Bulletin 2014–2015

Home , Columbia Water Center, Elizabeth Hillman

7/28/14 3:56 PM 2015 – BULLETIN BULLETIN 2014

Columbia | Engineering 2014 – 2 015 500 West 120th Street 120th West 500 NY 10027 York, New 40151 Cover.indd 1 Academic Calendar 2014–2015

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 2014 SPRING TERM 2015

August January 25–Sept. 1 New student orientation program. 13–16 Registration by appointment for all classes. 29 Registration by appointment for first-year 19 Birthday of Martin Luther King Jr. students. University holiday. 30 Last Day to apply for October degrees. 20 First day of classes. 20–23, Change of program by appointment. September 26–30 UNDERGRADUATE ADMISSIONS Need more information? 1 Labor Day. University holiday. 30 Last day to (1) register for academic credit, Office of Undergraduate Admissions You can find the contact information 2 First day of classes. (2) change course programs, (3) submit written notice of withdrawal from the 212 Hamilton Hall, Mail Code 2807 for the people who know in the 2–5, 8–12 Change of program by appointment. 12 Last day to (1) register for academic credit, spring term to the Dean of Student Affairs 1130 Amsterdam Avenue Columbia University Resource List (2) change course programs, (3) submit for full refund of tuition and special fees. New York, NY 10027 on pages 247–249 or visit the Columbia Engineering written notice of withdrawal from the fall No adjustment of fees for individual website, engineering.columbia.edu. Phone: 212-854-2522 term to the Dean of Student Affairs for courses dropped after this date. Last day Fax: 212-854-3393 full refund of tuition and special fees. No to confirm, update, or request a waiver For the most current information, visit our online E-mail: [email protected] adjustment of fees for individual courses from the Student Medical Insurance Plan. bulletin at bulletin.engineering.columbia.edu. undergrad.admissions.columbia.edu dropped after this date. 30 Last day to confirm, update, or request February a waiver from the Student Medical 11 February degrees conferred. FINANCIAL AID Insurance Plan. Office of Financial Aid and Educational Financing March Office: 618 Lerner Hall October 9 Midterm date. Mailing: 100 Hamilton Hall, Mail Code 2802 15 October degrees conferred. 16–20 Spring holiday. 1130 Amsterdam Avenue 16 Midterm date. 26 Last day to drop Engineering courses without academic penalty. Last day New York, NY 10027 November to change grading option. Phone: 212-854-3711 3 Last day to apply for February degrees. Fax: 212-854-5353 3 Academic holiday. April Undergraduate Inquiry E-mail: [email protected] 4 Election Day. University holiday. 13–17 Registration by appointment for fall 2015. Graduate Inquiry E-mail: [email protected] 10–14 Registration by appointment for spring 2014. cc-seas.financialaid.columbia.edu 14 Last day to drop Engineering courses May without academic penalty. Last day to 4 Last day for continuing students to apply GRADUATE STUDENT AFFAIRS change a grading option. for financial aid for the 2015–2016 27–28 Thanksgiving holiday. academic year. Graduate Admissions, Financial Aid, and Student Affairs 4 Last day of classes. 530 S. W. Mudd, Mail Code 4718 December 5–7 Study days. 500 West 120th Street 1 Last day to apply for May degrees. 8–15 Final examinations. New York, NY 10027 8 Last day of classes. 18 Baccalaureate Service. Phone: 212-854-6438 9–11 Study days. 19 Engineering Class Day. Fax: 212-854-5900 12–19 Final examinations. 20 2015 University Commencement. 20–Jan. 19 Winter holiday. E-mail: [email protected] gradengineering.columbia.edu

40151 Cover.indd 2 7/28/14 3:56 PM Bulletin 2014 – 2015 b

Mission Columbia Engineering, The Fu Foundation School of Engineering and Applied Science at Columbia University in the City of New York, prepares talented students to become innovative, socially responsible leaders in industry, government, and academia. Our education is grounded in the fundamental principles and creative approaches of engineering, while being critically informed by the broader perspective of a distinguished liberal arts education. This interdisciplinary education mission is enriched by a research endeavor focused on expanding the knowledge base of engineering and creating technological solutions that serve society. Columbia students, faculty, and alumni strive to improve the human condition locally, nationally, and globally with their enthusiasm to learn, to question, and to solve some of the world’s most pressing current and future challenges.

engineering 2014–2015 a message from the dean

elcome to Columbia University’s and incredible translation of these innovations Fu Foundation School of Engineering to entrpreneurial solutions that impact nearly W and Applied Science (SEAS). As every aspect of life. It has sparked a new way students here, you are among the very best of thinking, one that crosses disciplinary lines, and brightest of your generation, and you will so that today, engineering is not only informed be educated at a school that will empower by other fields, but now is informing other you to become the next leaders in the fields of fields. engineering and applied science. Our School has become the nexus that You are becoming part of a vibrant, connects the academic disciplines of our intellectually challenging school with a world-class sister schools at Columbia, helping distinguished history of transformational to shape the future of medicine, journalism, breakthroughs that have impacted the business, policy, science, the social sciences, world. As we continue to celebrate our even the arts and humanities. Beginning at sesquicentennial year, we are inspired by the undergraduate level with an emphasis on the path-breaking legacy of our academic the liberal arts of the Core Curriculum, we forebears, upon which our School continues now have pan disciplinary collaborations at to build. the graduate level, leading to many enriched Our first dean, Charles Frederick Chandler, academic opportunities at the vanguard of set the benchmark. A pioneering crusader, research and scholarship. he was also the president of New York City’s Columbia Engineering is an exciting and Metropolitan Board of Health, overseeing stimulating community and I encourage you purity of food and drugs, ensuring the safety to take full advantage of the exceptional of milk, conveying clean water into the city, opportunities for learning and advancement and establishing building codes. Bringing that await you here. engineering solutions to society’s greatest challenges continues to be a hallmark of With best wishes for the academic year, Columbia Engineering. Today, the pace of translating technological innovations into real world impact has never been faster, and our faculty and students remain at the forefront, pushing the frontiers of knowledge and of technology while, at the same time, providing solutions for some of the Mary C. Boyce world’s most intractable problems. Dean of Engineering I believe that Engineering is in a Morris A. and Alma Schapiro Professor Renaissance, and nowhere is that more apparent than at Columbia Engineering. This Renaissance is characterized by great research, great creativity and invention, great innovation,

engineering 2014–2015 table of contents

About the School and 1 Contact Information 36 Campus and Student Life 209 University Campus life 210 History of the School 2 Faculty and Administration 37 student services 215 Resources and Facilities 5 Departments and Academic 47 Scholarships, Fellowships, 219 Undergraduate Studies 9 Programs Awards, and Prizes the Undergraduate Programs 10 key to course listings 48 Endowed Scholarships and Grants 220 Policy on Degree Requirements 10 applied physics and 50 Endowed Fellowships 224 The First-Year/Sophomore Program 10 applied mathematics Outside Fellowship 226 Study Abroad 15 Medals and Prizes 226 Combined Plan Programs 16 biomedical engineering 64 Residence Hall Scholarships 230 The Junior-Senior Programs 16 Programs in Preparation for 17 chemical engineering 78 University and School 231 Other Professions civil engineering and 89 Policies, Procedures, and Joint Programs 18 engineering mechanics Undergraduate Admissions 18 Regulations computer engineering 101 academic procedures 232 Undergraduate TUITION, 19 program and standards FEES, AND PAYMENTS computer science 106 academic standing 236 FINANCIAL AID FOR 21 UNDERGRADUATE STUDY earth and environmental 119 policy on conduct and 238 Determining Eligibility 21 engineering discipline How to Apply for Financial Aid 21 electrical engineering 133 essential Policies for the Tax Withholding for Nonresident 22 columbia community 241 Alien Scholarship and industrial engineering 153 Fellowship Recipients and operations research student grievances, 242 academic concerns, and materials science and 170 Graduate Studies 23 complaints engineering program The graduate programs 24 The Master of Science Degree 24 mechanical engineering 178 Directory of University 245 Doctoral Degrees: Eng.Sc.D. 25 Resources and Ph.D. Undergraduate Minors 193 Columbia university 246 Special Nondegree Students 26 resource list

columbia video network 28 Interdisciplinary Courses 199 maps 249 and Courses in Other graduate admissions 29 Divisions of the University index 251 graduate tuition, fees, 31 Interdisciplinary 200 Academic Calendar (see inside back and payments engineering courses cover)

financial aid for graduate 33 courses in other divisions 201 study of the university Financing Graduate Education 33 Biological Sciences 201 Instructions for Financial Aid 33 Business 201 Applicants Chemistry 201 Graduate School Departmental 33 Earth and Environmental Sciences 202 Funding Humanities and Social Sciences 204 Alternative Funding Sources 34 Mathematics 205 Other Financial Aid—Federal 34 Physics 205 and Private Programs Statistics 207 Employment 35 About the School and University 2 history of the school

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

engineering 20134–20145 3

nuclear submarine, the 300-foot-long with cross-disciplinary research income from inventions created by Nautilus, launched in 1954. going on in biomedical imaging, its faculty. environmental chemistry, materials Columbia Engineering faculty science, medical digital libraries, have been instrumental in developing technology and beyond nanotechnology, digital government, and and establishing many of the widely Today, The Fu Foundation School of new media technologies. The School accepted global standards for storage Engineering and Applied Science, as and its departments have links to the and transmission of high-quality it was named in 1997, continues to Departments of Physics, Chemistry, audio and video data. Perhaps the provide leadership for scientific and Earth Science, and Mathematics, as most famous of these is the MPEG- educational advances. Even Joseph well as the College of Physicians and 2 data compression standard, which Engelberger, Class of 1946, the father Surgeons, the Graduate School of is embedded in millions of DVDs of modern robotics, could not have Journalism, Lamont-Doherty Earth and DVD players. With Columbia anticipated the revolutionary speed with Observatory, Teachers College, Engineering faculty continuing to play which cumbersome and expensive “big Columbia Business School, and the a key role in current and evolving science” computers would shrink to the Graduate School of Architecture, information technology, Columbia is size of a wallet. Planning and Preservation. The the only university actively participating No one could have imagined the transforming gift of The Fu Foundation in a broad range of standards-based explosive growth of technology and its has catapulted the School into the patent pools, including AVC (Advanced interdisciplinary impact. The Engineering forefront of collaborative research and Video Coding), the world standard for School is in a unique position to take teaching and has given students the audio/video compression that is now advantage of the research facilities opportunity to work with prize-winning one of the most commonly used HD and talents housed at Columbia to academicians, including Nobel laureates, formats and most commonly used in form relationships among and between from many disciplines. streaming media; ATSC, a standard other schools and departments developed by the Advanced Television within the University. The School’s Systems Committee for digital television newest department, Biomedical New Research frontiers transmission that is now the U.S. Engineering, with close ties to the Columbia is one of the top universities standard; MVC (Multi-View Coding), the Medical School, is but one example. in the world whose technology transfer standard for emerging 3D video; and Interdisciplinary centers are the norm, operations earn the largest patent Blu-ray Disc, the standard for recording

engineering 2014–2015 4 and retrieval of data and HD audio-visual Entrepreneurship A Forward-Looking media. Another hot area at Columbia Tradition Columbia Engineering also holds a Engineering is entrepreneurship. The But, for all its change, there is still host of exciting new patents in many School’s faculty and students are a continuous educational thread other emerging research areas. Among generating some 15 to 20 startups a that remains the same. Columbia these is a laser-based method that year in all kinds of fields, from medical to Engineering still remains an institution makes possible the sharper display cleantech to high-tech. of manageable size within a great screens found in high-end smart Throughout the academic year, university. Committed to the educational phones. Sequential lateral solidification the School hosts several activities philosophy that a broad, rigorous (SLS) is based on breakthrough research and networking events to support its exposure to the liberal arts provides the in understanding how a substance is active startup community, including surest chart with which an engineer can rapidly melted and solidified. The result the Columbia Engineering Fast Pitch navigate the future, all undergraduates is an optimal crystalline material that Competition, Columbia Venture must complete a modified but equally enables a new generation of smart Competition, and new Ignition Grants rigorous version of Columbia College’s phones, thin computers, and next- program, which funds ventures started celebrated Core Curriculum. It is these generation video displays. And, thanks by current students. selected courses in contemporary to the innovations taking place in Entrepreneurship has also emerged civilization in the West and other global Columbia Engineering labs, it may soon as an important central educational cultures that best prepare a student for be possible to put an entire computer theme at Columbia Engineering. The advanced course work; a wide range of on a sheet of glass or plastic. School promotes engineering innovation eventual professions; and a continuing, Other exciting technologies coming and engaged entrepreneurship through life-long pursuit of knowledge, out of Columbia Engineering labs a range of programs and offers a understanding, and social perspective. include technology for air carbon 15-credit, interdisciplinary minor in It is also these Core courses that most capture; medical robotics; Smart Grid entrepreneurship made up of both closely tie today’s student to the alumni technology for managing distribution and Engineering and Business School of centuries past. Through a shared maintenance of power grids and urban courses. The School also provides a exposure to the nontechnical areas, all infrastructure; and state-of-the-art DNA four-year entrepreneurship experience Columbia Engineering students—past, sequencing by synthesis technology that for all interested Columbia Engineering present, and future—gain the humanistic enables rapid and low-cost sequencing students, regardless of major. tools needed to build lives not solely as for future personalized medicine. technical innovators, but as social and political ones as well.

engineering 2014–2015 Resources and Facilities 5

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

engineering 2014–2015 6 also conducts ongoing research at Offering multiple programs of study, ColumbiA Engineering such facilities as Brookhaven National with facilities specifically designed and Computing Facilities Laboratory in Upton, NY, and the NASA equipped to meet the laboratory and The Botwinick Multimedia Learning Goddard Institute for Space Studies research needs of both undergraduate Laboratory at Columbia University located just off the Morningside campus. and graduate students, the School is has redefined the way engineers are the site of an almost overwhelming educated here. array of basic and advanced research The Morningside Heights Designed with both education and installations, from the Columbia Genome Campus interaction in mind, the lab provides Center and Nanoscale Science and students and instructors with 40 Apple The Fu Foundation School of Engineering Center to the Energy Mac Pro workstations connected Engineering and Applied Science is Frontier Research Center, which is to central servers and a network- located on Columbia’s Morningside examining new and more efficient ways based RAID storage array, a full set campus. One of the handsomest urban to extract solar energy. of professional-grade engineering institutions in the country, the 13.1 The latest addition to this group software tools, and a collaborative million gross square feet (gsf) of the of advanced research opportunities classroom learning environment to help Morningside campus comprise more and one that stems from a highly them engage in real-world interactions than 200 buildings of housing; off- interdisciplinary framework is Columbia’s with community clients, Engineering campus apartments and commercial new Institute for Data Sciences and faculty, and professional practitioners. buildings; recreation and research Engineering, housed within Columbia It is utilized in some of the School’s facilities; centers for the humanities Engineering with multiple partners introductory first-year engineering and social and pure sciences; and University-wide, including the Graduate projects, as well as advanced classes in professional schools in architecture, School of Arts and Sciences, the 3-D modeling and animation, technology business, the fine arts, journalism, law, Journalism School, and the Columbia and society, and entrepreneurship. and many other fields. University Medical Center. Supported at its founding by the City of New York, Central Computing The Fu Foundation School the Institute strives to be the single Resources of Engineering and Applied world-leading institution in research and Science education in the theory and practice Columbia University Information The Fu Foundation School of of the emerging and exciting field of Technology (CUIT) Engineering and Applied Science data science. Equally important to its Help Desk Support Center occupies four laboratory and mission is supporting and encouraging 202 Philosophy Hall classroom buildings at the north entrepreneurial ventures emerging from Monday–Friday: 10:00 a.m.–6:00 p.m. end of the campus, including the the research conducted by its students, recently completed Northwest Corner faculty, and collaborators. Phone: 212-854-1919 Science and Engineering Building, an Details about specific programs’ Monday–Thursday: 8:00 a.m.–11:00 p.m. interdisciplinary teaching and research laboratories and equipment can be Friday: 8:00 a.m.–7:00 p.m. building on the Morningside campus. It found in the sections describing those Saturday: 10:00 a.m.–6:00 p.m. was designed by the world-renowned programs. Sunday: 3:00 p.m.–11:00 p.m. architect Jose Rafael Moneo to serve E-mail: [email protected] cuit.columbia.edu/support as a physical and intellectual bridge, The Makerspace linking laboratories and maximizing Opening in the fall of 2014, Columbia CUIT provides Columbia University the ready sharing and exchange of Engineering’s brand new MakerSpace students, faculty, and staff with myriad ideas, resources, and information. will provide students a dedicated central computing and communications With its beehive-like setting, the new place at the School to collaborate, services, including Columbia’s wireless building is already enhancing existing learn, explore, experiment, and create and high-speed campus Ethernet collaborations and stimulating new prototypes. Students can utilize the network, available to all students ones, enabling researchers across the space to work on a variety of innovative in residence hall rooms. CUIT also University to work together to create projects, including independent or group manages an array of computer labs, new areas of knowledge, in fields where design projects, product development, terminal clusters, ColumbiaNet kiosk the biological, physical, and digital and new venture plans. Located in the stations, electronic classrooms, and worlds fuse. This pandisciplinary frontier Botwinick Laboratory on the 12th floor provides a variety of technical support is the nexus at which engineering and of the Mudd Building, this facility fosters services via the CUIT Helpdesk. applied scientific advances will provide student creativity by bringing together CUIT services include the following: innovative solutions to some of modern the workspace and tools for computer- society’s most challenging problems in aided design, physical prototyping, • E-mail accounts: CUIT provides a a wide range of sectors, from health to fabric arts, woodworking, electronics, web-based program for accessing cybersecurity and smart infrastructure to and software. Columbia e-mail. It provides a secure the environment. and convenient way to send and

engineering 2014–2015 receive mail from anywhere, using any also provides information on how to journals, ebooks (including handbooks), 7 web browser. protect your system, data, and privacy standards, patents, and society • Computer account IDs provide when working online. publications. Databases such as access to Columbia’s secure online • Electronic Data Service, run jointly Compendex, INSPEC, Scopus and information resources, campus by CUIT and the Libraries, provides Web of Science help patrons to pinpoint computer labs, and printing on CUIT computing support for researchers relevant engineering and science printers. All Columbia students, faculty, with data-intensive applications, research. and staff are assigned an ID account including statistical software, and (called University Network ID or UNI). finding and selecting appropriate data. Center for Career • Columbia’s website provides access • Telephone and cable TV service is Education to hundreds of online services available to students living in University East Campus, Lower Level and resources, including extensive residence halls. academic, scholarly, and administrative Mailing: 2960 Broadway, MC 5727 resources, myriad library catalogs and Delivery: 70–74 Morningside Drive columbia university references, the Directory of Classes, New York, NY 10027 Libraries registration information, campus Phone: 212-854-5609 Phone: 212-851-2950 publications, and events listings. Fax: 212-854-5640 E-mail: [email protected] • Technical support is available through E-mail: [email protected] library.columbia.edu the CUIT Help Desk, which provides careereducation.columbia.edu technical assistance to students on Columbia University Libraries/Information the Morningside campus online, by The Columbia University Center Services (CUL/IS) is one of the top five phone, or in person. (See beginning for Career Education (CCE) helps academic research library systems in of this section for hours and contact students and alumni develop the North America. The collections include information.) key competencies to make informed 11.9 million volumes, 168,000 current • CourseWorks is the University course decisions and take the necessary steps serial subscriptions, as well as extensive management system. It allows to achieve their career goals. CCE electronic resources, manuscripts, rare instructors to easily develop and establishes connections and facilitates books, microforms, maps, graphic and maintain course websites, distribute interaction among undergraduate audio-visual materials. The services and class materials, link to online reserves, students, graduate students, alumni, collections are organized into 21 libraries administer quizzes and tests, employers, and organizations to and various academic technology communicate with students, and generate opportunities that help centers. The Libraries employ more than promote online discussions. students pursue their personal and 550 professional and support staff. The • Electronic classrooms are equipped professional career objectives. website of the Libraries is the gateway with multimedia capabilities such as CCE encourages students and to its services and resources. computer and projection systems, alumni to visit the Center and to register The Science and Engineering Library, DVD and CD-ROM players, VCRs, and for Columbia’s job and internship located in 401 Northwest Corner audio systems. database, LionSHARE, to maximize the Building, focuses on research support • Public computer kiosks are available level of resources and assistance they for the fields of astronomy, biology, in various locations around the can receive. CCE develops relationships chemistry, engineering, physics, and Morningside campus for accessing with employers to connect students psychology, as well as providing a Columbia’s web resources and e-mail. with internships, full-time, part-time, collaborative environment supporting • Computer labs and clusters provide and temporary on- and off-campus rapidly expanding interdisciplinary students, faculty, and researchers with employment opportunities throughout science and engineering research. The access to a range of software. Some the year. In addition, CCE provides Science and Engineering Library is home locations have consultants to provide career development opportunities for to the Digital Science Center, where lab help. students beginning in their first year high-end computers are especially • Printing facilities are available at Columbia, offering externships, equipped with software and hardware throughout the Morningside campus internships, résumé and interviewing to support teaching, learning, research, and Barnard College. These high- preparation, site visits to employers, and innovation in the science and speed, high-volume printers are professionals in residence, career fairs, engineering disciplines. Group study, located in CUIT computer labs, alumni-student networking events, and individual carrels, and staff consultation libraries, residence halls, and other individual counseling. spaces along with printing and scanning computer clusters and electronic Highlights among career fairs include facilities are included in this new library, classrooms. the Engineering Career Fair in the fall which offers spectacular views of the • Computer security is extremely and the Startup Career Fair in the Columbia campus and Morningside important at Columbia and CUIT spring. Additionally, CCE partners with Heights. provides several resources online, Columbia Engineering on specialized Online, CUL provides access to including links to download antivirus events such as Speed Networking extensive collections of electronic and anti-spyware software. The site for Engineers, employer information

engineering 2014–2015 8 sessions, and workshops tailored to CCE also maintains a dossier The International Students and Scholars department and student club needs. service, managed by Interfolio, for Office (ISSO) offers many services for CCE has developed formal graduate students and alumni. A international students. Services for externship and internship programs in dossier consists of letters of reference international students include document partnership with alumni and employers, and other credentials that speak to and other immigration-related services, including the Science Technology a candidate’s scholarship, research and orientation programs. Engineering Program (STEP), the Virtual interests, and teaching experience. It is International students are urged Internship Program (VIP), and Columbia typically used in applying for teaching to make use of the services at the Experience Overseas (CEO), which positions at either the secondary school ISSO during their stay at the University offers internships in London, Hong or the college level and for graduate/ and are also invited to visit the ISSO Kong, Beijing, Shanghai, Singapore, professional school and fellowship website at columbia.edu/cu/isso, to Mumbai, and Amman. Alumni mentors applications. Undergraduate students or find comprehensive information for both are assigned to all students participating alumni with undergraduate degrees from prospective and current students. in these formal internship programs. Columbia Engineering work with the The International Students and New York–based spring internship Center for Student Advising for dossier Scholars Office is an essential source of programs include the Columbia Arts management. information regarding immigration and Experience and a civic engagement We welcome your visit to the Department of State regulations that program, Columbia Communities in Center for Career Education in person affect students studying in the United Action. CCE administers the Work at East Campus or via our website at States. The staff can also assist or Exemption Program and the Columbia cce.columbia.edu to learn more about make appropriate referrals with many Engineering Internship Fund to help our programs and resources. other nonacademic matters, including students undertake unpaid internships. adjustment to the University and the City CCE also fosters skill building through of New York. the International Students its Columbia Student Enterprises, which The office’s street address is 524 and Scholars Office are student led and staffed businesses. Riverside Drive in International House International House North Some of these programs are open to North, just north of 122nd Street. The 524 Riverside Drive, Suite 200 all students while others are open only orientation program for new international Mailing: 2960 Broadway, MC 5724 to undergraduate students. We invite students arriving for the September term New York, NY 10027 you to connect with CCE to learn about takes place during orientation week, eligibility requirements. usually the last week in August or the Phone: 212-854-3587 first week in September. For further Fax: 212-851-1235 information, consult the International E-mail: [email protected] Students and Scholars Office using the columbia.edu/cu/isso contact information above.

engineering 2014–2015 Undergraduate Studies 10 the Undergraduate Programs

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

engineering 2014–2015 in their professions and will require 4. ECON W1105: Principles of DRAMA AND THEATRE ARTS: All courses 11 sophisticated communication, planning, economics. (This course can except workshops, rehearsal, or performance and management skills. The Committee be satisfied through Advanced classes, THTR BC2120 Technical production, on Instruction established the School’s Placement; see the Advanced THTR BC3135 Set design, and THTR BC3134 nontechnical requirement so that Placement chart on page 14.) Note: Lighting design students would learn perspectives and Engineering students may not take EARTH AND ENVIRONMENTAL SCIENCES: principles of the humanities and social BC1003: Introduction to economic No courses sciences as part of a well-rounded and reasoning as a substitute for ECON multiperspective education. Through W1105. (4 points) EAST ASIAN LANGUAGES AND CULTURE: discussion, debate, and writing, All courses students improve their abilities to B. Elective Nontechnical Courses ECOLOGY, EVOLUTION, AND engage in ethical, analytic, discursive, (9–11 points of credit) ENVIRONMENTAL BIOLOGY: and imaginative thinking that will prove The following course listing by No courses except EEEB W4321 or W4700 indispensable later in life. department specifies the Columbia College, Barnard, or Columbia ECONOMICS: All courses except • E ngineering students must take 16 to Engineering courses that either fulfill W3025 Financial economics 18 points of credit of required courses or do not fulfill the nontechnical W3211 Intermediate microeconomics in list A and 9 to 11 elective points requirement. W3213 Intermediate macroeconomics chosen from the approved courses (Professional, workshop, lab, project, W3412 Introduction to econometrics in list B. The total combined number scientific, studio, music instruction, and W4020 Economics of uncertainty and information of nontechnical points (from lists A master’s-level professional courses do W4211 Advanced microeconomics and B, below) must add up to at least not satisfy the 27-point nontechnical W4213 Advanced macroeconomics 27. Neither list can be modified by requirement.) W4251 Industrial organization W4280 Corporate finance advising deans or faculty advisers. AFRICAN-AMERICAN STUDIES: All courses • Advanced Placement (AP) credit in W4412 Advanced econometrics appropriate subject areas can be AMERICAN STUDIES: All courses W4415 Game theory W4911 Seminar in microeconomics applied toward the 9-point elective ANCIENT STUDIES: All courses nontechnical requirement. W4913 Seminar in macroeconomics ANTHROPOLOGY: All courses in sociocultural W4918 Seminar in econometrics If electing Global Core, students must anthropology BC1003 Introduction to economic reasoning take two courses from the List of All courses in archaeology except field work (equivalent to ECON W1105) Approved Courses (college.columbia No courses in biological/physical anthro- BC1007 Mathematical methods for economics .edu/sites/default/files/global_core.pdf) pology [V1010, V1011, W3204, V3940, BC2411 Statistics for economics for a letter grade. G4147-G4148, W4200, G4700] BC3014 Entrepreneurship BC3018 Econometrics ARCHITECTURE: No courses A. Required Nontechnical Courses BC3033 Intermediate macroeconomic theory (16–18 points of credit) ART HISTORY AND ARCHEOLOGY: BC3035 Intermediate microeconomic theory These courses must be taken at All courses BC3038 International money and finance Columbia. ASIAN AMERICAN STUDIES: All courses EDUCATION: All courses 1. ENGL C1010: University writing (3 ASTRONOMY: No courses ENGINEERING: Only points) BMEN E4010 Ethics for biomedical engineers BIOLOGICAL SCIENCES: No courses 2. One of the following two-semester EEHS E3900 History of telecommunications sequences: HUMA C1001-C1002: BUSINESS: No courses ENGLISH AND COMPARATIVE Masterpieces of Western literature and CHEMISTRY: No courses LITERATURE: All courses philosophy (All students registering for this course should be prepared to CLASSICS: All courses FILM STUDIES: All courses except lab courses, discuss books 1–12 of the Iliad on the and COLLOQUIA: All courses first day of class) or W3850 Senior seminar in screenwriting COCI C1101-C1102: Introduction to COMPARATIVE ETHNIC STUDIES: All W4005 The film medium: script analysis contemporary civilization in the West courses FRENCH AND ROMANCE PHILOLOGY: or COMPARATIVE LITERATURE AND All courses Global Core: Any 2 courses from SOCIETY: All courses approved list (6–8 points) GERMANIC LANGUAGES: All courses COMPUTER SCIENCE: No courses 3. One of the following two courses: GREEK: All courses HUMA W1121: Masterpieces of CREATIVE WRITING: All courses HISTORY: A ll courses Western art, or HUMA W1123: (This is an exception to the workshop rule.) Masterpieces of Western music (3 HISTORY AND PHILOSOPHY OF SCIENCE: DANCE: All courses except performance classes points) All courses

engineering 2014–2015 12 HUMAN RIGHTS: All courses W3630 Seminar in social cognition world problems through classroom presentations and participation in an ITALIAN: All courses RELIGION: All courses in-depth, hands-on project. Along JAZZ STUDIES: All courses SLAVIC LANGUAGES: All courses the way, guest lecturers discuss social implications of technology, LATIN: All courses SOCIOLOGY: All courses except entrepreneurship, project management, SOCI W3020 Social Statistics LATINO STUDIES: All courses and other important nontechnical issues SPANISH AND PORTUGUESE: All courses affecting the practicing engineer. LINGUISTICS: All courses except CLLN W4202 While students need not officially SPEECH: No courses MATHEMATICS: No courses commit to a particular branch of STATISTICS: No courses engineering until the third semester, MEDIEVAL AND RENAISSANCE STUDIES: most programs recommend, and in All courses SUSTAINABLE DEVELOPMENT: No courses some cases may require, that particular MIDDLE EASTERN AND ASIAN LANGUAGE URBAN STUDIES: All courses courses be taken earlier for maximum AND CULTURES: All courses efficiency in program planning. VISUAL ARTS: No more than one course, For information concerning these MUSIC: All courses except performance which must be at the 3000-level or higher (This courses, instrument instruction courses, and is an exception to the workshop rule.) requirements, students should turn to workshops the individual program sections in this WOMEN AND GENDER STUDIES: All bulletin. PHILOSOPHY: All courses except courses F1401 Introduction to logic Professional-Level Courses for V3411 Symbolic logic Music Instruction Courses First- and Second-Year Students W4137 Nonclassical logics Music instruction and performance First- and second-year students G4431 Introduction to set theory courses do not count toward the 128 are required to take at least one G4424 Modal logic points of credit required for a B.S. professional-level course chosen from CSPH W4801 Mathematical logic I degree. Please note that this includes the list below. The faculty strongly CSPH G4802 Incompleteness results in logic courses taken at Teachers College, encourages students to schedule two Courses in logic Columbia College, and the School of of these courses. (ENGI E1102, which the Arts. PHYSICAL EDUCATION: No courses is required of every first-year student, is not included in this list.) PHYSICS: No courses Visual Arts Courses Each course is designed to acquaint Students are allowed to take courses in POLITICAL SCIENCE: All courses except Engineering students with rigorous the Visual Arts Department for general W3220 Logic of collective choice intellectual effort in engineering and credit to be applied toward the B.S. W3704 Data analysis and statisitcs for political applied science early in their academic degree. However, no more than one science research careers. If a student chooses to take visual arts course, which must be W3720 Scope and methods the second professional-level course, taken at the 3000 level or higher, may W4209 Game theory and political theory such a 1000-level course may, at the count toward the nontechnical elective W4210 Research topics in game theory discretion of each department, be used requirement. This 3000 course is an W4291 Advanced topics in quantitative research as an upper-level technical elective exception to the rule that no workshop W4292 Advanced topics in quantitative research normally satisfied by 3000-level or higher classes can fulfill the nontech elective W4360 Math methods for political science courses. requirement. W4365 Design and analysis of sample surveys The courses stipulate minimal W4368 Experimental research: design, analysis prerequisites. Each course serves as and interpretation Technical Course Requirements an introduction to the area of study W4910 Principles of quantitative political research The prescribed First Year–Sophomore in addition to teaching the subject W4911 Analysis of political data Program curriculum requires students to matter. Each course is taught by regular W4912 Multivariate political analysis complete a program of technical course department faculty and thus provides a work introducing them to five major double introduction to both subject area PSYCHOLOGY: Only areas of technical inquiry: engineering, and faculty. W1001 The science of psychology mathematics, physics, chemistry, and The courses are: W2235 Thinking and decision making computer science. W2240 Human communication APPH E1300y Physics of the human body All first-year Engineering W2280 Introduction to developmental psychology The human body analyzed from the basic undergraduate students take ENGI W2610 Introduction to personality principles of physics: energy balance in the E1102: The art of engineering (4 body, mechanics of motion, fluid dynamics of W2620 Abnormal behavior points). In this course, students see the heart and circulation, vibrations in speaking W2630 Social psychology how their high school science and and hearing, muscle mechanics, gas exchange W2640 Introduction to social cognition math knowledge can be applied in and transport in the lungs, vision, structural W2680 Social and personality development an engineering context to solve real- properties and limits, and other topics. W3615 Children at risk

engineering 2014–2015 APAM E1601y Introduction to computational ELEN E1201x and y Introduction to electrical Intercollegiate Athletics and Physical 13 mathematics and physics engineering Education. The physical education Mathematics and physics problems solved by Exploration of selected topics and their program offers a variety of activities in using computers. Topics include elementary application. Electrical variables, circuit laws, the areas of aquatics, fitness, martial interpolation of functions, solution of nonlinear nonlinear and linear elements, ideal and real arts, individual and dual lifetime sports, algebraic equations, curve-fitting and hypothesis sources, transducers, operational amplifiers in team sports, and outdoor education. testing, wave propagation, fluid motion, simple circuits, external behavior of diodes and Most activities are designed for the gravitational and celestial mechanics, and transistors, first order RC and RL circuits. Digital beginner/intermediate levels. Advanced chaotic dynamics. representation of a signal, digital logic gates, flip- flops. A lab is an integral part of the course. courses are indicated on the schedule. BMEN E1001x Engineering in medicine The majority of the activities are offered The present and historical role of engineering in GRAP E1115x and y Engineering graphics in ten time preferences. However, medicine and health care delivery. Engineering Visualization and simulation in virtual there are early-morning conditioning approaches to understanding organismic and environments; computer graphics methods for activities, Friday-only classes at Baker cellular function in living systems. Engineering presentation of data; 3D modeling; animation; Athletics Complex, and special courses in the diagnosis and treatment of disease. rendering; image editing; technical drawing. Medical imaging, medical devices: diagnostic that utilize off-campus facilities during MECE E1001x Mechanical engineering: and surgical instruments, drug delivery systems, weekends. The courses offered by the micro-machines to jumbo jets prostheses, artificial organs. Medical informatics department for each term are included The role of mechanical engineering in developing and organization of the health care system. in the online Directory of Classes, and a many of the fundamental technological advances Current trends in biomedical engineering description of the scheduled activities for on which today’s society depends. Topics research. each time preference is posted on the include airplanes, automobiles, robots, and www.dodgefitnesscenter.com website. CHEN E2100x Introduction to chemical modern manufacturing methods, as well as the engineering emerging fields of micro-electro-mechanical Students may register for only one This course serves as an introduction to the machines (MEMS) and nanotechnology. The section of physical education each term. chemical engineering profession. Students physical concepts that govern the operation of are exposed to concepts used in the analysis these technologies will be developed from basic Advanced Placement of chemical engineering problems. Rigorous principles and then applied in simple design Prior to entering Columbia, students analysis of material and energy balances on problems. Students will also be exposed to state- may have taken Advanced Placement open and closed systems is emphasized. of-the art innovations in each case study. examinations through the College An introduction to important processes in MSAE E1001y Atomic-scale engineering of Entrance Examination Board (CEEB) in the chemical and biochemical industries is new materials a number of technical and nontechnical provided. An introduction to the nanoscale science and areas. A maximum of 16 points may CIEN E1201y The art of structural design engineering of new materials. The control and be applied. Students may be assigned Basic scientific and engineering principles used manipulation of atomic structure can create to an advanced level course in for the design of buildings, bridges, and other new solids with unprecedented properties. mathematics or physics based on their parts of the built infrastructure. Application of Computer hard drives, compact disc players, and AP scores. these principles to the analysis and design liquid crystal displays (LCDs) are explored to In the required pure science areas, of a number of actual large-scale structures. understand the role of new materials in enabling the number of advanced placement History of major structural design innovations technologies. Group problem-solving sessions and the engineers who introduced them. Critical are used to develop understanding. academic credits awarded to students examination of the unique aesthetic/artistic of engineering and applied science varies from the levels awarded for liberal perspectives inherent in structural design. Physical Education Management, socioeconomic, and ethical issues arts programs, notably in mathematics, Two terms of physical education involved in the design and construction of physics, chemistry, and computer (C1001-C1002) are a degree large-scale structures. Recent developments in science. The benefit of advanced requirement for Columbia Engineering sustainable engineering, including green building placement is acceleration through students. No more than 4 points of design and adaptable structural systems. certain First Year–Sophomore Program physical education courses may be requirements and thus the opportunity of EAEE E2100x A better planet by design counted toward the degree. One point Development of the infrastructure for providing taking specialized courses earlier. of the physical education requirement safe and reliable resources (energy, water Each year the school reviews the can be fulfilled with a Barnard physical and other materials, transportation services) CEEB advanced placement curriculum education course or a Barnard dance to support human societies while attaining and makes determinations as to technique course. A student who environmental objectives. Introduction of a appropriate placements, credit, and/or intends to participate in an intercollegiate typology of problems by context, and common exemption. Please see the Advanced sport should register for the appropriate frameworks for addressing them through the Placement Credit Chart. application of appropriate technology and section of C1005: Intercollegiate policy. An interdisciplinary perspective that athletics. Intercollegiate athletes who focuses on the interaction between human attend regularly receive 1 point of credit and natural systems is provided. Alternatives up to the maximum of 4. Those who for resource provision and forecasts of their are advised to follow a restricted or potential environmental impacts through a adapted activity program should contact context provided by real-world applications and Professor Torrey in the Department of problems. engineering 2014–2015 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 W1121 Biology 4 or 5 3 no exemption Chemistry 4 or 5 3 requires completion of CHEM C1604 with grade of C or better 4 or 5 6 requires completion of CHEM C3045-C3046 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 W1105 (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 W1201 or POLS V1501 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 MATH V1102 with a grade of C or better Calculus BC 4 3** requires completion of MATH V1102 with a grade of C or better Calculus BC 5 6 requires completion of MATH V1201 (or V1207) with a grade of C or better Physics C-E&M 4 or 5 3 requires beginning with PHYS C2801 and earning grade of C or better C-MECH 4 or 5 3 requires beginning with PHYS C2801 and earning grade of C or better Physics B 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. **SEAS students with a 4 or 5 on Calculus AB or a 4 on Calculus BC must begin with Calculus II. If a SEAS student with these scores goes directly into Calculus III, he or she will not be awarded credit and may have to go back and complete Calculus II. Students with A-level or IB calculus credit must start with Calculus II.

International Baccalaureate (IB) British Advanced Level Examinations University. The appropriate transcript Entering students may be granted 6 Pending review by the appropriate should be submitted to the Center for points of credit for each score of 6 or 7 department at Columbia, students with Student Advising, 403 Lerner. on IB Higher Level Examinations if taken grades of A or B on British Advanced in disciplines offered as undergraduate Level examinations may be granted Other National Systems programs at Columbia. Students should 6 points of credit if the examinations Pending review by the appropriate consult their adviser at the Center for were taken in disciplines offered as department at Columbia, students Student Advising for further clarification. undergraduate programs at Columbia whose secondary school work was in

engineering 2014–2015 other national systems, such as the Dean for Undergraduate Student Affairs probation. Students must then register for 15 French Baccalauréat, may be granted and Global Programs and departmental their study abroad with the Office of Global credit in certain disciplines for sufficiently advisers will help students with their Programs by November 15 for spring high scores. The appropriate transcript course equivalencies for approved pro- programs and March 15 for summer, fall, should be submitted to the Center for grams so they can graduate on time. and academic year programs. Student Advising, 403 Lerner. Students can take nontechnical elec- Study-abroad students remain tives overseas, or with departmental enrolled at Columbia, and tuition is paid permission, they may choose technical to Columbia. Students participating Study Abroad electives or courses in their major. in Columbia-approved programs pay Engineering today is a global profession. housing costs directly to their host Engineers are increasingly being called It is essential that students begin or sponsoring institution. Students upon to work with other engineers from planning as early as possible—ideally receiving financial aid at Columbia will across the world, or they may even find this would be during their first year. remain eligible for financial aid when they themselves living abroad on an overseas Students are encouraged to meet with study abroad with Columbia’s approval. assignment. Learning problem-solving the Office of Global Programs to review Students who wish to be considered skills in a foreign context will help possible overseas destinations and for financial aid while studying abroad engineering students to expand their to decide on an appropriate abroad should consult the Office of Financial Aid horizons, and their adaptability to cross- experience. The Assistant Dean will and Educational Financing, 618 Lerner. cultural communication will make them a explain all Columbia Engineering study valuable addition to a team of engineers. abroad formalities and requirements. Program Information Study abroad allows engineering Students must obtain approval from Choosing the right university abroad is students to discover the field through their departmental advisers to ensure an important step in planning to study the perspective of engineers working that their work abroad meets the abroad. Study-abroad options vary widely in a different language and culture, requirements of their majors, as well as in size, geographical location, academic enabling them to learn the relationship of clearance from their Advising Dean in philosophy, language requirements, culture to science and develop the range the Center for Student Advising. living arrangements, and opportunities of transferable skills that employers for research and internships. Students are seeking today. Study abroad will Eligibility Requirements must establish a set of goals for the help students develop intellectually, In order to participate in a semester- study-abroad experience, taking into emotionally, culturally, and socially. long or yearlong study-abroad program, account their foreign-language skills Columbia Engineering undergraduate students must: and adaptability to new environments, students can study abroad for either a as well as their research objectives and semester (fall, spring, or summer) or, • Have at least a 3.0 GPA professional aspirations. exceptionally, for a full academic year. • Be making good progress toward Students must visit the Office of Global Students from every engineering major finishing the first and second year Programs’ website to review the various lists have studied abroad without adding any requirements of program options and then consult with time to their course of study at Columbia. • Although knowledge of the language the Assistant Dean for specific information Most do so in the spring semester of their of the study abroad country is not a or help in choosing an institution that offers sophomore year or in their junior year. requirement, students are encouraged the best courses in their engineering major. to have some foreign language skills Early planning is crucial so that study Engineering students have several study in order to enhance their cultural abroad plans can be integrated into the abroad options: competency and their overall study student’s curriculum plan. abroad experience. NOTE: For programs Summer study-abroad programs 1. Studying engineering at one of in countries where the language of allow students to earn credits for Columbia Engineering’s partner uni- instruction is not English, students must language instruction and nontechnical versities: University College London take all course work in the local language electives. Students can either participate (UK); Imperial College (UK); the École and will have to show proficiency in that in Columbia-approved summer Polytechnique (FR) or the École language prior to departure. programs for transfer credit or on Centrale de Paris (FR)—courses Columbia-sponsored programs for at these two institutions are pre- Students’ study-abroad plans must direct credit. The Columbia-sponsored dominantly taught in French; Bogazici be approved by the Office of Global summer programs include the Chinese University in Turkey. Programs by October 15 for spring Language Program in Beijing, the 2. Students can also choose a peer programs and March 15 for summer, Business Chinese and Internship university for direct enrollment or a fall and academic-year programs. A Program in Shanghai, the Italian program of study with a third-party review of each student’s academic and Cultural Studies Program in Venice, the provider, based on the student’s aca- disciplinary records is conducted as part Columbia University Summer Arabic demic interests. The Office of Global of this process. Students on academic or Language Program in Amman, Jordan, Programs will help students identify the disciplinary probation are not permitted and the Columbia University Programs in appropriate choice for their country of to study abroad during the term of their interest and their major. The Assistant Paris at Reid Hall.

engineering 2014–2015 16 Students who wish to have an Phone: 212-854-2522 are welcome to apply through our international experience but are unable Fax: 212-854-1209 competitive review process. to study abroad are encouraged to E-mail: [email protected] Visit the Office of Undergraduate consider the following options as viable undergrad.admissions.columbia.edu/ Admissions website for a complete list of alternatives to gaining such global apply/combined-plan affiliated schools, admission application experience and exposure. instructions, and curriculum requirements Non-credit-bearing internships, Columbia Engineering maintains for Combined Plan program admission. including the CEO program in London, cooperative program relationships with Please note that no change of major is Hong Kong, Singapore, Shanghai, Beijing, institutions nationwide and with other allowed after an admission decision has and Amman, are coordinated by the Columbia University undergraduate been rendered. Center for Career Education. Please visit divisions. The Combined Plan programs See page 25 for information on the the Center’s website for more information. (3-2 and 4-2) allow students to receive 4-2 Master of Science program, which In addition, the Summer Ecosystems both a degree in the liberal arts and in is administered through the Office of Experience for Undergraduate Education engineering. Combined plan students Graduate Student Affairs. through the Center for Environmental complete the requirements for the Research and Conservation (CERC) liberal arts degree along with required provides opportunities for engineering The Junior-Senior Programs prerequisite course work for their studies students in Brazil, Puerto Rico, the Students may review degree progress in engineering during the three or four Dominican Republic, and Jordan. via DARS (Degree Audit Reporting years at their liberal arts college before Other internship options may be System) as presented on Student entering the School of Engineering possible through Columbia Engineering Services Online. Required courses and Applied Science. They then must international partner institutions. that are not completed are detailed as complete all the requirements for the B.S. deficiencies and must be completed degree within four consecutive semesters. Academic Credit during summer session or carried as Students in Columbia-sponsored overload courses in later semesters. The Combined Plan Program within programs receive direct Columbia credit, Having chosen their program major Columbia University and the courses and grades appear in the second semester of their sopho- on students’ academic transcripts. Under this plan, the pre-engineering more year, students are assigned to a These include Reid Hall, Paris; the Berlin student studies in Columbia College, faculty adviser in the department in which Consortium for German Studies; the Kyoto Barnard College, or the School of General the program is offered. In addition to Center for Japanese Studies; the Columbia Studies for three or four years, then attends the courses required by their program, University Summer Arabic Language The Fu Foundation School of Engineering students must continue to satisfy cer- Program in Amman, Jordan, and the and Applied Science for two years, and tain distributive requirements, choosing Tsinghua University program in Beijing. is awarded the Bachelor of Arts degree elective courses that provide sufficient Credit from approved programs that and the Bachelor of Science degree in content in engineering sciences and engi- are not Columbia sponsored is certified engineering upon completion of the fifth neering design. The order and distribu- as transfer credit toward the Columbia or sixth year. This program is optional at tion of the prescribed course work may degree upon successful completion Columbia, but the School recommends it be changed with the adviser’s approval. of the program verifiable by academic to all students who wish greater enrichment Specific questions concerning course transcript. Students must earn a grade in the liberal arts and pure sciences. requirements should be addressed to of C or better in order for credits to the appropriate department or division. transfer. Course titles and grades for The Combined Plan with Other The Vice Dean’s concurrent approval is approved programs do not appear on Affiliated Colleges required for all waivers and substitutions. the Columbia transcript, and the grades There are more than one hundred are not factored into students’ GPAs. affiliated liberal arts colleges, including Tau Beta Pi Faculty from the Columbia those at Columbia, in which a student Tau Beta Pi is the nation’s second- Engineering academic departments can enroll in a Combined Plan program oldest honor society, founded at Lehigh have the responsibility to assess all leading to two degrees. Each college University in 1885. With the creed work completed abroad and make requires the completion of a specified “Integrity and excellence in engineering,” decisions about how these courses fit curriculum, including major and it is the only engineering honor society into major requirements. It is imperative degree requirements, to qualify for the that students gain course-by-course representing the entire engineering baccalaureate from that institution. Every approval from their department prior to profession. Columbia’s chapter, New affiliated school has a liaison officer who departure on a study-abroad program. York Alpha, is the ninth oldest and coordinates the program at his or her was founded in 1902. Many Columbia home institution. Students interested in buildings have been named for some Combined Plan Programs this program should inform the liaison of the more prominent chapter alumni: Office of Undergraduate Admissions officer as early as possible, preferably in Charles Fredrick Chandler, Michael 212 Hamilton Hall, MC 2807 the first year, in order to receive guidance Idvorsky Pupin, Augustus Schermerhorn, 1130 Amsterdam Avenue about completing program requirements. and, of course, Harvey Seeley Mudd. New York, NY 10027 Applicants from nonaffiliated schools Undergraduate students whose

engineering 2014–2015 scholarship places them in the top and applied science earned at Columbia in the fall of their sophomore year, when 17 eighth of their class in their next-to-last University prepares students to enter they also decide on a major. year or in the top fifth of their class a wide range of professions. Students In considering a minor, students must in their last college year are eligible are, however, encouraged to consider understand that all minors are not, and for membership consideration. These graduate work, at least to the master’s cannot, be available to all students. In scholastically eligible students are degree level, which is increasingly addition, the School cannot guarantee further considered on the basis of considered necessary for many that a selected minor can be completed personal integrity, breadth of interest professional careers. within the usual residence period need- both inside and outside engineering, The Engineering Accreditation ed for a major. Indeed, students choos- adaptability, and unselfish activity. Commission (EAC) of ABET, an ing minors should expect to encounter Benefits of membership include organization formed by the major scheduling difficulties. The potential for exclusive scholarships and fellowships. engineering professional societies, the successful completion of a minor Many networking opportunities for jobs accredits university engineering programs depends on the student’s major and and internships are also available, with on a nationwide basis. Completion of an the minor chosen, as well as the course 230 collegiate chapters and more than accredited program of study is usually schedules and availability, which may 500,000 members in Tau Beta Pi. the first step toward a professional change from year to year. The list of engineering license. Advanced minors, as well as their requirements, Taking Graduate Courses as an study in engineering at a graduate appear on pages 194–198. Undergraduate school sometimes presupposes the completion of an accredited program of With the faculty adviser’s approval, a Programs in Preparation undergraduate study. student may take graduate courses while for Other Professions still an undergraduate in the School. The following undergraduate The Fu Foundation School of Engineering Such work may be credited toward programs are accredited by the EAC of and Applied Science prepares its one of the graduate degrees offered by ABET: biomedical engineering, chemical students to enter any number of the Engineering Faculty, subject to the engineering, civil engineering, Earth and graduate programs and professions following conditions: (1) the course must be environmental engineering, electrical outside of what is generally thought of as accepted as part of an approved graduate engineering, and mechanical engineering. the engineering field. In an increasingly program of study; (2) the course must not technological society, where the line have been used to fulfill a requirement for The 4-1 Program at Columbia between humanities and technology the B.S. degree and must be so certified by College is becoming blurred, individuals with the Dean; and (3) the amount of graduate Students who are admitted as first-year a thorough grounding in applied credit earned by an undergraduate cannot students to the School of Engineering mathematics and the physical and exceed 15 points. Undergraduates may not and Applied Science and subsequently engineering sciences find themselves take CVN courses. complete the four-year program for highly sought after as professionals in the Bachelor of Science degree, have practically all fields of endeavor. the opportunity to apply for admission The Bachelor of Science Degree Engineering students interested in to either Columbia College or Barnard Students who complete a four-year pursuing graduate work in such areas College and, after one additional year of sequence of prescribed study are as architecture, business, education, study, receive the Bachelor of Arts degree. awarded the Bachelor of Science journalism, or law will find themselves The program will be selective, and degree. The general requirement for well prepared to meet the generally admission will be based on the following the Bachelor of Science degree is flexible admissions requirements of most factors: granting of the B.S. at Columbia the completion of a minimum of 128 professional schools. Undergraduate Engineering at the end of the fourth year; academic credits with a minimum students should, however, make fulfillment of the College Core requirements cumulative grade-point average (GPA) careful inquiry into the kinds of specific by the end of the fourth year at the of 2.0 (C) at the time of graduation. preparatory work that may be required School; a minimum GPA of 3.0 in the The program requirements, specified for admission into highly specialized College Core and other courses; and the elsewhere in this bulletin, include programs such as medicine. the first-year–sophomore course successful completion of any prerequisites for the College major or concentration. To requirements, the major departmental Premed requirements, and technical and be admitted to the program, a plan needs Engineering students seeking admission nontechnical elective requirements. to be in place for the student to complete to dental, medical, optometric, Students who wish to transfer points the major or concentration by the end of osteopathic, or veterinary schools of credit may count no more than 68 their fifth year. directly after college must complete all transfer points toward the degree, and Interested students should contact entrance requirements by the end of must satisfy the University’s residence their advising dean for further information. the junior year and should plan their requirements by taking at least 60 points program accordingly. Students should of credit at Columbia. Courses may not Minors consult with their adviser in the Center be repeated for credit unless it is stated Columbia Engineering undergraduates for Student Advising and Preprofessional otherwise in the course description. may choose to add minors to their Advising to plan an appropriate The bachelor’s degree in engineering programs. This choice should be made

engineering 2014–2015 18 program. Students should also connect training involving relational, syntactical, the sciences, of which 18 must be in the with Preprofessional Advising to learn and abstract thinking. A sound education area of the certification sought: chemistry, more about extracurricular and research is best for most prelaw students. While biology, physics, or Earth science. opportunities related to premed studies. selecting courses, keep in mind the Deadline for application, which includes It is necessary to apply for admission need to hone your writing skills, your an essay and letters of recommendation, to health professions schools a little over communication skills, and your capacity for is the first Monday in March of the one year in advance of the entry date. If logical analysis. student’s sophomore year. This allows candidates are interested in going directly Courses in history, political science, program faculty to support students on to health professions school following economics, statistics, and anthropology through program planning to ensure that graduation, they should complete all help students understand the structure students can meet the requirements for requirements and the Medical College of society and the problems of social certification. However, when space allows, Admissions Test (MCAT) by the summer ordering with which the law is concerned. applications will be considered through following the junior year. It is, however, The study of philosophy, literature, fine the fall of the junior year. Applications entirely acceptable to delay application arts, foreign languages, and other cultures from juniors are due no later than the and entrance to these schools several imparts familiarity with traditions of universal first Monday in October. Students who years beyond graduation. thought and trends that influence legal plan to study abroad during the spring of Candidates planning for an developments nationally and internationally. their junior year should apply during the application to medical or dental school The examination of human behavior fall semester of their sophomore year. will also need to be evaluated by the through sociology and psychology will aid Students should decide on their interest in Premedical Advisory Committee prior a prospective law student in understanding teacher certification by the end of the first to application. A Premedical Advisory the types and effects of behavior to which year in order to start course work in the Committee application is made available the law relates. sophomore year. each year in December. Please consult The systematic ordering of with Preprofessional Advising for more abstractions and ideas in logic and the Joint Programs information regarding this process. sciences contributes much to a prelaw Engineering’s curriculum covers many student’s ability to analyze, understand, School of International and Public of the premedical courses required by and rationally organize his or her Affairs medical schools. However, in addition to thoughts. Finally, it is useful in some fields completing the mathematics, chemistry, of law for a student to have a fundamental The Fu Foundation School of Engineering and physics courses required by the knowledge of technology, engineering, and Applied Science and the School of First Year–Sophomore Program, most computers, and accounting. International and Public Affairs offer a medical schools ask for a full year of joint program enabling a small number of organic chemistry, a full year of biology, Urban Teaching: New York State students to complete the requirements and a full year of English. Initial Certification in Adolescence for the degrees of Bachelor of Science The following courses are required by Education Grades 7–12 for Teachers and Master of International Affairs in medical schools: of Mathematics and the Sciences or five years instead of six. Not only an in Childhood Education Grades 1–6 excellent academic record but also • One year of calculus for some schools maturity, fluency in an appropriate foreign language, and pertinent experience will • One year of physics, with lab Barnard College Education Program determine admission to this program. For • One year of general chemistry, with lab 335-336 Milbank Hall more information, please contact your • One year of biology, with lab (BME 3009 Broadway advising dean. labs will qualify) New York, NY 10027 • One year of organic chemistry, with lab • One year of English Phone: 212-854-7072 Undergraduate Admissions • Biochemistry or additional biology education.barnard.edu Office of Undergraduate Admissions (required by some schools) 212 Hamilton Hall, MC 2807 The Barnard Education Program provides 1130 Amsterdam Avenue For further information, please courses leading to certification to teach in New York, NY 10027 consult Preprofessional Advising at New York State (with reciprocal agreements [email protected]. with 41 other states) at either the Phone: 212-854-2522 elementary or secondary level. Students Fax: 212-854-3393 Prelaw gain experience and develop skills in urban E-mail: [email protected] Students fulfilling the School of Engineering school classrooms. Required course work undergrad.admissions.columbia.edu and Applied Science’s curriculum are well includes psychology and education, a prepared to apply to and enter professional practicum, and student teaching, totaling For information about undergraduate schools of law, which generally do not 23–26 points of credit depending on the admissions, please visit the Office of require any specific prelaw course work. level of certification sought. Undergraduate Admissions website or Schools of law encourage undergraduate Certification to teach mathematics contact the office by phone or email. students to complete a curriculum requires 36 points in mathematics. Pure characterized by rigorous intellectual science courses required are: 36 points in

engineering 2014–2015 Undergraduate Tuition, Fees, and Payments 19

he 2014–2015 tuition and fees Tuition level of the Plan and billed for the are estimated. Tuition and fees Undergraduate students enrolled in The insurance premium in addition to the T are prescribed by statute and are Fu Foundation School of Engineering Health Service fee. Visit the Columbia subject to change at the discretion of and Applied Science pay a flat tuition Health website at health.columbia. the Trustees. charge of $24,323 per term, regardless edu for detailed information about University charges such as tuition, of the number of course credits taken. medical insurance coverage options fees, and residence hall and meal plans and directions for making confirmation, are billed in the first Student Account enrollment, or waiver requests. Mandatory Fees Statement of the term, which is sent out in July and December of each year Orientation fee: $416 (one-time charge Personal Expenses for the upcoming term. This account in the first term of registration) Students should expect to incur is payable and due in full on or before Student Life fee: $739 per term miscellaneous personal expenses for the payment due date announced in Health Service fee: $429 per term such items as clothing, linen, laundry, the Statement, typically at the end of International Services charge: $50 per dry cleaning, and so forth. Students August or early January before the term (international students only) should also add to the above expenses beginning of the billed term. Any student Transcript fee: $105 (one-time charge) the cost of two round trips between who does not receive the first Student home and the University to cover travel Account Statement is expected to pay Other Fees during the summer and the month-long, at registration. Application and late fees: midyear break. If the University does not receive The University advises students to the full amount due for the term on or • Application for undergraduate open a local bank account upon arrival before the payment due date of the admission: $85 in New York City. Since it often takes as first Statement, a late payment charge • Application for undergraduate transfer long as three weeks for the first deposit of $150 will be assessed. An additional admission: $85 to clear, students should plan to cover charge of 1 percent per billing cycle may • Late registration fee during late immediate expenses using either a credit be imposed on any amount past due registration: $50; card, traveler’s checks, or cash draft thereafter. after late registration: $100 drawn on a local bank. Students are Students with an overdue account urged not to arrive in New York without balance may be prohibited from Books and course materials: Depends sufficient start-up funds. registering, changing programs, or upon course obtaining a diploma or transcripts. In the case of persistently delinquent Laboratory fees: See course listings Laboratory Charges accounts, the University may utilize the Students may need to add another Room and board (estimated): $12,000 services of an attorney and/or collection $100 to $300 for drafting materials or agent to collect any amount past due. laboratory fees in certain courses. Each If a student’s account is referred for Health Insurance student taking laboratory courses must collection, the student may be charged Columbia University offers the Student furnish, at his or her own expense, the an additional amount equal to the cost Medical Insurance Plan, which provides necessary notebooks, blank forms, and of collection, including reasonable both Basic and Comprehensive levels similar supplies. In some laboratory attorney’s fees and expenses incurred of coverage. Full-time students are courses, a fee is charged to cover by the University. automatically enrolled in the Basic expendable materials and equipment

engineering 2013–2014 20 maintenance. Students engaged in Tuition and Fee Refunds For students receiving federal student special tests, investigations, theses, Students who make a complete aid, refunds will be made to the federal or research work are required to meet withdrawal from a term are assessed aid programs in accordance with the costs of expendable materials as a withdrawal fee of $75. Late fees, Department of Education regulations. may be necessary for this work and in application fees, withdrawal fees, tuition Refunds will be credited in the following accordance with such arrangements as deposits, special fees, computer fees, order: may be made between the student and special examination fees, and transcript Federal Unsubsidized Stafford Loans the department immediately concerned. fees are not refundable. Federal Stafford Loans The Health Service Fee, Health Federal Perkins Loans Insurance Premium, University facilities fees, Federal PLUS Loans (when disbursed Damages and student activity fees are not refundable through the University) All students will be charged for damage after the change of program period. Federal Pell Grants to instruments or apparatus caused by Students who withdraw within the Federal Supplemental Educational their carelessness. The amount of the first 60 percent of the academic period Opportunity Grants charge will be the actual cost of repair, are subject to a refund calculation, Other Title IV funds and, if the damage results in total loss of which refunds a portion of tuition based the apparatus, adjustment will be made on the percentage of the term remaining Withdrawing students should be in the charge for age or condition. To after the time of withdrawal. This aware that they will not be entitled ensure that there may be no question calculation is made from the date the to any portion of a refund until all as to the liability for damage, students student’s written notice of withdrawal is Title IV programs are credited and all should note whether the apparatus is in received by the Dean’s Office. outstanding charges have been paid. good condition before use and, in case of difficulty, request instruction in its Percentage Refund for Withdrawal proper operation. Where there is danger during First Nine Weeks of Term of costly damage, an instructor should Prorated for calendars of a different be requested to inspect the apparatus. duration: Liability for breakage will be decided by the instructor in charge of the course. 1st week 100% When the laboratory work is done 2nd week 90% by a group, charges for breakage will 3rd week 80% be divided among the members of the 4th week 80% group. The students responsible for any 5th week 70% damage will be notified that a charge is 6th week 60% being made against them. 7th week 60% The amount of the charge will be 8th week 50% stated at that time or as soon as it can 9th week 40% be determined. 10th week and after 0%

engineering 20134–20145 financial aid for undergraduate study 21

Office of Financial Aid and Eligibility for Columbia grant aid Satisfactory Academic Progress Educational Financing is normally limited to eight terms of Students must continue to make 618 Lerner Hall undergraduate study. Students must satisfactory academic progress toward 2920 Broadway, MC 2802 reapply for financial aid each year and the degree to remain eligible for financial New York, NY 10027 be registered for a minimum of 12 aid. Satisfactory academic progress is points during any term for which aid reviewed at the end of each term by Phone: 212-854-3711 is requested. Changes in the family’s the Committee on Academic Standing. Fax: 212-854-5353 circumstances—for example, increased All students are considered for financial E-mail: [email protected] income or a change in the number of aid purposes to be making satisfactory cc-seas.financialaid.columbia.edu family members attending college— academic progress as long as they are will result in changes in the family allowed to continue enrollment. For Columbia is committed to meeting contribution. In addition, the individual details of The Fu Foundation School the full demonstrated financial need elements in the financial aid package of Engineering and Applied Science’s of all applicants admitted as first-year may vary from year to year. process for evaluating students’ students. Financial aid is available for The Office of Financial Aid and academic progress, see the section on all four undergraduate years, provided Educational Financing reserves the right Conduct and Discipline in this bulletin. students continue to demonstrate to revise a financial aid award if the A student who is required to withdraw financial need. However, international student withdraws from school or if any because of failure to make satisfactory students who do not indicate their information reported on financial aid academic progress may appeal the intention to apply for financial aid in applications conflicts with information decision to the Committee on Academic their admission application are not on tax returns or other verification Standing. Upon returning to The Fu eligible to apply for financial aid in any documents. If a family’s financial Foundation School of Engineering and subsequent years. circumstances change after submission Applied Science following a required While transfer admission is need- of the financial aid application, an withdrawal period, a student regains blind, financial aid resources for transfer appeal may be made to the Office of eligibility for financial aid. students are limited. Therefore, The Fu Financial Aid and Educational Financing, Foundation School of Engineering and in writing, for a reconsideration of the How to Apply for Applied Science is unable to meet the financial aid package. Financial Aid full need of transfer applicants, with the Students who receive financial aid exception of students who transfer from from Columbia grant permission to the In order to be considered for need- Columbia College. Office of Financial Aid and Educational based institutional financial aid at Financing to release relevant personal, any time during their four years of academic, and financial information undergraduate study, students must Determining Eligibility to persons or organizations outside apply for financial aid at the time they Columbia determines the amount each Columbia in order to institute or to apply for admission. Exceptions may be family can contribute to educational continue financial assistance that they granted only in the case of extenuating costs through an evaluation of the might be eligible to receive from such circumstances that result in a significant family’s financial information as reported sources. Students can expect that change in the family’s financial situation. on the application forms described on Columbia will respect their right to Continuing students must reapply for the financial aid office website. privacy and release information only as financial aid each year. Financial aid necessary. applicants whose application materials are submitted after the published

engineering 20134–20145 22 deadlines cannot be guaranteed Certain countries have entered into International Students and institutional financial aid. tax treaties with the United States, Scholars Office All Columbia application materials which may serve to reduce this rate of International House North and deadlines can be accessed through withholding. However, even when such 524 Riverside Drive, Suite 200 cc-seas.financialaid.columbia.edu. a treaty applies, the student and the Mailing: 2960 Broadway, MC 5724 University must report the full amount New York, NY 10027 of such excess to the Internal Revenue Tax Withholding for Service. Nonresident Alien Phone: 212-854-3587 If a student claims tax treaty benefits, Scholarship and Fax: 212-851-1235 he or she must also report this amount Fellowship Recipients E-mail: [email protected] to his or her country of residence. columbia.edu/cu/isso United States tax law requires the The International Students and University to withhold tax at the rate Scholars Office has prepared a The tax law is complex and may vary of 14 percent on scholarship and packet of tax information, which is with regard to individual circumstances. fellowship grants paid to nonresident revised annually and is available to Therefore, as the University is not in a aliens which exceed the cost of tuition, students. position to offer individual tax advice, books, fees, and related classroom students are advised to consult with expenses. a qualified tax professional and/or the consulate of their country of residence.

engineering 20134–20145 Graduate Studies 24 the graduate programs

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

engineering 2014–2015 Master of Science programs may primarily of basic undergraduate course requirements in the Institute and 25 include from 35 to 45 points and may courses; during the second year, of satisfaction of the language requirement require three terms for completion. graduate courses in the selected field. (in any language indigenous to the Doctoral research credits cannot be The student must complete at least 30 former USSR), the student may qualify used toward M.S. degree requirements. credits of graduate study to qualify for for the professional certificate of the All degree requirements must be the degree. Harriman Institute. The manner in completed within five years of the A student whose background may which the Institute and departmental beginning of graduate study. Under require supplementary preparation in requirements are combined is to extraordinary circumstances, a written some specific area, or who has been be determined by the student in request for an extension of this time out of school for a considerable period, consultation with departmental and limit may be submitted to the student’s will have to carry a heavier than normal Institute advisers. Advanced studies department for approval by the department course load or extend the program and research may, where appropriate, chairman and the Assistant Dean beyond two years. be supervised by faculty members from or Director. A minimum grade-point Graduates of the 4-2 Master of both the School and the Institute. average of 2.5 is required for the M.S. Science program may not be eligible to degree. A student who, at the end of take the Fundamentals of Engineering Doctoral Degrees: any term, has not attained the grade- (FE) exam if their undergraduate degree Eng.Sc.D. and Ph.D. point average required for the degree is not in engineering or a related field. Two doctoral degrees in engineering may be asked to withdraw. Students should also check with are offered by the University: the Doctor After the first semester of enrollment, individual state boards to determine of Engineering Science, administered an M.S. student may submit an eligibility requirements for employment. by The Fu Foundation School of application to apply and transfer to Please contact the Office of Graduate Engineering and Applied Science and another academic program. If the Student Affairs, The Fu Foundation the Doctor of Philosophy, administered student is not successful with the School of Engineering and Applied by the Graduate School of Arts and application process, then he or she must Science, 530 S.W. Mudd, MC 4718, Sciences. Both doctoral programs are make sure requirements for the original 500 West 120th Street, New York, subject to review by the Committee academic program are completed. NY 10027; you should also contact on Instruction of the School. Doctoral your home institution’s Combined Plan students may submit a petition to the The 4-2 Master of Science Program liaison for program information. You Office of Graduate Student Affairs to The 4-2 Master of Science Program may, in addition, e-mail questions to change from the Eng.Sc.D. degree provides the opportunity for students [email protected]. to the Ph.D. degree or from the P.D. holding bachelor’s degrees from affiliated degree to the Eng.Sc.D. degree. The liberal arts colleges (see the listing under Dual Degree Program with the petition must be submitted within the heading The Combined Plan— School of Journalism in Computer the first year of enrollment or by the Affiliated Colleges and Universities) Science completion of 30 points. Any petitions with majors in mathematics, physics, The Graduate School of Journalism submitted after this period will not be chemistry, or certain other physical and the Engineering School offer a dual considered. Doctoral degree status sciences to receive the M.S. degree degree program leading to the degrees can be changed only once; students, after two years of study at Columbia in of Master of Science in Journalism and therefore, must determine which the following fields of engineering and the Master of Science in Computer doctoral degree program is most applied science: biomedical, chemical, Science. (See Computer Science.) appropriate for their academic and civil, computer science, Earth and professional endeavours. environmental, electrical, industrial, and Joint Program with the School of Departmental requirements may mechanical engineering; applied physics; Business in Industrial Engineering include comprehensive written and oral applied mathematics; engineering The Graduate School of Business qualifying examinations. A student must mechanics; operations research; and and the Engineering School offer a have a satisfactory grade-point average materials science. joint program leading to the degrees to be admitted to the doctoral qualifying Each applicant must produce of Master of Business Administration examination. Thereafter, the student evidence of an outstanding and Master of Science in Industrial must write a dissertation embodying undergraduate record, including Engineering. (See Industrial Engineering original research under the sponsorship superior performance in physics and Operations Research.) of a member of his or her department and mathematics through differential and submit it to the department. If equations. The program of study will Special Studies with the Harriman the department recommends the be individually designed in consultation Institute dissertation for defense, the student with a faculty adviser and will integrate A candidate for an advanced degree in applies for final examination, which is undergraduate work with the field of the Engineering School may combine held before an examining committee engineering or applied science the these studies with work in the Harriman approved by the appropriate Dean’s student chooses to follow. During Institute. Upon completion of the Office. This application must be made at the first year, the program will consist

engineering 2014–2015 26 least three weeks before the date of the of credit. Candidates for the Eng.Sc.D. circumstances warrant. Such extensions final examination. degree must, in addition to the 60-point are initiated by submitting a statement The defense of the dissertation requirement, accumulate 12 points of work in progress and a schedule for constitutes the final test of the of credit in the departmental course completion together with the sponsor’s candidate’s qualifications. It must be E9800: Doctoral research instruction recommendation to the department demonstrated that the candidate has (see below). The candidate for the chairman. made a contribution to knowledge in a degree of Doctor of Engineering Science chosen area. In content the dissertation must submit evidence that his or her Special Nondegree should, therefore, be a distinctly original dissertation has been filed in compliance Students contribution in the selected field of with requirements set by the faculty of Qualified persons who are not interested study. In form it must show the mastery Engineering and Applied Science. in a degree program but who wish of written English, which is expected of only to take certain courses may be a university graduate. Doctoral Research Instruction permitted to register as special students, An Eng.Sc.D. candidate is required to provided facilities are available. For the Ph.D. Degree complete 12 credits in the departmental Many graduate courses in The Fu A student must obtain the master’s course E9800: Doctoral research Foundation School of Engineering degree (M.S.) before enrolling as instruction in accordance with the and Applied Science are offered in the a candidate for the Ph.D. degree. following guidelines: late afternoon and evening in order Application for admission as a doctoral to make them available to working candidate may be made while a 1. After obtaining a master’s degree or individuals who wish to further their student is enrolled as a master’s degree advanced standing, at which time knowledge in the areas of engineering candidate. Candidates for the Ph.D. the student begins doctoral research, and applied science. Individuals who degree must register full time and the student is eligible to register for find it difficult or impossible to attend complete six Residence Units. The E9800 (3, 6, 9, or 12 points of credit). classes on the Columbia campus may minimum requirement in course work 2. Registration for E9800 at a time other be able to receive instruction from the for the doctoral degree is 60 points of than that prescribed above is not School through the Columbia Video credit beyond the bachelor’s degree. permitted, except by written Network without leaving their work sites. A master’s degree from an accredited permission of the Dean. Individuals interested in this program institution may be accepted in the form 3. The 12 points of E9800 required for should read the section describing of advanced standing as the equivalent the Eng.Sc.D. degree do not count the distance learning Columbia Video of one year of residence (30 points of toward the minimum residence Network (CVN), which follows in this credit and two Residence Units). An requirements, e.g. 30 points beyond bulletin. application for advanced standing must the master’s degree or 60 points Special students receive grades be completed during the first semester beyond the bachelor’s degree. and must maintain satisfactory of study. Ph.D. candidates will be 4. If a student is required to take course attendance and performance in classes required to complete not less than 30 work beyond the minimum residence or laboratories and will be subject to additional points of credit in residence requirements, the 12 points of the same rules as degree candidates. for a letter grade beyond the M.S.. doctoral research instruction must still Should a special student decide Ph.D. candidates should obtain a be taken in addition to the required to pursue a degree program, work copy of the bulletin of the Graduate course work. completed as a special student may be School of Arts and Sciences, in which 5. A student must register continuously considered for advanced standing, but are printed the requirements of the through the fall and the spring terms. no more than 15 points of course work department of major interest. This requirement does not include the completed as a special student may be summer session. counted toward a graduate degree. For the Eng.Sc.D. Degree For additional information and A student must obtain the master’s Completion of Requirements regulations pertaining to special degree (M.S.) before enrolling as a The requirements for the Eng.Sc.D. students, see Graduate Admissions. candidate for the Eng.Sc.D. degree. The degree must be completed in no more minimum requirement in course work for than seven years. The seven-year time the doctoral degree is 60 points of credit period begins at the time the student beyond the bachelor’s degree. Eng.Sc.D. becomes a candidate for the Eng.Sc.D. candidates will be required to complete degree and extends to the date on not less than 30 additional points of which the dissertation defense is held. credit in residence beyond the M.S. Extension of the time allowed for for a letter grade. A master’s degree completion of the degree may be from an accredited institution may be granted on recommendation of the accepted in the form of advanced student’s sponsor and the department standing as the equivalent of 30 points chairman to the Dean when special

engineering 2014–2015 27

engineering 2014–2015 28 columbia video network

Columbia Video Network prerecorded courses available. SEAS program. 540 S. W. Mudd, MC 4719 currently offers M.S. degrees in the Only CVN students may transfer 500 West 120th Street following disciplines through CVN: up to 6 credits from another university New York, NY 10027 toward an M.S. or P.D., subject to the • Applied physics approval of the student’s adviser and the Phone: 212-854-6447 • Applied physics and applied math department. E-mail: [email protected] • Biomedical engineering Columbia University students cvn.columbia.edu • Chemical engineering admitted to an on-campus program are • Civil engineering not eligible to take CVN courses. Background • Computer science Continuing a long-standing tradition of • Earth and environmental engineering academic excellence and innovation, • Electrical engineering Program Benefits Columbia University’s Fu Foundation • Engineering management systems The CVN program allows working School of Engineering and Applied • Industrial engineering—systems professionals to enroll in courses and Science established the Columbia engineering earn graduate engineering degrees Video Network (CVN) in 1986 to meet • Materials science and engineering without leaving their communities, a growing need within the engineering • Mechanical engineering their families, or their jobs. The key community for a graduate distance • Operations research component of CVN is flexibility without education program. Classes and • Operations research—methods in compromise to the high-caliber degrees offered through CVN are fully finance teaching, resources, and standards accredited; the degrees are granted by inherent in The Fu Foundation School of Columbia University. In addition, students admitted to Engineering and Applied Science. CVN Classes available through CVN the Doctor of Engineering Science can students are a part of the Columbia are taught on campus by Columbia complete the course work component community and may take classes on University faculty in multimedia of the program via CVN. campus. To further enhance the sense classrooms. Faculty and students meet of community, CVN has developed a in classrooms equipped with cameras, Student Registration completely automated online Student electronic writing tablets, and SMART™ Center. It provides a place where CVN Students who have earned an boards. The recorded lectures are fully students and faculty can communicate. undergraduate degree in engineering, downloadable for study at home, office, Homework and exams are submitted mathematics, or related field can apply or on the road. and graded there, and course notes and to take classes for credit or audit without CVN students take the same classes, other reference materials are available first enrolling in a degree program at the have the same homework assignments, for downloading. University or taking the GRE or TOEFL take the same exams, and earn the Professors and teaching assistants are exams by registering as nondegree same degrees as on-campus students available via e-mail, phone, or online office students. CVN also offers Certification of in Master of Science (M.S.) programs. hourse to address academic questions. Professional Achievement programs in CVN’s administrative staff is available various fields, which may lead to study to assist with registration procedures, Course Offerings and in a related M.S. or P.D. program. technical queries, and academic advising, Degree Programs Although you need not be admitted so working professionals can devote their CVN makes select SEAS graduate to a degree program to begin taking energies to their studies, their families, and courses available to off-campus classes through CVN, you should apply their careers. students in autumn (September– as soon as possible if you would like to December) and spring (January–May) earn a degree from Columbia University; terms. CVN administrators work closely up to 15 credits taken as a CVN with faculty representatives from each nondegree student may be counted department to select the classes that toward a degree when applying through best fit the needs of new and continuing CVN, subject to the approval of the students around the world. During the student’s departmental adviser. Earning summer semester (and on request in the credit as a nondegree student does not autumn and spring terms), CVN makes guarantee acceptance into a degree

engineering 2014–2015 graduate admissions 29

Office of Graduate Student Affairs applicant must obtain one official Language Program (ALP) at Columbia 530 S. W. Mudd, MC 4718 transcript from each postsecondary University. However, course credits 500 West 120th Street institution attended and upload it to the earned through ALP do not count New York, NY 10027 online application. Consideration for toward the minimum engineering admission will be based not only on the academic course work requirements. Phone: 212-854-6438 completion of an earlier course of study, Enrollment in ALP courses is solely the Fax: 212-854-5900 but also upon the quality of the record financial responsibility of the student. E-mail: [email protected] presented and upon such evidence As a rule, ISSO will not permit students gradengineering.columbia.edu as can be obtained concerning the to drop courses or fall below full-time candidate’s personal fitness to pursue registration for language proficiency The basic requirement for admission professional work. deficiencies. as a graduate student is a bachelor’s Additionally, candidates must provide degree received from an institution of three letters of recommendation and the Application Fee acceptable standing. Ordinarily, the results of required standardized exams. The nonrefundable application fee for applicant will have majored in the field The Graduate Record Examination all graduate degree and nondegree in which graduate study is intended, (general) is required for all candidates. programs is $85. but in certain programs, preparation in GRE scores are valid for five years a related field of engineering or science from the test date. The Test of English is acceptable. The applicant will be as a Foreign Language (TOEFL), the Graduate Admission admitted only if the undergraduate International English Language Testing Calendar record shows promise of productive and System (IELTS), or the Pearson Test of Applicants are admitted twice yearly, for effective graduate work. English (PTE) is required of all candidates the fall and spring semesters. Students who hold an appropriate who received their bachelor’s degree in a degree in engineering may apply for country in which English is not the official • Fall admission application deadlines: admission to study for the Ph.D. degree. and spoken language. TOEFL, IELTS, and December 15 for Ph.D., Eng.Sc.D., However, students are required to obtain PTE scores are valid for two years from and M.S. leading to Ph.D. programs the master’s degree first. Applications for the test date. Applicants can only apply to and February 15 for most M.S. only admission as a doctoral candidate may one degree program per admission term. and nondegree applicants. Please visit be made after completion of 15 points the Office of Graduate Student Affairs of work as a candidate for the master’s English Proficiency website for specific M.S. only program degree. deadlines. The Office of Graduate Student Students may be admitted in one • Spring admission application deadline: Affairs no longer requires students to of the following five classifications: October 1 for all departments and demonstrate English proficiency as candidate for the M.S. degree, candidate degree levels. a graduation requirement at The Fu for the M.S. degree leading to the Ph.D. Foundation School of Engineering and degree, candidate for the Doctor of Applicants who wish to be considered Applied Science. Regardless of TOEFL, Engineering Science degree, candidate for scholarships, fellowships, and IELTS, or PTE scores submitted for for the Doctor of Philosophy degree (see assistantships should file complete admission, students should continue to also the bulletin of the Graduate School applications for fall admission. work on maintaining adequate verbal of Arts and Sciences), or special student and/or written abilities for successful (not a degree candidate). Note: Not more integration within their classes and future EXPRESS APPLICATION than 15 points of credit completed as professional endeavors. Students are Columbia Engineering seniors already a special nondegree student may be highly encouraged to be proactive about enrolled in a B.S. program with a counted toward a degree. addressing their English proficiency by minimum GPA of 3.5 are eligible to utilizing the many resources available submit an express application. Application Requirements within Columbia University and This online application, which waives Applicants must submit an online throughout New York City. the submission of GRE scores, letters of application and required supplemental Students have the option of enrolling recommendation, and official transcripts, materials, as described below. The in courses offered through the American streamlines and simplifies the application

engineering 2014–2015 30 process for graduate study. Contact option is also appropriate for individuals Transfer Applicants your academic department or the Office who missed application deadlines. Master degree students are not eligible of Graduate Student Affairs for further Applications for special student status for transfer credits. details. are available at the Office of Graduate Students possessing a conferred Student Affairs and must be submitted M.S. degree may be awarded two during the first week of the fall or spring residence units toward their Ph.D., One-Term Special Student semester. as well as 30 points of advanced Status If a one-term special student standing toward their Ph.D. or Eng. Individuals who meet the eligibility subsequently wishes either to continue Sc.D. with approval from the academic requirements, who are U.S. citizens or taking classes the following term or to department and the Office of Graduate U.S. permanent residents, and who wish become a degree candidate, a formal Student Affairs. to take courses for enrichment, may application must be made through the secure faculty approval to take up to Office of Graduate Student Affairs. two graduate-level courses for one term only as a one-term special student. This

engineering 2014–2015 Graduate tuition, fees, and payments 31

he 2014–2015 tuition and fees Tuition $50 per term (international students are estimated. Tuition and fees Graduate students enrolled in M.S. only) T are prescribed by statute and are and Eng.Sc.D. programs pay $1,710 subject to change at the discretion of per credit, except when a special fee is Transcript fee: $105 (one-time charge) the Trustees. fixed. Graduate tuition for Ph.D. students University charges such as tuition, is $20,502 per Residence Unit. The Other Fees fees, and residence hall and meal plans Residence Unit, full-time registration for Application and late fees: are billed in the first Student Account one semester rather than for individual Statement of the term, which is sent out courses (whether or not the student is • Application for graduate admission: $85 in July and December of each year for the taking courses), provides the basis for • Late registration fee: upcoming term. This account is payable tuition charges. Ph.D. students should - during late registration: $50 and due in full on or before the payment consult the bulletin for the Graduate - after late registration: $100 due date announced in the Statement, School of Arts and Sciences. typically at the end of August or early Books and course materials: January before the beginning of the billed Comprehensive Fee/ Depends upon course term. Any student who does not receive Matriculation and the first Student Account Statement is Laboratory fees: See course listings Facilities expected to pay at registration. Eng.Sc.D. candidates engaged only If the University does not receive Health Insurance the full amount due for the term on or in research, and who have completed Columbia University offers the Student before the payment due date of the their twelve (12) credits of Doctoral Medical Insurance Plan, which provides first Statement, a late payment charge Research Instruction (see “The Graduate both Basic and Comprehensive levels of $150 will be assessed. An additional Programs” in this bulletin), are assessed of coverage. Full-time students are charge of 1 percent per billing cycle may a Comprehensive Fee of $1,892 per automatically enrolled in the Basic be imposed on any amount past due term by The Fu Foundation School of level of the Plan and billed for the thereafter. Engineering and Applied Science. insurance premium in addition to the Students with an overdue account Ph.D. candidates engaged only in Health Service fee. Visit the Columbia balance may be prohibited from research are assessed $1,836 per term Health website at www.health.columbia. registering, changing programs, or for Matriculation and Facilities by the edu for detailed information about obtaining a diploma or transcripts. Graduate School of Arts and Sciences. medical insurance coverage options In the case of persistently delinquent and directions for making confirmation, accounts, the University may utilize the Mandatory Fees enrollment, or waiver requests. services of an attorney and/or collection University facilities fee: agent to collect any amount past due. Personal Expenses If a student’s account is referred for • Full-time master’s programs: collection, the student may be charged $469 per term Students should expect to incur an additional amount equal to the cost • All other full-time programs: miscellaneous personal expenses for of collection, including reasonable $434 per term such items as food, clothing, linen, attorney’s fees and expenses incurred laundry, dry cleaning, and so forth. by the University. Health Service fee: $429 per term The University advises students to open a local bank account upon arrival International Services charge: in New York City. Since it often takes as

engineering 2014–2015 32 long as three weeks for the first deposit a group, charges for breakage will be Refund Policy When Dropping to clear, students should plan to cover divided among the members of the Individual Courses immediate expenses using either a credit group. The students responsible for any Tuition for courses dropped by the last card, traveler’s checks, or cash draft damage will be notified that a charge is day of the Change-of-Program period drawn on a local bank. Students are being made against them. The amount is refunded in full. There is no refund of urged not to arrive in New York without of the charge will be stated at that time tuition for individual courses dropped sufficient start-up funds. or as soon as it can be determined. after the last day of the Change-of- Program period. The Change-of- Laboratory Charges Tuition and Fee Refunds Program period is usually the first two weeks of the fall or spring semesters Students may need to add another Students who make a complete (please note that the first week of the $100 to $300 for drafting materials or withdrawal from a term are assessed semester usually begins on a Tuesday). laboratory fees in certain courses. Each a withdrawal fee of $75. Late fees, Please note: The prorated schedule student taking laboratory courses must application fees, withdrawal fees, tuition above does not pertain to individual furnish, at his or her own expense, the deposits, special fees, computer fees, classes dropped (unless your entire necessary notebooks, blank forms, and special examination fees, and transcript schedule consists of only one class). similar supplies. In some laboratory fees are not refundable. The prorated schedule pertains to courses, a fee is charged to cover The Health Service Fee, Health withdrawals. Withdrawal is defined as expendable materials and equipment Insurance Premium, University facilities dropping one’s entire program. maintenance; the amount of the fee fees, and student activity fees are not For students receiving federal student is shown with the descriptions in the refundable after the change of program aid, refunds will be made to the federal course listings. Students engaged in period. aid programs in accordance with special tests, investigations, theses, Students who withdraw within Department of Education regulations. or research work are required to meet the first 60 percent of the academic Refunds will be credited in the following the costs of expendable materials as period are subject to a pro rata refund order: may be necessary for this work and in calculation, which refunds a portion accordance with such arrangements as of tuition based on the percentage of Federal Unsubsidized Stafford Loans may be made between the student and the term remaining after the time of Federal Stafford Loans the department immediately concerned. withdrawal. This calculation is made Federal Perkins Loans from the date the student’s written Federal PLUS Loans (when disbursed notice of withdrawal is received by the Damages through the University) Office of Graduate Student Affairs. All students will be charged for damage Federal Pell Grants to instruments or apparatus caused by Federal Supplemental Educational Percentage Refund for Withdrawal their carelessness. The amount of the Opportunity Grants during First Nine Weeks of Term charge will be the actual cost of repair, Other Title IV funds and, if the damage results in total loss of Prorated for calendars of a different the apparatus, adjustment will be made duration, if the entire program is Withdrawing students should be in the charge for age or condition. To dropped: aware that they will not be entitled ensure that there may be no question to any portion of a refund until all as to the liability for damage, students 1st week 100% Title IV programs are credited and all should note whether the apparatus is in 2nd week 90% outstanding charges have been paid. good condition before use and, in case 3rd week 80% of difficulty, request instruction in its 4th week 80% proper operation. Where there is danger 5th week 70% of costly damage, an instructor should 6th week 60% be requested to inspect the apparatus. 7th week 60% Liability for breakage will be decided by 8th week 50% the instructor in charge of the course. 9th week 40% When the laboratory work is done by 10th week and after 0%

engineering 2014–2015 financial aid for graduate study 33

Financing Graduate Instructions for Engineering graduate programs is Education Financial Aid Applicants also used to apply for departmental The academic departments of funding. Outside scholarships for which Columbia Engineering and the Office of Deadlines you qualify must be reported to your Financial Aid and Educational Financing Apply for financial aid at the same time department and the Office of Financial seek to ensure that all academically that you apply for admission. Your Aid and Educational Financing. The qualified students have enough financial admissions application must be received School reserves the right to adjust your support to enable them to work by the December 1 deadline to be institutional award if you hold an outside toward their degree. Possible forms eligible for The Fu Foundation School scholarship, fellowship, or other outside of support for tuition, fees, books, of Engineering and Applied Science funding. and living expenses are: institutional departmental funding (institutional grants, fellowships, teaching and grants, fellowships, teaching and Institutional Grants research assistantships, readerships, research assistantships, readerships, Institutional grants are awarded to preceptorships, on- or off-campus and preceptorships). Spring admissions graduate students on the basis of employment, and student loans. The applicants will not be considered for academic merit. Recipients must Office of Financial Aid and Educational departmental funding. maintain satisfactory academic Financing works closely with students Incoming applicants and continuing standing. All applicants for admission to develop reasonable financial plans students must complete their FAFSA and continuing students maintaining for completing a degree. form after January 1 and by May 1. satisfactory academic standing will be Columbia University graduate Guidelines for continuing students considered for these funds. funds are administered by two are available from departmental advisers separate branches of the University, in advance of the established deadline. Fellowships and the application materials All continuing supported students Fellowships are financial and intellectual required by the two branches differ. must preregister for classes during the awards for academic merit that provide Institutional grants, fellowships, preregistration period. stipends to be used by fellows to further teaching and research assistantships, their research. If you are awarded a readerships, and preceptorships are Graduate School fellowship, you are expected to devote all departmentally-administered funds. Departmental Funding time to your own work, and you are not required to render any service to the Questions regarding these awards The graduate departments of Columbia University or donor. You may publish should be directed to your academic Engineering offer an extensive array of research produced by your fellowship department. Federal Student Loans funding. Funding decisions, based solely work. As a fellow, you may not engage (Unsubsidized, Graduate PLUS, and on merit, and contingent upon making in remunerative employment without Perkins) and private student loans are satisfactory academic progress, are consent of the Dean. All applicants administered by the Office of Financial made by the departments. Columbia for admission and continuing students Aid and Educational Financing. Engineering prospective and continuing maintaining satisfactory academic Questions about loans should be graduate students must complete their standing will be considered for these directed to the financial aid office. FAFSA in order to be considered for funds. Applicants should contact the all forms of graduate financing (both department directly for information. See departmentally-administered and the complete listing of fellowships on financial aid–administered funds). The application for admission to Columbia pages 224–226.

engineering 2014–2015 34 Assistantships obtain support for their educational request form is available at cc-seas Teaching and research assistantships, expenses from their government, a .financialaid.columbia.edu/educational available in many departments, foundation, or a private agency. -loans. It is your responsibility to provide tuition exemption and a International students who apply supply accurate and complete living stipend. Duties may include to doctoral programs of study by the information on the FAFSA and the teaching, laboratory supervision, December 1 deadline and are admitted online loan request form. You must participation in faculty research, and to a Columbia Engineering doctoral also notify the Office of Financial Aid other related activities. Teaching and program are automatically considered and Educational Financing immediately research assistantships require up for departmental funding (institutional of any changes in your enrollment to twenty hours of work per week. grants, fellowships, teaching and plans, housing status, or financial The appointments generally last from research assistantships, readerships, situation, including information nine to twelve months. If you are and preceptorships) upon completion of about any institutional or outside participating in faculty research that the required financial aid forms referred scholarships you will be receiving. fulfills degree requirements, you may to above. Spring admissions applicants Determination of your eligibility apply for a research assistantship. will not be considered for departmental for financial aid is based in part on Readers and preceptors receive partial funding. Continuing international the number of courses for which you tuition exemption and a stipend. students must preregister for classes register. If you enroll in fewer courses Assistantships are awarded on the during the preregistration period and than you initially reported on the loan basis of academic merit. All applicants complete an enrollment status form to request form, your loan eligibility may be for admission and continuing students be considered for departmental funding. reduced. maintaining satisfactory academic Most private student loan programs The FAFSA and the online loan standing will be considered for these are restricted to U.S. citizens and request form must be completed each funds. Applicants should contact the permanent residents. However, academic year, and you must maintain department directly for information. international students may be eligible to satisfactory academic progress as apply for these domestic loan programs defined in “The Graduate Programs” with a creditworthy cosigner who is section in order to remain eligible for Alternative Funding a citizen or permanent resident in the federal student loans. Sources United States. Depending on the loan program, you may need a valid U.S. Veterans’ Benefits External Awards Social Security number. Various Department of Veterans Affairs Because it is not possible to offer full Students who study at Columbia programs provide educational benefits grant and fellowship support to all Engineering on temporary visas for sons, daughters, and spouses of graduate students and because of the should fully understand the regulations deceased or permanently disabled prestige inherent in holding an award concerning possible employment under veterans as well as for veterans and through open competition, applicants those visas. Before making plans for in-service personnel who served on are encouraged to consider major employment in the United States, active duty in the U.S. Armed Forces national and international fellowship international students should consult with after January 1, 1955. In these opportunities. It is important that the International Students and Scholars programs the amount of benefits varies. prospective graduate students explore Office (ISSO), located at 524 Riverside Under most programs the student pays every available source of funding for Drive, Suite 200; 212-854-3587. Their tuition and fees at the time of registration graduate study. website is columbia.edu/cu/isso. but receives a monthly allowance from In researching outside funding you Veterans Affairs. may look to faculty advisers, career Other Financial Aid— Since interpretation of regulations services offices, deans of students, and Federal and Private governing veterans’ benefits is offices of financial aid where frequently Programs subject to change, veterans and their you may find resource materials, books, U.S. citizens and permanent residents dependents should keep in touch with and grant applications for a wide enrolled at least half-time in a degree- the Department of Veterans Affairs. For variety of funding sources. You must granting program are eligible to apply additional information and assistance in notify both your Columbia Engineering for federal student loans. To apply completing the necessary forms, contact academic department and the Office of for federal student loans, you must 1-800-827-1000, or consult their Financial Aid and Educational Financing first complete a Free Application for website (www.va.gov). of any outside awards that you will be Federal Student Aid (FAFSA) using Detailed information regarding receiving. Columbia University’s Title IV school the veteran population at Columbia code 002707. The preferred deadline and policies including the Veteran’s Funding for International Students for filing the FAFSA is May 1 for fall Readmission Provision may be found To secure a visa, international students enrollment. Additionally, you must on the Veterans Affairs website must demonstrate that they have complete the online loan request form. (veteranaffairs.columbia.edu). sufficient funding to complete the Information about the loan application degree. Many international students process as well as the online loan

engineering 2014–2015 35

Federal Student Loans loans is available at sfs.columbia.edu employment in the United States, /grad-private-loans. Once you have international students should consult Direct Unsubsidized Loan applied and been approved for a with the International Students and Direct Graduate PLUS Loan private student loan by the lender, Scholars Office (ISSO) located at 524 you must complete the online request Riverside Drive, Suite 200; 212-854- Perkins Loan form (cc-seas.financialaid.columbia 3587 or visit their website (columbia Detailed information regarding the above .edu/content/2014-2015_loan_app) .edu/cu/isso). Direct Loan programs may be found in order for the Office of Financial Aid on the Student Financial Services and Educational Financing to certify On-Campus Employment website at sfs.columbia.edu/direct-loan the loan. The Center for Career Education -program-overview. maintains an extensive listing of student Employment employment opportunities. The Center for Private Loans Students on fellowship support Career Education (CCE) is located at East Several private student loan programs must obtain the permission of the Campus, Lower Level, 212-854-5609, are available to both U.S. citizens and Dean before accepting remunerative careereducation.columbia.edu. international students. These loans employment. require that you have good credit Students who study at The Fu Off-Campus Employment in standing. International students may Foundation School of Engineering and New York City be elegible for a private loan with Applied Science on temporary visas One of the nation’s largest urban the assistance of a creditworthy should fully understand the regulations areas, the city offers a wide variety U.S. citizen or permanent resident concerning possible employment under of opportunities for part-time work. co-signer. More information on private those visas. Before making plans for Many students gain significant

engineering 2014–2015 36 experience in fields related to their Contact Information For questions about student loans, research and study while they For questions about institutional grants, contact: meet a portion of their educational fellowships, teaching and research Office of Financial Aid and expenses. assistantships, readerships, and Educational Financing preceptorships, contact your academic 618 Lerner Hall department. Mailing: 100 Hamilton Hall For questions about on- or off- 1130 Amsterdam Avenue, MC 2802 campus non-need-based employment, New York, NY 10027 contact the Center for Career Education, located at East Campus, Lower Level, Phone: 212-854-3711 212-854-5609, careereducation Fax: 212-854-5353 .columbia.edu. E-mail: [email protected] cc-seas.financialaid.columbia.edu

engineering 2013–2014 Faculty and Administration 38 Faculty and administration

Officers Guillaume Bal David M. Blei Lee C. Bollinger, J.D. Professor of Applied Mathematics Professor of Computer Science and of President of the University Diplôme, École Polytechnique (France), Statistics (Arts and Sciences) 1993; Ph.D., Université de Paris VI B.Sc., Brown, 1997; Ph.D., California John H. Coatsworth, Ph.D. (France), 1997 (Berkeley), 2004 Provost of the University Scott A. Banta Allen H. Boozer Mary C. Boyce, Ph.D. Associate Professor of Chemical Professor of Applied Physics Dean Engineering B.A., Virginia, 1966; Ph.D., Cornell, 1970 B.S., Maryland (Baltimore), 1997; M.S., Andrew Laine, D.Sc. Rutgers, 2000; Ph.D., 2002 Mary C. Boyce Secretary Morris A. and Alma Schapiro Professor Katayun Barmak and Professor of Mechanical Engineering Faculty Philips Electronics Professor of Applied S.B., Virginia Polytechnic Institute and Sunil Agrawal Physics and Applied Mathematics State University, 1981; S.M., MIT, 1983; Professor of Mechanical Engineering B.A., University of Cambridge (England), Ph.D., MIT, 1987 B.S., Indian Institute of Technology 1983; M.A., 1987; S.M., MIT, 1985; (India), 1984, M.S., Ohio State, 1986; Ph.D., 1989 Robert G. Bozic Lecturer in Chemical Engineering Ph.D., Stanford, 1990 Peter N. Belhumeur B.S., United States Military Academy, Professor of Computer Science 1989; M.E., Florida, 1999; Ph.D., Alfred V. Aho B.S., Brown, 1985; M.S., Harvard, Columbia, 2008 Lawrence Gussman Professor of 1991; Ph.D., 1993 Computer Science Michael P. Burke B.A.Sc., University of Toronto (Canada), Steven M. Bellovin Assistant Professor of Mechanical 1963; M.A., Princeton, 1965; Ph.D., 1967 Professor of Computer Science Engineering B.A., Columbia, 1972; M.S., North B.S., Pennsylvania State, 2005; Ph.D., Pejman Akbari Carolina (Chapel Hill), 1977; Ph.D., 1987 Princeton, 2011 Lecturer in Mechanical Engineering B.S., Sharif University (Iran), 1996; M.S., Keren Bergman Mark A. Cane 1998; Ph.D., Michigan State, 2004 Charles Batchelor Professor of Electrical G. Unger Vetlesen Professor of Earth Engineering and Environmental Sciences and Peter K. Allen B.S., Bucknell University, 1988; Professor of Applied Physics and Professor of Computer Science M.S., MIT, 1991; Ph.D., 1994 Applied Mathematics B.A., Brown, 1971; M.S., Oregon, 1976; B.A., Harvard, 1965; M.A., 1966; Ph.D., Pennsylvania, 1985 Raimondo Betti Ph.D., MIT, 1975 Professor of Civil Engineering and Dimitris Anastassiou Engineering Mechanics Charles Batchelor Professor of Electrical Adam Cannon B.S., Rome La Sapienza (Italy), 1985; M.S., Senior Lecturer in Machine Learning Engineering Southern California, 1988; Ph.D., 1991 B.S., California (Los Angeles), 1991; Dipl., National Technical University of M.S., 1994; M.A., Johns Hopkins, 1997; Athens (Greece), 1974; M.S., California Daniel Bienstock Ph.D., 2000 (Berkeley), 1975; Ph.D., 1979 Professor of Industrial Engineering and Operations Research and of Applied Agostino Capponi Gerard H. A. Ateshian Physics and Applied Mathematics Assistant Professor of Industrial Andrew Walz Professor of Mechanical B.S., Brandeis, 1982; Ph.D., MIT, 1985 Engineering and Operations Research Engineering and Professor of Biomedical B.S., University of Rome (Italy), 2001; Engineering Simon J. L. Billinge M.S., Caltech, 2006; Ph.D., 2009 B.S., Columbia, 1986; M.S., 1987; Professor of Materials Science and of M.Phil., 1990; Ph.D., 1991 Applied Physics and Applied Mathematics Luca Carloni B.A., University of Oxford (England), Associate Professor of Computer Science William E. Bailey 1986; Ph.D., Pennsylvania, 1992 B.S., University of Bologna (Italy), 1995; M.S., Associate Professor of Materials California (Berkeley), 1997; Ph.D., 2004 Science (Henry Krumb School of Mines) Jose H. Blanchet and of Applied Physics and Applied Associate Professor of Industrial Augustin Chaintreau Mathematics Engineering and Operations Research Assistant Professor of Computer Science B.A., B.S., Brown, 1993; B.S., Instituto Tecnológico Autónomo de Magistère, École Normale Supérieure M.S., Stanford, 1995; Ph.D., 1999 México (Mexico), 2000; M.S., Stanford, (France), 2001; D.E.A., Université 2001; Ph.D., 2004 Pierre et Marie Curie (France), 2002; Ph.D., INRIA-École Normale Supérieure (France), 2006

engineering 2014–2015 39

Siu-Wai Chan Michael J. Collins Christopher J. Durning Professor of Materials Science (Henry Vikram S. Pandit Professor of Professor of Chemical Engineering Krumb School of Mines) and of Applied Computer Science B.S., Columbia, 1978; M.A., Princeton, Physics and Applied Mathematics B.A., University of Cambridge 1979; Ph.D., 1982 B.S., Columbia, 1980; Sc.D., MIT, 1985 (England), 1992; M.Phil., 1993; Ph.D., Pennsylvania, 1999 Stephen A. Edwards Kartik Chandran Associate Professor of Computer Science Associate Professor of Earth and Patricia J. Culligan B.S., Caltech, 1992; M.S., California Environmental Engineering (Henry Professor of Civil Engineering and (Berkeley), 1994; Ph.D., 1997 Krumb School of Mines) Engineering Mechanics B.S., Indian Institute of Technology B.Sc., University of Leeds (England), Dan Ellis (India), 1995; Ph.D., Connecticut, 1999 1982; M.Phil., University of Cambridge Professor of Electrical Engineering (England), 1985; Ph.D., 1989 B.A., University of Cambridge (England), Shih-Fu Chang 1987; M.S., MIT, 1992; Ph.D., 1996 The Richard Dicker Professor of Gautam Dasgupta Telecommunications (Electrical Professor of Civil Engineering and Yaniv Erlich Engineering) and Professor of Computer Engineering Mechanics Assistant Professor of Computer Science Science and Senior Vice Dean B.Engr., University of Calcutta (India), B.S., Tel-Aviv University (Israel), 2006; B.S., National Taiwan University 1967; M.Engr., 1969; Ph.D., California Ph.D., 2010 (Taiwan), 1985; M.S., California (Berkeley), 1974 (Berkeley), 1991; Ph.D., 1993 Daniel Esposito George Deodatis Assistant Professor of Chemical Engineering Jingguang G. Chen The Santiago and Robertina B.S., Lehigh, 2006; Ph.D., Thayer Lindsley Professor of Chemical Calatrava Family Professor of Civil Delware, 2012 Engineering Engineering B.S., Nanjing University (P.R. China), B.S., National Technical University of Robert J. Farrauto 1982; Ph.D., Pittsburgh, 1988 Athens (Greece), 1982; M.S., Columbia, Professor of Professional Practice of 1984; Ph.D., 1987 Earth and Environmental Engineering Xi Chen B.S., Manhattan College, 1964; Ph.D., Assistant Professor of Computer Emanuel Derman Rensselaer Polytechnic Institute, 1968 Science Professor of Professional Practice of B.S., Tsinghua University (P.R. China), Industrial Engineering and Operations Steven K. Feiner 2003; Ph.D., 2007 Research Professor of Computer Science B.Sc., University of Cape Town (South A.B., Brown, 1973; Ph.D., 1985 Xi Chen Africa), 1965; M.A., Columbia, 1968; Associate Professor of Earth and Ph.D., 1973 Maria Q. Feng Environmental Engineering (Henry Renwich Professor of Civil Engineering Krumb School of Mines) Eleni Drinea and Engineering Mechanics B.E., Xi’an Jiaotong University (P.R. Lecturer in the Institute of Data Sciences B.S., Nanjing Institute of Technology China), 1994; M.E., Tsinghua University and Engineering (P.R. China), 1982; M.S., University of (P.R. China), 1997; S.M., Harvard, B.S./M.S., University of Patras Tokyo (Japan), 1987; Ph.D., 1992 1998; Ph.D., 2001 (Greece), 1999; M.Sc., Harvard, 2005; Ph.D., 2005 Jacob Fish Maria Chudnovsky Robert A. W. and Christine S. Carleton Professor of Industrial Engineering and Qiang Du Professor of Civil Engineering Operations Research The Fu Foundation School of B.S., Technion (Israel), 1982; M.S., 1985; B.A., Technion (Israel), 1996; M.Sc., 1999; Engineering and Applied Science Ph.D., Northwestern, 1989 M.A., Princeton, 2002; Ph.D., 2003 Professor of Applied Physics and Applied Mathematics George W. Flynn Matei Ciocarlie B.S., University of Science and Higgins Professor of Chemistry and Assistant Professor of Mechanical Technology of China, 1983; Ph.D., Professor of Chemical Engineering Engineering Carnegie Mellon, 1988 B.S., Yale, 1960; M.A., Harvard, 1962; B.S., Polytechnic University of Bucharest Ph.D., 1965; Postdoctoral Fellow, MIT, (Romania), 2003; M.S., Columbia, 2005; Paul F. Duby 1964–1966 Ph.D., 2010 Professor of Mineral Engineering (Earth and Environmental Engineering, Henry Guillermo M. Gallego Andrew J. Cole Krumb School of Mines) Liu Family Professor of Industrial Assistant Professor of Applied Physics Ing. Civil M.E., University of Brussels Engineering and Operations and Applied Mathematics (Belgium), 1956; Eng.Sc.D., Research B.A., Oregon, 2000; Ph.D., Texas Columbia, 1962 B.S., California (San Diego), 1980; (Austin), 2006 Ph.D., Cornell, 1988

engineering 2014–2015 40 Roxana Geambasu X. Edward Guo Julia B. Hirschberg Assistant Professor of Computer Professor of Biomedical Engineering Percy K. and Vida L. W. Hudson Science B.S., Peking University (P.R. China), Professor of Computer Science B.S., Polytechnic University of 1984; M.S., Harvard-MIT, 1990; B.A., Eckert College, 1968; Ph.D., Bucharest (Romania), 2005; M.S., Ph.D., 1994 Michigan, 1976; M.S.E.E., Pennsylvania, Washington (Seattle), 2007; Ph.D., 1982; Ph.D., 1985 2011 Martin B. Haugh Lecturer in Industrial Engineering and James C. Hone Pierre Gentine Operations Research Professor of Mechanical Engineering Assistant Professor of Earth and B.S., University College, Cork (Ireland), B.S., Yale, 1990; Ph.D., California Environmental Engineering (Henry 1993; M.S., 1993; M.S., Oxford, 1994; (Berkeley), 1998 Krumb School of Mines) Ph.D., MIT, 2001 B.Sc., SupAéro (France), 2002; M.S., Daniel Hsu MIT, 2006; M.S., Sorbonne (France), Xuedong He Assistant Professor of Computer Science 2009; Ph.D., MIT, 2009 Assistant Professor of Industrial B.S., California (Berkeley), 2004; M.S., Engineering and Operations Research California (San Diego), 2007; Ph.D., 2010 Javad Ghaderi B.S., Peking University (P.R. China), Assistant Professor of Electrical 2005; D.Phil., University of Oxford Clark T. Hung Engineering (England), 2009 Professor of Biomedical Engineering B.Sc., University of Tehran, 2006; Sc.B., Brown, 1990; M.S.E., M.A.Sc., University of Waterloo, 2008; Tony F. Heinz Pennsylvania, 1992; Ph.D., 1995 Ph.D., Illinois (Urbana-Champaign), David M. Rickey Professor of Optical 2013 Communications (Electrical Engineering) and James S. Im Professor of Physics (Arts and Sciences) Professor of Materials Science (Henry Donald Goldfarb B.S., Stanford, 1978; Ph.D., California Krumb School of Mines) and of Applied Alexander and Hermine Avanessians (Berkeley), 1982 Physics and Applied Mathematics Professor of Industrial Engineering and B.S., Cornell, 1984; Ph.D., MIT, 1989 Operations Research Christine P. Hendon B.Ch.E., Cornell, 1963; M.A., Princeton, Assistant Professor of Electrical Garud N. Iyengar 1965; Ph.D., 1966 Engineering Professor of Industrial Engineering and B.S., MIT, 2004; M.S., Case Western Operations Research Catherine Gorlé Reserve, 2007; Ph.D., 2010 B. Tech., Indian Institute of Technology Assistant Professor of Civil Engineering (India), 1993; M.S., Stanford, 1995; and Engineering Mechanics Irving P. Herman Ph.D., 1998 B.S., Delft University of Technology, Professor of Applied Physics 2002; M.S., 2005; Ph.D., Karman S.B., MIT, 1972; Ph.D., 1977 Christopher R. Jacobs Professor of Biomedical Engineering Institute for Fluid Dynamics and University B.S., Washington (St. Louis), 1988; of Antwerp, 2010 Henry Hess Associate Professor of Biomedical M.S., Stanford, 1989; Ph.D., 1994 Vineet Goyal Engineering Tony Jebara Assistant Professor of Industrial B.S., Technical University Clausthal Associate Professor of Computer Science Engineering and Operations Research (Germany), 1993; M.Sc., Technical B.Eng., McGill University (Canada), B.Tech., Indian Institute of Technology University Berlin (Germany), 1996; Ph.D., 1996; M.S., MIT, 1998; Ph.D., 2002 (India), 2003; M.S., Carnegie Mellon, Free University Berlin (Germany), 1999 2005; Ph.D., 2008 Predrag R. Jelenkovic Andreas H. Hielscher Professor of Electrical Engineering Luis Gravano Professor of Biomedical Engineering Dipl.Ing., Belgrade University (Serbia), Professor of Computer Science and of Electrical Engineering and of 1991; M.S., Columbia, 1993; M. Phil., B.S., Escuela Superior Latinoamericana Radiology (Health Sciences) 1995; Ph.D., 1996 de Informática (Argentina), 1990; B.S., University of Hannover (Germany), 1987; M.S., 1991; Ph.D., Rice, 1995 M.S., Stanford, 1994; Ph.D., 1997 Jingyue Ju Samuel Ruben–Peter G. Viele Professor Eitan Grinspun Michael I. Hill of Engineering (Chemical Engineering) Associate Professor of Computer Science Lecturer in Chemical Engineering Design B.S., Inner Mongolia University (P.R. B.A., University ofToronto (Canada), B.S., Columbia, 1983; M.S., 1989 China), 1985; M.S., Chinese Academy 1997; M.S., Caltech, 2000; Ph.D., 2003 of Sciences (P.R. China), 1988; Ph.D., Elizabeth M. C. Hillman Southern California, 1993 Jonathan L. Gross Associate Professor of Biomedical Engineering and of Radiology Professor of Computer Science Soulaymane Kachani (Health Sciences) B.S., MIT, 1964; M.A., Dartmouth, 1966; Professor of Professional Practice of M.Sci., University College London Ph.D., 1968 Operations Research (England), 1998; Ph.D., 2002 Diplôme, École Centrale Paris (France), 1998; M.S., MIT, 1999; Ph.D., 2002

engineering 2014–2015 Gail E. Kaiser Ioannis A. Kougioumtzoglou Javad Lavaei 41 Professor of Computer Science Assistant Professor of Civil Engineering Assistant Professor of Electrical Engineering Sc.B., MIT, 1979; M.S., Carnegie and Engineering Mechanics B.S., Sharif University of Technology (Iran), Mellon, 1980; Ph.D., 1985 B.S., National Technical University of 2003; M.A.Sc., Concordia University Athens (Greece), 2007; M.S., Rice, (Canada), 2007; Ph.D., Caltech, 2011 Lance C. Kam 2009; Ph.D., 2011 Associate Professor of Biomedical Aurel A. Lazar Engineering Harish Krishnaswamy Professor of Electrical Engineering B.S., Washington (St. Louis), 1991; M.S., Assistant Professor of Electrical B.S., Bucharest Polytechnical Institute Hawaii, 1994; Ph.D., RPI, 1999 Engineering (Romania), 1971; M.S., Darmstadt Institute B.Tech., Indian Institute of Technology of Technology (Germany), 1976; Shiho Kawashima (India), 2001; M.S., Southern California, Ph.D., Princeton, 1980 Assistant Professor of Civil Engineering 2003; Ph.D., 2009 and Engineering Mechanics Jae Woo Lee B.S., Columbia, 2007; M.S., Sanat K. Kumar Lecturer in Computer Science Northwestern, 2009; Ph.D., 2012 Professor of Chemical Engineering B.A., Columbia, 1994; M.S., 2006; B.Tech., Indian Institute of Technology Ph.D., 2012 John R. Kender (India), 1981; S.M., MIT, 1984; Sc.D., 1987 Professor of Computer Science Edward F. Leonard B.S., Detroit, 1970; M.S., Michigan, Aaron M. Kyle Professor of Chemical Engineering 1972; Ph.D., Carnegie Mellon, 1980 Lecturer in Biomedical Engineering Design B.S., MIT, 1953; M.S., Pennsylvania, B.S., Kettering University, 2002; 1955; Ph.D., 1960 Angelos D. Keromytis Ph.D., Purdue, 2007 Associate Professor of Computer Science Kam Leong B.Sc., University of Crete (Greece), 1996; Ioannis Kymissis Professor of Biomedical Engineering M.S., Pennsylvania, 1997; Ph.D., 2001 Associate Professor of Electrical B.S., California (Santa Barbara), 1977; Engineering Ph.D., Pennsylvania, 1987 Martha A. Kim S.B., MIT, 1998; M.Eng., 1999; Assistant Professor of Computer Science Ph.D., 2003 Pierre-David Létourneau B.A., Harvard, 2002; M.E., University Chu Assistant Professor of Applied of Lugano (Switzerland), 2003; M.S., Jeffrey W. Kysar Mathematics Washington (Seattle), 2005; Ph.D., 2008 Professor of Mechanical Engineering B.Eng., McGill University (Canada), B.S., Kansas State, 1987; M.S., 1992; 2008; M.S., Stanford, 2012; Ph.D., 2013 Philip Kim S.M., Harvard, 1993; Ph.D., 1998 Professor of Physics (Arts and Sciences) Allison Lewko B.S., Seoul National (South Korea), Klaus S. Lackner Assistant Professor of Computer Science 1990; S.M., 1992; M.S., Harvard, 1996; Maurice Ewing and J. Lamar Worzel A.B., Princeton, 2006; Ph.D., Texas Ph.D., 1999 Professor of Geophysics (Earth and (Austin), 2012 Environmental Engineering, Henry Peter R. Kinget Krumb School of Mines) Tim Siu-Tang Leung Professor of Electrical Engineering Vordiplom, University of Heidelberg Assistant Professor of Industrial Ph.D., Katholieke Universiteit Leuven (Germany), 1974; M.S., 1976; Ph.D., Engineering and Operations Research (Belgium), 1996 1978 B.S., Cornell, 2003; Ph.D., Princeton, 2008

