2021 – 2020 BULLETIN BULLETIN

Columbia | Engineering 2020 –2021 500 West 120th Street 120th West 500 NY 10027 York, New Academic Calendar 2020–2021 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 2020 SPRING TERM 2021

August January 22–Sept. 4 Graduate orientation and graduate department TBA Registration by appointment for all classes orientations TBA Graduate orientation 30–Sept. 7 New student orientation program TBA Registration by appointment (undergraduate and 3–7, 25–27 Registration by appointment (undergraduate) graduate) 11 First day of classes September 11–15, 19–22 Change of program by appointment 1 Last Day to apply for October degrees 15 Deadline to add Spring A courses 1–3 Registration by appointment (graduate) 18 Birthday of Martin Luther King Jr., 7 Labor Day, University holiday University holiday UNDERGRADUATE ADMISSIONS Need more information? 8 First day of classes 22 Deadline to add Spring (full term) courses Office of Undergraduate Admissions You can find the contact information 8–11, 14–18 Change of program by appointment 25 Deadline to drop a Spring A course 212 Hamilton Hall, Mail Code 2807 in the Columbia University Resource List 18 Last day to (1) register for academic credit, (2) change course programs, (3) submit written February 1130 Amsterdam Avenue on pages 225–228 or visit the Columbia Engineering 8 Deadline to declare pass/d/fail option for Spring A website, engineering.columbia.edu. notice of withdrawal from the fall term to the Dean New York, NY 10027 of Student Affairs for full refund of tuition and courses. Deadline to withdraw from a Spring A course Phone: 212-854-2522 special fees, (4) drop Core Curriculum classes. No 10 February degrees conferred For the most current information, visit our online Fax: 212-854-3393 adjustment of fees for individual courses dropped 23–26 Reading and final exam period for Spring A courses bulletin at bulletin.engineering.columbia.edu. [email protected] after this date. 22 Deadline to drop Fall A courses March undergrad.admissions.columbia.edu 30 Last day to confirm, update, or request 1–5 Spring recess Photography: a waiver from the Student Medical Insurance Plan. 8 First day of Spring B classes GRADUATE ADMISSIONS Nanfang Yu and Cheng-Chia Tsai. Butterflies have 18 Deadline to drop a course October 22 Deadline to drop a Spring B course (late drop) Graduate Admissions, Financial Aid, and Student Affairs specialized behaviors and wing scales to protect the 21 October degrees conferred 25 Last day to drop Engineering courses without living parts of their wings. 530 S. W. Mudd, Mail Code 4708 22 Midterm date academic penalty. Last day 500 West 120th Street 26 First day of Fall B courses to change grading option New York, NY 10027 Superimposed over this image is the emblem of the April 212-854-6438 School’s vision, Columbia Engineering for Humanity. November 5 Deadline to withdraw from a Spring B course. [email protected] 1 Last day to apply for February degrees 2 Academic holiday Deadline to declare the pass/d/fail option for a gradengineering.columbia.edu 3 Election Day. University holiday Spring B course. 9 Deadline to drop Fall B courses TBA Registration by appointment for fall 2021 FINANCIAL AID 16–20 Registration by appointment for spring 2021 15 Last day of Spring (full term) and Spring B classes 19 Last day to drop Engineering courses without 16–19 Study days Office of Financial Aid and Educational Financing academic penalty. Last day to change a grading 20–23 Final exam period for Spring (full term) and Spring B Office: 618 Lerner Hall option. courses Mailing: 100 Hamilton Hall, Mail Code 2802 TBA Registration by appointment (graduate) 26–30 Class Day and University Commencement will 1130 Amsterdam Avenue 25 Academic holiday take place during this week (specific dates to be 26–27 Thanksgiving holiday announced). New York, NY 10027

Phone: 212-854-3711 December May Fax: 212-854-5353 1 Last day to apply for May degrees 5 Last day for continuing students to apply [email protected] 7 Deadline to withdraw from a Fall B course for financial aid for the 2021–2022 academic year. cc-seas.financialaid.columbia.edu 14 Last day of classes 15–16 Study days SUMMER TERM 2021 17–23 Final examinations 24–Jan. 10 Winter recess May 3 First day of classes for Summer (full term) and Summer A courses June 28 First day of Summer B classes BULLETIN 2020– 2021 A MESSAGE FROM THE DEAN

elcome to Columbia University’s challenges of our time. We have a school Fu Foundation School of vision—Columbia Engineering for Humanity— W Engineering and Applied Science. that encapsulates our efforts to make a positive As students here, you are among the very best impact on society. It highlights the innovative and brightest of your generation. Together and interdisciplinary work that our faculty and with a talented group of students from around students are engaged in to create a more the world, you are embarking on a course sustainable, healthy, secure, connected, and of study that will enable you to become the creative world. next generation of leaders—leaders with a As you prepare for a new academic year, foundation in engineering. we urge you to reflect on this vision and Today, engineering is a foundational degree. embrace the many opportunities afforded to The breadth and depth of our curriculum and you by a world-class university. course offerings prepare students for a wealth There has never been a better time to be of pursuits in engineering and applied science a Columbia Engineer. I encourage you to seek and also provide a launch into many other out the exceptional opportunities for learning fields and industries. and advancement that await you here. Our community has a long history of scientific and engineering breakthroughs that With best wishes for the academic year, have impacted our world. From the School’s beginning in 1864 through today, the work of faculty, alumni, and students has pushed disciplinary frontiers to create, invent, and innovate devices, materials, and processes to make life better. Our first dean, Charles Frederick Chandler, Mary C. Boyce served as president of New York City’s Dean of Engineering Metropolitan Board of Health. In this role, he Morris A. and Alma Schapiro Professor crusaded to ensure the purity of food and drugs, the safety of milk, the availability of clean water in the city, and the introduction of Mission building codes. The mission of Columbia Engineering (The Fu Foundation School of Engineering and Applied Science) is to expand Today, our faculty and students continue knowledge and advance technology through research, while educating students to become leaders and innovators to bring their curiosity, creative drive, informed by an engineering foundation. Enriched with the intellectual resources of a global university in the City of New entrepreneurial energy, and an innovative York, we push disciplinary frontiers, confront complex issues, and engineer innovative solutions to address the grand engineering mindset to some of the biggest challenges of our time. We create a collaborative environment that embraces interdisciplinary thought, creativity, integrated entrepreneurship, cultural awareness, and social responsibility, and advances the translation of ideas into innovations that impact humanity.

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

ENGINEERING 2020–2021 ENGINEERING 2020–2021 TABLE OF CONTENTS­

About the School and 1 Financing Graduate Education 32 MECHANICAL ENGINEERING 186 University Instructions for Financial Aid 32 Applicants 203 About the School and University COLUMBIA ENGINEERING—­ 2 Undergraduate Minors YESTERDAY AND TODAY Graduate School Departmental 32 Funding Interdisciplinary Courses 209 Alternative Funding Sources 33 Undergraduate Studies 7 and Professional Development Other Financial Aid—Federal 33 and Leadership Program THE UNDERGRADUATE 8 and Private Programs INTERDISCIPLINARY 210 PROGRAMS Veterans Benefits 33 ENGINEERING COURSES Policy on Degree Requirements 9 Employment 34 The First-Year/Sophomore Program 9 Contact Information 34 PROFESSIONAL DEVELOPMENT 211 Study Abroad 13 AND LEADERSHIP Combined Plan Programs 14 Faculty and Administration 35 The Junior-Senior Programs 14 213 Programs in Preparation for 16 University and School 45 Other Professions Academic Departments Policies, Procedures, and Joint Programs 17 and Programs Regulations Undergraduate Admissions 17 KEY TO COURSE LISTINGS 46 ACADEMIC PROCEDURES 214 AND STANDARDS UNDERGRADUATE TUITION, 18 APPLIED PHYSICS AND 48 FEES, AND PAYMENTS APPLIED MATHEMATICS ACADEMIC STANDING 218

FINANCIAL AID FOR 20 BIOMEDICAL ENGINEERING 62 ACADEMIC INTEGRITY AND 221 UNDERGRADUATE STUDY DISCIPLINE CHEMICAL ENGINEERING 77

Graduate Studies 21 CIVIL ENGINEERING AND 87 Directory of University 225 THE GRADUATE PROGRAMS 22 ENGINEERING MECHANICS Resources COLUMBIA UNIVERSITY 226 The Master of Science Degree 22 COMPUTER ENGINEERING 101 RESOURCE LIST Doctoral Degrees: Eng.Sc.D. 24 PROGRAM and Ph.D. MAPS 230 Nondegree Students 25 COMPUTER SCIENCE 106 Office of Graduate Student Affairs 25 INDEX 232 EARTH AND ENVIRONMENTAL 122 COLUMBIA VIDEO NETWORK 26 ENGINEERING Academic Calendar (see inside back cover) GRADUATE ADMISSIONS 28 ELECTRICAL ENGINEERING 136

GRADUATE TUITION, FEES, 30 INDUSTRIAL ENGINEERING 157 AND PAYMENTS AND OPERATIONS RESEARCH

FINANCIAL AID FOR GRADUATE 32 MATERIALS SCIENCE AND 177 STUDY ENGINEERING PROGRAM 2 COLUMBIA ENGINEERING–YESTERDAY AND TODAY 3

A COLONIAL CHARTER A MODERN SCHOOL enemy aircraft ignition systems. After Since its founding in 1754, as King’s FOR MODERN TIMES the war, Armstrong improved his College, Columbia University has The School of Mines became the method of frequency modulation (FM), always been an institution both of and School of Mines, Engineering, and and by 1931, had both eliminated for the City of New York. And it has Chemistry in 1896, and its professors the static and improved the fidelity always been an institution of and for included Michael Idvorsky Pupin, a of radio broadcasting forever. The engineers. In its original charter, the graduate of the Columbia College Class historic significance of Armstrong’s college stated that it would teach, of 1883. As a professor at Columbia, contributions was recognized by the among other things, “the arts of Pupin did pioneering work in carrier- U.S. government when the Philosophy Number and Measuring, of Surveying wave detection and current analysis, Hall laboratory was designated a and Navigation, . . . the knowledge with important applications in radio National Historic Landmark in 2003. of . . . Meteors, Stones, Mines and broadcasting. He is perhaps most As the United States evolved into Minerals, Plants and Animals, and famous for having invented the “Pupin a major twentieth-century political Engelberger, Class of 1946, the father Institute, Teachers College, Columbia Video Coding), the world standard for everything useful for the Comfort, the coil,” which extended the range of power, the University continued to build of modern robotics, could not have Business School, and the Graduate audio/video compression that is now Convenience and Elegance of Life.” long-distance telephones. onto its undergraduate curriculum the anticipated the revolutionary speed with School of Architecture, Planning and one of the most commonly used HD An early student of Pupin’s was broad range of influential graduate which cumbersome and expensive “big Preservation. The transforming gift of formats and most commonly used Irving Langmuir. Langmuir, Class of and professional schools that define it THE GILDED AGE science” computers would shrink to the The Fu Foundation has catapulted the in streaming media; and ATSC, a 1903, enjoyed a long career at the today. Renamed once again in 1926, As the city grew, so did the School. size of a wallet. School into the forefront of collaborative standard developed by the Advanced General Electric research laboratory. the School of Engineering prepared King’s College was rechartered No one could have imagined the research and teaching and has given Television Systems Committee for There he invented a gas-filled tungsten students for careers not only as as Columbia College in 1784 and explosive growth of technology and students the opportunity to work with digital television transmission. It is now lamp, contributed to the development engineers of nuclear-age technology, relocated from the Wall Street area to its interdisciplinary impact. Columbia prize-winning academicians, including the U.S. standard for recording and of the radio vacuum tube, and but as leaders engaged with the far- what is now Midtown in 1857. Students Engineering is in a unique position to Nobel laureates from many disciplines. retrieval of data and HD audio-visual extended Gilbert Lewis’ work on reaching political implications of that began entering the new School of take advantage of the research facilities media. In addition to the standards, electron bonding and atomic structure. technology as well. Mines in 1864. Trained in mining, and talents housed at Columbia to form Columbia Engineering faculty have His research in monolayering and After receiving a master’s degree NEW RESEARCH FRONTIERS mineralogy, and engineering, Columbia relationships among and between other patents in areas as diverse as modular surface chemistry led to a Nobel Prize from the School in 1929, Admiral Columbia’s technology transfer office, graduates continued to make their schools and departments within the cameras, carbon capture, a search in chemistry in 1932. Hyman George Rickover served during Columbia Technology Ventures, mark both at home and abroad. University. Biomedical Engineering, with engine that matches facial features, and But early work on radio vacuum the Second World War as head of the works with faculty inventors to Working around the globe, William close ties to the Medical School, is but even methods to combat virtual reality tubes was not restricted to private electrical section of the Navy’s Bureau commercialize ideas and brings in Barclay Parsons, Class of 1882, was one example. Interdisciplinary centers sickness. industry. Working with Pupin, an of Ships. A proponent of nuclear sea millions in licensing revenue annually. an engineer on the Chinese railway and are the norm, with cross-disciplinary Increasingly, the inventions emerging engineering student named Edwin power, Rickover directed the planning Columbia Engineering faculty have the Cape Cod and Panama Canals. research going on in biomedical from Columbia Engineering are Howard Armstrong was conducting and construction of the world’s first been instrumental in developing some Most important for New York, he was imaging, environmental chemistry, developed in collaboration with other experiments with the Audion tube nuclear submarine, the 300-foot-long of the most successful inventions chief engineer of the city’s first subway. materials science, nanotechnology, researchers, expanding the potential in the basement of Philosophy Hall Nautilus, launched in 1954. in consumer electronics, as well Opened in 1904, the subway’s electric digital, and new media technologies. applications for their important work. when he discovered how to amplify as establishing many of the widely cars took passengers from City Hall The School and its departments have Programs such as the Columbia radio signals through regenerative accepted global standards for storage to Brooklyn, the Bronx, and the newly TECHNOLOGY AND BEYOND links to the Departments of Physics, Biomedical Technology Accelerator circuits. Armstrong, Class of 1913, and transmission of high-quality audio renamed and relocated Columbia Today, The Fu Foundation School of Chemistry, Earth Science, and (BiomedX), PowerBridgeNY, the was stationed in France during the and video data. Columbia is the only University in Morningside Heights. Engineering and Applied Science, as Mathematics, as well as the College of NYC Media Lab Combine program, First World War, where he invented university actively participating in it was named in 1997, continues to Physicians and Surgeons, the Graduate the COSMOS Wireless Testbed, the superheterodyne circuit to tune a broad range of standards-based provide leadership for scientific and School of Journalism, Lamont- the Columbia IBM-Center for in and detect the frequencies of patent pools, including AVC (Advanced educational advances. Even Joseph Doherty Earth Observatory, The Earth Blockchain and Data Transparency,

ENGINEERING 2020 –2021 ENGINEERING 2020–2021 4 and the Columbia Electrochemical remains the same. Committed to the theater from performance art in the Columbia University Irving Medical MANHATTANVILLE CAMPUS research programs in nanoscale 5 Energy Center are strengthening educational philosophy that a broad, East Village to musicals on Broadway; Center (CUIMC), which includes From Broadway and 125th Street West science and engineering. Shared interdisciplinary capacity and fostering rigorous exposure to the liberal arts food from around the world; and every Columbia’s College of Physicians and to a revitalized Hudson River waterfront, facilities and equipment to support an entrepreneurial and inventive energy provides the surest chart with which sport imaginable, New York is the Surgeons, the Mailman School of Public Columbia's 17-acre Manhattanville nano research at the Engineering within the School. Some of these an engineer can navigate the future, cultural crossroads of the world. Health, the New York State Psychiatric campus is a welcoming environment School include a state-of-the-art programs and centers have helped all undergraduates must complete a New York is also a major player in Institute, College of Dental Medicine, of publicly accessible open space, clean room in the Schapiro Center prepare ideas for commercialization, modified but equally rigorous version high-tech research and development, and School of Nursing. CUIMC is tree-lined streets, neighborhood- for Engineering and Physical Science including personalized robotics for of Columbia College’s celebrated where Fortune 500 companies traded the world’s first academic medical friendly retail, and innovative academic Research (CEPSR) and a Transmission use in physical rehabilitation and an Core Curriculum. It is these selected on Wall Street seek partnerships with center, and opened in 1928 when buildings that invite community Electron Microscope (TEM) Laboratory implantable device that acts as a courses in contemporary civilization in high-tech startups in Tribeca and Columbia’s health-related schools and engagement. It is home to the Jerome on the first floor of Havemeyer. minimally-invasive glucose sensor for the West and other global cultures that Brooklyn. As part of the research Presbyterian Hospital (now NewYork- L. Greene Science Center, Columbia's Founded in 2012 by Columbia diabetic patients. best prepare a student for advanced community themselves, Columbia Presbyterian Hospital) moved to the Mortimer B. Zuckerman Mind Brain Engineering, the Data Science Institute coursework; a wide range of eventual students have exceptional opportunities Washington Heights location. Columbia Behavior Institute, the Lenfest Center also sits on Morningside campus as professions; and a continuing, life-long for contact with industry both on and Engineering’s Biomedical Engineering for the Arts, and the University Forum, a University-wide resource that spans ENTREPRENEURSHIP pursuit of knowledge, understanding, off campus. Senior representatives of Department has offices on both the an event and meeting space. Columbia nine schools, including Journalism, Throughout the academic year, the and social perspective. It is also these companies often visit Columbia to Morningside campus and CUIMC. Business School will relocate to this the Graduate School of Arts and School hosts many activities and these Core courses that most closely lecture as adjunct faculty members or Beyond its schools and programs, campus by 2021, and plans are Sciences, and Columbia University networking events to support its tie today’s student to the alumni of as guest speakers, and undergraduate the measure of Columbia’s true underway to develop a new building Irving Medical Center. The mission of active startup community, including centuries past. Through a shared and graduate students frequently breadth and depth must take into here for Columbia Engineering, as well. the Data Science Institute is to train the Columbia Engineering Fast Pitch exposure to the nontechnical areas, undertake research or internships account its internationally recognized These spaces house cutting-edge data science innovators and develop Competition, Columbia Venture all Columbia Engineering students— with these and other companies, centers and institutions for specialized research and teaching in brain science, ideas for the social good. Competition, Design Challenges, past, present, and future—gain the oftentimes leading to offers of full-time research. These centers study an art gallery, screening room, and Details about specific programs’ Hackathons, and the Ignition Grants humanistic tools needed to build lives employment after graduation. everything from human rights to performance spaces, and space for laboratories and equipment can be program, which funds ventures started not solely as technical innovators, but In addition to its ties to private molecular recognition and hold close active community engagement. found in the sections describing those by current students. as social and political ones as well. industry, Columbia also has a affiliations with Teachers College, programs. An exciting way the School fosters historically close relationship with the Barnard College, the Juilliard School, entrepreneurship is with its BiomedX public sector of New York, stretching and both the Jewish and Union COLUMBIA ENGINEERING Columbia Engineering Computing Program. A major goal of the program is A COLLEGE WITHIN THE back to the eighteenth century. No Theological Seminaries. Columbia also Columbia Engineering (The Fu Facilities to educate researchers, clinicians, and UNIVERSITY other city in the world offers as many maintains major off-campus facilities Foundation School of Engineering students about the many aspects involved Combining the advantages of a small The Botwinick Multimedia Learning impressive examples of the built such as the Lamont-Doherty Earth and Applied Science) occupies four in commercializing biomedical innovation. college with the extensive resources of Laboratory at Columbia University environment—the world’s most famous Observatory in Palisades, NY and laboratory and classroom buildings Entrepreneurship remains an a major research university, students has redefined the way engineers are collection of skyscrapers, long-span the Nevis Laboratories in Irvington, at the north end of Morningside important central educational theme at Columbia Engineering pursue their educated here. bridges, road and railroad tunnels, and NY. Involved in many cooperative campus, including the Northwest at Columbia Engineering. The School academic interests under the guidance Designed with both education and one of the world’s largest subway and ventures, Columbia also conducts Corner Science and Engineering offers a range of programs and a of outstanding senior faculty members interaction in mind, the lab provides water supply systems. Involved in all ongoing research at such facilities as Building, an interdisciplinary teaching 15-credit, interdisciplinary minor in who teach both undergraduate and students and instructors with: aspects of the city’s growth and capital Brookhaven National Laboratory in and research building. In this building entrepreneurship made up of both graduate level courses. Encouraged by improvements over the years, Columbia Upton, NY, and the NASA Goddard researchers from across the University Engineering and Business School the faculty to undertake research at all • 48 desktops engineers have been responsible for the Institute for Space Studies located just work together to create new areas courses. The School also provides a levels, students at the School receive • A full set of professional-grade design, analysis, and maintenance of off the Morningside campus. of knowledge, in fields where the four-year entrepreneurship experience the kind of personal attention that only engineering software tools New York’s enormous infrastructure of biological, physical, and digital worlds for all interested Columbia Engineering Columbia’s exceptionally high faculty- • A collaborative classroom learning municipal services and communications fuse. This pandisciplinary frontier will students, regardless of major. student ratio affords. THE MORNINGSIDE HEIGHTS environment links, as well as its great buildings, advance some of modern society’s And for alumni, entrepreneurial CAMPUS most challenging problems in a wide bridges, tunnels, and monuments. The lab is utilized in some of the support continues. The Columbia Columbia Engineering is located on range of sectors, from health to THE NEW YORK ADVANTAGE School’s introductory first-year Startup Lab, a coworking facility Columbia’s Morningside campus. One cybersecurity, from smart infrastructure Besides the faculty, the single greatest engineering projects, as well as located in SoHo, provides subsidized THE UNIVERSITY AT LARGE of the handsomest urban institutions to the environment. resource for students is without doubt advanced classes in modeling and space for Columbia alumni Columbia University occupies three in the country, the 13.1 million gross Supporting multiple programs the City of New York. Within easy animation, technology and society, and entrepreneurs to house and nurture major campuses, as well as additional square feet (gsf) of the Morningside of study, the School's facilities are reach by walking, bus, subway, or entrepreneurship. their fledgling ventures. The Lab is the special-purpose facilities throughout campus comprise more than 200 designed and equipped to meet the taxi, New York’s broad range of social, result of a unique partnership between the area. The main campus is located buildings of housing; off-campus laboratory and research needs of both cultural, and business communities The Makerspace the deans of Columbia College and the on the Upper West Side in Morningside apartments and commercial buildings; undergraduate and graduate students. offer an unparalleled opportunity for Schools of Business, Engineering, Law, Heights, and the Manhattanville recreation and research facilities; The School is also the site of an Columbia Engineering’s Makerspace students to expand their horizons or and International and Public Affairs. campus is the newest addition to centers for the humanities and social almost overwhelming array of basic provides students with a dedicated deepen their understanding of almost Columbia University. This open and and pure sciences; and professional and advanced research installations, place to collaborate, learn, explore, any human endeavor imaginable. With environmentally sustainable campus schools in architecture, business, the such as the Columbia Genome Center experiment, and create prototypes. A FORWARD-LOOKING TRADITION art from small Chelsea galleries to will grow over the next decade to fine arts, journalism, law, and many and the Columbia Nano Initiative, Students can utilize the space to work But, for all its change, there is still a major museums; music from Harlem encompass more than 17 acres. Further other fields. established to serve as the hub for on a variety of innovative projects, continuous educational thread that jazz clubs to the Metropolitan Opera; uptown in Washington Heights is the multidisciplinary and collaborative including independent or group design

ENGINEERING 2020–2021 ENGINEERING 2020–2021 6 projects, product development, and Carleton Commons a dedicated and comfortable space to new venture plans. This facility fosters Located on the fourth floor (campus gather, relax between classes, or meet student creativity by bringing together level) of the Mudd Building, Carleton and work with one another on problem the workspace and tools for computer- Commons and Blue Java Café com- sets or projects. The new design also aided design, physical prototyping, prise 3,200 square feet with seating enables flexible and reconfigurable use fabric arts, woodworking, electronics, for 160 and areas for casual meetings, of the space for larger gatherings and and software. individual and group work, and quiet special events. study. Carleton Commons gives students

Undergraduate Studies

ENGINEERING 2020–2021 8 information and guidance to students Liberal Arts Core for global-core-requirement/) for a letter 9 THE UNDERGRADUATE PROGRAMS who plan a career in law or the health Columbia Engineering Students: grade. professions, through individual advising, 27-Point Nontechnical Requirement 3. One of the following two courses: workshops, and other events related This requirement provides a broad HUMA UN1121: Masterpieces of to professions of law and health. liberal arts component that enhances Western art, or HUMA UN1123: Preprofessional advisers work closely the Engineering professional curriculum Masterpieces of Western music (3 with other CSA advisers to support to help students meet the challenges points) students during their undergraduate of the twenty-first century. Our program of study. They also provide students are destined to be leaders 4. ECON UN1105: Principles of extensive individualized support to in their professions and will require economics. (This course can be students and alumni through their sophisticated communication, planning, satisfied through Advanced Placement; application process to professional and management skills. The Committee see the Advanced Placement chart on schools. on Instruction established the School’s page 12.) Note: Engineering students nontechnical requirement so that students may not take any Barnard class as a substitute for ECON UN1105. (4 points) POLICY ON DEGREE would learn perspectives and principles of the humanities and social sciences as part REQUIREMENTS B. Elective Nontechnical Courses of a well-rounded and multiperspective The Committee on Instruction and (9–11 points of credit) he undergraduate programs at While pursuing their own interests, academic advisement, exploration, education. Through discussion, debate, faculty of The Fu Foundation School of The following course listing by department Columbia Engineering not only undergraduate students are encouraged and counseling and writing, students improve their abilities Engineering and Applied Science review specifies the Columbia College, Barnard, are academically exciting and to participate in a broad range of ongoing • provides information on preprofessional to engage in ethical, analytic, discursive, T degree requirements and curricula or Columbia Engineering courses that technically innovative but also lead faculty research projects encompassed studies, major declaration, and and imaginative thinking that will prove matters each year, and the bulletin either fulfill or do not fulfill the nontechnical into a wide range of career paths for by the Student Research Program. completion of the degree, as well as indispensable later in life. reflects these faculty recommendations requirement. the educated citizen of the twenty-first Students can apply for available research various leadership, career, graduate and curricular changes in its yearly (Professional, workshop, lab, project, century. Whether you want to become a positions in Columbia Labs through the school, and research opportunities • Engineering students must take 16 to reprinting. School policy requires scientific, studio, music instruction, and professional engineer, work in industry or website at studentresearch.engineering. • interprets and disseminates 18 points of credit of required courses in students to fulfill all general degree master’s-level professional courses do government, or plan to pursue a career columbia.edu. information regarding University list A and 9 to 11 elective points chosen requirements as stated in the bulletin not satisfy the 27-point nontechnical in the physical and social sciences, In addition to in-depth exploration policies, procedures, resources, and from the approved courses in list B. The of the first year of their matriculation requirement.) medicine, law, business, or education, of engineering and applied science, programs total combined number of nontechnical into the School. Students declare their Columbia Engineering will provide you Columbia Engineering undergraduates • educates and empowers students to points (from lists A and B, below) must AFRICAN-AMERICAN STUDIES: All courses major during the first semester of their with an unparalleled education. explore the humanities and social take responsibility in making informed add up to at least 27. Neither list can sophomore year. Requirements for the AMERICAN STUDIES: All courses The School firmly believes that sciences with Columbia College decisions be modified by advising deans or faculty major or minor are in accordance with students gain the most when students through intellectually • refers students to additional campus advisers. ANCIENT STUDIES: All courses the bulletin during the year in which the engineering is brought up front, early challenging Core Curriculum courses resources • Advanced Placement (AP) credit in student declares the major or minor. ANTHROPOLOGY: All courses in sociocultural in the four-year curriculum. Therefore, taught by the Faculty of Arts and appropriate subject areas can be applied Every undergraduate is assigned anthropology each first-year student takes the Art Sciences. These courses in art, toward the 9-point elective nontechnical an adviser from the Berick Center for All courses in archaeology except field work of Engineering, which addresses the literature, music, major cultures, and THE FIRST-YEAR/SOPHOMORE requirement and for Principles of Student Advising for the duration of his Economics. No courses in biological/physical anthro- fundamental concepts of math and economics, among others, provide PROGRAM or her undergraduate career. Generally, pology [UN1010, UN1011, UN3204, UN3940, science in an engineering context, students with a broad, intellectually Students entering Columbia Engineering each matriculating student is assigned A. Required Nontechnical Courses GU4147-GU4148, GU4200, GU4700] as well as nontechnical issues in disciplined, cultural perspective on the to an advising dean, who is a liaison to are encouraged to consider the wide (16–18 points of credit) professional engineering practice such times they live in and the work they do. ARCHITECTURE: No courses the department the student indicated range of possibilities open to them, These courses must be taken at as ethics and project management. as his or her first intended major on the both academically and professionally. Columbia. ART HISTORY AND ARCHEOLOGY: Students in the Art of Engineering James H. and Christine Turk Berick Columbia application. When a student To this end, the first and second All courses choose a half-semester, hands-on 1. ENGL CC1010: University writing (3 Center for Student Advising declares a major, a faculty member is years of the four-year undergraduate project in one of the School’s nine points) ASIAN AMERICAN STUDIES: All courses 403 Lerner Hall, MC 1201 also appointed to advise him or her program comprise approximately half undergraduate engineering disciplines, 212-854-6378 for the next two years. Depending on the total number of credits required 2. One of the following two-semester ASTRONOMY: No courses followed by a half-semester general [email protected] their chosen major, students may be for the degree that expose students sequences: HUMA CC1001-CC1002: project that changes each year. BIOLOGICAL SCIENCES: No courses cc-seas.columbia.edu/csa assigned to a new advising dean who to a cross-fertilization of ideas from Masterpieces of Western literature and Depending on the project chosen, is a CSA liaison to their department. different disciplines within the University. philosophy (All students registering for BUSINESS: No courses students will solder, 3D print, laser cut, The James H. and Christine Turk Advising deans regularly refer students The sequence of study proceeds from this course should be prepared to dis- simulate, design websites, and much cuss books 1–12 of the Iliad on the first CHEMISTRY: No courses Berick Center for Student Advising to their academic departments to an engagement with engineering and more. These skills are further developed day of class) or (CSA) guides and supports receive expert advice about their scientific fundamentals, along with CLASSICS: All courses as students progress toward their senior COCI CC1101-CC1102: Introduction to undergraduates at Columbia College engineering course selections. humanities and social sciences, toward COLLOQUIA: year projects. Since the fall of 2014, and Columbia Engineering as they an increasingly focused training in the contemporary civilization in the West or All courses Columbia Engineering students have been third and fourth years designed to give Global Core: Any 2 courses from navigate their educations and lives at Preprofessional Advising COMPARATIVE ETHNIC STUDIES: able to utilize the School’s brand new students mastery of certain principles approved list (6–8 points) Columbia University. Individually and Preprofessional Advising is a specialized All courses Makerspace, a collaborative environment and arts central to engineering and If electing Global Core, students must collaboratively, each advising dean: advising unit within the James H. and where students can learn, explore, applied science. take two courses from the List of COMPARATIVE LITERATURE AND Christine Turk Berick Center for Student experiment, and create prototypes. • provides individual and group Approved Courses (bulletin.columbia. SOCIETY: All courses Advising. It is dedicated to providing edu/columbia-college/core-curriculum/

ENGINEERING 2020–2021 ENGINEERING 2020–2021 approaches to understanding organismic and on which today’s society depends. Topics 10 COMPUTER SCIENCE: No courses CHEN E4020 Protection of industrial and GU4732 Research topics in game theory visual arts course, which must be 11 intellectual property GU4791 Advanced topics in quantitative taken at the 3000 level or higher, may cellular function in living systems. Engineering in include airplanes, automobiles, robots, and CREATIVE WRITING: All courses EEHS E3900 History of telecommunications research count toward the nontechnical elective the diagnosis and treatment of disease. Medical modern manufacturing methods, as well as the (This is an exception to the workshop rule.) imaging, medical devices: diagnostic and surgical emerging fields of micro-electro-mechanical GU4792 Advanced topics in quantitative requirement. This 3000 course is an ENGLISH AND COMPARATIVE instruments, drug delivery systems, prostheses, machines (MEMS) and nanotechnology. The DANCE: All courses except performance research exception to the rule that no workshop LITERATURE: All courses artificial organs. Medical informatics and physical concepts that govern the operation of classes GU4700 Math methods for political science classes can fulfill the nontech elective organization of the health care system. Current these technologies will be developed from basic FILM STUDIES: All courses except lab courses, GU4765 Design and analysis of sample surveys requirement. DRAMA AND THEATRE ARTS: All courses trends in biomedical engineering research. principles and then applied in simple design and GU4768 Experimental research: design, analy- except workshops, rehearsal, or performance problems. Students will also be exposed to state- UN3920 Senior seminar in screenwriting sis and interpretation CHEN E2100x Introduction to chemical classes, THTR BC2120 Technical production, Technical Course Requirements of-the art innovations in each case study. UN2400 The film medium: script analysis GU4710 Principles of quantitative political engineering THTR BC3135 Set design, and THTR BC3134 research The prescribed First Year–Sophomore Serves as an introduction to the chemical Professional-Development and Lighting design FRENCH AND ROMANCE PHILOLOGY: GU4711 Analysis of political data Program curriculum requires students engineering profession. Students are exposed All courses to complete a program of technical to concepts used in the analysis of chemical Leadership Program EARTH AND ENVIRONMENTAL SCIENCES: GU4712 Multivariate political analysis coursework introducing them to engineering problems. Rigorous analysis of The Professional Development and No courses GERMANIC LANGUAGES: All courses PSYCHOLOGY: Only five major areas of technical inquiry: material and energy balances on open and Leadership (PDL) program educates EAST ASIAN LANGUAGES AND CULTURE: GREEK: All courses UN1001 The science of psychology engineering, mathematics, physics, closed systems is emphasized. An introduction students to maximize performance and All courses UN2280 Introduction to developmental chemistry, and computer science. to important processes in the chemical and achieve their full potential to become HISTORY: All courses psychology All first-year Engineering biochemical industries is provided. engineering leaders. Core sessions ECOLOGY, EVOLUTION, AND All courses on perception, attention, and cogni- HISTORY AND PHILOSOPHY OF SCIENCE: undergraduate students take ENGI CIEN E3000y The art of structural design focus on development of skills and ENVIRONMENTAL BIOLOGY: No courses tion topics numbered 2200s, 3200s, or 4200s All courses E1102: The art of engineering (4 Basic scientific and engineering principles used perspectives needed to compete and except EEEB GU4321 or GU4700 can be taken as nontech electives except for points). In this course, students see for the design of buildings, bridges, and other succeed in a fast-changing technical HUMAN RIGHTS: All courses PSYC UN2235 and UN4289. ECONOMICS: All courses except how their high school science and parts of the built infrastructure. Application of these climate. Topics include professional All courses on social, personality, and abnormal UN3025 Financial economics ITALIAN: All courses math knowledge can be applied in principles to the analysis and design of a number portfolio (resume, cover letter, business numbered 2600s, 3600s, or 4600s can be UN3211 Intermediate microeconomics an engineering context to solve real- of actual large-scale structures. History of major writing, social media presence), JAZZ STUDIES: All courses taken as nontech electives. UN3213 Intermediate macroeconomics world problems through classroom structural design innovations and the engineers who communication skills, leadership, ethics, introduced them. Critical examination of the unique UN3412 Introduction to econometrics LATIN: All courses RELIGION: All courses presentations and participation in an life management (stress, sleep, and aesthetic/artistic perspectives inherent in structural UN3981 Applied econometrics in-depth, hands-on project. Along time management) and more. Elective LATINO STUDIES: All courses SLAVIC LANGUAGES: All courses design. Management, socioeconomic, and ethical GU4020 Economics of uncertainty and sessions include effective presentations, the way, guest lecturers discuss issues involved in the design and construction of LINGUISTICS: All courses except CLLN information SOCIOLOGY: All courses except social implications of technology, large-scale structures. Recent developments in making small talk, Cloudproc/PySpark, GU4202 GU4211 Advanced microeconomics SOCI UN3020 Social Statistics entrepreneurship, project management, sustainable engineering, including green building and interview preparation. GU4213 Advanced macroeconomics and other important nontechnical issues design and adaptable structural systems. MATHEMATICS: No courses SPANISH AND PORTUGUESE: All courses GU4251 Industrial organization affecting the practicing engineer. Physical Education MEDIEVAL AND RENAISSANCE STUDIES: EAEE E2100x A better planet by design GU4260 Marketing design SPEECH: No courses While students need not officially Two terms of physical education All courses Introduction to design for a sustainable planet. GU4280 Corporate finance commit to a particular branch of STATISTICS: No courses Scientific understanding of the challenges. (PHED UN1001-PHED UN1002) are GU4301 Economic growth and development MIDDLE EASTERN AND ASIAN LANGUAGE engineering until the third semester, most Innovative technologies for water, energy, a degree requirement for Columbia GU4412 Advanced econometrics AND CULTURES: All courses SUSTAINABLE DEVELOPMENT: No courses programs recommend, and in some food, materials provision. Multiscale modeling Engineering students. No more than 4 GU4413 Econometrics of time series and cases may require, that particular courses MUSIC: All courses except performance URBAN STUDIES: All courses and conceptual framework for understanding points of physical education courses forecasting be taken earlier for maximum efficiency environmental, resource, human ecological, and courses, instrument instruction courses, and may be counted toward the degree. GU4415 Game theory VISUAL ARTS: No more than one course, in program planning. For information economic impacts and design performance, workshops The physical education requirement GU4505 International macroeconomics which must be at the 3000-level or higher (This concerning these requirements, students evaluation. Focus on linkages between planetary, can be fulfilled with Barnard dance GU4526 Transition reforms, globalization, PHILOSOPHY: All courses except is an exception to the workshop rule.) should turn to the individual program regional, and urban waste, energy, mineral, food, studio/technique courses. A student and financial crisis UN1401 Introduction to logic sections in this bulletin. climate, economic, and ecological cycles. Solution who intends to participate in an WOMEN AND GENDER STUDIES: All strategies for developed and developing country GU4911 Seminar in microeconomics UN3411 Symbolic logic intercollegiate sport should register courses settings. GU4913 Seminar in macroeconomics GU4137 Nonclassical logics Professional Development for the appropriate section of PHED GU4918 Seminar in econometrics GU4431 Introduction to set theory ELEN E1201x and y Introduction to electrical Music Instruction Courses Professional-Level Courses UN1005: Intercollegiate athletics. BC1003 Introduction to economic GU4424 Modal logic engineering Music instruction and performance The courses listed below may be Intercollegiate athletes who attend reasoning (equivalent to ECON UN1105) CSPH GU4801 Mathematical logic I Basic concepts of electrical engineering. courses do not count toward the 128 taken by first- and second-year regularly receive 1 point of credit up to BC1007 Mathematical methods for CSPH GU4802 Incompleteness results in logic Exploration of selected topics and their points of credit required for a B.S. students. Some departments require the maximum of 4. Students who are economics GU4810 Lattices and Boolean algebras application. Electrical variables, circuit laws, degree. Please note that this includes one of these courses; please consult advised to follow a restricted or adapted BC2411 Statistics for economics Courses in logic nonlinear and linear elements, ideal and real courses taken at Teachers College, with departmental charts for more activity program should contact the BC3014 Entrepreneurship sources, transducers, operational amplifiers in PHYSICAL EDUCATION: No courses Columbia College, and the School of information. Director of Physical Education and BC3018 Econometrics simple circuits, external behavior of diodes and the Arts. Each course serves as an Recreation. The physical education BC3033 Intermediate macroeconomic theory PHYSICS: No courses transistors, first order RC and RL circuits. Digital introduction to the area of study and is representation of a signal, digital logic gates, flip- program offers a variety of activities in BC3035 Intermediate microeconomic theory POLITICAL SCIENCE: All courses except taught by department faculty. flops. A lab is an integral part of the course. the areas of aquatics, fitness, martial BC3038 International money and finance Visual Arts Courses UN3220 Logic of collective choice The courses are: arts, individual and dual sports, team Students are allowed to take courses in MECE E1001x Mechanical engineering: EDUCATION: All courses UN3704 Data analysis and statistics for political sports, and outdoor education. Most the Visual Arts Department for general BMEN E1001x Engineering in medicine micro-machines to jumbo jets science research activities are designed for the introductory/ credit to be applied toward the B.S. Not offered in 2020–2021. Not offered in 2020–2021. ENGINEERING: Only UN3720 Scope and methods degree. However, no more than one The present and historical role of engineering in The role of mechanical engineering in developing beginner levels. Intermediate/advanced BMEN E4010 Ethics for biomedical engineers GU4730 Game theory and political theory medicine and health care delivery. Engineering many of the fundamental technological advances courses are indicated on the schedule.

