langmuir Center for Colloids and current research activities, 181–184 graduate programs, 159–163 Interfaces (LCCI), 121 facilities for teaching and research, joint programs, 25, 161–163 Latin, Greek or, minor in, 201 184 minors, 200–202 leave(s) of absence graduate programs, 187–190 undergraduate programs, 154–159 family, 244 undergraduate program, 185–187 Industry/University Cooperative involuntary, 244 medals and prizes, list of, 232–236 Research Center for Particulate and medical, 243 medical care and insurance, 20, 30, Surfactant Systems (CPaSS), 121 military, 244 221–222, 255 Institute of Flight Structures, 89 voluntary, 243–244 Medical College Admissions Test institutional grants, 32 Lenfest Center for Sustainable Energy, (MCAT), 17–18 Insurance, Student Medical Plan, 20, 121 medical leave of absence, 243 30, 222, 257 Lerner Hall, 216 medical physics, graduate program integrated circuits and systems, Library, Science & Engineering, 7, 258 in, 57 concentration in, 141 Libraries, Columbia University, 7, 258 medical services and Columbia Health integrity, academic, 245–247 lightwave (photonics) engineering, program, 221–222, 257 Intercollegiate Athletics, 217 concentration in, 140 mentorship, 215 Intercultural Resource Center (IRC), LionSHARE, 8 microelectronic devices, concentration 256 loans, student, 33 in, 141

ENGINEERING 2017–2018 266 Middle Eastern, South Asian, and P violation of rules of, 247 African Studies, minor in, 201 Residence Units, and the Ph.D., 26 payments military leave of absence, 244 Residential Life, 215, 256 timely and overdue, 20, 30 minors, academic, 17, 198–202 resources, Columbia University, list of, See also fees misconduct 256–259 Pearson Test of English (PTE), 28 academic, complaints about faculty Rules of University Conduct, 245–247 personal expenses of students, 20, 30 and staff, 252–253 philosophy, minor in, 202 scientific or scholarly, 254 physical education, 13 S Morningside Heights campus, 6 and intercollegiate athletics, 217, 258 maps of, 260–261 safety and security, campus, 217–218 Physical Education, Intercollegiate Multicultural Affairs, 215, 256 sanctions, for academic dishonesty, Athletics and, Department of, 217, multimedia networking, concentration 246 258 in, 140 scholarships Physics, Department of, 258 music and grants, endowed, list of, 224– courses for engineering students, instruction courses, 12 229 209–211 minor in, 201 residence hall, list of, 219 plagiarism, 245–247 School of Engineering. See Engineering plasma physics, graduate program School N in, 58 Science & Engineering Library, 7, 258 Plasma Physics Laboratory, 51 nanomaterials, 173 security resources, computer, 7 political science, minor in, 202 names, student, change of, 241 Sexual Violence Response, 222, 258 prelaw program, 18 New Student Orientation Program Social Security number, registration premed program, 17–18 (NSOP), 215 and, 238 preprofessional advising, 17–18, 214 New York City, 5 sociology, minor in, 202 printing facilities, 7 New York State solid-state physics, graduate program prizes, medals and, list of, 232–236 initial certification in adolescence in, 58 professions other than engineering, education, 18 solid-state science and engineering Engineering programs in preparation Nondegree students, 26, 29 areas of research, 176 for, 17–18 nondiscriminatory policies, equal graduate specialty in, 176 psychological services, counseling and, educational opportunity and sororities, fraternities and, 215, 219 221 student, 254 Special Interest Communities, 219 psychology, minor in, 202 nontechnical requirements, 10–12 sports, 13, 215, 217 Public Safety, Office of, 217–218, 258 Statistics, Department of, 258 courses for engineering students, O R 211–212 Off-Campus Housing Assistance statistics, minor in, 202 Rape Crisis/Anti-Violence Support (OCHA), 219 Student Advising, Center for, 214, 256 Center. See Sexual Violence officers of Columbia Engineering Student Conduct and Community Response list of, 36, 45–46 Standards, 216, 245, 259 readmission, 243 retired, list of, 44 Student Engagement, 215, 256 recreational programs, 217 Ombuds Office, 249, 252, 258 Student Financial Services. See refunds of tuition and fees, 21, 31 Ombuds Officer, 252 Student Service Center registrar, 258 operations research Student Governing Board (SGB), 215 See also Student Service Center graduate program in, 159 student grievances, academic registration, 238 minor in, 201–202 concerns, and complaints, 252–254 changes in, 239 undergraduate programs in, 154–159 student loans, 33 regulations, University, official, See also Industrial Engineering and Student Medical Insurance Plan, 20, 249–251 Operations Research, Department 30, 222, 257 religion, minor in, 202 of student organizations, 215–217 religious holidays, 249 optical and laser physics, graduate student records, rights pertaining to, report of grades, 240 program in, 58 247 Res. Inc., 215 orientation Student Research Program, 10 residence hall scholarships, list of, 236 graduate, 216 Student Service Center, 259 residence halls, 215, 219–220 undergraduate, 215 student services, 219–222

ENGINEERING 2017–2018 students telephone numbers of Columbia United Campus Ministries, 216 267 and campus life, 214–218 University departments and University Apartment Housing (UAH), contributions of, to educational resources, 256–259 219–220 costs, 20–21, 30–31 Test of English as a Foreign Language University Chaplain, Office of the, 216, employment and earnings of, 33–34 (TOEFL), 28 257 health insurance, 222 3-2 Combined Plan B.A./B.S. program, University ID card, 220–221 international, 8, 34 16 University regulations, official, 249–251 name changes of, 241 transcripts, 240 new, orientation for, 215, 216 transfer credits, 239 V personal expenses of, 20, 31 transfer students, 29 nondegree, status, 29 tuition Veteran Affairs, Department of, 33 transfer, 29 graduate, 30–31 veterans, educational benefits for, 33 See also engineering students; refunds of, 20, 31 visual arts courses, 12 graduate students; undergraduates undergraduate, 20–21 study abroad, 13–15 W sustainable energy U and materials, concentration in, Waste to Energy Research and 122–124 Undergraduate Student Life, 215, 256 Technology Council (WTERT),120 concentration in, 125 Undergraduate Financial Aid and water resources and climate risks, sustainable engineering, minor in, 202 Educational Financing, 257 concentration in, 122, 125 sustainable waste management, 125 undergraduates wireless and mobile communications, systems biology and neuroengineering, applications and admissions of, 19 concentration in, 141 concentration in, 141 degree requirements for, 10, 238– wireless network, 7 240 financial aid for, 22 T housing for, 219 Tau Beta Pi, 16 minor programs for, 17, 198–202 teacher certification, obtaining, 18 programs in Engineering School for, telecommunications engineering, 10–19 concentration in, 140 tuition and fees of, 20–21 telephone and cable TV services, 7 See also students

ENGINEERING 2017–2018