Jeffrey T. Koberstein Andrew F. Laine Qiao Lin Percy K. and Vida L. W. Hudson Percy K. and Vida L. W. Hudson Associate Professor of Mechanical Professor of Chemical Engineering Professor of Biomedical Engineering Engineering B.S., Wisconsin, 1974; Ph.D., and Professor of Radiology (Health B.S., Tsinghua University (P.R. China), Massachusetts, 1979 Sciences) 1985; M.S., 1988; Ph.D., Caltech, 1993 B.S., Cornell, 1977; M.S., Connecticut, Elisa E. Konofagou 1980; M.S., Washington (St. Louis), Hoe I. Ling Professor of Biomedical Engineering and 1983; D.Sc., 1989 Professor of Civil Engineering and of Radiology (Health Sciences) Engineering Mechanics B.S., Université de Paris VI (France), Upmanu Lall B.S., Kyoto University (Japan), 1988; M.S., 1992; M.S., University of London Alan and Carol Silberstein Professor of University of Tokyo (Japan), 1990; Ph.D., 1993 (England), 1993; Ph.D., Houston, 1999 Earth and Environmental Engineering (Henry Krumb School of Mines) and Richard W. Longman Zoran Kostic of Civil Engineering and Engineering Professor of Mechanical Engineering Associate Professor of Professional Mechanics and of Civil Engineering and Engineering Practice in Electrical Engineering B.Tech., Indian Institute of Technology Mechanics Dipl.Ing., University of Novi Sad (India), 1976; M.S., Texas, 1980; B.S., California (Riverside), 1965; (Yugoslavia), 1987; M.S., Rochester, Ph.D., 1981 M.S., California (San Diego), 1967; 1988; Ph.D., 1991 Ph.D., 1968, M.A., 1969

engineering 2014–2015 42 Helen H. Lu Vijay Modi Ibrahim S. Odeh Professor of Biomedical Engineering Professor of Mechanical Engineering Lecturer in Civil Engineering and B.S., Pennsylvania, 1992; M.S., 1997; B.Tech., Indian Institute of Technology Engineering Mechanics Ph.D., 1998 (India), 1978; Ph.D., Cornell, 1984 B.S., Jordan University of Science and Technology, 2000; M.B.A., St. Tal Malkin Barclay Morrison III Thomas, 2004; Ph.D., Illinois (Urbana– Associate Professor of Computer Science Associate Professor of Biomedical Champaign), 2010 B.S., Bar-Ilan University (Israel), 1993; Engineering M.S., Weizmann Institute of Science B.S., Johns Hopkins, 1992; M.S.E., Elizabeth S. Olson (Israel), 1995; Ph.D., MIT, 2000 Pennsylvania, 1994; Ph.D., 1999 Associate Professor of Biomedical Engineering and Auditory Biophysics (in Kyle Mandli Van C. Mow Otolaryngology/Head and Neck Surgery) Assistant Professor of Applied Stanley Dicker Professor of Biomedical B.A., Barnard, 1981; Ph.D., MIT, 1988 Mathematics Engineering and Professor of Orthopedic B.S., Wisconsin, 2004; M.Sc., Engineering (Orthopedic Surgery, Health Mariana Olvera-Cravioto Washington, 2005; Ph.D., 2011 Sciences) Associate Professor of Industrial B.A.E., RPI, 1962; Ph.D., 1966 Engineering and Operations Research Chris A. Marianetti B.S., Instituto Technológico Autónomo Associate Professor of Materials Kristin M. Myers de México (Mexico), 2000; Science (Henry Krumb School of Mines) Assistant Professor of Mechanical M.S., Stanford, 2004; Ph.D., 2006 and of Applied Physics and Applied Engineering Mathematics B.S., Michigan, 2002; M.S., MIT, 2005; Vanessa Ortiz B.S., Ohio State, 1997; M.S., 1998; Ph.D., 2008 Assistant Professor of Chemical Ph.D., MIT, 2004 Engineering Arvind Narayanaswamy B.S.E., University of Puerto Rico, 2002; Michael E. Mauel Associate Professor of Mechanical Ph.D., Pennsylvania, 2007 Professor of Applied Physics Engineering B.S., MIT, 1978; M.S., 1979; Sc.D., 1983 B.Tech., Indian Institute of Technology Richard M. Osgood Jr. (India), 1997; M.S., Delaware, 1999; Higgins Professor of Electrical Engineering Nicholas F. Maxemchuk Ph.D., MIT, 2007 and Professor of Applied Physics Professor of Electrical Engineering B.S., U.S. Military Academy, 1965; B.S., The City College of New York, Gerald A. Navratil M.S., Ohio State, 1968; Ph.D., MIT, 1973 1968; M.S., Pennsylvania, 1970; Thomas Alva Edison Professor Ph.D., 1975 of Applied Physics Ben O’Shaughnessy B.S., Caltech, 1973; M.S., Wisconsin, Professor of Chemical Engineering Kathleen McKeown 1974; Ph.D., 1976 B.Sc., University of Bristol (England), Henry and Gertrude Rothschild 1977; Ph.D., University of Cambridge Professor of Computer Science Shree K. Nayar (England), 1984 A.B., Brown, 1976; M.S., Pennsylvania, T. C. Chang Professor of Computer 1979; Ph.D., 1982 Science John Paisley B.S., Birla Institute of Technology (India), Assitant Professor of Electrical Engineering V. Faye McNeill 1984; M.S., North Carolina State, 1986; B.S.E., Duke, 2004; M.S., 2007; Associate Professor of Chemical Ph.D., Carnegie Mellon, 1990 Ph.D., 2010 Engineering B.S., Caltech, 1999; M.S., MIT, 2001; Ph.D., Jason Nieh Thomas Panayotidi 2005 Professor of Computer Science Lecturer in Civil Engineering and B.S., MIT, 1989; M.S., Stanford, 1990; Engineering Mechanics Nima Mesgarani Ph.D., 1999 B.S., Columbia, 1981; M.S., 1983; Assistant Professor of Electrical Ph.D., 1986 Engineering Steven M. Nowick B.Sc., Sharif University of Technology (Iran) Professor of Computer Science Ah-Hyung Alissa Park 1999; M.Sc., Maryland, 2005; Ph.D., 2008 B.A., Yale, 1976; M.A., Columbia, 1979; Lenfest Associate Professor in Ph.D., Stanford, 1993 Applied Climate Science Vishal Misra B.S., University of British Columbia Associate Professor of Computer Science Ismail Cevdet Noyan (Canada), 1998; M.S., 2000; Ph.D., Ohio B.Tech., Indian Institute of Technology Professor of Materials Science (Henry State, 2005 (India), 1992; M.S., Massachusetts Krumb School of Mines) and of Applied (Amherst), 1996; Ph.D., 2000 Physics and Applied Mathematics Dana Pe’er B.S., Middle East Technical University Associate Professor Biological Sciences Debasis Mitra (Turkey), 1978; Ph.D., Northwestern, and of Computer Science Professor of Electrical Engineering 1984 B.S., Hebrew University of Jerusalem B.Sc., London University (England), (Israel), 1995; M.S., 1999; Ph.D., 2003 1964; Ph.D., 1967

engineering 2014–2015 Itsik Pe’er Henning G. Schulzrinne Samuel K. Sia 43 Associate Professor of Computer Science Julian Clarence Levi Professor of Associate Professor of Biomedical B.S., Tel Aviv University (Israel), 1990; Mathematical Methods and Computer Engineering M.S., 1995; Ph.D., 2002 Science and Professor of Computer B.Sc., University of Alberta (Canada), Science and of Electrical Engineering 1997; Ph.D., Harvard, 2002 Feniosky Peña-Mora B.S., Technical University of Darmstadt Edwin Howard Armstrong Professor of Civil (Germany), 1984; M.S., Cincinnati, Karl Sigman Engineering and Engineering Mechanics 1987; Ph.D., Massachusetts (Amherst), Professor of Industrial Engineering and B.S., Universidad Nacional Pedro 1992 Operations Research Henríquez Ureña (Dominican Republic), B.A., California (Santa Cruz), 1980; 1987; S.M., MIT, 1991; Sc.D., 1994 Amiya K. Sen M.A., California (Berkeley), 1983; Professor of Electrical Engineering and M.S., 1984; Ph.D., 1986 Aron Pinczuk of Applied Physics Professor of Applied Physics and of Dipl., Indian Institute of Science Andrew W. Smyth Physics (Arts and Sciences) (India), 1952; M.S., MIT, 1958; Ph.D., Professor of Civil Engineering and Licenciado, Buenos Aires (Argentina), Columbia, 1963 Engineering Mechanics 1962; Ph.D., Pennsylvania, 1969 B.A., B.Sc., Brown, 1992; M.S., Rice, Mingoo Seok 1994; M.S., Southern California, 1997; Lorenzo M. Polvani Assistant Professor of Electrical Ph.D., 1998 Professor of Applied Mathematics and Engineering of Earth and Environmental Sciences B.S., Seoul National University (South Adam H. Sobel (Arts and Sciences) Korea), 2005; M.S., Michigan, 2007; Professor of Applied Physics and Applied B.Sc., McGill University (Canada), 1981; Ph.D., 2011 Mathematics and of Environmental M.Sc., 1982; Ph.D., MIT, 1988 Sciences (Arts and Sciences) Rocco A. Servedio B.A., Wesleyan, 1989; Ph.D., MIT, 1998 Katherine E. Reuther Associate Professor of Computer Science Lecturer in Biomedical Engineering A.B., Harvard, 1993; M.S., 1997; Ponisseril Somasundaran B.S.E., The College of New Jersey, Ph.D., 2001 LaVon Duddleson Krumb Professor of 2009; Ph.D., Pennsylvania, 2014 Mineral Engineering Simha Sethumadhavan B.Sc., Kerala University (India), 1958; Kenneth A. Ross Associate Professor of Computer B.E., Indian Institute of Science (India), Professor of Computer Science Science 1961; M.S., California (Berkeley), 1962; B.Sc., University of Melbourne B.S.E., University of Madras (India), Ph.D., 1964 (Australia), 1986; Ph.D., Stanford, 1991 2000; M.S., Texas, 2005; Ph.D., 2007 Marc W. Spiegelman Dan Rubenstein Arthur D. Storke Memorial Professor of Associate Professor of Computer Science Jay Sethuraman Earth and Environmental Sciences (Arts B.S., MIT, 1992; M.A., California (Los Professor of Industrial Engineering and and Sciences) and Professor of Applied Angeles), 1994; Ph.D., Massachusetts Operations Research Physics and Applied Mathematics (Amherst), 2000 B.E., Birla Institute of Technology and B.A. Harvard, 1985; Ph.D., University of Science (India), 1991; M.S., Indian Cambridge (England), 1989 Paul Sajda Institute of Science (India), 1994; Professor of Biomedical Engineering Ph.D., MIT, 1999 Clifford Stein and of Electrical Engineering and of Professor of Industrial Engineering and Radiology (Health Sciences) Michael P. Sheetz Operations Research and of Computer B.S., MIT, 1989; M.S., Pennsylvania, William R. Kenan Jr. Professor of Cell Science 1992; Ph.D., 1994 Biology and Professor of Biomedical B.S.E., Princeton, 1987; Engineering M.S., MIT, 1989; Ph.D., 1992 José I. Sánchez B.A., Albion, 1968; Ph.D., Caltech, Lecturer in Civil Engineering and 1972 Milan N. Stojanovic Engineering Mechanics Associate Professor of Biomedical B.A., Pontifica Universidad Católica Kenneth L. Shepard Engineering and of Medical Science Madre y Maestre (Dominican Republic), Professor of Electrical Engineering Ph.D., Harvard, 1995 1991; M.A., Pratt, 1994; M.S., and of Biomedical Engineering Columbia, 1996 B.S.E., Princeton, 1987; Fred R. Stolfi M.S., Stanford, 1988; Ph.D., 1992 Senior Lecturer in Mechanical Peter Schlosser Engineering Vinton Professor of Earth and Nasanobu Shinozuka Environmental Engineering (Henry B.S., Fordham, 1972; M.S., RPI, 1976; Professor of Civil Engineering and Krumb School of Mines) and Professor Ph.D., 2001 Engineering Mechanics of Earth and Environmental Sciences B.S., Kyoto University (Japan), 1953; Salvatore J. Stolfo (Arts and Sciences) M.S., 1955; Ph.D., Columbia, 1960 Professor of Computer Science B.S./M.S., University of Heidelberg B.S., Brooklyn, 1974; M.S., New York (Germany), 1981; Ph.D., 1985 University, 1976; Ph.D., 1979

engineering 2014–2015 44 WaiChing Steve Sun Gordana Vunjak-Novakovic Chee Wei Wong Assistant Professor of Civil Engineering The Mikati Foundation Professor of Associate Professor of Mechanical and Engineering Mechanics Biomedical Engineering and Professor of Engineering B.S., California (Davis), 2005; M.S. Medical Sciences B.A., B.S., California (Berkeley), 1999; Stanford, 2007; M.A., Princeton, 2008; B.S., University of Belgrade (Serbia), M.S., MIT, 2001; Ph.D., 2003 Ph.D., Northwestern, 2011 1972; S.M., 1975; Ph.D., 1980 John Wright Michael K. Tippett Haim Waisman Assistant Professor of Electrical Engineering Lecturer in Applied Physics and Applied Associate Professor of Civil Engineering B.S., Illinois (Urbana-Champaign), 2004; Mathematics and Engineering Mechanics M.S., 2007; Ph.D., 2009 B.S., North Carolina State, 1987; B.S., Technion (Israel), 1999; M.S., M.S., New York University, 1990; 2002; Ph.D., RPI, 2005 Cheng-Shie Wuu Ph.D., 1992 Professor of Clinical Radiation Oncology, Qi Wang and of Environmental Health Sciences, Joseph F. Traub Assistant Professor of Biomedical and of Applied Physics Edwin Howard Armstrong Professor of Engineering B.S., National Tsing Hua University Computer Science B.S., North China University of Electric (Taiwan), 1979; M.S., 1982; B.S., College of the City of New York, Power (P.R. China), 1992; M.S., Harbin Ph.D., Kansas, 1985 1954; M.S., Columbia, 1955; Ph.D., 1959 Institute of Technology (P.R. China), 1995; Ph.D., 1999; Ph.D., McGill Junfeng Yang Van-Anh Truong University (Canada), 2006 Associate Professor of Computer Science Assistant Professor of Industrial B.S., Tsinghua University (P.R. Engineering and Operations Research Wen I. Wang China), 2000; M.S., Stanford, 2002; B.S., University of Waterloo (Canada); Thayer Lindsley Professor of Electrical Ph.D., 2007 Ph.D., Cornell, 2007 Engineering and Professor of Applied Physics Mihalis Yannakakis Yannis P. Tsividis B.S., National Taiwan University (Taiwan), Percy K. and Vida L. W. Hudson Charles Batchelor Memorial Professor of 1975; M.E.E., Cornell, 1979; Ph.D., 1981 Professor of Computer Science Electrical Engineering Dipl., National Technical University of B.E., Minnesota, 1972; M.S., California Xiaodong Wang Athens (Greece), 1975; (Berkeley), 1973; Ph.D., 1976 Professor of Electrical Engineering Ph.D., Princeton, 1979 B.S., Shanghai Jiao Tong University (P.R. David G. Vallancourt China), 1992; M.S., Purdue, 1995; David D. W. Yao Senior Lecturer in Circuits and Ph.D., Princeton, 1998 Professor of Industrial Engineering and Systems in the Department of Electrical Operations Research Engineering Anthony C. Webster M.A.Sc., University of Toronto (Canada), B.S., Columbia, 1981; M.S., 1984; Lecturer in Finance in the Department 1981; Ph.D., 1983 Ph.D., 1987 of Industrial Engineering and Operations Research Y. Lawrence Yao Latha Venkataraman B.S., Rutgers, 1980; M.S., Columbia, Professor of Mechanical Engineering Associate Professor of Applied Physics 1983; M.B.A., 1999 B.E., Shanghai Jiao Tong University B.S., MIT, 1993; M.S., Harvard, 1997; (P.R. China), 1982; M.S., Wisconsin Ph.D., 1999 Michael I. Weinstein (Madison), 1984; Ph.D., 1988 Professor of Applied Mathematics Venkat Venkatasubramanian B.S., Union College, 1977; M.S., Tuncel M. Yegulalp Samuel Ruben–Peter G. Viele Courant Institute-NYU, 1979; Ph.D., 1982 Professor of Mining (Earth and Professor of Engineering (Chemical Environmental Engineering, Henry Engineering) Alan C. West Krumb School of Mines) B.Tech., University of Madras (India), Samuel Ruben-Peter G. Viele Professor M.S., Technical University (Turkey), 1961; 1977; M.S., Vanderbilt, 1979; Ph.D., of Electrochemistry (Chemical Engineering) Eng.Sc.D., Columbia, 1968 Cornell, 1984 B.S., Case Western Reserve, 1985; Ph.D., California (Berkeley), 1989 Huiming Yin Francesco A. Volpe Associate Professor of Civil Engineering Assistant Professor of Applied Physics Ward Whitt and Engineering Mechanics Laurea, University of Pisa (Italy), Wai T. Chang Professor of Industrial B.S.E., Hohai University (P.R. China), 1998; Ph.D., University of Greifswald Engineering and Operations Research 1995; M.S., Peking University (P.R. China), (Germany), 2003 A.B., Dartmouth, 1964; 1998; Ph.D., Iowa, 2004 Ph.D., Cornell, 1969 Sinisa Vukelic Nanfang Yu Lecturer in Mechanical Engineering Chris H. Wiggins Assistant Professor of Applied Physics Dipl.Ing., University of Belgrade, Associate Professor of Applied Mathematics B.S., Peking University (China), 2004; 2004; M.S., Columbia, 2005; B.A., Columbia, 1993; Ph.D., Harvard, 2009 Ph.D., 2009 Ph.D., Princeton, 1998

engineering 2014–2015 Changxi Zheng Edward G. Coffman Jordan L. Spencer 45 Assistant Professor of Computer Science Professor Emeritus of Electrical Engineering Professor Emeritus of Chemical B.Eng., Shanghai Jiao Tong University Engineering (P.R. China), 2005; Ph.D., Cornell, 2012 Paul Diament Professor Emeritus of Electrical Engineering Thomas E. Stern Yuan Zhong Dicker Professor Emeritus of Electrical Assistant Professor of Industrial Frank L. DiMaggio Engineering Engineering and Operations Research Robert A. W. and Christine S. Carleton B.A., University of Cambridge (England), Professor Emeritus of Civil Engineering Robert D. Stoll 2006; M.A., Caltech, 2008; Ph.D., MIT, Professor Emeritus of Civil Engineering 2012 Zvi Galil Professor Emeritus of Computer Science Horst Stormer Charles Zukowski I. I. Rabi Professor Emeritus of Physics Professor of Electrical Engineering Atle Gjelsvik (Arts and Sciences) and Professor B.S., MIT, 1982; M.S., 1982; Professor Emeritus of Civil Engineering Emeritus of Applied Physics Ph.D., 1985 Fletcher H. Griffis Malvin Carl Teich Gil Zussman Professor Emeritus of Civil Engineering Professor Emeritus of Engineering Associate Professor of Electrical Science Engineering Robert A. Gross B.A., B.Sc., Technion (Israel), 1995; Percy K. and Vida L. W. Hudson Rene B. Testa M.Sc., 1999; Ph.D., 2004 Professor Emeritus of Applied Physics Professor Emeritus of Civil Engineering and Dean Emeritus and Engineering Mechanics Faculty Members-at-Large Carlos J. Alonso Herbert H. Kellogg Nickolas J. Themelis Dean, Graduate School of Arts and Stanley-Thompson Professor Emeritus Stanley-Thompson Professor Emeritus Sciences of Chemical Metallurgy of Chemical Metallurgy (Earth and Environmental Engineering, Henry Peter B. deMenocal John T. F. Kuo Krumb School of Mines) Chair, Department of Earth and Maurice Ewing and J. Lamar Worzel Environmental Sciences Professor Emeritus of Geophysics Stephen H. Unger Professor Emeritus of Computer Science Liang Tong W. Michael Lai and of Electrical Engineering Chair, Department of Biological Sciences Professor Emeritus of Mechanical Engineering Rimas Vaicaitis R. Glenn Hubbard Renwick Professor Emeritus of Civil Dean, Columbia Business School Leon Lidofsky Engineering Professor Emeritus of Applied Physics Ioannis Karatzas and Nuclear Engineering Howard W. Vreeland Chair, Department of Mathematics Professor Emeritus of Graphics Eugene S. Machlin Ann McDermott Henry Marion Howe Professor Emeritus Omar Wing Chair, Department of Chemistry of Metallurgy Professor Emeritus of Electrical Engineering James J. Valentini Thomas C. Marshall Dean, Columbia College Professor Emeritus of Applied Physics Henryk Wozniakowski Professor Emeritus of Computer Science William Zajc Henry E. Meadows Jr. Chair, Department of Physics Professor Emeritus of Electrical Engineering Edward S. Yang Professor Emeritus of Electrical Engineering Emeriti and Retired Christian Meyer Officers (Not in Residence) Professor Emeritus of Civil Engineering Yechiam Yemini Daniel N. Beshers and Engineering Mechanics Professor Emeritus of Computer Science Professor Emeritus of Metallurgy Glenn K. Rightmire Administrative officers Huk Yuk Cheh Associate in Mechanical Engineering and STAFF Samuel Ruben-Peter G. Viele Professor Mary C. Boyce Emeritus of Electrochemistry Enders Robinson Dean Maurice Ewing and J. Lamar Worzel Rene Chevray Professor Emeritus of Applied Daniel P. Alicea Professor Emeritus of Mechanical Engineering Geophysics Business Manager, Institute for Data Sciences and Engineering C. K. Chu Mischa Schwartz Fu Foundation Professor Emeritus of Charles Batchelor Professor Emeritus Stephanie D. Allred Applied Mathematics of Electrical Engineering Assistant Director, Parents Fund engineering 2014–2015 46 Rumana Ashraf Idrija Ibrahimagic Israel Rodriguez Coordinator, Grants and Contracts Financial Coordinator, Institute for Data Facilities Manager Sciences and Engineering Ellie Bastani Elaine Rooney Assistant Director, Graduate Student Jessie Jones Executive Assistant to the Dean Services Administrative Assistant, Graduate Student Affairs Nancy Rubin Janezee Bond Executive Director of Distance and Development Coordinator, Major Gifts Soulaymane Kachani Online Education Vice Dean of Academic Programs Vladimir Boucheu Starling Sawyer Systems Administrator Margaret Kelly Director, Alumni Relations Executive Director, Communications Kimberly Bregenzer Anthony Schmitt Executive Director, Budget and Financial Peggy Maher Manager, Grants and Contracts Planning Associate Dean of Advancement Ivy Schultz Leora Brovman Elizabeth Manchester Associate Director of Entrepreneurship Assistant Dean of Undergraduate Alumni Programs Coordinator Programs Student Affairs and Global Programs Jessica L. Marinaccio Tiffany M. Simon Shih-Fu Chang Dean of Undergraduate Admissions and Associate Dean of Graduate Student Senior Vice Dean Financial Aid Affairs

Louis Cohen Kathleen McKeown David Simpson Technical Specialist, Columbia Video Director, Institute for Data Sciences and Administrative Assistant Network Engineering Jonathan R. Stark Timothy Cross Nicholas Mider Director of Operations, Institute for Data Advancement Communications Officer Associate Director, Alumni Relations Sciences and Engineering

Ralph Cruz Jocelyn Morales Michelle R. Stevenson Financial Analyst Associate Director, Graduate Student Coordinator, Columbia Video Network Services Patricia Culligan Dawn M. Strickland Associate Director, Institute for Data Jane Nisselson Director, Graduate Student Services and Sciences and Engineering Associate Director, Multimedia Postdoctoral Affairs Communications Scott DeHart Jessie Tong Associate Director of Human Resources Quy O Assistant Director of Academic Associate Director of Technology Administration Holly Evarts Services Director, Strategic Communications Yannis P. Tsividis and Media Relations Clarissa Peña Undergraduate Curriculum Adviser to Student Services Officer, Graduate the Dean Michelle Failing Student Affairs Associate Director, Web Communications Jeffrey Urstadt Lourdes Pineiro Senior Financial Analyst Melanie Farmer Development Assistant Associate Director, Communications Sofia Yagaeva Jennifer Piro Assistant Director, Columbia Video Network Jennifer Feierman Institutional Research Coordinator Assistant Director, Engineering Annual Fund William Yandolino DeShanda Porter Director, Budget and Financial Planning Emily Ford Financial Analyst Director of Outreach Programs Brian K. Powell Katherine B. Hickey Associate Dean of Faculty Affairs, Financial Support Specialist, Center for Human Resources, and Administration Computational Learning Systems Ashley Robinson Zachary Howell Fund Coordinator Leadership Gifts Officer, Engineering Annual Fund

engineering 2014–2015 Departments and Academic Programs 48 KEY to course listings

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

engineering 2014–2015 49

IEME Industrial Engineering and How Courses Are Numbered Directory of Classes Mechanical Engineering The course number that follows each Room assignments, days and hours, IEOR Industrial Engineering and designator consists of a capital letter and course changes for all courses are Operations Research followed by four digits. The capital available online at columbia.edu/cu/ letter indicates the University division or bulletin/uwb. INAF International Affairs affiliate offering the course: The School reserves the right to INTA Earth and Environmental Engineering, B Business withdraw or modify the courses of Civil Engineering, and instruction or to change the instructors International and Public Affairs C Columbia College at any time. MATH Mathematics E Engineering and Applied Science MEBM Mechanical Engineering and G Graduate School of Arts and Sciences Biomedical Engineering P Mailman School of Public Health MECE Mechanical Engineering S Summer Session MEEM Mechanical Engineering and Engineering Mechanics U International and Public Affairs MSAE Materials Science and Engineering V Interschool course with Barnard MSIE Management Science and Industrial W Interfaculty course Engineering and Operations Research Z American Language Program MUSI Music The first digit indicates the level of PHED Physical Education the course, as follows: PHIL Philosophy 0 Course that cannot be credited PHYS Physics toward any degree PLAN Planning 1 Undergraduate course POLS Political Science 2 Undergraduate course, intermediate PSLG Physiology 3 Undergraduate course, advanced PSYC Psychology 4 Graduate course that is open to qualified undergraduates RELI Religion SCNC Science 6 Graduate course SIEO Statistics and Industrial Engineering 8 Graduate course, advanced and Operations Research 9 Graduate research course or seminar SOCI Sociology An x following the course number SPAN Spanish means that the course meets in the fall STAT Statistics semester; y indicates the spring semester. URBS Urban Studies VIAR Visual Arts

engineering 2014–2015 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 Marc W. Spiegelman Jerome Meli Jacek Chowdhary Adjunct Associate Ismail C. Noyan Wen I. Wang, Electrical Ron L. Miller Jerry I. Dadap Research Scientists 208 S. W. Mudd Engineering Thomas Morgan Darren Garnier Manolis Antonoyiannakis Michael I. Weinstein Stephen L. Ostrow Igor Geogdzhayev Camille Jones Department Cheng-Shie Wuu, Thomas S. Pedersen Qiancheng Ma Conal Murray Administrator Radiation Oncology Lawrence N. Rothenberg George Tselioudes Dina Amin Stephen A. Sabbagh Yuanchong Zhang VISITING Research Associate George Tselioudes Scientist Professors Professors Shalom J. Wind Adjunct REsearch Hanquan Wang Guillaume Bal William E. Bailey ScientistS Katayun Barmak Eitan Grinspun, Adjunct Associate Mark Holzer Postdoctoral Daniel Bienstock, Computer Science Professors Emmanuel Yashchin Research Scientists Industrial Engineering Chris A. Marianetti Brian Cairns Jia Chen and Operations Latha Venkataraman Alexander Casti VISITING Research Pierre Darancet Research Chris H. Wiggins David Maurer Scientist Chris Hansen Simon J. L. Billinge Hanquan Wang Kristen Jensen Allen H. Boozer Assistant Adjunct Assistant Dalal Kanan Mark A. Cane, Earth Professors Professors Associate Research Myoung-Hwan Kim and Environmental Andrew J. Cole Camille Jones Scientists Eric Olofsson Sciences Pierre-David Létourneau Andrew Martin Mikhail Alexandrov Hyowon Park Siu-Wai Chan Kyle Mandli Anastasia Romanou Michael Bauer Jasmin Remillard Qiang Du Tiffany Shaw, Earth Yonghua Chen Abraham Solomon Irving P. Herman and Environmental Senior Research Robert Field Nicholas Vaxelaire James S. Im Sciences Scientists Jeremy Hanson Michael E. Mauel Francesco A. Volpe James Bialek Seung Yub Lee Associate Gerald A. Navratil Nanfung Yu Rainer Bleck Jeffrey Levesque John C. Arbo Ismail C. Noyan Steven A. Sabbagh Li Liu Richard M. Osgood Jr., Lecturer in Shalom J. Wind Catherine Naud Special Lecturers Electrical Engineering Discipline Young Seouk Park Daniel N. Beshers Aron Pinczuk Michael K. Tippett Adjunct Senior Carlos Perez Garcia- C. K. Chu Lorenzo M. Polvani Research ScientistS Pando Malvin A. Ruderman, Adjunct C. Julian Chen Jan Perlwitz Special Research Physics Professors David E. Keyes Denis Potapenko Scientists Christopher H. Scholz, Vittorio M. Canuto Yigal Komem Anastasia Romanou Leonard Druyan Earth and Barbara E. Carlson John Marshall Francesca Turco Thomas C. Marshall Environmental C. Julian Chen Shuguang Wang Sciences Anthony Del Genio Research Jingbo Wu Scientists Amiya K. Sen, Electrical Supratik Guha Mark Adams Engineering Timothy M. Hall John Berkery Adam Sobel David E. Keyes

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 172–174. techniques; and (5) the development of is conducted in the theory of plasma

engineering 2014–2015 equilibrium and stability, active control Columbia’s Institute for Data Sciences with laboratory magnetospheres 51 of MHD instabilities, the kinetic theory and Engineering (IDSE), the Department and advanced models for space of turbulence and transport, and the of Systems Biology, and the Department weather and radiation belt dynamics. development of techniques based on of Statistics. Extensive collaborations The stellarator known as Columbia the theory of general coordinates and exist with national climate research Nonneutral Torus (CNT) conducts dynamical systems. The work is applied centers (the Geophysical Fluid Dynamics research on the magnetohydrodynamic to magnetic fusion, nonneutral and Laboratory and the National Center for stability, microwave heating, and space plasmas. Atmospheric Research) and with national microwave diagnostics of neutral laboratories of the U.S. Department of stellarator plasmas. Two smaller Optical and laser physics. Active Energy, custodians of the nation’s most devices investigate respectively an areas of research include inelastic light 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 and instruction with Collisionless Terrella Experiment solid-state physics covers nanoscience the NASA Goddard Institute for Space investigates plasma transport in and nanoparticles, electronic transport Studies and the Lamont-Doherty Earth magnetospheric geometry and the and inelastic light scattering in low- Observatory. Six faculty members share generation of strong plasma flow from dimensional correlated electron appointments with the Department of nonlinear electrostatic potentials. systems, fractional quantum Hall Earth and 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 Center for Integrated Science and electronics, nanostructure analysis, students from other departments, and Engineering and the School of Mines. and electronic structure calculations. visiting scientists. Facilities include laser processing and Research opportunities also exist spectroscopic apparatus, ultrahigh within the NSF Nanoscale Science and Laboratory and Computation vacuum chambers for surface analysis, Engineering Center, which focuses Facilities in Applied Physics and picosecond and femtosecond lasers, on electron transport in molecular Applied Mathematics a molecular beam epitaxy machine, nanostructures; and the DOE Energy and a clean room that includes photo- The Plasma Physics Laboratory, Frontier Research Center, which focuses lithography and thin film fabrication founded in 1961, is one of the leading on conversion of sunlight into electricity systems. Within this field, the Laser university laboratories for the study of in nanometer-sized thin films. Diagnostics and Solid-State Physics plasma physics in the United States. Laboratory conducts studies in laser There are four experimental facilities. Applied mathematics. Current research spectroscopy of nanomaterials and The Columbia High-Beta Tokamak encompasses analytical and numerical semiconductor thin films, and laser (HBT-EP) supports the national program analysis of deterministic and stochastic diagnostics of thin film processing. to develop controlled fusion energy. partial differential equations, large-scale The Laser Lab focuses on the study It utilizes high voltage, pulsed power scientific computation, fluid dynamics, of materials under high pressure, laser systems, and laser and magnetic dynamical systems and chaos, as surface chemical processing, and new diagnostics to study the properties well as applications to various fields of semiconductor structures. Research of high-beta plasmas and the use physics and biology. The applications is also conducted in the shared of feedback stabilization to increase to physics include quantum and characterization laboratories and clean the achievable beta. A collaborative condensed-matter physics, materials room operated by the NSF Nanoscale program with the Princeton Plasma science, electromagnets and optics, Science and Engineering Center. Physics Laboratory and the DIII-D plasma physics, medical imaging, and The department maintains an tokamak group at General Atomics is the earth sciences, notably atmospheric, extensive network of computing studying the properties of high-beta clusters and desktop computers. oceanic, and climate science, and plasmas in order to maximize fusion The research of the Plasma Lab solid earth geophysics (see below). power production in these large, neutral is supported by a dedicated data The applications to biology include beam-heated tokamaks and spherical acquisition/data analysis system, and machine learning and biophysical tori. The plasma physics group the applied math group has access to a modeling, including collaborations with and MIT conduct joint experiments Beowulf cluster. Materials Science and

engineering 2014–2015 52 Applied Physics program: first and second Years

Semester i Semester iI Semester iII Semester iV

MATH V1202 (3) mathematics1 MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) and ODE (3)2

physics C1401 (3) C1402 (3) C1403 (3) C1494 (3) (three tracks, C1601 (3.5) C1602 (3.5) C2601 (3.5) Lab C2699 (3) choose one) C2801 (4.5) C2802 (4.5) Lab W3081 (2)

chemistry/ CHEM C1403 (3), or higher or biology (choose one course) BIOL W2001 (4) or BIOL C2005 (4), or higher

english C1010 (3) composition (three tracks, Z1003 (0) C1010 (3) choose one) Z0006 (0) Z1003 (0) C1010 (3)

HUMA C1001, HUMA C1002, COCI C1101, COCI C1102, required or Global Core (3–4) or Global Core (3–4) nontechnical electives HUMA W1121 or ECON W1105 (4) and W1123 (3) W1155 recitation (0)

required (3) Student’s choice, see list of first- and second-year technical electives tech electives (professional-level courses; see pages 12–13)

computer ENGI E1006 (3) any semester science

physical C1001 (1) C1002 (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 E1210). 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.

Applied Physics built an intel-based Current Research Activities and number of electives in these programs, 600 core computing cluster that is Laboratory Facilities in Materials students can tailor their programs to fit dedicated to performing first-principles Science and Engineering their personal and career interests. By computations of materials. Researchers See page 171. focusing their technical electives, students in the department are additionally using can obtain a strong base of knowledge supercomputing facilities at the National in a specialized area. In addition to formal Center for Atmospheric Research; Undergraduate Programs minors, some areas of specialization that the San Diego Supercomputing The Department of Applied Physics are available are described on pages Center; the National Energy Research and Applied Mathematics offers three 55–56. All technical electives are normally Supercomputer Center in Berkeley, undergraduate programs: applied phys- at the 3000 level or above. California; the National Leadership ics, applied mathematics, and materials Class Facility at Oak Ridge, Tennessee; science. The materials science program Undergraduate Programs various allocations via XSEDE; and is described on pages 171–172. in Applied Physics others. The Amazon Elastic Compute The applied physics and applied The applied physics program stresses Cloud (EC2) is also utilized to mathematics programs provide an excellent the basic physics that underlies most supplement computing resources in preparation for graduate study or for careers developments in engineering and the times of high demand. in which mathematical and technical sophistication are important. Using the large mathematical tools that are important

engineering 2014–2015 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 E lectives

total points 16 15 16 17

1 They must include at least 2 points of laboratory courses. If PHYS W3081 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.

to both physicists and engineers. Since physics program to participate in this In addition to these courses, courses the advances in most branches of research through part-time employment listed in the Specialty Areas in Applied technology lead to rapid changes in during the academic year and full-time Physics can be used to satisfy this state-of-the-art techniques, the applied employment during the summer, either requirement with preapproval of the physics program provides the student at Columbia or as part of the NSF REU applied physics adviser. with a broad base of fundamental program nationwide. Practical research All students must take 30 points of science and mathematics while retaining experience is a valuable supplement to electives in the third and fourth years, the opportunity for specialization through the formal course of instruction. Applied of which 17 points must be technical technical electives. physics students participate in an informal courses approved by the adviser. The 17 The applied physics curriculum offers undergraduate seminar to study current points include 2 points of an advanced students the skills, experience, and and practical problems in applied physics, laboratory in addition to APPH E4018. preparation necessary for several career and obtain hands-on experience in at least Technical electives must be at the 3000 options, including opportunities to minor two advanced laboratory courses. level or above unless prior approval is in economics and to take business- Majors are introduced to two areas of obtained from the department. A number related courses. In recent years, applied application of applied physics (AP) by a of approved technical electives are physics graduates have entered graduate course in each of two areas. Approved listed in the section on specialty areas. programs in many areas of applied areas and courses are The remaining points of electives are physics or physics, enrolled in medical intended primarily as an opportunity to school, or been employed in various DYNAMICAL SYSTEMS: complete the absolutely mandatory four- technical or financial areas immediately APMA E4101 or PHYS G4003 year, 27-point nontechnical requirement after receiving the B.S. degree. OPTICAL OR LASER PHYSICS: for the B.S. degree, but if this 27-point Opportunities for undergraduate APPH E4110 or E4112 nontechnical requirement has been met research exist in the many research NUCLEAR SCIENCE: APPH E4010 already, then any type of coursework can programs in applied physics. These satisfy these elective points. PLASMA PHYSICS: APPH E4301 include fusion and space plasma physics, optical and laser physics, and condensed PHYSICS OF FLUIDS: APPH E4200 Undergraduate Programs matter physics. Undergraduate students SOLID STATE/CONDENSED MATTER in Applied Mathematics can receive course credit for research PHYSICS: PHYS G4018 The applied mathematics program is or an independent project with a faculty BIOPHYSICAL modeling: APMA E4400 flexible and intensive. A student must member. Opportunities also exist for take the required courses listed below, undergraduate students in the applied

engineering 2014–2015 54 Applied mathematics program: first and second Years

Semester i Semester iI Semester iII Semester iV

MATH V1202(3) mathematics1 MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) and ODE (3)2

physics C1401 (3) C1402 (3) C1403 (3) C1494 (3) (three tracks, C1601 (3.5) C1602 (3.5) C2601 (3.5) Lab C2699 (3) choose one) C2801 (4.5) C2802 (4.5) Lab W3081 (2)

chemistry/ CHEM C1403 (3), or higher or BIOL W2001 (4) biology (choose one course) or BIOL C2005 (4), or higher

english C1010 (3) composition (three tracks, Z1003 (0) C1010 (3) choose one) Z0006 (0) Z1003 (0) C1010 (3)

HUMA C1001, HUMA C1002, COCI C1101, COCI C1102, required or Global Core (3–4) or Global Core (3–4) nontechnical electives HUMA W1121 or ECON W1105 (4) and W1123 (3) W1155 recitation (0)

required (3) Student’s choice, see list of first- and second-year technical electives tech electives (professional-level courses; see pages 12–13)

computer ENGI E1006 (3) any semester science

physical C1001 (1) C1002 (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 E1210). 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.

or prove equivalent standing, and find employment directly in industry, undergraduate Double then may elect the other courses from government, education, or o’ther fields. Major in applied physics mathematics, computer science, physics, Of the 27 points of elective content and applied mathematics Earth and environmental sciences, in the third and fourth years, at least 15 Students satisfy all requirements for biophysics, economics, business and points of technical courses approved both majors, except for the seminar finance, or other application fields. Each by the adviser must be taken. The requirements. They are required to take student tailors his or her own program in remaining points of electives are both senior seminars, APMA E4903 and close collaboration with an adviser. He intended primarily as an opportunity to APPH E4903 (taking one in the junior or she must also register for the applied complete the absolutely mandatory four- year and one in the senior year, due mathematics seminar during both the year, 27-point nontechnical requirement to timing conflicts), but not the junior junior and senior years. During the junior for the B.S. degree, but if this 27-point seminars, APMA E4901 and APPH year, the student attends the seminar nontechnical requirement has been met E4901. A single course may be used lectures for 0 points; during the senior already, then any type of coursework to fulfill a requirement in both majors. year, he or she attends the seminar can satisfy these elective points. Students must maintain a GPA at or lectures as well as tutorial problem Transfers into the applied above 3.75, and must graduate with at sessions for 3 or 4 points. mathematics program from other majors least 143 points, 15 above the regular While it is common for students require a GPA of 3.0 or above, and the 128-point requirement. These extra 15 in the program to go on to graduate approval of the applied mathematics points should be technical electives school, many graduating seniors will program chair. appropriate for one or both majors.

engineering 2014–2015 55 Applied mathematics: Third and Fourth Years

Semester V Semester VI Semester VII Semester VIII

APMA E3101 (3)1 APMA E3102 (3)1 Linear algebra Partial differential MATH W4061 (3) (Applied math, I) equations Modern analysis (Applied math, II) APMA E3900 (3)3 APMA E4901 (0) APMA E4101 (3) Research Required Seminar Course from Group A Introduction to Courses or Group B2 dynamical systems Courses designated Course from Group A (Applied math, III) MATH, APMA, or STAT (3) or Group B2 APMA E4300 (3) Introduction to numerical APMA E4903 (4) APMA E4204 (3)1 methods (Computational Seminar Complex variables math, I)

Tech4 3 points 3 points 3 points 6 points

NonTech 3 points 3 points 3 points 3 points E lectives

total points 15 15 16 15

1 MATH V2010 may be substituted for APMA E3101; MATH V3028 may be substituted for APMA E3102; MATH V3007 may be substituted for APMA E4204. 2 One course from Group A and one course from Group B required for graduation. Group A: IEOR E3658: Probability; STAT W4105: Probability; SIEO W3600: Introduction to probability and statistics; SIEO W4150: Introduction to probability and statistics; STAT W3105: Introduction to probability; MATH W4155: Probability theory. Group B: STAT W3107: Statistical inference; STAT W4107: Statistical inference; STAT W4109: Probability and statistical inference; SIEO W 4606: Elementary stochastic processes; IEOR E3106: Introduction to stochastic models; IEOR E4106: Introduction to operations research: 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.

To apply, a student first obtains Technical Electives Atmosphere, Oceans, and Climate the approval of both the general • Applications of Physics APPH E4008y: Intro to atmospheric science undergraduate AP adviser and the Courses that will give a student a broad APPH E4200x: Physics of fluids APPH E4210y: Geophysical fluid dynamics general undergraduate AM adviser, and background in applications of physics: EESC W4925x: Principles of physical then the approval of the Dean. ELEN E3000x: Circuits, systems, and oceanography electronics (J) EESC W4930y: Earth’s oceans and atmosphere Specialty Areas in APAM MSAE E3103x: Elements of materials science (J) Solid Earth Geophysics Both applied physics and applied math- APPH E4010x: Intro to nuclear science EESC W4001x: Advanced general geology ematics students can focus their tech- PHYS G4018y: Solid-state physics EESC W4113x: Intro to mineralogy nical electives and develop a strong APMA E4101y: Intro to dynamical systems APPH E4200x: Physics of fluids base of knowledge in a specialty area. APPH E4110x: Modern optics EESC W4701y: Intro to igneous petrology There is no requirement to focus elec- APPH E4112y: Laser physics EESC W4941y: Principles of geophysics EESC W4950x: Mathematical methods in the tives, so students may take as many or APPH E4200x: Physics of fluids Earth sciences as few of the recommended courses APPH E4301y: Intro to plasma physics in a specialty area as is appropriate to • Earth and Atmospheric Sciences (See also courses listed under their schedules and interests. Some The Earth sciences provide a wide Scientific Computation and Computer specialties are given below, but this range of problems of interest to Science on page 56.) is not an exclusive list and others can physicists and mathematicians ranging be worked out in coordination with the • Basic Physics and Astrophysics from the dynamics of the Earth’s student’s adviser. The courses that are Fundamental physics and astrophysics climate to earthquake physics to often taken, or in some cases need to can be emphasized. Not only is dynamics of Earth’s deep interior. The be taken, in the junior year are denoted astrophysics providing a deeper Lamont-Doherty Earth Observatory, with a “J.” understanding of the universe, but it is which is part of Columbia University, also testing the fundamental principles provides enormous resources for of physics. students interested in this area.

engineering 2014–2015 56 PHYS W3002y: From quarks to the cosmos: • Quantitative Biology MATH V3020x: Number theory and cryptography (J) applications of modern physics Traditionally biology was considered a COMS W3137x,y: Data structures and ASTR C3601x: General relativity, black holes, descriptive science in contrast to the algorithms (or COMS W3139y: and cosmology (J) Honors data structures and quantitative sciences that are based ASTR C3602y: Physical cosmology (J) algorithms) (J) ASTR G4001y: Astrophysics, I on mathematics, such as physics. This COMS W3157x,y: Advanced programming (J) APMA E4101x: Intro to dynamical systems view no longer coincides with reality. COMS W3203x,y: Discrete mathematics: intro Researchers from biology as well as to combinatorics and graph • Business and Finance from the physical sciences, applied theory (J) The knowledge of physics and math- mathematics, and computer science COMS W4203y: Graph theory APMA E4300y: Intro to numerical methods ematics that is gained in the applied are rapidly building a quantitative base APMA E4301x: Numerical methods for partial physics and applied mathematics of biological knowledge. Students can differential equations programs is a strong base for a career acquire a strong base of knowledge in AMCS E4302x: Parallel scientific computing in business or finance. quantitative biology, both biophysics COMS W4701x,y: Artificial intelligence and computational biology, while COMS W4771y: Machine learning Economics completing the applied physics or ECON W3211x,y: Intermed microeconomics (J) applied mathematics programs. • Solid-State Physics ECON W3213x,y: Intermed macroeconomics(J) Much of modern technology is based on solid-state physics, the study of I ndustrial Engineering Professional-level Course: solids and liquids. Courses that will and Operations Research APPH E3400y: Physics of the human body build a strong base for a career in this IEOR E4003x: Industrial economics Recommended: area are IEOR E4201x: The eng of management, I BIOL C2005x-C2006y: Intro biology, I and II IEOR E4202y: The eng of management, II APMA E4400y: Intro to biophysical modeling PHYS W3083y: Electronics laboratory (J) Finance MSAE E3103x: Elements of material science (J) Other Technical Electives (a course ELEN E3106x: Solid-state devices and MATH W4071x: Mathematics of finance in at least two areas recommended): IEOR E4106y: Intro to operations research: materials (J) stochastic models (J) Biological Materials MSAE E4100x: Crystallography SIEO W4150x,y: Probability and statistics (J) BIOL W4070x: The biology and physics of PHYS G4018y: Solid-state physics ECIE W4280: Corporate finance single molecules MSAE E4206x: Electronic and magnetic IEOR E4700x: Intro to financial engineering CHEN E4650x: Biopolymers properties of solids MSAE E4207y: Lattice vibrations and crystal defects • Mathematics Applicable to Physics Biomechanics Applied physics students can specialize BMEN E3320y: Fluid biomechanics (J) in the mathematics that is applicable BMEN E4300y: Solid biomechanics (J) Undergraduate Program to physics. This specialization is in Materials Science Genomics and Bioinformatics particularly useful for students See page 171. interested in theoretical physics. BIOL W3037y: Whole genome bioinformatics (J) ECBM E3060x: Intro to genomic information MATH V3386x: Differential geometry science and technology (J) Graduate Programs APMA E4001y: Principles of applied mathematics CBMF W4761y: Computational genomics APMA E4101x: Intro to dynamical systems Financial aid is available for students pursuing a doctorate. Fellowships, APMA E4301x: Numerical methods for partial Neurobiology differential equations scholarships, teaching assistantships, BIOL W3004x: Neurobiology , I (J) APMA E4302x: Parallel scientific computing and graduate research assistantships BIOL W3005y: Neurobiology, II (J) PHYS G4019y: Mathematical methods of physics ELEN G4011x: Computational neuroscience are awarded on a competitive basis. The Aptitude Test of the Graduate Record • Fundamental Mathematics in Applied The second term of biology will be Examination is required of candidates Mathematics considered a technical elective if a for admission to the department and This specialization is intended for student has credits from at least two for financial aid; the Advanced Tests are students who desire a more solid other of the recommended courses in recommended. foundation in the mathematical quantitative biology at the 3000 level methods and underlying theory. For or above. M.S. Program in Applied Physics example, this specialization could be The program of study leading to the followed by students with an interest in • Scientific Computation and degree of Master of Science, while graduate work in applied mathematics. Computer Science emphasizing continued work in basic Advanced computation has become physics, permits many options in MATH V3386x: Differential geometry several applied physics specialties. The APMA E4101x: Intro to dynamical systems a core tool in science, engineering, program may be considered simply as APMA W4150x: Applied functional analysis and mathematics and provides MATH W4032x: Fourier analysis challenges for both physicists additional education in areas beyond MATH W4062y: Modern analysis, II and mathematicians. Courses the bachelor’s level, or as preparatory to SIEO W4150x,y: Intro to probability and that build on both practical and doctoral studies in the applied physics statistics (J) theoretical aspects of computing and fields of plasma physics, laser physics, PHYS W4386x-W4387y: Geometrical computation include: or solid-state physics. Specific course concepts in physics requirements for the master’s degree

engineering 2014–2015 are determined in consultation with the Industrial engineering/operations APPH E4330: Radiobiology 57 program adviser, but must include four research elective courses include: APPH E4500: Health physics of the six core courses listed below. APPH E4600: Dosimetry The core courses provide a IEOR E4003: Industrial economics APBM E4650: Anatomy for physicists and engineers student with a solid foundation in the IEOR E4004: Intro to operations research: APPH E6319: Clinical nuclear medicine physics or APPH E6330: Diagnostic radiology physics fundamentals of applied physics, but deterministic models APPH E6335: Radiation therapy physics with the approval of the faculty adviser, IEOR E4007: Optimization: models and methods IEOR E4106: Intro to operations research: or APPH E6336: Advanced topics in radiation other graduate-level courses with APPH stochastic models therapy designators not listed below may also SIE0 W4150: Intro to probability and statistics count as core courses. IEOR E4403: Advanced engineering and corporate This is a part-time nondegree program. economics Students are admitted to the department APPH E4100x: Quantum physics of matter IEOR E4407: Game theoretic models of operations as certificate-track students. APPH E4110x: Modern optics STAT W4606: Elementary stochastic processes APPH E4112y: Laser physics IEOR E4700: Intro to financial engineering APPH E4200x: Physics of fluids Ph.D. and Eng.Sc.D. Programs APPH E4300x: Applied electrodynamics Other elective courses include: After completing the M.S. program APPH E4301y: Introduction to plasma physics MECE E4100: Mechanics of fluids in applied physics, doctoral students MSAE E4215: Mechanical behavior of structural specialize in one applied physics field. M.S. Program in Applied Physics/ materials Some specializations have specific Concentration in Applied EEME E6601: Intro to control theory course requirements for the doctorate; Mathematics elective courses are determined in This 30-point program leads to an M.S. M.S. Program in Materials Science consultation with the program adviser. degree. Students must complete five and Engineering Successful completion of an approved core courses and five electives. The See page 172. 30-point program of study is required in core courses provide a student with addition to successful completion of a written qualifying examination taken after a foundation in the fundamentals of M.S. Program in Medical Physics two semesters of graduate study. An oral applied mathematics and contribute This CAMPEP-approved 36-point 15 points of graduate credit toward the examination, taken within one year after program in medical physics leads to the the written qualifying examination, and a degree. Students must complete five of M.S. degree. It is administered by faculty the following seven courses: thesis proposal examination, taken within from the School of Engineering and two years after the written qualifying Applied Science in collaboration with APMA E4001: Principles of applied mathematics examination, are required of all doctoral faculty from the College of Physicians APMA E4101: Intro to dynamical systems candidates. APMA E4150: Applied functional analysis and Surgeons and the Mailman School of Public Health. It provides preparation APMA E4200: Partial differential equations Applied Mathematics toward certification by the American APMA E4204: Functions of a complex variable This graduate specialty, for students APMA E4300: Intro to numerical methods Board of Radiology. The program registered in the Department of Applied APMA E4301: Numerical methods for partial consists of a core curriculum of medical Physics and Applied Mathematics, differential equations and nuclear physics courses, anatomy, emphasizes applied mathematics APMA E6301: Analytic methods for partial lab, seminar, a tutorial, one elective, research in nonlinear dynamics, fluid differential equations and two practicums. Specific course APMA E6302: Numerical analysis for partial mechanics, and scientific computation, requirements are APPH E4010, E4330, differential equations with a current emphasis on geophysical, E4710, E4500, E4501, E4550, E4600, biophysical, and plasma physics E6319, E6330, E6335, and APBM applications. A student must select five elective E4650. Approved electives include Applied mathematics deals with courses from those listed below (or any APPH E4711, APPH E6336, APAM the use of mathematical concepts of those not used to satisfy the core E6650, and a third practicum. Up to and techniques in various fields of requirements from the list above) for 6 points of this 36-point program may science and engineering. Historically, a total of 15 points of graduate credit. be waived based on prior equivalent mathematics was first applied with great Additional courses not listed below academic work. A passing grade on a success in astronomy and mechanics. can be applied toward the elective comprehensive examination is required Then it developed into a main tool of requirements, subject to the approval of for graduation. This examination, on physics, other physical sciences, and the faculty adviser. Computer science subjects covered in the curriculum, is engineering. It is now important in elective courses include: taken after two terms of study. the biological, geological, and social CSOR W4231: Analysis of algorithms, I sciences. With the coming of age of COMS W4236: Intro to computational complexity Certification of Professional the computer, applied mathematics has COMS W4241: Numerical algorithms and Achievement in Medical Physics transcended its traditional style and now complexity This graduate program of instruction COMS W4252: Computational learning theory assumes an even greater importance leads to the Certification of Professional and a new vitality. Achievement and requires satisfactory Compared with the pure mathematician, completion of six of the following the applied mathematician is more courses: interested in problems coming from

engineering 2014–2015 58 other fields. Compared with the engineer ultrafast dynamical properties of solids, using Fortran 90. Students develop familiarity with and the physical scientist, he or she is with an aim to understanding them basic and advanced concepts of modern numerical more concerned with the formulation of in terms of the atomic and electronic programming and acquire practical experience problems and the nature of solutions. structure. The field emphasizes the solving representative problems in math and Compared with the computer scientist, formation, processing, and properties of physics. he or she is more concerned with the thin films, low-dimensional structures— APPH E3200x Mechanics: fundamentals and accuracy of approximations and the such as one- and two-dimensional applications interpretation of results. Needless to say, electron gases, nanocrystals, surfaces 3 pts. Lect: 3. Professor Cole. even in this age of specialization, the of electronic and optoelectronic interest, Prerequisites: PHYS C1402, C1402; MATH E1210, work of mathematicians, scientists, and and molecules. Facilities include a or equivalent. Basic non-Euclidean coordinate systems, Newtonian mechanics, oscillations, engineers frequently overlaps. Applied microelectronics laboratory, high-pressure Green’s functions, Newtonian gravitation, mathematics, by its very nature, has diamond anvil cells, a molecular beam Lagrangian mechanics, central force motion, occupied a central position in this interplay epitaxy machine, ultrahigh vacuum two-body collisions, noninertial reference frames, and has remained a field of fascination systems, lasers, equipment for the study rigid body dynamics. Applications, including GPS and excitement for active minds. of optical properties and transport on the and feedback control systems, are emphasized nanoscale, and the instruments in the throughout. Materials Science shared facilities overseen by the Center APPH E3300y Applied electromagnetism and Engineering Program for Integrated Science and Engineering 3 pts. Lect: 3. Professor Venkataraman. See page 173. (CISE). There are also significant Corequisite: APMA E3102. Vector analysis, resources for electrical and optical electrostatic fields, Laplace’s equation, multipole expansions, electric fields in matter: dielectrics, Plasma Physics experimentation at low temperatures and high magnetic fields. Specific course magnetostatic fields, magnetic materials, and This graduate specialty is designed to superconductors. Applications of electromagnetism emphasize preparation for professional requirements for the solid-state physics to devices and research areas in applied physics. doctoral specialization are set with the careers in plasma research, controlled APPH E3400y Physics of the human body fusion, and space research. This academic adviser, in consultation with the Committee on Materials Science and 3 pts. Lect: 3. Not offered in 2014–2015. includes basic training in relevant areas Prerequisites: PHYS C1201 or C1401, and Engineering/Solid-State Science and of applied physics, with emphasis Calculus I; corequisites: PHYS C1202 or on plasma physics and related areas Engineering. C1402, and Calculus II. This introductory leading to extensive experimental and course analyzes the human body from the basic theoretical research in the Columbia principles of physics. Topics covered include Courses in Applied Physics the energy balance in the body, the mechanics University Plasma Physics Laboratory. APAM E1601y Introduction to computational of motion, fluid dynamics of the heart and Specific course requirements for the circulation, vibrations in speaking and hearing, plasma physics doctoral program are mathematics and physics 3 pts. Lect: 3. Not offered in 2014–2015. muscle mechanics, gas exchange and transport APPH E4018, E4200, E4300, E6101, Introduction to computational methods in applied in the lungs, vision, structural properties and E6102, and E9142 or E9143, or mathematics and physics. Students develop limits, electrical properties and the development equivalents taken at another university. solutions in a small number of subject areas to and sensing of magnetic fields, and basics of acquire experience in the practical use of computers equilibrium and regulatory control. In each case, a simple model of the body organ, property, or Optical and Laser Physics to solve mathematics and physics problems. function will be derived and then applied. This graduate specialty involves a basic Topics change from year to year. Examples include elementary interpolation of functions, solution of training in relevant areas of applied APPH E3900x and y Undergraduate research nonlinear algebraic equations, curve-fitting and physics with emphasis in quantum in applied physics hypothesis testing, wave propagation, fluid motion, 0–4 pts. Members of the faculty. mechanics, quantum electronics, and gravitational and celestial mechanics, and chaotic Prerequisite: Written permission from instructor related areas of specialization. Some dynamics. Basic requirement for this course is and approval from adviser. This course may be active areas of research in which the one year of college-level calculus and physics; repeated for credit, but no more than 6 points of student may concentrate are laser programming experience is not required. this course may be counted toward the satisfaction of the B.S. degree requirements. Candidates for modification of surfaces, optical APPH E3100y Introduction to quantum the B.S. degree may conduct an investigation in diagnostics of film processing, inelastic mechanics applied physics or carry out a special project under 3 pts. Lect: 3. Professor Herman. light scattering in nanomaterials, the supervision of the staff. Credit for course is Prerequisites: PHYS C1403 or equivalent, and nonlinear optics, ultrafast optoelectronics contingent upon the submission of an acceptable differential and integral calculus. Corequisites: photonic switching, optical physics thesis or final report. APMA E3101 or equivalent. Basic concepts and of surfaces, and photon integrated assumptions of quantum mechanics, Schrodinger’s APPH E4008x Introduction to atmospheric circuits. Specific course requirements equation, solutions for one-dimensional problems, science for the optical and laser physics doctoral including square wells, barriers, and the harmonic 3 pts. Lect: 3. Professor Polvani. specialization are set with the academic oscillator, introduction to the hydrogen atom, Prerequisites: Advanced calculus and general adviser. atomic physics and X-rays, electron spin. physics, or instructor’s permission. Basic physical processes controlling atmospheric structure: APAM E3105x Programming methods for thermodynamics; radiation physics and radiative Solid-State Physics scientists and engineers transfer; principles of atmospheric dynamics; cloud This graduate specialty encompasses 3 pts. Lect: 2.5. Lab: 1. Not offered in 2014–2015. processes; applications to Earth’s atmospheric the study of the electrical, optical, Introduction to modern techniques of computer general circulation, climatic variations, and the programming for the numerical solutions to magnetic, thermal, high-pressure, and atmospheres of the other planets. problems in physics, mathematics, and engineering

engineering 2014–2015 APPH E4010x Introduction to nuclear science of Helmholtz and Gibbs free energies and for measurement of plasma properties. Illustrative 59 3 pts. Lect: 3. Professor Ostrow. open systems. Correlation times and lengths. problems in fusion, space, and nonneutral or beam Prerequisites: MATH V1202 and E1210 and PHYS Exploration of phase space and observation time plasmas. C1403 or equivalents. Introductory course for scale. Correlation functions. Fermi-Dirac and APPH E4330y Radiobiology for medical individuals with an interest in medical physics and Bose-Einstein statistics. Fluctuation-response physicists other branches of radiation science. Topics include theory. Applications to ideal gases, interfaces, 3 pts. Lect: 3. Professor Zaider. basic concepts, nuclear models, semiempirical liquid crystals, microemulsions and other complex Prerequisite: APPH E4010 or equivalent or mass formula, interaction of radiation with matter, fluids, polymers, Coulomb gas, interactions between Corequisite: APPH E4010. Interface between nuclear detectors, nuclear structure and instability, charged polymers and charged interfaces, ordering clinical practice and quantitative radiation radioactive decay process and radiation, particle transitions. accelerators, and fission and fusion processes and biology. Microdosimetry, dose-rate effects technologies. APPH E4130x Physics of solar energy and biological effectiveness thereof; radiation 3 pts. Lect: 3. Professor Chen. biology data, radiation action at the cellular APPH E4018y Applied physics laboratory Prerequisites: General physics (PHYS C1403 and tissue level; radiation effects on human 2 pts. Lab: 4. Professor Volpe. or C1602) and mathematics, including ordinary populations, carcinogenesis, genetic effects; Prerequisite: ELEN E3401 or equivalent. differential equations and complex numbers radiation protection; tumor control, normal- Typical experiments are in the areas of plasma (such as MATH V1202 or E1210) or instructor’s tissue complication probabilities; treatment plan physics, microwaves, laser applications, optical permission. The physics of solar energy including optimization. spectroscopy physics, and superconductivity. solar radiation, the analemma, atmospheric efforts, APPH E4500y Health physics thermodynamics of solar energy, physics of solar APPH E4090y Nanotechnology 3 pts. Lect: 3. Professor Morgan. cells, energy storage and transmission, and 3 pts. Lect: 3. Professor Wind. Prerequisite: APPH E4600 or Corequisite: APPH physics and economics in the solar era. Prerequisites: APPH E3100 and MSAE E3103 E4600. Fundamental principles and objectives of or their equivalents with instructor’s permission. APPH E4200x Physics of fluids health physics (radiation protection), quantities of The science and engineering of creating 3 pts. Lect: 3. Professor Mauel. radiation dosimetry (the absorbed dose, equivalent materials, functional structures and devices on the Prerequisites: APMA E3102 or equivalent; PHYS dose, and effective dose) used to evaluate human nanometer scale. Carbon nanotubes, nanocrystals, C1401 or C1601 or equivalent. An introduction radiation risks, elementary shielding calculations quantum dots, size dependent properties, self- to the physical behavior of fluids for science and and protection measures for clinical environments, assembly, nanostructured materials. Devices engineering students. Derivation of basic equations characterization and proper use of health physics and applications, nanofabrication. Molecular of fluid dynamics: conservation of mass, momentum, instrumentation, and regulatory and administrative engineering, bionanotechnology. Imaging and and energy. Dimensional analysis. Vorticity. requirements of health physics programs in manipulating at the atomic scale. Nanotechnology Laminar boundary layers. Potential flow. Effects general and as applied to clinical activities. in society and industry. of compressibility, stratification, and rotation. APPH E4501y Medical health physics tutorial Waves on a free surface; shallow water equations. APPH E4100x Quantum physics of matter 0 pts. Turbulence. 3 pts. Lect: 3. Professor Herman. Prerequisite: Permission of the course coordinator. Prerequisite: APPH E3100. Corequisite: APMA APPH E4210y Geophysical fluid dynamics Required for, and limited to, M.S. degree candidates E3102 or equivalent. Basic theory of quantum 3 pts. Lect: 3. Professor Sobel. in the Medical Physics Program. Course addresses mechanics, well and barrier problems, the Prerequisites: APMA E3101, E3102 (or procedures for personnel and area monitoring, harmonic oscillator, angular momentum identical equivalents) and APPH E4200 (or equivalent), or radiation and contamination surveys, instrument particles, quantum statistics, perturbation theory permission from instructor. Fundamental concepts calibration, radioactive waste disposal, radiation and applications to the quantum physics of atoms, in the dynamics of rotating, stratified flows. safety compliance, licensure requirements, molecules, and solids. Geostrophic and hydrostatic balances, potential and other matters contributing to professional APPH E4110x Modern optics vorticity, f and beta plane approximations, gravity competence in the field of medical health physics. 3 pts. Lect: 3. Professor Yu. and Rossby waves, geostrophic adjustment Course includes lectures, seminars, tours, and Prerequisite: APPH E3300. Ray optics, matrix and quasigeostrophy, baroclinic and barotropic hands-on experience. This two-week tutorial is formulation, wave effects, interference, Gaussian instabilities, Sverdrup balance, boundary offered immediately following spring semester final beams, Fourier optics, diffraction, image formation, currents, Ekman layers. examinations and is taken for Pass/Fail only. electromagnetic theory of light, polarization and APPH E4300y Applied electrodynamics APPH E4550y Medical physics seminar crystal optics, coherence, guided wave and fiber 3 pts. Lect: 3. Professor Navratil. 0 pts. Lect: 1. Professor Arbo. optics, optical elements, photons, selected topics Prerequisite: APPH E3300. Overview of properties Required for all graduate students in the Medical in nonlinear optics. and interactions of static electric and magnetic Physics Program. Practicing professionals and APPH E4112y Laser physics fields. Study of phenomena of time dependent faculty in the field present selected topics in 3 pts. Lect: 3. Professor Yu. electric and magnetic fields including induction, medical physics. waves, and radiation as well as special relativity. Recommended but not required: APPH E3100 APPH E4600x Fundamentals of radiological Applications are emphasized. and E3300 or their equivalents. Optical resonators, physics and radiation dosimetry interaction of radiation and atomic systems, APPH E4301y Introduction to plasma physics 3 pts. Lect: 3. Professor Meli. theory of laser oscillation, specific laser systems, 3 pts. Lect: 3. Professor Navratil. Prerequisite: APPH E4010 or equivalent or rate processes, modulation, detection, harmonic Prerequisite: PHYS W3008 or APPH E3300. Corequisite: APPH E4010. Basic radiation physics: generation, and applications. Definition of a plasma. Plasmas in laboratories radioactive decay, radiation producing devices, and nature, plasma production. Motion of charged CHAP E4120y Statistical mechanics characteristics of the different types of radiation particles in electric and magnetic fields, adiabatic 3 pts. Lect: 3. Professor O’Shaughnessy. (photons, charged and uncharged particles) and invariants. Heuristic treatment of collisions, Prerequisite: CHEN E3210 or equivalent mechanisms of their interactions with materials. diffusion, transport, and resistivity. Plasma as a thermodynamics course, or instructor’s Essentials of the determination, by measurement conducting fluid. Electrostatic and magnetostatic permission. Fundamental principles and underlying and calculation, of absorbed doses from ionizing equilibria of plasmas. Waves in cold plasmas. assumptions of statistical mechanics. Boltzmann’s radiation sources used in medical physics (clinical) Demonstration of laboratory plasma behavior, entropy hypothesis and its restatement in terms situations and for health physics purposes.

engineering 2014–2015 60 APBM E4650x Anatomy for physicists and Mathematics who may need relevant work APPH E6110x Laser interactions with matter engineers experience as part of their program of study. Final 3 pts. Lect: 3. Not offered in 2014–2015. 3 pts. Lect: 3. Professors Lignelli and report required. This course may not be taken for Prerequisites: APPH E4112 or equivalent, and Rozenshtein. pass/fail or audited. quantum mechanics. Principles and applications Prerequisite: Engineering or physics background. of laser-matter coupling, nonlinear optics, three- APPH E6081x Solid state physics, I Systemic approach to the study of the human body and four-wave mixing, harmonic generation, 3 pts. Lect: 3. Professor Pinczuk. from a medical imaging point of view: skeletal, laser processing of surfaces, laser probing of Prerequisites: APPH E3100 or the equivalent. respiratory, cardiovascular, digestive, and urinary materials, spontaneous and stimulated light Knowledge of statistical physics on the level systems, breast and women’s issues, head and scattering, saturation spectroscopy, multiphoton of MSAE E3111 or PHYS G4023 strongly neck, and central nervous system. Lectures are excitation, laser isotope separation, transient recommended. Crystal structure, reciprocal reinforced by examples from clinical two- and optical effects. lattices, classification of solids, lattice dynamics, three-dimensional and functional imaging (CT, MRI, anharmonic effects in crystals, classical electron APPH E6319y Clinical nuclear medicine PET, SPECT, U/S, etc.). models of metals, electron band structure, and physics APPH E4710x Radiation instrumentation and low-dimensional electron structures. 3 pts. Lect: 3. Professor Esser. measurement laboratory, I Prerequisite: APPH E4010 or equivalent APPH E6082y Solid state physics, II 3 pts. Lect: 1. Lab: 4. Professor Arbo. recommended. Introduction to the 3 pts. Lect: 3. Professor Altshuler. Prerequisite or corequisite: APPH E4010. Lab instrumentation and physics used in clinical Prerequisite: APPH E6081 or instructor’s fee: $50. Theory and use of alpha, beta, gamma, nuclear medicine and PET with an emphasis permission. Semiclassical and quantum mechanical and X-ray detectors and associated electronics on detector systems, tomography and quality electron dynamics and conduction, dielectric for counting, energy spectroscopy, and dosimetry; control. Problem sets, papers, and term project. properties of insulators, semiconductors, defects, radiation safety; counting statistics and error magnetism, superconductivity, low-dimensional propagation; mechanisms of radiation emission APPH E6330y Diagnostic radiology physics structures, and soft matter. and interaction. (Topic coverage may be revised.) 3 pts. Lect: 3. Professors Jambalwalikar and APPH E6085x Computing the electronic Liang. APPH E4711x or y Radiation instrumentation structure of complex materials Prerequisite: APPH E4600. Physics of medical and measurement laboratory, II 3 pts. Lect: 3. Not offered in 2014–2015. imaging. Imaging techniques: radiography, 3 pts. Lect: 1. Lab: 4. Professor Arbo. Prerequisite: APPH E3100 or equivalent. Basics of fluoroscopy, computed tomography, Prerequisite: APPH E4710. Lab fee: $50. Additional density functional theory (DFT) and its application mammography, ultrasound, magnetic resonance. detector types; applications and systems including to complex materials. Computation of electronics Includes conceptual, mathematical/theoretical, and coincidence, low-level, and liquid scintillation and mechanical properties of materials. Group practical clinical physics aspects. counting; neutron activation; TLD dosimetry, theory, numerical methods, basis sets, computing, APPH E6333x or y Radiation therapy physics gamma camera imaging. (Topic coverage may be and running open source DFT codes. Problem sets revised.) practicum and a small project. 3 pts. Lab: 6. Professors Amols and Wuu. APPH E4901x Seminar: problems in applied APPH E6091y Magnetism and magnetic Prerequisites: Grade of B+ or better in APPH physics materials E6335 and instructor’s permission. Students 1 pt. Lect: 1. Professor Mauel. 3 pts. Lect. 3. Offered in alternate years. spend two to four days per week studying the This course is required for, and can be taken Professor Bailey. clinical aspects of radiation therapy physics. only by, all applied physics majors and minors Prerequisites: MSAE E4206, APPH E6081, or Projects on the application of medical physics in the junior year. Discussion of specific and equivalent. Types of magnetism. Band theory in cancer therapy within a hospital environment self-contained problems in areas such as applied of ferromagnetism. Magnetic metals, insulators, are assigned; each entails one or two weeks of electrodynamics, physics of solids, and plasma and semiconductors. Magnetic nanostructures: work and requires a laboratory report. Two areas physics. Topics change yearly. ultrathin films, superlattices, and particles. Surface are emphasized: 1. computer-assisted treatment APPH E4903x Seminar: problems in applied magnetism and spectroscopies. High speed planning (design of typical treatment plans for physics magnetization dynamics. Spin electronics. various treatment sites including prostate, breast, 2 pts. Lect: 1. Tutorial: 1. Professor Mauel. head and neck, lung, brain, esophagus, and APPH E6101x Plasma physics, I This course is required for, and can be taken only cervix) and 2. clinical dosimetry and calibrations 3 pts. Lect: 3. Professor Volpe. by, all applied physics majors in the senior year. (radiation measurements for both photon and Prerequisite: APPH E4300. Debye screening. Discussion of specific and self-contained problems electron beams, as well as daily, monthly, and Motion of charged particles in space- and in areas such as applied electrodynamics, physics part of annual QA). time-varying electromagnetic fields. Two-fluid of solids, and plasma physics. Formal presentation description of plasmas. Linear electrostatic and APPH E6335y Radiation therapy physics of a term paper required. Topics change yearly. electromagnetic waves in unmagnetized and 3 pts. Lect: 3. Professor Wuu. APPH E4990x and y Special topics in applied magnetized plasmas. The magnetohydrodynamic Prerequisites: APPH E4600; APPH E4330 physics (MHD) model, including MHD equilibrium, stability, recommended. Review of X-ray production and 1–3 pts. Not offered in 2014–2015. and MHD waves in simple geometries. fundamentals of nuclear physics and radioactivity. Prerequisite: Instructor’s permission. This Detailed analysis of radiation absorption and course may be repeated for credit. Topics and APPH E6102y Plasma physics, II interactions in biological materials as specifically instructors change from year to year. For advanced 3 pts. Lect: 3. Professor Cole. related to radiation therapy and radiation therapy undergraduate students and graduate students in Prerequisite: APPH E6101. Magnetic coordinates. dosimetry. Surveys of use of teletherapy isotopes engineering, physical sciences, and other fields. Equilibrium, stability, and transport of torodial and X-ray generators in radiation therapy plus plasmas. Ballooning and tearing instabilities. the clinical use of interstitial and intracavitary APAM E4999x and y–S4999 Supervised Kinetic theory, including Vlasov equation, Fokker- isotopes. Principles of radiation therapy treatment internship Planck equation, Landau damping, kinetic transport planning and isodose calculations. Problem sets 1–3 pts. Members of the faculty. theory. Drift instabilities. taken from actual clinical examples are assigned. Prerequisite: Obtained internship and approval from adviser. Only for master’s students in the Department of Applied Physics and Applied

engineering 2014–2015 APPH E6336x Advanced topics in radiation APAM E6650x and y–S6650 Research project APMA E3102y Partial differential equations 61 therapy 1–6 pts. Members of the faculty. 3 pts. Lect: 3. Professor Mandli. 3 pts. Lect: 3. Professors Amols and Wuu. Prerequisite: Written permission from instructor Prerequisite: MATH E1210 or equivalent. Prerequisite: APPH E6335. Advanced technology and approval from adviser. This course may be Introduction to partial differential equations; applications in radiation therapy physics, repeated for credit. A special investigation of a integral theorems of vector calculus. Partial including intensity modulated, image guided, problem in nuclear engineering, medical physics, differential equations of engineering in rectangular, stereotactic, and hypofractionated radiation applied mathematics, applied physics, and/or cylindrical, and spherical coordinates. Separation therapy. Emphasis on advanced technological, plasma physics consisting of independent work on of the variables. Characteristic-value problems. engineering, clinical and quality assurance issues the part of the student and embodied in a formal Bessel functions, Legendre polynomials, other associated with high-technology radiation therapy report. orthogonal functions; their use in boundary value and the special role of the medical physicist in problems. Illustrative examples from the fields APPH E9142x-E9143y Applied physics seminar the safe clinical application of these tools. of electromagnetic theory, vibrations, heat flow, 3 pts. Sem: 3. Not offered in 2014–2015. and fluid mechanics. APPH E6340x or y Diagnostic radiology These courses may be repeated for credit. practicum Selected topics in applied physics. Topics and APAM E3105x Programming methods for 3 pts. Lab: 6. Members of the faculty. instructors change from year to year. scientists and engineers Prerequisites: Grade of B+ or better in APPH 3 pts. Lect: 2.5. Lab: 1. Not offered in 2014–2015. APAM E9301x and y–S9301 Doctoral research E6330 and instructor’s permission. Practical Introduction to modern techniques of computer 0–15 pts. Members of the faculty. applications of diagnostic radiology for various programming for the numerical solutions to Prerequisite: Qualifying examination for the measurements and equipment assessments. familiarity with basic and advanced concepts doctorate. Required of doctoral candidates. Instruction and supervised practice in radiation of modern numerical programming and acquire safety procedures, image quality assessments, APAM E9800x and y–S9800 Doctoral practical experience solving representative regulatory compliance, radiation dose evaluations research instruction problems in math and physics. and calibration of equipment. Students participate 3, 6, 9, or 12 pts. Members of the faculty. APMA E3900x and y Undergraduate research in clinical QC of the following imaging equipment: A candidate for the Eng.Sc.D. degree must register in applied mathematics radiologic units (mobile and fixed), fluoroscopy for 12 points of doctoral research instruction. 0–4 pts. Members of the faculty. units (mobile and fixed), angiography units, Registration for APAM E9800 may not be used Prerequisite: Written permission from instructor mammography units, CT scanners, MRI units and to satisfy the minimum residence requirement for and approval from adviser. This course may be ultrasound units. The objective is familiarization the degree. repeated for credit, but no more than 6 points of in routine operation of test instrumentation this course may be counted toward the satisfaction and QC measurements utilized in diagnostic APAM E9900x and y–S9900 Doctoral dissertation of the B.S. degree requirements. Candidates for medical physics. Students are required to submit 0 pts. Members of the faculty. the B.S. degree may conduct an investigation in QC forms with data on three different types of A candidate for the doctorate may be required applied mathematics or carry out a special project radiology imaging equipment. to register for this course every term after the under the supervision of the staff. Credit for the APPH E6365x or y Nuclear medicine course work has been completed, and until the course is contingent upon the submission of an practicum dissertation has been accepted. acceptable thesis or final report. 3 pts. Lab: 6. Members of the faculty. APMA E4001y Principles of applied Prerequisites: Grade of B+ or better in APPH mathematics Courses in Applied E6319 and instructor’s permission. Practical 3 pts. Lect: 3. Professor Du. applications of nuclear medicine theory and Mathematics Prerequisites: Introductory Linear Algebra required. application for processing and analysis of APMA E2101y Introduction to applied Ordinary Differential Equations recommended. clinical images and radiation safety and quality Review of finite-dimensional vector spaces and assurance programs. Topics may include mathematics 3 pts. Lect: 3. Professor Tippett. elementary matrix theory. Linear transformations, tomography, instrumentation, and functional Prerequisite: Calculus III. A unified, single-semester change of basis, eigenspaces. Matrix representation imaging. Reports. introduction to differential equations and linear of linear operators and diagonalization. APPH E6380x or y Health physics practicum algebra with emphases on (1) elementary Applications to difference equations, Markov 3 pts. Lab: 6. Members of the faculty. analytical and numerical technique and (2) processes, ordinary differential equations, and Prerequisites: Grade of B+ or better in APPH discovering the analogs on the continuous and stability of nonlinear dynamical systems. Inner E4500 and instructor’s permission or Corequisite: discrete sides of the mathematics of linear product spaces, projection operators, orthogonal APPH E4500 and permission of the instructor. operators: superposition, diagonalization, bases, Gram-Schmidt orthogonalization. Least Radiation protection practices and procedures for fundamental solutions. Concepts are illustrated squares method, pseudo-inverses, singular value clinical and biomedical research environments. with applications using the language of engineering, decomposition. Adjoint operators, Hermitian and Includes design, radiation safety surveys of the natural sciences, and the social sciences. unitary operators, Fredholm Alternative Theorem. diagnostic and therapeutic machine source Students execute scripts in Mathematica and Fourier series and eigenfunction expansions. facilities, the design and radiation protection MATLAB (or the like) to illustrate and visualize Introduction to the theory of distributions and the protocols for facilities using unsealed sources of course concepts (programming not required). Fourier Integral Transform. Green’s functions. radioactivity—nuclear medicine suites and sealed Application to Partial Differential Equations. APMA E3101x Linear algebra sources—brachytherapy suites. Also includes 3 pts. Lect: 3. Professor Tippett. APMA E4101x Introduction to dynamical radiation protection procedures for biomedical Matrix algebra, elementary matrices, inverses, systems research facilities and the administration rank, determinants. Computational aspects of 3 pts. Lect: 3. Professor Weinstein. of programs for compliance to professional solving systems of linear equations: existence- Prerequisites: APMA E2101 (or MATH V1210) and health physics standards and federal and state uniqueness of solutions, Gaussian elimination, APMA E3101 or their equivalents, or instructor’s regulatory requirements for the possession and scaling, ill-conditioned systems, iterative permission. An introduction to the analytic and use of radioactive materials and machine sources techniques. Vector spaces, bases, dimension. geometric theory of dynamical systems; basic of ionizing and nonionizing radiations in clinical Eigenvalue problems, diagonalization, inner existence, uniqueness and parameter dependence situations. Individual topics are decided by the products, unitary matrices. of solutions to ordinary differential equations; student and the collaborating Clinical Radiation constant coefficient and parametrically forced Safety Officer. engineering 2014–2015 62 systems; Fundamental solutions; resonance; limit APMA E4301x Numerical methods for partial APMA E4903x Seminar: problems in applied points, limit cycles and classification of flows in the differential equations mathematics plane (Poincare-Bendixson Theorem); conservative 3 pts. Lect: 3. Professor Spiegelman. 3–4 pts. Lect: 1. Tutorial: 2. Professor Wiggins. and dissipative systems; linear and nonlinear Prerequisites: APMA E4300 and E3102 or E4200 This course is required for all applied mathematics stability analysis of equilibria and periodic solutions; or equivalents. Numerical solution of partial majors in the senior year. Prerequisites or stable and unstable manifolds; bifurcations, e.g., differential equations (PDE) arising in various corequisites: APMA E4200 and E4204 or their Andronov-Hopf; sensitive dependence and chaotic physical fields of application. Finite difference, equivalents. For 4 pts. credit, term paper required. dynamics; selected applications. finite element, and spectral methods. Elementary Examples of problem areas are nonlinear dynamics, finite volume methods for conservation laws. asymptotics, approximation theory, numerical APMA E4150x Applied functional analysis Time stepping, method of lines, and simultaneous methods, etc. Approximately three problem areas 3 pts. Lect: 3. Professor Weinstein. space-time discretization. Direct and iterative are studied per term. Prerequisites: Advanced calculus and course methods for boundary-value problems. Applied in basic analysis, or instructor’s permission. APMA E4990x and y Special topics in applied numerical analysis of PDE, including sources Introduction to modern tools in functional analysis mathematics of numerical error and notions of convergence that are used in the analysis of deterministic and 1–3 pts. Lect: 3. Not offered in 2014–2015. and stability, to an extent necessary for successful stochastic partial differential equations and in Prerequisites: Advanced calculus and junior numerical modeling of physical phenomena. the analysis of numerical methods: metric and year applied mathematics, or their equivalents. Applications will include the Poisson equation, heat normed spaces, Banach space of continuous This course may be repeated for credit. Topics equation, wave equation, and nonlinear equations functions, measurable spaces, the contraction and instructors from the Applied Mathematics of fluid, solid, and gas dynamics. Homework mapping theorem, Banach and Hilbert spaces Committee and the staff change from year to assignments will involve substantial programming. bounded linear operators on Hilbert spaces and year. For advanced undergraduate students their spectral decomposition, and time permitting AMCS E4302x Parallel scientific computing and graduate students in engineering, physical distributions and Fourier transforms. 3 pts. Lect: 3. Not offered in 2014–2015. sciences, biological sciences, and other fields. Prerequisites: APMA E3101, E3102, and E4300, or APMA E6209x Approximation theory APMA E4200x Partial differential equations their equivalents. Corequisites: APMA E4301, and 3 pts. Lect: 3. Professor Spiegelman. 3 pts. Lect: 2. Not offered in 2014–2015. programming ability in C/C++ or FORTRAN/F90. Prerequisite: Course in ordinary differential Prerequisite: MATH W4061 or some knowledge An introduction to the concepts, the hardware and equations. Techniques of solution of partial of modern analysis. Theory and application software environments, and selected algorithms differential equations. Separation of the variables. of approximate methods of analysis from the and applications of parallel scientific computing, Orthogonality and characteristic functions, viewpoint of functional analysis. Approximate with an emphasis on tightly coupled computations nonhomogeneous boundary value problems. numerical and analytical treatment of linear and that are capable of scaling to thousands of Solutions in orthogonal curvilinear coordinate nonlinear algebraic, differential, and integral processors. Includes high-level descriptions of systems. Applications of Fourier integrals, Fourier equations. Topics include function spaces, motivating applications and low-level details of and Laplace transforms. Problems from the fields operators in normed and metric spaces, fixed point implementation, in order to expose the algorithmic of vibrations, heat conduction, electricity, fluid theorems and their applications. kernels and the shifting balances of computation dynamics, and wave propagation are considered. and communication between them. Students run APMA E6301y Analytic methods for partial APMA E4204x Functions of a complex demonstration codes provided on a Linux cluster. differential equations variable Modest programming assignments using MPI and 3 pts. Lect: 2. Professor Bal. 3 pts. Lect. 3. Professor Letourneau. PETSc culminate in an independent project leading Prerequisites: Advanced calculus, basic concepts Prerequisite: MATH V1202 or equivalent. Complex to an in-class report. in analysis, APMA E3101, and E4200 or their numbers, functions of a complex variable, equivalents, or instructor’s permission. Introduction APMA E4400y Introduction to biophysical differentiation and integration in the complex plane. to analytic theory of PDEs of fundamental and modeling Analytic functions, Cauchy integral theorem and applied science; wave (hyperbolic), Laplace and 3 pts. Lect: 3. Professor Wiggins. formula, Taylor and Laurent series, poles and Poisson equations (elliptic), heat (parabolic) and Prerequisites: PHYS W1401 or equivalent, and residues, branch points, evaluation of contour Schroedinger (dispersive) equations; fundamental APMA E2101 or MATH E1210 or equivalent. integrals. Conformal mapping. Schwarz-Christoffel solutions, Green’s functions, weak/distribution Introduction to physical and mathematical models transformation. Applications to physical problems. solutions, maximum principle, energy estimates, of cellular and molecular biology. Physics at the variational methods, method of characteristics; cellular scale (viscosity, heat, diffusion, statistical APMA E4300y Introduction to numerical elementary functional analysis and applications mechanics). RNA transcription and regulation methods to PDEs; introduction to nonlinear PDEs, shocks; 3 pts. Lect: 3. Professor Letourneau. of genetic expression. Genetic and biochemical selected applications. Prerequisites: MATH V1201, MATH E1210, networks. Bioinformatics as applied to reverse- and APMA E3101 or their equivalents. Some engineering of naturally-occurring networks and APMA E6302x Numerical analysis of partial programming experience and MATLAB will be to forward-engineering of synthetic biological differential equations extremely useful. Introduction to fundamental networks. Mathematical and physical aspects of 3 pts. Lect: 2. Not offered in 2014–2015. algorithms and analysis of numerical methods functional genomics. Prerequisite: APMA E3102 or E4200. Numerical commonly used by scientists, mathematicians analysis of initial and boundary value problems APMA E4901x Seminar: problems in applied and engineers. This course is designed to give for partial differential equations. Convergence mathematics a fundamental understanding of the building and stability of the finite difference method, the 0 pts. Lect: 1. Professor Wiggins. blocks of scientific computing that will be used in spectral method, the finite element method and This course is required for, and can be taken only more advanced courses in scientific computing applications to elliptic, parabolic, and hyperbolic by, all applied mathematics majors in the junior and numerical methods for PDEs. Topics include equations. year. Prerequisites or corequisites: APMA E4200 numerical solutions of algebraic systems, linear least- and E4204 or their equivalents. Introductory APMA E6304y Integral transforms squares, eigenvalue problems, solution of nonlinear seminars on problems and techniques in applied 3 pts. Lect: 2. Not offered in 2014–2015. systems, optimization, interpolation, numerical mathematics. Typical topics are nonlinear Prerequisites: APMA E4204 and MATH E1210, or integration and differentiation, initial value problems dynamics, scientific computation, economics, their equivalents. Laplace, Fourier, Hankel, and and boundary value problems for systems of ODEs. operations research, etc. Mellin transforms. Selection of suitable transform All programming exercises will be in MATLAB. for a given partial differential equation boundary

engineering 2014–2015 value problem. Operational properties of transforms. Asymptotic treatment of ordinary and partial research in problems at the interface between 63 Inversion theorems. Approximate evaluation of differential equations in problems arising in applied applied mathematics and earth and environmental inversion integrals for small and large values of mathematics. Asymptotic series. Asymptotic sciences. parameter. Application to the solution of integral evaluation of integrals. Expansion of solutions of APMA E9815x or y Geophysical fluid equations. ordinary differential equations: connection problem dynamics seminar and turning points. Stoke’s phenomenon. Differential APMA E6901x and y–E6901y Special topics in 1–3 pts. May be repeated for up to 10 points of equations with a parameter: “boundary layer” applied mathematics credit. Not offered in 2014–2015. phenomenon. Application to partial differential 3 pts. Lect: 3. Not offered in 2014–2015. Prerequisite: Instructor’s permission. Problems in equations: problems from fl uid dynamics, wave Prerequisites: Advanced calculus and junior the dynamics of geophysical fluid flows. propagation theory, electromagnetic theory. year applied mathematics, or their equivalents. This course may be repeated for credit. Topics APMA E9101x-E9102y Research and instructors from the Applied Mathematics 1–4 pts. Members of the faculty. Courses in Materials Committee and the staff change from year to year. Prerequisite: Permission of the supervising faculty science and engineering For students in engineering, physical sciences, member. This course may be repeated. Advanced See page 175. biological sciences, and other fields. study in a special area. APMA E8308y Asymptotic methods in applied APMA E9810x or y SEAS colloquium in mathematics climate science 3 pts. Lect: 2. Not offered in 2014–2015. 0 pts. Lect: 1. Professors Polvani and Sobel. Prerequisite: APMA E4204 or equivalent. Prerequisite: Instructor’s permission. Current

engineering 2014–2015 64 biomedical engineering 351 Engineering Terrace, MC 8904 Phone: 212-854-4460 E-mail: [email protected] bme.columbia.edu

Chair Laboratory Andrew F. Laine, Assistant Adjunct Associate Andrew F. Laine, Manager Percy K. and Vida Professor Professor Percy K. and Vida Keith Yeager L. W. Hudson Qi Wang Alayar Kangarlu L. W. Hudson Professor of Professor of Computer Systems Biomedical Lecturers Affiliates Biomedical Administrator Engineering Aaron M. Kyle Peter K. Allen, Professor Engineering Robert J. Foster Edward F. Leonard Katherine Reuther of Computer Science Helen H. Lu Dimitris Anastassiou, VICE CHAIR GRANTS Kam W. Leong Joint Faculty Charles Batchelor Barclay Morrison III COORDINATOr Van C. Mow, Shunichi Homma, Professor of Electrical Ariella Ghanooni Stanley Dicker Professor of Medicine Engineering Department Professor Elizabeth S. Olson, Kung-Ming Jan, Administrator Chair of Paul Sajda Associate Professor of Associate Professor of Shila Maghji Undergraduate Gordana Vunjak- Otolaryngology/Head Clinical Medicine Studies Novakovic, The Mikati and Neck Surgery Jung-Chi Liao, Business Manager X. Edward Guo Foundation Professor Michael P. Sheetz, Assistant Professor Kidest Shenkoru of Biomedical William R. Kenan Jr. of Mechanical Chair of Graduate Engineering Professor of Cell Engineering Administrative Studies Biology Lawrence Schwartz, Coordinator for Helen H. Lu Associate Kenneth Shepard, James Picker Student Affairs Professors Professor of Electrical Professor of Radiology Jarmaine Lomax Ombuds Henry Hess Engineering Scott A. Small, Lance Kam Elizabeth Hillman Milan N. Stojanovic, Bob and Rose Katz Administrative Lance C. Kam Associate Professor of Professor of Neurology Assistant for Professors Barclay Morrison III Medical Science (in the Taub Institute, Fiscal Affairs Gerard H. A. Ateshian Samuel K. Sia Sergievsky Center and Michelle Cintron X. Edward Guo Adjunct in Radiology) Andreas H. Hielscher ProfessorS Henry M. Spotnitz, Administrative Clark T. Hung Nicolas W. Chbat Professor of Surgery Assistant for Christopher R. Jacobs David Elad Binsheng Zhao, Departmental Elisa E. Konofagou Ernest Feleppa Associate Professor Affairs of Clinical Radiology Paulette Louissaint (Physics)

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 2014–2015 to interdisciplinary research is important practices in biomedical engineering and engineering or related fields; 65 to the quality and strength of the related sciences. 3. Attendance at medical, dental, or other program. Research facilities of the Biomedical professional schools. Educational programs at all Engineering faculty include the Liu The undergraduate program in levels are based on engineering Ping Laboratory for Functional Tissue biomedical engineering will prepare and biological fundamentals. From Engineering (Professor Mow), the graduates who will have: this basis, the program branches Heffner Biomedical Imaging Laboratory into concentrations along three (Professor Laine), the Laboratory (a) an ability to apply knowledge tracks: biomechanics, cell and tissue for Intelligent Imaging and Neural of mathematics, science, and engineering, and biosignals and Computing (Professor Sajda), the engineering biomedical imaging. The intrinsic Biophotonics and Optical Radiology (b) an ability to design and conduct breadth of these tracks, and a Laboratory (Professor Hielscher), experiments, as well as to analyze substantial elective content, prepare the Bone Bioengineering Laboratory and intepret data bachelor’s and master’s students to (Professor Guo), the Cell and Tissue (c) an ability to design a system, commence professional activity in any Engineering Laboratory (Professor component, or process to meet area of biomedical engineering or to Hung), the Biomaterial and Interface desired needs within realistic go on to graduate school for further Tissue Engineering Laboratory contraints such as economic, studies in related fields. The program (Professor Lu), the Neurotrauma environmental, social, political, also provides excellent preparation for and Repair Laboratory (Professor ethical, health and safety, the health sciences and the study of Morrison), the Laboratory for Stem manufacturability, and sustainability medicine. Graduates of the doctoral Cells and Tissue Engineering (Professor (d) an ability to function on program are prepared for research Vunjak-Novakovic), the Ultrasound multidisciplinary teams (e) an ability to identify, formulate, and activities at the highest level. and Elasticity Imaging Laboratory solve engineering problems Areas of particular interest to (Professor Konofagou), the Microscale (f) an understanding of professional and Columbia faculty include biomechanics Biocomplexity Laboratory (Professor ethical responsibility (Professors Ateshian, Guo, Hess, Kam), the Molecular and Microscale (g) an ability to communicate effectively Jacobs, Morrison, and Mow), cellular and Bioengineering Laboratory (Professor (h) the broad education necessary to tissue engineering and artificial organs Sia), the Laboratory for Functional understand the impact of engineering (Professors Hung, Kam, Leonard, Leong, Optical Imaging (Professor Hillman), solutions in a global, economic, Lu, Morrison, Sia, and Vunjak-Novakovic), the Cell and Molecular Biomechanics environmental, and societal context auditory biophysics (Professor Olson), Laboratory (Professor Jacobs), the (i) a recognition of the need for, and an and biosignals and biomedical imaging Nanobiotechnology and Synthetic ability to engage in life-long learning (Professors Guo, Hielscher, Hillman, Biology Laboratory (Professor Hess), (j) a knowledge of contemporary issues Konofagou, Laine, Sajda, and Wang). the Neural Engineering and Control (k) an ability to use the techniques, Laboratory (Professor Wang), and skills, and modern engineering tools Facilities the Laboratory for Nanomedicine and necessary for engineering practice The Department of Biomedical Regenerative Medicine (Professor (l) an understanding of biology and Engineering has been supported by Leong). These laboratories are physiology grants obtained from NIH, NSF, DoT, supplemented with core facilities, (m) the capability to apply advanced DoD, New York State, numerous including a tissue culture facility, a mathematics (including differential research foundations, and University histology facility, a confocal microscope, equations and statistics), science, funding. The extensive new facilities an atomic force microscope, a and engineering, to solve the that have recently been added 2-photon microscope, epifluorescence problems at the interface of both at the Medical Center and microscopes, a freezer room, engineering and biology Morningside campus include new biomechanics facilities, a machine (n) the ability to make measurements teaching and research laboratories shop, and a specimen preparation on and interpret data from living that provide students with unusual room. systems, addressing the problems access to contemporary research associated with the interaction between living and nonliving materials equipment specially selected for its Undergraduate Program relevance to biomedical engineering. and systems. The objectives of the undergraduate An undergraduate wet laboratory program in biomedical engineering are devoted to biomechanics and cell The undergraduate curriculum is as follows: and tissue engineering has been designed to provide broad knowledge added, together with a biosignals of the physical and engineering 1. Professional employment in and biomedical imaging and data sciences and their application to the areas such as the medical device processing laboratory. Each laboratory solution of biological and medical industry, engineering consulting, and incorporates equipment normally problems. Students are strongly biotechnology; reserved for advanced research and encouraged to take courses in the 2. Graduate studies in biomedical provides exceptional access to current order specified in the course tables;

engineering 2014–2015 66 implications of deviations must meet the 27-point total of nontechnical In the fields of biomedical engineering, be discussed with a departmental electives required for graduation. experimental techniques and principles adviser before registration. The are fundamental skills that good first two years provides a strong First and Second Years biomedical engineers must master. grounding in the physical and chemical As outlined in this bulletin, in the first Beginning in junior year, all students sciences, engineering fundamentals, two years, all engineering students take the two-semester sequence mathematics, and modern biology. This are expected to complete a sequence Biomedical engineering laboratory, I & II (BMEN E3810, E3820). In this two- background is used to provide a unique of courses in mathematics, physics, semester series, students learn through physical approach to the study of chemistry, computer science, hands-on experience the principles biological systems. The last two years engineering, modern biology, English and methods of biomedical engineering of the undergraduate program provide composition, and physical education, as experimentation, measurement substantial exposure to fundamentals in well as nontechnical electives including techniques, quantitative theories of biomedical engineering with emphasis the humanities. For most of these biomedical engineering, data analysis, on the integration of principles of sequences, the students may choose and independent design of biomedical biomedical engineering, quantitative from two or more tracks. If there is a engineering experiments, in parallel to analysis of physiology, and experimental question regarding the acceptability of a the Biomedical engineering I & II and quantification and measurements of course as a nontechnical elective, please Quantitative physiology I & II courses. In biomedical systems. The common consult the approved listing of courses addtion, all students must take BMEN core biomedical engineering curriculum beginning on page 11 or contact your E4110: Biostatistics for engineers. In provides a broad yet solid foundation advising dean for clarification. the senior year, students are required in biomedical engineering. The Please see the charts in this to take a two-semester capstone flexible choice of technical electives section for a specific description of design course, Biomedical engineering in the Department of Biomedical course requirements. design (BMEN E3910 and E3920), in Engineering, other departments in For students who are interested which students work within a team to the Engineering School, as well as in the biomedical engineering major, tackle an open-ended design project in in other departments in the arts and they must take E1201: Introduction to biomedical engineering. The underlying sciences allows students to broaden electrical engineering. For the computer philosophy of these core requirements their biomedical engineering education science requirement, students must is to provide our biomedical engineering to their individualized interests for a take ENGI W1006. They must take students with a broad knowledge and personalized curriculum. These qualities the two-semester BIOL C2005 and understanding of topics in the field allow the faculty to prepare students C2006: Introduction to Biology I & II in of biomedical engineering. Parallel to for acivity in all contemporary areas the second year, which gives students these studies in core courses, students of biomedical engineering. Graduates a comprehensive overview of modern are required to take flexible technical of the program are equipped for biology from molecular to organ system elective courses (21 points) to obtain an employment in the large industrial levels. In addition, all students must take in-depth understanding of their chosen sector devoted to health care, which APMA E2101: Introduction to applied interests. A technical elective is defined includes pharmaceuticals, medical mathematics in their second year. as a 3000-level or above course taught devices, artificial organs, prosthetics in SEAS or 3000-level or above courses and sensory aids, diagnostics, medical Third and Fourth Years in biology, chemistry, or biochemistry. instrumentation, and medical imaging. The biomedical engineering programs At least 15 points (five courses) of Graduates also accept employment at Columbia at all levels are based these technical electives must have in oversight organizations (FDA, on engineering and biological engineering content, while at least two NIH, OSHA, and others), medical fundamentals. This is emphasized in of the five courses have to be from the centers, and research institutes. They our core requirements. All students Department of Biomedical Engineering. are prepared for graduate study in must take the two-semester The curriculum prepares students who biomedical engineering and several introduction to biomedical engineering wish to pursue careers in medicine related areas of engineering and the course, BMEN E3010 and E3020: by satisfying most requirements in the health sciences. Students can meet Biomedical engineering I & II, which pre-medical programs with no more entrance requirements for graduate provide a broad yet solid foundation than three additional courses. Some of training in the various allied health in the biomedical engineering these additional courses may also be professions. No more than three discipline. In parallel, all students counted as nonengineering technical additional courses are required to take the two-semester Quantitative electives. Please see the course tables satisfy entrance requirements for most physiology, I and II sequence (BMEN for schedules leading to a bachelor’s U.S. medical schools. E4001-E4002), which is taught by degree in biomedical engineering. All biomedical engineering students biomedical engineering faculty and It is strongly advised that students take required courses during the specific are expected to register for nontechnical emphasizes quantitative applications of term that they are designated in the electives, both those specifically required engineering principles in understanding course tables, as scheduling conflicts by the School of Engineering and biological systems and phenomena may arise if courses are taken out of Applied Science and those needed to from molecular to organ system levels. sequence.

engineering 2014–2015 Technical Elective Requirements a. Department of Applied Physics and BIOMECHANICS 67 Students are required to take at least Applied Mathematics BMEN E3100: Mechanics of fluids (3) 48 points of engineering content course b. Department of Computer Science EMEN E3105: Mechanics (4) work toward their degree. The 48-point c. Department of Industrial MECE E3113: Mechanics of solids (3) requirement is a criterion established Engineering and Operations MECE E3301: Thermodynamics (3) BMEN E3320: Fluid biomechanics (3) by ABET. Taking into consideration the Research BMEN E4300: Solid biomechanics (3) number of engineering content points d. Program of Materials Science and BMEN E4340: Biomechanics of cells (3) conferred by the required courses Engineering of the BME curriculum, a portion of technical electives must be clearly Once 48 points of engineering BIOSIGNALS AND BIOMEDICAL IMAGING engineering in nature (Engineering content are satisfied, students may ELEN E3810: Signals and systems (3.5) Content Technical Electives), specifically choose any course above the 3000 BMEN E4410: Ultrasound imaging (3) BMEN E4420: Biosignal process and modeling (3) as defined below: level in Columbia Engineering as well as BMEN E4430: Principles of MRI (3) biology, chemistry, and biochemistry as ELEN E4810: Digital signal processing (3) 1. Technical elective courses with technical electives. BMEN E4894: Biomedical imaging (3) sufficient engineering content that The accompanying charts describe the BMEN E4898: Biophotonics (3) can count toward the 48 units of eight-semester degree program schedule engineering courses required for of courses leading to the bachelor’s NEURAL ENGINEERING ABET accreditation: degree in biomedical engineering. ELEN E3810: Signals and systems (3.5) The undergraduate Biomedical a. All 3000-level or higher courses BMEB W4020: Computational neuroscience: Engineering program is designed in the Department of Biomedical circuits in the brain (3) to provide a solid biomedical BMEE E4030: Neural control engineering (3) Engineering, except BMEN E4010, engineering curriculum through its BMEN E4420: Biosignal process and modeling (3) E4103, E4104, E4105, E4106, core requirements while providing BMEN E4430: Principles of MRI (3) E4107, and E4108. (Note that only flexibility to meet the individualized ELEN E4810: Digital signal processing (3) 3 points of BMEN E3998 may be interests of the students. The following BMEN E4894: Biomedical imaging (3) counted toward technical elective are suggested sample courses for degree requirements.) GENOMICS AND SYSTEMS BIOLOGY b. All 3000-level or higher courses various topic areas that students may ELEN E3810: Signals and systems (3.5) in the Department of Mechanical consider. Note that students are not ECBN E4060: Introduction to genomic information Engineering, except MECE limited to these choices. All students are encouraged to design their own science and technology (3) E4007: Creative engineering and CHBM E4321: The genome and the cell (3) educational paths through flexible entrepreneurship BMEN E4420: Biosignal process and modeling (3) c. All 3000-level or higher courses technical electives while meeting the CHEN E4700: Principles of genomic technologies in the Department of Chemical following requirements: (1) courses (3) Engineering, except CHEN E4020: must be at the 3000-level or above; (2) CHEN E4760: Genomics sequence laboratory (3) Safeguarding intellectual and five of the seven electives must meet CHEN E4800: Protein engineering (3) business property the above criteria to be considered d. All 3000-level or higher engineering content; and (3) two of the QUANTITATIVE BIOLOGY courses in the Department of seven electives must be biomedical BMEN E3320: Fluid biomechanics (3) Electrical Engineering, except engineering courses. To help students BMEB W4020: Computational neuroscience: EEHS E3900: History of choose their electives, the following circuits in the brain (3) telecommunications: from the suggested sample curricula in various ECBN E4060: Introduction to genomic information telegraph to the Internet interest fields in biomedical engineering science and technology (3) BIOL W4070: The biology and physics of single e. All 3000-level or higher courses are provided. Students do not need to molecules (3.5) in the Civil Engineering and follow them rigidly and may substitute BMEN E4300: Solid biomechanics (3) Engineering Mechanics program, other courses, provided they meet the APMA E4400: Introduction to biological modeling except CIEN E4128, E4129, requirements above. (3) E4130, E4131, E4132, E4133, CHEN E4650: Biopolymers (3) E4134, E4135, E4136, and CELL AND TISSUE ENGINEERING E4140 BIOINDUCTIVE AND BIOMIMETIC MATERIALS f. All 3000-level or higher courses CHEM C3443: Organic chemistry I (3.5) CHEM C3444: Organics chemistry II (3.5) CHEM C3443: Organic chemistry I (3.5) in the Earth and Environmental BMCH E3500: Biological transport process (3) BMCH E3500: Biological transport process (3) Engineering program BMEN E4501: Tissue engineering I (3) BMEN E4501: Tissue engineering I (3) BMEN E4502: Tissue engineering II (3) BMEN E4502: Tissue engineering II (3) 2. Courses from the following BMEN E4210: Thermodynamics of biological CHEN E4620: Introduction to polymers and soft departments are not allowed to systems (3) materials (3) count toward the required 48 units of BMEN E4550: Micro- and nanostructures in CHEN E4640: Polymer surface and interface (3) engineering courses: cellular engineering (3) CHEN E4800: Protein engineering (3)

engineering 2014–2015 68 BIOMATERIALS interest. In addition, sufficient knowledge Curriculum and Exam CHEM C3443: Organic chemistry I (3.5) is acquired in other areas to facilitate Requirements BMCH E3500: Biological transport process (3) broad appreciation of problems and BMEN E4300: Solid biomechanics (3) effective collaboration with specialists Master’s Degree BMEN E4301: Structure, mechanics, and from other scientific, medical, and In consultation with an appointed faculty adaptation of bone (3) engineering disciplines. The Department BMEN E4501: Tissue engineering I (3) adviser, M.S. students should select of Biomedical Engineering offers a BMEN E4502: Tissue engineering II (3) a program of 30 points of credit of ELEN E4944: Principles of device microfabrication graduate program leading to the Master graduate courses (4000 level or above) (3) of Science degree (M.S.), the Doctor appropriate to their career goals. This of Philosophy degree (Ph.D.), and the BIOMEMS AND NANOTECHNOLOGY program must include the course in Doctor of Engineering Science degree computational modeling of physiological MECE E3100: Mechanics of fluids (3) (Eng.Sc.D.). Applicants who have a EMEN E3105: Mechanics (4) systems (BMEN E6003); two semesters Master of Science degree or equivalent MECE E3113: Mechanics of solids (3) of BMEN E9700: Biomedical engineering may apply directly to the doctoral degree MSAE E4090: Nanotechnology (3) seminar; at least four other biomedical MECE E4212: Microelectromechanical systems (3) program. All applicants are expected engineering courses; and at least one MEBM E4550: Micro- and nanostructures in cellular to have earned the bachelor’s degree graduate-level mathematics course engineering (3) in engineering or in a cognate scientific (excluding statistics). Up to 6 credits of BMEN E4590: BioMEMS: cellular and molecular program. The Graduate Record Exam- Master’s Research BMEN E9100 may applications (3) ination (General Test only) is required of be taken to fulfill degree requirements. all applicants. Students whose bachelor’s Students with deficiency in physiology ROBOTICS AND CONTROL OF BIOLOGICAL degree was not earned in a country course work are required to take the SYSTEMS where English is the dominant spoken BMEN E4001-E4002 sequence before MECE E3100: Mechanics of fluids (3) language are required to take the TOEFL taking BMEN E6003. Candidates must EMEN E3105: Mechanics (4) test. In addition, for the doctoral program, achieve a minimum grade-point average MECE E3113: Mechanics of solids (3) the individual tracks require applicants of 2.5. A thesis based on experimental, BMEE E4030: Neural control engineering (3) to have taken the following foundation computational, or analytical research MECE E4431: Space vehicle dynamics and courses: is optional and may be counted in lieu controls (3) of 6 points of course work. Students MEBM E4439: Modeling and identification of • Biomechanics: One year of biology dynamic systems (3) wishing to pursue the Master’s Thesis and/or physiology, solid mechanics, MECE E4602: Introduction to robotics (3) option should register for BMEN E9100 statics and dynamics, fluid mechanics, Master’s Research and consult with ordinary differential equations. their BME faculty adviser. PRE-MED AND PRE-HEALTH PROFESSIONAL • Cell and Tissue Engineering: One MECE E3100: Mechanics of fluids (3) year of biology and/or physiology, Doctoral Degree EMEN E3105: Mechanics (4) one year of organic chemistry or Doctoral students must complete MECE E3113: Mechanics of solids (3) biochemistry with laboratory, fluid a program of 30 points of credit BMEN E3320: Fluid biomechanics (3) mechanics, rate processes, ordinary CHEM C3443: Organic chemistry I (3.5) beyond the M.S. degree. The core differential equations. CHEM C3444: Organic chemistry II (3.5) course requirements (9 credits) for the BMEN E4300: Solid biomechanics (3) • Biosignals and Biomedical Imaging: doctoral program include the course in One year of biology and/or physiology computational modeling of physiological and/or biochemistry. Linear algebra, systems (BMEN E6003), plus at least To meet entrance requirements of most ordinary differential equations, Fourier two graduate mathematics courses U.S. medical schools, students will analysis, digital signal processing. (excluding statistics). If BMEN E6003 or need to take CHEM C3543 Organic a graduate level mathematics course chemistry laboratory (3), PHYS C1493: Applicants lacking some of these has already been taken for the master’s Introduction to experimental physics courses may be considered for degree, a technical elective can be (3), and PSYC W1001: The science of admission with stipulated deficiencies used to complete the core course psychology (3) as well. that must be satisfied in addition to the requirements. Students must register for requirements of the degree program. BMEN E9700: Biomedical engineering Graduate Programs Columbia Engineering does not admit seminar and for research credits during students holding the bachelor’s degree The graduate curriculum in biomedical the first two semesters of doctoral study. directly to doctoral studies; admission engineering is track free at the master’s Remaining courses should be selected is offered either to the M.S. program or level while at the doctoral level, it in consultation with the student’s faculty to the M.S. program/doctoral track. The consists of three tracks: biomechanics, adviser to prepare for the doctoral Department of Biomedical Engineering cell and tissue engineering, and qualifying examination and to develop also admits students into the 4-2 biosignals and biomedical imaging. expertise in a clearly identified area of program, which provides the opportunity Initial graduate study in biomedical biomedical engineering. for students holding a bachelor’s degree engineering is designed to expand the All graduate students admitted to from certain physical sciences to receive student’s undergraduate preparation the doctoral degree program must the M.S. degree after two years of study in the direction of the concentration of satisfy the equivalent of two semesters’ at Columbia.

engineering 2014–2015 69 biomedical engineering program: first and second Years (Class of 2015–2016)

Semester i Semester iI Semester iII Semester iV

mathematics MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) MATH V1202 (3)

physics C1401 (3) C1402 (3) C1403 (3) (three tracks, C1601 (3.5) C1602 (3.5) C2601 (3.5) choose one) C2801 (4.5) C2802 (4.5)

C1403 (3.5) C1404 (3.5) C3443 (3.5) chemistry and Lab C1500 (3) either semester (three tracks, choose one) C1604 (3.5) C2507 (3) C3443 (3.5) C3045 (3.5) C3046 (3.5), C2507 (3)

english C1010 (3) composition (three tracks, Z1003 (0) C1010 (3) choose one) Z0006 (0) Z1003 (0) C1010 (3)

computer COMS W1005 (3) MATLAB (in semester I or III) science

physical C1001 (1) C1002 (1) education

THE ART OF ENGI E1102 (4) either semester ENGINEERING

HUMA C1002, COCI C1102, HUMA C1001, HUMA W1121 (3) or Global Core (3–4) nontechnical COCI C1101, requirements or W1123 (3) or Global Core (3–4) ECON W1105 (4) and W1155 recitation (0)

APMA E2101 Intro. to applied math (3) ELEN E1201 Intro. to EE (3.5) ENME E3105 technical requirements Mechanics (4)

STAT W1211 (3) Intro. to statistics (either semester)

experience in teaching (one semester Doctoral Qualifying Examination grade-point average of 3.2 is required to for M.D./Ph.D. students). This may Doctoral candidates are required to register for this examination. include supervising and assisting pass a qualifying examination. This undergraduate students in laboratory examination is given once a year, and Doctoral Committee and Thesis experiments, grading, and preparing it should be taken after the student has Students who pass the qualifying lecture materials to support the completed 30 points of graduate study. examination choose a faculty member teaching mission of the department. The qualifying examination consists of to serve as their research adviser. The Department of Biomedical an oral exam during which the student Each student is expected to submit Engineering is the only engineering presents an analysis of assigned a research proposal and present it department that offers Ph.D. training to scientific papers, as well as answers to a committee that consists of three M.D./Ph.D. students. These candidates to questions in topics covering applied BME faculty members. The committee are expected to complete their mathematics, quantitative biology and considers the scope of the proposed Ph.D. program within 3.5 years, with physiology, and track-specific material. A research, its suitability for doctoral otherwise the same requirements as written analysis of the assigned scientific research and the appropriateness those outlined for the Doctoral Degree papers must be submitted prior to of the research plan. The committee program. the oral exam. A minimum cumulative

engineering 2014–2015 70 biomedical engineering: Third and Fourth Years (Class of 2015–2016)

Semester V Semester VI Semester VII Semester VIII

BIOL C2005 (4) BIOL C2006 (4) Introductory biol. I Introductory biol. II BMEN E3910 (4) BMEN E3920 (4) BME design, I BME design, II Required BMEN E3810 (3) BMEN E3820 (3) Courses: BME laboratory, I BME laboratory, II all tracks BMEN E3830 (3) BMEN E4010 (2)1 BME laboratory, III Ethics for BMEs BMEN E4001 (3) BMEN E4002 (3) Quantitative physiol., I Quantitative physiol., II

nontech 0–3 points 3 points 0–3 points 3 points electives

BMEN E2500 (0) BMEN E4501 (3) BMEN E4502 (3) BMCH E3500 (3) cell and BMEN E4210 (4) Tissue eng., I Tissue eng., II tissue Biol. transport. proc. engineering2 Thermo. biol. sys. Technical elective (6) Technical elective (3) MSAE E3103 (3) Elements of mat. sci.