ENGINEERING 2020–2021 ENGINEERING 2020–2021 12 Advanced Placement Credit Chart The majority of the activities are offered may be granted 6 points of credit if the opportunities. Students must obtain 13 In order to receive AP credit, students must be in possession of appropriate transcripts or scores and send official score reports to Columbia. in ten time preferences. Additionally, there examinations were taken in disciplines approval from their departmental The CEEB code is 2116. are early-morning conditioning activities, offered as undergraduate programs at advisers to ensure that their work abroad Friday-only classes at Baker Athletics Columbia University. The appropriate meets the requirements of their majors, AP AP Complex, and special courses that utilize transcript should be submitted to the as well as clearance from their Advising Subject Score Credit Requirements or Placement Status Credit off-campus facilities during weekends and James H. and Christine Turk Berick Dean in the James H. and Christine Turk Art History 5 3 No exemption from HUMA UN1121 vacation periods. The courses offered by Center for Student Advising, 403 Lerner. Berick Center for Student Advising. Biology 5 3 No exemption the department for each term are included Chemistry 4 or 5 3 Requires completion of CHEM UN1604 with grade of C or better in the online Directory of Classes, and a Other National Systems Eligibility Requirements 4 or 5 6 Requires completion of CHEM UN2045-UN2046 with grade of C or better description of the scheduled activities for Students whose secondary school work In order to participate in a semester- Computer each time preference is posted on was in other national systems, such as long or yearlong study-abroad program, Science A 4 or 5 3 Exemption from COMS W1004 perec.columbia.edu. Students may the French Baccalauréat, may be granted students must: Principles 4 or 5 3 Exemption from COMS W1001 only register for one section of physical credit in certain disciplines for sufficiently • Be an enrolled student in good Economics education each term. high scores. The appropriate transcript Micro & Macro 5 and 4 4* Exemption from ECON UN1105. Exams must be taken in both micro and macro, should be submitted to the James H. academic and disciplinary standing • Have at least a 3.0 GPA with a score of 5 in one and at least 4 in the other. Advanced Placement and Christine Turk Berick Center for • Be making adequate progress toward English Prior to entering Columbia, students Student Advising, 403 Lerner. finishing the first and second year  Language and may have taken Advanced Placement requirements Composition 5 3 No exemption examinations through the College STUDY ABROAD Literature and • Have declared a major Composition 5 3 No exemption Entrance Examination Board (CEEB) in Engineering today is a global profession. a number of technical and nontechnical Study abroad allows engineering French Finances areas. A maximum of 16 points may students to discover the field through the Language 4 or 5 3 • Fall/spring (academic year) be applied. Students may be assigned perspective of engineers working in a Literature 4 or 5 3 • Billed by Columbia: tuition and to an advanced level course in different language and culture, enabling German health insurance mathematics or physics based on their them to learn the relationship of culture Language 4 or 5 3 • Billed by abroad institution/external AP scores. to science and develop the range of Government vendors: room, board, living and In the required pure science areas, the transferable skills that employers are and Politics travel expenses number of advanced placement academic seeking today. Study abroad will help United States 5 4* Exemption from POLS UN1201. • Still eligible for financial aid credits awarded to students of engineering students develop intellectually, emotionally, Comparative 5 4* Exemption from POLS UN1501. • Summer and applied science varies from the levels culturally, and socially. History • Student pays most expenses awarded for liberal arts programs, notably Columbia Engineering undergraduate European 5 3 directly to the program and external in mathematics, physics, chemistry, students can study abroad for either a United States 5 3 vendors and computer science. The benefit of semester (fall, spring, or summer) or, Italian Language 4 or 5 3 • Not eligible for financial aid advanced placement is acceleration exceptionally, for a full academic year. Latin Literature 5 3 through certain First Year–Sophomore Students from every engineering major Academic Credit Mathematics Program requirements and thus the have studied abroad, and most do so in • Students in Columbia-sponsored Calculus AB 4 or 5 3 Requires completion of MATH UN1102 with a grade of C or better. opportunity of taking specialized courses the spring semester of their sophomore Credit is reduced to 0 if MATH UN1101 is taken. programs receive direct Columbia earlier. year or in their junior year. Although not a Calculus BC 4 3 Requires completion of MATH UN1102 with a grade of C or better. credit, and the courses and grades Each year the school reviews the requirement, students are encouraged to Credit is reduced to 0 if MATH UN1101 is taken. appear on students' academic Calculus BC 5 6 Requires completion of APMA E2000 with a grade of C or better. CEEB advanced placement curriculum have some foreign language skills in order transcripts. Credit is reduced to 0 if MATH UN1101 is taken, or to 3 if MATH 1102 is taken. and makes determinations as to to enhance their cultural competency and • Cr edit from approved programs that appropriate placements, credit, and/or their overall study abroad experience. Physics Maximum of six credits. are not Columbia sponsored is certified C-E&M 4 or 5 3 Credit is reduced to 0 if PHYS UN1401 or 1601 is taken. Credit is reduced to 0 if PHYS UN2801 exemption. Please see the Advanced The Center for Undergraduate Global Engagement will help students identify as transfer credit toward the Columbia is taken and the final grade is C- or lower. Placement Credit Chart. C-MECH 4 or 5 3 Credit is reduced to 0 if PHYS UN1401 or 1601 is taken. Credit is reduced to 0 if PHYS UN2801 the appropriate choice for their country of degree upon successful completion is taken and the final grade is C- or lower. interest and their major. Undergraduate of the program verifiable by academic International Baccalaureate (IB) Physics 1 and 2 4 or 5 3 No exemption. Both AP Physics 1 and 2 must be taken to receive credit. Student Affairs advisers and departmental transcript. Students must earn a grade Entering students may be granted 6 Spanish advisers will help students with their course of C or better in order for credits to be Language 4 or 5 3 points of credit for each score of 6 or 7 equivalencies for approved programs so transferred. Course titles and grades for Literature 4 or 5 3 on IB Higher Level Examinations if taken they can graduate on time. Students can approved programs do not appear on in disciplines offered as undergraduate *AP credits may be applied toward minor requirements depending on the specific rules of the minor. When the rules of the minor allow AP take nontechnical electives overseas, or the Columbia transcript, and grades are credit to fulfill a requirement, then only one course for a minor may be replaced by advanced placement credit. programs at Columbia. Students should with departmental permission, they may not factored into students' GPAs. consult their adviser at the James H. **Columbia Engineering Students with a 4 or 5 on Calculus AB or a 4 on Calculus BC must begin with MATH UN1102 (Caculus II). If a choose technical electives or courses in • Faculty from the Columbia Engineering Columbia Engineering student with these scores goes directly into APMA E2000 (Multivariable Calculus), he or she will have to go back and and Christine Turk Berick Center for their major. academic departments have the complete MATH UN1102 (Calculus II). Students with A-level or IB calculus credit must start with MATH UN1102 (Calculus II). Student Advising for further clarification. It is essential that students begin responsibility to assess all work planning as early as possible. Students completed abroad and make decisions British Advanced Level Examinations are encouraged to meet with advisers about how these courses fit into Students with grades of A or B on in the Center for Undergraduate Global major requirements. It is imperative British Advanced Level examinations Engagement to review possible global that students gain course-by-course

ENGINEERING 2020–2021 ENGINEERING 2020–2021 14 approval from their department prior to then attends The Fu Foundation School a faculty adviser in the department in 15 departure on a study-abroad program. of Engineering and Applied Science for which the program is offered. In addi- two years, and is awarded the Bachelor tion to the courses required by their Deadlines of Arts degree and the Bachelor of program, students must continue to • Spring trips: October 1st Science degree in engineering upon satisfy certain distributive requirements, • Fall trips: March 1st completion of the fifth or sixth year. This choosing elective courses that provide • Summer trips: May 1st program is optional at Columbia, but the sufficient content in engineering sci- • Year-long trips: March 1st School recommends it to all students ences and engineering design. The who wish greater enrichment in the liberal order and distribution of the prescribed For more information on study arts and pure sciences. coursework may be changed with abroad, students should contact: the adviser’s approval. Specific ques- Center for Undergraduate Global The Combined Plan with Other tions concerning course requirements Engagement Affiliated Colleges should be addressed to the appropriate 606 Kent Hall, MC 3948 There are more than one hundred department or division. The Vice Dean’s 1140 Amsterdam Avenue affiliated liberal arts colleges, including concurrent approval is required for all New York, NY 10027 those at Columbia, in which a student waivers and substitutions. 212-854-2559 can enroll in a Combined Plan program [email protected] leading to two degrees. Each college Double Major uge.columbia.edu requires the completion of a specified Students who wish to apply for a curriculum, including major and second major must consult their SEAS Undergraduate Student Affairs degree requirements, to qualify for the advising dean about next steps. A [email protected] baccalaureate from that institution. proposal to double major must be Every affiliated school has a liaison approved by both departments and COMBINED PLAN PROGRAMS officer who coordinates the program at then forwarded to the Vice Dean for Undergraduate Admissions his or her home institution. Students Undergraduate Programs for a final 212 Hamilton Hall, MC 2807 interested in this program should decision. 1130 Amsterdam Avenue inform the liaison officer as early as Courses cannot be cross-counted New York, NY 10027 possible, preferably in the first year, between dual majors. Please consult 212-854-2522 in order to receive guidance about with an adviser and the respective further considered on the basis of The Bachelor of Science Degree are, however, encouraged to consider [email protected] completing program requirements. departments to find alternative courses personal integrity, breadth of interest Students who complete a four-year graduate work, at least to the master’s undergrad.admissions.columbia.edu/ Applicants from nonaffiliated schools for duplicate requirements. both inside and outside engineering, sequence of prescribed study are degree level, which is increasingly apply/combined-plan are welcome to apply. 3-2 students are not eligible to have adaptability, and unselfish activity. awarded the Bachelor of Science considered necessary for many Visit the Undergraduate Admissions a second major due to the time con- Benefits of membership include degree. The general requirement for professional careers. Columbia Engineering maintains website for a complete list of affili- straints of their program. exclusive scholarships and fellowships. the Bachelor of Science degree is The Engineering Accreditation cooperative program relationships with ated schools, admission application Many networking opportunities for jobs the completion of a minimum of 128 Commission (EAC) of ABET, an institutions nationwide and with other instructions, information on financial Tau Beta Pi and internships are also available, with academic credits with a minimum organization formed by the major Columbia University undergraduate aid, and curriculum requirements for Tau Beta Pi is the nation’s second- 230 collegiate chapters and more than cumulative grade-point average (GPA) engineering professional societies, divisions. The Combined Plan Combined Plan program admission. oldest honor society, founded at 500,000 members in Tau Beta Pi. of 2.0 (C) at the time of graduation. accredits university engineering programs (3-2 and 4-2) allow students Please note that no change of major Lehigh University in 1885. With the The program requirements, specified programs on a nationwide basis. to receive a degree both in the liberal is allowed after an admission decision creed “Integrity and excellence in Taking Graduate Courses as an elsewhere in this bulletin, include Completion of an accredited program arts and in engineering. Combined Plan has been rendered. engineering,” it is the only engineering Undergraduate the first-year–sophomore course of study is usually the first step toward students complete the requirements See page 23 for information on the honor society representing the entire With the faculty adviser’s approval, a requirements, the major departmental a professional engineering license. 4-2 Master of Science Program, which for the liberal arts degree along with engineering profession. Columbia’s student may take graduate courses requirements, and technical and Advanced study in engineering is administered through the Office of required prerequisite coursework for chapter, New York Alpha, is the ninth while still an undergraduate in the nontechnical elective requirements. at a graduate school sometimes Graduate Student Affairs. their studies in engineering during the oldest and was founded in 1902. Many School. Such work may be credited Students who wish to transfer points presupposes the completion of an three or four years at their liberal arts Columbia buildings have been named toward one of the graduate degrees of credit may count no more than 68 accredited program of undergraduate study. college before entering the School THE JUNIOR-SENIOR PROGRAMS for some of the more prominent chapter offered by the Engineering Faculty, transfer points toward the degree and The following undergraduate of Engineering and Applied Science. Students may review degree progress alumni: Charles Fredrick Chandler, subject to the following conditions: (1) must satisfy the University’s residence programs are accredited by the EAC They then must complete all the via DARS (Degree Audit Reporting Michael Idvorsky Pupin, Augustus the course must be accepted as part requirements by taking at least 60 of ABET: biomedical engineering, requirements for the B.S. degree within System) as presented on Student Schermerhorn, and, of course, Harvey of an approved graduate program of points of credit while enrolled in The Fu Foundation School of Engineering and chemical engineering, civil engineering, four consecutive semesters. Services Online. Required courses Seeley Mudd. study; (2) the course must not have Applied Science. Courses may not be Earth and environmental engineering, that are not completed are detailed as Undergraduate students whose been used to fulfill a requirement repeated for credit unless it is stated electrical engineering, and mechanical The Combined Plan Program within deficiencies and must be completed scholarship places them in the top for the B.S. degree and must be so certified by the Dean; and (3) the otherwise in the course description. engineering. Columbia University during summer session or carried as eighth of their class in their next-to-last amount of graduate credit earned by The bachelor’s degree in engineering Under this plan, the pre-engineering overload courses in later semesters. year or in the top fifth of their class an undergraduate cannot exceed 15 and applied science earned at Columbia Minors student studies in Columbia College, Having chosen their program major in their last college year are eligible points. Undergraduates may not take University prepares students to enter Columbia Engineering undergraduates Barnard College, or the School of in the second semester of their sopho- for membership consideration. These CVN courses. a wide range of professions. Students may choose to add minors to their General Studies for three or four years, more year, students are assigned to scholastically eligible students are

ENGINEERING 2020–2021 ENGINEERING 2020–2021 16 programs. This choice should be made Premed • One semester of introductory by rigorous intellectual training involving requirements for certification. However, Interested students should 17 in the fall of their sophomore year, when Medical, dental, and other health psychology relational, syntactical, and abstract when space allows, applications will contact their advising dean for further they also decide on a major. professional schools prefer that thinking. While selecting courses, keep in be considered through the fall of the information. In considering a minor, students must undergraduates complete a four-year As you prepare for this path, you mind the need to hone your writing skills, junior year. Applications from juniors understand that all minors are not, and program of study toward the bachelor's should consult regularly with both your communication skills, and your are due no later than the first Monday School of International and Public cannot, be available to all students. In degree. All health professional schools your assigned adviser and one of the capacity for logical analysis. in October. Students who plan to Affairs addition, the School cannot guarantee require prerequisite coursework, but premedical advisers in the James H. While engineering students may find study abroad during the spring of their The Fu Foundation School of that a selected minor can be completed they do not prefer one type of major or Christine Turk Berick Center for Student interests in many areas of the law, for junior year should apply during the Engineering and Applied Science and within the usual residence period need- scholarly concentration. Students with Advising. These individuals will help to intellectual property and patent law, a fall semester of their sophomore year. the School of International and Public ed for a major. Indeed, students choos- all types of engineering backgrounds are guide you in your course selection and science and technology background will Students should decide on their interest Affairs offer a joint program enabling a ing minors should expect to encounter highly valued. planning, and introduce you to extracur- be greatly valued if not essential. in teacher certification by the end of the small number of students to complete scheduling difficulties. The potential for It is important to note, however, ricular and research opportunities related first year in order to start coursework in the requirements for the degrees of the successful completion of a minor that each medical school in the to your interests in health and medicine. Urban Teaching: New York State the sophomore year. Bachelor of Science and Master of depends on the student’s major and United States and Canada individually Preprofessional Advising maintains an Initial Certification in Adolescence International Affairs in five years instead the minor chosen, as well as the course determines its own entrance online list of many different clinical volun- Education Grades 7–12 for Teachers of six. Not only an excellent academic JOINT PROGRAMS schedules and availability, which may requirements, including prerequisite teer and research opportunities across of Mathematics and the Sciences or record but also maturity, fluency in change from year to year. The list of New York City and beyond. Exploration in Elementary Education Grades 1–6 coursework and/or competencies. Each The 4-1 Program at Columbia an appropriate foreign language, and minors, as well as their requirements, of the career and sustained interactions medical school also sets its own rules Barnard College Education Program College pertinent experience will determine appear on pages 203–208. regarding acceptable courses or course with patients is viewed by many medi- 335-336 Milbank Hall admission to this program. For more Students who are admitted as first-year equivalents. It is therefore essential cal schools as essential preparation and 3009 Broadway information, please contact your students to the School of Engineering that students plan early and confirm therefore students are strongly encour- New York, NY 10027 advising dean. PROGRAMS IN PREPARATION FOR and Applied Science and subsequently the premedical requirements for those aged to spend time volunteering/work- 212-854-7072 OTHER PROFESSIONS complete the four-year program for schools to which they intend to apply. ing in clinical and research environments education.barnard.edu the Bachelor of Science degree have The Engineering curriculum covers many before applying to medical school. UNDERGRADUATE ADMISSIONS James H. and Christine Turk Berick the opportunity to apply for admission of the prerequisite courses required by Students must apply for admission The Barnard Education Program provides Undergraduate Admissions Center for Student Advising to either Columbia College or Barnard medical schools, however, in addition to to health professional schools more than courses leading to certification to teach 212 Hamilton Hall, MC 2807 403 Lerner Hall, MC 1201 College and, after one additional completing the mathematics, chemistry, one year in advance of the entry date. in New York State (with reciprocal 1130 Amsterdam Avenue 212-854-6378 year of study, receive the Bachelor of and physics courses required by the Students who are interested in going agreements with 41 other states) at New York, NY 10027 [email protected] Arts degree. The fifth year of study First Year–Sophomore Program, most directly on to health professional schools either the elementary or secondary level. 212-854-2522 cc-seas.columbia.edu/preprofessional/ commences in the fall semester and schools ask for a full year of organic following graduation should complete Students gain experience and develop [email protected] students are required to conclude their chemistry, a full year of biology, a full all prerequisite courses required for the skills in urban school classrooms. undergrad.admissions.columbia.edu The Fu Foundation School of studies while enrolled for two full-time year of English, a semester of statistics, MCAT by the end of the junior year. It Required coursework includes Engineering and Applied Science semesters. and a semester of biochemistry. is entirely acceptable (and most com- psychology and education, a practicum, For information about undergradu- prepares its students to enter any The program is selective, and Advanced Placement credit is accepted mon) for students to take time between and student teaching, totaling 23–26 ate admissions, please visit the number of graduate programs and admission is based on the following in fulfillment of these requirements by undergraduate and health professional points of credit depending on the level of Undergraduate Admissions website or professions outside of what is generally factors: granting of the B.S. at some schools but not all. Students school and thus delay application to certification sought. contact the office by phone or email. thought of as the engineering field. In Columbia Engineering at the end of the are responsible for monitoring the these schools for one or more years. Certification to teach mathematics an increasingly technological society, fourth year; fulfillment of the College requirements of each school to which Students planning to apply to medical requires 36 points in mathematics. Pure where the line between humanities Core requirements by the end of the they intend to apply. Generally, students or dental school should be evaluated science courses required are: 36 points and technology is becoming blurred, fourth year at the School; a minimum with Advanced Placement credit are by the Premedical Advisory Committee in the sciences, of which 18 must be individuals with a thorough grounding GPA of 3.0 in the College Core and strongly advised to take further courses prior to application. A Premedical in the area of the certification sought: in applied mathematics and the other courses; and the successful in the field in which they have received Advisory Committee application is made chemistry, biology, physics, or Earth physical and engineering sciences completion of any prerequisites for such credit. available each year in December. For science. find themselves highly sought after as the College major or concentration. In addition to medical school more information regarding this process The deadline for application, which professionals in practically all fields of Students apply at the end of their junior requirements, all medical schools and other premedical-related questions, includes an essay and letters of endeavor. year at the School; to be admitted to currently require applicants to sit for please consult with a premedical adviser recommendation, is the first Monday in Engineering students interested in the program, the student needs to have the Medical College Admissions Test in the Berick Center for Student Advising March of the student’s sophomore year. pursuing graduate work in such areas a plan in place to complete the College (MCAT). The recommended preparation or peruse their website: www.cc-seas. This allows program faculty to support as architecture, business, education, major or concentration by the end of for this exam is: columbia.edu/preprofessional/health/ students through program planning journalism, or law will find themselves their fifth year. • One year of general chemistry and to ensure that students can meet the well prepared to meet the generally general chemistry lab Prelaw flexible admissions requirements of most • One year of organic chemistry and Students fulfilling the School of professional schools. Undergraduate organic chemistry lab Engineering and Applied Science’s students should, however, make • One year of introductory biology and curriculum are well prepared to apply careful inquiry into the kinds of specific biology lab to and enter professional schools of preparatory work that may be required • One semester of biochemistry law, which generally do not require any for admission into highly specialized • One year of general physics and specific prelaw coursework. Schools of programs such as medicine. physics lab law encourage undergraduate students to complete a curriculum characterized

ENGINEERING 2020–2021 ENGINEERING 2020–2021 18 student taking laboratory courses must TUITION AND FEE REFUNDS Federal Unsubsidized Stafford Loans 19 UNDERGRADUATE TUITION, FEES, AND PAYMENTS furnish, at his or her own expense, the Students who make a complete Federal Stafford Loans necessary notebooks, blank forms, and withdrawal from a term are assessed Federal Perkins Loans similar supplies. In some laboratory a withdrawal fee of $75. Late fees, Federal PLUS Loans (when disbursed courses, a fee is charged to cover application fees, withdrawal fees, tuition through the University) expendable materials and equipment deposits, special fees, computer fees, Federal Pell Grants maintenance. Students engaged in special examination fees, and transcript Federal Supplemental Educational special tests, investigations, theses, fees are not refundable. Opportunity Grants or research work are required to meet The Health Service Fee, Health Other Title IV funds the costs of expendable materials as Insurance Premium, University facilities may be necessary for this work and in fees, and student activity fees are not Withdrawing students should be accordance with such arrangements as refundable. aware that they will not be entitled may be made between the student and Students who withdraw within the to any portion of a refund until all the department immediately concerned. first 60 percent of the academic period Title IV programs are credited and all are subject to a refund calculation, outstanding charges have been paid. which refunds a portion of tuition based DAMAGES on the percentage of the term remaining All students will be charged for damage he 2020–2021 tuition and fees TUITION HEALTH INSURANCE after the time of withdrawal. This to instruments or apparatus caused by are estimated. Tuition and fees Undergraduate students enrolled in The Columbia University offers the Student calculation is made from the date the their carelessness. The amount of the are prescribed by statute and are Fu Foundation School of Engineering Medical Insurance Plan, which provides student’s written notice of withdrawal is T charge will be the actual cost of repair, subject to change at the discretion of and Applied Science pay a flat tuition both Basic and Comprehensive levels received by the Dean’s Office. and, if the damage results in total loss of the Trustees. charge of $30,049 per term, regardless of coverage. Full-time students are the apparatus, adjustment will be made University charges such as tuition, of the number of course credits taken. automatically enrolled in the Basic Percentage Refund for Withdrawal in the charge for age or condition. To fees, and residence hall and meal plans Postgraduate special students and level of the Plan and billed for the during First Nine Weeks of Term ensure that there may be no question are billed in the first Student Account degree candidates enrolled for a ninth insurance premium in addition to the Prorated for calendars of a different as to the liability for damage, students Statement of the term, which is sent term are billed according to the per-point Health Service fee. Visit the Columbia duration: should note whether the apparatus is in out in July and December of each year system; the per-point cost is $2,008. Health website at health.columbia. good condition before use and, in case 1st week 100% for the upcoming term. This account edu for detailed information about of difficulty, request instruction in its 2nd week 100% is payable and due in full on or before medical insurance coverage options MANDATORY FEES proper operation. Where there is danger 3rd week 90% the payment due date announced in and directions for making confirmation, Orientation fee: $485 (one-time charge of costly damage, an instructor should 4th week 80% the Statement, typically at the end of enrollment, or waiver requests. in the first term of registration) 5th week 70% August or early January before the be requested to inspect the apparatus. Student Life fee: On-campus students: 6th week 60% beginning of the billed term. Any student Liability for breakage will be decided by $623 fall / $908 spring 7th week 50% who does not receive the first Student PERSONAL EXPENSES the instructor in charge of the course. Remote students: $501 fall / $908 spring 8th week 40% Account Statement is expected to pay Students should expect to incur When the laboratory work is done Health and Related Services fee: $610 9th week and after 0% at registration. miscellaneous personal expenses for by a group, charges for breakage will per term For students receiving federal student If the University does not receive such items as clothing, linen, laundry, be divided among the members of the International Services charge: $110 per aid, refunds will be made to the federal the full amount due for the term on or dry cleaning, and so forth. Students group. The students responsible for any term (international students only) aid programs in accordance with before the payment due date of the should also add to the above expenses damage will be notified that a charge is Document fee: $105 (one-time charge) Department of Education regulations. first Statement, a late payment charge the cost of two round trips between being made against them. The amount Refunds will be credited in the following of $150 will be assessed. An additional home and the University to cover travel of the charge will be stated at that time during the summer and the month-long, order: charge of 1.5 percent per billing cycle OTHER FEES or as soon as it can be determined. midyear break. may be imposed on any amount past Application and late fees: The University advises students to due thereafter. • Application for undergraduate open a local bank account upon arrival Students with an overdue account admission: $85 in New York City. Since it often takes as balance may be prohibited from • Application for undergraduate transfer long as three weeks for the first deposit registering, changing programs, or admission: $85 to clear, students should plan to cover obtaining a diploma or transcripts. • Late registration fee during late immediate expenses using either a credit In the case of persistently delinquent registration: $50; card, traveler’s checks, or cash draft accounts, the University may utilize the after late registration: $100 services of an attorney and/or collection drawn on a local bank. Students are agent to collect any amount past due. Books and course materials: Depends urged not to arrive in New York without If a student’s account is referred for upon course sufficient start-up funds. collection, the student may be charged Laboratory fees: See course listings an additional amount equal to the cost LABORATORY CHARGES of collection, including reasonable Students may need to add another Room and board (estimated): $15,130 attorney’s fees and expenses incurred $100 to $300 for drafting materials or by the University. laboratory fees in certain courses. Each

ENGINEERING 2020–2021 ENGINEERING 2020–2021 20 FINANCIAL AID FOR UNDERGRADUATE STUDY

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

ENGINEERING 2020–2021 22 beginning of graduate study. Under liberal arts colleges (see the listing Dual Degree Program with the School 23 THE GRADUATE PROGRAMS extraordinary circumstances, a written under the heading The Combined Plan of Journalism in Computer Science request for an extension of this time Program with Other Affiliate Colleges) The Graduate School of Journalism and limit may be submitted to the student’s with majors in mathematics, physics, the Engineering School offer a dual degree department for approval by the chemistry, or certain other physical program leading to the degrees of Master department chair and the Assistant sciences to receive the M.S. degree of Science in Journalism and the Master Dean. A minimum cumulative grade- after two years of study at Columbia in of Science in Computer Science. (See point average of 2.5 is required for the the following fields of engineering and Computer Science.) M.S. degree. A student who, at the end applied science: biomedical, chemical, of any term, has not attained the grade- civil, computer science, Earth and Joint Program with the School of point average required for the degree environmental, electrical, industrial, and Business in Industrial Engineering may be asked to withdraw. mechanical engineering; applied physics; The Graduate School of Business After the first semester of enrollment, applied mathematics; engineering and the Engineering School offer a an M.S. student may submit an application mechanics; operations research; and joint program leading to the degrees to apply and transfer to another academic materials science. of Master of Business Administration program. If the student is not successful Each applicant must produce evidence and Master of Science in Industrial with the application process, then he or of an outstanding undergraduate record, Engineering. (See Industrial Engineering raduate programs of study in For residence requirements for students THE MASTER OF SCIENCE DEGREE she must make sure requirements for the including superior performance in physics and Operations Research.) The Fu Foundation School of registered in the Graduate School of Arts The Master of Science degree is offered original academic program are completed. and mathematics through differential G Engineering and Applied Science and Sciences or those wishing to change in many fields of engineering and applied equations. The program of study will Master of Science in Data Science are not formally prescribed, but are planned from the Eng.Sc.D. degree to the Ph.D. science upon the satisfactory completion Professional Development be individually designed in consultation Candidates for the Master of Science to meet the particular needs and interests degree, see the bulletin of the Graduate of a minimum of 30 points of credit of Leadership M.S. Requirement with a faculty adviser and will integrate in Data Science are required to of each individual student. Departmental School of Arts and Sciences. approved graduate study extending over (ENGI E4000) undergraduate work with the field of complete a minimum of 30 graduate- requirements for each degree, which Students admitted to graduate study at least one academic year. The Professional Development and engineering or applied science the student level credits, which includes seven supplement the general requirements given are expected to enter upon the term for While a suitable Master of Science Leadership (PDL) program educates chooses to follow. During the first year, required courses: Algorithms for Data below, appear in the sections on individual which they are admitted and continue program will necessarily emphasize students to maximize performance and the program will consist primarily of basic Science, Machine Learning for Data graduate programs. their studies in each succeeding regular some specialization, the program achieve their full potential to become undergraduate courses; during the second Science, Exploratory Data Analysis and Applicants for a graduate program term of the academic year. Any such should be well balanced, including basic engineering leaders. The core modules year, of graduate courses in the selected Visualization, Probability and Statistics are required to have completed an student who fails to register for the subjects of broad importance as well as focus on development of professional skills field. The student must complete at least for Data Science, Statistical Inference & undergraduate degree and to furnish following term will be assumed to have theory and applications. The history of and perspectives needed to succeed in a 30 credits of graduate study to qualify for Modeling, Computer Systems for Data an official transcript as part of the withdrawn unless a leave of absence has modern economic, social, and political fast-changing technical climate. the degree. Science, and Data Science Capstone admissions application. Ordinarily the been granted by the Office of Graduate institutions is important in engineering, M.S. students must complete A student whose background may & Ethics. A minimum of 9 credits of candidate for a graduate degree will have Student Affairs. and this is recognized in the prescribed the professional development and require supplementary preparation in elective coursework are chosen in completed an undergraduate course in While many candidates study on a undergraduate program of the School. leadership course, ENGI E4000, as a some specific area, or who has been consultation with the student's adviser the same field of engineering in which full-time basis, it is usually possible to If the candidate’s undergraduate graduation requirement. out of school for a considerable period, and should be technical in nature he or she seeks a graduate degree. obtain all or a substantial part of the credit education has been largely confined to will have to carry a heavier than normal and must be a 4000-level graduate However, if the student’s interests have requirement for the master’s or Eng.Sc.D. course load or extend the program course or higher that expands the changed, it may be necessary to make pure science and technology, a program Professional Development degrees through part-time study. beyond two years. student's expertise in data science. up such basic undergraduate courses as of general studies, totaling from 6 to 8 Leadership Ph.D. Requirement Under special conditions, and with the Graduates of the 4-2 Master of M.S. students must complete the are essential to graduate study in his or points, may be required. Supplementary (ENGI E6001–6004) prior approval of the department of his Science program may not be eligible to professional development and her new field of interest. statements covering these special The Professional Development and or her major interest and of the Assistant take the Fundamentals of Engineering leadership course, ENGI E4000, as a A maximum of 15 points of credit of requirements are issued by the School’s Leadership (PDL) program educates Dean, a student may be permitted to (FE) exam if their undergraduate degree graduation requirement. graduate-level coursework, completed separate departments. An applicant students to maximize performance and take a required subject at another school. is not in engineering or a related field. at Columbia University before the new who lacks essential training will be achieve their full potential during and after However, credit for such courses will not Students should also check with Certificate of Professional program is approved and not used toward required to strengthen or supplement the doctoral program. The goal is to cul- reduce the 30-point minimum that must individual state boards to determine Achievement in Data Science another degree, may be counted toward the undergraduate work by taking or tivate future scholars and leaders in their be taken. eligibility requirements for employment. the degree. Students registered in the repeating certain undergraduate courses Graduate Online delivery is also available For graduation, a candidate for respective fields. The modules are tailored School have a minimum requirement before proceeding to graduate study. No Please contact the Office of Graduate for this program. Candidates for the any degree except a doctoral degree for each stage of the doctoral program, for each Columbia degree of 30 points graduate credit (that is, credit toward the Student Affairs, The Fu Foundation School Certification of Professional Achievement must file an Application for Degree or with a focus on the development of aca- of credit of coursework completed at minimum 30-point requirement for the of Engineering and Applied Science, in Data Science, a nondegree part-time Certificate on the date specified in the demic, research, and professional skills. Columbia University. The student must Master of Science degree) will be allowed 530 S. W. Mudd, MC 4718, 500 West program, are required to complete a Academic Calendar. Candidates for a Ph.D. candidates are strongly encouraged enroll for at least 15 of these points while for such subjects. Accordingly, Master of 120th Street, New York, NY 10027; you minimum of 12 credits, including four doctoral degree must apply for the final to complete ENGI E6001–6004 and registered as a matriculating student in Science programs may include from 35 should also contact your home institution’s required courses: Algorithms for Data examination. If the degree is not earned should consult their program for PDL a degree program in the Engineering Combined Plan liaison for program Science, Probability and Statistics for by the next regular time for the issuance to 45 points and may require three terms requirements. School. (See also the section Nondegree information. You may, in addition, email of diplomas subsequent to the date of for completion. Doctoral research credits Data Science, Machine Learning for Students and the chapter Columbia Video questions to [email protected]. filing, the application must be renewed. cannot be used toward M.S. degree The 4-2 Master of Science Program Data Science, and Exploratory Data Network.) Students wishing to change requirements. Analysis and Visualization. Degrees are awarded three times a The 4-2 Master of Science Program from the Ph.D. degree to the Eng.Sc.D. All degree requirements must be year—in October, February, and May. provides the opportunity for students degree must therefore enroll for at least completed within five years of the 15 points while registered in the School. holding bachelor’s degrees from affiliated

ENGINEERING 2020–2021 ENGINEERING 2020–2021 24 Master of Science Program in examination. Thereafter, the student credit beyond the bachelor’s degree. at the time of enrollment and extends to or impossible to attend classes on the is integral to the School’s teaching, 25 Management Science and Engineering must write a dissertation embodying Eng.Sc.D. candidates will be required the date on which the dissertation defense Columbia campus may be able to receive research, and service mission and works In collaboration with the Graduate original research under the sponsorship to complete a minimum of 30 additional is held. instruction from the School through to enhance the educational opportuni- School of Business' Decision, Risk of a member of his or her department points of credit in residence beyond Extension of the time allowed for the Columbia Video Network without ties available to students. This office and Operations Division, the Industrial and submit it to the department. If the the M.S. for a letter grade. A master’s completion of the degree may be leaving their work sites. Individuals provides leadership for the integration Engineering and Operations Research department recommends the dissertation degree from an accredited institution may granted on recommendation of the interested in this program should read the of educational programs and services department offers a master’s degree for defense, the student applies for final be accepted in the form of advanced student’s sponsor and the department section describing the distance learning that enhance recruitment, retention, and program focused on management examination, which is held before an standing as the equivalent of 30 points chair to the Dean when special Columbia Video Network (CVN), which quality of campus life for graduate stu- and engineering perspectives examining committee approved by the of credit. Candidates for the Eng.Sc.D. circumstances warrant. Such extensions follows in this bulletin. dents at Columbia Engineering. It strives in solving problems of complex appropriate Dean’s Office. This application degree must, in addition to the 60-point are initiated by submitting a statement Nondegree students receive grades to demonstrate sensitivity and concern systems. (See Industrial Engineering must be made at least three weeks requirement, accumulate 12 points of of work in progress and a schedule for and must maintain satisfactory attendance in addressing the needs of the School’s and Operations Research.) before the date of the final examination. credit in the departmental course E9800: completion together with the sponsor’s and performance in classes or laboratories population. The office is dedicated to The defense of the dissertation Doctoral research instruction (see below). recommendation to the department chair. and will be subject to the same rules as providing service to prospective, new, Master of Science Program in constitutes the final test of the candidate’s The candidate for the degree of Doctor of Please contact the Office of Graduate degree candidates. Should a nondegree and continuing students pursuing a Business Analytics qualifications. It must be demonstrated Engineering Science must submit evidence Student Affairs for more information. student decide to pursue a degree graduate education in engineering or that the candidate has made a contribution that his or her dissertation has been filed program, work completed as a nondegree applied science. In partnership with the Graduate to knowledge in a chosen area. In content in compliance with requirements set by student may be considered for advanced School of Business' Decision, Risk NONDEGREE STUDENTS the dissertation should, therefore, be the faculty of Engineering and Applied standing, but no more than 15 points of and Operations Division and Marketing Qualified persons who are not interested a distinctly original contribution in the Science. coursework completed as a nondegree Division, the Industrial Engineering and in a degree program but who wish selected field of study. In form it must student may be counted toward a Operations Research department offers only to take certain courses may be show the mastery of written English, which Doctoral Research Instruction graduate degree. a master’s degree program designed for permitted to register as nondegree is expected of a university graduate. An Eng.Sc.D. candidate is required to For additional information and those who want to focus on learning the students, provided facilities are available. complete 12 credits in the departmental regulations pertaining to nondegree modeling techniques and data science Many graduate courses in The Fu For the Ph.D. Degree course E9800: Doctoral research students, see Graduate Admissions. tools that help businesses use data to Foundation School of Engineering and instruction in accordance with the make better decisions. (See Industrial A student must obtain the master’s Applied Science are offered in the late following guidelines: Engineering and Operations Research.) degree (M.S.) before enrolling as afternoon and evening in order to make OFFICE OF GRADUATE a candidate for the Ph.D. degree. them available to working individuals STUDENT AFFAIRS Application for admission as a doctoral 1. After obtaining a master’s degree or who wish to further their knowledge in The Office of Graduate Student DOCTORAL DEGREES: candidate may be made while a student is advanced standing, at which time the areas of engineering and applied Affairs at The Fu Foundation School ENG.SC.D. AND PH.D. enrolled as a master’s degree candidate. the student begins doctoral research, science. Individuals who find it difficult of Engineering and Applied Science Two doctoral degrees in engineering Candidates for the Ph.D. degree the student is eligible to register for are offered by the University: the Doctor must register full time and complete E9800 (3, 6, 9, or 12 points of credit of Engineering Science, administered six Residence Units. The minimum per term). by The Fu Foundation School of requirement in coursework for the doctoral 2. Registration for E9800 at a time other Engineering and Applied Science and degree is 60 points of credit beyond the than that prescribed above is not per- the Doctor of Philosophy, administered bachelor’s degree. A master’s degree from mitted, except by written by the Graduate School of Arts and an accredited institution may be accepted permission of the Dean. Sciences. Both doctoral programs are in the form of advanced standing as the 3. The 12 points of E9800 required for subject to review by the Committee equivalent of one year of residence (30 the Eng.Sc.D. degree do not count on Instruction of the School. Doctoral points of credit and two Residence Units). toward the minimum residence students may submit a petition to the An application for advanced standing requirements, e.g., 30 points beyond Office of Graduate Student Affairs to must be completed during the first the master’s degree or 60 points change from the Eng.Sc.D. degree to semester of study. Ph.D. candidates will beyond the bachelor’s degree. the Ph.D. degree or from the Ph.D. be required to complete a minimum of 30 4. If a student is required to take degree to the Eng.Sc.D. degree. The additional points of credit in residence for coursework beyond the minimum res- petition must be submitted within the a letter grade beyond the M.S. idence requirements, the 12 points of first year of enrollment in the doctoral Ph.D. candidates should obtain a doctoral research instruction must still program. Any petitions submitted after copy of the bulletin of the Graduate be taken in addition to the required this period will not be considered. School of Arts and Sciences, in which coursework. Doctoral degree status can be changed are printed the requirements of the 5. A student must register continuously only once; students, therefore, must department of major interest. through the fall and the spring terms. determine which doctoral degree This requirement does not include the program is most appropriate for their For the Eng.Sc.D. Degree summer session. academic and professional endeavors. A student must obtain the master’s Departmental requirements may degree (M.S.) before enrolling as a Completion of Requirements include comprehensive written and oral candidate for the Eng.Sc.D. degree. The The requirements for the Eng.Sc.D. degree qualifying examinations. A student must minimum requirement in coursework must be completed in no more than seven have a satisfactory grade-point average for the doctoral degree is 60 points of years. The seven-year time period begins to be admitted to the doctoral qualifying

ENGINEERING 2020–2021 ENGINEERING 2020–2021 26 Doctor of Engineering Science (DES) Certification of Professional Certification Application 27 COLUMBIA VIDEO NETWORK Degree Programs (Hybrid) Achievement Programs The certification application requires The DES requires 30 credits of online CVN offers 12-credit, four-course a minimum cumulative undergraduate courses and a research project that is Certification of Professional Achievement GPA of 3.0, a resume/CV, a 250-word completed on campus with a faculty programs in various fields for those personal/professional statement, adviser. Applicants must already who desire graduate-level coursework an unofficial transcript for each have an M.S. in a related field prior for professional advancement. Up to university attended, three letters to applying to the DES program. The six credits earned in the Certification of of recommendation, and a $150 DES must be completed within seven Professional Achievement program can application fee. Applications are years. Applicants must select their be applied towards an M.S .degree at reviewed on a rolling basis and decisions faculty advisers prior to submitting CVN. Students enrolled in the certificate are issued within a week of submission. their applications. program must complete the program Applications must be submitted via the within two years and earn a GPA of 3.0 application portal on cvn.columbia.edu. Fields of Study: or higher. • Computer Science* Nondegree Courses Fields of Study: • Earth and Environmental Engineering Students who have earned an • Electrical Engineering • Applied Mathematics undergraduate degree in engineering, Columbia Video Network CVN graduates earn the same degrees • Computer Science (9 tracks) • Mechanical Engineering • Business and Technology mathematics, or a related field may take 540 S. W. Mudd, MC 4719 as on-campus students. Professors and – Computational Biology • Civil Engineering one or two courses as a nondegree 500 West 120th Street teaching assistants are available via email, – Computer Security *Only available to applicants who have • Construction Management student. Any of the CVN courses listed New York, NY 10027 phone, or online office hours to address – Foundations of Computer Science earned an M.S. in Computer Science from • Data Science on the CVN website may be taken as academic questions. CVN’s administrative – Machine Learning Columbia University. • Earth and Environmental 212-854-6447 a non-degree course, provided that the staff is available to assist with registration – Natural Language Processing Engineering [email protected] student has met the prerequisites for procedures, technical queries, and – Network Systems DES Application • Electrical Engineering cvn.columbia.edu that course. academic advising. – Personalized Track The DES application requires a minimum • Financial Engineering Up to six credits earned as a non- – Software Systems cumulative undergraduate GPA of 3.0, • Industrial Engineering degree student may be applied BACKGROUND – Vision Graphics, Interactions, an M.S. in a related field, a resume/ • Information Systems towards the MS course requirements. Columbia University’s Fu Foundation PROGRAMS OF STUDY and Robotics CV, a 250-word personal/professional • Low Carbon and Efficiency Earning credit as a non-degree student School of Engineering and Applied CVN offers part-time online graduate • Earth and Environmental Engineering statement, an unofficial transcript for Technology does not guarantee acceptance into a Science established the Columbia degree, certificate, and non-degree • Electrical Engineering each university attended, three letters • Manufacturing Engineering degree program. Video Network (CVN) in 1986 to meet programs. CVN students may enroll • Industrial Engineering: Systems of recommendation, self-reported GRE • Materials Science a growing need within the engineering in select SEAS graduate courses in Nondegree Application Engineering General Test scores (GRE scores are • Multimedia Networking community for a graduate distance Fall, Spring, and Summer terms. CVN The application requires a minimum • Materials Science and Engineering valid for five years), TOEFL/IELTS scores • Nanotechnology education program. Over 30 years administrators work closely with faculty cumulative undergraduate GPA of 3.0, • Mechanical Engineering (if applicable), a $150 application fee, • Networking and Systems later, our part-time fully online programs members from each department to a resume/CV, a 250-word personal/ • Operations Research: Methods and the name of a prospective faculty • New Media Engineering provide working professionals high select courses that best fit the needs of professional statement, and unofficial in Finance adviser. Applications must be submitted • Operations Research quality graduate engineering education our students. transcripts from every university via the application portal on • Sustainable Energy in a convenient and flexible format. attended. There is no application fee. M.S. Application cvn.columbia.edu. Applications are • Systems Engineering Applications are reviewed on a rolling Master of Science (M.S.) The M.S. application requires a minimum reviewed on a rolling basis and decisions • Telecommunications basis and decisions are issued within a PROGRAM BENEFITS Degree Programs cumulative undergraduate GPA of 3.0, are issued 4–6 weeks after submission. • Wireless and Mobile week of submission. Applications must At CVN, the #1 ranked Best Graduate a resume/CV, a 250-word personal/ Communications The M.S. is a coursework-based be submitted via the application portal Online Engineering Program by the 2020 professional statement, an unofficial master's, which requires 30 credits of on cvn.columbia.edu. U.S. News & World Report, students online coursework. The M.S. must be transcript for each university attended, can enroll in online courses and earn completed within five years. Students three letters of recommendation, self- graduate engineering degrees without are required to maintain continuous reported GRE General Test scores (GRE ever having to set foot on campus. enrollment, which is a minimum of two scores are valid for five years), TOEFL/ CVN courses are taught by Columbia classes per year, one in the Fall and one IELTS scores (if applicable), and a University faculty, offering students in the Spring semesters. $150 application fee. Applications are flexibility coupled with the high-caliber reviewed on a rolling basis and decisions teaching, resources, and standards Fields of Study: are issued 4–6 weeks after submission. inherent in The Fu Foundation School of • Applied Mathematics Applications must be submitted via the Engineering and Applied Science. • Applied Physics application portal on cvn.columbia.edu. CVN students view the same lectures • Biomedical Engineering Accepted students can begin and complete the same homework, • Chemical Engineering coursework up to one year after projects, and exams as those offered to • Civil Engineering admission into CVN. students enrolled in on-campus SEAS • Civil Engineering: Construction courses. Students have access to online Engineering and Management university resources and are a part of the Columbia Community.

ENGINEERING 2020–2021 ENGINEERING 2020–2021 28 demonstrate English proficiency as and February 15 for most M.S. only as a one-term nondegree student. This 29 GRADUATE ADMISSIONS a graduation requirement at The Fu and nondegree applicants. Please option is also appropriate for individuals Foundation School of Engineering and visit the Office of Graduate Student who missed application deadlines. Applied Science. Regardless of TOEFL, Affairs website for specific M.S. only Applications for the one-term nondegree IELTS, or PTE scores submitted for program deadlines. student status are available at the Office admission, students should continue to • Spring admission application deadline: of Graduate Student Affairs and must be work on maintaining adequate verbal October 1 for all departments and submitted during the first week of the fall and/or written abilities for successful degree levels. or spring semester. integration within their classes and future If a one-term nondegree student Applicants who wish to be considered professional endeavors. Students are subsequently wishes either to continue for scholarships, fellowships, and highly encouraged to be proactive about taking classes the following term or to assistantships should file complete addressing their English proficiency by become a degree candidate, a formal applications for fall admission. utilizing the many resources available application must be made through the within Columbia University and Office of Graduate Student Affairs. throughout New York City. EXPRESS APPLICATION Students have the option of enrolling Columbia Engineering, Columbia TRANSFER APPLICANTS in communication courses offered College, General Studies, and Barnard Master's degree students are not eligible Office of Graduate Student Affairs student (not a degree candidate). Note: described below. An official transcript through Columbia Engineering's seniors as well as alumni from the for transfer credits. 530 S. W. Mudd, MC 4708 Not more than 15 points of credit from each postsecondary institution Professional Development and same schools, who have graduated Students admitted to the doctoral 500 West 120th Street completed as a nondegree student may attended, personal statement, and Leadership courses (noncredit, tuition within three years, may be eligible to program who have been conferred New York, NY 10027 be counted toward a degree. resume or curriculum vitae must free) and the American Language apply to a master's program using the an appropriate M.S. degree may be The applicant must submit all be submitted. Consideration for Program (ALP) at Columbia University express application process. A minimum awarded two residence units toward 212-854-6438 materials directly, not through an agent or admission will be based not only on the (credited). Course credits earned through cumulative GPA of 3.50 in an approved their Ph.D., as well as 30 points of [email protected] third-party vendor, with the sole exception completion of an earlier course of study, ALP, however, do not count toward undergraduate program is required to advanced standing toward their Ph.D. gradengineering.columbia.edu of submissions by the U.S. Department but also upon the quality of the record the minimum engineering academic be eligible to submit an M.S. Express or Eng.Sc.D. with approval from the of State's Fulbright Program and its presented and upon such evidence coursework requirements. Enrollment application. For more information about academic department and the Office of The basic requirement for admission three partner agencies IIE, LASPAU and as can be obtained concerning the in ALP courses is solely the financial eligibility, visit the Office of Graduate Graduate Student Affairs. as a graduate student is a bachelor’s AMIDEAST, and by the Danish-American applicant’s personal fitness to pursue responsibility of the student. As a rule, Student Affairs website. degree received from an institution of Fulbright Commission (DAF), Deutscher professional work. ISSO will not permit students to drop The M.S. Express online applica- acceptable standing. Ordinarily, the Akademischer Austauschdienst (DAAD), Additionally, applicants must provide courses or fall below full-time registration tion, which waives the submission of applicant will have majored in the field and Vietnam Education Fund (VEF). In three letters of recommendation and the for language proficiency deficiencies. GRE scores, letters of recommendation, in which graduate study is intended, addition, the applicant will be required to results of required standardized exams. and official transcripts, streamlines and but in certain programs, preparation in attest to the accuracy and authenticity of The Graduate Record Examination APPLICATION FEE simplifies the application process for a related field of engineering or science all information and documents submitted (general) is required for all candidates. The nonrefundable application fee for graduate study. Contact your academic is acceptable. The applicant will be to Columbia. If you have any questions Applicants to the doctoral program in all graduate degree and nondegree department or the Office of Graduate admitted only if the undergraduate about this requirement, please contact applied physics are also required to programs is $85. Student Affairs for further details. record shows promise of productive and the admissions office at seasgradmit@ submit official GRE Physics Test scores. effective graduate work. columbia.edu. GRE general and subject test scores Students who hold an appropriate Academic integrity is the cornerstone are valid for five years from the test GRADUATE ADMISSION ONE-TERM NONDEGREE degree in engineering may apply for of a university education. Failure to administration date according to the CALENDAR STUDENT STATUS admission to study for the Ph.D. degree. submit complete, accurate, and authentic Educational Testing Service (ETS). English Applicants are admitted twice yearly, for Individuals who meet the eligibility However, students are required to obtain application documents consistent with language test scores are required of all the fall and spring semesters. requirements, who are U.S. citizens, the master’s degree first. Students these instructions may result in denial or applicants who received their bachelor's U.S. permanent residents, or hold an currently enrolled in the School's M.S. revocation of admission, cancellation of degree in a country in which English is not • Fall admission application deadlines: appropriate visa, and who wish to take program may apply for admission to academic credit, suspension, expulsion, the official and widely spoken language. December 15 for Ph.D., Eng.Sc.D., courses for enrichment, may secure the doctoral program after completing or eventual revocation of degree. The Test of English as a Foreign Language and M.S. leading to Ph.D. programs faculty approval to take up to two 15 points of coursework. Completion of Applicants may be required to assist (TOEFL), International English Language graduate-level courses for one term only a relevant master's degree is required admissions staff and faculty involved in Testing System (IELTS), or Pearson Test prior to entry into the Ph.D. program. admission reviews in the verification of of English (PTE) scores satisfy the test Students may be admitted in one all documents and statements made in requirement and are valid for two years of the following five classifications: documents submitted by students as according to the test organizations. candidate for the M.S. degree, candidate part of the application review process. Applicants may be asked to for the M.S. degree leading to the Ph.D. participate in an interview as part of the degree, candidate for the Doctor of application process. APPLICATION REQUIREMENTS Engineering Science degree, candidate Applicants can only apply to one degree for the Doctor of Philosophy degree (see program per admission term. Applicants ENGLISH PROFICIENCY also the bulletin of the Graduate School must submit an online application and The Office of Graduate Student of Arts and Sciences), or nondegree required supplemental materials, as Affairs no longer requires students to