ENME E3113 (3) Mech. of solids BMEN E2300 (0) BMEN 4300 (3) BMEN E3320 (3) Solid biomech. biomechanics3 MECE E3301 (3) MECE E3100 (3) Fluid biomech. Thermodynamics Mech. of fluids Technical elective (3) Technical elective (6)

ELEN E4810 (3) Dig. sig. processing

track-s p ecific c o urses BMEN E4410 (3) Princ. Ultrasound BMEN E2400 (0) BMEN E4894 (3) biosignals BMEN E4420 (3) or Biomed. imaging and Biosig. proc. and BMEN E4898 (3) biomedical ELEN E3801 (3.5) 4 modeling Biophotonics imaging Signals and systems BMEN E4430 (3) Principles of MRI Technical elective (3) Technical elective (3)

total points 16–17 16 19 15

1 BMEN E4010: Ethics for biomedical engineers is a SEAS nontechnical course. 2 In the cell and tissue engineering track, of the 9 points of technical electives, at least 4.5 must be from engineering courses. 3 In the biomechanics track, of the 9 points of technical electives, at least 2.5 points must be from engineering courses. 4 In the imaging track, core requirements satisfy the 48 points of engineering content.

may approve the proposal without appointment in another department Courses in Biomedical reservation or may recommend or school or university. Every doctoral Engineering modifications. In general, the student candidate is required to have had is expected to submit his/her research accepted at least one first-author BMEN E1001x Engineering in medicine 3 pts. Lect: 3. Professors Hung, Konofagou, proposal after five semesters of full-length paper for publication in and Mow. doctoral studies. In accordance with a peer-reviewed journal prior to The present and historical role of engineering regulations of the Graduate School recommendation for award of the in medicine and health care delivery. of Arts and Sciences, each student degree. Engineering approaches to understanding is expected to submit a thesis and organismic and cellular function in living defend it before a committee of five systems. Engineering in the diagnosis and faculty, one of whom holds primary treatment of disease. Medical imaging, medical

engineering 2014–2015 71 biomedical engineering program: first and second Years (CLass 2017 and beyond)

Semester i Semester iI Semester iII Semester iV

mathematics MATH V1102 (3) MATH V1201 (3) MATH V1202 (3)

physics C1401 (3) C1402 (3) C1403 (3) (three tracks, C1601 (3.5) C1602 (3.5) C2601 (3.5) choose one) C2801 (4.5) C2802 (4.5)

C1403 (3.5) C1404 (3.5) chemistry C1500 (3) (or semester 1) (three tracks, choose one) C1604 (3.5) C2507 (3) C3045 (3.5) C3046 (3.5), C2507 (3)

english C1010 (3) composition (or any semester)

computer ENGI W1006 (3) science (or semester II)

physical C1001 (1) C1002 (1) education1

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

HUMA C1002, COCI C1102, HUMA C1001, HUMA W1121 (3) or Global Core (3–4) nontechnical COCI C1101, requirements1 or W1123 (3) or Global Core (3–4) ECON W1105 (4) and W1155 recitation (0)

ELEN E1201 APMA E2101 (3) Intro. to EE (3.5) Intro. to applied math technical requirements BIOL C2005 BIOL C2006 (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 devices: diagnostic and surgical instruments, BMEN E2400x or y Biosignals and biomedical sophomore year if they choose the cell and tissue drug delivery systems, prostheses, artificial imaging track engineering track. organs. Medical informatics and organization 0 pts. Professor Morrison. BMEN E3010x Biomedical engineering, I of the health care system. Current trends in Rising juniors (class of 2015–2016) are required 3 pts. Lect: 3. Not offered in 2014–2015 biomedical engineering research. to register for this course in the spring of their Prerequisites: BIOL C2005 and C2006, or sophomore year if they choose the biosignals and BMEN E2300x or y Biomechanics track instructor’s permission. Corequisites: BMEN 0 pts. Professor Morrison. biomedical imaging track. E4001, BMEN E3810. Various concepts within Rising juniors (class of 2015–2016) are required BMEN E2500x or y Cellular and tissue the field of biomedical engineering, foundational to register for this course in the spring of their engineering track knowledge of engineering methodology applied sophomore year if they choose the biomechanics 0 pts. Professor Morrison. to biological and/or medical problems through track. Rising juniors (class of 2015-2016) are required modules in biomechanics, biomaterials, and cell to register for this course in the spring of their and tissue engineering.

engineering 2014–2015 72 biomedical engineering: Third and Fourth Years (Class 2017 and Beyond)

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 (3) Technical elective (3)1 Biostat. for engineers

nontech 3 points 3 points 3 points electives

total points 15 15 16 13

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

BMEN E3020x Biomedical engineering, II BMCH E3500x Biological transport and BMEN E3830x Biomedical engineering 3 pts. Lect: 3. Not offered in 2014–2015 rate processes laboratory, III Prerequisites: BIOL C2005 and C2006, or 3 pts. Lect: 3. Professor Vunjak-Novakovic. 3 pts. Lab: 4. Professor Kyle. instructor’s permission. Corequisites: BMEN Prerequisites: CHEM C3443, APMA E2101. Experimental design. Cell adhesion, membrane E4002, BMEN E3820. Various concepts within Corequisites: BIOL C2005. Convective and transport, osmosis, ultrasound, design of the field of biomedical engineering, foundational diffusive movement and reaction of molecules cell encapsulation and drug delivery system, knowledge of engineering methodology applied in biological systems. Kinetics of homogeneous respiratory impedance. Selected clinical to biological and/or medical problems through and heterogeneous reactions in biological demonstrations: body compositions, magnetic modules in biomechanics, bioinstrumentation, and environments. Mechanisms and models of resonance imaging, echocardiography, blood biomedical imaging. transport across membranes. Convective diffusion pressure. with and without chemical reaction. Diffusion in BMEN E3910x-E3920y Biomedical engineering ECBM E3060x Introduction to genomic restricted spaces. Irreversible thermodynamic information science and technology approaches to transport and reaction in biological design, I and II 3 pts. Lect: 3. Professor Varadan. systems. 4 pts. Lect: 1. Lab: 3. Professor Kyle. Introduction to the information system paradigm of A two-semester design sequence to be taken in molecular biology. Representation, organization, BMEN E3810x Biomedical engineering the senior year. Elements of the design process, structure, function and manipulation of the laboratory, I with specific applications to biomedical engineering: biomolecular sequences of nucleic acids and 3 pts. Lab: 4. Professor Kyle. concept formulation, systems synthesis, design proteins. The role of enzymes and gene regulatory Statistical analysis of experimental measurements: analysis, optimization, biocompatibility, impact elements in natural biological functions as well normal distribution, test of significance, linear on patient health and comfort, health care costs, as in biotechnology and genetic engineering. regression, correlation, error analysis and regulatory issues, and medical ethics. Selection Recombination and other macromolecular propagation. MATLAB programming, EKG signal and execution of a project involving the design processes viewed as mathematical operations with acquisition and processing, microscopy, cell of an actual engineering device or system. counting and scaffold encapsulation, mechanical Introduction to entrepreneurship, biomedical start- simulation and visualization using simple computer testing of linear and nonlinear biomaterials. ups, and venture capital. Semester I: statistical programming. This course shares lectures with analysis of detection/classification systems ECBM E4060, but the work requirements differ BMEN E3820y Biomedical engineering (receiver operation characteristic analysis, logistic somewhat. laboratory, II regression), development of design prototype, 3 pts. Lab: 4. Professor Kyle. BMEN E3320y Fluid biomechanics need, approach, benefits and competition analysis. Statistical analysis of experimental measurements: 3 pts. Lect: 3. Professor Elad. Semester II: spiral develop process and testing, analysis of variance, power analysis. Circuit Prerequisite: APMA E2101. The principles of iteration and refinement of the initial design/ implementation of nerve conduction, alginate bead continuum mechanics as applied to biological prototype, and business plan development. A lab formation, mechanical testing and optical strain fluid flows and transport. Course covers fee of $100 each is collected. analysis, galvanotaxis, image segmentation and continuum formulations of basic conservation analysis of cells, computer aided design, library BMEN E3998x or y Projects in biomedical laws, Navier-Stokes equations, mechanics of resources. engineering arterial and venous blood flow, blood rheology 1–3 pts. Hours to be arranged. Members of the and non-Newtonian properties, flow and transport faculty. in the microcirculation, oxygen diffusion, capillary Independent projects involving experimental, filtration. theoretical, computational, or engineering design

engineering 2014–2015 work. May be repeated, but no more than 3 points BMEE E4030x Neural control engineering BMEN E4105x Anatomy of the extremities 73 of this or any other projects or research course 3 pts. Lect: 3. Professor Wang. 2 pts. Lect: 2. Professor April. may be counted toward the technical elective Prerequisites: ELEN E3801. Topics include: Prerequisite: Graduate standing in Biomedical degree requirements as engineering technical basic cell biophysics, active conductance and Engineering. This course is designed for the electives. the Hodgkin-Huxley model, simple neuron Biomedical Engineering graduate student models, ion channel models and synaptic interested in acquiring in-depth knowledge of BMEN E4000x Special topics models, statistical models of spike generation, anatomy relevant to his/her doctoral research. 3 pts. Lect: 3. Professor Morrison. Wilson-Cowan model of cortex, large-scale Lectures and tutorial sessions may be taken Additional current topics in biomedical electrophysiological recording methods, with or without the associated laboratory (BMEN engineering taught by regular or visiting sensorimotor integration and optimal state faculty. The same subject matter is not usually E4106). estimation, operant conditioning of neural considered in different years. activity, nonlinear modeling of neural systems, BMEN E4106x Anatomy laboratory: BMEN E4001x Quantitative physiology, I: cells sensory systems: visual pathway and extremities and molecules somatosensory pathway, neural encoding 2 pts. Lab: 2. Professor April. 3 pts. Lect: 3. Professor Kam. model: spike triggered average (STA) and spike Prerequisites: Graduate standing in Biomedical Prerequisites: BIOL C2005 and C2006. triggered covariance (STC) analysis, neuronal Engineering. Corequisites: BMEN E4105. Corequisites: BMEN E3010 and E3810. response to electrical micro-stimulation, DBS BMEN E4107x Anatomy of the head and neck Physiological systems at the cellular and molecular for Parkinson’s disease treatment, motor neural 2 pts. Lect: 2. Professor April. level are examined in a highly quantitative context. prostheses, and sensory neural prostheses. Prerequisite: Graduate standing in Biomedical Topics include chemical kinetics, molecular binding Engineering. This course is designed for the ECBM E4060x Introduction to genomic and enzymatic processes, molecular motors, Biomedical Engineering graduate student information biological membranes, and muscles. interested in acquiring in-depth knowledge of 3 pts. Lect: 3. Professor Varadan. anatomy relevant to his/her doctoral research. BMEN E4002y Quantitative physiology, II: Prerequisites: None. Introduction to the Lectures and tutorial sessions may be taken with or organ systems information system paradigm of molecular biology. without the associated laboratory (BMEN E4108). 3 pts. Lect: 3. Professor Morrison. Representation, organization, structure, function Prerequisites: BIOL C2005 and C2006. and manipulation of the biomolecular sequence of BMEN E4108x Anatomy laboratory: head Corequisites: BMEN E3020, E3820. Students are nucleic acids and proteins. The role of enzymes and neck introduced to a quantitative, engineering approach and gene regulatory elements in natural biological 2 pts. Lab: 2. Professor April. to cellular biology and mammalian physiology. functions as well as in biotechnology and Prerequisites: Graduate standing in Biomedical Beginning with biological issues related to the cell, genetic engineering. Recombination and other Engineering. Corequisites: BMEN E4107. the course progresses to considerations of the macromolecular processes viewed as mathematical BMEN E4110x Biostatistics for engineers major physiological systems of the human body operations with simulation and visualization using 3 pts. Lect: 3. Not offered in 2014–2015. (nervous, circulatory, respiratory, renal). simple computer programming. Prerequisites: MATH V1202 and APMA E2101. BMEN E4010y Ethics for biomedical engineers ECBM E4090x or y Brain computer interfaces Fundamental concepts of probability and 2 pts. Lect: 2. Professor Loike. (BCI) laboratory statistics applied to biology and medicine. Prerequisite: senior status in biomedical 3 pts. Lect: 2. Lab: 3. Professor Mesgarani. Probability distributions, hypothesis testing and engineering or the instructor’s permission. Prerequisite: ELEN E3801. Hands-on experience inference, summarizing data and testing for Covers a wide range of ethical issues expected to with basic neural interface technologies. trends. Signal detection theory and the receiver confront graduates as they enter the biotechnology Recording EEG (electroencephalogram) signals operator characteristic. Lectures accompanied industry, research, or medical careers. Topics vary using data acquisition systems (noninvasive by data analysis assignments using MATLAB and incorporate guest speakers from Physicians scalp recordings). Real-time analysis and as well as discussion of case studies in and Surgeons, Columbia Law School, Columbia monitoring of brain responses. Analysis of biomedicine. College, and local industry. intention and perception of external visual and BMEN E4150x The cell as a machine BMEB W4020x Computational neuroscience: audio signals. 3 pts. Lect: 3. Professors Sheetz and Kam. circuits in the brain BMEN E4103x Anatomy of the thorax and Prerequisite: MATH V1101 or equivalent. 3 pts. Lect: 3. Professor Lazar. Corequisites: One semester of BIOL C2005 Prerequisite: ELEN E3801 or BIOL W3004. The abdomen 2 pts. Lect: 2. Professor April. or BIOC C3501, and one semester of PHYS biophysics of computation: modeling biological C1401 or equivalent. Cells as complex micron- Prerequisite: Graduate standing in Biomedical neurons, the Hodgkin-Huxley neuron, modeling sized machines, basic physical aspects of cell Engineering. This course is designed for the channel conductances and synapses as components (diffusion, mechanics, electrostatics, Biomedical Engineering graduate student memristive systems, bursting neurons and central hydrophobicity), energy transduction (motors, interested in acquiring in-depth knowledge of pattern generators, I/O equivalence and spiking transporters, chaperones, synthesis complexes), anatomy relevant to his/her doctoral research. neuron models. Information representation and basic cell functions. Biophysical principles, Lectures and tutorial sessions may be taken neural encoding: stimulus representation with feedback controls for robust cell function, with or without the associated laboratory (BMEN time encoding machines, the geometry of time adaptation to environmental perturbations. encoding, encoding with neural circuits with E4104). feedback, population time encoding machines. BMEN E4210y Thermodynamics of biological BMEN E4104x Anatomy laboratory: thorax Dendritic computation: elements of spike processing systems and abdomen and neural computation, synaptic plasticity and 4 pts. Lect: 4. Professor Sia. 2 pts. Lect: 2. Professor April. learning algorithms, unsupervised learning and Prerequisites: CHEM C1404 and MATH Prerequisites: Graduate standing in Biomedical spike time-dependent plasticity, basic dendritic V1202. Corequisite: BIOL C2005 or equivalent. Engineering. Corequisites: BMEN E4103. integration. Projects in MATLAB. Introduction to the thermodynamics of biological systems, with a focus on connection microscopic molecular properties to macroscopic states. Both classical and statistical thermodynamics are

engineering 2014–2015 74 applied to biological systems; phase equilibria, and intracellular signal transduction will be used questions on specific data sets in modalities chemical reactions, and colligative properties. to illustrate switching of intracellular processes, such as ECG, EEG, MEG, ultrasound. Lectures Topics in modern biology, macromolecular behavior transient and permanent gene activation, and cell accompanied by data analysis assignments using in solutions and interfaces, protein-ligand binding, commitment, development, and death. MATLAB. and the hydrophobic effect. BMEN E4340x Biomechanics of cells BMEN E4430x Principles of magnetic BMEN E4300y Solid biomechanics 3 pts. Lect: 3. Not offered in 2014–2015. resonance imaging 3 pts. Lect: 3. Professor Jacobs. Prerequisites: BMEN E3320 and BMEN E4300 or 3 pts. Lect: 3. Professor Kangarlu. Prerequisites: ENME-MECE E3105 and ENME equivalents. Survey of experiments and theoretical Prerequisites: PHYS C1403 and APMA E2101, or E3113. This course introduces applications of analyses of the mechanical behavior of individual instructor’s permission. Fundamental principles continuum mechanics to the understanding of living nonmuscle cells. Emphasis on quantitative of Magnetic Resonance Imaging (MRI), including various biological tissues properties. The structure, analytic description using continuum mechanics the underlying spin physics and mathematics function, and mechanical properties of various and molecular level theory from the standpoint of image formation with an emphasis on the tissues in biological systems, such as blood of statistical mechanics and mechanical models. application of MRI to neuroimaging, both vessels, muscle, skin, brain tissue, bone, tendon, Mechanics of erythrocytes, leukocytes, endothelial anatomical and functional. The course examines cartilage, ligaments, etc., are examined. The cells, and fibroblasts; models of aggregation, both theory and experimental design techniques. focus is on the establishment of basic governing adhesion, locomotion, amoeba motility, cell division mechanical principles and constitutive relations for and morphogenesis; molecular level models of MEBM E4439x Modeling and identification of each tissue. Experimental determination of various actin, myosin, microtubules, and intermediate dynamic systems tissue properties is introduced and demonstrated. filaments and relation to mechanical properties 3 pts. Lect: 3. Professor Chbat. The important medical and clinical implications of cells and cytoskeleton. Alternative models of Prerequisites: APMA E2101, ELEN E3801 tissue mechanical behavior are emphasized. cytoskeletal mechanics, foam theory, tensegrity. or corequisite EEME E3601, or instructor’s Analysis of experimental techniques including permission. Generalized dynamic system modeling BMEN E4301x Structure, mechanics, and micropipette studies, optical and magnetic and simulation. Fluid, thermal, mechanical, diffusive, adaptation of bone cytometry, and nanoindentation. electrical, and hybrid systems are considered. 3 pts. Lect: 3. Not offered in 2014–2015. Nonlinear and high order systems. System Introduction to structure, physiology, and BMEE E4400x Wavelet applications in identification problem and Linear Least Squares biomechanics of bone. Structure, function, biomedical image and signal processing method. State-space and noise representation. and physiology of skeletal bones; linear elastic 3 pts. Lect: 3. Not offered in 2014–2015. Kalman Filter. Parameter estimation via prediction- properties of cortical and trabecular bone; Prerequisite: APMA E2101 or E3101 or equivalent. error and subspace approaches. Iterative and anisotropy and constitutive models of bone tissue; An introduction to methods of wavelet analysis bootstrap methods. Fit criteria. Wide applicability: failure and damage mechanics of bone; bone and processing techniques for the quantification medical, energy, others. MATLAB and Simulink adaptation and fracture healing; experimental of biomedical images and signals. Topics include: environments. determination of bone properties; and morphological frames and overcomplete representations, analysis of bone microstructure. multiresolution algorithms for denoising and image BMEN E4440y Physiological control systems restoration, multiscale texture segmentation 3 pts. Lect: 3. Professor Chbat. BMEN E4305y Cardiac mechanics and classification methods for computer aided Prerequisites: MEBM E4439 and APMA E2101, 3 pts. Lect: 3. Not offered in 2014–2015. diagnosis. or instructor’s permission. Fundamentals of Prerequisites: BMEN E3310 and BMEN E3320 or time and frequency domains analyses and equivalents. Cardiac anatomy, passive myocardial BMEN E4410y Ultrasound in diagnostic stability. Frequency domain controller design. constitutive properties, electrical activation, imaging Cardiovascular and respiratory systems ventricular pump function, ventricular-vascular 3 pts. Lect: 3. Professor Konofagou. simulation. Endogenous control systems: coupling, invasive and noninvasive measures of Prerequisites: MATH V1202 or equivalent. Fourier baroreflex, chemoreflex, thermoregulation, regional and global function, models for predicting analysis. Physics of diagnostic ultrasound and pupillary light reflex. Open and closed loop ventricular wall stress. Alterations in muscle principles of ultrasound imaging instrumentation. physiological systems. Exogenous control properties and ventricular function resulting Propagation of plane waves in lossless medium; systems: ventilators, infusion pumps. Nonlinear from myocardial infarction, heart failure, and left ultrasound propagation through biological tissues; actuators and delayed feedback systems. Acute ventricular assist. single-element and array transducer design; disease simulation and clinical decision support pulse-echo and Doppler ultrasound instrumentation, in the intensive care unit. MATLAB and Simulink CHBM E4321y The genome and the cell performance evaluation of ultrasound imaging environments utilized. 3 pts. Lect: 3. Not offered in 2014–2015. systems using tissue-mimicking phantoms, Prerequisites: BIOL C2005 and MATH E1210. The ultrasound tissue characterization; ultrasound BMEN E4450y Dental and craniofacial tissue utility of genomic information lies in its capacity to nonlinearity and bubble activity; harmonic imaging; engineering predict the behavior of living cells in physiological, acoustic output of ultrasound systems; biological 3 pts. Lect: 3. Not offered in 2014–2015. developmental, and pathological situations. The effects of ultrasound. Prerequisites: MSAE E3103, BMEN E4210, E4501, effect of variations in genome structure between or equivalent. Principles of dental and craniofacial individuals within a species, including those BMEN E4420y Biomedical signal processing bioengineering, periodontal tissue engineering: deemed healthy or diseased, and among species, and signal modeling beyond guided tissue regeneration, craniofacial can be inferred statistically by comparisons of 3 pts. Lect: 3. Professor Sajda. regeneration by stem cells and engineered sequences with behaviors and mechanistically, by Prerequisites: ELEN E3801 and either APMA scaffolds, biomaterials: Engineering approaches in studying the action of molecules whose structure E2101 or E3101 or instructor’s permission. tissue regeneration, bone biology and development: is encoded within the genome. This course Fundamental concepts of signal processing instructive cues for tissue engineers. examines known mechanisms that elucidate the in linear systems and stochastic processes. combined effect of environmental stimulation Estimation, detection, and filtering methods applied BMEN E4501x Tissue engineering, I: and genetic makeup on the behavior of cells to biomedical signals. Harmonic analysis, auto- biomaterials and scaffold design in homeostasis, disease states, and during regressive model, Wiener and Matched filters, 3 pts. Lect: 3. Professor Hess. development, and includes assessments of the linear discriminants, and independent components. Prerequisites: BIOL C2005-C2006; BMEN probable effect of these behaviors on the whole Methods are developed to answer concrete E4001-E4002. An introduction to the strategies and organism. Quantitative models of gene translation fundamental bioengineering design criteria in the

engineering 2014–2015 development of biomaterials and tissue engineered and hydrogen bonds are reviewed, in relation Introduction to modeling and simulation 75 grafts. Material structural-functional relationships, to the structure/properties of the body fluid. techniques, and modern biophysical techniques biocompatibility in terms of material and host Selected physiological processes are examined in such as single molecule FRET, optical responses. Through discussions, readings, and physical-chemical terms for polymers. traps, AFM, and superresolution imaging,for a group design project, students acquire an understanding molecular mechanics and BMEN E4590x BioMems: cellular and understanding of cell-material interactions and dynamics. identify the parameters critical in the design molecular applications and selection of biomaterials for biomedical 3 pts. Lect: 3. Professor Sia. BMEN E4737x Computer control of medical applications. Prerequisites: Chemistry, CHEM C3443, or instrumentation CHEN C3545 or equivalent, MATH V1201, 3 pts. Lect: 2. Lab: 1. Not offered in 2014–2015. BMEN E4502y Tissue engineering, II: BIOL W2005 and W2006. Topics include Prerequisite: Basic knowledge of the C programming biological tissue substitutes biomicroelectromechanical, microfluidic, and lab- language. Acquisition and presentation of data 3 pts. Lect: 3. Professor Hung. on-a-chip systems in biomedical engineering, with for medical interpretation. Operating principles of Prerequisites: BIOL C2005-C2006, BMEN a focus on cellular and molecular applications. medical devices: technology of medical sensors, E4001-E4002. An introduction to the strategies and Microfabrication techniques, biocompatibility, algorithms for signal analysis, computer interfacing fundamental bioengineering design criteria behind miniaturization of analytical and diagnostic and programming, interface design. Laboratory the development of cell-based tissue substitutes. devices, high-throughput cellular studies, assignments cover basic measurement technology, Topics include biocompatibility, biological grafts, microfabrication for tissue engineering, and in interfacing techniques, use of Labview software gene therapy-transfer, and bioreactors. vivo devices. instrument interrogation and control, automated ECG analysis, ultrasonic measurements, image BMEN E4540y Bioelectrochemistry BMEN E4601y Cellular electricity processing applied to X-ray images and CAT 3 pts. Lect: 3. Not offered in 2014–2015. 3 pts. Lect: 2. Lab: 1. Not offered in scans. Prerequisites: CHEM C3079 and C3443 or 2014–2015. equivalent. Application of electrochemical kinetics Bioelectricity of the cell membrane. Basis of cell BMEN E4738y Transduction and acquisition to interfacial processes occurring in biomedical resting voltage, voltage changes that lead to the of biomedical data systems. Basics of electrochemistry, electrochemical action potential and electrical oscillations used 3 pts. Lect: 2. Lab: 1. Not offered in 2014–2015. instrumentation, and relevant cell and electrophysiology in sensing systems. Laboratory includes building Data transduction and acquisition systems used in reviewed. Applications to interpretation of excitable electronic circuits to measure capacitance of biomedicine. Assembly of biotransducers and the and nonexcitable membrane phenomena, with artificial membranes and ion pumping in frog skin. analog/digital circuitry for acquiring electrocardiogram, emphasis on heterogeneous mechanistic steps. Lab required. electromyogram, and blood pressure signals. Each Examples of therapeutic devices created as a small group will develop and construct a working APBM E4650x Anatomy for physicists and result of bioelectrochemical studies. data acquisition board, which will be interfaced engineers with a signal generator to elucidate the dynamics BMEN E4550y Micro- and nanostructures in 3 pts. Lect: 3. Professors Lignelli and of timing constraints during retrieval of biodata. cellular engineering Rozenshtein. Lab required. 3 pts. Lect: 3. Not offered in 2014–2015. Prerequisite: Engineering or physics background. Prerequisites: BIOL W2005 and W2006 or A systemic approach to the study of the human BMEE E4740y Bioinstrumentation equivalent. Design, fabrication, and application of body from a medical imaging point of view: 3 pts. Lect: 1. Lab: 3. Professor Kyle. micro-/nanostructured systems for cell engineering. skeletal, respiratory, cardiovascular, digestive, and Prerequisites: ELEN E1201, COMS W1005. Recognition and response of cells to spatial urinary systems, breast and women’s issues, head Hands-on experience designing, building, and aspects of their extracellular environment. Focus and neck, and central nervous system. Lectures testing the various components of a benchtop on neural, cardiac, coculture, and stem cell are reinforced by examples from clinical two- and cardiac pacemaker. Design instrumentation systems. Molecular complexes at the nanoscale. three-dimensional and functional imaging (CT, MRI, to measure biomedical signals as well as to BMEN E4560y Dynamics of biological PET, SPECT, U/S, etc.). actuate living tissues. Transducers, signal conditioning electronics, data acquisition boards, membranes BMME E4702x Advanced musculoskeletal the Arduino microprocessor, and data acquisition 3 pts. Lect: 3. Not offered in 2014–2015. biomechanics and processing using MATLAB will be covered. Prerequisites: BIOL C2005, BMEN E4001, 3 pts. Lect: 2.5. Lab: 0.5. Professor Guo. Various devices will be discussed throughout the or equivalent. The structure and dynamics of Advanced analysis and modeling of the course, with laboratory work focusing on building biological (cellular) membranes are discussed, musculoskeletal system. Topics include an emulated version of a cardiac pacemaker. with an emphasis on biophysical properties. Topics advanced concepts of 3D segmental kinematics, include membrane composition, fluidity, lipid musculoskeletal dynamics, experimental BMEN E4750y Sound and hearing asymmetry, lipid-protein interactions, membrane measurements of joint kinematics and anatomy, 3 pts. Lect: 3. Not offered in 2014–2015. turnover, membrane fusion, transport, lipid phase modeling of muscles and locomotion, multibody Prerequisites: PHYS C1401 and MATH V1105- behavior. In the second half of the semester, joint modeling, introduction to musculoskeletal MATH V1106. Introductory acoustics, basics of students will lead discussions of recent journal surgical simulations. waves and discrete mechanical systems. The articles. mechanics of hearing—how sound is transmitted MEBM E4703y Molecular mechanics in through the external and middle ear to the inner BMEN E4570x Science and engineering of biology ear, and the mechanical processing of sound within body fluids 3 pts. Lect: 3. Professor Chbat. the inner ear. 3 pts. Lect: 3. Not offered in 2014–2015. Prerequisites: ENME E3105, APMA E2101, Prerequisites: General chemistry, organic or instructor’s permission. Mechanical CBMF W4761y Computational genomics chemistry, and basic calculus. Body fluids as a understanding of biological structures including 3 pts. Lect: 3. Professor Pe’er. dilute solution of polyelectrolyte molecules in proteins, DNA and RNA in cells and tissues. Prerequisites: Working knowledge of at least one water. Study of physical behavior as affected Force response of proteins and DNA, mechanics programming language, and some background in by the presence of ions in surrounding of membranes, biophysics of molecular motors, probability and statistics. Computational techniques environments. The physics of covalent, ionic, mechanics of protein-protein interactions. for analyzing and understanding genomic data,

engineering 2014–2015 76 including DNA, RNA, protein and gene expression quantitative analysis of selected physiological of constitutive models for biological tissues data. Basic concepts in molecular biology relevant systems from molecules to organs. Selected into existing finite element software packages. to these analyses. Emphasis on techniques from systems are analyzed in depth with an emphasis Model generation from biomedical images by artificial intelligence and machine learning. String- on modeling methods and quantitative analysis. extraction of tissue geometry, inhomogeneity and matching algorithms, dynamic programming, Topics may include cell signaling, molecular anisotropy. Element-by-element finite element hidden Markov models, expectation-maximization, transport, excitable membranes, respiratory solver for large-scale image based models neural networks, clustering algorithms, support physiology, nerve transmission, circulatory of trabecular bone. Implementation of tissue vector machines. Students with life sciences control, auditory signal processing, muscle remodeling simulations in finite element models. backgrounds who satisfy the prerequisites are physiology, data collection and analysis. MEBM E6310x-E6311y Mixture theories for encouraged to enroll. EEBM E6020y Methods of computational biological tissues, I and II BMCH E4810y Artificial organs neuroscience 3 pts. Lect: 3. Not offered in 2014–2015. 3 pts. Lect: 3. Not offered in 2014–2015. 4.5 pts. Lect: 3. Not offered in 2014–2015. Prerequisites: MECE E6422 and APMA E4200, or Analysis and design of replacements for the heart, Prerequisite: BMEB W4020. Formal methods in equivalent Development of governing equations for kidneys, and lungs. Specification and realization of computational neuroscience including methods mixtures with solid matrix, interstitial fluid, and ion structures for artificial organ systems. of signal processing, communications theory, constituents. Formulation of constitutive models for information theory, systems and control, system biological tissues. Linear and nonlinear models of BMEN E4840y Functional imaging for the identification and machine learning. Molecular fibrillar and viscoelastic porous matrices. Solutions brain models of transduction pathways. Robust adaptation to special problems, such as confined and 3 pts. Lect: 3. Lab: 1. Professor Razlighi. and integral feedback. Stimulus representation unconfined compression, permeation, indentation Prerequisites: APMA E2101, APMA E4200, ELEN and groups. Stochastic and dynamical systems and contact, and swelling experiments. E3801, or instructor’s permission. Fundamentals models of spike generation. Neural diversity and of modern medical functional imaging. In-depth BMEN E6400x Analysis and quantification of ensemble encoding. Time encoding machines and exploration of functional magnetic resonance medical images neural codes. Stimulus recovery with time decoding imaging (fMRI), arterial spin labeling (ASL), 3 pts. Lect: 3. Professor Laine. machines. MIMO models of neural computation. and positron emission tomography (PET). Novel methods of mathematical analysis Synaptic plasticity and learning algorithms. Major Human brain anatomy, physiology, and applied to problems in medical imaging. Design project(s) in MATLAB. neurophysiological bases underlying each requirements for screening protocols, treatment functional imaging. Statistical and digital signal BMEE E6030x Neural modeling and therapies, and surgical planning. Sensitivity and processing methods specific for functional image neuroengineering specificity in screening mammography and chest analysis. Final cumulative project requiring 3 pts. Lect: 3. Not offered in 2014–2015. radiographs, computer aided diagnosis systems, coding in MATLAB, Python, R, or C. Prerequisites: ELEN E3801, and either APMA surgical planning in orthopaedics, quantitative E2101 or E3101, or equivalent, or instructor’s analysis of cardiac performance, functional BMEN E4894x Biomedical imaging permission. Engineering perspective on the study magnetic resonance imaging, positron emission 3 pts. Lect: 3. Professor Hielscher. of multiple levels of brain organization, from tomography, and echocardiography data. This course covers image formation, methods of single neurons to cortical modules and systems. analysis, and representation of digital images. BMEN E6420y Advanced microscopy: Mathematical models of spiking neurons, neural Measures of qualitative performance in the context fundamentals and applications dynamics, neural coding, and biologically-based of clinical imaging. Algorithms fundamental to 3 pts. Lect: 3. Not offered in 2014–2015. computational learning. Architectures and learning the construction of medical images via methods Prerequisites: Physics C1401, C1402, C1403 principles underlying both artificial and biological of computed tomography, magnetic resonance, or C1601, C1602, C2601 or C2801, C2802, neural networks. Computational models of cortical and ultrasound. Algorithms and methods for or equivalent (general Physics sequence). processing, with an emphasis on the visual the enhancement and quantification of specific Fundamentals of techniques including confocal, system. Applications of principles in neuroengineering; features of clinical importance in each of these two-photon, atomic force and electron microscopy. neural prostheses, neuromorphic systems and modalities. Application of methods to modern biomedical biomimetics. Course includes a computer simulation imaging targets. Analysis and interpretation of BMEN E4898y Biophotonics laboratory. Lab required. microscopy data. Enrollment beyond the cap 3 pts. Lect: 3. Professor Hielscher. EEBM E6090-6099x or y Topics in must be completed using an add/drop form in Prerequisites: BMEN E4894 Biomedical computational neuroscience and consultation with class instructor. imaging, PHYS C1403 Classical and quantum neuroengineering waves, or instructor’s permission. This course BMEN E6500x Tissue and molecular 3 pts. Lect: 2. Professor Sajda. provides a broad-based introduction into the engineering laboratory Prerequisite: Instructor’s permission. Selected field of Biophotonics. Fundamental concepts of 4 pts. Lect: 1. Lab: 3. Not offered in 2014–2015. advanced topics in computational neuroscience optical, thermal, and chemical aspects of the Prerequisites: Biology BIOL C2005 and BIOL and neuroengineering. Content varies from year to light-tissue interactions will be presented. The C2006 or permission of instructor. Hands-on year, and different topics rotate through the course application of these concepts for medical therapy experiments in molecular and cellular techniques, numbers 6090-6099. and diagnostics will be discussed. The course including fabrication of living engineered tissues. includes theoretical modeling of light-tissue BMEN E6301y Modeling of biological tissues Covers sterile technique, culture of mammalian interactions as well as optical medical instrument with finite elements cells, microscopy, basic subcloning and gel design and methods of clinical data interpretation. 3 pts. Lect: 3. Not offered in 2014–2015. electrophoresis, creation of cell-seeded scaffolds, Prerequisite: MECE E6422, or ENME E6315, and the effects of mechanical loading on the BMEN E6003x Computational modeling of or equivalent. Structure-function relations and metabolism of living cells or tissues. Theory, physiological systems linear/nonlinear constitutive models of biological background, and practical demonstration for each 3 pts. Lect: 3. Professor Morrison. tissues: anisotropic elasticity, viscoelasticity, technique will be presented. Lab required. Prerequisites: BMEN E4001 and E4002 or porous media theories, mechano-electrochemical equivalent, and APMA E4200 or equivalent. models, infinitesimal and large deformations. Advanced computational modeling and Emphasis on the application and implementation

engineering 2014–2015 BMEN E6505x Advanced scaffold design and EEBM E9070y Massively parallel neural BMEN E9700x or y Biomedical engineering 77 engineering complex tissues computation seminar 3 pts. Lect: 2.5. Lab: 0.5. Professor Lu. 3 pts. Lect: 3. Professor Lazar 0 pts. Sem: 1. Professor Hess. Prerequisites: BMEN E4501 or equivalent. Prerequisites: BMEB W4020 or permission of All matriculated graduate students are required Corequisites: BMEN E4001 or E4002. Advanced instructor. Drosophila connectomics. Detailed to attend the seminar as long as they are in biomaterial selection and biomimetic scaffold description of the fruit fly’s olfactory and vision residence. No degree credit is granted. The design for tissue engineering and regenerative systems. Parallel processing on GPSs. seminar is the principal medium of communication medicine. Formulation of bio-inspired design among those with biomedical engineering interests BMEN E9100x or y Master’s research criteria, scaffold characterization and testing, within the University. Guest speakers from other 1–6 pts. Members of the faculty. and applications on forming complex tissues or institutions, Columbia faculty, and students within Candidates for the M.S. degree may conduct organogenesis. Laboratory component includes the department who are advanced in their studies an investigation of some problem in biomedical basic scaffold fabrication, characterization and in frequently offer sessions. engineering culminating in a thesis describing the vitro evaluation of biocompatibility. Group projects results of their work. No more than 6 points in this BMEN E9800x or y Doctoral research target the design of scaffolds for select tissue course may be counted for graduate credit, and instruction engineering applications. this credit is contingent upon the submission of an 3–12 pts. Members of the faculty. BMEN E8001y Current topics in acceptable thesis. A candidate for the Eng.Sc.D. degree in biomedical nanobiotechnology and synthetic biology engineering must register for 12 points of doctoral BMEN E9500x or y Doctoral research 3 pts. Lect: 3. Not offered in 2014–2015. research instruction. Registration may not be used 1–6 pts. Members of the faculty. Targeted toward graduate students; undergraduate to satisfy the minimum residence requirement for Doctoral candidates are required to make an student may participate with permission of the the degree. original investigation of a problem in biomedical instructor. Review and critical discussion of recent engineering, the results of which are presented in BMEN E9900x or y Doctoral dissertation literature in nanobiotechnology and synthetic the dissertation. 0 pts. Members of the faculty. biology. Experimental and theoretical techniques, A candidate for the doctorate in biomedical critical advances. Quality judgments of scientific engineering or applied biology may be required impact and technical accuracy. Styles of written and to register for this course in every term after the graphical communication, the peer review process. student’s course work has been completed and until the dissertation has been accepted.

engineering 2014–2015 78 Chemical Engineering 801 S. W. Mudd, MC 4721 Phone: 212-854-4453 cheme.columbia.edu

Chair George W. Flynn, Edward F. Leonard Associate Adjunct Sanat K. Kumar Higgins Professor of Ben O’Shaughnessy Professors Professors Chemistry Venkat Scott A. Banta Stanley Leshaw Department Jingyue Ju, Venkatasubramanian V. Faye McNeill Robert I. Pearlman Administrator Samuel Ruben–Peter Samuel Ruben–Peter Carlos Rosas Teresa Colaizzo G. Viele Professor of G. Viele Professor of Assistant Engineering Engineering ProfessorS Adjunct Associate Professors Jeffrey T. Koberstein, Alan C. West, Samuel Daniel Esposito Professor Jingguang G. Chen Percy K. and Vida Ruben–Peter G. Vanessa A. Ortiz Aghavni Bedrossian- Thayer Lindsley L. W. Hudson Viele Professor of Omer Professor of Chemical Professor of Chemical Electrochemistry LECTURERs Engineering Engineering Robert Bozic Christopher J. Durning Sanat K. Kumar Michael I. Hill

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

engineering 2014–2015 careers in medicine, law, management, simulation and theory of unique “living” research programs are aimed at 79 banking and finance, politics, and polymerization processes important developing methods for patterning so on. For those interested in the to synthetic polymer production and biological surfaces in order to prepare fundamentals, a career of research and biological systems; theory and simulation new biocompatible surfaces as well as teaching is a natural continuation of of irreversible polymer adsorption. to fabricate antigen/antibody and protein their undergraduate studies. Whichever arrays for diagnostic applications. path the student may choose after Genomics Engineering. Research graduation, the program offers a deep and development of novel bioanalytical Interfacial Engineering and understanding of the physical and reagents, systems, and processes using Electrochemistry. Research efforts chemical nature of things and provides chemical science, engineering principles, within the department are focused on an insight into an exploding variety and experimental biological approaches mass transfer and reaction mechanisms of new technologies that are rapidly to study problems in genomics are in electrochemical systems, and the reshaping the society we live in. actively pursued in the Department of effects that such variables have on Chemical Engineering in collaboration process design and materials properties. Current Research Activities with the Columbia Genome Center: Applications of the research program Science and Engineering of Polymers high-throughput DNA sequencing; novel include fuel cells, electrodeposition, and Soft Materials. Theoretical gene chip development and fundamental and corrosion. Both electrochemical and experimental studies of novel or understanding of the processes involved; and microscopy methods are used important macromolecules and their applying the cutting-edge genomic extensively for characterization. applications, especially surface-active technologies to study fundamental A significant numerical simulation species: ultrasonic sensor, scanning biology and for disease gene discovery. component of the research programs probe microscopy and reflectivity studies also exists. of adsorption and self-assembly of highly Biophysics and Soft Matter Physics. branched “dendrimers” at the solid- Theoretical and experimental biophysics Facilities for Teaching and liquid interface, with the aim of creating of biological soft matter: actin filament Research novel surface coatings; fluorescence growth kinetics and its role in living The Department of Chemical Engineering tracer studies of molecular level mobility cell motility; DNA hybridization, melting is continually striving to provide access to in ultrathin polymer films with the aim and unzipping; DNA microarrays in state-of-the-art research instrumentation of improving resolution in lithography; biotechnology; model gene circuits; DNA and computational facilities for its reflectivity studies and computer mobility in 2D microfluidics. Physics of undergraduate and graduate students, simulation of flexible polymer adsorption synthetic soft matter: nanoparticles in postdoctoral associates, and faculty. and the response of adsorbed polymer mesostructured polymer phases and Departmental equipment is considered to layers to imposed flows with the aim phase transitions; universal scaling be in most cases shared, which means of improving polymer processing laws in reacting polymer systems and that equipment access is usually open to operations; optical microscopy studies polymerization phenomena; polymer- all qualified individuals with a need to use and numerical simulation of microporous interface adsorption phenomena; particular instrumentation. polymer membrane formation with polymer interfacial reactions; diffusion The most extensive collection of the aim of improving ultrafiltration of particles in thin polymer films; instrumentation in the department membrane technology; synthesis and interactions of charged polymer minigels is associated with the polymer and structural characterization of bioactive with interfaces. soft matter research faculty. Faculty polymer surfaces in order to realize banded together to create a unique new in-vivo devices; contact angle, Bioinductive and Biomimetic shared-facilities laboratory, completed X-ray photoelectron spectroscopy, and Materials. The thrust of this research at the end of 2001. The shared facilities reflectivity analysis, and lattice model is to develop new strategies for the include a fully equipped polymer simulation, of responsive polymer molecular design of polymeric and soft synthesis lab with four fumes hoods, surfaces based on unique polymeric materials for biological and biomedical a 10'x16' soft wall clean room, metal “surfactants” in order to develop “smart” applications. Ongoing research pertains evaporator system, a Milligen 9050 surface-active materials; preparation and to the development of bioactive hydrogel peptide synthesizer, and polymer IR/fluorescence characterization of DNA- coatings for applications in glucose thin film preparation and substrate decorated surfaces for “recognition” sensors. The objective of the coatings is cleaning stations. Also installed are new, of DNA in solution in order to further to control the tissue-sensor interactions computer-controlled thermal analysis, medical diagnostic technologies; by incorporating cell-signaling motifs rheometric, and light-scattering setups. preparation and characterization into the hydrogel in such a manner that Specialized instrumentation for surface via TEM, AFM, and reflectivity of the hydrogel induces the formation of analysis includes an optical/laser system nanoparticle-block copolymer new vascular tissue within the surface dedicated to characterization of polymer composites with the aim of very high coating. In this fashion, the biosensor surface dynamics by Fluorescence density magnetic storage media; self- can continue to operate in vivo, even if Recovery after Photobleaching and consistent field theory of nanoparticle- there is an immune response leading to a PHI 5500 X-ray photoelectron block copolymer composites; computer fibrous encapsulation. Complementary spectrophotometer with monochromator

engineering 2014–2015 80 that is capable of angle-dependent Chemistry Department. Access to Undergraduate Program depth profiling and XPS imaging. NMR and mass spectrometry facilities is The system can also perform SIMS possible through interactions with faculty Chemical Engineering and ion scattering experiments. A members who also hold appointments The undergraduate program in chemical digital image analysis system for the in the Chemistry Department. The NMR engineering at Columbia has five formal characterization of sessile and pendant facility consists of a 500 MHz, a 400 educational objectives: drop shapes is also available for MHz, and two 300 MHz instruments that the purpose of polymer surface and are operated by students and postdocs 1. Prepare students for careers in interfacial tension measurements as after training. The mass spectrometry industries that require technical well as contact angle analysis. An X-ray facility is run by students for routine expertise in chemical engineering. reflectometer that can perform X-ray samples and by a professional mass standing wave–induced fluorescence spectrometrist for more difficult 2. Prepare students to assume measurements is also housed in the samples. The Chemistry Department leadership positions in industries new shared equipment laboratory, along also provides access to the services of that require technical expertise in with instrumentation for characterizing a glass blower and machine shop and chemical engineering. the friction and wear properties of to photochemical and spectroscopic 3. Enable students to pursue polymeric surfaces. The laboratory facilities. These facilities consist of (1) graduate-level studies in chemical also houses an infrared spectrometer two nanosecond laser flash photolysis engineering and related technical or (Nicolet Magna 560, MCT detector) instruments equipped with UV-VIS, scientific fields (e.g., biomedical or with a variable angle grazing incidence, infrared, EPR, and NMR detection; environmental engineering, materials temperature-controlled attenuated- (2) three EPR spectrometers; (3) two science). total-reflectance, transmission, and fluorescence spectrometers; (4) a single liquid cell accessories. These facilities photon counter for analysis of the 4. Provide a strong foundation for are suitable for mid-IR, spectroscopic lifetimes and polarization of fluorescence students to pursue alternative career investigations of bulk materials as well and phosphorescence; and (5) a high- paths, especially careers in business, as thin films. The laboratory also has performance liquid chromatographic management, finance, law, medicine, a UV-Vis spectrometer (a Cary 50), an instrument for analysis of polymer or education. SLM Aminco 8000 spectrofluorimeter, molecular weight and dispersity. and a high-purity water system 5. Establish in students a commitment (Millipore Biocel) used for preparation Columbia Genome Center. Because of to life-long learning and service of biological buffers and solutions. its affiliation with the Columbia Genome within their chosen profession and Facilities are available for cell tissue Center (CGC), the Department of society. culture and for experiments involving Chemical Engineering also has access biocompatibilization of materials or The expertise of chemical engineers to more than 3,000 sq. ft. of space cellular engineering. In addition, gel is essential to production, marketing, equipped with a high-throughput DNA electrophoresis apparatus is available for and application in such areas as sequencer (Amersham Pharmacia the molecular weight characterization of pharmaceuticals, high performance Biotech Mega-Bace 1000), a nucleic nucleic acids. A total-internal-reflection- materials as in the automotive and acid synthesizer (PE Biosystems 8909 fluorescence (TIRF) instrument with aerospace industries, semiconductors Expedite Nucleic Acid/Peptide Synthesis an automated, temperature-controlled in the electronics industry, paints and System), an UV/VIS spectrophotometer flow cell has been built for dedicated plastics, consumer products such as (Perkin-Elmer Lambda 40), a investigations of surface processes food and cosmetics, petroleum refining, fluorescence spectrophotometer (Jobin involving fluorescently tagged biological industrial chemicals, synthetic fibers, Yvon, Inc. Fluorolog-3), Waters HPLC, and synthetic molecules. The instrument and just about every bioengineering and and a sequencing gel electrophoresis can operate at different excitation biotechnology area from artificial organs apparatus (Life Technologies Model wavelengths (typically HeNe laser, to biosensors. Increasingly, chemical S2), as well as the facilities required 633 nm, using Cy5 labeled nucleic engineers are involved in exciting new for state-of-the-art synthetic chemistry. acids). Fluorescence is collected by technologies employing highly novel The division of DNA sequencing and a highly sensitive photomultiplier tube materials, whose unusual response at chemical biology at the Columbia and logged to a personal computer. the molecular level endows them with Genome Center consists of 6,000 sq. Because fluorescence is only excited unique properties. Examples include ft. of laboratory space and equipment in the evanescent wave region near an controlled release drugs, materials necessary for carrying out the state-of- interface, signals from surface-bound with designed interaction with in vivo the-art DNA analysis. The laboratory fluorescent species can be determined environments, “nanomaterials” for with minimal background interference has one Amersham Pharmacia Biotech electronic and optical applications, from fluorophores in bulk solution. MegaBace 1000 sequencer, three ABI agricultural products, and a host of 377 sequencers with complete 96 land others. This requires a depth and upgrades, a Qiagen 9600 Biorobot, a breadth of understanding of physical Hydra 96 microdispenser robot, and and chemical aspects of materials and standard molecular biology equipment. their production that is without parallel.

engineering 2014–2015 The chemical engineering degree The table also shows that a new areas, or perhaps to explore 81 also serves as a passport to exciting significant fraction of the junior-senior familiar subjects in greater depth, or you careers in directly related industries as program is reserved for electives, both may wish to gain experience in actual diverse as biochemical engineering, technical and nontechnical. Nontechnical laboratory research. Up to 6 points of environmental management, and electives are courses that are not CHEN E3900: Undergraduate research pharmaceuticals. Because the deep quantitative, such as those taught in project may be counted toward the and broad-ranging nature of the degree the humanities and social sciences. technical elective content. (Note that has earned it a high reputation across These provide an opportunity to pursue if more than 3 points of research are society, the chemical engineering interests in areas other than engineering. pursued, an undergraduate thesis is degree is also a natural platform from A crucial part of the junior-senior required.) which to launch careers in medicine, program is the 21-point (7 courses) The program details discussed law, management, banking and finance, technical elective requirement. Technical above apply to undergraduates who politics, and so on. Many students electives are science and/or technology are enrolled at Columbia as first-years choose it for this purpose, to have a based and feature quantitative analysis. and declare the chemical engineering firm and respected basis for a range Generally, technical electives must be major in the sophomore year. of possible future careers. For those 3000 level or above but there are a However, the chemical engineering interested in the fundamentals, a career few exceptions: PHYS C1403, PHYS program is designed to be readily of research and teaching is a natural C2601, BIOL C2005, BIOL C2006, and accessible to participants in any of continuation of undergraduate studies. BIOL W2501. The technical electives are Columbia’s Combined Plans and to The first and sophomore years subject to the following constraints: transfer students. In such cases, the of study introduce general principles guidance of one of the departmental of science and engineering and • Two technical electives must be within advisers in planning your program is include a broad range of subjects in chemical engineering (e.g., with the required (contact information for the the humanities and social sciences. designator BMCH, CHEN, CHEE, or departmental UG advisers is listed on Although the program for all engineering CHAP). the department’s website: cheme students in these first two years is to .columbia.edu). • One technical elective must be within some extent similar, there are a few Columbia’s program in chemical SEAS but taken outside of chemical important differences for chemical engineering leading to the B.S. degree engineering (that is, a course with a engineering majors. Those wishing is fully accredited by the Engineering designator other than BMCH, CHEN, to learn about, or major in, chemical Accreditation Commission of ABET. CHEE, or CHAP). engineering should take the professional elective CHEN E2100 Introduction • Two technical electives must be within Requirements for a Minor in to chemical engineering in term III, SEAS (may or may not be within Chemical Engineering taught by the Chemical Engineering chemical engineering). See page 195. Department. This course is a • Two technical electives must contain requirement for the chemical engineering Requirements for a Minor in “advanced science” course work, major. It can also possibly serve as a Biomedical Engineering technical elective for other engineering which can include chemistry, physics, Students majoring in chemical majors. Those wishing to major in biology, and certain engineering engineering who wish to include in chemical engineering should also take courses. Qualifying engineering their records a minor in biomedical ENGI E1006 Introduction to computing courses are determined by Chemical engineering may do so by taking BMEN for engineering and applied scientists Engineering Department advisers. E4001 or E4002; BIOL C2005; BMEN in term II. Chemical engineering majors At least one of these classes must E4501 and E4502; and any one of receive additional instruction in their be taken outside of SEAS (e.g., in a several chemical engineering courses junior year on the use of computational science department at Columbia; see approved by the BME Department. See methods to solve chemical engineering listing of possible courses above). also, Minor in Biomedical Engineering, problems. • At most, only one computer science page 195. In the junior-senior sequence one (COMS) class can be counted towards specializes in the chemical engineering the technical elective requirement. major. The table on page 83 spells Graduate Programs out the core course requirements, The junior-senior technical electives The graduate program in chemical which are split between courses provide the opportunity to explore engineering, with its large proportion emphasizing engineering science and new, interesting areas beyond the core of elective courses and independent those emphasizing practical and/or requirements of the degree. Often, research, offers experience in any professional aspects of the discipline. students satisfy the technical electives of the fields of departmental activity Throughout, skills required of practicing by taking courses from another SEAS mentioned in previous sections. For engineers are developed (e.g., writing department in order to obtain a minor both chemical engineers and those and presentation skills, competency with from that department. Alternately, you with undergraduate educations in other computers). may wish to take courses in several related fields such as physics, chemistry,

engineering 2014–2015 82 chemical engineering PROGRAM: first and second Years

Semester i Semester iI Semester iII Semester iV

MATH V1202 (3) and one of the following: MATH E1210 (3) mathematics MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) Ord. diff. equations or APMA E2101 (3) Intro. to appl. math.

physics C1401 (3) C1402 (3) Lab C1493 (3) (three tracks, C1601 (3.5) C1602 (3.5) choose one) C2801 (4.5) C2802 (4.5) Lab W3081 (2)

C1403 (3.5) and C1404 (3.5) C3443 (3.5) chemistry Lab C1500 (3) C2507 (3) (three tracks, choose one) C1604 (3.5) C3046 (3.5) and C3045 (3.5) Lab C2507 (3)

english C1010 (3) composition (three tracks, Z1003 (0) C1010 (3) choose one) Z0006 (0) Z1003 (0) C1010 (3)

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 C1001 (1) C1002 (1) education

THE ART OF ENGI E1102 (4) either semester ENGINEERING

total points3 16.5 17.5 16.5 17

1 Four core humanities electives should be taken as follows: In Semester III, HUMA C1001, C1101 (4), or any initial course in one of the Global Core sequences offered by the College (3–4); in Semester IV, HUMA C1002, C1102 (4), or the second course in the Global Core sequence elected in Semester III (3–4); also in Semester IV, ECON W1105 (4) with W1105 recitation (0) and either HUMA C1121 or C1123 (3). 2 Should be taken in Semester III, but may be moved upon adviser’s approval to Semester V if CHEM C3543: 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.

and biochemistry, the Ph.D. program chemical engineering thermodynamics master’s degree in chemical engineering. provides the opportunity to become (CHEN E4130)/Statistical mechanics This program enables such students to expert in research fields central to (CHAP E4120); and (2) 18 points of avoid having to take all undergraduate modern technology and science. 4000- or 6000-level courses, approved courses in the bachelor’s degree program. by the graduate coordinator or research M.S. Degree adviser, of which up to 6 may be Master’s Doctoral Degrees The requirements are (1) the core research (CHEN 9400). Students with The Ph.D. and D.E.S. degrees have courses: Chemical process analysis undergraduate preparation in physics, essentially the same requirements. (CHEN E4010), Transport phenomena, chemistry, biochemistry, pharmacy, and All students in a doctoral program III (CHEN E4110), Advanced chemical related fields may take advantage of a must (1) earn satisfactory grades kinetics (CHEN E4300), and Advanced special program leading directly to the in the three core courses (CHEN

engineering 2014–2015 83 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

CHEN C3543 (3)1 CHEN E4300 (2) CHEN 3810 (3) Required labs 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 E lectives

total points (normal track) 18 15 15 15

1 May be taken in Semester III with adviser’s permission if CHEN E3100: Material and energy balances is taken in Semester V. 2 The total of 15 points (5 courses) of required technical electives must include two chemical engineering courses, one engineering course outside of chemical engineering, and 9 points (3 courses) of “advanced natural science” (i.e., courses in chemistry, physics, biology, and certain engineering courses—contact a departmental adviser for details).

E4010, E4110, E4330, E4130/CHAP graduate concentration are suggested the variety of fascinating microscopic E4120); (2) pass a qualifying exam; below, with associated recommended structures, from the simple orientational (3) defend a proposal of research courses. Each concentration provides order of a nematic liquid crystal to within 12 months of passing the students with the opportunity to gain the full periodic “crystalline” order of qualifying exam; (4) defend their thesis; in-depth knowledge about a particular block copolymer mesophases. Soft and (5) satisfy course requirements research field of central importance to materials provide ideal testing grounds beyond the three core courses. For the department. Graduate students for such fundamental concepts as the detailed requirements, please consult outside the department are very interplay between order and dynamics the departmental office or graduate welcome to participate in these course or topological defects. They are of coordinator. Students with degrees concentrations, many of which are highly primary importance to the paint, food, in related fields such as physics, interdisciplinary. The department strongly petroleum, and other industries as well chemistry, biochemistry, and others encourages interdepartmental dialogue as a variety of advanced materials and are encouraged to apply to this highly at all levels. devices. In addition, most biological interdisciplinary program. materials are soft, so that understanding Science and Engineering of Polymers of soft materials is very relevant Areas of Concentration and Soft Materials. Soft materials to improving our understanding of After satisfying the core requirement include diverse organic media with cellular function and therefore human of Chemical process analysis (CHEN supramolecular structure having scales pathologies. At Columbia Chemical E4010), Transport phenomena, III in the range 1–100 nm. Their small- Engineering, we focus on several (CHEN E4110), Advanced chemical scale structure imparts unique, useful unique aspects of soft matter, such kinetics (CHEN E4330), and Advanced macroscopic properties. Examples as their special surface and interfacial chemical engineering thermodynamics include polymers, liquid crystals, properties. This concentration is similar (CHEN E4130)/Statistical mechanics colloids, and emulsions. Their “softness” in thrust to that of the “Biophysics and (CHAP E4120), chemical engineering refers to the fact that they typically flow Soft Matter” concentration, except here graduate students are free to choose or distort easily in response to moderate there is greater emphasis on synthetic their remaining required courses as they shear and other external forces. They rather than biological soft matter, desire, subject to their research adviser’s exhibit a great many unique and useful with particular emphasis on interfacial approval. However, a number of areas of macroscopic properties stemming from properties and materials with important

engineering 2014–2015 84 related applications. Synthetic polymers CHAP E4120: Statistical mechanics requirements or have the instructor’s are by far the most important material in CHEN E6920: Physics of soft matter permission. All lecture courses in the this class. BIOC G6300: Biochemistry/molecular biology— program are available through the eukaryotes, I Columbia Video Network, which offers a BIOC G6301: Biochemistry/molecular biology— CHEE E4252: Introduction to surface and colloid eukaryotes, II certificate for those students completing chemistry CHEN E4750: The genome and the cell a prescribed set of the courses. CHEN E4620: Introduction to polymers and soft CMBS G4350: Cellular molecular biophysics The course Introduction to genomic materials information science and technology CHEN E4640: Polymer surfaces and interfaces CHEN E6620y: Physical chemistry of macro- Genomic Engineering. Genomic (ECBM E4060) provides the essential molecules engineering may be defined as the concepts of the information system CHEN E6910: Theoretical methods in polymer development and application of paradigm of molecular biology and physics novel technologies for identifying and genetics. Principles of genomic CHEN E6920: Physics of soft matter evaluating the significance of both technology (CHEN E4700) provides selected and all nucleotide sequences students with a solid basis for Biophysics and Soft Matter Physics. in the genomes of organisms. An understanding both the principles that Soft matter denotes polymers, gels, interdisciplinary course concentration underlie genomic technologies and self-assembled surfactant structures, in genomic engineering is available to how these principles are applied. The colloidal suspensions, and many other graduate students, and to selected Genomics sequencing laboratory (CHEN complex fluids. These are strongly undergraduate students. The National E4760) provides hands-on experience fluctuating, floppy, fluid-like materials that Science Foundation is sponsoring the in high-throughput DNA sequencing, can nonetheless exhibit diverse phases development of this concentration, as conducted in a bioscience research with remarkable long-range order. In the which is believed to be the first of its laboratory. The genome and the cell last few decades, statistical physics has kind. Courses in the concentration equip (CHEN E4750) conveys a broad but achieved a sound understanding of the students in engineering and computer precise, organized, and quantitative scaling and universality characterizing science to help solve technical problems overview of the cell and its genome: large length scale properties of much encountered in the discovery, assembly, how the genome, in partnership with synthetic soft condensed matter. More organization, and application of genomic extragenomic stimuli, influences the recently, ideas and techniques from soft information. The courses impart an behavior of the cell and how mechanisms condensed matter physics have been understanding of the fundamental goals within the cell enable genomic regulation. applied to biological soft matter such and problems of genomic science and Computational genomics (CBMF W4761) as DNA, RNA, proteins, cell membrane gene-related intracellular processes; introduces students to basic and surfactant assemblies, actin and tubulin elucidate the physical, chemical, and advanced computational techniques for structures, and many others. The aim is instrumental principles available to analyzing genomic data. to shed light on (1) fundamental cellular extract sequence information from the Interested parties can obtain processes such as gene expression genome; and teach the concepts used further information, including a list of or the function of cellular motors and to organize, manipulate, and interrogate cognate courses that are available (2) physical mechanisms central to the genomic database. and recommended, from Professor the exploding field of biotechnology The concentration consists of five Leonard ([email protected]). involving systems such as DNA courses that address the principal areas microarrays and methods such as of genomic technology: sequencing Interfacial Engineering and genetic engineering. The practitioners in and other means of acquiring genomic Electrochemistry. Electrochemical this highly interdisciplinary field include information; bioinformatics as a means processes are key to many alternative physicists, chemical engineers, biologists, of assembling and providing structured energy systems (batteries and fuel biochemists, and chemists. access to genomic information; cells), to electrical and magnetic- The “Biophysics and Soft Matter” and methods of elucidating how device manufacturing (interconnects concentration is closely related to the genomic information interacts with the and magnetic-storage media), and “Science and Engineering of Polymers developmental state and environment to advanced materials processing. and Soft Materials” concentration, of cells in order to determine their Electrochemical processes are also but here greater emphasis is placed behavior. Professor E. F. Leonard involved in corrosion and in some on biological materials and cellular directs the program and teaches CHEN waste-treatment systems. Key biophysics. Both theory and experiment E4750. The other instructors are Profs. employers of engineers and scientists are catered to. Students will be D. Anastassiou (ECBM E4060), Jingyue with knowledge of electrochemical/ introduced to statistical mechanics and Ju (CHEN E4700, E4730), and C. Leslie interfacial engineering include its application to soft matter research (CBMF W4761). The Departments of companies from the computer, and to cellular biophysics. In parallel, Chemical, Biomedical, and Electrical automotive, and chemical industries. the student will learn about genomics Engineering and of Computer Knowledge of basic electrochemical and cellular biology to develop an Science credit these courses toward principles, environmental sciences, and/ understanding of what the central and requirements for their doctorates. or materials science can be useful to a fascinating biological issues are. Students may take individual courses career in this area. so long as they satisfy prerequisite

engineering 2014–2015 CHEN E4201: Engineering applications of CHEN E3110x Transport phenomena, I CHEN E3810y Chemical engineering 85 electrochemistry 3 pts. Lect: 3. Professor McNeill. laboratory CHEN E4252: Introduction to surface and colloid Prerequisites: mechanics, vector calculus, ordinary 3 pts. Lab: 3. Professor Ju. science differential equations. Corequisite: CHEN E3020. Prerequisites: Completion of core chemical CHEN E6050: Advanced electrochemistry Analysis of momentum and energy transport engineering curricula through the fall semester CHEN E3900: Undergraduate research project processes at molecular, continuum, and system of senior year (includes: CHEN E3110, E3120, scales for systems of simple fluids (gases and low- E4230, E3100, E3010, E3210, E4140, E4500), or Bioinductive and Biomimetic molecular-weight liquids). Molecular-level origins of instructor’s permission. The course emphasizes Materials. This is a rapidly emerging fluid viscosity, continuum fluid mechanics analysis active, experiment-based resolution of open-ended of laminar flows, and the resulting dimensionless problems involving use, design, and optimization area of research, and the department’s correlations of kinematic and mechanical of equipment, products, or materials. Under course concentration is under characteristics of a system needed for engineering faculty guidance students formulate, carry out, development. At present, students design (e.g., friction factor vs. Reynolds number validate, and refine experimental procedures, interested in this area are recommended correlations). Molecular origins of fluid conductivity, and present results in oral and written form. The to attend Polymer surfaces and continuum heat transfer analysis, and the resulting course develops analytical, communications, and interfaces (CHEN E4640); and Physical correlations of a system’s thermal characteristics cooperative problem-solving skills in the context chemistry of macromolecules (CHEN useful in engineering design (e.g., Nusselt of problems that span from traditional, large number correlations). Examples are reviewed scale separations and processing operations to E6620). Other courses in the “Science of analyses typical in chemical engineering molecular level design of materials or products. and Engineering of Polymers and technologies. Essential mathematical methods are Sample projects include: scale up of apparatus, Soft Materials” concentration are reviewed or introduced in context. process control, chemical separations, microfluidics, also relevant. When complete, the surface engineering, molecular sensing, and CHEN E3120y Transport phenomena, II concentration will include courses alternative energy sources. Safety awareness is 3 pts. Lect: 3. Professor West. integrated throughout the course. directly addressing biomaterials and Prerequisite: CHEN E3110. Corequisite: CHEN immunological response. E3220. Developments in Transport I are extended CHEN E3900x and y Undergraduate research to handle turbulence. Topics include: Turbulent project energy cascade, wall-bounded turbulent shear 1–6 pts. Members of the faculty. Courses in Chemical flow, time-averaging of the equations of change, Candidates for the B.S. degree may conduct Engineering Prandtl’s mixing length hypothesis for the Reynolds an investigation of some problem in chemical See also section for Biomedical stress, the Reynolds analogy, continuum modeling engineering or applied chemistry or carry out a special Engineering. Note: Check the of turbulent flows and heat transfer processes, project under the supervision of the staff. Credit for department website for the most current friction factor, and Nusselt number correlations for the course is contingent upon the submission of course offerings and descriptions. turbulent conditions. Then, macroscopic (system- an acceptable thesis or final report. No more than level) mass, momentum, and energy balances for 6 points in this course may be counted toward the CHEN E2100x Introduction to chemical one-component systems are developed and applied satisfaction of the B.S. degree requirements. engineering to complex flows and heat exchange processes. 3 pts. Lect: 3. Professor Chen. The final part focuses on mass transport in mixtures CHEN E4001x Essentials of chemical Prerequisites: First year chemistry and physics, or of simple fluids: Molecular-level origins of diffusion engineering—A equivalent. This course serves as an introduction phenomena, Fick’s law and its multi-component 3 pts. Lect: 3. Professor Hill. to the chemical engineering profession. Students generalizations, continuum-level framework for Prerequisites: First-year chemistry and physics, are exposed to concepts used in the analysis of mixtures and its application to diffusion dominated vector calculus, ordinary differential equations, chemical engineering problems. Rigorous analysis processes, diffusion with chemical reaction, and and the instructor’s permission. Part of an of material and energy balances on open and forced/free convection mass transport. accelerated consideration of the essential chemical closed systems is emphasized. An introduction engineering principles from the undergraduate CHEN E3210y Chemical engineering to important processes in the chemical and program, including topics from Reaction Kinetics thermodynamics biochemical industries is provided. and Reactor Design, Chemical Engineering 3 pts. Lect: 3. Professor Koberstein. Thermodynamics, I and II, and Chemical and CHEE E3010x Principles of chemical Prerequisites: CHEE E3010 and CHEN E3100. Biochemical Separations. While required for all engineering thermodynamics Corequisite: CHEN E3220. This course deals with M.S. students with Scientist to Engineer status, the 3 pts. Lect: 3. Professor Kumar. fundamental and applied thermodynamic principles credits from this course may not be applied toward Prerequisite: CHEM C1403. Corequisite: that form the basis of chemical engineering any chemical engineering degree. CHEN E3020. Introduction to thermodynamics. practice. Topics include phase equilibria, methods Fundamentals are emphasized: the laws of to treat ideal and nonideal mixtures, and estimation CHEN E4002x Essentials of chemical thermodynamics are derived and their meaning of properties using computer-based methods. engineering—B explained and elucidated by applications to 3 pts. Lect: 3. Professor Hill. BMCH E3500y Transport in biological engineering problems. Pure systems are treated, Prerequisites: First-year chemistry and physics, systems followed by an introduction to mixtures and phase vector calculus, ordinary differential equations, 3 pts. Lect: 3. Not offered in 2014–2015. equilibrium. and the instructor’s permission. Part of an Prerequisites: CHEM C3443 and MATH E1210. accelerated consideration of the essential CHEN E3020x Analysis of chemical Corequisites: BIOL C2005. Convective and chemical engineering principles from the engineering problems diffusive movement and reaction of molecules in undergraduate program, including topics from 3 pts. Lect: 1.5. Lab: 1.5. Professor Ortiz. biological systems. Kinetics of homogeneous and Chemical Engineering Thermodynamics, I and Prerequisites: Vector calculus, ordinary heterogeneous reactions in biological environments. II, Chemical and Biochemical Separations. differential equations. Corequisites: CHEE Mechanisms arid models of transport across Reaction Kinetics and Reactor Design. While E3010, CHEN E3110. Computational membranes. Convective diffusion with and without required for all M.S. students with Scientist to solutions of chemical engineering problems in chemical reaction. Diffusion in restricted spaces. Engineer status, the credits from this course thermodynamics, transport phenomena, and Irreversible thermodynamic approaches to transport may not be applied toward any chemical reaction design. and reaction in biological systems. engineering degree.

engineering 2014–2015 86 CHEN E4010x and y Mathematical methods of Helmholtz and Gibbs free energies and for CHEN E4300x Chemical engineering control in chemical engineering open systems. Correlation times and lengths. 2 pts. Lab: 2. Professors Venkatasubramanian 3 pts. Lect: 3. Professor Hill. Exploration of phase space and observation and Bedrossian. Mathematical description of chemical engineering timescale. Correlation functions. Fermi-Dirac and Prerequisites: Material and energy balances. problems and the application of selected methods Bose-Einstein statistics. Fluctuation-response Ordinary differential equations including Laplace for their solution. General modeling principles, theory. Applications to ideal gases, interfaces, transforms. Reactor Design. An introduction to including model hierarchies. Linear and nonlinear liquid crystals, microemulsions and other complex process control applied to chemical engineering ordinary differential equations and their systems, fluids, polymers, Coulomb gas, interactions through lecture and laboratory. Concepts include including those with variable coefficients. Partial between charged polymers and charged interfaces, the dynamic behavior of chemical engineering differential equations in Cartesian and curvilinear ordering transitions. systems, feedback control, controller tuning, and coordinates. Analytic functions of complex process stability. CHEN E4130x Advanced chemical variables. Application of the Laplace transform for engineering thermodynamics CHEN E4320y Molecular phenomena in solving linear ODEs and PDEs, and inversion by 3 pts. Lect: 3. Professor Koberstein. the method of residues. chemical engineering Prerequisite: Successful completion of an 3 pts. Lect: 3. Professor McNeill. CHEN E4020x Protection of industrial and undergraduate thermodynamics course. The course Prerequisites: CHEN E3120 or instructor’s intellectual property provides a rigorous and advanced foundation in permission. This course introduces a molecular- 3 pts. Lect: 3. Not offered in 2014–2015. chemical engineering thermodynamics suitable for level understanding of topics in modern chemical To expose engineers, scientists and technology chemical engineering Ph.D. students expected to engineering. It builds upon and validates the concepts managers to areas of the law they are most likely undertake diverse research projects. Topics include presented in the rest of the chemical engineering to be in contact with during their career. Principals intermolecular interactions, nonideal systems, curriculum via a molecular perspective. are illustrated with various case studies together mixtures, phase equilibria and phase transitions CHBM E4321x The genome and the cell with active student participation. and interfacial thermodynamics. 3 pts. Lect: 3. Professor Leonard. Prerequisites: CHEE E4050y Principles of industrial CHEE E4140x Engineering separations BIOL C2005, MATH E1210. The utility of electrochemistry processes genomic information lies in its capacity to predict 3 pts. Lect: 3. Not offered in 2014–2015. 3 pts. Lect: 3. Professor Banta. the behavior of living cells in physiological, Prerequisites: CHEE E3010 or equivalent. A Prerequisites: CHEN E3100, E3120, and E3210 developmental, and pathological situations. The presentation of the basic principle underlying or permission of instructor. Design and analysis of effect of variations in genome structure between electrochemical processes. Thermodynamics, unit operations employed in chemical engineering individuals within a species, including those electrode kinetics, and ionic mass transport. separations. Fundamental aspects of single and deemed healthy or diseased, and among species, Examples of industrial and environmental multistaged operations using both equilibrium and can be inferred statistically by comparisons of applications illustrated by means of laboratory rate-based methods. Examples include distillation, sequences with behaviors, and mechanistically, by experiments: electroplating, refining, and winning in absorption and stripping, extraction, membranes, studying the action of molecules whose structure aqueous solutions and in molten salts; electrolytic crystallization, bioseparations, and environmental is encoded within the genome. This course treatment of wastes; primary, secondary, and fuel applications. examines known mechanisms that elucidate the cells. combined effect of environmental stimulation CHEN E4201x Engineering applications of and genetic makeup on the behavior of cells CHEN E4110y Transport phenomena, III electrochemistry in homeostasis, disease states, and during 3 pts. Lect: 3. Professor Durning. 3 pts. Lect: 3. Professor West. development, and includes assessments of the Prerequisite: CHEN E3120. Tensor analysis; Prerequisites: Physical chemistry and a course probable effect of these behaviors on the whole kinematics of continua; balance of laws for one- in transport phenomena. Engineering analysis of organism. Quantitative models of gene translation component media; constituitive laws for free electrochemical systems, including electrode kinetics, and intracellular signal transduction will be used energy and stress in one-component media; exact transport phenomena, mathematical modeling, to illustrate switching of intracellular processes, and asymptotic solutions to dynamic problems and thermodynamics. Common experimental transient and permanent gene activation, and cell in fluids and solids; balance laws for mixtures; methods are discussed. Examples from common commitment, development, and death. constitutive laws for free energy, stress and applications in energy conversion and metallization diffusion fluxes in mixtures; solutions to dynamic are presented. CHEN E4330x Advanced chemical kinetics problems in mixtures. 3 pts. Lect: 3. Professor Esposito. CHEN E4230y Reaction kinetics and reactor Prerequisite: CHEN E4230 or instructor’s CHEN E4115y Topics in transport phenomena design permission. Complex reactive systems. Catalysis. 3 pts. Instructor to be announced. 3 pts. Lect: 3. Professor Banta. Heterogeneous systems, with an emphasis on Prerequisites: Undergraduate fluid mechanics, or Prerequisites: CHEE E3010. Reaction kinetics, coupled chemical kinetics and transport phenomena. transport phenomena, or instructor’s permission. applications to the design of batch and continuous Reactions at interfaces (surfaces, aerosols, Self-contained treatments of selected topics reactors. Multiple reactions, nonisothermal bubbles). Reactions in solution. in transport phenomena (e.g., rheology, reactors. Analysis and modeling of reactor nonequilibrium thermodynamics, molecular-level behavior. Recitation section required. CHEN E4400x Chemical process development aspects of transport turbulence). Topics and 3 pts. Lect: 3. Instructor to be announced. instrutor may change from year to year. Intended CHEE E4252x Introduction to surface and Prerequisites: CHEM C3443 or equivalent or for junior/senior level undergraduates and graduate colloid chemistry instructor’s permission. Process development students in engineering and the physical sciences. 3 pts. Lect: 3. Professor Somasundaran. for new compounds, including fine and specialty Prerequisites: Elementary physical chemistry. chemicals, pharmaceuticals, biologicals, and CHAP E4120y Statistical mechanics Thermodynamics of surfaces, properties of agrochemicals. Experimental strategy and methods 3 pts. Lect: 3. Professor O’Shaughnessy. surfactant solutions and surface films, electrostatic for process scale-up from bench to pilot plant. Prerequisites: CHEE E3010 or equivalent and electrokinetic phenomena at interfaces, Evaluation of process economis. Hazard and risk thermodynamics course, or instructor’s permission. adsorption; interfacial mass transfer and modern evaluation for environmental and industrial hygiene Fundamental principles and underlying experimental techniques. safety. Capture and use of process know-how for assumptions of statistical mechanics. Boltzmann’s process and plant design, regulatory approvals, entropy hypothesis and its restatement in terms and technology transfer to first manufacture.

engineering 2014–2015 CHEN E4410x Environmental control CHEN E4610y Chemical product design on those based on main-group elements. Main 87 technology 3 pts. Lect: 3. Professor Joback topics are characterization methods, polysiloxanes, 3 pts. Lect: 3. Not offered in 2014–2015. Prerequisite: CHEN E3210 and CHEM C3443 or polysilanes, polyphosphazenes, ferrocene-based Prerequisites: CHEN E3010x or the equivalent. equivalent, or instructor’s permission. Application polymers, other phosphorous-containing Causes of pollution and effect on life. Legal of chemical and engineering knowledge to the polymers, boron-containing polymers, preceramic aspects, OSHA and EPA rules. Pollution at home design of new chemical products. Relationships inorganic polymers, and inorganic-organic hybrid and at work; radon, fumes, and dust; ventilation, between composition and physical properties. composites. The focus of the second part of the dust collection, carbon adsorption. Fuel and Strategies for achieving desired volumetric, course, taught by Prof. Koberstein, is on gels, acid gases, smog and dispersion. Treatment rheological, phase equilibrium, thermal, and both physical and chemical. Topics will include of ground, saline, and wastewater. Primary environmental behavior. Case studies, including gel chemistry, including epoxies, polyurethanes, and secondary (biological) treatment. Tertiary separation solvents, blood substitutes, polyester, vinyl esters and hydrogels, as well as water treatment with membranes, ion excahnge, refrigerants, and aircraft deicing fluids. theoretical methods used to characterize the gel carbon, and sieves. Solid hazardous waste. Visit CHEN E4620y Introduction to polymers and point and gel properties. New York City wastewater treatment plant. soft materials CHEN E4680x Soft materials laboratory CHEN E4500x Process and product design, I 3 pts. Lect: 3. Professor Durning. 3 pts. Lect/lab: 3. Not offered in 2014–2015. 4 pts. Lect: 4. Professors Hill, Kumar, and Prerequisite: An elementary course in physical Prerequisites: Two years of undergraduate Leshaw. chemistry or thermodynamics. Organic chemistry, science courses and the instructor’s permission. Prerequisites: CHEN E2100x, CHEN E4140x. statistics, calculus and mechanics are helpful, but Corequisites: Limited to 15 students. Covers The practical application of chemical engineering not essential. An introduction to the chemistry and modern characterization methods for soft materials principles for the design and economic evaluation physics of soft material systems (polymers, colloids, (polymers, complex fluids, biomaterials). of chemical processes and plants. Use of ASPEN organized surfactant systems and others), Techniques include differential scanning calorimetry, Plus for complex material and energy balances emphasizing the connection between microscopic dynamic light scattering, gel permeation of real processes. Students are expected to structure and macroscopic physical properties. chromatography, rheology, and spectroscopic build on previous course work to identify creative To develop an understanding of each system, methods. Team-taught by several faculty and open solutions to two design projects of increasing illustrative experimental studies are discussed complexity. Each design project culminates in an to graduate and advanced undergraduate students. along with basic theoretical treatments. High Lab required. oral presentation, and in the case of the second molecular weight organic polymers are discussed project, a written report. first (basic notions, synthesis, properties of single CHEN E4700x Principles of genomic CHEN E4510y Process and product design, II polymer molecules, polymer solution and blend technologies 4 pts. Lect: 4. Professors Koberstein, Joback, and thermodynamics, rubber and gels). Colloidal 3 pts. Lect: 3. Professor Ju. Venkatasubramanian. systems are treated next (dominant forces in Prerequisites: Undergraduate-level biology, Prerequisite: CHEN E4500. Students carry out a colloidal systems, flocculation, preparation and organic chemistry, and instructor’s permission. semester long process or product design course manipulation of colloidal systems) followed by a Chemical and physical aspects of genome with significant industrial involvement. The project discussion of self-organizing surfactant systems structure and organization, genetic information culminates with a formal written design report and (architecture of surfactants, micelles and flow from DNA to RNA to protein. Nucleic acid a public presentation. Recitation section required. surfactant membranes, phase behavior). hybridization and sequence complexity of DNA and RNA. Genome mapping and sequencing CHEE E4530y Corrosion of metals CHEN E4630y Topics in soft materials methods. The engineering of DNA polymerase for 3 pts. Lect: 3. Professor Duby. 3 pts. Instructor to be announced. DNA sequencing and polymerase chain reaction. Prerequisite: CHEE E3010 or equivalent. The Prerequisite: Physical chemistry or instructor’s Fluorescent DNA sequencing and high-throughput theory of electrochemical corrosion, corrosion permission. Self-contained treatments of DNA sequencer development. Construction of tendency, rates, and passivity. Application to selected topics in soft materials (e.g., polymers, gene chip and micro array for gene expression various environments. Cathodic protection and colloids, amphiphiles, liquid crystals, glasses, analysis. Technology and biochemical approach coatings. Corrosion testing. powders). Topics and instructor may change for functional genomics analysis. Gene discovery from year to year. Intended for junior/senior CHEN E4540y Energy and process integration and genetics database search method. The level undergraduates and graduate students in 3 pts. Lect: 3. Instructor to be announced. application of genetic database for new therapeutics engineering and the physical sciences. Prerequisite: CHEN E4500 or equivalent. Energy discovery. optimization of chemical processes through CHEN E4640x Polymer surfaces and identification of thermodynamically attainable interfaces CHEN E4740x Biological transport and rate minimum energy targets. Energy cascade 3 pts. Lect: 3. Professor Koberstein. phenomena, II diagrams. Composite curves. Identification of Prerequisite: CHEN E4620 or consent of instructor. 3 pts. Lect: 3. Not offered in 2014–2015. energy saving opportunities. Maximum energy A fundamental treatment of the thermodynamics Prerequisites: Any two of the following: CHEN recovery networks. Euler’s Principle. Capital cost and properties relating to polymer surfaces and E3110; BIOL C2005; CHEN E3210 or BMCH targeting. Introduction to combined heat and power interfaces. Topics include the characterization E3500. Analysis of transport and rate phenomena site integration. of interfaces, theoretical modeling of interfacial in biological systems and in the design of biomimetic thermodynamics and structure, and practical transport-reaction systems for technological and CHEN E4600x Atmospheric aerosols therapeutic applications. Modeling of homogeneous 3 pts. Lect: 3. Professor McNeill. means for surface modification. and heterogeneous biochemical reactions. The Prerequisite: CHEN E3120 or instructor’s permission. CHEN E4645x Inorganic polymers, hybrid Bases of biological transport: roles of convection, Atmospheric aerosols and their effects on materials and gels ordinary diffusion, forced diffusion. Systems atmospheric composition and climate. Major topics 3 pts. Lect: 3. Not offered in 2014–2015. where reaction and transport interact strongly. are aerosol sources and properties, field and Prerequisite: Organic chemistry. The focus of the Applications to natural and artificial tissue beds, laboratory techniques for characterization, gas- first part of the course, taught by Prof. Mark, is on aerosol interactions, secondary organic aerosols, tumor modeling, controlled release, natural and the preparation, characterization, and applications aerosol direct and indirect effects on climate. artificial organ function. of inorganic ploymers, with a heavy emphasis

engineering 2014–2015 88 CHEN E4760y Genomics sequencing conducting research involving electrochemical motility, DNA transcription in gene circuits, protein laboratory technologies. networks, recombinant DNA technology, aging, and 3 pts. Lect: 1. Lab: 2. Professor Ju. gene therapy. CHEE E6220y Equilibria and kinetics in Prerequisites: Undergraduate level biology, hydrometallurgical systems CHEN E9000x and y Chemical engineering organic chemistry, and instructor’s permission. 3 pts. Lect: 3. Professor Duby. colloquium The chemical, biological and engineering principles Prerequisite: Instructor’s permission. An advanced 0 pts. Col: 1. Professor Banta. involved in the genomics sequencing process will overview of the fundamentals of electrochemistry, All graduate students are required to attend the be illustrated throughout the course for engineering with examples taken from modern applications. department colloquium as long as they are in students to develop the hands-on skills in conducting An emphasis is placed on mass transfer and residence. No degree credit is granted. genomics research. scaling phenomena. Principles are reinforced CHEN E9400x and y Master’s research through the development of mathematical models CHEN E4780x or y Quantitative methods in 1–6 pts. Members of the faculty. of electrochemical systems. Course projects cell biology Prescribed for M.S. and Ch.E. candidates; will require computer simulations. The course 3 pts. Lect: 3. Professor O’Shaughnessy. elective for others with the approval of the is intended for advanced graduate students, Prerequisites: Elementary calculus, physics and Department. Degree candidates are required conducting research involving electrochemical biology, or instructor’s permission. Quantitative to conduct an investigation of some problem in technologies. statistical analysis and mathematical modeling chemical engineering or applied chemistry and in cell biology for an audience with diverse CHEE E6252y Applied surface and colloid to submit a thesis describing the results of their backgrounds. The course presents quantitative chemistry work. No more than 6 points in this course may methods needed to analyze complex cell biological 3 pts. Lect: 2. Lab: 3. Professor Somasundaran. be counted for graduate credit, and this credit is experimental data and to interpret the analysis Prerequisites: CHEN 4252. Applications of contingent upon the submission of an acceptable in terms of the underlying cellular mechanisms. surface chemistry principles to wetting, flocculation, thesis. The concentration in pharmaceutical Optical and electrical experimental methods to flotation, separation techniques, catalysis, mass engineering requires a 2-point thesis internship. study cells and basic image analysis techniques transfer, emulsions, foams, aerosols, membranes, CHEN E9500x and y–S9500 Doctoral research are described. Methods of statistical analysis of biological surfactant systems, microbial surfaces, 1–15 pts. Members of the faculty. experimental data and techniques to test and enhanced oil recovery, and pollution problems. Prerequisites: The qualifying examinations for the compare mathematical models against measured Appropriate individual experiments and projects. doctorate. Open only to certified candidates for the statistical properties will be introduced. Concepts Lab required. and techniques of mathematical modeling will be Ph.D. and Eng.Sc.D. degrees. Doctoral candidates illustrated by applications to mechanosensing in CHEN E6620y Physical chemistry of in chemical engineering are required to make an cells, the mechanics of cytokinesis during cell macromolecules original investigation of a problem in chemical division and synaptic transmission in the nervous 3 pts. Lect: 3. Not offered in 2014–2015. engineering or applied chemistry, the results of system. Image analysis, statistical analysis, and Prerequisite: CHEN E4620 or the instructor’s which are presented in their dissertations. No more model assessment will be illustrated for these permission. Modern studies of static and dynamic than 15 points of credit toward the degree may be systems. behavior in macromolecular systems. Topics granted when the dissertation is accepted by the include single-chain behavior adsorption, solution department. CHEN E4800x Protein engineering thermodynamics, the glass transition, diffusion, and CHEN E9600x and y Advanced research 3 pts. Lect: 3. Professor Banta. viscoelastic behavior. The molecular understanding problems Prerequisite: CHEN E4230, may be taken of experimentally observed phenomena is 2–10 pts. Members of the faculty. concurrently, or the instructor’s permission. stressed. Fundamental tools and techniques currently Prerequisites: Recommendation of the professor used to engineer protein molecules. Methods CHEN E8001 M.S. chemical engineering concerned and approval of the master’s research used to analyze the impact of these alterations colloquium department. For postdoctoral students and other on different protein functions with specific 0 pts. Professor West. qualified special students who wish to pursue emphasis on enzymatic catalysis. Case studies Required for all M.S. students in residence in research under the guidance of members of the reinforce concepts covered, and demonstrate their first semester. Topics related to professional department. Not open to undergraduates or to the wide impact of protein engineering research. development and the practice of chemical candidates for the degrees of Ch.E., M.S., Ph.D., Application of basic concepts in the chemical engineering are discussed. No degree credit is or Eng.Sc.D. granted. This course is not intended for M.S./ engineering curriculum (reaction kinetics, CHEN E9800x and y Doctoral research mathematical modeling, thermodynamics) to Ph.D. students or doctoral students. instruction specific approaches utilized in protein engineering. CHEN E8100y Topics in biology 3, 6, 9 or 12 pts. Members of the faculty. BMCH E4810y Artificial organs 3 pts. Lect: 3. Professor O’Shaughnessy. A candidate for the Eng.Sc.D. degree in 3 pts. Lect: 3. Professor Leonard. Prerequisites: Instructor’s permission. This chemical engineering must register for 12 Analysis and design of replacements for the heart, research seminar introduces topics at the points of doctoral research instruction. kidneys, and lungs. Specification and realization of forefront of biological research in a format and Registration in CHEN E9800 may not be used to structures for artificial organ systems. language accessible to quantitative scientists and satisfy the minimum residence requirement for engineers lacking biological training. Conceptual the degree. CHEN E6050x Advanced electrochemistry and technical frameworks from both biological CHEN E9900x and y–S9900 Doctoral 3 pts. Lect: 3. Not offered in 2014–2015. and physical science disciplines are utilized. dissertation Prerequisite: Instructor’s permission. An advanced The objective is to reveal to graduate students 0 pts. Members of the faculty. overview of the fundamentals of electrochemistry, where potential lies to apply techniques from Open only to certified doctoral candidates. with examples taken from modern applications. their own disciplines to address pertinent A candidate for the doctorate in chemical An emphasis is placed on mass transfer and biological questions in their research. Classes engineering may be required to register for this scaling phenomena. Principles are reinforced entail reading, criticism and group discussion of course in every term after the student’s course through the development of mathematical models research papers and textbook materials providing work has been completed, and until the dissertation of electrochemical systems. Course projects overviews to various biological areas including: has been accepted. will require computer simulations. The course evolution, immune system, development and is intended for advanced graduate students, cell specialization, the cytoskeleton and cell

engineering 2014–2015 civil engineering and engineering mechanics 89 610 S. W. Mudd, MC 4709 Phone: 212-854-3143 civil.columbia.edu

Chair Hoe I. Ling Adjunct FACULTY Bojidar Yanev George Deodatis Richard W. Longman, Ali Ashrafi Theodore P. Zoli Mechanical Engineering James Barrett Department Feniosky Peña-Mora William Becker DIRECTOR OF Administrator Masanobu Shinozuka Eli B. Gottlieb RESEARCH, CARLETON Elaine MacDonald Andrew Smyth Paul Haining LABORATORY William M. Hart Andrew Smyth graduate admissions Associate Professors Wilfred Laufs and student affairs Haim Waisman Samuel A. Leifer MANAGER, CARLETON officer Huiming Yin Elisabeth Malsch LABORATORY Scott Kelly Nasri Munfakh Adrian Brügger Assistant Professors Catherine Gorlé Robert D. Mutch Professors Mysore Nagaraja Information Raimondo Betti Shiho Kawashima Technology Manager Ioannis Kougioumtzoglou Reza Nikain Bruno A. Boley King-Tung Chan WaiChing Sun Gary F. Panariello Patricia J. Culligan Daniel Peterson Gautam Dasgupta LecturerS in Bettina Quintas George Deodatis discipline Robert Ratay Maria Q. Feng Julius Chang Robert A. Rubin Jacob Fish Ibrahim Odeh Lixun Sun Upmanu Lall, Earth Thomas Panayotidi Vincent Tirolo and Environmental José I. Sánchez Richard L. Tomasetti Engineering Pawel Woelke

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

engineering 2014–2015 90 Structures: dynamics, stability, and analysis); software development and and graphics terminals exist throughout design of structures, structural failure parallel computing. the department, and a PC lab is and damage detection, fluid and soil available to students in the department structure interaction, ocean structures Multiscale mechanics: solving in addition to the larger school-wide subjected to wind-induced waves, various engineering problems that facility. inelastic dynamic response of reinforced have important features at multiple concrete structures, earthquake- spatial and temporal scales, such as Laboratories resistant design of structures. predicting material properties or system The Robert A. W. Carleton Strength of behavior based on information from finer Materials Laboratory is a very large facility Geotechnical engineering: soil scales; focus on information reduction equipped for research into all types of behavior, constitutive modeling, methods that provide balance between engineering materials and structural reinforced soil structures, geotechnical computational feasibility and accuracy. elements. The Heffner Laboratory earthquake engineering, liquefaction for Hydrologic Research is a newly and numerical analysis of geotechnical Construction engineering and established facility for both undergraduate systems. management: contracting strategies; instruction and research in all aspects of alternative project delivery systems, such fluid mechanics and its applications. The Structural materials: cement-based as design-build, design-build-operate, Eugene Mindlin Laboratory for Structural materials, micro- and macromodels of and design-build-finance-operate; Deterioration Research is a teaching and fiber-reinforced cement composites, minimizing project delays and disputes; research facility dedicated to all facets utilization of industrial by-products advanced technologies to enhance of the assessment of structures and the and waste materials, beneficiation of productivity and efficiency; strategic processes of deterioration of structural dredged material. decisions in global engineering and performance. The concrete laboratory is construction markets. equipped to perform a wide spectrum of Earthquake engineering: response of experimental research in cement-based structures to seismic loading, seismic Infrastructure delivery and materials. The Donald M. Burmister Soil risk analysis, active and passive control management: decision support systems Mechanics Laboratory is used in both of structures subject to earthquake for infrastructure asset management; undergraduate and graduate instruction excitation, seismic analysis of long-span assessing and managing infrastructure for static and dynamic testing of soils cable-supported bridges. assets and systems; capital budgeting and foundations. The 200G geotechnical processes and decisions; innovative centrifuge located in the Carleton Flight structures: aeroelasticity, financing methods; procurement Laboratory is used for geotechnical and aeroacoustics, active vibration and strategies and processes; data geoenvironmental research. noise control, smart structures, management practices and systems; noise transmission into aircraft, and indicators of infrastructure performance The Institute of Flight Structures vibroacoustics of space structures. and service. The Institute of Flight Structures was established within the department Advanced materials: multifunctional through a grant by the Daniel and Facilities engineering materials, advanced Florence Guggenheim Foundation. It The offices and laboratories of the energy materials, durable infrastructure provides a base for graduate training department are in the S. W. Mudd materials, new concretes/composites in aerospace and aeronautical related Building and the Engineering Terrace. using nanotubes, nanoparticles, and applications of structural analysis and other additives with alternative binders, design. sustainable manufacturing technologies, Computing rheological characterization for The department manages a substantial Center for Infrastructure Studies advanced cement/concrete placement computing facility of its own in addition The Center was established in the to being networked to all the systems processes. department to provide a professional operated by the University. The environment for faculty and students from department facility enables its users Computational mechanics: aimed at a variety of disciplines to join with industry to perform symbolic and numeric understanding and solving problems in and government to develop and apply computation, three-dimensional science and engineering, topics include the technological tools and knowledge graphics, and expert systems multiscale methods in space and time bases needed to deal with the massive development. Connections to wide-area (e.g., homogenization and multigrid problems of the city, state, and regional networks allow the facility’s users to methods); multiphysics modeling; infrastructure. The Center is active in communicate with centers throughout material and geometric nonlinearities; major infrastructure projects through a the world. All faculty and student strong and weak discontinuities (e.g., offices and department laboratories consortium of universities and agencies. cracks and inclusions); discretization are hardwired to the computing facility, techniques (e.g., extended finite element which is also accessible remotely to methods and mixed formulations); users. Numerous personal computers verification and validation (e.g., error

engineering 2014–2015 Undergraduate Programs the sophomore year and that the student • Structural engineering: applications 91 The Department of Civil Engineering have obtained a grade of B or better. to steel and concrete buildings, and Engineering Mechanics focuses bridges, and other structures • Geotechnical engineering: soil on two broad areas of instruction and Civil Engineering research. The first, the classical field mechanics, foundation engineering, The prerequisites for this program of civil engineering, deals with the tunneling, and geodisasters are the courses listed in the First planning, design, construction, and • Construction engineering and Year–Sophomore Program (page maintenance of structures and the management: capital facility planning 92) or their equivalents. The civil infrastructure. These include buildings, and financing, strategic management, engineering program offers three areas foundations, bridges, transportation managing engineering and of concentration: civil engineering and facilities, nuclear and conventional construction processes, construction construction management, geotechnical power plants, hydraulic structures, and industry law, construction techniques, engineering or structural engineering, other facilities essential to society. The managing civil infrastructure systems, and water resources/environmental second is the science of mechanics and civil engineering and construction engineering. In the junior and senior its applications to various engineering entrepreneurship years, 15 credits of technical electives disciplines. Frequently referred to as • Environmental engineering and are allocated. applied mechanics, it includes the water resources: transport of The department offers a first-year study of the mechanical properties of water-borne substances, hydrology, design course, CIEN E1201: The art of materials, stress analysis of stationary sediment transport, hydrogeology, structural design, which all students are and movable structures, the dynamics and geoenvironmental design of required to take in the spring semester and vibrations of complex structures, containment systems of the first year or later. An equivalent aero- and hydrodynamics, micro- and course could be substituted for E1201. nanomechanics, and the mechanics of Engineering Mechanics biological and energy systems. Minor in Architecture Programs in engineering mechanics offer Civil engineering program students may comprehensive training in the principles Program Objectives want to consider a minor in architecture of applied mathematics and continuum 1. Graduates with a broad and (see page 194). mechanics and in the application of fundamental technical base will be these principles to the solution of able to enter the professional civil engineering problems. The emphasis is engineering workforce either with a Graduate Programs on basic principles, enabling students B.S. to develop specialized expertise The Department of Civil Engineering to choose from among a wide range by way of apprenticeship or through and Engineering Mechanics offers of technical areas. Students may work the increasingly common path of a graduate programs leading to the on problems in such disciplines as specialized M.S. degree of Master of Science (M.S.), and systems analysis, acoustics, and stress the degrees of Doctor of Engineering analysis, and in fields as diverse as 2. Graduates with a firm foundation Science (Eng.Sc.D.) and Doctor of transportation, environmental, structural, in the basic math, science, and Philosophy (Ph.D.). These programs are nuclear, and aerospace engineering. engineering science which underlie flexible and may involve concentrations Program areas include: all technological development will be in structures, construction engineering, well equipped to adapt to changing reliability and random processes, • Continuum mechanics: solid and technology in the profession. soil mechanics, fluid mechanics, fluid mechanics, theories of elastic hydrogeology, continuum mechanics, 3. Graduates equipped with a broad and inelastic behavior, and damage finite element methods, computational technical background will be able to mechanics mechanics, experimental mechanics, follow other technical or nontechnical • Vibrations: nonlinear and random vibrations and dynamics, earthquake career paths. vibrations; dynamics of continuous engineering, forensic structural media, of structures and rigid bodies, 4. Graduates will practice their engineering, or any combination thereof, and of combined systems, such as profession with effective writing such as fluid-structure interaction. fluid-structure interaction; active, and communication skills, with The Graduate Record Examination passive, and hybrid control systems professional ethics, as well as with (GRE) is required for admission to the for structures under seismic loading; awareness of societal issues. department. dynamic soil-structure interaction effects on the seismic response of Engineering Mechanics Civil Engineering structures • Random processes and reliability: The prerequisites for this program are By selecting technical electives, students problems in design against failure the courses listed in the First Year– may focus on one of several areas of under earthquake, wind, and wave Sophomore Program (page 94) or their concentration or prepare for future loadings; noise, and turbulent flows; equivalents, with the provision that endeavors such as architecture. Some analysis of structures with random ENME E3105: Mechanics be taken in typical concentrations are:

engineering 2014–2015 92 civil engineering program: first and second Years

Semester i Semester iI Semester iII Semester iV

APMA E2101 (3) mathematics MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) Intro. to applied math.

C1401 (3) C1402 (3) Lab C1493 (3) physics or chem. lab (three tracks, choose one) C1601 (3.5) C1602 (3.5) C2801 (4.5) C2802 (4.5) Lab W3081 (2)

one-semester lecture (3–4): C1403 or C1404 or C3045 or C1604 chemistry Chem lab C1500 (3) either semester or physics lab

geology EESC V1011 (4) or EESC W4001 (4)

mechanics ENME-MECE E3105 (4) either semester

CIEN E3004 (3) civil engineering CIEN E1201 (3) or equivalent Urban infra. systems

english C1010 (3) composition (three tracks, Z1003 (0) C1010 (3) choose one) Z0006 (0) Z1003 (0) C1010 (3)

HUMA C1001, HUMA C1002, COCI C1101, COCI C1102, required or Global Core (3–4) or Global Core (3–4) nontechnical electives HUMA W1121 or ECON W1105 (4) and W1123 (3) W1155 recitation (0)

computer Computer Language: W1005 (3) (any semester) science

physical C1001 (1) C1002 (1) education

THE ART OF ENGI E1102 (4) either semester ENGINEERING

properties ics, mathematics, fluid dynamics, flight bridges, and other parts of the built infrastructure. • Fluid mechanics: turbulent flows, structures, and control. The program Application of these principles to the analysis two-phase flows, fluid-structure is a part of the Guggenheim Institute and design of a number of actual large-scale interaction, fluid-soil interaction, flow in of Flight Structures in the department. structures. Experimental verification of these principles through laboratory experiments. porous media, computational methods Specific information regarding degree Coverage of the history of major structural design for flow and transport processes, and requirements is available in the depart- innovations and of the engineers who introduced flow and transport in fractured rock ment office. them. Critical examination of the unique aesthetic/ under mechanical loading artistic perspectives inherent in structural design. • Computational mechanics: finite Courses in Civil Consideration of management, socioeconomic, element and boundary element and ethical issues involved in the design and Engineering techniques, symbolic computation, construction of large-scale structures. Introduction See also Courses in Engineering and bioengineering applications. to some recent developments in sustainable Mechanics at the end of this section. engineering, including green building design and A flight structures program is CIEN E1201y The art of structural design adaptable structural systems. designed to meet the needs of industry 3 pts. Lect: 3. Professor Deodatis. in the fields of high-speed and space An introduction to basic scientific and engineering flight. The emphasis is on mechan- principles used for the design of buildings,

engineering 2014–2015 93 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) A first course in finite elements geotech ENME E3114 (4) Exper. mech. of materials eng. (GE) ENME E3106 (3) CIEN E3127 (3) or Dynamics and vibrations Struct. design projects Struct. CIEN E3121 (3) (SE) Eng. (SE) Struct. anal. or 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.) o ns c o ncentrati

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. CIEN 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 16 18 18.5 13

CIEN E3004y Urban infrastructure systems infrastructure. Emphasis upon the purposes that resources / environmental engineering, geotechnical 3 pts. Lect: 3. Professor Chang. these systems serve, the factors that influence engineering and construction engineering and Introduction to: (a) the infrastructure systems their performance, the basic mechanisms that management topics. that support urban socioeconomic activities, and govern their design and operation, and the impacts (b) fundamental system design and analysis that they have regionally and globally. Student methods. Coverage of water resources, vertical, teams complete a semester-long design/analysis transportation, communications and energy project with equal emphasis given to water

engineering 2014–2015 94 engineering mechanics program: first and second Years

Semester i Semester iI Semester iII Semester iV

MATH V1202 (3) mathematics MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) and ODE (3)

C1401 (3) C1402 (3) Lab C1493 (3) physics or chem. lab (three tracks, choose one) C1601 (3.5) C1602 (3.5) C2801 (4.5) C2802 (4.5) Lab C3081 (2)

one-semester lecture (3–4): C1403 or C1404 or C3045 or C1604 chemistry Chem lab C1500 (3) either semester or physics lab

mechanics ENME-MECE E3105 (4) any semester

english C1010 (3) composition (three tracks, Z1003 (0) C1010 (3) choose one) Z0006 (0) Z1003 (0) C1010 (3)

HUMA C1001, HUMA C1002, COCI C1101, COCI C1102 required or Global Core (3–4) or Global Core (3–4) nontechnical electives HUMA W1121 or ECON W1105 (4) and W1123 (3) W1155 recitation (0)

required (3) Student’s choice, see list of first- and second-year technical electives tech electives (professional-level courses; see pages 12–13).

computer Computer Language: W1005 (3) (any semester) science

physical C1001 (1) C1002 (1) education

THE ART OF ENGI E1102 (4) either semester ENGINEERING

CIEN E3111x Uncertainty and risk in civil CIEN E3125y Structural design CIEN E3128y Design projects infrastructure systems 3 pts. Lect: 3. Professor Panayotidi. 4 pts. Lect: 4. Professor Panayotidi. 3.5 pts. Lect: 3. Instructor to be announced. Prerequisite: ENME E3113. Design criteria for Prerequisites: CIEN E3125 and E3126. Prerequisite: Working knowledge of calculus. varied structural applications, including buildings Capstone design project in civil engineering. Introduction to basic probability; hazard and bridges; design of elements using steel, This project integrates structural, geotechnical function; reliability function; stochastic models concrete, masonry, wood, and other materials. and environmental/water resources design of natural and technological hazards; extreme problems with construction management tasks CIEN E3126y Computer-aided structural value distributions; statistical inference and sustainability, legal and other social issues. design methods; Monte Carlo simulation techniques; Project is completed in teams, and communication 1 pt. Lect: 1. Lab: 1. Professor Panayotidi. fundamentals of integrated risk assessment skills are stressed. Outside lecturers will address Corequisite: CIEN E3125. Introduction to software and risk management; topics in risk-based important current issues in engineering practice. for structural analysis and design with lab. insurance; case studies involving civil Every student in the course will be exposed with Applications to the design of structural elements infrastructure systems, environmental systems, equal emphasis to issues related to geotechnical and connections. Lab required. mechanical and aerospace systems, construction engineering, water resources/environmental management. CIEN E3127x Structural design projects engineering, structural engineering, and 3 pts. Lect: 3. Professor Panayotidi. construction engineering and management. CIEN E3121y Structural analysis Prerequisites: CIEN E3125 and E3126 or the 3 pts. Lect: 3. Professor Yin. instructor’s permission. Design projects with Methods of structural analysis. Trusses, arches, various structural systems and materials. cables, frames; influence lines; deflections; force method; displacement method; computer applications.

engineering 2013–2014 95 engineering mechanics: Third and Fourth Years

Semester V Semester VI Semester VII Semester VIII

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

tech 3 points 6 points 6 points 9 points

nontech 3 points 3 points E lectives

total points 16 16 18 15

CIEN E3129x Project management for CIEE E3255y Environmental control and CIEN E4010y Transportation engineering construction pollution reduction systems 3 pts. Lect: 3. Professor Peterson. 3 pts. Lect: 3. Professor Chang. 3 pts. Lect: 3. Instructor to be announced. An overview of the planning, design, operation, Prerequisite: Senior standing in Civil Engineering Prerequisite: ENME E3161 or MECE E3100. and construction of urban highways and mass or instructor’s permission. Introduction to Review of engineered systems for prevention and transportation systems. Transportation planning Project Management for design and construction control of pollution. Fundamentals of material and and traffic studies; traffic and highway engineering; processes. Elements of planning, estimating, energy balances and reaction kinetics. Analysis rapid transit and railroad engineering. scheduling, bidding, and contractual relationships. of engineered systems to address environmental CIEN E4021x Elastic and plastic analysis of Computer scheduling and cost control. Critical path problems, including solid and hazardous waste, structures method. Design and construction activities. Field and air, water, soil and noise pollution. Life cycle 3 pts. Lect: 3. Professor Kawashima. supervision. assessments and emerging technologies. Prerequisite: CIEN E3121 or the equivalent. CIEN E3141y Soil mechanics CIEE E3260y Engineering for developing Overview of classical indeterminate structural 4 pts. Lect: 3. Lab 3. Instructor to be announced. communities analysis methods (force and displacement methods), Prerequisite: ENME E3113. Index properties Lect: 3. 3 pts. Professor Culligan. approximate methods of analysis, plastic analysis and classification; compaction; permeability and Introduction to engineering problems faced methods, collapse analysis, shakedown theorem, seepage; effective stress and stress distribution; by developing communities and exploration of structural optimization. shear strength of soil; consolidation; slope stability. design solutions in the context of a real project CIEN E4022y Bridge design and management with a community client. Emphasis is on the CIEE E3250y Hydrosystems engineering 3 pts. Lect: 3. Professor Yanev. design of sustainable solutions that take account 3 pts. Lect: 3. Instructor to be announced. Prerequisite: CIEN E3125 or the equivalent. Bridge of social, economical, and governance issues, Prerequisites: CHEN E3110 or ENME E3161 or design history, methods of analysis, loads: static, and that can be implemented now or in the near equivalent, SIEO W3600 or equivalent, or the live, dynamic. Design: allowable stress, ultimate future. The course is open to all undergraduate instructor’s permission. A quantitative introduction to strength, load resistance factor, supply/demand. engineering students. Multidisciplinary teamwork hydrologic and hydraulic systems, with a focus on Steel and concrete superstructures: suspension, and approaches are stressed. Outside lecturers integrated modeling and analysis of the water cycle cable stayed, prestressed, arches. Management are used to address issues specific to developing and associated mass transport for water resources of the assets, life-cycle cost, expected useful life, communities and the particular project under and environmental engineering. Coverage of unit inspection, maintenance, repair, reconstruction. consideration. hydrologic processes such as precipitation, Bridge inventories, condition assessments, data evaporation, infiltration, runoff generation, CIEN E3303x and y Independent studies in acquisition and analysis, forecasts. Selected case open channel and pipe flow, subsurface flow civil engineering for juniors histories and field visits. and well hydraulics in the context of example 1–3 pts. By conference. Members of the faculty. CIEN E4100y Earthquake and wind watersheds and specific integrative problems such A project on civil engineering subjects approved engineering as risk-based design for flood control, provision of by the chairman of the department. Lab fee: 3 pts. Lect: 3. Professor Ashrafi. water, and assessment of environmental impact $200. or potential for nonpoint source pollution. Spatial Prerequisite: ENME E3106 or the equivalent. Basic hydrologic analysis using GIS and watershed CIEN E3304x and y Independent studies in concepts of seismology. Earthquake characteristics, models. Note: This course is to be joint listed with civil engineering for seniors magnitude, response spectrum, dynamic response CIEN and replaces the previous CIEN 3250. 1–3 pts. By conference. Members of the faculty. of structures to ground motion. Base isolation A project on civil engineering subjects approved by and earthquake-resistant design. Wind loads and the chairman of the department. Lab fee: $200. aeroelastic instabilities. Extreme winds. Wind effects on structures and gust factors. engineering 2014–2015 96 CIEN E4111x Uncertainty and risk in construction industry and the actions that result CIEN E4138x Real-estate finance for infrastructure systems in disputes. Emphasis on procedures required to construction management 3 pts. Lect: 3. Instructor to be announced. prevent disputes and resolve them quickly and 3 pts. Lect: 3. Professor Webster. Introduction to basic probability, hazard function, cost-effectively. Case studies requiring oral and Prerequisites: IEOR E2261, CIEN E3129 or reliability function, stochastic models of natural written presentations. permission of instructor. Introduction to financial and technological hazards, extreme value mechanics of public and private real-estate CIEN E4133x or y Capital facility planning and distributions, Monte Carlo simulation techniques, development and management. Working from financing fundamentals of integrated risk assessment and perspectives of developers, investors and 3 pts. Lect: 3. Professor Chang. risk management, topics in risk-based insurance, taxpayers, financing of several types of real- Prerequisite: CIEN E4129 or equivalent. Planning estate and infrastructure projects are covered. case studies involving civil infrastructure systems, and financing of capital facilities with a strong Basics of real-estate accounting and finance, environmental systems, mechanical and aerospace emphasis upon civil infrastructure systems. Project followed by in-depth studies of private, public, systems, construction management. Not open to feasibility and evaluation. Design of project delivery and public/private-partnership projects and their undergraduate students. systems to encourage best value, innovation financial structures. Focused on U.S.-based and private sector participation. Fundamentals CIEN E4128y Civil engineering management financing, with some international practices of engineering economy and project finance. 3 pts. Available only on CVN. introduced and explored. Financial risks and Elements of life cycle cost estimation and decision Principles of engineering management with a rewards, and pertinent capital markets and analysis. Environmental, institutional, social and strong emphasis on planning of infrastructure their financing roles. Impacts and incentives of political factors. Case studies from transportation, systems. The course stresses leadership, creativity, various government programs, such as LEED water supply and wastewater treatment. and management analysis. Program planning with certification and solar power tax credits. Case optimization under financial and environmental CIEN E4134y Construction industry law studies provide opportunity to compare U.S. constraints; project planning and scheduling using 3 pts. Lect: 3. Professors Quintas and Rubin. practices to several international methods. deterministic and stochastic network theories; Prerequisite: Graduate standing or the instructor’s CIEN E4139x Theory and practice of virtual production rate development and control using permission. Practical focus upon legal concepts design and construction statistical, heuristic, simulation, and queuing applicable to the construction industry. Provides 3 pts. Lect: 3. Professor Barrett. theory approaches. Students prepare and formally sufficient understanding to manage legal aspects, Prerequisites: CIEN E4129 or instructor’s present term projects. instead of being managed by them. Topics include permission. History and development of Building contractual relationships, contract performance, CIEN E4129x and y Managing engineering and Information Modeling (BIM), its uses in design and contract flexibility and change orders, liability and construction processes construction, and introduction to the importance negligence, dispute avoidance/resolution, surety 3 pts. Lect: 3. Professors Odeh and Nagaraja. of planning in BIM implementation. Role of visual bonds, insurance and site safety. Prerequisite: Graduate standing in Civil design and construction concepts and methodologies, Engineering, or instructor’s permission. CIEN E4135y Strategic management global including integrated project delivery form in Introduction to the principles, methods and tools design and construction architecture, engineering, and construction necessary to manage design and construction 3 pts. Lect: 3. Not offered in 2014–2015. industries from project design, cost estimating, processes. Elements of planning, estimating, Core concepts of strategic planning, management scheduling, coordination, fabrication, installation, scheduling, bidding and contractual relationships. and analysis within the construction industry. and financing. Industry analysis, strategic planning models Valuation of project cash flows. Critical path CIEN E4140x Environmental, health, and and industry trends. Strategies for information method. Survey of construction procedures. Cost safety concepts in construction processes technology, emerging markets and globalization. control and effectiveness. Field supervision. 3 pts. Lect: 3. Professor Haining. Case studies to demonstrate key concepts in real- Prerequisite: Graduate standing in Civil CIEN E4130x Design of construction systems world environments. 3 pts. Lect: 3. Professor Tirolo. Engineering and Engineering Mechanics. A Prerequisite: CIEN E3125 or the equivalent, or the CIEN E4136y Global entrepreneurship in civil definitive review of and comprehensive introduction instructor’s permission. Introduction to the design engineering to construction industry best practices and of systems that support construction activities 3 pts. Lect: 3. Not offered in 2014–2015. fundamental concepts of environmental health and operations. Determination of design loads Capstone practicum where teams develop and safety management systems (EH&S) for the during construction. Design of excavation support strategies and business plans for a new enterprise construction management field. How modern systems, earth retaining systems, temporary in the engineering and construction industry. EH&S management system techniques and supports and underpinning, concrete formwork Identification of attractive market segments and theories not only result in improved safe work and shoring systems. Cranes and erection locations; development of an entry strategy; environments but ultimately enhance operational systems. Tunneling systems. Instrumentation and acquisition of financing, bonding and insurance; processes and performance in construction monitoring. Students prepare and present term organizational design; plans for recruiting and projects. projects. retaining personnel; personnel compensation/ incentives. Invited industry speakers. CIEE E4163x Environmental engineering: CIEN E4131x Principles of construction wastewater techniques CIEN E4137y Managing civil infrastructure 3 pts. Lect: 3. Professor Becker. 3 pts. Lect: 3. Professor Hart. systems Prerequisites: Introductory chemistry (with Prerequisite: CIEN 4129 or equivalent. Current 3 pts. Lect: 3. Professor Chang. laboratory) and fluid mechanics. Fundamentals methods of construction, cost-effective designs, Prerequisites: IEOR E4003, CIEN E4133, or of water pollution and wastewater characteristics. maintenance, safe work environment. Design equivalent. Examination of the fundamentals of Chemistry, microbiology, and reaction kinetics. functions, constructability, site and environmental infrastructure planning and management, with a Design of primary, secondary, and advanced issues. focus on the application of rational methods that treatment systems. Small community and support infrastructure decision-making. Institutional residential systems. CIEN E4132x or y Prevention and resolution environment and issues. Decision-making under of construction disputes certainty and uncertainty. Capital budgeting and CIEN E4210x Forensic structural engineering 3 pts. Lect: 3. Professor Nikain. financing. Group decision processes. Elements of 3 pts. Lect: 3. Professor Ratay. Prerequisite: CIEN E 4129 or equivalent. decision and finance theory. Prerequisites: Working knowledge of structural Contractual relationships in the engineering and

engineering 2014–2015 analysis and design; graduate student standing CIEN E4234y Design of large-scale building types of tunnel, including cut and cover tunnel, 97 or instructor’s permission. Review of significant structures rock tunnel, soft ground tunnel, immersed tub failures, civil/structural engineering design and 3 pts. Lect: 3. Professor Tomasetti. tunnel, and jacked tunnel. The design for the liner, construction practices, ethical standards and Prerequisites: CIEN E3121 and E3127. Modern excavation, and instrumentation are also covered. the legal positions as necessary background to challenges in the design of large-scale building A field trip will be arranged to visit the tunneling forensic engineering. Discussion of standard- structures will be studied. Tall buildings, large site. of-care. Study of the process of engineering convention centers, and major sports stadiums CIEN E4246y Earth retaining structures evaluation of structural defects and failures present major opportunities for creative solutions 3 pts. Lect: 3. Professor Leifer. in construction and in service. Examination and leadership on the part of engineers. This Prerequisite: CIEN E3141. Retaining structures, course is designed to expose the students to of the roles, activities, conduct and ethics of bulkheads, cellular cofferdams, and braced this environment by having them undertake the the forensic consultant and expert witness. excavations. Construction dewatering and complete design of a large structure from initial Students are assigned projects of actual cases underpinning. Instrumentation to monitor actual design concepts on through all the major design of nonperformance or failure of steel, concrete, performances. Ground improvement techniques, decisions. The students work as members of a masonry, geotechnical, and temporary structures, including earth reinforcement, geotextiles, and design team to overcome the challenges inherent in order to perform, discuss, and report their own grouting. To alternate with CIEN E4243. investigations under the guidance of the instructor. in major projects. Topics include overview of major projects, project criteria and interface with CIEN E4250y Waste containment design and CIEN E4212y Structural assessment and architecture, design of foundations and structural practice failure systems, design challenges in the post 9/11 3 pts. Lect: 3. Not offered in 2014–2015. 3 pts. Lect: 3. Not offered in 2014–2015. environment, and roles, responsibilities, and legal Prerequisites: ENME E3161 and CIEN E3141, Prerequisites: ENME E3113 and CIEN E3121. issues. or equivalents. Strategies for the containment Laboratory and field test methods in assessment of buried wastes. Municipal and hazardous CIEN E4241x Geotechnical engineering of structures for rehabilitation and to determine waste landfill design; bioreactor landfills; vertical fundamentals causes of failure; ASTM and other applicable barriers, evapotranspiration barriers and capillary 3 pts. Lect: 3. Professor Ling. standards; case histories of failures and barriers; hydraulic containment; in situ stabilization Prerequisite: CIEN E3141 or instructor’s permission. rehabilitation in wood, steel, masonry, and and solidification techniques; site investigation; Bearing capacity and settlement of shallow concrete structures. monitoring and stewardship of buried wastes; and deep foundations; earth pressure theories; options for land reuse/redevelopment. CIEN E4213x Elastic and inelastic buckling of retaining walls and reinforced soil retaining walls; structures sheet pile walls; braced excavation; slope stability. CIEE E4252x Environmental engineering 3 pts. Lect: 3. Professor Laufs. 3 pts. Lect: 3. Professor Chandran. CIEN E4242x Geotechnical earthquake Stability of framed structures in the elastic and Prerequisites: CHEM C1403 or equivalent; ENME engineering inelastic ranges. Lateral buckling of beams. E3161 or the equivalent. Engineering aspects of 3 pts. Lect: 3. Instructor to be announced. Torsional buckling of compression members. problems involving human interaction with the Prerequisite: CIEN E3141 or equivalent. Seismicity, natural environment. Review of fundamentals Buckling of plates of plate-stiffener combinations. earthquake intensity, propagation of seismic principles that underlie the discipline of Linear stability analysis of cylindrical shells and waves, design of earthquake motion, seismic site environmental engineering, i.e., constituent discussion of its limitations. Discussion of the response analysis, in situ and laboratory evaluation transport and transformation processes in semiempirical nature of the elastoplastic relations of dynamic soil properties, seismic performance of environmental media such as water, air and used in the case of plates and shells. underground structures, seismic performance of ecosystems. Engineering applications for port and harbor facilities, evaluation and mitigation CIEN E4226y Advanced design of steel addressing environmental problems such as water of soil liquefaction and its consequences. Seismic structures quality and treatment, air pollutant emissions, earth pressures, slopes stability, safety of dams 3 pts. Lect: 3. Professor Woelke. and hazardous waste remediation. Presented and embankments, seismic code provisions and Prerequisite: CIEN E3125 or equivalent. Review in the context of current issues facing practicing practice. To alternate with E4244. of loads and structural design approaches. engineers and government agencies, including Material considerations in structural steel design. CIEN E4243y Foundation engineering legal and regulatory framework, environmental Behavior and design of rolled steel, welded, cold- 3 pts. Lect: 3. Professor Sun. impact assessments, and natural resource formed light-gauge, and composite concrete/steel Prerequisite: CIEN E3141 or equivalent. management. members. Design of multistory buildings and space Conventional types of foundations and foundation CIEN E4253y Finite elements in geotechnical structures. problems: subsurface exploration and testing. engineering Performance of shallow and deep foundations and CIEN E4232y Advanced design of concrete 3 pts. Lect: 3. Not offered in 2014–2015. evaluation by field measurements. Case histories structures Prerequisites: CIEN E3141 and E4332. to illustrate typical design and construction 3 pts. Lect: 3. Professor Panayotidi. State-of-the-art computer solutions in geotechnical problems. To alternate with CIEN E4246. Prerequisite: CIEN E3125 or equivalent. Design engineering; 3D consolidation, seepage flows, of concrete slabs, deep beams, walls, and CIEN E4244x Geosynthetics and waste and soil-structure interaction; element and mesh other plane structures; introduction to design of containment instabilities. To be offered in alternate years with prestressed concrete structures. 3 pts. Lect: 3. Not offered in 2014–2015. CIEN E4254. Prerequisite: CIEN E4241 or the equivalent. CIEN E4233x Design of large-scale bridges CIEE E4257x Contaminant transport in Properties of geosynthetics. Geosynthetic design 3 pts. Lect: 3. Professor Zoli. subsurface systems for soil reinforcement. Geosynthetic applications in Prerequisites: CIEN E3121 or equivalent, and 3 pts. Lect: 3. Professor Mutch. solid waste containment system. To alternate with CIEN E3127 or equivalent. Design of large-scale Prerequisites: CIEE E3250 or equivalent. Single CIEN E4242. and complex bridges with emphasis on cable- and multiple phase transport in porous media; supported structures. Static and dynamic loads, CIEN E4245x or y Tunnel design and contaminant transport in variably saturated component design of towers, superstructures construction heterogeneous geologic media; physically based and cables; conceptual design of major bridge 3 pts. Lect: 3. Professor Munfakh. numerical models of such processes. types including arches, cable stayed bridges and Engineering design and construction of different suspension bridges.

engineering 2014–2015 98 CIEN E4260x Urban ecology studio CIEN E9101x and y–S9101 Civil engineering Courses in Engineering 4 pts. Lect: 3. Lab: 3. Not offered in 2014–2015. research Mechanics Prerequisites: Graduate standing and instructor’s 1–4 pts. Members of the faculty. See also Courses in Civil Engineering at permission. Conjoint studio run with the Graduate Advanced study in a specialized field under the School of Architecture, Planning and Preservation supervision of a member of the department staff. the beginning of this section. (GSAPP) that explores solutions to problems of Before registering, the student must submit an ENME E3105x or y Mechanics urban density. Engineering and GSAPP students outline of the proposed work for approval of the 4 pts. Lect: 4. Professors Hone and Feng. will engage in a joint project that address habitability supervisor and the department chair. Prerequisites: PHYS C1401 and MATH and sustainability issues in an urban environment, CIEN E9120x and y–S9120 Independent V1101-V1102 and V1201. Elements of statics; and also provides community service. Emphasis dynamics of a particle and systems of particles; studies in flight sciences will be on the integration of science, engineering dynamics of rigid bodies. and design within a social context. Interdisciplinary 3 pts. By conference. approaches and communication will be stressed. Prerequisite: Instructor’s permission. This course ENME E3106x Dynamics and vibrations is geared toward students interested in flight 3 pts. Lect: 2. Professor Smyth. CIEN E6132y Advanced systems and sciences and flight structures. Topics related to Prerequisite: Math E1201. Corequisite: ENME E3105. technologies for global project collaboration aerodynamics, propulsion, noise, structural dynamics, Kinematics of rigid bodies; momentum and energy 3 pts. Lect: 3. Not offered in 2014–2015. aeroelasticity, and structures may be selected for methods; vibrations of discrete and continuous Prerequisite: CIEN E4129 or the equivalent. supervised study. A term paper is required. systems; eigenvalue problems, natural frequencies Systems and technologies that support and modes. Basics of computer simulation of CIEN E9130x and y–S9130 Independent collaborative work in global projects. Information dynamics problems using MATLAB or Mathematica. technologies for design, visualization, project studies in construction management, and collaboration in globally 3 pts. By conference. ENME E3113x Mechanics of solids distributed networks of design, fabrication, and Prerequisites: Permission by department chair 3 pts. Lect: 3. Professor Betti. construction organizations, including web-based, and instructor. Independent study of engineering Pre- or corequisite: ENME E3105 or equivalent. parametric computer-aided modeling, project and construction industry problems. Topics Stress and strain. Mechanical properties of organizational simulation, and other emerging related to capital planning and financing, project materials. Axial load, bending, shear, and torsion. applications. Global team project with students at management, contracting strategies and risk Stress transformation. Deflection of beams. Buckling collaborating universities abroad. allocation, dispute mitigation and resolution, and of columns. Combined loadings. Thermal stresses. infrastructure assessment and management may CIEN E6133y Advanced construction and be selected for supervised study. A term paper ENME E3114y Experimental mechanics of infrastructure risk management using real is required. materials options 4 pts. Lect: 2. Lab: 3. Professor Kawashima. CIEN E9165x and y–S9165 Independent 3 pts. Lect: 3. Not offered in 2014–2015. Prerequisite: ENME E3113. Material behavior Prerequisite: CIEN E6131. Advanced concepts studies in environmental engineering and constitutive relations. Mechanical properties of risk analysis and management applied to civil 4 pts. By conference. of metals and cement composites. Structural engineering systems. Identifying and valuing Prerequisite: CIEN E4252 or the equivalent. materials. Modern construction materials. flexibility in construction and operation. Tools Emphasizes a one-on-one study approach to Experimental investigation of material properties to perform risk analysis in flexible civil specific environmental engineering problems. and behavior of structural elements including infrastructure systems. Valuation methods for real Students develop papers or work on design fracture, fatigue, bending, torsion, buckling. options. Risk flexibility analysis; integrating real problems pertaining to the treatment of solid and liquid waste, contaminant migration, ENME E3161x Fluid mechanics options analysis with quantitative risk analysis. 4 pts. Lect: 3. Lab: 3. Professor Waisman. Applications to case studies on construction and monitoring and sampling programs for remediation design. Prerequisites: ENME E3105 and ordinary differential management, life-cycle cost analysis for equations. Fluid statics. Fundamental principles infrastructure assets, public-private partnerships CIEN E9201x and y–S9201 Civil engineering and concepts of flow analysis. Differential and projects, real estate developments, and renewable reports finite control volume approach to flow analysis. energy infrastructure projects. 1–4 pts. By conference. Dimensional analysis. Application of flow analysis: A project on some civil engineering subject CIEN E6232x Advanced topics in concrete flow in pipes, external flow, flow in open channels. approved by department chair. engineering ENME E3332 A first course in finite elements 3 pts. Lect: 3. Not offered in 2014–2015. CIEN E9800x and y–S9800 Doctoral research 3 pts. Lect: 3. Professor Fish. Prerequisite: CIEN E3125 or the equivalent. instruction Prerequisite: Senior standing or instructor’s permission. Behavior of concrete under general states of 3–12 pts. May be taken for 3, 6, 9, or 12 points, Recommended corequisite: differential equations. stress, numerical modeling of steel and concrete, dependent on instructor’s permission. Focus on formulation and application of the finite finite element analysis of reinforced concrete, A candidate for the Eng.Sc.D. degree in civil element to engineering problems such as stress design of slabs and their shell concrete structures. engineering must register for 12 points of doctoral analysis, heat transfer, fluid flow, and electromagnetics. research instruction. Registration in CIEN E9800 Topics include finite element formulation for one- CIEN E6246y Advanced soil mechanics may not be used to satisfy the minimum residence dimensional problems, such as trusses, electrical 3 pts. Lect: 2.5. Instructor to be announced. requirement for the degree. and hydraulic systems; scalar field problems in two Prerequisite: CIEN E3141. Stress-dilatancy of dimensions, such as heat transfer; and vector field sand; failure criteria; critical state soil mechanics; CIEN E9900x and y–S9900 Doctoral dissertation problems, such as elasticity and finally usage of the limit analysis; finite element method and case Members of the faculty. commercial finite element program. Students taking histories of consolidation analysis. A candidate for the doctorate may be required ENME E3332 cannot take ENME E4332. to register for this course every term after the CIEN E6248x Experimental soil mechanics student’s course work has been completed and ENME E4113x Advanced mechanics of solids 3 pts. Lect: 2.5. Professor Ling. until the dissertation has been accepted. 3 pts. Lect: 3. Professor Yin. Stress and Prerequisite: CIEN E3141. Advanced soil testing, deformation formulation in two-and three- including triaxial and plane strain compression dimensional solids; viscoelastic and plastic material tests; small-strain measurement. Model testing; in one and two dimension energy methods. application (of test results) to design.

engineering 2014–2015 ENME E4114y Mechanics of fracture ENME E4363y Multiscale computational swelling, fracture, or liquefaction. These 99 and fatigue science and engineering coupling phenomena are important for numerous 3 pts. Lect: 3. Instructor to be announced. 3 pts. Lect: 3. Professor Fish. disciplines, including geophysics, biomechanics, Prerequisite: Undergraduate mechanics of solids Prerequisites: ENME E4332, elementary and material sciences. Fundamental principles of course. Elastic stresses at a crack; energy and computer programming, linear algebra. poromechanics essential for engineering practice stress intensity criteria for crack growth; effect Introduction to multiscale analysis. Information- and advanced study on porous media. Topics of plastic zone at the crack; fracture testing passing bridging techniques: among them, include balance principles, Biot’s poroelasticity, applications. Fatigue characterization by stress-life generalized mathematical homogenization mixture theory, constitutive modeling of path and strain-life; damage index; crack propagation; theory, the heterogeneous multiscale method, independent and dependent multiphase fail safe and safe life analysis. variational multiscale method, the discontinuous materials, numerical methods for parabolic and Galerkin method and the kinetic Monte hyperbolic systems, inf-sup conditions, and EMME E4115y Micromechanics of composite Carlo–based methods. Concurrent multiscale common stabilization procedures for mixed materials techniques: domain bridging, local enrichment, finite element models, explicit and implicit time 3 pts. Lect: 3. Professor Yin. and multigrid-based concurrent multiscale integrators, and operator splitting techniques for Prerequisite: ENME E4113 or instructor’s methods. Analysis of multiscale systems. poromechanics problems. approval. An introduction to the constitutive modeling of composite materials: Green’s ENME E6215y Principles and applications of ENME E6333y Finite element analysis, II functions in heterogenous media, Eshelby’s sensors for structural health monitoring 3 pts. Lect: 3. Professor Waisman. equivalent inclusion methods, eigenstrains, 3 pts. Lect: 2.5. Lab: 0.5. Professor Feng. Prerequisite: ENME E4332. FE formulation spherical and ellipsoidal inclusions, Prerequisite: ENME E4215. Concepts, principles, for beams and plates. Generalized eigenvalue dislocations, homogenization of elastic and applications of various sensors for sensing problems (vibrations and buckling). FE fields, elastic, viscoelastic and elastoplastic structural parameters and nondestructive formulation for time-dependent parabolic and constitutive modeling, micromechanics-based evaluation techniques for subsurface inspection, hyperbolic problems. Nonlinear problems, models. data acquisition, and signal processing linearization, and solution algorithms. Geometric techniques. Lectures, demonstrations, and and material nonlinearities. Introduction to ENME E4202y Advanced mechanics hands-on laboratory experiments. continuum mechanics. Total and updated 3 pts. Lect: 3. Professor Smyth. Lagrangian formulations. Hyperelasticity and ENME E6216y Structural health monitoring Prerequisite: ENME E3105 or equivalent. plasticity. Special topics: fracture and damage 3 pts. Lect: 3. Not offered in 2014–2015. Differentiation of vector functions. Review of mechanics, extended finite element method. kinematics. Generalized coordinates and constraint Prerequisites: ENME E4215 and ENME equations. Generalized forces. Lagrange’s E4332. Principles of traditional and emerging ENME E6364x Nonlinear computational equations. Impulsive forces. Collisions. sensors, data acquisition and signal processing mechanics Hamiltonian. Hamilton’s principle. techniques, experimental modal analysis (input- 3 pts. Lect: 3. Professor Fish. output), operational modal analysis (output- Prerequisites: ENME 4332 or equivalent, ENME E4214y Theory of plates and shells only), model-based diagnostics of structural elementary computer programming, linear 3 pts. Lect: 3. Not offered in 2014–2015. integrity, long-term monitoring and intelligence algebra. The formulations and solution strategies Prerequisite: ENME E3113. Static flexural maintenance. Lectures and demonstrations, for finite element analysis of nonlinear problems response of thin, elastic, rectangular, and circular hands-on laboaratory experiments. are developed. Topics include the sources of plates. Exact (series) and approximate (Ritz) nonlinear behavior (geometric, constitutive, ENME E6220x Random processes in solutions. Circular cylindrical shells. Axisymmetric boundary condition), derivation of the governing mechanics and nonaxisymmetric membrane theory. Shells of discrete equations for nonlinear systems such 3 pts. Lect: 3. Professor Deodatis. arbitrary shape. as large displacement, nonlinear elasticity, rate Prerequisites: CIEN E4111 and ENME E4215 (or independent and dependent plasticity and other ENME E4215x Theory of vibrations equivalent). Review of random variables. Random nonlinear constitutive laws, solution strategies 3 pts. Lect: 3. Professor Betti. process theory: stationary and ergodic processes, for nonlinear problems (e.g., incrementation, Frequencies and modes of discrete and continuous correlation functions, power spectra. Nonstationary iteration), and computational procedures for large elastic systems. Forced vibrations-steady-state and non-Gaussian processes. Linear random systems of nonlinear algebraic equations. and transient motion. Effect of damping. Exact and vibration theory. Crossing rates, peak distributions, approximate methods. Applications. and response analysis of nonlinear structures to ENME E8310x Advance continuum mechanics random loading. Major emphasis on simulation of 3 pts. Lect: 3. Not offered in 2014–2015. ENME E4332x Finite element analysis, I various types of random processes. Monte Carlo Prerequisites: MECE E6422 and E6423. This 3 pts. Lect: 3. Professor Waisman. simulation. Prerequisites: Mechanics of solids, structural course is open to Ph.D. students and to M.S. students with instructor’s permission. Review of analysis, elementary computer programming ENME E6315x Theory of elasticity continuum mechanics in Cartesian coordinates; (MATLAB) is recommended, linear algebra 3 pts. Lect: 2.5. Not offered in 2014–2015. tensor calculus and the calculus of variation; large and ordinary differential equations. Direct Foundations of continuum mechanics. General deformations in curvilinear coordinates; electricity stiffness approach for trusses. Strong and theorems of elasticity. Application to stress analysis problems and applications, weak forms for one-dimensional problems. and wave propagation. Galerkin finite element formulation, shape ENME E8320y Viscoelasticity and plasticity functions, Gauss quadrature, convergence. ENME E6320x Computational poromechanics 3 pts. Lect: 3. Professor Sun. 4 pts. Lect: 3. Not offered in 2014–2015. Multidimensional scalar field problems (heat Prerequisite: ENME E6315 or equivalent, or conduction), triangular and rectangular elements, Prerequisite: ENME E3332 or instructor’s permission. A fluid infiltrating porous solid is a instructor’s permission. Constitutive equations Isoparametric formulation. Multidimensional of viscoelastic and plastic bodies. Formulation vector field problems (linear elasticity). Practical multiphase material whose mechanical behavior is significantly influenced by the pore fluid. and methods of solution of the boundary value, FE modeling with commercial software (ABAQUS). problems of viscoelasticity and plasticity. Computer implementation of the finite element Diffusion, advection, capillarity, heating, cooling, method. Advanced topics. Not open to and freezing of pore fluid, buildup of pore undergraduate students. pressure, and mass exhanges among solid and fluid constituents all influence the stability and integrity of the solid skeleton, causing shrinkage,

engineering 2014–2015 100 ENME E8323y Nonlinear vibrations that are suitable for 3D printing, CNC Milling, simulation for mechanical models, structural 3 pts. Lect: 2.5. Not offered in 2014–2015. Injection Molding and Laser Cutting for buildings. models, kinematics models, design visualization, Prerequisite: ENME E4215 or equivalent. Free Different models and drawing specifications and other applications of 3D software and forced motion of simple oscillators with taught that are required by different manufacturing technologies. Introduction to advanced nonlinear damping and stiffness. Exact, perturbation, technologies. 3D modeling and visualization tools such iteration, and graphical methods of solution. as SolidWorks, Maya, Revit, Photoshop, GRAP E2005y Computer-aided engineering Stability of motion. Chaotic vibrations. Illustrator, and Final Cut Pro. Different uses and graphics applications taught in the context of engineering 3 pts. Lect: 1.5. Lab: 2.5. Not offered in 2014–2015. design, industrial design, process visualization, Courses in Graphics Prerequisite: MATH V1105. Basic concepts needed assembly visualization, and finite element to prepare and understand engineering drawings analysis (FEA). GRAP E1115x and y Engineering graphics and computer-aided representations: preparation 3 pts. Lect: 1. Lab: 3. Professor Sánchez. of sketches and drawings, preparation and GRAP E4005y Computer graphics in Focus on 3D software design for applications transmission of graphic information. Lectures and engineering in engineering design, manufacturing, and demonstrations, hands-on computer-aided graphics 3 pts. Lect: 3. Not offered in 2014–2015. graphics presentations. Introduction to 3D design laboratory work. Term project. Prerequisites: Any programming language and using advanced 3D modeling and visualization linear algebra. Numerical and symbolic (algebraic) GRAP E3115y Advanced computer modeling technologies using Maya and SolidWorks. The problem solving with Mathematica. Formulation design process includes idea conception, 3D and animation for graphics application in civil, mechanical, model development as well as 3D printing and 3 pts. Lect: 1. Lab: 3. Professor Sánchez. and bioengineering. Example of two-and three- CNC Milling manufacturing specifications derived Focus on the use of 3D modeling, animation, dimensional curve and surface objects in C++ directly from 3D models produced in class. and simulation technologies for 3D design, and Mathematica; special projects of interest to Introduction to the process of creating 3D models 3D analysis, design presentations, and electrical and computer science. manufacturing. Modeling, animation, and

engineering 2014–2015 Computer Engineering Program 101 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 Assistant Professor of Computer Science Associate Professor of Computer Science 1026 CEPSR Vishal Misra, Kenneth L. Shepard, Associate 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, Assistant Professor of Electrical Professor of Electrical Engineering Engineering Gil Zussman, 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 www.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. Students will have the prerequisites to Undergraduate Program 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 2014–2015 102 computer engineering program: first and second Years early-starting students

Semester i Semester iI Semester iII Semester iV

MATH V1202 (3) mathematics MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) and APMA E2101 (3)1

C1401 (3) C1402 (3) Lab C1493 (3) or chem. lab C1500 (3)

physics C1601 (3.5) C1602 (3.5) Lab C1493 (3) or (three tracks, choose one) chem. lab C1500 (3) C2801 (4.5) C2802 (4.5) Lab W3081 (2) or chem. lab C1500 (3)

one-semester lecture (3–4) C1403 or C1404 or C3045 or C1604 chemistry Lab C1500 (3) either semester or physics lab C1493 (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

english C1010 (3) composition (three tracks, Z1003 (0) C1010 (3) choose one) Z0006 (0) Z1003 (0) C1010 (3)

HUMA C1001, HUMA C1002, COCI C1101, COCI C1102, required or Global Core (3–4) or Global Core (3–4) nontechnical electives2 HUMA W1121 or ECON W1105 (4) and W1123 (3)1 W1155 recitation (0)

COMS W1004 (3) or COMS W3203 (3) computer ENGI E1006 (3) science W1007 (3) Discrete math.

physical C1001 (1) C1002 (1) education

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 APMA E2101 may be replaced by MATH E1210 and either APMA E3101 or MATH V2010. 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.

engineering 2014–2015 103 computer engineering: Third and Fourth Years early-starting students

Semester V Semester VI Semester VII Semester VIII

ELEN E3331 (3) IEOR E3658 (3) Electronic circuits Probability COMS W4118 (3) COMS W4115 (3) Operating systems Programming lang. COMS W3261 (3) core Required COMS W3157 (4) Computer sci. theory Courses Advanced programming

ELEN E3201 (3.5) CSEE W4823 (3) CSEE W4119 (3) Circuit analysis or Advanced logic design Computer networks

EECS E4340 (3) Computer hardware design ELEN E3081 (1) ELEN E3083 (1) or CSEE W4840 (3) required labs Circuit analysis lab Electronic circuits lab Embedded sys. design or CSEE W4140 (3) Networking 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) E lecti v e s

total points1 17.5 17 15 15

For a discussion about programming languages used in the program, please see www.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.

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: ELEN E3000, EEHS one semester after that. For sample GPA in technical courses. The Graduate E3900/4900, EEJR E4901, COMS “early-starting” and “late-starting” Record Examination (GRE), General Test W3101, W4400, W4405, courses programs, see the degree track charts. only, is required of all applicants. used for other computer engineering It must be emphasized that these Students must take at least 30 points requirements and courses that have charts present examples only; actual of courses at Columbia University at or significant overlap with other required schedules may be customized in above the 4000 level. These must include or elective courses (e.g., COMS consultation with academic advisers. at least 15 points from the courses W3134 and W3137). Courses at the listed below that are deemed core to 3000 level or higher in other areas of computer engineering. At least 6 points Graduate Program engineering, math, and science can must be included from each department. The Computer Engineering Program be considered for approval, as long as CSEE and EECS courses can count offers a course of study leading to the they do not significantly overlap with toward either department minimum. degree of Master of Science (M.S.). other required or elective courses. Other courses may be chosen with the The basic courses in the M.S. program Economics courses cannot be used as prior approval of a faculty adviser in the come from the Electrical Engineering technical electives. Computer Engineering Program. and Computer Science Departments. Students completing the program are

engineering 2014–2015 104 computer engineering program: first and second Years late-starting students

Semester i Semester iI Semester iII Semester iV

MATH V1202 (3) mathematics MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) and APMA E2101 (3)1

C1401 (3) C1402 (3) Lab C1493 (3) or chem. lab C1500 (3)

physics C1601 (3.5) C1602 (3.5) Lab C1493 (3) or (three tracks, choose one) chem. lab C1500 (3) C2801 (4.5) C2802 (4.5) Lab W3081 (2) or chem. lab C1500 (3)

one-semester lecture (3–4) C1403 or C1404 or C3045 or C1604 chemistry Lab C1500 (3) either semester or physics lab C1493 (3)

core required ELEN E1201 (3.5)2 courses Intro. to elec. eng. (either semester)

english C1010 (3) composition (three tracks, Z1003 (0) C1010 (3) choose one) Z0006 (0) Z1003 (0) C1010 (3)

HUMA C1001, HUMA C1002, COCI C1101, COCI C1102, required or Global Core (3–4) or Global Core (3–4) nontechnical electives HUMA W1121 or ECON W1105 (4) and W1123 (3) W1155 recitation (0)

COMS W1004 (3) or W3203 (3) computer ENGI E1006 (3) science W1007 (3) Discrete math.

physical C1001 (1) C1002 (1) education

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 APMA E2101 may be replaced by MATH E1210 and either APMA E3101 or MATH V2010. 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.

engineering 2014–2015 105 computer engineering: Third and Fourth Years late-starting students

Semester V Semester VI Semester VII Semester VIII

IEOR E3658 (3)1 COMS W3157 (4) COMS W4118 (3) COMS W4115 (3) Probability Advanced programming Operating systems Programming lang.

COMS W3134 (3) or ELEN E3331 (3) W3137 (4) Electronic circuits core Required Data structures Courses COMS W3261 (3)2 ELEN E3201 (3.5) Models of comp. CSEE W4119 (3) or CSEE W4823 (3) Circuit analysis Computer networks Advanced logic design CSEE W3827 (3) ELEN E3801 (3.5) Fund. of computer Signals and systems systems

EECS E4340 (3) ELEN E3081 (1)3 ELEN E3083 (1)3 Computer hardware design Circuit analysis lab Electronic circuits lab or CSEE W4840 (3) required labs Embedded sys. design ELEN E3084 (1)3 ELEN E3082 (1)3 or CSEE W4140 (3) Signals and systems lab Digital systems lab Networking 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) E lecti v e s

total points5 15 18 15 18

For a discussion about programming languages used in the program, please see www.compeng.columbia.edu. 1 SIEO W3600, STAT W4105, and SIEO W4150 can be used instead of IEOR E3658, but W3600 and W4150 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 STAT W1211. 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 E1210 and either APMA E3101 or MATH V2010. 5 Assuming technical electives taken Semesters VII and VIII, and 9 points of nontechnical electives taken Semesters VI, VII, and VIII.

Core Computer Engineering Courses COMS E6118: Operating systems, II* ELEN E6951: Wireless and mobile networking, II COMS W4115: Programming languages and CSEE E6180: Modeling and performance evaluation COMS W6998: T opic: Formal verification of translators COMS E6181: Advanced Internet services hardware/software systems COMS W4118: Operating systems, I EECS E6321: Advanced digital electronic circuits * Occasionally offered CSEE W4119: Computer networks ELEN E6350: VLSI design laboratory* The overall program must include at COMS W4130: Principles and practice of parallel ELEN E6488: Optical interconnects and least 15 points of 6000-level ELEN, programming interconnection networks CSEE W4140: Networking laboratory ELEN E6761: Computer communication EECS, CSEE, or COMS courses COMS W4180: Network security networks, I (exclusive of seminars). No more than EECS E4321: Digital VLSI circuits ELEN E6762: Computer communication networks, II* 9 points of research may be taken CSEE E6824: Parallel computer architecture EECS E4340: Computer hardware design for credit. No more than 3 points of ELEN E4350: VLSI design laboratory* CSEE E6831: Sequential logic circuits* CSEE E6832: Topics in logic design theory* a nontechnical elective (at or above ELEN E4702: Digital communications the 4000 level) may be included. A ELEN E4810: Digital signal processing CSEE E6847: Distributed embedded systems minimum GPA of at least 2.7 must be CSEE W4823: Advanced logic design ELEN E6850: Visual information systems CSEE W4824: Computer architecture ELEN E6860: Advanced digital signal processing maintained, and all degree requirements CSEE W4825: Digital systems design* CSEE E6861: Computer-aided design of digital must be completed within five years of ELEN E4830: Digital image processing systems the beginning of the first course credited CSEE W4840: Embedded systems CSEE E6868: System-on-chip platforms toward the degree. ELEN E4896: Music signal processing ELEN E6950: Wireless and mobile networking, I

engineering 2014–2015 106 Computer Science 450 Computer Science, MC 0401 Phone: 212-939-7000 cs.columbia.edu

Chair Professors Associate SENIOR Lecturer in Senior Research Julia B. Hirschberg Alfred V. Aho Professors Discipline Scientists 450 Computer Science Peter K. Allen Luca Carloni Adam Cannon Arthur G. Werschulz 212-939-7004 Peter N. Belhumeur Stephen A. Edwards Moti Yung Steven M. Bellovin Eitan Grinspun Lecturer in discipline Vice Chair Michael J. Collins Tony Jebara Jae Woo Lee Research Scientists Rocco A. Servedio Steven K. Feiner Angelos D. Keromytis Rebecca Passonneau 512 Computer Science Luis Gravano Tal Malkin Associated Faculty Owen Rambow* 212-939-7065 Jonathan L. Gross Vishal Misra David Blei Anargyros Papageorgiou Julia B. Hirschberg Itsik Pe’er Shih-Fu Chang Associate Chair Gail E. Kaiser Daniel S. Rubenstein Edward G. Coffman Jr. Associate Research for Undergraduate John R. Kender Rocco A. Servedio Dana Pe’er Scientists Education Kathleen R. McKeown Simha Sethumadhavan Clifford Stein Marta Arias* Adam Cannon Shree Kumar Nayar Junfeng Yang Steven H. Unger, Jiang Chen* 459 Computer Science Jason Nieh Professor Emeritus Wei Chu* 212-939-7016 Steven M. Nowick Assistant Vladimir Vapnik* Mona Diab* Kenneth A. Ross Professors Henryk Wozniakowski Mohit Gupta Department Henning G. Schulzrinne Augustin Chaintreau Yechiam Yemini, Nizar Habash* Administrator Salvatore J. Stolfo Xi Chen Professor Emeritus Claire Monteleoni* Patricia Hervey Joseph F. Traub Roxana Geambasu Michail Polychronakis Mihalis Yannakakis Daniel Hsu Cynthia Rudin* Martha Allen Kim Ansaf Salleb-Audissi* Allison Lewko Changxi Zheng *Columbia Center for Computational Learning Systems

he function and influence of computational complexity and the student laboratory, featuring 17 Mac- the computer is pervasive analysis of algorithms, combinatorial mini machines and 33 Linux towers T in contemporary society. methods, computer architecture, each with 8 cores and 24GB memory; Today’s computers process the daily computer-aided digital design, a remote Linux cluster with 17 servers, transactions of international banks, the computer communications, databases, a large Linux computer cluster and data from communications satellites, the mathematical models for computation, a number of computing facilities for images in video games, and even the optimization, and software systems individual research labs. In addition, fuel and ignition systems of automobiles. the data center houses a computer Computer software is as Laboratory Facilities cluster consisting of a Linux cloud commonplace in education and The department has well-equipped lab with 43 servers each with 2 Nehalem recreation as it is in science and areas for research in computer graphics, processors, 8 cores and 24GB memory. business. There is virtually no field or computer-aided digital design, computer This cloud can support approximately profession that does not rely upon vision, databases and digital libraries, 5000 of VMware instances. computer science for the problem- data mining and knowledge discovery, Research labs contain Puma 500 solving skills and the production distributed systems, mobile and and IBM robotic arms; a UTAH-MIT expertise required in the efficient wearable computing, natural-language dexterous hand; an Adept-1 robot; processing of information. Computer processing, networking, operating three mobile research robots; a real-time scientists, therefore, function in a wide systems, programming systems, defocus range sensor; PC interactive 3D variety of roles, ranging from pure robotics, user interfaces, and real-time graphics workstations with 3D position theory and design to programming and multimedia. and orientation trackers; prototype marketing. The computer facilities include a wearable computers, wall-sized stereo The computer science curriculum shared infrastructure of Sun and Linux projection systems; see-through at Columbia places equal emphasis multiprocessor file servers, NetApp headmounted displays; a networking on theoretical computer science and file servers, a student interactive testbed with three Cisco 7500 mathematics and on experimental teaching and research lab of high- backbone routers, traffic generators; an computer technology. A broad range end multimedia workstations, a load IDS testbed with secured LAN, Cisco of upper-level courses is available in balanced web cluster with 6 servers routers, EMC storage and Linux servers; such areas as artificial intelligence, and business process servers, a large a simulation testbed with several Sun

engineering 2014–2015 107 computer science program: first and second Years

Semester i Semester iI Semester iII Semester iV

mathematics MATH V1101 (3) MATH V1102 (3) MATH V1201 (3)

physics C1401 (3) C1402 (3) (three tracks, C1601 (3.5) C1602 (3.5) Chemistry or physics lab: choose one) C2801 (4.5) C2802 (4.5) PHYS C1493 (3) or PHYS W3081 (2) or CHEM W1500 (3) or chemistry/ CHEM C1403 (3) or higher or CHEM W2507 (3) or BIOLOGY EEEB W2001 (4) or C2005 (4) or higher CHEM C3085 (4) (choose one course) either semester

english C1010 (3) composition (three tracks, Z1003 (0) C1010 (3) choose one) Z0006 (0) Z1003 (0) C1010 (3)

ECON W1105 (4) and W1105 recitation (0) any semester

HUMA C1002 or required COCI C1102 or nontechnical electives HUMA C1001 or Major Cultures (3–4) COCI C1101 or Major Cultures (3–4) HUMA W1121 or W1123 (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 C1001 (1) C1002 (1) education

THE ART OF ENGI E1102 (4) either semester ENGINEERING

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

engineering 2014–2015 108 computer science: Third and Fourth Years

Semester V Semester VI Semester VII Semester VIII

COMS W3251 (3) Computational lin. algebra and COMS W3261 (3) Required Computer sci. theory Courses and SIEO W4150 (3) or SIEO W3600 (4) Prob. and stat.

nonTech 3 points 6 points 3 points

Tech 6 points 12 points 9 points 9 points ELECTI V E S

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 exam.

Ongoing faculty projects include For further information on the All technical electives except those algorithmic analysis, computational undergraduate computer science noted in each track must be approved complexity, software tool design, program, please see the home page by the faculty adviser. Technical electives distributed computation, modeling and (cs.columbia.edu/education/undergrad) not noted in the track must be at the performance evaluation, computer and the Quick Guide (cs.columbia.edu 3000 level or above and in mathematics, networks, computer architecture, CAD /education/undergrad/seasguide). science, engineering or closely related for digital systems, computer graphics, disciplines. programming environments, expert Technical Electives Students who pass the Computer systems, natural language processing, Students are encouraged to select Science Advanced Placement (AP) computer vision, robotics, computational one of the following six preapproved Exam with a 4 or 5 will receive 3 points biology, computer security, groupings of electives called “tracks.” of credit and exemption from COMS multicomputer design, user interfaces, An advanced version of each track W1004. VLSI applications, artificial intelligence, is available by invitation for qualified Note: A maximum of one course combinatorial modeling, virtual students who wish an extra opportunity worth no more than 4 points passed environments, and microprocessor for advanced learning. An additional with a grade of D may be counted applications. Students are strongly 15 points of technical elective points toward the major or minor. encouraged to arrange for participation beyond those used to satisfy the track by consulting individual faculty members requirements are also required. Track 1: Foundations of CS Track and by attending the Computer Science The following courses are required The foundations track is suitable for Research Fair held at the beginning of as a preparation for all tracks: COMS students who plan to concentrate on each semester. W1004 or W1007, W3134 or W3137, theoretical computer science in graduate Most graduates of the computer W3157, W3203, W3251, W3261, CSEE school or in mathematical topics such science program at Columbia step W3827, and SIEO W4150 (SIEO W3600 as communications security or scientific directly into career positions in computer is an acceptable substitute for W4150). computation in their career plans. science with industry or government, Collectively these courses are called Register for track course COMS E0001. or continue their education in graduate the CS Core Curriculum. In addition, Required: 9 points degree programs. Many choose to all students are required to take ENGI combine computer science with a CSOR W4231: Analysis of algorithms E1006 Introduction to computing for COMS W4236: Introduction to computational second career interest by taking engineers and applied scientists in their complexity additional programs in business first year. Students considering a career COMS W4241: Numerical algorithms and complexity administration, medicine, or other in scientific computing or finance are Electives: 12 points from the following list: professional studies. encouraged to take COMS W3210 COMS W3902: Undergraduate thesis* Scientific computation.

engineering 2014–2015 COMS W3998: Projects in Computer Science* 9 Points from: * With adviser approval, may be repeated for credit 109 IEOR E4010: Graph theory: A combinatorial view COMS W4701: Artificial intelligence Note: No more than 6 units of project/thesis COMS W4203: Graph theory COMS W4705: Natural language processing courses (COMS W3902, W3998, W4901, E6901) COMS W4205: Combinatorial theory COMS W4706: Spoken language processing can count toward the major. COMS W4252: Computational learning theory COMS W4731: Computer vision COMS W4261: Introduction to cryptography COMS W4733: Computational aspects of robotics COMS W4281: Quantum computing COMS W4771: Machine learning Track 5: Vision and Graphics Track COMS W4444: Programming and problem solving The vision and graphics track exposes Electives: 12 points required COMS W4771: Machine learning students to interesting new fields and Up to 12 points from the following list: COMS W4772: Advanced machine learning focuses on visual information with topics COMS W4901: Projects in Computer Science* Any COMS W40xx course with adviser approval in vision, graphics, human-computer COMS W4995: Math foundations of machine COMS W4165: Pixel processing learning COMS E6232: Analysis of COMS W4252: Computational learning theory interaction, robotics, modeling, algorithms, II Any COMS W47xx course if not used as a and learning. Students learn about COMS E6261: Advanced cryptography required course fundamental ways in which visual ELEN E6717: Information theory COMS W4995: Special topics, I* information is captured, manipulated, COMS E6901: Projects in Computer Science* COMS W4996: Special topics, II* and experienced. Register for track Any COMS W67xx course COMS E6998: Approximation algorithms course COMS E0005. COMS E6998: T opics in computer science, I (with * With adviser approval, may be repeated for credit adviser approval) Required: 6 points from: Note: No more than 6 units of project/thesis COMS E6999: Topics in computer science, II (with COMS W4160: Computer graphics courses (COMS W3902, W3998, W4901, and adviser approval) COMS W4731: Computer vision E6901) can count toward the major. Up to 6 points from the following list: COMS W4761: Computer animation COMS W3902: U ndergraduate thesis* Electives: 15 points from the following list: Track 2: Software Systems Track COMS W3998: U ndergraduate projects in computer COMS W3902: Undergraduate thesis* The software systems track is for science* COMS W3998: U ndergraduate projects in students interested in networks, COMS W4901: Projects in computer science* computer science* programming languages, operating COMS E6901: Projects in computer science* COMS W4162: Advanced computer graphics systems, and software systems. Up to 3 points from the following list: COMS W4165: Pixel processing COMS W4167: Computer animation Register for track course COMS E0002. COMS W4111: Database systems COMS W4170: User interface design COMS W4160: Computer graphics Required: 9 points COMS W4172: 3D user interface design COMS W4170: User interface design COMS W4115: Programming languages and COMS W4701: Artificial intelligence COMS W4999: Computing and the humanities translators COMS W4733: Computational aspects of robotics COMS W4118: Operating systems * With adviser approval, may be repeated for credit COMS W4735: Visual interfaces to computers CSEE W4119: Networking COMS W4771: Machine learning Note: No more than 6 units of project/thesis COMS W4901: Projects in computer science* courses (COMS W3902, W3998, W4901, E6901) Electives: 12 points from the following list: COMS W4995: Video game technology and design can count toward the major. COMS W3902: Undergraduate thesis* COMS W4995-W4996: Special topics in computer COMS W3998: Undergraduate projects in computer science, I and II (with adviser science* Track 4: Applications Track approval) Any COMS W41xx course The applications track is for students COMS E6901: Projects in computer science* COMS W4444: Programming and problem solving interested in the implementation of Any COMS E691x course (with adviser approval) Any COMS W48xx course COMS W4901: Projects in computer science* interactive multimedia applications for * With adviser approval, may be repeated for credit the Internet and wireless networks. COMS W4995-W4996: Special topics in computer Note: No more than 6 units of project/thesis science Register for track course COMS E0004. courses (COMS W3902, W3998, W4901, E6901) Any COMS E61xx or E68xx course (with adviser Required: 6 points can count toward the major. approval) COMS E6901: Projects in computer science* COMS W4115: Programming languages and translators Track 6: Digital Systems Track * With adviser approval, may be repeated for credit COMS W4170: User interface design The digital systems track is for students Note: No more than 6 units of project/thesis courses Electives: 15 points from the following list: interested in working at the interface of (COMS W3902, W3998, W4901, E6901) can count COMS W3902: U ndergraduate thesis* hardware and software. Subjects include toward the major. COMS W3998: U ndergraduate projects in computer digital design, computer architecture science* (both sequential and parallel) and Track 3: Intelligent Systems Track Any COMS W41xx course embedded systems. Register for track The intelligent systems track is for Any COMS W47xx course course COMS E0006. students interested in machine learning, COMS W4901: Projects in computer science* COMS W4995-W4996: Special topics in computer Required: 3 points robots, and systems capable of science, I and II (with adviser CSEE W4824: Computer architecture exhibiting “human-like” intelligence. approval) A total of seven required and elective COMS E6901: Projects in computer science* or Plus 3 points from: courses are to be chosen from the other COMS E69xx course (with EECS E4340: Computer hardware design following schedule. Register for track adviser approval) CSEE W4823: Advanced logic design course COMS E0003. Any COMS E69xx course (with adviser approval) CSEE W4840: Embedded systems

engineering 2014–2015 110 Plus 3 points from: The Graduate Record Examination Engineering and Applied Science. COMS W4115: Programming languages and (GRE) is required for admission to Admitted students will enroll for a translators the department’s graduate programs. total of four semesters. In addition to COMS W4118: Operating systems Applicants for September admission taking classes already offered at the COMS W4130: Parallel programming should take the GREs by October of the journalism and engineering schools, Electives: 12 points from the following list: preceding year. Applicants for January students will attend a seminar and COMS W3902: Undergraduate thesis admission should take these exams by workshop designed specifically for COMS E3998: U ndergraduate projects in computer April of the preceding year. the joint program. The seminar will science The course requirements in all teach students about the impact of Any COMS/CSEE W41xx course programs are flexible, and each student digital techniques on journalism; the Any COMS/CSEE W48xx course emerging role of citizens in the news COMS E4901: Projects in computer science is urged to design his or her own CSEE E6824: Parallel computer architecture* program under the guidance of a faculty process; the influence of social media; CSEE E6827: Distributed embedded systems* adviser. The student’s program should and the changing business models CSEE E6861: C AD of digital systems* focus on a particular field of computer that will support newsgathering. In the CSEE E6868: System-on-chip platforms science. Among the fields of graduate workshop, students will use a hands- COMS E6901: Projects in computer science study in computer science are analysis on approach to delve deeply into * With adviser approval, may be repeated for credit of algorithms, artificial intelligence, information design, focusing on how Note: No more than 6 units of project/thesis expert systems, natural language to build a site, section, or application courses (COMS W3902, W3998, W4901, E6901) understanding, computer vision, from concept to development, can count toward the major. multicomputer design, VLSI applications, ensuring the editorial goals are kept combinatorial modeling, combinatorial uppermost in mind. Track 7: Advanced optimization, computational complexity, The advanced track of the B.S. in computer architecture and design, courses in computer Computer Science provides extra computer communications networks, science opportunity for advanced learning. computer graphics, database machines In the listing below, the designator It comprises accelerated versions of and systems, microprocessors, COMS (Computer Science) is the other six tracks. Entry is only by parallel computation, programming understood to precede all course collective faculty invitation, extended to environments, programming languages, numbers for which no designator is students who have already completed robotics, user interfaces, software indicated. NOTE: Students may receive the core courses and the required design, computational biology, computer credit for only one of the following two courses for one of those tracks. security, and machine learning. courses: COMS W1004 and W1005. Required Track Courses Graduate students are encouraged Likewise, students may receive credit for A student designates one of the six other track actively to pursue research. Faculty only one of the following three courses: areas and completes the set of required track members of the Department of COMS W3134, W3136, or W3137. courses for that track, prior to entry into the Computer Science are engaged in Advanced Track. There are two or three courses, experimental and theoretical research COMS W1001x and y Introduction to information science depending on the designated area. in most of the fields in which courses 3 pts. Lect: 3. Instructor to be announced. Electives are offered. The degree of doctor of Basic Introduction to concepts and skills At least 6 points of 4000-level lecture courses philosophy requires a dissertation based in Information Sciences: human-computer from the menu for the designated track, plus 6 on the candidate’s original research, interfaces, representing information digitally, points of 6000-level courses in the designated which is supervised by a faculty member. organizing and searching information on the track area. For information on the M.S. World Wide Web, principles of algorithmic Thesis program, please see cs.columbia.edu/ problem solving, introduction to database There is a required 6-point senior thesis. education/MS and for information on concepts, introduction to programming in the Ph.D. program, see cs.columbia. Python. Invitation edu/education/phd. Only the top 20 percent of computer science majors in course performance in computer science courses will be considered for invitation during the Dual Degree Program in junior year. (A student in the advanced track who Journalism and Computer does not maintain this status may be required to Science return to his or her previously selected track area.) The Graduate School of Journalism and the School of Engineering Graduate Programs and Applied Science offer a dual The Department of Computer Science degree program leading to the M.S. offers graduate programs leading to degree from the Graduate School of the degree of Master of Science and Journalism and the M.S. degree in the degree of Doctor of Philosophy. Computer Science from the School of

engineering 2014–2015 COMS W1004x and y Introduction to as in biotechnology and genetic engineering. professional software construction, including 111 computer science and programming in Java Recombination and other macromolecular learning how to write code to given specifications 3 pts. Lect: 3. Professor Cannon. processes viewed as mathematical operations with as well as document the results. Provides A general introduction to computer science for simulation and visualization using simple computer introductory overview of C and C++ in a UNIX science and engineering students interested in programming. This course shares lectures with environment, for students with Java background. majoring in computer science or engineering. ECBM E4060, but the work requirements differ Also introduces scripting languages (Perl) and Covers fundamental concepts of computer science, somewhat. basic web programming. UNIX programming algorithmic problem-solving capabilities, and utilities are also covered. Lab required. COMS W3101x and y Programming languages introductory Java programming skills. Assumes 1 pt. Lect: 1. COMS W3203x and y Discrete mathematics: no prior programming background. Columbia Prerequisite: Fluency in at least one programming introduction to combinatorics and graph University students may receive credit for only one language. Introduction to a programming language. theory of the following two courses: 1004 and 1005. Each section is devoted to a specific language. 3 pts. Lect: 3. Professor Strickland. COMS W1005x and y Introduction to Intended only for those who are already fluent in Prerequisite: Any introductory course in computer computer science and programming in at least one programming language. Sections may programming. Logic and formal proofs, sequences MATLAB meet for one hour per week for the whole term, for and summation, mathematical induction, binomial 3 pts. Lect: 3. Professor Blaer. three hours per week for the first third of the term, coefficients, elements of finite probability, Prerequisites: None. Corequisites: None. A or for two hours per week for the first six weeks. recurrence relations, equivalence relations and general introduction to computer science concepts, May be repeated for credit if different languages partial orderings, and topics in graph theory algorithmic problem-solving capabilities, and are involved. (including isomorphism, traversability, planarity, programming skills in MATLAB. Assumes no prior and colorings). COMS W3134x and y Data structures in Java programming background. Columbia University 3 pts. Lect: 3. Instructor to be announced. COMS W3210y Scientific computation students may receive credit for only one of the Prerequisite: COMS W1004 or knowledge of 3 pts. Lect: 3. Professor Traub. following two courses: 1004 and 1005. Java. Data types and structures: arrays, stacks, Prerequisites: Two terms of calculus. Introduction ENGI E1006x and y Introduction to computing singly and doubly linked lists, queues, trees, to computation on digital computers. Design for engineers and applied scientists sets, and graphs. Programming techniques and analysis of numerical algorithms. Numerical 3 pts. Lect: 3. Professor Cannon. for processing such structures: sorting and solution of equations, integration, recurrences, Prerequisite: None. An interdisciplinary course in searching, hashing, garbage collection. Storage chaos, differential equations. Introduction to computing intended for first year SEAS students. management. Rudiments of the analysis of Monte Carlo methods. Properties of floating point Introduces computational thinking, algorithmic algorithms. Taught in Java. Note: Due to arithmetic. Applications to weather prediction, problem solving and Python programming with significant overlap, students may receive credit computational finance, computational science, applications in science and engineering. Assumes for only one of the following three courses: COMS and computational engineering. no prior programming background. W3134, W3136, or W3137. COMS W3251x Computational linear algebra COMS W1007x Honors introduction to COMS W3136y Data structures with C/C++ 3 pts. Lect: 3. Professor Papageorgiou. computer science 4 pts. Lect: 3. Professor Lee. Prerequisites: Two terms of calculus. 3 pts. Lect: 3. Professor Kender. Prerequisite: COMS W1004, W1005, W1007, Computational linear algebra, solution of linear Prerequisite: AP Computer Science with a grade or ENGI E1006. A second programming course systems, sparse linear systems, least squares, of 4 or 5 or similar experience. An honors-level intended for nonmajors with at least one semester eigenvalue problems, and numerical solution of introduction to computer science, intended of introductory programming experience. Basic other multivariate problems as time permits. primarily for students considering a major in elements of programming in C and C++, array- COMS W3261x and y Computer science theory computer science. Computer science as a science based data structures, heaps, linked lists, C 3 pts. Lect: 3. Professor Yannakakis. of abstraction. Creating models for reasoning programming in UNIX environment, object-oriented Prerequisite: COMS W3203. Corequisite: COMS about and solving problems. The basic elements of programming in C++, trees, graphs, generic W3134, W3136, or W3137. Regular languages: computers and computer programs. Implementing programming, hash tables. deterministic and nondeterministic finite automata, abstractions using data structures and algorithms. COMS W3137y Honors data structures and regular expressions. Context-free languages: Taught in Java. algorithms context-free grammars, push-down automata. COMS W1404x and y Emerging scholars 4 pts. Lect: 3. Instructor to be announced. Turing machines, the Chomsky hierarchy, and the program seminar Prerequisite: COMS W1004 or W1007. Church-Turing thesis. Introduction to complexity 1 pt. Sem: 1. Professor Cannon. Corequisite: COMS W3203. An honors introduction theory and NP-completeness. Corequisite: COMS W1004/1007 or ENGI E1006. to data types and structures: arrays, stacks, singly CSEE W3827x and y Fundamentals of Enrollment with instructor permission only. Peer-led and doubly linked lists, queues, trees, sets, and computer systems weekly seminar intended for first- and second-year graphs. Programming techniques for processing 3 pts. Lect: 3. Professors Rubenstein and Kim. undergraduates considering a major in computer such structures: sorting and searching, hashing, Prerequisite: An introductory programming science. Pass/Fail only. garbage collection. Storage management. Design course. Fundamentals of computer organization and analysis of algorithms. Taught in Java. Note: ECBM E3060x Introduction to genomic and digital logic. Boolean algebra, Karnaugh Due to significant overlap, students may receive information science and technology maps, basic gates and components, flip-flops credit for only one of the following three courses: 3 pts. Lect: 3. Professor Anastassiou. and latches, counters and state machines, basics COMS W3134, W3136, or W3137. Introduction to the information system paradigm of of combinational and sequential digital design. molecular biology. Representation, organization, COMS W3157x and y Advanced programming Assembly language, instruction sets, ALUs, structure, function and manipulation of the 4 pts. Lect: 4. Professor Lee. single-cycle and multi-cycle processor design, biomolecular sequences of nucleic acids and Prerequisite: Two terms of programming introduction to pipelined processors, caches, and proteins. The role of enzymes and gene regulatory experience. Practical, hands-on introduction virtual memory. elements in natural biological functions as well to programming techniques and tools for

engineering 2014–2015 112 COMS W3902x and y Undergraduate thesis database management systems. Storage methods include task and data decomposition, load- 1–6 pts. and indexing, query processing and optimization, balancing, reasoning about correctness, Prerequisite: Agreement by faculty member to materialized views, transaction processing and determinacy, safety, and deadlock-freedom. serve as thesis adviser. An independent theoretical recovery, object-relational databases, parallel and Application of techniques through semester-long or experimental investigation by an undergraduate distributed databases, performance considerations. design project implementing performant, parallel major of an appropriate problem in computer Programming projects are required. application in a modern parallel programming science carried out under the supervision of COMS W4115x and y Programming languages language. a faculty member. A formal written report is and translators mandatory and an oral presentation may also CSEE W4140x or y Networking laboratory 3 pts. Lect: 3. Professor Edwards. be required. May be taken over more than one 3 pts. Lect: 3. Professor Zussman. term, in which case the grade is deferred until Prerequisites: COMS W3134, W3136, or W3137 Prerequisite: CSEE 4119 or equivalent. In this all 6 points have been completed. Consult the (or equivalent), W3261, and CSEE W3827, or course, students will learn how to put “principles department for section assignment. instructor’s permission. Modern programming into practice,” in a hands-on networking lab languages and compiler design. Imperative, object- course. The course will cover the technologies COMS W3995x or y Special topics in oriented, declarative, functional, and scripting and proctocols of the Internet using equipment computer science languages. Language syntax, control structures, currently available to large Internet service 3 pts. Lect: 3. data types, procedures and parameters, binding, providers such as CISCO routers and end Prerequisite: Instructor’s permission. Consult the systems. A set of laboratory experiments provides department for section assignment. Special topics scope, run-time organization, and exception hands-on experience with engineering wide- arranged as the need and availability arise. Topics handling. Implementation of language translation area networks and will familiarize students with are usually offered on a one-time basis. Since tools including compilers and interpreters. Lexical, the Internet Protocol (IP), Address Resolution the content of this course changes each time it is syntactic, and semantic analysis; code generation; Protocol (ARP), Internet Control Message offered, it may be repeated for credit. introduction to code optimization. Teams implement Protocol (ICMP), User Datagram Protocol (UDP) a language and its compiler. COMS W3998x and y Undergraduate projects and Transmission Control Protocol (TCP), the in computer science COMS W4117x or y Compilers and interpreters Domain Name System (DNS), routing protocols 1–3 pts. 3 pts. Lect: 3. Professor Aho. (RIP, OSPF, BGP), network management Prerequisite: Approval by a faculty member who Prerequisite: COMS W4115 or instructor’s protocols (SNMP, and application-level protocols agrees to supervise the work. Independent project permission. Continuation of COMS W4115, (FTP, TELNET, SMTP). involving laboratory work, computer programming, with broader and deeper investigation into the COMS W4156x Advanced software engineering analytical investigation, or engineering design. design and implementation of contemporary 3 pts. Lect: 3. Professor Kaiser. May be repeated for credit, but not for a total of language translators, be they compilers or Prerequisite: Substantial software development more than 3 points of degree credit. Consult the interpreters. Topics include: parsing, semantic experience in Java, C++ or C# beyond the level department for section assignment. analysis, code generation and optimization, run- of COMS W3157. Recommended corequisite: time environments, and compiler-compilers. A ECBM E4060x Introduction to genomic COMS W4111. Software lifecycle from the programming project is required. information viewpoint of designing and implementing N-tier 3 pts. Lect: 3. Professor Anastassiou. COMS W4118x and y Operating systems, I applications (typically utilizing web browser, Introduction to the information system paradigm of 3 pts. Lect: 3. Professor Nieh. web server, application server, database). Major molecular biology. Representation, organization, Prerequisites: CSEE W3827 and knowledge of emphasis on quality assurance (code inspection, structure, function, and manipulation of the C and programming tools as covered in W3136, unit and integration testing, security and stress testing). Centers on a student-designed team biomolecular sequences of nucleic acids and W3157, or W3101, or instructor’s permission. project that leverages component services (e.g., proteins. The role of enzymes and gene regulatory Design and implementation of operating systems. transactions, resource pooling, publish/subscribe) elements in natural biological functions as well Topics include process management, process as in biotechnology and genetic engineering. for an interactive multi-user application such as a synchronization and interprocess communication, Recombination and other macromolecular simple game. memory management, virtual memory, interrupt processes viewed as mathematical operations with COMS W4160y Computer graphics simulation and visualization using simple computer handling, processor scheduling, device 3 pts. Lect: 3. Professor Zheng. programming. This course shares lectures with management, I/O, and file systems. Case study of Prerequisite: COMS W3134, W3136, or W3137; ECBM E3060, but the work requirements differ the UNIX operating system. A programming project W4156 is recommended. Strong programming somewhat. is required. background and some mathematical familiarity COMS W4111x and y Introduction to databases CSEE W4119x and y Computer networks including linear algebra is required. Introduction 3 pts. Lect: 3. Professor Biliris. 3 pts. Lect: 3. Professor Chaintreau or Misra. to computer graphics. Topics include 3D viewing Prerequisites: COMS W3134, W3136, or W3137, Corequisite: SIEO W3600 or IEOR E3658 or and projections, geometric modeling using spline fluency in Java; or instructor’s permission. The equivalent. Introduction to computer networks and curves, graphics systems such as OpenGL, fundamentals of database design and application the technical foundations of the Internet, including lighting and shading, and global illumination. development using databases: entity-relationship applications, protocols, local area networks, Significant implementation is required: the final modeling, logical design of relational databases, algorithms for routing and congestion control, project involves writing an interactive 3D video relational data definition and manipulation security, elementary performance evaluation. game in OpenGL. languages, SQL, XML, query processing, physical Several written and programming assignments COMS W4162x or y Advanced computer database tuning, transaction processing, security. required. graphics Programming projects are required. COMS W4130x Principles and practice of 3 pts. Lect: 3. COMS W4112y Database system parallel programming Prerequisite: COMS W4160 or equivalent, or implementation 3 pts. Lect: 2.5. Professor Kim. instructor’s permission. A second course in 3 pts. Lect: 2.5. Professor Gravano. Prerequisites: Experience in Java, basic computer graphics covering more advanced Prerequisites: COMS W4111; fluency in Java understanding of analysis of algorithms. COMS topics including image and signal processing, or C++. CSEE W3827 is recommended. The W3134, W3136, or W3137 (or equivalent). geometric modeling with meshes, advanced principles and practice of building large-scale Principles of parallel software design. Topics image synthesis including ray tracing and global engineering 2014–2015 illumination, and other topics as time permits. COMS W4187x or y Security architecture and COMS W4252x or y Introduction to 113 Emphasis will be placed both on implementation engineering computational learning theory of systems and important mathematical and 3 pts. Lect: 3. Professor Bellovin. 3 pts. Lect: 3. Professor Servedio. geometric concepts such as Fourier analysis, Prerequisite: COMS W4118; W4180 and/or W4119 Prerequisites: CSOR W4231 or COMS W4236 mesh algorithms and subdivision, and Monte recommended. Secure programming. Cryptograhic or W3203 and instructor’s permission or Carlo sampling for rendering. Note: Course will engineering and key handling. Access controls. COMS W3261 and instructor’s permission. be taught every two years. Trade-offs in security design. Design for security. Possibilities and limitations of performing learning by computational agents. Topics include COMS W4167x or y Computer animation COMS W4203y Graph theory computational models of learning, polynomial time 3 pts. Lect: 3. Professor Grinspun. 3 pts. Lect: 3. Instructor to be announced. learnability, learning from examples and learning Prerequisite: Multivariable calculus, linear algebra, Prerequisite: COMS W3203. General introduction from queries to oracles. Computational and C++ programming proficiency. COMS W4156 to graph theory. Isomorphism testing, algebraic statistical limitations of learning. Applications to recommended. Theory and practice of physics- specification, symmetries, spanning trees, Boolean functions, geometric functions, automata. based animation algorithms, including animated traversability, planarity, drawings on higher-order clothing, hair, smoke, water, collisions, impact, surfaces, colorings, extremal graphs, random COMS W4261x or y Introduction to and kitchen sinks. Topics covered: integration graphs, graphical measurement, directed graphs, cryptography of ordinary differential equations, formulation Burnside-Polya counting, voltage graph theory. 3 pts. Lect: 2.5. Professor Malkin. of physical models, treatment of discontinuities Prerequisites: Comfort with basic discrete math COMS W4205x Combinatorial theory including collisions/contact, animation control, and probability. Recommended: COMS W3261 3 pts. Lect: 3. Professor Gross. constrained Lagrangian Mechanics, friction/ or CSOR W4231. An introduction to modern Prerequisites: COMS W3203 and course in dissipation, continuum mechanics, finite elements, cryptography, focusing on the complexity- calculus. Sequences and recursions, calculus of rigid bodies, thin shells, discretization of Navier- theoretic foundations of secure computation and finite differences and sums, elementary number Stokes equations. General education requirement: communication in adversarial environments; a theory, permutation group structures, binomial quantitative and deductive reasoning (QUA). rigorous approach, based on precise definitions coefficients, Stilling numbers, harmonic numbers, and provably secure protocols. Topics include COMS W4170x User interface design generating functions. private and public key encryption schemes, 3 pts. Lect: 3. Professor Feiner. CSOR W4231x Analysis of algorithms, I digital signatures, authentication, pseudorandom Prerequisite: COMS W3134, W3136, or W3137. 3 pts. Lect: 3. Professor Yannakakis, Chen, or generators and functions, one-way functions, Introduction to the theory and practice of computer Stein. trapdoor functions, number theory and user interface design, emphasizing the software Prerequisites: COMS W3134, W3136 or W3137, computational hardness, identification and zero design of graphical user interfaces. Topics include and W3203. Introduction to the design and knowledge protocols. basic interaction devices and techniques, human analysis of efficient algorithms. Topics include factors, interaction styles, dialogue design, and COMS W4281x or y Introduction to quantum models of computation, efficient sorting and software infrastructure. Design and programming computing searching, algorithms for algebraic problems, projects are required. 3 pts. Lect: 3. Professor Papageorgiou. graph algorithms, dynamic programming, Prerequisite: Knowledge of linear algebra. COMS W4172y 3D user interfaces and probabilistic methods, approximation algorithms, Prior knowledge of quantum mechanics is augmented reality and NP-completeness. not required although helpful. Introduction to 3 pts. Lect: 3. Professor Feiner. COMS W4236y Introduction to computational quantum computing. Shor’s factoring algorithm, Prerequisite: COMS W4160 or W4170 or complexity Grover’s database search algorithm, the quantum instructor’s permission. Design, development, 3 pts. Lect: 3. Professor Servedio. summation algorithm. Relationship between and evaluation of 3D user interfaces. Interaction Prerequisite: COMS W3261. Develops a classical and quantum computing. Potential power techniques and metaphors, from desktop to quantitative theory of the computational difficulty of quantum computers. immersive. Selection and manipulation. Travel of problems in terms of the resources (eg., time, and navigation. Symbolic, menu, gestural, and EECS E4340x Computer hardware design space) needed to solve them. Classification of multimodal interaction. Dialogue design. 3D 3 pts. Lect: 2. Professor Sethumadhavan. problems into complexity classes, reductions software support. 3D interaction devices and Prerequisites: ELEN E3331 plus ELEN E3910 and completeness. Power and limitations displays. Virtual and augmented reality. Tangible or CSEE W3827. Practical aspects of computer of different modes of computation such as user interfaces. Review of relevant 3D math. hardware design through the implementation, nondeterminism, randomization, interaction and simulation, and prototyping of a PDP-8 processor. COMS W4180x or y Network security parallelism. High-level and assembly languages, I/O, interrupts, 3 pts. Lect: 3. Professor Keromytis. COMS W4241y Numerical algorithms and datapath and control design, piplelining, busses, Prerequisites: COMS W3134, W3136, or W3137, complexity memory architecture. Programmable logic and and W4119, or instructor’s permission. Introduction 3 pts. Lect: 3. Professor Traub. hardware prototyping with FPGAs. Fundamentals to network security concepts and mechanisms. Prerequisite: Knowledge of a programming of VHDL for register-transfer level design. Testing Foundations of network security and an in-depth language. Some knowledge of scientific and validation of hardware. Hands-on use of review of commonly used security mechanisms computation is desirable. Modern theory and industry CAD tools for simulation and synthesis. and techniques, security threats and network- practice of computation on digital computers. Lab required. based attacks, applications of cryptography, Introduction to concepts of computational authentication, access control, intrusion detection COMS W4444x Programming and problem complexity. Design and analysis of numerical and response, security protocols (IPsec, SSL, solving algorithms. Applications to computational finance, Kerberos), denial of service, viruses and worms, 3 pts. Lect: 3. Professor Ross. computational science, and computational software vulnerabilities, web security, wireless Prerequisites: COMS W3134, W3136, or W3137, engineering. security, and privacy. and CSEE W3827. Hands-on introduction to solving open-ended computational problems. Emphasis on creativity, cooperation, and

engineering 2014–2015 114 collaboration. Projects spanning a variety COMS W4705x Natural language processing COMS W4733x or y Computational aspects of areas within computer science, typically 3 pts. Lect: 3. Professor Collins. of robotics requiring the development of computer programs. Prerequisite: COMS W3134, W3136, or W3137 3 pts. Lect: 3. Professor Allen. Generalization of solutions to broader problems, (or equivalent), or instructor’s permission. Prerequisite: COMS W3134, W3136, or W3137. and specialization of complex problems to make Computational approaches to natural language Introduction to robotics from a computer science them manageable. Team-oriented projects, generation and understanding. Recommended perspective. Topics include coordinate frames and student presentations, and in-class participation preparation: Some previous or concurrent kinematics, computer architectures for robotics, required. exposure to AI or machine learning. Topics integration and use of sensors, world modeling include information extraction, summarization, systems, design and use of robotic programming COMS W4460y Principles of innovation and machine translation, dialogue systems, and languages, and applications of artificial intelligence entrepreneurship emotional speech. Particular attention is for planning, assembly, and manipulation. 3 pts. Lect: 3. Professor Yemini. given to robust techniques that can handle Prerequisites: COMS W3134, W3136, or W3137 COMS W4735x or y Visual interfaces to understanding and generation for the large (or equivalent), or instructor’s permission. Team computers amounts of text on the web or in other large project-centered course focused on principles 3 pts. Lect: 3. Professor Kender. corpora. Programming exercises in several of of planning, creating, and growing a technology Prerequisite: COMS W3134, W3136, or W3137. these areas. venture. Topics include: identifying and analyzing Visual input as data and for control of computer opportunities created by technology paradigm COMS W4706y Spoken language processing systems. Survey and analysis of architecture, shifts, designing innovative products, protecting 3 pts. Lect: 3. Professor Hirschberg. algorithms, and underlying assumptions intellectual property, engineering innovative Prerequisite: COMS W3134, W3136, or W3137 of commercial and research systems that business models. (or equivalent), or instructor’s permission. recognize and interpret human gestures, Computational approaches to speech analyze imagery such as fingerprint or iris COMS W4560x Introduction to computer generation and understanding. Topics include patterns, generate natural language descriptions applications in health care and biomedicine speech recognition and understanding, speech of medical or map imagery. Explores foundations 3 pts. Lect: 3. in human psychophysics, cognitive science, and analysis for computational linguistics research, Prerequisites: Experience with computers and artificial intelligence. and speech synthesis. Speech applications a passing familiarity with medicine and biology. including dialogue systems, data mining, COMS W4737x or y Biometrics Undergraduates in their senior or junior years summarization, and translation. Exercises 3 pts. Lect: 3. Professor Belhumeur. may take this course only if they have adequate involve data analysis and building a small text- Prerequisite: A background at the sophomore background in mathematics and receive permission to-speech system. level in computer science, engineering, or like from the instructor An overview of the field of discipline. Corequisites: None. In this course we biomedical informatics, combining perspectives COMS W4725x or y Knowledge representation will explore the latest advances in biometrics as from medicine, computer science, and social and reasoning well as the machine learning techniques behind science. Use of computers and information in 3 pts. Lect: 3. them. Students will learn how these technologies health care and the biomedical sciences, covering Prerequisite: COMS W4701. General aspects work and how they are sometimes defeated. specific applications and general methods, current of knowledge representation (KR). The two Grading will be based on homework assignments issues, capabilities and limitations of biomedical fundamental paradigms (semantic networks and and a final project. There will be no midterm or informatics. Biomedical Informatics studies the frames) and illustrative systems. Topics include final exam. This course shares lectures with COMS organization of medical information, the effective hybrid systems, time, action/plans, defaults, E6737. Students taking COMS E6737 are required management of information using computer abduction, and case-based reasoning. Throughout to complete additional homework problems and technology, and the impact of such technology the course particular attention is paid to design undertake a more rigorous final project. Students on medical research, education, and patient trade-offs between language expressiveness and will only be allowed to earn credit for COMS care. The field explores techniques for assessing reasoning complexity, and issues relating to the W4737 or COMS E6737 but not both. current information practices, determining the use of KR systems in larger applications. information needs of health care providers and CBMF W4761x or y Computational genomics COMS W4731x or y Computer vision patients, developing interventions using computer 3 pts. Lect: 3. Professor Pe’er. 3 pts. Lect: 3. Professor Nayar. Prerequisites: Introductory probability and technology, and evaluating the impact of those Prerequisites: The fundamentals of calculus, linear statistics and basic programming skills. Provides interventions. algebra, and C programming. Students without any comprehensive introduction to computational COMS W4701x or y Artificial intelligence of these prerequisites are advised to contact the techniques for analyzing genomic data including 3 pts. Lect: 3. Professor Pasik. instructor prior to taking the course. Introductory DNA, RNA and protein structures; microarrays; Prerequisite: COMS W3134, W3136, or W3137. course in computer vision. Topics include image transcription and regulation; regulatory, metabolic Provides a broad understanding of the basic formation and optics, image sensing, binary and protein interaction networks. The course techniques for building intelligent computer images, image processing and filtering, edge covers sequence analysis algorithms, dynamic systems. Topics include state-space problem extraction and boundary detection, region growing programming, hidden Markov models, phylogenetic representations, problem reduction and and-or and segmentation, pattern classification methods, analysis, Bayesian network techniques, neural graphs, game playing and heuristic search, brightness and reflectance, shape from shading networks, clustering algorithms, support vector predicate calculus, and resolution theorem and photometric stereo, texture, binocular stereo, machines, Boolean models of regulatory networks, proving, AI systems and languages for knowledge optical flow and motion, 2D and 3D object flux based analysis of metabolic networks and representation, machine learning and concept representation, object recognition, vision systems scale-free network models. The course provides self-contained introduction to relevant biological formation, and other topics such as natural and applications. mechanisms and methods. language processing may be included as time permits.

engineering 2014–2015 COMS W4771y Machine learning machines (ASMs); introduction to hardware COMS E6113y Topics In database systems 115 3 pts. Lect: 3. Professor Jebara. description languages (VHDL or Verilog); 3 pts. Lect: 2. Prerequisites: Any introductory course in linear system-level modelling and simulation; design Prerequisite: COMS W4111. Concentration on algebra and any introductory course in statistics examples. some database paradigm, such as deductive, are both required. Highly recommended: COMS heterogeneous, or object-oriented, and/or CSEE W4824x Computer architecture W4701 or knowledge of artificial intelligence. some database issue, such as data modeling, 3 pts. Lect: 3. Professor Carloni. Topics from generative and discriminative distribution, query processing, semantics, or Prerequisite: CSEE W3827 or equivalent. Focuses machine learning including least squares transaction management. A substantial project is on advanced topics in computer architecture, methods, support vector machines, kernel typically required. May be repeated for credit with illustrated by case studies from classic and methods, neural networks, Gaussian distributions, instructor’s permission. modern processors. Fundamentals of quantitative linear classification, linear regression, maximum analysis. Pipelining. Memory hierarchy design. COMS E6117x or y Topics in programming likelihood, exponential family distributions, Instruction-level and thread-level parallelism. Data- languages and translators Bayesian networks, Bayesian inference, mixture level parallelism and graphics processing units. 3 pts. Lect: 2. Professor Aho. models, the EM algorithm, graphical models and Multiprocessors. Cache coherence. Interconnection Prerequisite: COMS W4115 or instructor’s hidden Markov models. Algorithms implemented networks. Multi-core processors and systems-on- permission. Concentration on the design and in Matlab. chip. Platform architectures for embedded, mobile, implementation of programming languages, and COMS W4772x Advanced machine learning and cloud computing. tools focused on advanced applications in new areas in software verification, distributed systems, 3 pts. Lect: 3. Professors Jebara and Hsu. CSEE W4840y Embedded systems Prerequisites: COMS W4771 or instructor’s programming in the large, and web computing. 3 pts. Lect: 3. Professor Edwards. A substantial project is typically required. May be permission; knowledge of linear algebra and Prerequisite: CSEE W4823. Embedded system repeated for credit. introductory probability or statistics is required. design and implementation combining hardware An exploration of advanced machine learning and software. I/O, interfacing, and peripherals. COMS E6118y Operating systems, II tools for perception and behavior learning. Weekly laboratory sessions and term project on 3 pts. Lect: 2. How can machines perceive, learn from, and design of a microprocessor-based embedded Prerequisite: COMS W4118. Corequisite: COMS classify human activity computationally? Topics system including at least one custom peripheral. W4119. Continuation of COMS W4118, with include appearance-based models, principal and Knowledge of C programming and digital logic emphasis on distributed operating systems. independent components analysis, dimensionality required. Lab required. Topics include interfaces to network protocols, reduction, kernel methods, manifold learning, distributed run-time binding, advanced virtual COMS W4901x and y Projects in computer latent models, regression, classification, Bayesian memory issues, advanced means of interprocess science methods, maximum entropy methods, real-time communication, file system design, design for 1–3 pts. tracking, extended Kalman filters, time series extensibility, security in a distributed environment. Prerequisite: Approval by a faculty member who prediction, hidden Markov models, factorial Investigation is deeper and more hands-on than agrees to supervise the work. A second-level HMMs, input-output HMMs, Markov random fields, in COMS W4118. A programming project is independent project involving laboratory work, variational methods, dynamic Bayesian networks, required. computer programming, analytical investigation, and Gaussian/Dirichlet processes. Links to or engineering design. May be repeated for COMS E6121x Reliable software cognitive science. credit, but not for a total of more than 3 points of 3 pts. Lect: 3. Professor Yang. COMS W4776x Machine learning for data degree credit. Consult the department for section Prerequisite: at least one of COMS W4118, science assignment. W4115, or W4117, or significant software development experiences. Topics include: 3 pts. Lect: 3. Professor Jebara. COMS W4995x or y Special topics in automated debugging, automated software Prerequisites: SIEO W3600 or W4150 or computer science, I repair, concurrent software reliability, software equivalent, COMS W3251 or equivalent. 3 pts. Lect: 3. Introduction to machine learning, emphasis on Prerequisite: Instructor’s permission. Special topics error detection, and more. data science. Topics include least square methods, arranged as the need and availability arises. Topics COMS E6123x or y Programming Gaussian distributions, linear classification, linear are usually offered on a one-time basis. Since environments and software tools (PEST) regression, maximum likelihood, exponential the content of this course changes each time it is 3 pts. Lect: 2. Professor Kaiser. family distributions, Bayesian networks, Bayesian offered, it may be repeated for credit. Consult the Prerequisites: At least one COMS W41xx or inference, mixture models, the EM algorithm, department for section assignment. COMS E61xx course and/or COMS W4444, or graphical models, hidden Markov models, support instructor’s permission. Strongly recommended: vector machines kernel methods. Emphasizes COMS W4996x or y Special topics in computer science, II COMS W4156. Software methodologies and methods and problems relevant to big data. technologies concerned with development and Students may not receive credit for both COMS 3 pts. Lect: 3. Prerequisite: Instructor’s permission. A continuation operation of today’s software systems. Reliability, W4771 and W4776. of COMS W4995 when the special topic extends security, systems management and societal CSEE W4823x or y Advanced logic design over two terms. issues. Emerging software architectures such as enterprise and grid computing. Term paper and 3 pts. Lect: 3. Professor Nowick. COMS E6111y Advanced database systems programming project. Seminar focus changes Prerequisite: CSEE W3827, or a half-semester 3 pts. Lect: 2. Professor Gravano. frequently to remain timely. introduction to digital logic, or equivalent. An Prerequisites: COMS W4111 and knowledge introduction to modern digital system design. COMS E6125y Web-enhanced information of Java or instructor’s permission. Continuation Advanced topics in digital logic: controller of COMS W4111, covers latest trends in both management (WHIM) synthesis (Mealy and Moore machines); database research and industry: information 3 pts. Lect: 2. Professor Kaiser. adders and multipliers; structured logic retrieval, web search, data mining, data Prerequisites: At least one COMS W41xx or COMS blocks (PLDs, PALs, ROMs); iterative circuits. warehousing, OLAP, decision support, multimedia E61xx course and/or COMS W4444, or instructor’s Modern design methodology: register transfer databases, and XML and databases. Programming permission. Strongly recommended: COMS level modelling (RTL); algorithmic state projects required. W4111. History of hypertext, markup languages,

engineering 2014–2015 116 groupware and the web. Evolving web protocols, COMS E6183x or y Advanced topics in COMS E6253y Advanced topics in formats and computation paradigms such as network security computational learning theory HTTP, XML and Web Services. Novel application 3 pts. Lect: 3. Professor Keromytis. 3 pts. Lect: 3. domains enabled by the web and societal issues. Prerequisites: COMS W4180, CSEE W4119 Prerequisite: CSOR W4231 or equivalent; COMS Term paper and programming project. Seminar and COMS W4261 recommended. Review W4252 or W4236 helpful but not required. focus changes frequently to remain timely. the fundamental aspects of security, including In-depth study of inherent abilities and limitations of computationally efficient learning algorithms. COMS E6160x or y Topics in computer authentication, authorization, access control, Algorithms for learning rich Boolean function graphics confidentiality, privacy, integrity, and availability. Review security techniques and tools, and their classes in online, Probably Approximately 3 pts. Lect: 2. Professor Belhumeur. Correct, and exact learning models. Connections Prerequisite: COMS W4160 or instructor’s applications in various problem areas. Study the with computational complexity theory permission. An advanced graduate course, state of the art in research. A programming project emphasized. Substantial course project or term involving study of an advanced research topic is required. paper required. in Computer Graphics. Content varies between COMS E6184y Seminar on anonymity and offerings, and the course may be repeated for privacy COMS E6261x or y Advanced cryptography credit. Recent offerings have included appearance 3 pts. Lect: 3. 3 pts. Lect: 3. Professor Malkin or Lewko. models in graphics, and high quality real-time Prerequisite: COMS W4261 or W4180 or Prerequisite: COMS W4261. A study of advanced rendering. CSEE W4119 or instructor’s permission. This cryptographic research topics such as: secure computation, zero knowledge, privacy, anonymity, COMS E6174y Interaction design: a course covers the following topics: Legal and cryptographic protocols. Concentration on perceptual approach social framework for privacy. Data mining and theoretical foundations, rigorous approach, 3 pts. Lect: 3. databases. Anonymous commerce and Internet and provable security. Content varies between Prerequisite: COMS W4170 or instructor’s usage. Traffic analysis. Policy and national offerings. May be repeated for credit. permission. Design methology for special-purpose security considerations. Classes are seminars user interfaces. Emphasis on how psychology and with students presenting papers and discussing COMS E6291x or y Theoretical topics in perception inform good design. Interviewing and them. Seminar focus changes frequently to computer science task modeling, participatory design, and low-fidelity remain timely. prototyping. Applications of brain research, graphic 3 pts. Lect: 3. design and art to develop custom user interfaces COMS E6185x or y Intrusion and anomaly Prerequisite: Instructor’s permission. Concentration components, screen layouts, and interaction detection systems on some theoretical aspect of computer science. techniques for application-specific systems. 2 pts. Lect: 2. Professor Stolfo. Content varies from year to year. May be repeated Pre- or corequisite: COMS W4180 Network for credit. COMS E6176x or y User interfaces for mobile security. The state of threats against computers, COMS E6732x or y Computational imaging and wearable computing and networked systems. An overview of computer 3 pts. Lect: 3. Professor Nayar. 3 pts. Lect: 2. Professor Feiner. security solutions and why they fail. Provides a Prerequisite: COMS W4731 or instructor’s Prerequisite: COMS W4170 or instructor’s detailed treatment for network and host-based permission. Introduction to research on user permission. Computational imaging uses a intrusion detection and intrusion prevention combination of novel imaging optics and a interfaces for mobile and wearable computing systems. Considerable depth is provided on through lectures, invited talks, student-led computational module to produce new forms anomaly detection systems to detect new attacks. of visual information. Survey of the state of art discussions of important papers, and programming Covers issues and problems in e-mail (spam, and projects. Designing and authoring for mobility in computational imaging. Review of recent viruses) and insider attacks (masquerading and papers on: omnidirectional and panoramic and wearability. Ubiquitous/pervasive computing. impersonation). Collaboration with other users. Display, imaging, catadioptric imaging, high dynamic interaction, and communication technologies. COMS E6204x or y Topics in graph theory range imaging, mosaicing and superresolution. Sensors for tracking position, orientation, motion, 3 pts. Lect: 2. Professor Gross. Classes are seminars with the instructor, guest speakers, and students presenting papers and environmental context, and personal context. Prerequisite: COMS W4203 or instructor’s discussing them. Applications and social consequences. permission. Content varies from year to year. This course may be repeated for credit. Concentration CSEE E6180x or y Modeling and performance COMS E6733x or y 3D photography on some aspect of graph theory, such as 3 pts. Lect: 2. Professor Misra. 3 pts. Lect: 2. Professor Allen. topological graph theory, algebraic graph theory, Prerequisites: COMS W4118 and SIEO W4150. Prerequisite: Experience with at least one of the enumerative graph theory, graphical optimization Introduction to queuing analysis and simulation following topics: Computer graphics, computer techniques. Evaluation of time-sharing and problems, or matroids. vision, pixel processing, robotics or computer-aided design, or permission of instructor. Programming multiprocessor systems. Topics include priority COMS E6206x or y Topics in combinatorial queuing, buffer storage, and disk access, proficiency in C, C++, or JAVA. 3D Photography— theory the process of automatically creating 3D, interference and bus contention problems, and 3 pts. Lect: 2. Professor Gross. modeling of program behaviors. texture-mapped models of objects in detail. Prerequisite: COMS W4203 or W4205, or Applications include robotics, medicine, graphics, COMS E6181x or y Advanced Internet instructor’s permission. Concentration on some virtual reality, entertainment and digital movies services aspect of combinatorial theory. Content varies etc. Topics include 3D data acquisition devices, 3 pts. Lect: 2. Professor Schulzrinne. from year to year. This course may be repeated 3D modeling systems and algorithms to acquire, In-depth survey of protocols and algorithms for credit. create, augment, manipulate, render, animate and physically build such models. needed to transport multimedia information COMS E6232x or y Analysis of algorithms, II across the Internet, including audio and video 3 pts. Lect: 2. COMS E6734y Computational photography encoding, multicast, quality-of-service, voice-over Prerequisites: CSOR W4231. Continuation of 3 pts. Lect: 3. Professor Belhumeur. IP, streaming media and peer-to-peer multimedia CSOR W4231. Prerequisites: COMS W4160, W4731, or a working systems. Includes a semester-long programming knowledge of photography are recommended. project. Students should have knowledge in any of three

engineering 2014–2015 core areas: computer vision, computer graphics, metastability. Analysis of latches to determine CSEE E6868x or y System-on-chip platforms 117 or photography. Computational techniques are key parameters. Bounds of input rates. Clocking 3 pts. Lect: 3. Professor Carloni. used to produce a new level of images and visual schemes for synchronous systems. Synthesis Prerequisites: COMS 3157 and CSEE 3827 representations. Topics include HDR imaging, of self-timed systems using 4-phase or 2-phase Design and programming of system-on-chip feature matching using RANSAC, image mosaics, handshakes. (SoC) platforms. Topics include: overview of image-based rendering, motion magnification, technology and economic trends, methodologies CSEE E6832x or y Topics in logic design camera lens arrays, programmable lighting, face and supporting CAD tools for system-level design theory detection, single and multiview geometry, and and verification, software simulation and virtual more. 3 pts. Lect: 3. platforms, models of computation, the SystemC Prerequisite: CSEE W3827 or any introduction to language, transaction-level modeling, hardware- COMS E6735y Visual databases logic circuits. A list of topics for each offering of software partitioning, high-level synthesis, 3 pts. Lect: 3. the course is available in the department office memory organization, device drivers, on-chip Prerequisite: COMS W3134, W3136, or W3137 one month before registration. May be taken more communication architectures, power management (or equivalent). COMS W4731 and W4735 helpful than once if topics are different Iterative logic and optimization, integration of programmable but not required. Contact instructor if uncertain. circuits applied to pattern recognition. Finite state cores and specialized accelerators. Case studies The analysis and retrieval of large collections of machines; alternative representations, information of modern SoC platforms for various classes of image and video data, with emphasis on visual loss, linear circuits, structure theory. Reliability and applications. semantics, human psychology, and user interfaces. testability of digital systems. Low-level processing: features and similarity EECS E6870x or y Speech recognition CSEE E6847y Distributed embedded systems measures; shot detection; key frame selection; 3 pts. Lect: 3. machine learning methods for classification. 3 pts. Lect: 2. Prerequisites: Basic probability and statistics. Middle-level processing: organizational rules for Prerequisite: Any COMS W411X, CSEE Theory and practice of contemporary automatic videos, including unedited (home, educational), W48XX, or ELEN E43XX course, or instructor’s speech recognition. Gaussian mixture distributions, semiedited (sports, talk shows), edited (news, permission. An interdisciplinary graduate-level hidden Markov models, pronunciation modeling, drama); human memory limits; progressive seminar on the design of distributed embedded decision trees, finite-state transducers, and refinement; visualization techniques; incorporation systems. System robustness in the presence language modeling. Selected advanced topics will of audio and text. High-level processing: extraction of highly variable communication delays and be covered in more depth. of thematic structures; ontologies, semantic filters, heterogeneous component behaviors. The and learning; personalization of summaries and study of the enabling technologies (VLSI COMS E6900x and y Tutorial in computer interfaces; detection of pacing and emotions. circuits, communication protocols, embedded science Examples and demonstrations from commercial processors, RTOSs), models of computation, 1–3 pts. and research systems throughout. Substantial and design methods. The analysis of modern Prerequisite: Instructor’s permission. A reading course project or term paper required. domain-specific applications including on-chip course in an advanced topic for a small number of micro-networks, multiprocessor systems, fault- students, under faculty supervision. COMS E6737x or y Biometrics tolerant architectures, and robust deployment of 3 pts. Lect: 3. Professor Belhumeur. embedded software. Research challenges such COMS E6901x Projects in computer science Prerequisite: Background at the sophomore as design complexity, reliability, scalability, safety, 1–12 pts. level in computer science, engineering, or like and security. The course requires substantial Prerequisite: Instructor’s permission. Software or discipline. Corequisites: None In this course we reading, class participation and a research hardware projects in computer science. Before will explore the latest advances in biometrics as project. registering, the student must submit a written well as the machine learning techniques behind proposal to the instructor for review. The proposal them. Students will learn how these technologies CSEE E6861y Computer-aided design of should give a brief outline of the project, estimated work and how they are sometimes defeated. digital systems schedule of completion, and computer resources Grading will be based on homework assignments 3 pts. Lect: 2. Professor Nowick. needed. Oral and written reports are required. and a final project. There will be no midterm Prerequisites: (i) one semester of advanced May be taken over more than one semester, in or final exam. This course shares lectures with digital logic (CSEE W4823 or equivalent, which case the grade will be deferred until all 12 COMS W4737. Students taking COMS E6737 or instructor’s permission); and (ii) a basic points have been completed. No more than 12 are required to complete additional homework course in data structures and algorithms points of COMS E6901 may be taken. Consult the problems and undertake a more rigorous final COMS W3134, W3136, W3137, W3157, or department for section assignment. equivalent, and familiarity with programming. project. Students will only be allowed to earn credit COMS E6902x and y Thesis for COMS W4737 or COMS E6737 but not both. Introduction to modern digital CAD synthesis and optimization techniques. Topics include: 1–9 pts. CSEE E6824y Parallel computer architecture modern digital system design (high-level Available to M.S. and CSE candidates. An 3 pts. Lect: 2. Professor Sethumadhavan. synthesis, register-transfer level modeling, independent investigation of an appropriate Prerequisite: CSEE W4824. Parallel computer algorithmic state machines, optimal scheduling problem in computer science carried out under the principles, machine organization and design of algorithms, resource allocation and binding, supervision of a faculty member. A formal written parallel systems including parallelism detection retiming), controller synthesis and optimization, report is essential and an oral presentation may methods, synchronization, data coherence and exact and heuristic two-level logic minimization, also be required. May be taken over more than interconnection networks. Performance analysis advanced multilevel logic optimization, optimal one semester, in which case the grade will be and special purpose parallel machines. technology mapping to library cells (for delay, deferred until all 9 points have been completed. No power and area minimization), advanced more than 9 points of COMS E6902 may be taken. CSEE E6831y Sequential logic circuits data structures (binary decision diagrams), Consult the department for section assignment. 3 pts. Lect: 3. SAT solvers and their applications, static Prerequisite: CSEE W3827 or any introduction COMS E6910x and y Fieldwork timing analysis, and introduction to testability. to logic circuits. Generation and manipulation of 1 pt. Members of the faculty. Includes hands-on small design projects using flow table descriptions to asynchronous sequential Prerequisites: Obtained internship and approval and creating CAD tools. functions. Coding of flow tables to satisfy from faculty adviser. Only for M.S. students in the various design criteria. Delays, races, hazards, Computer Science Department who need relevant work experience as part of their program of study.

engineering 2014–2015 118 Final report required. This course may not be COMS E6999x and y Topics in computer approve the number of credits. May be repeated taken for pass/fail credit or audited. science, II for credit. This course is only for M.S. candidates 3 pts. holding GRA or TA appointments. Note: It is NOT COMS E6915y Technical writing for computer Prerequisite: COMS E6998. Continuation of required that a student take Graduate research, I scientists and engineers COMS E6998. prior to taking Graduate research, II. Consult the 3 pts. Members of the faculty. department for section assignment. Available to M.S. or Ph.D. candidates in CS/ COMS E9800x and y Directed research in CE. Topics to help CS/CE graduate students’ computer science COMS E9911x and y Graduate research, II communication skills. Emphasis on writing, 1–15 pts. 1-15 pts. presenting clear, concise proposals, journal Prerequisites: Submission of outline of proposed Prerequisites: Submission of an outline of the articles, conference papers, theses, and technical research for approval by faculty member who proposed research for approval by the faculty presentations. May be repeated for credit. Credit will supervise. The department must approve the member who will supervise. The department must may not be used to satisfy degree requirements. number of points. May be repeated for credit. This approve the number of points. May be repeated course is only for Eng.Sc.D. candidates. for credit. This course is only for M.S./Ph.D. track COMS E6998x and y Topics in computer and Ph.D. students. Note: It is NOT required that science COMS E9910x and y Graduate research, I a student take Graduate research, I prior to taking 3 pts. Members of the faculty. 1–6 pts. Graduate research, II. Consult the department for Prerequisite: Instructor’s permission. Selected Prerequisites: Submission of an outline of the section assignment. topics in computer science. Content varies from proposed research for approval by the faculty year to year. May be repeated for credit. member who will supervise. The department must

engineering 2014–2015 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 Professor of Adjunct Professors Lamont Associate Associate Research Paul F. Duby professional William Becker Research Scientists Practice Raymond S. Farinato Professor Irina Chernyshova Department Robert Farrauto Vasilis M. Fthenakis Wade McGillis Hongkeun Park Administrator D. R. Nagaraj Partha Patra Anna Kovács Associate Special Research Professors Adjunct Associate Scientist Professors Kartik Chandran Professor Nickolas J. Themelis Paul F. Duby Xi Chen Marco J. Castaldi Klaus S. Lackner Ah-Hyung (Alissa) Park Senior Research Upmanu Lall Adjunct Assistant Scientist Ismail C. Noyan Assistant Professor Professors Vasilis M. Fthenakis Peter Schlosser Pierre Gentine Yuri Gorokhovich Ponisseril Somasundaran Christoph Meinrenken Tuncel M. Yegulalp Srinivasan Rangarajan

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 (MSE). This program, administered students who want to enrich their of Mines at Columbia by the Department of Applied academic record by concentrating University Physics and Applied Mathematics, is some of their technical electives on The School of Mines of Columbia described on page 171. Earth/Environment subjects. There is close collaboration between EEE and University was established in 1864 and • The Earth Engineering Center the Departments of Civil Engineering was the first mining and metallurgy (seas.columbia.edu/earth). The and Earth and Environmental Sciences, department in the U.S. It became the current research areas include energy, including several joint appointments. foundation for Columbia’s School of materials, and water resources. Engineering and Applied Sciences and has been a pioneer in many areas of

engineering 2014–2015 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 mangement 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 tecnologies 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 (www chains, and risk management using renewable energy integration into .wtert.org) has sister organizations in novel structural and financial tools. electricity grids. It is developing 14 countries including Canada, China, America’s Water is the third models for evaluating and optimizing Germany, Greece, India, Italy, Mexico, major initiative. It is driven by the energy storage units for ramping and the U.K. Over the years, WTERT goal of developing sustainable water rate control in photovoltaic power research at Columbia has engaged management and infrastructure plants, optimizing penetration of st many M.S. and Ph.D. students on all design paradigms for the 21 century, solar and wind resources, and aspects of waste management (see recognizing the linkages between urban unit commitment and economic www.wtert.org, Publications, Theses). functioning, food, water, energy, and dispatch of conventional generators EEC conducts a biannual survey of climate. It seeks to pull together a to compensate for solar and wind waste management in the 50 states of comprehensive understanding of the variability in large-scale penetrations. the Union. issues facing water infrastructure in • Resource assessment and recycling the USA. These include the financing of critical energy materials variability:

engineering 2014–2015 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. of colloids and interfaces with science and engineering disciplines. The Center encompasses detailed surfactants and macromolecules. LCCI At the same time, it integrates structure-property assessment of several activities involve significant interaction technological research with analysis classes of surface-active molecules, with industrial sponsors and adopt of the institutional, economic, and including oligomeric, polymeric, and an interdisciplinary approach toward political context within which energy bio-molecules. The aim of CPaSS state-of-the-art resarch on interfacial technologies are commercialized and is to develop and characterize novel phenomena. Major areas of research deployed. For more information: energy surfactants for industrial applications at LCCI are thin films, surfactant and .columbia.edu. such as coatings, dispersions, polymer adsorption, environmental deposition, gas hydrate control, personal problems, enhanced oli recovery, care products, soil decontamination, computer tomography, corrosion and Scholarships, Fellowships, waste treatment, corrosion prevention, catalysis mechanisms, membrance and Internships flotation, and controlled chemical technology, novel separations of The department arranges for reactions. The proposed research thus minerals, biocolloids, microbial surfaces, undergraduate summer internships focuses on the design and development and interfacial spectroscopy. after the sophomore and junior years. of specialty surfactants, characterization Undergraduates can also participate in Lenfest Center for Sustainable Energy. of their solution and interfacial behavior, graduate research projects under the The mission of the Lenfest Center and 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 2014–2015 122 Undergraduate Program of past, present, and future industrial to 4000-level courses of any Columbia The Bachelor of Science (B.S.) degree activities; and analysis and design of Engineering department, as well as in Earth and Environmental Engineering processes for remediation, recycling, courses listed in the section “Courses in prepares students for careers in the and disposal of used materials. Other Divisions” in this bulletin. However, public and private sector concerned with 4. Graduates will practice their at least four of the six junior/senior primary materials (minerals, fuels, water) profession with excellent written electives must consist of engineering and the environment. Graduates are and communication skills and topics. Alternatives for sophomore-year also prepared to continue with further with professional ethics and science courses are shown in the EEE studies in Earth/Environmental sciences responsibilities. program table. and engineering, business, public policy, A student may also choose to international studies, law, and medicine. The Curriculum develop an individual concentration The EEE program is accredited as an The first two years of the EEE program conforming to his/her specific interests, environmental engineering program are similar to those of other engineering provided that it satisfies ABET by the Engineering Accreditation programs. Students are provided with engineering accreditation criteria. Commission of ABET. a strong foundation in basic sciences Therefore, this must be developed in and mathematics, as well as the liberal close consultation with and approved by What Is Earth and Environmental arts core. Specific to the EEE program a faculty adviser. Engineering? is an early and sustained introduction It is now recognized by the U.S. and to Earth science and environmental Water Resources and Climate Risks other nations that continuing economic engineering, and options for a number Concentration development must be accompanied by of science courses to meet the specific Preapproved course sequence: intelligent use of Earth’s resources and interests of each student. The junior PHYS C1403: Introduction to classical and quantum waves (SEM III) that engineers can contribute much and senior years of the program consist of a group of required courses EESC V2100: Climate system (SEM III) to the global efforts for sustainable EAEE E4006: Field methods for environmental in engineering science and a broad development. The technologies that engineering (SEM VI) have been developed for identifying, selection of technical electives organized EAEE E4009: G IS for resource, environmental, extracting, and processing primary into three distinct concentrations, and infrastructure management materials are also being applied to representing major areas of focus within (SEM VII) the twenty-first-century problems of the department. EAEE E4350: Planning and management of urban resource recovery from used materials, Several Columbia departments, hydrologic systems (SEM VII) EAEE E4257: Environmental data analysis and pollution prevention, and environmental such as Civil Engineering, Mechanical Engineering, and Earth and Environ- modeling (SEM VIII) remediation. The EEE undergraduate ECIA W4100: M anagement and development of mental Sciences (Lamont-Doherty Earth program encompasses these water systems (SEM VIII) technologies. Observatory), as well as the Mailman CIEE E4257: G roundwater contaminant transport School of Public Health, contribute and remediation Undergraduate Program Objectives courses to the EEE program. EEE students are strongly encouraged to Alternatives for junior/senior electives: 1. Graduates equipped with the work as summer interns in industry or EAEE E4001: Industrial ecology of Earth resources necessary tools (mathematics, agencies on projects related to Earth EESC W4008: Introduction to atmospheric science chemistry, physics, Earth sciences, and Environmental Engineering. The CIEE E4163: E nvironmental engineering: wastewater and engineering science) will APPH E4200: Physics of fluids department helps students get summer understand and implement the CIEN E4250: Waste containment design and practice internships. underlying principles used in the CIEN E4255: Flow in porous media engineering of processes and EESC W4401: Quantitative models of climate- systems. Technical Elective Concentrations sensitive natural and human systems EESC W4404: R egional dynamics, climate and 2. Graduates will be able to pursue Students majoring in Earth and Environ climate impacts careers in industry, government mental Engineering select one of the agencies, and other organizations following three preapproved technical Sustainable Energy and Materials concerned with the environment elective concentrations. Note that Concentration and the provision of primary and the eight-course sequence for each secondary materials and energy, preapproved concentration includes two Preapproved course sequence: science courses during sophomore year CHEM C3443: O rganic chemistry (SEM III) as well as continue their education EESC V2200: Solid earth system (SEM III) (fall semester) and six technical elective as graduate students in related EESC W4001: Advanced general geology (SEM III) disciplines. courses during junior and senior years. MECE E3311: H eat transfer (SEM VI) 3. Graduates will possess the basic skills Any deviations from a preapproved EAEE E4001: Industrial ecology of Earth needed for the practice of Earth and concentration must be approved by resources (SEM VII) Environmental Engineering, including an undergraduate faculty adviser. EAEE E4361: Economics of Earth resource Alternatives for junior/senior electives industries (SEM VII) measurement and control of material EAEE E4190: Photovoltaic systems engineering within each concentration are listed, and flows through the environment; and sustainability (SEM VII) assessment of environmental impact others may be considered among 3000- MECE E4302: A dvanced thermodynamics (SEM VIII)

engineering 2014–2015 123 earth and environmental engineering program: first and second Years

Semester i Semester iI Semester iII Semester iV

MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) APMA E2101 (3) mathematics or MATH V1207 (4) MATH V1208 (4) MATH E1210 (3) ODE

C1401 (3) C1402 (3)

physics or C1601 (3.5) C1602 (3.5) CHEM C3443 (3.5) or C2801 (4.5) C2802 (4.5) or PHYS C1403 (3) or C1403 (3.5) C1404 (3.5) and Lab C1500 (3) either semester PHYS C2601 (3.5) or BIOL C2005 (4) chemistry or C1604 (3.5) C2507 (3)

or C3045 (3.5) C3046 (3.5) and Lab C2507 (3)

HUMA C1001, HUMA C1002, COCI C1101, COCI C1102, or Global Core (3–4) or Global Core (3–4) C1010 (3) required or nontechnical Z1003 (4) C1010 (3) ECON W1105 (4) and electives or W1155 recitation (0) ALP0006 (0) Z1003 (4) or C1010 (3) HUMA C1121 or C1123 (3)

EESC W4001 (4) or EESC V2100 (4.5) required or EESC V2200 (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 C1001 (1) C1002 (1) education

THE ART OF ENGI E1102 (4) either semester ENGINEERING

EESC W3015: T he Earth’s carbon cycle (SEM VIII) EAEE E4210: Thermal treatment of waste and EAEE E4006: Field methods for environmental MECE E4211: E nergy: sources and conversion biomass materials engineering (SEM VI) (SEM VIII) CHEM G4230: Statistical thermodynamics EAEE E4009: G IS for resource, environmental CHEE E4140: Engineering separations processes EAEE E4550: Catalysis for emissions control and infrastructure management EACE E4560: Particle technology (SEM VII) Alternatives for junior/senior electives: EHSC P6300: Environmental health sciences CHEM C3071: Introduction to inorganic chemistry (SEM VII) MSAE E3103: Elements of materials science Environmental Health Engineering EAEE E4257: E nvironmental data analysis and CHEN E3110: T ransport phenomena, I Concentration modeling (SEM VIII) CHEN E3120: T ransport phenomena, II Preapproved course sequence: EAEE E4150: A ir pollution prevention and control EESC W4008: Introduction to atmospheric science CHEM C3443: O rganic chemistry (SEM III) (SEM VIII) EESC V2100: Climate system (SEM III)

engineering 2014–2015 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 transportation 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 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: G roundwater 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 phenomena while being employed. For students with a B.S. in 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 Graduate Programs engaged in mineral processing ventures, the environmental industry, environmental points (total of sixteen courses) may be groups in all industries, and for city, state, required for makeup courses. Students M.S. in Earth and Environmental and federal agencies responsible for may carry out a research project and Engineering (M.S.-EEE) the environment and energy/resource write a thesis worth 3–6 points. A The M.S.-EEE program is designed conservation. At the present time, the number of areas of study are available for engineers and scientists who plan U.S. environmental industry comprises for the M.S.-EEE, and students may to pursue, or are already engaged in, nearly 30,000 big and small businesses choose courses that match their interest environmental management/development with total revenues of more than $150 and career plans. The areas of study careers. The focus of the program is billion. Sustainable development and include: the environmentally sound mining and environmental quality has become a top

engineering 2014–2015 • Alternative energy and carbon • Models for design and operation of with environmental sciences and energy 125 management water resource systems, considering engineering will be another aspect of the • Climate risk assessment and climate and other uncertainties concentration. Additional specialization management • Integrated risk assessment and may consider region-specific energy • Environmental health engineering management across water resources development. • Integrated waste management and related sectors • Natural and mineral resource Integrated Waste Management (IWM) development and management Sustainable Energy Humanity generates nearly 2 billion tons • Novel technologies: surfacial and Building and shaping the energy of municipal solid wastes (MSW) annually. colloidal chemistry and infrastructure of the twenty-first century Traditionally, these wastes have been nanotechnology is one of the central tasks for modern discarded in landfills that have a finite • Urban environments and spatial analysis engineering. The purpose of the lifetime and then must be replaced by Additionally, there are three optional sustainable energy concentration is converting more greenfields to landfills. concentrations in the program, in each to expose students to modern energy This method is not sustainable because of which there are a number of required technologies and infrastructures and to it wastes land and valuable resources. specific core courses and electives. The the associated environmental, health, Also, it is a major source of greenhouse concentrations are described briefly and resource limitations. Emphasis gases and of various contaminants of below; details and the lists of specific will be on energy generation and use air and water. In addition to MSW, the courses for each track are available from technologies that aim to overcome the U.S. alone generates billions of tons of the department. limits to growth that are experienced industrial and extraction wastes. Also, today. Energy and economic well-being the by-product of water purification is a Water Resources and Climate Risks are tightly coupled. Fossil fuel resources sludge or cake that must be disposed are still plentiful, but access to energy is in some way. The IWM concentration Climate-induced risk is a significant limited by environmental and economic prepares engineers to deal with the component of decision making for the constraints. A future world population major problem of waste generation planning, design, and operation of water of 10 billion people trying to approach by exposing them to environmentally resource systems, and related sectors the standard of living of the developed better means for dealing with wastes: such as energy, health, agriculture, nations cannot rely on today’s energy waste reduction, recycling, composting, ecological resources, and natural hazards technologies and infrastructures without and waste-to-energy via combustion, control. Climatic uncertainties can be severe environmental impacts. Concerns anaerobic digestion, or gasification. broadly classified into two areas: (1) over climate change and changes in Students are exposed not only to the those related to anthropogenic climate ocean chemistry require reductions in technical aspects of integrated waste change; (2) those related to seasonal- carbon dioxide emissions, but most management but also to the associated to century-scale natural variations. alternatives to conventional fossil economic, policy, and urban planning The climate change issues impact the fuels, including nuclear energy, are too issues. design of physical, social, and financial expensive to fill the gap. Yet access Since the initiation of the Earth and infrastructure systems to support to clean, cheap energy is critical for environmental engineering program in the sectors listed above. The climate providing minimal resources: water, 1996, there have been several graduate variability and predictability issues impact food, housing, and transportation. research projects and theses that systems operation, and hence design. Concentration-specific classes will exemplify the engineering problems that The goal of the M.S. concentration in sketch out the availability of resources, will be encompassed in this concentration: water resources and climate risks is to their geographic distribution, the provide (1) a capacity for understanding economic and environmental cost of • Design of an automated materials and quantifying the projections for resource extraction, and avenues for recovery facility climate change and variability in the increasing energy utilization efficiency, • Analysis of the bioreactor landfill context of decisions for water resources such as cogeneration, district heating, • Generation of methane by anaerobic and related sectors of impact; and (2) and distributed generation of energy. digestion of organic materials skills for integrated risk assessment and Classes will discuss technologies for • Design of corrosion inhibitors management for operations and design, efficiency improvement in the generation • Flocculation modeling as well as for regional policy analysis and and consumption sector; energy • Analysis of formation of dioxins in high- management. Specific areas of interest recovery from solid wastes; alternatives temperature processes include: to fossil fuels, including solar and wind • Combination of waste-to-energy and energy, and nuclear fission and fusion; anaerobic digestion • Numerical and statistical modeling of and technologies for addressing the • Application of GIS in siting new WTE global and regional climate systems environmental concerns over the use of facilities and attendant uncertainties fossil fuels and nuclear energy. Classes • Corrosion phenomena in WTE • Methods for forecasting seasonal to on climate change, air quality, and health • Combustion chambers interannual climate variations and their impacts focus on the consequences of • Mathematical modeling of transport sectoral impacts energy use. Policy and its interactions phenomena in a combustion chamber

engineering 2014–2015 126 • Effect of oxygen enrichment on at least one course in each core area technology. Introduction to carbon dioxide capture combustion of paper and other types of during their first two semesters at Columbia and carbon dioxide disposal as a means of solid wastes (see website for up-to-date course listing). sustaining the fossil fuel option. • Feasibility study and design of WTE In case the student declares an explicit EAEE E2100x A better planet by design facilities minor in another department, the qualifying 3 pts. Lect: 3. Professors Lall and Park. exam requirements will be modified in Introduction to design for a sustainable planet. Doctoral Programs consultation with the graduate committee. Scientific understanding of the challenges. The minor has to be approved by both Innovative technologies for water, energy, EEE offers two doctoral degrees: food, materials provision. Multiscale modeling departments. (1) the Eng.Sc.D. degree, administered by and conceptual framework for understanding Columbia Engineering; and (2) the Ph.D. The engineering objectives of EEE environmental, resource, human, ecological, degree, administered by the Graduate research and education include: and economic impacts and design performance School of Arts and Sciences. evaluation. Focus on the linkages between • Provision and disposal of materials: planetary, regional, and urban water, energy, mineral, food, climate, economic, and ecological Doctoral Qualifying Examination and environmentally sustainable extraction and processing of primary cycles. Solution strategies for developed and Research Proposal developing country settings. materials; manufacturing of derivative Before the end of the first semester in the products; recycling of used materials; CHEE E3010x Principles of chemical doctoral program, the student and her/his management of industrial residues engineering thermodynamics adviser will set up an advisory committee and used products; materials-related 3 pts. Lect: 3. Professor Kumar. of two or three faculty members. This application of industrial ecology. Prerequisite: CHEM C1403. Corequisite: CHEN committee will meet at least once a E3030. Introduction to thermodynamics. • Management of water resources: semester to assess academic and Fundamentals are emphasized: the laws of understanding, prediction, and research progress of the student and to thermodynamics are derived and their meaning management of the processes that recommend corrective action in case of explained and elucidated by applications to govern the quantity and quality of engineering problems. Pure systems are treated, emerging or existing deficiencies. water resources, including the role with an emphasis on phase equilibrium. Doctoral students are required to of climate; development/operation of pass a qualifying exam soon after the EAEE E3101y Earth resource production water resource facilities; management of completion of their first year into the systems water-related hazards. program (spring or fall). They will submit 3 pts. Lect: 3. Not offered in 2014–2015. • Energy resources and carbon Technologies and equipment common to a wide and defend their research proposal management: mitigation of range of surface and subsurface engineering approximately one year after successful environmental impacts of energy activities: mine reclamation, hazardous waste completion of the qualifying exam. production; energy recovery from waste remediation, discovering and operating surface Submission of the dissertation and thesis and underground mines, detection and removal materials; advancement of energy defense will follow general University rules. of hidden underground objects, waste disposal, efficient systems; new energy sources; The qualifying examination will be an dredging and harbor rehabilitation, and tunneling development of carbon sequestration oral exam administered by four faculty for transportation or water distribution systems. strategies. These methods and equipment are examined members. The adviser of the student will • Sensing and remediation: as they apply across the spectrum from mining be a member of the exam committee understanding of transport processes at to environmental engineering projects. The aim but may not be the chair. The students different scales and in different media; is to provide a broad background for earth and will be examined in their understanding environmental engineers in careers involving containment systems; modeling flow of fundamentals as they apply in the minerals and industrial, large-scale environmental and transport in surface and subsurface four general areas of research of the projects. systems; soil/water decontamination department: water resources, materials and bioremediation. EAEE E3103x Energy, minerals, and materials processing, energy, and chemical and systems biochemical processes. It is expected 3 pts. Lect: 3. Professors Park and Yegulalp. that each question period will last about Prerequisites: MSAE E3111 or MECE E3301 20 minutes, of which 15 minutes will be courses in earth and ENME E3161 or MECE E3100 or equivalent led by the faculty member from the area and environmental Corequisites: MSAE E3111 or MECE E3301 and ENME E3161 or MECE E3100 or equivalent. and the remaining 5 minutes will be open engineering Overview of energy resources, resource for questions by all faculty present at the EAEE E2002x Alternative energy resources management from extraction and processing to exam. There will be a final period of 20 3 pts. Lect: 3. Instructor to be announced. recycling and final disposal of wastes. Resources minutes for general questions. Unconventional, alternative energy resources. availability and resource processing in the context All graduate students are expected Technological options and their role in the world of the global natural and anthropogenic material to have a background equivalent to energy markets. Comparison of conventional cycles; thermodynamic and chemical conditions the required core of our undergraduate and unconventional, renewable and non- including nonequilibrium effects that shape the resource base; extractive technologies and their program. They have, of course, an renewable energy resources and analysis of the consequences of various technological choices impact on the environment and the biogeochemical opportunity to make up for any deficiency cycles; chemical extraction from mineral ores, and in their master’s program. In order to be and constraints. Economic considerations, energy availability, and the environmental consequences metallurgical processes for extraction of metals. prepared for the exam, students can take of large-scale, widespread use of each particular In analogy to metallurgical processing, power

engineering 2014–2015 generation and the refining of fuels are treated as introduction to hydrologic and hydraulic the submission of an acceptable thesis or final 127 extraction and refining processes. Large scale of systems, with a focus on integrated report. This course cannot substitute for the power generation and a discussion of its impact on modeling and analysis of the water cycle Undergraduate design project (EAEE E3999 or the global biogeochemical cycles. and associated mass transport for water EAEE E3999). EAEE E3112y Introduction to rock mechanics resources and environmental engineering. EAEE E3901y Environmental microbiology 3 pts. Lect: 3. Not offered in 2014–2015. Coverage of unit hydrologic processes such 3 pts. Lect: 3. Professor Chandran. Prerequisites: EAEE E3101 and ENME 3111, or as precipitation, evaporation, infiltration, Prerequisite: CHEM C1404 or equivalent. their equivalents. Rock as an engineering material, runoff generation, open channel and pipe flow, Fundamentals of microbiology, genetics and geometry and strength of rock joints, geotechnical subsurface flow and well hydraulics in the molecular biology, principles of microbial nutrition, classification of rock masses, strength and failure context of example watersheds and specific energetics and kinetics, application of novel and of rock, field investigations prior to excavation in integrative problems such as risk-based state-of-the-art techniques in monitoring the rock, rock reinforcement, analysis and support of design for flood control, provision of water, structure and function of microbial communities rock slopes and tunnels, and case histories. and assessment of environmental impact in the environment, engineered processes for or potential for non-point source pollution. biochemical waste treatment and bioremediation, MSAE E3141y Processing of metals and Spatial hydrologic analysis using GIS and microorganisms and public health, global microbial semiconductors watershed models. elemental cycles. 3 pts. Lect: 3. Professor Duby. Prerequisite: MSAE E3103 or equivalent. CIEE E3255y Environmental control and EAEE E3998x-E3999y Undergraduate design Synthesis and production of metals and pollution reduction systems project semiconductors with engineered microstructures 3 pts. Lect: 3. Professor Farrauto. 2 pts. (each semester). Lect: 1. Lab: 2. for desired properties. Includes high-temperature, Prerequisite: EAEE E3200 or ENME E3161 or Professor Farrauto. aqueous, and electrochemical processing; thermal MECE E3100. Review of engineered systems for Prerequisite: senior standing. Students must enroll and mechanical processing of metals and alloys; prevention and control of pollution. Fundamentals for both 3998x and 3999y during their senior casting and solidification; diffusion, microstructural of material and energy balances and reaction year. Selection of an actual problem in Earth and evolution, and phase transformations; modification kinetics. Analysis of engineered systems to environmental engineering, and design of an and processing of surfaces and interfaces; address environmental problems including solid engineering solution including technical, economic, deposition and removal of thin films. Processing of and hazardous waste, air, water, soil and noise environmental, ethical, health and safety, social Si and other materials for elemental and compound pollution. Life cycle assessments and emerging issues. Use of software for design, visualization, semiconductor-based electronic, magnetic, and technologies. economic analysis, and report preparation. optical devices. Students may work in teams. Presentation of EAEE E3800y Earth and environmental results in a formal report and public presentation. EAEE E3185y Summer fieldwork for Earth and engineering laboratory, I environmental engineers 2 pts. Lect: 1. Lab: 3. Professors Farrauto and Duby. EAEE E4001x Industrial ecology of earth 0.5 pt. Not offered in 2014–2015. Prerequisite: CHEE E3010. Corequisite: EAEE resources Undergraduates in Earth and environmental E3255. Experiments on fundamental aspects 3 pts. Lect: 3. Professor Meinrenken. engineering may spend up to 3 weeks in the field of Earth and environmental engineering with Industrial ecology examines how to reconfigure under staff direction. The course consists of mine, emphasis on the applications of chemistry, industrial activities so as to minimize the adverse landfill, plant, and major excavation site visits and biology and thermodynamics to environmental environmental and material resource effects on the brief instruction of surveying methods. A final report processes: energy generation, analysis and planet. Engineering applications of methodology is required. purification of water, environmental biology, and of industrial ecology in the analysis of current processes and products and the selection or EAEE E3200x Applied transport and chemical biochemical treatment of wastes. Students will learn the laboratory procedures and use analytical design of environmentally superior alternatives. rate phenomena equipment firsthand, hence demonstrating Home assignments of illustrative quantitative 3 pts. Lect: 3. Professor Chen. experimentally the theoretical concepts learned problems. Prerequisite: APMA E2101. Fluid statics. Basics in class. of flow analysis. Dimensional analysis. Pipe flow. EAEE E4003x Introduction to aquatic chemistry Fluid dynamics, heat and mass transfer. Effects of EAEE E3801x Earth and environmental 3 pts. Lect: 3. Professor Duby. velocity, temperature, and concentration gradients engineering laboratory, II Prerequisite: CHEE E3010. Principles of physical and material properties on fluid flow, heat and 2 pts. Lect: 1. Lab: 3. Professors Farrauto and Duby. chemistry applied to equilibria and kinetics of mass transfer. Applications to environmental Prerequisite: EAEE E3800. Corequisite: EAEE aqueous solutions in contact with minerals and engineering problems. E4003. A continuation of EAEE E3800, with anthropogenic residues. The scientific background for addressing problems of aqueous pollution, EAEE E3221x Environmental geophysics emphasis on the principles underlying water analysis for inorganic, organic, and bacterial water treatment, and sustainable production of 3 pts. Lect: 3. Not offered in 2014–2015. contaminants. Lab required. materials with minimum environmental impact. Introduction to applied and environmental Hydrolysis, oxidation-reduction, complex formation, geophysics methods. Overview of principles of EAEE E3900x and y–S3900 Undergraduate dissolution and precipitation, predominance geophysics, geophysical methods and techniques research in Earth and environmental diagrams; examples of natural water systems, (seismic, ground penetrating radar, resistivity, engineering processes for water treatment and for the frequency em, and magnetics), and theory and 0–3 pts. Directed study. Members of the faculty. production of inorganic materials from minerals. practical aspects of data processing and inversion. This course may be repeated for credit, but Examination of geophysical case studies for no more than 3 points of this course may be EAEE E4004x Physical processing and engineering and environmental purposes. counted towards the satisfaction of the B.S. recovery of solids 3 pts. Lect: 3. Not offered in 2014–2015. CIEE E3250y Hydrosystems engineering degree requirements. Candidates for the B.S. Generalized treatment of processes for solids 3 pts. Lect: 3. Professor Lall. degree may conduct an investigation in Earth and Environmental Engineering, or carry out a separation. Applications to materials processing Prerequisites: CHEN E3110 or ENME E3161 and handling; mining; solid waste, recycling, and or equivalent, SIEO W3600 or equivalent, special project under the supervision of EAEE faculty. Credit for the course is contingent on resource recovery; construction materials and or instructor’s permission. A quantitative debris; scrap materials, yard and park wastes.

engineering 2014–2015 128 Economic considerations and context. Relevant balance, flooding, asset management, and water and wastewater treatment, or distribution materials properties and bulk materials analyses. emergency response to natural or man-made system evaluation and improvement. Process system flow-sheets and analysis. Solid/ hazards. Technical content includes geography and CHEE E4140x Engineering separations solid, solid/liquid, and solid/gas separation process. map projections, spatial statistics, database design Liberation, concentration, and auxiliary processes. and use, interpolation and visualization of spatial processes Design of separation machines: types and surfaces and volumes from irregularly spaced data, 3 pts. Lect: 3. Professor Park. intensities of force involved; scalling-up factors. and decision analysis in an applied setting. Taught Prerequisites: CHEN E3100, E3120, and Laboratory demonstrations and a field trip will be in a laboratory setting using ArcGIS. Access to E3210 or permission of instructor. Design included. New York City and other standard databases. Term and analysis of unit operations employed in projects emphasize information synthesis towards chemical engineering separations. Fundamental EAEE E4005x Near-surface engineering the solution of a specific problem. aspects of single and multistaged operations geophysics using both equilibrium and rate-based methods. EAEE E4010y Remote sensing and 3 pts. Lect: 3. Not offered in 2014–2015. Examples include distillation, absorption and environmental change Geophysical methods as applicable to stripping, extraction, membranes, crystallization, engineering problems. Principles of geophysics 3 pts. Lect: 3. Professors Bell and Ceccato. bioseparations, and environmental applications. and noninvasive imaging techniques (inversion Prerequisite: EAEE E4009 or EESC W4050 or technology) and benefits and pitfalls of geophysics instructor’s permission. Practical and theoretical EAEE E4150y Air pollution prevention and vs. direct imaging methods. Discussion of theory foundations for the application of remote sensing control of each method. Discussion of data acquisition, techniques to identification and monitoring of 3 pts. Lect: 3. Professor Fthenakis. processing and interpretation for each method. environmental change. Designing and applying Adverse effects of air pollution, sources and Treatment of several case studies. Class-wide spectral indices for assessment and monitoring, transport media, monitoring and modeling of planning and execution of small-scale geophysical time series analysis of remote sensing data for air quality, collection and treatment techniques, survey. analyzing environmental problems. Discussions pollution prevention through waste minimalization of published literature relevant to the central topic and clean technologies, laws, regulations, EAEE E4006y Field methods for covered in class. Analysis of remote sensing data standards, and guidelines. environmental engineering using IRI data library. 3 pts. Lect: 1.5. Lab: 2. Professor McGillis. EAEE E4160y Solid and hazardous waste Prerequisite: ENME E3161 or equivalent or EAEE E4011y Industrial ecology for management instructor’s permission Principles and methods for manufacturing 3 pts. Lect: 3. Professor Somasundaran. designing, building and testing systems to sense 3 pts. Lect: 3. Not offered in 2014–2015. Generation, composition, collection, transport, the environment. Monitoring the atmosphere, water Prerequisite: EAEE E4001. Application of industrial storage and disposal of solid and hazardous bodies and boundary interfaces between the two. ecology to Design for Environment (DFE) of waste. Impact on the environment and public Sensor systems for monitoring heat and mass processes and products using environmental health. Government regulations. Recycling and flows, chemicals, and biota. Measurements of indices of resources consumption and pollution resource recovery. velocity, temperature, flux and concentration in the loads. Introduction of methodology for Life Cycle field. The class will involve planning and execution Assessment (LCA) of manufactured products. CIEE E4163x Sustainable water treatment of a study to sense a local environmental system. Analysis of several DFE and LCA case studies. and reuse Term project required on use of DFE/LCA on 3 pts. Lect: 3. Professor Becker. EAEE E4007y Environmental geophysics field a specific product/process: (a) product design Prerequisites: Introductory chemistry (with lab) studies complete with materials and process selection, and fluid mechanics, or the equivalent. Theory and 3 pts. Lect: 3. Not offered in 2014–2015. energy consumption, and waste loadings; (b) LCA application of the physical and chemical processes Application of geophysical methods to noninvasive of an existing industrial or consumer product using for treating potable water and reusing wastewater. assessment of the near surface. First part consists a commercially established method. Disinfection/oxidation, coagulation and floccuation, of series of two-hour lectures of physics and clarification, filtration, ion exchange, adsorption, math involved in instrumental methods and data CHEE E4050x Industrial and environmental membrane processes, advanced oxidation acquisition and processing. the field (nine field electrochemistry processes, activated sludge, and anaerobic sludge days) students plan surveys; collect and analyze 3 pts. Lect: 3. Professor Duby. digestion. geophysical data in teams; learn how to integrate Prerequisite: CHEN E3010 or equivalent. A geophysical data with invasive data, hydrological, presentation of the basic principle underlying EAEE E4190x Photovoltaic systems geological, engineering, and contaminant transport electrochemical processes. Thermodynamics, engineering and sustainability models; and develop a comprehensive and electrode kinetics, and ionic mass transport. 3 pts. Lect: 3. Professor Fthenakis. justifiable model of the subsurface. Geophysical Examples of industrial and environmental Prerequisite: Senior standing or instructor’s methods include GPR (Ground Penetrating applications illustrated by means of laboratory permission. Corequisites: N/A. A systems approach Radar), conductivity, and magnetic and seismic experiments: electroplating, refining, and for intermittent renewable energy involving the methods. Field applications include infrastructure/ winning in aqueous solutions and in molten study of resources, generation, demand, storage, environmental assessment, archeological studies, salts; electrolytic treatment of wastes; primary, transmission, economics and politic. Study of and high resolution geology. secondary, and fuel cells. current and emerging photovoltaic technologies, with focus on basic sustainability metrics EAEE E4009x Geographic information ECIA W4100y Management and development (e.g., cost, resource availability, and life-cycle systems (GIS) for resource, environmental of water systems environmental impacts). The status and potential and infrastructure management 3 pts. Lect: 3. Professor Lall. of first- and second-generation photovoltaic 3 pts. Lect: 3. Professor Gorokhovich. Decision analytic framework for operating, technologies (e.g., crystalline and amorphous Si, Prerequisite: Permission of the instructor. Basic managing, and planning water systems, CdTe, CIGS) and emerging third-generation ones. concepts of geomatics, spatial data representation considering changing climate, values and needs. Storage options to overcome the intermittency and organization, and analytical tools that Public and private sector models explored through constraint. Large scales of renewable energy comprise GIS are introduced and applied to a U.S.-international case studies on topics ranging technologies and plug-in hybrid electric cars. variety of problems including watershed protection, from integrated watershed management to the environmental risk assessment, material mass analysis of specific projects for flood mitigation,

engineering 2014–2015 EAEE E4200y Production of inorganic water resources and environmental engineering. EAEE E4257y Environmental data analysis 129 materials Coverage of unit hydrologic processes such as and modeling 3 pts. Lect: 3. Professor Duby. precipitation, evaporation, infiltration, runoff 3 pts. Lect: 3. Professor Yegulalp. Prerequisite: CHEE E3010 or equivalent. generation, open channel and pipe flow, Prerequisite: SIEO W3600 or W4250 or equivalent. Production and recycling of inorganic materials in subsurface flow and well hydraulics in the context Statistical methods for the analysis of the aqueous and high temperature systems. Industrial of example watersheds and specific integrative space and time structure in environmental data. and environmental applications of hydrometallurgy, problems such as risk-based design for flood Application to problems of climate variation and pyrometallurgy, and electrometallurgy. Reactor control, provision of water, and assessment of change; hydrology; air, water and soil pollution systems for, e.g., leaching, precipitation, and environmental impact or potential for non-point dynamics; disease propagation; ecological solvent extraction, bath and flash smelting source pollution. Spatial hydrologic analysis using change; and resource assessment. Applications reactors, rotary kilns, and fluid bed reactors. GIS and watershed models. are developed using the ArcView Geographical Thermodynamic and kinetic factors and Information System (GIS), integrated with currently CHEE E4252x Introduction to surface and materials/energy balances involved in the design available statistical packages. Team projects colloid chemistry and performance of such reactors in typical that lead to publication-quality analyses of data 3 pts. Lect: 3. Professor Somasundaran. applications. in various environmental fields of interest. An Prerequisite: Elementary physical chemistry. interdisciplinary perspective is emphasized in this EAIA E4200y Alternative energy resources Thermodynamics of surfaces, properties of applications-oriented class. 3 pts. Lect: 3. Instructor to be announced. surfactant solutions and surface films, electrostatic Unconventional, alternative energy resources. and electrokinetic phenomena at interfaces, EAEE E4300x or y Introduction to carbon Technological options and their role in the world adsorption; interfacial mass transfer and modern management energy markets. Comparison of conventional and experimental techniques. 3 pts. Lect: 3. Professor Schlosser. unconventional, renewable and nonrenewable, Prerequisites: Undergraduate level mathematics CIEE E4252y Environmental engineering energy resources and analysis of the and science, or instructor’s permission. 3 pts. Lect: 3. Professor Chandran. consequences of various technological choices Introduction to natural and anthropogenic carbon Prerequisites: CHEM C1403, or equivalent; and constraints. Economic considerations, energy cycle, and carbon and climate. Rationale and need ENME E3161 or equivalent. Engineering aspects availability, and the environmental consequences to manage carbon and tools with which to do so of problems involving human interaction with of large-scale, widespread use of each particular (basic science, psychology, economics and policy the natural environment. Review of fundamental technology. Introduction to carbon dioxide disposal background, negotiations and society; emphasis principles that underlie the discipline of as a means of sustaining the fossil fuel option. on interdisciplinary and inter-dependent approach). environmental engineering, i.e., constituent Recitation section required. Simple carbon emission model to estimate the transport and transformation processes in impacts of a specific intervention with regard to EAEE E4210x Thermal treatment of waste and environmental media such as water, air, and national, per capita, and global emissions. Student- biomass materials ecosystems. Engineering applications for led case studies (e.g., reforestation, biofuels, addressing environmental problems such as water 3 pts. Lect: 3. Professor Castaldi. CCS, efficiency, alternative energy) to illustrate quality and treatment, air pollution emissions, Prerequisite: CHEE E3010 or the equivalent necessary systems approach required to tackle and hazardous waste remediation. Presented in or instructor’s permission. Origins, quantities global challenges. generated, and characterization of solid wastes. the context of current issues facing the practicing Chemical and physical phenomena in the engineers and government agencies, including EAEE E4301y Carbon storage combustion or gasification of wastes. Application legal and regulatory framework, environmental 3 pts. Lect: 3. Professor Lackner. of thermal conversion technologies, ranging impact assessments, and natural resource Prerequisites: Undergraduate level mathematics from combustion to gasification and pyrolysis. management. and science, or instructor’s permission. Major Quantitative description of the dominant waste technologies to capture carbon dioxide via new or EAEE E4255x River and coastal to energy processes used worldwide, including retro-fitted power plant designs, during industrial hyrdrodynamics feedstock preparation, moving grate and fluid bed processes, and from ambient air. In addition 3 pts. Lect: 3. Professor Cioffi. combustion, heat transfer from combustion gases to basic science and engineering challenges Prerequisites: CHEN E3110 or ENME E3161 or the to steam, mitigation of high-temperature corrosion, of each technology, full spectrum of economic, equivalent. Dynamics of flow and waves in rivers electricity generation, district heating, metal environmental, regulatory, and political/policy and coastal settings, with applications to flooding recovery, emission control, and beneficial use of aspects, and their implication for regional and and mixing of saline and fresh waters, sediment ash residues. global carbon management strategies of the transport. Integrative hydrodynamics modeling future. Combination of lectures, class debates EAEE E4241x Solids handling and transport experience using numerical and analytical tools and breakout groups, student presentations, and systems applied to complex real world setting, including independent final projects. 3 pts. Lect: 3. Not offered in 2014–2015. concerns of anthropogenic change in rivers and Analysis and design of transportation systems estuaries and sea level fluctuations at the river- EAEE E4302x or y Carbon capture for bulk solids in tunnels, mines, and large estuary boundary. 3 pts. Lect: 3. Professor Lackner. excavations. Design of hoisting, cable transport, Prerequisites: Undergraduate level math CIEE E4257y Groundwater contaminant rail and trackless haulage systems, conveyor and science or instructor’s permission. Major transport and remediation belts, selection of loaders, excavators, off-highway technologies to store carbon dioxide, geological, 3 pts. Lect: 3. Professor Mutch. trucks, and draglines for large excavations. ocean, and in the carbon chemical pool. Carbon Prerequisite: CIEE E3250 or equivalent. Sources dioxide transport technologies also covered. CIEE E4250y Hydrosystems engineering and types of groundwater contamination. In addition to basic science and engineering 3 pts. Lect: 2.5. Professors Lall and Gentine. Groundwater hydrology. Groundwater contaminant challenges of each technology, full spectrum of Prerequisites: CHEN E3110 or ENME E3161 or rate and transport. Flow and transport in the economic, environmental, regulatory, and political/ equivalent, SIEO W3600 or equivalent, or the unsaturated zone. Nonaqueous phase liquids and policy aspects, and their implication for regional instructor’s permission. A quantitative introduction multiphase flow. Physical and numerical models and global carbon management strategies of the to hydrologic and hydraulic systems, with a for contaminant transport. Characterization and future. Combination of lectures, class debates focus on integrated modeling and analysis of the assessment of contaminated sites. Groundwater and breakout groups, student presentations, and water cycle and associated mass transport for remediation alternatives. Regulations. independent final projects.