ENGINEERING 2020–2021 ENGINEERING 2020–2021 30 GRADUATE TUITION, FEES, AND PAYMENTS HEALTH INSURANCE charge will be the actual cost of repair, 6th week 60% 31 Columbia University offers the Student and, if the damage results in total loss of 7th week 50% Medical Insurance Plan, which provides the apparatus, adjustment will be made 8th week 40% both Basic and Comprehensive levels in the charge for age or condition. To 9th week and after 0% of coverage. Full-time students are ensure that there may be no question automatically enrolled in the Basic level as to the liability for damage, students Refund Policy When Dropping of the Plan and billed for the insurance should note whether the apparatus is in Individual Courses premium in addition to the Health Service good condition before use and, in case Tuition for courses dropped by the last fee. Visit the Columbia Health website of difficulty, request instruction in its day of the Change-of-Program period at health.columbia.edu for detailed proper operation. Where there is danger is refunded in full. There is no refund of information about medical insurance of costly damage, an instructor should tuition for individual courses dropped coverage options and directions for be requested to inspect the apparatus. after the last day of the Change-of- making confirmation, enrollment, or Liability for breakage will be decided by Program period. The Change-of- waiver requests. the instructor in charge of the course. Program period is usually the first two When the laboratory work is done by weeks of the fall or spring semesters a group, charges for breakage will be (please note that the first week of the PERSONAL EXPENSES divided among the members of the semester usually begins on a Tuesday). Students should expect to incur he 2020–2021 tuition and fees TUITION • Health and Related Services fee: group. The students responsible for any Please note: The prorated schedule miscellaneous personal expenses for are estimated. Tuition and fees Graduate students enrolled in M.S. and $610 per term damage will be notified that a charge is above does not pertain to individual such items as food, clothing, linen, are prescribed by statute and are Eng.Sc.D. programs pay $2,196 per • International Services charge: being made against them. The amount classes dropped (unless your entire T laundry, dry cleaning, and so forth. subject to change at the discretion of credit, except when a special fee is $110 per term (international of the charge will be stated at that time schedule consists of only one class). The University advises students to the Trustees. fixed. Graduate tuition for Ph.D. students students only) or as soon as it can be determined. The prorated schedule pertains to open a local bank account upon arrival University charges such as tuition, is $24,512 per Residence Unit. The • Document fee: $105 (one-time charge) withdrawals. Withdrawal is defined as in New York City. Since it often takes as fees, and residence hall and meal plans Residence Unit, full-time registration for dropping one’s entire program. long as three weeks for the first deposit TUITION AND FEE REFUNDS are billed in the first Student Account one semester rather than for individual For students receiving federal OTHER FEES to clear, students should plan to cover Students who make a complete Statement of the term, which is sent out courses (whether or not the student is student aid, refunds will be made to Activities fees for master's programs: immediate expenses using either a credit withdrawal from a term, including the in July and December of each year for the taking courses), provides the basis for the federal aid programs in accordance • First year full-time students (12 or more card, traveler’s checks, or cash draft summer, are assessed a withdrawal upcoming term. This account is payable tuition charges. Ph.D. students should with Department of Education credits): $300 drawn on a local bank. Students are fee of $75. Late fees, application and due in full on or before the payment consult the bulletin for the Graduate regulations. Refunds will be credited in • Continuing full-time students (12 or urged not to arrive in New York without fees, withdrawal fees, tuition deposits, due date announced in the Statement, School of Arts and Sciences. the following order: more credits): $200 sufficient start-up funds. special fees, computer fees, special typically at the end of August or early • First year part-time students (less than examination fees, and transcript fees January before the beginning of the billed Federal Unsubsidized Stafford Loans COMPREHENSIVE FEE/ 12 credits): $150 are not refundable. term. Any student who does not receive LABORATORY CHARGES Federal Stafford Loans MATRICULATION AND • Continuing part-time students (less than The Health Service Fee, Health the first Student Account Statement is Students may need to add another Federal Perkins Loans FACILITIES 12 credits): $100 Insurance Premium, University expected to pay at registration. Federal PLUS Loans (when disbursed Eng.Sc.D. candidates engaged only $100 to $300 for drafting materials or facilities fees, and student activity If the University does not receive laboratory fees in certain courses. Each through the University) in research, and who have completed All full-time and part-time M.S.-Ph.D. fees are not refundable. the full amount due for the term on or student taking laboratory courses must Federal Pell Grants their twelve (12) credits of Doctoral track and Ph.D. students shall be Students who withdraw within before the payment due date of the furnish, at his or her own expense, the Federal Supplemental Educational Research Instruction (see “The Graduate charged, per term, a student activities the first 60 percent of the academic first Statement, a late payment charge necessary notebooks, blank forms, and Opportunity Grants Programs” in this bulletin), are assessed fee of $25. period are subject to a pro rata refund of $150 will be assessed. An additional similar supplies. In some laboratory Other Title IV funds a Comprehensive Fee of $2,344 per calculation, which refunds a portion charge of 1.5 percent per billing cycle courses, a fee is charged to cover term by The Fu Foundation School of Application and late fees: of tuition based on the percentage of Withdrawing students should be may be imposed on any amount past expendable materials and equipment Engineering and Applied Science. • Application for graduate admission: $85 the term remaining after the time of aware that they will not be entitled due thereafter. maintenance; the amount of the fee Ph.D. candidates engaged only in • Late registration fee: withdrawal. This calculation is made to any portion of a refund until all Students with an overdue account is shown with the descriptions in the research are assessed $2,344 per term - during late registration: $50 from the date the student’s written Title IV programs are credited and all balance may be prohibited from course listings. Students engaged in for Matriculation and Facilities by the - after late registration: $100 notice of withdrawal is received by the outstanding charges have been paid. registering, changing programs, or special tests, investigations, theses, Graduate School of Arts and Sciences. Office of Graduate Student Affairs. obtaining a diploma or transcripts. Books and course materials: or research work are required to meet In the case of persistently delinquent • Depends upon course the costs of expendable materials as Percentage Refund for Withdrawal accounts, the University may utilize the MANDATORY FEES may be necessary for this work and in during First Nine Weeks of Term services of an attorney and/or collection University service and support fee: Laboratory fees: See course listings accordance with such arrangements as agent to collect any amount past due. Prorated for calendars of a different • On-campus full-time master's IEOR master’s program fee: may be made between the student and If a student’s account is referred for duration, if the entire program is dropped: programs: $305 fall / $575 spring • Full-time master’s program: $1,000 the department immediately concerned. collection, the student may be charged • On-campus all other full-time • Part-time master’s program: $500 an additional amount equal to the cost 1st week 100% programs: $261 fall / $531 spring of collection, including reasonable DAMAGES 2nd week 100% • On-campus part-time master's attorney’s fees and expenses incurred All students will be charged for damage 3rd week 90% programs: $176 fall / $446 spring by the University. to instruments or apparatus caused by 4th week 80% their carelessness. The amount of the 5th week 70%

ENGINEERING 2020–2021 ENGINEERING 2020–2021 32 are participating in faculty research Most private student loan programs progress as defined in “The Graduate 33 FINANCIAL AID FOR GRADUATE STUDY that fulfills degree requirements, you are restricted to U.S. citizens and Programs” section in order to remain may apply for a research assistantship. permanent residents. However, eligible for federal student loans. Assistantships are awarded on the basis international students may be eligible to of academic merit. apply for these domestic loan programs VETERANS BENEFITS with a creditworthy cosigner who is The U.S. Department of Veterans ALTERNATIVE FUNDING a citizen or permanent resident in the Affairs, as well as state and local SOURCES United States. Depending on the loan government, offers a number of program, you may need a valid U.S. educational assistance programs for External Awards Social Security number. veterans of the U.S. Armed Forces Because it is not possible to offer full Students who study at Columbia and their dependents. Based on the grant and fellowship support to all Engineering on temporary visas time and length of service, as well as graduate students and because of the should fully understand the regulations current status, veterans can be eligible prestige inherent in holding an award concerning possible employment under for one or more of these programs. through open competition, applicants those visas. Before making plans for Many benefits are available to advance are encouraged to consider major employment in the United States, the education and skills of veterans national and international fellowship international students should consult with and service members. Spouses and FINANCING GRADUATE admissions application must be received apply for departmental funding. Outside opportunities. It is important that the International Students and Scholars family members may also be eligible EDUCATION by the December 15 deadline to be scholarships for which you qualify must prospective graduate students explore Office (ISSO), located at 524 Riverside for education and training assistance. The academic departments of eligible for The Fu Foundation School be reported to your department and the every available source of funding for Drive, Suite 200; 212-854-3587. Its Please visit Vets.gov to apply for Columbia Engineering and the Office of Engineering and Applied Science Office of Student Financial Planning. graduate study. website is isso.columbia.edu. education benefits. of Student Financial Planning seek to departmental funding (institutional The School reserves the right to adjust In researching outside funding you To qualify for deferred tuition ensure that all academically qualified grants, fellowships, and teaching your institutional award if you hold an may look to faculty advisers, career OTHER FINANCIAL AID— payments, please provide a copy of students have enough financial support and research assistantships). Spring outside scholarship, fellowship, or other services offices, deans of students, and FEDERAL AND PRIVATE your Certificate of Eligibility and DD-214 to enable them to work toward their admissions applicants will not be outside funding. offices of financial aid where frequently PROGRAMS (please note the DD-214 is not required degree. Possible forms of support for considered for departmental funding. you may find resource materials, books, U.S. citizens and permanent residents for dependents) to the Columbia Office tuition, fees, books, and living expenses Incoming applicants and continuing Institutional Grants and grant applications for a wide variety enrolled at least half-time in a degree- of Military & Veterans Affairs (OMVA). are: institutional grants, fellowships, students should complete the FAFSA by Institutional grants are awarded to of funding sources. You must notify both granting program are eligible to apply teaching and research assistantships, May 5 for fall enrollment. graduate students on the basis of your Columbia Engineering academic for federal student loans. To apply • In person to 202 Kent Hall on- or off-campus employment, and Guidelines for continuing students academic merit. Recipients must department and the Office of Student for federal student loans, students • Scan and email to veterans@ student loans. The Office of Student are available from departmental advisers maintain satisfactory academic standing. Financial Planning of any outside should complete the Free Application columbia.edu Financial Planning assists students in advance of the established deadline. awards that you will be receiving. for Federal Student Aid (FAFSA) using • Fax to 212-854-2818 with developing financing plans for All continuing supported students Fellowships Columbia University’s school code must preregister for classes during the completing a degree. Fellowships are financial and intellectual Funding for International Students 002707 by May 5 for fall enrollment For assistance with utilizing your benefits preregistration period. Columbia University graduate funds awards for academic merit that provide To secure a visa, international students Several private student loan as well as understanding the timeline are administered by two separate stipends to be used by fellows to further must demonstrate that they have programs are available to both U.S. of payments please contact a School citizens and international students. Certifying Official at 212-854-3161 or branches of the University, and the GRADUATE SCHOOL their research. If you are awarded a sufficient funding to complete the These loans require that you have a [email protected]. application materials required by DEPARTMENTAL FUNDING fellowship, you are expected to devote degree. Many international students good credit standing. International For questions related to the status the two branches differ. Institutional The graduate departments of Columbia time to your own work, and you are not obtain support for their educational students may be eligible for a private of the VA application or entitlement grants, fellowships, and teaching Engineering offer an extensive array required to render any service to the expenses from their government, a loan with a creditworthy U.S. citizen or eligibility, contact the Department of and research assistantships are all of funding. Funding decisions, based University or donor. You may publish foundation, or a private agency. permanent resident cosigner. Veterans Affairs at 1-888-442-4551. departmentally-administered funds. solely on merit, and contingent upon research produced by your fellowship International students who apply Detailed information and application Additional resources and veterans Questions regarding these awards making satisfactory academic progress, work. As a fellow, you may not engage to doctoral programs of study by instructions for student loans may be news can be found at sfs.columbia.edu/ should be directed to your academic are made by the departments. All in remunerative employment without the December 15 deadline and are found at the Office of Student Financial departments/veterans-service. department. Federal Student Loans applicants for admission and continuing consent of the Dean. Applicants should admitted to a Columbia Engineering Planning website at sfs.columbia.edu/ (Unsubsidized and Graduate PLUS) students maintaining satisfactory contact the department directly for doctoral program are automatically sfp-grad-engin. Veterans Benefits and Transition Act and private student loans are academic standing will be considered information. considered for departmental funding Determination of your eligibility of 2018 administered by the Office of Student for departmental funds. Applicants (institutional grants, fellowships, and for financial aid is based in part on Financial Planning. Questions about should contact their department directly Assistantships teaching and research assistantships, In accordance with Title 38 US Code the number of courses for which you loans should be directed to the for information. Columbia Engineering Teaching and research assistantships, upon completion of the required 3679 subsection (e), this school adopts register. If you enroll in fewer courses financial aid office. prospective and continuing graduate available to doctoral students in all financial aid forms referred to above. the following additional provisions for than you initially reported on the loan students must complete their FAFSA in departments, provide tuition exemption Spring admissions applicants will not be any students using U.S. Department of request form, your loan eligibility may be order to be considered for all forms of and a living stipend. Duties may include considered for departmental funding. Veterans Affairs (VA) Post 9/11 G.I. Bill® INSTRUCTIONS FOR reduced. graduate financing (both departmentally- teaching, laboratory supervision, Continuing international students (Ch. 33) or Vocational Rehabilitation and FINANCIAL AID APPLICANTS The FAFSA, planned enrollment administered and financial aid– participation in faculty research, and must preregister for classes during the Employment (Ch. 31) benefits, while Deadlines form, and the loan request form must administered funds). The application other related activities. Teaching and preregistration period and complete an payment to the institution is pending Apply for financial aid at the same time be completed each academic year, and for admission to Columbia Engineering research assistantships require up to enrollment status form to be considered from the VA. This school will not: that you apply for admission. Your you must maintain satisfactory academic graduate programs is also used to twenty hours of work per week. If you for departmental funding.

ENGINEERING 2020–2021 ENGINEERING 2020–2021 34 • Prevent nor delay the student's Off-Campus Employment in For the specific Columbia Gainful enrollment; New York City Employment Disclosures, please • Assess a late penalty fee to the One of the nation’s largest urban review them both at essential-policies. student; areas, the city offers a wide variety columbia.edu/files_facets/imce_shared/ • Require the student to secure of opportunities for part-time work. isclosure_CU_Template_2019_Engineer_ alternative or additional funding; Many students gain significant of_Mines.pdf and essential-policies. • Deny the student access to any experience in fields related to their columbia.edu/files_facets/imce_shared/ resources available to other students research and study while they sure_CU_Template_2019_Metallurgical_ who have satisfied their tuition and meet a portion of their educational Engineer.pdf. fee bills to the institution, including expenses. but not limited to access to classes, CONTACT INFORMATION libraries, or other institutional Gainful Employment Disclosures For questions about institutional grants, facilities. Programs: Engineer of Mines and fellowships, and teaching and research Metallurgical Engineer assistantships, contact your academic However, to qualify for this provision, These programs are designed to be department. such students may be required to: completed in 32 weeks. For questions about on- or off- These programs will cost $71,998 campus non-need-based employment, • Produce the Certificate of Eligibility if completed within the normal time. contact the Center for Career Education, by the first day of class; There may be additional costs for living located at East Campus, Lower Level, • Provide written request to be expenses. These costs were accurate 212-854-5609, careereducation. certified; at the time of the posting but may columbia.edu. • Provide additional information have changed. For questions about student loans, needed to properly certify the Fewer than 10 students completed contact: enrollment as described in other this program within the normal time. This institutional policies. number has been withheld to preserve Office of Student Financial Planning the confidentiality of the students. 202 Kent Hall, MC 9205 Further information can be found at The following states/territories do 1140 Amsterdam Avenue sfs.columbia.edu/content/information. not have licensure requirements for this New York, NY 10027 profession: Alabama, Alaska, American EMPLOYMENT Samoa, Arizona, Arkansas, California, Phone: 212-854-7040 Students on fellowship support Colorado, Connecticut, Delaware, Fax: 212-854-2818 must obtain the permission of the District of Columbia, Federated States [email protected] Dean before accepting remunerative of Micronesia, Florida, Georgia, sfs.columbia.edu/sfp-grad-engin employment. Guam, Hawaii, Idaho, Illinois, Indiana, Students who study at Columbia Iowa, Kansas, Kentucky, Louisiana, Engineering on temporary visas Maine, Marshall Islands, Maryland, should fully understand the regulations Massachusetts, Michigan, Minnesota, concerning possible employment under Mississippi, Missouri, Montana, those visas. Before making plans for Nebraska, Nevada, New Hampshire, employment in the United States, New Jersey, New Mexico, New York, international students should consult North Carolina, North Dakota, Northern with the International Students and Marianas, Ohio, Oklahoma, Oregon, Scholars Office (ISSO) located at 524 Palau, Pennsylvania, Puerto Rico, Rhode Riverside Drive, Suite 200; 212-854- Island, South Carolina, South Dakota, 3587. Its website is isso.columbia.edu. Tennessee, Texas, Utah, Vermont, Virgin Islands, Virginia, Washington, West On-Campus Employment Virginia, Wisconsin, and Wyoming. The Center for Career Education For more information about maintains an extensive listing of student graduation rates, loan repayment rates, employment opportunities. The Center for and postenrollment earnings about this Career Education (CCE) is located at East institution and other postsecondary Campus, Lower Level, 212-854-5609, institutions please read further on careereducation.columbia.edu. collegescorecard.ed.gov.

ENGINEERING 2020–2021 Faculty and Administration 36 Asaf Cidon Daniel Esposito Ronghui Gu 37 FACULTY AND ADMINISTRATION Assistant Profesor of Electrical Associate Professor of Chemical Assistant Professor of Computer Engineering Engineering Science OFFICERS Elias Bareinboim Robert G. Bozic Lee C. Bollinger, J.D. Assistant Professor of Computer Lecturer in Chemical Engineering Matei T. Ciocarlie Yuri Faenza X. Edward Guo President of the University Science Associate Professor of Mechanical Assistant Professor of Industrial Stanley Dicker Professor of Biomedical Michael P. Burke Engineering Engineering and Operations Research Engineering Ira Katznelson Katayun Barmak Vaziri Assistant Professor of Mechanical Interim Provost of the University Philips Electronics Professor of Applied Engineering Michael J. Collins Raymond Farinato Christine P. Hendon Physics and Applied Mathematics Vikram S. Pandit Professor of Professor of Professional Practice of Associate Professor of Electrical Mary C. Boyce, Ph.D. Adam Cannon Computer Science Earth and Environmental Engineering Engineering Dean Daniel Bauer Senior Lecturer in Machine Learning Lecturer in Computer Science (Computer Science) Tal Danino Robert J. Farrauto Irving P. Herman Andrew Laine, D.Sc. Assistant Professor of Biomedical Professor of Professional Practice of Edward Howard Armstrong Professor of Secretary Peter N. Belhumeur Agostino Capponi Engineering Earth and Environmental Engineering Applied Physics Professor of Computer Science Assistant Professor of Industrial Engineering and Operations Research Gautam Dasgupta Steven K. Feiner Henry S. Hess FACULTY Steven M. Bellovin Professor of Civil Engineering and Professor of Computer Science Professor of Biomedical Engineering Perry K. and Vida L. W. Hudson Luca Carloni Engineering Mechanics Shipra Agrawal Elizabeth M. C. Hillman Professor of Computer Science Professor of Computer Science Maria Q. Feng Assistant Professor of Industrial Tony Dear Renwick Professor of Civil Engineering Associate Professor of Biomedical Engineering and Operations Research Engineering and of Radiology Keren Bergman Augustin Chaintreau Lecturer in Computer Science and Engineering Mechanics (Physics) Charles Batchelor Professor of Electrical Associate Professor of Computer Sunil Agrawal Engineering Science George Deodatis Jacob Fish Professor of Mechanical Engineering Ali Hirsa The Santiago and Robertina Calatrava Robert A. W. and Christine S. Carleton Professor of Practice Industrial Raimondo Betti Siu-Wai Chan Family Professor of Civil Engineering Professor of Civil Engineering Peter K. Allen Engineering and Operations Research Professor of Civil Engineering and Professor of Materials Science (Henry Professor of Computer Science Emanuel Derman Engineering Mechanics Krumb School of Mines) and of Applied Alexander Gaeta Julia B. Hirschberg Professor of Professional Practice of David M. Rickey Professor of Applied Dimitris Anastassiou Physics and Applied Mathematics Percy K. and Vida L. W. Hudson Daniel Bienstock Industrial Engineering and Operations Physics and of Materials Science Charles Batchelor Professor of Electrical Professor of Computer Science Liu Family Professor of Industrial Kartik Chandran Research Engineering Engineering and Operations Research Professor of Earth and Environmental Oleg Gang James C. Hone Engineering (Henry Krumb School of Xuan Sharon Di Professor of Chemical Engineering James Anderson and Professor of Applied Physics and Wang Fong-Jen Professor of Mechanical Applied Mathematics Mines) Assistant Professor of Civil Engineering Engineering Assistant Professor of Electrical and Engineering Mechanics Roxana Geambasu Engineering Simon J. L. Billinge Julius Chang Associate Professor of Computer Science Daniel J. Hsu Lecturer in Civil Engineering and Antonius Dieker Associate Professor of Computer Alexandr Andoni Professor of Materials Science and of Engineering Mechanics Associate Professor of Industrial Pierre Gentine Science Associate Professor of Computer Science Applied Physics and Applied Mathematics Engineering and Operations Research Associate Professor of Earth and Shih-Fu Chang Environmental Engineering (Henry Krumb Clark T. Hung Gerard A. Ateshian Kyle J. M. Bishop The Richard Dicker Professor of Chris Dolan School of Mines) Professor of Biomedical Engineering Andrew Walz Professor of Mechanical Associate Professor of Chemical Telecommunications (Electrical Lecturer in Industrial Engineering and Engineering and Professor of Biomedical Engineering Engineering) and Professor of Computer Operations Research Javad Ghaderi Dehkordi James S. Im Engineering Science Professor of Materials Science (Henry Paul Blaer Associate Professor of Electrical Eleni Drinea Engineering Krumb School of Mines) and of Applied Elham Azizi Senior Lecturer in Computer Science Jingguang G. Chen Lecturer in the Data Science Institute Physics and Applied Mathematics Assistant Professor of Biomedical Thayer Lindsley Professor of Engineering and in Computer Science Marco Giometto David M. Blei Garud N. Iyengar Engineering (Chemical Engineering) Assistant Professor of Civil Engineering Professor of Computer Science and of Professor of Industrial Engineering and Qiang Du and Engineering Mechanics William E. Bailey Statistics (Arts and Sciences) Operations Research Xi Chen The Fu Foundation Professor of Applied Associate Professor of Materials Associate Professor of Computer Mathematics Donald Goldfarb Allen H. Boozer Joshua Jacobs Science (Henry Krumb School of Mines) Science Alexander and Hermine Avanessians Professor of Applied Physics Assistant Professor of Biomedical and of Applied Physics and Applied Christopher J. Durning Professor of Industrial Engineering and Mathematics Xi Chen Engineering Athanasios Bourtsalas Professor of Chemical Engineering Operations Research Professor of Earth and Environmental Lecturer in Earth and Environmental Suman Jana Eric Balkanski Engineering (Henry Krumb School of Stephen A. Edwards Vineet Goyal Engineering Assistant Professor of Computer Science Assistant Professor of Industrial Mines) Associate Professor of Computer Science Associate Professor of Industrial Engineering and Operations Research Christopher Boyce Engineering and Operations Research Lydia Chilton Predrag R. Jelenkovic Assistant Professor of Chemical Adam Elmachtoub Scott A. Banta Assistant Professor of Computer Professor of Electrical Engineering Engineering Assistant Professor of Industrial Luis Gravano Professor of Chemical Engineering Science Engineering and Operations Research Professor of Computer Science Xiaofan Fred Jiang Mary C. Boyce Assistant Professor of Electrical Morris A. and Alma Schapiro Professor Engineering and Professor of Mechanical Engineering

ENGINEERING 2020–2021 ENGINEERING 2020–2021 38 Hardeep V. Johar Zoran Kostic Qiao Lin Vishal Misra John Paisley Timothy Roughgarden 39 Senior Lecturer in Industrial Engineering Associate Professor of Professional Professor of Mechanical Engineering Professor of Computer Science Associate Professor of Electrical Professor of Computer Science and Operations Research Practice in Electrical Engineering Engineering Hoe I. Ling Debasis Mitra Dan Rubenstein Cedric Josz Ioannis A. Kougioumtzoglou Professor of Civil Engineering and Professor of Electrical Engineering Thomas Panayotidi Associate Professor of Computer Science Assistant Professor of Industrial Assistant Professor of Civil Engineering Engineering Mechanics Lecturer in Civil Engineering and Engineering and Operations Research and Engineering Mechanics Vijay Modi Engineering Mechanics Amir Sagiv Hod Lipson Professor of Mechanical Engineering Assistant Professor of Applied Physics Jingyue Ju Harish Krishnaswamy Professor of Mechanical Engineering Christos Papadimitriou and Applied Mathematics Samuel Ruben–Peter G. Viele Professor Associate Professor of Electrical Aaron Moment Donovan Family Professor of Computer of Engineering (Chemical Engineering) Engineering Michal Lipson Professor of Practice in Chemical Science Paul Sajda Eugene Higgins Professor of Electrical Engineering Professor of Biomedical Engineering Christoph W. Juchem Christian Kroer Engineering Ah-Hyung Alissa Park and of Electrical Engineering and of Associate Professor of Biomedical Assistant Professor of Industrial Barclay Morrison III Lenfest Earth Institute Associate Radiology (Health Sciences) Engineering Engineering and Operations Research Richard W. Longman Professor of Biomedical Engineering Professor in Climate Change (Earth and Professor of Mechanical Engineering Environmental Engineering) Ansaf Salleb-Aouissi Soulaymane Kachani Sanat K. Kumar and of Civil Engineering and Engineering Kristin M. Myers Lecturer in Computer Science Professor of Professional Practice of Bykhovsky Professor of Chemical Mechanics Associate Professor of Mechanical Carlos Paz-Soldan Industrial Engineering and Operations Engineering Engineering Associate Professor of Applied Physics P. James Schuck Research Helen H. Lu and Applied Mathematics Associate Professor of Mechanical Aaron M. Kyle Professor of Biomedical Engineering D. R. Nagaraj Engineering Gail E. Kaiser Senior Lecturer in Biomedical Engineering Professor of Practice in Earth and Itsik Pe’er Professor of Computer Science Design Tal Malkin Environmental Engineering Associate Professor of Computer Science Henning G. Schulzrinne Associate Professor of Computer Science Julian Clarence Levi Professor of Lance C. Kam Ioannis Kymissis Arvind Narayanaswamy Feniosky Peña-Mora Mathematical Methods and Computer Professor of Biomedical Engineering Professor of Electrical Engineering Kyle Mandli Associate Professor of Mechanical Edwin Howard Armstrong Professor Science and Professor of Electrical Assistant Professor of Applied Engineering of Civil Engineering and Engineering Engineering Karen Kasza Jeffrey W. Kysar Mathematics Mechanics and Professor of Earth Clare Boothe Luce Assistant Professor Professor of Mechanical Engineering Gerald A. Navratil and Environmental Engineering and of Mingoo Seok of Mechanical Engineering Lauren Marbella Thomas Alva Edison Professor Computer Science Associate Professor of Electrical Daniel Lacker Assistant Professor of Chemical of Applied Physics Engineering Ethan Katz-Bassett Assistant Professor of Industrial Engineering Aron Pinczuk Associate Professor of Electrical Engineering and Operations Research Shree K. Nayar Professor of Applied Physics and of Rocco A. Servedio Engineering Chris A. Marianetti T. C. Chang Professor of Computer Physics (Arts and Sciences) Professor of Computer Science Andrew F. Laine Associate Professor of Materials Science Shiho Kawashima Percy K. and Vida L. W. Hudson Science (Henry Krumb School of Mines) Lorenzo M. Polvani Simha Sethumadhavan Associate Professor of Civil Engineering Professor of Biomedical Engineering and and of Applied Physics and Applied Nandan Nerurkar Professor of Applied Mathematics and Associate Professor of Computer Science and Engineering Mechanics Professor of Radiology (Health Sciences) Mathematics Assistant Professor of Biomedical of Earth and Environmental Sciences Engineering (Arts and Sciences) Jay Sethuraman John R. Kender Upmanu Lall Mike Massimino Professor of Industrial Engineering and Professor of Computer Science Alan and Carol Silberstein Professor of Professor of Professional Practice of Jason Nieh Dylan Possamai Operations Research Earth and Environmental Engineering Mechanical Engineering Professor of Computer Science Assistant Professor of Industrial Dion Khodagholy (Henry Krumb School of Mines) and of Civil Engineering and Operations Research Kenneth L. Shepard Assistant Professor of Electrical Engineering and Engineering Mechanics Ismail Cevdet Noyan Lau Family Professor of Electrical Engineering Michael E. Mauel Professor of Applied Physics Professor of Materials Science (Henry Matthias Preindl Engineering and Professor of Biomedical Kwai Hung Henry Lam Krumb School of Mines) and of Applied Assistant Professor of Electrical Engineering Martha A. Kim Associate Professor of Industrial Physics and Applied Mathematics Engineering Associate Professor of Computer José McFaline-Figueroa Engineering and Operations Research Samuel K. Sia Science Assistant Professor of Biomedical Engineering Allie C. Obermeyer Baishakhi Ray Professor of Biomedical Engineering Peter R. Kinget Aurel A. Lazar Assistant Professor of Chemical Assistant Professor of Computer Science Karl Sigman Bernard J. Lechner Professor of Professor of Electrical Engineering Kathleen McKeown Engineering Professor of Industrial Engineering and Electrical Engineering Henry and Gertrude Rothschild Martin Reiman Jae Woo Lee Professor of Computer Science Ibrahim S. Odeh Professor of Industrial Engineering and Operations Research David Knowles Senior Lecturer in Computer Science Senior Lecturer in Civil Engineering and Operations Research Mijo Simunovic Assistant Professor of Computer V. Faye McNeill Engineering Mechanics Science Sophia Hyoseon Lee Associate Professor of Chemical Kui Ren Assistant Professor of Chemical Lecturer in Discipline, English Engineering Elizabeth S. Olson Professor of Applied Physics and Applied Engineering Elisa E. Konofagou Proficiency Professor of Biomedical Engineering and Mathematics Robert and Margaret Hariri Professor of Nima Mesgarani Auditory Biophysics (in Otolaryngology/ Brian Smith Biomedical Engineering and Professor of Kam Leong Associate Professor of Electrical Head and Neck Surgery) Katherine E. Reuther Assistant Professor of Computer Science Radiology (Health Sciences) Samuel Y. Sheng Professor of Engineering Lecturer in Biomedical Engineering Biomedical Engineering Ben O’Shaughnessy Andrew W. Smyth Professor of Chemical Engineering Kenneth A. Ross Professor of Civil Engineering and Professor of Computer Science Engineering Mechanics

ENGINEERING 2020–2021 ENGINEERING 2020–2021 40 Adam H. Sobel Alexander Urban-Artrith Michael I. Weinstein 41 Professor of Applied Physics and Applied Assistant Professor of Chemical Professor of Applied Mathematics Mathematics and of Environmental Engineering Sciences (Arts and Sciences) Omri Weinstein David G. Vallancourt Assistant Professor of Computer Ponisseril Somasundaran Senior Lecturer in Circuits and Systems Science LaVon Duddleson Krumb Professor (Electrical Engineering) of Mineral Engineering (Earth and Renata Maria Mattosinho Environmental Engineering) Vladimir Vapnik Wentzcovitch Professor of Computer Science Professor of Materials Science and Shuran Song Applied Physics, and Earth and Assistant Professor of Computer Science John T. Vaughan Environmental Science Professor of Biomedical Engineering in Marc W. Spiegelman the Mortimer B. Zuckerman Mind Brain Alan C. West Arthur D. Storke Memorial Professor of Behavior Institute Samuel Ruben-Peter G. Viele Professor Earth and Environmental Sciences (Arts of Electrochemistry (Chemical and Sciences) and Professor of Applied Vijay Vedula Engineering) Physics and Applied Mathematics Assistant Professor of Mechanical Engineering Harry West Clifford Stein Professor of Professional Practice in Professor of Industrial Engineering and Latha Venkataraman Industrial Engineering and Operations Operations Research and of Computer Professor of Applied Physics and Research Science Chemistry Ward Whitt Daniel Steingart Venkat Venkatasubramanian Wai T. Chang Professor of Industrial Stanley-Thompson Associate Professor of Samuel Ruben–Peter G. Viele Engineering and Operations Research Chemical Metallurgy Professor of Engineering (Chemical Engineering) Chris H. Wiggins Milan N. Stojanovic Associate Professor of Applied Mathematics Professor of Biomedical Engineering and Nakul Verma Y. Lawrence Yao Xunyu Zhou Robert Mawhinney of Medical Science (in Medicine) Lecturer in Computer Science Jeannette Wing Professor of Mechanical Engineering Liu Family Professor of Industrial Chair, Department of Physics Professor of Computer Science Engineering and Operations Research Fred R. Stolfi Carl Vondrick Yevgeniy Yesilevskiy EMERITI AND RETIRED Senior Lecturer in Mechanical Assistant Professor of Computer Science John Wright Lecturer in Mechanical Engineering Charles Zukowski Engineering Associate Professor of Electrical Professor of Electrical Engineering OFFICERS (NOT IN RESIDENCE) Sinisa Vukelic Engineering Huiming Yin Salvatore J. Stolfo Lecturer in Mechanical Engineering Associate Professor of Civil Engineering Gil Zussman Alfred V. Aho Professor of Computer Science Eugene Wu and Engineering Mechanics Associate Professor of Electrical Lawrence Gussman Professor Emeritus Gordana Vunjak-Novakovic Assistant Professor of Computer Science Engineering of Computer Science WaiChing Steve Sun University Professor and Mikati Ngai Yin Yip Assistant Professor of Civil Engineering Foundation Professor of Biomedical Cheng-Shie Wuu Assistant Professor of Earth and Daniel N. Beshers FACULTY MEMBERS-AT-LARGE and Engineering Mechanics Engineering Professor of Clinical Radiation Oncology, Environmental Engineering Professor Emeritus of Metallurgy (Earth Carlos J. Alonso and of Environmental Health Sciences, and Environmental Engineering) Dean, Graduate School of Arts and Wenpin Tang Haim Waisman and of Applied Physics Drew Youngren Sciences Assistant Professor of Industrial Associate Professor of Civil Engineering Lecturer in Applied Physics and Applied Mark A. Cane G. Unger Vetlesen Professor Emeritus Engineering and Operations Research and Engineering Mechanics Bolun Xu Mathematics Sidney R. Hemming of Earth and Climate Sciences and Assistant Professor of Earth and Chair, Department of Earth and Professor Emeritus of Applied Physics James Teherani Kaizheng Wang Environmental Engineering Nanfang Yu Environmental Sciences and Applied Mathematics Assistant Professor of Electrical Assistant Professor of Industrial Associate Professor of Applied Physics Engineering and Operations Research Junfeng Yang Engineering Liang Tong Huk Yuk Cheh Associate Professor of Computer Science Zhou Yu Chair, Department of Biological Sciences Samuel Ruben-Peter G. Viele Professor Michael K. Tippett Qi Wang Assistant Professor of Computer Science Emeritus of Electrochemistry Associate Professor of Applied Physics Assistant Professor of Biomedical Yuan Yang Costis Maglaras Engineering Assistant Professor of Applied Physics and Applied Mathematics Dean, Columbia Business School Rene Chevray and Applied Mathematics Henry Yuen Assistant Professor of Computer Professor Emeritus of Mechanical Van-Anh Truong Wen I. Wang David Reichman Science Engineering Associate Professor of Industrial Thayer Lindsley Professor in the Faculty Mihalis Yannakakis Chair, Department of Chemistry Engineering and Operations Research of Engineering and Applied Science Percy K. and Vida L. W. Hudson Lu Zhang C. K. Chu (Electrical Engineering) and Professor of Professor of Computer Science Michael Thaddeus Assistant Professor of Applied Physics Fu Foundation Professor Emeritus Yannis P. Tsividis Applied Physics Chair, Department of Mathematics and Applied Mathmatics of Applied Physics in the Faculty of Edwin Howard Armstrong Professor of David Da-Wei Yao Engineering and Applied Science Electrical Engineering Xiaodong Wang Piyasombatkul Family Professor of James J. Valentini Changxi Zheng Professor of Electrical Engineering Industrial Engineering and Operations Dean, Columbia College Associate Professor of Computer Science Research

ENGINEERING 2020–2021 ENGINEERING 2020–2021 42 Edward G. Coffman Enders Robinson Tuncel M. Yegulalp Ervis Dinkel Shadman Islem Liam Maserjian 43 Professor Emeritus of Electrical Engineering Maurice Ewing and J. Lamar Worzel Professor Emeritus of Mining (Earth Financial Business Manager Manager, Graduate Student Affairs CVN Production Manager and of Computer Science Professor Emeritus of Applied and Environmental Engineering, Henry Geophysics (Earth and Environmental Krumb School of Mines) Ivy Elkins Meaghan Jameyson Janine Nadia Maslov Paul Diament Engineering) Career Placement Officer, Computer Assistant Director of Graduate Graduate Admissions Officer Professor Emeritus of Electrical Engineering Yechiam Yemini Science Admissions Peter Schlosser Professor Emeritus of Computer Science Betty Matias Hsu Frank L. DiMaggio Maurice Ewing and J. Lamar Worzel Allison Elliott Soulaymane Kachani Assistant Director of Graduate Student Robert A. W. and Christine S. Carleton Professor Emeritus of Geophysics Communications Writer Senior Vice Dean Services Professor Emeritus of Civil Engineering and Professor Emeritus of Earth and ADMINISTRATIVE OFFICERS Environmental Sciences AND STAFF Holly Evarts Asha Kaufman Bianca Matthew Zvi Galil Mary C. Boyce Director, Strategic Communications Director of Annual Giving Student Services Officer Julian Clarence Leu Professor Emeritus Mischa Schwartz Dean and Media Relations of Mathematical Methods and of Charles Batchelor Professor Emeritus Lauren Kopac Neil McClure Computer Science and Dean Emeritus of Electrical Engineering Rumana Ashraf Mindy Farabee Institutional Research Analyst Senior Associate Dean of Faculty Affairs Manager, Grants and Contracts, Pre- Associate Director, Communications and Chief Administrative Officer Fletcher H. Griffis Michael P. Sheetz Award Mercedes Kriesel Professor Emeritus of Civil Engineering William R. Kenan Jr. Professor Emeritus Jennifer Feierman de Lannoy Career Placement Officer, Financial Emily Anne McCormack of Cell Biology and Professor Emeritus Mark Beer Director of Development, Graduate Engineering Associate Director, Career Placement Jonathan L. Gross of Biomedical Engineering Systems Engineer Programs for Civil Engineering and Mechanical Professor Emeritus of Computer Science Jackson Lau Engineering Jordan L. Spencer Yannick Brookes Samantha Fellers System Administrator Jeffrey T. Koberstein Professor Emeritus of Chemical Assistant Dean of Graduate Student Development Coordinator, Major Gifts, Joan McDowell Percy K. and Vida L. W. Hudson Engineering Affairs SEAS Abby Lee Associate Director of Human Resources Professor Emeritus of Chemical Video Producer, Columbia Video Engineering Thomas E. Stern Leora Brovman David Fitzgerald Network Theresa A. McKenzie Dicker Professor Emeritus of Electrical Senior Associate Dean of Undergraduate Career Placement Officer, Operations Executive Director of Budget and Jennifer Lee John T. F. Kuo Engineering and Graduate Student Affairs Research Finance Maurice Ewing and J. Lamar Worzel Career Placement Officer, Electrical Professor Emeritus of Geophysics Horst Stormer Alexander Browne Rachel Fitzgerald Engineering Ryan Michels I. I. Rabi Professor Emeritus of Physics Assistant Manager, CVN Production Facilities Specialist Institutional Research Analyst, Academic Logan Lee W. Michael Lai (Arts and Sciences) and Professor Programs Professor Emeritus of Mechanical Emeritus of Applied Physics Cecily Castle Genevieve Fleming Alumni Programs Coordinator Engineering and of Orthopedic Leadership Giving Officer Special Projects Manager Alexis Moore Mindi Levinson Bioengineering (Orthopedic Surgery) Malvin Carl Teich Assistant Director of Academic Director of Career Placement, Professor Emeritus of Engineering Nancy Cedeno Emily Ford Administration Management Science and Engineering, Eugene S. Machlin Science Financial Coordinator Director of Outreach Programs and Henry Marion Howe Professor Emeritus Special Projects Industrial Engineering Mairead Moore of Metallurgy Rene B. Testa Shih-Fu Chang Director of Alumni Relations Raaya Lewis Professor Emeritus of Civil Engineering Senior Executive Vice Dean Gabrielle Gannon Recruitment and Marketing Manager Thomas C. Marshall and Engineering Mechanics Director of Graduate Admissions Barclay Morrison Professor Emeritus of Applied Physics Karen Cheng Vice Dean of Undergraduate Programs Gabriella Lilienthal Nickolas J. Themelis Outreach Program Specialist Julie Han Program Manager, Professional Henry E. Meadows Jr. Professor Emeritus of Earth and Admissions Operations Officer Jane Nisselson Development and Leadership Professor Emeritus of Electrical Engineering Environmental Engineering Tom Chow Associate Director, Multimedia Director of IT Keely Henderson Communications Alan Lin Van C. Mow Stephen H. Unger Senior Associate Dean of Advancement, Financial Analyst Stanley Dicker Professor Emeritus of Professor Emeritus of Computer Science Jaclyn Chu SEAS Quy O Biomedical Engineering and Professor Senior Major Gifts Officer Associate Director of Technology and of Electrical Engineering Christina Liu Emeritus of Orthopedic Engineering Kristen Henlin Services Reunion Coordinator (Orthopedic Surgery) Rimas Vaicaitis Brianne Cortese Career Placement Officer, Applied Assistant Director of Admissions and Physics and Applied Mathematics and Kwame Osei-Sarfo Renwick Professor Emeritus of Civil Jenny Mak Academic Affairs Biomedical Engineering Director, Bridge to the Ph.D. Program Steven M. Nowick Engineering Executive Director, Graduate Professor of Computer Science and Career Placement and Professional Gerald Cotiangco Michele Hoos Timur Pakay Electrical Engineering Omar Wing Development and Leadership Professor Emeritus of Electrical Career Placement Officer, Business Executive Director of Communications Associate Director of Executive Richard M. Osgood Jr. Engineering Analytics Jessica L. Marinaccio Education Programs Higgins Professor Emeritus of Electrical Shu-Yi Hsu Dean of Undergraduate Admissions and Dylan Pappas Engineering and Professor Emeritus Henryk Wozniakowski Rafael Cruz Assistant Director, Online Learning Financial Aid of Applied Physics and Applied Professor Emeritus of Computer Science Assistant Director of Procurement and Senior Analyst, Budget and Finance Mathematics Compliance John Hyde Mathieu Marthe Darcelle Paul Edward S. Yang Assistant Director of Career Associate Project Manager Professor Emeritus of Electrical Engineering Asha De Costa Development and Alumni Services, Data Program Specialist Associate Director of Wellness Science

ENGINEERING 2020–2021 ENGINEERING 2020–2021 44 Kayla Quinnies Ivy Schultz Alex J. Vervoort Outreach Program Manager Director of Entrepreneurship Programs Associate Director of Alumni Relations

Madeline Ramos Esther Schwartz Eric Vieira Faculty Affairs Officer Executive Assistant to the Dean Director of Strategic Collaborations

Raina Ranaghan Dempsey Simonis Emma Williams Career Placement Officer, Chemical Assistant Director for Annual Giving, Assistant Director of Alumni Relations Engineering and Earth and SEAS Environmental Engineering Nancy Wong David Simpson Marketing and Strategic Planning Officer, Adrieanna Reyes Administrative Assistant Annual Giving, SEAS Undergraduate Student Affairs Program Officer Michelle R. Stevenson Sofia Yagaeva Coordinator, Columbia Video Network Assistant Director, Columbia Video Alvaro Rojas-Caamano Network Associate Director of Graduate Student Elizabeth Strauss Services Associate Director of Professional William Yandolino Development and Leadership Executive Director of Finance and Jessica Rosa Operations Academic Departments Assistant Dean of Graduate Student Maura Swisher Services Senior Analyst, Budget and Finance Nicole Yarnold Assistant Director of Donor Relations Eric Ruberte Malcom Thaxton and Stewardship and Programs Facilities Manager Financial Coordinator Marina Zamalin Stan Sakry Dario Vasquez Executive Director of Online Learning Director of Facilities and Space Planning Program Specialist

Anthony Schmitt Tania Velimirovici Manager, Grants and Contracts, Pre- Academic Programs and Special Award Projects Manager

ENGINEERING 2020–2021 EESC Earth and Environmental Sciences MSAE Materials Science and Engineering U International and Public Affairs 46 KEY TO COURSE LISTINGS 47 EHSC Environmental Health Sciences MSIE Management Science and Industrial W Interfaculty course Engineering and Operations Research ELEN Electrical Engineering Z American Language Program MUSI Music ENGI Engineering Arts and Sciences ORCA Operations Research, Computer ENGL English Science and Applied Mathematics CC Columbia College EMME Engineering Mechanics PHED Physical Education UN Undergraduate and Mechanical Engineering PHIL Philosophy GU Undergraduate, Graduate ENME Engineering Mechanics PHYS Physics GR Graduate Only FINC Finance PLAN Planning FREN French The first digit indicates the level of the POLS Political Science GERM German course, as follows: PSLG Physiology GRAP Graphics 0 Course that cannot be credited PSYC Psychology toward any degree HIST History his section contains a descrip- BIOC Biology and Chemistry COSA Computer Science, Industrial RELI Religion 1 Undergraduate course Engineering and Operations Research, HSAM History and Applied Mathematics tion of the curriculum of each BIOL Biology SCNC Science 2 Undergraduate course, intermediate Statistics, and Applied Physics and Applied department in the School, along HUMA Humanities T BIST Biostatistics Mathematics SIEO Statistics and Industrial Engineering 3 Undergraduate course, advanced with information regarding undergradu- IEME Industrial Engineering and and Operations Research ate and graduate degree requirements, BMCH Biomedical and Chemical Engineering CSEE Computer Science and Mechanical Engineering 4 Graduate course that is open to qualified elective courses, and suggestions about Electrical Engineering SOCI Sociology undergraduates BMEB Biomedical Engineering, Electrical courses and programs in related fields. IEOR Industrial Engineering and Engineering, and Biology CSEN Computer Science and Operations Research SPAN Spanish 6 Graduate course All courses are listed, whether or not English they are being offered during the current BMEE Biomedical Engineering and INAF International Affairs STAT Statistics 8 Graduate course, advanced Electrical Engineering CSOR Computer Science and year; if a course is not being given, that STCS Statistics and Computer Science 9 Graduate research course or seminar Operations Research INTA Earth and Environmental Engineering, is indicated. Included as well are cours- BMEN Biomedical Engineering Civil Engineering, and URBS Urban Studies es cross-listed with other departments DNCE Dance BMME Biomedical Engineering and International and Public Affairs An x following the course number and undergraduate divisions within the VIAR Visual Arts means that the course meets in the fall Mechanical Engineering DRAN Decision, Risk, and Operations MATH Mathematics University. semester; y indicates the spring semester. BUSI Business DROM Decision, Risk, and Operations MEBM Mechanical Engineering and HOW COURSES ARE NUMBERED Management Biomedical Engineering CBMF Computer Science, Biomedical DESIGNATORS The course number that follows each DIRECTORY OF CLASSES EACH Earth and Environmental Engineering Each course is preceded by a four-letter Engineering and Medical Informatics MECE Mechanical Engineering designator consists of one or two capital and Chemical Engineering Room assignments, days and hours, designator, which indicates the department CEOR Civil Engineering and Operations MECH Mechanical Engineering and letters followed by four digits. The capital and course changes for all courses are or departments presenting the course. Research EAEE Earth and Environmental Engineering Chemical Engineering letter indicates the University division or available online at columbia.edu/cu/ affiliate offering the course: CHAP Chemical Engineering and EAIA Earth and Environmental Engineering MECS Mechanical Engineering and bulletin/uwb. Course Designator Department Subject Applied Physics and Applied Math and International and Public Affairs Computer Science B Business The School reserves the right to withdraw or modify the courses of AHIS Art History CHBM Chemical Engineering and ECBM Electrical Engineering, Computer MEEM Mechanical Engineering and E Engineering and Applied Science instruction or to change the instructors Biomedical Engineering Science and Biomedical Engineering Engineering Mechanics AMCS Applied Math and Computer Science P Mailman School of Public Health at any time. CHCB Chemistry, Biology and ECIA Earth and Environmental and Civil MEIE Mechanical Engineering and AMST American Studies S Summer Session Computer Science Engineering and International and Public Industrial Engineering APAM Applied Physics and Applied Math Affairs CHEE Chemical Engineering and APBM Applied Physics and Earth and Environmental Engineering ECIE Economics and Industrial Engineering Biomedical Engineering CHEM Chemistry ECON Economics APCH Applied Physics and CHEN Chemical Engineering EEBM Electrical Engineering and Chemical Engineering Biomedical Engineering CIEE Civil Engineering and APMA Applied Mathematics Earth and Environmental Engineering EECS Electrical Engineering and APPH Applied Physics Computer Science CIEN Civil Engineering ARCH Architecture EEHS Electrical Engineering and History CMBS Cellular, Molecular, and ASCE Asian Civilization: East Asian Biophysical Studies EEME Electrical Engineering and Mechanical Engineering ASCM Asian Civilization: Middle East COCI Contemporary Civilization EEOR Electrical Engineering and COMS Computer Science ASTR Astronomy Operations Research