engineering 2014–2015 130 EAEE E4303x or y Carbon measurement and production, global trade, consumption of mineral stoichiometric parameters. Engineering design monitoring commodities and fuels. Economics of recycling of several bioreactor configurations employed 3 pts. Lect: 3. Professor Meinrenken. and substitution. Methods of project evaluation: for biochemical waste treatment. Mathematical Prerequisites: Undergraduate level math and estimation of operating costs and capital modeling of engineered biological reactors using science or instructor permission. Sources of requirements, project feasibility, risk assessment, state-of-the-art simulation packages. various GHGs (whether fossil/industrial or and environmental compliance. Cost estimation EAEE E4951x Engineering systems for water biogenic), their chemical behavior, interactions, for reclamation/remediation projects. Financing of treatment and reuse and global warming potential once airborne; reclamation costs at abandoned mine sites and waste-disposal post-closure liability. 3 pts. Lect: 3. Professors Becker and Chandran. available measurement, monitoring, and detection Prerequisites: CIEE E4163 and EAEE 3901, or the technologies to track gas emissions, including CHEE E4530y Corrosion of metals instructor’s permission. Application of fundamental leakage from storage sites. Carbon accounting 3 pts. Lect: 3. Professor Duby. principles to designing water treatment and and reporting methodologies such as life cycle Prerequisite: CHEN E3010 or equivalent. The reuse plants. Development of process designs analysis, and corporate carbon footprinting. theory of electrochemical corrosion, corrosion for a potable water treatment plant, a biological In addition to basic science and engineering tendency, rates, and passivity. Application to wastewater treatment plant, or a water reclamation challenges of each technology, full spectrum of various environments. Cathodic protection and and reuse facility by students working in teams. economic, environmental, regulatory, and political/ coatings. Corrosion testing. Student work in evaluation of water quality and policy aspects, and their implication for regional pilot plant data, screeening process alternatives, EAEE E4550x Catalysis for emissions control and global carbon management strategies of the conducting regulatory reviews and recommending 3 pts. Lect: 3. Professor Farrauto. future. Combination of lectures, class debates a process for implementation, supported by Prerequisites: ENME E3161 and MSAE E3111 and breakout groups, student presentations, and engineering drawings and capital operating or equivalent. Fundamentals of heterogeneous independent final projects. costs. Periodic oral progress reports and a full catalysis including modern catalytic preparation engineering report are required. Presentations EAEE W4304x Closing the carbon cycle techniques. Analysis and design of catalytic by practicing engineers, utility personnel, and 3 pts. Lect: 3. Professor Eisenberger. emissions control systems. Introduction to current regulators; and field trips to water, wastewater, and Prerequisites: Calculus, basic inorganic chemistry, industrial catalytic solutions for controlling gaseous water reuse facilities. and basic physics, including thermodynamics, or emissions. Introduction to future catalytically instructor’s permission. Introduction to complex enabled control technologies. EAEE E4980 Urban environmental technology and policy systems, their impact on our understanding EACE E4560y Particle technology and predictability of the carbon cycle, the use 3 pts. Lect: 3. Not offered in 2014–2015. 3 pts. Lect: 3. Professor Park. of systems analysis and modeling tools, as well Progress of urban pollution engineering via Prerequisites: ENME E3161 and MSAE E3111 as Bayesian statistics and decision theory for contaminant abatement technology, government or equivalent. Introduction to engineering evaluating various solutions to close the carbon policy, and public action in urban pollution. processes involving particulates and powders. cycle, a detailed examination of the geochemical Pollutant impact on modern urban environmental The fundamentals of particle characterization, carbon cycle, major conceptual models that quality, natural resources, and government, multiphase flow behavior, particle formation, couple its changes to climate change, analysis of municipal, and social planning and management processing and utilization of particles in various the anthropogenic carbon sources and sinks and programs. Strong emphasis on current and engineering applications with examples in role of carbon in energy production, closing the twentieth-century waste management in New energy and environment related technologies. carbon cycle impacts on energy security, economic York City. Engineering of functionalized particles and development and climate change protection, design of multiphase reactors and processing EAEE E6132y Numerical methods in analysis of solutions to close the carbon cycle. units with emphasis on fluidization technology. geomechanics EAEE E4350x Planning and management of Particle technology is an interdisciplinary field. 3 pts. Lect: 3. Professor Chen. urban hydrologic systems Due to the complexity of particulate systems, Prerequisites: EAEE E3112 and CIEN E4241 3 pts. Lect: 3. Professor Rangarajan. particle technology is often treated as art rather or instructor’s permission. A detailed survey Prerequisite: ENME E3161 or equivalent. than science. In this course, the fundamental of numerical methods used in geomechanics, Introduction to runoff and drainage systems in an principles governing the key aspects of particle emphasizing the Finite Element Method (FEM). urban setting, including hydrologic and hydraulic science and technology are introduced along with Review of the behavior of geological materials. analyses, flow and water quality monitoring, various industrial examples. Water and heat flow problems. FEM techniques for solving nonlinear problems, and simulating common regulatory issues, and mathematical EAEE E4901y Environmental microbiology modeling. Applications to problems of climate incremental excavation and loading on the surface 3 pts. Lect: 3. Professor Chandran. variation, land use changes, infrastructure and underground. Basic microbiological principles; microbial operation and receiving water quality, developed metabolism; identification and interactions EAEE E6150y Industrial catalysis using statistical packages, public-domain models, of microbial populations responsible for the 3 pts. Lect: 3. Professor Farrauto. and Geographical Information Systems (GIS). biotransformation of pollutants; mathematical Prerequisite: EAEE E4550 or equivalent, or Team projects that can lead to publication quality modeling of microbially mediated processes; instructor’s permission. Fundamental principles analyses in relevant fields of interest. Emphasis on biotechnology and engineering applications using of kinetics, characterization and preparation of the unique technical, regulatory, fiscal, policy, and microbial systems for pollution control. catalysts for production of petroleum products other interdisciplinary issues that pose a challenge for conventional transportation fuels, specialty to effective planning and management of urban EAEE E4950x Environmental biochemical chemicals, polymers, food products, hydrogen hydrologic systems. processes and fuel cells and the application of catalysis 3 pts. Lect: 3. Professor Chandran. EAEE E4361y Economics of earth resource in biomass conversion to fuel. Update of the Prerequisite: EAEE 4901, E4003, CIEE E4252, or industries ever changing demands and challenges in instructor’s approval. Qualitative and quantitative 3 pts. Lect: 3. Professor Yegulalp. environmental applications, focusing on advanced considerations in engineered environmental Prerequisite: EAEE E3103 or instructor’s catalytic applications as described in modern biochemical processes. Characterization of permission. Definition of terms. Survey of literature and patents. multiple microbial reactions in a community and Earth resource industries: resources, reserves, techniques for determining associated kinetic and

engineering 2014–2015 EAEE E6151y Applied geophysics instructor’s permission. New technologies for flotation, separation techniques, catalysis, mass 131 3 pts. Lect: 3. Not offered in 2014–2015. capturing carbon dioxide and disposing of it away transfer, emulsions, foams, aerosols, membranes, Potential field data, prospecting, wave equations. from the atmosphere. Detailed discussion of the biological surfactant systems, microbial surfaces, Huygens’ principle, Green’s functions, Kirchoff extent of the human modifications to the natural enhanced oil recovery, and pollution problems. equation, WKB approximation, ray tracing. Wave carbon cycle, the motivation and scope of future Appropriate individual experiments and projects. propagation, parameters. Computer applications. carbon management strategies and the role of Lab required. Wavelet processing, filters and seismic data. carbon sequestration. Introduction of several EAEE E6255x-E6256y Methods and Stratified Earth model, seismic processing and carbon sequestration technologies that allow for profiling. Radon transform and Fourier migration. the capture and permanent disposal of carbon applications of analytical decision making in Multidimensional geological interpretation. dioxide. Engineering issues in their implementation, mineral industries economic impacts, and the environmental issues 3 pts. Lect: 3. Not offered in 2014–2015. EAEE E6200y Theory and applications of raised by the various methods. Prerequisites: Instructor’s permission. Advanced extreme value statistics in engineering and study of decision-making problems with critical earth sciences CHEE E6220y Equilibria and kinetics in survey and applications of quantitative decision- 3 pts. Lect: 3. Professor Yegulalp. hydrometallurgical systems making techniques in mineral industries. Prerequisite: STAT W4107 or equivalent 3 pts. Lect: 3. Professor Duby. Systematic development of methods of the background in probability and statistical inference, Prerequisite: CHEE E4050 or EAEE E4003. formulation, analysis, and resolution of these or instructor’s permission. Introduction of Detailed examination of chemical equilibria problems. fundamental concepts in extreme value statistics. in hydrometallurgical systems. Kinetics and EAEE E8229x Selected topics in processing The exact and asymptotic theory of extremes. mechanisms of homogeneous and heterogeneous Development of statistical methodology for reactions in aqueous solutions. minerals and wastes estimating the parameters of asymptotic extremal 3 pts. Lect: 2. Lab: 3. Professor Nagaraj. EAEE E6220x Remedial and corrective action distributions from experimental data. Examples of Prerequisite: CHEE E4252 or instructor’s applications of extreme value statistics to regional 3 pts. Lect: 3. Not offered in 2014–2015. permission. Critical discussion of current research and global earthquake forecasting, laboratory Prerequisite: EAEE E4160 or equivalent. Integrates topics and publications in the area of flotation, the engineering aspects of cleanup of hazardous testing of rocks and metals, fatigue failure, floods, flocculation, and other mineral processing materials in the environment. Site assessment/ droughts, extreme wind velocities, and rainfalls. techniques, particularly mechanisms of adsorption, investigation. Site closure, containment, and EAEE E6208y Combustion chemistry and control techniques and technologies. Techniques interactions of particles in solution, thinning of processes used to treat hazardous materials in the liquid films, and optimization techniques. 3 pts. Lect: 3. Professor Castaldi. environment, in situ and removal for treatment, EAEE E8231y Selected topics in hydro- and Prerequisite: EAEE E4900 or equivalent or focusing on those aspects that are unique to the electrometallurgy instructor’s permission. The fundamentals application of those technologies in an uncontrolled 3 pts. Lect: 3. Professor Duby. of combustion phenomena and the intrinsic natural environment. Management, safety, and Prerequisites: EAEE E4003 and CHEE chemistry of combustion processes. The theory training issues. E4050, or instructor’s permission. Review of of the essential combustion processes such as EAEE E6228y Theory of flotation current research and literature in the field of ignition, sustained reaction, stability and flame hydrometallurgy, electrometallurgy, and corrosion. quenching. Processes that govern reactant 3 pts. Lect: 3. Not offered in 2014–2015. Prerequisite: CHEE E4252 or instructor’s Topics will be selected by the instructor to consumption and product formation, in particular illustrate the application of thermodynamics and by-products that are formed that result in pollutant permission. A detailed study of the physicochemical principles of the flotation process. rate phenomena to the design and control of emissions, and the impacts and implications electrochemical engineering processes. that combustion has locally and globally on the EAEE E6240x or y Physical hydrology environment. Detailed examination of the entire 3 pts. Lect: 3. Professor Gentine. EAEE E8233x and y Research topics in range of combustion systems from diffusion flame Prerequisite: Engineering hydrology or equivalent. particle processing processes to current developing technologies Spatial/temporal dynamics of the hydrologic cycle 0 pts. Professor Somasundaran. including millisecond catalytic combustion and its interactions with landforms and vegetation. Emergent findings in the interactions of particles processes, noncarbon fueled combustion, fuel Hydroclimatology at regional to planetary scales, with reagents and solutions, especially inorganics, cells, and plasma combustion. focusing on mechanisms of organization and surfactants, and polymers in solution, and variation of water fluxes as a function of season, their role in grinding, flotation, agglomeration, EAEE E6210x Quantitative environmental risk filtration, enhanced oil recovery, and other mineral analysis location, reservoir (ocean, atmosphere, land), and time scale. Land-atmosphere interaction and the processing operations. 3 pts. Lect: 3. Professor Yegulalp. role of vegetation and soil moisture. Topography Prerequisite: EAEE E3101, SIEO W4150, or EAEE E8273x-E8274y Mining engineering as an organizing principle for land water fluxes. equivalent. Comprises the tools necessary for reports Geomorphology and the evolution of river technical professionals to produce meaningful 0–4 pts. Professor Yegulalp. networks. Sedimentation, erosion and hill slope risk analyses. Review of relevant probability and May substitiute for formal thesis, EAEE E9271, hydrology. Dynamics of water movement over land, statistics; incorporation of probability in facility upon recommendation of the student’s adviser. in rivers and in the subsurface, with an emphasis failure analysis. Availability, assessment, and on modeling interfaces. Integrated models and the EAEE E9271x and y–S9271 Earth and incorporation of risk-related data. Contaminant scale problem. Emphasis on data-based spatial/ environmental engineering thesis transport to exposed individuals; uptake, morbidity, temporal modeling and exploration of outstanding and mortality. Computational tools necessary to 0–6 pts. Members of the faculty. theoretical challenges. risk modeling. Use and applicability of resulting Research work culminating in a creditable dissertation on a problem of a fundamental measurements of risk, and their use in public CHEE E6252y Advanced surface and colloid nature selected in conference between student policy and regulation. chemistry and adviser. Wide latitude is permitted in choice 3 pts. Lect: 2. Lab: 3. Professors Farinato and EAEE E6212y Carbon sequestration of a subject, but independent work of distinctly 3 pts. Lect: 3. Professor Lackner. Somasundaran. graduate character is required in its handling. Prerequisite: EAEE E4900 or equivalent or Prerequisite: CHEE E4252. Applications of surface chemistry principles to wetting, flocculation,

engineering 2014–2015 132 EAEE E9273x-E9274y Earth and the four key issues that limit the expansion EAEE E9800x and y–S9800 Doctoral research environmental engineering reports of nuclear energy: cost, safety, proliferation instruction 0–4 pts. concerns, and long-term disposal of radioactive 3, 6, 9, or 12 pts. Members of the faculty. May substitute for the formal master’s thesis, wastes. Through readings, research, and class A candidate for the Eng.Sc.D. degree in mineral EAEE E9271, upon recommendation of the discussions, it engages students to critically engineering must register for 12 points of doctoral department. evaluate arguments both for and against nuclear research instruction. Registration in EAEE E9800 power. The course builds basic literacy in nuclear may not be used to satisfy the minimum residence EAEE E9280x and y Earth and environmental technology and is open to students with technical, requirement for the degree. engineering colloquium policy, or economic backgrounds. 0 pts. Lect: 1.5. Professor Gentine. EAEE E9900x and y–S9900 Doctoral All graduate students are required to attend the EAEE E9302x and y Mining engineering dissertation departmental colloquium as long as they are in research 0 pts. Members of the faculty. residence. Advanced doctoral students may be 0–4 pts. Professor Yegulalp. A candidate for the doctorate may be required excused after three years of residence. No degree Graduate research directed toward solution of to register for this course every term after the credit is granted. technicoscientific problems in mining. student’s course work has been completed, and until the dissertation has been accepted. EAEE E9281x Prospects for nuclear energy– EAEE E9305x and y–S9305 Earth and earth and environmental engineering seminar environmental engineering research 0–1 pt. Lect: 1.5. Professors Gazze and Lackner. 0–12 pts. Members of the faculty. This seminar course examines the prospects for Graduate research directed toward solution of nuclear energy as a source of safe, secure, and a problem in mineral processing or chemical environmentally sustainable energy both in the metallurgy. U.S. and internationally. In particular, it analyzes

engineering 2014–2015 Electrical Engineering 133 1300 S. W. Mudd, MC 4712 Phone: 212-854-3105 ee.columbia.edu

Chair Steven Nowick, Associate Adjunct Associate Associate ResearcH Keren Bergman Computer Science Professor of Professors Scientists 1305 S. W. Mudd Richard M. Osgood Jr. Professional Timothy Dickson Dong Liu Henning G. Schulzrinne, Practice Rogerio Ferris Noam Ohpir Vice Chair Computer Science Zoran Kostic Wilfried Haensch Vladimir Sokolov Charles A. Zukowski Amiya K. Sen Benjamin Lee 1026 CEPSR Kenneth L. Shepard Senior Lecturer Jiang Libin Postdoctoral Yannis P. Tsividis David Vallancourt Ching-Yung Lin Research Department Wen I. Wang Deepak Turaga Scientists Adjunct Administrator Xiaodang Wang Subhabrata Professors Janice Savage Charles A. Zukowski Adjunct Assistant Bhattacharya 1303 S. W. Mudd Yves Baeyens Professors Tao Chen Doru Calin Associate Mohammad Ali Maddah- Guy Grebla Liangliang Cao Professors Professors Ali Andreas Hartel Mark Feuer Dimitris Anastassiou Ioannis (John) Kymissis Neda Cvijetic Krishna Jayant Irving Kalet Keren Bergman Gil Zussman Urs Niesen Hongki Kang Shih-Fu Chang Jeffrey Kash Yi Sun Jianxun Lin Robert Laibowitz Dan Ellis Assistant Chao Tian Vladimir Sokolov Andreas H. Hielscher, Professors Ta-Hsin Li Jun Wang David Meng-Ting Tsai Biomedical Engineering Javad Ghaderi Truong-Thao Nguyen Kai Yang Sefi Vernick Tony F. Heinz Christine Hendon Bhuvana Ramabhadran Predrag Jelenkovic Javad Lavaei Krishan Sabnani Senior Research Postdoctoral Peter Kinget Harish Krishnaswamy Vinay Vaishampayan Scientist Research fellow Aurel A. Lazar Nima Mesgarani Vinay Varadan Robert Laibowitz David Meng-Ting Tsai Nicholas Maxemchuk John Paisley Harish Viswanathan Debasis Mitra Mingoo Seok Anwar Walid John Wright Shalom Wind Thomas Woo

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 2014–2015 134 Research Activities conductors, pin diodes, avalanche Photonics Laboratory, Plasma Physics The research interests of the faculty photodiodes, optical interconnects, and Laboratory (in conjunction with the encompass a number of rapidly growing quantum optics. A major effort is the Department of Applied Physics). areas, vital to the development of future picosecond optoelectronics program, Laboratory instruction is provided in technology, that will affect almost every focusing on the development of new the Introduction to Electrical Engineering aspect of society: communications devices and their applications to high- Laboratory, Marcellus-Hartley Electronics and information processing; solid-state speed optoelectronic measurement Laboratory, Microprocessor Laboratory, devices; ultrafast optics and photonics; systems, photonic switching, and optical Microwave Laboratory, Optical microelectronic circuits, integrated logic. In addition, research is being Electronics Laboratory, Solid-State systems and computer-aided design; performed in detection techniques for Laboratory, VLSI Design Laboratory, and systems biology; and electromagnetics optical communications and radar. Student Projects Laboratory, all on the and plasmas. Details on all of Members of the photonics group play twelfth floor of the S. W. Mudd Building. these areas can be found at a leading role in a multi-university consortium: The National Center for ee.columbia.edu/research. Undergraduate Program Integrated Photonics Technology. Communications research focuses The educational objective of the Integrated systems research involves on wireless communication, multimedia Electrical Engineering program, in the analysis and design of analog, digital, networking, real-time Internet, support of the mission of the School, is and mixed-signal microelectronic circuits lightwave (fiber optic) communication to prepare graduates to achieve success and systems. These include novel signal networks, optical signal processing in one or more of the following within a processors and related systems, data and switching, service architectures, few years after graduation: network management and control, converters, radio frequency circuits, low noise and low power circuits, and the processing of image and video A. Graduate or professional studies—as fully integrated analog filters that share information, and media engineering. evidenced by admission to a top-tier the same chip with digital logic. VLSI Current studies include wireless and program, attainment of advanced architectures for parallel computation, mobile computing environments, degrees, research contributions, or packet switching, and signal processing broadband kernels, object-oriented professional recognition. are also under investigation. Computer- network management, real-time B. Engineering practice—as evidenced aided design research involves the monitoring and control, lightwave by entrepreneurship; employment in development of techniques for the network architectures, lightweight industry, government, academia, or analysis and design of large-scale protocol design, resource allocation and nonprofit organizations in engineering; integrated circuits and systems. networking games, real-time Internet patents; or professional recognition. Electromagnetics research ranges services, future all-digital HDTV systems, C. Careers outside of engineering that from the classical domains of microwave coding and modulation. take advantage of an engineering generation and transmission and wave Solid-state device research education—as evidenced by propagation in various media to modern is conducted in the Columbia contributions appropriate to the applications involving lasers, optical Microelectronics Sciences Laboratories. chosen field. This is an interdisciplinary facility, fibers, plasmas, and solid-state devices. Problems relevant to controlled thermo- involving aspects of electrical The B.S. program in electrical nuclear fusion are under investigation. engineering and applied physics. It engineering at Columbia University seeks includes the study of semiconductor to provide a broad and solid foundation physics and devices, optical electronics, Laboratory Facilities in the current theory and practice of and quantum optics. The emphasis is Current research activities are fully electrical engineering, including familiarity on laser processing and diagnostics supported by more than a dozen well- with basic tools of math and science, for submicron electronics, fabrication equipped research laboratories run by an ability to communicate ideas, and of compound semiconductor the department. Specifically, laboratory a humanities background sufficient to optoelectronic devices by molecular research is conducted in the following understand the social implications of beam epitaxy, physics of superlattices laboratories: Multimedia Networking engineering practice. Graduates should and quantum wells, and interface Laboratory, Lightwave Communications be qualified to enter the profession devices such as Schottky barriers, Laboratory, Systems Laboratory, Image of engineering, to continue toward a MOS transistors, heterojunctions, and and Advanced Television Laboratory, career in engineering research, or to bipolar transistors. Another area of Laser Processing Laboratory, Molecular enter other fields in which engineering activity is the physics and chemistry of Beam Epitaxy Laboratory, Surface knowledge is essential. Required microelectronics packaging. Analysis Laboratory, Microelectronics nontechnical courses cover civilization Research in photonics includes Fabrication Laboratory, Device and culture, philosophy, economics, development of semi conductor light Measurement Laboratory, Ultrafast and a number of additional electives. sources such as LEDs and injection Optoelectronics Laboratory, Columbia English communication skills are an lasers, fabrication and analysis of Integrated Systems Laboratory (CISL), important aspect of these courses. quantum confined structures, photo Lightwave Communications Laboratory, Required science courses cover basic

engineering 2014–2015 135 electrical engineering PROGRAM: FIRST and SECOND Years early-starting students

Semester i Semester iI Semester iII Semester iV

MATH V1202 (3) mathematics MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) and APMA E2101 (3)1

physics C1401 (3) C1402 (3) (three tracks, C1601 (3.5) C1602 (3.5) choose one) C2801 (4.5) C2802 (4.5)

one-semester lecture (3–4) chemistry C1403 or C1404 or C3045 or C1604

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

english C1010 (3) composition (three tracks, Z1003 (0) C1010 (3) choose one) Z0006 (0) Z1003 (0) C1010 (3)

required HUMA C1001, COCI C1101, or Major Cultures (3–4); HUMA W1121 or W1123 (3); HUMA C1002, COCI nontechnical C1102, or Global Core (3–4); ECON W1105 (4) and W1155 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 C1001 (1) C1002 (1) education

the art of ENGI E1102 (4) either semester engineering

1 APMA E2101 may be replaced by MATH E1210 and either APMA E3101 or MATH V2010. 2 If possible, these labs should be taken along with their corresponding lecture courses. 3 ENGI E1006 may not be offered every semester. See www.ee.columbia.edu for more discussion about the Computer Science sequences.

chemistry and physics, whereas math Topics include a sequence of two theoretical work. Simple creative design requirements cover calculus, differential courses on circuit theory and electronic experiences start immediately in this equations, probability, and linear algebra. circuits, one course on semiconductor first-year course. Following this is a Basic computer knowledge is also devices, one on electromagnetics, one sequence of lab courses that parallel included, with an introductory course on on signals and systems, one on digital the core lecture courses. Opportunities using engineering workstations and two systems, and one on communications for exploring design can be found rigorous introductory computer science or networking. Engineering practice is both within these lab courses and courses. Core electrical engineering developed further through a sequence in the parallel lecture courses, often courses cover the main components of laboratory courses, starting with a coupled with experimentation and of modern electrical engineering and first-year course to introduce hands- computer simulation, respectively. The illustrate basic engineering principles. on experience early and to motivate culmination of the laboratory sequence

engineering 2014–2015 136 electrical engineering: Third and Fourth Years early-starting students

Semester V Semester VI Semester VII Semester VIII

C1403 (3) Lab C1494 (3)1 physics (tracks continued) C2601 (3.5) Lab C2699 (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 41054; and COMS W3136 (or W3133, 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)

breadth At least two technical electives outside the chosen depth area; must be engineering courses tech (see ee.columbia.edu)

E lecti v e s other Additional technical electives (consisting of more depth or breadth courses, or further options listed at tech ee.columbia.edu/academics/undergrad) 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 1500) 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 W4150 cannot generally be used to replace IEOR E3658 or STAT W4105. 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 E1210 and either APMA E3101 or MATH V2010. 7 “Total points” assumes that 20 points of nontechnical electives and other courses are included.

and the design experiences introduced core program, encourages creativity, technical electives are required, chosen throughout earlier courses is a senior explores practical aspects of engineering to provide both breadth and depth in a design course (capstone design practice, and provides additional specific area of interest. More detailed course), which includes a significant experience with communication skills in program objectives and outcomes are design project that ties together the an engineering context. Finally, several posted at ee.columbia.edu.

engineering 2014–2015 137 electrical engineering program: first and second Years late-starting students

Semester i Semester iI Semester iII Semester iV

MATH V1202 (3) mathematics MATH V1101(3) MATH V1102 (3) MATH V1201 (3) and APMA E2101 (3)1

physics C1401 (3) C1402 (3) C1403 (3) Lab C1494 (3)2 (three tracks, C1601 (3.5) C1602 (3.5) C2601 (3.5) Lab C2699 (3) choose one) C2801 (4.5) C2802 (4.5) Lab W3081 (2)

one-semester lecture (3–4) chemistry C1403 or C1404 or C3045 or C1604

electrical ELEN E1201 (3.5) either semester3 engineering

english C1010 (3) composition (three tracks, Z1003 (0) C1010 (3) choose one) Z0006 (0) Z1003 (0) C1010 (3)

HUMA C1001, HUMA C1002, COCI C1101, COCI C1102, required or Global Core (3–4) or Global Core (3–4) nontechnical electives HUMA W1121 or ECON W1105 (4) and W1123 (3) W1155 recitation (0)

computer ENGI E1006 (3) any semester4 science

physical C1001 (1) C1002 (1) education

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 APMA E2101 may be replaced by MATH E1210 and either APMA E3101 or MATH V2010. 2 Chemistry lab (CHEM C1500) 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 www.ee.columbia.edu for more discussion about the Computer Science sequences.

The program in electrical engineering EE Core Curriculum Technical Electives leading to the B.S. degree is accredited All electrical engineering (EE) students The 18-point technical elective by the Engineering Accreditation must take a set of core courses, which requirement for the electrical engineering Commission of ABET. collectively provide the student with program consists of three components: There is a strong interaction between fundamental skills, expose him/her depth, breadth, and other. A general the Department of Electrical Engineering to the breadth of EE, and serve as a outline is provided here, and more and the Departments of Computer springboard for more advanced work, or specific course restrictions can be found Science, Applied Physics and Applied for work in areas not covered in the core. at ee.columbia.edu. For any course not Mathematics, Industrial Engineering These courses are shown on the charts clearly listed there, adviser approval is and Operations Research, Physics, and in Undergraduate Degree Tracks. A full necessary. Chemistry. curriculum checklist is also posted at The depth component must consist of ee.columbia.edu. at least 6 points of electrical engineering courses in one of four defined areas: (a) photonics, solid-state devices,

engineering 2014–2015 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 W41053; and COMS W3136 (or W3133, 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.)

breadth At least two technical electives outside the chosen depth area; must be tech engineering courses (see ee.columbia.edu)

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 W4150 cannot generally be used to replace IEOR E3658 or STAT W4105. 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 E1210 and either APMA E3101 or MATH V2010. 6 “Total points” assumes that 9 points of nontechnical electives are included.

and electromagnetics; (b) circuits and and exposure to the process of exploring consist of at least 6 additional points of electronics; (c) signals and systems; and a discipline in depth—an essential engineering courses that are outside of (d) communications and networking. process that can be applied later to other the chosen depth area. These courses The depth requirement provides an disciplines, if desired. can be from other departments within opportunity to pursue particular interests The breadth component must the School. The breadth requirement engineering 2014–2015 precludes overspecialization. Breadth Plan 2: This plan is for students who Applicants who, for good reasons, 139 is particularly important today, as have taken a course equivalent to ELEN are unable to submit GRE test results innovation requires more and more E1201 at their school of origin, including by the deadline date but whose of an interdisciplinary approach, and a laboratory component. See the bulletin undergraduate record is clearly superior exposure to other fields is known to help for a description of this course. Many may file an application without the GRE one’s creativity in one’s own main field. pre-engineering programs and physics scores. An explanatory note should be Breadth also reduces the chance of departments at four-year colleges offer added to ensure that the application will obsolescence as technology changes. such courses. Such students can start be processed even while incomplete. If Any remaining technical elective taking circuits at Columbia immediately, the candidate’s admissibility is clear, the courses, beyond the minimum 12 points and thus can choose circuits and decision may be made without the GRE of depth and breadth, do not have to be electronics as a depth area. scores; otherwise, it may be deferred engineering courses (except for students until the scores are received. It is stressed that ELEN E1201 or without ELEN E1201 or approved transfer There are no prescribed course its equivalent is a key part of the EE credit for ELEN E1201) but must be requirements in any of the regular curriculum. The preparation provided by technical. Generally, math and science graduate degree programs. Students, in this course is essential for a number of courses that do not overlap with courses consultation with their faculty advisers, other core courses. used to fill other requirements are allowed. design their own programs, focusing on Sample programs for both Plan 1 particular fields of electrical engineering. and Plan 2 transfer students can be Among the fields of graduate study are Starting Early found at ee.columbia.edu. The EE curriculum is designed to allow microelectronics, communications and signal processing, integrated circuit students to start their study of EE in their B.S./M.S. Program first year. This motivates students early and system analysis and synthesis, The B.S./M.S. degree program is open and allows them to spread nontechnical photonics, electromagnetic theory to a select group of undergraduate requirements more evenly. It also makes and applications, plasma physics, and students. This double degree program evident the need for advanced math and quantum electronics. makes possible the earning of both physics concepts, and motivates the Graduate course charts for the Bachelor of Science and Master of study of such concepts. Finally, it allows several focus areas can be found at Science degrees simultaneously. Up to 6 more time for students to take classes ee.columbia.edu. points may be credited to both degrees, in a chosen depth area, or gives them and some graduate classes taken in more time to explore before choosing Master of Science Degree the senior year may count toward the a depth area. Students can start with Candidates for the M.S. degree in M.S. degree. Both degrees may be ELEN E1201: Introduction to electrical electrical engineering must complete 30 conferred at the same time. Interested engineering in the second semester of points of credit beyond the bachelor’s students can find further information at their first year, and can continue with degree. A minimum of 15 points of www.ee.columbia.edu and can discuss other core courses one semester after credit must be at the 6000 level or options directly with their faculty adviser. that, as shown in the “early-starting higher. No credit will be allowed for Students must be admitted prior to students” chart. It is emphasized that undergraduate courses (3000 or lower). the start of their seventh semester at both the early- and late-starting sample At least 15 points must be in Columbia Engineering. Students in the programs shown in the charts are Electrical Engineering, as defined at 3-2 Combined Plan undergraduate examples only; schedules may vary ee.columbia.edu/academics/masters. program are not eligible for admission to depending on student preparation and Courses to be credited toward the this program. interests. M.S. degree can be taken only upon prior approval of a faculty adviser in the Transfer Students Graduate Programs Department of Electrical Engineering. Transfer students coming to The Department of Electrical Engineering This applies to the summer session as Columbia as juniors with sufficient offers graduate programs leading to the well as the autumn and spring terms. general background can complete all degree of Master of Science (M.S.), and Certain 4000-level courses will not requirements for the B.S. degree in the degrees of Doctor of Engineering be credited toward the M.S. degree, electrical engineering. Such students fall Science (Eng.Sc.D.) and Doctor of and no more than 6 points of research into one of two categories: Philosophy (Ph.D.). The Graduate may be taken for credit. Up to 3 points Record Examination (General Test only) of credit for approved graduate courses Plan 1: Students coming to Columbia is required of all applicants except outside of engineering and science without having taken the equivalent of special students. An undergraduate may be allowed. The general school ELEN E1201 must take this course in grade-point average equivalent to B or requirements listed earlier in this bulletin, their junior year. This requires postponing better from an institution comparable to such as minimum GPA, must also be the core courses in circuits and Columbia is expected. satisfied. All degree requirements must electronics until the senior year, and thus be completed within five years of the does not allow taking electives in that beginning of the first course credited area; thus, such students cannot choose toward the degree. circuits and electronics as a depth area.

engineering 2014–2015 140

More details and a checklist for doctoral program. information on available courses, visit adviser approvals can be found at More detailed information regarding the Electrical Engineering home page at ee.columbia.edu. the requirements for the doctoral degree ee.columbia.edu. may be obtained in the department Doctoral Degree office and at ee.columbia.edu. Concentration in Multimedia The requirements for the Ph.D. and Eng. Networking Sc.D. degrees are identical. Both require Optional M.S. Concentrations Advisers: Professors Henning a dissertation based on the candidate’s Students in the electrical engineering Schulzrinne, Predrag Jelenkovic original research, conducted under the M.S. program often choose to use supervision of a faculty member. The work some of their electives to focus on 1. Satisfy M.S. degree requirements. may be theoretical or experimental or both. a particular field. Students may pick 2. Both ELEN E6761: Computer Students who wish to become one of a number of optional, formal communication networks, I and candidates for the doctoral degree in concentration templates or design their ELEN E6950: Wireless and mobile electrical engineering have the option of own M.S. program in consultation with networking, I. applying for admission to the Eng.Sc.D. an adviser. These concentrations are not 3. Either COMS W4118: Operating program or the Ph.D. program. Students degree requirements. They represent systems or COMS W4111: Database who elect the Eng.Sc.D. degree register suggestions from the faculty as to how systems. in the School of Engineering and Applied one might fill one’s programs so as to 4. COMS E6181: Advanced Internet Science; those who elect the Ph.D. focus on a particular area of interest. services or ELEN E6776: Topic: degree register in the Graduate School Students may wish to follow these content distribution networks. of Arts and Sciences. suggestions, but they need not. The Doctoral candidates must obtain degree requirements are quite flexible With an adviser’s approval, any of the a minimum of 60 points of formal and are listed in the Master of Science courses above can be replaced by the course credit beyond the bachelor’s Degree section, above. All students, following closely related subjects: CSEE degree. A master’s degree from an whether following a formal concentration E4140: Networking laboratory; CSEE accredited institution may be accepted template or not, are expected to W4119: Computer networks; COMS as equivalent to 30 points. A minimum include breadth in their program. Not W4180: Network security; ELEN E6762: of 30 points beyond the master’s degree all of the elective courses listed here Computer communication networks, must be earned while in residence in the are offered every year. For the latest II; ELEN E6850: Visual information

engineering 2014–2015 systems; ELEN E6951: Wireless and E4110: Modern optics; CHAP E4120: Concentration in Integrated Circuits 141 mobile networking, II. Statistical mechanics; APPH E4112: and Systems Laser physics; APPH E4130: Physics Advisers: Professors Peter Kinget, Concentration in Telecommunications of solar energy; APPH E6081: Solid Harish Krishnaswamy, Mingoo Seok, Engineering state physics, I; APPH E6082: Solid Kenneth Shepard, Yannis Tsividis, Advisers: Professors Henning state physics, II; APPH E6091: Charles Zukowski Schulzrinne, Pedrag Jelenkovic, Magnetism and magnetic materials; Ed Coffman, Nicholas Maxemchuk, APPH E6110: Laser interactions 1. Satisfy M.S. degree requirements. Gil Zussman with matter; MSAE E4202: 2. One digital course from: EECS E4321: Thermodynamics and reactions in Digital VLSI circuits or EECS E6321: 1. Satisfy M.S. degree requirements. solids; MSAE E4206: Electronic Advanced digital electronic circuits. 2. One basic hardware or software and magnetic properties of solids; 3. One analog course from: ELEN course such as: EECS E4321: MSAE E4207: Lattice vibrations E4312: Analog electronic circuits; Digital VLSI circuits; ELEN E4411: and crystal defects; MSAE E6120: ELEN E6312: Advanced analog Fundamentals of photonics; COMS Grain boundaries and interfaces; integrated circuits; ELEN E6316: W4118: Operating systems, I; COMS MSAE E6220: Crystal physics; Analog circuits and systems in W4111: Database systems. MSAE E6229: Energy and particle VLSI; ELEN E4314: Communication 3. One basic systems course such beam processing of materials; MSAE circuits; ELEN E6314: Advanced as: ELEN E4702: Communication E6225: Techniques in X-ray and communication circuits; ELEN E6320: theory; ELEN E4703: Wireless neutron diffraction. Millimeter-wave IC design. communications; CSEE W4119: 4. Two additional courses such as: Computer networks; ELEN E6761: Concentration in Wireless and Mobile Other courses from 2. and 3.; ELEN Computer communication networks, I. Communications E6350: VLSI design laboratory; ELEN 4. At least two approved courses from Adviser: Professors Gil Zussman, E6304: Topics in electronic circuits; a focus area such as Signal/Image Predrag Jelenkovic, Xiaodong Wang ELEN E6318: Microwave circuit Processing and Telecommunications/ design; ELEN E9303: Seminar in Multimedia Networks. 1. Satisfy M.S. degree requirements. electronic circuits. 2. One basic circuits course such as: 5. At least one additional approved Concentration in Lightwave ELEN E4312: Analog electric circuits; course in integrated circuits and (Photonics) Engineering ELEN E4314: Communication systems or a related area. Advisers: Professors Keren Bergman, circuits; ELEN E6314: Advanced Paul Diament, Richard Osgood, communication circuits; ELEN E6312: Concentration in Microelectronic Amiya Sen, Tony Heinz, Ioannis Advanced analog ICs. Devices (John) Kymissis 3. Two communications or networking Advisers: Professors Wen Wang, courses such as: CSEE W4119: Richard Osgood, Ioannis (John) Kymissis 1. Satisfy M.S. degree requirements. Computer networks; ELEN E4702: 2. Take both ELEN E4411: Digital communications; ELEN 1. Satisfy M.S. degree requirements. Fundamentals of photonics and ELEN E4703: Wireless communications; 2. One basic course such as: ELEN E6412: Lightware devices (or an ELEN E6711: Stochastic signals E4301: Introduction to semiconductor E&M course, such as APPH E4300: and noise; ELEN E4810: Digital devices or ELEN E4411: Applied electrodynamics or PHYS signal processing; ELEN E6950: Fundamentals of photonics. G6092: Electromagnetic theory). Wireless and mobile networking, 3. One advanced course such as: ELEN 3. One more device/circuits/photonics I; ELEN E6951: Wireless and E4193: Modern display science course such as: ELEN E6413: mobile networking, II; ELEN E6761: and technology; ELEN E4944: Lightwave systems; ELEN E6414: Computer communication networks, Principles of device microfabrication; Photonic integrated circuits; ELEN I; ELEN E6712: Communication ELEN E4503: Sensors, actuators, E4314: Communication circuits; theory; ELEN E6713: Topics in and electromechanical systems; ELEN E4488: Optical systems; ELEN communications; ELEN E6717: ELEN E6151: Surface physics and E6488: Optical interconnects and Information theory; ELEN E677x: analysis of electronic materials; ELEN interconnection networks; ELEN Topics in telecommunication E6331: Principles of semiconductor E4193: Modern display science and networks. physics, I; ELEN E6332: Principles technology. 4. At least two additional approved of semiconductor physics, II; ELEN 4. At least two additional approved courses in wireless communications or E6333: Semiconductor device courses in photonics or a related a related area. physics; ELEN E6945: Nanoscale area. Options also include courses fabrication and devices. outside EE such as APPH E4090: 4. At least two other approved courses Nanotechnology; APPH E4100: in devices or a related area. Options Quantum physics of matter; APPH also include courses outside EE such

engineering 2014–2015 142 as APPH E4090: Nanotechnology; models in information systems; ELEN E3081x Circuit analysis laboratory APPH E4100: Quantum physics of ELEN E6860: Advanced digital signal 1 pt. Lab: 3. Professor Zukowski. matter; APPH E4110: Modern optics; processing; EEBM E6090: Topics Prerequisite: ELEN E1201 or equivalent. CHAP E4120: Statistical mechanics; in computational neuroscience and Corequisite: ELEN E3201. Companion lab course APPH E4112: Laser physics; APPH neuroengineering; ELEN E6261: for ELEN E3201. Experiments cover such topics as: use of measurement instruments; HSPICE E4130: Physics of solar energy; Computational methods of circuit simulation; basic network theorems; linearization of APPH E6081: Solid state physics, analysis. nonlinear circuits using negative feedback; op-amp I; APPH E6082: Solid state physics, circuits; integrators; second order RLC circuits. II; APPH E6091: Magnetism and courses in electrical The lab generally meets on alternate weeks. magnetic materials; APPH E6110: engineering Laser interactions with matter; ELEN E3082y Digital systems laboratory 1 pt. Lab: 3. Professor Shepard. MSAE E4202: Thermodynamics and ELEN E1101x or y The digital information age Corequisite: CSEE W3827. Recommended reactions in solids; MSAE E4206: 3 pts. Lect: 3. Professor Vallancourt. preparation: ELEN E1201 or equivalent. Electronic and magnetic properties An introduction to information transmission and Companion lab course for CSEE W3827. storage, including technological issues. Binary of solids; MSAE E4207: Lattice Experiments cover such topics as logic gates; numbers; elementary computer logic; digital vibrations and crystal defects; flip-flops; shift registers; counters; combinational speech and image coding; basics of compact MSAE E6120: Grain boundaries and logic circuits; sequential logic circuits; disks, telephones, modems, faxes, UPC bar interfaces; MSAE E6220: Crystal programmable logic devices. The lab generally codes, and the World Wide Web. Projects physics; MSAE E6229: Energy and meets on alternate weeks. include implementing simple digital logic systems particle beam processing of materials; and Web pages. Intended primarily for students ELEN E3083y Electronic circuits laboratory MSAE E6225: Techniques in X-ray outside the School of Engineering and Applied 1 pt. Lab: 3. Professor Vallancourt. and neutron diffraction. Science. The only prerequisite is a working Prerequisite: ELEN E3081. Corequisite: ELEN knowledge of elementary algebra. E3331. Companion lab course for ELEN Concentration in Systems Biology E3331. Experiments cover such topics as ELEN E1201x and y Introduction to electrical macromodeling of nonidealities of opamps and Neuroengineering engineering Advisers: Professors Dimitris 3.5 pts. Lect: 3. Lab:1. Professor Vallancourt. using SPICE; Schmitt triggers and astable Anastassiou, Christine Fleming, Pedrag Prerequisite: MATH V1101. Basic concepts of multivibrations using opamps and diodes; logic inverters and amplifiers using bipolar junction Jelenkovic, Aurel Lazar, Nima Mesgarani, electrical engineering. Exploration of selected transistors; logic inverters and ring oscillators Kenneth Shepard, Xiaodong Wang, topics and their application. Electrical variables, using MOSFETs; filter design using op-amps. Charles Zukowski circuit laws, nonlinear and linear elements, ideal and real sources, transducers, operational The lab generally meets on alternate weeks. 1. Satisfy M.S. degree requirements. amplifiers in simple circuits, external behavior ELEN E3084x Signals and systems laboratory of diodes and transistors, first order RC and RL 2. Take both ECBM E4060: Introduction 1 pt. Lab: 3. Professor X. Wang. circuits. Digital representation of a signal, digital Corequisite: ELEN E3801. Companion lab to genomic information science logic gates, flip-flops. A lab is an integral part of course for ELEN E3801. Experiments cover and technology and BMEB W4020: the course. Required of electrical engineering topics such as: introduction and use of MATLAB Computational neuroscience, I: and computer engineering majors. for numerical and symbolic calculations; circuits in the brain linearity and time invariance; continuous-time 3. Take at least one course from BMEE ELEN E3043x Solid state, microwave, and fiber optics laboratory convolution; Fourier-series expansion and signal E4030: Neural control engineering; 3 pts. Lect: 1. Lab: 6. Professor W. Wang. reconstruction; impulse response and transfer CBMF W4761: Computational Prerequisites: ELEN E3106 and ELEN E3401. function; forced response. The lab generally genomics; BIST P8139: Theoretical Optical electronics and communications. meets on alternate weeks. genetic modeling (Biostatistics); ELEN Microwave circuits. Physical electronics. ELEN E3106x Solid-state devices and materials E6010: Systems biology; EEBM 3.5 pts. Lect: 3. Recit: 1. Professor Kymissis. E6020: Methods in computational ECBM E3060x Introduction to genomic information science and technology Prerequisite: MATH V1201 or equivalent. neuroscience; BMEE E6030: Neural 3 pts. Lect: 3. Professor Anastassiou. Corequisite: PHYS C1403 or PHYS C2601 or modeling and neuroengineering; Introduction to the information system paradigm of equivalent. Crystal structure and energy band APMA E4400: Introduction to molecular biology. Representation, organization, theory of solids. Carrier concentration and biophysical modeling; CHEN E4700: structure, function and manipulation of the transport in semiconductors. P-n junction and Principles of genomic technologies; biomolecular sequences of nucleic acids and junction transistors. Semiconductor surface CHEN E4760: Genomics sequencing proteins. The role of enzymes and gene regulatory and MOS transistors. Optical effects and lab; ELEN E4312: Analog electronic elements in natural biological functions as well optoelectronic devices. circuits. as in biotechnology and genetic engineering. ELEN E3201x Circuit analysis 4. Take at least one course from ELEN Recombination and other macromolecular 3.5 pts. Lect: 3. Recit: 1. Professor Zukowski. E608x: Topics in systems biology; processes viewed as mathematical operations with Prerequisite: ELEN E1201 or equivalent. ELEN E6717: Information theory; simulation and visualization using simple computer Corequisite: MATH V1201. A course on analysis of ELEN E6201: Linear systems theory; programming. This course shares lectures with linear and nonlinear circuits and their applications. ECBM E4060, but the work requirements differ EEME E6601: Introduction to control Formulation of circuit equations. Network somewhat. theory; ELEN E6711: Stochastic theorems. Transient response of first and second order circuits. Sinusoidal steady state-analysis.

engineering 2014–2015 Frequency response of linear circuits. Poles and theorem on channel capacity, and elements of Wilson-Cowan model of cortex, large-scale 143 zeros. Bode plots. Two-port networks. coding theory. electrophysiological recording methods, sensorimotor integration and optimal state ELEN E3331y Electronic circuits ELEN E3801x Signals and systems estimation, operant conditioning of neural activity, 3 pts. Lect: 3. Professor Vallancourt. 3.5 pts. Lect: 3. Professor X. Wang. nonlinear modeling of neural systems, sensory Prerequisites: ELEN E3201. Operational Corequisite: MATH V1201. Modeling, description, systems: visual pathway and somatosensory amplifier circuits. Diodes and diode circuits. and classification of signals and systems. pathway, neural encoding model: spike triggered MOS and bipolar junction transistors. Biasing Continuous-time systems. Time domain analysis, average (STA) and spike triggered covariance techniques. Small-signal models. Single-stage convolution. Frequency domain analysis, transfer (STC) analysis, neuronal response to electrical transistor amplifiers. Analysis and design of functions. Fourier series. Fourier and Laplace micro-stimulation, DBS for Parkinson’s disease CMOS logic gates. A/D and D/A converters. transforms. Discrete-time systems and the Z treatment, motor neural prostheses, and sensory transform. ELEN E3390y Electronic circuit design neural prostheses. laboratory CSEE W3827x and y Fundamentals of ECBM E4060x Introduction to genomic 3 pts. Lab: 6. Professor Vallancourt. computer systems information science and technology Prerequisites: ELEN E3082, E3083, E3331, 3 pts. Lect: 3. Professors Kim and Rubenstein. 3 pts. Lect: 3. Professor Anastassiou. Prerequisites: An introductory programming E3401, E3801. Advanced circuit design Introduction to the information system course. Fundamentals of computer organization laboratory. Students work in teams to specify, paradigm of molecular biology. Representation, and digital logic. Boolean algebra, Karnaugh design, implement and test an engineering organization, structure, function and manipulation maps, basic gates and components, flipflops and prototype. The work involves technical as of the biomolecular sequences of nucleic latches, counters and state machines, basics well as non-technical considerations, such as acids and proteins. The role of enzymes and of combinational and sequential digital design. manufacturability, impact on the environment, gene regulatory elements in natural biological Assembly language, instruction sets, ALUs, and economics. The projects may change from functions as well as in biotechnology and single-cycle and multi-cycle processor design, year to year. genetic engineering. Recombination and introduction to pipelined processors, caches, and other macromolecular processes viewed as ELEN E3399x Electrical engineering practice virtual memory. 1 pt. Professor Vallancourt. mathematical operations with simulation and visualization using simple computer programming. Design project planning, written and oral ELEN E3998x and y Projects in electrical engineering This course shares lectures with ECBM E3060, technical communication, practical aspects of 0 to 3 pts. but the work requirements differ somewhat. engineering as a profession, such as career Prerequisite: Requires approval by a faculty development and societal and environmental ECBM E4090x or y Brain computer interfaces member who agrees to supervise the work. impact. Generally taken senior year. (BCI) laboratory May be repeated for credit, but no more than 3 pts. Lect: 2. Lab: 3. Professor Mesgarani. ELEN E3401y Electromagnetics 3 total points may be used for degree credit. Prerequisites: ELEN E3801. Hands-on 4 pts. Lect: 3. Professor Diament. Independent project involving laboratory work, experience with basic neural interface computer programming, analytical investigation, Prerequisite: MATH V1201, PHYS C1402 technologies. Recording EEG or engineering design. or PHYS C1602, or equivalents. Basic (electroencephalogram) signals using data field concepts. Interaction of time-varying BMEB W4020x Computational neuroscience: acquisition systems (noninvasive, scalp electromagnetic fields. Field calculation of circuits in the brain recordings). Real-time analysis and monitoring lumped circuit parameters. Transition from 3 pts. Lect: 3. Professor Lazar. of brain responses. Analysis of intention and electrostatic to quasistatic and electromagnetic Prerequisite: ELEN E3801 or BIOL W3004. perception of external visual and audio signals. regimes. Transmission lines. Energy transfer, The biophysics of computation: modeling CSEE W4119x and y Computer networks dissipation, and storage. Waveguides. Radiation. biological neurons, the Hodgkin-Huxley neuron, 3 pts. Lect: 3. Professor Misra. modeling channel conductances and synapses EEME E3601x Classical control systems Corequisite: IEOR E3658 or SIEO W3600 or as memristive systems, bursting neurons and 3 pts. Lect: 3. Professor Longman. equivalents. Introduction to computer networks central pattern generators, I/O equivalence Prerequisite: MATH E1210. Analysis and design and the technical foundations of the Internet, and spiking neuron models. Information of feedback control systems. Transfer functions; including applications, protocols, local area representation and neural encoding: stimulus block diagrams; proportional, rate, and integral networks, algorithms for routing and congestion representation with time encoding machines, the controllers; hardware; implementation. Routh control, security, elementary performance geometry of time encoding, encoding with neural stability criterion, root locus, Bode and Nyquist evaluation. Several written and programming circuits with feedback, population time encoding plots, compensation techniques. assignments required. machines. Dendritic computation: elements ELEN E3701y Introduction to communication of spike processing and neural computation, CSEE W4140x or y Networking laboratory systems synaptic plasticity and learning algorithms, 3 pts. Lect: 3. Professor Zussman. 3 pts. Lect: 3. Professor Kalet. unsupervised learning and spike time-dependent Prerequisite: CSEE W4119 or equivalent. In this Prerequisite: ELEN E3801. Corequisite: IEOR plasticity, basic dendritic integration. Projects in course, students learn how to put “principles E3658. A basic course in communication Matlab. into practice,” in a hands-on-networking lab course. The technologies and protocols of the theory, stressing modern digital communication BMEE E4030 y Neural control engineering Internet are covered, using equipment currently systems. Nyquist sampling, PAM and PCM/ 3 pts. Lect: 3. available to large Internet service providers DPCM systems, time division multipliexing, Prerequisite: ELEN E3801. Topics include: such as CISCO routers and end-systems. A set high frequency digital (ASK, OOK, FSK, Basic cell biophysics, active conductance and of laboratory experiments provides hands-on PSK) systems, and AM and FM systems. An the Hodgkin-Huxley model, simple neuron experience with engineering wide-area networks introduction to noise processes, detecting models, ion channel models and synaptic and familiarizes students with the Internet signals in the presence of noise, Shannon’s models, statistical models of spike generation,

engineering 2014–2015 144 Protocol (IP), Address Resolution Protocol and BiCMOS device modeling. Integrated circuit homojunction and heterojunction laser diodes. (ARP), Internet Control Message Protocol fabrication and layout. Interconnect and parasitic Semiconductor photon detectors: p-n, p-i-n, (ICMP), User Datagram Protocol (UDP) and elements. Static and dynamic techniques. and heterostructure photo diodes; avalanche Transmission Control Protocol (TCP), the Worst-case design. Heat removal and I/O. Yield photodiodes. Domain Name System (DNS), routing protocols and circuit reliability. Logic gates, pass logic, ELEN E4488x Optical systems (RIP, OSPF, BGP), network management latches, PLAs, ROMs, RAMs, receivers, drivers, protocols (SNMP), and application-level protocols repeaters, sense amplifiers. 3 pts. Lect: 3. Professor Bergman. (FTP, TELNET, SMTP). Prerequisite: ELEN E3401 or equivalent. EECS E4340x Computer hardware design Introduction to optical systems based on physical ELEN E4193x or y Modern display science 3 pts. Lect: 2. Lab: 3. Professor Sethumadhavan. design and engineering principles. Fundamental and technology Prerequisites: ELEN E3331 and CSEE W3827. geometrical and wave optics with specific 3 pts. Lect: 3. Professor Kymissis. Practical aspects of computer hardware design emphasis on developing analytical and numerical Prerequisites: Linear algebra, differential through the implementation, simulation, and tools used in optical engineering design. Focus equations, and basic semiconductor physics. prototyping of a PDP-8 processor. High-level on applications that employ optical systems and Introduction to modern display systems in and assembly languages, I/O, interrupts, networks, including examples in holographic an engineering context. The basis for visual datapath and control design, pipelining, imaging, tomography, Fourier imaging, confocal perception, image representation, color busses, memory architecture. Programmable microscopy, optical signal processing, fiber optic space, metrics of illumination. Physics of logic and hardware prototyping with FPGAs. communication systems, optical interconnects luminescence, propagation and manipulation Fundamentals of VHDL for register-transfer and networks. of light in anisotropic media, emissive displays, level design. Testing and validation of hardware. and spatial light modulators. Fundamentals Hands-on use of industry CAD tools for ELEN E4501x Electromagnetic devices and of display addressing, the Alt-Pleshko simulation and synthesis. energy conversion theorem, multiple line addressing. Large area 3 pts. Lect: 3. Professor Sen. BMEE E4400x Wavelet applications in electronics, fabrication, and device integration of Prerequisite: ELEN E3401. Linear and nonlinear biomedical image and signal processing commercially important display types. A series of magnetic circuits. Electric and magnetic energy 3 pts. Lect: 3. short laboratories will reinforce material from the storage, loss, and transfer. Circuit behavior of Prerequisites: APMA E2101 or E3101 or lectures. Enrollment may be limited. energy storage and transfer devices. Field theory equivalent. An introduction to methods of of moving bodies. Dynamical equations of an ELEN E4301y Introduction to semiconductor wavelet analysis and processing techniques devices for the quantification of biomedical images and electromechanical system. Electromechanical 3 pts. Lect: 3. Professor Laibowitz. signals. Topics include: frames and overcomplete and thermo-electric sensors and actuators. Prerequisite: ELEN E3106 or equivalent. representations, multiresolution algorithms for Rotating electric energy converters. Semiconductor physics. Carrier injection and denoising and image restoration, multiscale Superconductivity and applications. recombination. P-n junction and diodes: Schottky texture segmentation and classification methods ELEN E4503x Sensors, actuators and barrier and heterojunctions, solar cells and light- for computer aided diagnosis. electromechanical systems emitting diodes. Junction and MOS field-effect ELEN E4401x Wave transmission and fiber 3 pts. Lect: 3. transistors, bipolar transistors. Tunneling and optics Prerequisites: ELEN E3201 and E3401, charge-transfer devices. 3 pts. Lect: 3. Professor Diament. or equivalents. Electromagnetic energy ELEN E4312x Analog electronic circuits Prerequisite: ELEN E3401 or equivalent. Waves storage, loss, and transfer. Dynamics of 3 pts. Lect: 3. Professor Tsividis. and Maxwell’s equations. Field energetics, electromechanical systems. Linearization Prerequisites: ELEN E3331 and E3801. dispersion, complex power. Waves in dielectrics of nonlinear coupled dynamical equations Differential and multistage amplifiers; small- and in conductors. Reflection and refraction. and equivalent circuits. Electromechanical signal analysis; biasing techniques; frequency Oblique incidence and total internal reflection. actuators: acoustic, IC processed response; negative feedback; stability criteria; Transmission lines and conducting waveguides. micromachines. Electromechanical sensors: frequency compensation techniques. Analog Planar and circular dielectric waveguides; acoustic, pressure, and acceleration. Thermal layout techniques. An extensive design project is integrated optics and optical fibers. Hybrid and sensors: polysilicon thermopiles and bipolar an integral part of the course. LP modes. Graded-index fibers. Mode coupling; transistor temperature sensors. Electro-optic sensors: visible light, infrared, and X-ray. ELEN E4314y Communication circuits wave launching. 3 pts. Lect: 3. Professor Tsividis. ELEN E4411x Fundamentals of photonics ELEN E4510x or y Solar energy and smart Prerequisite: ELEN E4312. Principles of 3 pts. Lect: 3. Professor Osgood. grid power systems electronic circuits used in the generation, Prerequisite: ELEN E3401 or equivalent. Planar 3 pts. Lect: 3. Professors Kymissis and Schwartz. transmission, and reception of signal waveforms, resonators. Photons and photon streams. Prerequisite: Background in circuits. Inorganic as used in analog and digital communication Photons and atoms: energy levels and band solar cell semiconductor physics. Single and systems. Nonlinearity and distortion; power structure; interactions of photons with matter; tandem junction design. Measures of spectral amplifiers; tuned amplifiers; oscillators; absorption, stimulated and spontaneous and energy efficiency. Introduction to organic multipliers and mixers; modulators and emission; thermal light, luminescence light. solar cells and thin film inorganic cells. demodulators; phase-locked loops. An extensive Laser amplifiers: gain, saturation, and phase Batteries and other energy storage systems. design project is an integral part of the course. shift; rate equations; pumping. Lasers: theory of Introduction to legacy power networks: Single EECS E4321x Digital VLSI circuits oscillation; laser output characteristics. Photons phase equivalents to three-phase networks. 3 pts. Lect: 3. Professor Shepard. in semiconductors: generation, recombination, Reactive and real power. Equivalent circuits Recommended preparation: ELEN E3106, and injection; heterostructures; absorption of synchronous machines, transformers, and E3331, and CSEE W3827. Design and analysis and gain coefficients. Semiconductor photon transmission lines. Smart grid technology: of high speed logic and memory. Digital CMOS sources: LEDs; semiconductor optical amplifiers; Control and management of distributed solar

engineering 2014–2015 energy and other intermittent renewable power actuate living tissues. Transducers, signal computer architecture, illustrated by recent 145 sources connected to legacy power networks. conditioning electronics, data acquisition boards, case studies. Fundamentals of quantitative Microgrid concept. “Small world” networks and the Arduino microprocessor, and data scquisition analysis. Pipelined, out-of-order, and fault management. Communication over power and processing using MATLAB will be covered. speculative execution. Superscalar, VLIW and lines. Smart metering. Various devices will be discussed throughout the vector processors. Embedded processors. course, with laboratory work focusing on building Memory hierarchy design. Multiprocessors and ELEN E4511x or y Power systems analysis an emulated version of a cardiac pacemaker. thread-level parallelism. Synchronization and and control Lab required. cache coherence protocols. Interconnection 3 pts. Lect: 3. Professor Lavaei. networks. Prerequisites: ELEN E3201 and E3401, or ELEN E4750x or y Signal processing and equivalents, or instructor’s permission. Modeling communications on mobile multicore ELEN E4830y Digital image processing of power networks, steady-state and transient processors 3 pts. Lect: 3. behaviors, control and optimization, electricity 3 pts. Lect: 2. Lab: 3. Professor Kostic. Introduction to the mathematical tools and market, and smart grid. Prerequisite: ELEN E4702 or E4810 or algorithmic implementation for representation instructor’s permission. Methods for deploying and processing of digital pictures, videos, and EEME E4601y Digital control systems signal processing and communications visual sensory data. Image representation, 3 pts. Lect: 3. Professor Longman. algorithms on contemporary mobile processors filtering, transform, quality enhancement, Prerequisite: ELEN E3801 or EEME E3601, with heterogeneous computing infrastructures restoration, feature extraction, object or equivalent. Real-time control using digital consisting of a mix of general purpose, segmentation, motion analysis, classification, computers. Solving scalar and state-space graphics, and digital signal processors. Using and coding for data compression. A series of difference equations. Discrete equivalents of programming languages such as OpenCL and programming assignments reinforces material continuous systems fed by holds. Z-transfer CUDA for computational speedup in audio, from the lectures. functions. Creating closed-loop difference image, and video processing and computational equation models by Z-transform and state data analysis. Significant design project. ELEN E4835 Introduction to adaptive signal variable approaches. The Nyquist frequency representations ELEN E4810x Digital signal processing and sample rate selection. Classical- and 3 pts. Lect: 3. Professor Ellis. 3 pts. Lect: 2. Professor Wright. modern-based digital control laws. Digital system Prerequisite: ELEN E3801. Digital filtering in Prerequisites: Linear algebra (APMA E3101, MATH identification. time and frequency domain, including properties V2010, or equivalent), probability (IEOR E3658 or equivalent), and signals and systems (ELEN EEOR E4650x or y Convex optimization for of discrete-time signals and systems, sampling E3801), or instructor’s permission.Introduces electrical engineering theory, transform analysis, system structures, numerical tools for adaptive processing of signals. 3 pts. Lect: 3. Professor Lavaei. IIR and FIR filter design techniques, the discrete Signal representations, sparsity in overcomplete Prerequisite: ELEN E3801 or instructor’s Fourier transform, fast Fourier transforms. bases. Techniques for sparse recovery, permission. Theory of convex optimization; ELEN E4815y Random signals and noise applications to inpainting and denoising. Adaptive numerical algorithms; applications in circuits, 3 pts. Lect: 3. representations: principal component analysis, communications, control, signal processing and Prerequisite: IEOR E3658 or equivalent. clustering and vector quantization, dictionary power systems. Characterization of stochastic processes as learning. Source separation: independent ELEN E4702x or y Digital communications models of signals and noise; stationarity, component analysis and matrix factorizations. 3 pts. Lect: 3. Professor Cvijetic. ergodicity, correlation functions, and power Signal classification: support vector machines Prerequisite: ELEN E3701 or equivalent. Digital spectra. Gaussian processes as models of and boosting, learning with invariances. Hashing communications for both point-to-point and noise in linear and nonlinear systems; linear and and signal retrieval. Case studies from image switched applications is further developed. nonlinear transformations of random processes; processing, audio, multimedia. Optimum receiver structures and transmitter orthogonal series representations. Applications to CSEE W4840y Embedded systems signal shaping for both binary and M-ary signal circuits and devices, to communication, control, 3 pts. Lect: 3. transmission. An introduction to block codes and filtering, and prediction. convolutional codes, with application to space Prerequisite: CSEE W4823 or equivalent. CSEE W4823x or y Advanced logic design communications. Embedded system design and implementation 3 pts. Lect: 3. Professor Nowick. combining hardware and software. I/O, ELEN E4703y Wireless communications Prerequisite: CSEE W3827 or equivalent. An interfacing, and peripherals. Weekly laboratory 3 pts. Lect: 3. Professor Diament. introduction to modern digital system design. sessions and term project on design of a Prerequisite: ELEN E3701 or equivalent. Advanced topics in digital logic: controller microprocessor-based embedded system Wireless communication systems. System design synthesis (Mealy and Moore machines); adders including at least one custom peripheral. fundamentals. Trunking theory. Mobile radio and multipliers; structured logic blocks (PLDs, Knowledge of C programming and digital logic propagation. Reflection of radio waves. Fading PALs, ROMs); iterative circuits. Modern design required. and multipath. Modulation techniques; signal methodology: register transfer level modeling ELEN E4896y Music signal processing space; probability of error, spread spectrum. (RTL); algorithmic state machines (ASMs); 3 pts. Lect: 3. Diversity. Multiple access. introduction to hardware description languages Prerequisite: ELEN E3801, E4810, or the (VHDL or Verilog); system-level modeling and BMEE E4740y Bioinstrumentation equivalent. An investigation of the applications simulation; design examples. 3 pts. Lect: 1. Lab: 3. Professor Kyle. of signal processing to music audio, spanning Prerequisites: COMS W1005, ELEN E1201. CSEE W4824x or y Computer architecture the synthesis of musical sounds (including Hands-on experience designing, building, and 3 pts. Lect: 3. Professor Carloni. frequency modulation [FM], additive sinusoidal testing the various components of a benchtop Prerequisite: CSEE W3827 or equivalent. synthesis, and linear predictive coding cardiac pacemaker. Design instrumentation Focuses on advanced topics in modern [LPC]), the modification of real and synthetic to measure biomedical signals as well as to

engineering 2014–2015 146 sounds (including reverberation and time/ Matlab. time-sharing and multiprocessor systems. Topics pitch scaling), and the analysis of music include priority queuing, buffer storage, and disk EEBM E6020y Methods of computational audio to extract musical information (including access, interference and bus contention problems, neuroscience pitch tracking, chord transcription, and music and modeling of program behaviors. 4.5 pts. Lect: 3. matching). Emphasis on practical, hands-on Prerequisite: BMEB W4020 or instructor’s ELEN E6201x Linear system theory experimentation, with a wide range of software permission. Formal methods in computational 3 pts. Lect: 3. Professor Fishler. implementations introduced and modified within neuroscience including methods of signal Prerequisites: ELEN E3801 and APMA E3101, the class. processing, communications theory, information or equivalents. Abstract objects, the concepts of ELEN E4944x or y Principles of device theory, systems and control, system identification state. Definition and properties of linear systems. microfabrication and machine learning. Molecular models of Characterization of linear continuous-time and discrete-time, fixed, and time-varying systems. 3 pts. Lect: 3. Professor Yardley. transduction pathways. Robust adaptation and State-space description; fundamental matrix, Science and technology of conventional and integral feedback. Stimulus representation and calculation by computer and matrix methods. advanced microfabrication techniques for groups. Stochastic and dynamical systems Modes in linear systems. Adjoint systems. electronics, integrated and discrete components. models of spike generation. Neural diversity and Controllability and observability. Canonical Topics include diffusion; ion implantation, ensemble encoding. Time encoding machines forms and decompositions. State estimators. thin-film growth including oxides and metals, and neural codes. Stimulus recovery with time Lyapunov’s method and stability. molecular beam and liquid-phase epitaxy; decoding machines. MIMO models of neural optical and advanced lithography; and plasma computation. Synaptic plasticity and learning ELEN E6312y Advanced analog integrated and wet etching. algorithms. Major project(s) in Matlab. circuits 3 pts. Lect: 2. ELEN E4998x or y Intermediate projects in BMEE E6030x Neural modeling and Prerequisite: ELEN E4312. Integrated circuit electrical engineering neuroengineering device characteristics and models; temperature- 0–3 pts. 3 pts. Lect: 3. Professor Sajda. and supply-independent biasing; IC operational Prerequisite: Requires approval by a faculty Prerequisites: ELEN E3801 and either APMA amplifier analysis and design and their member who agrees to supervise the work. May E2101 or E3101, or equivalent, or instructor’s applications; feedback amplifiers, stability and be repeated for credit, but no more than 3 total permission. Engineering perspective on the frequency compensation techniques; noise in points may be used for degree credit. Substantial study of multiple levels of brain organization, circuits and low-noise design; mismatch in circuits independent project involving laboratory work, from single neurons to cortical modules and and low-offset design. Computer-aided analysis computer programming, analytical investigation, systems. Mathematical models of spiking techniques are used in homework or a design or engineering design. neurons, neural dynamics, neural coding, project. ELEN E6001x-E6002y Advanced projects in and biologically based computational learning. ELEN E6314x Advanced communication Architectures and learning principles underlying electrical engineering circuits both artificial and biological neural networks. 1–4 pts. Members of the faculty. 3 pts. Lect: 2. Computational models of cortical processing, Prerequisite: Requires approval by a faculty Prerequisites: ELEN E4314 and E6312. with an emphasis on the visual system. member who agrees to supervise the work. Overview of communication systems, modulation Applications of principles in neuroengineering; May be repeated for up to 6 points of credit. and detection schemes. Receiver and transmitter neural prostheses, neuromorphic systems and Graduate-level projects in various areas of architectures. Noise, sensitivity, and dynamic biomimetics. Course will include a computer electrical engineering and computer science. range. Nonlinearity and distortion. Low-noise simulation laboratory. In consultation with an instructor, each student RF amplifiers, mixers, and oscillators. Phase- designs his or her project depending on the ELEN E6080–6089x or y Topics in systems locked loops and frequency synthesizers. student’s previous training and experience. biology Typical applications discussed include wireless Students should consult with a professor in their 3 pts. Lect: 2. RF transceivers or data links. Computer-aided area for detailed arrangements no later than the Prerequisite: Instructor’s permission. Selected analysis techniques are used in homework(s) or last day of registration. advanced topics in systems biology. Content a design project. varies from year to year, and different topics ELEN E6010y Systems biology: design ELEN E6316y Analog systems in VLSI rotate through the course numbers 6080 to principles for biological circuits 3 pts. Lect: 3. 6089. 4.5 pts. Lect: 3. Prerequisite: ELEN E4312. Analog-digital Prerequisite: ECBM E4060 or instructor’s EEBM E6090–6099x or y Topics in computational interfaces in very large scale integrated circuits. permission. Beyond bioinformatics, cells as neuroscience and neuroengineering Precision sampling; A/D and D/A converter systems. Metabolic networks, transcription 3 pts. Lect: 2. architectures; continuous-time and switched regulatory networks, signaling networks. Prerequisite: Instructor’s permission. Selected capacitor filters; system considerations. A design Deterministic and stochastic kinetics. advanced topics in computational neuroscience project is an integral part of this course. and neuroengineering. Content varies from year Mathematical representation of reconstructed ELEN E6318x or y Microwave circuit design networks. Network motifs. Signal transduction to year, and different topics rotate through the course numbers 6090 to 6099. 3 pts. Lect: 3. and neuronal networks. Robustness. Prerequisites: ELEN E3331 and E3401, Bacterial chemotaxis and patterning in fruit fly CSEE E6180x or y Modeling and performance or equivalents. Introduction to microwave development. Kinetic proofreading. Optimal evaluation engineering and microwave circuit design. Review gene circuit design. Rules for gene regulation. 3 pts. Lect: 2. of transmission lines. Smith chart, S-parameters, Random networks and multiple time scales. Prerequisites: COMS W4118 and SIEO W4150 or microwave impedance matching, transformation Biological information processing. Numerical permission of the instructor. Introduction to queuing and power combining networks, active and and simulation techniques. Major project(s) in analysis and simulation techniques. Evaluation of passive microwave devices, S-parameter-

engineering 2014–2015 based design of RF and microwave amplifiers. and recombination of excess carriers. Schottky, and entangled states of light. 147 A microwave circuit design project (using P-N, MOS, and heterojunction diodes. Field ELEN E6488y Optical interconnects and microwave CAD) is an integral part of the course. effect and bipolar junction transistors. Dielectric interconnection networks and optical properties. Optical devices including ELEN E6320x or y Millimeter-wave IC design 3 pts. Lect: 2. Professor Bergman. semiconductor lamps, lasers, and detectors. 3 pts. Lect: 3. Professor Krishnaswamy. Prerequisite: ELEN E4411 or E4488 or an Prerequisites: ELEN E3401 or equivalent, ELEN E6412y Lightwave devices equivalent photonics course. Introduction ELEN E4314 and E6312. Principles behind the 3 pts. Lect: 2. to optical interconnects and interconnection implementation of millimeter-wave (30GHz- Prerequisites: ELEN E4411. Electro-optics: networks for digital systems. Fundamental 300GHz) wireless circuits and systems in principles; electro-optics of liquid crystals and optical interconnects technologies, optical silicon-based technologies. Silicon-based photo-refractive materials. Nonlinear optics: interconnection network design, characterization, active and passive devices for millimeter- second-order nonlinear optics; third-order and performance evaluation. Enabling photonic wave operation, millimeter-wave low-noise nonlinear optics; pulse propagation and solitons. technologies including free-space structures, amplifiers, power amplifiers, oscillators and Acousto-optics: interaction of light and sound; hybrid and monolithic integration platforms for VCOs, oscillator phase noise theory, mixers and acousto-optic devices. Photonic switching photonic on-chip, chip-to-chip, backplane, and frequency dividers for PLLs. A design project is and computing: photonic switches; all-optical node-to-node interconnects, as well as photonic an integral part of the course. switches; bistable optical devices. Introduction networks on-chip. to fiber-optic communications: components of EECS E6321y Advanced digital electronic EEME E6601x Introduction to control theory the fiber-optic link; modulation, multiplexing circuits 3 pts. Lect: 3. Professor Longman. and coupling; system performance; receiver 4.5 pts. Lect: 3. Professor Seok. Prerequisite: MATH E1210. A graduate-level sensitivity; coherent optical communications. Prerequisite: EECS E4321. Advanced topics in introduction to classical and modern feedback the design of digital integrated circuits. Clocked ELEN E6413y Lightwave systems control that does not presume an undergraduate and non-clocked combinational logic styles. 3 pts. Lect: 2. background in control. Scalar and matrix Timing circuits: latches and flip-flops, phase- Prerequisites: ELEN E4411. Recommended differential equation models, and solutions in locked loops, delay-locked loops. SRAM and preparation: ELEN E6412. Fiber optics. Guiding, terms of state transition matrices. Transfer DRAM memory circuits. Modeling and analysis dispersion, attenuation, and nonlinear properties functions and transfer function matrices, block of on-chip interconnect. Power distribution of fibers. Optical modulation schemes. Photonic diagram manipulations, closed-loop response. and power-supply noise. Clocking, timing, and components, optical amplifiers. Semiconductor Proportional, rate, and integral controllers, synchronization issues. Circuits for chip-to-chip laser transmitters. Receiver design. Fiber optic and compensators. Design by root locus and electrical communication. Advanced technology telecommunication links. Nonregenerative frequency response. Controllability, observability. issues that affect circuit design. The class may transmission using erbium-doped fiber amplifier Luenberger observers, pole placement, and include a team circuit design project. chains. Coherent detection. Local area networks. linear-quadratic cost controllers. Advanced topics in light wave networks. ELEN E6331y Principles of semiconductor EEME E6602y Modern control theory physics, I ELEN E6414y Photonic integrated circuits 3 pts. Lect: 3. 3 pts. Lect: 2. 3 pts. Lect: 3. Prerequisite: EEME E6601 or E4601 or ELEN Prerequisite: ELEN E4301. Designed for Photonic integrated circuits are important E6201, or instructor’s permission. Singular value students interested in research in semiconductor subsystem components for telecommunications, decomposition. ARX model and state-space model materials and devices. Topics include energy optically controlled radar, optical signal system identification. Recursive least squares bands: nearly free electron and tight-binding processing, and photonic local area networks. filters and Kalman filters. LQR, H, linear robust approximations, the k.p. method, quantitative An introduction to the devices and the design of control, predictive control. Learning control, calculation of band structures and their these circuits. Principle and modelling of dielectic repetitive control, adaptive control. Liapunov applications to quantum structure transistors, waveguides (including silica on silicon and InP and Popov stability. Nonlinear adaptive control, photodetectors, and lasers; semiconductor based materials), waveguide devices (simple and nonlinear robust control, sliding mode control. statistics, Boltzmann transport equation, star couplers), and surface diffractive elements. scattering processes, quantum effect in transport Discussion of numerical techniques for modelling EEOR E6616x or y Convex optimization phenomena, properties of heterostructures. circuits, including beam propagation and finite 3 pts. Lect: 2.5. Quantum mechanical treatment throughout. difference codes, and design of other devices: Prerequisites: IEOR E6613 and EEOR E4650. optical isolators, demultiplexers. ELEN E6332y Principles of semiconductor Convex sets and functions, and operations preserving convexity. Convex optimization physics, II ELEN E6430x or y Applied quantum optics 3 pts. Lect: 2. 3 pts. Lect: 2. problems. Convex duality. Applications of Prerequisites: ELEN E6331. Optical properties Prerequisites: Background in electromagnetism convex optimization problems ranging from signal including absorption and emission of radiation, (ELEN E3401, E4401, E4411, or PHYS G6092) processing and information theory to revenue electron-phonon interactions, radiative and and quantum mechanics (APPH E3100, management. Convex optimization in Banach phonon-mediated processes, excitons, plasmons, E4100, or PHYS G402x). An introduction to spaces. Algorithms for solving constrained convex polaritons, carrier recombination and generation, fundamental concepts of quantum optics and optimization problems. and related optical devices, tunneling phenomena, quantum electrodynamics with an emphasis ELEN E6711x Stochastic models in superconductivity. Quantum mechanical treatment on applications in nanophotonic devices. information systems throughout, heavy use of perturbation theory. The quantization of the electromagnetic field; 4.5 pts. Lect: 3. Professor Baryshnikov. coherent and squeezed states of light; interaction ELEN E6333y Semiconductor device physics Prerequisite: IEOR E3658. Foundations: between light and electrons in the language 3 pts. Lect: 2. probability review, Poisson processes, discrete- of quantum electrodynamics (QED); optical Prerequisites: ELEN E4301 or equivalent. Physics time Markov models, continuous-time Markov resonators and cavity QED; low-threshold lasers; and properties of semiconductors. Transport models, stationarity, and ergodicity. The course

engineering 2014–2015 148 presents a sample-path (time domain) treatment ELEN E6770–6779x or y Topics in scheduling, and admission control), compressed of stochastic models arising in information telecommunication networks video editing, and synchronization issues of systems, including at least one of the following 3 pts. Lect: 2. stored video/audio signals. Programming projects areas: communications networks (queueing Further study of areas such as communication and final presentations are required. systems), biological networks (hidden Markov protocols and architectures, flow and congestion ELEN E6860y Advanced digital signal control in data networks, performance evaluation models), Bayesian restoration of images (Gibbs processing in integrated networks. Content varies from year fields), and electric networks (random walks). 3 pts. Lect: 2. Professor Nguyen. to year, and different topics rotate through the ELEN E6712x Communication theory Prerequisite: ELEN E4810. This course is course numbers 6770 to 6779. 3 pts. Lect: 3. designed as an extension to ELEN E4810, Prerequisite: ELEN E4815, or equivalent, or ELEN E6820y Speech and audio processing with emphasis on emerging techniques in the instructor’s permission. Representation of and recognition area of digital signal processing. Topics include bandlimited signals and systems. Coherent 4.5 pts. Lect: 3. multirate signal processing, multidimensional and incoherent communications over Prerequisite: ELEN E4810 or instructor’s signal processing, short-time Fourier transform, Gaussian channels. Basic digital modulation permission. Fundamentals of digital speech signal expansion in discrete and continuous time, schemes. Intersymbol inference channels. processing and audio signals. Acoustic and filter banks, multiresolution analysis, wavelets, Fading multipath channels. Carrier and clock perceptual basics of audio. Short-time Fourier and their applications to image compression and synchronization. analysis. Analysis and filterbank models. Speech understanding. Other topics may be included to ELEN E6713y Topics in communications and audio coding, compression, and reconstruction. reflect developments in the field. Acoustic feature extraction and classification. 3 pts. Lect: 3. CSEE E6861y Computer-aided design of Recognition techniques for speech and other Prerequisite: ELEN E6712 or E4702 or E4703 or digital systems sounds, including hidden Markov models. equivalent, or instructor’s permission. Advanced 3 pts. Lect: 2. topics in communications, such as turbo codes, CSEE E6824y Parallel computer architecture Prerequisites: (i) one semester of advanced LDPC codes, multiuser communications, network 3 pts. Lect: 2. digital logic (CSEE W4823 or equivalent, coding, cross-layer optimization, cognitive radio. Prerequisite: CSEE W4824. Parallel computer or instructor’s permission); and (ii) a basic Content may vary from year to year to reflect the principles, machine organization and design of course in data structures and algorithms latest development in the field. parallel systems including parallelism detection (COMS W3133, 3134, 3137, 3139 or 3157, or ELEN E6717x Information theory methods, synchronization, data coherence and equivalent, and familiarity with programming. 3 pts. Lect: 2. interconnection networks. Performance analysis Introduction to modern digital CAD synthesis Prerequisite: IEOR E3658 or a course in stochastic and special purpose parallel machines. and optimization techniques. Topics include: modern digital system design (high-level processes. Corequisite: ELEN E4815. Mutual CSEE E6847y Distributed embedded systems synthesis, register-transfer level modeling, information and entropy. The source coding 3 pts. Lect: 2. algorithmic state machines, optimal scheduling theorem. The capacity of discrete memoryless Prerequisite: Any COMS W411X, CSEE algorithms, resource allocation and binding, channels and the noisy channel coding theorem. W48XX, or ELEN E43XX course, or instructor’s The rate distortion function. Discrete memoryless retiming), controller synthesis and optimization, permission. An interdisciplinary graduate-level sources and single-letter distortion measures. exact and heuristic two-level logic minimization, seminar on the design of distributed embedded Bhattacharya bounds, convolutional codes, and advanced multi-level logic optimization, optimal systems. System robustness in the presence the Viterbi algorithm. technology mapping to library cells (for delay, of highly variable communication delays and power and area minimization), advanced data ELEN E6718y Algebraic coding theory heterogeneous component behaviors. The structures (binary decision diagrams), SAT 3 pts. Lect: 2. study of the enabling technologies (VLSI solvers and their applications, static timing Prerequisite: IEOR E3658. Elementary concepts circuits, communication protocols, embedded analysis, and introduction to testability. Includes of error control codes. Linear block codes. processors, RTOSs), models of computation, hands-on small design projects using and Elements of algebra: Galois fields. Cyclic and design methods. The analysis of modern creating CAD tools. codes: BCH, Reed Solomon, Goppa codes. domain-specific applications including on-chip CSEE E6868x or y System-on-chip platforms Coder, decoder implementation. Decoding micro-networks, multiprocessor systems, fault- 3 pts. Lect: 3. algorithms based on spectral techniques. tolerant architectures, and robust deployment Prerequisites: COMS W3157 and CSEE W3827. Convolutional codes. of embedded software. Research challenges Design and programming of system-on-chip such as design complexity, reliability, scalability, ELEN E6761x Computer communication (SoC) platforms. Topics include: overview of networks I safety, and security. The course requires technology and economic trends, methodologies 3 pts. Lect: 3. Professor Maxemchuk. substantial reading, class participation and a and supporting CAD tools for system-level Prerequisites: IEOR E3658 and CSEE W4119 research project. design and verification, software simulation and or equivalent, or instructor’s permission. Focus ELEN E6850x Visual information systems virtual platforms, models of computation, the on architecture protocols and performance 3 pts. Lect: 2. SystemC language, transaction-level modeling, evaluation of geographically distributed and Prerequisite: ELEN E4830 or instructor’s hardware-software partitioning, high-level local area data networks. Emphasis on layered permission. Introduction to critical image synthesis, memory organization, device drivers, protocols. Data link layer. Network layer: flow technologies in advanced visual information on-chip communication architectures, power and congestion control routing. Transport layer. systems, such as content-based image management and optimization, integration Typical Local and Metropolitan Area Network databases, video servers, and desktop video of programmable cores and specialized standards: Ethernet, DQDB, FDDI. Introduction editors. Intended for graduate students. accelerators. Case studies of modern SoC platforms for various classes of applications. to Internetting. Review of relevant aspects Topics include visual data representation and of queueing theory to provide the necessary compression, content-based visual indexing and analytical background. retrieval, storage system design (data placement,

engineering 2014–2015 EECS E6870x or y Speech recognition photon, electron, ion and atom, scanning probe, member who is to supervise the work of the 149 3 pts. Lect: 2. soft lithography, and nanoimprinting; pattern student. Prerequisites: Basic probability and statistics. transfer; self-assembly; process integration; and ELEN E9800x and y Doctoral research Theory and practice of contemporary applications. instruction automatic speech recognition. Gaussian ELEN E6950x Wireless and mobile networking, I 3, 6, 9 or 12 pts. mixture distributions, hidden Markov models, 4.5 pts. Lect: 2. Lab: 1. Professor Jelenkovic. A candidate for the Eng.Sc.D. degree in pronunciation modeling, decision trees, finite- Corequisite: ELEN E6761 or instructor’s electrical engineering must register for 12 points state transducers, and language modeling. permission. Overview of mobile and wireless of doctoral research instruction. Registration Selected advanced topics will be covered in networking. Fundamental concepts in mobile in ELEN E9800 may not be used to satisfy the more depth. wireless systems: propagation and fading, minimum residence requirement for the degree. ELEN E6873x or y Detection and estimation cellular systems, channel assignment, power ELEN E9900x and y–9900 Doctoral dissertation theory control, handoff. Examples of second-generation 0 pts. 3 pts. Lect: 2. circuits-switched systems and standards. A candidate for the doctorate may be required Prerequisite: ELEN E4815. Introduction to Quantitative homework assignments may require to register for this course every term after the the fundamental principles of statistical signal use of a mathematical software package. student’s course work has been completed, and processing related to detection and estimation. ELEN E6951y Wireless and mobile networking, II until the dissertation has been accepted. Hypothesis testing, signal detection, parameter 3 pts. Lect: 2. Lab: 1. Professor Zussman. estimation, signal estimation, and selected Prerequisite: CSEE W4119, ELEN E6761, or advanced topics. Suitable for students doing instructor’s permission. Third-generation packet Courses in Electrical research in communications, control, signal switched systems, wireless LANs, mobile Engineering Offered processing, and related areas. computing and communications. Study of some Occasionally ELEN E6880-6889x or y Topics in signal current research topics. Quantitative homework EEHS E3900y History of telecommunications: processing assignments may require use of a mathematical from the telegraph to the Internet 3 pts. Lect: 2. software package. A project based on readings 3 pts. Lect: 3. Prerequisite: ELEN E4810. Advanced topics from the literature will be required. Historical development of telecommunications in signal processing, such as multidimensional ELEN E6999 Fieldwork from the telegraphy of the mid-1800s to signal processing, image feature extraction, 0.5–1.5 pts. the Internet at present. Included are the image/video editing and indexing, advanced Prerequisites: Obtained internship and approval technologies of telephony, radio, and computer digital filter design, multirate signal processing, from a faculty adviser. May be repeated for communications. The coverage includes both adaptive signal processing, and wave-form credit, but no more than 3 total points may the technologies themselves and the historical coding of signals. Content varies from year to be used for degree credit. Only for electrical events that shaped, and in turn were shaped by, year, and different topics rotate through the engineering and computer engineering graduate the technologies. The historical development, course numbers 6880 to 6889. students who include relevant off-campus work both the general context and the particular EECS E6890-6899x or y Topics in information experience as part of their approved program of events concerning communications, is presented processing study. Final report required. May not be taken for chronologically. The social needs that elicited 3 pts. Lect: 2. pas/faill credit or audited. new technologies and the consequences of their Advanced topics spanning electrical adoption are examined. Throughout the course, EEME E8601y Advanced topics in control engineering and computer science such as relevant scientific and engineering principles theory speech processing and recognition, image and are explained as needed. These include, 3 pts. Lect: 3. multimedia content analysis, and other areas among others, the concept and effective use See entry under “Courses in Mechanical drawing on signal processing, information theory, of spectrum, multiplexing to improve capacity, Engineering” for description. machine learning, pattern recognition, and digital coding, and networking principles. There related topics. Content varies from year to year, ELEN E9001x and y–E9002 Research are no prerequisites, and no prior scientific or and different topics rotate through the course 0–6 pts. engineering knowledge is required. Engineering numbers 6890 to 6899. Prerequisite: Requires approval by a faculty students may not count this course as a member who agrees to supervise the work. technical elective. The course shares lectures ELEN E6900–6909x or y Topics in electrical Points of credit to be approved by the with EEHS E4900, but the work requirements and computer engineering department. Requires submission of an outline of differ somewhat. 3 pts. Lect: 2. the proposed research for approval by the faculty Prerequisite: Instructor’s permission. Selected ELEN E3999x or y Electrical engineering member who is to supervise the work of the topics in electrical and computer engineering. design challenge student. The research facilities of the department Content varies from year to year, and different 1 pt. are available to qualified students interested in topics rotate through the course numbers 6900 Prerequisite: Approval by a faculty member who advanced study. to 6909. agrees to supervise the work. May be repeated ELEN E9011x and y–E9012 Doctoral research for credit, but no more than 3 total points may be ELEN E6945x or y Device nanofabrication 0–6 pts. used for degree credit. Short-term design project 3 pts. Lect: 3. Prerequisite: Requires approval by a faculty organized as a faculty-led team competition. Prerequisites: ELEN E3106 and E3401, or member who agrees to supervise the work. Particular design targets are set that vary by equivalents. Recommended: ELEN E4944. Points of credit to be approved by the semester. A set of hardware and software This course provides an understanding of department. Open only to doctoral students constraints is specified. The project takes place the methods used for structuring matter on who have passed the qualifying examinations. over an advertised subset of the semester, the nanometer length: thin-film technology; Requires submission of an outline of the beginning around the third week. lithographic patterning and technologies including proposed research for the approval of the faculty

engineering 2014–2015 150 ELEN E4215y Analog filter synthesis and tested the following term. Lectures cover use aperture radiation, system properties, pattern design of computer-aided design tools, design issues synthesis); electrodynamics (special relativity, 3 pts. Lect: 3. specific to the projects, and chip integration radiation by charged particles, relativistic beams, Prerequisites: ELEN E3201 and ELEN E3801, issues. This course shares lectures with E6350, free electron lasers). or equivalent. Approximation techniques for but the complexity requirements of integrated ELEN E4741x Introduction to biological magnitude, phase, and delay specifications , circuits are lower. sensory systems transfer function realization sensitivity, passive LC ELEN E4405x Classical nonlinear optics 3 pts. Lect: 3. filters, active RC filters, MOSFET-C filters, Gm-C 3 pts. Lect: 3. Corequisite: IEOR E3658. Introduction to vision filters, switched-capacitor filters, automatic tuning Prerequisite: ELEN E4401. Waves in anisotropic and hearing using engineering principles. techniques for integrated filters. Filter noise. A media. Maxwell’s equations and constitutive Nature of sound and light; minimum detectable design project is an integral part of the course. relations. Fresnel equations. Optical waves in energy for human observers; excitation of the ELEN E4302x or y Magnetic sensors and anisotropic crystals. Birefringence. Waves in visual and hearing systems; rods, cones, and instruments for medical imaging nonlinear media. Plasma model. Electro-optic, hair-cell receptors; the experiment of Hecht, 3 pts. Lect: 2.5, Lab: 0.5. Pockels, and Kerr effects. Second harmonic Shlaer, and Pirenne; Poisson counting statistics; Prerequisite: ELEN E3106, ELEN E3401, or generation and phase matching. Parametric stimulus-based modeling; detection and false- instructor’s permission. Physics of nuclear amplification. Backward-wave oscillator. alarm probabilities; de Vries-Rose square-root magnetic resonance (NMR) and superconducting Acousto-optic beam deflection and light law; Weber’s law; relation of sensory and quantum interference device (SQUID). Design modulation. communication systems. and operation of superconducting DC magnet, ELEN E4420x Topics in electromagnetics CSEE W4825y Digital systems design RF receiver, Josephson junction, and integrated 3 pts. Lect: 3. 3 pts. Lect: 3. SQUID. Principles of biomedical sensoring systems Prerequisites: Undergraduate electromagnetic Prerequisite: CSEE W3827. Dynamic logic, including Magnetic Resonance Imaging (MRI), theory. Selected topics in the theory and practice field programmable gate arrays, logic design SQUID magnetometer, and NMR spectroscopy. of electromagnetics, varying from year to year. languages, multipliers. Special techniques for Medical image formation and processing. Topic for current term will be available in the multilevel NAND and NOR gate circuits. Clocking ELEN E4350y VLSI design laboratory department office one month before registration. schemes for one- and two-phase systems. Fault 3 pts. Lab: 3. This course may be taken more than once when checking: scan method, built-in-test. Survey of Prerequisites: ELEN E4321 and E4312, or topics are different. Possible topics: microwave logic simulation methods. Other topics to be instructor’s permission. Design of a CMOS theory and design (generalized waveguides, added as appropriate. mixed-signal integrated circuit. The class divides excitation and coupling of waveguides, junctions, up into teams to work on mixed-signal integrated microwave networks, periodic structures, optical circuit designs. The chips are fabricated to be fibers); antennas (filamentary antennas, arrays,

engineering 2014–2015 ELEN E6140x Gallium arsenide materials ELEN E6304x or y Topics in electronic interference, and propagation effects. Modulation 151 processing circuits methods, earth terminals, and standards. Digital 3 pts. Lect: 3. 3 pts. Lect: 3. transmission and advanced systems. Prerequisite: ELEN E4301 or instructor’s Prerequisite: Instructor’s permission. State-of- ELEN E6762y Computer communication permission. Materials and device aspects of the-art techniques in integrated circuits. Topics networks, II GaAs and compound technologies, electronic may change from year to year. 3 pts. Lect: 2. properties of GaAs, growth techniques (bulk ELEN E6350y VLSI design laboratory Prerequisite: ELEN E6761. Broadband and epitaxial), surface and etching properties, 3 pts. Lab: 3. ISDN, services and protocols; ATM. Traffic implantation, MESFETS, transferred electron Prerequisites: ELEN E4321 and E4312, or characterization and modeling: Markov- devices, Impatt diodes, HEMTS, HBTs. instructor’s permission. Design of a CMOS modulated Poisson and Fluid Flow processes; ELEN E6151y Surface physics and analysis of mixed-signal integrated circuit. The class divides application to voice, video, and images. Traffic electronic materials up into teams to work on mixed-signal integrated Management in ATM networks: admission 3 pts. Lect: 2. circuit designs. The chips are fabricated to be and access control, flow control. ATM switch Prerequisite: Instructor’s permission. Basic tested the following term. Lectures cover use architectures; input/output queueing. Quality of physical principles of methods of surface of computer-aided design tools, design issues service (QoS) concepts. analysis, surfaces of electronic materials specific to the projects, and chip integration ELEN E6763y Digital circuit switched networks including structure and optical properties (auger issues. This course shares lectures with E4350 3 pts. Lect: 2. electron spectroscopy, X-ray photoemission, but the complexity requirements of integrated Prerequisite: ELEN E6761 or instructor’s ultraviolet photoelectron spectroscopy, circuits are higher. permission. Current topics in digital circuit electron energy loss spectroscopy, inverse ELEN E6403y Classical electromagnetic theory switching: introduction to circuit switching, photoemission, photo stimulated desorption, 4.5 pts. Lect: 3. comparison with packet switching, elements and low energy electron diffraction), physical Prerequisite: One term of undergraduate of telephone traffic engineering, space and principles of each approach. electromagnetic theory. A mathematical physics time switching, call processing in digital ELEN E6211x or y Circuit theory approach to electromagnetic phenomena. circuit-switched systems, overload control 3 pts. Lect: 3. Poisson, Laplace equations; Green’s functions. mechanisms, nonhierarchical routing, common Prerequisites: ELEN E3331 and ELEN E3801. Theorems of electrostatics. Multipole expansions. channel signaling, introduction to integrated An axiomatic development of circuit theory. Energy relations and stress tensor. Maxwell’s services digital networks. Examples of current Circuit theorems, circuit topology, general equations in stationary and moving media. systems are introduced throughout. Emphasis on methods of circuit analysis. Normal form The wave equation, energy and momentum modeling and quantitative performance analysis. characterizations. Scattering characterization theorems, potentials, choice of gauge. Queueing models introduced where possible. and sensitivity function. Basic network synthesis EEME E6610x Optimal control theory ELEN E6781y Topics in modeling and methods: immittance and transfer function 3 pts. Lect: 3. analysis of random phenomena realization, multiport realization, approximation Prerequisite: ELEN E6201 or EEME E6601. 3 pts. Lect: 3. techniques. Objectives of optimal control. Continuous and Prerequisite: ELEN E6711. Recommended ELEN E6261y Computational methods of discrete control problems. Calculus of variations: preparation: a course on real analysis circuit analysis Mayer and Bolza; Pontryagin’s maximum principle. and advanced probability theory. Current 3 pts. Lect: 3. Bang-bang and singular controls. Existence methodology in research in stochastic processes Prerequisites: ELEN E3331 and APMA E3101. of optimal control. Hamilton-Jacobi theory and applied to communication, control, and signal Computational algorithms for DC, transient, dynamic programming. Numerical methods. processing. Topics vary from year to year to and frequency analysis of linear and nonlinear Optimal feedback control regulatory problems. reflect student interest and current developments circuits. Formulation of equations: state Linear-quadratic-Gaussian estimation. Applications. in the field. equations, hybrid equations, sparse tableaux. EEME E6612x or y Control of nonlinear CSEE E6831y Sequential logic circuits Solution techniques: iterative methods to solve dynamic systems 3 pts. Lect: 3. nonlinear algebraic equations; piecewise linear 3 pts. Lect: 3. Prerequisite: CSEE W3827 or any introduction methods; sparse matrix techniques; numerical Prerequisites: EEME E6601 or ELEN E6201 and to logic circuits. Generation and manipulation of integration of stiff, nonlinear differential an undergraduate controls course. Fundamental flow table descriptions to asynchronous sequential equations, companion network models; waveform properties of nonlinear systems; qualitative functions. Coding of flow tables to satisfy relaxation. analysis of nonlinear systems; nonlinear various design criteria. Delays, races, hazards, ELEN E6302x or y MOS transistors controllability and observability; nonlinear stability; metastability. Analysis of latches to determine 3 pts. Lect: 2. zero dynamics and inverse systems; feedback key parameters. Bounds of input rates. Clocking Prerequisite: ELEN E3106 or equivalent. stabilization and linearization; sliding control schemes for synchronous systems. Synthesis Operation and modelling of MOS transistors. theory; nonlinear observers; describing functions. of self-timed systems using 4-phase or 2-phase MOS two- and three-terminal structures. The handshakes. ELEN E6731y Satellite communication MOS transistor as a four-terminal device; general systems CSEE E6832x or y Topics in logic design charge-sheet modelling; strong, moderate, 3 pts. Lect: 2. Not offered in 2014–2015. theory and weak inversion models; short-and-narrow- Prerequisite: ELEN E4702. Introduction to 3 pts. Lect: 3. channel effects; ion-implanted devices; scaling satellite communication, with emphasis on Prerequisite: CSEE W3827 or any introduction to considerations in VLSI; charge modelling; large- characterization and systems engineering of the logic circuits. A list of topics for each offering of signal transient and small-signal modelling for transmission channel. Power budgets, antennas, the course is available in the department office quasistatic and nonquasistatic operation. transponders, multiple access, and frequency one month before registration. May be taken re-use techniques. Noise, intermodulation, more than once if topics are different. Iterative

engineering 2014–2015 152 logic circuits applied to pattern recognition. Finite topics in classical and quantum phenomena ELEN E9404x or y Seminar in lightwave state machines; alternative representations, that are based on ion and electron beams, communications information loss, linear circuits, structure theory. gas discharges, and related excitation 3 pts. Lect: 2. Reliability and testability of digital systems. sources. Application to new laser sources and Open to doctoral candidates, and to qualified microelectronic fabrication. M.S. candidates with instructor’s approval. ELEN E6920x or y Topics in VLSI systems Recent theoretical and experimental design ELEN E9201x or y Seminar in circuit theory developments in light wave communications 3 pts. Lect: 2. 3 pts. Lect: 2. research. Examples of topics that may be Prerequisite: ELEN E4321. Design automation: Open to doctoral candidates, and to qualified treated include information capacity of light layout, placement, and routing. Circuit simulation M.S. candidates with instructor’s permission. wave channels, photonic switching, novel light algorithms and optimization of performance Study of recent developments in linear, wave network architectures, and optical neural and area. Multiprocessor computing systems. nonlinear, and distributed circuit theory and networks. Verification of testing. Topics may change from analysis techniques important to the design of year to year. very large scale integrated circuits. ELEN E9501x or y Seminar in electrical power networks ELEN E8701y Point processes in information ELEN E9301x or y Seminar in electronic 3 pts. Lect: 2. and dynamical systems devices Prerequisites: Open to doctoral candidates, and 3 pts. Lect: 3. 3 pts. Lect: 2. to qualified M.S. candidates with the instructor’s Prerequisite: ELEN E6711 or equivalent. Open to doctoral candidates, and to qualified permission. Recent developments in control & Recommended preparation: Course in M.S. candidates with instructor’s permission. optimization for power systems, design of smart measure theory or advanced probability theory. Theoretical and experimental studies of grid, and related topics. Probability and point processes. Random semiconductor physics, devices, and technology. intensity rate, martingales, and the integral ELEN E9701x or y Seminar in information and ELEN E9303x or y Seminar in electronic representation of point process martingales. communication theories circuits Recursive estimation, the theory of innovations, 3 pts. Lect: 2. 3 pts. Lect: 2. state estimate for queues. Markovian queueing Open to doctoral candidates, and to qualified Open to doctoral candidates, and to qualified networks. Hypothesis testing, the separation M.S. candidates with instructor’s permission. M.S. candidates with instructor’s permission. between filtering and detection. Mutual Recent developments in telecommunication Study of recent developments in electronic information and capacity for the Poisson- networks, information and communication circuits. type channel. Stochastic control, dynamic theories, and related topics. programming for intensity control. ELEN E9402x or y Seminar in quantum ELEN E9801x or y Seminar in signal electronics ELEN E9060x or y Seminar in systems biology processing 3 pts. Lect: 2. 3 pts. Lect: 2. 3 pts. Lect: 2. Open to doctoral candidates, and to qualified Open to doctoral candidates, and to qualified Open to doctoral candidates, and to qualifies M.S. candidates with instructor’s permission. M.S. candidates with instructor’s permission. M.S. candidates with instructor’s approval. Recent experimental and theoretical Study of recent developments in the field of Recent developments in theory and applications developments in various areas of quantum systems biology. of signal processing, machine learning, content electronics research. Examples of topics that analysis, and related topics. EEBM E9070x or y Seminar in computational may be treated include novel nonlinear optics, neuroscience and neuroengineering lasers, transient phenomena, and detectors. 3 pts. Lect: 2. ELEN E9403x or y Seminar in photonics Open to doctoral candidates and qualified 3 pts. Lect: 2. M.S. candidates with instructor’s permission. Prerequisite: ELEN E4411. Open to doctoral Study of recent developments in computational candidates, and to qualified M.S. candidates with neuroscience and neuroengineering. instructor’s permission. Recent experimental ELEN E9101x or y Seminar in physical and theoretical developments in various areas of electronics photonics research. Examples of topics that may 3 pts. Lect: 2. be treated include squeezed-light generation, Prerequisites: Quantum electronics and ELEN quantum optics, photon detection, nonlinear E4944, or instructor’s permission. Advanced optical effects, and ultrafast optics.

engineering 2014–2015 Industrial Engineering and Operations Research 153 313 S. W. Mudd, MC 4704 Phone: 212-854-2941 ieor.columbia.edu

Chair Director: Professors Associate Adjunct Faculty Garud Iyengar Undergraduate Daniel Bienstock Professors Siddhartha Dastidar 326 S. W. Mudd Programs Mark Broadie, Jose Blanchet David DeRosa Karl Sigman Business School Mariana Olvera-Cravioto Robert Farrokhnia Executive Director Maria Chudnovsky Leon S. Gold Jenny S. Mak Director: Master Awi Federgruen, Assistant David Gulley 324 S. W. Mudd of Science Business School Professors Mark Herman Programs Guillermo Gallego Augustino Capponi Mark Higgins associate director: Soulaymane Kachani Paul Glasserman, Vineet Goyal Ali Hirsa admissions and Business School Xuedong He Ebad Jahangir Student Affairs Director: Financial Donald Goldfarb Tim Leung Iraj Kani Engineering Adina Berrios Brooks Garud Iyengar Van Anh Truong Michael D. Lipkin Program Jay Sethuraman Yuan Zhong Hanan Luss Emanuel Derman CAREER MANAGEMENT Karl Sigman Allan Malz TEAM Clifford Stein Lecturers in Cyrus Mohebbi Director: Doctoral Mindi Levinson Garrett van Ryzin, Discipline Gerard Neumann Darbi Roberts Programs Martin Haugh Lucius J. Riccio Jay Sethuraman Business School Tamar Senderowicz Ward Whitt Anthony Webster Moshe Rosenwein Leon Tatevossian David D. Yao Director: Leo Tilman Executive Sheldon Weinig professors of Education Larry Wright Soulaymane Kachani professional practice Emanuel Derman Soulaymane Kachani

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

engineering 2014–2015 154 Current Research Activities The Computational Optimization behaviors, and communicate their In industrial engineering, research is Research Center (CORC) at Columbia solutions and recommendations conducted in the area of logistics, University is an interdisciplinary group effectively through written, oral, and routing, scheduling, production and of researchers from a variety of electronic presentations; supply chain management, inventory departments on the Columbia campus. 3. To familiarize students with the control, revenue management, and Its permanent members are Professors historical development of industrial quality control. Daniel Bienstock, Don Goldfarb, Garud engineering tools and techniques and In operations research, new Iyengar, Jay Sethuraman, and Cliff with the contemporary state of the developments are being explored Stein, from the Industrial Engineering art, and to instill the need for lifelong in mathematical programming, and Operations Research Department, learning within their profession; and combinatorial optimization, stochastic and Professor David Bayer, from 4. To instill in our students an modeling, computational and the Department of Mathematics at understanding of ethical issues mathematical finance, queueing Barnard College. Researchers at and professional and managerial theory, reliability, simulation, and both CORC specialize in the design and responsibilities. deterministic and stochastic network implementation of state-of-the-art flows. algorithms for the solution of large-scale B.S. in Operations Research In engineering and management optimization problems arising from a The operations research program systems, research is conducted in wide variety of industrial and commercial is one of several applied science the areas of logistics, supply chain applications. programs offered at the School. At optimization, and revenue and risk the undergraduate level, it offers management. undergraduate programs basic courses in probability, statistics, In financial engineering, research applied mathematics, simulation, is being carried out in portfolio and optimization as well as more B.S. in Industrial Engineering management; option pricing, including professionally oriented operations The undergraduate program is exotic and real options; computational research courses. The curriculum is well designed to develop the technical finance, such as Monte Carlo simulation suited for students with an aptitude for skills and intellectual discipline needed and numerical methods; as well as data mathematics applications. by our graduates to become leaders mining and risk management. It prepares graduates for professional in industrial engineering and related Projects are sponsored and employment as operations research professions. The program is distinctive supported by leading private firms analysts, e.g., with management in its emphasis on quantitative, and government agencies. In addition, consultant and financial service economic, computer-aided approaches our students and faculty are involved organizations, as well as for graduate to production and service management in the work of three research and studies in operations research or problems. It is focused on providing educational centers: the Center for business. It is flexible enough to be an experimental and mathematical Applied Probability (CAP), the Center adapted to the needs of future medical problem-formulating and problem- for Financial Engineering (CFE), and and law students. the Computational and Optimization solving framework for industrial engineering work. The curriculum Research Center (CORC). These centers B.S. in Operations Research: provides a broad foundation in the are supported principally by grants from Engineering Management Systems the National Science Foundation. current ideas, models, and methods of industrial engineering. It also includes a This operations research option is The Center for Applied Probability designed to provide students with (CAP) is a cooperative center involving substantial component in the humanities and social sciences to help students an understanding of contemporary the School of Engineering and Applied technology and management. It is Science, several departments in the understand the societal implications of their work. for students who are interested in a Graduate School of Arts and Sciences, technical-management background and the Graduate School of Business. The industrial engineering program objectives are: rather than one in a traditional Its interests are in four applied areas: engineering field. It consists of required mathematical and computational finance, 1. To provide students with the requisite courses in industrial engineering and stochastic networks, logistics and operations research, economics, distribution, and population dynamics. analytical and computational skills to assess practical situations and business, and computer science, The Center for Financial Engineering intended to provide a foundation (CFE) at Columbia University encourages academic problems, formulate models of the problems represented for dealing with engineering and interdisciplinary research on financial management systems problems. engineering and mathematical modeling or embedded therein, design potential solutions, and evaluate their Elective courses are generally intended in finance and promoting collaboration to provide a substantive core in at least between Columbia faculty and financial impact; 2. To prepare students for the workplace one technology area and at least one institutions, through the organization management area. of research seminars, workshops, and by fostering their ability to participate in teams, understand and practice Due to the flexibility of this option, it the dissemination of research done by can incorporate the varied educational members of the Center. interpersonal and organizational engineering 2014–2015 155 industrial engineering program: first and second Years

Semester i Semester iI Semester iII Semester iV

mathematics MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) Linear algebra (3)1

Chemistry or physics lab: PHYS C1493 (3) or C1401 (3) C1402 (3) physics PHYS W3081 (2) or (three tracks, C1601 (3.5) C1602 (3.5) CHEM C1500 (3) or choose one) C2801 (4.5) C2802 (4.5) CHEM C2507 (3) or CHEM C3085 (4) or

chemistry C1403 (3) or C1404 (3) or (choose one course) C1604 (3.5) or C3045 (3.5)

english C1010 (3) composition (three tracks, Z1003 (0) C1010 (3) choose one) Z0006 (0) Z1003 (0) C1010 (3)

HUMA C1001, HUMA C1002, COCI C1101, COCI C1102, or Global core (3–4) or Global core (3–4) required ECON W1105 (4) and W1155 recitation (0) nontechnical electives either semester HUMA W1121 or W1123 (3) either semester

first- and Second-Year Professional-level course (3) (see pages 12–13) IEOR E2261 (3) SIEO W3600 (4)2 Dept. Requirements

COMS W1004 (3) and COMS W3134 (3) computer ENGI E1006 (3) COMS W3136 (3)3 science or and or COMS W1007 (3) and COMS W3137 (4)

physical C1001 (1) C1002 (1) education

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 The linear algebra requirement may be filled by either MATH V2010 or APMA E3101. 2 If taking IEOR E3658, students must take IEOR E4307 to complete the SIEO W3600 requirement. 3 COMS W3136 will be offered beginning in Spring 2013.

industrial engineering: Third and Fourth Years

Semester V Semester VI Semester VII Semester VIII

MATH E1210 (3) Ordinary diff. equations IEOR E4003 (3) IEOR E4405 (3) Industrial econ. Prod. scheduling IEOR E3106 (3) IEOR E3402 (4) Stochastic models Production planning IEOR E4207 (3) IEOR E4412 (3) Required Human factors Courses1 Quality control and IEOR E3608 (4) IEOR E4404 (4) management Mathematical prog. Simulation IEOR E4205 (3) Studies in operations IEOR E4510 (3) COMS W4111 (3) research Project management Database systems

technical Choose one (3 pts.): Please consult the list on the departmental website: ieor.columbia.edu electives

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

Industrial Engineering Choose two (6 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.

engineering 2014–2015 156 operations research program: first and second Years

Semester i Semester iI Semester iII Semester iV

mathematics MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) Linear algebra (3)1

chemistry C1403 (3) or C1404 (3) or (choose one course) C1604 (3.5) or C3045 (3.5)

english C1010 (3) composition (three tracks, Z1003 (0) C1010 (3) choose one) Z0006 (0) Z1003 (0) C1010 (3)

HUMA C1001, HUMA C1002, COCI C1101, COCI C1102, or Global Core (3–4) or Global Core (3–4) required ECON W1105 (4) and W1155 recitation (0) nontechnical electives either semester HUMA W1121 or W1123 (3) either semester

first- and Second- Year Dept. Professional-level course (3) (see pages 12–13) IEOR E2261 (3) SIEO W3600 (4)2 Requirements

COMS W1004 (3) and COMS W3134 (3) computer ENGI E1006 (3) COMS W3136 (3)3 science or and or COMS W1007 (3) and COMS W3137 (4)

physical C1001 (1) C1002 (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

IEOR E4003 (3) MATH E1210 (3) Industrial econ. Ordinary diff. equations IEOR E4405 (3) IEOR E3402 (4) IEOR E4407 (3) Prod. scheduling Production planning IEOR E3106 (3) Game theoretic models of Stochastic models operations Required IEOR E4404 (4) Courses1 Simulation IEOR E3608 (4) Mathematical prog. Choose one: IEOR E4600 (3) IEOR E4505 Operations research for public policy Applied integer prog. COMS W4111 (3) IEOR E4507 Healthcare operations management Database systems IEOR E4615 Service engineering IEOR E4700 Introduction to FE

operations Choose four OR electives (12 pts. total): 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.

engineering 2014–2015 157 OPERATIONS RESEARCH: engineering management systems program: first and second Years

Semester i Semester iI Semester iII Semester iV

mathematics MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) Linear algebra (3)1

chemistry C1403 (3) or C1404 (3) or (choose one course) C1604 (3.5) or C3045 (3.5)

english C1010 (3) composition (three tracks, Z1003 (0) C1010 (3) choose one) Z0006 (0) Z1003 (0) C1010 (3)

first- and Second- Professional-level course (3) (see pages 12–13) IEOR E2261 (3) SIEO W3600 (4)2 Year Dept. Requirements

COMS W1004 (3) and COMS W3134 (3) computer ENGI E1006 (3) COMS W3136 (3)3 science or and or COMS W1007 (3) and COMS W3137 (4)

physical C1001 (1) C1002 (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 E1210 (3) IEOR E4003 (3) Ordinary diff. equations Industrial econ. IEOR E4001 (3) IEOR E3402 (4) Design and mgmt. of prod. Production planning IEOR E3106 (3) IEOR E4404 (4) and service systems Stochastic models Simulation Required ECON W3213 (3) Courses1 Macroeconomics IEOR E3608 (4) Mathematical prog. COMS W4111 (3) Choose one: Database systems IEOR E4550 Entrepreneurial business creation ECON W3211 (3) IEOR E4998 Managing technological innovations Microeconomics

tech Technical electives (12 pts. total)2

Management electives (9 pts. total): management Please consult lists posted on IEOR website: ieor.columbia.edu E lecti v es 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 www.ieor.columbia.edu.

engineering 2014–2015 158 OPERATIONS RESEARCH: FINANCIAL engineering programming: first and second Years

Semester i Semester iI Semester iII Semester iV

Linear algebra (3)1 mathematics MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) and ODE (3)

Physics or chemistry lab: PHYS C1493 (3) or C1401 (3) C1402 (3) physics PHYS W3081 (2) or (three tracks, C1601 (3.5) C1602 (3.5) CHEM C1500 (3) or choose one) C2801 (4.5) C2802 (4.5) CHEM C2507 (3) or CHEM C3085 (4) or

chemistry C1403 (3.5) or C1404 (3.5) or (choose one course) C1604 (3.5) or C3045 (3.5)

english C1010 (3) composition (three tracks, Z1003 (0) C1010 (3) choose one) Z0006 (0) Z1003 (0) C1010 (3)

first- and IEOR E2261 (4) Second-Year Professional-level course (3) (see pages 12–13) Dept. Requirements IEOR E3658 (3) IEOR E4307 (3)2

COMS W1004 (3) and COMS W3134 (3) computer ENGI E1006 (3) COMS W3136 (3)3 science or and or COMS W1007 (3) and COMS W3137 (4)

physical C1001 (1) C1002 (1) education

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 The linear algebra requirement may be filled by either MATH V2010 or APMA E3101. 2 Students may also take STAT W3107 or W4107; however, the department strongly recommends IEOR E4307 in the spring term. 3 COMS W3136 will be offered beginning in Spring 2013.

OPERATIONS RESEARCH: FINANCIAL engineering: Third and Fourth Years

Semester V Semester VI Semester VII Semester VIII

IEOR E3402 (4) IEOR E4407 (3) Production planning Game theoretic models ECON W3213 (3) of operations IEOR E4630 (3) Macroeconomics IEOR E4404 (4) Asset allocation Simulation IEOR E4620 (3) IEOR E3106 (3) Pricing models for FE Stochastic models Required IEOR E4700 (3) Courses Intro. to FE IEOR E3608 (4) Mathematical prog. IEOR E4500 (3) COMS W4111 (3) Applications prog. for FE Database systems IEOR E4003 (3) Industrial econ. ECON E3412 (3) ECON W3211 (3) Intro. to econometrics Microeconomics

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

E lecti v es nontech Complete 27-point requirement; see page 10 or engineering.columbia.edu for details

engineering 2014–2015 needs of preprofessional students higher-level IEOR courses, including the of 3.0 (B) or its equivalent in an 159 interested in law, medicine, business, following: undergraduate engineering program and finance. In addition, most students is required for admission to the M.S. IEOR E4004 instead of IEOR E3608 are encouraged to add a minor in programs. At a minimum, students are IEOR E4106 instead of IEOR E3106 economics or computer science to their expected, on entry, to have completed IEOR E4403 instead of IEOR E4003 standard course schedules. courses in ordinary differential and MATH V2500 equations, linear algebra, probability, B.S. in Operations Research: Students successfully completing and a programming language such as Financial Engineering the requirements of the undergraduate C or Java. The operations research concentration advanced track will receive recognition in financial engineering is designed to on their academic record. M.S. in Financial Engineering provide students with an understanding The department offers a full-time of the application of engineering Minors only M.S. in Financial Engineering. methodologies and quantitative A number of minors are available for This program is intended to provide methods to finance. Financial students wishing to add them to their a unique technical background for engineering is a multidisciplinary programs. These minors are described students interested in pursuing career field integrating financial theory with starting on page 194 of this bulletin. opportunities in financial analysis and economics, methods of engineering, IEOR program students may want risk management. tools of mathematics, and practice of to consider minors in economics In addition to the basic requirements programming. Students graduating with or computer science. In addition, for graduate study, students are this concentration are prepared to enter operations research and engineering expected, on entry, to have attained a careers in securities, banking, financial and management systems majors may high level of mathematical and computer management, and consulting industries, elect to minor in industrial engineering, programming skills, particularly in and fill quantitative roles in corporate and industrial engineering majors may probability, statistics, linear algebra, and treasury and finance departments of elect to minor in operations research. the use of a programming language general manufacturing and service firms. The department does not offer a such as C or JAVA. Work experience is Students who are interested in minor in engineering management desirable but not required. pursuing the rigorous concentration in systems or financial engineering. The program consists of 36 points financial engineering must demonstrate (12 courses), starting the fall semester. proficiency in calculus, computer Graduate Programs Students may complete the program programming, linear algebra, ordinary in June, August, or December of The Department of Industrial differential equations, probability, the following year. The requirements Engineering and Operations Research and statistics. Applications to the include six required core courses and offers courses and M.S. programs in concentration are accepted during additional elective courses chosen from (1) financial engineering on a full-time the fall and spring semesters of the a variety of departments or schools basis only; (2) management science and sophomore year, and students will be at Columbia. In addition, the program engineering on a full-time basis only; (3) notified of the departmental decision requires its students to attend the Financial industrial engineering on either a full- by the end of that spring semester. The Engineering Seminar Series and submit or part-time basis; and (4) operations department is seeking students who learning journals. research on either a full- or part-time demonstrate strength and consistency The MSFE Program offers five basis. The Department’s M.S. program iin all the above-mentioned areas. concentrations, including (1) Computation in Management Science and Egineering Application to this concentration is and Programming; (2) Finance and is offered in conjunction with the available online: ieor.columbia.edu Economics; (3) Derivatives; (4) Asset Columbia Graduate School of Business. /pages/undergraduate/financial_eng Management; and (5) Computational Graduate programs leading to a Ph.D. /bsfe_app.html. Finance and Trading Systems. A sample or Eng.Sc.D. in industrial engineering schedule is available in the department or operations research. In addition, the office and on the IEOR website: ieor Undergraduate Advanced Track department and the Graduate School .columbia.edu. The undergraduate advanced of Business offer combined M.S./ The six required core courses for the track is designed for advanced M.B.A. degree programs in industrial financial engineering program are IEOR undergraduate students with the desire engineering, in financial engineering, and E4007, E4701, E4703, E4706, E4707, to pursue further higher education in operations research. and E4709. after graduation. Students with a All degree program applicants In addition, students select two minimum cumulative GPA of 3.4 and are required to take the Aptitude semicore courses from a group of faculty approval have the opportunity Tests of the Graduate Record specialized offerings in both the fall and to participate. Students are invited to Examination. M.S./M.B.A. candidates spring terms. Students may select from apply to the track upon the completion are also required to take the Graduate a variety of approved electives from the of their sophomore year. Advanced Management Admissions Test. department, the School of Business, track students are required to take A minimum grade-point average and the Graduate School of Arts and

engineering 2014–2015 160 Sciences. Courses taken at the School of Continuing Education will not be M.S. in Financial Engineering—June 2015 Completion (36 points)1 counted towards the M.S. degree (e.g., courses with the following prefixes: Fall Semester Spring Semester Summer and/or Fall Semester ACTU, BUSI, COPR, IKNS, SUMA, (9 points)2 (9 points)2 (For remaining credits)2 FUND, and more). Please consult with your academic adviser regarding Required core courses: Required core courses: IEOR E4708 Seminar on electives offered in other departments important papers in financial and schools, prior to registration. IEOR E4007 Optimization mod- IEOR E4703 Monte Carlo engineering The department requires that els and methods for financial simulation engineering IEOR E4714 (1.5) Risk manage- students achieve grades of B– or IEOR E4707 Continuous time ment, financial systems, and higher in each of the three fundamental IEOR E4701 Stochastic models finance financial crisis core courses offered in the first fall. for financial engineering IEOR E4709 Data analysis for Poor performance in these courses is IEOR E4715 Commodity IEOR E4706 Foundations of financial engineering derivatives (1.5) indicative of inadequate preparation financial engineering and is very likely to lead to serious IEOR E4722 Introduction to problems in completing the program. Plus semi-core electives, 3-6 algorithmic trading (1.5) As a result, students failing to meet this 3 Plus semi-core electives, 3-6 points IEOR E4733 Algorithmic trading criterion will be asked to withdraw from points 3 the program. IEOR E4734 Foreign exchange and related derivatives instruments (1.5) M.S. in Management Science and Engineering IEOR E4735 Introduction to The Master of Science program in structured and hybrid products Management Science and Engineering

(MS&E), offered by the IEOR Department 1 Students may conclude the program in June, August, or December 2015. Please visit the departmental in conjunction with Columbia Business website (ieor.columbia.edu/ms-financial-engineering) for more information. School, is the first such program 2 All courses listed are for 3 points, unless stated otherwise. 3 between Columbia Engineering and The list of semi-core MSFE electives can be found at ieor.columbia.edu/ms-financial-engineering Columbia Business School. It reflects the next logical step in the longstanding and insurance firms. Electives are selected under the close collaboration between the IEOR The MS&E program is a three- advisement of the student’s faculty Department at the Engineering School semester program (36 points) that can adviser. Courses taken at the School and the Decision, Risk, and Operations be completed in a single calendar year. of Continuing Education will not be (DRO) Division at the Business School. Students enter in the fall term and can counted toward the M.S. degree (e.g., This program was formed and either finish their course work at the end courses with the following prefixes: structured following many interactions of the following August, or alternatively, ACTU, BUSI, COPR, IKNS, SUMA, with corporations, alumni, and students. have the option to take the summer FUND, and more). It emphasizes both management and term off (e.g., for an internship) and The department requires that stu- engineering perspectives in solving complete their course work by the end dents achieve grades of B– or higher problems, making decisions, and of the following fall term. Students are in each of the three fundamental core managing risks in complex systems. required to take the equivalent of 12 courses. Poor performance in these Students pursuing this degree program 3-point courses (36 points). courses is indicative of inadequate are provided with a rigorous exposure to Students must take at least six preparation and is very likely to lead optimization and stochastic modeling, courses within the IEOR Department, to serious problems in completing the and a deep coverage of applications in four to six courses at the Business program. As a result, students failing to the areas of operations engineering and School, and the remaining courses (if meet this criterion will be asked to with- management. any) within the School of Engineering, draw from the program. Graduates from this program are the School of International and expected to assume positions as Public Affairs, the Law School, or M.S. in Industrial Engineering analysts and associates in consulting the Departments of Economics, The department’s graduate program firms, business analysts in logistics, Mathematics, and Statistics. Students in in industrial engineering is generally supply chain, operations, or revenue residence during the summer term take intended to enable students with management departments of large two to four Business School courses in industrial engineering bachelor’s degrees corporations, and as financial the third (summer) semester in order to to enhance their undergraduate training analysts in various functions (e.g., risk complete their program. with studies in special fields such as management) of investment banks, production planning, inventory control, hedge funds, credit-card companies, scheduling, and industrial economics.

engineering 2014–2015 However, the department also offers 161 broader master’s programs for engineers M.S. in Management Science and Engineering (36 points) whose undergraduate training is not in industrial engineering. Required Core IEOR E4004 Intro to OR: deterministic models (first fall semester) M.S. degree candidates are required Courses (12) IEOR E4111 Operations consulting (starts first fall semester, all-year course) to satisfy a core program of graduate IEOR E4575 Probability models for management science and engineering courses in production management, (first fall semester) probability theory, statistics, simulation, IEOR E4576 Stochastic models for management science and engineering and operations research. Students with (spring semester) B.S. degrees in industrial engineering will Plus Semi-Core Courses (DRO, Analaysis, and Management Electives (18) usually have satisfied this core in their undergraduate programs. All students Decision, Risk, and DROM B8106-060 Operations strategy (1.5) (summer—second half) must take at least 18 points of graduate Operations Electives DROM B8107-060 Service operations (fall semester) work in industrial engineering and at (9) DROM B8108-060 Supply chain management (spring semester) least 30 points of graduate studies at DROM B8111-060 Analytics for business research (1.5) (summer—second half) Columbia. Master’s degree programs DROM B8122-060 MSE game-theoretic business strategy (spring semester) may include concentrations in: DROM B9106-001 Applied multivariate statistics (summer) engineering and management systems DROM B9122-001 Computing for business research (fall semester) production and operations management MGMT B8510-060 Managerial negotiations (with game theoretical analysis) manufacturing (fall and spring semester) industrial regulation studies MRKT B8617-001 Marketing research (summer) Additional details regarding Analysis and ECON W4280 Corporate finance (by application, fall and spring semester) these concentrations are available Management IEME E4310 The manufacturing enterprise (fall semester) in the department office. A thesis Electives (9) IEOR E4205 Studies in operations research (fall or spring semester) is not required. Students who Management Group IEOR E4505 Operations research in public policy (spring semester) plan post–master’s degree studies At least one of the IEOR E4510 Project management (spring semester) should give due consideration to the following: IEOR E4520 Applied systems engineering (fall semester) course, examination, and admission IEOR E4521 Systems engineering tools and methods requirements of these programs. Students may select from a IEOR E4550 Entrpreneurial business creation for engineers (fall or spring semester) variety of approved electives from the IEOR E4573 Design and Agile Project Management Engineerng Lab department, the School of Business, (fall semester) and the Graduate School of Arts and IEOR E4573 Lean LaunchPad (weeklong course in mid-January, by Sciences. Courses taken at the School application only) of Continuing Education will not be IEOR E4711 Global capital markets (fall semester) counted toward the M.S. degree (e.g., IEOR E4998 Managing technological innovation and entrpreneurship (fall or courses with the following prefixes: spring semester) ACTU, BUSI, COPR, IKNS, SUMA, FINC B8307 Advanced corporate finance (spring semester) FUND, and more). Please consult with your academic adviser regarding Analysis and IEOR E4000 Production and operations management (fall semester) electives offered in other departments Management IEOR E4403 Advanced engineering and corporate economics (fall semester) and schools, prior to registration. Electives (9) IEOR E4404 Simulation (fall or spring semester) Analysis Group The department requires that IEOR E4405 Production scheduling (spring semester) students in the program achieve At least one of the following: IEOR E4407 Game theoretic models of operations (fall semester) grades of B– or higher in each of the IEOR E4418 Logistics and transportation management (spring semester) fundamental core courses (IEOR E4004 IEOR E4507 Operations management: with application to healthcare management and E4106). Poor performance in these (fall semester) courses is indicative of inadequate IEOR E4570 Machine learning for OR and FE (spring semester) preparation and is very likely to lead IEOR E4601 Dynamic pricing and revenue optimization (spring semester) to serious problems in completing the IEOR E4611 Decision models and applications (spring semester) program. In addition, students must IEOR E4615 Service engineering (spring semester) maintain a cumulative GPA equivalent to a B– during every term enrolled. A Breadth Electives: student failing to meet these criteria The breadth electives can be selected from the Business School, the School of Engineering, the School of may be asked to withdraw from his/her International and Public Affairs, the Law School, or the Departments of Economics, Mathematics, and Statistics. program.

engineering 2014–2015 162 M.S. in Operations Research (30 points)

Required Core Courses SIEO W4150 Intro to probability and statistics IEOR E4004 Intro to OR: deterministic models (12 points) IEOR E4106 Intro to OR: stochastic models IEOR E4004 Simulation

Electives for conceNtration

Applied Probability IEOR E4000 Production and 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: OPMN B8815 Supply chain management DRAN B8839 Demand and supply analytics

Business Analytics Technical Courses Management Courses The department recommends taking: IEOR E4570 Machine learning for OR and FE and At least two of: IEOR E4205 Studies in operations research At least two of: IEOR E4408 Resources allocation: models, algorithms, and IEOR E4000 Production and operations management applications IEOR E4307 Applied statistical models in operations research IEOR E4510 Project management IEOR E4500 Applications programming for financial engineering IEOR E4520 Applied systems engineering business creation for IEOR E4722 Topics in quantitative finance engineers IEOR E4726 Experimental finance IEOR E4550 Entrepreneurial business creation for engineers OPMN B8862 Demand and supply analytics IEOR E4611 Decision models and applications OPMN B9835 Computing for business research IEOR E4998 Managing technological innovation and entrpreneurship

Financial and Managerial Corporate Finance Courses Derivatives Pricing Courses Management Courses Applications IEOR E4403 Adv. engineering and IEOR E4700 Intro to financial engineering At least one of: The department corporate economics recommends taking: And at least one of: IEOR E4205 Studies in operations research And at least one of: IEOR E4602 Quantitative risk IEOR E4505 OR in public policy IEOR E4721 Global capital market management IEOR E4507 Healthcare operations FINC B8301 Advanced corporate finance IEOR E4620 Pricing models management ECON W4280 Corporate finance IEOR E4630 Asset allocation IEOR E4510 Project management or INAF U6022 Economics of finance IEOR E4731 Credit risk and credit IEOR E4550 Entrepreneurial business creation derivatives for engineers DRAN B8835 Quantitative finance: models IEOR E4611 Decision models and applications and computation IEOR E4998 Managing technological innovation

Logistics and Supply Technical Courses Management Courses Chain Management At least three of: At least two of: The department recommends taking: IEOR E4000 Production and operations management IEOR E4205 Studies in operations research IEOR E4403 Adv. engineering and corporate economics IEOR E4310 The manufacturing enterprise IEOR E4405 Production scheduling IEOR E4408 Resource allocation: models, algorithms and IEOR E4505 OR in public policy applications IEOR E4507 Healthcare operations management IEOR E4510 Project management IEOR E4600 Applied integer programming IEOR E4520 Applied systems engineering IEOR E4601 Dynamic pricing and revenue management IEOR E4550 Entrepreneurial business creation for engineers IEOR E4602 Quantitative risk management IEOR E4611 Decision models and applications IEOR E4615 Service engineering IEOR E4998 Managing technological innovation OPMN B8815 Supply chain management DRAN B8839 Demand and supply analytics

Optimization IEOR E4000 Production and operations management IEOR E4405 Production scheduling The department IEOR E4408 Resource allocation: models, algorithms and applications IEOR E4505 Operations research in public policy recommends taking at IEOR E4507 Healthcare operations management IEOR E4510 Project management least three of the following IEOR E4520 Applied systems engineering IEOR E4600 Applied integer programming elective courses: IEOR E4611 Decision models and applications IEOR E4615 Service engineering IEOR E4630 Asset allocation OPMN B8815 Suppy chain management

engineering 2014–2015 M.S. in Operations Research courses in ordinary differential equations, conducted under the supervision of a 163 The graduate program in this area is in linear algebra, and in a programming faculty member. The dissertation work designed to enable students to concen- language such as C or Java. may be theoretical or computational trate their studies in methodological areas The department requires that or both. Doctoral students are also such as mathematical programming, sto- students in the program achieve required to select a concentration for chastic models, and simulation. However, grades of B– or higher in each of the their studies and complete a certain the department also has a broadly based fundamental core courses (IEOR E4004 amount of course work in one of the master’s degree program that enables and E4106). Poor performance in these following fields: applied probability, students with engineering or other courses is indicative of inadequate mathematical programming, financial undergraduate majors that include strong preparation and is very likely to lead engineering, or supply chain manage- mathematics preparation to complete to serious problems in completing the ment and logistics. Doctoral candidates work in two terms of full-time study. program. In addition, students must must obtain a minimum of 60 points of M.S. degree candidates are required maintain a cumulative GPA equivalent formal course credit beyond the bach- to satisfy a core set of graduate courses to a B– during every term enrolled. A elor’s degree. A master’s degree from an in probability, statistics, linear program- student failing to meet these criteria accredited institution may be accepted ming, and simulation. All students must may be asked to withdraw from his/her as equivalent to 30 points. A minimum complete at least 18 points of opera- program. of 30 points beyond the master’s degree tions research courses and at least 30 must be earned while in residence in the points of graduate work at Columbia. Joint M.S. and M.B.A. doctoral program. Detailed information The department considers it desir- The department and the Graduate regarding the requirements for the able that students construct balanced School of Business offer a joint doctoral degree may be obtained in programs involving deterministic and master’s program in industrial the department office or online at ieor stochastic models, as well as substan- engineering. Prospective students .columbia.edu/phd_ieor.html. tive areas for application. for this special program must submit The M.S. degree program may be separate applications to the School of Courses in industrial constructed to include the following Engineering and Applied Science and engineering and areas of focus: the Graduate School of Business and be operations research admitted to both schools for entrance applied probability For up-to-date course offerings, please into the joint program. financial and managerial application of visit ieor.columbia.edu. operations research Admissions requirements are the logistics and supply chain management same as those for the regular M.S. IEOR E2261x and y Introduction to optimization programs and for the M.B.A. This joint accounting and finance program is coordinated so that both 3 pts. Lect: 3. Professor Webster. Prerequisite: ECON W1105 Principles of Students may select from a degrees can be obtained after five terms economics. For undergraduates only. This course variety of approved electives from the of full-time study (30 points in two terms is required for all undergraduate students majoring department, the School of Business, while registered in SEAS and 45 points in IE, OR:EMS, OR:FE, and OR. This course and the Graduate School of Arts and in three terms while registered in the examines the fundamental concepts of financial Sciences. Courses taken at the School Graduate School of Business). accounting and finance, from the perspective of Continuing Education will not be Students in the joint program must of both managers and investors. Key topics counted toward the M.S. degree (e.g., complete certain courses by the end covered include: principles of accrual accounting; recognizing and recording accounting transactions; courses with the following prefixes: of their first year of study. Students in preparation and analysis of financial statements; ACTU, BUSI, COPR, IKNS, SUMA, the IE joint program should take IEOR ratio analysis; pro-forma projections; time value of FUND, and more). Please consult E4000, E4004, and SIEO W4150. money (present values, future values and interest/ with your academic adviser regarding If a substantial equivalent has been discount rates); inflation; discounted-cash-flow electives offered in other departments completed during undergraduate (DCF) project evaluation methods; deterministic and schools, prior to registration. studies, students should consult with and probabilistic measures of risk; capital Additional details regarding these a faculty adviser in order to obtain budgeting. concentrations are available in the exemption from a required course. IEOR E3106x Introduction to operations department office. A thesis is not research: stochastic models required. Students who plan to continue Doctoral Studies 3 pts. Lect: 3. Professor Whitt. their studies beyond the master’s degree The requirements for the Ph.D. in Prerequisite: SIEO W3600. For undergraduates only. This course is required for all undergraduate level should give due consideration to industrial engineering and operations students majoring in IE, OR:EMS, OR:FE, and OR. the course, examination, and grade-point research are identical. Both require the requirements of doctoral programs. The This class must be taken during (or before) the student to pass two qualifying examina- fifth semester. Some of the main stochastic models M.S. degree program can be taken on a tions—respectively covering stochastic used in engineering and operations research part-time basis or completed in one year and deterministic models—as well as applications: discrete-time Markov chains, Poisson of full-time study. Students planning to submit and defend a dissertation based processes, birth and death processes and other complete this program in one year are on the candidate’s original research, continuous Markov chains, renewal reward expected, on entry, to have completed

engineering 2014–2015 164 processes. Applications: queueing, reliability, IEOR E3658x Probability IEOR E4007x Optimization models and inventory, and finance. IEOR E3106 must be 3 pts. Lect: 3. Members of the faculty. methods for financial engineering completed by the fifth term. Only students with Prerequisite: Calculus. For undergraduates 3 pts. Lect: 3. Professor Iyengar. special academic circumstances may be allowed only. This course is required for the OR:FE Prerequisite: Linear algebra. This course is for to take these courses in alternative semesters concentration. This class must be taken during MSFE students only. Linear, quadratic, nonlinear, with the consultation of CSA and Departmental (or before) the third semester. Fundamentals dynamic, and stochastic programming. Some advisers. of probability theory. Distributions of one or discrete optimization techniques will also be more random variables. Moments, generating introduced. The theory underlying the various IEOR E3402y Production inventory planning functions, law of large numbers and central limit optimization methods is covered. The emphasis and control theorem. is on modeling and the choice of appropriate 4 pts. Lect: 3. Recit: 1. Professor Truong. optimization methods. Applications from financial Prerequisites: SIEO W3600 Probability and IEOR E3900x and y Undergraduate research engineering are discussed. Statistics and IEOR E3608 Introduction to OR: or project Mathematical programming. For undergraduates 1–3 pts. Members of the faculty. CSOR E4010y Graph theory: a combinatorial view only. This course is required for all undergraduate Prerequisite: Approval by a faculty member who 3 pts. Lect: 3. Professor Chudnovsky. students majoring in IE, OR:EMS, OR:FE, and agrees to supervise the work. Independent work Prerequisites: Linear algebra, or instructor’s OR. This class must be taken during (or before) involving experiments, computer programming, permission. An introductory course in graph theory the sixth semester. Inventory management and analytical investigation, or engineering design. with emphasis on its combinatorial aspects. Basic production planning. Continuous and periodic IEOR E4000x Production and operations definitions, and some fundamental topics in graph review models: optimal policies and heuristic management theory and its applications. Topics include trees solutions, deterministic and probabilistic demands. 3 pts. Lect: 3. Professor Gallego. and forests graph coloring, connectivity, matching Material requirements planning. Aggregate Prerequisites or Corequisite: Probability theory theory and others. planning of production, inventory, and work force. and linear programming. Required course for Multi-echelon integrated production-inventory IEOR E4106x and y Introduction to operations MSIE. An introduction to production management systems. Production scheduling. Term project. research: stochastic models for students not having an industrial engineering Recitation section required. 3 pts. Lect: 3. Professors Olvera and Yao. bachelor’s degree. Topics include deterministic Prerequisites: SIEO W4150 or probability theory. SIEO W3600y Introduction to probability inventory models, aggregate production planning, This is a required course for MSEMS, MSIE, and and statistics material requirements planning, forecasting, MSOR students. This is also required for students 4 pts. Lect: 3. Recit: 1. Members of the faculty. stochastic inventory models and supply chain in the Undergraduate Advanced Track. Some of Prerequisite: Calculus. For undergraduates only. management. Emphasis is on modeling and its the main stochastic models used in engineering This course is required for undergraduate students implications for managerial decisions. and operations research applications: discrete-time majoring in IE, OR:EMS, and OR. This class must IEOR E4001y Design and management of Markov chains, Poisson processes, birth and death be taken during the fourth semester. Fundamentals production and service systems processes and other continuous Markov chains, of probability and statistics used in engineering 3 pts. Lect: 3. Professor Riccio. renewal reward processes. Applications: queueing, and applied science. Probability: random variables, Prerequisite: IEOR E4000 or E3402. This course reliability, inventory, and finance. useful distributions, expectations, law of large is required for undergraduate students majoring in numbers, central limit theorem. Statistics: point and SIEO W4150x Introduction to probability and OR:EMS. Design and management problems in confidence interval estimation, hypothesis tests, statistics production and service systems: process design linear regression. SIEO W3600 must be completed 3 pts. Lect: 3. Professor Sigman. and capacity management, inventory system by the fourth term. Only students with special Prerequisite: Calculus. Fundamentals of probability design and management, aggregate planning, staff academic circumstances may be allowed to take theory and statistical inference used in engineering scheduling, and quality control system design. these courses in alternative semesters with the and applied science. Probabilistic models, random consultation of CSA and Departmental advisers. IEOR E4003x Industrial economics variables, useful distributions, expectations, law Recitation section required. 3 pts. Lect: 3. Professor Mohebbi. of large numbers, central limit theorem. Statistical Prerequisites or corequisites: Probability theory inference: point and confidence interval estimation, IEOR E3608x Introduction to mathematical and linear programming. This course is required hypothesis tests, linear regression. programming for all undergraduate students majoring in IE, 4 pts. Lect: 3. Recit: 1. Professor Sethuraman. IEOR E4205x and y Studies in operations OR:EMS, OR:FE, and OR. Introduction to the Prerequisite: MATH V2010 Linear algebra. research economic evaluation of industrial projects. Economic Corequisite: COMS W3134 (or COMS W3137 3 pts. Lect: 3. Professor Riccio. equivalence and criteria. Deterministic approaches to Data structures). For undergraduates only. Prerequisites: IEOR E3608 or E4004, and IEOR economic analysis. Multiple projects and constraints. This course is required for all undergraduate E3106 or E4106, or instructor’s permission. Analysis and choice under risk and uncertainty. students majoring in IE, OR:EMS, OR:FE, and Applications of operations research models OR. This class must be taken during (or before) IEOR E4004x and y Introduction to operations in practice; examples of successful projects; the fifth semester. Introduction to mathematical research: deterministic models discussion of difficulties in applying operations programming models and computational 3 pts. Lect: 3. Professors Goldfarb and research techniques in practice; understanding the techniques. Linear programming and the Strickland factors leading to successful applications. Students simplex method, dynamic programming, implicit This is a required course for MSEMS, MSIE, and will be required to do a project that may involve enumeration for integer programs; production MSOR students. This is also required for students the following: project management and budgeting, planning applications. IEOR E3608 must be in the Undergraduate Advanced Track. For contract preparation, change-order negotiations, completed by the fifth term. Only students with students who have not studied linear programming. progress reporting, organizational and personal special academic circumstances may be allowed Some of the main methods used in IEOR dynamics, client communications and relationships, to take these courses in alternative semesters applications involving deterministic models: linear and presentation skills. with the consultation of CSA and Departmental programming, the simplex method, nonlinear, advisers. Recitation section required. integer and dynamic programming.

engineering 2014–2015 IEOR E4207x Human factors: performance development, and strategic planning as currently Prerequisites: Linear programming (IEOR E3608 165 3 pts. Lect: 3. Professor Gold. practiced in industry. or E4004), basic knowledge of nonlinear and This course is required for undergraduate integer programming. Overview of resource IEOR E4403x Advanced engineering and students majoring in IE. Sensory and cognitive allocation models. Single resource allocation with corporate economics (brain) processing considerations in the design, concave returns; equitable resource allocation; 3 pts. Lect: 3. Professor Mohebbi. development, and operations of systems, products, lexicographic minmax/maxmin optimization; Prerequisites: Probability theory and linear and tools. User or operator limits and potential in extensions to substitutable resources; multi- programming This course is required for period resource allocation; equitable allocation in sensing, perceiving decision making, movement students in the Undergraduate Advanced multicommodity network flow models; equitable coordination, memory, and motivation. Track. Key measures and analytical tools to content distribution in networks; equitable IEOR E4208y Seminar in human factors design assess the financial performance of a firm and perform the economic evaluation of resource allocation with discrete decision 3 pts. Lect: 3. Professor Gold. variables. Prerequisite: IEOR E4207 or instructor’s industrial projects. Deterministic mathematical permission. This course is an elective programming models for capital budgeting. IEOR E4412y Quality control and management undergraduate students majoring in IE. An in-depth Concepts in utility theory, game theory and 3 pts. Lect: 3. Professor Ullman. exploration of the application potential of human real options analysis. Prerequisite: SIEO W3600 or W4150. This course factor principles for the design of products and IEOR E4404x and y Simulation is required for undergraduate students majoring processes. Applications to industrial products, 4 pts. Lect: 3. Recit: 1. Professor Zhong. in IE. Statistical methods for quality control and tools, layouts, workplaces, and computer displays. Prerequisites: SIEO W3600 or SIEO W4150, improvement: graphical methods, introduction to Consideration to environmental factors, training computer programming. Corequisite: IEOR E3106 experimental design and reliability engineering and and documentation. Term project. or IEOR E4106. This course is required for all the relationships between quality and productivity. undergraduate students majoring in IE, OR:EMS, Contemporary methods used by manufacturing OPMN B8815/IEOR E4210y Supply chain and service organizations in product and process OR:FE, and OR. This course is also required management design, production and delivery of products and for MSIE and MSOR. Generation of random 3 pts. Lect: 3. Members of the faculty. services. Prerequisite: IEOR E3402, E4000, or numbers from given distributions; variance permission of instructor. This is a IE elective for reduction; statistical output analysis; introduction IEOR E4418y Logistics and transportation undergraduate students majoring in IE. Major to simulation languages; application to financial, management issues in supply chain management, including, telecommunications, computer, and production 3 pts. Lect: 3. Professor Truong. definition of a supply chain; role of inventory; systems. Graduate students must register for 3 Prerequisite: IEOR E3608 or E4404 or permission supply contracts; bullwhip effect and information points. Undergraduate students must register for of instructor. Introduces quantitative techniques sharing; vendor-managed inventories and 4 points. NOTE: Students who have taken IEOR and state-of-the-art practice of operations research other distribution strategies; third-party logistics E4703 Monte Carlo simulation may not register relevant to the design and both the tactical providers; managing product variety; information for this course for credit. Recitation section and strategic management of logistical and technology and supply chain management; required. transportation systems. Discusses a wide variety of international issues. Emphasis on quantitative IEOR E4405y Production scheduling passenger and freight systems, including air, urban models and analysis. 3 pts. Lect: 3. Professor Sethuraman. and highway traffic, rail, and maritime systems. Explores the practice of revenue management and ORAN B8839/IEOR E4220y Demand and Prerequisites: SIEO W3600, IEOR E3608, dynamic pricing. Through case studies, analyzes supply analytics computer programming. This course is required 3 pts. Lect: 3. Members of the faculty. for undergraduate students majoring in IE and successes and failures in third-party logistics, Prerequisites: IEOR E4004 (or E3608), IEOR OR. Job shop scheduling: parallel machines, postal, truck and rail pickup and delivery systems. E4106 (or E3608). Tools to efficiently manage machines in series; arbitrary job shops. Algorithms, Investigates large-scale integrated logistics and supply and demand networks. Topics include complexity, and worst-case analysis. Effects transportation systems and studies the underlying service and inventory trade-offs, stock allocation, of randomness: machine breakdowns, random principles governing transportation planning, pricing, markdown management and contracts, processing time. Term project. investment and operations. timely product distribution to market while avoiding IEOR E4407x Game theoretic models of IEOR E4500x Applications programming for excess inventory, allocating adequate resources to financial engineering the most profitable products and selling the right operations 3 pts. Lect: 3. Professor Goyal. 3 pts. Lect: 3. Professor Bienstock. product to the right customer at the right price and Prerequisite: Computer programming or at the right time. Prerequisites: IEOR E4004 (or E3608), IEOR E4106 (or E3106), familiarity with differential instructor’s approval. This course is required IEOR E4307y Applied statistical models in equations and computer programming; for undergraduate students majoring in operations research or instructor’s permission. This course is OR:FE. In this course we will take a hands-on 3 pts. Lect: 3. Professor Wright. required for undergraduate students majoring approach to developing computer applications Prerequisites: probability, linear algebra. in OR:FE and OR. A mathematically rigorous for Financial Engineering. Special focus will be placed on high-performance numerical Descriptive statistics, central limit theorem, study of game theory and auctions, and applications that interact with a graphical parameter estimation, sufficient statistics, their application to operations management. interface. In the course of developing such hypothesis testing, regression, logistic regression, Topics include introductory game theory, applications we will learn how to create DLLs, goodness-of-fit tests, applications to operations private value auction, revenue equivalence, how to integrate VBA with C/C++ programs, research models. mechanism design, optimal auction, multiple- and how to write multithreaded programs. unit auctions, combinatorial auctions, IEME E4310x The manufacturing enterprise Examples of problems settings that we incentives, and supply chain coordination with 3 pts. Lect: 3. Professor Weinig. consider include simulation of stock price contracts. No previous knowledge of game The strategies and technologies of global evolution, tracking, evaluation and optimization theory is required. manufacturing and service enterprises. of a stock portfolio; optimal trade execution. In Connections between the needs of a global IEOR E4408x Resource allocation: models, the course of developing these applications, we enterprise, the technology and methodology algorithms, and applications review topics of interest to OR:FE in a holistic needed for manufacturing and product 3 pts. Lect: 3. Professor Luss. fashion.

engineering 2014–2015 166 IEOR E4507y Healthcare operations knowledge necessary in creating a business entity, IEOR E4600y Applied integer programming management defending your business assets, and in promoting 3 pts. Lect: 3. Professor Bienstock. 3 pts. Lect: 3. Professor Truong. effective interaction with other individuals and Prerequisites: Linear programming, linear algebra, Prerequisite(s): for senior undergraduate organizations. and computer programming. This course is Engineering students: SIEO W3600 and required for undergraduate students majoring in IEOR E4572x Operations research in IEOR E3608; for Engineering graduate OR. Applications of mathematical programming telecommunications students (M.S. or Ph.D.): Probability and techniques, especially integer programming, with 3 pts. Lect: 3. Professor Luss. statistics at the level of SIEO W4150, and emphasis on software implementation. Typical Prerequisites: IEOR E3608 or E4004, IEOR deterministic models at the level of IEOR applications: capacity expansion, network design, E3106 or E4106, or instructor’s permission. This E4004; for Healthcare Management students: and scheduling. course is recommended for graduate and senior P8529 Analytical methods for health services undergraduate students in IEOR and related IEOR E4601y Dynamic pricing and revenue management. Analytic methods for health programs. Background in telecommunications is services management. Develops modeling, management not assumed. Operations research models and 3 pts. Lect: 3. Professor Gallego. analytical, and managerial skills of Engineering algorithms used to solve diverse, contemporary Prerequisites: SIEO W4150 and IEOR E4004. and Healthcare Management students. Enables problems in the telecommunications industry. Focus on capacity allocation, dynamic pricing and students to master an array of fundamental Problems include routing and design of core revenue management. Perishable and/or limited Operations Management tools adapted to the networks with an emphasis on IP networks and product and pricing implications. Applications to management of healthcare systems. Through on optical networks. Various robust network various industries including service, airlines, hotel, real-world business cases, students learn design methods are explored that provide resource rentals, etc. to identify, model, and analyze operational networks that can survive any failure. Such improvements and innovations in a range of IEOR E4602y Quantitative risk management methods include shared mesh restoration, rinf healthcare contexts. 3 pts. Lect: 3. Professor Haugh. networks, and pcycles. Examination of various Prerequisites: SIEO W4150 and IEOR E4106. IEOR E4510y Project management OR problems encountered in access networks Risk management models and tools; measure risk 3 pts. Lect: 3. Professor Rosenwein. including content distribution network used, for Prerequisites: IEOR E4004 (or IEOR E3608). example, for video-on-demand applications. Other using statistical and stochastic methods, hedging Management of complex projects and the tools topics include wireless networks, such as cellular and diversification. Examples include insurance that are available to assist managers with such networks and ad-hoc networks, fair networks that risk, financial risk, and operational risk. Topics projects. Topics include: project selection, achieve equitable loads throughout a network, covered include VaR, estimating rare events, project teams and organizational issues, and sensor networks with homeland security extreme value analysis, time series estimation of project monitoring and control, project risk applications. Topics may vary according to interest. extremal events; axioms of risk measures, hedging management, project resource management, Discussion of similarities and differences between using financial options, credit risk modeling, and and managing multiple projects. telecommunications networks and networks in various insurance risk models. other application areas, such as transportation and IEOR E4611y Decision models and IEOR E4520y Applied systems engineering the electrical grid. 3 pts. Lect: 3. Professor Jahangir. applications Prerequisites: B.S. in Engineering or IEOR E4573x or y Topics in operations 3 pts. Lect: 3. Professor Webster. Applied Sciences; professional experience research: Design and Agile Project Prerequisites: For undergraduates: SIEO W3600/ recommended; Calculus, Probability and Management Engineering Lab (DAPME-Lab) SIEO W4150 or equivalent and IEOR E3608/ Statistics, Linear Algebra. Introduction to 3 pts. Professor Farrokhnia. IEOR E4004 or equivalent. For graduate students: fundamental methods used in Systems Intensive project-based seminar with emphasis Instructor’s permission required. Corequisite: IEOR Engineering. Rigorous process that translates on multidisciplinary approach to front-end product E4404 or equivalent. Introduction to deterministic customer needs into a structured set of specific design, strategy formulation, implementation, and stochastic decision tools used by leading requirements; synthesizes a system architecture and agile application of tech-driven concepts corporations and applied researchers. Real- that satisfies those requirements and in actual business settings. Focus on practical world problems in engineering and finance are allocates them in a physical system, meeting development and execution of inventive design- discussed. cost, schedule, and performance objectives centric solutions coupled with deep industrial, IEOR E4615y Service engineering throughout the product life-cycle. Sophisticated operational, and business analyses. Topics 3 pts. Lect: 3. Professor Whitt. modeling of requirements optimization and include industrial product and web design, UX Prerequisite(s): Introductory courses in probability dependencies, risk management, probabilistic and UI, Scrum, Kanban, and the dynamics of and statistics such as SIEO W3600, and scenario scheduling, verification matrices, and entrepreneurial/venture-capital financing relevant introductory courses in stochastic processes such systems-of-systems constructs are synthesized to technical (co-)founders. Guest speakers, field as IEOR E3106 or IEOR E4106. Focus on service to define the meta-workflow at the top of every trips, and interaction with domain experts. Projects systems viewed as stochastic networks, exploiting major engineering project. include work with a Fortune 500 corporation and the theoretical framework of queueing theory. an entrpreneurial portfolio company. Social good IEOR E4550x and y Entrepreneurial business Includes multidisciplinary perspectives involving project of a New York–based small or not-for- creation for engineers Statistics, Psychology, and Marketing. Significant profit business. Best practices in lean start-ups, 3 pts. Lect: 3. Professor Gulley. emphasis on data analysis, exploiting data from product development, team management, and Prerequisite: ENGI W2261. This course is required banks, hospitals, and call centers to demonstrate business planning. Product Design Sprint and for undergraduate students majoring in OR:EMS. the use of decision support tools. Analytical Agile Development, working on all aspects of Introduces the basic concepts and methodologies models, flow models of service networks, Little’s exploration, ideation, design, refinement, prototype that are used by the nonengineering part of the law, measuring methods in face-to-face and buildup, and validation. Simultaneous work on world in creating, funding, investing in, relating to, computerized systems, forecasting methods, engineering and tech-driven briefs (including field- and operating entrepreneurial ventures. The first stability of service systems, operational quality testing) addressing real life business challenges. half of the course focuses on the underpinning of service, economies of scale, staffing, complex Limited enrollment by application: requires signing principles and skills required in recognizing, service networks, skill-based routing. of Non-Disclosure Agreement for class projects. analyzing, evaluating, and nurturing a business Proficiency in math, statistics, coding, and/or idea. The second half focuses on basic legal database management/analysis recommended.

engineering 2014–2015 IEOR E4620x Pricing models for financial Simulation may not register for this course for credit. aspect of behavioral finance and briefly touches 167 engineering others. Compared with classical theory of portfolio IEOR E4706 Foundations of financial 3 pts. Lect: 3. Professor DeRosa. choice, behavioral portfolio choice features human engineering Prerequisite: IEOR E4700. This course is being’s psychological biases. It builds both on 3 pts. Lect: 3. Professor Leung. required for undergraduate students majoring in behavioral preference structures different from Prerequisites: IEOR E4701, E4702, and linear OR:FE. Characteristics of commodities or credit mean variance theory and expected utility theory algebra. This course is for MSFE students only, derivatives. Case study and pricing of structures and on systematic biases against rational beliefs offered during the summer session. Discrete-time and products. Topics covered include swaps, such as Bayesian rule. models of equity, bond, credit, and foreign- credit derivatives, single tranche CDO, hedging, exchange markets. Introduction to derivative IEOR E4714x Risk management, financial convertible arbitrage, FX, leverage leases, debt markets. Pricing and hedging of derivative system and financial crisis markets, and commodities. securities. Complete and incomplete markets. 1.5 pts. Professor Malz. IEOR E4630y Asset allocation Introduction to portfolio optimization and the Prerequisites: None. Risk-taking and risk 3 pts. Lect: 3. Members of the faculty. capital asset pricing model. management are at the heart of the financial system, and of the current financial crisis. An Prerequisite: IEOR E4700. Models for pricing IEOR E4707y Financial engineering: and hedging equity, fixed-income, credit- introduction to risk management both from an continuous-time asset pricing individual financial firm’s and from a public derivative securities, standard tools for hedging 3 pts. Lect: 3. Professor Leung. and risk management, models and theoretical policy viewpoint. Overview of the contemporary Prerequisites: IEOR E4701. This course is for financial system, focusing on innovations of foundations for pricing equity options (standard MSFE students only. Modeling, analysis, and European, American equity options, Asian the past few decades that have changed how computation of derivative securities. Applications financial risk is generated and distributed among options), standard Black-Scholes model (with of stochastic calculus and stochastic differential market participants, such as the growth of non- multiasset extension), asset allocation, portfolio equations. Numerical techniques: finite-difference, bank financial intermediaries, the increased optimization, investments over longtime binomial method, and Monte Carlo. prevalence of leverage and liquidity risk, and horizons, and pricing of fixed-income derivatives the development of structured credit products. (Ho-Lee, Black-Derman-Toy, Heath-Jarrow- IEOR E4708y Seminar on important papers in Introduction to the basic quantitative tools used Morton interest rate model). financial engineering 3 pts. Lect: 3. Not offered in 2014–2015. in market, credit, and liquidity risk management. IEOR E4700x and y Introduction to financial Prerequisites: IEOR E4703, E4706, probability The two strands of the course are brought engineering and statistics. Selected topics of special interest to together to help understand how the financial 3 pts. Lect: 3. Professors He and Yao. Financial Engineering M.S. students. If topics are crisis arose and is playing out, examining the Prerequisite: IEOR E4106 or E3106. This course different then this course can be taken more than mechanics of runs and the behavior of asset is required for undergraduate students majoring once for credit. prices during crises. Attempt to understand in OR:FE. Introduction to investment and financial the emergency programs deployed by central IEOR E4709y Data analysis for financial instruments via portfolio theory and derivative bankers and other policy makers to address engineering crises historically and today. securities, using basic operations research/ 3 pts. Lect: 3. Professor He. engineering methodology. Portfolio theory, Prerequisites: Probability and IEOR E4702. IEOR E4715x Commodity derivatives arbitrage; Markowitz model, market equilibrium, Corequisites: IEOR E4706, E4707. This course is 1.5 pts. Professor Higgins. and the capital asset pricing model. General for MSFE students only. Empirical analysis of asset Commodities markets have been much in the models for asset price fluctuations in discrete prices: heavy tails, test of the predictability of stock public eye recently as volatility has increased and and continuous time. Elementary introduction to returns. Financial time series: ARMA, stochastic they changed from markets dominated by physical Brownian motion and geometric Brownian motion. volatility, and GARCH models. Regression models: participants to ones which have a significant Option theory; Black-Scholes equation and call linear regression and test of CAPM, nonlinear investor component. The largest banks either option formula. Computational methods such as regression and fitting of term structures. already have profitable commodities franchises or Monte Carlo simulation. are actively building them, and money managers IEOR E4710s Term structure models and funds are increasingly including these assets IEOR E4701 Stochastic models for financial 3 pts. Lect: 3. Professor Leung. in their portfolio mix. The end result is a dramatic engineering Prerequisites: IEOR E4706, E4707, and computer increase in focus on these markets from all 3 pts. Lect: 3. Professor Blanchet. programming. Interest rate models and numerical aspects of the financial markets, including the Prerequisite: SIEO W4105. This course is for MSFE techniques for pricing and hedging interest rate quantitative end. students only, offered during the summer session. contracts and fixed income securities. Review of elements of probability theory, Poisson IEOR E4718y Introduction to the implied IEOR E4711x Global capital markets processes, exponential distribution, renewal theory, volatility smile 3 pts. Lect: 3. Professor Dastidar. Wald’s equation. Introduction to discrete-time 3 pts. Lect: 3. Professor Derman. Prerequisites: Refer to course syllabus. An Markov chains and applications to queueing theory, Prerequisites: IEOR E4706, knowledge of introduction to capital markets and investments inventory models, branching processes. derivatives valuation models. During the past 15 providing an overview of financial markets and years the behavior of market options prices have IEOR E4703y Monte Carlo simulation tools for asset valuation. Topics covered include shown systematic deviations from the classic 3 pts. Lect: 3. Professor Capponi. the pricing of fixed-income securities (treasury Black-Scholes model. The course examines Prerequisite: IEOR E4701. This course is for markets, interest rate swaps futures, etc.), the empirical behavior of implied volatilities, in MSFE students only. Multivariate random number discussions on topics in credit, foreign exchange, particular the volatility smile that now characterizes sovereign ad securitized markets—private equity generation, bootstrapping, Monte Carlo simulation, most markets, the mathematics and intuition and hedge funds, etc. efficiency improvement techniques. Simulation behind new models that can account for the smile, output analysis, Markov-chain Monte Carlo. IEOR E4712x Behavioral finance and their consequences for hedging and valuation. Applications to financial engineering. Introduction 3 pts. Lect: 3. Professor He. to financial engineering simulation software and Prerequisite: IEOR E4700. Behavioral finance exposure to modeling with real financial data. is the application of behavioral psychology to NOTE: Students who have taken IEOR E4404 financial decision making. Focus on the portfolio

engineering 2014–2015 168 IEOR E4720x and y–E4729 Topics in Some of the background in Financial Engineering IEOR E4734y Foreign exchange and related quantitative finance will be provided. The course will build on derivatives instruments 1.5–3 pts. Lect: 2–2.5. Members of the faculty. knowledge from IEOR E4728. 1.5 pts. Lect: 1.5. Professor DeRosa. Prerequisites: IEOR E4700; additional Prerequisite: IEOR E4700. Foreign exchange IEOR S4729 Financial markets, risk, and prerequisites will be announced depending on market and its related derivative instruments—the institutions offering. Selected topics of interest in the area of latter being forward contracts, futures, options, 1.5 pts. Lect: 1.5. Not offered in 2014–2015. quantitative finance. Offerings vary each year; some and exotic options. What is unusual about foreign Corequisites: IEOR E4701, E4702, E4706. topics include: energy derivatives, experimental exchange is that although it can rightfully claim to This course is for MSFE students only, offered finance, foreign exchange and related derivative be the largest of all financial markets, it remains during the summer session. This core curriculum instruments, inflation derivatives, hedge fund an area where very few have any meaningful course introduces students pursuing a graduate management, modeling equity derivatives in Java, experience. Virtually everyone has traded stocks, degree in financial engineering to the main mortgage-backed securities, numerical solutions of bonds, and mutual funds. Comparatively few areas and concepts of modern finance. Topics partial differential equations, quantitative portfolio individuals have ever traded foerign exchange. include financial analytics; fixed income and management, risk management, trade and In part that is because foreign exchange is an equity markets; macroeconomic aspects of technology in financial markets. interbank market. Ironically the foreign exchange investment decisions; portfolio and utility markets may be the best place to trade derivatives IEOR E4722x Introduction to algorithmic theories; introduction to risk management; and to invent new derivatives—given the massive trading financial crises. The course’s objective is to two-way flow of trading that goes through bank 1.5 pts. Professor Fishler. provide the broadest possible perspective dealing rooms virtually twenty-four hours a day. Prerequisite: IEOR E4700. An introductory-level on how financial theory and real-life practice And most of that is transacted at razor-thin course on the various aspects of algorithmic and interact, preparing students for successful margins, at least comparatively speaking, a fact quantitative trading, putting significant emphasis on careers in the financial industry and paving the that makes the foreign echange market an ideal topics related to execution and to a greater extent way for in-depth studies that follow. platform for derivatives. The emphasis is on to quantitative trading. Large emphasis on practical IEOR E4731y Credit risk modeling and credit familiarizing the student with the nature of the consideration in the general area of quantitative derivatives foreign exchange market and those factors that trading, and in particular in the equities of the 3 pts. Lect: 3. Professor He. make it special among financial markets, enabling world. Topics covered include market participants, Prerequisites: IEOR E4701 and E4707. the student to gain a deeper understanding of the the mechanics of trading, order books, exchanges, Introduction to quantitative modeling of credit risk, related market for derivatives on foreign exchange. ATS, ECNs, etc. Market micro structure, routing, with a focus on the pricing of credit derivatives. rules, market impact, covariance matrix estimation IEOR E4735y Introduction to structured and Focus on the pricing of single-name credit in various time frames, dynamic and optimal hybrid products derivatives (credit default swaps) and collateralized trading, statistical arbitrage, portfolio optimization. 3 pts. Lect: 3. Professor Kani. debt obligations (CDOs). Detail topics include Homework includes working with data sets at Prerequisite: IEOR E4700. Conceptual and default and credit risk, multiname default barrier various frequencies. practical understanding of structured and hybrid models and multiname reduced form models. products from the standpoint of relevant risk IEOR E4728x Advanced programming for IEOR E4732y Computational methods in factors, design goals and characteristics, pricing, financial engineering, I derivatives pricing hedging, and risk management. Detailed analysis 3 pts. Professors Kaddoura and Haugh. 3 pts. Professor Hirsa. of the underlying cash-flows, embedded derivative Prerequisites: Refer to course syllabus. This Prerequisite: IEOR E4700. Introduction and instruments, and various structural feautures course is part of the programming track for the application of various computational techniques of these transactions, both from the investor M.S. in Financial Engineering (FE) program and in pricing derivatives and risk management. and issuer perspectives, and analysis of the only suitably qualified M.S. in FE and M.S. in Transform techniques, numerical solutions of impact of the prevailing market conditions and OR students will be admitted (preference will be partial differential equations (PDEs) and partial parameters on their pricing and risk characteristics. given to M.S. in FE students in the event that the integro-differential equations (PIDEs) via finite Numerical methods for valuing and managing course is over-subscribed). Python 2.7 will be the differences, Monte-Carlo simulation techniques, risk of structured/hybrid products and their “default” programming language for the course, calibration techniques, and parameter estimation imbedded derivatives and their application to but we will also use SQL, Excel-VBA, Bloomberg and filtering techniques. The computational equity, interest rates, commodities and currencies, and the Bloomberg APIs. We will use Microsoft’s platform will be Java/C++. The primary application inflation, and credit-related products. Conceptual SQL Server Express as our database “server.” focus will be pricing of financial derivatives and and mathematical principles underlying these Details on downloading the various components calibration. These techniques are useful for various techniques, and practical issues that arise in and configuring the programming environment will other problems in financial modeling and practical their implementations in the Microsoft Excel/VBA be provided in the first lecture. Prior knowledge implementations from the theory of mathematical and other programming environments. Special of how to code and familiarity with object-oriented finance. contractual provisions encountered in structured programming is expected. This course will and hybrid transactions, and incorporation of therefore focus as much on applications and the IEOR E4733y Algorithmic trading yield curves, volatility smile, and other features core project as it will on programming. These 3 pts. Professor Kani. of the underlying processes into pricing and Prerequisite: IEOR E4700. Large and amorphous applications will draw mainly from finance but we implementation framework for these products. collection of subjects ranging from the study will also consider some simple applications from of market microstructure, to the analysis of IEOR E4736x or y Experimental finance “data-science” if time permits. optimal trading strategies, to the development of 3 pts. Lect: 2.5. Professors Lipkin and Stanton. IEOR E4729y Advanced programming for computerized, high-frequency trading strategies. Prerequisites: IEOR E4700 or equivalent. Intense laboratory to introduce students to event-driven financial engineering, II Analysis of these subjects, the scientific and finance using SQL query language to perform data 3 pts. Lect: 3. Professors DeRosa. practical issues they involve, and the extensive explorations in the Optionmetrics IVY database. Prerequisite: IEOR E4007. This course will body of academic literature they have spawned. develop the ability to deploy high-performance Attempt to understand and uncover the economic implementations of selected Financial and financial mechanisms that drive and ultimately Engineering topics using modern techniques. relate them.

engineering 2014–2015 IEOR E4900x and y Master’s research or methods for unconstrained problems, active set, of queueing, reliability, manufacturing, insurance 169 project penalty set, interior point, augmented Lagrangian risk, financial engineering and other engineering 1–3 pts. Members of the faculty. and sequential quadratic programming methods applications. Review of elements of probability Prerequisite: Approval by a faculty member who for constrained problems. Introduction to theory; exponential distribution; renewal agrees to supervise the work. Independent work nondifferentiable optimization and bundle methods. theory; Wald’s equation; Poisson processes. involving experiments, computer programming, Introduction to both discrete and continuous-time IEOR E6613x Optimization, I analytical investigation, or engineering design. Markov chains; introduction to Brownian motion. 4.5 pts. Lect: 3. Professor Goyal. IEOR E4998x and y Managing technological Prerequisite: Linear algebra. Theory and geometry IEOR E6712y Stochastic models, II innovation and entrepreneurship of linear programming. The simplex method. 4.5 pts. Lect: 3. Professor Yao. 3 pts. Lect: 3. Professor Neumann. Duality theory, sensitivity analysis, column Prerequisite: IEOR E6711 or equivalent. This is a required course for undergraduate generation and decomposition. Interior point Continuation of IEOR E6711, covering further students majoring in OR:EMS. Focus on the methods. Introduction to nonlinear optimization: topics in stochastic modeling in the context of management and consequences of technology- convexity, optimality conditions, steepest descent, queueing, reliability, manufacturing, insurance based innovation. Explores how new industries and Newton’s method, active set, and barrier risk, financial engineering, and other engineering are created, how existing industries can be methods. applications. Topics from among generalized transformed by new technologies, the linkages semi-Markov processes; processes with a IEOR E6614y Optimization, II between technological development and the nondiscrete state space; point processes; 4.5 pts. Lect: 3. Professor Sethuraman. creation of wealth and the management challenges stochastic comparisons; martingales; introduction Prerequisite: Linear algebra. An introduction to of pursuing strategic innovation. to stochastic calculus. combinatorial optimization, network flows and IEOR E4999x and y Fieldwork discrete algorithms. Shortest path problems, IEOR E8100x and y Advanced topics in IEOR 1–3 pts. Professor Derman. maximum flow problems. Matching problems, 1–3 pts. Members of the faculty. Prerequisites: Obtained internship and approval bipartite and cardinality nonbipartite. Introduction Prerequisite: Faculty adviser’s permission. from faculty adviser. Only for IEOR graduate to discrete algorithms and complexity theory: Selected topics of current research interest. May students who need relevant work experience NP-completeness and approximation algorithms. be taken more than once for credit. as part of their program of study. Final reports required. This course may not be taken for pass/ IEOR E6703y Advanced financial engineering IEOR E9101x and y Research fail credit or audited. 3 pts. Lect: 2. Not offered in 2014–2015. 1–6 pts. Members of the faculty. Prerequisites: Probability theory and advanced Before registering, the student must submit an MSIE W6408y Inventory theory stochastic models at the SIEO W6501 level. outline of the proposed work for approval by 3 pts. Lect: 3. Not offered in 2014–2015. Review of basic mathematics, including renewal the supervisor and the chair of the Department. Prerequisites: Probability theory, dynamic theory and stochastic calculus. Martingale Advanced study in a specialized field under the programming. Construction and analysis of approach to Black-Scholes formula. Optimal supervision of a member of the department staff. mathematical models used in the design and stopping and American options. Pricing of This course may be repeated for credit. analysis of inventory systems. Deterministic and continuous and discrete exotic options. Term IEOR E9800x and y Doctoral research stochastic demands and lead times. Optimality structure models and pricing of bond options. instruction of (s, S) policies. Multiproduct and multiechelon Jump diffusion models. Applications, including 3, 6, 9, or 12 pts. Members of the faculty. systems. Computational methods. pricing of real and electricity options and hedging A candidate for the Eng.Sc.D. degree in of real options. IEOR E6602y Nonlinear programming industrial engineering or operations research 3 pts. Lect: 3. IEOR E6711x Stochastic models, I must register for 12 points of doctoral research Prerequisite: Ph.D.-level linear programming. 4.5 pts. Lect: 3. Professor Whitt. instruction. Registration in IEOR E9800 may Convex sets and functions, convex duality and Prerequisite: SIEO W4105 or equivalent. Advanced not be used to satisfy the minimum residence optimality conditions. Computational methods: treatment of stochastic modeling in the context requirement for the Ph.D. degree. steepest descent, Newton and quasi-newton

engineering 2014–2015 170 Materials Science and Engineering Program 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 Committee on Louis E. Brus James S. Im Ponisseril Somasundaran Materials Science and Materials Science and Professor of Chemistry Professor of Materials Professor of Mineral Engineering Engineering/Solid-State Siu-Wai Chan Science Engineering Professor Katayun Barmak Science and Engineering Professor of Materials Chris A. Marianetti Yasutomo Uemura 1137 S. W. Mudd William E. Bailey Science Associate Professor of Professor of Physics Associate Professor of Paul F. Duby Materials Science Wen I. Wang In Charge of Solid- Materials Science Professor of Mineral Richard M. Osgood Jr. Professor of Electrical State Science and Katayun Barmak Engineering Professor of Electrical Engineering Engineering Professor of Materials Christopher J. Durning Engineering Chee Wei Wong Professor Siu-Wai Chan Science Professor of Aron Pinczuk Associate Professor of 1136 S. W. Mudd Simon J. Billinge Chemical Engineering Professor of Applied Physics Mechanical Engineering Professor Irving P. Herman Professor of Materials Irving P. Herman and Physics 208 S. W. Mudd Science Professor of Applied Physics

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

engineering 2014–2015 Current Research Activities Undergraduate Program at most two may be in the Type B 171 Current research activities in the in materials science category. The Type B electives are listed materials science and engineering This program provides the basis under different materials subdisciplines program at Columbia focus on thin films for developing, improving, and for guidance. Still, some courses listed and electronic materials that enable understanding materials and processes under different categories may appeal to significant advances in information for electronic, structural, and other students interested in a given area. For technologies. Specific topics under applications. It draws from physics, example, CHEE E4252: Intro to surface investigation include interfaces, stresses, chemistry, and other disciplines to and colloidal chemistry should also be and grain boundaries in thin films; provide a coherent background for considered by students interested in lattice defects and electrical properties immediate application in engineering biomaterials and environmental materials. of semiconductors; laser processing or for subsequent advanced study. Type A electives are: and ultrarapid solidification of thin films; The emphasis is on fundamentals CHEE E4530: Corrosion of metals nucleation in condensed systems; relating atomic-to microscopic-scale MSAE E4207: Lattice vibrations and crystal optical and electrical properties of phenomena to materials properties defects semiconductors and metals; synthesis and processing, including design and MSAE E4250: Ceramics and composites of nanocrystals, carbon nanotubes, control of industrially important materials ELEN E4944: Principles of device microfabrication and nanotechnology-related materials; processes. Core courses and electives deposition, in-situ characterization, combine rigor with flexibility and provide Type B electives are: electronic testing, and ultrafast opportunities for focusing on such BIOMATERIALS spectroscopy of magnetoelectronic areas as electronic materials, polymers, BMEN E4300: Solid biomechanics ultrathin films and heterostructures. In ceramics, biomaterials, structural BMEN E4301: Structure, mechanics, and addition, there is research in surface materials, and metals and mineral adaptation of bone and colloid chemistry involving both processing. There are also opportunities BMEN E4501: T issue engineering, I inorganic and organic materials such for combining materials science with ELECTRONIC MATERIALS as surfactants, polymers, and latexes, interests in areas such as medicine, APPH E3100: Intro to quantum mechanics with emphasis on materials/environment business, law, or government. APPH E3300: Applied electromagnetism interactions. The unifying theme of understanding APPH E4100: Quantum physics of matter The research activities in solid-state and interrelating materials synthesis, APPH E4110: Modern optics science and engineering are described processing, structure, and properties ELEN E4301: Intro to semiconductor devices later in this section. forms the basis of our program and is ELEN E4411: Fundamentals of photonics evident in the undergraduate curriculum ENVIRONMENTAL MATERIALS and in faculty research activities. These Laboratory Facilities EAEE E4001: Industrial ecology of Earth resources activities include work on polycrystalline EAEE E4160: Solid and hazardous waste mgmt Facilities and research opportunities silicon for flat panel displays; high- also exist within the interdepartmental MECHANICAL PROPERTIES OF MATERIALS temperature superconductors for Nanoscale Science and Engineering ENME E3114: Experimental mechanics of solids power transmission and sensors; Center (NSEC), and Energy Frontier ENME E4113: Advanced mechanics of solids semiconductors for laser and solar cell ENME E4114: Mechanics of fracture and fatigue Research Center (EFRC), which applications; magnetic heterostructures MECE E3610: Manufacturing processes focus on complex films formed from for information storage and novel nanoparticles, molecular electronics, and SOFT MATERIALS AND SURFACES computation architectures; electronic solar energy conversion, respectively. CHEE C3443: O rganic chemistry ceramics for batteries, gas sensors, Modern clean room facilities with (note that C3444 is not allowed) and fuel cells; electrodeposition and optical and e-beam lithography, thin CHEE E4252: Intro to surface and colloid chemistry corrosion of metals; and the analysis APMA E4400: Intro to biophysical modeling film deposition, and surface analytical and design of high-temperature probes (STM, SPM, XPS) are available. OTHER reactors and first principle calculations. More specialized equipment exists in MSAE E3900: U ndergrad research in materials Through involvement with our research individual research groups in solid state science groups, students gain valuable hands- engineering and materials science and Alternative courses can be taken on experience and are often engaged engineering. The research facilities in as electives with the approval of the in joint projects with industrial and solid-state science and engineering undergraduate adviser. Of the 24 government laboratories. are listed in the sections for each host points of elective content in the third The undergraduate curriculum department. Facilities, and research and fourth years, at least 12 points requires 17 courses in the third and opportunities, also exist within the of restricted electives approved by fourth years, of which four are restricted interdepartmental clean room, shared the adviser must be taken. Of the electives. This program allows students materials characterization laboratories, remaining 12 points of electives to specialize in a subdiscipline of and electron microscopy facility allotted, a sufficient number must Materials Science if they so choose. (SEM, TEM). actually be taken so that no fewer Students must take 13 required courses than 64 points of courses are credited and four electives. At least two electives to the third and fourth years. Those must be in the Type A category, and

engineering 2014–2015 172 materials science PROgram: first and second Years

Semester i Semester iI Semester iII Semester iV

MATH V1202 (3) mathematics1 MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) and ODE (3)

physics C1401 (3) C1402 (3) C1403 (3) C1494 (3) (three tracks, C1601 (3.5) C1602 (3.5) C2601 (3.5) Lab C2699 (3) choose one) C2801 (4.5) C2802 (4.5) Lab W3081 (2)

C1403 (3.5) C1404 (3) chemistry Lab C1500 (2) either semester (three tracks, choose one) C1604 (3.5) C2507 (3) C3045 (3.5) C3046 (3), Lab C2507 (3) C3545 (3)

english C1010 (3) composition (three tracks, Z1003 (0) C1010 (3) choose one) Z0006 (0) Z1003 (0) C1010 (3)

HUMA C1001, HUMA C1002, COCI C1101, COCI C1102, required or Global Core (3–4) or Global Core (3–4) nontechnical electives HUMA W1121 (3) ECON W1105 (4) and or W1123 (3) W1155 recitation (0)

required tech (3) Student’s choice, see list of first-and second-year technical electives electives (professional-level courses; see pages 12–13).

computer ENGI E1006 (3) any semester science

physical C1001 (1) C1002 (1) education

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 Students with advanced standing may start the calculus sequence at a higher level.

remaining points of electives are The following five courses (15 points) which may be Type I or Type II: intended primarily as an opportunity are required for the degree: • Type I Electives: to complete the four-year, 27-point nontechnical requirement, but any type 15 points: MSAE E4090: Nanotechnology of course work can satisfy them. MSAE E4100: Crystallography MSAE E4132: F undamentals of polymers and MSAE E4101: Structural analysis of materials ceramics MSAE E4206: Electronic and magnetic properties MSAE E4207: Lattice vibrations and crystal defects Graduate Programs in of solids MSAE E4250: Ceramics and composites Materials Science and MSAE E4202: T hermodynamics and reactions MSAE E4990: Special topics in materials science and engineering Engineering in solids MSAE E4215: Mechanical behavior of structural MSAE E6091: Magnetism and magnetic materials materials MSAE E6225: T echniques in X-ray and neutron Master of Science Degree diffraction Candidates for the Master of Science If a candidate has already taken one MSAE E6229: Energy and particle beam processing of materials degree in Materials Science and or more of these courses at Columbia MSAE E6230: Kineticsof phase transformations Engineering will follow a program of University, substitutions from the Type I Elective list may be approved. MSAE E6251: Thin films and layers study formulated in consultation with MSAE E6273: Materials science reports The remaining 15 points will be and approved by a faculty adviser. MSAE E8235: Selected topics in materials science Thirty points of credit are required at a chosen from elective courses, 9 points MSAE E4000-, 6000- or 8000-level courses not minimum. of which must be Type I and 6 points of listed here

engineering 2014–2015 173 materials science Program: third and fourth Years

Semester V Semester VI Semester VII Semester VIII

MSAE E3156 (3) Design project MSAE E3103 (3) MSAE E3104 (3) MSAE E3157 (3) Elements of mat. sci. Laboratory in mat. sci. Design project MSAE E4100 (3) Crystallography MSAE E 3111 (3) MSAE E3141 (3) MSAE E4202 (3) Thermodynamics, Processing of metals Thermodynamics and Required MSAE E4101 (3) Courses kinetic theory, and and semiconductors reactions in solids Structural analysis statistical mechanics of materials MSAE E3142 (3)2 MSAE E4215 (3) ENME E3113 (3)1 Processing of ceramics Mechanical behavior MSAE E4206 (3) Mechanics of solids and polymers of materials Electronic and magnetic properties of solids

Electives 6 points3 6 points3 3 points3 9 points3

total points 15 15 15 15

1 Students wishing to have advance preparation for ENME E3113 may take ENME-MECE E3105: Mechanics as an elective in Semester IV. 2 Juniors substitute E4132 for E3142 when offered. 3 At least 6 of the 24 points of electives must be Type A. Another 6 points must be from the Type A and Type B elective lists.

• Type II Electives: Doctoral Program Areas of Research BMEN E4300: Solid biomechanics At the end of the first year of graduate Materials science and engineering is BMEN E4301: Structure, mechanics, and study in the doctoral program, concerned with synthesis, processing, adaptation of bone candidates are required to take a structure, and properties of metals, BMEN E4501: T issue engineering, I comprehensive written qualifying ceramics, polymers, and other materials, APPH E4100: Quantum physics of matter examination, which is designed to test with emphasis on understanding APPH E4110: Modern optics the ability of the candidate to apply and exploiting relationships among APPH E4130: Physics of solar energy APPH E6081: Solid state physics, I course work in problem solving and structure, properties, and applications APPH E6082: Solid state physics, II creative thinking. The standard is first- requirements. Our graduate research ELEN E4301: Intro to semiconductor devices year graduate level. There are two programs encompass projects in areas ELEN E4411: F undamentals of photonics four-hour examinations over a two-day as diverse as polycrystalline silicon, ELEN E4944: Principles of device microfabrication period. electronic ceramics grain boundaries EAEE E4001: Industrial ecology of earth resources Candidates in the program must and interfaces, microstructure and EAEE E4160: Solid and hazardous waste take an oral examination within one year stresses in microelectronics thin films, management ENME E4113: A dvanced mechanics of solids of taking the qualifying examination. oxide thin films for novel sensors and ENME E4114: Mechanics of fracture and fatigue Within two years of taking the qualifying fuel cells, optical diagnostics of thin-film ENME E4608: Manufacturing processes examination, candidates must submit processing, ceramic nanocomposites, CHEE E4252: Intro to surface and colloid a written proposal and defend it orally electrodeposition and corrosion chemistry before a Thesis Proposal Defense processes, structure, properties, and CHEE E4530: Corrosion of metals Committee consisting of three transmission electron microscopy and APMA E4101: Intro to dynamical systems members of the faculty, including the crystal orientation mapping, magnetic APMA E4200: Partial differential equations APMA E4300: Intro to numerical methods adviser. Doctoral candidates must thin films for giant and colossal APMA E4400: Intro to biophysical modeling submit a thesis to be defended before magnetoresistance, chemical synthesis a Dissertation Defense Committee of nanoscale materials, nanocrystals, Columbia Video Network (CVN) consisting of five faculty members, carbon nanotubes, nanostructure students may have their programs including two professors from outside analysis using X-ray and neutron approved by faculty. Special reports (3 the doctoral program. Requirements diffraction techniques, and electronic points) are required of CVN students. for the Eng.Sc.D. (administered by the structure calculation of materials using All degree requirements must be School of Engineering and Applied density functional and dynamical completed within five years. A candidate Science) and the Ph.D. (administered mean-field theories. Application targets is required to maintain at least a 2.5 by the Graduate School of Arts and for polycrystalline silicon are thin film GPA. Applicants for admission are Sciences) are listed elsewhere in this transistors for active matrix displays required to take the Graduate Record bulletin. and silicon-on-insulator structures for Examinations.

engineering 2014–2015 174 ULSI devices. Novel applications are optical, and thermal properties. The Billinge, Applied Physics and Applied being developed for oxide thin films, science of solids is concerned with Mathematics); electronic structure including uncooled IR focal plane arrays understanding these properties in calculations of materials (Professor and integrated fuel cells for portable terms of the atomic and electronic Marianetti, Applied Physics and equipment. Long-range applications structure of the materials in question. Applied Mathematics); and optical of high-temperature superconductors Insulators (dielectrics), semiconductors, nanostructures (Professor Wong, include efficient power transmission and ceramics, and metallic materials are all Mechanical Engineering). highly sensitive magnetic field sensors. studied from this viewpoint. Quantum Thin film synthesis and processing and statistical mechanics are key Program of Study in this program include evaporation, background subjects. The engineering The applicant for the graduate specialty sputtering, electrodeposition, and aspects deal with the design of materials must be admitted to one of the plasma and laser processing. For to achieve desired properties and the participating programs: applied physics analyzing materials structures and assembling of materials into systems to and applied mathematics, or electrical properties, faculty and students employ produce devices of interest to modern engineering. A strong undergraduate electron microscopy, scanning probe technology, e.g., for computers and for background in physics or chemistry and microscopy, cathodoluminescence energy production and utilization. in mathematics is important. and electron beam–induced current The doctoral student must meet the imaging, photoluminescence, dielectric Areas of Research formal requirements for the Eng.Sc.D. or and anelastic relaxation techniques, The graduate specialty in solid-state Ph.D. degree set by the department in ultrasonic methods, magnetotransport science and engineering includes which he or she is registered. However, measurements, and X-ray diffraction research programs in semiconductor the bulk of the program for the specialty techniques. Faculty members have nanocrystals (Professor Brus, will be arranged in consultation with research collaborations with Lucent, Chemistry/Chemical Engineering); a member of the interdepartmental Exxon, IBM, and other New York area optics of semiconductors and Committee on Materials Science and research and manufacturing centers, nanomaterials (Professor Herman, Engineering/ Solid-State Science and as well as major international research Applied Physics and Applied Engineering. At the end of the first year centers. Scientists and engineers from Mathematics); chemical physics of of graduate study, doctoral candidates these institutions also serve as adjunct surfaces and photoemission (Professor are required to take a comprehensive faculty members at Columbia. The Osgood, Electrical Engineering/ written examination concentrating on National Synchrotron Light Source at Applied Physics and Applied solid-state science and engineering. Brookhaven National Laboratory is used Mathematics); molecular beam The following are regarded as core for high-resolution X-ray diffraction and epitaxy leading to semi-conductor courses of the specialty: absorption measurements. devices (Professor Wang, Electrical Entering students typically have Engineering/Applied Physics and APPH E4100: Quantum physics of matter undergraduate degrees in materials Applied Mathematics); metamaterials APPH E4110: Modern optics APPH E4112: Laser physics science, metallurgy, physics, chemistry, and infrared optoelectronic devices APPH-MSAE E6081-E6082: Solid state physics, or other science and engineering (Professor Yu, Applied Physics and I and II disciplines. First-year graduate courses Applied Mathematics); and inelastic CHEM G4230: Statistical thermodynamics provide a common base of knowledge light scattering in low-dimensional and technical skills for more advanced or electron gases within semiconductors CHAP E4120: Statistical mechanics courses and for research. In addition (Professor Pinczuk, Applied Physics ELEN E4301: Intro to semiconductor devices to course work, students usually and Applied Mathematics/Physics); ELEN E4944: Principles of device microfabrication begin an association with a research large-area electronics and thin-film ELEN E6331-E6332: Principles of semiconductor group, individual laboratory work, and transistors (Professor Im, Henry Krumb physics participation in graduate seminars during School of Mines/Applied Physics ELEN E6403: Classical electromagnetic theory their first year. and Applied Mathematics); structural or analysis and high Tc superconductors PHYS G6092: Electromagnetic theory, I MSAE E4100: Crystallography Graduate Specialty in (Professor Chan, Henry Krumb School of Mines/Applied Physics and Applied MSAE E4206: Electronic and magnetic properties Solid-State Science and of solids Mathematics); X-ray microdiffraction Engineering MSAE E4207: Lattice vibrations and crystal and stresses (Professor Noyan, Henry Solid-state science and engineering defects Krumb School of Mines/Applied Physics is an interdepartmental graduate MSAE E6220: Crystal physics and Applied Mathematics); electronic specialty that provides coverage of an MSAE E6240: Impurities and defects in and magnetic metal thin films (Professor semiconductor materials important area of modern technology Barmak, Applied Physics and Applied MSAE E6241: Theory of solids that no single department can provide. It Mathematics); magnetic properties of PHYS G6018: Physics of the solid state encompasses the study of the full range PHYS G6037: Quantum mechanics thin films (Professor Bailey, Applied of properties of solid materials, with Physics and Applied Mathematics); the special emphasis on electrical, magnetic, structure of nanomaterials (Professor

engineering 2014–2015 Courses in Materials MSAE E3142y Processing of ceramics and MSAE E4100x Crystallography 175 Science and Engineering polymers 3 pts. Lect: 3. Professor Barmak. For related courses, see also Applied 3 pts. Lect: 3. Instructor to be announced. Prerequisites: CHEM C1403, PHYS C1403, Prerequisite: MSAE E3103 or equivalent. APMA E2101, or equivalent. A first course on Physics and Applied Mathematics, Established and novel methods involved in crystallography. Crystal symmetry, Bravais lattices, Chemical Engineering, Earth and the processing of polymers and ceramics. point groups, space groups. Diffraction and Environmental Engineering, and The fundamental aspects of the structure and diffracted intensities. Exposition of typical crystal Electrical Engineering. properties of polymers and ceramic materials; structures in engineering materials, including strategy in the preparatory, synthesis,, and metals, ceramics, and semiconductors. Crystalline MSAE E1001y Atomic-scale engineering of new materials processing methods for obtaining them. anisotropy. Topics include polymer synthesis, elastomers, 3 pts. Lect: 3. Professor Noyan. MSAE E4101x Structural analysis of materials thermoplastics, thermoset materials, design An introduction to the nanoscale science and 3 pts. Lect: 3. Professor Barmak. and molding processes. Ceramics: inorganic engineering of new materials. The control and Prerequisites or corequisite: MSAE E3103 or glasses and composites, materials production manipulation of atomic structure can create new instructor’s permission. Geometry of crystals, basic and principle inorganic chemistry. Processing solids with unprecedented properties. Computer diffraction theory. X-ray diffraction. Techniques methodology, conditioning, drying, forming, hard drives, compact disc players, and liquid and theory of electron microscopy. Analysis of sintering, and microstructure development. crystal displays (LCDs) are explored to understand crystal structures and orientations. Microstructure Relevant aspects of transport phenomena, colloid the role of new materials in enabling technologies. characterization and analysis of crystalline defects. Group problem-solving sessions are used to and sol-gel science, contemporary issues in develop understanding. modern polymer and ceramic processing. MSAE E4132y Fundamentals of polymers and ceramics MSAE E3156x-E3157y Design project MSAE E3103x Elements of materials science 3 pts. Lect: 3. Not offered in 2014-2105. 3 pts. Lect: 3. Professor Noyan. 3 pts. Members of the faculty. Prerequisite: MSAE E3103 or instructor’s Prerequisites: CHEM C1404 and PHYS C1011. Prerequisite: Senior standing. Written permission permission. The science and engineering of Atomic and crystal structures, structural defects, from instructor and approval from adviser. May be polymer, ceramic and composite inorganic alloying and phase diagrams. The influence repeated with the permission of the undergraduate materials. Fundamental aspects of structure, of microstructure on the strength and physical adviser. E3156: A design problem in materials processing and properties. Polymers: classification, properties of metals and alloys, semiconductors, science or metallurgical engineering selected jointly synthesis, elastomers, thermoplastics, thermosets; ceramics, glasses, and polymers. by the student and a professor in the department. ceramics: Crystal structure, morphology, The project requires research by the student, MSAE E3104y Laboratory in materials science classification, oxides, nitrides, carbides, silicates. directed reading, and regular conferences with 3 pts. Lect: 1. Lab: 4. Professor Jones. Electrical, mechanical, thermal and optical the professor in charge. E3157: Completion of Corequisite: MSAE E3103. Metallographic properties. Common and advanced technological the research, directed reading, and conferences, specimen preparation, optical microscopy, applications, electrical/optical devices, catalytic and culminating in a written report and an oral quantitative metallography, hardness and tensile environmental applications. presentation to the department. testing, plastic deformation, annealing, phase MSAE E4202y Thermodynamics and reactions diagrams, brittle fracture of glass, temperature and MSAE E3900x and y Undergraduate research in solids strain rate dependent deformation of polymers, in materials science 3 pts. Lect: 3. Professor Im. written and oral reports. 0–4 pts. Members of the faculty. Prerequisite: Instructor’s permission. Free energy Prerequisite: Written permission from instructor MSAE E3111x Thermodynamics, kinetic of phases, the relationship between phase and approval from adviser. This course may be theory and statistical mechanics diagrams and metastability. Thermodynamics of repeated for credit, but no more than 6 points 3 pts. Lect: 3. Professor Billinge. surfaces and interfaces, effect of particle size of this course may be counted toward the An introduction to the basic thermodynamics on phase equilibria, Gibbs adsorption of solute satisfaction of the B.S. degree requirements. of systems, including concepts of equilibrium, at interfaces, grain boundaries, surface energy. Candidates for the B.S. degree may conduct an entropy, thermodynamic functions, and phase Nucleation and growth, spinodal decomposition investigation in materials science or carry out changes. Basic kinetic theory and statistical of phases. Diffusion in metals, intermetallic a special project under the supervision of the mechanics, including diffusion processes, concept compounds and ionic crystals. Diffusion along staff. Credit for the course is contingent upon the of phase space, classical and quantum statistics, interfaces. and applications thereof. submission of an acceptable thesis or final report. MSAE E4206x Electronic and magnetic MSAE E4090y Nanotechnology MSAE E3141y Processing of metals and properties of solids 3 pts. Lect: 3. Professor Wind. semiconductors 3 pts. Lect: 3. Professor Bailey. Prerequisites: APPH E3100 and MSAE E3103 3 pts. Lect: 3. Professor Duby. Prerequisite: PHYS C1401-3 or equivalent. A or their equivalents with instructor’s permission. Prerequisite: MSAE E3103 or the equivalent. survey course on the electronic and magnetic The science and engineering of creating Synthesis and production of metals and properties of materials, oriented towards materials, functional structures and devices on the semiconductors with engineered microstructures materials for solid state devices. Dielectric nanometer scale. Carbon nanotubes, nanocrystals, for desired properties. Includes high-temperature, and magnetic properties, ferroelectrics and quantum dots, size dependent properties, self- aqueous, and electrochemical processing; thermal ferromagnets. Conductivity and superconductivity. assembly, nanostructured materials. Devices and mechanical processing of metals and alloys; Electronic band theory of solids: classification of and applications, nanofabrication. Molecular casting and solidification; diffusion, microstructural metals, insulators, and semiconductors. Materials engineering, bionanotechnology. Imaging and evolution, and phase transformations; modification in devices: examples from semiconductor lasers, manipulating at the atomic scale. Nanotechnology and processing of surfaces and interfaces; cellular telephones, integrated circuits, and in society and industry. Offered in alternate years. deposition and removal of thin films. Processing of magnetic storage devices. Topics from physics Si and other materials for elemental and compound are introduced as necessary. semiconductor-based electronic, magnetic, and optical devices.

engineering 2014–2015 176 MSAE E4207y Lattice vibrations and crystal MSAE E4999x or y–S4999 Supervised boundary interactions with crystal defects, defects internship boundaries as short-circuit diffusion paths, 3 pts. Lect: 3. Professor Chan. 1 pt. Members of the faculty. applications of boundary concepts to interfaces, An introductory course in topics of solid state Prerequisite: Internship and approval from and roles of grain boundaries in material properties physics other than electronics and magnetic adviser must be obtained in advance. Only for and in kinetic phenomena in polycrystalline properties. Elastic waves in solids. Phonons master’s students in the Department of Applied materials. and lattice vibrations. Brillouin zones. Thermal Physics and Applied Mathematics who may need MSAE E6220x Crystal physics properties of solids. Defects, such as point defects relevant work experience as part of their program 3 pts. Lect: 3. Not offered in 2014–2015. in metals, ionic crystals, semiconductors, and of study. Final report required. This course may not Prerequisite: MSAE E4206 or instructor’s ceramics. be taken for pass/fail or audited. permission. The course develops the idea of MSAE E4215y Mechanical behavior of MSAE E6020y Electronic ceramics a tensor and applies it to stress and, together structural materials 3 pts. Lect: 3. Not offered in 2014–2015. with considerations of crystal symmetry, to the 3 pts. Lect: 3. Professor Barmak. Structure and bonding of ceramics and glasses. study of the physical constants of crystals, such Prerequisite: MSAE E3103. Recommended Point defects and diffusion. Electronic and ionic as diamagnetic and paramagnetic susceptibility, preparation: A course in mechanics of materials. conduction. Dielectric, ferroelectric, magnetic, and dielectric constants, thermal expansivity, Review of states of stress and strain and optical ceramics. piezoelectric constants, and others. The physical their relations in elastic, plastic, and viscous properties are also studied against the background MSAE E6081x Solid state physics, I materials. Dislocation and elastic-plastic concepts material of MSAE E4206. 3 pts. Lect: 3. Professor Pinczuk. introduced to explain work hardening, various Prerequisite: APPH E3100 or equivalent. Knowledge MSAE E6221x Introduction to dislocation materials-strengthening mechanisms, ductility, of statistical physics on the level of MSAE E3111 theory and toughness. Macroscopic and microstructural or PHYS G4023 strongly recommended. Crystal 3 pts. Lect: 3. Not offered in 2014–2015. aspects of brittle and ductile fracture mechanics, structure; reciprocal lattices; classification of solids; Prerequisite: MSAE E4215 or course in theory of creep and fatigue phenomena. Case studies lattice dynamics; anharmonic effects in crystals; elasticity, or instructor’s permission. Point and line used throughout, including flow and fracture of stress and strain; classical electron models of imperfections. Theory of dislocations. Relation structural alloys, polymers, hybrid materials, metals; and periodic, nearly periodic, and more between imperfections and structure-sensitive composite materials, ceramics, and electronic advanced analysis of electron band structure. properties. materials devices. Materials reliability and fracture prevention emphasized. MSAE E6082y Solid state physics, II MSAE E6225y Techniques in X-ray and 3 pts. Lect: 3. Professor Altshuler. neutron diffraction MSAE E4250x Ceramics and composites Prerequisite: MSAE E6081 or instructor’s 3 pts. Lect: 3. Not offered in 2014–2015. 3 pts. Lect: 3. Professor Martin. permission. Semiclassical and quantum Prerequisite: MSAE E4101. Crystal symmetry, Prerequisites or corequisites: MSAE E3142 and mechanical electron dynamics and conduction; diffraction, reciprocal space and Ewald sphere E3104, or instructor’s permission. The course dielectric properties of insulators; semiconductors; construction, radiation sources, analytical will cover some of the fundamental processes defects; magnetism; superconductivity; low- representation of diffraction peaks, diffraction of atomic diffusion, sintering and microstructural dimensional structures; and soft matter. line broadening, Fourier analysis of peak shape, evolution, defect chemistry, ionic transport, and texture analysis, diffraction analysis of stress electrical properties of ceramic materials. Following MSAE E6085x Computing the electronic structure of complex materials and strain, diffraction analysis of order-disorder this, we will examine applications of ceramic thermal diffuse scattering, small angle scattering, materials, specifically, ceramic thick and thin film 3 pts. Lect: 3. Not offered in 2014–2015. Prerequisite: APPH E3100 or equivalent. Basics instrumentation in diffraction experiments, error materials in the areas of sensors and energy of density functional theory (DFT) and its analysis. conversion/storage devices such as fuel cells, and application to complex materials. Computation batteries. The course work level assumes that the MSAE E6229x Energy and particle beam of electronics and mechanical properties of processing of materials student has already taken basic courses in the materials. Group theory, numerical methods, 3 pts. Lect: 3. Professor Im. thermodynamics of materials, diffusion in materials, basis sets, computing, and running open source Prerequisites: MSAE E4202 or instructor’s and crystal structures of materials. DFT codes. Problem sets and a small project. permission. Laser-, electron-, and ion-beam MSAE E4301x and y Materials science MSAE E6091y Magnetism and magnetic modification of materials to achieve unique laboratory materials microstructures and metastable phases 1–3 pts. Members of the faculty. 3 pts. Lect. 3. Not offered in 2014–2015. for electronic and structural applications. Prerequisite: Instructor’s permission. Materials Prerequisite: MSAE E4206, APPH E6081, or Fundamentals of energy deposition and heat science laboratory work so conducted as to fulfill equivalent. Types of magnetism. Band theory of flow during laser- and electron-beam irradiation. particular needs of special students. ferromagnetism. Magnetic metals, insulators, and Atomic displacement processes in ion-irradiated MSAE E4990x and y Special topics in semiconductors. Magnetic nanostructures: ultrathin materials. Beam-induced microstructural evolution, materials science and engineering films, superlattices, and particles. Surface magnetism crystallization, surface alloying, rapid solidification, 1–3 pts. Instructor to be announced. and spectroscopies. High speed magnetization and metastable phase formation. Review of current Prerequisite: Instructor’s permission. This dynamics. Spin electronics. Offered in alternate years. industrial applications. course may be repeated for credit. Topics and MSAE E6120x Grain boundaries and interfaces MSAE E6230y Kinetics of phase transformations instructors change from year to year. For advanced 3 pts. Lect: 2. Not offered in 2014–2015. 3 pts. Lect: 3. Not offered in 2014-2015. undergraduate students and graduate students in Prerequisites: the instructor’s permission. Prerequisite: MSAE E4202 or instructor’s engineering, physical sciences, and other fields. Suggested background: basic knowledge of permission. Principles of nonequilibrium materials science, dislocations and point defects. thermodynamics; stochastic equations; nucleation, The course gives an overview of the classic growth, and coarsening reactions in solids; approaches in studying grain boundaries. Topics spinodal decomposition; eutectic and eutectoid include boundary geometry and structure, transformations.

engineering 2014–2015 MSAE E6251y Thin films and layers MSAE E8236y Anelastic relaxations in MSAE E9309x and y–S9309 Proposal of 177 3 pts. Lect: 3. Not offered in 2014–2015. crystals Research for the Doctorate Vacuum basics, deposition methods, nucleation 3 pts. Lect: 3. Not offered in 2014–2015. 0–3 pts. Members of the faculty. and growth, epitaxy, critical thickness, defects Prerequisite: Instructor’s permission. Formal theory A written report prepared by the prospective properties, effect of deposition procedure, of anelastic relaxation phenomena. Detailed study doctoral candidate defining the proposed research mechanical properties, adhesion, interconnects, of the mechanisms of anelasticity and internal for the dissertation, and oral defense of the and electromigration. friction in crystals, including the role of point defects, proposal at the time of the qualifying examinations. dislocations, grain boundaries, electron-phonon MSAE E6273x and y–S6273x Materials MSAE E9800x and y–S9800 Doctoral research interactions, and ferromagnetic domain effects. science reports instruction 0 to 6 pts. Members of the faculty. MSAE E9000x and y Materials science and 3, 6, 9, or 12 pts. Professor Barmak. Prerequisite: Written permission from instructor engineering colloquium A candidate for the Eng.Sc.D. degree must register and approval from adviser. Formal written reports 0 pts. Professor Im. for 12 points of doctoral research instruction. and conferences with the appropriate member Speakers from industry are invited to speak on the Registration in MSAE E9800 may not be used to of the faculty on a subject of special interest to recent impact of materials science and engineering satisfy the minimum residence requirement for the the student but not covered in the other course innovations. degree. offerings. MSAE E9259x-E9260y Research topics MSAE E9900x and y–S9900 Doctoral MSAE E8235x and y Selected topics in in materials science and metallurgical dissertation materials science engineering 0 pts. Members of the faculty. 3 pts. Lect: 3. Professor Marianetti. 1 pt. Lect: 1. Members of the faculty. A candidate for the doctorate may be required to This course may be repeated for credit. Selected Discussion of a group of technical papers related register for this course every term after the course topics in materials science. Topics and instructors to a topic of current research interest. work has been completed and until the dissertation has been accepted. change from year to year. For students in MSAE E9301x-S9301 Doctoral research engineering, physical sciences, biological sciences, 0–15 pts. Members of the faculty. and related fields. Prerequisite: Qualifying examination for doctorate. Required of doctoral candidates.

engineering 2014–2015 178 Mechanical Engineering 220 S. W. Mudd, MC 4703 Phone: 212-854-2965 me.columbia.edu

Chair Professors Associate senior Lecturer Elias Panides Jeffrey W. Kysar Sunil Agrawal Professors Fred Stolfi Aleksandra Popovic 248 S. W. Mudd Gerard A. Ateshian Qiao Lin V. T. Rajan Mary C. Boyce Arvind Narayanaswamy Lecturers in Graham Walker Department James Hone Chee Wei Wong discipline Administrator Jeffrey W. Kysar Pejman Akbari Manager of Sandra Morris Richard W. Longman Assistant Sinisa Vukelic Instructional 220 S. W. Mudd Vijay Modi Professors Laboratories Y. Lawrence Yao Michael P. Burke Adjunct faculty Robert G. Stark Matei Ciocarlie Nicholas Chbat Kristin Myers John C. Leylegian Mohammad H. N. Naraghi

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

engineering 2014–2015 Biomechanics and Mechanics of they are also studied as a means of with molecular diffusion and inertia are 179 Materials. Some of the current assessing damage in civil engineering presently being investigated. Other research in biomechanics is concerned structures from earthquake data. areas of investigation include the fluid with the application of continuum (Longman) mechanics of inkjet printing, drop on theories of mixtures to problems of Robotics research focuses on demand, the suppression of satellite electromechanical behavior of soft design of novel rehabilitation machines droplets, shock wave propagation, and biological tissues, contact mechanics, and training algorithms for functional remediation in high-frequency printing lubrication of diarthrodial joints, and rehabilitation of neural impaired adults systems. (Modi) cartilage tissue engineering. (Ateshian) and children. The research also aims In the area of nanoscale thermal In the area of the mechanics of to design intelligent machines using transport, our research efforts center on materials, research is performed to better nonlinear system theoretic principles, the enhancement of thermal radiation understand material constitutive behavior computational algorithms for planning, transport across interfaces separated by at the micro- and mesolength scales. and optimization. a nanoscale gap. The scaling behavior This work is experimental, theoretical, and Robotic Systems Engineering (ROSE) of nanoscale radiation transport is computational in nature. The ultimate goal Lab develops technology capable measured using a novel heat transfer is to formulate constitutive relationships of solving difficult design problems, measurement technique based on that are based on physical concepts such as cable-actuated systems, the deflection of a bimaterial atomic rather than phenomenology, as in the under-actuated systems, and others. force microscope cantilever. Numerical case of plasticity power-law hardening. Robotics and Rehabilitation (ROAR) simulations are also performed to In addition, the role that the constitutive Lab focuses on developing new and confirm these measurements. The relations play in the fracture and failure of innovative technologies to improve the measurements are also used to infer materials is emphasized. (Kysar) quality of care and patient outcomes. extremely small variations of van der Other areas of biomechanics The lab designs novel exoskeletons Waals forces with temperature. This include characterizing the structure- for upper and lower limbs training of enhancement of radiative transfer will function behavior of the cervix during stroke patients, and mobile platforms ultimately be used to improve the power the remodeling events of pregnancy to improve socialization in physically density of thermophotovoltaic energy and characterizing the mechanical impaired infants (Agrawal). conversion devices. (Narayanaswamy) properties of the eye-wall in relation to In the area of advanced Also in the area of energy, research glaucoma. Research in our lab includes manufacturing processes and systems, is being performed to improve the the mechanical testing of biological soft current research concentrates on laser thermochemical models used in tissues, the biochemical analysis of tissue materials processing. Investigations accelerating development of cleaner, microstructure, and material modeling are being carried out in laser more fuel-efficient engines through based on structure-mechanical property micromachining; laser forming of sheet computational design. In particular, relationships. In collaboration with metal; microscale laser shock-peening, data-driven approaches to creating clinicians, our goal is to understand the material processing using improved high-accuracy, uncertainty-quantified etiologies of tissue pathology and disease. laser-beam quality. Both numerical and thermochemicals models are being (Myers) experimental work is conducted using developed that utilize both theoretical state-of-the-art equipment, instruments, and experimental data. Special Control, Robotics, Design, and and computing facilities. Close ties emphasis is placed on the generation Manufacturing. Control research with industry have been established for and analysis of data across the full emphasizes iterative learning control collaborative efforts. (Yao) range of relevant scales—from the (ILC) and repetitive control (RC). ILC small-scale electronic behavior that creates controllers that learn from Energy, Fluid Mechanics, and Heat/ governs molecular reactivity to the large- previous experience performing a Mass Transfer. In the area of energy, one scale turbulent, reactive phenomena that specific command, such as robots effort addresses the design of flow/mass govern engine performance. (Burke) on an assembly line, aiming for high- transport systems for the extraction precision mechanical motions. RC learns of carbon dioxide from air. Another MEMS and Nanotechnology. In these to cancel repetitive disturbances, such effort addresses the development of areas, research activities focus on power as precision motion through gearing, distributed sensors for use in micrositing generation systems, nanostructures for machining, satellite precision pointing, and performance evaluation of energy photonics, fuel cells and photovoltaics, particle accelerators, etc. Time optimal and environmental systems. The design and microfabricated adaptive cooling control of robots is being studied for and testing of components and systems skin and sensors for flow, shear, and increased productivity on assembly for micropower generation is part of the wind speed. Basic research in fluid lines through dynamic motion planning. thermofluids effort as well as part of the dynamics and heat/mass transfer Research is also being conducted on MEMS effort. (Modi) phenomena at small scales also support improved system identification, making In the area of fluid mechanics, study these activities. (Hone, Lin, Modi, mathematical models from input-output of low-Reynolds-number chaotic flows Narayanaswamy, Wong) data. The results can be the starting is being conducted both experimentally We study the dynamics of point for designing controllers, but and numerically, and the interactions microcantilevers and atomic force

engineering 2014–2015 180 microscope cantilevers to use them exploiting polymer structures to binding between biomolecules and as microscale thermal sensors based enable micro/nanofluidic manipulation, receptor molecules to enable selective on the resonance frequency shifts and integrating MEMS sensors with purification, concentration, and of vibration modes of the cantilever. microfluidics for measuring physical label-free detection of nucleic acid, Bimaterial microcantilever-based properties of biomolecules. (Lin) protein, and small molecule analytes; sensors are used to determine the miniaturized instruments for label-free thermophysical properties of thin films. Biological Engineering and characterization of thermodynamic (Narayanaswamy) Biotechnology. Active areas of research and other physical properties of Research in the area of nanotechnology in the musculoskeletal biomechanics biomolecules; and subcutaneously focuses on nanomaterials such as laboratory include theoretical and implantable MEMS affinity biosensors for nanotubes and nanowires and experimental analysis of articular continuous monitoring of glucose and their applications, especially in cartilage mechanics; theoretical and other metabolites. (Lin) nanoelectromechanical systems experimental analysis of cartilage Mass radiological triage is critical (NEMS). A laboratory is available for lubrication, cartilage tissue engineering, after a large-scale radiological event the synthesis of carbon nanotubes and bioreactor design; growth and because of the need to identify and semiconductor nanowires using remodeling of biological tissues; cell those individuals who will benefit chemical vapor deposition (CVD) mechanics; and mixture theory for from medical intervention as soon as techniques and to build devices using biological tissues with experiments and possible. The goal of the ongoing NIH- electron-beam lithography and various computational analysis (Ateshian). funded research project is to design etching techniques. This effort will seek The Hone group is involved in a a prototype of a fully automated, ultra to optimize the fabrication, readout, number of projects that employ the high throughput biodosimetry. This and sensitivity of these devices for tools of micro- and nanofabrication prototype is supposed to accommodate numerous applications, such as sensitive toward the study of biological multiple assay preparation protocols detection of mass, charge, and magnetic systems. With collaborators in biology that allow the determination of the resonance. (Hone, Wong, Modi) and applied physics, the group has levels of radiation exposure that a Research in the area of optical developed techniques to fabricate patient received. The input to this fully nanotechnology focuses on devices metal patterns on the molecular scale autonomous system is a large number smaller than the wavelength of light, (below 10 nanometers) and attach of capillaries filled with blood of patients for example, in photonic crystal biomolecules to create biofunctionalized collected using finger sticks. These nanomaterials and NEMS devices. nanoarrays. The group is currently capillaries are processed by the system A strong research group with using these arrays to study molecular to distill the micronucleus assay in facilities in optical (including ultrafast) recognition, cell spreading, and protein lymphocytes, with all the assays being characterization, device nanofabrication, crystallization. Professor Hone is a co-PI carried out in situ in multi-well plates. and full numerical intensive simulations of the NIH-funded Nanotechnology The research effort on this project is available. Current efforts include Center for Mechanics in Regenerative involves the automation system design silicon nanophotonics, quantum Medicine, which seeks to understand and integration including hierarchical dot interactions, negative refraction, and modify at the nanoscale force- and control algorithms, design and control dramatically enhanced nonlinearities, geometry-sensing pathways in health of custom built robotic devices, and and integrated optics. This effort seeks and disease. The Hone group fabricates automated image acquisition and to advance our understanding of many of the tools used by the center to processing for sample preparation and nanoscale optical physics, enabled now measure and apply force on a cellular analysis. (Yao) by our ability to manufacture, design, level. (Hone) A technology that couples the and engineer precise subwavelength Microelectromechanical systems power of multidimensional microscopy nanostructures, with derived applications (MEMS) are being exploited to enable (three spatial dimensions, time, and in high-sensitivity sensors, high- and facilitate the characterization and multiple wavelengths) with that of bandwidth data communications, manipulation of biomolecules. MEMS DNA array technology is investigated and biomolecular sciences. Major technology allows biomolecules to in an NIH-funded project. Specifically, ongoing collaborations across national be studied in well-controlled micro/ a system is developed in which laboratories, industrial research centers, nanoenvironments of miniaturized, individual cells selected on the and multiuniversities support this integrated devices, and may enable basis of optically detectable multiple research. (Wong) novel biomedical investigations not features at critical time points in Research in BioMEMS aims to attainable by conventional techniques. dynamic processes can be rapidly design and create MEMS and micro/ The research interests center on the and robotically micromanipulated into nanofluidic systems to control the development of MEMS devices and reaction chambers to permit amplified motion and measure the dynamic systems for label-free manipulation DNA synthesis and subsequent array behavior of biomolecules in solution. and interrogation of biomolecules. analysis. Customized image processing Current efforts involve modeling and Current research efforts primarily involve and pattern recognition techniques understanding the physics of micro/ microfluidic devices that exploit specific are developed, including Fisher’s nanofluidic devices and systems, and reversible, stimulus-dependent linear discriminant preprocessing with

engineering 2014–2015 neural net, a support vector machine components of the microcomputer undergraduate program 181 with improved training, multiclass cell architecture. The laboratory is divided The objectives of the undergraduate detection with error correcting output into work centers for two-person program in mechanical engineering are coding, and kernel principal component student laboratory teams. Each work as follows: analysis. (Yao) center is equipped with several power The Mechanical Engineering supplies (for low-power electronics Department at Columbia University is Facilities for Teaching and Research and higher power control), a function dedicated to graduating mechanical The undergraduate laboratories, generator, a multimeter, a protoboard engineers who: occupying an area of approximately for building circuits, a microcomputer 6,000 square feet of floor space, are circuit board (which includes the 1. Practice mechanical engineering in a the site of experiments ranging in microcomputer and peripheral broad range of industries complexity from basic instrumentation components), a microcomputer 2. Pursue advanced education, research and fundamental exercises to advanced programmer, and a personal computer and development, and other creative experiments in such diverse areas as that contains a data acquisition board. and innovative efforts in science, automatic controls, heat transfer, fluid The data acquisition system serves engineering, and technology, as well mechanics, stress analysis, vibrations, as an oscilloscope, additional function as other professional careers microcomputer-based data acquisition, generator, and spectrum analyzer for 3. Conduct themselves in a responsible, and control of mechanical systems. the student team. The computer also professional, and ethical manner Equipment includes microcomputers contains a complete microcomputer 4. Participate as leaders in their fields of and microprocessors, analog-to-digital software development system, including expertise and in activities that support and digital-to-analog converters, editor, assembler, simulator, debugger, service and economic development lasers and optics for holography and C compiler. The laboratory nationally and throughout the world and interferometry, a laser-Doppler is also equipped with a portable Highly qualified students are velocimetry system, a Schlieren oscilloscope, an EPROM eraser (to permitted to pursue an honors course system, dynamic strain indicators, a erase microcomputer programs from the consisting of independent study under servohydraulic material testing machine, erasable chips), a logic probe, and an the guidance of a member of the faculty. a photoelastic testing machine, analog filter bank that the student teams Upon graduation the student may an internal combustion engine, a share, as well as a stock of analog and wish to enter employment in industry dynamometer, subsonic and supersonic digital electronic components. or government, or continue with wind tunnels, a cryogenic apparatus, The department maintains a modern graduate study. Alternatively, training in computer numerically controlled vertical computer-aided design laboratory mechanical engineering may be viewed machine centers (VMC), a coordinate equipped with fifteen Silicon Graphics as a basis for a career in business, measurement machine (CMM), and workstations and software tools. The patent law, medicine, or management. a rapid prototyping system. A CNC research facilities are located within Thus, the department’s undergraduate wire electrical discharge machine individual or group research laboratories program provides a sound foundation (EDM) is also available for the use of in the department, and these facilities for a variety of professional endeavors. specialized projects for students with are being continually upgraded. To The program in mechanical prior arrangement. The undergraduate view the current research capabilities engineering leading to the B.S. degree laboratory also houses experimental please visit the various laboratories is accredited by the Engineering setups for the understanding and within the research section of the Accreditation Commission of ABET. performance evaluation of a complete department website. The students Undergraduates who wish to small steam power generation system, and staff of the department can, by declare mechanical engineering as a heat exchanger, a solar cell system, prior arrangement, use much of the their major should do so prior to the a fuel cell system, and a compressor. equipment in these research facilities. start of their junior year. Students who Part of the undergraduate laboratory is Through their participation in the NSF- wish to declare during or after the fall a staffed machine shop with machining MRSEC center, the faculty also have semester of their junior year must first tools such as standard vertical milling access to shared instrumentation and obtain approval from the Mechanical machines, engine and bench lathes, the clean room located in the Schapiro Engineering Department. programmable surface grinder, band Center for Engineering and Physical Of the 21 points of elective content saw, drill press, tool grinders, and a Science Research. Columbia University’s in the third and fourth years, at least 12 power hacksaw. The shop also has a extensive library system has superb points of technical courses, including at tig welder. scientific and technical collections. least 6 points from the Department of A mechatronics laboratory affords E-mail and computing services are Mechanical Engineering, must be taken. the opportunity for hands-on experience maintained by Columbia University Those remaining points of electives are with microcomputer-embedded control Information Technology (CUIT) (columbia intended primarily as an opportunity of electromechanical systems. Facilities .edu/cuit). to complete the four-year, 27-point for the construction and testing of nontechnical requirement. Consistent analog and digital electronic circuits with professional accreditation aid the students in learning the basic

engineering 2014–2015 182 mechanical engineering program: first and second Years standard track

Semester i Semester iI Semester iII Semester iV

MATH V1202 (3)

APMA E2101 (3)1 mathematics MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) or Linear Algebra (3)2 and ODE (3)3

physics C1401 (3) C1402 (3) C1403 (3)4 (three tracks, C1601 (3.5) C1602 (3.5) C2601 (3.5)4 choose one) C2801 (4.5) C2802 (4.5)

one semester lecture (3–4) chemistry C1403 or C1404 or Lab C1500 (3)5 C3045 or C1604

english C1010 (3) composition (three tracks, Z1003 (0) C1010 (3) choose one) Z0006 (0) Z1003 (0) C1010 (3)

HUMA C1001, HUMA C1002, COCI C1101, COCI C1102, required or Global Core (3–4) or Global Core (3–4) nontechnical courses HUMA W1121 or ECON W1105 (4) and W1123 (3) W1155 recitation (0)

required (3) Student’s choice, see list of technical first- and second-year technical electives ENME-MECE E3105 (4) either semester courses (professional-level courses; see pages 12–13)6

computer Computer language: COMS W1005 (3) or ENGI E1006 (3) (in semester I or III) science

physical C1001 (1) C1002 (1) education

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 Students who take APMA E2101 must additionally purpose 3 points of their 12 points of technical elective requirement toward a course with the following course designators: MATH, PHYS, CHEM, BIOL, STAT, APMA, SIEO, or EEEB. 2 Linear algebra may be fulfilled by either APMA E3101 or MATH V2010. 3 Ordinary differential equations may be fulfilled by either MATH V3027 or MATH V1210. 4 May substitute EEEB W2001, BIOL C2005, or higher. 5 May substitute Physics Lab C1493 (3), C1494 (3), or W3081 (2). 6 ELEN E1201 (see Semester VI) satisfies this requirement. However, MECE E1001 is strongly encouraged.

standards, courses in engineering course in linear algebra (either APMA course in numerical methods (APAM science and courses in design must E3101 or MATH V2010) and a stand- E3105 or APMA E4300) as technical have a combined credit of 48 points. alone course in ordinary differential electives. Ideally, planning for these Students should see their advisers for equations (either MATH V3027 or courses should start at the beginning of details. V1210), instead of the combined topics the sophomore year. Undergraduate students interested course APMA E2101. In addition, such in pursuing a graduate degree in students are encouraged to take a engineering are strongly encouraged to course in partial differential equations take the combination of a stand-alone (APMA E3102 or E4200) as well as a

engineering 2014–2015 183 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 MECE E3038 (3) Lab III MECE E3408 (3) MECE E3100 (3) Graphics and design Fluids I MECE E3409 (3) Machine design MECE E3311 (3) MECE E3430 (3) MECE E3301 (3) Required Heat transfer Engineering design: Courses Thermodynamics MECE E3420 (1) creation Engineering design: MECE E3610 (3) ENME E3105 (4)1 concept Materials and processes Mechanics in manufacturing EEME E3601 (3) ENME E3113 (3) Classical control sys. ELEN E1201 (3.5) Mechanics of solids Intro. elec. eng.

technical 6 points 6 points Electives2

NONTECH 6 points Electives

total points3 16 15.5 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 purpose 3 points of their 12 points of technical elective requirement toward a course with the following course designators: MATH, PHYS, CHEM, BIOL, STAT, APMA, SIEO, or EEEB. 3 Students must complete 128 points to graduate.

Fundamentals of Engineering (FE) to simulate the testing experience. The quality for this program, your cumulative Exam FE exam is given in the fall and spring of GPA should be at least 3.5. For more The FE exam is a state licensing exam each year. The review course is offered information on requirements and access and the first step toward becoming in the spring semester, concluding to an application form, please visit a Professional Engineer (P.E.). P.E. before the spring exam. me.columbia.edu/integrated-bsms licensure is important for engineers -program. to obtain—it shows a demonstrated Integrated B.S./M.S. Program commitment to professionalism and The Integrated B.S./M.S. Program is graduate programS an established record of abilities that open to a select group of Columbia will help a job candidate stand out in juniors and makes possible the Master of Science Degree Program the field. Ideally, the FE exam should earning of both a B.S. and an M.S. be taken in the senior year while the degree simultaneously. Benefits of this The program leading to the Master technical material learned while pursuing program include optimal matching of of Science degree in mechanical the undergraduate degree is still fresh in graduate courses with corresponding engineering requires completion of a the student’s mind. In addition to the FE undergraduate prerequisites, greater minimum of 30 points of approved exam, achieving P.E. licensure requires ability to plan ahead for most course work consisting of no fewer some years of experience and a second advantageous course planning, than ten courses. A thesis based on examination, which tests knowledge opportunities to do research for credit either experimental, computational, or gained in engineering practice. For more during the summer after senior year, and analytical research is optional and may information, please see http://ncees.org up to 6 points of 4000-level technical be counted in lieu of up to 6 points of /exams/fe-exam/. electives from the B.S. requirement course work. In general, attainment of The Mechanical Engineering may count toward the fulfillment of the the degree requires one academic year Department strongly encourages all point requirement of the M.S. degree. of full-time study, although it may also seniors to take this exam and offers a Additional benefits include simplified be undertaken on a part-time basis review course covering material relevant application process, no GRE is required, over a correspondingly longer period. A to the exam, including a practice exam and no reference letters are required. To minimum grade-point average of 2.5 is required for graduation.

engineering 2014–2015 184 mechanical engineering program: first and second Years early decision track

Semester i Semester iI Semester iII Semester iV

MATH V1202 (3)

APMA E2101 (3)1 mathematics MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) or Linear algebra (3)2 and ODE (3)3

physics C1401 (3) C1402 (3) C1403 (3)4 (three tracks, C1601 (3.5) C1602 (3.5) C2601 (3.5)4 choose one) C2801 (4.5) C2802 (4.5)

one semester lecture (3–4) chemistry C1403 or C1404 or Lab C1500 (3)5 C3045 or C1604

english C1010 (3) composition (three tracks, Z1003 (0) C1010 (3) choose one) Z0006 (0) Z1003 (0) C1010 (3)

required HUMA C1001, HUMA C1002, nontechnical COCI C1101, COCI C1102, courses or Global Core (3–4) or Global Core (3–4)

(3) Student’s choice, ELEN E1201 (3.5) see list of first- and Intro. to elec. eng. required second-year technical ENME E3105 (4) ENME E3113 (3) technical electives Mechanics Mechanics of solids courses MECE E3408 (3) (professional-level courses; Graphics and design see page 12)6

computer Computer language: COMS W1005 (3) or ENGI E1006 (3) (in semester I and III) science

physical C1001 (1) C1002 (1) education

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 Students who take APMA E2101 must additionally purpose 3 points of their 12 points of technical elective requirement toward a course with the following course designators: MATH, PHYS, CHEM, BIOL, STAT, APMA, SIEO, or EEEB. 2 Linear algebra may be fulfilled by either APMA E3101 or MATH V2010. 3 Ordinary differential equations may be fulfilled by either MATH V3027 or MATH V1210. 4 May substitute EEEB W2001, BIOL C2005, or higher. 5 May substitute Physics Lab C1493 (3), C1494 (3), or W3081 (2). 6 ELEN E1201 (see Semester IV) satisfies this requirement. However, MECE E1001 is strongly encouraged.