ENGINEERING 2020–2021 ENGINEERING 2020–2021 48 development of techniques based on collaborations exist with national climate devices investigate respectively an 49 APPLIED PHYSICS AND APPLIED MATHEMATICS the theory of general coordinates and research centers (the Geophysical Fluid innovative tokamak-stellarator hybrid 200 S. W. Mudd, MC 4701 dynamical systems. The work is applied Dynamics Laboratory and the National plasma confinement concept and the 212-854-4457 to magnetic fusion, nonneutral and Center for Atmospheric Research) and use of toroidal electron-heated plasmas Applied Physics and Applied Mathematics: apam.columbia.edu/ space plasmas. with national laboratories of the U.S. as sources of ions for accelerators. Materials Science and Engineering: matsci.apam.columbia.edu Department of Energy, custodians of the The Columbia Linear Machine (CLM) is Optical and laser physics. Active nation’s most powerful supercomputers. a continuously operating, linear mirror areas of research include inelastic light device for the study of collisionless CHAIR Christopher H. Scholz, ADJUNCT ADJUNCT SENIOR ADJUNCT ASSOCIATE scattering in nanomaterials, optical Atmospheric, oceanic, and earth plasma instabilities, plasma, transport, Irving P. Herman Professor Emeritus, PROFESSORS RESEARCH SCIENTISTS RESEARCH SCIENTISTS diagnostics of film processing, flat physics. Current research focuses on and feedback stabilization. Columbia’s 208 S. W. Mudd Earth and Environmental Vittorio M. Canuto C. Julian Chen Emmanouil optics, metasurfaces, nonlinear optics, Sciences Peter F. Caracappa Jay Kesner Antonogiannakis the dynamics of the atmosphere and the Collisionless Terrella Experiment DEPARTMENT Adam Sobel Barbara E. Carlson Yigal Komem Pedro Rodrigo Castro da ultrafast optoelectronics, photonic ocean, climate modeling, cloud physics, investigates plasma transport in ADMINISTRATOR Marc W. Spiegelman C. Julian Chen John Marshall Silveira switching, optical physics of surfaces, radiation transfer, remote sensing, magnetospheric geometry and the Stella M. Lau Anthony Del Genio Patricia Mooney Thomas A. Caswell Latha Venkataraman laser-induced crystallization, and photon geophysical/geological fluid dynamics, generation of strong plasma flow from Wen I. Wang, Electrical Timothy M. Hall David Yuen Gabriel Chiado integrated circuits. PROFESSORS Engineering David E. Keyes Lingjie Du geochemistry. The department engages nonlinear electrostatic potentials. Katayun Barmak Michael I. Weinstein Jerome Meli RESEARCH Chris Hansen in ongoing research with the NASA Experimental research in solid- Solid-state physics. Research in Daniel Bienstock, Renata M. Wentzcovitch Ron L. Miller SCIENTISTS Seung Yub Lee Goddard Institute for Space Studies and state physics and laser physics is Industrial Engineering Jacek Chowdhary solid-state physics covers nanoscience Cheng-Shie Wuu, Stephen L. Ostrow Robert Rosenberg the Lamont-Doherty Earth Observatory. conducted within the department and and Operations Radiation Oncology Thomas S. Pedersen Igor Geogdzhayev and nanoparticles, electronic transport Catherine Naud POSTDOCTORAL Seven faculty members share also in association with the Columbia Research Lawrence N. Rothenberg and inelastic light scattering in low- Simon J. L. Billinge ASSOCIATE Stephen A. Sabbagh Yoshitomo Okawachi RESEARCH SCIENTISTS appointments with the Department of Nano Initiative. Facilities include dimensional correlated electron Allen H. Boozer PROFESSORS George Tselioudis Rei Chemke Earth and Environmental Sciences. laser processing and spectroscopic ADJUNCT RESEARCH Qian Cheng systems, heterostructure physics and Mark A. Cane, Professor William E. Bailey Shalom J. Wind In addition to the faculty and apparatus, ultrahigh vacuum chambers Emeritus, Earth Eitan Grinspun, Marco Zaider SCIENTISTS Bithi De applications, grain boundaries and graduate students, many others for surface analysis, picosecond and and Environmental Computer Science Pat Zanzonico Conal C. Murray Ran Gu interfaces, nucleation in thin films, femtosecond lasers, and a clean Sciences Kyle Mandli Emmanuel Yashchin Mohammed Jadidi participate in these projects, including molecular electronics, nanostructure Siu-Wai Chan Chris A. Marianetti ADJUNCT ASSOCIATE Joseph Kiaisler full-time research faculty, faculty and room that includes photo-lithography ASSOCIATE RESEARCH Qiang Du Michael K. Tippett PROFESSORS Yang Sun analysis, and electronic structure students from other departments, and and thin film fabrication systems. Alexander Gaeta Chris H. Wiggins Brian Cairns SCIENTISTS Boyuan Zhang calculations. Jae Heon Ahn visiting scientists. Within this field, the Laser Diagnostics Oleg Gang Yuan Yang Payel Das Mikhail Alexandrov Applied physics is part of the and Solid-State Physics Laboratory Irving P. Herman Nanfang Yu Yuan He POSTDOCTORAL Columbia Quantum Initiative. Research James S. Im Anastasia Romanou Michael Bauer RESEARCH FELLOWS Laboratory and Computation conducts studies in laser spectroscopy Michal Lipson, Electrical ASSISTANT Anna Rozenshtein Greggory Ellsaesser Miriam Blau opportunities also exist within the of nanomaterials and semiconductor Robert Field Facilities in Applied Physics and Engineering PROFESSORS Kevin DallaSanta Columbia Nano Initiative (CNI), including thin films, and laser diagnostics of thin Jeremy Hanson Alvin Zhang Applied Mathematics Michael E. Mauel Ami Sagiv ADJUNCT ASSISTANT the NSF Materials Research Science film processing. The Laser Lab focuses Gerald A. Navratil PROFESSORS Jae Kyung Jang The Plasma Physics Laboratory, and Engineering Center, which focuses on the study of laser surface chemical Ismail C. Noyan AFFILIATED FACULTY Dorian Goldman Yanzheng Jiang SPECIAL LECTURERS founded in 1961, is one of the leading Jeffrey Levesque Daniel N. Beshers processing and new semiconductor Richard M. Osgood Jr., John Wright, Electrical Jacob Hofman on low dimensional materials. university laboratories for the study of Li Liu C. K. Chu structures. Research is also conducted Professor Emeritus, Engineering plasma physics in the United States. Electrical Engineering SENIOR RESEARCH Katherine Marvel Monique C. Katz Applied mathematics. Current research in the shared characterization SCIENTISTS Young Seok Park There are four experimental facilities. Aron Pinczuk LECTURER IN encompasses analytical and numerical laboratories and clean room operated Lorenzo M. Polvani DISCIPLINE John Berkery Francesca Turco SPECIAL RESEARCH The Columbia High-Beta Tokamak analysis of deterministic and stochastic by CNI. Kui Ren Drew Youngren James Bialek Inigo Urteaga SCIENTIST (HBT-EP) supports the national program Thomas C. Marshall Shuguang Wang Shalom J. Wind partial differential equations, large-scale The department maintains an Malvin A. Ruderman, to develop controlled fusion energy. Steven A. Sabbagh Jingbo Wu scientific computation, fluid dynamics, extensive network of computing clusters Physics It utilizes high voltage, pulsed power dynamical systems and chaos, and desktop computers. The research systems, and laser and magnetic inverse problems, algorithms for data of the Plasma Lab is supported by he Department of Applied Physics The results from our fusion science diagnostics to study the properties Current Research Activities in and learning, as well as applications a dedicated data acquisition/data and Applied Mathematics experiments are used as a basis of high-beta plasmas and the use Applied Physics and Applied to various fields of physical and analysis system, and the applied includes undergraduate and for collaboration with large national of feedback stabilization to increase T Mathematics biological sciences. The applications to math group has access to a Beowulf graduate studies in the fields of and international experiments. For the achievable beta. A collaborative Applied Physics. physical science include quantum and cluster. Materials Science and Applied applied physics, applied mathematics, Plasma physics and fusion energy. example, methods of active feedback program with the Princeton Plasma condensed-matter physics, materials Physics built an intel-based 600 core and materials science and engineering. In experimental plasma physics, research control of plasma instability developed Physics Laboratory and the DIII-D science, electromagnetics, optics, computing cluster that is dedicated to The graduate program in applied at Columbia University are guiding tokamak group at General Atomics is is being conducted on (1) equilibrium, performing first-principles computations physics includes plasma physics and research on NSTX at the Princeton photonics, plasma physics, medical studying the properties of high-beta stability, and transport in fusion of materials. Researchers in the controlled fusion; solid-state physics; Plasma Physics Laboratory, on the imaging, and the earth sciences, notably plasmas in order to maximize fusion plasmas: high-beta tokamaks, spherical department are additionally using optical and laser physics and medical DIII-D tokamak at General Atomics, and atmospheric, oceanic, and climate power production in these large, neutral tokamaks, and levitated dipoles; (2) supercomputing facilities at the National physics. The graduate program in for the design of the next generation science, and solid earth geophysics beam-heated tokamaks and spherical magnetospheric physics: trapped Center for Atmospheric Research; applied mathematics includes research burning plasma experiment, ITER. In (see below). Other applications include tori. The stellarator known as Columbia particle instabilities and stochastic the San Diego Supercomputing in applied analysis, data science, theoretical plasma physics, research machine learning and biophysical Nonneutral Torus (CNT) conducts particle motion; (3) confinement Center; the National Energy Research and atmospheric, oceanic, and earth is conducted in the theory of plasma modeling, including collaborations with research on the magnetohydrodynamic of toroidal nonneutral plasmas; (4) Supercomputer Center in Berkeley, physics. The graduate programs in equilibrium and stability, active control Columbia’s Data Science Institute (DSI), stability, microwave heating, and plasma source operation and heating California; the National Leadership materials science and engineering are of MHD instabilities, the kinetic theory the Department of Systems Biology, and microwave diagnostics of neutral techniques; and (5) the development of Class Facility at Oak Ridge, Tennessee; described on pages 181–183. of turbulence and transport, and the the Department of Statistics. Extensive stellarator plasmas. Two smaller new plasma measurement techniques. various allocations via XSEDE; and

ENGINEERING 2020–2021 ENGINEERING 2020–2021 50 51 APPLIED PHYSICS PROGRAM: FIRST AND SECOND YEARS APPLIED PHYSICS: THIRD AND FOURTH YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

APMA E2000 (4) either semester APPH E3200 (3) APPH E4300 (3) APPH E3100 (3) Mechanics Applied electrodynamics MATHEMATICS1 MATH UN1101 (3) MATH UN1102 (3) Intro. to quantum mechanics and ODE (3)2 MSAE E3111 (3) APPH E4100 (3) Course in second Thermodynamics Quantum physics AP area (3) REQUIRED APPH E3300 (3) COURSES Applied electromagnetism UN1401 (3) UN1402 (3) UN1403 (3) APMA E3101 (3) Course in first APPH E4018 (2) PHYSICS Lab UN1494 (3) Linear algebra AP area (3) Laboratory (three tracks, UN1601 (3.5) UN1602 (3.5) UN2601 (3.5) APMA E3102 (3) choose one) UN2801 (4.5) UN2802 (4.5) Lab UN3081 (2) Partial differential APPH E4901 (1) APPH E4903 (2) equations Seminar Seminar CHEMISTRY/ CHEM UN1403 (3), or higher or BIOLOGY BIOL UN2001 (4) or BIOL UN2005 (4), or higher (choose one course) TECH1 3 points 3 points 2 points 9 points

UNIVERSITY CC1010 (3) either semester WRITING NONTECH 3 points 3 points 3 points 3 points ELECTIVES OR TECH HUMA CC1001, HUMA CC1002, COCI CC1101, COCI CC1102, REQUIRED or Global Core (3–4) or Global Core (3–4) NONTECHNICAL TOTAL POINTS 16 15 16 17 ELECTIVES HUMA UN1121 or ECON UN1105 (4) and UN1123 (3) UN1155 recitation (0) 1 They must include at least 2 points of laboratory courses. If PHYS UN3081 is taken as part of the first two years of the program, these technical electives need not include laboratory courses. Technical electives must be at the 3000 level or above unless prior approval is obtained. REQUIRED (3) Student’s choice TECH ELECTIVES specialization through technical electives. undergraduate seminar to study current Technical electives must be at the 3000 The applied physics curriculum offers and practical problems in applied physics, level or above unless prior approval is COMPUTER ENGI E1006 (3)3 any semester students the skills, experience, and and obtain hands-on experience in at obtained from the department. A number SCIENCE preparation necessary for several career least two advanced laboratory courses. of approved technical electives are options, including opportunities to minor Majors are introduced to two areas listed in the section on specialty areas. PHYSICAL UN1001 (1) UN1002 (1) in economics and to take business- of application of applied physics (AP) by The remaining points of electives are EDUCATION related courses. In recent years, applied a course in each of two areas. Approved intended primarily as an opportunity to physics graduates have entered graduate areas and courses are complete the absolutely mandatory four- THE ART OF ENGI E1102 (4) either semester ENGINEERING programs in many areas of applied year, 27-point nontechnical requirement physics or physics, enrolled in medical DYNAMICAL SYSTEMS: for the B.S. degree, but if this 27-point 1 With the permission of the faculty adviser, students with advanced standing may start the calculus sequence at a higher level. APMA E4101 or PHYS GU4003 2 school, or been employed in various nontechnical requirement has been met Applied physics majors should satisfy their ODE requirement with the Mathematics Department (ordinarily MATH UN2030). OPTICAL OR LASER PHYSICS: 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 technical or financial areas immediately already, then any type of coursework can APPH E4110 or E4112 faculty adviser. after receiving the B.S. degree. satisfy these elective points. 3 With permission of faculty adviser, students demonstrating familiarity with computational mathematics using Python may waive course requirement and use 3 credits Opportunities for undergraduate NUCLEAR SCIENCE: APPH E4010 for another technical course. research exist in the many research PLASMA PHYSICS: APPH E4301 UNDERGRADUATE PROGRAM programs in applied physics. These others. The Amazon Elastic Compute science. The materials science program electives are normally at the 3000 level PHYSICS OF FLUIDS: APPH E4200 IN APPLIED MATHEMATICS include fusion and space plasma physics, Cloud (EC2) is also utilized to is described on pages 178–181. or above. The applied mathematics program is optical and laser physics, and condensed SOLID STATE/CONDENSED MATTER supplement computing resources in The applied physics and applied flexible and intensive. A student must matter physics. Undergraduate students PHYSICS: PHYS GU4018 times of high demand. mathematics programs provide an take the required courses listed below, UNDERGRADUATE PROGRAM can receive course credit for research BIOPHYSICAL MODELING: APMA E4400 excellent preparation for graduate study or prove equivalent standing, and IN APPLIED PHYSICS or an independent project with a faculty Current Research Activities and or for careers in which mathematical and In addition to these courses, courses then may elect the other courses from The applied physics program stresses member. Opportunities also exist for technical sophistication are important. listed in the Specialty Areas in Applied mathematics, computer science, physics, Laboratory Facilities in Materials the basic physics that underlies most undergraduate students in the applied Using the large number of electives in Physics can be used to satisfy this Earth and environmental sciences, Science and Engineering developments in engineering and the physics program to participate in this these programs, students can tailor their requirement with preapproval of the biophysics, economics, business and See pages 177–178. mathematical tools that are important to research through part-time employment programs to fit their personal and career applied physics adviser. finance, or other application fields. Each both physicists and engineers. Since the during the academic year and full-time interests. By focusing their technical All students must take 30 points of student tailors his or her own program in UNDERGRADUATE PROGRAMS advances in most branches of technology employment during the summer, either electives, students can obtain a strong electives in the third and fourth years, close collaboration with an adviser. He The Department of Applied Physics lead to rapid changes in state-of-the-art at Columbia or as part of the NSF REU base of knowledge in a specialized area. of which 17 points must be technical or she must also register for the applied and Applied Mathematics offers three techniques, the applied physics program program nationwide. Practical research In addition to formal minors, some areas courses approved by the adviser. The 17 mathematics seminar during both the undergraduate programs: applied phys- provides the student with a broad base experience is a valuable supplement to of specialization that are available are points include 2 points of an advanced junior and senior years. During the junior ics, applied mathematics, and materials of fundamental science and mathematics the formal course of instruction. Applied described on pages 53–54. All technical laboratory in addition to APPH E4018. year, the student attends the seminar while retaining the opportunity for physics students participate in an informal

ENGINEERING 2020–2021 ENGINEERING 2020–2021 52 53 APPLIED MATHEMATICS PROGRAM: FIRST AND SECOND YEARS APPLIED MATHEMATICS: THIRD AND FOURTH YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

APMA E2000 (4) either semester APMA E3101 (3)1 Linear algebra 1 MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) (Applied math, I) MATH GU4061 (3)1 APMA E3102 (3)1 2 Modern analysis and ODE (3) Partial differential APMA E4204 (3)1 equations APMA E3900 (3)3 Complex variables APMA E4101 (3) (Applied math, II) Research UN1401 (3) UN1402 (3) UN1403 (3)3 REQUIRED Introduction to PHYSICS Lab UN1494 (3)4 APMA E4300 (3) dynamical systems (three tracks, UN1601 (3.5) UN1602 (3.5) UN2601 (3.5) COURSES Course from Group A2 Courses designated 4 Introduction to numerical (Applied math, III) choose one) UN2801 (4.5) UN2802 (4.5) Lab UN3081 (2) MATH, APMA, or STAT (3) methods (Computational Course from Group B2 math, I) APMA E4903 (3 or 4) Seminar CHEMISTRY/ CHEM UN1403 (3), or higher BIOL UN2001 (4) or APMA E4901 (0) BIOLOGY BIOL UN2005 (4), or higher (choose one course) or Seminar

UNIVERSITY CC1010 (3) either semester 4 WRITING TECH 3 points 3 points 3 points 6 points

HUMA CC1001, HUMA CC1002, COCI CC1101, COCI CC1102, NONTECH 3 points 3 points 3 points 3 points REQUIRED or Global Core (3–4) or Global Core (3–4) ELECTIVES NONTECHNICAL ELECTIVES HUMA UN1121 or ECON UN1105 (4) and UN1123 (3) UN1155 recitation (0) TOTAL POINTS 15 15 16 15

REQUIRED (3) Student’s choice 1 MATH UN2010 may be substituted for APMA E3101; MATH UN3028 may be substituted for APMA E3102; MATH UN3007 may be substituted for APMA E4204; TECH ELECTIVES MATH UN2500 may be substituted for MATH GU4061. 2 One course from Group A and one course from Group B required for graduation. Group A: IEOR E3658: Probability for engineers; STAT GU4105: Probability; COMPUTER ENGI E1006 (3) any semester SIEO W3600: Introduction to probability and statistics; STAT GU4001: Introduction to probability and statistics; STAT UN3105: Introduction to probability; MATH SCIENCE W4155: Probability theory. Group B: STAT UN3107: Statistical inference; STAT GU4107: Statistical inference; STAT GU4109: Probability and statistical inference; SIEO GU4606: Elementary stochastic processes; IEOR E3106: Stochastic systems and applications; IEOR E4106: Stochastic models; IEOR E4703: Monte Carlo PHYSICAL simulation; COMS W4771: Machine learning. UN1001 (1) UN1002 (1) 3 EDUCATION With an adviser’s permission, an approved technical elective may be substituted. 4 Any course in science or engineering at the 3000 level or above qualifies as a technical elective, except for required or elective courses in the minor in entrepreneurship and innovation which do not count as technical electives unless authorized by an adviser. Other elective courses may be chosen from other THE ART OF E1102 (4) either semester departments in SEAS and Arts and Sciences, e.g., the Departments of Mechanical Engineering, Electrical Engineering, Mathematics, and Statistics. ENGINEERING

To apply, a student first obtains Technical Electives Lamont-Doherty Earth Observatory, 1 With the permission of the faculty adviser, students with advanced standing may start the calculus sequence at a higher level. the approval of both the general which is part of Columbia University, 2 • Applications of Physics Applied mathematics majors should satisfy their ODE requirement with the Mathematics Department (ordinarily MATH UN2030). Students who take APMA E2101 undergraduate Applied Physics adviser provides enormous resources for prior to declaring their major in applied mathematics may use this course to satisfy their ODE requirement with the permission of the faculty adviser. Courses that will give a student a broad 3 Transfer students who have not fulfilled the physics requirement prior to enrolling at Columbia may substitute this course with PHYS BC3001. and the general undergraduate Applied background in applications of physics: students interested in this area. 4 Or a lab course in Astronomy, Astrophysics, Biology, or Chemistry. Mathematics adviser, and then the ELEN E3000x: Circuits, systems, and approval of the Dean. ATMOSPHERE, OCEANS, AND CLIMATE electronics (J) EESC GU4008x: Intro to atmospheric science lectures for 0 points; during the senior year, 27-point nontechnical requirement requirements. They are required to take MSAE E3010x: Introduction to materials APPH E4200x: Physics of fluids year, he or she attends the seminar for the B.S. degree, but if this 27-point both senior seminars, APMA E4903 and science, I SPECIALTY AREAS IN APAM APPH E4210y: Geophysical fluid dynamics lectures as well as tutorial problem nontechnical requirement has been met APPH E4903 (taking one in the junior APPH E4010x: Intro to nuclear science Both applied physics and applied math- EESC GU4925x: Principles of physical sessions for 3 or 4 points. already, then any type of coursework year and one in the senior year, due PHYS GU4018y: Solid-state physics oceanography ematics students can focus their technical APMA E4101x: Intro to dynamical systems While it is common for students can satisfy these elective points. to timing conflicts), but not the junior EESC GU4930y: Earth’ s oceans and electives and develop a strong base of APPH E4110y: Modern optics in the program to go on to graduate Transfers into the applied seminars, APMA E4901 and APPH atmosphere knowledge in a specialty area. There is no APPH E4112x: Laser physics school, many graduating seniors will mathematics program from other majors E4901. A single foundational course may requirement to focus electives, so students APPH E4200x: Physics of fluids SOLID EARTH GEOPHYSICS find employment directly in industry, require a GPA of 3.0 or above, and the be used to fulfill a requirement in both may take as many or as few of the recom- APPH E4301y: Intro to plasma physics EESC GU4001x: Advanced general geology government, education, or other fields. approval of the applied mathematics majors. Students must maintain a GPA mended courses in a specialty area as is EESC GU4113x: Intro to mineralogy Of the 27 points of elective content program chair. at or above 3.75, and must graduate APPH E4200x: Physics of fluids appropriate to their schedules and inter- • Earth and Atmospheric Sciences in the third and fourth years, at least 15 with at least 143 points, 15 above the The Earth sciences provide a wide EESC GU4701y: Intro to igneous petrology ests. Some specialties are given below, but points of technical courses approved regular 128-point requirement. These range of problems of interest to EESC GU4941y: Principles of geophysics UNDERGRADUATE DOUBLE this is not an exclusive list and others can EESC GU4950x: Mathematical methods in the by the adviser must be taken. The extra 15 points should be technical physicists and mathematicians ranging MAJOR IN APPLIED PHYSICS be worked out in coordination with the stu- Earth sciences remaining points of electives are electives appropriate for one or both from the dynamics of the Earth’s AND APPLIED MATHEMATICS dent’s adviser. The courses that are often intended primarily as an opportunity to majors. climate to earthquake physics to Students satisfy all requirements for taken, or in some cases need to be taken, complete the absolutely mandatory four- dynamics of Earth’s deep interior. The both majors, except for the seminar in the junior year are denoted with a “J.”

ENGINEERING 2020–2021 ENGINEERING 2020–2021 Functions of a complex variable (See also courses listed under methods and underlying theory. For • Scientific Computation and requirement. Ph.D. candidates are APMA E4204: M.S. Program in Materials Science 54 APMA E4300: Intro to numerical methods 55 Scientific Computation and Computer example, this specialization could be Computer Science strongly encouraged to complete APMA E4301: Numerical methods for partial and Engineering Science below.) followed by students with an interest in ENGI E6001–6004 and should consult Advanced computation has become differential equations See page 181. graduate work in applied mathematics. a core tool in science, engineering, their program for PDL requirements. APMA E6301: Analytic methods for partial • Basic Physics and Astrophysics and mathematics and provides Ethics training is required of all MATH UN3386x: Differential geometry differential equations M.S. Program in Medical Physics Fundamental physics and astrophysics challenges for both physicists students pursuing a doctorate. APMA E4101x: Intro to dynamical systems APMA E6302: Numerical analysis for partial This CAMPEP-approved 36-point can be emphasized. Not only is APMA E4150x: Applied functional analysis and mathematicians. Courses differential equations program in medical physics leads to the astrophysics providing a deeper MATH GU4032x: Fourier analysis that build on both practical and M.S. Program in Applied Physics M.S. degree. It is administered by faculty understanding of the universe, but it is MATH GU4062y: Modern analysis, II theoretical aspects of computing and The program of study leading to the Students must also take a required from the School of Engineering and also testing the fundamental principles STAT GU4001x, y: Intro to probability and computation include: degree of Master of Science, while Research Seminar course, APMA E6100 Applied Science in collaboration with of physics. statistics (J) PHYS GU4386x-GU4387y: Geometrical MATH UN3020x: Number theory and emphasizing continued work in basic x or y faculty from the College of Physicians PHYS UN3002y: From quarks to the cosmos: concepts in physics cryptography (J) physics, permits many options in and Surgeons and the Mailman applications of modern COMS W3137x,y: Data structures and several applied physics specialties. The A student must select five elective School of Public Health. It provides physics algorithms (or COMS W3139y: • Quantitative Biology program may be considered simply as courses from those listed below (or any preparation toward certification by the ASTR UN3601x: General relativity, black holes, Honors data structures and additional education in areas beyond of those not used to satisfy the core and cosmology (J) Traditionally biology was considered a algorithms) (J) American Board of Radiology. The ASTR UN3602y: Physical cosmology (J) descriptive science in contrast to the COMS W3157x,y: Advanced programming (J) the bachelor’s level, or as preparatory to requirements from the list above) for program consists of a core curriculum ASTR GU4001y: Astrophysics, I quantitative sciences that are based COMS W3203x,y: Discrete mathematics: intro doctoral studies in the applied physics a total of 15 points of graduate credit. of medical and nuclear physics courses, APMA E4101x: Intro to dynamical systems on mathematics, such as physics. This to combinatorics and graph fields of plasma physics, laser physics, Additional courses not listed below anatomy, lab, seminar, a tutorial, one view no longer coincides with reality. theory (J) or solid-state physics. Specific course can be applied toward the elective elective, and two practicums. Specific COMS W4203y: Graph theory • Business and Finance Researchers from biology as well as requirements for the master’s degree requirements, subject to the approval of course requirements are APPH E4010, The knowledge of physics and math- APMA E4300x: Intro to numerical methods are determined in consultation with the the faculty adviser*. from the physical sciences, applied APMA E4301y: Numerical methods for partial E4330, E4710, E4500, E4550, E4600, program adviser, but must include four ematics that is gained in the applied mathematics, and computer science differential equations *Courses from the Department of E6319, E6330, E6335, and APBM of the six core courses listed below. physics and applied mathematics are rapidly building a quantitative base APMA E4302x: Methods in computational Economics, School of Business, School E4650. Approved electives include The core courses provide a programs is a strong base for a career of biological knowledge. Students can science of International and Public Affairs, or APPH E4711, APPH E6336, APAM student with a solid foundation in the in business or finance. acquire a strong base of knowledge in COMS W4701x,y: Artificial intelligence quantitative courses offered by the School E6650, and a third practicum. Up to COMS W4771y: Machine learning fundamentals of applied physics, but quantitative biology, both biophysics of Professional Studies may not be 6 points of this 36-point program may ECONOMICS with the approval of the faculty adviser, and computational biology, while counted as electives toward the degree. be waived based on prior equivalent ECON UN3211x,y: Intermed microeconomics (J) • Solid-State Physics other graduate-level courses with APPH academic work. A student who enters ECON UN3213x,y: Intermed macroeconomics(J) completing the applied physics or Much of modern technology is based designators not listed below may also Computer science elective courses the 36-point M.S. Program in Medical applied mathematics programs. on solid-state physics, the study of INDUSTRIAL ENGINEERING count as core courses. include: Physics having satisfactorily completed, RECOMMENDED: solids and liquids. Courses that will AND OPERATIONS RESEARCH CSOR W4231: Analysis of algorithms, I prior to beginning the Program, a BIOL UN2005x-UN2006y: Intro biology, I and II build a strong base for a career in this IEOR E4003x: Industrial economics APPH E4100: Quantum physics of matter COMS W4236: Intro to computational complexity APPH E3400y: Physics of the human body area are course determined by the faculty to IEOR E4201x: The eng of management, I APPH E4110: Modern optics COMS W4241: Numerical algorithms and be equivalent in content to a required IEOR E4202y: The eng of management, II APMA E4400y: Intro to biophysical modeling PHYS UN3083y: Electronics laboratory (J) APPH E4112: Laser physics complexity course within the Program may be MSAE E3110x: Introduction to materials APPH E4200: Physics of fluids COMS W4252: Computational learning theory FINANCE OTHER TECHNICAL ELECTIVES (A COURSE science, I APPH E4300: Applied electrodynamics considered to have satisfied that MATH GU4071x: Mathematics of finance IN AT LEAST TWO AREAS RECOMMENDED): content requirement, may be allowed ELEN E3106x: Solid-state devices and APPH E4301: Introduction to plasma physics Industrial engineering/operations IEOR E4106y: Intro to operations research: BIOLOGICAL MATERIALS materials (J) to have that requirement waived, and research elective courses include**: stochastic models (J) BIOL GU4070x: The biology and physics of MSAE E4100x: Crystallography may be permitted to graduate from M.S. Program in Applied STAT GU4001x,y: Probability and statistics (J) single molecules PHYS GU4018y: Solid-state physics the M.S. Program in Medical Physics ECON GU4280x,y: Corporate finance IEOR E4003: Industrial economics CHEN E4650x: Biopolymers MSAE E4206x: Electronic and magnetic Mathematics with fewer than 36 points, but not IEOR E4700x: Intro to financial engineering properties of solids This 30-point program leads to a IEOR E4004: Intro to operations research: deterministic models fewer than the 30-point minimum BIOMECHANICS Master of Science degree. Students IEOR E4007: Optimization: models and methods required by the School of Engineering • Mathematics Applicable to Physics BMEN E3320y: Fluid biomechanics (J) must complete five core courses and Applied physics students can specialize UNDERGRADUATE PROGRAM IEOR E4106:  Stochastic models and Applied Science. Evaluation of BMEN E4300y: Solid biomechanics (J) five electives. All degree requirements STAT GU4001: Intro to probability and statistics in the mathematics that is applicable IN MATERIALS SCIENCE prior coursework may include review must be completed within five years. IEOR E4403:  Advanced engineering and of syllabi, comparison of textbooks, to physics. This specialization is GENOMICS AND BIOINFORMATICS See page 178. A candidate is required to maintain corporate economics consultation with instructors, and/or particularly useful for students BIOL UN3037y: Whole genome bioinformatics (J) at least a 2.5 grade point average. IEOR E4407: Game theoretic models of written or oral examination administered interested in theoretical physics. ECBM E3060x: Intro to genomic information If a student admitted to the Applied operations GRADUATE PROGRAMS by Program faculty. A passing grade on science and technology (J) Mathematics M.S. only program is STAT GU4606: Elementary stochastic processes MATH UN3386x: Differential geometry Financial aid is available for students a comprehensive examination is required APMA E4001y: Principles of applied mathematics CBMF W4761y: Computational genomics interested in the Ph.D. program, the IEOR E4700: Intro to financial engineering pursuing a doctorate. Fellowships, for graduation. This examination, on APMA E4101x: Intro to dynamical systems student must reapply for admission. NEUROBIOLOGY scholarships, teaching assistantships, **Please check IEOR website for registration subjects covered in the curriculum, is APMA E4301y: Numerical methods for partial The core courses provide a student differential equations BIOL UN3004x: Neurobiology , I (J) and graduate research assistantships procedures required of non-IEOR students. taken after two terms of study. with a foundation in the fundamentals APMA E4302x: Methods in computational BIOL UN3005y: Neurobiology, II (J) are awarded on a competitive basis. of applied mathematics and contribute science ELEN E4011x: Computational neuroscience The Aptitude Test of the Graduate Other elective courses may be cho- 15 points of graduate credit toward the Certification of Professional PHYS GU4019y: Mathematical methods of physics Record Examination is required of sen from other departments in SEAS degree. Students must complete five of Achievement in Medical Physics The second term of biology will be candidates for admission to the and Arts and Sciences, e.g., the the following nine courses: This graduate program of instruction • Fundamental Mathematics in Applied considered a technical elective if a department and for financial aid; the Departments of Mechanical Engineering, leads to the Certification of Professional Mathematics student has credits from at least two Advanced Tests are recommended. APMA E4001: Principles of applied mathematics Electrical Engineering, Mathematics, Achievement and requires satisfactory This specialization is intended for other of the recommended courses in M.S. students must complete the APMA E4101: Intro to dynamical systems and Statistics. completion of six of the following courses: students who desire a more solid quantitative biology at the 3000 level professional development and leadership APMA E4150: Applied functional analysis foundation in the mathematical or above. course, ENGI E4000, as a graduation APMA E4200: Partial differential equations

ENGINEERING 2020–2021 ENGINEERING 2020–2021 equilibrium and regulatory control. In each case, approaches in soft condensed matter with 56 mathematician is more concerned with Applied Physics a molecular beam epitaxy machine, 57 a simple model of the body organ, property, or emphasis on biomolecular systems. Covers the APPH E4330: Radiobiology the accuracy of approximations and the This doctoral program has three ultrahigh vacuum systems, lasers, Health physics function will be derived and then applied. broad range of molecular, nanoscale and colloidal APPH E4500: interpretation of results. Needless to say, specialties. APPH E4018 Applied equipment for the study of optical APPH E4600: Dosimetry phenomena with revealing their mechanisms and even in this age of specialization, the physics laboratory is required for each properties and transport on the APPH E3900x and y Undergraduate research APBM E4650: Anatomy for physicists and engineers physical foundations. The relationship between work of mathematicians, scientists, and of the three specialties in the first year nanoscale, and the instruments in in applied physics APPH E6319: Clinical nuclear medicine physics 0–4 pts. Members of the faculty. molecular architecture and interactions and engineers frequently overlaps. Applied of the doctoral program, in addition to the shared facilities overseen by the or APPH E6330: Diagnostic radiology physics Prerequisite: Written permission from instructor macroscopic behavior are discussed for the broad mathematics, by its very nature, has Columbia Nano Initiative (CNI). There APPH E6335: Radiation therapy physics any specific courses required of each and approval from adviser. May be repeated range of soft and biological matter systems, occupied a central position in this interplay or APPH E6336: Advanced topics in radiation specialty. are also significant resources for for credit, but no more than 6 points may be from surfactants and liquid crystals to polymers, therapy and has remained a field of fascination electrical and optical experimentation counted toward the satisfaction of the B.S. degree nanoparticles, and biomolecules. Modern and excitement for active minds. Plasma Physics at low temperatures and high magnetic requirements. Candidates for the B.S. degree characterization methods for soft materials, The Applied Analysis specialty may conduct an investigation in applied physics or including X-ray scattering, molecular force probing, This is a part-time nondegree program. This graduate specialty is designed to fields. Specific course requirements includes research on analytical and carry out a special project under the supervision of and electron microcopy are reviewed. Example Students are admitted to the department emphasize preparation for professional for the solid-state physics doctoral numerical partial differential equations; the staff. Credit for course is contingent upon the problems, drawn from the recent scientific as certificate-track students. careers in plasma research, controlled specialization are set with the academic mathematical foundations of data submission of an acceptable thesis or final report. literature, link the studied materials to the actively fusion, and space research. This adviser, in consultation with the analytics, uncertainty quantification, developed research areas. Course grade based PH.D. AND ENG.SC.D. PROGRAMS includes basic training in relevant areas Committee on Materials Science and APAM E3999x, y or s Undergraduate fieldwork on midterm and final exams, weekly homework stochastic analysis; large-scale 1–2 pts. Members of the faculty. After completing the M.S. program, of applied physics, with emphasis Engineering/Solid-State Science and assignments, and final individual/team project. scientific computation; fluid dynamics Prerequisite(s): Obtained internship and approval doctoral students specialize in one area Engineering. and continuum mechanics; dynamical on plasma physics and related areas from adviser. Restricted to ENAPMA, ENAPPH, APPH E4090y Nanotechnology of their programs. Some specializations systems and chaos; and applications to leading to extensive experimental and ENMSAE. May be repeated for credit, but no 3 pts. Lect: 3. Not offered in 2020–2021. have specific course requirements for various fields of data and physical and life theoretical research in the Columbia COURSES IN APPLIED PHYSICS more than 3 total points may be used toward the Prerequisites: APPH E3100 and MSAE E3010 the doctorate; elective courses are sciences. University Plasma Physics Laboratory. 128-credit degree requirement. Only for APAM or their equivalents with instructor’s permission. APPH E3100y Introduction to quantum determined in consultation with the The Atmospheric, Oceanic, and Earth Specific course requirements for the undergraduate students who include relevant The science and engineering of creating program adviser. Successful completion plasma physics doctoral program are mechanics off-campus work experience as part of their materials, functional structures and devices on the Physics specialty includes research on 3 pts. Lect: 3. Professor Herman. of an approved 30-point program of APPH E4018, E4200, E4300, E6101, approved program of study. Final report and letter nanometer scale. Carbon nanotubes, nanocrystals, dynamics of the atmosphere and the Prerequisites: PHYS UN1403 or equivalent, and study is required in addition to successful of evaluation required. Fieldwork credits may not quantum dots, size dependent properties, self- ocean; climate modeling; cloud physics; E6102, and E9142 or E9143, or differential and integral calculus. Corequisites: completion of a written qualifying equivalents taken at another university. count toward any major core, technical, elective, assembly, nanostructured materials. Devices radiation transfer; remote sensing; APMA E3101 or equivalent. Basic concepts and and nontechnical requirements. May not be taken and applications, nanofabrication. Molecular examination taken after two semesters geophysical/geological fluid dynamics; assumptions of quantum mechanics, Schrodinger’s of graduate study. An oral examination, for pass/fail credit or audited. engineering, bionanotechnology. Imaging and and geochemistry. Optical and Laser Physics equation, solutions for one-dimensional problems, manipulating at the atomic scale. Nanotechnology taken within one year after the written APPH E4008x Introduction to atmospheric This graduate specialty involves a basic including square wells, barriers, and the harmonic in society and industry. qualifying examination, and a thesis science Courses: training in relevant areas of applied oscillator, introduction to the hydrogen atom, 3 pts. Lect: 3. Professor Polvani. proposal examination, taken within APMA E4001: Principles of applied mathematics atomic physics and X-rays, electron spin. APPH E4100x Quantum physics of matter physics with emphasis in quantum Prerequisites: Advanced calculus and general two years after the written qualifying APMA E4101: Intro to dynamical systems 3 pts. Lect: 3. Professor Venkataraman. mechanics, quantum electronics, and APPH E3200x Mechanics: fundamentals and physics, or instructor’s permission. Basic physical examination, are required of all doctoral APMA E4150: Applied functional analysis Prerequisite: APPH E3100. Corequisite: APMA related areas of specialization. Some applications processes controlling atmospheric structure: E3102 or equivalent. Basic theory of quantum candidates, as is training in research and APMA E4200: Partial differential equations 3 pts. Lect: 3. Instructor to be announced. active areas of research in which the thermodynamics; radiation physics and radiative mechanics, well and barrier problems, the professional ethics in the first two years APMA E4204: Functions of a complex variable Prerequisites: PHYS UN1402, MATH UN2030, or student may concentrate are laser transfer; principles of atmospheric dynamics; cloud harmonic oscillator, angular momentum identical of the doctoral program. APMA E4300: Intro to numerical methods equivalent. Basic non-Euclidean coordinate systems, processes; applications to Earth’s atmospheric particles, quantum statistics, perturbation theory APMA E4301: Numerical methods for partial modification of surfaces, optical Newtonian mechanics, oscillations, Green’s general circulation, climatic variations, and the and applications to the quantum physics of atoms, differential equations diagnostics of film processing, inelastic functions, Newtonian gravitation, Lagrangian Applied Mathematics atmospheres of the other planets. molecules, and solids. Applied mathematics deals with APMA E4302: Intro to computational science light scattering in nanomaterials, nonlinear mechanics, central force motion, two-body collisions, APMA E4400: Intro to biophysical modeling APPH E4010x Introduction to nuclear science mathematical concepts and techniques optics, ultrafast optoelectronics photonic noninertial reference frames, rigid body dynamics. APPH E4110y Modern optics APMA E6301: Analytic methods for partial Applications, including GPS and feedback control 3 pts. Lect: 3. Professor Ostrow. 3 pts. Lect: 3. Professor Yu. used in various fields of science and switching, optical physics of surfaces, Prerequisites: MATH UN1202 or APMA E2000, differential equations systems, are emphasized throughout. Prerequisite: APPH E3300. Ray optics, matrix engineering. Historically, mathematics and photon integrated circuits. Specific and UN2030 and PHYS UN1403 or equivalents. APMA E6302: Numerical analysis for partial formulation, wave effects, interference, Gaussian was first applied with great success course requirements for the optical and APPH E3300y Applied electromagnetism Introductory course for individuals with an interest differential equations beams, Fourier optics, diffraction, image formation, laser physics doctoral specialization are 3 pts. Lect: 3. Professor Navratil. in medical physics and other branches of radiation in astronomy and mechanics. Then it electromagnetic theory of light, polarization and Corequisite: APMA E3102. Vector analysis, science. Topics include basic concepts, nuclear developed into a main tool for physics, Related courses of specialization: set with the academic adviser. electrostatic fields, Laplace’s equation, multipole models, semiempirical mass formula, interaction crystal optics, coherence, guided wave and fiber other physical science, and engineering. APMA E6901: Special topics in applied mathematics expansions, electric fields in matter: dielectrics, of radiation with matter, nuclear detectors, nuclear optics, optical elements, photons, selected topics It is now becoming important in the APMA E8308: Asymptotic methods in applied Solid-State Physics magnetostatic fields, magnetic materials, and structure and instability, radioactive decay process in nonlinear optics. biological, geological, economics, mathematics This graduate specialty encompasses superconductors. Applications of electromagnetism and radiation, particle accelerators, and fission and APPH E4112x Laser physics business, etc. With the coming of age APPH E4210: Geophysical fluid dynamics the study of the electrical, optical, to devices and research areas in applied physics. fusion processes and technologies. 3 pts. Lect: 3. Professor Yu. of the computer, applied mathematics APMA E9815: Geophysical fluid dynamics seminar magnetic, thermal, high-pressure, and APPH E3400y Physics of the human body Recommended but not required: APPH E3100 transcended its traditional style and now COMS E4205: Combinatorial theory APPH E4018y Applied physics laboratory ultrafast dynamical properties of solids, 3 pts. Lect: 3. Not offered in 2020–2021. and E3300 or their equivalents. Optical resonators, assumes an even greater importance and COMS E4241: Numerical algorithms and 2 pts. Lab: 4. Professor Mauel. with an aim to understanding them Prerequisites: PHYS UN1201 or UN1401, Prerequisite: APPH E3300 or ELEN E3401 interaction of radiation and atomic systems, a new vitality. complexity EESC GU4008: Introduction to atmospheric in terms of the atomic and electronic and Calculus I. Corequisites: PHYS UN1202 or equivalent. Typical experiments are in the theory of laser oscillation, specific laser systems, Compared with the pure science structure. The field emphasizes the or UN1402, and Calculus II. This introductory areas of plasma physics, microwaves, laser rate processes, modulation, detection, harmonic mathematician, the applied mathematician course analyzes the human body from the basic generation, and applications. PHYS GU4019: Mathematical methods in physics formation, processing, and properties of applications, optical spectroscopy physics, and is more interested in problems coming principles of physics. Topics covered include MATH GU4032: Fourier analysis thin films, low-dimensional structures— superconductivity. CHAP E4120y Statistical mechanics from other fields. Compared with the the energy balance in the body, the mechanics such as one- and two-dimensional 3 pts. Lect: 3. Professor O’Shaughnessy. engineer and the physical scientist, the of motion, fluid dynamics of the heart and APCH E4080x Soft condensed matter electron gases, nanocrystals, surfaces Prerequisite: CHEN E3210 or equivalent applied mathematician is more concerned Materials Science circulation, vibrations in speaking and hearing, 3 pts. Lect: 3. Professor Gang. muscle mechanics, gas exchange and transport Prerequisite(s): MSAE E3111, CHEE E3010, or thermodynamics course, or instructor’s permission. with the formulation of problems and and Engineering Program of electronic and optoelectronic interest, and molecules. Facilities in the lungs, vision, structural properties and CHEN E3120 or equivalent. Course is aimed at Fundamental principles and underlying assumptions the nature of solutions. Compared with See page 182. of statistical mechanics. Boltzmann’s entropy include a microelectronics laboratory, limits, electrical properties and the development senior undergraduate and graduate students. the computer scientist, the applied and sensing of magnetic fields, and basics of hypothesis and its restatement in terms of Helmholtz high-pressure diamond anvil cells, Introduces fundamental ideas, concepts, and