The M.S. degree in mechanical Alternatively, M.S. students can pick controls, and power generation. engineering requires a student to take from a set of predefined concentrations, Nevertheless, the following guidelines a sequence of courses that shows or special tracks. must be adhered to: a “clearly discernible specialty or Typical choices of concentration concentration.” In consultation with his/ in the standard track include such 1. The sequence of courses selected her adviser an M.S. student can develop subjects as mechanics of solids and must not be haphazard but rather a concentration specifically tailored to fluids, thermodynamics, heat transfer, show a clearly discernible specialty. his/her interests and objectives, and manufacturing engineering, robotics, 2. All courses must be at the graduate we refer to this as the standard track. kinematics, dynamics and vibrations, level, i.e., numbered 4000 or higher,

engineering 2014–2015 185 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 W1121 or ECON W1105 (4) and nontechnical Courses W1123 (3) W1155 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 purpose 3 points of their 12 points of technical elective requirement toward a course with the following course designators: MATH, PHYS, CHEM, BIOL, STAT, APMA, SIEO, or EEEB. 2 Students must complete a minimum of 128 points to graduate.

with some 6000-level courses tracks are listed below. MECE E4210: Energy infrastructure planning included. MECE E4211: Energy: sources and conversion 3. Every program must contain at M.S. in Mechanical Engineering with MECE E4302: Advanced thermodynamics MECE E4304: Turbomachinery least one course in mathematics Concentration in Energy Systems MECE E4305: Mechanics and thermodynamics (APMA, MATH, STAT, SIEO course Advisers: Professors Vijay Modi and propulsion designations) covering material Arvind Narayanaswamy MECE E4312: Solar thermal engineering beyond what the student has taken MECE E4314: Energy dynamics of green buildings previously. It should appear early in The concentration in energy systems MECE E4320: Intro to combustion the sequence in order to serve as a provides the M.S. candidate with a MECE E4330: Thermofluid systems design basis for the technical course work. global understanding of current energy MECE E6100: Advanced mechanics of fluids MECE E6104: Case studies in computational fluid 4. Out-of-department study is challenges. Advanced thermofluidic dynamics encouraged, but at least five courses knowledge is provided to design and optimize energy systems, with MECE E6313: Advanced heat transfer should be in mechanical engineering. APPH E4130: Physics of solar energy a strong emphasis on renewable ELEN E4511: Power systems analysis Rather than apply for the standard track, energies. Courses related to energy and EAEE E6126: Carbon sequestration students can apply for a special track environmental policy, two strong areas EAEE E6208: Combustion chemistry or processes in either energy systems or in micro/ of Columbia as a global university, can nanoscale engineering. The require- be integrated into the course sequence. One 3-point research course can be ments for a special track are identical This concentration is a suitable counted towards the concentration if the to those of the standard track, with one preparation for careers in energy research is approved by the student’s exception: a special track student must production and energy consultation. adviser and is energy related. take at least 15 of his/her points from a Requirements: While satisfying It is recommended that Energy Track list determined by a special track adviser the general mechanical engineering students take at least one course in in consultation with a special track requirements, take at least five courses STAT/SIEO. advisory committee. The name of the from: special track will be listed on a student’s transcript. The currently available special

engineering 2014–2015 186 M.S. in Mechanical Engineering with Doctoral Degree Program suitable for doctoral research, whether Concentration in Micro/Nanoscale When a student becomes a the plan of attack is well formulated and Engineering prospective candidate for either the appropriate to the problem, and whether Advisers: Professors James Hone and Doctor of Engineering Science (Eng. the student is adequately prepared. Jeff Kysar Sc.D.) or Doctor of Philosophy (Ph.D.) It may approve the plan without degree, a faculty adviser is assigned reservation, or it may recommend The concentration in micro/nanoscale whose task is to help choose a modifications or additions. This is the last engineering provides the M.S. candidate program of courses, provide general formal requirement until the dissertation with an understanding of engineering advice on academic matters, and is submitted for approval. challenges and opportunities in micro- monitor academic performance. All doctoral students are required to and nanoscale systems. The curriculum The doctoral candidate is expected successfully complete four semesters addresses fundamental issues of to attain a level of mastery in some of the mechanical engineering seminar mechanics, fluid mechanics, optics, heat area of mechanical engineering, and MECE E9500. transfer, and manufacturing at small-size must therefore choose a field and scales. Application areas include MEMS, concentrate in it by taking the most bio-MEMS, microfluidics, thermal courseS in mechanical advanced courses offered. This choice systems, and carbon nanostructures. engineering of specialty is normally made by the time Requirements: While satisfying the student has completed 30 points of MECE E1001x Mechanical engineering: the general mechanical engineering credit beyond the bachelor’s degree, at micromachines to jumbo jets requirements, take at least five courses 3 pts. Lect: 3. Professor Myers. which time a complete course program from: Corequisite: MATH V1101 Calculus I. This is prepared and submitted to the introductory course explores the role of Mechanical MECE E4212: Microelectromechanical systems departmental doctoral committee for Engineering in developing many of the fundamental MECE E4213: BioMEMS approval. The student must maintain a technological advances on which today’s society MECE E6105: T ransport phenomena in the grade-point average of 3.2 or better in depends. Students will be exposed to several presence of interfaces graduate courses. mature and emerging technologies through a MECE E6700: Carbon nanotubes The department requires the series of case studies. Topics include: airplanes, MECE E6710: Nanofabrication laboratory prospective candidate to pass a automobiles, robots, modern manufacturing MECE E6720: Nano/microscale thermal transport methods as well as the emerging fields of qualifying examination. Given once a processes microelectromechanical machines (MEMS) and MECE E8990: Small scale mechanical behavior year, in January, it is usually taken after nanotechnology. The physical concepts that govern ELEN E4503: Sensors, actuators, and the student has completed 30 points the operation of these technologies will be developed electromechanical systems beyond the bachelor’s degree. However, from basic principles and then applied in simple ELEN E6945: Device nanofabrication it may not be delayed past the next design problems. Students will also be exposed to BMEN E4590: BioMEMS: cellular and molecular examination given after completion of state-of-the art innovations in each case study. applications 45 points. The examination comprises MECE E1304x or y Naval ship systems, I MSAE E4090: Nanotechnology a written test, given in two parts over 3 pts. Lect: 3. Instructor to be announced. two days, in which questions may be A study of ship characteristics and types including Express M.S. Program selected from a broad set in all areas ship design, hydrodynamic forces, stability, The Express M.S. Program is offered to of mechanical engineering and applied compartmentation, propulsion, electrical and auxiliary systems, interior communications, ship current seniors, including 3-2 students, mathematics, devised to test the who are enrolled in the BS program. In control, and damage control; theory and design candidate’s ability to think creatively. of steam, gas turbine, and nuclear propulsion; the Express M.S. Program, a master’s There is also an oral examination based shipboard safety and firefighting. This course is degree can be earned seamlessly. on some research project the student part of the Naval ROTC program at Columbia but Graduate classes are available for has undertaken. A candidate who fails will be taught at SUNY Maritime. Enrollment may seniors to apply toward their M.S. the examination may be permitted to be limited; priority is given to students participating degree and the advanced courses that repeat it once in the following year. in Naval ROTC. This course will not count as a technical elective. Students should see a faculty will be taken have been designed to After passing the qualifying have the exact prerequisites completed adviser as well as Columbia NROTC staff (nrotc@ examination, the student chooses a columbia.edu) for more information. as an undergraduate. Other advantages faculty member in the pertinent area include the opportunity for better course of specialization who then serves as MECE E3018x Mechanical engineering planning and creating a streamlined set the research adviser. This adviser laboratory, I 3 pts. Lect: 3. Professor Kysar. of courses more possible. Additional helps select a research problem and benefits include simplified application Experiments in instrumentation and measurement: supervises the research, writing, and optical, pressure, fluid flow, temperature, stress, process, no GRE is required and no defense of the dissertation. Once a and electricity; viscometry, cantilever beam, digital reference letters are required. To qualify specific problem has been identified data acquisition. Probability theory: distribution, for this program, your cumulative and a tentative plan for the research functions of random variables, tests of significance, GPA should be at least 3.5. For more prepared, the student submits a research correlation, ANOVA, linear regression. A lab fee of information on requirements and proposal and presents it to a faculty $50.00 is collected. access to an application, please visit committee. The committee considers me.columbia.edu/ms-express whether the proposed problem is -application-1.

engineering 2014–2015 187

MECE E3028y Mechanical engineering ENME E3105x and y Mechanics analytical and graphical synthesis of mechanism, laboratory, II 4 pts. Lect: 4. Professor Hone. displacement analysis, velocity analysis, 3 pts. Lect: 3. Professor Akbari. Prerequisites: PHYS C1401 and MATH V1101, acceleration analysis of linkages, dynamics of Experiments in engineering and physical V1102, and V1201. Elements of statics, dynamics mechanism, cam design, gear and gear trains, and phenomena: aerofoil lift and drag in wind tunnels, of a particle, systems of particles, and rigid bodies. computer-aided mechanism design. laser Doppler anemometry in immersed fluidic ENME E3113x Mechanics of solids MECE E3408y Computer graphics and design channels, supersonic flow and shock waves, 3 pts. Lect: 3. Professor Deodatis. 3 pts. Lect: 3. Instructor to be announced. Rankine thermodynamical cycle for power Introduction to drafting, engineering graphics, generation, and structural truss mechanics and Pre- or corequisite: ENME E3105 or equivalent. computer graphics, solid modeling, and mechanical analysis. A lab fee of $50.00 is collected. Stress and strain. Mechanical properties of materials. Axial load, bending, shear, and engineering design. Interactive computer graphics MECE E3038x Mechanical engineering torsion. Stress transformation. Deflection of and numerical methods applied to the solution laboratory, III beams. Buckling of columns. Combined loadings. of mechanical engineering design problems. A 3 pts. Lect: 3. Professor Stolfi. Thermal stresses. laboratory fee of $175 is collected. Mechatronic control of mechanical and MECE E3409x Machine design electromechanical systems. Control of various MECE E3301x Thermodynamics 3 pts. Lect: 3. Professor Agrawal. thermodynamic cycles, including internal 3 pts. Lect: 3. Professor Vukelic. Prerequisite: MECE E3408. Computer-aided combustion engine (Otto cycle). Reverse Classical thermodynamics. Basic properties and analysis of general loading states and deformation engineering of an electromechanical product. A lab concepts, thermodynamic properties of pure of machine components using singularity functions fee of $50.00 is collected. substances, equation of state, work, heat, the first and second laws for flow and nonflow processes, and energy methods. Theoretical introduction to MECE E3100x Introduction to mechanics energy equations, entropy, and irreversibility. static failure theories, fracture mechanics, and of fluids Introduction to power and refrigeration cycles. fatigue failure theories. Introduction to conceptual 3 pts. Lect: 3. Professor Vukelic. design and design optimization problems. Design Prerequisite: ENME E3105. Basic continuum MECE E3311y Heat transfer of machine components such as springs, shafts, concepts. Liquids and gases in static equilibrium. 3 pts. Lect: 3. Professor Narayanaswamy. fasteners, lead screws, rivets, welds. Modeling, Continuity equation. Two-dimensional kinematics. Steady and unsteady heat conduction. Radiative analysis, and testing of machine assemblies for Equation of motion. Bernoulli’s equation and heat transfer. Internal and external forced and free prescribed design problems. Problems will be applications. Equations of energy and angular convective heat transfer. Change of phase. Heat drawn from statics, kinematics, dynamics, solid momentum. Dimensional analysis. Two- exchangers. modeling, stress analysis, and design optimization. dimensional laminar flow. Pipe flow, laminar, and MECE E3401x Mechanics of machines MECE E3411y Fundamentals of engineering turbulent. Elements of compressible flow. 3 pts. Lect: 3. Professor Lin. 1 pt. Lect: 3. Professor Stolfi. Prerequisites: ENME E3105 and MECE E3408. Prerequisite: Senior standing. Review of core Introduction to mechanisms and machines, courses in mechanical engineering, including

engineering 2014–2015 188 mechanics, strength of materials, fluid mechanics, MECE E3900x-E3901y Honors tutorial in lectures on infrastructure finance, regulation and thermodynamics, heat transfer, materials and mechanical engineering public-private partnerships. processing, control, and mechanical design and 3 pts. Lect: 3. Members of the faculty. MECE E4211x or y Energy: sources and analysis. Review of additional topics, including Individual study; may be selected after the first engineering economics and ethics in engineering. term of the junior year by students maintaining a conversion The course culminates with a comprehensive 3.2 grade-point average. Normally not to be taken 3 pts. Lect: 3. Professor Modi. examination, similar to the Fundamentals of in a student’s final semester. Course format may Prerequisite: MECE E3301. Energy sources such Engineering examination. This course meets the vary from individual tutorial to laboratory work as oil, gas, coal, gas hydrates, hydrogen, solar, first 4.5 weeks only. to seminar instruction under faculty supervision. and wind. Energy conversion systems for electrical Written application must be made prior to power generation, automobiles, propulsion and MECE E3420x Engineering concept and registration outlining proposed study program. refrigeration. Engines, steam and gas turbines, design Projects requiring machine-shop use must be wind turbines; devices such as fuel cells, 1 pt. Lect: 1. Professor Stolfi. approved by the laboratory supervisor. thermoelectric converters, and photovoltaic cells. Prerequisite: Senior standing. Corequisite: MECE Specialized topics may include carbon-dioxide E3409. A preliminary design for an original project MECE E3998x and y Projects in mechanical sequestration, cogeneration, hybrid vehicles and is a prerequisite for the capstone design course. engineering energy storage devices. This course will focus on the steps required for 1-3 pts. Members of the faculty. generating a preliminary design concept. Included Prerequisite: Approval by faculty member who MECE E4212x or y Microelectromechanical will be a brainstorming concept generation phase, agrees to supervise the work. Normally not to be systems a literature search, and the production of a layout taken in a student’s final semester. Independent 3 pts. Lect: 1.5. Lab: 3. Professor Wong. drawing of the proposed capstone design project in project involving theoretical, computational, MEMS markets and applications; scaling laws; a Computer Aided Design (CAD) software package experimental or engineering design work. May silicon as a mechanical material; Sensors and (i.e., ProEngineer). be repeated, but no more than 3 points may be actuators; micromechanical analysis and design; counted toward degree requirements. Projects substrate (bulk) and surface micromachining; MECE E3430y Engineering design requiring machine-shop use must be approved by computer aided design; packaging; testing and 3 pts. Lect: 2. Lab: 4. Professor Stolfi. the laboratory supervisor. characterization; microfluidics. Prerequisite: MECE E3420. Building on the preliminary design concept, the detailed elements MECE E4058x and y Mechatronics and MECE E4213y Biomicroelectromechanical of the design process are completed: systems embedded microcomputer control systems (BioMEMS): design, fabrication, and synthesis, design analysis optimization, and 3 pts. Lect: 3. Professor Stolfi. analysis Computer Aided Design (CAD) component part Prerequisite: ELEN E1201. Recommended: 3 pts. Lect: 3. Professor Lin. drawings. Execution of a project involving the ELEN E3000. Enrollment limited to 12 students. Prerequisites: MECE E3100 and E3311, course in design, fabrication, and performance testing of an Mechatronics is the application of electronics and transport phenomena, or instructor’s permission. actual engineering device or system. A laboratory microcomputers to control mechanical systems. Silicon and polymer micro/nanofabrication fee of $125 is collected. Systems explored include on/off systems, techniques; hydrodynamic microfluidic control; solenoids, stepper motors, DC motors, thermal MECE E3450y Computer-aided design electrokinetic microfluidic control; microfluidic systems, magnetic levitation. Use of analog and 3 pts. Lect: 3. Professor Ateshian. separation and detection; sample preparation; Prerequisites: ENME E3105, E3113, MECE digital electronics and various sensors for control. micro bioreactors and temperature control; E3408, E3311. Introduction to numerical methods Programming microcomputers in Assembly and C. implantable MEMS, including sensors, actuators and their applications to rigid body mechanics for A lab fee of $75.00 is collected. Lab required. and drug delivery devices. mechanisms and linkages. Introduction to finite MECE E4100y Mechanics of fluids MECE E4302y Advanced thermodynamics element stress analysis for deformable bodies. 3 pts. Lect: 3. Professor Lin. 3 pts. Lect: 3. Professor Leylegian. Computer-aided mechanical engineering design Prerequisite: MECE E3100 or equivalent. Fluid Prerequisite: MECE E3301. Advanced classical using established software tools and verifications dynamics and analyses for mechanical engineering thermodynamics. Availability, irreversibility, against analytical and finite difference solutions. and aerospace applications: boundary layers generalized behavior, equations of state for EEME E3601x Classical control systems and lubrication, stability and turbulence, and nonideal gases, mixtures and solutions, phase and 3 pts. Lect: 3. Professor Longman. compressible flow. Turbomachinery as well as chemical behavior, combustion. Thermodynamic Prerequisite: MATH E1210. Analysis and design additional selected topics. properties of ideal gases. Applications to automotive and aircraft engines, refrigeration and of feedback control systems. Transfer functions; MECE E4210x or y Energy infrastructure air conditioning, and biological systems. block diagrams; proportional, rate, and integral planning controllers; hardware, implementation. Routh 3 pts. Lect: 3. Professor Modi. MECE E4304x Turbomachinery stability criterion, root locus, Bode and Nyquist Prerequisites: One year each of college level 3 pts. Lect: 3. Professor Akbari. plots, compensation techniques. physics, chemistry, and mathematics. Energy This course will introduce you to the basics MECE 3610y Materials and processes in infrastructure planning with specific focus on of theory, design, selection and applications manufacturing countries with rapidly growing infrastructure of turbomachinery. Turbomachines are widely 3 pts. Lect: 3. Professor Yao. needs. Spatiotemporal characteristics, scale, and used in many engineering applications such as Prerequisites: ENME E3113 or the equivalent. environmental footprints of energy resources, energy conversion, power plants, air-conditioning, Introduction to microstructures and properties power generation and storage, modeling pumping, refrigeration and vehicle engines, of metals, polymers, ceramics and composites; demand growth, technology choices and learning as there are pumps, blowers, compressors, typical manufacturing processes: material removal, for planning. Computer-assisted decision gas turbines, jet engines, wind turbines etc. shaping, joining, and property alteration; behavior support and network design/optimization tools. Applications are drawn from energy conversion of engineering materials in the manufacturing Similarities, differences and interactions among technologies, HVAC and propulsion. The course processes. electricity, gas, information, transportation and provides a basic understanding of the different water distribution networks. Penetration of kinds of turbomachines. renewable and/or decentralized technologies into existing or new infrastructure. Special guest

engineering 2014–2015 MECE E4305y Mechanics and Prerequisites: MECE E3100, E3301, E3311, satellite attitude dynamics, gravity gradient 189 thermodynamics of propulsion or equivalent. Thermodynamics and kinetics of stabilization of satellites, spin-stabilized satellites, 3 pts. Lect: 3. Professor Akbari. reacting flows; transport phenomena, laminar dual-spin satellites, satellite attitude control, Prerequisites: MECE E3301x Thermodynamics premixed and nonpremixed flames, droplet modeling, dynamics, and control of large flexible and MECE E3311y Heat transfer; MECE combustion, critical phenomena, detonations, spacecraft. E4304x Turbomachinery (or instructor approval). turbulent flames, oxidation of common fuel MEBM E4439x Modeling and identification of Principles of propulsion. Thermodynamic cycles molecules, pollutant chemistry, applications for air- dynamic systems of air breathing propulsion systems including breathing and rocket propulsion. ramjet, scramjet, turbojet, and turbofan engine 3 pts. Lect: 3. Professor Chbat. and rocket propulsion system concepts. Turbine MECE E4330x Thermofluid systems design Prerequisite: APMA E2101, ELEN E3801, or engine and rocket performance characteristics. 3 pts. Lect: 3. Professor Vukelic. corequisite EEME E3601, or permission of Component and cycle analysis of jet engines and Prerequisites: MECE E3100, E3301, E3311. instructor. Generalized dynamic system modeling turbomachinery. Advanced propulsion systems. Theoretical and practical considerations, and and simulation. Fluid, thermal, mechanical, Columbia Engineering interdisciplinary course. design principles, for modern thermofluids diffusive, electrical, and hybrid systems are systems. Topics include boiling, condensation, considered. Nonlinear and high order systems. MECE E4306x or y Introduction to phase change heat transfer, multi-mode heat System identification problem and Linear aerodynamics transfer, heat exchangers, and modeling Least Squares method. State-space and noise 3 pts. Lect: 3. Professor Akbari. of thermal transport systems. Emphasis on representation. Kalman filter. Parameter estimation Principles of flight, incompressible flows, applications of thermodynamics, heat transfer, via prediction-error and subspace approaches. compressible regimes. Inviscid compressible and fluid mechanics to modeling actual physical Iterative and bootstrap methods. Fit criteria. Wide aerodynamics in nozzles (wind tunnels, jet systems. Term project on conceptual design and applicability: medical, energy, others. MATLAB and engines), around wings (aircraft, space shuttle) presentation of a thermofluid system that meets Simulink environments. and around blunt bodies (rockets, reentry specified criteria. MECE E4501y Geometrical modeling vehicles). Physics of normal shock waves, oblique 3 pts. Lect: 3. Professor Rajan. shock waves, and explosion waves. MECE E4400x and y Computer laboratory access 0 pts. Professor Kysar. Prerequisite: COMS W1005. Relationship between IEME E4310x The manufacturing enterprise Sign up for this class to obtain a computer account 3D geometry and CAD/CAM; representations 3 pts. Lect: 3. Professor Weinig. and access to the Department of Mechanical of solids; geometry as the basis of analysis, The strategies and technologies of global Engineering Computer Laboratory. design, and manufacturing; constructive solid manufacturing and service enterprises. geometry and the CSG tree; octree representation Connections between the needs of a global MECE E4404x or y Tribology: friction, and applications; surface representations and enterprise, the technology and methodology lubrication, and wear intersections; boundary representation and needed for manufacturing and product 3 pts. Lect: 3. Not offered in 2014–2015. boundary evaluation; applied computational development, and strategic planning as currently Prerequisites: MECE E3100, E3311, and ENME geometry; analysis of geometrical algorithms practiced in industry. E3113, or permission of the instructor. Friction, and associated data structures; applications of lubrication, and wear between sliding surfaces. geometrical modeling in vision and robotics. MECE E4312x Solar thermal engineering Surface metrology, contact mechanics, and sliding 3 pts. Lect: 3. Professor Narayanaswamy. friction. Deformation, wear, and temperature rise of MECE E4502x Computational geometry for Prerequisite: MECE E3311 (Heat transfer). nonlubricated, liquid-lubricated, and solid-lubricated CAD/CAM Fundamentals of solar energy transport: rolling and sliding materials. The theories of 3 pts. Lect: 3. Professor Rajan. Prerequisite: COMS W1005 FORTRAN or radiation heat transfer, convention, conduction boundary, elastohydrodynamic, hydrodynamic, PASCAL. Analysis of geometric problems and and phase change processes. Heat exchangers hydrostatic, and solid-phase lubrication. Lubricant the design of efficient methodologies to obtain and solar collectors: basic methods of thermal flow and load-carrying capacity in bearings. Special solutions to these problems. Algorithms to be design, flow arrangements, effects of variable applications such as geartrains, cam/tappets, and studied include geometric searching, convex hulls, conditions, rating procedures. Solar energy micro- and nanoscale tribological interfaces. concentration. Piping Systems: series and triangulations, Voronoi diagrams, intersections, parallel arrangements, fluid movers. Thermal MECE E4430y Automotive dynamics hidden surfaces. Emphasis will be on practical response and management of photovoltaic 3 pts. Lect: 3. Professor Honarmandi. aspects of these algorithms, and on applications of energy conversion. Solar energy storage. Solar Prerequisite: ENME 3105 or equivalent; the solutions in computer-aided product design and cooling, solar thermal power and cogeneration. recommended: ENME 3106 or equivalent. manufacturing. Applications to the design of solar thermal Automobile dynamic behavior is divided into three EEME E4601y Digital control systems engineering systems. subjects: vehicle subsystems, ride, and handling. 3 pts. Lect: 3. Professor Longman. Vehicle subsystems include: tire, steering, MECE E4314y Energy dynamics of green Prerequisite: EEME E3601 or ELEN E3201. Real- mechanisms, suspensions, gearbox, engine, time control using digital computers. Solving scalar buildings clutch, etc. Regarding ride, vibrations and ride and state-space difference equations. Discrete 3 pts. Lect: 3. Professor Naraghi. comfort are analyzed, and suspension optimization equivalents of continuous systems fed by holds. Prerequisites: MECE E3301 and E3311. of a quarter car model is treated. Regarding Z-transer functions. Creating closed-loop difference Introduction to analysis and design of heating, handling, vehicle dynamic behavior on the road is equation models by Z-transform and state variable ventilating and air-conditioning systems. Heating analyzed, with emphasis on numerical simulations approaches. The Nyquist frequency and sample and cooling loads. Humidity control. Solar gain and using planar as well as roll models. rate selection. Classical and modern based digital passive solar design. Global energy implications. control laws. Digital system identification. Green buildings. Building-integrated photovoltaics. MECE E4431x or y Space vehicle dynamics Roof-mounted gardens and greenhouses. Financial and control MECE E4602x Introduction to robotics assessment tools and case studies. Open to 3 pts. Lect: 3. Professor Longman. 3 pts. Lect: 3. Professor Popovic. Mechanical Engineering graduate students only. Prerequisite: ENME-MECE E3105; ENME E4202 Overview of robot applications and capabilities. recommended. Space vehicle dynamics and Linear algebra, kinematics, statics, and MECE E4320x Introduction to combustion control, rocket equations, satellite orbits, initial dynamics of robot manipulators. Survey of 3 pts. Lect: 3. Professor Leylegian. trajectory designs from earth to other planets, sensor technology: force, proximity, vision,

engineering 2014–2015 190 compliant manipulators. Motion planning and biopohysical techniques such as single molecule variables, turbulence modeling, and coordinate artificial intelligence; manipulator programming FRET, optical traps, AFM, and superresolution transformations. requirements and languages. imaging, for understanding molecular mechanics MECE E6103x Compressible flow and dynamics. MECE E4604x Product design for 3 pts. Lect: 3. Professor Akbari. manufacturability IEME E4810y Introduction to human Prerequisites: APMA E4200, MECE E3100 and 3 pts. Lect: 3. Professor Walker. spaceflight E3301. Fundamental analysis of compressible Prerequisites: Manufacturing process, computer 3 pts. Lect: 3. Professor Massimino. flows and its applications for various sonic/ graphics, engineering design, mechanical design. Prerequisites: Department permission and supersonic elements including supersonic airfoils/ General review of product development process; knowledge of MATLAB or equivalent. Introduction projectiles, nozzles, and shock tubes. Steady market analysis and product system design; to human spaceflight from a systems engineering and unsteady shock/expansion waves, oblique principles of design for manufacturing; strategy perspective. Historical and current space programs shock waves. Shock reflections, methods of for material selection and manufacturing process and spacecraft. Motivation, cost, and rationale characteristic. choice; component design for machining; casting; for human space exploration. Overview of space MECE E6104y Case studies in computational molding; sheet metal working and inspection; environment needed to sustain human life and fluid dynamics general assembly processes; product design health, including physiological and psychological 3 pts. Lect: 3. Professor Panides. for manual assembly; design for robotic and concerns in space habitat. Astronaut selection and Prerequisites: APAM E4200 and MECE E6100. automatic assembly; case studies of product training processes, spacewalking, robotics, mission Corequisites: APAM E4300 and MECE E4400. design and improvement. operations, and future program directions. Systems Hands-on case studies in computational fluid integration for successful operation of a spacecraft. MECE E4609y Computer-aided manufacturing dynamics, including steady and transient Highlights from current events and space research, 3 pts. Lect: 3. Professor Walker. flows, heat and mass transfer, turbulence, Space Shuttle, Hubble Space Telescope, and Prerequisites: Introductory course on manufacturing compressible flow and multiphase flow. International Space Station (ISS). Includes a processes and knowledge of computer-aided design, Identifying assumptions, computational domain design project to assist International Space Station and mechanical design or instructor’s permission. selection, model creation and setup, boundary astronauts. Computer-aided design, free-form surface modeling, conditions, choice of convergence criteria, tooling and fixturing, computer numeric control, MECE E4990x or y Special topics in visualization and interpretation of computed rapid prototyping, process engineering, fixed and mechanical engineering results. Taught in the Mechanical Engineering programmable automation, industrial robotics. 3 pts. Lect: 3. Instructor to be announced. Computer Laboratory with Computational Fluid MECE E4610x Advanced manufacturing Prerequisites: Permission of the instructor. Topics Dynamics software. and Instructors change from year to year. For processes MECE E6105y Transport phenomena in the advanced undergraduate students and graduate 3 pts. Lect: 3. Professor Yao. presence of interfaces students in engineering, physical sciences, and Prerequisites: Introductory course on 3 pts. Lect: 3. Not offered in 2014–2015. other fields. manufacturing processes, and heat transfer, Prerequisites: MECE E3301 Thermodynamics knowledge of engineering materials, or MECE E4999x, y or s Curricular practical training and MECE E3311 Heat transfer; MECE E4100 instructor’s permission. Principles of nontraditional 1 pt. Professor Kysar. Mechanics of fluids, or equivalent or instructor’s manufacturing, nontraditional transport and media. Prerequisite: Instructor’s written approval. Only for permission; CHEE E4252 Introduction to surface Emphasis on laser assisted materials processing, ME graduate students who need relevant intern and colloid chemistry, or the equivalent, or the laser material interactions with applications to or field-work experience as part of their program instructor’s permission. Surface energy and laser material removal, forming, and surface of study as determined by the instructor. Written capillary phenomena. Wetting and spreading modification. Introduction to electrochemical application must be made prior to registration of liquids, wetting line pinning and hysteresis, machining, electrical discharge machining and outlining proposed study program. Final reports dynamics of wetting. Surfactants. Bubbles: abrasive water jet machining. required. This course may not be taken for pass/ nucleation, stability, dynamics, microstreaming. BMME E4702x Advanced musculoskeletal fail credit or audited. International students must Jets and Drops: generation, dynamics, stability and biomechanics also consult with the International Students and impact with surfaces. Measurement of transport 3 pts. Lect: 3. Professor Guo. Scholars Office. phenomena involving interfaces. Interfacial transport phenomena involvng thermal, chemical Advanced analysis and modeling of the MECE E6100x Advanced mechanics of fluids or electrical gradients. Applications in microfluidic musculoskeletal system. Topics include 3 pts. Lect: 3. Professor Panides. systems. advanced concepts of 3D segmental kinematics, Prerequisites: MATH E1210 and MECE E3100. musculoskeletal dynamics, experimental Eulerian and Lagrangian descriptions of motion. MECE E6200y Turbulence measurements of joints kinematics and anatomy, Stress and strain rate tensors, vorticity, integral 3 pts. Lect: 3. Not offered in 2014–2015. modeling of muscles and locomotion, multibody and differential equations of mass, momentum, Prerequisite: MECE E6100. Introductory concepts joint modeling, introduction to musculoskeletal and energy conservation. Potential flow. and statistical description. Kinematics of random surgical simulations. velocity fields, dynamics of vorticity, and scalar MECE E6102y Computational heat transfer quantities. Transport processes in a turbulent MEBM E4703x Molecular mechanics in and fluid flow medium. Turbulent shear flows: deterministic and biology 3 pts. Lect: 3. Not offered in 2014–2015. random structures. Experimental techniques, 3 pts. Lect: 3. Not offered in 2014–2015. Prerequisites: MECE E3100 and E3311; COMS prediction methods, and simulation. Prerequisite: ENME E3105, APMA E2101, or W1005 FORTRAN. Mathematical description of instructor’s permission. Mechanical understanding pertinent physical phenomena. Basics of finite- MEBM E6310x-E6311y Mixture theories for of biological structures including proteins, DNA difference methods of discretization, explicit biological tissues, I and II and RNA in cells and tissues. Force response and implicit schemes, grid sizes, stability, and 3 pts. Lect: 3. Not offered in 2014–2015. of protenis and DNA, mechanics of membranes, convergence. Solution of algebraic equations, Prerequisites: MECE E6422 and APMA E4200 or biophysics of molecular motors, mechanics relaxation. Heat conduction. Incompressible equivalent. Development of governing equations of protein-protein interactions. Introduction to fluid flow, stream function-vorticity formulation. for mixtures with solid matrix, interstitial fluid, modeling and simulation techniques, and modern Forced and natural convection. Use of primitive and ion constituents. Formulation of constitutive

engineering 2014–2015 models for biological tissues. Linear and nonlinear the study of the equilibrium and stability of surfaces. and classification of signals using a selection 191 models of fibrillar and viscoelastic porous matrices. of tools borrowed from different disciplines. EEME E6601x Introduction to control theory Solutions to special problems, such as confined Applications include human biometrics, imaging, 3 pts. Lect: 3. Professor Longman. and unconfined compression, permeation, geophysics, machinery, electronics, networking, Prerequisite: MATH E1210. A graduate-level indentation and contact, and swelling experiments. languages, communications, and finance. introduction to classical and modern feedback Practical algorithms are covered in signal MECE E6313x Advanced heat transfer control that does not presume an undergraduate generation, modeling, feature extraction, metrics 3 pts. Lect: 3. Professor Naraghi. background in control. Scalar and matrix for comparison and classification, parameter Prerequisites: MECE E3311. Corequisites: MECE differential equation models and solutions in terms estimation, supervised, unsupervised and E6100. Application of analytical techniques to the of state transition matrices. Transfer functions hierarchical clustering and learning, optimization, solution of multidimensional steady and transient and transfer function matrices, block diagram scaling and alignment, signals as codes emitted problems in heat conduction and convection. manipulations, closed loop response. Proportional, from natural sources, information, and extremely Lumped, integral, and differential formulations. rate, and integral controllers, and compensators. large-scale search techniques. Topics include use of sources and sinks, laminar/ Design by root locus and frequency response. turbulent forced convection, and natural convection Controllability and observability. Luenberger MECE E6700x Carbon nanotube science and in internal and external geometries. observers, pole placement, and linear-quadratic technology cost controllers. 3 pts. Lect: 3. Not offered in 2014–2015. MECE E6400y Advanced machine dynamics Prerequisite: Knowledge of introductory solid 3 pts. Lect: 3. Professor Chbat. EEME E6602y Modern control theory state physics (e.g., PHYS G4018, APPH E6081, Prerequisite: MECE E3401. Review of classical 3 pts. Lect: 3. Not offered in 2014–2015. or MSAE E3103) or instructor’s permission. dynamics, including Lagrange’s equations. Analysis Prerequisite: EEME E6601 or E4601 or ELEN Basic science of solid state systems. Crystal of dynamic response of high-speed machine E6201, or instructor’s permission. Singular value structure, electronic and phonon band structures elements and systems, including mass-spring decomposition. ARX model and state space of nanotubes. Synthesis of nanotubes and other systems, cam-follower systems, and gearing; model system identification. Recursive least nanomaterials. Experimental determination shock isolation; introduction to gyrodynamics. squares filters and Kalman filters. LQR, Hlinear of nanotube structures and techniques for robust control, predictive control, adaptive MECE E6422x–E6423y Introduction to the nanoscale imaging. Theory and measurement of control. Liapunov and Popov stability. Nonlinear theory of elasticity, I and II mechanical, thermal, and electronic properties of adaptive control, nonlinear robust control, sliding 3 pts. Lect: 3. Professors Ateshian and Kysar. nanotubes and nanomaterials. Nanofabrication and mode control. Corequisite: APMA E4200. Analysis of stress nanoelectronic devices. Applications of nanotubes. and strain. Formulation of the problem of elastic EEME E6610y Optimal control theory MECE E6710y Nanofabrication laboratory equilibrium. Torsion and flexure of prismatic bars. 3 pts. Lect: 3. Not offered in 2014–2015. 3 pts. Lect: 3. Not offered in 2013–2014. Problems in stress concentration, rotating disks, Prerequisite: EEME E6601 or E4601 or instructor’s Prerequisite: ELEN E6945 or instructor’s shrink fits, and curved beams; pressure vessels, permission. Covers topics in calculus of variations, permission. Laboratory in techniques for contact and impact of elastic bodies, thermal Pontryagin maximum principle, quadratic cost fabrication at the nanometer scale. Electron- stresses, propagation of elastic waves. optimal control, predictive control, dynamic beam lithography. Plasma etching and 3D programming for optimal control, Kalman filtering, MECE E6424x Vibrations in machines, I nanofabrication. Thin film deposition. Self- numerical methods for solution. Some applications 3 pts. Lect: 3. Professor Honarmandi. assembly and “bottom up” nanofabrication. discussed include: minimum energy subway Prerequisite: MECE E3401. Review of vibration Fabrication of and testing of complete operation (our solution saved 11% in tests on the analysis of systems and mechanisms with one nanodevices. A lab fee of $300 is required. Flushing Line, and the method was adopted by the degree of freedom. Natural frequencies. Forced transit authority, saving many millions of dollars per MECE E6720x Nano/microscale thermal vibrations. Effects of dry and viscous friction. year), minimum time robot optimal control allowing transport process Energy methods of Rayleigh and Ritz. Suppression one to run assembly lines faster for increased 3 pts. Lect: 3. Not offered in 2014–2015. and elimination of vibration. Vibration isolation. productivity. Nano- and microscale origins of thermal Measuring instruments. Critical speeds in machinery. transport phenomena by molecules, electrons, Synchronous whirl. Half-frequency whirl. Influence of MECE E6614x or y Advanced topics in phonons, and photons. Quantum mechanics bearing characteristics on critical speeds. Effect of robotics and mechanism synthesis and statistical physics. Density of states. gyroscopic moments. Systems with multiple degrees 3 pts. Lect: 3. Professor Agrawal. Kinetic theory of gases. Boltzmann transport of freedom. Dynamic vibration absorbers. Self-tuning Prerequisites: APMA E2101, E3101, MECE E4602 equation (BTE), classical and quantum size absorbers of pendulum and roller types. Lagrangian (or COMS W4733). Recommended: MECE E3401 effects. Landauer formalism for transport equations of motion as applied to vibrating systems. or instructor’s permission. Kinematic modeling via nanostructures. Macroscopic constitutive General equations for transverse critical speeds of methods for serial, parallel, redundant, wire- equations from BTE. Application to electronics shafts. Surging of helical springs. actuated robots and multifingered hands with cooling, thermoelectric and thermophotovoltaic discussion of open research problems. Introduction MECE E6432y Small-scale mechanical devices, and energy conversion. to screw theory and line geometry tools for behavior kinematics. Applications of homotropy continuation MECE E8020x-E8021y Master’s thesis 3 pts. Lect: 3. Professor Kysar. methods and symbolic-numerical methods for 1–3 pts. Members of the faculty. Prerequisites: ENME E3113 or equivalent; APMA direct kinematics of parallel robots and synthesis of Interpretive research in graduate areas in E4200 or equivalent. Mechanics of small-scale mechanisms. Course uses mechanical engineering and engineering science. materials and structures require nonlinear kinematics textbook materials as well as a collection of recent and/or nonlinear stress vs. strain constitutive MECE E8100y Advanced topics in fluid research papers. relations to predict mechanical behavior. Topics mechanics include: variational calculus, deformation and MECE E6620x or y Applied signal recognition 3 pts. Lect: 3. Not offered in 2014–2015. vibration of beam, strings, plates, and membranes; and classification Prerequisite: MECE E6100. This course may fracture, delamination, bulging, buckling of thin 3 pts. Lect: 3. Not offered in 2014–2015. be taken more than once, since its content has films, among others. Thermodynamics of solids Prerequisites: MATH E1210, APMA E3101, minimal overlap between consecutive years. will be reviewed to provide the basis for a detailed knowledge of a programming language, or Selected topics from viscous flow, turbulence, discussion of nonlinear elastic behavior as well as permission of instructor. Applied recognition compressible flow, rarefied gas dynamics,

engineering 2014–2015 192 computational methods, and dynamical systems EEME E8601y Advanced topics in control theory MECE E9500x and y Graduate seminar theory, non-Newtonian fluids, etc. 3 pts. Lect: 3. Not offered in 2014–2015. 0 pts. Pass/fail only. Professor Myers. Prerequisites: EEME E6601 and E4601 or All doctoral students are required to complete MECE E8501y Advanced continuum instructor’s permission This course may be taken successfully four semesters of the mechanical biomechanics more than once, since the content changes from engineering seminar MECE E9500. 3 pts. Lect: 2. Professor Myers. year to year, electing different topics from control MECE E9800x and y Doctoral research Prerequisite: Instructor’s permission. The theory such as learning and repetitive control, instruction essentials of finite deformation theory of solids and adaptive control, system identification, Kalman 3, 6, 9, or 12 pts. Members of the faculty. fluids needed to describe mechanical behavior of filtering, etc. biological tissue: kinematics of finite deformations, A candidate for the Eng.Sc.D. degree in balance laws, principle of material objectivity, MECE E8990x and y Special topics in mechanical engineering must register for 12 points theory of constitutive equations, concept of simple mechanical engineering of doctoral research instruction. Registration in solids and simple fluids, approximate constitutive 3 pts. Lect: 3. Instructor to be announced. MECE E9800 may not be used to satisfy the equations, some boundary-value problems. Topics Prerequisite: Instructor’s permission. This course minimum residence requirement for the degree. include one- and two-point tensor components may be taken for credit more than once. The MECE E9900x and y Doctoral dissertation with respect to generalized coordinates; finite instructor from the Mechanical Engineering 0 pts. Members of the faculty. deformation tensors, such as right and left Department and the topics covered in the course A candidate for the doctorate may be required to Cauchy-Green tensors; rate of deformation will vary from year to year. This course is intended register for this course every term after his/her tensors, such as Rivlin-Ericksen tensors; various for students with graduate standing in Mechanical course work has been completed and until the forms of objective time derivatives, such as Engineering and other engineering and applied dissertation has been accepted. co-rotational and convected derivatives of tensors; sciences. viscometric flows of simple fluids; examples of rate MECE E9000x-E9001y and E9002s Graduate and integral type of constitutive equations. research and study 1–3 pts. Members of the faculty. Theoretical or experimental study or research in graduate areas in mechanical engineering and engineering science.

engineering 2014–2015 Undergraduate Minors 194 undergraduate minors

ndergraduate minors are Minor in ANTHROPOLOGY Minor in Applied Physics designed to allow engineering 1. ANTH V1002: The interpretation of culture (3) Prospective students should consult the U and applied science students or ANTH V1008: The rise of civilization (3) first- and second-year requirements for to study, to a limited extent, a discipline applied physics majors to ensure that Note: V1002 serves as a preview to other than their major. Besides sociocultural anthropology, while V1008 prerequisites for the applied physics engineering minors offered by Columbia serves as a preview to archaeology. minor are satisfied in the first two years. Engineering departments, liberal arts Course work counting toward the 2–5. Any four courses in the Anthropology minors are available. applied physics minor may not include department, in ethnomusicology, or taught A minor requires at least 15 points of by an Anthropology instructor, regardless of advanced placement credits. credit, and no more than one course can department. No distribution requirement. 1. APPH E4901: Problems in applied physics (1) be taken outside of Columbia or met through AP or IB credit. This includes 2. APPH E3200: Mechanics (3) courses taken through study abroad. Minor in Applied 3. APPH E3100: Intro to quantum mechanics (3) In Engineering departments with more Mathematics 4. APPH E3300: Applied electromagnetism (3) than one major program, a minor in the Prospective students should consult second program may be permitted, if the first- and second-year requirements 5. MSAE E3111: Thermodynamics, kinetic theory, and statistical mechanics (3) approved by the department. for applied mathematics majors to No substitutions or changes of any ensure that prerequisites for the applied 6. Two of the following courses kind from the approved minors are mathematics minor are satisfied in the APPH E4010: Intro to nuclear science (3) permitted (see lists below). No appeal first two years. APPH E4100: Quantum physics of matter (3) APPH E4110: Modern optics (3) for changes will be granted. Please Course work counting toward the APPH E4112: Laser physics (3) applied mathematics minor may not note that the same courses may not be APPH E4300: Applied electrodynamics (3) used to satisfy the requirements of more include advanced placement credits. APPH E4301: Intro to plasma physics (3) than one minor. No courses taken for Any substitutions for the courses listed pass/fail may be counted for a minor. below require the approval of the applied Minor in Architecture Minimum GPA for the minor is 2.0. mathematics program adviser. 1. Studio: One of the following courses Departments outside the Engineering 1. APMA E3101: Linear algebra (3) ARCH V1020: Intro to architectural design and School have no responsibility for or MATH V2010: Linear algebra (3) visual culture (3) nonengineering minors offered by 2. APMA E3102: Partial differential equations (3) ARCH V3101: Abstraction (4) Engineering. or MATH V3028: Partial differential equations (3) ARCH V3103: Perception (4) For a student to receive credit for 2–4. History/theory courses (see Note below) a course taken while studying abroad, 3–5. Three of the following courses: APMA E4300: Intro to numerical methods (3) the department offering the minor must 5. Elective: must be either an approved second APMA E4204: Func of complex variable (3) design studio or an additional history/theory approve the course in writing, ahead of APMA E4101: Intro to dynamical systems (3) course the student’s study abroad. MATH V2500: Analysis and optimization (3) Students must expect a course load SIEO W4150: Intro to probablity and statistics (3) Note: A list of the approved history/theory that is heavier than usual. In addition, STAT W4107: Statistical inference (3) courses is available at the departmental unforeseen course scheduling changes, or any other course designated APMA, MATH, office each semester. STAT, IEOR, or COMS that is approved by the problems, and conflicts may occur. The applied mathematics program adviser School cannot guarantee a satisfactory completion of the minor.

engineering 2014–2015 Minor in Art History Minor in Civil Engineering 1–2. History/criticism: Two of the following: 195 DNCE BC2565: World dance history 1. CIEN E3121: Structural analysis (3) 1–7. Seven courses in art history, covering DNCE BC2570: Dance in New York City or ENME E3161: Fluid mechanics (4) four of the following areas: (a) ancient DNCE BC2575: Choreography for the American or MECE E3100: Intro to mech of fluids (3) Mediterranean, (b) medieval Europe, musical (c) Renaissance and baroque, (d) 18th, 2. ENME E3105: Mechanics (4) DNCE BC3000: From the page to the dance stage 19th, and 20th century, and (e) non- 3. ENME E3113: Mechanics of solids (3) Western DNCE BC3001: Western theatrical dance from 4–6. Electives: Three of the following courses: the Renaissance to the 1960s CIEN E1201: Design of buildings, bridges, and DNCE BC3200: Dance in film Minor in Biomedical spacecraft (3) DNCE BC3567: Dance in Asia Engineering ENME E3161: Fluid mechanics (4) DNCE BC3570: Latin American and Caribbean The Biomedical Engineering program ENME E3114: Exp mechanics of materials (4) dance offers a minor that consists of the ENME E3332: A first course in finite elements (3) DNCE BC3574: Seminar on contemporary MECE E3414: Adv strength of materials (3) choreographers and their works following six courses. Participation in the CIEN E3125: Structural design (3) DNCE BC3576: Dance criticism minor is subject to the approval of the CIEN E4241: Geotech eng fundamentals (3) DNCE BC3577: Performing the political major program adviser. CIEE E3250: Hydrosystems engineering (3) DNCE BC3578: Traditions of African-American CIEE E4163: Environ eng: wastewater (3) dance CIEN E3129: Project mgmt for construction (3) 1. BIOL C2005: Introduction to biology, I (3) 3–4. Performance/choreography: Two of the CIEN E4131: Prin of construction tech (3) following: 2. BIOL C2006: Introduction to biology, II (3) Note: At least three of the courses must DNCE BC2563: Dance composition: form 2. BMEN E3010: Biomedical engineering, I (3) be courses that are not required in the DNCE BC2564: Dance composition: content DNCE BC2567: Music for dance 2. BMEN E3020: Biomedical engineering, II (3) student’s major. DNCE BC2580: Tap as an American art form 2. BMEN E4010: Quantitative physiology (3) DNCE BC3565: Composition: collaboration and Minor in Computer Science the creative process 2. BMEN E4020: Quantitative physiology , II (3) Students who pass the Computer DNCE BC3601-3604: Rehearsal and Science Advanced Placement Exam, performance in dance Minor in Chemical either A or AB, with a 4 or 5 will receive 5. One elective Engineering 3 points and exemption from COMS Of the six courses required, at least W1004. Taking COMS W1007 is Minor in Earth and three must have the CHEN, CHEE, or recommended but not required for those Environmental CHAP designator: students exempt from COMS W1004. Engineering 1. CHEN E2100: Intro to chemical engineering (3) Participation in the minor is subject to the approval of the major program adviser. 1–3. Three of the following courses: 2. CHEE E3010: Prin of chemical engineering EAEE E3103: Energy, minerals, and mat syst (3) thermodynamics (3) For further information, please see the QuickGuide at www.cs.columbia.edu/ CIEE E3255: Environmental control and or MSAE E3111: Thermodynamics, kinetic pollution reduction systems (3) education/undergrad/seasguide. theory, and statistical mechanics (3) EAEE E4001: Industrial ecology of Earth res (3) or MECE E3301: Thermodynamics (3) 1. COMS W1004: Intro to computer science and EAEE E4003: Intro to aquatic chemistry (3) or BMEN E4210: Thermodynamics of biological programming in Java (3) EAEE E4004: Physical processing and recovery systems (3) or COMS W1007: Honors intro to comp sci (3) of solids (3) 3. CHEN E3110: Transport phenomena, I (3) EAEE E4006: Field methods for environ eng (3) 2. COMS W3134: Data structures in Java (3) or EAEE E4900: Applied transport and EAEE E4009: GIS for resource, environment, or COMS W3137: Honors data structures and chemical rate phenomena (3) and infrastructure management (3) algorithms (4) or MECE E3100: Intro to mech of fluids (3) EAEE E4150: Air pollution prevention and or ENME E3161: Fluid mechanics (4) 3. COMS W3157: Advanced programming (4) control (3) EAEE E4160: Solids and hazardous waste 4. COMS W3203: Discrete mathematics (3) 4. CHEN E4230: Reaction kinetics and management (3) reactor design (3) 5. COMS W3261: Comp science theory (3) EAEE E4200: Prod of inorganic materials (3) 5–6. Two of the following courses: EAEE E4257: Environ data analysis and 6. CSEE W3827: Fund of computer systems (3) Any 3000-level or higher BMCH, CHEN, CHAP, modeling (3) or a 4000-level COMS technical elective or CHEE course EAEE E4361: Econ of Earth res industries (3) APMA E3101: Linear algebra (3) 7. COMS W3251: Comp linear algebra (3) EACE E4560: Particle technology (3) or COMS W3210: Scientific computation (3) APMA E3102: Partial differential equations (3) 4–6. Three of the following courses: or SIEO W3600 (or W4150): Intro to probability BMEN E3320: Fluid biomechanics (3) CHEE E3010: Prin of chemical engineering and statistics (3) BMEN E4001: Quantitative physiology, I (3) thermodynamics (3) BMEN E4002: Quantitative physiology, II (3) CHEE E3110: Transport phenomena, I (3) ELEN E3201: Circuit analysis (3.5) Minor in Dance CIEN E3141: Soil mechanics (3) ELEN E3331: Electronic circuits (3) CIEE E3250: Hydrosystems engineering (3) SIEO W3600: Intro to probability and statistics (4) The dance minor consists of five 3-point courses. Please note that no SIEO W3600: Intro to probability and statistics (4) IEOR W4105: Probability (3) ECIA W4100: Mgmt and dev of water systems (3) performance/choreography courses IEOR W4106: Stochastic models (3) CIEE E4163: Environ eng: wastewater (3) MSAE E3103: Elements of mat sci (3) below count toward the nontech EAEE E4190: Photovoltaic systems eng (3) MSAE E3142: Ceramics and polymers (3) requirement for Engineering students. MECE E4211: Energy: sources and conv (3)

engineering 2014–2015 196 CIEN E4250: Waste contain design and prac (3) ECON W4480: Gender and applied economics 6. ELEN E3106: Solid-state dev and mat (3.5) CHEE E4252: Intro to surface and colloid ECON W4490: Economics of the Internet or ELEN E3401: Electromagnetics (4) chem (3) ECON W4500: International trade CIEE E4252: Environmental engineering (3) ECON W4505: Int’l monetary theory and policy Note: Not available to computer CIEE E4257: Groundwater contaminant ECON W4615: Law and economics engineering majors transport and remediation (3) ECON W4625: Economics of the environment CHEN E4410: Environmental control technology (3) ECON W4750: Globalization and its risks Minor in Engineering Note: Electives may be taken only after the Mechanics Minor in East Asian Studies completion of both W3211 and W3213, 1. ENME E3105: Mechanics (4) 1–5. Any two of the survey courses on with the exception of W2257, which may Chinese, Japanese, Korean, or Tibetan be taken after completion of W1105. Some 2. ENME E3113: Mechanics of solids (3) civilization (ASCE V2359, V2361, V2363, of the elective courses listed above have 3. ENME E3161: Fluid mechanics (4) V2365), plus three elective courses additional prerequisites. Courses may or MECE E3100: Intro to mech of fluids (3) dealing with East Asia. The elective be taken only after the completion of all courses may be taken in departments prerequisites. Please see the Columbia 4–6. Electives: Three of the following: outside of East Asian Languages and College bulletin for course descriptions and ENME E3106: Dynamics and vibrations (3) Cultures. The minor does not include complete lists of prerequisites. ENME E3114: Exp mechanics of materials (4) a language requirement. However, one or MECE E3414: Adv strength of materials (3) semester of an East Asian language 7. Statistics: One of the following three CIEN E3121: Structural analysis (3) class may be used to fulfill one of the probability and statistics options (course ENME E4202: Advanced mechanics (3) three electives, as long as at least two or sequence): ENME E4113: Advanced mechanics of solids (3) semesters of that language have been a. SIEO W3600 (or W4150): Intro to probability ENME E4114: Mech of fracture and fatigue (3) taken. Placement exams may not be and statistics ENME E4214: Theory of plates and shells (3) used in place of these courses. b. IEOR E3658: Probablity and ENME E4215: Theory of vibrations (3) E4307: Applied statistical models MECE E3301: Thermodynamics (3) Minor in Economics c. STAT W3105 (or W4105): Intro to Note: At least three of the courses must probability and statistics and STAT W3107 1. ECON W1105: Principles of economics be courses that are not required in the (or W4107): Stat inference student’s major. 2. ECON W3211: Intermediate microeconomics Notes: 3. ECON W3213: Intermediate macroeconomics • T he statistics course must be finished Minor in English and before taking W3412, and it is 4. ECON W3412: Introduction to econometrics Comparative Literature recommended that students take W3412 Note: W1105 is a prerequisite for W3211, in the semester following the statistics 1–5. Any five courses in the English W3213, and W3412. Students must have course. Department with no distribution completed Calculus I before taking W3213, • Some courses done as part of the requirement. No speech courses, only one Calculus III before taking W3211, and one economics minor may count toward writing course as above and excluding fulfilling the School’s nontechnical of the introductory statistics courses (see ENGL C1010, may be taken; total 15 points. list) before taking W3412. requirements. However, other courses, such as W3412: Intro to econometrics, MINOR IN Entrepreneurship 5–6. Electives: Two of the following courses: may not be applied toward satisfaction ECON W2257: Global economy of the nontechnical course requirements. and Innovation ECON W4280: Corporate finance To determine which economic class Minimum: 15 points ECON V3025: Financial economics can count toward the nontech elective 1–2. Required courses: ECON V3265: Econ of money and banking requirement, please consult the nontech IEOR E2261: Intro to acct and finance (3) ECON W4020: Econ of uncertainty and info elective section of this bulletin for further and IEOR E4998: Managing technological ECON W4080: Globalization, incomes and details. innovation and entrepreneurship (3) inequality • Students with AP credit for economics ECON W4211: Advanced microeconomics and an exemption for W1105 may use 3–5. Electives: Three of the following courses: ECON W4213: Advanced macroeconomics the credit toward the minor. BIOT W4180: Entrpreneurship in biotech (3) ECON W4228: Urban economics • Transfer or study abroad credits may not BMEN E3998: Projects in biomedical eng (3) ECON G4235: Historical foundations of modern be applied to fulfill the requirements of BUSI W3021: Marketing management (3) economics the economics minor. CHEN E4020: Protection of industrial and ECON W4251: Industrial organization intellectual property (3) ECON G4301: Economic growth and develop Minor in Electrical CIEN E4136: Global entrepreneurship in civil ECON W4321: Economic development Engineering engineering (3) ECON W4329: Economics of sustainable develop COMS W4444: Program and problem solving (3) ECON W4345: World economic problems 1. ELEN E1201: Intro to electrical eng (3.5) COMS W4460: Principles of innovation in ECON W4370: Political economy (May be replaced by a similar course or roughly biotechnolgy (3) ECON W4400: Labor economics equivalent experience) ECON E4280: Corporate finance (3) ECON W4412: Advanced econometrics IEOR E4003: Industrial economics (3) 2. ELEN E3201: Circuit analysis (3.5) ECON W4415: Game theory IEOR E4510: Project management (3) ECON W4438: Economics of race in the U.S. 3. CSEE W3827: Fund of computer systems (3) IEOR E4550: Entrepreneurial business creation ECON W4457: Industrial organization of art, for engineers (3) 4. ELEN E3081 and ELEN E3082: entertainment and communications IEOR E4573: Design and agile project Electrical engineering labs (2) ECON W4465: Public economics management (3) 5. ELEN E3801: Signals and systems (3.5) (Fall semester by application only)

engineering 2014–2015 IEOR E4573: Lean LaunchPad (3) requirements. Transfer or study-abroad or EAEE E4900: App transport and chemical 197 (by application only with adviser approval) credits may not be applied. rate phenomena (3) IEOR E4705: Studies in operations research (3) ENME E3105: Mechanics (4) IEME E4310: The manufacturing enterprise (3) Minor in Industrial MECE E3301: Thermodynamics (3) or CHEE E3010: Principles of chemical Engineering Minor in French engineering thermodynamics (3) 1. SIEO W3600: Intro to probability and statistics (4) or MSAE E3111: Thermodynamics, kinetic 1–2. FREN W3333: Major literary works to 1800 (3) theory, and statistical mechanics (3) and W3334: Major literary works since 1800 (3) 2. IEOR E3608: Intro to math programming (4) ENME E3113: Mechanics of solids (3) MECE E3408: Comp graphics and design (3) 3–5. Three additional courses in French 3. IEOR E3402: Production inventory planning and beyond satisfaction of the language control (3) MECE E3311: Heat transfer (3) requirement MECE E3610: Materials and processes in 4. IEOR E4003: Industrial economics (3) manufacturing (3) 5–6. Electives: Two IEOR courses of interest MECE E3409: Machine design (3) Minor in French and and approved by a faculty adviser EEME E3601: Classical control systems (3) Francophone Studies 5–6. Electives: Two additional mechanical Required: 15 points beyond second-year French Note: In addition to the required courses, students majoring in operations research engineering courses from either the above 1–2. FREN W3420 and W3421: Intro to French and its concentrations (EMS or FE) list or the following (not all courses in this and francophone studies, I and II (3, 3) minoring in industrial engineering must take list are given every year): MECE E3401: Mechanics of machines (3) 3–5. Three additional courses in French three industrial engineering courses that MECE E4058: Mechatronics and embedded beyond satisfaction of the language are not used to satisfy the requirements of microcomputer control (3) requirement their major. MECE E4100: Mechanics of fluids (3) MECE E4211: Energy: sources and conversion (3) Minor in German Minor in Materials Science MECE E4212: Microelectromechanical sys (3) Required: 15 points beyond second-year German and Engineering MECE E4302: Advanced thermodynamics (3) MECE E4404: Tribology (3) 1. MSAE E3103: Elements of mat sci (3) 1. GERM V3001 or V3002: Adv German, I or II (3) MECE E4501: Geometrical modeling (3) 2. GERM W3333: Intro to German literature (3) 2–3. Two of the following courses: MECE E4502: Comp geometry for CAD/CAM (3) MSAE E3111: Thermodynamics, kinetic theory, EEME E4601: Digital control systems (3) 3. One of the period survey courses in and statistical mechanics (3) MECE E4602: Intro to robotics (3) German literature and culture, GERM MSAE E3141: Metals and semiconductors (3) MECE E4604: Product design for manufact (3) W3442, W3443, W3444, W3445 MSAE E3142: Ceramics and polymers (3) MECE E4609: Computer-aided manufacturing (3) 4–5. Two courses taken from any 3000/4000- MSAE E4090: Nanotechnology (3) MECE E4610: Adv manufacturing processes (3) level German or CompLit-German courses MSAE E4100: Crystallography (3) Note: Equivalent substitution courses taught in German or English MSAE E4101: Struc analysis of materials (3) require the approval of the Mechanical MSAE E4206: Electronic and magnetic Engineering Program Adviser. Minor in Greek or Latin properties of solids (3) MSAE E4215: Mech behavior of materials (3) 1–4. A minimum of 13 points in the chosen MSAE E4250: Ceramics and composites (3) Minor in Middle Eastern, language at the 1200 level or higher 4–6. Three of the following courses South Asian, and African 5. 3 points in ancient history of the (other materials-related courses may be Studies acceptable): appropriate civilization 1–5. Five courses, to be chosen with the approval APPH E4100: Quantum physics of matter (3) CHEE E4050: Industrial electrochemistry (3) of the MESAAS Director of Undergraduate Minor in Hispanic Studies CHEE E4252: Intro to surface and colloid chem (3) Studies; no elementary or intermediate 1. SPAN W3300: Adv language through content (3) CHEE E4530: Corrosion of metals (3) language courses may be counted. CHEN E4620: Polymers and soft materials (3) 2. SPAN W3330: Intro to the study of Hispanic CHEN E4630: Polymer laboratory (3) Minor in Music cultures (3) CHEM C3443-C3444: Organic chemistry (3.5) 3-4. SPAN W3349 and W3350: Hispanic cultures, ELEN E4411: Fundamentals of photonics (3) 1. MUSI V2318-V2319: Diatonic harmony, I and II (3, 3) I and II (3, 3) ELEN E4301: Intro to semiconductor 2. MUSI V1312-V1313: Intro ear training (1) devices (3) 5. One additional 3000-level elective course ELEN E4944: Prin of dev microfabrication (3) 3. MUSI V2314: Ear training, I (1) in the Department of Latin American and ENME E4113: Adv mechanics of solids (3) Iberian Cultures 4. One of the following courses: ENME E4114: Mech of fracture and fatigue (3) MUSI V3128: History of Western music, I (3) Note: Please see the director of MECE E3610: Manufacturing processes (3) MUSI V3129: History of Western music, II (3) undergraduate studies in the Department MECE E4701: Introductory biomechanics (3) of Latin American and Iberian Cultures for 5–6. Any two electives at the 3000 or 4000 level. See also the Engineering-approved more information and to declare the minor. Minor in Mechanical nontechnical electives in music Engineering (page 12). Minor in History 1–4. Four of the following courses: Notes: 1–5. Minimum 15 points in the History MECE E3100: Intro to mechanics of fluids (3) • Students must successfully place out of Department with no distribution or seminar or ENME E3161: Fluid mechanics (4) MUSI V1002: Fundamentals of Western or CHEN E3110: Transport phenomena, I (3)

engineering 2014–2015 198 music (3.0 points). Minor in Psychology MINOR IN SUSTAINABLE • Steps 4 and 5 must be completed ENGINEERING to fulfill the nontechnical elective Minimum: 15 points requirement for graduation. 1. PSYC W1001: The science of psychology (3) Total of six courses from the following • Students are strongly encouraged to lists required with no substitutions take HUMA W1123: Masterpieces of 2–5. Any four courses from, at a minimum, two allowed: Western music (3.0 points) from the list of the three groups below: 1–4. Four of the following courses: of nontechnical electives. I. PERCEPTION AND COGNITION EAEE E2002: Alternative energy sources Courses numbered in the 2200s, 3200s, or EAEE E2100: Better planet by design 4200s. Also PSYC W1420, W1480, or W1490 Minor in Operations CIEE/EAEE 3260: Eng for developing comm Research II. PSYCHOBIO LOGY AND NEUROSCIENCE EAEE E3901: Environmental microbiology PSYC W1010: Mind, brain, and behavior (3) EAEE E4001: Industrial ecology 1. IEOR E3106: Stochastic models (3) Courses numbered in the 2400s, 3400s, or ECIA W4100: Mgmt and dev of water systems 2. SIEO W3600: Intro to probability and statistics (4) 4400s; also PSYC W1440 APPH E4130: Physics of solar energy EAEE E4190: Photovoltaic systems eng and III. SOCIA L, PERSONALITY, AND ABNORMAL 3. IEOR E3608: Intro to math programming (4) sustainability Courses numbered in the 2600s, 3600s, or MECE E4211: Energy sources and conversion 4. IEOR E4404: Simulation (3) 4600s; also PSYC W1450 or W1455 MECE E4312: Solar thermal engineering 5–6. Electives: Two IEOR courses of interest MECE E4314: Dynamics of green buildings and approved by a faculty adviser. IEOR Minor in Religion EESC W4404: Regional climate and climate E3402: Production-inventory planning and impacts control 3.0 points is strongly recommended. 1–5. Five courses (total 15 points), one of which must be at the 2000 level 5. One of the following courses: Note: In addition to the required courses, ECON W2257: Global economy students majoring in industrial engineering PLAN 4151: Found of urban economic analysis must take three operations research Minor in Sociology PLAN 4304: Intro to housing courses that are not used to satisfy the ECON 4321: Economic development 1. SOCI W1000: The social world (3) requirements of their major. PLAN 4501: Local econ development planning 2. SOCI W2200: Evaluation of evidence (3) ECON G4527: Econ org and develop of China Interdisciplinary planning for health Minor in Philosophy 3. SOCI W3000: Social theory (3) PLAN 4540: PLAN 4579: Environmental planning 1–5. Any five courses in the Philosophy 4–5. Any two 2000-, 3000-, or 4000-level PLAN 4609: Intro to international planning Department with no distribution courses offered by the Department of ECON W4625: Economics of the environment requirement; total 15 points. See also Sociology; total 6 points the list of exceptions under Elective 6. One of the following courses: POLS V3212: Environmental politics Nontechnical Courses. Minor in Statistics POLS V3313: American urban politics Note: Please be aware that some SOCI W3235: Social movements 1. STAT W1001: Intro to statistical reason (3) philosophy courses may not count as SOCI W3670: Culture markets and consumption or W1111: Intro to statistics (w/o calculus) (3) SOCI W4424: Global urbanism nontechnical electives. or W1211: Intro to statistics (w/calculus) (3) 2. STAT W2024: App linear regression analysis (3) Minor in Political Science 3. STAT W2025: App statistical methods (3) 1–2. Two of the following courses: POLS W1201: American govt and politics (3) 4. STAT W2026: Stat appl and case studies (3) POLS V1501: Comparative politics (3) 5. STAT W3026: Applied data mining (3) POLS V1601: International politics (3) 6. STAT W3997: Independent research 3–5. Any three courses in the Political Science or any Statistics Department offering numbered Department with no distribution requirement; 4201 or above. total 9 points Notes: • The curriculum is designed for students seeking practical training in applied statistics; students seeking a foundation for advanced work in probability and statistics should consider substituting W3105, W3107, W3315, and W4606. • Students may, with permission of the Director of Undergraduate Studies in Statistics, substitute for courses. Students may count up to two courses toward both the Statistics minor and another Engineering major.

engineering 2014–2015 Interdisciplinary Courses and Courses in Other Divisions of the University 200 Interdisciplinary Engineering Courses

f the following courses, telephony, radio, and computer communications. CHEN E4020x Protection of industrial and some may be requirements The coverage includes both the technologies intellectual property for degree programs, and themselves and the historical events that shaped, 3 pts. Lect: 3. Professor Pearlman. O and in turn were shaped by, the technologies. To expose engineers, scientists, and technology others may be taken as electives. See The historical development, both the general managers to areas of the law they are most likely your departmental program of study context and the particular events concerning to be in contact with during their career. Principles or consult with an adviser for more communications, is presented chronologically. The are illustrated with various case studies together information. social needs that elicited new technologies and with active student participation. the consequences of their adoption are examined. ENGI E1102x and y The art of engineering Throughout the course, relevant scientific and IEOR E4998x and y Managing technological 4 pts. Lect: 4. Professor Vallancourt. engineering principles are explained as needed. innovation and entrepreneurship Core requirement for all entering SEAS students. These include, among others, the concept and 3 pts. Lect: 3. Members of the faculty. This course is a bridge between the science- effective use of spectrum, multiplexing to improve Focus on the management and consequences of oriented, high school way of thinking and the capacity, digital coding, and networking principles. technology-based innovation. Explores how new engineering point of view. Fundamental concepts There are no prerequisites, and no prior scientific industries are created, how existing industries of math and science are reviewed and re-framed in or engineering knowledge is required. Engineering can be transformed by new technologies, the an engineering context, with numerous examples students may not count this course as a technical linkages between technological development of each concept drawn from all disciplines of elective. and the creation of wealth, and the management engineering represented at Columbia. Non- challenges of pursuing strategic innovation. technical issues of importance in professional engineering practice such as ethics, engineering project management, and societal impact are addressed. Lab fee: $350. IEOR E2261x and y Introduction to accounting and finance 3 pts. Lect: 3. Professor Webster. Prerequisite: ECON W1105. For undergraduates only. This course examines the fundamental concepts of financial accounting and finance, from the perspective of both managers and investors. Key topics covered include: principles of accrual accounting; recognizing and recording accounting transactions; preparation and analysis of financial statements, including balance sheets, income statements, cash flow statements, and statements of owners’ equity; ratio analysis; pro-forma projections; time value of money (present values, future values, and interest/discount rates); inflation; discounted-cash-flow (DCF) project evaluation methods; deterministic and probabilistic measures of risk; capital budgeting. The course is targeted toward students pursuing careers in engineering, economics, finance, or business. EEHS E3900y History of telecommunications: from the telegraph to the internet 3 pts. Lect: 3. Historical development of telecommunications from the telegraphy of the mid-1800s to the Internet at present. Included are the technologies of

engineering 2014–2015 Courses in Other Divisions of the University 201

his listing of courses has been BIOC C3501 Biochemistry: structure and Chemistry selected with specific engineering metabolism Placement Exam program requirements in mind. 4 pts. Professor Stockwell. T Prerequisites: BIOL W2001 or C2005 and one For information on these courses All students must take the placement year of organic chemistry. Lecture and recitation. and additional courses offered by exam during Orientation week. The Students wishing to cover the full range of results of the placement exam are these departments, please consult modern biochemistry should take both BIOC used to advise students which track to the bulletins of Columbia College, the C3501 and C3512. C3501 covers subject matters pursue. School of Continuing Education, the in modern biochemistry, including chemical School of General Studies, and the biology and structural biology, discussing the Graduate School of Arts and Sciences. structure and function of both proteins and small Courses of Instruction molecules in biological systems. Proteins are the Pre-engineering students should primary class of biological macromolecules and refer to the First Year–Sophomore Biological Sciences serve to carry out most cellular functions. Small Program to determine the chemistry organic molecules function in energy production BIOL C2005x Introductory biology, I: and creating building blocks for the components requirements for admission to particular biochemistry, genetics, and molecular biology of cells and can also be used to perturb the Junior-Senior Programs. Special 4 pts. Professors Chasin and Mowshowitz. functions of proteins directly. The first half of the attention should be given to the Prerequisite: one year of college chemistry, or a course covers protein structure, enzyme kinetics requirements for admission to chemical strong high school chemistry background. Lecture and enzyme mechanism. The second half of the engineering, biomedical engineering, and recitation. Recommended as the introductory course explores how small molecules are used materials science and metallurgical biology course for biology and related majors, and endogenously by living systems in metabolic for premedical students. Fundamental principles engineering, and other related fields. and catabolic pathways; this part of the course of biochemistry, molecular biology, and genetics. focuses on mechanistic organic chemistry Website: columbia.edu/cu/biology/courses/c2005 involved in metabolic pathways. Laboratory Fee BIOL C2006y Introductory biology, II: cell The laboratory fee covers the cost of biology, development, and physiology nonreturnable items, chemicals, and Business 4 pts. Professor Mowshowitz. reasonable breakage. In addition, Prerequisite: EEEB W2001 or BIOL C2005, or BUSI W3021x and y Marketing management students may be charged for lab the instructor’s permission. Lecture and recitation. 3 pts. Lect: 3. Professors Jedidi, Jerath, and handouts and excessive breakage, for Recommended second term of biology for majors Kivetz cleaning of equipment returned dirty, in biology and related majors, and for premedical Designed to provide students with an students. Cellular biology and development; and for checking out late. understanding of the fundamental marketing physiology of cells and organisms. Website: concepts and their application by business CHEM C1403x-C1404y General chemistry columbia.edu/cu/biology/courses/c2006 and non-business organizations. The goal 3.5 pts. Lect: 3.5. Members of the faculty. BIOL W2501x or y Contemporary biology is to expose students to these concepts as Prerequisites: Concurrent registration in MATH laboratory they are used in a wide variety of settings, V1101; for C1404: CHEM C1403 or W1403. 3 pts. Professor Hazen. including consumer goods firms, manufacturing Preparation equivalent to one year of high school Strongly recommended prerequisite or corequisite: and service industries, and small and large chemistry is assumed, and concurrent registration BIOL C2005 or F2401. Experiments focus on businesses. The course gives an overview in Calculus I. Students lacking such preparation genetics and molecular biology, with an emphasis of marketing strategy issues, elements of a should plan independent study of chemistry over the on data analysis and experimental techniques. market (company, customers, and competition), summer or take CHEM W0001 before taking C1403. Topics include stoichiometry, states of matter, The class also includes a study of mammalian as well as the fundamental elements of the chemical equilibria, acids and bases, chemical anatomy and histology. Each section is limited to marketing mix (product, price, placement/ thermodynamics, nuclear properties, electronic 28 students. Lab fee: $150. distribution, and promotion). structures of atoms, periodic properties, chemical bonding, molecular geometry, introduction to organic and biological chemistry, solid state and materials science, polymer science and macromolecular

engineering 2014–2015 202 structures, chemical kinetics, coordination chemistry, CHEM C3071y Introduction to inorganic include stereochemistry, reactions of organic and electrochemistry. Although C1403 and C1404 chemistry molecules, mechanisms of organic reactions, are separate courses, students are expected to take 3 pts. Lect: 3. Professor Owen. syntheses and degradations of organic molecules, both terms sequentially. The order of presentation of Corequisite: CHEM C3444 or C3046. Principles and spectroscopic techniques of structure topics may differ from the order presented here, and governing the structure and reactivity of inorganic determination. Recitation section required. from year to year. Recitation section required. compounds surveyed from experimental and CHEM W3543x or y Organic chemistry theoretical viewpoints. Topics include inorganic CHEM W1500x or y General chemistry laboratory solids, aqueous and nonaqueous solutions, the laboratory 3 pts. Lab: 3. Professors Ghurbanyan and chemistry of selected main group elements, 3 pts. Lab: 3. Professors Hansen and Ulichny. Sedbrook. transition metal chemistry, metal clusters, metal Corequisite: CHEM C1403 or W1403. Lab Prerequisite: CHEM W1500. Corequisite: CHEM carbolyls, and organometallic chemistry. Recitation fee: $140. An introduction to basic techniques C3443 or W3343. Lab fee: $125. Students section required. of modern experimental chemistry, including planning to take a full year of laboratory should quantitative procedures and chemical analysis. A CHEM C3079x-C3080y Physical chemistry, I enroll in CHEM W3543 and W3546. Techniques of lab lecture section is also required for this course and II experimental organic chemistry, with emphasis on (W1501). 4 pts. Professors Berne and Cacciuto. understanding fundamental principles underlying Prerequisites: CHEM C1403 and C1404, or C1604, the experiments in methodology of solving CHEM C1604x Second semester general or C3045 and C3046; PHYS V1201-V1202 is laboratory problems involving organic molecules. chemistry (intensive) acceptable, PHYS C1401-C1402 is recommended, 3.5 pts. Professor Brus. CHEM W3545x Intensive organic chemistry or the equivalent; and MATH V1101-V1102 or Prerequisite: A grade of “B” or better in CHEM laboratory V1207-V1208. Recommended corequisite: CHEM C1403 or W1403 or acceptable performance on 3 pts. Lab: 3. Professor Ng. C3085-C3086. Elementary but comprehensive the Department placement exam. Corequisite: Prerequisites: CHEM C3045 and C3046 and treatment of the fundamental laws governing the Calculus II. Topics include gases (kinetic W2507. Lab fee: $125. The course covers the behavior of individual atoms and molecules and theory of gases); binary collision model for same material as CHEM W3543, but is intended collections of them. C3079: The thermodynamics of chemical reactions; chemical kinetics; acid-base for those students who have taken Intensive chemical systems at equilibrium and the chemical equilibria; thermochemistry (Thermodynamics Organic Chemistry for First-Year Students, CHEM kinetics of nonequilibrium systems. C3080: The I); spontaneous processes (Thermodynamics quantum mechanics of atoms and molecules, the C3045-C3046. II); chemical bonding in polyatomic molecules. quantum statistical mechanics of chemical systems, Recitation section required. CHEM W3546y Advanced organic chemistry and the connection of statistical mechanics to laboratory CHEM W2507x or y Intensive general thermodynamics. Recitation section required. 3 pts. Lab: 3. Professor Ng. chemistry laboratory CHEM C3085x-C3086y Physical and analytical Prerequisite: CHEM W3543 or W3545. Corequisite: 3 pts. Lab: 3. Professor Avila. chemistry laboratory CHEM C3444 or W3444. Lab fee: $125. A project Prerequisite: CHEM C1604 or C3045. Lab fee: 4 pts. Lab: 4. Professor Avila. laboratory with emphasis on complex synthesis $140. An introduction to basic techniques and Prerequisite: CHEM C3085 is prerequisite for and advanced techniques including qualitative practices of modern experimental chemistry, C3086. Corequisites: CHEM C3079 for CHEM organic analysis and instrumentation. including qualitative procedures and chemical C3085 and C3080 for C3080. Fee: $125 per term. analysis. This course differs from CHEM W1500 Techniques of experimental physical chemistry in its emphasis on instrumentation and methods. Earth and Environmental and instrumental analysis, including infrared Students must also attend the compulsory Sciences and ultraviolet spectrophotometry, magnetic mentoring session. Please check the Directory of resonance, electroanalytical methods, calorimetry, Undergraduates in the four-year course Classes for details. reaction kinetics, hydrodynamic methods, and of study in the School of Engineering CHEM C3045x-C3046y Intensive organic applications of digital computers to the analysis of and Applied Science may take courses chemistry for first-year students (lecture) experimental data. numbered up to 4999 but may enter 3.5 pts. Professors Breslow and Leighton. CHEM C3098x or y Supervised independent courses of higher numbers only if Prerequisites: A grade of 5 on the Chemistry research Advanced Placement exam and an acceptable 4 pts. Lab: 4. Professor Gasperov. (1) the course is expressly included in grade on the Department placement exam. Not Prerequisite: Permission of the professor in charge the prescribed curriculum or open to students who have taken other courses for entrance and permission of the departmental in college-level chemistry. Premedical students (2) special permission is obtained representative for aggregate points in excess may take CHEM C3045, C3046, and C3545 to from the Department of Earth and of 12 or less than 4. Laboratory fee: $105 per meet the minimum requirements for admission Environmental Sciences. term. This course may be repeated for credit (see to medical school. This course covers the major and concentration requirements). Individual same material as CHEM C3443-C3444, but research under the supervision of a member of the is intended for students who have learned EESC V1011x Earth: origin, evolution, staff. Research areas include organic, physical, the principles of general chemistry in high processes, future inorganic, analytical, and biological chemistry. school. The level of instruction is appropriate 4 pts. Lect: 3. Lab: 1. Professor Tolstoy. for those who have not had a college course CHEM C3443x-C3444y Organic chemistry Students who wish to take only the lectures should in general chemistry. Students enrolled in (lecture) register for V1411. What is the nature of our CHEM C3045-C3046 are expected to enroll 3.5 pts. Professors Campos, Cornish, and planet and how did it form? From geochemical concurrently in CHEM W2507. Recitation Nuckolls. and geophysical perspectives we explore section required. Prerequisites: CHEM C1404 or W1404 or Earth’s internal structure, its dynamical character C1604, and C1500 or W1500. The principles of expressed in plate tectonics, and ask if its future organic chemistry. The structure and reactivity behavior can be known. Students who wish to take of organic molecules are examined from the only the lectures should register for V1411. standpoint of modern theories of chemistry. Topics

engineering 2014–2015 EESC V1030x Oceanography and technology arise in current debates on WMD. EESC W4113x Introduction to mineralogy 203 3 pts. Lect: 3. Professor Hoenisch. What aspects of the manufacture of WMD are 4 pts. Not offered in 2014–2015. Explore the geology of the sea floor, understand easily addressed, and what aspects are technically Prerequisites: introductory geology or the what drives ocean currents and how ocean challenging? It may be expected that current equivalent, elementary college physics and ecosystems operate. Case studies and discussions events/headlines will be discussed in class. chemistry, or the instructor’s permission. centered on ocean-related issues facing society. Elementary crystallography and crystal structures, EESC W4001x Advanced general geology optical properties of minerals, mineral associations, EESC V1201y Environmental risks and 4 pts. Lect: 3. Lab: 1. Professor Anders. economic minerals. Laboratory: identification disasters Prerequisites: one term of college-level calculus, of minerals in hand specimens and use of the 3 pts. Lect: 3. Professor Ekstrom. physics, and chemistry. A concentrated introduction petrographic microscope. Lab required. Prerequisites: high school science and math. to the solid Earth, its interior, and near-surface First-years and sophomores will have priority. geology. Intended for students with good EESC W4230y Crustal deformation An introduction to risks and hazards in the backgrounds in the physical sciences but none in 3 pts. Lect: 3. Professors Anders and Scholz. environment. Different types of hazards are geology. Laboratory and field trips. Prerequisites: introductory geology and one year of analyzed and compared: natural disasters, such calculus. Recommended preparation: higher levels as tornados, earthquakes, and meteorite impacts; EESC W4008x Introduction to atmospheric of mathematics. Introduction to the deformation acute and chronic health effects caused by science processes in the Earth’s crust. Fundamental exposure to radiation and toxic substances such 3 pts. Lect: 3. Professor Polvani. theories of stress and strain; rock behavior as radon, asbestos, and arsenic; long-term societal Prerequisites: advanced calculus and general in both brittle and ductile fields; earthquake effects due to environmental change, such as physics, or the instructor’s permission. Basic processes; ductile deformation; large-scale crustal sea level rise and global warming. Emphasizes physical processes controlling atmospheric contractional and extensional events. the basic physical principles controlling the structure: thermodynamics; radiation physics EESC W4300x The Earth’s deep interior hazardous phenomena and develops simple and radiative transfer; principles of atmospheric dynamics; cloud processes; applications to Earth’s 3 pts. Lect: 3. Offered in alternate years. Not quantitative methods for making scientifically offered in 2014–2015. reasoned assessments of the threats (to health atmospheric general circulation, climatic variations, and the atmospheres of the other planets. Prerequisites: calculus, differential equations, one and wealth) posed by various events, processes, year of college physics, and EESC W4950 or its and exposures. Discusses methods of risk EESC W4009x. Chemical geology equivalent. An introduction to properties of the mitigation and sociological, psychological, and 4 pts. Offered in alternate years. Not offered in Earth’s mantle, fluid outer core, and solid inner economic aspects of risk control and management. 2014–2015. core. Current knowledge of these features is Discussion section required. Prerequisite: physical chemistry or the instructor’s explored, using observations of seismology, heat permission. Thermodynamics as applied to earth EESC V1600x Earth resources and flow, gravity, and geomagnetism, plus information systems. sustainable development on the Earth’s bulk composition. 3 pts. Lect: 3. Professor Kelemen. EESC W4050x Global assessment and EESC W4600x Earth resources and Prerequisites: none. High school chemistry monitoring using remote sensing sustainable development recommended. Survey of the origin and extent 3 pts. Professor Small. 3 pts. Lect: 3. Professor Kelemen. of mineral resources, fossil fuels, and industrial Prerequisite: Calculus I and Physics I and II. Prerequisites: none. High school chemistry materials, that are non-renewable, finite Enrollment limited to 24 students. General recommended. Survey of the origin and extent resources, and the environmental consequences introduction to fundamentals of remote sensing and of mineral resources, fossil fuels, and industrial of their extraction and use, using the textbook image analysis. Example applications in the Earth materials, that are nonrenewable, finite resources, Earth Resources and the Environment, by James and environmental sciences are explored through and the environmental consequences of their Craig, David Vaughan and Brian Skinner. This the analysis of remote sensing imagery in a state-of- extraction and use, using the textbook Earth course provides an overview but includes focus the-art visualization laboratory. Lab required. Resources and the Environment, by James Craig, on topics of current societal relevance, including David Vaughan and Brian Skinner. This course EESC W4076y Geologic mapping provides an overview, but includes focus on topics estimated reserves and extraction costs for 3 pts. Lect: 3. Professor Anders. of current societal relevance, including estimated fossil fuels, geological storage of CO2, sources Prerequisite: Permission of instructor. Fieldwork reserves and extraction costs for fossil fuels, and disposal methods for nuclear energy fuels, on weekends in April and two weeks in mid-May, geological storage of CO2, sources and disposal sources and future for luxury goods such as gold immediately following the end of examinations. methods for nuclear energy fuels, sources and future and diamonds, and special, rare materials used in Enrollment limited. Estimated expense: $250. The for luxury goods such as gold and diamonds, and consumer electronics (e.g., “Coltan,” mostly from principles and practices of deciphering geologic special, rare materials used in consumer electronics Congo) and in newly emerging technologies such history through the observation of rocks in the (e.g., “Coltan,” mostly from Congo) and in newly as superconducting magnets and rechargeable field, mapmaking, construction of geological cross- emerging technologies such as superconducting batteries (e.g., heavy rare earth elements, mostly sections, and short written reports. Please be magnets and rechargeable batteries (e.g., heavy rare from China). Guest lectures from economists, advised: graduating undergraduate seniors may earth elements, mostly from China). Guest lectures commodity traders and resource geologists will have to miss graduation. provide “real world” input. Discussion session from economists, commodity traders and resource required. EESC W4085x Geodynamics geologists will provide “real world” input. Required 3 pts. Lect: 3. Offered in alternate years. Not recitation session. EESC W3018y Weapons of mass destruction offered in 2014–2015. EESC W4701y Introduction to igneous 3 pts. Lect: 3. Not offered in 2014–2015. Prerequisites: calculus, differential equations, Prerequisites: high school science and math. introductory physics. An introduction to how the petrology A review of the history and environmental Earth and planets work. The focus is on physical 4 pts. Offered in alternate years. Not offered in consequences of nuclear, chemical, and biological processes that control plate tectonics and the 2014–2015. weapons of mass destruction (WMD); of how evolution of planetary interiors and surfaces; Prerequisite: introductory geology or the equivalent. Recommended preparation: EESC these weapons work, what they cost, how they analytical descriptions of these processes; weekly W4113 and knowledge of chemistry. Compositional have spread, how they might be used, how they physical model demonstrations. characteristics of igneous and metamorphic rocks are currently controlled by international treaties and how they can be used as tools to investigate and domestic legislation, and what issues of policy

engineering 2014–2015 204 earth processes. Development of igneous and water and air. Overview of the stratification and Why such an economy has fluctuations and how metamorphic rocks in a plate-tectonic framework. circulation of Earth’s oceans and atmosphere and they may be controlled. Recitation section required. their governing processes; ocean-atmosphere EESC W4885y The chemistry of continental interaction; resultant climate system; natural and ENGL C1010x or y University writing waters anthropogenic forced climate change. 3 pts. Members of the faculty. 3 pts. Lect: 3. Not offered in 2014–2015. Teaches general techniques and strategies for Recommended preparation: a solid background in EESC W4947y Plate tectonics academic reading and writing. Students read and basic chemistry. Introduction to geochemical cycles 3 pts. Lect: 3. Professor Abers. discuss a range of published essays, complete involving the atmosphere, land, and biosphere; Prerequisite: A course in solid earth geology or regular reading and writing exercises, write several chemistry of precipitation, weathering reactions, geophysics. Prepares students for research and oral longer essays, and undertake a collaborative rivers, lakes, estuaries, and groundwaters; exams with cross-disciplinary analysis of the plate- research and writing project designed by the class. students are introduced to the use of major and tectonic cycle. Driving forces and mantle convection, Students placed in C1010 whose names fall in the minor ions as tracers of chemical reactions and plate kinematics, magmatism, structure, thermal first part of the alphabet must take the course in biological processes that regulate the chemical and chemical evolution of mid-ocean ridges and the fall. Students whose names fall in the second composition of continental waters. subduction zones, continental rifts and collisions, part of the alphabet take the course in the spring. and hot spots. Includes literature readings of great The alphabet will be split somewhere between K EESC W4924y Introduction to atmospheric debates, and emphasizes integration of geophysical, chemistry and O. The exact place for the split will be posted geological and geochemical observations and before fall registration. 3 pts. Lect: 3. Professor Fiore. processes. Prerequisites: PHYS V1201, CHEM C1403, Global Core Calculus III, or equivalent or instructor’s EESC W4949x Introduction to seismology The Global Core requirement asks students to permission. EESC V2100 preferred. Physical and 3 pts. Lect: 3. Professor Waldhauser. engage directly with the variety of civilizations and chemical processes determining atmospheric Prerequisites: Solid Earth dynamics (V3201 or the diversity of traditions that, along with the West, equivalent), differential equations (APMA E3102, composition and the implications for climate and have formed the world and continue to interact in it E4200, or equivalent). Methods and underpinnings regional air pollution. Atmospheric evolution and today. Courses in the Global Core typically explore human influence; basics of greenhouse effect, of seismology including seismogram analysis, the cultures of Africa, Asia, the Americas, and the photolysis, reaction kinetics; atmospheric transport elastic wafe propogation theory, earthquake sourde Middle East in an historical context. These courses of trace species; stratospheric ozone chemistry; characterization, instrumentation, inversion of are organized around a set of primary materials tropospheric hydrocarbon chemistry; oxidizing seismic data to infer Earth structure. produced in these traditions and may draw from power, nitrogen, oxygen, sulfur, carbon, mercury texts or other forms of media, as well as from oral cycles; chemistry-climate-biosphere interactions; sources or performance. Global Core courses fall aerosols, smog, acid rain. Discussion section Humanities and Social into two categories: those that focus on a specific required. Sciences culture or civilization, tracing its existence across EESC W4925x Principles of physical For listings of additional courses of a significant span of time; and those that address oceanography interest to engineering students, consult a common theme or set of analytic questions 3 pts. Lect: 3. Professors Abernathey and the bulletins of Columbia College; the comparatively (and may include Europe and the Gordon. School of General Studies; the Graduate West). Recommended preparation: a solid background School of Architecture, Planning, and in mathematics, physics, and chemistry. Physical HUMA C1001x-C1002y Masterpieces of Preservation; the Graduate School of Western literature and philosophy properties of seawater, water masses and their Business; and the Graduate School of distribution, sea-air interaction influence on the ocean 4 pts. Lect: 4. Instructor to be announced. Arts and Sciences. structure, basic ocean circulation pattern, relation of Taught by members of the Departments of Classics, English and Comparative Literature, diffusion and advection with respect to distribution COCI C1101x-C1102y Introduction to French, German, Italian, Middle East and Asian of ocean properties, ocean tides and waves, contemporary civilization in the West Languages and Cultures, Philosophy, Religion, turbulence, and introduction to ocean dynamics. 4 pts. Lect: 4. Members of the faculty. Slavic Languages, and Spanish; and members of Taught by members of the Departments of EESC W4926y Principles of chemical the Society of Fellows in the Humanities. Major Anthropology, Classics, English and Comparative oceanography works by over twenty authors, ranging in time, Literature, French, German, History, Middle East 3 pts. Lect: 3. Instructor to be announced. theme, and genre from Homer to Virginia Woolf. and Asian Languages and Cultures, Philosophy, Prerequisites: Instructor’s permission for students Students are expected to write at least two papers, Political Science, Religion, Slavic Languages, without one year of chemistry. Course open to complete two examinations each semester, and and Sociology; and members of the Society of to undergraduates with one year of chemistry. to participate actively in class discussions. Recommended preparation: a solid background Fellows. A study in their historical context of major in mathematics, physics, and chemistry. Factors contributions to the intellectual traditions that HUMA W1121x or y Masterpieces of controlling the concentration and distribution underpin contemporary civilization. Emphasis is Western art of dissolved chemical species within the sea. on the history of political, social, and philosophical 3 pts. Lect: 3. Instructor to be announced. Application of tracer and natural radioisotope thought. Students are expected to write at least Discussion and analysis of the artistic qualities methods to large-scale mixing of the ocean, the three papers to complete two examinations, and to and significance of selected works of painting, geological record preserved in marine sediments, participate actively in class discussions. sculpture, and architecture from the Parthenon in the role of ocean processes in the global carbon Athens to works of the 20th century. ECON W1105x and y Principles of economics cycle, and biogeochemical processes influencing 4 pts. Professors Gulati, Musatti, Salanie, and the distribution and fate of elements in the ocean. HUMA W1123x or y Masterpieces of Zaniboni. Western music EESC W4930y Earth’s oceans and Corequisites: ECON W1155 recitation section 3 pts. Lect: 3. Instructor to be announced. atmosphere with the same instructor. How a market economy Popularly known as “Music Hum,” this course aims 3 pts. Lect: 3. Professor Gordon. determines the relative prices of goods, factors of to instill in students a basic comprehension of the Recommended preparation: a good background production, and the allocation of resources and many forms of the Western musical imagination. in the physical sciences. Physical properties of the circumstances under which it does it efficiently. The course involves students actively in the

engineering 2014–2015 process of critical listening, both in the classroom Placement BC calculus exam. The second term MATH W4041x-W4042y Introduction to 205 and in concerts. Although not a history of Western of this course may not be taken without the first. modern algebra music, the course is taught in chronological Multivariable calculus and linear algebra from a 3 pts. Lect: 3. Professors Deopurkar, Khovano, format and includes masterpieces by Josquin rigorous point of view. and Neumann. des Prez, Monteverdi, Bach, Handel, Mozart, The second term of this course may not be MATH E1210x or y Ordinary differential Haydn, Beethoven, Verdi, Wagner, Schoenberg, taken without the first. Prerequisites: MATH equations Stravinsky, Louis Armstrong, and Duke Ellington, V1102-V1202 and V2010 or equivalent. 3 pts. Lect: 3. Professors Chang, Chen, and among others. Groups, homomorphisms, rings, ideals, fields, Savin. polynominals, and field extensions, Galois theory. Prerequisite: MATH V1201 or the equivalent. Mathematics Special differential equations of order one. Linear MATH W4061x-W4062y Introduction to differential equations with constant and variable modern analysis Courses for First-Year Students coefficients. Systems of such equations. Transform 3 pts. Lect: 3. Professors Gallagher and Zhang. Depending on the program, completion and series solution techniques. Emphasis on The second term of this course may not be taken of Calculus III or IV satisfies the basic applications. without the first. Prerequisite: MATH V1202 or equivalent and V2010. Real numbers, metric mathematics requirement. Normally MATH V2010 x or y Linear algebra spaces, elements of general topology. Continuous students who have taken an AP Calculus 3 pts. Lect: 3. Professors Bayer, Maulik, and and differentiable functions. Implicit functions. course begin with either Calculus II or Stein. Integration, change of variables. Function spaces. Calculus III. Refer to the AP guidelines Prerequisite: MATH V1201 or equivalent. Matrices, on page 14 for placement information. vector spaces, linear transformations, eigenvalues MATH W4065x Honors complex variables The sequence ends with MATH E1210: and eigenvectors, canonical forms, applications. 3 pts. Lect: 3. Professor Urban. Prerequisite: MATH V1207 and V1208, or W4061. Ordinary differential equations. MATH V2500x or y Analysis and optimization A theoretical introduction to analytic functions. Students who wish to transfer 3 pts. Lect: 3. Professors Dubedat, Hongler, and Holomorphic functions, harmonic functions, power Pinkham. from one calculus course to another series, Cauchy-Riemann equations, Cauchy’s Prerequisites: MATH V1102-V1201 or equivalent, are allowed to do so beyond the date integral formula, poles, Laurent series, residue and V2010. Mathematical methods for economics. specified on the Academic Calendar. theorem. Other topics as time permits: elliptic Quadratic forms, Hessian, implicit functions. They are considered to be adjusting functions, the gamma and zeta functions, the Convex sets, convex functions. Optimization, Riemann mapping theorem, Riemann surfaces, their level, not changing their program. constrained optimization, Kuhn-Tucker conditions. Nevanlinna theory. They must, however, obtain the approval Elements of the calculus of variations and optimal of the new instructor and the Center for control. Student Advising before reporting to the MATH V3007y Complex variables Physics Registrar. 3 pts. Lect: 3. Professor Gallagher. The general four-term preengineering MATH V1101x or y Calculus, I Prerequisite: MATH V1202. An elementary course physics sequence consists of PHYS 3pts. Lect: 3. in functions of a complex variable. Fundamental C1401, C1402, C1403, and C1494 Functions, limits, derivatives, introduction to properties of the complex numbers, differentiability, (laboratory); or PHYS C1601, C1602, integrals. Cauchy-Riemann equations, Cauchy integral C2601, and C2699 (laboratory). theorem, Taylor and Laurent series, poles, and MATH V1102x or y Calculus, II essential singularities. Residue theorem and PHYS C1401x Introduction to mechanics and 3 pts. Lect: 3. conformal mapping. thermodynamics Prerequisite: MATH V1101 or equivalent. Methods 3 pts. Lect: 2.5. Professors Hughes and MATH V3027x Ordinary differential equations of integration, applications of integral, Taylor’s Zelevinsky. 3 pts. Lect: 3. Professor Daskalopoulos. theorem, infinite series. Corequisite: MATH V1101 or equivalent. Prerequisite: MATH V1201 or equivalent. Fundamental laws of mechanics, kinematics and MATH V1201x or y Calculus, III Corequisite: MATH V2010. Equations of order dynamics, work and energy, rotational dynamics, 3 pts. Lect: 3. one, systems of linear equations, second-order oscillations, gravitation, fluids, temperature Prerequisite: MATH V1101 with a grade of B equations, series solutions at regular and singular and heat, gas laws, first and second laws of or better or V1102 or equivalent. Vectors in points, boundary value problems, selected thermodynamics. dimensions 2 and 3, complex numbers and the applications. complex exponential function with applications to PHYS C1402y Introduction to electricity, MATH V3028y Partial differential equations differential equations, Cramer’s rule, vector-valued magnetism, and optics 3 pts. Lect: 3. Professor Daskalopoulos. functions of one variable, scalar-valued functions 3 pts. Lect: 2.5. Members of the faculty. Prerequisite: MATH V3027 and V2010 or of several variables, partial derivatives, gradients, Prerequisite: PHYS C1401. Corequisite: MATH equivalent. Introduction to partial differential surfaces, optimization, the method of Lagrange V1102 or equivalent. Electric fields, direct equations. First-order equations. Linear second- multipliers. currents, magnetic fields, alternating currents, order equations, separation of variables, solution electromagnetic waves, polarization, geometrical MATH V1202x or y Calculus, IV by series expansions. Boundary value problems. 3 pts. Lect: 3. optics, interference and diffraction. MATH W4032x Fourier analysis Prerequisite: MATH V1102, V1201, or equivalent. PHYS C1403x Introduction to classical and 3 pts. Lect: 3. Professor Hongler. Multiple integrals, Taylor’s formula in several quantum waves Prerequisites: three terms of calculus and linear variables, line and surface integrals, calculus of 3 pts. Lect: 2.5. Professor Brooijmans. algebra or four terms of calculus. Fourier series vector fields, Fourier series. Prerequisite: PHYS C1402. Corequisite: MATH and integrals, discrete analogues, inversion V1201 or equivalent. Classical waves and the MATH V1207x-V1208y Honors math A-B and Poisson summation, formulae, convolution, wave equation, Fourier series and integrals, normal 4 pts. Lect and recit. Professors Gallagher and Heisenberg uncertainty principle. Stress on the modes, wave-particle duality, the uncertainty Wang. application of Fourier analysis to a wide range of principle, basic principles of quantum mechanics, Prerequisite: Score of 5 on the Advanced disciplines.

engineering 2014–2015 206 energy levels, reflection and transmission Experiments in mechanics, thermodynamics, PHYS W3081x or y Intermediate laboratory coefficients, applications to atomic physics. electricity, magnetism, optics, wave motion, atomic work and nuclear physics. 2 pts. Lab: 2. Members of the faculty. PHYS C1493x Introduction to experimental Prerequisite: PHYS C2601 or C2802. Primarily physics PHYS C2801x-C2802y Accelerated physics, for junior and senior physics majors. Other 3 pts. Lab: 3. Instructor to be announced. I and II majors require the instructor’s permission. May Prerequisites: PHYS C1401 and C1402. 4.5 pts. Lect: 3.5. Rec: 1 hour weekly to be be repeated for credit by performing different Laboratory work associated with the two arranged. Professor Cole. experiments. The laboratory has 15 individual prerequisite lecture courses. Experiments Prerequisite: Advanced placement in physics experiments available, of which two are required in mechanics, thermodynamics, electricity, and mathematics, or equivalent, and instructor’s per 2 points. Each experiment is chosen by magnetism, optics, wave motion, atomic and permission. (A special placement meeting is the student in consultation with the instructor. nuclear physics. (Students cannot receive credit for held during Orientation.) This accelerated two- Each section meets one afternoon per week, both PHYS C1493 and C1494.) semester sequence covers the subject matter of with registration in each section limited by the PHYS C1601, C1602, and C2601 and is intended PHYS C1494y Introduction to experimental laboratory capacity. Experiments (classical and for students who have an exceptionally strong physics modern) cover topics in electricity, magnetism, background in both physics and mathematics. The 3 pts. Lab: 3. Professor Veicht. optics, atomic physics, and nuclear physics. Prerequisites: PHYS C1401 and C1402. course is preparatory for advanced work in physics Laboratory work associated with the two and related fields. There is no accompanying PHYS W3083y Electronics laboratory prerequisite lecture courses. Experiments laboratory; however, students are encouraged to 3 pts. Lab: 3. Professor Parsons. in mechanics, thermodynamics, electricity, take the intermediate laboratory, PHYS W3081, in Registration is limited to the capacity of the magnetism, optics, wave motion, atomic and the following year. laboratory. Corequisite or prerequisite: PHYS nuclear physics. (Students cannot receive credit for W3003 or W3007. A sequence of experiments in PHYS W3002y From quarks to the cosmos: solid-state electronics, with introductory lectures. both PHYS C1493 and C1494.) applications of modern physics PHYS C1601x Physics, I: mechanics and 3.5 pts. Lect: 3.5. Not offered in 2014–2015. PHYS G4003y Advanced mechanics relativity Prerequisite: PHYS C2601 or C2802. This course 3 pts. Lect: 2.5. Professor Rosen. Prerequisites: Differential and integral calculus, 3.5 pts. Lect: 2.5. Professor Dodd. reinforces basic ideas of modern physics through differential equations, and PHYS W3003 or Corequisite: MATH V1102 or equivalent. applications to nuclear physics, high-energy equivalent. Lagrange’s formulation of mechanics, Fundamental laws of mechanics, kinematics and physics, astrophysics, and cosmology. The calculus of variations and the Action Principle, dynamics, work and energy, rotational dynamics, ongoing Columbia research programs in these Hamilton’s formulation of mechanics, rigid body oscillations, gravitation, fluids, introduction to fields are used as practical examples. The course motion, Euler angles, continuum mechanics, is preparatory for advanced work in physics and special relativity and relativistic kinematics. The Introduction to chaotic dynamics. course is preparatory for advanced work in physics related fields. PHYS G4018y Solid-state physics and related fields. PHYS W3003x Mechanics 3 pts. Lect: 2.5. Professors Pinczuk and Uemura. 3 pts. Lect: 2.5. Professor Millis. PHYS C1602y Physics, II: thermodynamics, Prerequisites: PHYS G4021 and G4023, or Prerequisites: General physics; differential electricity, and magnetism equivalent. Introduction to solid-state physics: and integral calculus. Newtonian mechanics, 3.5 pts. Lect: 2.5. Professors Dodd and Zajc. crystal structures, properties of periodic lattices, Prerequisite: PHYS C1601. Corequisite: oscillations and resonance, conservative forces electrons in metals, band structure, transport MATH V1201 or equivalent. Temperature and and potential energy, central forces, noninertial properties, semiconductors, magnetism, and heat, gas laws, the first and second laws of frames of reference, rigid body motion, an superconductivity. thermodynamics, kinetic theory of gases, introduction to Lagrange’s formulation of electric fields, direct currents, magnetic fields, mechanics, coupled oscillators, and normal modes. PHYS G4019x Mathematical methods of physics alternating currents, electromagnetic waves. PHYS W3007y Electricity and magnetism The course Is preparatory for advanced work in 3 pts. Lect: 3. Professor Nicolis. 3 pts. Lect: 2.5. Professor Pasupathy. Prerequisites: Differential and integral calculus; physics and related fields. Prerequisite: General physics; differential linear algebra; PHYS W3003 and W3007 or PHYS C2601x Physics, III: classical and and integral calculus. Electrostatics and instructor’s permission. Presents a wide variety quantum waves magnetostatics, Laplace’s equation and boundary- of mathematical ideas and techniques used in 3.5 pts. Lect: 2.5. Professor Hailey. value problems, multipole expansions, dielectric the study of physical systems. Topics include: Prerequisite: PHYS C1602 or C1402. Corequisite: and magnetic materials, Faraday’s law, AC ordinary and partial differential equations, MATH V1202 or equivalent. Classical waves circuits, Maxwell’s equations, Lorentz covariance, generalized functions, integral transforms, Green’s and the wave equation, geometrical optics, and special relativity. functions, nonlinear equations, chaos and solitons, Hilbert space and linear operators, Feynman interference and diffraction, Fourier series and PHYS W3008x Electromagnetic waves and path integrals, Riemannian manifolds, tensor integrals, normal modes, wave-particle duality, optics the uncertainty principle, basic principles of analysis, probability and statistics. Discussion of 3 pts. Lect: 2.5. Professor Metzger. applications to classical mechanics, fluid dynamics, quantum mechanics, energy levels, reflection and Prerequisite: PHYS W3007. Maxwell’s equations transmission coefficients, the harmonic oscillator. electromagnetism, plasma physics, quantum and electromagnetic potentials, the wave mechanics, and general relativity. The course is preparatory for advanced work in equation, propagation of plane waves, reflection physics and related fields. and refraction, geometrical optics, transmission PHYS G4021x-G4022y Quantum mechanics, PHYS C2699y Experiments in classical and lines, wave guides, resonant cavities, radiation, I and II 3 pts. Lect: 2.5. Professor Weinberg. modern physics interference of waves, and diffraction. Prerequisite: PHYS C2601 or C2802, or 3 pts. Lab: 3. Professor Veicht. equivalent. Formulation of quantum mechanics Prerequisites: PHYS C1601 (or C1401), C1602 (or in terms of state vectors and linear operators, C1402), and C2601. Laboratory work associated three-dimensional spherically symmetric potentials, with the three prerequisite lecture courses. theory of angular momentum and spin, time-

engineering 2014–2015 independent and time-dependent perturbation Please note that STAT W3000 STAT W3103x Mathematical methods for 207 theory, scattering theory, and identical particles. has been renumbered as W3105 and statistics Selected phenomena from atomic physics, nuclear STAT W3659 has been renumbered as 6 pts. Professor Mukherjee. physics, and elementary particle physics are Prerequisite: MATH V1101 or instructor’s permission. W3107. For a description of the following described and then interpreted using quantum A fast-paced coverage of those aspects of the mechanical models. course offered jointly by the Departments differential and integral calculus of one and several of Statistics and Industrial Engineering variables and of the linear algebra required for the PHYS G4023x Thermal and statistical physics and Operations Research, see “Industrial core courses in the Statistics major. The mathematical 3 pts. Lect: 2.5. Professor Denef. topics are integrated with an introduction to Prerequisite: PHYS G4021 or equivalent. Engineering and Operations Research.” computing. Students seeking more comprehensive Thermodynamics, kinetic theory, and methods STAT W2024x Applied linear regression background should replace this course with MATH of statistical mechanics; energy and entropy; analysis V1102 and V2010, and any COMS course numbered Boltzmann, Fermi, and Bose distributions; ideal 3 pts. Instructor to be announced. from W1003 to W1009. and real gases; blackbody radiation; chemical Prerequisite: One of STAT W1001, W1111, or equilibrium; phase transitions; ferromagnetism. W1211. Develops critical thinking and data STAT W3105x Introduction to probability 3 pts. Professor Lo. PHYS G4040x Introduction to general analysis skills for regression analysis in science Prerequisites: MATH V1101 and V1102 or relativity and policy settings. Simple and multiple linear equivalent. A calculus-based introduction to 3 pts. Lect: 2.5. Professor Beloborodov. regression, nonlinear and logistic models, probability theory. A quick review of multivariate Prerequisites: PHYS W3003 and W3007, or equiv- random-effects models, penalized regression calculus is provided. Topics covered include alent. Tensor algebra, tensor analysis, introduction methods. Implementation in a statistical package. random variables, conditional probability, to Riemann geometry. Motion of particles, fluid, Optional computer-lab sessions. Emphasis on expectation, independence, Bayes’ rule, important and fields in curved spacetime. Einstein equation. real-world examples and on planning, proposing, distributions, joint distributions, moment generating Schwarzschild solution; test-particle orbits and light implementing, and reporting. functions, central limit theorem, laws of large bending. Introduction to black holes, gravational STAT W2025y Applied statistical methods numbers and Markov’s inequality. waves, and cosmological models. 3 pts. Professors Landwehr and Whalen. Prerequisite: STAT W2024. Classical STAT W3107y Introduction to statistical nonparametric methods, permutation tests; inference Statistics contingency tables, generalized linear models, 3 pts. Professor ElBarmi. Engineering students interested in a missing data, causal inference, multiple Prerequisite: STAT W3105 or W4105, or survey of the mathematical theory of comparisons. Implementation in statistical equivalent. Calculus-based introduction to the probability and statistics should consider software. Emphasis on conducting data analyses theory of statistics. Useful distributions, law of large numbers and central limit theorem, point the pair STAT W3105: Probability theory and reporting the results. Optional weekly estimation, hypothesis testing, confidence W3107: Statistical inference computer-lab sessions. and . Students intervals maximum likelihood, likelihood ratio tests, seeking a quicker overview that focuses STAT W2026x Statistical applications and nonparametric procedures, theory of least squares, more on probability theory should consider case studies and analysis of variance. SIEO W4150. STAT W4109 (6 pts) covers 3 pts. Professor Stodden. STAT W3315x Linear regression models the same material as W3105 and W3107 Prerequisite: STAT W2025. A sample of topics and application areas in applied statistics. 3 pts. Professor Neath. in a single semester. STAT W3315: Topic areas may include Markov processes and Prerequisites: STAT W3107 (or W4150) and STAT Linear regression models takes W3105 queuing theory; meta-analysis of clinical trial W3103 (or MATH V1101, V1102, and V2110). and W3107 as prerequisites; like other research; receiver-operator curves in medical Theory and practice of regression analysis. Simple advanced offerings in statistics, it covers diagnosis; spatial statistics with applications in and multiple regression, testing, estimation, both theory and practical aspects of geology, astronomy, and epidemiology; multiple prediction, and confidence procedures, modeling, regression diagnostics and plots, polynomial modeling and data analysis. comparisons in bio-informatics; causal modeling regression, colinearity and confounding, model STAT W4105, W4107, and W4315 with missing data; statistical methods in genetic epidemiology; stochastic analysis of neural spike selection, geometry of least squares. Extensive are the equivalent of W3105, W3107, train data; graphical models for computer and use of the computer to analyze data. Equivalent to and W3315, respectively; but graduate social network data. STAT W4315 except that enrollment is limited to students may not register for W3105, undergraduate students. W3107, or W3315. STAT W3026x Applied data mining 3 pts. Professor Emir. STAT W3997x and y Independent research Advanced offerings in probability Data mining is a dynamic and fast growing field at 1 pt. Members of the faculty. theory, stochastic processes, and the interface of Statistics and Computer Science. Prerequisite: Permission of a member of the mathematical finance generally take The emergence of massive datasets containing department. May be repeated for credit. This STAT W3105 as a prerequisite; millions or even billions of observations provides course provides a mechanism for students who advanced offerings in statistical theory the primary impetus for the field. Such datasets undertake research with a faculty member from the and methods generally take STAT arise, for instance, in large-scale retailing, Department of Statistics to receive academic credit; students should only register for this course with W4107 and, in several cases, W3315 telecommunications, astronomy, computational and statistical challenges. This course will provide permission of their project mentor. as prerequisites; an exception is STAT an overview of current practice in data mining. SIEO W4150x and y Introduction to W4220: Data mining, which has a Specific topics covered include databases and course in computer programming probability and statistics data warehousing, exploratory data analysis and 3 pts. Members of the faculty. as prerequisite and STAT W3107 as visualization, descriptive modeling, predictive Prerequisites: MATH V1101 and V1102 or corequisite. STAT 4201 is an advanced modeling, pattern and rule discovery, text mining, equivalent. A quick calculus-based tour of the survey of applied statistical methods. Bayesian data mining, and causal inference. The fundamentals of probability theory and statistical use of statistical software will be emphasized. inference. Probabilistic models, random variables,

engineering 2014–2015 208 useful distributions, expectations, laws of large and estimation of yield curves statistical methods response and transfer function. Fourier series, the numbers, central limit theorem, point and confidence for financial time series, value at risk, term fast Fourier transform, autocorrelation function, and interval estimation, hypothesis tests, linear structure models and fixed income research, and spectral density. Univariate Box-Jenkins modeling regression. Students seeking a more thorough estimation and modeling of volatilities. Hands-on and forecasting. Emphasis on applications. introduction to probability and statistics should experience with financial data. Examples from the physical sciences, social consider STAT W3105 and W3107. sciences, and business. Computing is an integral STAT W4315x and y Linear regression models part of the course. STAT W4201x and y Advanced data analysis 3 pts. Professors Feng, Huang, and Sobel. 3 pts. Professors Alemayehu and Liu. Prerequisites: STAT W3107 or equivalent, MATH STAT W4543y Survival analysis Prerequisite: STAT W4315. At least one of W4290, V1101, V1102, V2010 or permission of program Professor Shnaidman. W4325, W4330, W4437, W4413, W4543 is adviser. Theory and practice regression analysis, Prerequisite: STAT W4315. Survival distributions, recommended. This is a course on getting the simple and multiple regression, including testing, types of censored data, estimation for various most out of data. The emphasis will be on hands- estimation and confidence procedures, modeling, survival models, nonparametric estimation of on experience, involving case studies with real regression diagnostics and plots, polynomial survival distributions, the proportional hazard data and using common statistical packages. The regression, colinearity and confounding, model and accelerated lifetime models for regression course covers, at a very high level, exploratory selection, geometry of least squares. Extensive analysis with failure-time data. Extensive use of data analysis, model formulation, goodness of use of the computer to analyze data. the computer. fit testing, and other standard and nonstandard STAT W4325y Generalized linear models statistical procedures, including linear regression, STAT W4606x and y Elementary stochastic 3 pts. Professor Sobel. analysis of variance, nonlinear regression, processes Prerequisite: STAT W4315. Statistical methods generalized linear models, survival analysis, time 3 pts. Professors Brown and Hogan. for rates and proportions, ordered and nominal series analysis, and modern regression methods. Prerequisite: STAT W3105, W4105, or equivalent. categorical responses, contingency tables, odds- Students will be expected to propose a data set of Review of elements of probability theory. Poisson ratios, exact inference, logistic regression, Poisson their choice for use as case study material. processes. Renewal theory. Wald’s equation. regression, generalized linear models. Introduction to discrete and continuous time STAT W4240x Data mining Markov chains. Applications to queueing theory, STAT W4330x Multilevel models 3 pts. Professors Cunningham and Hannah. inventory models, branching processes. 3 pts. Instructor to be announced. Prerequisite: COMS W1003, W1004, W1005, Prerequisites: STAT W4315. Theory and practice, W1007, or the equivalent. Corequisites: Either STAT W4635y Stochastic processes for including model-checking, for random and mixed- STAT W3105 or W4105, and either STAT W3107 finance effects models (also called hierarchical, multi- or W4107. Data Mining is a dynamic and fast 3 pts. Professor Hogan. level models). Extensive use of the computer to growing field at the interface of Statistics and Prerequisite: STAT W3105, W4105, or equivalent. analyze data. Computer Science. The emergence of massive This course covers theory of stochastic processes applied to finance. It covers concepts datasets containing millions or even billions of STAT W4335x Sample surveys of Martingales, Markov chain models, Brownian observations provides the primary impetus for the 3 pts. Professors Sobel and Wu. motion. Stochastic Integration, Ito’s formula field. Such datasets arise, for instance, in large- Prerequisite: STAT W3107 or W4107. Introductory as a theoretical foundation of processes used scale retailing, telecommunications, astronomy, course on the design and analysis of sample in financial modeling. It also introduces basic computational and statistical challenges. This surveys. How sample surveys are conducted, discrete and continuous time models of asset price course will provide an overview of current why the designs are used, how to analyze survey evolutions in the context of the following problems research in data mining and will be suitable for results, and how to derive from first principles in finance: portfolio optimization, option pricing, graduate students from many disciplines. Specific the standard results and their generalizations. spot rate interest modeling. topics covered with include databases and data Examples from public health, social work, opinion warehousing, exploratory data analysis and polling, and other topics of interest. STAT W4840x Theory of interest visualization, descriptive modeling, predictive 3 pts. Professors Qadir and Szeto. STAT W4413y Nonparametric statistics modeling, pattern and rule discovery, text mining, Prerequisite: MATH V1101 or equivalent. 3 pts. Professors Maleki and Sen. Bayesian data mining, and causal inference. Introduction to the mathematical theory of interest Prerequisite: STAT W3107 or W4107. Statistical as well as the elements of economic and financial STAT W4290y Statistical methods in finance inference without parametric model assumption. theory of interest. Topics include rates of interest 3 pts. Professors Xing and Ying. Hypothesis testing using ranks, permutations, and and discount; simple, compound, real, nominal, Prerequisite: STAT W3107 or W4107. A fast- order statistics. Nonparametric analogs of analysis effective, dollar (time)-weighted; present, current, paced introduction to statistical methods used in of variance. Nonparametric regression, smoothing future value; discount function; annuities; stocks quantitative finance. Financial applications and and model selection. statistical methodologies are intertwined in all and other instruments; definitions of key terms lectures. Topics include regression analysis and STAT W4437x and y Time series analysis of modern financial analysis; yield curves; spot applications to the Capital Asset Pricing Model and 3 pts. Professors Davis, Motta, and Zhang. (forward) rates; duration; immunization; and short multifactor pricing models, principal components Prerequisite: STAT W4315 or equivalent. Least sales. The course will cover determining equivalent and multivariate analysis, smoothing techniques squares smoothing and prediction, linear systems, measures of interest; discounting; accumulating; Fourier analysis, and spectral estimation. Impulse determining yield rates; and amortization.

engineering 2014–2015 Campus and Student Life 210 campus life

he Fu Foundation School Center for undergraduate career. When each of Engineering and Applied Student Advising student matriculates, they are assigned T Science attracts and admits an 403 Lerner Hall, MC 1201 to an advising dean. When a student exceptionally interesting, diverse, and Phone: 212-854-6378 declares a major, a faculty member is multicultural group of students, and E-mail: [email protected] also appointed to advise him or her it takes steps to provied a campus studentaffairs.columbia.edu/csa for the next two years. Depending on environment that promotes the their chosen major, students may be continued expansion of each student’s The Center for Student Advising (CSA) assigned to a new advising dean who ideas and perspectives. reflects the mission of the University is a CSA liaison to their department. This begins within the residence in striving to support and challenge Advising deans regularly refer students halls, in which nearly all first-year the intellectual and personal growth to their academic departments to undergraduate students live. The of its students and by creating a receive expert advice about their University assigns rooms to both developmental, diverse, and open engineering course selections. Engineering and Columbia College learning environment. Individually and undergraduate students, ensuring that collaboratively, each advising dean: Preprofessional Advising all students will live either with or near Preprofessional Advising works closely • provides individual and group a student attending the other program. with other staff members of the Center academic advisement, exploration, Once students have moved into their for Student Advising and with the and counseling new campus home, they will find Center for Career Education to provide • provides information on themselves part of a residential system information for students who plan a preprofessional studies, study abroad, that offers undergraduates a network career in law or the health professions. and major declaration and completion, of social and academic support (more The office advises and assists students as well as various leadership, career, information about the residence halls throughout their four years, but works graduate school, and research can be found in the chapter “Housing most closely with students during their opportunities and Residence Life” in this bulletin). application year and with alumni who • designs and facilitates programming In addition to robust residential apply for admission after graduation. to meet the unique developmental offerings, a blend of academic, Information sheets, forms, and helpful needs of each class and to enhance educational, social, and cocurricular resources are available from the community among students, faculty, activities enhances the Columbia Preprofessional Advising website. and administrators experience through integrated efforts Students will still work with their advising • interprets and disseminates of numerous units including the Center deans as their primary advisers; these information regarding University for Student Advising, Undergraduate advisers will be instrumental in writing polices, procedures, resources, and Student Life, Parent and Family committee evaluations for some programs Programs, and the Office of Judicial professional schools. • educates and empowers students to Affairs and Community Standards. take responsibility in making informed While the School is large enough to decisions support a wide variety of programs, it is Undergraduate Student • refers students to additional campus also small enough to promote the close Life resources interaction among students, faculty, and The Undegraduate Student Life administration that has created a strong Every undergraduate is assigned team works to foster a vibrant and sense of community on campus. an adviser from the Center for Student welcoming undergraduate community Advising for the duration of their through organizational advising,

engineering 2014–2015 leadership development, advocacy, traditions, understand how to access a greater awareness and appreciation 211 diversity education, civic engagement, campus resources and support services, of cultural history within and between and community programming. The and meet the Columbia community communities on campus. Multicultural team includes Student Engagement, through the New Student Orientaion Affairs endeavors to empower students, Multicultural Affairs, and Residential Program (NSOP). faculty, and staff with the tools to be Life. Knowing that students’ learning able to successfully navigate their continues beyond the classroom, Orientation environments and thus be able to Columbia University strongly encourages All new students are required to positively change and impact the students to become involved in participate in an orientation program community at large. programs and activities to enhance that is designed to acquaint them with Programs and services provided their educational experience and the University and its traditions, the by Multicultural Affairs include the personal growth. A wide array of student administration and faculty of The Fu Columbia Mentoring Initiative, a organizations addresses both student Foundation School of Engineering and program connecting incoming students interests and professional concerns, Applied Science, upperclass students, with returning students, and returning including the arts, politics, identity, and New York City. The New Student students with alumni; Respecting culture, and religion. Joining such Orientation Program (NSOP) for new Ourselves and Others Through groups offers an exciting and dynamic undergraduate students begins the Education (ROOTED), a peer diversity opportunity to develop leadership skills week prior to the start of the fall faciliation program; Under1Roof, that will serve students well throughout semester. NSOP is intended to assist a program during orientation that their lives. all new students with the transition to explores how to create an inclusive college life. community at Columbia University; Student Engagement Orientation is busy, exciting, and a and the Intercultural House (ICH), a Student Engagement is committed lot of fun, but it is also a week in which unique residential experience that to building a strong sense of campus important academic decisions are is supportive of Multicultural Affairs’ community by helping students made. Scheduled into the program are social justice goals. enhance their leadership skills, engage information sessions and opportunities in their communities, and explore the to meet with academic advisers. Residential Life cocurricular opportunities available at Through large group programs and The staff strives to enhance the quality Columbia University. small group activities, students will be of residential life by cultivating an This unit supports many of the introduced to faculty members, deans, atmosphere conducive to educational student organizations on campus and resident advisers, and other students. pursuits and the development of aids them in meeting the objectives NSOP includes walking tours of New community within the student body. of their student group or organization. York City, social events, and information These contributions form an integral Staff will assist students who are sessions on University services and part of a Columbia education by looking for advisement on running an co-curricular opportunities. During stimulating mutual understanding and organization, planning an event, sorting NSOP, new students have the campus by fostering an atmosphere based on their organization’s financial records, to themselves. This provides students the appreciation of the differences and or starting a student group. They with a unique opportunity to make similarities characterizing such a diverse are there to guide students through friends and settle into life at Columbia cultural community. formal University processes, help them before classes begin. The undergraduate student navigate Columbia’s resources, or simply Undergraduate students may e-mail staff, resident advisers (RAs), and brainstorm new ideas with students. [email protected] for additional community advisers (CAs) serve as Here are just a few ways to get information on NSOP. role models for their residents. They involved with campus life through the Orientation for graduate students is facilitate discussions about community programs of Student Engagement: scheduled during the week prior to the standards, provide community building tackle a civic engagement project during beginning of each semester. For more programs, and serve as a resource your time away from campus through information on orientation for graduate for the residents. RAs/CAs serve the Alternative Break Program and students, contact the Office of Graduate as the front line of a layered on-call make a difference in a community that Student Affairs. system and are trained to respond to matters to you; explore and enjoy New the variety of issues that emerge in York City’s performing arts scene over Multicultural Affairs community life. spring break with the Alternative Spring Multicultural Affairs is devoted to The Faculty-in-Residence Program Break: NYC Performing Arts program promoting a just society and explores allows students, alumni, and faculty to or throughout the spring semester with issues of interculturalism and diversity meet formally and informally throughout Urban New York; take a break from your within and beyond the Columbia the year. Faculty members who reside classes and studies with Live at Lerner’s University community. By promoting in three residence halls invite students educational, cultural, and entertainment forums that address diversity issues, to dine in their apartments; organize events that take place in the student self-discovery takes place along with special programs around issues of center—all after you learn about campus interest; provide opportunities for

engineering 2014–2015 212 academic growth and challenges within Working in conjunction with the Student Council (EGSC). The EGSC the residence halls; and help students Student Council, the Activities Board is a recognized group that consists of establish links with major cultural, at Columbia (ABC), Student Governing representatives from each of the nine political, and professional institutions in Board (SGB), InterGreek Council (IGC), academic departments at SEAS. The New York City. In addition, the faculty Community Impact (CI), Club Sports, objectives of the EGSC are to foster member in residence partners with the and Interschool Governing Board interaction among graduate engineering Engineering alumni office to provide (IGB) oversee the management and students, to serve as a voice for opportunities for students to network funding of more than 500 student graduate engineering students, and to and gain exposure to a variety of organizations. sponsor social and educational events careers. The ABC provides governance for of interest to the graduate engineering Begun in fall 2006, Res. Inc., formerly recognized student organizations, community. known as the Gateway Residential including cultural organizations, Initiative, allows Engineering first-years, performance-based and theatrical Office of Judicial Affairs sophomores, juniors, and seniors to live groups, media and publications and Community Standards together clustered in the Living Learning groups, competition and special The Office of Judicial Affairs and Center (LLC) housed in Hartley and interests groups and preprofessional Community Standards was created Wallach Halls. This initiative seeks to organizations and societies. The to assist students in the maintenance bridge the academic and co-curricular preprofessional organizations and of a safe, honest, and responsible experience for Engineering students and societies are of special interest to campus community. To achieve this encourages and supports engineers engineering students. These societies goal, the Office of Judicial Affairs and with entrepreneurial ideas. Mentorship reflect the range of academic Community Standards partners with between students, connection among disciplines and interests to be found administrators and faculty to create the class years, and alumni interaction among students and include the programs designed to educate students are the foundations for the success of National Society of Black Engineers, regarding the potential impact of their the program. the Society of Women Engineers, actions on both their individual lives and Fraternities and sororities are an the American Institute of Aeronautics the community at large. In addition, the active and vibrant community, adding and Astronautics, and the Biomedical Office of Judicial Affairs and Community diversity to the residential experience. Engineering Society, just to name a Standards works with student groups Some fraternities and sororities have few. to facilitate the development of skills brownstones near campus, and some of The SGB provides governance and processes students can use to the organizations without brownstones for recognized student organizations hold each other accountable when they have a suite within the residence halls. that are faith-based, spiritual, political, encounter inappropriate behavior. The Residential Life provides guidance activist, and humanitarian and Office of Judicial Affairs and Community and support to the Greek community, that encourage open interreligious Standards also holds students advising the four student-governing and political dialogue at Columbia accountable for inappropriate behavior Greek councils: the Intergreek Council University’s Morningside campus. The through the Dean’s Discipline process (IGC), InterFraternity Council (IFC), IGB recognizes student organizations when necessary. Panhellenic Council, and Multicultural whose membership spans across the Greek Council (MGC). Fraternity and various undergraduate and graduate sorority members share in service, schools. Office of the scholastic, philanthropic, cultural, and For more information on the University Chaplain leadership experiences. IGC, see Residential Life. For more Columbia is home to a community information on Club Sports, see of scholars, students, and staff from Student Organizations Intercollegiate Athletics Program (page many different religious backgrounds. Programs and activities at Columbia 213), and for more information on The Office of the University Chaplain are shaped primarily by students who Community Impact see Office of the ministers to their individual faiths and assume leadership and volunteer University Chaplain (page 214). All the supports individual spirituality, while positions in hundreds of organizations governing groups provide networking, promoting interreligious understanding. across the campus. The Engineering leadership, and professional The University Chaplain oversees Student Council and its associated class development opportunities for students. the work of the United Campus councils are the elected representative Columbia University graduate Ministries—a fellowship of more than body of undergraduates at Columbia students can participate in and enjoy twenty religious life advisers representing Engineering. Its members represent hundreds of diverse, University-affiliated specific faith traditions. The University student interests on committees and social, religious, cultural, academic, Chaplain also fosters learning through projects addressing a wide range of athletic, political, literary, professional, spiritual, ethical, religious, political, issues facing the Columbia community public service, and other organizations. and cultural exchanges and hosts and help shape the quality of life for At SEAS, graduate students are programs on matters of justice, faith, Columbia students. encouraged to become active and spirituality. Through these and members of the Engineering Graduate other means, the Office of the University

engineering 2014–2015 Chaplain cultivates interfaith and Office of Graduate the University’s athletic facilities. The 213 intercultural awareness. Student AFFAIRS Baker Field Athletics Complex, a few The University Chaplain is available The Office of Graduate Student miles up the Hudson River on the for confidential pastoral counseling to Affairs at The Fu Foundation School northern tip of Manhattan, has been individuals, couples, and families in the of Engineering and Applied Science completely rebuilt and expanded. Columbia University community. The is integral to the School’s teaching, The complex features Robert K. Kraft Office of the University Chaplain may research, and service mission, and Field at Lawrence A. Wien Stadium, also assist with private ceremonies such works to enhance the educational a 17,000-seat football and lacrosse as weddings, christenings, and memorial opportunities available to students. facility; Robertson Field at Satow services. We warmly welcome your This Office provides leadership for the Stadium, home of the baseball program; interest, questions, and participation. integration of educational programs softball and field hockey venues; and For more information, please call and services that enhance recruitment, an Olympic-quality synthetic track. At the Earl Hall Center at 212-854-1474 or retention, and quality of campus life Columbia’s Dick Savitt Tennis Center at 212-854-6242 or visit columbia.edu for graduate students at Columbia the Baker Athletics Complex there are /cu/earl. Engineering. It strives to demonstrate six cushioned hard tennis courts, all of sensitivity and concern in addressing the which are covered by a state-of-the-art air dome for winter use. The Remmer Lerner Hall needs of the School’s population. The Office is dedicated to providing service and 1929 Boathouse includes a three- Lerner Hall is dedicated to student to prospective, new, and continuing bay shell house, complete with an upper life at Columbia University. A students pursuing a graduate education level that includes an erg and weight 225,000-square-foot facility located in engineering or applied science. room. The Campbell Sports Center, the on the southwest corner of campus, newest athletics building at the Baker Lerner Hall was designed by Bernard Athletics Complex, features coaches, Tschumi, the former Dean of Columbia’s Intercollegiate Athletics offices, a strength and conditioning Graduate School of Architecture, Program center, a theatre-style meeting room, Planning and Preservation. The building Columbia has a long tradition of success as well as a student-athlete lounge and features a glass facade and ramps to in intercollegiate athletics, and The Fu study space. offer those within Lerner scenic views Foundation School of Engineering and Columbia’s Dodge Physical Fitness of campus and to allow those on Applied Science has always been an Center draws thousands of students campus to clearly view the activities active participant in these programs. each day for recreation, physical within the building. While Columbia’s intercollegiate athletics education classes, intramural play, club Opened in 1999, Lerner Hall contains program is governed by Ivy League competition, and varsity sport contests an auditorium that seats up to 1,100, a regulations, Columbia is also a member and practices. The Center houses fully operational cinema, a party space, of the National Collegiate Athletic most indoor sports and is available to plus a diverse offering of meeting, Association. Columbia sponsors men’s all registered students. Major athletic rehearsal, and performance spaces, varsity teams in baseball, basketball, facilities on campus include two full-size computer labs and kiosks, and 7,000 cross-country, fencing, football, golf, gymnasiums for basketball, volleyball, student mailboxes. rowing (heavyweight and lightweight), and badminton; eight squash and The building also features the soccer, squash, swimming and diving, handball courts; the eight-lane Uris University Bookstore, two dining tennis, track and field (indoor and pool with three diving boards; a fully facilities, a banking center and ATM, outdoor), and wrestling. equipped three-level exercise and weight Package Center, and the Ticket and Women in all undergraduate divisions room facility; two aerobic dance/martial Information Center. Lerner Hall is home of Columbia and in Barnard College arts rooms; a fencing room; a wrestling to many critical University resources compete together as members of room; an indoor running track; and two such as Undergraduate Student Life, the University-wide athletic teams. The fully equipped saunas. Center for Student Advising, University arrangement, called a consortium under Chaplain, University Event Management, NCAA rules, is one of only three in the Eligibility for Intercollegiate Athletics and Health Services. nation and the only one on a Division Any student in the Engineering School Lerner Hall is much more than a I level. Currently, there are women’s who is pursuing the undergraduate building for performances and events — varsity teams in archery, basketball, program or an approved combined it is the center of student and campus cross-country, fencing, field hockey, program toward a first degree is eligible activity at Columbia. golf, lacrosse, rowing, soccer, softball, for intercollegiate athletics. To be For more information visit lernerhall squash, swimming and diving, tennis, eligible for athletic activities, the student .columbia.edu. track and field (indoor and outdoor), and must: volleyball. Columbia’s commitment to success • Be a candidate for a bachelor’s in intercollegiate athletics competition degree has been matched by the determination • Be registered for at least 12 points of of alumni and administrators to upgrade credit

engineering 2014–2015 214 • Make appropriate progress offers a comprehensive Intramural Campus Safety toward the degree as defined by and Club Sports Program. Through and Security the NCAA, the Ivy League, and intramurals, students have the Columbia University prepares an annual Columbia University. These criteria opportunity to participate in both security report, which is available to are monitored by the Director of individual and team sports. Individual all current and prospective employees Compliance and certified by the activities function through tournaments, and students. The report includes Office of the Registrar. while team activities feature both statistics for the three previous • Have attended the University for not league and tournament competition. years concerning reported crimes more than eight terms Club sports are designed to allow that occurred on campus, in certain • Not have completed the requirements groups of individuals who share a off campus buildings or property for the bachelor’s degree common athletics interest to organize owned or controlled by Columbia and collectively pursue this activity. Questions about athletic eligibility University, and on public property Clubs are organized on recreational, should be referred to the appropriate within, or immediately adjacent to and instructional, and competitive levels. academic adviser or the Director of accessible from, the campus. The Activities range from organized Compliance in the Department of report also includes institutional policies instruction to intercollegiate and Intercollegiate Athletics and Physical concerning campus security, such as tournament competition. A list of the Education. policies concerning sexual assault, intramural activities and sports clubs and other matters. You can obtain a as well as all information regarding the Recreational Programs copy of this report by contacting the program can be obtained in the Office Director of Administration and Planning, In addition to the required physical of Intramurals and Club Sports, 331 Public Safety at 212-854-3815 or education courses (see page 13), Dodge Fitness Center or on the website by accessing the following website: the Department of Intercollegiate at gocolumbialions.com. columbia.edu/cu/publicsafety Athletics and Physical Education /SecurityReport.pdf.