ENGINEERING 2020–2021 ENGINEERING 2020–2021 electron dynamics and conduction, dielectric APPH E6330y Diagnostic radiology physics radiologic units (mobile and fixed), fluoroscopy 58 and Gibbs free energies and for open systems. APPH E4330y Radiobiology for medical for counting, energy spectroscopy, and dosimetry; 59 Correlation times and lengths. Exploration of phase physicists radiation safety; counting statistics and error properties of insulators, semiconductors, defects, 3 pts. Lect: 3. Professor Jambalwalikar. units (mobile and fixed), angiography units, space and observation time scale. Correlation 3 pts. Lect: 3. Professor Zaider. propagation; mechanisms of radiation emission magnetism, superconductivity, low-dimensional Prerequisite: APPH E4600. Physics of medical mammography units, CT scanners, MRI units and functions. Fermi-Dirac and Bose-Einstein statistics. Prerequisite: APPH E4010 or equivalent or and interaction. (Topic coverage may be revised.) structures, and soft matter. imaging. Imaging techniques: radiography, ultrasound units. The objective is familiarization Fluctuation-response theory. Applications to ideal Corequisite: APPH E4010. Interface between fluoroscopy, computed tomography, in routine operation of test instrumentation APPH E4711x or y Radiation instrumentation MSAE E6085y Computing the electronic gases, interfaces, liquid crystals, microemulsions clinical practice and quantitative radiation mammography, ultrasound, magnetic resonance. and QC measurements utilized in diagnostic and measurement laboratory, II structure of complex materials and other complex fluids, polymers, Coulomb gas, biology. Microdosimetry, dose-rate effects Includes conceptual, mathematical/theoretical, and medical physics. Students are required to submit 3 pts. Lect: 1. Lab: 4. Not offered in 2020–2021. 3 pts. Lect: 3. Professor Wentzcovitch. interactions between charged polymers and charged and biological effectiveness thereof; radiation practical clinical physics aspects. QC forms with data on three different types of Prerequisite: APPH E4710. Lab fee: $50. Additional Prerequisite: APPH E3100 or equivalent. Basics of interfaces, ordering transitions. biology data, radiation action at the cellular radiology imaging equipment. detector types; applications and systems including density functional theory (DFT) and its application APPH E6333x or y Radiation therapy physics and tissue level; radiation effects on human APPH E4130x Physics of solar energy coincidence, low-level, and liquid scintillation to complex materials. Computation of electronics practicum APPH E6365x or y Nuclear medicine populations, carcinogenesis, genetic effects; 3 pts. Lect: 3. Professor Chen. counting; neutron activation; TLD dosimetry, and mechanical properties of materials. Group 3 pts. Lab: 6. Professor Wuu. practicum radiation protection; tumor control, normal- Prerequisites: General physics (PHYS UN1403 gamma camera imaging. (Topic coverage may be theory, numerical methods, basis sets, computing, Prerequisites: Grade of B+ or better in APPH 3 pts. Lab: 6. Members of the faculty. tissue complication probabilities; treatment plan and running open source DFT codes. Problem sets or UN1602) and mathematics, including ordinary revised.) E6335 and instructor’s permission. Students Prerequisites: Grade of B+ or better in APPH optimization. and a small project. differential equations and complex numbers (such spend two to four days per week studying the E6319 and instructor’s permission. Practical APPH E4901x Seminar: problems in applied as MATH UN1202 or UN2030) or instructor’s APPH E4500x Health physics clinical aspects of radiation therapy physics. applications of nuclear medicine theory and physics APPH E6091y Magnetism and magnetic permission. The physics of solar energy including 3 pts. Lect: 3. Professor Caracappa. Projects on the application of medical physics application for processing and analysis of 1 pt. Lect: 1. Professor Mauel. materials solar radiation, the analemma, atmospheric efforts, Prerequisite: APPH E4600 or Corequisite: APPH in cancer therapy within a hospital environment clinical images and radiation safety and quality Required for, and can be taken only by, all applied 3 pts. Lect. 3. Not offered in 2020–2021. thermodynamics of solar energy, physics of solar E4600. Fundamental principles and objectives of are assigned; each entails one or two weeks of assurance programs. Topics may include physics majors and minors in the junior year. Prerequisites: MSAE E4206, APPH E6081, or cells, energy storage and transmission, and health physics (radiation protection), quantities of work and requires a laboratory report. Two areas tomography, instrumentation, and functional Discussion of specific and self-contained problems equivalent. Types of magnetism. Band theory physics and economics in the solar era. radiation dosimetry (the absorbed dose, equivalent are emphasized: 1. computer-assisted treatment imaging. Reports. in areas such as applied electrodynamics, physics of ferromagnetism. Magnetic metals, insulators, dose, and effective dose) used to evaluate human planning (design of typical treatment plans for APPH E4200x Physics of fluids of solids, and plasma physics. Topics change and semiconductors. Magnetic nanostructures: APPH E6380x or y Health physics practicum radiation risks, elementary shielding calculations various treatment sites including prostate, breast, 3 pts. Lect: 3. Not offered in 2020–2021. yearly. ultrathin films, superlattices, and particles. Surface 3 pts. Lab: 6. Professor Caracappa and protection measures for clinical environments, head and neck, lung, brain, esophagus, and Prerequisites: APMA E3102 or equivalent; PHYS magnetism and spectroscopies. High speed Prerequisites: Grade of B+ or better in APPH characterization and proper use of health physics APPH E4903x Seminar: problems in applied cervix) and 2. clinical dosimetry and calibrations UN1401 or UN1601 or equivalent. An introduction magnetization dynamics. Spin electronics. E4500 and instructor’s permission or Corequisite: instrumentation, and regulatory and administrative physics (radiation measurements for both photon and to the physical behavior of fluids for science and APPH E4500 and permission of the instructor. requirements of health physics programs in 2 pts. Lect: 1. Tutorial: 1. Professor Mauel. APPH E6101x Plasma physics, I electron beams, as well as daily, monthly, and engineering students. Derivation of basic equations Radiation protection practices and procedures for general and as applied to clinical activities. Required for, and can be taken only by, all applied 3 pts. Lect: 3. Professor Navratil. part of annual QA). of fluid dynamics: conservation of mass, momentum, clinical and biomedical research environments. physics majors in the senior year. Discussion of Prerequisite: APPH E4300. Debye screening. and energy. Dimensional analysis. Vorticity. APPH E4550y Medical physics seminar APPH E6335y Radiation therapy physics Includes design, radiation safety surveys of specific and self-contained problems in areas such Motion of charged particles in space- and Laminar boundary layers. Potential flow. Effects of 0 pts. Lect: 1. Professor Wuu. 3 pts. Lect: 3. Professors Wuu and Homacher. diagnostic and therapeutic machine source as applied electrodynamics, physics of solids, and time-varying electromagnetic fields. Two-fluid compressibility, stratification, and rotation. Waves on Required for all graduate students in the Medical Prerequisites: APPH E4600; APPH E4330 facilities, the design and radiation protection plasma physics. Formal presentation of a term description of plasmas. Linear electrostatic and a free surface; shallow water equations. Turbulence. Physics Program. Practicing professionals and recommended. Review of X-ray production and protocols for facilities using unsealed sources of paper required. Topics change yearly. electromagnetic waves in unmagnetized and faculty in the field present selected topics in fundamentals of nuclear physics and radioactivity. radioactivity—nuclear medicine suites and sealed APPH E4210y Geophysical fluid dynamics magnetized plasmas. The magnetohydrodynamic medical physics. APPH E4990x and y Special topics in applied Detailed analysis of radiation absorption and sources—brachytherapy suites. Also includes 3 pts. Lect: 3. Professor Sobel. (MHD) model, including MHD equilibrium, stability, physics interactions in biological materials as specifically radiation protection procedures for biomedical Prerequisites: APMA E3101, E3102 (or and MHD waves in simple geometries. APPH E4600x Fundamentals of radiological 1–3 pts. Professor Gaeta. related to radiation therapy and radiation therapy research facilities and the administration equivalents) and APPH E4200 (or equivalent), or physics and radiation dosimetry Prerequisite: Instructor’s permission. May be APPH E6102y Plasma physics, II dosimetry. Surveys of use of teletherapy isotopes of programs for compliance to professional permission from instructor. Fundamental concepts 3 pts. Lect: 3. Professor Meli. repeated for credit. Topics and instructors change 3 pts. Lect: 3. Professor Mauel. and X-ray generators in radiation therapy plus health physics standards and federal and state in the dynamics of rotating, stratified flows. Prerequisite: APPH E4010 or equivalent or from year to year. For advanced undergraduate Prerequisite: APPH E6101. Magnetic coordinates. the clinical use of interstitial and intracavitary regulatory requirements for the possession and Geostrophic and hydrostatic balances, potential Corequisite: APPH E4010. Basic radiation physics: students and graduate students in engineering, Equilibrium, stability, and transport of toroidal isotopes. Principles of radiation therapy treatment use of radioactive materials and machine sources vorticity, f and beta plane approximations, gravity radioactive decay, radiation producing devices, physical sciences, and other fields. plasmas. Ballooning and tearing instabilities. planning and isodose calculations. Problem sets of ionizing and nonionizing radiations in clinical and Rossby waves, geostrophic adjustment characteristics of the different types of radiation Kinetic theory, including Vlasov equation, Fokker- taken from actual clinical examples are assigned. situations. Individual topics are decided by the and quasigeostrophy, baroclinic and barotropic APAM E4999x and y–S4999 Supervised (photons, charged and uncharged particles) and Planck equation, Landau damping, kinetic transport student and the collaborating Clinical Radiation instabilities, Sverdrup balance, boundary internship APPH E6336x Advanced topics in radiation mechanisms of their interactions with materials. theory. Drift instabilities. Safety Officer. currents, Ekman layers. 1–3 pts. Members of the faculty. therapy Essentials of the determination, by measurement Prerequisite: Obtained internship and approval APPH E6110x Laser interactions with matter 3 pts. Lect: 3. Professors Wuu and Amols. APAM E6650x and y–S6650 Research project and calculation, of absorbed doses from ionizing APPH E4300x Applied electrodynamics from adviser. Only for master’s students in the 3 pts. Lect: 3. Not offered in 2020–2021. Prerequisite: APPH E6335. Advanced technology 1–6 pts. Members of the faculty. 3 pts. Lect: 3. Professor Gaeta. radiation sources used in medical physics (clinical) Department of Applied Physics and Applied Prerequisites: APPH E4112 or equivalent, and applications in radiation therapy physics, Prerequisite: Written permission from instructor Prerequisite: APPH E3300. Overview of properties situations and for health physics purposes. Mathematics who may need relevant work quantum mechanics. Principles and applications including intensity modulated, image guided, and approval from adviser. May be repeated for and interactions of static electric and magnetic APBM E4650x Anatomy for physicists and experience as part of their program of study. Final of laser-matter coupling, nonlinear optics, three- stereotactic, and hypofractionated radiation credit. A special investigation of a problem in fields. Study of phenomena of time dependent engineers report required. May not be taken for pass/fail or and four-wave mixing, harmonic generation, laser therapy. Emphasis on advanced technological, nuclear engineering, medical physics, applied electric and magnetic fields including induction, 3 pts. Lect: 3. Professors Rozenshtein and Katz. audited. processing of surfaces, laser probing of materials, engineering, clinical and quality assurance issues mathematics, applied physics, and/or plasma waves, and radiation as well as special relativity. Prerequisite: Engineering or physics background. spontaneous and stimulated light scattering, associated with high-technology radiation therapy physics consisting of independent work on the part Applications are emphasized. APPH E6081x Solid state physics, I Systemic approach to the study of the human body saturation spectroscopy, multiphoton excitation, and the special role of the medical physicist in of the student and embodied in a formal report. 3 pts. Lect: 3. Professor Pinczuk. from a medical imaging point of view: skeletal, laser isotope separation, transient optical effects. the safe clinical application of these tools. APPH E4301y Introduction to plasma physics Prerequisites: APPH E3100 or the equivalent. APPH E9142x-E9143y Applied physics seminar 3 pts. Lect: 3. Not offered in 2020–2021. respiratory, cardiovascular, digestive, and urinary Knowledge of statistical physics on the level APPH E6319y Clinical nuclear medicine APPH E6340x or y Diagnostic radiology 3 pts. Sem: 3. Not offered in 2020–2021. Prerequisite: PHYS UN3008 or APPH E3300. systems, breast and women’s issues, head and of MSAE E3111 or PHYS GU4023 strongly physics practicum These courses may be repeated for credit. Definition of a plasma. Plasmas in laboratories neck, and central nervous system. Lectures are recommended. Crystal structure, reciprocal 3 pts. Lect: 3. Professor Zanzonico. 3 pts. Lab: 6. Members of the faculty. Selected topics in applied physics. Topics and and nature, plasma production. Motion of charged reinforced by examples from clinical two- and lattices, classification of solids, lattice dynamics, Prerequisite: APPH E4010 or equivalent Prerequisites: Grade of B+ or better in APPH instructors change from year to year. particles in electric and magnetic fields, adiabatic three-dimensional and functional imaging (CT, MRI, anharmonic effects in crystals, classical electron recommended. Introduction to the E6330 and instructor’s permission. Practical invariants. Heuristic treatment of collisions, diffusion, PET, SPECT, U/S, etc.). APAM E9301x and y–S9301 Doctoral research models of metals, electron band structure, and instrumentation and physics used in clinical applications of diagnostic radiology for various transport, and resistivity. Plasma as a conducting 0–15 pts. Members of the faculty. APPH E4710x Radiation instrumentation and low-dimensional electron structures. nuclear medicine and PET with an emphasis measurements and equipment assessments. fluid. Electrostatic and magnetostatic equilibria of Prerequisite: Qualifying examination for the measurement laboratory, I on detector systems, tomography and quality Instruction and supervised practice in radiation plasmas. Waves in cold plasmas. Demonstration of APPH E6082y Solid state physics, II doctorate. Required of doctoral candidates. 3 pts. Lect: 1. Lab: 4. Professor Ostrow. control. Problem sets, papers, and term project. safety procedures, image quality assessments, laboratory plasma behavior, measurement of plasma 3 pts. Lect: 3. Professor Pasupathy. Prerequisite or corequisite: APPH E4010. Lab regulatory compliance, radiation dose evaluations APAM E9800x and y–S9800 Doctoral Prerequisite: APPH E6081 or instructor’s properties. Illustrative problems in fusion, space, fee: $50. Theory and use of alpha, beta, gamma, and calibration of equipment. Students participate research instruction permission. Semiclassical and quantum mechanical and nonneutral or beam plasmas. and X-ray detectors and associated electronics in clinical QC of the following imaging equipment: 3, 6, 9, or 12 pts. Members of the faculty.

ENGINEERING 2020–2021 ENGINEERING 2020–2021 A candidate for the Eng.Sc.D. degree must register APMA E3102y Partial differential equations differential equations; constant coefficient and optimization, interpolation, numerical integration of problem areas are nonlinear dynamics, Prerequisites: APMA E4204 and MATH UN2030, 60 for 12 points of doctoral research instruction. 3 pts. Lect: 3. Professor Tippett. parametrically forced systems; Fundamental and differentiation, initial value problems, and asymptotics, approximation theory, numerical or their equivalents. Laplace, Fourier, Hankel, 61 Registration for APAM E9800 may not be used Prerequisite: MATH UN2030 or equivalent. solutions; resonance; limit points, limit cycles boundary value problems for systems of ODE’s. All methods, etc. Approximately three problem areas and Mellin transforms. Selection of suitable to satisfy the minimum residence requirement for Introduction to partial differential equations; and classification of flows in the plane (Poincare- programming exercises will be in Python. are studied per term. transform for a given partial differential equation the degree. integral theorems of vector calculus. Partial Bendixson Theorem); conservative and dissipative boundary value problem. Operational properties APMA E4301y Numerical methods for partial APMA E4990x and y Special topics in applied differential equations of engineering in rectangular, systems; linear and nonlinear stability analysis of transforms. Inversion theorems. Approximate APAM E9900x and y–S9900 Doctoral differential equations mathematics cylindrical, and spherical coordinates. Separation of equilibria and periodic solutions; stable and evaluation of inversion integrals for small and large dissertation 3 pts. Lect: 3. Professor Mandli. 1–3 pts. Lect: 3. Members of the faculty. of the variables. Characteristic-value problems. unstable manifolds; bifurcations, e.g., Andronov- values of parameter. Application to the solution of 0 pts. Members of the faculty. Prerequisites: APMA E4300 and APMA E3102 Prerequisites: Advanced calculus and junior year Bessel functions, Legendre polynomials, other Hopf; sensitive dependence and chaotic dynamics; integral equations. A candidate for the doctorate may be required or APMA E4200 or equivalents. Numerical applied mathematics, or their equivalents. May orthogonal functions; their use in boundary value selected applications. to register for this course every term after the solution of differential equations, in particular be repeated for credit. Topics and instructors APMA E6901x and y–E6901y Special topics in problems. Illustrative examples from the fields of coursework has been completed, and until the APMA E4150x Applied functional analysis partial differential equations arising in various from the Applied Mathematics Committee and applied mathematics electromagnetic theory, vibrations, heat flow, and dissertation has been accepted. 3 pts. Lect: 3. Professor Weinstein. fields of application. Presentation emphasizes the staff change from year to year. For advanced 3 pts. Lect: 3. Members of the faculty. fluid mechanics. Prerequisites: Advanced calculus and course finite difference approaches to present theory on undergraduate students and graduate students in Prerequisites: Advanced calculus and junior year APAM E3105x Programming methods for in basic analysis, or instructor’s permission. stability, accuracy, and convergence with minimal engineering, physical sciences, biological sciences, applied mathematics, or their equivalents. May COURSES IN APPLIED scientists and engineers Introduction to modern tools in functional analysis coverage of alternate approaches (left for other and other fields. Examples of topics include be repeated for credit. Topics and instructors MATHEMATICS 3 pts. Lect: 2.5. Lab: 1. Not offered in 2020–2021. that are used in the analysis of deterministic and courses). Method coverage includes explicit and multiscale analysis and Applied Harmonic Analysis. from the Applied Mathematics Committee and the Introduction to modern techniques of computer stochastic partial differential equations and in implicit time-stepping methods, direct and iterative staff change from year to year. For students in APMA E2000x and y Multivariable calculus for APMA E6100x or y Research Seminar programming for the numerical solutions to the analysis of numerical methods: metric and solvers for boundary-value problems. engineering, physical sciences, biological sciences, engineers and applied scientists 0 pts. Lect: 1. Members of the faculty. familiarity with basic and advanced concepts normed spaces, Banach space of continuous and other fields. Examples of topics include 4 pts. Lect: 3. Professor Youngren and Sagiv. APMA E4302x Methods in computational Prerequisites: MATH UN3027 or APMA E4101, of modern numerical programming and acquire functions, measurable spaces, the contraction uncertainty quantification. Differential and integral calculus of multiple science MATH UN3028 or APMA E4200, MATH UN2010 practical experience solving representative mapping theorem, Banach and Hilbert spaces variables. Topics include partial differentiation; 3 pts. Lect: 3. Professor Mandli. or APMA E3101 or their equivalents. An M.S. APMA E8308y Asymptotic methods in applied problems in math and physics. bounded linear operators on Hilbert spaces and optimization of functions of several variables; Prerequisites: APMA E4300, application and degree requirement. Students attend at least mathematics their spectral decomposition, and time permitting line, area, volume, and surface integrals; vector APMA E3900x and y Undergraduate research knowledge in C, Fortran or similar compiled three Applied Mathematics research seminars 3 pts. Lect: 2. Not offered in 2020–2021. distributions and Fourier transforms. functions and vector calculus; theorems of Green, in applied mathematics language. Introduction to the key concepts and within the Department of Applied Physics and Prerequisite: APMA E4204 or equivalent. Gauss, and Stokes; applications to selected 0–4 pts. Members of the faculty. APMA E4200x Partial differential equations issues in computational science aimed at getting Applied Mathematics and submit reports on Asymptotic treatment of ordinary and partial problems in engineering and applied science. Prerequisite: Written permission from instructor 3 pts. Lect: 3. Professor Du. students to a basic level of understanding where each. differential equations in problems arising in applied and approval from adviser. May be repeated Prerequisite: Course in ordinary differential they can run simulations on machines aimed at mathematics. Asymptotic series. Asymptotic APMA E2101y Introduction to applied APMA E6209x Approximation theory for credit, but no more than 6 points may be equations. Techniques of solution of partial a range of applications and sizes from a single evaluation of integrals. Expansion of solutions mathematics 3 pts. Lect: 2. Not offered in 2020–2021. counted toward the satisfaction of the B.S. degree differential equations. Separation of the variables. workstation to modern super-computer hardware. of ordinary differential equations: connection 3 pts. Lect: 3. Professor He. Prerequisite: MATH GU4061 or some knowledge requirements. Candidates for the B.S. degree may Orthogonality and characteristic functions, Topics include but are not limited to basic problem and turning points. Stoke’s phenomenon. Prerequisite: Calculus III. A unified, single- of modern analysis. Theory and application conduct an investigation in applied mathematics nonhomogeneous boundary value problems. knowledge of unix shells, version control systems, Differential equations with a parameter: semester introduction to differential equations and of approximate methods of analysis from the or carry out a special project under the supervision Solutions in orthogonal curvilinear coordinate reproducibility, OpenMP, MPI, and many-core “boundary layer” phenomenon. Application to linear algebra with emphases on (1) elementary viewpoint of functional analysis. Approximate of the staff. Credit for the course is contingent systems. Applications of Fourier integrals, Fourier technologies. Applications will be used throughout partial differential equations: problems from analytical and numerical technique and (2) numerical and analytical treatment of linear and upon the submission of an acceptable thesis and Laplace transforms. Problems from the fields to demonstrate the various use cases and pitfalls fluid dynamics, wave propagation theory, discovering the analogs on the continuous and nonlinear algebraic, differential, and integral or final report. of vibrations, heat conduction, electricity, fluid of using the latest computing hardware. electromagnetic theory. discrete sides of the mathematics of linear equations. Topics include function spaces, dynamics, and wave propagation are considered. operators: superposition, diagonalization, APMA E4001y Principles of applied APMA E4400y Introduction to biophysical operators in normed and metric spaces, fixed point APMA E9101x-E9102y Research fundamental solutions. Concepts are illustrated mathematics APMA E4204x Functions of a complex modeling theorems and their applications. 1–4 pts. Members of the faculty. with applications using the language of 3 pts. Lect: 3. Professor Zhang. variable 3 pts. Lect: 3. Not offered in 2020–2021. Prerequisite: Permission of the supervising faculty APMA E6301y Analytic methods for partial engineering, the natural sciences, and the social Prerequisites: Introductory Linear Algebra required. 3 pts. Lect. 3. Professor Ren. Prerequisites: PHYS UN1401 or equivalent, and member. May be repeated. Advanced study in a differential equations sciences. Students execute scripts in Mathematica Ordinary Differential Equations recommended. Prerequisite: MATH UN1202 or APMA E2000 APMA E2101 or MATH UN2030 or equivalent. special area. 3 pts. Lect: 2. Not offered in 2020–2021. and MATLAB (or the like) to illustrate and visualize Review of finite-dimensional vector spaces and or equivalent. Complex numbers, functions of a Introduction to physical and mathematical models Prerequisites: Advanced calculus, basic concepts APMA E9810x or y SEAS colloquium in course concepts (programming not required). elementary matrix theory. Linear transformations, complex variable, differentiation and integration of cellular and molecular biology. Physics at the in analysis, APMA E3101 or E4200 or their climate science change of basis, eigenspaces. Matrix representation in the complex plane. Analytic functions, Cauchy cellular scale (viscosity, heat, diffusion, statistical APAM - HSAM W2901y Data: past, present equivalents, or instructor’s permission. Introduction 0 pts. Lect: 1. Professors Polvani and Sobel. of linear operators and diagonalization. integral theorem and formula, Taylor and Laurent mechanics). RNA transcription and regulation and future to analytic theory of PDEs of fundamental and Prerequisite: Instructor’s permission. Current Applications to difference equations, Markov series, poles and residues, branch points, evaluation of genetic expression. Genetic and biochemical 3 pts. Lect: 1.5. Lab: 1.5. Professors Wiggins applied science; wave (hyperbolic), Laplace and research in problems at the interface between processes, ordinary differential equations, and of contour integrals. Conformal mapping. Schwarz- networks. Bioinformatics as applied to reverse- and Jones. Poisson equations (elliptic), heat (parabolic) and applied mathematics and earth and environmental stability of nonlinear dynamical systems. Inner Christoffel transformation. Applications to engineering of naturally-occurring networks and Prerequisites: Instructor's permission. Critical Schroedinger (dispersive) equations; fundamental sciences. product spaces, projection operators, orthogonal physical problems. to forward-engineering of synthetic biological thinking and practice regarding the past, present, solutions, Green’s functions, weak/distribution bases, Gram-Schmidt orthogonalization. Least networks. Mathematical and physical aspects of APMA E9815x or y Geophysical fluid and future of data. Readings covering how APMA E4300x Computational math: solutions, maximum principle, energy estimates, squares method, pseudo-inverses, singular value functional genomics. dynamics seminar students, scholars, and citizens can make sense introduction to numerical methods variational methods, method of characteristics; decomposition. Adjoint operators, Hermitian and 1–3 pts. May be repeated for up to 10 points of of data in science, public policy, and our personal 3 pts. Lect: 3. Professor Spiegelman. APMA E4901x Seminar: problems in applied unitary operators, Fredholm Alternative Theorem. elementary functional analysis and applications credit. Not offered in 2020–2021. lives. Labs covering descriptive, predictive, and Prerequisites: MATH UN1201 or APMA E2000, mathematics Fourier series and eigenfunction expansions. to PDEs; introduction to nonlinear PDEs, shocks; Prerequisite: Instructor’s permission. Problems in prescriptive modeling of data. UN2030, and APMA E3101 and ENGI E1006 0 pts. Lect: 1. Professor Wiggins. Introduction to the theory of distributions and the selected applications. the dynamics of geophysical fluid flows. or their equivalents. Programming experience Required for, and can be taken only by, all Fourier Integral Transform. Green’s functions. APMA E6302x Numerical analysis of partial APMA E3101x Linear algebra in Python extremely useful. Introduction applied mathematics majors in the junior Application to Partial Differential Equations. differential equations 3 pts. Lect: 3. Professor He. to fundamental algorithms and analysis of year. Introductory seminars on problems and 3 pts. Lect: 2. Not offered in 2020–2021. COURSES IN MATERIALS Matrix algebra, elementary matrices, inverses, APMA E4101x Introduction to dynamical numerical methods commonly used by scientists, techniques in applied mathematics. Typical topics Prerequisite: APMA E3102 or E4200. Numerical rank, determinants. Computational aspects of systems mathematicians, and engineers. Designed to are nonlinear dynamics, scientific computation, SCIENCE AND ENGINEERING analysis of initial and boundary value problems solving systems of linear equations: existence- 3 pts. Lect: 3. Professor Sagiv. give a fundamental understanding of the building economics, operations research, etc. See page 183. for partial differential equations. Convergence and uniqueness of solutions, Gaussian elimination, Prerequisites: APMA E3101 or MATH UN2010 blocks of scientific computing that will be used in APMA E4903x Seminar: problems in applied stability of the finite difference method, the spectral scaling, ill-conditioned systems, iterative (Linear Algebra), and MATH UN2030 (ODE), or more advanced courses in scientific computing mathematics method, the finite element method and applications techniques. Vector spaces, bases, dimension. their equivalents, or instructor’s permission. An and numerical methods for PDEs (e.g., APMA 3–4 pts. Lect: 1. Tutorial: 2. Professor Wiggins. to elliptic, parabolic, and hyperbolic equations. Eigenvalue problems, diagonalization, inner introduction to the analytic and geometric theory of E4301, APMA E4302). Topics include numerical Required for all applied mathematics majors in products, unitary matrices. dynamical systems; basic existence, uniqueness solutions of algebraic systems, linear least-squares, the senior year. Term paper required. Examples APMA E6304y Integral transforms and parameter dependence of solutions to ordinary eigenvalue problems, solution of nonlinear systems, 3 pts. Lect: 2. Not offered in 2020–2021.

ENGINEERING 2020–2021 ENGINEERING 2020–2021 62 BIOMEDICAL ENGINEERING interdisciplinary research is important to and biomedical imaging and data UNDERGRADUATE PROGRAM 63 the quality and strength of the program. processing laboratory. Each laboratory The program in biomedical engineering 351 Engineering Terrace, MC 8904 Educational programs at all incorporates equipment normally leading to the B.S. degree is accredited 212-854-4460 levels are based on engineering and reserved for advanced research and by the Engineering Accreditation [email protected] biological fundamentals. From this provides exceptional access to current Commission of ABET, http://www.abet. bme.columbia.edu basis, the program branches into practices in biomedical engineering and org. concentrations of contemporary related sciences. The objectives of the undergraduate CHAIR CAREER PLACEMENT Andrew F. Laine, SENIOR LECTURERS EMERITUS FACULTY biomedical engineering fields. Research facilities of the Biomedical X. Edward Guo OFFICER Percy K. and Vida Aaron M. Kyle Van C. Mow, Stanley program in biomedical engineering are Kristen Henlin L. W. Hudson Katherine Reuther Dicker Professor The intrinsic breadth of these Engineering faculty include the Synthetic as follows: VICE CHAIR Professor of Emeritus of Biomedical concentrations, and a substantial Biological Systems Laboratory (Professor 1. Professional employment in Paul Sajda COMMUNICATIONS AND Biomedical JOINT FACULTY Engineering elective content, prepare bachelor’s Danino), the Heffner Biomedical Imaging areas such as the medical device EVENTS MANAGER Engineering Gerard A. Ateshian, and master’s students to commence Laboratory (Professor Laine), the industry, engineering consulting, and CHAIR OF Alexis M. Newman Helen H. Lu Andrew Walz ADJUNCT UNDERGRADUATE Kam W. Leong, Professor of PROFESSORS professional activity in any area of Laboratory for Intelligent Imaging and biotechnology; STUDIES GRANTS MANAGER Samuel Y. Sheng Mechanical Hariklia Deligianni biomedical engineering or to go on Neural Computing (Professor Sajda), 2. Graduate studies in biomedical Lance C. Kam Monica Ionescu-Albu Professor of Engineering David Elad to graduate school for further studies the Biophotonics and Optical Radiology engineering or related fields; Biomedical Shunichi Homma, Ernest Feleppa in related fields. The program also Laboratory (Professor Hielscher), 3. Attendance at medical, dental, or other CHAIR OF GRADUATE GRANTS ANALYST Engineering Margaret Miliken Mark Gelfand provides excellent preparation for the Bone Bioengineering Laboratory STUDIES TBA Barclay Morrison III Hatch Professor of Howard Levin professional schools. Henry S. Hess Paul Sajda Medicine the health sciences and the study of (Professor Guo), the Cellular Engineering FINANCIAL ASSISTANT Samuel K. Sia Sachin Jambawalikar ADJUNCT ASSOCIATE medicine. Graduates of the doctoral Laboratory (Professor Hung), the The undergraduate program in DIRECTOR OF Michelle Cintron Gerard Karsenty, Paul PROFESSOR J. Thomas Vaughan program are prepared for research Biomaterial and Interface Tissue biomedical engineering will prepare FINANCE AND Karen Evans Gordana Vunjak- A. Marks Professor Alayar Kangarlu activities at the highest level. Engineering Laboratory (Professor Lu), ADMINISTRATION Novakovic, University of Genetics and graduates who will have: Mindaugas Paunksnis PROFESSORS Professor and the Development AFFILIATES Areas of particular interest to the Neurotrauma and Repair Laboratory X. Edward Guo, Stanley Mikati Foundation Edward F. Leonard Sunil Agrawal Columbia faculty include biomechanics (Professor Morrison), the Laboratory 1. an ability to identify, formulate, and BUSINESS MANAGER Dicker Professor Professor of Andrew Marks, Clyde Nadeen Chahine (Professors Ateshian, Guo, Hess, for Stem Cells and Tissue Engineering solve complex engineering problems Maria Leah Kim of Biomedical '56 and Helen Wu Anthony Fitzpatrick Biomedical Morrison, Mow, and Nerurkar), cellular (Professor Vunjak-Novakovic), the Engineering Engineering Professor of Molecular Jennifer Gelinas by applying principles of engineering, STUDENT AFFAIRS Henry S. Hess Cardiology (in Christine Hendon and tissue engineering (Professors Ultrasound and Elasticity Imaging science, and mathematics MANAGER Andreas H. Hielscher ASSOCIATE Medicine) Karen Kasza Danino, Hung, Kam, Leonard, Leong, Lu, Laboratory (Professor Konofagou), 2. an ability to apply engineering design Helen Cen Elizabeth M. C. Hillman PROFESSOR Elizabeth S. Olson Wei Min Morrison, Sia, and Vunjak-Novakovic), the Magnetic Resonance Scientific to produce solutions that meet Clark T. Hung Kenneth L. Shepard, Kristin Myers Joshua Jacobs auditory biophysics (Professor Olson), Engineering for Clinical Excellence specified needs with consideration STUDENT AFFAIRS Lance C. Kam Christoph Juchem Lau Family Professor Raju Tomer SPECIALIST Elisa E. Konofagou, Qi Wang of Electrical Stephen Tsang biomaterials (Professors Danino, Hess, Laboratory (Professor Juchem), the of public health, safety, and welfare, Jocelyn McArthur Robert and Margaret Engineering Binsheng Zhao Kam, Leong, Lu, Sia, and Vunjak- Microscale Biocomplexity Laboratory as well as global, cultural, social, Hariri Professor ASSISTANT Milan N. Stojanovic Novakovic), biosignals and biomedical (Professor Kam), the Molecular and environmental, and economic factors of Biomedical LABORATORY PROFESSORS Stavros Thomopoulos, imaging (Professors Guo, Hielscher, Microscale Bioengineering Laboratory 3. an ability to communicate effectively MANAGER Engineering and Elham Azizi Robert E. Carroll with a range of audiences Arthur Autz Radiology Tal Danino and Jane Chace Hillman, Jacobs, Juchem, Konofagou, (Professor Sia), the Laboratory for Nandan Nerurkar Carroll Professor of Laine, Sajda, Vaughan, and Wang), Functional Optical Imaging (Professor 4. an ability to recognize ethical and Biomechanics neuroengineering (Professors Hillman, Hillman), the Cognitive Electrophysiology professional responsibilities in Jacobs, Konofagou, Laine, Morrison, Laboratory (Professor J. Jacobs), the engineering situations and make Sajda, and Wang) and Machine Learning Nanobiotechnology and Synthetic informed judgments, which must iomedical engineering is an sophisticated approaches to of other Engineering departments, in Biomedical Engineering (Azizi, Laine, Biology Laboratory (Professor Hess), consider the impact of engineering evolving discipline in engineering measurement, data acquisition and and faculty from other University Sajda). the Raymond and Beverly Sackler solutions in global, economic, Bthat draws on collaboration analysis, simulation, and systems divisions who have strong interests and Laboratory for Neural Engineering environmental, and societal contexts 5. an ability to function effectively among engineers, physicians, and identification. These approaches involvement in biomedical engineering. Facilities and Control (Professor Wang), the on teams whose members scientists to provide interdisciplinary are useful in the study of individual Several of the faculty hold joint The Department of Biomedical Morphogenesis and Developmental together provide leadership, create insight into medical and biological cells, organs, entire organisms, appointments in Biomedical Engineering Engineering has been supported by Biomechanics Lab (Professor Nerurkar), a collaborative and inclusive problems. The field has developed its and populations of organisms. The and other University departments. grants obtained from NIH, NSF, DoT, the Laboratory for Nanomedicine and environment, establish goals, plan own knowledge base and principles increasing value of mathematical Courses offered by the Department Regenerative Medicine (Professor DoD, New York State, numerous tasks, and meet objectives that are the foundation for the academic models in the analysis of living systems of Biomedical Engineering are Leong), and the Computational Cancer research foundations, and University 6. an ability to develop and conduct programs designed by the Department is an important sign of the success of complemented by courses offered by Biology Laboratory (Professor Azizi). funding. The extensive facilities that are appropriate experimentation, of Biomedical Engineering at Columbia. contemporary activity. The programs other departments in The Fu Foundation These laboratories are supplemented at the Medical Center and Morningside analyze and interpret data, and The programs in biomedical offered in the Department of Biomedical School of Engineering and Applied with core facilities, including a tissue campus include teaching and research use engineering judgment to draw engineering at Columbia (B.S., Engineering seek to emphasize the Science and by many departments in culture facility, a histology facility, a laboratories that provide students conclusions M.S., Ph.D., Eng.Sc.D., and M.D./ confluence of basic engineering the Faculty of Medicine, the College confocal microscope, an atomic force with unusual access to contemporary 7. an ability to acquire and apply Ph.D.) prepare students to apply science and applied engineering with of Dental Medicine, and the Mailman research equipment specially selected microscope, a 2-photon microscope, new knowledge as needed, using engineering and applied science to the physical and biological sciences, School of Public Health, as well as the for its relevance to biomedical epifluorescence microscopes, a appropriate learning strategies. problems in biology, medicine, and particularly in the areas of biomechanics, science departments within the Graduate engineering. Another addition is an freezer room, biomechanics facilities, the understanding of living systems cell and tissue engineering, and School of Arts and Sciences. The undergraduate wet laboratory devoted a machine shop, and a specimen The undergraduate curriculum is and their behavior, and to develop biosignals and biomedical imaging. availability of these courses in a university to biomechanics and cell and tissue preparation room. designed to provide broad knowledge biomedical systems and devices. Programs in biomedical engineering that contains a large medical center engineering, together with a biosignals of the physical and engineering sciences Modern engineering encompasses are taught by its own faculty, members and enjoys a basic commitment to

ENGINEERING 2020–2021 ENGINEERING 2020–2021 64 and their application to the solution All biomedical engineering students faculty and emphasizes quantitative electives. Please see the course tables f. All 3000-level or higher courses individualized interests of the students. 65 of biological and medical problems. are expected to register for nontechnical applications of engineering principles in for schedules leading to a bachelor’s in the Earth and Environmental The following are suggested sample Students are strongly encouraged to electives, both those specifically required understanding biological systems and degree in biomedical engineering. Engineering program courses for various topic areas that take courses in the order specified by the School of Engineering and phenomena from molecular to organ It is strongly advised that students students may consider. Note that in the course tables; implications of Applied Science and those needed to system levels. In the fields of biomedical take required courses during the 2. Courses from the following students are not limited to these deviations must be discussed with a meet the 27-point total of nontechnical engineering, experimental techniques specific term that they are designated departments are not allowed to choices. All students are encouraged departmental adviser before registration. electives required for graduation. and principles are fundamental skills that in the course tables, as scheduling count toward the required 48 units of to design their own educational paths The first two years provides a strong good biomedical engineers must master. conflicts may arise if courses are taken engineering courses: through flexible technical electives while Beginning in junior year, all students grounding in the physical and chemical First and Second Years out of sequence. a. Department of Applied Physics and meeting the following requirements: (1) take the two-semester sequence sciences, engineering fundamentals, As outlined in this bulletin, in the first Applied Mathematics courses must be at the 3000-level or Biomedical engineering laboratory, I ­­& mathematics, and modern biology. two years, all engineering students Technical Elective Requirements b. Department of Computer Science above; (2) five of the seven electives II (BMEN E3810, E3820). In this two- This background is used to provide a are expected to complete a sequence Students are required to take at least c. Department of Industrial must meet the above criteria to be semester series, students learn through unique physical approach to the study of courses in mathematics, physics, 48 points of engineering content Engineering and Operations considered engineering content; and hands-on experience the principles and of biological systems. The last two years chemistry, computer science, coursework toward their degree. The Research (3) two of the seven electives must be methods of biomedical engineering of the undergraduate program provide engineering, modern biology, English 48-point requirement is a criterion d. Program of Materials Science and biomedical engineering courses. To help experimentation, measurement substantial exposure to fundamentals in composition, and physical education, as established by ABET. Taking into Engineering students choose their electives, the techniques, quantitative theories of biomedical engineering with emphasis consideration the number of engineering following suggested sample curricula well as nontechnical electives including biomedical engineering, data analysis, on the integration of principles of content points conferred by the required Once 48 points of engineering in various interest fields in biomedical the humanities. For most of these and independent design of biomedical biomedical engineering, quantitative courses of the BME curriculum, a content are satisfied, students may engineering are provided. Students do sequences, the students may choose engineering experiments, in parallel to analysis of physiology, and experimental portion of technical electives must be choose any course above the 3000 not need to follow them rigidly and may from two or more tracks. If there is a the Biomedical engineering I & II and quantification and measurements of clearly engineering in nature (Engineering level in Columbia Engineering as well substitute other courses, provided they question regarding the acceptability of Quantitative physiology I & II courses. In biomedical systems. Content Technical Electives), specifically as biology, chemistry, biochemistry, and a course as a nontechnical elective, addition, all students must take BMEN meet the requirements above. The common core biomedical as defined below: biotechnology as technical electives. please consult the approved listing of E4110: Biostatistics for engineers. In CELL AND TISSUE ENGINEERING engineering curriculum provides courses beginning on page 9 or contact If the 3000-level course is greater the senior year, students are required 1. Technical elective courses with CHEM UN2443: Organic chemistry I (3.5) a broad yet solid foundation in your advising dean for clarification. than or equal to the course cross to take a two-semester capstone sufficient engineering content that CHEM UN2444: Organics chemistry II (3.5) biomedical engineering. The flexible Please see the charts in this listed, its eligibility as an engineering BMCH E4500: Biological transport and rate design course, Biomedical engineering can count toward the 48 units of choice of technical electives in section for a specific description of content technical elective is determined processes (3) design (BMEN E3910 and E3920), in engineering courses required for the Department of Biomedical course requirements. which students work within a team to by the call letters of the first (owning) BMEN E4510: T issue engineering (3) ABET accreditation: BMEN E4590: BioMems: cellular and molecular Engineering, other departments in For students who are interested tackle an open-ended design project in department in the course name a. All 3000-level or higher courses applications (3) the Engineering School, as well as in the biomedical engineering major, designation. The department owning the biomedical engineering. The underlying in the Department of Biomedical BMEN E4210: Driving forces of biological systems in other departments in the arts and course must be ABET accredited to be they must take E1201: Introduction to philosophy of these core requirements Engineering, except BMEN E4010, (3) sciences allows students to broaden considered engineering. electrical engineering. For the computer is to provide our biomedical engineering E4103, E4104, E4105, E4106, BMEN E4550: Micro- and nanostructures in their biomedical engineering education For example, APBM E4560 Anatomy science requirement, students must students with a broad knowledge and E4107, E4108, and E6510; cellular engineering (3) to their individualized interests for a take ENGI E1006. They must take understanding of topics in the field of for physicists & engineers does not additionally, BMEN E4000 001 in BIOMECHANICS personalized curriculum. These qualities the two-semester BIOL UN2005 and biomedical engineering. count as engineering content technical fall 2019. (Note that only 3 points MECE E3100: Introduction to mechanics of fluids (3) allow the faculty to prepare students Parallel to these studies in core elective, since the course is owned UN2006: Introduction to Biology I & II in of BMEN E3998 may be counted EMEN E3105: Mechanics (4) for activity in all contemporary areas by Applied Physics (and cross-listed the second year, which gives students courses, students are required to take toward technical elective degree MECE E3113: Mechanics of solids (3) of biomedical engineering. Graduates a comprehensive overview of modern flexible technical elective courses (21 requirements.) with Biomedical Engineering). BMCH MECE E3301: Thermodynamics (3) of the program are equipped for biology from molecular to organ system points) to obtain an in-depth under- b. All 3000-level or higher courses E4810 Artificial organs is counted as an BMEN E4310: Solid biomechanics (3) employment in the large industrial levels. In addition, all students must take standing of their chosen interests. A in the Department of Mechanical engineering content technical elective, BMEN E4320: Fluid biomechanics (3) sector devoted to health care, which APMA E2101: Introduction to applied technical elective is defined as a 3000- Engineering, except MECE as the course is owned by Biomedical BMEN E4340: Biomechanics of cells (3) includes pharmaceuticals, medical Engineering (and cross listed with mathematics in their second year. level or above course taught in SEAS or E4007: Creative engineering and BIOSIGNALS AND BIOMEDICAL IMAGING devices, artificial organs, prosthetics Chemical Engineering). 3000-level or above courses in biology, entrepreneurship ELEN E3810: Signals and systems (3.5) and sensory aids, diagnostics, medical Third and Fourth Years chemistry, biochemistry, or biotechnol- c. All 3000-level or higher courses Based on the above for Engineering BMEN E4410: Ultrasound imaging (3) instrumentation, and medical imaging. The biomedical engineering programs ogy. Exceptions include organic chem- in the Department of Chemical Technical Electives, a cross-listed course BMEN E4420: Biosignal process and modeling (3) Graduates also accept employment at Columbia are based on engineering istry lecture courses and laboratory Engineering, except CHEN E4020: that is greater than or equal to 3000 BMEN E4430: Principles of MRI (3) in oversight organizations (FDA, and biological fundamentals. This is (which are 2000-level courses). At least Safeguarding intellectual and level and with BMEN as its starting call ELEN E4810: Digital signal processing (3) BMEN E4894: Biomedical imaging (3) NIH, OSHA, and others), medical emphasized in our core requirements, 15 points (five courses) of these technical business property letters will qualify as a BME Engineering BMEN E4898: Biophotonics (3) centers, and research institutes. They which cannot be waived nor substituted. electives must have engineering content, d. All 3000-level or higher courses Technical Elective. are prepared for graduate study in All students must take the two-semester while at least two of the five courses have in the Department of Electrical The accompanying charts describe NEURAL ENGINEERING biomedical engineering and several introduction to biomedical engineering to be from the Department of Biomedical Engineering, except EEHS E3900: the eight-semester degree program ELEN E3810: Signals and systems (3.5) related areas of engineering and the courses, BMEN E3010 and E3020: Engineering. The curriculum prepares History of telecommunications: schedule of courses leading to the BMEB W4020: Computational neuroscience: health sciences. Students can meet Biomedical engineering I & II, which students who wish to pursue careers in from the telegraph to the internet bachelor’s degree in biomedical circuits in the brain (3) entrance requirements for graduate provide a broad yet solid foundation in medicine by satisfying most requirements e. All 3000-level or higher courses engineering. BMEE E4030: Neural control engineering (3) BMEN E4420: Biosignal process and modeling (3) training in the various allied health the biomedical engineering discipline. in the premedical programs with no more in the Civil Engineering and The undergraduate Biomedical BMEN E4430: Principles of MRI (3) professions. No more than three Engineering Mechanics program, In parallel, all students take the two- than three additional courses. Some of Engineering program is designed to ELEN E4810: Digital signal processing (3) except CIEN E4128, E4129, E4130, additional courses are required to semester Quantitative physiology, I and II these additional courses may also be provide a solid biomedical engineering BMEN E4894: Biomedical imaging (3) satisfy entrance requirements for most sequence (BMEN E4001-E4002), which counted as nonengineering technical E4131, E4132, E4133, E4134, curriculum through its core requirements U.S. medical schools. is taught by biomedical engineering E4135, E4136, E4138, and E4140 while providing flexibility to meet the

ENGINEERING 2020–2021 ENGINEERING 2020–2021 MECE E4602: Introduction to robotics (3) 66 GENOMICS AND SYSTEMS BIOLOGY of medical students with world-class 67 ECBN E4060: Introduction to genomic information BMEE E4740: Bioinstrumentation (3) training in biomedical engineering at BIOMEDICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS science and technology (3) PREMED AND PRE-HEALTH PROFESSIONAL the graduate-level. This interdisciplinary BMEN E4150: The cell as a machine (3) MECE E3100: Introduction to mechanics of educational experience will prepare CHBM E4321: The genome and the cell (3) SEMESTER I SEMESTER II SEMESTER III SEMESTER IV fluids (3) students to become innovative leaders BMEN E4420: Biosignal process and modeling (3) EMEN E3105: Mechanics (4) in science, engineering, and medicine. CHEN E4700: Principles of genomic technologies MATH UN1102 (3) APMA E2000 (4) either semester MECE E3113: Mechanics of solids (3) MATHEMATICS (3) The program is open to a select group CHEM UN2443: Organic chemistry I (3.5) CHEN E4760: Genomics sequence laboratory (3) of Columbia medical students and CHEM UN2444: Organic chemistry II (3.5) CHEN E4800: Protein engineering (3) makes possible the earning of both PHYSICS UN1401 (3) UN1402 (3) UN1403 (3) BMEN E4310: Solid biomechanics (3) the M.D. and M.S. degree in 5 years (three tracks, UN1601 (3.5) UN1602 (3.5) UN2601 (3.5) QUANTITATIVE BIOLOGY BMEN E4320: Fluid biomechanics (3) choose one) (4 years for the M.D. program, 1 year UN2801 (4.5) UN2802 (4.5) BMEB W4020: Computational neuroscience: for the M.S. program). Six points from circuits in the brain (3) To meet entrance requirements the M.D. degree, through completion UN1403 (4) UN1404 (4) ECBN E4060: Introduction to genomic information of most U.S. medical schools, stu- of anatomy coursework, will also count CHEMISTRY UN1500 (3) (or semester 1) science and technology (3) dents will need to take BIOC UN3501 (three tracks, toward the Master of Science degree. choose one) UN1604 (4) UN1507 (3) BIOL GU4070: The biology and physics of single Biochemistry: Structure and metabolism UN2045 (4) UN2046 (4), UN1507 (3) molecules (3.5) Students must apply separately to the (4), CHEM UN2545 Organic chem- BMEN E4310: Solid biomechanics (3) Department of Biomedical Engineering. istry laboratory (3), PHYS UN1493: BMEN E4320: Fluid biomechanics (3) For more information on requirements UNIVERSITY CC1010 (3) either semester Introduction to experimental physics (3), WRITING APMA E4400: Introduction to biological modeling and application process, please visit and PSYC UN1001: The science of psy- (3) bme.columbia.edu. CHEN E4650: Biopolymers (3) chology (3) as well. COMPUTER ENGI E1006 (3) SCIENCE (or semester II) BIOINDUCTIVE AND BIOMIMETIC MATERIALS GRADUATE PROGRAMS CHEM UN2443: Organic chemistry I (3.5) DUAL DEGREE PROGRAMS The graduate curriculum in biomedical PHYSICAL BMCH E4500: Biological transport and rate 1 UN1001 (1) UN1002 (1) processes (3) Integrated B.S./M.S. Program in engineering is track-free at the master’s EDUCATION BMEN E4510: T issue engineering (3) Biomedical Engineering level while at the doctoral level, it BMEN E4590: BioMems: cellular and molecular The B.S./M.S. degree program is consists of three tracks: biomechanics, THE ART OF ENGI E1102 (4) 1 applications (3) open to a select group of Columbia cell and tissue engineering, and ENGINEERING (or in semester I) CHEN E4620: Introduction to polymers and soft juniors and makes possible the biosignals and biomedical imaging. materials (3) earning of both the B.S. and M.S. Initial graduate study in biomedical CHEN E4640: Polymer surface and interface (3) HUMA CC1002, engineering is designed to expand the COCI CC1102, degrees in an integrated fashion. HUMA CC1001, CHEN E4800: Protein engineering (3) HUMA UN1121 (3) Global Core (3–4) Benefits of this program include the student’s undergraduate preparation NONTECHNICAL COCI CC1101, or REQUIREMENTS1 or UN1123 (3) BIOMATERIALS matching of graduate courses with the in the direction of the concentration of or Global Core (3–4) ECON UN1105 (4) and CHEM UN2443: Organic chemistry I (3.5) corresponding prerequisites, a greater interest. In addition, sufficient knowledge UN1155 recitation (0) BMCH E3000: Biological transport process (3) ability to plan ahead for optimal course is acquired in other areas to facilitate BMEN E4301: Structure, mechanics, and planning, and a simplified application broad appreciation of problems and adaptation of bone (3) ELEN E1201 APMA E2101 (3) process with no GRE required. Up effective collaboration with specialists BMEN E4310: Solid biomechanics (3) from other scientific, medical, and Intro. to EE­ (3.5) Intro. to applied math BMEN E4510: T issue engineering (3) to 6 points from the B.S. degree TECHNICAL engineering disciplines. The Department REQUIREMENTS BMEN E4590: BioMems: cellular and molecular requirements, specifically BMEN BIOL UN2005 BIOL UN2006 (4) applications (3) E4001 and E4002, will also count of Biomedical Engineering offers a Intro. to Biology, I (4) Intro to Biology, II ELEN E4944: Principles of device toward fulfilling the M.S. degree course graduate program leading to the Master of Science degree (M.S.), the Doctor microfabrication (3) requirements. To qualify for this program, 202 192 14.52 152 of Philosophy degree (Ph.D.), and the TOTAL POINTS BIOMEMS AND NANOTECHNOLOGY students must have a cumulative GPA Doctor of Engineering Science degree MECE E3100: Introduction to mechanics of fluids (3) of at least 3.4 and should apply for the (Eng.Sc.D.). Applicants who have a 1 EMEN E3105: Mechanics (4) program by April 30 in their junior year. Students can mix these requirements according to what is available. Master of Science degree or equivalent 2 Estimations MECE E3113: Mechanics of solids (3) For more information on requirements may apply directly to the doctoral MSAE E4090: Nanotechnology (3) and application process, please visit degree program. All applicants are • Biomechanics: One year of biology ordinary differential equations, Fourier Department of Biomedical Engineering MECE E4212: Microelectromechanical systems (3) bme.columbia.edu. BMEN E4550: Micro- and nanostructures in expected to have earned the bachelor’s and/or physiology, solid mechanics, analysis, digital signal processing. also admits students into the 4-2 cellular engineering (3) degree in engineering or in a cognate statics and dynamics, fluid mechanics, program, which provides the opportunity BMEN E4590: BioMems: cellular and molecular M.D./M.S. Program in Biomedical scientific program. The Graduate ordinary differential equations. Applicants lacking some of these for students holding a bachelor’s degree applications (3) Engineering Record Examination (General Test only) • Cell and Tissue Engineering: One courses may be considered for from certain physical sciences to receive The Doctor of Medicine/Master of ROBOTICS AND CONTROL OF BIOLOGICAL is required of all applicants. Students year of biology and/or physiology, admission with stipulated deficiencies the M.S. degree after two years of study Science in Biomedical Engineering SYSTEMS whose bachelor’s degree was not one year of organic chemistry or that must be satisfied in addition to the at Columbia. (M.D./M.S.) program is an integrated MECE E3100: Introduction to mechanics of earned in a country where English is the biochemistry with laboratory, fluid requirements of the degree program. M.S. students must complete the fluids (3) program offered between The Fu dominant spoken language are required mechanics, rate processes, ordinary Columbia Engineering does not admit professional development and leadership EMEN E3105: Mechanics (4) Foundation School of Engineering and to take the TOEFL test. In addition, for differential equations. students holding the bachelor’s degree course, ENGI E4000, as a graduation MECE E3113: Mechanics of solids (3) Applied Science and the College of the doctoral program, the individual • Biosignals and Biomedical Imaging: directly to doctoral studies; admission requirement. Ph.D. candidates are strongly BMEE E4030: Neural control engineering (3) Physicians and Surgeons at Columbia tracks require applicants to have taken One year of biology and/or physiology is offered either to the M.S. program or encouraged to complete ENGI E6001– MEBM E4439: Modeling and identification of University. The purpose of this program the following foundation courses: and/or biochemistry. Linear algebra, to the M.S. program/doctoral track. The 6004 and should consult their program dynamic systems (3) is to supplement the current training for PDL requirements.

ENGINEERING 2020–2021 ENGINEERING 2020–2021 BMEN E6505: Advanced biomaterials and tissue EEME E6610: Optimal control theory (3) 68 Doctoral Qualifying Examination 69 engineering (3) MECE E6614: Advanced topics in robotics and Doctoral candidates are required to BIOMEDICAL ENGINEERING: THIRD AND FOURTH YEARS BMEN E9100: Master's research (3) mechanism synthesis (3) MECE E6615: Robotic manipulation (3) pass a qualifying examination. This BIOMECHANICS SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII BMEN E9100: Master's research (3) examination is given once a year, and MECE E4100: Mechanics of fluids (3) it should be taken after the student has BMEN E4301: Structure, mechanics, and BMEN E3010 (3) completed 30 points of graduate study. BMEN E3020 (3) adaptation of bone (3) Doctoral Degree Biomedical eng., I The qualifying examination consists of Biomedical eng., II BMEN E3910 (4) BMEN E3920 (4) BMEN E4302: Biomechanics of musculoskeletal Doctoral students must complete BME design, I BME design, II an oral exam during which the student BMEN E3810 (3) soft tissues (3) a program of 30 points of credit BMEN E3820 (3) BMEN E4305: Cardiac mechanics (3) presents an analysis of assigned BME laboratory, I 1 1 beyond the M.S. degree. The core REQUIRED BME laboratory, II Technical elective (3) Technical elective (3) BMEN E4310: Solid biomechanics (3) scientific papers, as well as answers course requirements (9 credits) for the COURSES BMEN E4001 (3) BMEN E4570: Science and engineering of body to questions in topics covering applied BMEN E4002 (3) Technical elective (3)1 Technical elective (3)1 doctoral program include the course in Quantitative physiol., I fluids (3) mathematics, quantitative biology and Quantitative physiol., II computational modeling of physiological Technical elective (3)1 Technical elective (3)1 BMME E4702: Advanced musculoskeletal physiology, and track-specific material. BMEN E4110 (4) Technical elective (3)1 biomechanics (3) systems (BMEN E6003), plus at least Biostat. for engineers The committee consists of the thesis MEBM E4703: Molecular mechanics in biology. (3) two graduate mathematics courses adviser and two BME core faculty MEBM E4710: Morphogenesis: shape and (one of these can be a graduate-level members approved by the graduate structure in biological materials (3) NONTECH 3 points 3 points 3 points Biostatistics course). If BMEN E6003 studies committee. A written analysis of ELECTIVES BMEN E4750: Sound and hearing (3) has already been taken for the master’s the assigned scientific papers must MECE E6100: Advanced mechanics of fluids (3) degree, a technical elective can be BMEN E6301: Modeling of biological tissues with be submitted prior to the oral exam. TOTAL POINTS 16 15 16 13 used to complete the core course finite elements (3) A minimum cumulative grade-point requirement. If one or both graduate MEBM E6310-E6311: Mixture theories for average of 3.2 without research 1 level mathematics courses have been Five of seven technical electives must have engineering content, and two of them must be from the Biomedical Engineering Department. biological tissues, I and II (3) credit grades is required to register taken for the master's degree, technical MECE E6422-E6423: Introduction to the theory of for this examination. elasticity, I and II (3) elective(s) can be used as a substitution. CURRICULUM AND EXAM 6003, Applied Math, BMEN 9700, four BMEN E4894: Biomedical imaging (3) BMEN E9070: Massively parallel neural MECE E8501: Advanced continuum biomechanics Students must register for BMEN REQUIREMENTS BMEN courses, three SEAS courses, computation (3) (3) E9700: Biomedical engineering seminar Doctoral Committee and Thesis and 1 SEAS/non-SEAS course), with BMEN E9100: Master's research (3) BMEN E9100: Master's tesearch (3) and for research credits during the Students who pass the qualifying Master’s Degree one exception: students must take at examination must have a core BME DESIGN, INNOVATION, AND BIOMEDICAL IMAGING first two semesters of doctoral study. In consultation with an appointed least 12 credits from a list of courses. faculty member who will serve as their ENTREPRENEURSHIP BMEN E4410: Ultrasound in diagnostic imaging(3) Remaining courses should be selected faculty adviser, M.S. students should BIOINFORMATICS AND MACHINE LEARNING primary research adviser or co-adviser. ENGI W4100: Research to revenue (3) BMEN E4420: Biomedical signal processing and in consultation with the student’s faculty select a program of 30 points of credit Each student is expected to submit BINF G4006: Translational bioinformatics (3) BIOT GU4180: Entrepreneurship in biotechnology signal modeling (3) adviser to prepare for the doctoral of graduate courses (4000 level or BINF G4015: Computational systems biology: (3) BMEN E4430: Principles of magnetic resonance qualifying examination and to develop a research proposal and present it above) appropriate to their career proteins, networks, functions (3) BIOT W4200: Biopharmaceutical development imaging (3) expertise in a clearly identified area of to a committee that consists of three ECBM E4040: Neural networks and deep learning goals. This program must include the and regulation (3) BMEE E4740: Bioinstrumentation (3) biomedical engineering. Students should core BME faculty members (including (3) course in computational modeling of IEME E4200: Intro to human centered design ELEN E4810: Digital signal processing (3) not receive more than two "C" or below research adviser) before the end of STAT GU4241: Statistical machine learning (3) BMEN E4840: Functional imaging for the brain (3) physiological systems (BMEN E6003); (3) letter grades. year 4. The committee considers the COMS W4252: Introduction to computational BMEN E4894: Biomedical imaging (3) two semesters of BMEN E9700: IEME E4310: Manufacturing enterprise (3) All graduate students admitted scope of the proposed research, its learning theory (3) MECE E4604: Product design for BMEN E4895: Analysis and quantification of Biomedical engineering seminar; at to the doctoral degree program suitability for doctoral research and BMEN E4420: Biomedical signal processing and manufacturability (3) medical images (3) least four other biomedical engineering signal modeling (3) MECE E4610: Advanced manufacturing processes BMEN E4898: Biophotonics (3) must satisfy the equivalent of two the appropriateness of the research courses where BME is the course's BMEN E4520: Synthetic biology: principles of (3) BMEN E6410 : Principles and practices of in vivo semesters’ experience in teaching (one plan. The committee may approve owning department; and at least one genetic circuits (3) IEOR E4570: Entrepreneurship bootcamp (1.5) magnetic resonance spectroscopy (3) semester for M.D./Ph.D. students). the proposal without reservation or graduate-level mathematics course BMEN E4460: Deep learning in Biomedical BMEE E4740: Bioinstrumentation (3) BMEN E9100: Master's research (3) This may include supervising and may recommend modifications. In Engineering (3) (excluding statistics). Up to 6 credits of BMEN E6005: Biomedical innovation I (3) assisting undergraduate students general, the student is expected to COMS W4701: Artificial intelligence (3) ROBOTICS AND CONTROL OF BIOLOGICAL Master’s Research BMEN E9100 may BMEN E6006: Biomedical innovation II (3) submit his/her research proposal after CBMF W4761: Computational genomics (3) SYSTEMS in laboratory experiments, grading, be taken to fulfill degree requirements. BMEN E6007: Lab-to-market: commercializing and preparing lecture materials to five semesters of doctoral studies. COMS W4771: Machine learning (3) biomedical innovations (3) BMEE E4030: Neural control engineering (3) Students with deficiency in physiology COMS W4772 (E6772): Advanced machine MECE E4058: Mechatronics and embedded support the teaching mission of the In accordance with regulations of coursework are required to take the learning (3) BIOMATERIALS AND TISSUE ENGINEERING microcomputer control (3) department. The requirement must be the Graduate School of Arts and BMEN E4001-E4002 sequence before BMEN E4895: Analysis and quantification of BMEN E4210: Driving forces of biological systems BMEN E4420: Biomedical signal processing and completed by the 3rd year of graduate Sciences, each student is expected to taking BMEN E6003. Candidates must medical images (3) (3) signal modeling (3) studies. The Department of Biomedical submit a thesis and defend it before achieve a minimum grade-point average BMEN E9100: Master's research (3) BMCH E4500: Biological transport and rate MEBM E4439: Modeling and identification of Engineering is the only engineering a committee of five faculty, one of processes (3) dynamic systems (3) of 2.5. A thesis based on experimental, NEURAL ENGINEERING department that offers Ph.D. training whom holds primary appointment EEME E4601: Digital control systems (3) computational, or analytical research is BMEN E4501: Biomaterials (3) to M.D./Ph.D. students. These in another department or school or BMEB W4020: Computational neuroscience: BMEN E4510: Tissue engineering (3) MECE E4602: Introduction to robotics (3) optional. Students wishing to pursue the candidates are expected to complete university. Every doctoral candidate is circuits in the brain (3) BMEN E4530: Drug and gene delivery (3) MECS E4603: Applied robotics: algorithms and Master’s Thesis option should register their Ph.D. program within 3.5 years, required to have had at least one first- BMEE E4030: Neural control engineering (3) BMEN E4550: Micro- and nanostructures in software (3) for BMEN E9100 Master’s Research and BMEN E4050: Electrophysiology of human cellular engineering (3) MECE E4606: Digital manufacturing (3) with otherwise the same requirements author full-length paper accepted for consult with their BME faculty adviser. memory and navigation (3) BMEN E4580: Fundamentals of nanobioscience BMME E4702: Advanced musculoskeletal as those outlined for the Doctoral publication in a peer-reviewed journal M.S. students can also declare BMEN E4420: Biomedical signal processing and and nanobiotechnology (3) biomechanics (3) Degree program. prior to recommendation for award of a concentration listed below. The signal modeling (3) BMEN E4590: BioMems: cellular and molecular BMEE E4740: Bioinstrumentation (3) the degree. requirements for these elective BMEN E4430: Principles of magnetic resonance applications (3) MECE E6400: Advanced machine dynamics (3) concentrations are identical to those imaging (3) BMEN E6500: Tissue and molecular engineering EEME E6601: Introduction to control theory (3) ELEN E4810: Digital signal processing (3) of the standard track (including BMEN laboratory (4) EEME E6602: Modern control theory (3)

ENGINEERING 2020–2021 ENGINEERING 2020–2021 testing. Statistical analysis of experimental molecular level are examined in a highly ECBM E4040x or y Neural networks and deep external visual and audio signals. sized machines, basic physical aspects of cell 70 COURSES IN BIOMEDICAL 71 measurements. Analysis of variance, post hoc quantitative context. Topics include chemical learning components (diffusion, mechanics, electrostatics, BMEN E4103x Anatomy of the thorax and ENGINEERING testing. Fluid shear and cell adhesion, neuro- kinetics, molecular binding and enzymatic 3 pts. Lect: 3. Professor Kostic. hydrophobicity), energy transduction (motors, abdomen BMEN E1001x Engineering in medicine electrophysiology, soft tissue biomechanics, processes, molecular motors, biological mem- Prerequisites: BMEB W4020 or BMEE E4030 or transporters, chaperones, synthesis complexes), 2 pts. Lect: 2. Not offered in 2020–2021. 3 pts. Lect: 3. Not offered in 2020–2021. biomedical imaging and ultrasound, branes, and muscles. ECBM E4090 or ELEN E4750 or COMS W4771 basic cell functions. Biophysical principles, Prerequisite: Graduate standing in Biomedical The present and historical role of engineering in characterization of excitable tissues, microfluidics. or an equivalent. Developing features and inter- feedback controls for robust cell function, BMEN E4002y Quantitative physiology, II: Engineering. Designed for the Biomedical medicine and health care delivery. Engineering nal representations of the world, artificial neural adaptation to environmental perturbations. BMEN E3910x-E3920y Biomedical engineering organ systems Engineering graduate student interested in approaches to understanding organismic and networks, classifying handwritten digits with design, I and II 3 pts. Lect: 3. Professor Morrison. acquiring in-depth knowledge of anatomy relevant BMEN E4210y Driving forces of biological cellular function in living systems. Engineering in logistics regression, feedforward deep networks, 4 pts. Lect: 1. Lab: 3. Professors Hillman and Prerequisites: BIOL UN2005 and UN2006. to his/her doctoral research. Lectures and tutorial systems the diagnosis and treatment of disease. Medical back propagation in multilayer perceptrons, Sajda. Corequisites: BMEN E3020, E3820. Students are sessions may be taken with or without the 4 pts. Lect: 4. Professor Sia. imaging, medical devices: diagnostic and surgical regularization of deep or distributed models, opti- A two-semester design sequence to be taken in introduced to a quantitative, engineering approach Prerequisites: CHEM UN1404 and MATH UN1202 instruments, drug delivery systems, prostheses, associated laboratory (BMEN E4104). the senior year. Elements of the design process, to cellular biology and mammalian physiology. mization for training deep models, convolutional or AMPA E2000. Corequisite: BIOL UN2005 or artificial organs. Medical informatics and with specific applications to biomedical engineering: Beginning with biological issues related to the cell, neural networks, recurrent and recursive neural BMEN E4104x Anatomy laboratory: thorax equivalent. Introduction to the statistical mechanics organization of the health care system. Current concept formulation, systems synthesis, design the course progresses to considerations of the networks, deep learning in speech, and object and abdomen and thermodynamics of biological systems, with trends in biomedical engineering research. analysis, optimization, biocompatibility, impact major physiological systems of the human body recognition. 2 pts. Lect: 2. Not offered in 2020–2021. a focus on connecting microscopic molecular Prerequisites: Graduate standing in Biomedical BMEN E3010x Biomedical engineering, I on patient health and comfort, health care costs, (nervous, circulatory, respiratory, renal). BMEN E4050x or y Electrophysiology of properties to macroscopic states. Both classical regulatory issues, and medical ethics. Selection and Engineering. Corequisites: BMEN E4103. and statistical thermodynamics will be applied 3 pts. Lect: 3. Professor Wang. BMEN E4010y Ethics for biomedical engineers human memory and navigation execution of a project involving the design of an to biological systems; phase equilibria, chemical Prerequisites: BIOL UN2005 and UN2006, or 2 pts. Lect: 2. Not offered in 2020–2021. 3 pts. Lect: 3. Professor Jacobs. BMEN E4105x Anatomy of the extremities actual engineering device or system. Introduction reactions, and colligative properties. Topics in instructor’s permission. Corequisites: BMEN Prerequisite: senior status in biomedical Prerequisites: Instructor's permission. Human 2 pts. Lect: 2. Not offered in 2020–2021. to entrepreneurship, biomedical start-ups, and modern biology, macromolecular behavior in E4001, BMEN E3810. Various concepts within engineering or the instructor’s permission. memory, including working, episodic, and Prerequisite: Graduate standing in Biomedical venture capital. Semester I: statistical analysis of solutions and interfaces, protein-ligand binding, the field of biomedical engineering, foundational Covers a wide range of ethical issues expected to procedural memory. Electrophysiology of cognition, Engineering. Designed for the Biomedical detection/classification systems (receiver operation and the hydrophobic effect. knowledge of engineering methodology applied confront graduates as they enter the biotechnology noninvasive and invasive recordings. Neural Engineering graduate student interested in to biological and/or medical problems through characteristic analysis, logistic regression), industry, research, or medical careers. Topics vary basis of spatial navigation, with links to spatial acquiring in-depth knowledge of anatomy relevant BMEN E4301x Structure, mechanics, and modules in biomechanics, biomaterials, and cell development of design prototype, need, approach, and incorporate guest speakers from Physicians and episodic memory. Computational models of to his/her doctoral research. Lectures and tutorial adaptation of bone and tissue engineering. benefits and competition analysis. Semester II: and Surgeons, Columbia Law School, Columbia memory, brain stimulation, lesion studies. sessions may be taken with or without the spiral develop process and testing, iteration and 3 pts. Lect: 3. Not offered in 2020–2021. College, and local industry. BMEN E3020y Biomedical engineering, II refinement of the initial design/prototype, and ECBM E4060x Introduction to genomic associated laboratory (BMEN E4106). Introduction to structure, physiology, and 3 pts. Lect: 3. Professor Lu. biomechanics of bone. Structure, function, business plan development. A lab fee of $100 each BMEB W4020x Computational neuroscience: information BMEN E4106x Anatomy laboratory: and physiology of skeletal bones; linear elastic Prerequisites: BIOL UN2005 and UN2006, or is collected. circuits in the brain 3 pts. Lect: 3. Professor Anastassiou. extremities properties of cortical and trabecular bone; instructor’s permission. Corequisites: BMEN 3 pts. Lect: 3. Professor Lazar. Prerequisites: None. Introduction to the BMEN E3998x or y Projects in biomedical 2 pts. Lab: 2. Not offered in 2020–2021. anisotropy and constitutive models of bone tissue; E4002, BMEN E3820. Various concepts within Prerequisite: ELEN E3801 or BIOL UN3004. The information system paradigm of molecular engineering Prerequisites: Graduate standing in Biomedical failure and damage mechanics of bone; bone the field of biomedical engineering, foundational biophysics of computation: modeling biological biology. Representation, organization, structure, 1–3 pts. Hours to be arranged. Members of the Engineering. Corequisites: BMEN E4105. adaptation and fracture healing; experimental knowledge of engineering methodology applied neurons, the Hodgkin-Huxley neuron, modeling function and manipulation of the biomolecular faculty. determination of bone properties; and morphological to biological and/or medical problems through channel conductances and synapses as sequence of nucleic acids and proteins. The role of BMEN E4107x Anatomy of the head and neck Independent projects involving experimental, analysis of bone microstructure. modules in biomechanics, bioinstrumentation, and memristive systems, bursting neurons and central enzymes and gene regulatory elements in natural 2 pts. Lect: 2. Not offered in 2020–2021. theoretical, computational, or engineering design biomedical imaging. pattern generators, I/O equivalence and spiking biological functions as well as in biotechnology Prerequisite: Graduate standing in Biomedical BMEN E4302x Biomechanics of work. May be repeated, but no more than 3 points Engineering. Designed for the Biomedical neuron models. Information representation and and genetic engineering. Recombination and musculoskeletal soft tissues ECBM E3060x Introduction to genomic of this or any other projects or research course may Engineering graduate student interested in neural encoding: stimulus representation with other macromolecular processes viewed as 3 pts. Lect: 3. Professor Reuther. information science and technology be counted toward the technical elective degree acquiring in-depth knowledge of anatomy relevant time encoding machines, the geometry of time mathematical operations with simulation and Prerequisite: ENME E3113 or equivalent. 3 pts. Lect: 3. Professor Varadan. requirements as engineering technical electives. to his/her doctoral research. Lectures and tutorial encoding, encoding with neural circuits with visualization using simple computer programming. Restricted to seniors and graduate students. Introduction to the information system paradigm of sessions may be taken with or without the BMEN E3999x, y or s Fieldwork feedback, population time encoding machines. Biomechanics of orthopaedic soft tissues molecular biology. Representation, organization, ECBM E4070y Computing with brain circuits associated laboratory (BMEN E4108). 1–2 pts. Professor Kam. Dendritic computation: elements of spike processing (cartilage, tendon, ligament, meniscus, etc.). structure, function and manipulation of the of model organisms Prerequisites: Obtained internship and approval and neural computation, synaptic plasticity and biomolecular sequences of nucleic acids and 3 pts. Lect: 3. Professor Lazar. BMEN E4108x Anatomy laboratory: head Basic and advanced viscoelasticity applied to from faculty adviser. BMEN undergraduate learning algorithms, unsupervised learning and proteins. The role of enzymes and gene regulatory Prerequisites: ELEN E3801 or BIOL W3004, and and neck the musculoskeletal system. Topics include students only. May be used toward the 128-credit spike time-dependent plasticity, basic dendritic elements in natural biological functions as well Python programming experience, or instructor's 2 pts. Lab: 2. Not offered in 2020–2021. mechanical properties, applied viscoelasticity degree requirement. Only for BMEN undergraduate integration. Projects in MATLAB. as in biotechnology and genetic engineering. permission. Building the functional map of the fruit Prerequisites: Graduate standing in Biomedical theory, and biology of orthopaedic soft tissues. students who include relevant off-campus work Recombination and other macromolecular BMEE E4030x Neural control engineering fly brain. Molecular transduction and spatio-temporal Engineering. Corequisites: BMEN E4107. experience as part of their approved program of BMEN E4305y Cardiac mechanics processes viewed as mathematical operations with 3 pts. Lect: 3. Professor Wang. encoding in the early visual system. Predictive study. Final report and letter of evaluation required. BMEN E4110x Biostatistics for engineers 3 pts. Lect: 3. Not offered in 2020–2021. simulation and visualization using simple computer Prerequisites: ELEN E3801. Topics include coding in the Drosophila retina. Canonical circuits Fieldwork credits may not count toward any 4 pts. Lect: 4. Professor Jacobs. Prerequisites: BMEN E4310 and BMEN E4320 or basic cell biophysics, active conductance and in motion detection. Canonical navigation circuits programming. Shares lectures with ECBM E4060, major core, technical, elective, and nontechnical Prerequisites: MATH UN1202 or APMA E2000 equivalents. Cardiac anatomy, passive myocardial the Hodgkin-Huxley model, simple neuron in the central complex. Molecular transduction but the work requirements differ somewhat. requirements. May not be taken for pass/fail credit and APMA E2101. Fundamental concepts of constitutive properties, electrical activation, models, ion channel models and synaptic and combinatorial encoding in the early olfactory BMEN E3810x Biomedical engineering or audited. probability and statistics applied to biology and ventricular pump function, ventricular-vascular models, statistical models of spike generation, system. Predictive coding in the antennal lobe. The medicine. Probability distributions, hypothesis laboratory, I coupling, invasive and noninvasive measures of BMEN E4000x or y Special topics Wilson-Cowan model of cortex, large-scale functional role of the mushroom body and the later- testing and inference, summarizing data and 3 pts. Lab: 4. Professor Hess. regional and global function, models for predicting 3 pts. Lect: 3. Members of the Faculty. electrophysiological recording methods, al horn. Canonical circuits for associative learning testing for trends. Signal detection theory and Fundamental considerations of wave mechanics; ventricular wall stress. Alterations in muscle Current topics in biomedical engineering. sensorimotor integration and optimal state and innate memory. Projects in Python. the receiver operator characteristic. Lectures design philosophies; reliability and risk concepts; properties and ventricular function resulting Subject matter will vary by year. Instructors estimation, operant conditioning of neural accompanied by data analysis assignments basics of fluid mechanics; design of structures ECBM E4090x or y Brain computer interfaces from myocardial infarction, heart failure, and left may impose prerequisites depending on the activity, nonlinear modeling of neural systems, using MATLAB and R as well as discussion of subjected to blast; elements of seismic design; (BCI) laboratory ventricular assist. topic. sensory systems: visual pathway and bioethics and case studies in biomedicine. elements of fire design; flood considerations; 3 pts. Lect: 2. Lab: 3. Professor Mesgarani. somatosensory pathway, neural encoding BMEN E4310x or y Solid biomechanics advanced analysis in support of structural design. BMEN E4001x Quantitative physiology, I: cells Prerequisite: ELEN E3801. Hands-on experience model: spike triggered average (STA) and spike BMEN E4150x The cell as a machine 3 pts. Lect: 3. Professor Guo. and molecules with basic neural interface technologies. Recording 3 pts. Lect: 3. Not offered in 2020–2021. BMEN E3820y Biomedical engineering triggered covariance (STC) analysis, neuronal Prerequisites: ENME-MECE E3105 and ENME 3 pts Lect: 3. Professor Kam. EEG (electroencephalogram) signals using data Prerequisite: MATH UN1101 or equivalent. E3113. Applications of continuum mechanics to laboratory, II response to electrical micro-stimulation, DBS Prerequisites: BIOL UN2005 and UN2006. acquisition systems (noninvasive scalp recordings). Corequisites: One semester of BIOL UN2005 the understanding of various biological tissues 3 pts. Lab: 4. Professor Hung. for Parkinson’s disease treatment, motor neural Corequisites: BMEN E3010 and E3810. Real-time analysis and monitoring of brain or BIOC UN3501, and one semester of PHYS properties. The structure, function, and mechanical Biomedical experimental design and hypothesis prostheses, and sensory neural prostheses. Physiological systems at the cellular and responses. Analysis of intention and perception of UN1401 or equivalent. Cells as complex micron- properties of various tissues in biological systems,

ENGINEERING 2020–2021 ENGINEERING 2020–2021 such as blood vessels, muscle, skin, brain tissue, equivalents. Survey of experiments and theoretical BMEN E4430x Principles of magnetic neural networks and recurrent neural networks. substitutes. Topics include biocompatibility, asymmetry, lipid-protein interactions, membrane 72 73 bone, tendon, cartilage, ligaments, etc., are analyses of the mechanical behavior of individual resonance imaging Deep autoencoders for denoising. Segmentation biological grafts, gene therapy-transfer, and turnover, membrane fusion, transport, lipid phase examined. The establishment of basic governing living nonmuscle cells. Emphasis on quantitative 3 pts. Lect: 3. Professor Juchem. and classification of biological tissues and bioreactors. behavior. In the second half of the semester, mechanical principles and constitutive relations for analytic description using continuum mechanics Prerequisites: PHYS UN1403 and APMA E2101, biomarker of disease. Theory and methods students will lead discussions of recent journal BMEN E4520x Synthetic biology: principles of each tissue. Experimental determination of various and molecular level theory from the standpoint or instructor’s permission. Fundamental principles lectures will be accompanied with examples from articles. tissue properties. Medical and clinical implications of statistical mechanics and mechanical models. of Magnetic Resonance Imaging (MRI), including biomedical image including analysis of neurological genetic circuits of tissue mechanical behavior. Mechanics of erythrocytes, leukocytes, endothelial the underlying spin physics and mathematics images of the brain (MRI), CT images of the 3 pts. Lect: 3. Professor Danino. BMEN E4570x Science and engineering of cells, and fibroblasts; models of aggregation, of image formation with an emphasis on the lung for cancer and COPD, cardiac ultrasound. Basic principles of synthetic biology and survey body fluids BMEN E4320x or y Fluid biomechanics adhesion, locomotion, amoeba motility, cell division application of MRI to neuroimaging, both Programming assignments will use tensorflow/ of the field. Fundamentals of biological circuits, 3 pts. Lect: 3. Not offered in 2020–2021. 3 pts. Lect: 3. Professor Guo. and morphogenesis; molecular level models of anatomical and functional. The course examines Pytorch and Jupyter Notebook. Examinations and including circuit design, modern techniques for Prerequisites: General chemistry, organic Prerequisites: APMA E2101, ENME E3105, actin, myosin, microtubules, and intermediate both theory and experimental design techniques. a final project will also be required. DNA assembly, quantitative characterization of chemistry, and basic calculus. Body fluids as a and MECE E4100. The principles of continuum filaments and relation to mechanical properties genetic circuits, and ODE modeling of biological dilute solution of polyelectrolyte molecules in BMEN E4480x Statistical machine learning for mechanics as applied to biological fluid flows of cells and cytoskeleton. Alternative models of MEBM E4439x Modeling and identification of circuits with MATLAB. Knowledge of biology, water. Study of physical behavior as affected and transport. Continuum formulations of basic cytoskeletal mechanics, foam theory, tensegrity. dynamic systems genomics ordinary differential equations, and MATLAB will be by the presence of ions in surrounding conservation laws, Navier-Stokes equations, Analysis of experimental techniques including 3 pts. Lect: 3. Professor Chbat. 3 pts. Lect: 3. Professor Azizi. assumed. Intended for advanced undergraduate environments. The physics of covalent, ionic, Prerequisites: APMA E2101, MATH UN1202, mechanics of arterial and venous blood flow, blood micropipette studies, optical and magnetic Prerequisites: APMA E2101, ELEN E3801 and graduate students. and hydrogen bonds are reviewed, in relation or corequisite EEME E3601, or instructor’s MATH UN2010, Proficiency in Python/R rheology and non-Newtonian properties, flow and cytometry, and nanoindentation. to the structure/properties of the body fluid. permission. Generalized dynamic system programming, and background in probability/ BMEN E4530x Drug and gene delivery transport in the microcirculation, oxygen diffusion, Selected physiological processes are examined in BMEE E4400x Wavelet applications in modeling and simulation. Fluid, thermal, statistics. Recommended: COMS W4771. 3 pts. Lect: 3. Professor Leong. capillary filtration. physical-chemical terms for polymers. biomedical image and signal processing mechanical, diffusive, electrical, and hybrid Introduction to statistical machine learning Prerequisites: BMEN E3010. Application of CHBM E4321y The genome and the cell 3 pts. Lect: 3. Not offered in 2020–2021. systems are considered. Nonlinear and high methods using applications in genomic data polymers and other materials in drug and gene BMEN E4580y Foundations of nanobioscience 3 pts. Lect: 3. Not offered in 2020–2021. Prerequisite: APMA E2101 or E3101 or equivalent. order systems. System identification problem and and in particular high-dimensional single-cell delivery, with focus on recent advances in field. and nanobiotechnology Prerequisites: BIOL UN2005 and MATH UN2030. An introduction to methods of wavelet analysis Linear Least Squares method. State-space and data. Concepts of molecular biology relevant Basic polymer science, pharmacokinetics, and 3 pts. Lect: 3. Not offered in 2020–2021. The utility of genomic information lies in its and processing techniques for the quantification noise representation. Kalman Filter. Parameter to genomic technologies, challenges of high- biomaterials, cell-substrate interactions, drug Prerequisites: BIOL UN2005, UN2006, BMEN capacity to predict the behavior of living cells in of biomedical images and signals. Topics include estimation via prediction-error and subspace dimensional genomic data analysis, bioinformatics delivery system fabrication from nanoparticles E4001-E4002 or instructor's permission. physiological, developmental, and pathological frames and overcomplete representations, approaches. Iterative and bootstrap methods. Fit preprocessing pipelines, dimensionality reduction, to microparticles and electrospun fibrous Fundamentals of nanobioscience and situations. The effect of variations in genome multiresolution algorithms for denoising and image criteria. Wide applicability: medical, energy, others. unsupervised learning, clustering, probabilistic membranes. Applications include cancer therapy, nanobiotechnology, scientific foundations, structure between individuals within a species, restoration, multiscale texture segmentation MATLAB and Simulink environments. modeling, hidden Markov models, Gibbs immunotherapy, gene therapy, tissue engineering, engineering principles, current and envisioned including those deemed healthy or diseased, and classification methods for computer aided sampling, deep neural networks, gene regulation, and regenerative medicine. Course readings BMEN E4440y Physiological control systems applications. Includes discussion of and among species, can be inferred statistically diagnosis. Programming assignments and final project will include textbook chapters and journal papers. 3 pts. Lect: 3. Professor Chbat. intermolecular forces and bonding, of kinetics and by comparisons of sequences with behaviors be required. Homework assignments take format of assay BMEN E4410x Ultrasound in diagnostic Prerequisites: MEBM E4439 and APMA E2101, thermodynamics of self-assembly, of nanoscale and mechanistically, by studying the action of responding to open-ended question. Term paper molecules whose structure is encoded within imaging or instructor’s permission. Fundamentals of BMCH E4500x or y Biological transport and transport processes arising from actions of and 30-minute PowerPoint presentation required at the genome. Examines known mechanisms that 3 pts. Lect: 3. Professor Konofagou. time and frequency domains analyses and rate processes biomolecular motors, computation and control in end of semester. elucidate the combined effect of environmental Prerequisites: MATH UN1202 or APMA E2000 or stability. Frequency domain controller design. 3 pts. Lect: 3. Not offered in 2020–2021. biomolecular systems, and of mitochondrium as an stimulation and genetic makeup on the behavior equivalent. Fourier analysis. Physics of diagnostic Cardiovascular and respiratory systems Prerequisites: CHEM UN2443, APMA E2101. BMEN E4540y Bioelectrochemistry example of nanoscale factory. ultrasound and principles of ultrasound imaging simulation. Endogenous control systems: Corequisites: BIOL UN2005. Convective and of cells in homeostasis, disease states, and during 3 pts. Lect: 3. Not offered in 2020–2021. BMEN E4590x BioMems: cellular and development, and includes assessments of the instrumentation. Propagation of plane waves baroreflex, chemoreflex, thermoregulation, diffusive movement and reaction of molecules Prerequisites: CHEM UN3079 and UN2443 molecular applications probable effect of these behaviors on the whole in lossless medium; ultrasound propagation pupillary light reflex. Open and closed loop in biological systems. Kinetics of homogeneous or equivalent. Application of electrochemical 3 pts. Lect: 3. Professor Sia. organism. Quantitative models of gene translation through biological tissues; single-element physiological systems. Exogenous control and heterogeneous reactions in biological kinetics to interfacial processes occurring in Prerequisites: Chemistry, CHEM UN3443, or and intracellular signal transduction will be used and array transducer design; pulse-echo and systems: ventilators, infusion pumps. Nonlinear environments. Mechanisms and models of biomedical systems. Basics of electrochemistry, Doppler ultrasound instrumentation, performance CHEM UN3545 or equivalent, MATH UN1201 or to illustrate switching of intracellular processes, actuators and delayed feedback systems. Acute transport across membranes. Convective diffusion electrochemical instrumentation, and relevant evaluation of ultrasound imaging systems using disease simulation and clinical decision support with and without chemical reaction. Diffusion in APMA E2000, BIOL UN2005, and UN2006. Topics transient and permanent gene activation, and cell cell and electrophysiology reviewed. Applications tissue-mimicking phantoms, ultrasound tissue in the intensive care unit. MATLAB and Simulink restricted spaces. Irreversible thermodynamic include biomicroelectromechanical, microfluidic, commitment, development, and death. to interpretation of excitable and nonexcitable characterization; ultrasound nonlinearity and environments utilized. approaches to transport and reaction in biological and lab-on-a-chip systems in biomedical membrane phenomena, with emphasis on BMEN E4350y Biomechanics of bubble activity; harmonic imaging; acoustic systems. engineering, with a focus on cellular and molecular heterogeneous mechanistic steps. Examples developmental biology output of ultrasound systems; biological effects of BMEN E4450y Dental and craniofacial tissue applications. Microfabrication techniques, of therapeutic devices created as a result of 3 pts. Lect: 3. Professor Nerurkar. ultrasound. engineering BMEN E4501x Biomaterials biocompatibility, miniaturization of analytical Prerequisites: Undergraduate-level course in 3 pts. Lect: 3. Not offered in 2020–2021. 3 pts. Lect: 3. Not offered in 2020–2021. bioelectrochemical studies. and diagnostic devices, high-throughput cellular mechanics (e.g. MECE E3113, BMEN E4310) and BMEN E4420y Biomedical signal processing Prerequisites: MSAE E3103, BMEN E4210, E4501, Prerequisites: BIOL UN2005, UN2006, BMEN BMEN E4550y Micro- and nanostructures in studies, microfabrication for tissue engineering, cell biology (e.g. BIOL UN2005/6) or by instructor's and signal modeling or equivalent. Principles of dental and craniofacial E4001, and E4002. An introduction to the cellular engineering and in vivo devices. permission. Biophysical mechanisms of tissue 3 pts. Lect: 3. Not offered in 2020–2021. bioengineering, periodontal tissue engineering: strategies and fundamental bioengineering design 3 pts. Lect: 3. Professor Kam. organization during embryonic development: Prerequisites: ELEN E3801 and either APMA beyond guided tissue regeneration, craniofacial criteria in the development of biomaterials and BMEN E4601y Cellular electricity Prerequisites: BIOL UN2005 and UN2006 or conservation laws, reaction-diffusion, finite E2101 or E3101 or instructor’s permission. regeneration by stem cells and engineered tissue engineered grafts. Materials structural- 3 pts. Lect: 2. Lab: 1. Not offered in equivalent. Design, fabrication, and application of elasticity, and fluid mechanics reviewed and Fundamental concepts of signal processing scaffolds, biomaterials: Engineering approaches in functional relationships, biocompatibility in 2020–2021. micro-/nanostructured systems for cell engineering. applied to topics in developmental biology, in linear systems and stochastic processes. tissue regeneration, bone biology and development: terms of material and host responses. Through Bioelectricity of the cell membrane. Basis of cell from early development to later organogenesis Estimation, detection, and filtering methods applied instructive cues for tissue engineers. discussions, readings, and a group design project, Recognition and response of cells to spatial resting voltage, voltage changes that lead to the of the central nervous, cardiovascular, to biomedical signals. Harmonic analysis, auto- students acquire an understanding of cell-material aspects of their extracellular environment. Focus action potential and electrical oscillations used BMEN E4460y Deep learning in biomedical musculoskeletal, respiratory, and gastrointestinal regressive model, Wiener and Matched filters, interactions and identify the parameters critical on neural, cardiac, coculture, and stem cell in sensing systems. Laboratory includes building imaging systems. Subdivided into modules on patterning linear discriminants, and independent components. in the design and selection of biomaterials for systems. Molecular complexes at the nanoscale. 3 pts. Lect: 3. Professor Laine. electronic circuits to measure capacitance of (conversion of diffusible cues into cell fates) and Methods are developed to answer concrete biomedical applications. Prerequisites: MATH UN1202 or APMA E2000 BMEN E4560y Dynamics of biological membranes artificial membranes and ion pumping in frog skin. morphogenesis (shaping of tissues). Includes questions on specific data sets in modalities and APMA E2101. Recommended: background BMEN E4510x or y Tissue engineering 3 pts. Lect: 3. Not offered in 2020–2021. Lab required. lectures, problem sets, reading of primary such as ECG, EEG, MEG, ultrasound. Lectures in Python programming. Introduction to methods 3 pts. Lect: 3. Professor Hung. Prerequisites: BIOL UN2005, BMEN E4001, literature, and a final project. accompanied by data analysis assignments using APBM E4650x Anatomy for physicists and or equivalent. The structure and dynamics of MATLAB. deep learning, with focus on applications to Prerequisites: BIOL UN2005, UN2006, BMEN engineers BMEN E4340x Biomechanics of cells quantitative problems in biomedical imaging and E4001, E4002. An introduction to the strategies biological (cellular) membranes are discussed, 3 pts. Lect: 3. Professors Katz and Rozenshtein. 3 pts. Lect: 3. Not offered in 2020–2021. Artificial Intelligence (AI) in medicine. Network and fundamental bioengineering design criteria with an emphasis on biophysical properties. Topics Prerequisite: Engineering or physics background. Prerequisites: BMEN E3320 and BMEN E4300 or models: Deep feedforward networks, convolutional behind the development of cell-based tissue include membrane composition, fluidity, lipid A systemic approach to the study of the human