engineering 2014–2015 student services 215

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

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a cooperative relationship with two 50 and 250 miles from campus). All First-Year Dining Plans New York City real estate/relocation continuing students and applications agencies, Citihabitats and Douglas from Zone 3 areas (within 50 miles) are 1. 19 meals per week and 75 Dining Elliman, which also offer a discounted automatically placed on a waiting list. Dollars per term, plus 15 floating broker fee. Only students/affiliates UAH-approved students can begin meals and 6 faculty meals with a UNI or admission acceptance moving in during the last week of August 2. 15 meals per week and 125 Dining letter are permitted to use the for the fall term, and early January for the Dollars per term, plus 10 floating Registry. Office hours and instructions spring term. Students will be properly meals and 6 faculty meals are posted on the website at columbia notified of Graduate Orientation and 3. 19 meals per week, $50 Flex and .edu/ocha. Registration, which are generally held the 25 Dining Dollars per term, plus 15 UAH application information is sent week before the first day of class. If a floating meals and 6 faculty meals along with acceptance packets from student needs to move in earlier, proper The dining plans are transacted through the Office of Graduate Student Affairs. documentation from the department in Columbia’s ID Card, called the Columbia Information on applying for housing is support of the request is necessary. Card, which serves as a convenient way also available in the Office of Graduate to enjoy dining all over campus without Student Affairs and the UAH Office. You Columbia Dining carrying cash. can also seek additional information on the Columbia Students Page: columbia. Meals edu/cu/students. First-Year Students Due to the growing demand for All first-year students in residence are The meals portion of the dining plan housing, graduate housing is no required to enroll in one of three dining enables students to help themselves longer guaranteed, but every effort plans, each of which is comprised of a to unlimited servings of food served is made to accommodate you. It is varying number of meals served in John in John Jay Dining Hall, Ferris Booth critical that you follow the instructions Jay Dining Hall, Ferris Booth Commons, Commons, or JJ’s Place. The hours in your acceptance packet. Housing or JJ’s Place, and Dining Dollars, which of operations for these locations offer applications received after the set can be used at the 12 dining locations dining options for breakfast, lunch, dates are not guaranteed housing. on campus. Plan 3 is the only first-year dinner, and late-night, with continuous The order of priority for selection is: plan that also includes Off Campus dining from 8:00 a.m. to 1:00 a.m. graduate fellowship recipients, Zone 1 Flex. This plan is designed for students students (those who live further than who are on campus during breaks (fall, Dining Dollars 250 miles from campus), and then Zone Thanksgiving, and spring), when the In addition to meals, Dining Dollars 2 students (those who live between dining halls are closed. comprise the other portion of the first-

engineering 2014–2015 year dining plan. Each Dining Dollar is either the First Year Dining Plan or students may also enroll in the Columbia 217 equal to one dollar and operates as a the Upperclass Dining Plan options, Health Program and Columbia Plan. declining balance account, much like a according to the student’s status, then debit card. elects to enroll in the Kosher Dining Benefits and Services of the Columbia Dining maintains 12 dining Plan. The addition of the Kosher Columbia Health Program facilities conveniently located on campus. Dining Plan adds 10 percent to the The Columbia Health Program Each of the locations accepts Dining cost of the selected plan. For more compromises five departments and Dollars, an alternative to cash payment details, a dining plan comparison, and more than 130 individuals to meet your that is accessed by the Columbia Card additional tools, visit the Columbia health needs on campus. (student ID card). Dining website at dining.columbia.edu. With Dining Dollars, students will Medical Services enjoy the ease and flexibility of cashless Locations/Menus/Hours John Jay Hall, 3rd and 4th Floors transactions as well as the savings of Locations, menus, and hours of all Phone: 212-854-7426 sales tax on all food purchases. Dining campus dining facilities can be found at health.columbia.edu/pcms Dollars will roll over from year to year dining.columbia.edu. You can also view Medical Services provides routine and until graduation. photos and take a virtual tour of some of urgent medical care, travel medicine, our facilities. Menus and hours are also and immunizations, as well as sexual Upperclass and Graduate Students available on the Dine@CU iPhone app. health services, reproductive and Many upperclass and graduate students gynecological services, LGBTQ health who dine on campus open a Dining Nutrition, Food Allergies, and care, and confidential HIV testing. Dollars account; however, some choose Special Diets Students can make appointments to enroll in an upperclass/graduate Registered Dietitian Kristie Koerner online with their health care provider student dining plan. is available on site as well as online and are encouraged to do so (bios and Columbia Dining offers four plans—all to address individual questions and photos are available online). are accessed by the Columbia Card and concerns related to food allergies, can be used for meals in John Jay Dining intolerances, and dietary preferences. Counseling and Psychological Services Hall, Ferris Booth Commons, or JJ’s Place. Kristie can be contacted via e-mail at Lerner Hall, 8th Floor The hours of operations for these locations [email protected] or by phone Phone: 212-854-2878 offers dining options for breakfast, lunch, at 212-854-3353 with questions, to health.columbia.edu/cps dinner, and late-night, with continuous schedule a consultation, or to discuss Counseling and Psychological dining from 8:00 a.m. to 1:00 a.m. personal meal planning. For more Services offers short-term individual Upperclass, GS, and Graduate Dining information and a nutrition calculator, counseling, referrals for longer-term Plans visit the Columbia Dining website. therapy, consultations for couples, Nutrition data can also be accessed on student-life support groups, medication A. 14 meals per week and 200 Dining the Dine@CU iPhone app. consultation, and emergency Dollars per term, plus 15 floating consultation. Students are welcome to meals and 6 faculty meals Columbia health select a mental-health clinician (bios and B. 175 meals and 200 Dining Dollars per Phone: 212-854-2284 photos are available online). term, plus 6 guest meals After-hours Urgent Health Disability Services C. 100 meals and 125 Dining Dollars per Concerns: 212-854-9797 Lerner Hall, 7th Floor term, plus 4 guest meals health.columbia.edu D. 75 meals and 75 Dining Dollars per Phone: 212-854-2388 health.columbia.edu/ods term, plus 2 guest meals Columbia Health is an integrated program that provides extensive on- and Disability Services facilitates equal Kosher Dining Plan off-campus health care and services access for students with disabilities All students who participate in a dining for you while you are enrolled at the by coordinating accommodations and plan, including first-year, upperclass, University. The Columbia Health Program support services, including assistive General Studies, or graduate students, and an accepted medical insurance technology, networking groups, are eligible for the Columbia Kosher plan work together to meet your health academic skills workshops, and learning Dining Plan. Signing up for this dining care needs. Columbia requires all full- specialists. Disability documentation plan allows access to a restricted time students to enroll in both. To meet and registration guidelines are available kosher area within John Jay Dining the insurance requirement, you must online. Hall as well as Express Meals to go. either confirm your enrollment in the CU kosher meals can also, for an Columbia Student Medical Insurance Alice! Health Promotion additional charge, be exchanged for Plan (Columbia Plan) or provide proof Wien Hall, 1st Floor a kosher meal at Barnard’s Hewitt of alternate coverage that meets Phone: 212-854-5453 Hall (kosher to kosher only). To sign the established criteria listed on the health.columbia.edu/alice up, the student selects a plan from Columbia Health website. Part-time

engineering 2014–2015 218 Alice! Health Promotion connects edu before September 30 (February 1 university campuses. Columbia students individuals and groups with information for new spring term enrollment, or June must make an informed decision about and resources, cultivates healthy 14 for newly arrived full-time summer being vaccinated and certify their attitudes and behaviors, promotes trimester students). All waiver requests decision online. Full instructions are health-supporting policy, and fosters are considered but approval is not given at www.health.columbia.edu and a culture that values and supports guaranteed. the process takes two to three minutes individual and community health. Optional coverage for early arrival to complete. You must formally indicate students or eligible dependents of insured your decision about being vaccinated Sexual Violence Response students and a separate dental plan are before you will be permitted to register Lerner Hall, 3rd Floor available through Aetna Student Health. for classes. Phone: 212-854-3500 For more up-to-date information, visit Deadline: Decisions must be health.columbia.edu/svprp the Columbia Health website at health recorded online before classes begin. Sexual Violence Response works to .columbia.edu or www.aetnastudent Students will not be permitted to register promote behaviors that support positive, health.com/columbiadirect.html. until a decision is recorded. healthy, and consensual relationships, Documentation of Immunity to Measles, and supports survivors and co-survivors Immunization Compliance Mumps, and Rubella (MMR) of violence through advocacy, Wien Hall, 1st Floor New York State public health law connection to resources, community Phone: 212-854-7210 requires all Columbia students taking education, training, and engagement. six or more credits must document There are two immunization requirements their immunity to measles, mumps, and that all new students must meet before Student Health Insurance rubella. Instructions and the Columbia arrival on campus: Wien Hall, 1st Floor University MMR Form are available at Phone: 212-854-3286 Meningococcal Meningitis Vaccination health.columbia.edu. New York State public health law Deadline: Completed forms must All full-time students are automatically requires that students receive be mailed or faxed 30 days before enrolled in the Basic level of the information from their institutions about registering for classes. Columbia Plan. To request a waiver meningococcal meningitis and the from automatic enrollment, you must vaccine that protects against most Please visit us at health.columbia submit a request at health.columbia. strains of the disease that can occur on .edu or contact us for questions.

engineering 2014–2015 Scholarships, Fellowships, Awards, and Prizes 220 Scholarships, Fellowships, Awards, and Prizes

Endowed Scholarships Cesare Barbieri Scholarship (1953) Burns and Roe, Arthur J. Fiehn and Grants Gift of Cesare Barbieri Fund. Scholarship (1989) All endowed scholarships are awarded Gifts from various donors in memory of annually to undergraduate students as William S. Barstow Scholarship (1935) Arthur J. Fiehn ’46. part of Columbia’s financial aid program. Gift of William S. Barstow. We are unable to accept applications Samuel J. Clarke Scholarship (1960) Edwin D. Becker Scholarship Fund for these awards independent of this Bequest of Agnes Robertson Clarke. (1993) process. Gift of Edwin D. Becker ’56. Preference Class of 1885 (1910) Leslie Abbot Scholarship is given to students from the Rocky Gift of the Class of 1885 School of For an undergraduate student Mountain states. Mines in commemoration of the twenty- pursuing course of study in mechanical fifth anniversary of their graduation. John E. Bertram Memorial engineering. Scholarship (1990) Class of 1889 (1939) Cvi Abel Memorial Scholarship (2003) Gift of Mrs. Lucy Bertram and friends Gift of the Class of 1889 College and Gift of Jack Abel ’71. in honor of John E. Bertram. Awarded Engineering. to students in electrical engineering or Aigrain Family Scholarship (2008) computer science. Class of 1900 (1940) Gift of Jacques and Nicolleta Aigrain Gift of the Class of 1900 College and P’08. Preference is given to international Jerry and Evelyn Bishop Scholarship Engineering. students studying civil or mechanical (1984) Class of 1902 (1952) engineering. Gift of Jerry ’42 and Evelyn Bishop for students in the Combined Plan Gift of the Class of 1902 College and Walter H. Aldridge (1936) Program. Preference is given to students Engineering. Gift of Walter H. Aldridge. in the program who attended Columbia College. Class of 1906 (1940) Alvey-Ferguson Company Gift of the Class of 1906 in honor of Scholarship (1948) Paul H. Blaustein Scholarship (1994) Frank D. Fackenthal 1906. Gift of the Alvey-Ferguson Company. Gift of Barbara Blaustein, Stacey Blaustein Divack, and Joshua Divack. Class of 1907 (1937) Erwin H. Amick Memorial Scholarship Gift of the Class of 1907. Preference is (1970) Philip P. Bonanno Scholarship (1999) given to sons and descendants of class Gift of various donors for students Donated by Philip P. Bonanno ’55. members. in chemical engineering and applied Class of 1909 (1959) chemistry. Cecil Ane and Tullio J. Borri Family Scholarship Gift of the Class of 1909 in honor of Nathaniel Arbiter Scholarship (1985) Gift of Tullio J. ’51 and Cecil Ane John J. Ryan. Gift of various donors in honor of Borri. Preference for students who are Class of 1913 (1963) Professor Nathaniel Arbiter for students majoring in or studying civil engineering. Gift of the Class of 1913 in in the following specializations in order of commemoration of the fiftieth preference: mineral beneficiation, mines, Cornelius A. Boyle Scholarship (1962) anniversary of their graduation. and physical metallurgy. Bequest of Cornelius A. Boyle. Class of 1914 (1937) Attardo Scholarship (1999) Lauren Breakiron Scholarships (1999) Gift of the Class of 1914 College and Gift of Michael J. Attardo ’63. Gift of Lauren P. Breakiron ’56. Engineering for a pre-engineering or pre- Jee Yin and Choi Heung Au Edwin W. and Mary Elizabeth architecture student. Scholarship Fund (2002) Bright Scholarship in Mechanical Class of 1945 50th Reunion Gift of Michael M. Au ’90. Preference is Engineering (1985) Scholarship given to students who have graduated Gift of Edwin W. ’42 and Mary Elizabeth Gift of the Class of 1945. from Stuyvesant High School in New Bright to support students studying York City. mechanical engineering. Class of 1950 Endowed Scholarship (2000) Frank and Harriet Ayer Scholarship Lewis G. Burnell Memorial Gift of members of the Class of 1950 (1977) Scholarship (2001) in commemoration of the fiftieth Bequest of Frank A. Ayer. Graduates Gift of Roger W. Burnell in memory of anniversary of their graduation. of Deerfield Academy are given first his father, Lewis G. Burnell ’32. preference.

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Class of 1951 Endowed Scholarship to support a deserving minority Sarah E. Grant Memorial Scholarship (2001) undergraduate who has demonstrated (1997) Gift of members of the Class of 1951 academic achievement. Gift of Geoffrey T. ’82 and Annette M. in commemoration of the fiftieth Grant in memory of their daughter, anniversary of their graduation. Stancliffe Bazen Downes Scholarship Sarah. Designated to support students (1945) who have demonstrated academic Class of 1952 Endowed Scholarship Bequest of Bezena Treat Downes achievement and are student athletes. (2002) Merriman in honor of her brother, for a Established by Alexander Feiner ’52. student in civil engineering. Adam R. Greenbaum Memorial Scholarship Fund Hugo Cohn Scholarship (1984) Brooke Lynn Elzweig Scholarship (2002) Established in memory of Adam R. Gift of Hugo Cohn 1909. Preference is Gift of Gary Elzweig ’77. Preference Greenbaum by his parents, relatives, given to electrical engineering students. is given to students with high financial and friends following his death in need. February 2001, when he was a Herbert J. Cooper Scholarship (1999) sophomore. The scholarship is given to Gift of Mrs. Deborah Cooper and the Jack B. Freeman Scholarship (1994) a SEAS sophomore who was named to Estate of Herbert J. Cooper ’46. Gift of Jack B. Freeman ’55. Designated the Dean’s List as a first-year, as Adam to support students who are members was, with a preference to students from Milton L. Cornell Scholarship (1958) of the varsity baseball team. New Jersey and New York. Gift of various donors in memory of Milton L. Cornell. Pier-Luigi Focardi Scholarship (1964) Luther E. Gregory Scholarship (1963) Bequest of Clara G. Focardi. Bequest of Luther E. Gregory 1893. Paul and Lillian Costallat Scholarship (1972) Ford/EEOC Scholarship Robert Gross Fund (1999) Gift of Paul and Lillian Costallat. Designated for minorities and women. Gifts of friends of Robert Gross to Preference is given to Ford employees, support a student in applied physics. Frederick Van Dyke Cruser their spouses, or children. Scholarship (1980) Wallace K. Grubman-Graham Bequest of Maude Adelaide Cruser Z. Y. Fu Scholarship (1993) Scholarship (1998) to support students in chemical Gift of The Fu Foundation for Gift of Wallace Grubman ’50 and engineering with financial need. undergraduate scholarship support. the Grubman Graham Foundation to support a student in chemical Cytryn Family Scholarship (2002) Jewell M. Garrelts Scholarship engineering. Gift from Allan ’72, ’79 and Carol Cytryn. Gift of Jewell Garrelts; preference for a junior or senior in the Department of Civil Lawrence A. Gussman Scholarship Frank W. Demuth Scholarship (1965) Engineering and Engineering Mechanics. (1987) Bequest of Frank W. Demuth 1914. Gift of Lawrence Gussman ’38. Awarded General Motors Scholarship annually to students studying computer Freda Imber Dicker Endowed Designated for minorities and women. science. Scholarship Fund (2000) Preference is given to General Motors Gift of Dr. Stanley Dicker ’61 in honor employees, their spouses, or children. Haight Family Scholarship (2004) of the hundredth anniversary of Gift of Deborah E. Haight ’00. his mother’s birth (March 5, 1900). Ben and Ethelyn Geschwind Preference is given to juniors and Endowed Scholarship (2004) Ralph W. Haines Scholarship (2002) seniors in the Department of Biomedical Gift of Benjamin and Ethelyn ’84 Gift of Ralph W. Haines ’69 for needy Engineering. Geschwind. and deserving students in Columbia Engineering. Jack Dicker Endowed Scholarship Alger C. Gildersleeve Scholarship (2003) (1955) A. A. Halden Scholarship (1962) Gift of Dr. Stanley Dicker ’61 in honor Bequest of Josephine M. Gildersleeve, in Established by bequests from Dorothy of his father. Preference is given to honor of Alger G. Gildersleeve 1889. C. Halden and Barbara Schwartz in juniors and seniors in the Department of memory of Alfred A. Halden. Biomedical Engineering. Frederick A. Goetze Scholarship (1960) Gift of William A. Baum, in honor of the Albert M. Hall Scholarship James and Donna Down Scholarship former Dean of Columbia Engineering. Preference for students in metallurgy or (1997) materials science. Gift of James ’73 and Donna Down

engineering 2014–2015 222 The Hamann Scholarship (1970) Sheldon E. Isakoff Endowed Frank H. Lee Memorial Scholarships Bequest of Adolf M. Hamann 1910. Scholarship Fund (2000) (1986) Gift of Sheldon E. ’45 and Anita Isakoff Awarded to a student in the Combined Alfred M. and Cornelia H. Haring to support chemical engineering Plan Program in honor of Professor Scholarship (1965) student. Frank H. Lee. Gift of the Aeroflex. Alfred L. Jaros Memorial Scholarship Leung Endowed Scholarship (2006) H. Field Haviland Scholarship Fund (1967) Gift of Lawrence Leung P’10, P’15. (1988) Gift of various donors, in memory of Bequest of Henry F. Haviland 1902. Alfred L. Jaros 1911. James F. Levens Scholarship (1973) Scholarships are awarded equally Bequest of Ola Levens Poole for between Columbia Engineering and Cavalier Hargrave Jouet Scholarship students in chemical engineering and Columbia College. (1941) applied chemistry. Bequest of Belinda Hearn Jouet, in Harold T. Helmer Scholarship (1965) memory of C. H. Jouet 1882. George J. Lewin Scholarship (1965) Bequest of Harold T. Helmer. Gift of George J. Lewin 1917 and family. Alfred E. Kadell Scholarship (1995) Preference given to hearing-impaired David Bendel Hertz College/Engineering Bequest of the Estate of Alfred E. Kadell students. Interschool Scholarship (1989) 1921. Gift of David B. Hertz ’39. Awarded in Alvin and Richard H. Lewis alternate years to the College and to the Wayne Kao Scholarship (1988) Scholarship Engineering School to a student electing Gift of Mabel C. Kao in memory of Gift of Alvin and Helen S. Lewis in to receive a B.A. from Columbia College Wayne Kao ’49. memory of their son, Richard Lewis ’63. and a B.S. from Columbia Engineering. Ruth Katzman Scholarship (2011) James M. and Elizabeth S. Li Edward Gurnee Hewitt Scholarship Bequest from Ruth Katzman in loving Endowed Scholarship (2006) (1980) memory of her parents, Max and Lilian Gift of James ’68, ’70, ’76 and Elizabeth Bequest of Mary Louise Cromwell. Katzman. Li. Awarded to students majoring in industrial engineering and operations. Prentice Hiam Memorial Scholarship Stanley A. and Minna Kroll (2007) Scholarship for Engineering and Robert D. Lilley Memorial Scholarship Gift of Atul Khanna ’83. Preference given Computer Science (1987) (1988) to international students. Gift of Stanley A. Kroll ’28 to support For students who are in their final year students who are studying electrical of the 3-2 Combined Plan Program and James T. Horn Scholarship (1938) engineering or computer science. who have a commitment to community Gift of Sarah L. and Mary T. Horn, in service. memory of their brother, James T. Horn Henry Krumb Scholarship (1945) 1884. Gift of Henry Krumb for annual Bruce and Doris Lister Endowed scholarships in mining engineering, Scholarship (2000) Richard and Janet Hunter Scholarship metallurgy, and ore dressing. Gift of Bruce A. Lister ’43, ’47 to (2000) support a needy and deserving Gift of Richard ’67 and Janet Hunter. Jacob Kurtz Memorial Scholarship undergraduate student. Scholarship awarded to 3-2 program (1982) participants entering Columbia Gift of Kulite Semiconductor Products, Lu Lo Family Scholarship Engineering with preference given to Inc., and Kulite Tungsten, for Gift of Lu Lo. Established to provide graduates of Whitman College. undergraduates, preferably studying in scholarships to undergraduate students, the fields of metallurgy or solid-state with a preference for students from Jonathan Lewis Isaacs Memorial physics. In memory of Jacob Kurtz 1917. China. Scholarship (2001) This scholarship was endowed in 2001 Ronald A. Kurtz Scholarship Fund Anna Kazanjian and Guy Longobardo by Gary F. Jonas ’66 and Jonathan L. (1990) Scholarship (2007) Isaacs ’66 as the Future Entrepreneurs Gift of Kulite Tungsten. Gift of Anna Kazanjian ’49, ’52 and Scholarship to acknowledge the thirty- Guy Longobardo ’49, ’50, ’62. fifth anniversary of their graduation from Lahey Scholarship (1932) Preference given to students studying Columbia Engineering. On April 30, Bequest of Richard Lahey. mechanical engineering who have 2003, Mr. Isaacs died at the young age demonstrated academic excellence. of fifty-seven, and the scholarship was Charles and Sarah Lapple then renamed in his memory by Gary F. Scholarship (2004) Donald D. MacLaren Scholarship Jonas, with the support of Jon’s wife, Bequest from the Estate of Charles E. (1995) Charlotte Isaacs. Lapple and Sarah V. Lapple to be used Established by Donald D. MacLaren ’45 to provide scholarships to deserving to support a student who is studying undergraduate students. biochemical engineering. engineering 2014–2015 Manelski Family Scholarship (2004) David Novick Scholarship (2011) The Frederick Roeser Fund for 223 Gift of Darren E. Manelski ’91. Bequest of David Novick ’48, ’54 to Student Aid (1934) support civil engineering students. An annual loan to help pay educational Ernest Marquardt Scholarship (1968) expenses, which is awarded to Bequest of Ernest Marquardt 1912. Parker Family Endowed Scholarship students chosen by the Committee on (2001) Scholarships. The amount is individually Louis F. Massa Scholarship (1952) Gift of Peter D. Parker ’72, ’74. determined and is to be repaid only if Bequest of Louis F. Massa 1890. and when the student can do so without Robert I. Pearlman Scholarship (1989) personal sacrifice. Repayments go into Ralph Edward Mayer Scholarship Gift of Robert I. Pearlman ’55. the Frederick Roeser Research Fund for (1924) Preference is given to students from research in physics and chemistry. Contributed by friends in memory of single-parent households. Professor Ralph Edward Mayer. Edgar Lewisohn Rossin Scholarship Robert Peele Scholarship (1925) (1949) Henry Michel Scholarship (2005) Gift of E. E. Olcott 1874. Bequest of Edgar L. Rossin, to provide Gift of Mrs. Mary-Elizabeth Michel in a scholarship for students in mining memory of Henry Michel ’49 to support Brainerd F. Phillipson Scholarship (1936) engineering. civil engineering majors. Gift of an anonymous donor in memory of Brainerd F. Phillipson. Harry B. Ryker (1947) Stuart Miller Endowed Scholarship in Bequest of Miss Helen L. Ryker in Engineering (2003) Andre Planiol Scholarship (1967) memory of her brother, Harry Benson Gift of Stuart Miller. Bequest of Andre Planiol for a student Ryker 1900. from France. John K. Mladinov Scholarship (1994) Thomas J. Sands Endowed Gift of Barbara P. Mladinov in honor of Roy Howard Pollack Scholarship (1998) Scholarship Fund (2001) her husband, John K. Mladinov ’43. Bequest of Roy Howard Pollack to be Gift of Thomas J. Sands ’86. Awarded to a deserving undergraduate used for scholarships for junior or senior with a minor in liberal arts. students. Peter K. Scaturro Scholarship Fund (1997) Frank C. Mock and Family Polychrome-Gregory Halpern Gift of Peter K. Scaturro ’82, ’85 Scholarship (1987) Scholarship to support students at Columbia Bequest of Frank C. Mock 1913. For For students in chemical engineering Engineering or Columbia College, with students in electrical engineering with and applied chemistry. preference given to scholar-athletes from financial need. Archbishop Molloy H.S. in Briarwood, Rodman K. Reef Scholarship (1999) Queens, NY. New Hope Foundation Scholarship Gift of Rodman Reef ’69, ’78. (2006) Norman A. Schefer Scholarship (1999) Gift of Lee and Margaret Lau P’09 Professor William H. Reinmuth Gift of Norman A. Schefer ’50 and Fay P’10CC. Preference is given to students Scholarship (1988) J. Lindner Foundation. from Ontario, Canada, or mainland Gift of Curtis Instruments, Inc., awarded in alternate years to Columbia College China. Mark Schlowsky-Fischer Scholarship and Columbia Engineering. Preference (2005) A. Peers Montgomery Memorial will be given to college students Gift of George Schlowsky ’65 in memory Scholarship (1990) studying chemistry and to engineering of Mark Schlowsky-Fischer ’97 to Gift of the family of A. Peers students studying electrochemistry. support students studying computer Montgomery ’26. Established in honor of Professor William science. H. Reinmuth. John J. Morch Scholarship (1963) Ralph J. Schwarz Scholarship (1993) Bequest of John J. Morch. Patricia Remmer Scholarship (2004) Gift of the Class of 1943 and other Bequest of Patricia Cady Remmer donors in memory of Ralph J. Schwarz Seeley W. Mudd Scholarship (1958) ’45BC. ’43. To be awarded to academically Gift of the Seeley W. Mudd Foundation. outstanding students who require Brenda and Dave Rickey Endowed financial aid. Mary Y. Nee Endowed Scholarship Scholarship Fund (2008) (2008) Gift of David ’79 and Brenda Rickey David C. and Gilbert M. Serber Gift of Mary Yuet-So Nee ’84. P’08 to benefit undergraduate students Memorial Scholarship (1950) from California. Frederick Noel Nye Scholarship Gift of the Serber family in honor of David Serber 1896. Designated to (1971) Kevin T. Roach Endowed Scholarship support a student in civil engineering. Bequest of Frederick Noel Nye ’27. (2003) Gift of Kevin T. Roach ’77.

engineering 2014–2015 224 Varsha H. Shah Scholarship (2003) Grace C. Townsend Scholarship William F. Wurster Scholarship (1974) Gift of Hemant and Varsha Shah to (1941) Gifts of William F. Wurster 1913. support undergraduate female minority Bequest of Miss Grace C. Townsend. Awarded to a student of chemical students. engineering and applied chemistry. Theodosios and Ekaterine Typaldos Jared K. Shaper Scholarship Endowed Scholarship Fund (2000) Robert H. and Margaret H. Wyld For deserving and qualified candidates Gift of Andreas ’69 and Renee Typaldos Scholarship for degrees in engineering. and the Community Foundation of New Gift of Robert H. 1904 and Margaret H. Jersey. Preference is given to Greek- Wyld. Samuel Y. Sheng Scholarship (2007) American students. Gift of Samuel Y. Sheng ’51, Lauren Max Yablick Memorial Scholarship Wong Sheng ’76, Kent Sheng, and Upton Scholarship (1986) Jean Sheng. Awarded to students who For the children of employees of D. Bequest of Max Yablick 1914. demonstrate academic excellence. C. Heath and Company of Lexington, Preference is given to graduates of Massachusetts. Hebrew day schools and to students Edith Shih Interschool Scholarship in the Combined Plan Program with Fund (2008) Valeiras Family Scholarship (2009) Yeshiva University. Gift of Edith Shih, Esq. ’77TC, ’78TC. Gift of Horacio and Amy Valeiras P’09 Preference is given to international and Peter Valeiras ’09. Theresa Ann Yeager Memorial students. Scholarship (1983) Kenneth Valentine Memorial Gift of the family of Theresa Ann Yeager Silent Hoist and Crane Company (1950) Scholarship (1986) ’81 to support a woman who is enrolled Gift of the Silent Hoist and Crane Company. Bequest of Julia H. Valentine, in memory Columbia Engineering. of Kenneth Valentine 1914. Preference David W. Smyth Scholarship (1957) is given to students in chemical Yu Family Scholarship Bequest of Mrs. Millicent W. Smyth, engineering. Gift of Richard ’82 and Jean Yu. in memory of her husband, David W. Smyth 1902. Frank Vanderpoel Scholarship (1936) Endowed Fellowships Bequest of Frank Vanderpoel. Fritz and Emma Spengler Memorial All endowed fellowships are awarded Scholarship (2005) William E. Verplanck Scholarship annually to graduate students. Gift of Manfred Spengler ’56, ’55CC (1957) Preference is given to students who to support student athletes in the 3-2 Gift of Mrs. T. Bache Bleecker and serve as teaching assistants. Graduate Combined Plan Program. Edward F. Verplanck 1912 in memory of students who qualify for these awards their father, William E. Verplanck 1876. will be contacted directly for application Gene F. Straube Fund (2007) materials. Gift of Gene F. Straube ’50, ’49 CC. Arnold Von Schrenk Scholarship (1943) Preference is given to students who Bequest of Mrs. Helen von Schrenk in H. Dean Baker Fellowship (1982) graduated from a high school or prep memory of her husband, Arnold von Awarded to support deserving graduate school in northern California, and Schrenk. students in mechanical engineering. who are pursing studies in electrical engineering, computer engineering, or George Wascheck Scholarship Boris A. Bakhmeteff Research computer science. Bequest of George Wascheck ’26. Fellowship in Fluid Mechanics Provides a stipend for the academic Steve Tai and Kin-Ching Wu Endowed J. Watumull Scholarship (1989) year with tuition exemption to be Scholarship Fund (2001) For students in the Graduate School arranged by the recipient’s department, Gift of Steve Tai ’80. of Arts and Sciences and in the to a candidate for a doctoral degree in Engineering School who are of East any department at Columbia University Tai Family Scholarship (2003) Indian ancestry. whose research is in fluid mechanics. Gift of Timothy Tai P’06 to be used to support Asian students demonstrating Wells and Greene Scholarship Quincy Ward Boese Fellowships financial need and outstanding academic Bequest of Josephine Wells Greene. Pre-doctoral fellowships for students potential, with preference given to Hong studying under the Faculty of Engineering Kong, Taiwanese, mainland Chinese, Herbert A. Wheeler Scholarship (1923) and Applied Science. and Chinese-American applicants for Gift of Herbert A. Wheeler. admission. A T. Tai Family Scholar will Roy S. Bonsib Memorial Fellowship be named in a first-year class, and with Frederick C. Winter Scholarship (1957) suitable academic achievement and (1966) Awarded to worthy students for advanced continuing need, would retain that honor Gift of various donors in memory of study or research in engineering. until graduation. Frederick C. Winter ’43.

engineering 2014–2015 Arthur Brant Fellowship (1997) Robert F. Gartland Fellowship Edward J. Ignall Research Fellowship 225 Gift of Arthur Brant. Awarded to students Gift of Robert Gartland, an IEOR Gift of family, friends, and former of the Henry Krumb School of Mines in alumnus. The fellowship is designated students in memory of Professor the field of applied geophysics. to support students in the Master Edward J. Ignall. Awarded to encourage of Science in Financial Engineering and help support the research activities Samuel Willard Bridgham-William program who have demonstrated of a graduate student in the Department Petit Trowbridge Fellowship academic excellence and professional of Industrial Engineering and Operations A combined fellowship awarded annually promise. Students are awarded a Research. for research. certificate and monetary prize. George M. Jaffin Fellowship Byron Fellowship (1980) GEM Fellowship Awarded for graduate study and Bequest of Verna and Oscar Byron 1914. The GEM fellowship provides African- research leading to the Ph.D. degree Americans, Hispanic Americans, and in orthopedic biomechanics by the William Campbell Fellowships for Native Americans access to graduate Department of Bioengineering of the Encouraging Scientific Research education. The fellowship includes Hospital for Joint Diseases, Orthopedic Four or five fellowships for research in tuition, fees, a stipend, and a paid Institute, and the Department of the general field of metals. summer internship. Applicants for Mechanical Engineering. this fellowship must be engineering or Robert A.W. and Christine S. Carleton applied science majors. Herbert H. Kellogg Fellowship (1988) Fellowships in Civil Engineering Funded by former students and friends Fellowships awarded to students in the Governor’s Committee on Scholarship of Professor Emeritus H. H. Kellogg and Department of Civil Engineering and Achievement the generous contribution of Professor Engineering Mechanics. One year awards based on financial Kellogg. Awarded to students of mineral need. Renewal is based on academic engineering and chemical metallurgy. Chiang Chen Fellowship (2004) progress, financial need, and availability Gift of the Chiang Chen Industrial Charity of funds. The student applies directly to Otto Kress Fellowship (1990) Foundation. Awarded to students in the GCSA; the awards are matched by Bequest of Mrs. Florence T. Kress in mechanical engineering. the School and are not in supplement to memory of her husband, Otto Kress. initial School awards. Awarded to postgraduate students. Professor Bergen Davis Fellowship Gift of Dr. Samuel Ruben. To be Carl Gryte Fellowship (2007) Henry Krumb Fellowships awarded to a student in chemical Gift from friends of Professor Carl Annual fellowships in mining engineering, engineering and applied chemistry Campbell Gryte. Awarded to students metallurgy, and ore dressing. upon the recommendation of the senior who are studying chemical engineering. professor in chemical engineering active John F. T. Kuo Fellowship (1992) in electrochemistry research. Daniel and Florence Guggenheim Established by Dr. I. J. Won and other Fellowships students of Professor Emeritus Kuo George W. Ellis Fellowships Two fellowships for the study of engineering for the support of graduate students in Awarded annually for graduate study in mechanics in the Institute of Flight Structures. applied geophysics. any division of the University. Open to students who are residents of the state M. D. Hassialis Memorial Fellowship Charles and Sarah Lapple Fellowship of Vermont or who have been graduated (2002) (2004) from a Vermont college or university. Gift of former students of the late Krumb Bequest of Charles ’36, ’37 and Sarah Professor Emeritus Hassialis. Awarded Lapple. Awarded to support deserving Herbert French Fellowship (2010) to students of the Henry Krumb School students in the Department of Chemical Bequest of Ralph S. French ’42CC. of Mines in the field of Earth resources Engineering. economics and management. Michael Frydman Endowed Kuo and Grace Li Memorial Fellowship (2000) Higgins Fellowships Fellowship (1993) Established in 2000, a generous gift Designated to support first-year Gift from the Li Foundation Inc. Awarded of a SEAS alumnus, Michael Frydman. graduate students. to students interested in mining, mineral Fellowship is designed to support resources, metallurgy, and materials science. academically gifted graduate students in Leta Stetter Hollingworth Fellowship the Department of Industrial Engineering Gift of Harry L. Hollingworth in memory Ralph H. McKee Fellowship (1979) and Operations Research, particularly of his wife to support women who are Bequest of Ralph H. Mckee to support in the Management Science program. graduates of the University of Nebraska, fellowships in the fields of mathematics Students are awarded a certificate and with preference given to those who were or chemical engineering. monetary prize. born in Nebraska or received their earlier education there.

engineering 2014–2015 226 Walter Mielziner Fellowship (2011) for at least two years after completing American Society of Civil Engineers— Bequest of Walter Mielziner ‘49 to studies at Columbia; holders are eligible Student Chapter Service Award support fellowships for students for reappointment. Established in 2008 to reward one studying computer science, automatic or more students who have been controls or communications. Samuel N. Rubinstein Endowed particularly active in the Student Steel Fellowship (2005) Bridge Competition. Benjamin Miller Memorial Fellowship Bequest of Leo Rubinstein ’63 and gift Awarded to a student in the Department of Frederick Rubinstein. Awarded to American Society of Civil Engineers— of Industrial Engineering and Operations students studying applied mathematics Younger Member Forum Award Research. Preference is given to or industrial design. Awarded annually to that member of the students concerned with work in graduating class in civil engineering who government-industry regulatory policy, Frank E. Stinchfield Fellowship in has been most active in promoting the procurement procedures and trade Orthopedic Biomechanics aims of the Society. regulations. Awarded for graduate study and research in the Department of American Society of Mechanical Nickolaus Fellowship Mechanical Engineering through the Engineers Gift of Nicholas Nickolaus ’50. Orthopedic Research Laboratory of In recognition of outstanding efforts the Department of Orthopedic Surgery, and accomplishments on behalf of the Anthony Pesco Fellowship (2006) College of Physicians and Surgeons, it American Society of Mechanical Engineers Gift of Dr. Anthony Pesco ’82, ’83, ’87 carries tuition exemption and a twelve- Student Section at Columbia University. to support students in the Chemical month stipend of up to $15,000. Engineering Department who wish to Applied Mathematics Faculty Award pursue careers in academia. Nickolas and Liliana Themelis Awarded to an outstanding senior in the Fellowship in Earth and applied mathematics program. Presidential Distinguished Fellowships Environmental Engineering (2000) These fellowships are awarded annually Gift of Nickolas and Liliana Themelis to Applied Physics Faculty Award to selected incoming Ph.D., Eng. support students in the Department of Awarded to an outstanding graduating Sc.D., and master’s/Ph.D. students. Earth and Environmental Engineering. senior in the applied physics program. Fellowships include tuition plus an annual stipend of $24,000 for up to Erwin S. and Rose F. Wolfson The Edwin Howard Armstrong four years, including three months of Memorial Engineering Fellowship Memorial Award summer research. All applications for (1979) Awarded by the Faculty of Electrical admission are considered for these new Gift of Erwin S. and Rose F. Wolfson. Engineering to one outstanding fellowships. graduating senior and one outstanding candidate for the M.S. degree, to honor outside fellowship Bernard R. Queneau Fellowship the late Edwin Howard Armstrong, Gift of Bernard R. Queneau ’32CC, ’33. professor of electrical engineering Wei Family Private Foundation Awarded to a student in the Department and noted inventor of wideband Fellowship of Earth and Environmental Engineering. FM broadcasting, the regenerative The Wei Family Private Foundation circuit, and other basic circuits of is a 501(c)(3) nonprofit organization David M. Rickey Endowed Fellowship communications and electronics. (2000) established to honor the memory of Dr. Gift of David M. Rickey ’79. Awarded to Chung Kwai Lui Wei and Mr. Hsin Hsu The Theodore R. Bashkow Award students studying electrical engineering Wei. The purpose of the foundation is A cash award presented to a computer under the holder of the David M. Rickey to award scholarship grants to students science senior who has excelled in Professorship. of Chinese heritage with high academic independent projects. This is awarded credentials who are pursuing a graduate in honor of Professor Theodore R. Lydia C. Roberts Graduate degree in Electrical Engineering. Visit Bashkow, whose contributions as a Fellowships www.wfpf888.org for more information. researcher, teacher, and consultant Open to persons born in Iowa who have have significantly advanced the art of been graduated from an Iowa college or Medals and Prizes computer science. university. In addition to the stipend, the fellow is reimbursed the cost of traveling The Charles F. Bonilla Medal American Society of Civil Engineers— once from Iowa to New York City and The Bonilla Medal is an award for The Robert Ridgway Award back. Special provisions: holders may outstanding academic merit. It is Awarded to the senior showing the most not concentrate their studies in law, presented annually to that student in promise for a professional career in civil medicine, dentistry, veterinary medicine, the graduating class in the Department engineering. or theology, and each holder must, of Chemical Engineering who best when accepting the award, state that it exemplifies the qualities of Professor is his or her purpose to return to Iowa Charles F. Bonilla.

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The Tullio J. Borri ’51 Award in Civil Computer Science Department Award the graduating class in mechanical Engineering of Excellence engineering. A certificate and cash prize presented A $512 cash prize to a student who has annually by the Department of Civil demonstrated outstanding ability in the The Adam J. Derman Memorial Award Engineering and Engineering Mechanics field of computer science. Established in 1989 by family and to a senior for outstanding promise of friends in memory of Adam J. Derman scholarly and professional achievement The Edward A. Darling Prize in ’89 and graduate student in the in civil engineering. This award has Industrial Engineering and Operations Department of Industrial Engineering been made possible by gifts from the Research and Operations Research. A certificate stockholder/employees and the board Established in 1903 by a gift from and cash prize awarded annually by the of directors of the Damon G. Douglas the late Edward A. Darling, formerly Department of Industrial Engineering Company, a New Jersey-based general superintendent of Buildings and and Operations Research to a member contractor, in appreciation of Mr. Borri’s Grounds; a certificate and prize of the graduating class who has many years of dedicated service and awarded annually to the most faithful demonstrated exceptional ability to visionary leadership as chairman and and deserving student of the graduating make computer-oriented contributions president. class in industrial engineering and to the fields of industrial engineering and operations research. operations research. Computer Engineering Award of Excellence The Edward A. Darling Prize in Electrical Engineering Department Awarded each year by vote of the Mechanical Engineering Research Award computer engineering faculty to an Established in 1903 by a gift from Awarded by the faculty of Electrical outstanding senior in the computer the late Edward A. Darling, formerly Engineering to one outstanding engineering program. superintendent of Buildings and graduating senior who has Grounds; a certificate and $100 cash demonstrated outstanding passion and prize awarded annually to the most accomplishment in research. faithful and deserving student of

engineering 2014–2015 228 Electrical Engineering Department The Stephen D. Guarino Memorial his forty years of teaching. The medal is Service Award Award in Industrial Engineering and made possible by Dr. Myron A. Coler. Awarded by the faculty of Electrical Operations Research Engineering to one outstanding A certificate and cash prize established The Yuen-huo Hung and Chao-chin graduating senior who has made by a gift from Roger Guarino (1951) in Huang Award in Biomedical significant contributions to the memory of his son. To be awarded to Engineering department and community at large. one outstanding senior in the Industrial This award has been endowed to Engineering and Operations Research honor the grandfathers of Professor Zvi Galil Award for Improvement in Department who, in the opinion of Clark T.Hung in the Department of Engineering Student Life the faculty and Board of Managers Biomedical Engineering. His paternal Given annually to the student group that of the Columbia Engineering School grandfather,Yuen-huo Hung, was a most improves engineering student life Alumni Association, has been active surgeon in Taipei who was renowned during the academic year. Established in undergraduate activities and has for his practice of medicine and for his in honor of Zvi Galil, Dean of the School displayed leadership, school spirit, and compassion toward patients. Professor from 1995 to 2007. scholarship achievement. Hung’s maternal grandfather, Chao- chin Huang, was a famous politician The Jewell M. Garrelts Award The Wlliam A. Hadley Award in in Taiwan who dedicated his life to Awarded to an outstanding graduating Mechanical Engineering the citizens of his country, serving as senior who will pursue graduate study Established in 1973 by Lucy Hadley in mayor of Taipei, speaker ofthe Taiwan in the department that was so long and memory of her husband. The award Provincial Assembly, and consul general successfully shepherded by Professor is made annually in the form of a to the United States. This award is given Jewell M. Garrelts. This award is made certificate and cash to that student to a graduating doctoral student in the possible by gifts from alumni and friends in the graduating class in mechanical Department of Biomedical Engineering of Professor Garrelts and from the engineering who has best exemplified who embodies the collective attributes Garrelts family in honor of an outstanding the ideals of character, scholarship, and of these distinguished individuals. engineer, educator, and administrator. service of Professor William A. Hadley. This student will have demonstrated great potential for making significant The Carl Gryte Prize The Thomas “Pop” Harrington Medal contributions to the fields of biomedical Awarded annually to an undergraduate Presented annually to the student who engineering and public health, and for student for service to the Department of best exemplifies the qualities of character serving as an ambassador of biomedical Chemical Engineering. that Professor Harrington exhibited during engineering.

engineering 2014–2015 The Illig Medal Eliahu I. Jury Award Mechanical Engineering Certificate 229 Established in 1898 by a bequest Established 1991 for outstanding of Merit from William C. Illig, E.M., 1882, and achievement by a graduate student or In recognition of excellence in awarded by the faculty to a member of recent graduate in the areas of systems, undergraduate studies. the graduating class for commendable communications, signal processing, or proficiency in his or her regular circuits. The Henry L. Michel Award in Civil studies. Engineering Charles Kandel Award Established by the Columbia Industrial Engineering and Operations Medal and cash prize presented Engineering School Alumni Association Research Academic Excellence annually by the Columbia Engineering in memory of Henry M. Michel ’49, who Award School Alumni Association to that built Parsons Brinkerhoff into one of the Given to exceptional students who member of the graduating class who world’s leading engineering companies. completed both B.S. and M.S. in has best promoted the interests of A certificate and cash prize is presented the IEOR Department consecutively. the School through participation in annually by the Department of Civil Students are awarded a certificate and extracurricular activities and student- Engineering and Engineering Mechanics monetary prize. alumni affairs. to a student or group of students in the Civil Engineering Department who Industrial Engineering and Operations Andrew P. Kosoresow Memorial demonstrate outstanding promise of Research Graduate Fellowship Award for Excellence in Teaching, leadership and professional achievement Gift from the IEOR Department, nominated TA-ing, and Service in civil and construction engineering. by the faculty. This fellowship is designated Awarded each year by the Department The award is in support of a project with to support graduate students pursuing of Computer Science to up to three emphasis on the construction industry in degrees in operations research or industrial computer science students for which the students participate. engineering. Recipients have demonstrated outstanding contributions to teaching in academic excellence and professional the department and exemplary service Paul Michelman Award for Exemplary promise in the fields. Students are awarded to the department and its mission. Service to the Computer Science a certificate and monetary prize. Department Dongju Lee Memorial Award This award is given to a Ph.D. Industrial Engineering and Operations Established in 2005 by family and student in computer science who Research Academic Outstanding friends in memory of Dongju Lee (DJ), has performed exemplary service to Service Award graduate student in the Department the department, devoting time and In recognition of significant contributions of Civil Engineering and Engineering effort beyond the call to further the to the IEOR Department, this award Mechanics, 1999–2003. A certificate department’s goals. It is given in goes to graduate students who have and cash prize awarded annually memory of Dr. Paul Michelman ’93, represented the department with grace by the department to a doctoral who devoted himself to improving and intelligence through their work as student specializing in geotechnical/ our department through service while ambassadors, student leaders, etc. geoenvironmental engineering and of excelling as a researcher. Students are awarded a certificate and outstanding promise for a career in monetary prize. research and academia. Millman Award A certificate and prize, in honor of Jacob The Bernard Jaffe Prize for the The Sebastian B. Littauer Award Millman, awarded to two of the most Encouragement of Inventiveness in Established in 1979 in honor of Professor outstanding teaching assistants for the Engineering Littauer, a certificate and cash prize academic year. Gift of Fern Jaffe in honor of her late presented annually by the Department husband, Bernard Jaffe ’38, ’39. of Industrial Engineering and Operations The Russell C. Mills Award Given annually to an undergraduate Research to a senior for outstanding Presented to a computer science major and graduate engineering and promise of scholarly and professional for excellence in computer science in applied science student who exhibits achievement in operations research. memory of Russell C. Mills, a Ph.D. exceptional qualities of curiosity candidate in computer science who toward the engineered world and a Robert D. Lilley Award for Socially exemplified academic excellence by his predisposition toward inventiveness and Responsible Engineering boundless energy and intellectual curiosity. novel problem solving in both theoretical Established in 2013 by a gift from and physical contexts. Preference is Helen M. Lilley, this award supports the The Mindlin Scholar in Civil given to students whose endeavors are activities of student clubs at the School Engineering and Engineering directed toward the betterment of the that have as their primary focus socially Mechanics human condition. responsible engineering. This award will be made each year to a graduate student in the Department of Civil Engineering and Engineering Mechanics in recognition

engineering 2014–2015 230 of outstanding promise of a creative who shows the greatest promise of an inspirational teacher and scholar career in research and/or practice. success in applying the discipline who taught students and colleagues This award is made possible by gifts of chemical engineering to the to appreciate the value of broad of friends, colleagues, and former improvement of biological products interactions between engineering students of Professor Raymond and medical devices. and medicine, particularly in the D. Mindlin, and, above all, by the fields of cardiovascular mechanics, Mindlin family. It is intended to honor The Francis B. F. Rhodes Prize tissue engineering, and orthopedics. the Mindlin brothers, Raymond, Established in 1926 by Eben Erskine The Richard Skalak Memorial Prize Eugene, and Rowland, who excelled Olcott 1874, in memory of his is awarded annually to a senior in their respective scientific fields of classmate, Francis Bell Forsyth Rhodes, biomedical engineering student engineering research, engineering School of Mines, 1874, and awarded who exemplifies the qualities of practice, and medical practice. from time to time to the member of the outstanding engineering scholarship graduating class in materials science and breadth of scientific curiosity that The Moles’ Student Award in Civil and metallurgical engineering who has form the basis for lifelong learning Engineering shown the greatest proficiency in his or and discovery. Awarded to the student in engineering her course of study. whose academic achievement Professor Rene B. Testa Award and enthusiastic application show School of Engineering and Applied A prize that will be given to graduate outstanding promise of personal Science Scholar Athlete Award and undergraduate students who have development leading to a career Presented from time to time by the achieved excellence in their academic in construction engineering and Office of the Dean to that graduating program and have actively participated management. student who has distinguished himself in the research and testing mission of or herself as a varsity athlete and the Carleton Laboratory. The James F. Parker Memorial Award scholar. (Mechanical Engineering Design Award) The George Vincent Wendell James F. Parker served and represented School of Engineering and Applied Memorial Medal Columbia engineering students as Science Student Activities Award Established in 1924 by the friends in the their Dean from 1975 to 1984. He also This award is presented to an alumni and faculty of the late Professor distinguished himself in the pursuit undergraduate degree candidate in George Vincent Wendell to honor and and analysis of two-dimensional art. In Columbia Engineering who by virtue perpetuate his memory; a certificate recognition of his special combination of of his or her willingness, energy, and medal awarded annually by choice talents and their integration, the School and leadership has significantly of the class and the faculty to that of Engineering and Applied Science contributed to the co-curricular life member of the graduating class who salutes the graduate student who has of the School. best exemplifies his ideals of character, distinguished her- or himself as a designer. scholarship, and service. A person of creative and innovative Robert Simon Memorial Prize inclination receives the James Parker The Robert Simon Memorial Prize was Residence Hall Medal, as evidenced by outstanding established in 2001 to honor Robert Scholarships performance in courses integrating Simon, a Columbia alumnus who spent engineering analysis and design. a lifetime making valuable contributions to computational and mathematical Class of 1887 Mines Residence The Robert Peele Prize sciences, and is awarded annually by Scholarship A prize of $500 awarded from time to the Department of Applied Physics and Awarded annually to a third-year degree time to that member of the graduating Applied Mathematics to the doctoral candidate, with preference given to class in mining engineering who has student who has completed the most descendants of members of the Class of shown the greatest proficiency in his or outstanding dissertation. Should no 1887 Mines. her course of studies. dissertation qualify in a given year, the Class of 1896 Arts and Mines prize may be awarded to either the Scholarship The Claire S. and Robert E. Reiss most outstanding student who has Awarded annually to a degree candidate in Award in Biomedical Engineering completed a Master of Science degree Columbia College, Columbia Engineering, This award is given by Robert E. Reiss, in the department or to the most or the Graduate School of Architecture B.S.’66, and his wife, Claire S., to outstanding graduating senior in the and Planning, with preference given to the graduating senior(s) in biomedical department. engineering judged by faculty of the descendants of members of the Class of program as most likely to contribute The Richard Skalak Memorial Prize 1896 Arts and Mines. substantially to the field. The Richard Skalak Memorial Prize Class of 1916 College and was founded in recognition of the Engineering Fund The Robert Edward Reiss Award in pioneering contributions of Richard Gift of the Class of 1916 College and Chemical Engineering Skalak to the development of the Engineering. Awarded annually to the student in the biomedical engineering program at Department of Chemical Engineering Columbia University. Dr. Skalak was engineering 2014–2015 University and School Policies, Procedures, and Regulations 232 Academic Procedures and Standards

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

engineering 2014–2015 undergraduate registration is defined is a special student is considered to Undergraduate students may obtain 233 as at least 12 semester credits per be making normal progress if at the academic credit toward the B.S. term. However, in order to complete the completion of 9 credits, he or she degree by completing course work at degree, students must be averaging has earned a cumulative GPA of 2.5. other accredited four-year institutions. 16 points per term. Students may not Candidates in the Doctor of Engineering Normally, this credit is earned during register for point loads greater than 21 Science (Eng.Sc.D.) program are the summer. To count as credit toward points per term without approval from expected to achieve a 3.0 grade-point the degree, a course taken elsewhere the Committee on Academic Standing. average at the completion of 9 points of must have an equivalent at Columbia To be eligible to receive the Bachelor course work. University and the student must achieve of Science degree, a student must Thereafter, graduate students are a grade of at least B. An exception to complete the courses prescribed in a considered to be making minimum this policy is made for students enrolled faculty-approved major/program (or satisfactory progress if they successfully in an approved study abroad program. faculty-authorized substitutions) and complete at least 75 percent of all Students in an approved study abroad achieve a minimum cumulative grade- courses they have registered for as program will receive transfer credit if point average (GPA) of 2.0. Although candidates for the degree with grades they earn a grade of C or higher. To the minimum number of academic of C– or better. Students placed on transfer credit, a student must obtain credits is 128 for the B.S. degree, some academic probation because of their prior approval from his or her adviser programs of the School require a greater grades are nonetheless considered and the department before taking such number of credits in order to complete to be making minimum satisfactory courses. A course description and all the requirements. Undergraduate progress for their first term on probation syllabus should be furnished as a part engineering degrees are awarded only to (see chapter “Academic Standing,” of the approval process. Courses taken students who have completed at least following). Degree requirements for before the receipt of the high school 60 points of course work at Columbia. master’s degrees must be completed diploma may not be credited toward the No credit is earned for duplicate courses, within five years; those for the doctoral B.S. degree. A maximum of 6 credits including courses that are taken pass/fail degrees must be completed within may be applied toward the degree for the first time and the final grade is a P. seven years. A minimum cumulative college courses taken following the Undergraduates in the programs grade-point average of 2.5 (in all receipt of a high school diploma and accredited by the Engineering courses taken as a degree candidate) is initial enrollment at Columbia University. Accreditation Commission of ABET required for the M.S. degree; a minimum Master degree students are not (biomedical engineering, chemical GPA of 3.0 is required for the Doctor of eligible for transfer credits. engineering, civil engineering, Earth Engineering Science (Eng.Sc.D.) degree. Students possessing a conferred and environmental engineering, The minimum residence requirement for M.S. degree may be awarded 2 electrical engineering, and mechanical each Columbia degree is 30 points of residence units toward their Ph.D., as engineering) satisfy ABET requirements course work completed at Columbia. well as 30 points of advanced standing by taking the courses in prescribed toward their Ph.D. or Eng.Sc.D. with programs, which have been designed Changes in Registration departmental approval. by the departments so as to meet the A student who wishes to drop or add ABET criteria. courses or to make other changes in Examinations his or her program of study after the Midterm examinations: Instructors Attendance change of program period must obtain generally schedule these in late October Students are expected to attend the signature of his or her adviser. A and mid-March. their classes and laboratory periods. student who wishes to drop or add a Final examinations: These are given Instructors may consider attendance in course in his or her major must obtain at the end of each term. The Master assessing a student’s performance and department approval. The deadline for University Examination Schedule is may require a certain level of attendance making program changes in each term available online and is confirmed by for passing a course. is shown in the Academic Calendar. November 1 for the fall term and April After this date, undergraduate students 1 for the spring term. This schedule is Graduate must petition their Committee on sent to all academic departments and Graduate students are required Academic Standing; graduate students is available for viewing on the Columbia to complete the School’s degree must petition the Office of Graduate website. Students should consult with requirements as outlined on pages 24–27 Student Affairs. For courses dropped their instructors for any changes to the (The Graduate Programs). Full-time after these dates, no adjustment of fees exam schedule. Examinations will not graduate registration is defined as at least will be made. Failure to attend a class be rescheduled to accommodate 12 credits per term. Students may not without officially dropping the class will travel plans. register for point loads greater than 21 result in a grade indicating permanent Note: If a student has three final credits per term. unofficial withdrawal (UW). examinations scheduled during one A graduate student who has calendar day, as certified by the matriculated in an M.S. program or Transfer Credits Registrar, an arrangement may be made with one of the student’s instructors

engineering 2014–2015 234 to take that examination at another, course for R, or who, with the approval in an effort to improve his or her final mutually convenient time during the of the instructor, file written notice of grade. The privilege is granted only final examination period. This refers to a change of intention with the registrar when there is a wide discrepancy calendar day, not a 24-hour time period. not later than the last day for change of between the quality of the student’s Undergraduate students unable to make program. Students wishing to change work during the term and his or her suitable arrangements on their own to R credit after this date are required to performance on the final examination, should contact their adviser. Graduate submit the dean’s written approval to the and when, in the instructor’s judgment, students should contact the Office of registrar. A course which has been taken the reasons justify a make-up Graduate Student Affairs. for R credit may not be repeated later examination. A student may be granted for examination credit. The mark of R is the mark of MU in only two courses in Transcripts and Certifications automatically given in Doctoral Research one term, or, alternatively, in three or For information on the Federal Family Instruction courses. more courses in one term if their total Education Rights and Privacy Act The mark of UW (unofficial point value is not more than 7 credits. (FERPA) of 1974, please visit http:// withdrawal): given to students who The student must remove MU by taking facets.columbia.edu—Essential Policies discontinue attendance in a course but a special examination administered as for the Columbia Community. Information are still officially registered for it, or who soon as the instructor can schedule it. on obtaining University transcripts and fail to take a final examination without an The mark of P/F (pass/fail): certifications will be found as a subhead authorized excuse. Undergraduate students may take up under Essential Resources. The mark of IN (incomplete): granted to 6 credits of the 9-11 nontechnical only in the case of incapacitating illness elective credit on a P/F basis. These Report of Grades as certified by the Health Services at courses must be at the 3000-level or Columbia, serious family emergency, or higher and must be courses that can Grades can be viewed by using the circumstances of comparable gravity. be taken P/F by students attending Student Services Online feature located Undergraduate students request an IN Columbia College (e.g. instruction on the Student Services home page at by filling out the Incomplete Request classes in foreign language and core columbia.edu/students. If you need an Form with their advising dean prior curriculum classes are not eligible). official printed report, you must request to the final exam for the course in These courses may not count toward a transcript (please see Transcripts and the semester of enrollment. Students the minor, and cannot be uncovered Certifications above). requesting an IN must gain permission under any circumstances. Students may All graduate students must have a from both the Committee on Academic take only one class P/F per semester to current mailing address on file with the Standing (CAS) and the instructor. count toward the 128 points, exclusive Registrar’s Office. Graduate students should contact their of physical education credit and any instructor. If granted an IN, students other course that is taught only on a Transcript Notations must complete the required work P/F basis. Please note that physical The grading system is as follows: A, within a period of time stipulated by the education classes are the only courses excellent; B, good; C, satisfactory; instructor but not to exceed one year. taught solely on a P/F basis that may D, poor but passing; F, failure (a final After a year, the IN will be automatically apply toward the 128 credits for the grade not subject to re-examination). changed into an F or the contingency degree. The P/F option does not Occasionally, P (Pass) is the only grade. count toward degree requirements for passing option available. The grade- The mark of YC (year course): a mark graduate students. point average is computed on the basis given at the end of the first term of a The mark of W (official withdrawal): a of the following index: A=4, B=3, C=2, course in which the full year of work mark given to students who are granted D=1, F=0. Designations of + or – (used must be completed before a qualitative a leave of absence after the drop only with A, B, C) are equivalent to 0.33 grade is assigned. The grade given at deadline for the semester. The grade (i.e., B+=3.33; B–=2.67). Grades of P, the end of the second term is the grade of W, meaning “official withdrawal,” will INC, UW, and MU will not be included for the entire course. be recorded as the official grade for in the computation of the grade-point The mark of CP (credit pending): the course in lieu of a letter grade. The average. given only in graduate research courses grade of W will zero out the credits for The mark of R (registration credit; no in which student research projects the class so the student’s GPA will not qualitative grade earned): not accepted regularly extend beyond the end of be affected. for degree credit in any program. R the term. Upon completion, a final credit is not available to undergraduate qualitative grade is then assigned and Name Changes students for academic classes. In some credit allowed. The mark of CP implies Students may change their name of divisions of the University, the instructor satisfactory progress. record by submitting a name change may stipulate conditions for the grade The mark of MU (make-up affidavit to the Student Service Center. and report a failure if those conditions examination): given to a student who Affidavits are available from this office or are not satisfied. The R notation will has failed the final examination in a online at registrar.columbia.edu. be given only to those students who course but who has been granted the indicate, upon registration and to the privilege of taking a second examination instructor, their intention to take the Graduation

engineering 2014–2015 Columbia University awards degrees Philosophy degrees should inquire at Diplomas 235 three times during the year: in February, their departments but must also follow There is no charge for the preparation May, and October. There is one the instructions of the Dissertation and conferral of an original diploma. commencement ceremony in May. Office, 107 Low Library. If your diploma is lost or damaged, General deadlines for applying for there will be a charge of $100 for Application or Renewal of graduation are November 1 for February, a replacement diploma. Note that Application for the Degree December 1 for May, and August 1 for replacement diplomas carry the In general, students pick up and file October. (When a deadline falls on a signatures of current University an application for a degree at their weekend or holiday, the deadline moves officials. Applications for replacement schools or departments, but there are to the next business day.) Doctoral diplomas are available on our website: several exceptions. Candidates for students must deposit their dissertations registrar.columbia.edu/registrar-forms/ Master of Science degree may pick up two days before the above conferral application-replacement-diploma. and file their application for the degree dates in order to graduate. Any questions regarding graduation with the Diploma Division, 210 Kent Students who fail to earn the degree or diploma processing should be Hall, or through the registrar’s website: by the conferral date for which they addressed to [email protected]. registrar.columbia.edu/registrar-forms/ applied must file another application for application-degree-or-certificate. a later conferral date. Candidates for doctoral and Master of

engineering 2014–2015 236 Academic standing

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

engineering 2014–2015 and by the student’s departmental withdrawal from Columbia Engineering may request permission to return after one 237 adviser when the student has for a nonmedical reason. Students semester as long as they can demonstrate declared a major. All proposed considering a voluntary leave must that they can remain on sequence with courses will be reviewed by the discuss this option in advance with their coursework and have the prior appropriate faculty who teach the their advising dean. Voluntary leaves are approval of the departmental adviser. equivalent classes at Columbia granted for a period of one academic Students who decide not to return University. All courses that are being year only; VLOAs will not be granted for must notify the Center for Student taken to fulfill a major requirement one semester, or for more than one year. Advising of their decision. The date of or as a technical elective must Students must be in good academic separation for the leave of absence will be approved by the student’s standing at the time of the leave, and be the date of separation for withdrawal. departmental adviser. Courses being must be able to complete their major Leaves may not extend beyond four taken to count as a nontech elective and degree in eight semesters. Students semesters. Students who do not notify or to count as general credit would may not take courses for transferable the Center for Student Advising of their only require the approval of the credit while on leave. Finally, students intentions by the end of the two-year Committee on Academic Standing. who choose to take voluntary leaves period will be permanently withdrawn. The existing procedures for the are not guaranteed housing upon approval of outside credit will be return to the University. International Leave for Military Duty followed in these cases. Students students should contact the International Please refer to Military Leave of must receive a grade of B or better Students and Scholars Office to ensure Absence Policy in Essential Policies for the credit to be transferred. that a leave will not jeopardize their for the Columbia Community (facets. ability to return to Columbia Engineering. columbia.edu) for recent updates Medical Leave of Absence regarding leave for military duty. A medical leave of absence for an undergraduate emergency undergraduate student is granted by the family leave of absence Involuntary Leave Center for Student Advising to a student CC and SEAS students who must of Absence Policy whose health prevents him or her from leave the university for urgent family Please refer to Involuntary Leave of successfully pursuing full-time study. reasons that necessitate a semester- Absence Policy in Essential Policies Undergraduates who take a medical leave long absence (e.g., family death or for the Columbia Community (facets. of absence are guaranteed housing upon serious illness in the family) may request columbia.edu). their return. A medical leave of absence an emergency family leave of absence. for a graduate student is granted by the Documentation of the serious nature Office of Graduate Student Affairs, so of the emergency must be provided. Required Medical Leave please consult with this office for more Students must request an emergency for Students with information. Documentation from a family leave of absence from their advising Eating Disorders physician or counselor must be provided dean in the Center for Student Advising. Please refer to Required Medical Leave before such a leave is granted. In order to When an emergency family leave of for Students with Eating Disorders in apply for readmission following a medical absence is granted during the course Essential Policies for the Columbia leave, a student must submit proof of of the semester, the semester will be Community (facets.columbia.edu). recovery from a physician or counselor. deleted if the leave begins prior to the A medical leave is for a minimum of one drop deadline. If after the drop deadline, year and cannot be longer than two the course grades will normally be W Readmission years. If the student does not return within (official withdrawal) in all courses. In Students seeking readmission to The Fu the two-year time frame, he or she will be certain circumstances, a student may Foundation School of Engineering and permanently withdrawn from the School. qualify for an incomplete, which would Applied Science must submit evidence During the course of the leave, students have to be completed by the first week that they have achieved the purposes for are not permitted to take any courses of the semester in which the student which they left. Consequently, specific for the purpose of transferring credit and returns to Columbia. If the Incomplete is readmission procedures are determined are not permitted to be on the campus. not completed by that time, a W will be by the reasons for the withdrawal. For more information about the medical inserted. Further information for undergraduate leave of absence policy, consult your To return, students must notify the students is available in the Center for advising dean. Center for Student Advising as soon Student Advising. Graduate students as possible, ideally by October 1 for should see the Office of Graduate the spring semester and April 1 for the Student Affairs. Voluntary Leave fall semester. Students must request Students applying for readmission of Absence readmission in writing and submit a should complete all parts of the A voluntary leave of absence (VLOA) statement describing their readiness to appropriate readmission procedures may be granted by the Committee on return. Once readmission is granted, by June 1 for the autumn term or Academic Standing to undergraduate housing will be guaranteed. SEAS students November 1 for the spring term. students who request a temporary

engineering 2014–2015 238 Policy on Conduct and Discipline

Life in the We expect that in and out of the • refusal to show identification at the Academic Community classroom, on and off campus, each request of a University official; failure The Fu Foundation School of student in the School will act in an to respond to the legitimate request Engineering and Applied Science within honest way and will respect the rights of a University official exercising his or Columbia University is a community. of others. Freedom of expression is an her duty Admitted students, faculty, and essential part of University life, but it • threatening, harrassing, or abusing administrators come together and does not include intimidation, threats of others work through committees and other violence, or the inducement of others to • violating local, state, or federal laws representative bodies to pursue and to engage in violence or in conduct which • violating the “Rules of University promote learning, scholarly inquiry, and harasses others. We state emphatically Conduct” (copies of which are free discourse. As in any community, that conduct which threatens or available in 406 Low Library and other principles of civility and reasoned harasses others because of their race, locations mentioned above) interaction must be maintained. Thus, sex, religion, disability, sexual orientation, • violating the rules of the residence methods for addressing social as well as or for any other reason is unacceptable halls as outlined in the “Guide to academic behaviors exist. and will be dealt with very severely. If Living”; this also applies to all fraternity each of us at Columbia can live up to and sorority housing these standards, we can be confident • violating the University’s Alcohol Policy Rules of that all in our community will benefit fully • violating the University’s Sexual University Conduct from the diversity to be found here. Any Assault Policy Rules of University Conduct are included undergraduate student who believes • violating the rules governing Columbia under University Regulations in Essential he or she has been victimized should University Information Technology Policies for the Columbia Community speak with an adviser in the Center (CUIT) policies and procedures (facets.columbia.edu). for Student Advising, a member of the • representing any commercial interest Residential Life staff, or a member of the on campus or operating any business STUDent conduct Office of Judicial Affairs and Community on campus without authorization from The continuance of each student upon Standards; graduate students should the Associate Dean of Career Services the rolls of the University, the receipt speak with an officer in the Office of Graduate Student Affairs. of academic credits, graduation, and Academic Integrity While every subtlety of proper the conferring of the degree are strictly Academic integrity defines a university behavior cannot be detailed here, subject to the disciplinary powers of the and is essential to the mission of examples of other actions subject to University. education. At Columbia students are discipline are: Although ultimate authority on expected to participate in an academic matters of student discipline is vested in • dishonesty in dealings with University community that honors intellectual work the Trustees of the University, the Dean officials, including members of the and respects its origins. In particular, of the School and his staff are given faculty the abilities to synthesize information responsibility for establishing certain • knowingly or recklessly endangering and produce original work are key standards of behavior for Columbia the health or safety of others components in the learning process. As Engineering students beyond the • intentionally or recklessly destroying, such, a violation of academic integrity regulations included in the Statutes damaging, or stealing property is one of the most serious offenses a of the University and for defining • possession, distribution, or use of student can commit at Columbia and procedures by which discipline will be illegal drugs can result in dismissal. administered. • possession of weapons

engineering 2014–2015 Students rarely set out with the in intellectual development. Plagiarism, Academic Integrity Policies and 239 intent of engaging in violations of the use of words, phrases, or ideas Expectations academic integrity. But classes are belonging to another, without properly Violations of policy may be intentional challenging at Columbia, and students citing or acknowledging the source, or unintentional and may include will often find themselves pressed for is considered one of the most serious dishonesty in academic assignments time, unprepared for an assignment or violations of academic integrity and or in dealing with University officials, exam, or feeling that the risk of earning is a growing problem on university including faculty and staff members. a poor grade outweighs the need to campuses. Moreover, dishonesty during the Dean’s be thorough. Such circumstances One of the most prevalent forms Discipline hearing process may result in lead some students to behave in of plagiarism involves students using more serious consequences. a manner that compromises the information from the Internet without Common types of academic integrity integrity of the academic community, proper citation. While the Internet violations: disrespects their instructors and can provide a wealth of information, classmates, and deprives them of an sources obtained from the web must • Plagiarism: the use of words, phrases, opportunity to learn. In short, they be properly cited just like any other or ideas belonging to another, without cheat. Students who find themselves in source. If you are uncertain how to properly citing or acknowledging the such circumstances should immediately properly cite a source of information source contact their instructor and adviser for that is not your own, whether from the • Self-plagiarism: the submission of one advice. Internet or elsewhere, it is critical that piece of work in more than one course The easiest way to avoid the you do not hand in your work until without the explicit permission of the temptation to cheat in the first place you have learned the proper way to instructors involved is to prepare yourself as best you can. use in-text references, footnotes, and • Falsification or misreprensentation Here are some basic suggestions to bibliographies. Faculty members are of information in course work or lab help you along the way: available to help as questions arise work; on any application, petition, or about proper citations, references, forms submitted to the School • Understand instructor expectations and the appropriateness of group • Fabrication of credentials in materials and policies. work on assignments. You can also submitted to the University for • Clarify any questions or concerns check with the Undergraduate Writing administrative or academic review about assignments with instructors as Program. Ignorance of proper citation • Violating the limits of acceptable early as possible. methods does not exonerate one from collaboration in course work set by a • Develop a timeline for drafts and responsibility. faculty member or department final edits of assignments and begin • Facilitating academic dishonesty by preparation in advance. Personal Responsibility, Finding enabling another to engage in such • Avoid plagiarism: acknowledge Support, and More Information behavior people’s opinions and theories by A student’s education at Columbia • Cheating on examinations, tests, or carefully citing their words and always University is comprised of two homework assignments indicating sources. complementary components: a • Unauthorized collaboration on an • Utilize the campus’s resources, mastery over intellectual material assignment such as the advising centers and within a discipline and the overall • Receiving unauthorized assistance on Counseling and Psychological development of moral character an assignment Services, if feeling overwhelmed, and personal ethics. Participating • Copying computer programs burdened, or pressured. in forms of academic dishonesty • Unauthorized distribution of • Assume that collaboration in the violates the standards of our assignments and exams completion of assignments is community at Columbia and severely • Lying to a professor or University prohibited unless specified by the inhibits a student’s chance to grow officer instructor. academically, professionally, and • Obtaining advance knowledge of socially. As such, Columbia’s approach exams or other assignments without Plagiarism and to academic integrity is informed by permission Acknowledgment of Sources its explicit belief that students must Columbia has always believed that take full responsibility for their actions, Disciplinary Procedures writing effectively is one of the most meaning you will need to make Many policy violations that occur in the important goals a college student can informed choices inside and outside Residence Halls rules are handled by achieve. Students will be asked to do the classroom. Columbia offers a the Associate Directors of Residential a great deal of written work while at wealth of resources to help students Life. Some serious offenses are referred Columbia: term papers, seminar and make sound decisions regarding directly to the Office of Judicial Affairs laboratory reports, and analytic essays academics, extracurricular activities, and Community Standards. Violations of different lengths. These papers play and personal issues. If you don’t know in University Apartment Housing are a major role in course performance, but where to go, see your advising dean. handled by building managers and more important, they play a major role

engineering 2014–2015 240 housing officials. Some incidents are the normal operations of the institution, the violation of Columbia policy(ies) may referred directly to the School’s housing or to the safety of himself or herself request a review of the decision if: (1) liaison in the Office of Graduate Student or others or to the property of the the student believes a procedural error Affairs. University or others. occurred, which the student feels may Most violations of rules concerning When a complaint is received, the change or affect the outcome of the fraternities or sororities as organizations Office of Judicial Affairs and Community decision; (2) the student has substantive are handled by the Associate Director Standards or Office of Graduate Student new evidence that was not available at of Greek Life and Leadership. Some Affairs determines whether Dean’s the time of the hearing and that may serious offenses are referred directly Discipline is an appropriate response change the outcome; or (3) the student to the Office of Judicial Affairs and or if the complaint should be referred feels that the severity of the sanction Community Standards. elsewhere. If a Dean’s Discipline hearing is inappropriate given the details In matters involving rallies, picketing, is to occur, a student is informed in of the case. The request for review and other mass demonstrations, the writing of the complaint made against must be made in writing as directed Rules of University Conduct outlines him/her and of the next step in the in the hearing outcome letter. For procedures. process. At the hearing, at least two more information about the discipline The Office of Judicial Affairs and staff members will present the accused process for undergraduate students, Community Standards is responsible student with the information that please visit the Office of Judicial for all disciplinary affairs concerning supports the allegation that he/she has Affairs and Community Standards undergraduate students that are not violated Columbia Engineering or other website (studentaffairs.columbia.edu/ reserved to some other body. The University policy(ies). The student is then judicialaffairs). For more information Office of Graduate Student Affairs is asked to respond and will be given an about the discipline process for responsible for all disciplinary affairs opportunity to present information on his graduate students, please visit the Office concerning graduate students that are or her behalf. of Graduate Student Affairs website not reserved to some other body. At the conclusion of the hearing, (engineering.columbia.edu/graduate the hearing officers will make a -student-affairs). Dean’s Discipline Process for determination, based on all of the Undergraduate and Graduate information available to them, regarding Confidentiality Students whether the accused student is In general, under University policy and The purpose of the Dean’s Discipline responsible for the violation(s). The federal law, a student’s record, including process is twofold. First, it is used standard of proof used to make this information about Dean’s Discipline pro- to determine the accused student’s determination is the preponderance of ceedings, is confidential; however, there responsibility for the alleged violation(s) the evidence standard. This standard are certain exceptions to this rule. One of Columbia Engineering or University allows for a finding of responsibility if exception to this principle is that the policy(ies). In addition, it is an the information provided shows that it outcome of Dean’s Disciplinary proceed- opportunity for the student to engage is more likely than not that a violation ings alleging a crime of violence may in a meaningful conversation regarding of Columbia policy(ies) occurred. If the be disclosed both to the accuser and his or her role as a member of the student is found responsible, the degree the accused. To read more about the Columbia community. The Dean’s of seriousness of the offense and the exceptions that apply to the disclosure Discipline process is not an adversarial student’s previous disciplinary record, of student records information, please process, nor is it a legalistic one, and if any, will determine the severity of the visit facets.columbia.edu/policy-access- therefore the technical rules of evidence sanction that will be issued. The student student-records-ferpa. applicable to civil and criminal court will be notified of the outcome of the Students found responsible for cases do not apply. hearing in writing. reportable violations of conduct, includ- In a situation requiring immediate A student found responsible after ing academic integrity violations, may action, a student may be removed from a hearing has the right to request an face reports of such offenses on future housing, if applicable, and/or placed on appeal of the decision and the resulting recommendations for law, medical, or interim suspension if it is determined sanctions. There are three grounds upon graduate school. The parents or guard- that the student’s behavior makes his which an appeal of the decision may be ians of undergraduate students may also or her presence on campus a danger to made. A student found responsible for be notified.

engineering 2014–2015 Essential Policies for the Columbia Community 241

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

engineering 2014–2015 242 Student Grievances, Academic Concerns, and Complaints

The following procedures are part dishonesty, or issues of behavioral procedure below also applies to of a process to ensure that stu- concerns as they relate to student complaints against instructional and dent concerns about experiences conduct (see item B). They also should administrative staff): in the classroom or with faculty are not be used when students believe that Students are encouraged to addressed in an informed and appro- they have been the victim of sexual seek a resolution to their complaints priate 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 e-mail 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 A. Complaints about offers several informal paths for office and on the departmental faculty and staff students to use, as described in this website. Students may also ask the academic 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 atomosphere 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. the student should consult the performance. They should confine • Students may bring their concerns to procedures of the school in which their classes to the subject matter the University’s Ombuds Officer, who they serve. covered by their courses and not use serves as an informal, confidential For academic complaints relating them to advocate any political or social resource for assisting members of the to Engineering faculty, these cause” (2008 Faculty Handbook). University with conflict resolution. The procedures, like those of other A fuller description of faculty rights Ombuds Officer provides information, schools, provide for a final appeal and obligations may be found in the counseling, and referrals to to the University Provost. Faculty Handbook (columbia.edu/ appropriate University offices and will The procedures under item A do cu/vpaa/handbook). Students who also mediate conflicts if both parties not take the place of the grievance feel that members of the Engineering agree. The Ombuds Officer does procedures already established to faculty have not met those obligations not have the authority to adjudicate address disputes over grades, academic may take the following steps (the

engineering 2014–2015 disputes and does not participate (undergraduate students), who acts member are all subject to appeal. A 243 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 B. 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 2014–2015 244 and believe that a procedural issue is C. Discrimination, Discrimination and Harassment and in involved, they should bring the matter to Harassment, and Gender- Gender-Based Misconduct Policies for the attention of the Vice Dean. The Vice based misconduct Students Dean will work with the student and the If the alleged misconduct involves faculty to determine whether there has discrimination, harassment, gender- D. Scientific or been a procedural breach and if so, take based or sexual misconduct, a scholarly misconduct immediate steps to remedy the matter. If student should file a complaint with Complaints against the School’s the Vice Dean, together with appropriate the Associate Provost for Equal faculty that allege scientific or scholarly faculty other than the instructor, decides Opportunity and Affirmative Action. The misconduct are evaluated using other that there is no need for further action, procedures for handling such complaints procedures. These are contained in the the student will be informed and the are described in the statements Columbia University Institutional Policy decision will be final. Student Policies and Procedures on on Misconduct in Research.

engineering 2014–2015 Directory of University Resources 246 columbia university resource list

Admissions (Undergraduate) Megan Rigney, [email protected] All inquiries concerning Lit Hum should Senior Assistant Dean, Preprofessional be directed to the Center for the Core Office of Undergraduate Admissions Advising Curriculum (listed above) 212 Hamilton, MC 2807 212-854-2522 Nathaniel Wood Jr., [email protected] Undergraduate Writing Program undergrad.admissions.columbia.edu Assistant Dean 310 Philosophy, MC 4995 [email protected] 212-854-3886 Center for Career Education [email protected] Jessica Marinaccio East Campus, Lower Level, MC 5727 Dean of Undergraduate Admissions and 212-854-5609 Nicole Wallack, Director Financial Aid careereducation.columbia.edu Columbia Video Network Joanna May, [email protected] [email protected] 540 S. W. Mudd, MC 4719 Associate Dean of Undergraduate 212-854-6447 Admissions Columbia College 208 Hamilton, MC 2805 cv.columbia.edu Peter Johnson, [email protected] 212-854-2441 [email protected] Director of Undergraduate Admissions James J. Valentini Meaghan McCarthy, [email protected] Dean of Columbia College Undergraduate Student Life Director of Programming and Outreach 510–515 Lerner, MC 2601 Kathryn B. Yatrakis, [email protected] 212-854-3612 David Buckwald, [email protected] Dean of Academic Affairs Senior Associate Director and Director Todd Smith-Bergollo, ts2488@columbia. of Engineering Recruitment Core Curriculum Program edu Interim Dean of Undergraduate Student Diane McKoy, [email protected] Offices Life Senior Associate Director Center for the Core Curriculum Beth Venderputten Perlongo, bv2145@ 202 Hamilton, MC 2811 James Minter, [email protected] columbia.edu 212-854-2453 Senior Associate Director Director of Operations Roosevelt Montás, [email protected] Advising (Undergraduate) Director of the Center for the Core Multicultural Affairs Center for Student Advising Curriculum 510 Lerner, MC 2607 403 Lerner Hall, MC 1201 212-854-0720 Art Humanities 212-854-6378 826 Schermerhorn, MC 5517 Melinda Aquino, [email protected] studentaffairs.columbia.edu/csa 212-854-4505 Associate Dean of Multicultural Affairs [email protected] Branden Jospeh, [email protected] Chia-Ying Sophia Pan, cp2804@ Monique Rinere Director of Undergraduate Studies columbia.edu Dean of Advising Director of Education, Outreach, and Music Humanities International Student Support Sixto Fernandez, [email protected] 621 Dodge, MC 1813 Director of Operations 212-854-3825 Intercultural Resource Center (IRC) Andrew Plaa, [email protected] 552 West 114th Street, MC 5755 Susan Boynton, [email protected] Associate Dean of Advising 212-854-7461 Director of Undergraduate Studies Lavinia Lorch, [email protected] Marta Esquilin, [email protected] Contemporary Civilization Senior Assistant Dean and Director of Intercultural and Social Justice 514 Fayerweather, MC 2811 Director of Scholars Program Programming 212-854-5682 Angie Carrillo, [email protected] James Zetzel, [email protected] Residential Life Assistant Dean, Community Outreach Director of Undergraduate Studies 515 Lerner, MC 4205 A. Alex España, [email protected] 212-854-6805 Senior Assistant Dean Literature Humanities 202 Hamilton, 212-854-2453 Cristen Scully Kromm, [email protected] Robert Ferraiuolo, [email protected] Mail Code 2811 Associate Dean of Residential Life Assistant Dean, Advising Specialites

engineering 2014–2015 247

Anna Schmidt-Mackenzie, as4393@ Financial Aid (Undergraduate) CU-EMS (Ambulance) columbia.edu 212-854-5555 or 4-5555 from a campus Director of Residential Life Office of Undergraduate Financial Aid phone and Educational Financing Brad Badgley, [email protected] Office: 618 Lerner Insurance and Immunization Director of Fraternity and Sorority Life Mailing: 100 Hamilton, MC 2802 Compliance Offices Lerner, 5th Floor, MC 2605 Student Engagement 212-854-3711 Insurance Office: 212-854-3286 515 Lerner, MC 2601 [email protected] Immunization Compliance Office: 212-854-3611 Kathryn Tuman 212-854-7210 Joshua Lucas, [email protected] Executive Director of Financial Aid Director of Student Community Programs Pamela Mason, [email protected] Student Medical Insurance Plan Sallee Spearman, [email protected] Senior Associate Director Administrators: Aetna Student Health Director of Student Financial Advising 1-800-859-8471 Leah Bestmann, [email protected] www.aetnastudenthealth.com/ Annie Virkus, [email protected] Assistant Director columbiadirect.html Director of Leadership and Civic Engagement Financial Aid (Graduate) Alice! Health Promotion Lerner, 5th Floor, MC 2605 Benjamin Young, [email protected] Federal Financial Aid (Loans, Work Study) 212-854-5453 Director of Broadcasting and Operations Financial Aid and Educational Financing health.columbia.edu/alice 615 Lerner, MC 2802 computing support center 212-854-3711 Counseling and Psychological Services Client Services Help Desk Jacqueline Perez, Associate Director Lerner, 8th floor, MC 2606 202 Philosophy, MC 4926 [email protected] 212-854-2878 212-854-1919 Marjorie Ortiz, [email protected] Disability Services [email protected] Assistant Director 108A Wien Hall, MC 3711 The earl hall center Institutional Financial Aid Voice/TTY: 212-854-2388 (Grants, Fellowships, Assistantships) Medical Services Office of the University Chaplain Office of Graduate Student Affairs John Jay Hall, 3rd and 4th Floors Office: W710 Lerner 530 S. W. Mudd, MC 4718 212-854-7426 (Appointments) Mailing: 202 Earl Hall, MC 2008 212-854-6438 212-854-6242, 212-854-1493 212-854-6655 (Gay Health Advocacy Project) Jewelnel Davis, [email protected] Office of graduate Student University Chaplain Affairs Sexual Violence Response 530 S.W. Mudd, MC 4718 Rape Crisis/Anti-Violence Support office of equal Opportunity 212-854-6438 Center 105 Hewitt (Barnard Quad) and Affirmative Action Tiffany M. Simon, [email protected] 212-854-HELP 103 Low Library, MC 4333 Associate Dean 212-854-5511 Dawn M. Strickland, [email protected] Housing and Dining Melissa Rooker, [email protected] Director of Graduate Student Services Columbia Housing Associate Provost and Postdoctoral Affairs 118 Hartley, MC 3003 Student Services for Gender-Based Jocelyn Morales, [email protected] 212-854-2946 and Sexual Misconduct Associate Director [email protected] Wien Hall, Suite 108C 212-854-1717 columbia Health Columbia Dining 125 Wallach, MC 3003 Rosalie Siler, [email protected] General Info: 212-854-2284 212-854-4076 Assistant Director After-hours Urgent Health Concerns: 212-854-9797 [email protected] health.columbia.edu

engineering 2014–2015 248 Intercollegiate Athletics and Earth and Environmental Sciences Registrar Physical Education 106 Geoscience, Lamont-Doherty 210 Kent, MC 9202 Earth Observatory, 845-365-8550 Dodge Physical Fitness Center Barry Kane, [email protected] 212-854-3439 Sidney Hemming, [email protected] University Registrar Codirector of Undergraduate Studies Ken Torrey, [email protected] Monica Avitsur, [email protected] Walter C. Pitman, [email protected] Director of Undergraduate Studies Deputy Registrar Codirector of Undergraduate Studies Jacqueline Blackett, [email protected] Terry Plank, [email protected] Jennifer Caplan, [email protected] Senior Associate Athletics Director/SWA Codirector of Undergraduate Studies Associate Registrar Sheila Serrano, [email protected] International Students and Mathematics Associate Registrar Scholars Office 410 Mathematics, MC 4426 524 Riverside Drive, Suite 200 212-854-2432 James Cunha, [email protected] 212-854-3587 Panagiota Daskalopoulos, Assistant Registrar Mailing: 2960 Broadway, MC 5724 [email protected] Lenore Hubner, [email protected] Director of Undergraduate Studies Assistant Registrar office of Judicial Affairs and community standards Physics Kristabelle Munson, [email protected] 609 Lerner, MC 4205 704 Pupin, Mail Code 5255 Associate Director 212-854-3348 212-854-6872 Lisa Wade-Stewart, [email protected] Jeri Henry, [email protected] Jeremy Dodd, [email protected] Associate Director Associate Dean of Judicial Affairs and Director of Undergraduate Studies Jeanelle Folkes, [email protected] Community Standards Statistics Operations and Systems Support Specialist 1255 Amsterdam Avenue Libraries George Voorhis, [email protected] Room 1005 SSW, MC 4690 Technical Specialist for Client Support Butler Library Information 212-851-2132 535 W 114th Street Daniel Rabinowitz, [email protected] student Service Center 212-854-7309 Director of Undergraduate Studies 205 Kent, MC 9202 212-854-4400 Science & Engineering Library Ombuds Office Cashiering: 212-854-1518 401 Northwest Corner 600 Schermerhorn Ext., MC 5558 For quick answers to your questions, 212-851-2950 212-854-1234 visit: askus.columbia.edu

Math/Science Departments Public Safety Office Melbourne Francis, [email protected] 111 Low Library, MC 4301 Biological Sciences Associate Director 212-854-2797 (24 hours a day) 600 Fairchild, MC 2402 [email protected] 212-854-4581 Deborah Mowshowitz, [email protected] Campus Emergencies: Director of Undergraduate Programs 212-854-5555 (4-5555)

Chemistry Escort Service: 344 Havemeyer, MC 3178 212-854-SAFE (4-7233) 212-854-2202 James F. McShane Vesna Gasperov, [email protected] Vice President for Public Safety Undergraduate Program Coordinator

engineering 2014–2015 Columbia University 249 The Morningside Campus & Environs

engineering 2014–2015 250 The Morningside Heights Area of New York City

engineering 2014–2015 index 251

A applications biomedical engineering for degrees, 24, 235 courses in, 70–77 academic advising. See Center for Student Advising graduate, 29 minor in, 82, 195 academic calendar, inside back cover undergraduate, 18 Biomedical Engineering, Department academic community, conduct applied chemistry. See Chemical of, 64–77 expected in, 238 Engineering, Department of graduate programs, 68–70 academic concerns, grievances, and applied mathematics undergraduate program, 65–68 complaints, student, 242–244 courses in, 61–63 biophysics and soft matter physics, academic discipline, 239–240 minor in, 194 program in, 84 academic dishonesty, 239 applied physics Bookstore, Columbia University, 213 academic honors, 236 courses in, 58–61 Botwinick Multimedia Learning academic integrity, 238–239 minor in, 194 Laboratory, 6 academic monitoring, 236 Applied Physics and Applied Business, Graduate School of academic procedures and standards, Mathematics, Department of, 50–63 courses for engineering students, 232–235 current research activities, 50–51 201 academic progress, satisfactory, 21, graduate programs, 56–58 joint programs with, 25, 163 232–234 laboratory facilities, 51–52 Butler Library, 248 academic standing, 236–237 specialty areas, 55–56 undergraduate programs, 52–56 ABET, 17, 67, 81, 122, 137, 181, 233 C addresses of Columbia University architecture, minor in, 91, 194 departments and resources, 246–248 art history, minor in, 195 cable TV service, 7 administrative officers, lists of, 38, assault, sexual, policy on, 238, 244 calendar 45–46 assistantships, 34 academic, inside back cover admissions Associate Provost for Equal for graduate admissions, 29 graduate, 29–30. See also Graduate Opportunity and Affirmative Action, campus life, 210–214 Student Affairs 244 campus safety and security, 214 undergraduate, 18, 246 athletic programs, 13, 213–214 career counseling, 7–8 advanced placement, 11, 13, 14 attendance, 233 Center for Applied Probability (CAP), 154 advanced standing, of transfer Center for Career Education (CCE), 7–8, 35, 246 students, 30 B advising centers. See Center for Center for Financial Engineering, 154 Student Advising Bachelor of Science degree (B.S.), 17 Center for Infrastructure Studies, 90 Alice! Columbia University’s Health Baker Field Athletics Complex, 213 Center for Life Cycle Analysis (LCA), 120 Promotion program, 217–218, 247 Barnard Education Program, 18 Center for Student Advising, 210, 246 American Language Program (ALP), 29 bioinductive and biomimetic materials, Certification of Professional anthropology, minor in, 194 program in, 67, 85 Achievement program, 29, 58 Biological Sciences, Department of, 248 Chaplain, University, Office of the, courses for engineering students, 201 212–213, 247

engineering 2014–2015 252 chemical engineering e-mail addresses, list of, 246–248 key to listings, 48–49 courses in, 85–88 website, 7 in other divisions of the University, minor in, 82, 195 Columbia University Bookstore, 213 of interest to engineering students, Chemical Engineering, Department of, Columbia University Information 201–208 78–88 Technology (CUIT), 6–7 in Engineering School departments. current research activities, 79 Columbia University Libraries, 7 See individual departments facilities and laboratories, 79–80 Columbia University’s Health Promotion CourseWorks, 7 graduate programs, 81–85 Program (Alice!), 217–218, 247 credit, points of, required for degree undergraduate program, 80–81 Columbia Video Network (CVN), 28, graduate, 26–27, 233 Chemistry, Department of, 248 246 undergraduate, 10–13, 232–233 courses for engineering students, application to, 28 201–202 Columbia Water Center, 120 D facilities and laboratories, 79–80 Combined Plan programs, 16 civil engineering commencement ceremony, 235 damages, payment for, 20, 32 courses in, 92–98 Committee on Academic Standing, dance, minor in, 195 minor in, 195 233, 236 Dean’s discipline, 240 Civil Engineering and Engineering Committee on Instruction, 10, 26, 236 Dean’s List, 236 Mechanics, Department of, complaints, academic concerns, and Degree Audit Reporting System 89–100 grievances, student, 242–244 (DARS), 16 current research activities, 89–90 Computational and Optimization degrees facilities and laboratories, 90 Research Center (CORC), 154 application for, 235 graduate programs, 91–92 computer accounts, obtaining, 6 doctoral, requirements, 26, 233 undergraduate programs, 91 Computer Engineering Program, 101–105 See also individual degrees classes graduate program, 103–105 Dining Dollars, 216–217 attendance at, 233 undergraduate program, 101–103 dining facilities, locations, 217 registration and enrollment in, 232 computer kiosks, public, 7 diplomas, 235 classrooms, electronic, 7 computer labs and clusters, 7 direct loans, 35 Club Sports, 212, 214 computer science Disability Services, University Office of, colleges and universities in Combined courses in, 110–118 217, 241, 247 Plan program, 16 minor in, 195 discipline, academic, 239–240 Columbia Arts Experience, 8 Computer Science, Department of, Dean’s, 240 Columbia Card (ID card), 216 106–118 procedures for administering, Columbia College and engineering dual degree program, with School of 239–240 students, 210–214 Journalism, 25, 110 discrimination Columbia Dining, 216–217, 248 laboratory facilities, 106–107 and harassment, and gender-based Columbia Dining Dollars, 216–217 graduate programs, 110 misconduct policy and procedure, Columbia Experience Overseas (CEO), 8 undergraduate program, 107–110 244 Columbia Genome Center (CGC), 80 computer security resources, 7 dishonesty, academic, 239 Columbia Health, 217–218, 247 computing facilities, University, 6–7 disputes over grades or other academic Columbia Housing, 215–216, 247 Computing Support Center, 247 evaluations, 243–244 Columbia Microelectronic Sciences conduct distance education. See Columbia Laboratories, 134 expected in the academic Video Network Columbia Student Enterprises (CSE), 8 community, 238 Doctor of Engineering Science (Eng. Columbia University unacceptable, subject to discipline, Sc.D.), 25–26 campuses, schools, affiliations, and 239–240 Doctor of Philosophy (Ph.D.), 25–26 research facilities, 5–8 Core Curriculum of Columbia Dodge Physical Fitness Center, 213, history of, 2–4 University, 4 248 maps of campus, 249, 250 program offices, 246 dual degree new York City roots of, 5 Counseling and Psychological Services with the School of Journalism, in policy, procedures, and regulations, (CPS), 217, 247 computer science, 25, 110 232–244 courses See also joint programs Provost, 243 for professions other than reservation of rights, 241 engineering, 17–18 resources, phone numbers, and interdisciplinary engineering, 200

engineering 2014–2015 E Engineering Accreditation Commission lists of, 38–45 253 (EAC), 17 members-at-large, list of, 45 Earl Hall Center, 214, 247 engineering courses, interdisciplinary, Faculty in Residence, 211 Earth and environmental engineering 200 family contributions to educational courses in, 126–133 Engineering Graduate Student Council costs, 21 minor in, 195–196 (EGSC), 212 Family Educational Rights and Privacy Earth and Environmental Engineering, Engineering Library, 248 Act (FERPA), 234, 240 Department of (DEEE), 119–132 engineering management science federal financial aid, 34–35 graduate programs, 124–126 graduate program in, 160 Federal Graduate PLUS Loan, 35 research centers, 120–121 undergraduate program in, 154–159 federal income tax returns, 22 scholarshihps, fellowships, and engineering mechanics Federal Perkins Loan, 35 internships, 121 courses in, 98–100 Federal Unsubsidized Loan, 35 undergraduate program, 122–124 graduate program in, 91–92 fees See also Henry Krumb School of minor in, 196 graduate, 31–32 Mines undergraduate program in, 91 refunds of, 20, 32 Earth and Environmental Engineering See also Civil Engineering and undergraduate, 19–20 (EEE) program, 119 Engineering Mechanics, See also payments Earth and Environmental Sciences, Department of fellowships, 33 Department of (Columbia College), Engineering, School of endowed, list of, 224–226 248 courses. See individual departments outside, 226 courses for engineering students, Dean of, 238 financial aid 202–204 department and course codes, 48–49 eligibility for, 21 Earth Engineering Center, 120 departments and programs, 50–192 employment and, 35 East Asian studies, faculty and administration, 38–46 federal, 34, 35 minor in, 196 history of, 2–4 to graduate students, 33–36, 247 economics resources and facilities, 5–8 how to apply for, 21–22 minor in, 196 vice Dean of, 243 private programs, 35 electrical engineering engineering students tax withholding from, for nonresident courses in, 142–152 and campus life, 210–214 aliens, 22 minor in, 196 courses for, offered by other to undergraduate students, 21–22, Electrical Engineering, Department of, University divisions, 201–208 247 133–152 interdisciplinary courses for, 200 Financial Aid and Educational B.S./M.S. program, 139 See also students Financing, Office of, 15, 21, 33, 34, concentration options in the M.S. Engineering Student Council, 212 35, 247 program, 140–142 English and comparative literature, financial engineering graduate programs, 139–142 minor in, 196 graduate program in, 159–160 laboratory facilities, 134 English proficiency requirement, 29 joint programs in, 163 research activities, 134 enrollment, 232 undergraduate program in, 159 undergraduate program, 134–139 entrepreneurship and innovation, minor First Year–Sophomore Program course electronic classrooms, 7 in, 196–197 requirements Electronic Data Service, 7 environmental health engineering, nontechnical, 10–12 e-mail concentration in, 123–124 professional-level, 12–13 addresses of Columbia University Environmental Tracer Group, 121 technical, 12 resources and staff, 246–248 Equal Opportunity and Affirmative 4-2 Combined Plan B.S. program, 16 as service of CUIT, 6 Action, Office of, 247 4-2 Combined Plan M.S. program, 25 emergency resources, 247, 248 Equal Opportunity and fraternities and sororities, 212 emeriti and retired officers, list of, 45 Nondiscrimination Policies, 241 Free Application for Federal Student employment, student, 35 examinations, midterm and final, 233–234 Aid (FAFSA), 33 endowed fellowships, list of, 224–226 French endowed scholarships and grants, and francophone studies, minor in, list of, 220–224 F 197 faculty minor in, 197 and staff academic misconduct, complaints about, 242–243

engineering 2014–2015 254 Fu Foundation School of Engineering Henry Krumb School of Mines (HKSM), International Research Center for and Applied Science, The. See 119 Climate Prediction (IRI), 121 Engineering, School of See also Earth and Environmental International Students and Scholars Fundamentals of Engineering (FE) Engineering, Department of Office (ISSO), 8, 22, 248 exam, 183 Hispanic studies, minor in, 197 Internet access, 7 history, minor in, 197 Interschool Governing Board, 212 honors, academic, 236 internships, 121 G housing, University and off-campus, Intramural and Club Sports Program, Gateway Residential Initiative, 212 215–216 214 genomic engineering, program in, 84 See also residence halls German, minor in, 197 Humanities and Social Sciences, J grade-point average (GPA), 234 Department of, grades, report of, 234 courses for engineering students, John Jay Dining Hall, 216, 217 grading system, explained, 234 204–205 joint programs graduate courses, taking as an with the Graduate School of undergraduate, 17 Business, in industrial engineering, I graduate programs, 24–27 25, 163 admission to, 29–30 immunization requirements, 218 with the Harriman Institute, 25 applying to, 29–30 industrial engineering with the School of International and requirements, 24–27, 233 courses in, 163–169 Public Affairs, 18 See also individual programs minor in, 197 See also dual degree Graduate Record Examination (GRE), 29 Industrial Engineering and Operations Judicial Affairs and Community Graduate Student Affairs, Office of, Research, Department of, 153–169 Standards, Office of, 212, 238–240, 213, 247 current research activities, 154 248 graduate students graduate programs, 159–163 Junior-Senior programs, 16–17 degree requirements for, 233 joint programs, 25, 163 discipline process for, 239–240 minors, 159 L financial aid for, 33–35, 247 undergraduate programs, 154–159 housing, 215–216 Industry/University Cooperative laboratory charges, 19–20, 32 special students as, 26–27, 30 Research Center for Particulate and Langmuir Center for Colloids and tuition and fees, 31–32 Surfactant Systems (CPaSS), 121 Interfaces (LCCI), 121 graduation, 235 Institute of Flight Structures, 90 Latin, Greek or, minor in, 197 grants and scholarships institutional grants, 33 leave(s) of absence endowed, list of, 220–224 Insurance, Student Medical Plan, 19, family, 237 graphics, courses in, 100 31, 218, 247 involuntary, 237 Greek or Latin, minor in, 197 integrated circuits and systems, medical, 237 grievance procedures, 243 concentration in, 141–142 military, 237 grievances, academic concerns, and integrated waste management, voluntary, 237 complaints, student, 242–244 concentration in, 125–126 Lenfest Center for Sustainable Energy, integrity, academic, 238–239 121 Intercollegiate Athletics Lerner Hall, 213 H eligibility for, 213–214 Library, Science & Engineering, 7, 248 harassing or threatening behavior, 244 program in, 213–214 Libraries, Columbia University, 7, 248 harrassment Intercultural Resource Center (IRC), 246 lightwave (photonics) engineering, discriminatory, 244 interdisciplinary engineering courses, 200 concentration in, 141 gender-based misconduct, 244 interfacial engineering and LionSHARE, 7 Harriman Institute, Special Studies electrochemistry, program in, 84–85 loans, student, 33, 34, 35 with, 25 Inter-Greek Council, 212 health insurance, 19, 31, 218 International and Public Affairs, School health service. See Columbia Health of, joint programs with, 18 International English Language Testing System (IELTS), 29

engineering 2014–2015 M misconduct P 255 academic, complaints about faculty Makerspace, 6 parents and staff, 242–244 management science and engineering, contributions to educational costs, 22 scientific or scholarly, 244 graduate program in, 160 payments sexual. See harassment maps of Columbia Morningside Heights timely and overdue, 19, 31 Morningside Heights campus, 6 campus, 249, 250 See also fees maps of, 249, 250 marks. See grading system Pearson Test of English (PTE), 29 Multicultural Affairs, 211, 246 Master of Science degree (M.S.), Perkins Loans, 35 multimedia networking, concentration 24–25 personal expenses of students, 19, in, 141 materials science and engineering 31–32 music courses in, 175–177 philosophy, minor in, 198 instruction courses, 12 minor in, 197 physical education, 13 minor in, 197–198 Materials Science and Engineering and intercollegiate athletics, 213–214 program (MSE), 119, 170–177 Physical Education, Intercollegiate current research activities, 171 N Athletics and, Department of, graduate programs, 172–174 213–214 names, student, change of, 234 graduate specialty in solid-state Physics, Department of, 248 New Student Orientation Program science and engineering, 174 courses for engineering students, (NSOP), 211 interdepartmental committee and, 170 205–207 New York City, 5 laboratory facilities, 171 plagiarism, 239 New York State undergraduate program, 171–172 plasma physics, graduate program in, 58 initial certification in adolescence Mathematics, Department of, 248 Plasma Physics Laboratory, 51 education, 18 courses for engineering students, 205 political science, minor in, 198 nondiscriminatory policies, equal meal plans. See dining plans polymers and soft materials, science educational opportunity and mechanical engineering and engineering of, program in, 83–84 student, 241 courses in, 186–192 prelaw program, 18 nontechnical requirements, 10–12 minor in, 197 premed program, 17 Mechanical Engineering, Department preprofessional advising, 17–18, 211 of, 178–192 O printing facilities, 7 current research activities, 178–181 prizes, medals and, list of, 226–230 Off-Campus Housing Assistance facilities for teaching and research, professions other than engineering, (OCHA), 215 181 Engineering programs in preparation officers of Columbia Engineering graduate programs, 183–186 for, 17–18 list of, 38, 45–46 undergraduate program, 181–183 psychological services, counseling and, retired, list of, 45 medals and prizes, list of, 226–230 217 Ombuds Office, 242, 243, 248 medical care and insurance, 19, 31, psychology, minor in, 198 Ombuds Officer, 242 218, 247 Public Safety, Office of, 214, 248 operations research Medical College Admissions Test courses in, 163–169 (MCAT), 18 graduate program in, 163 R medical leave of absence, 237 minor in, 198 medical physics, graduate program Rape Crisis/Anti-Violence Support undergraduate programs in, 154–159 in, 57 Center. See Sexual Violence See also Industrial Engineering and medical services and Columbia Health Response Operations Research, Department of program, 217–218, 247 readmission, 237 optical and laser physics, graduate Mentoring Initiative, Columbia, 211 recreational programs, 214 program in, 58 microelectronic devices, concentration refunds of tuition and fees, 20, 32 orientation, 211 in, 142 registrar, 248 Middle Eastern, South Asian, and See also Student Service Center African Studies, minor in, 197 registration, 232 military leave of absence, 237 changes in, 233 minors, academic, 17, 194–198 regulations, University, official, 232, 238, 241 religion, minor in, 198

engineering 2014–2015 256 report of grades, 234 concerns, and complaints, 242–244 transfer credits, 233 Res. Inc., 212 student loans, 33, 34, 35 transfer students, 30 residence hall scholarships, list of, 230 Student Medical Insurance Plan, 19, tuition residence halls, 212, 215–216 31, 218, 247 graduate, 31–32 violation of rules of, 238 student organizations, 212 refunds of, 20, 32 Residence Units, and the Ph.D., 26 student records, rights pertaining to, 234 undergraduate, 19–20 Residential Life, 211, 246 Student Research Involvement resources, Columbia University, list of, Program, 10 U 246–248 Student Service Center, 248 Respecting Ourselves and Others student services, 215–218 Undergraduate Student Life, 210–212 Through Education (ROOTED), 211 students Undergraduate Financial Aid and Rules of University Conduct, 238 and campus life, 210–214 Educational Financing, 247 contributions of, to educational undergraduates costs, 21 applications and admissions of, 18 S employment and earnings of, 35 degree requirements for, 10, 232– safety and security, campus, 214 health insurance, 218 233 sanctions, for academic dishonesty, international, 8, 34 financial aid for, 21–22 239 name changes of, 234 housing for, 215 scholarships new, orientation for, 211 minor programs for, 17, 194–198 and grants, endowed, list of, 220–224 personal expenses of, 19, 31–32 programs in Engineering School for, residence hall, list of, 230 special, status, 26, 30 10–18 School of Engineering. See Engineering transfer, 30 tuition and fees of, 19–20 School See also engineering students; See also students Science & Engineering Library, 7, 248 graduate students; undergraduates United Campus Ministries, 212 science and engineering of polymers study abroad, 15–16 University Apartment Housing (UAH), and soft materials, program in, 83–84 summer courses at other institutions, 233 215–216 security resources, computer, 7 sustainable energy University Chaplain, Office of the, sexual assault policy and procedures, and materials, concentration in, 212–213, 248 241, 244 122–123 University regulations, official, 232–235, Sexual Violence Response, 218, 247 concentration in, 125 241 Social Security number, registration sustainable engineering, minor in, 198 and, 232 systems biology and neuroengineering, V sociology, minor in, 198 concentration in, 142 solid-state physics, graduate program Veteran Affairs, Department of, 34 in, 58 veterans, educational benefits for, 34 T solid-state science and engineering Vice Dean, 243 areas of research, 174 Tau Beta Pi, 16–17 Virtual Internship Program (VIP), 8 graduate specialty in, 174 tax withholding, on tuition aid to visual arts courses, 12 sororities, fraternities and, 212 nonresident alien students, 22 Special Interest Communities, 215 teacher certification, obtaining, 18 W special student status, 26, 30 technical elective concentrations, 122 sports, 13, 213–214 telecommunications engineering, Waste to Energy Research and Stafford Loans, 20, 32 concentration in, 141 Technology Council, 120 Statistics, Department of, 248 telephone and cable TV services, 7 water resources and climate risks, courses for engineering students, telephone Helpdesk, 6 concentration in, 122, 125 207–208 telephone numbers of Columbia wireless and mobile communications, statistics, minor in, 198 University departments and concentration in, 141 Student Advising, Center for, 210, 246 resources, 246–248 wireless network, 6 Student Engagement, 211, 246 Test of English as a Foreign Language women’s athletics, 213 Student Financial Services. See (TOEFL), 29 Student Service Center 3-2 Combined Plan B.A./B.S. program, Student Governing Board (SGB), 212 16 student grievances, academic transcripts, 234

engineering 2014–2015 Academic Calendar 2014–2015

FALL TERM 2014 SPRING TERM 2015

August January 25–Sept. 1 New student orientation program. 13–16 Registration by appointment for all classes. 29 Registration by appointment for first-year 19 Birthday of Martin Luther King Jr. students. University holiday. 30 Last Day to apply for October degrees. 20 First day of classes. 20–23, Change of program by appointment. September 26–30 Undergraduate Admissions Need more information? 1 Labor Day. University holiday. 30 Last day to (1) register for academic credit, Office of Undergraduate Admissions You can find the contact information 2 First day of classes. (2) change course programs, (3) submit written notice of withdrawal from the 212 Hamilton Hall, Mail Code 2807 for the people who know in the 2–5, 8–12 Change of program by appointment. 12 Last day to (1) register for academic credit, spring term to the Dean of Student Affairs 1130 Amsterdam Avenue Columbia University Resource List (2) change course programs, (3) submit for full refund of tuition and special fees. New York, NY 10027 on pages 247–249 or visit the Columbia Engineering written notice of withdrawal from the fall No adjustment of fees for individual website, engineering.columbia.edu. Phone: 212-854-2522 term to the Dean of Student Affairs for courses dropped after this date. Last day Fax: 212-854-3393 full refund of tuition and special fees. No to confirm, update, or request a waiver For the most current information, visit our online E-mail: [email protected] adjustment of fees for individual courses from the Student Medical Insurance Plan. bulletin at bulletin.engineering.columbia.edu. undergrad.admissions.columbia.edu dropped after this date. 30 Last day to confirm, update, or request February a waiver from the Student Medical 11 February degrees conferred. Financial Aid Insurance Plan. Office of Financial Aid and Educational Financing March Office: 618 Lerner Hall October 9 Midterm date. Mailing: 100 Hamilton Hall, Mail Code 2802 15 October degrees conferred. 16–20 Spring holiday. 1130 Amsterdam Avenue 16 Midterm date. 26 Last day to drop Engineering courses without academic penalty. Last day New York, NY 10027 November to change grading option. Phone: 212-854-3711 3 Last day to apply for February degrees. Fax: 212-854-5353 3 Academic holiday. April Undergraduate Inquiry E-mail: [email protected] 4 Election Day. University holiday. 13–17 Registration by appointment for fall 2015. Graduate Inquiry E-mail: [email protected] 10–14 Registration by appointment for spring 2014. cc-seas.financialaid.columbia.edu 14 Last day to drop Engineering courses May without academic penalty. Last day to 4 Last day for continuing students to apply Graduate Student affairs change a grading option. for financial aid for the 2015–2016 27–28 Thanksgiving holiday. academic year. Graduate Admissions, Financial Aid, and Student Affairs 4 Last day of classes. 530 S. W. Mudd, Mail Code 4718 December 5–7 Study days. 500 West 120th Street 1 Last day to apply for May degrees. 8–15 Final examinations. New York, NY 10027 8 Last day of classes. 17 Baccalaureate Service. Phone: 212-854-6438 9–11 Study days. 18 Engineering Class Day. Fax: 212-854-5900 12–19 Final examinations. 20 2015 University Commencement. 20–Jan. 19 Winter holiday. E-mail: [email protected] gradengineering.columbia.edu 7/28/14 3:56 PM 2015 – BULLETIN BULLETIN 2014

Columbia | Engineering 2014 – 2 015 500 West 120th Street 120th West 500 NY 10027 York, New 40151 Cover.indd 1