ENGINEERING 2020–2021 ENGINEERING 2020–2021 body from a medical imaging point of view: instrument interrogation and control, automated ECG Prerequisites: APMA E2101, APMA E4200, ELEN Current topics in biomedical engineering. computational neuroscience including methods solver for large-scale image based models 74 75 skeletal, respiratory, cardiovascular, digestive, and analysis, ultrasonic measurements, image processing E3801, or instructor’s permission. Fundamentals Subject matter will vary by year. Instructors may of signal processing, communications theory, of trabecular bone. Implementation of tissue urinary systems, breast and women’s issues, head applied to X-ray images and CAT scans. of modern medical functional imaging. In-depth impose prerequisites depending on the topic. information theory, systems and control, system remodeling simulations in finite element models. and neck, and central nervous system. Lectures exploration of functional magnetic resonance identification and machine learning. Molecular BMEN E4738y Transduction and acquisition BMEN E6001x Current topics in MEBM E6310x-E6311y Mixture theories for are reinforced by examples from clinical two- and imaging (fMRI), arterial spin labeling (ASL), and models of transduction pathways. Robust adaptation of biomedical data nanobiotechnology and synthetic biology biological tissues, I and II three-dimensional and functional imaging (CT, MRI, positron emission tomography (PET). Human brain and integral feedback. Stimulus representation 3 pts. Lect: 2. Lab: 1. Not offered in 2020–2021. 3 pts. Lect: 3. Not offered in 2020–2021. 3 pts. Lect: 3. Not offered in 2020–2021. PET, SPECT, U/S, etc.). anatomy, physiology, and neurophysiological bases and groups. Stochastic and dynamical systems Data transduction and acquisition systems used Targeted toward graduate students; undergraduate Prerequisites: MECE E6422 and APMA E4200, or underlying each functional imaging. Statistical models of spike generation. Neural diversity and BMME E4702x Advanced musculoskeletal in biomedicine. Assembly of biotransducers students may participate with permission of the equivalent Development of governing equations for and digital signal processing methods specific for ensemble encoding. Time encoding machines and biomechanics and the analog/digital circuitry for acquiring instructor. Review and critical discussion of recent mixtures with solid matrix, interstitial fluid, and ion functional image analysis. Final cumulative project neural codes. Stimulus recovery with time decoding 3 pts. Lect: 2.5. Lab: 0.5. Not offered in 2020–2021. electrocardiogram, electromyogram, and blood literature in nanobiotechnology and synthetic constituents. Formulation of constitutive models for requiring coding in MATLAB, Python, R, or C. machines. MIMO models of neural computation. Advanced analysis and modeling of the pressure signals. Each small group will develop biology. Experimental and theoretical techniques, biological tissues. Linear and nonlinear models of Synaptic plasticity and learning algorithms. Major musculoskeletal system. Topics include and construct a working data acquisition board, BMEN E4894x Biomedical imaging critical advances. Quality judgments of scientific fibrillar and viscoelastic porous matrices. Solutions project(s) in MATLAB. advanced concepts of 3D segmental kinematics, which will be interfaced with a signal generator to 3 pts. Lect: 3. Not offered in 2020–2021. impact and technical accuracy. Styles of written and to special problems, such as confined and musculoskeletal dynamics, experimental elucidate the dynamics of timing constraints during Covers image formation, methods of analysis, graphical communication, the peer review process. BMEE E6030x Neural modeling and unconfined compression, permeation, indentation measurements of joint kinematics and anatomy, retrieval of biodata. Lab required. and representation of digital images. Measures neuroengineering and contact, and swelling experiments. BMEN E6003y Computational modeling of modeling of muscles and locomotion, multibody of qualitative performance in the context of 3 pts. Lect: 3. Not offered in 2020–2021. BMEE E4740y Bioinstrumentation physiological systems BMEN E6400x Analysis and quantification of joint modeling, introduction to musculoskeletal clinical imaging. Algorithms fundamental to the Prerequisites: ELEN E3801, and either APMA 3 pts. Lect: 3. Not offered in 2020–2021. 3 pts. Lect: 3. Professor Reuther. medical images surgical simulations. construction of medical images via methods of E2101 or E3101, or equivalent, or instructor’s Prerequisites: ELEN E1201, COMS W1005. Prerequisites: BMEN E4001 and E4002 or 3 pts. Lect: 3. Not offered in 2020–2021. computed tomography, magnetic resonance, permission. Engineering perspective on the study MEBM E4703y Molecular mechanics in Hands-on experience designing, building, and equivalent, and APMA E4200 or equivalent. Novel methods of mathematical analysis and ultrasound. Algorithms and methods for of multiple levels of brain organization, from biology testing the various components of a benchtop Advanced computational modeling and applied to problems in medical imaging. Design the enhancement and quantification of specific single neurons to cortical modules and systems. 3 pts. Lect: 3. Professor Chbat. cardiac pacemaker. Design instrumentation to quantitative analysis of selected physiological requirements for screening protocols, treatment features of clinical importance in each of these Mathematical models of spiking neurons, neural Prerequisites: ENME E3105, APMA E2101, or measure biomedical signals as well as to actuate systems from molecules to organs. Selected therapies, and surgical planning. Sensitivity and modalities. dynamics, neural coding, and biologically-based instructor’s permission. Mechanical understanding living tissues. Transducers, signal conditioning systems are analyzed in depth with an emphasis specificity in screening mammography and chest computational learning. Architectures and learning of biological structures including proteins, DNA electronics, data acquisition boards, the Arduino BMEN E4895x or y Analysis and on modeling methods and quantitative analysis. radiographs, computer aided diagnosis systems, principles underlying both artificial and biological and RNA in cells and tissues. Force response microprocessor, and data acquisition and quantification of medical images Topics may include cell signaling, molecular surgical planning in orthopaedics, quantitative neural networks. Computational models of cortical of proteins and DNA, mechanics of membranes, processing using MATLAB will be covered. Various 3 pts. Lect: 3. Not offered in 2020–2021. transport, excitable membranes, respiratory analysis of cardiac performance, functional processing, with an emphasis on the visual biophysics of molecular motors, mechanics devices will be discussed throughout the course, Prerequisite: BMEN E4894. Corequisite: BMEN physiology, nerve transmission, circulatory magnetic resonance imaging, positron emission system. Applications of principles in neuroengineering; of protein-protein interactions. Introduction to with laboratory work focusing on building an E4894. Novel methods of mathematical analysis control, auditory signal processing, muscle tomography, and echocardiography data. neural prostheses, neuromorphic systems and modeling and simulation techniques, and modern emulated version of a cardiac pacemaker. applied to problems in medical imaging. Design physiology, data collection and analysis. biomimetics. Course includes a computer simulation BMEN E6410x Principles and practices of in biophysical techniques such as single molecule requirements for screening protocols, treatment BMEN E4750y Sound and hearing BMEN E6005x Biomedical innovation I laboratory. Lab required. vivo magnetic resonance spectroscopy FRET, optical traps, AFM, and superresolution therapies, and surgical planning. Sensitivity and 3 pts. Lect: 3. Not offered in 2020–2021. 3 pts. Lect: 3. Professor Reuther. 3 pts. Lect: 3. Professors Juchem and Kegeles. imaging,for understanding molecular mechanics specificity in screening mammography and chest ECBM E6070-6079x or y Topics in Prerequisites: PHYS UN1401 and MATH UN1105- Master's students only. Project-based design Corequisite: Quantitative Physiology I or II. and dynamics. radiographs, computer-aided diagnosis systems, neuroscience and deep learning MATH UN1106. Introductory acoustics, basics experience for graduate students. Elements of Magnetic resonance spectroscopy (MRS) as a surgical planning in orthopaedics, quantitative 3 pts. Lect: 2. Members of the faculty. MEBM E4710x or y Morphogenesis: shape tool for assessing key aspects of brain metabolism of waves and discrete mechanical systems. The analysis of cardiac performance, functional design process, including need identification, Prerequisites: the instructor's permission. Selected and clinical conditions in biomedical research and and structure in biological materials mechanics of hearing—how sound is transmitted magnetic resonance imaging, positron emission concept generation, concept selection, and advanced topics in neuroscience and deep learn- clinical diagnostics. All aspects of in vivo MRS from 3 pts. Lect: 3. Not offered in 2020–2021. through the external and middle ear to the inner tomography, and echocardiography data. implementation. Development of design prototype ing. Content varies from year to year, and different theory to experiment, data acquisition to derivation Prerequisites: Courses in mechanics, ear, and the mechanical processing of sound within and introduction to entrepreneurship and topics rotate through the course numbers 6070 thermodynamics, and ordinary differential BMEN E4898y Biophotonics of metabolic signatures, and study design to the inner ear. implementation strategies. Real-world training in to 6079. equations at the undergraduate level or instructor's 3 pts. Lect: 3. Not offered in 2020–2021. biomedical design and innovation. clinical interpretation analyzed. Note: restricted to permission. Introduction to how shape and CBMF W4761y Computational genomics Prerequisites: BMEN E4894 Biomedical imaging, EEBM E6090-6099x or y Topics in MS and Ph.D. students from SEAS, GSAS, and structure are generated in biological materials 3 pts. Lect: 3. Professor Pe’er. PHYS UN1403 Classical and quantum waves, BMEN E6006y Biomedical innovation II computational neuroscience and CUMC. using engineering approach emphasizing Prerequisites: Working knowledge of at least one or instructor’s permission. Provides a broad- 3 pts. Lect 3. Professor Reuther. neuroengineering BMEN E6500x Tissue and molecular application of fundamental physical concepts to a programming language, and some background in based introduction into the field of Biophotonics. Second semester of project-based design 3 pts. Lect: 2. Professor Sajda. engineering laboratory diverse set of problems. Mechanisms of pattern probability and statistics. Computational techniques Fundamental concepts of optical, thermal, and experience for graduate students. Elements of Prerequisite: Instructor’s permission. Selected 4 pts. Lect: 1. Lab: 4. Professor Reuther. formation, self-assembly, and self-organization for analyzing and understanding genomic data, chemical aspects of the light-tissue interactions design process, with focus on skills development, advanced topics in computational neuroscience Prerequisites: Biology BIOL UN2005 and BIOL in biological materials, including intracellular including DNA, RNA, protein and gene expression will be presented. The application of these prototype development and testing, and business and neuroengineering. Content varies from year to UN2006 or permission of instructor. Hands-on structures, cells, tissues, and developing embryos. data. Basic concepts in molecular biology relevant concepts for medical therapy and diagnostics will planning. Real-world training in biomedical year, and different topics rotate through the course experiments in molecular and cellular techniques, Structure, mechanical properties, and dynamic to these analyses. Emphasis on techniques from be discussed. The course includes theoretical design, innovation, and entrepreneurship. numbers 6090-6099. including fabrication of living engineered tissues. behavior of these materials. Discussion of artificial intelligence and machine learning. String- modeling of light-tissue interactions as well as BMEN E6007y Lab-to-market: commercializing Covers sterile technique, culture of mammalian experimental approaches and modeling. Course matching algorithms, dynamic programming, optical medical instrument design and methods of BMEN E6301y Modeling of biological tissues biomedical innovations cells, microscopy, basic subcloning and gel uses textbook materials as well as collection of hidden Markov models, expectation-maximization, clinical data interpretation. with finite elements 3 pts. Lect: 3. Professor Reuther. research papers. neural networks, clustering algorithms, support 3 pts. Lect: 3. Not offered in 2020–2021. electrophoresis, creation of cell-seeded scaffolds, Introduction to and application of vector machines. Students with life sciences BMEN E4999x and y Graduate fieldwork Prerequisite: MECE E6422, or ENME E6315, and the effects of mechanical loading on the BMEN E4737x Computer control of medical commercialization of biomedical innovations. backgrounds who satisfy the prerequisites are 1–2 pts. Professor Reuther. or equivalent. Structure-function relations and metabolism of living cells or tissues. Theory, instrumentation Topics include needs clarification, stakeholder encouraged to enroll. Prerequisites: Obtained internship and approval linear/nonlinear constitutive models of biological background, and practical demonstration for each 3 pts. Lect: 2. Lab: 1. Not offered in 2020–2021. from faculty adviser. BMEN graduate students analysis, market analysis, value proposition, tissues: anisotropic elasticity, viscoelasticity, technique will be presented. Lab required. Prerequisite: Basic knowledge of the C programming BMCH E4810y Artificial organs only. Only for BMEN graduate students who business models, intellectual property, regulatory, porous media theories, mechano-electrochemical BMEN E6505x or y Advanced biomaterials & language. Acquisition and presentation of data 3 pts. Lect: 3. Not offered in 2020–2021. need relevant work experience as part of their and reimbursement. Development of path-to- models, infinitesimal and large deformations. tissue engineering for medical interpretation. Operating principles of Analysis and design of replacements for the heart, program of study. Final reports required. May market strategy and pitch techniques. Emphasis on the application and implementation 3 pts. Lect: 2.5. Lab: 0.5. Professor Lu. medical devices: technology of medical sensors, kidneys, and lungs. Specification and realization of not be taken for pass/fail credit or audits. EEBM E6020y Methods of computational of constitutive models for biological tissues algorithms for signal analysis, computer interfacing structures for artificial organ systems. Prerequisites: BMEN E4501 or equivalent. BMEN E6000x and y Graduate special topics neuroscience into existing finite element software packages. Corequisites: BMEN E4001 or E4002. Advanced and programming, interface design. Laboratory Model generation from biomedical images by assignments cover basic measurement technology, BMEN E4840y Functional imaging for the brain in biomedical engineering 4.5 pts. Lect: 3. Not offered in 2020–2021. biomaterial selection and biomimetic scaffold 3 pts. Lect: 3. Not offered in 2020–2021. 3 pts. Lect: 3. Members of the faculty. Prerequisite: BMEB W4020. Formal methods in extraction of tissue geometry, inhomogeneity and design for tissue engineering and regenerative interfacing techniques, use of Labview software anisotropy. Element-by-element finite element

ENGINEERING 2020–2021 ENGINEERING 2020–2021 medicine. Formulation of bio-inspired design BMEN E9100x or y Master’s research BMEN E9800x or y Doctoral research 76 77 criteria, scaffold characterization and testing, 1–6 pts. Members of the faculty. instruction CHEMICAL ENGINEERING and applications on forming complex tissues or Candidates for the M.S. degree may conduct 3–12 pts. Members of the faculty. 801 S. W. Mudd, MC 4721 organogenesis. Laboratory component includes an investigation of some problem in biomedical A candidate for the Eng.Sc.D. degree in biomedical 212-854-2965 basic scaffold fabrication, characterization and in engineering culminating in a thesis describing the engineering must register for 12 points of doctoral cheme.columbia.edu vitro evaluation of biocompatibility. Group projects results of their work. No more than 6 points may research instruction. Registration may not be used target the design of scaffolds for select tissue be counted for graduate credit, and this credit is to satisfy the minimum residence requirement for engineering applications. contingent upon the submission of an acceptable the degree. thesis. BMEN E6510y Stem cell, genome engineering, BMEN E9900x or y Doctoral dissertation CHAIR Christopher J. Durning Ben O’Shaughnessy Daniel Esposito ADJUNCT Jingguang Chen PROFESSORS and regenerative medicine BMEN E9500x or y Doctoral research 0 pts. Members of the faculty. George W. Flynn, Daniel Steingart Alissa Park Higgins Professor of Venkat Elias Mattas 3 pts. Lect: 3. Professors Tsang, Egli, and 1–6 pts. Members of the faculty. A candidate for the doctorate in biomedical DIRECTOR OF Chemistry Venkatasubramanian, ASSISTANT Kenneth Spall Vunjak-Novakovic. Doctoral candidates are required to make an engineering or applied biology may be required FINANCE AND Oleg Gang Samuel Ruben–Peter PROFESSORS Christos Tsiamis Prerequisites: Biology, Cell Biology, BMEN E4001 original investigation of a problem in biomedical to register for this course in every term after the ADMINISTRATION Jingyue Ju, G. Viele Professor of Christopher Boyce or BMEN E4002. General lectures on stem engineering, the results of which are presented in student’s coursework has been completed and Kathy Marte-Garcia Samuel Ruben–Peter Engineering Lauren Marbella ADJUNCT ASSOCIATE cell biology followed by student presentations the dissertation. until the dissertation has been accepted. G. Viele Professor of Alan C. West, Samuel Allie Obermeyer PROFESSORS and discussion of primary literature. Themes PROFESSORS Engineering Ruben–Peter G. Mijo Simunovic Aghavni Bedrossian- BMEN E9700x or y Biomedical engineering presented include: basic stem cell concepts; basic Scott A. Banta Sanat K. Kumar, Viele Professor of Alexander Urban Omer seminar cell and molecular biological characterization Jingguang G. Chen, Bykhovsky Professor Electrochemistry Hartoun Hartounian 0 pts. Sem: 1. Professors Danino, Juchem, and LECTURERS Gregory Hounsell of endogenous stem cell populations; concepts Thayer Lindsley of Chemical Olson. Professor Robert Bozic related to reprogramming; directed differentiation of Engineering ASSOCIATE All matriculated graduate students are required of Chemical Edward F. Leonard PROFESSORS Aaron Moment stem cell populations; use of stem cells in disease to attend the seminar as long as they are in Engineering V. Faye McNeill Kyle Bishop modeling or tissue replacement/repair; clinical residence. No degree credit is granted. The translation of stem cell research. seminar is the principal medium of communication EEBM E9070y Massively parallel neural among those with biomedical engineering interests hemical engineering is a importance employing DNA- or protein- the theoretical work involves analytical computation within the University. Guest speakers from other highly interdisciplinary field based chemical sensors, controlled- mathematical physics, numerical 3 pts. Lect: 3. Professor Mesgarani. institutions, Columbia faculty, and students within C concerned with materials and release drugs, new agricultural simulations, and data science. Prerequisites: BMEB W4020 or permission of the department who are advanced in their studies processes at the heart of a broad range products, nanoparticle-based materials, Interested students will have the instructor. Drosophila connectomics. Detailed frequently offer sessions. of technologies. Practicing chemical bio-nanoparticle conjugates, and many opportunity to conduct research in description of the fruit fly’s olfactory and vision engineers are the experts in charge others. these and other areas. The Department systems. Parallel processing on GPSs. of the development and production of Driven by this diversity of of Chemical Engineering at Columbia diverse products in traditional chemical applications, chemical engineering is committed to a leadership role in industries as well as many emerging is perhaps the broadest of all research and education in frontier new technologies. The chemical engineering disciplines: chemistry, areas of research and technology engineer guides the passage of the physics, mathematics, biology, and where progress derives from the product from the laboratory to the computing are all deeply involved. The conjunction of many different traditional marketplace, from ideas and prototypes research of the faculty of Columbia’s research disciplines. Increasingly, to functioning articles and processes, Chemical Engineering Department is new technologies and fundamental from theory to reality. This requires correspondingly broad. Some of the research questions demand this type of a remarkable depth and breadth areas under active investigation are: interdisciplinary approach. of understanding of physical and protein engineering, fundamentals and The undergraduate program chemical aspects of materials and their engineering of polymers, biopolymers, provides a chemical engineering degree production. and other soft materials, colloidal that is a passport to many careers in The expertise of chemical engineers machines, atmospheric chemistry directly related industries as diverse as is essential to production, marketing, and air quality, fundamentals and biochemical engineering, environmental and application in such areas as applications of electrochemistry for management, and pharmaceuticals. The pharmaceuticals, high-performance energy storage and manufacturing, degree is also used by many students materials in the aerospace and multiphase flows, carbon capture and as a springboard from which to launch automotive industries, biotechnologies, utilization, catalysis, and electrocatalysis, careers in medicine, law, consulting, semiconductors in the electronics solar fuels, the bioengineering of management, banking and finance, industry, paints and plastics, petroleum artificial organs, the engineering and and so on. For those interested in the refining, synthetic fibers, artificial organs, biochemistry of sequencing the human fundamentals, a career of research and biocompatible implants and prosthetics genome, emergent phenomena in teaching is a natural continuation of and numerous others. Increasingly, complex and dynamical systems, the their undergraduate studies. Whichever chemical engineers are involved in new biophysics of cellular processes in living path the student may choose after technologies employing highly novel organisms, and DNA-guided assembly graduation, the program offers a deep materials, whose unusual response at of inorganic and biological nanoscale understanding of the physical and the molecular level endows them with objects. chemical nature of things and provides unique properties. Examples include Many experimental approaches are an insight into an exploding variety environmental technologies, emerging employed, from magnetic resonance of new technologies that are rapidly biotechnologies of major medical imaging to synchrotron techniques, and reshaping the society in which we live.

ENGINEERING 2020–2021 ENGINEERING 2020–2021 78 79 CHEMICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS CHEMICAL ENGINEERING: THIRD AND FOURTH YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

APMA E2000 (4) either semester CHEN E3110 (3) CHEN E3120 (3) Transp. phenomena, I Transp. phenomena, II CHEN E4500 (4) MATH UN1101 (3) MATH UN1102 (3) Process and product MATHEMATICS CHEE E3010 (3) CHEN E3210 (3) MATH UN2030 (3) ODE design, I MATH elective (3)4 or REQUIRED Principles of chem. Chem. eng. eng. thermodynamics thermodynamics APMA E2101 (3) COURSES CHEE E4140 (3) Eng. separations CHEN E3020 (3) CHEN E3230 (3) processes Analysis of Reaction kinetics and PHYSICS UN1401 (3) UN1402 (3) Lab UN1494 (3) (three tracks, UN1601 (3.5) UN1602 (3.5) chem. eng. problems, I reactor design choose one) UN2801 (4.5) UN2802 (4.5) Lab UN3081 (2)

CHEM UN2495 (1.5)1 CHEM UN2496 (1.5)1 CHEN E4300 (3) CHEN E3810 (3) Org. chem. lab I Org. chem. lab II UN1403 (4) and UN1404 (4) UN2443 (4) REQUIRED LABS Chem. eng. control Chem. eng. lab CHEMISTRY Lab UN1500 (3) UN1507 (3) and CHEM UN2493 (0) and CHEM UN2494 (0) (three tracks, choose one) UN1604 (4) UN2046 (4) and

UN2045 (4) Lab UN1507 (3) NONTECH 3 points 3 points 3 points

UNIVERSITY CC1010 (3) either semester WRITING TECH2 3 points 3 points 3 points 12 points REQUIRED ELECTIVES

REQUIRED One core humanities Three core humanities NONTECHNICAL elective (3–4 points)1 electives (11 points)1 ELECTIVES TOTAL POINTS 16.5 16.5 16 15 (normal track)

CHEN E2100 (3)2 1 May be taken in Semester III and IV with adviser’s permission. Additional option is that Intensive organic chemistry lab course UN2545 (3) can count in place of CHEM. ENG. Intro to chemical UN2495 and UN2496. REQUIREMENT engineering 2 The total of 21 points (7 courses) of required technical electives must include five engineering courses, two of which must be in chemical engineering and one must be outside chemical engineering, and 6 points (2 courses) of "advanced science" (i.e., courses in chemistry, physics, biology, and certain engineering courses, one of which must be outside engineering). COMPUTER ENGI E1006 (3) SCIENCE UNDERGRADUATE PROGRAM environment, establish goals, plan Upon graduation, we expect our tasks, and meet objectives PHYSICAL UN1001 (1) UN1002 (1) students to have: EDUCATION Chemical Engineering 6. an ability to develop and conduct Graduates of the Chemical Engineering appropriate experimentation, 1. an ability to identify, formulate, and analyze and interpret data, and THE ART OF ENGI E1102 (4) either semester Program achieve success in one or ENGINEERING more of the following within a few years solve complex engineering problems use engineering judgment to draw of graduation: by applying principles of engineering, conclusions TOTAL POINTS3 17 18 16.5 18 science, and mathematics 7. an ability to acquire and apply 1. Careers in industries that require 2. an ability to apply engineering design new knowledge as needed, using 1 Four core humanities electives should be taken as follows: In Semester III, HUMA CC1001or COCI CC1101 (4) or any initial course in one of the Global Core technical expertise in chemical to produce solutions that meet appropriate learning strategies. sequences offered by the College (3–4); in Semester IV, HUMA CC1002 or COCI CC1102 (4) or ASCM UN2002 or the second course in the Global Core sequence engineering. specified needs with consideration elected in Semester III (3–4); also in Semester IV, ECON UN1105 (4) with UN1155 recitation (0) and either HUMA UN1121 or UN1123 (3). 2. Leadership positions in industries that of public health, safety, and welfare, Columbia’s program in chemical 2 Should be taken in Semester III, but may be moved upon adviser’s approval to Semester V if CHEM UN2543: Organic chemistry lab is taken in Semester III. This course fulfills the SEAS professional engineering elective requirement. require technical expertise in chemical as well as global, cultural, social, engineering leading to the B.S. degree 3 Taking the first track in each row and E1102 in Semester II. engineering. environmental, and economic factors is accredited by the Engineering 5 Elective options include APMA E3101, MATH UN2010, APMA E3102, APMA E4001, APMA E4150, APMA E4300, STAT GU4001, or another course approved by 3. Graduate-level studies in chemical 3. an ability to communicate effectively Accreditation Commission of ABET, the major adviser. engineering and related technical or with a range of audiences http://www.abet.org. scientific fields (e.g. biomedical or 4. an ability to recognize ethical and The first and sophomore years Waters HPLC system, a SpectraMax laboratory facilities exist in the Columbia Facilities for Teaching and environmental engineering, materials professional responsibilities in of study introduce general principles spectrophotometer, a rotating disk Electrochemical Energy Center, the Soft Research science). engineering situations and make of science and engineering and electrode and potentiostat, a fixed bed Materials laboratory, and the Columbia The Department of Chemical 4. Careers outside of engineering that informed judgments, which must include a broad range of subjects in adsorption unit, a solar cell/electrolyzer/ Genome Center. Engineering provides access to state- take advantage of an engineering consider the impact of engineering the humanities and social sciences. fuel cell apparatus, flow and temperature Chemical engineering students, of-the-art research instrumentation education, such as business, solutions in global, economic, Although the program for all engineering control equipment, an IR camera, two faculty, and research staff also and computational facilities for its environmental, and societal contexts students in these first two years is PhyMetrix Bench-top Moisture Analyzer have access to shared NMR, MRI, management, finance, law, medicine, undergraduate and graduate students, 5. an ability to function effectively to some extent similar, there are units, and 15 computer work stations. photochemical, spectroscopic, and or education. postdoctoral associates, and faculty. on teams whose members a few important differences for State-of-the-art specialized research mass spectrometry facilities in the 5. A commitment to life-long learning The recently renovated chemical together provide leadership, create chemical engineering majors. Those equipment are housed within individual Department of Chemistry. and service within their chosen engineering undergraduate laboratory profession. a collaborative and inclusive wishing to learn about, or major in, features equipment including a faculty laboratories. Shared research

ENGINEERING 2020–2021 ENGINEERING 2020–2021 CHEN E3120y Transport phenomena, II include scale up of apparatus, process control, 80 chemical engineering should take the CHAP, or MECH). At least one must fields of departmental activity mentioned are encouraged to apply to this highly 81 professional elective CHEN E2100 be outside chemical engineering. in previous sections. For both chemical interdisciplinary program. 3 pts. Lect: 3. Professor Durning. chemical separations, microfluidics, surface Prerequisite: CHEN E3110. Corequisite: CHEN engineering, molecular sensing, and alternative Introduction to chemical engineering engineers and those with undergraduate • The remaining technical elective E3220. Developments in Transport I are extended energy sources. Safety awareness is integrated in term III, taught by the Chemical educations in other related fields such to handle turbulence. Topics include turbulent throughout the course. courses must contain "advanced COURSES IN CHEMICAL Engineering Department. This course as physics, chemistry, and biochemistry, energy cascade, wall-bounded turbulent shear ENGINEERING CHEN E3900x and y Undergraduate research is a requirement for the chemical science" coursework, which includes the Ph.D. program provides the flow, time-averaging of the equations of change, Note: Check the department website project engineering major. It can also possibly the natural sciences and certain opportunity to become expert in Prandtl’s mixing length hypothesis for the Reynolds for the most current course offerings 1–6 pts. Members of the faculty. serve as a technical elective for other engineering coursework. At least one of research fields central to modern stress, the Reynolds analogy, continuum modeling and descriptions. Candidates for the B.S. degree may conduct engineering majors. Those wishing to these courses must be taken outside technology and science. of turbulent flows and heat transfer processes, friction factor, and Nusselt number correlations for an investigation of some problem in chemical major in chemical engineering should of SEAS (e.g., in a science department M.S. students must complete the CHEN E2100x Introduction to chemical turbulent conditions. Then, macroscopic (system- engineering or applied chemistry or carry out at Columbia). Qualifying engineering professional development and leadership engineering also take ENGI E1006 Introduction level) mass, momentum, and energy balances for a special project under the supervision of the courses are determined by Chemical 3 pts. Lect: 3. Professor Banta. to computing for engineering and course, ENGI E4000, as a graduation one-component systems are developed and applied staff. Credit for the course is contingent upon the Prerequisites: First-year chemistry and physics, applied scientists in term II. Chemical Engineering department advisers. requirement. Ph.D. candidates are to complex flows and heat exchange processes. submission of an acceptable thesis or final report. or equivalent. Serves as an introduction to the No more than 6 points may be counted toward the engineering majors receive additional strongly encouraged to complete The final part focuses on mass transport in mixtures The junior-senior technical electives chemical engineering profession. Students are ENGI E6001–6004 and should consult of simple fluids: Molecular-level origins of diffusion satisfaction of the B.S. degree requirements. instruction in their junior year on the exposed to concepts used in the analysis of provide the opportunity to explore phenomena, Fick’s law and its multicomponent use of computational methods to solve their program for PDL requirements. chemical engineering problems. Rigorous analysis CHEN E3999x, y, or s Undergraduate new, interesting areas beyond the generalizations, continuum-level framework for chemical engineering problems. of material and energy balances on open and fieldwork core requirements of the degree. mixtures and its application to diffusion dominated closed systems is emphasized. An introduction 1–2 pts. Members of the faculty. In the junior-senior sequence one M.S. Degree processes, diffusion with chemical reaction, and Often, students satisfy the technical to important processes in the chemical and Prerequisites: Obtained internship and approval specializes in the chemical engineering The requirements are (1) the core forced/free convection mass transport. electives by taking courses from biochemical industries is provided. from adviser. Restricted to CHEN undergraduate major. The table on page 79 spells courses: Mathematical methods in another SEAS department in order to CHEN E3210y Chemical engineering students. Provides work experience on chemical out the core course requirements, chemical engineering (CHEN E4010)/ CHEE E3010x Principles of chemical engineering in relevant intern or fieldwork obtain a minor from that department. thermodynamics which are split between courses Partial differential equations (APMA engineering thermodynamics experience as part of their program of study as Alternately, you may wish to take 3 pts. Lect: 3. Professor Obermeyer. 3 pts. Lect: 3. Professor Kumar. determined by the instructor. Written application emphasizing engineering science and E4200), Transport phenomena, III Prerequisites: CHEE E3010 and CHEN E2100. courses in several new areas, or Prerequisite: CHEM UN1403. Corequisite: must be made prior to registration outlining those emphasizing practical and/or (CHEN E4110), Advanced chemical Corequisite: CHEN E3220. Deals with fundamental perhaps to explore familiar subjects CHEN E3020. Introduction to thermodynamics. proposed internship/study program. A written report professional aspects of the discipline. kinetics (CHEN E4130), and Advanced and applied thermodynamic principles that form in greater depth, or you may wish to Fundamentals are emphasized: the laws of describing the experience and how it relates to the Throughout, skills required of practicing chemical engineering thermodynamics the basis of chemical engineering practice. Topics thermodynamics are derived and their meaning chemical engineering core curriculum is required. gain experience in actual laboratory include phase equilibria, methods to treat ideal and engineers are developed (e.g., writing (CHEN E4130)/Statistical mechanics explained and elucidated by applications to Employer feedback on student performance and research. Up to 6 points of CHEN nonideal mixtures, and estimation of properties and presentation skills, competency (CHAP E4120); and (2) 18 points of engineering problems. Pure systems are treated, the quality of the report are the basis of the grade. E3900: Undergraduate research project using computer-based methods. with computers). 4000- or 6000-level courses, approved followed by an introduction to mixtures and phase May not be taken for pass/fail or audited. May not may be counted toward the technical The table also shows that a by the graduate coordinator or research equilibrium. BMCH E3500y Transport in biological be used as a technical or nontechnical elective. elective content. (Note that if more than systems May be repeated for credit, but no more than significant fraction of the junior-senior adviser, of which up to 6 may be Master’s CHEN E3020x Analysis of chemical 3 points of research are pursued, an 3 pts. Lect: 3. Not offered in 2020–2021. 3 points total of CHEN E3999 may be used for program is reserved for electives, both research (CHEN 9400). Students with engineering problems undergraduate thesis is required.) Prerequisites: CHEM UN2443 and MATH UN2030. degree credit. technical and nontechnical. Nontechnical undergraduate preparation in physics, 3 pts. Lect: 1.5. Lab: 1.5. Professor West. The program details discussed Corequisite: BIOL UN2005. Convective and electives are courses that are not chemistry, biochemistry, pharmacy, and Prerequisites: Vector calculus, ordinary CHEN E4001x Essentials of chemical above apply to undergraduates who diffusive movement and reaction of molecules differential equations. Corequisites: CHEE engineering—A quantitative, such as those taught in related fields may take advantage of a in biological systems. Kinetics of homogeneous are enrolled at Columbia as first-years E3010, CHEN E3110. Computational 3 pts. Lect: 3. Professor Banta. the humanities and social sciences. special program leading directly to the and heterogeneous reactions in biological and declare the chemical engineering solutions of chemical engineering problems in Prerequisites: First-year chemistry and physics, These provide an opportunity to pursue master’s degree in chemical engineering. environments. Mechanisms arid models of major in the sophomore year. thermodynamics, transport phenomena, and vector calculus, ordinary differential equations, transport across membranes. Convective interests in areas other than engineering. This program enables such students to reaction design. and the instructor’s permission. Part of an However, the chemical engineering diffusion with and without chemical reaction. A crucial part of the junior-senior avoid having to take all undergraduate accelerated consideration of the essential chemical program is designed to be readily CHEN E3110x Transport phenomena, I Diffusion in restricted spaces. Irreversible program is the 21-point (7 courses) courses in the bachelor’s degree program. engineering principles from the undergraduate accessible to participants in any of 3 pts. Lect: 3. Professor McNeill. thermodynamic approaches to transport and technical elective requirement. Technical program, including topics from Mass and Energy Columbia’s Combined Plans and to Prerequisites: mechanics, vector calculus, ordinary reaction in biological systems. balances, Process Control, and Transport I electives are science and/or technology Doctoral Degrees differential equations. Corequisite: CHEN E3020. transfer students. In such cases, the CHEN E3810y Chemical engineering and II. While required for all M.S. students with based and feature quantitative analysis. The Ph.D. and D.E.S. degrees have Analysis of momentum and energy transport guidance of one of the departmental laboratory Scientist to Engineer status, the credits from this Generally, technical electives must be processes at molecular, continuum, and system advisers in planning your program is essentially the same requirements. 3 pts. Lab: 3. Professors Ju and Bedrossian. course may not be applied toward any chemical scales for systems of simple fluids (gases and low- 3000 level or above but there are a few All students in a doctoral program Prerequisites: Completion of core chemical engineering degree. required (contact information for the molecular-weight liquids). Molecular-level origins of exceptions including: PHYS UN1403, must (1) earn satisfactory grades in engineering curricula through the fall semester departmental UG advisers is listed fluid viscosity, continuum fluid mechanics analysis CHEN E4002x Essentials of chemical PHYS UN2601, BIOL UN2005, BIOL of senior year (includes: CHEN E3110, E3120, on the department’s website: the four core courses (CHEN E4010, of laminar flows, and the resulting dimensionless UN2006, BIOL UN2501, and CHEM E4230, E2100, E3210, E4140, E4500, CHEE engineering—B cheme.columbia.edu). E4110, E4330, E4130/CHAP E4120); correlations of kinematic and mechanical E3010), or instructor’s permission. Emphasizes 3 pts. Lect: 3. Professor Banta. UN2444. The technical electives are (2) pass a qualifying exam; (3) defend characteristics of a system needed for engineering active, experiment-based resolution of open-ended Prerequisites: First-year chemistry and physics, subject to the following constraints: a proposal of research within 12 design (e.g., friction factor vs. Reynolds number Requirements for a Minor in problems involving use, design, and optimization vector calculus, ordinary differential equations, correlations). Molecular origins of fluid conductivity, months of passing the qualifying of equipment, products, or materials. Under and the instructor’s permission. Part of an • Of the seven elective courses, at least Chemical Engineering continuum heat transfer analysis, and the resulting exam; (4) defend their thesis; and (5) faculty guidance students formulate, carry out, accelerated consideration of the essential five must be within SEAS. Among See page 205. correlations of a system’s thermal characteristics satisfy course requirements beyond validate, and refine experimental procedures, and chemical engineering principles from the those courses, at least four must have useful in engineering design (e.g., Nusselt number present results in oral and written form. Develops undergraduate program, including topics from the four core courses. For detailed correlations). Examples are reviewed of analyses significant engineering content (i.e. are analytical, communications, and cooperative Chemical Engineering Thermodynamics, I and II, GRADUATE PROGRAMS requirements, please consult the typical in chemical engineering technologies. not mathematical or computational in problem-solving skills in the context of problems Chemical and Biochemical Separations. Reaction The graduate program in chemical departmental office or graduate Essential mathematical methods are reviewed or nature). At least two must be within that span from traditional, large scale separations Kinetics and Reactor Design. While required engineering, with its large proportion coordinator. Students with degrees introduced in context. chemical engineering (e.g., with the and processing operations to molecular level for all M.S. students with Scientist to Engineer of elective courses and independent in related fields such as physics, status, the credits from this course may not be designator BMCH, CHEN, CHEE, design of materials or products. Sample projects research, offers experience in any of the chemistry, biochemistry, and others applied toward any chemical engineering degree.

ENGINEERING 2020–2021 ENGINEERING 2020–2021 CHEN E4010x Mathematical methods connections to molecular/microscopic mechanisms undergraduate thermodynamics course. The course and catalytic properties of surfaces. Kinetics of environmental stimulation and genetic makeup CHEN E4500x Process and product design, I 82 83 in chemical engineering for "conductive"transport. Continuum balances provides a rigorous and advanced foundation in and thermodynamics in adsorption, reaction, on the behavior of cells in homeostasis, disease 4 pts. Lect: 4. Professor Bozic. 3 pts. Lect: 3. Professor Bozic. of mass and momentum; continuum-level chemical engineering thermodynamics suitable for desorption, and diffusion processes on surfaces. states, and during development, and includes Prerequisites: CHEN E2100, CHEN E4140. The Prerequisites: CHEN E3120 and E4230, or development of conductive momentum flux (stress chemical engineering Ph.D. students expected to Effects of transport in modifying surface reaction assessments of the probable effect of these practical application of chemical engineering equivalent, or instructor’s permission. Mathematical tensor) for simple fluids; applications of continuum undertake diverse research projects. Topics include kinetics. Applies basic concepts in the chemical behaviors on the whole organism. Quantitative principles for the design and economic evaluation description of chemical engineering problems framework for simple fluids (lubrication flows, intermolecular interactions, nonideal systems, engineering curriculum (mathematical modeling, models of gene translation and intracellular of chemical processes and plants. Use of ASPEN and the application of selected methods for their creeping flows). Microscopic developments of mixtures, phase equilibria and phase transitions reaction kinetics, thermodynamics, transport) to signal transduction will be used to illustrate Plus for complex material and energy balances solution. General modeling principles, including stress for simple and/or complex fluids; kinetic and interfacial thermodynamics. surface reactions. switching of intracellular processes, transient and of real processes. Students are expected to model hierarchies. Linear and nonlinear ordinary theory and/or liquid state models for transport permanent gene activation, and cell commitment, build on previous coursework to identify creative CHEN E4140x Engineering separations differential equations and their systems, including coefficients in simple fluids; Langevin/Fokker- EACH E4252x Introduction to surface and development, and death. solutions to two design projects of increasing processes those with variable coefficients. Partial differential Plank/Smoluchowski framework for stress in colloid chemistry complexity. Each design project culminates in an 3 pts. Lect: 3. Professor Durning. CHEN E4325y Bioseparations equations in Cartesian and curvilinear coordinates complex fluids; stress in active matter; applications 3 pts. Lect: 3. Professors Farinato and oral presentation, and in the case of the second Prerequisites: CHEN E2100, E3120, and E3210 3 pts. Lect: 3. Professor Hartounian. for the solution of chemical engineering problems. for complex fluids. Somasundaran. project, a written report. or permission of instructor. Design and analysis of Prerequisite: Elemental physical chemistry. The Prerequisites: CHEN E2100 or CHEN E3230, CHEN E4020y Protection of industrial and CHEN E4112y Transport phenomena in fluids unit operations employed in chemical engineering principles of surfaces and colloid chemistry critical or equivalent. Design and analysis of the CHEN E4501y Chemical engineering process intellectual property and mixtures separations. Fundamental aspects of single and to range of technologies indispensable to modern concentration, recovery, and isolation of biological safety 3 pts. Lect: 3. Professor Spall. 3 pts. Lect: 3. Professor Durning. multistaged operations using both equilibrium and life. Surface and colloid chemistry has significance molecules relevant in biotechnology. The unit 3 pts. Lect.: 3. Professor Bozic. To expose engineers, scientists and technology Prerequisites: CHEN E3110 and E3120 rate-based methods. Examples include distillation, to life sciences, pharmaceuticals, agriculture, envi- operations used in recovery and purification Aimed at seniors and graduate students. Provides managers to areas of the law they are most likely or equivalent. Develops and applies non- absorption and stripping, extraction, membranes, ronmental remediation and waste management, of biological molecules. Theory and design classroom experience on chemical engineering to be in contact with during their career. Principles equilibrium thermodynamics for modeling crystallization, bioseparations, and environmental earth resources recovery, electronics, advanced of filtration, microfiltration, centrifugation, cell process safety as well as Safety in Chemical are illustrated with various case studies together of transport phenomena in fluids and their applications. materials, enhanced oil recovery, and emerging disruption, extraction, adsorption, chromatography, Engineering certification. Process safety and with active student participation. extraterrestrial mining. Topics include: thermody- precipitations, ultrafiltration, crystallization, and mixtures. Continuum balances of mass, CHEN E4150y Computational fluid dynamics process control emphasized. Application of basic namics of surfaces, properties of surfactant solu- drying. Students will have an understanding of CHEE E4050y Principles of industrial energy, and momentum for pure fluids; non- in chemical engineering chemical engineering concepts to chemical tions and surface films, electrokinetic phenomena basic principles of downstream processing, design electrochemistry equilibrium thermodynamic development of 3 pts. Lect: 3. Professor Boyce. reactivity hazards, industrial hygiene, risk at interfaces, principles of adsorption and mass and operations of various unit operations used 3 pts. Lect: 3. Not offered in 2020–2021. Newton's law of viscosity and Fourier's law; Fundamentals of numerical algorithms for modeling assessment, inherently safer design, hazard transfer and modern experimental techniques. in recovery of biological products, examining Prerequisites: CHEE E3010 or equivalent. A applications (conduction dominated energy dynamics of fluid flow computationally. Includes operability analysis, and engineering ethics. Leads to deeper understanding of interfacial traditional unit operations, as well as new concepts presentation of the basic principle underlying transport, forced and free convection energy various approaches to discretize time and space Application of safety to full spectrum of chemical engineering, particulate dispersions, emulsions, and emerging technologies that are likely to benefit electrochemical processes. Thermodynamics, transport in fluids); balance laws for fluid on structured and unstructured grids with a variety engineering operations. foams, aerosols, polymers in solution, and soft biochemical product recovery in the future. electrode kinetics, and ionic mass transport. mixtures; non-equilibrium thermodynamic of boundary conditions. Involves programming matter topics. CHEN E4510y Process and product design, II development of Fick's law; applications of basic CFD codes in MATLAB or Python to CHEN E4330y Advanced chemical kinetics Examples of industrial and environmental 4 pts. Lect: 4. Professor Venkatasubramanian. (diffusion-reaction problems, analogy between test example problems in fluid mechanics with 3 pts. Lect: 3. Professor Esposito. applications illustrated by means of laboratory CHEN E4300x Chemical process control and Prerequisite: CHEN E4500. Students carry out a energy and mass transport process, transport different discretization schemes. Uses open-source Prerequisite: CHEN E4230 or instructor’s experiments: electroplating, refining, and process safety semester long process or product design course in electrolyte solutions, sedimentation). software OpenFOAM to investigate more complex permission. Complex reactive systems, winning in aqueous solutions and in molten 3 pts. Lect: 1. Lab: 2. Professor McNeill. with significant industrial involvement. The project salts; electrolytic treatment of wastes; primary, geometries and numerical approaches. Introduction Prerequisites: Material and energy balances. molecular view of reaction kinetics, reactions in CHEN E4115y Topics in transport phenomena culminates with a formal written design report and secondary, and fuel cells. to simulation of multiphase flow. Course grade Ordinary differential equations including Laplace liquid, reactions at surfaces, diffusion-reaction 3 pts. Instructor to be announced. a public presentation. Recitation section required. based on homework assignments and final project transforms. Reactor Design. An introduction to systems. Applications to the design of batch and APCH E4080x Soft condensed matter Prerequisites: Undergraduate fluid mechanics, or report and presentation. process control applied to chemical engineering continuous reactors. CHEE E4530y Corrosion of metals 3 pts. Lect: 3. Professor Gang. transport phenomena, or instructor’s permission. through lecture and laboratory. Concepts include 3 pts. Lect: 3. Prerequisites: MSAE E3111, CHEE E3010, or Self-contained treatments of selected topics in CHEN E4201x Engineering applications of CHEN E4400x Chemical process development the dynamic behavior of chemical engineering Prerequisite: CHEE E3010 or equivalent. The CHEN E3120 or equivalent. Course is aimed at transport phenomena (e.g., rheology, non- electrochemistry 3 pts. Lect: 3. Professor Mattas. systems, feedback control, controller tuning, and theory of electrochemical corrosion, corrosion senior undergraduate and graduate students. equilibrium thermodynamics, molecular-level 3 pts. Lect: 3. Professor West. Prerequisites: CHEM UN2443 or equivalent or process stability. Introduction to the fundamentals tendency, rates, and passivity. Application to Introduces fundamental ideas, concepts, and aspects of transport turbulence). Topics and Prerequisites: Physical chemistry and a course instructor’s permission. Process development of process safety and hazard analysis. various environments. Cathodic protection and approaches in soft condensed matter with instructor may change from year to year. Intended in transport phenomena. Engineering analysis of for new compounds, including fine and specialty coatings. Corrosion testing. emphasis on biomolecular systems. Covers the for junior/senior level undergraduates and graduate electrochemical systems, including electrode kinetics, CHEN E4320y Molecular phenomena in chemicals, pharmaceuticals, biologicals, and broad range of molecular, nanoscale, and colloidal students in engineering and the physical sciences. transport phenomena, mathematical modeling, chemical engineering agrochemicals. Experimental strategy and methods CHEN E4580x Artificial intelligence in phenomena with revealing their mechanisms and and thermodynamics. Common experimental for process scale-up from bench to pilot plant. Chemical Engineering CHAP E4120y Statistical mechanics 3 pts. Lect: 3. Not offered in 2020–2021. physical foundations. The relationship between methods are discussed. Examples from common Evaluation of process economics. Hazard and risk 3 pts. Lect: 3. Professor Venkatasubramanian. 3 pts. Lect: 3. Professor O’Shaughnessy. Prerequisites: CHEN E3120 or instructor’s molecular architecture and interactions and applications in energy conversion and metallization evaluation for environmental and industrial hygiene Prerequisites: Background in chemical engineering Prerequisites: CHEE E3010 or equivalent permission. Introduces a molecular-level macroscopic behavior are discussed for the broad are presented. safety. Capture and use of process know-how for and Python/MATLAB. Introduction to AI methods thermodynamics course, or instructor’s permission. understanding of topics in modern chemical range of soft and biological matter systems, engineering. It builds upon and validates the concepts process and plant design, regulatory approvals, including knowledge-based systems and deep Fundamental principles and underlying CHEN E4231x Solar fuels from surfactants and liquid crystals to polymers, presented in the rest of the chemical engineering and technology transfer to first manufacture. learning in the context of chemical engineering assumptions of statistical mechanics. Boltzmann’s 3 pts. Lect: 3. Professors Esposito and West. nanoparticles, and biomolecules. Modern curriculum via a molecular perspective. applications. Topics include chemical engineering entropy hypothesis and its restatement in terms Prerequisite: Graduate standing or CHEN CHEN E4410x Environmental control characterization methods for soft materials, modeling approaches, knowledge representation, of Helmholtz and Gibbs free energies and for E4230. Fundamentals and applications of solar technology including X-ray scattering, molecular force probing, CHBM E4321x The genome and the cell symbolic reasoning and inference, knowledge-based open systems. Correlation times and lengths. energy conversion, especially technologies for 3 pts. Lect: 3. Not offered in 2020–2021. and electron microcopy are reviewed. Example 3 pts. Lect: 3. Not offered in 2020–2021. systems, statistical data analysis, and machine Exploration of phase space and observation conversion of sunlight into storable chemical Prerequisites: CHEN E3010 or the equivalent. problems, drawn from the recent scientific Prerequisites: BIOL UN2005, MATH UN2030. The learning methods such as clustering, neural networks, timescale. Correlation functions. Fermi-Dirac and energy or solar fuels. Topics include fundamentals Causes of pollution and effect on life. Legal literature, link the studied materials to the actively utility of genomic information lies in its capacity to random forests, Bayesian networks, and directed Bose-Einstein statistics. Fluctuation-response of photoelectrochemistry, kinetics of solar fuels aspects, OSHA and EPA rules. Pollution at home developed research areas. Course grade based predict the behavior of living cells in physiological, evolution. Chemical engineering case studies in theory. Applications to ideal gases, interfaces, production, solar harvesting technologies, solar and at work; radon, fumes, and dust; ventilation, on midterm and final exams, weekly homework developmental, and pathological situations. The process monitoring, diagnosis, and control, process/ liquid crystals, microemulsions and other complex reactors, and solar thermal production of solar dust collection, carbon adsorption. Fuel and assignments, and final individual/team project. effect of variations in genome structure between product design, scheduling, and process hazards fluids, polymers, Coulomb gas, interactions fuels. Applications include solar fuels technology acid gases, smog and dispersion. Treatment individuals within a species, including those analysis. Development of hybrid models that combine CHEN E4110y Mechanisms of transport between charged polymers and charged interfaces, for grid-scale energy storage, chemical industry, of ground, saline, and wastewater. Primary deemed healthy or diseased, and among species, first-principles knowledge of the underlying physics phenomena in fluids ordering transitions. manufacturing, environmental remediation. and secondary (biological) treatment. Tertiary can be inferred statistically by comparisons of & chemistry with data-driven techniques and the 3 pts. Lect: 3. Professor Durning. sequences with behaviors, and mechanistically, by water treatment with membranes, ion exchange, CHEN E4130x Advanced chemical CHEN E4235x Surface reactions and kinetics development of causal mechanism-based models. Prerequisite: CHEN E3110 and E3120 or studying the action of molecules whose structure carbon, and sieves. Solid hazardous waste. Visit engineering thermodynamics 3 pts. Lect: 3. Professor Chen. equivalent. Continuum framework for modeling is encoded within the genome. Examines known New York City wastewater treatment plant. 3 pts. Lect: 3. Professor O'Shaughnessy. Fundamental concepts and techniques to non-equilibrium phenomena in fluids with clear mechanisms that elucidate the combined effect Prerequisite: Successful completion of an describe electronic, structural, chemical,

ENGINEERING 2020–2021 ENGINEERING 2020–2021 CHEN E4600x Atmospheric aerosols CHEN E4660x Biochemical engineering E3110; BIOL UN2005; CHEN E3210 or BMCH kidneys, and lungs. Specification and realization of approaches and hands-on experience in using state- biologics, and vaccine manufacturing illustrated 84 85 3 pts. Lect: 3. Not offered in 2020–2021. 3 pts. Lect.: 3. Professor Obermeyer. E3500. Analysis of transport and rate phenomena structures for artificial organ systems. of-the-art (free and open source) simulation software. through examples, and quantitative engineering Prerequisite: CHEN E3120 or instructor’s permission. Prerequisite: CHEN E4320 or instructor’s in biological systems and in the design of biomimetic Practical examples focus on inorganic materials approaches applied as appropriate. Small molecules, CHEN E4850x or y Contaminated site cleanup Atmospheric aerosols and their effects on permission. Engineering of biochemical and transport-reaction systems for technological and mostly in crystalline solids, though methods taught biologics, vaccines, solid oral formulations, sterile 3 pts. Lect: 3. Professor Tsiamis. atmospheric composition and climate. Major topics microbiological reaction systems. Kinetics, reactor therapeutic applications. Modeling of homogeneous are transferable to other materials classes. Course processing, and design of experiments (DoE) treated Aimed at senior undergraduate and graduate are aerosol sources and properties, field and analysis, and design of batch and continuous and heterogeneous biochemical reactions. The grades based on reports for practical assignments. along with a module on regulatory requirements. students. Introduces the science fundamentals laboratory techniques for characterization, gas- fermentation and enzyme processes. Recovery and Bases of biological transport: roles of convection, and the policies and regulations that govern the CHEN E4890x or y Biopharmaceuticals, CHEN E4930y Biopharmaceutical process aerosol interactions, secondary organic aerosols, separations in biochemical engineering systems. ordinary diffusion, forced diffusion. Systems cleanup of sites contaminated with hazardous entrepreneurship, and chemical engineering laboratory aerosol direct and indirect effects on climate. where reaction and transport interact strongly. CHEN E4670x Chemical engineering data materials and discusses the processes used 3 pts. Lect: 3. Professor Hartounian. 3 pts. Lect: 3. Professor Moment. Applications to natural and artificial tissue beds, CHEN E4610y Chemical product design analysis for their treatment and safe disposal. Covers Aimed at graduate students of Chemical Prerequisites: Organic Chemistry Lab I, tumor modeling, controlled release, natural and 3 pts. Lect: 3. Instructor to be announced. 3 pts. Lect: 3. Professor Bishop. the methods used to investigate the extent Engineering. Examines the application of Chemical Undergraduate organic Chemistry. Laboratory- artificial organ function. Prerequisite: CHEN E3210 and CHEM UN2443 or Prerequisites: CHEN E4230, CHEN E3120, and of contamination in soil, groundwater, and Engineering fundamentals and entrepreneurship based course intended for junior and senior equivalent, or instructor’s permission. Application CHEN E3210 or equivalents. Course is aimed CHEN E4760y Genomics sequencing sediment. Uses case studies to illustrate the in starting up a biopharmaceutical company and in undergraduate and graduate students interested in of chemical and engineering knowledge to the at senior undergraduate and graduate students. laboratory application of technologies used to address developing a biopharmaceutical product. Serves gaining hands-on experience in biopharmaceutical design of new chemical products. Relationships industry, including tableting, dissolution, Introduces fundamental concepts of Bayesian 3 pts. Lect: 1. Lab: 2. Not offered in 2020–2021. different categories of contaminants (metals, as a description of the major stages of developing between composition and physical properties. disintegration, fermentation, chromatography, data analysis as applied to chemical engineering Prerequisites: Undergraduate level biology, volatile and semivolatile organics). Applies basic a biopharmaceutical product. Topics presented Strategies for achieving desired volumetric, tangential flow filtration, mixing, and crystallization. problems. Covers basic elements of probability organic chemistry, and instructor’s permission. concepts in the chemical engineering curriculum will include drug discovery, preclinical and clinical rheological, phase equilibrium, thermal, and Connections between process parameters, theory, parameter estimation, model selection, The chemical, biological and engineering principles to specific approaches utilized in characterizing development, IP, manufacturing, and regulatory environmental behavior. Case studies, including chemical and molecular properties, process and experimental design. Advanced topics such involved in the genomics sequencing process will the fate and transport of contaminants and for process. In addition, implementation of the lean separation solvents, blood substitutes, parameters, chemical and molecular properties, as nonparametric estimation and Markov chain be illustrated throughout the course for engineering designing the engineering processes utilized for startup methodology, business valuation, and refrigerants, and aircraft deicing fluids. Monte Carlo (MEME) techniques are introduced. their treatment. financial considerations for a biopharmaceutical process performance, and product attributes students to develop the hands-on skills in conducting illustrated through combination of lectures (given CHEN E4620y Introduction to polymers and Example problems and case studies drawn startup will be offered. Basic topics in the genomics research. CHEN E4860x NMR for bio, soft, and energy during lab time) experiments, and report writing. soft materials from chemical engineering practice are used to chemical engineering curriculum (reaction materials 3 pts. Lect: 3. Not offered in 2020–2021. highlight the practical relevance of the material. CHEN E4780x or y Quantitative methods in kinetics, mathematical modeling, unit operations, CHEN E4999x and y Fieldwork 3 pts. Lect: 3. Professor Marbella. Prerequisite: An elementary course in physical Theory reduced to practice through programming cell biology thermodynamics), as well as specific topics in 1.5–3 pts. Lect: 3. Members of the faculty. in Mathematica. Course grade based on midterm Prerequisites: PHYS UN1401, CHEE E3010, chemistry or thermodynamics. Organic chemistry, 3 pts. Lect: 3. Professor O’Shaughnessy. developing biopharmaceuticals will be discussed Prerequisite: M.S. student. Intended only for and final exams, biweekly homework assignments, or instructor’s permission. Note: junior/senior statistics, calculus and mechanics are helpful, but Prerequisites: Elementary calculus, physics and in this course. M.S. students. Provides work experience on and final team project. undergraduates and graduate (M.S.) students not essential. An introduction to the chemistry and biology, or instructor’s permission. Quantitative chemical engineering in relevant intern or statistical analysis and mathematical modeling only. Course focuses on the fundamentals of CHEN E4900x or y Topics in chemical physics of soft material systems (polymers, colloids, CHOR E4690y Managing systemic risk in fieldwork experience as part of their program in cell biology for an audience with diverse nuclear magnetic resonance (NMR) spectroscopy engineering organized surfactant systems and others), complex systems of study as determined by the instructor. A backgrounds. The course presents quantitative and imaging in fields ranging from biomedical 3 pts. Members of the faculty. emphasizing the connection between microscopic 3 pts. Lect: 3. Professor Venkatasubramanian. written report describing their experience and methods needed to analyze complex cell engineering to electrochemical energy storage. Prerequisite: Instructor's permission. Additional structure and macroscopic physical properties. how it relates to the chemical engineering core Prerequisites: Senior or graduate standing in biological experimental data and to interpret Covers basic NMR theory, instrumentation current topics in chemical engineering taught by To develop an understanding of each system, curriculum is required. Employer feedback on SEAS or instructor's permission. Course will the analysis in terms of the underlying cellular (including in situ/operando setup), data regular or visiting faculty. Special topics arranged illustrative experimental studies are discussed student performance and the quality of the report introduce systems engineering concepts and mechanisms. Optical and electrical experimental interpretation, and experimental design to couple as the need and availability arise. Topics usually along with basic theoretical treatments. High are the basis of the grade. May not be taken for tools such as digraphs, fault trees, probabilistic methods to study cells and basic image with other materials characterization strategies. offered on a one-time basis. Since the content of molecular weight organic polymers are discussed pass/fail credit or audited. Only 3 points of CHEN risk assessment, HAZOP, FMEA, etc., for analysis techniques are described. Methods Course grade based on problem sets, quizzes, this course changes each time it is offered, it may first (basic notions, synthesis, properties of single E4999 can be credited toward the M.S. degree. modeling enterprise-wide risk in complex of statistical analysis of experimental data and and final project presentation. be repeated for credit. polymer molecules, polymer solution and blend Furthermore, students who take CHEN E4999 systems. Important industrial accidents will be techniques to test and compare mathematical thermodynamics, rubber and gels). Colloidal CHEN E4870y Synthetic organogenesis CHEN E4910x and y Solid state chemistry in can use only a maximum of 3 points of CHEN E discussed as case studies. models against measured statistical properties 3 pts. Lect: 3. Professor Simunovic. pharmaceutical development 9400 in fulfillment of the M.S. degree. systems are treated next (dominant forces in will be introduced. Concepts and techniques colloidal systems, flocculation, preparation and CHEN E4700x Principles of genomic Prerequisites: Any quantitative undergraduate 3 pts. Lect: 3. Not offered in 2020–2021. of mathematical modeling will be illustrated by CHEN E6050x Advanced electrochemistry manipulation of colloidal systems) followed by a technologies course with elements of biology, such as Prerequisites: Thermodynamics (any) or General applications to mechanosensing in cells, the 3 pts. Lect: 3. Not offered in 2020–2021. discussion of self-organizing surfactant systems 3 pts. Lect: 3. Professor Ju. Chemistry, Biochemical Engineering/Biochemistry, Chemistry. Fundamentals of solid state as related mechanics of cytokinesis during cell division and to pharmaceutical development, and is intended Prerequisite: Instructor’s permission. An (architecture of surfactants, micelles and Prerequisites: Undergraduate-level biology, Biophysics, or at the instructor's permission. synaptic transmission in the nervous system. for junior and senior undergraduates and graduate advanced overview of the fundamentals of surfactant membranes, phase behavior). organic chemistry, and instructor’s permission. Synthetic organogenesis to use stem cells to Image analysis, statistical analysis, and model electrochemistry, with examples taken from Chemical and physical aspects of genome reconstitute aspects of embryo development and students. Theoretical and practical aspects assessment will be illustrated for these systems. modern applications. An emphasis is placed CHEN E4630y Topics in soft materials structure and organization, genetic information organ formation in vitro. Examines the molecular are covered, including segments on thermal on mass transfer and scaling phenomena. 3 pts. Instructor to be announced. flow from DNA to RNA to protein. Nucleic acid CHEN E4800x Protein engineering basis of human embryogenesis. Introduces and spectroscopic analytical instrumentation. Topics include crystal structure, polymorphism, Principles are reinforced through the development Prerequisite: Physical chemistry or instructor’s hybridization and sequence complexity of DNA 3 pts. Lect: 3. Professor Banta. synthetic organogenesis as an interdisciplinary crystallization processes, pharmaceutical of mathematical models of electrochemical permission. Self-contained treatments of and RNA. Genome mapping and sequencing Prerequisite: CHEN E4230, may be taken field. Students learn to recognize generic properties, amorphous solids, solid state reactions, systems. Course projects will require computer selected topics in soft materials (e.g., polymers, methods. The engineering of DNA polymerase concurrently, or the instructor’s permission. molecular mechanisms behind signaling and cell stability testing, solid oral formulation, particle simulations. The course is intended for advanced colloids, amphiphiles, liquid crystals, glasses, for DNA sequencing and polymerase chain Fundamental tools and techniques currently used lineage specification. Covers recent advances in size control, and dissolution testing. Connections graduate students, conducting research involving powders). Topics and instructor may change reaction. Fluorescent DNA sequencing and to engineer protein molecules. Methods used applying engineering and contemporary biology from year to year. Intended for junior/senior between molecular structure, physical structure electrochemical technologies. high-throughput DNA sequencer development. to analyze the impact of these alterations on to creating organoids and organs on chips using level undergraduates and graduate students in (e.g., particle size distribution), and product Construction of gene chip and micro array for different protein functions with specific emphasis human stem cells. EACH E6181x Advanced electrochemical engineering and the physical sciences. on enzymatic catalysis. Case studies reinforce performance will be focus of class. gene expression analysis. Technology and CHEN E4880x or y Atomistic simulations for energy storage concepts covered, and demonstrate the wide CHEN E4650y Polymer physics biochemical approach for functional genomics science and engineering CHEN E4920x and y Pharmaceutical industry 3 pts. Lect: 3. Professor Steingart. impact of protein engineering research. Application 3 pts. Lect.: 3. Professor Kumar. analysis. Gene discovery and genetics database 3 pts. Lect: 3. Not offered in 2020–2021. for engineers Prerequisites: EAEE E4180, EAEE E4002. of basic concepts in the chemical engineering Prerequisites: CHEN E3110, CHEN E3120 and search method. The application of genetic Prerequisites: statistical mechanics or 3 pts. Lect: 3. Not offered in 2020–2021. Most modern commercial implementations curriculum (reaction kinetics, mathematical database for new therapeutics discovery. thermodynamics or instructor's permission. Aimed at Prerequisites: General Chemistry and Organic of electrochemical energy storage are not E4620. Senior undergraduate/first-year graduate modeling, thermodynamics) to specific approaches course on the physics of polymer systems. Topics senior undergraduates and graduate students. Covers Chemistry. Overview of biopharmaceutical design, fully deterministic: provides context and best- CHEN E4740x Biological transport and rate utilized in protein engineering. include scaling behavior of chains under different atomistic simulation techniques for applications at development, manufacturing, and regulatory hypotheses for modern challenges. Topics include: phenomena, II requirements from an engineering perspective. conditions, mixing thermodynamics, networks and BMCH E4810y Artificial organs interface of chemical engineering and materials current understanding of LithiumLithium Anode 3 pts. Lect: 3. Not offered in 2020–2021. Unit operations, equipment selection, and process generation, polymer dynamics, including reptation 3 pts. Lect: 3. Professor Leonard. science. Theoretical background of various simulation Solid-Electrolyte-Interphase, Reversible and Prerequisites: Any two of the following: CHEN development associated with small molecule, and entanglements. Special topics: nanocomposites. Analysis and design of replacements for the heart, techniques ranging from empirical to first-principles Irreversible Side Reactions in Redox flow systems,

ENGINEERING 2020–2021 ENGINEERING 2020–2021 electrochemically correlated mechanical fracture at studies, research, technical writing, and to conduct an investigation of some problem in 86 87 multiple scales, relationships between electrolyte professionalism. Covers manuscript preparation, chemical engineering or applied chemistry and CIVIL ENGINEERING AND ENGINEERING MECHANICS solvation and electrode insertion, roughening, proposal preparation, protection of intellectual to submit a thesis describing the results of their 610 S. W. Mudd, MC 4709 smoothing, and detachment behavior of metal property, professional ethics, etc. Topics include: work. No more than 6 points may be counted for 212-854-3143 anodes, best practices in structural, chemical, and (1) laboratory safe practices including rules graduate credit, and this credit is contingent upon civil.columbia.edu microscopic characterization, morphological vs. administered by EHRS and preparation for the submission of an acceptable thesis. macro-homogenous transport models, particle to obtaining the required NYFD Certificate of Fitness, CHEN E9500x and y–S9500 Doctoral research electrode to cell nonlinearity. (2) expectations and responsibilities of teaching 1–15 pts. Members of the faculty. CHAIR PROFESSORS Marco Giometto Mysore Nagaraja MANAGER, CARLETON assistants (TAs) and (3) rules, milestones, and CHEE E6201x or y Topics in electrochemical Prerequisites: The qualifying examinations for the Jacob Fish Raimondo Betti LECTURERS IN Michele O'Connor LABORATORY assessment of progress within the Chemical William A. Hunnicutt energy storage and conversion doctorate. Open only to certified candidates for the Gautam Dasgupta DISCIPLINE Daniel Peterson Engineering graduate program. DEPARTMENT George Deodatis Julius Chang 3 pts. Lect: 3. Professor West. Ph.D. and Eng.Sc.D. degrees. Doctoral candidates Alan Poeppel ADMINISTRATOR Maria Q. Feng Ibrahim Odeh Kevin Riordan MANAGER, Prerequisite: CHEN E4201 or instructor’s CHEN E8100y Topics in biology in chemical engineering are required to make an Alma Levin Jacob Fish Thomas Panayotidi Robert A. Rubin CENTRIFUGE permission. Selected topics in electrochemical 3 pts. Lect: 3. Professor O’Shaughnessy. original investigation of a problem in chemical Upmanu Lall, Earth Matthew Sisul LABORATORY Prerequisites: Instructor’s permission. This engineering or applied chemistry, the results of energy storage and/or conversion. Experimental, GRADUATE and Environmental ADJUNCT FACULTY Vincent Tirolo Liming Li research seminar introduces topics at the which are presented in their dissertations. No more theoretical, technological topics vary. Critical ADMISSIONS AND Engineering Amr Aly Richard L. Tomasetti analysis of scientific and engineering literature. forefront of biological research in a format and than 15 points of credit toward the degree may be STUDENT AFFAIRS Hoe I. Ling Ali Ashrafi Mario Valenti SENIOR LABORATORY Team projects and student-led discussions. Topics language accessible to quantitative scientists and granted when the dissertation is accepted by the OFFICER Richard W. Longman, Luciana Balsamo Christopher Vitolano TECHNICIAN and instructor may change from year to year. Note: engineers lacking biological training. Conceptual department. Scott Kelly Mechanical Emily Belote George Wheeler Travis Simmons and technical frameworks from both biological Engineering Adrian Brügger recommended for Ph.D. students. CHEN E9600x and y Advanced research Philip White and physical science disciplines are utilized. ASSOCIATE DIRECTOR, Feniosky Peña-Mora Richard F. Carbonaro Bojidar Yanev SENIOR LABORATORY problems CHEE E6220y Equilibria and kinetics in The objective is to reveal to graduate students CAREER PLACEMENT Andrew Smyth Steven Charney Songtao Yang ENGINEER 2–10 pts. Members of the faculty. hydrometallurgical systems where potential lies to apply techniques from Emily-Anne McCormack Raymond Daddazio Theodore P. Zoli Freddie E. Wheeler ASSOCIATE 3 pts. Lect: 3. Not offered in 2020–2021. their own disciplines to address pertinent Prerequisites: Recommendation of the professor Jonathan David PROFESSORS Prerequisite: Instructor’s permission. An concerned and approval of the master’s research FINANCIAL ANALYST Rudolph Frizzi DIRECTOR, CARLETON biological questions in their research. Classes Laura Lichtblau Shiho Kawashima advanced overview of the fundamentals of entail reading, criticism and group discussion of department. For postdoctoral students and other Marc Gallagher LABORATORY qualified special students who wish to pursue Ioannis Kougioumtzoglou Eli B. Gottlieb Adrian Brügger electrochemistry, with examples taken from research papers and textbook materials providing WaiChing Sun research under the guidance of members of the SYSTEM Paul Haining modern applications. An emphasis is placed overviews to various biological areas including: ADMINISTRATOR Haim Waisman on mass transfer and scaling phenomena. department. Not open to undergraduates or to William M. Hart FACULTY DIRECTOR, evolution, immune system, development and Michael Smith Huiming Yin CARLETON Principles are reinforced through the development candidates for the degrees of Ch.E., M.S., Ph.D., George Leventis cell specialization, the cytoskeleton and cell Elisabeth Malsch LABORATORY of mathematical models of electrochemical or Eng.Sc.D. ADMINISTRATIVE ASSISTANT motility, DNA transcription in gene circuits, protein Tim McManus Andrew Smyth systems. Course projects will require computer ASSISTANT PROFESSORS networks, recombinant DNA technology, aging, and CHEN E9800x and y Doctoral research Virginia Mosquera simulations. The course is intended for advanced Nathalie Benitez Sharon (Xuan) Di gene therapy. instruction Robert D. Mutch graduate students, conducting research involving 3, 6, 9 or 12 pts. Members of the faculty. electrochemical technologies. CHEN E9000x and y Chemical engineering colloquium A candidate for the Eng.Sc.D. degree in CHEE E6252y Applied surface and colloid 0 pts. Col: 1. Professor Esposito. chemical engineering must register for 12 he Department of Civil Engineering breadth needed to follow diverse career engineering, social, financial, and decision- chemistry Graduate students on the Ph.D. track are required points of doctoral research instruction. 3 pts. Lect: 2. Lab: 3. Professors Somasundaran to attend the department colloquium as long as Registration in CHEN E9800 may not be used to and Engineering Mechanics paths, whether in the profession via making perspectives of the problem are and Farinato. they are in residence. No degree credit is granted. satisfy the minimum residence requirement for focuses on two broad areas of advanced study or apprenticeship, or as examined in an integrated manner. the degree. T Prerequisites: CHEE E4252. Applications of instruction and research. The first, the a base for other pursuits. CHEN E9001x M.S. Chemical engineering Probabilistic mechanics: random surface chemistry principles to wetting, flocculation, CHEN E9900x and y–S9900 Doctoral classical field of civil engineering, deals flotation, separation techniques, catalysis, mass colloquium processes and fields to model uncertain dissertation with the planning, design, construction, transfer, emulsions, foams, aerosols, membranes, 0 pts. Lect.: 1. Professor Bozic. Current Research Activities loads and material/soil properties, 0 pts. Members of the faculty. and maintenance of the built biological surfactant systems, microbial surfaces, Required for all M.S. students in residence in Current research activities in the Open only to certified doctoral candidates. nonlinear random vibrations, reliability enhanced oil recovery, and pollution problems. their first semester. Topics related to professional environment. This includes buildings, Department of Civil Engineering and A candidate for the doctorate in chemical and safety of structural systems, Appropriate individual experiments and projects. development and the practice of chemical foundations, bridges, transportation engineering may be required to register for Engineering Mechanics are centered computational stochastic mechanics, Lab required. engineering. No degree credits granted. Intended facilities, nuclear and conventional this course in every term after the student’s in the areas outlined below. A number stochastic finite element and boundary for M.S. students only. power plants, hydraulic structures, and CHEN E6543x Chemical engineering research coursework has been completed, and until the of these activities impact directly on element techniques, Monte Carlo other facilities essential to society. The methodology CHEN E9400x and y Master’s research dissertation has been accepted. problems of societal importance, such simulation techniques, random second is the science of mechanics and 1 pts. Professor Bishop. 1–6 pts. Members of the faculty. as rehabilitation of the infrastructure, micromechanics. For first year graduate students entering the Prescribed for M.S. and Ch.E. candidates; its applications to various engineering mitigation of natural or man-made Ph.D. program. Serves as a "survival skills" elective for others with the approval of the disciplines. Frequently referred to as disasters, and environmental concerns. Structural control and health course to familiarize students with graduate Department. Degree candidates are required applied mechanics, it includes the study monitoring: topics of research in this of the mechanical and other properties Solid mechanics: mechanical properties highly cross-disciplinary field include the of materials, stress analysis of stationary of new and exotic materials, constitutive development of “smart” systems for the and movable structures, the dynamics equations for geologic materials, failure mitigation and reduction of structural and vibrations of complex structures, of materials and components, properties vibrations, assessment of the health aero- and hydrodynamics, and the of fiber-reinforced cement composites, of structural systems based on their mechanics of biological systems. damage mechanics. vibration response signatures, and the Multihazard risk assessment and modeling of nonlinear systems based mitigation: integrated risk studies of on measured dynamic behavior. MISSION the civil infrastructure form a multihazard The department aims to provide Fluid mechanics: numerical and perspective, including earthquake, wind, students with a technical foundation theoretical study of fluid flow and flooding, fire, blast, and terrorism. The anchored in theory together with the transport processes, non-equilibrium

ENGINEERING 2020–2021 ENGINEERING 2020–2021 88 fluid dynamics and thermodynamics, rheological characterization for strategies and processes; data to gain a unique appreciation of modern ry component of the ENME E3161 Fluid UNDERGRADUATE PROGRAMS 89 turbulence and turbulent mixing, advanced cement/concrete placement management practices and systems; experimental approaches to material sci- Mechanics course and includes multiple The Department of Civil Engineering boundary-layer flow, urban and processes. indicators of infrastructure performance ence and engineering mechanics. hydraulic benches with a full array of and Engineering Mechanics focuses vegetation canopy flow, particle-laden and service; market analysis. The Carleton Laboratory serves as experimental modules. Computational mechanics: aimed at on two broad areas of instruction and flow, wind loading, flow through porous the hub of instruction for classes offered research. The first, the classical field understanding and solving problems in The Eugene Mindlin Laboratory for media, and flow and transport in by the Department of Civil Engineering of civil engineering, deals with the science and engineering, topics include FACILITIES Structural Deterioration Research fractured rock. and Engineering Mechanics, most planning, design, construction, and multiscale methods in space and time The offices and laboratories of the The Mindlin Laboratory has been devel- prominently ENME E3114 Experimental maintenance of structures and the Environmental engineering/water (e.g., homogenization and multigrid department are in the S. W. Mudd oped for teaching and research dedicated Mechanics of Materials, ENME E3106 infrastructure. These include buildings, resources: modeling of flow and methods); multiphysics modeling; Building and the Engineering Terrace. to all facets of the assessment of struc- Dynamics and Vibrations, and CIEN foundations, bridges, transportation pollutant transport in surface and material and geometric nonlinearities; tures, deterioration of structural perfor- E3141 Soil Mechanics. The Laboratory facilities, nuclear and conventional subsurface waters, unsaturated strong and weak discontinuities (e.g., Computing mance and surface coatings, dynamic test- also hosts and advises the AISC Steel power plants, hydraulic structures, and zone hydrology, geoenvironmental cracks and inclusions); discretization The department manages a substantial ing for earthquakes, and other applications. Bridge Team in the design, fabrication, other facilities essential to society. The containment systems, analysis of techniques (e.g., extended finite element computing facility of its own in addition The commissioning of a state-of-the-art and construction phases of their bridge, second is the science of mechanics and watershed flows including reservoir methods and mixed formulations); 150 kN Instron universal testing machine, a to being networked to all the systems which goes to regional and national simulation. verification and validation (e.g., error QUV ultraviolet salt spray corrosion system, its applications to various engineering operated by the University. The depart- competition annually. analysis); software development and a freeze-thaw tester, a Keyence optical disciplines. Frequently referred to as Structures: dynamics, stability, and ment facility enables its users to perform Additionally, the Carleton Laboratory parallel computing. microscope and surface analyzer have applied mechanics, it includes the design of structures, structural failure symbolic and numeric computation, has a fully outfitted machine shop further expanded the Mindlin Laboratory’s study of the mechanical properties of and damage detection, fluid and soil Multiscale mechanics: solving three-dimensional graphics, and expert capable of machining parts, fittings, and capabilities in material testing and char- materials, stress analysis of stationary structure interaction, ocean structures various engineering problems that systems development. Connections to testing enclosures in steel, nonferrous acterization. The Mindlin Laboratory also and movable structures, the dynamics subjected to wind-induced waves, have important features at multiple wide-area networks allow the facility’s metals, acrylic, and wood. The Carleton serves as a state-of-the-art medium scale and vibrations of complex structures, inelastic dynamic response of reinforced spatial and temporal scales, such as users to communicate with centers Machine Shop’s machine tool pool is non-destructive structural health monitoring aero- and hydrodynamics, micro- and concrete structures, earthquake- predicting material properties or system throughout the world. All faculty and state-of-the-art, either of the latest gen- facility, allowing the conduct of research in nanomechanics, and the mechanics of resistant design of structures. behavior based on information from finer student offices and department labora- eration or recently rebuilt and modern- the assessment of our nation’s degrading biological and energy systems. scales; focus on information reduction tories are hardwired to the computing Geotechnical engineering: soil ized. The machine shop is open for use civil infrastructure. methods that provide balance between facility, which is also accessible remotely behavior, constitutive modeling, by undergraduate students performing Program Objectives computational feasibility and accuracy. to users. Numerous personal computers independent research and is supported reinforced soil structures, geotechnical The Pao Sustainable Engineering and 1. Graduates with a broad and funda- and graphics terminals exist throughout earthquake engineering, liquefaction Transportation engineering: by the Lab’s senior lab technician. mental technical base will be able to the department, and a PC lab is available Materials Laboratory and numerical analysis of geotechnical understanding and modeling enter the professional civil engineer- to students in the department in addition The Donald M. Burmister Soil The Pao Sustainable Engineering systems. transportation systems that are ing workforce either with a B.S. to to the larger school-wide facility. Mechanics Laboratory and Materials Laboratory (Pao Lab) radically evolving due to emerging develop specialized expertise by Structural materials: cement-based The Burmister Laboratory contains is located off-campus at 7 Industry communication and sensing Street, Poughkeepsie, NY 12603 and way of apprenticeship or through the materials, micro- and macromodels of Laboratories equipment and workspace to carry out technologies; leveraging large data hosts major research projects of the increasingly common path of a spe- fiber-reinforced cement composites, Robert A. W. Carleton Strength of all basic soil mechanics testing for our collected from various traffic sensors NSF IUCRC Center for Engineering cialized M.S. utilization of industrial by-products Materials Laboratory undergraduate and graduate programs. to understand transformation in travel Harvesting Materials and Systems 2. Graduates with a firm foundation and waste materials, beneficiation of The Carleton Laboratory serves as the Several unique apparatuses have been behavior patterns; modeling travel (CEHMS). Cooperating with CEHMS' in the basic math, science, and dredged material. central laboratory for all experimental acquired or fabricated for advanced soil behavior using a game theory approach industry members, researchers and engineering science that underlie all work performed in the Department testing and research: automated plain Earthquake engineering: response of to help decision-makers understand students can access a modern technological development will be of Civil Engineering and Engineering strain/triaxial apparatus for stress path structures to seismic loading, seismic upcoming changes and prepare for multifunctional weathering system well equipped to adapt to changing Mechanics. It is the largest laboratory testing at both drained and undrained risk analysis, active and passive control effective planning and management of anchored by the Henry Mitchell Weitzner technology in the profession. at Columbia University’s Morningside conditions, direct sheer device for mini- of structures subject to earthquake next generation transportation systems. Environmental Chamber for life-cycle 3. Graduates equipped with a broad campus and is equipped for teaching mum compliance, and a unique sand excitation, seismic analysis of long-span performance evaluation of infrastructure technical background will be able to Construction engineering and and research in all types of engineer- hopper which prepares foundations and cable-supported bridges. materials and surface coatings. The follow other technical or nontechnical management: contracting strategies; ing materials and structural elements, slopes for small scale model testing. The Flight structures: composite materials, Pao Lab serves some laboratory career paths. alternative project delivery systems; as well as damage detection, fatigue, Laboratory has established a link and smart and multifunctional structures, components for the CIEE E4116 4. Graduates will practice their minimizing project delays and disputes; vibrations, and sensor networks. The cooperation for large-scale testing for multiscale and failure analysis, vibration Energy Harvesting course and some profession with effective writing advanced technologies to enhance Laboratory has a full-time staff who earthquake and geosynthetic applica- control, computational mechanics and experimental modules of other courses. and communication skills, with productivity and efficiency; strategic provide assistance in teaching and tions with NRIAE, the centrifuge facilities finite element analysis, fluid-structure professional ethics, as well as with decisions in global engineering and research. The Laboratory is equipped at the Rensselaer Polytechnic Institute interaction, aeroelasticity, optimal design, awareness of societal issues. construction markets; industry trends with a strong floor that allows for the and the Tokyo Institute of Technology. The Institute of Flight Structures and environmental degradation of and challenges. testing of full-scale structural compo- The Institute of Flight Structures was structures. The Heffner Hydrologic Research established within the department through Student Outcomes Infrastructure delivery and nents such as bridge decks, beams, and Laboratory a grant by the Daniel and Florence 1. an ability to identify, formulate, and Advanced materials: multifunctional management: decision support systems columns. Furthermore, it is equipped The Heffner Laboratory is a facility for Guggenheim Foundation. It provides a solve complex engineering problems engineering materials, advanced for infrastructure asset management; with universal testing machines ranging both undergraduate instruction and base for graduate training in aerospace by applying principles of engineering, energy materials, durable infrastructure assessing and managing infrastructure in capacity from 150 kN (30,000 lbs.) research in aspects of fluid mechanics, and aeronautical related applications of science, and mathematics materials, new concretes/composites assets and systems; capital budgeting to 3 MN (600,000 lbs.). The seamless environmental applications, and water structural analysis and design. 2. an ability to apply engineering design using nanotubes, nanoparticles, and integration of both research and teach- processes and decisions; innovative resources. The Heffner Laboratory hous- to produce solutions that meet other additives with alternative binders, ing in the same shared space allows civil financing methods; procurement es the facilities for teaching the laborato- specified needs with consideration sustainable manufacturing technologies, engineering students of all degree tracks

ENGINEERING 2020–2021 ENGINEERING 2020–2021 90 91 CIVIL ENGINEERING PROGRAM: FIRST AND SECOND YEARS CIVIL ENGINEERING: THIRD AND FOURTH YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

APMA E2101 (3) CIEN E3125 (3) MATH UN1101 (3) MATH UN1102 (3) APMA E2000 (4) MATHEMATICS Intro. to applied math. 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) Computer-aided UN1401 (3) UN1402 (3) Lab UN1494 (3) REQUIRED Design projects PHYSICS or chem. lab COURSES ENME E3161 (4) struct. design CIEN E3129 (3) (three tracks, UN1601 (3.5) UN1602 (3.5) Fluid mech. Proj. mgmt. for choose one) UN2801 (4.5) UN2802 (4.5) Lab UN3081 (2) CIEN E3141 (4) construction Soil mech.

one-semester lecture (3–4): UN1403 or UN1404 or UN2045 or UN1604 CHEMISTRY Chem lab UN1500 (3) either semester or physics lab ENME E3332 (3) ENME E3106 (3) A first course in finite Dynamics and vibrations elements GEOTECH GEOLOGY EESC UN1011 (4) or equivalent ENG. (GE) ENME E3114 (4) CIEN E3127 (3) OR Exper. mech. of materials Struct. design projects STRUCT. (SE) MECHANICS ENME-MECE E3105 (4) either semester ENG. (SE) CIEN E3121 (3) or Struct. anal. CIEN E4241 (3) CIEE E3260 (3) Geotech. eng. fund. (GE) CIEN E3000 (3) (Spring semester; recommended but not required) CIVIL ENGINEERING Eng for dev communities

TECH 3 points 3 points 9 points ELECTIVES UNIVERSITY CC1010 (3) either semester WRITING CIEN E4133 (3) ENME E3114 (4) Capital facility planning HUMA CC1001, HUMA CC1002, Exper. mech. of materials COCI CC1101, COCI CC1102, and financing CIVIL ENG. REQUIRED or Global Core (3–4) or Global Core (3–4) CIEN E3121 (3) CIEN E4131 (3) NONTECHNICAL AND CIEN E3127 (3) Struct. anal. Princ. of constr. tech. ELECTIVES CONSTR. Struct. design projects HUMA UN1121 or ECON UN1105 (4) and MGMT. or or UN1123 (3) UN1155 recitation (0) CIEE E3250 (3) CIEN E4241 (3) Hydrosystems eng. Geotech. eng. fund.) CONCENTRATIONS COMPUTER Computer Language: ENGI E1006 (3) or equivalent (any semester) SCIENCE TECH 6 points 3 points 6 points ELECTIVES PHYSICAL UN1001 (1) UN1002 (1) EDUCATION CIEE E3255 (3) Environ. control / pollution CIEE E4163 (3) THE ART OF ENGI E1102 (4) either semester Sust. water treat. / reuse ENGINEERING EAEE E4006 (3) WATER RES./ CIEE E3250 (3) Field methods for ENVIRON. Hydrosystems eng. CIEE E4257 (3) ENG. environ. eng. of public health, safety, and welfare, tasks, and meet objectives the student have obtained a grade of Ground contam. transport CIEN E3303 (1) / remed. as well as global, cultural, social, 6. an ability to develop and conduct B or better. Independent studies environmental, and economic factors appropriate experimentation, 3. an ability to communicate effectively analyze and interpret data, and Civil Engineering TECH 6 points 3 points 6 points with a range of audiences use engineering judgment to draw The prerequisites for this program are the ELECTIVES 4. an ability to recognize ethical and conclusions courses listed in the First and Second professional responsibilities in 7. an ability to acquire and apply Years Program (see above) or their NONTECH 3 points 3 points 3 points engineering situations and make new knowledge as needed, using ELECTIVES equivalents. The civil engineering program informed judgments, which must appropriate learning strategies. offers three areas of concentration: consider the impact of engineering civil engineering and construction TOTAL POINTS 13 21 18.5 13 solutions in global, economic, Engineering Mechanics management, geotechnical engineering environmental, and societal contexts The prerequisites for this program or structural engineering, and water 5. an ability to function effectively are the courses listed in the First and resources/environmental engineering. In on teams whose members Second Years Program (page 92) or the junior and senior years, 15 credits of together provide leadership, create their equivalents, with the provision technical electives are allocated. a collaborative and inclusive that ENME E3105: Mechanics be Columbia’s program in civil environment, establish goals, plan taken in the sophomore year and that engineering leading to the B.S. degree

ENGINEERING 2020–2021 ENGINEERING 2020–2021 92 93 ENGINEERING MECHANICS PROGRAM: FIRST AND SECOND YEARS ENGINEERING MECHANICS: THIRD AND FOURTH YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

APMA E2101 (3) APMA E3102 (3) MATH UN1101 (3) MATH UN1102 (3) APMA E2000 (4) MATHEMATICS Intro. to applied math. ENME E3113 (3) Applied math., II ENME E3332 (3) Mech. of solids A first course in finite ENME E3106 (3) elements ENME E3161 (4) Dynamics and vibrations UN1401 (3) UN1402 (3) Lab UN1494 (3) CORE ENME E4202 (3) PHYSICS Fluid mechanics ENME E4113 (3) or chem. lab REQUIRED Advanced mech. (three tracks, COURSES ENME E3114 (4) Advanced solids choose one) UN1601 (3.5) UN1602 (3.5) UN2801 (4.5) UN2802 (4.5) Lab UN3081 (2) APMA E3101 (3) Experimental mech. Applied math., I ENME E4215 (3) CIEN E3121 (3) Theory of vibrations one-semester lecture (3–4): UN1403 or UN1404 or UN2045 or UN1604 Structural analysis CHEMISTRY Chem lab UN1500 (3) either semester or physics lab

TECH 3 points 6 points 6 points 9 points MECHANICS ENME-MECE E3105 (4) any semester

3 points 3 points ELECTIVES NONTECH UNIVERSITY CC1010 (3) either semester WRITING

13 19 18 15 HUMA CC1001, HUMA CC1002, TOTAL POINTS COCI CC1101, COCI CC1102 REQUIRED or Global Core (3–4) or Global Core (3–4) NONTECHNICAL ELECTIVES HUMA UN1121 or ECON UN1105 (4) and • Construction Engineering and the M.S. degree. Candidates for the managing engineering and UN1123 (3) UN1155 recitation (0) Management Eng.Sc.D. degree must also accumulate construction processes, construction • Engineering Mechanics 12 credits in the departmental course industry law, construction techniques, • Environmental Engineering and Water CIEN E9800 Doctoral Research managing civil infrastructure systems, REQUIRED (3) Student’s choice, see list of first- and second-year technical electives TECH ELECTIVES Resources Instruction. In addition to coursework civil engineering and construction • Forensic (Structural) Engineering requirements, doctoral degree students entrepreneurship COMPUTER Computer Language: ENGI E1006 (3) or equivalent (any semester) • Geotechnical Engineering must write a dissertation embodying • Environmental Engineering and SCIENCE • Structural Engineering original research under the sponsorship Water Resources: transport of of their faculty adviser. water-borne substances, hydrology, PHYSICAL UN1001 (1) UN1002 (1) EDUCATION Doctoral Degree Programs Major research thrusts for the sediment transport, hydrogeology, Two doctoral degrees in engineering doctoral degree programs include: and geoenvironmental design of Computational mechanics containment systems THE ART OF ENGI E1102 (4) either semester are offered within the department: ENGINEERING the Doctor of Engineering science Multiscale mechanics • Geotechnical Engineering: soil (Eng.Sc.D.), administered by The Fu Poromechanics mechanics, foundation engineering, Foundation School of Engineering and Dynamics and vibrations earth-retaining structures, slopes, and of these areas. There are no required is accredited by the Engineering Master of Science Degree Program Applied Science, and the Doctor of Infrastructure monitoring geotechnical earthquake engineering courses at the M.S. level. Every student Accreditation Commission of ABET, The Department of Civil Engineering and Philosophy (Ph.D.), administered by the Cementitious materials and concrete • Forensic (Structural) Engineering: is assigned a faculty member as an http://www.abet.org. Engineering Mechanics offers a graduate Graduate School of Arts and Science. Advanced infrastructure materials investigation and determination of academic adviser. Student and adviser program leading to the degree of Master The Eng.Sc.D. and Ph.D. programs have Structural safety and reliability the causes of structural failures meet regularly and plan together the Minor in Architecture of Science (M.S.) in Civil Engineering nearly identical academic requirements Probabilistic mechanics of buildings, bridges, and other sequence of courses that best fit the Civil engineering program students may and Engineering Mechanics. The Master with regard to courses, qualifying Sustainable/green infrastructure constructed facilities student's interests. While a suitable want to consider a minor in architecture of Science degree is awarded upon the examinations, and the dissertation, but Geomechanics • Structural Engineering: applications M.S. program will necessarily entail (see page 204). satisfactory completion of a minimum of differ in residence requirements and in Fluid mechanics to steel and concrete buildings, some degree of specialization, the 30 points of credit of approved graduate certain administrative details. A student Autonomous transportation bridges, and other structures program of study established between study extending over at least two must obtain the master's degree (M.S.) Disasters and natural hazards GRADUATE PROGRAMS the student and the adviser should be semesters. before enrolling as a candidate for either Engineering Mechanics M.S. students must complete the well balanced, including basic subjects The M.S. program is very flexible and the Ph.D. or Eng.Sc.D. degree. Civil Engineering Programs in engineering mechanics offer professional development and of broad importance as well as theory includes concentrations in Construction In conjunction with their faculty By selecting technical electives, students comprehensive training in the principles leadership course, ENGI E4000, and applications Students may take Engineering and Management, adviser, doctoral degree students may focus on one of several areas of of applied mathematics and continuum as a graduation requirement. Ph.D. graduate-level courses from across Engineering Mechanics, Environmental plan an appropriate course of study concentration or prepare for future mechanics and in the application of candidates are strongly encouraged various concentrations within the Engineering and Water Resources, related to their area of focus within the endeavors such as architecture. these principles to the solution of to complete the ENGI E6001–6004 department. Forensic (Structural) Engineering, department. Doctoral degree students • Construction Engineering and engineering problems. The emphasis is and should consult their program for The Master of Science Geotechnical Engineering, and must complete a minimum of 30 credits Management: capital facility planning on basic principles, enabling students PDL requirements. concentrations are: Structural Engineering, or combinations of graduate-level coursework beyond and financing, strategic management, to choose from among a wide range

ENGINEERING 2020–2021 ENGINEERING 2020–2021 CIEN E3000y The art of structural design Corequisite: CIEN E3125. Introduction to software runoff generation, open channel and pipe flow, and traffic studies; traffic and highway engineering; considering changing climate, values, and needs. 94 of technical areas. Students may work 95 on problems in such disciplines as 3 pts. Lect: 3. Professor Deodatis. for structural analysis and design with lab. subsurface flow and well hydraulics in the context rapid transit and railroad engineering. Public and private sector models explored through Basic scientific and engineering principles for the Applications to the design of structural elements of example watersheds and specific integrative U.S.-international case studies on topics ranging systems analysis, acoustics, and stress CEOR E4011y Infrastructure systems design of buildings, bridges, and other parts of and connections. Lab required. problems such as risk-based design for flood from integrated watershed management to the optimization analysis, and in fields as diverse as the built infrastructure. Application of principles control, provision of water, and assessment of analysis of specific projects for flood mitigation, CIEN E3127x Structural design projects 3 pts. Lect: 3. Professor Di. transportation, environmental, structural, to analysis and design of actual large-scale environmental impact or potential for nonpoint water and wastewater treatment, or distribution 3 pts. Lect: 3. Professor Panayotidi. Prerequisites: Basic linear algebra. Basic nuclear, and aerospace engineering. structures. Coverage of the history of major source pollution. Spatial hydrologic analysis using system evaluation and improvement. Prerequisites: CIEN E3125 and E3126 or the probability and statistics. Engineering economic Program areas include: structural design innovations and of the engineers GIS and watershed models. Note: This course instructor’s permission. Design of steel members in concepts. Basic spreadsheet analysis and CIEN E4111x Uncertainty and risk in who introduced them. Critical examination of the is to be joint listed with CIEN and replaces the accordance with AISC 360: moment redistribution programming skills. Subject to instructor's infrastructure systems • Continuum mechanics: solid and unique aesthetic/artistic perspectives inherent in previous CIEN 3250. in beams; plastic analysis; bearing plates; beam- permission. Infrastructure design and systems 3 pts. Lect: 3. Professor Kougioumtzoglou. fluid mechanics, theories of elastic structural design. Consideration of management, columns: exact and approximate second-order CIEE E3255y Environmental control and concepts, analysis, and design under competing/ Introduction to basic probability, hazard function, and inelastic behavior, and damage socioeconomic, and ethical issues involved in analysis; design by the Effective Length method pollution reduction systems conflicting objectives, transportation network reliability function, stochastic models of natural and mechanics design and construction of large-scale structures. and the Direct Analysis method. Design of 3 pts. Lect: 3. Professor Farrauto. models, traffic assignments, optimization, and the technological hazards, extreme value distributions, • Vibrations: nonlinear and random Introduction to recent developments in sustainable concrete members in accordance with ACI 318: bar Prerequisite: EAEE E3200 or ENME E3161 or simplex algorithm. Monte Carlo simulation techniques, fundamentals vibrations; dynamics of continuous engineering, including green building design and anchorage and development length, bar splices, MECE E3100. Review of engineered systems for CIEN E4011y Big data analytics in of integrated risk assessment and risk management, media, of structures and rigid bodies, adaptable structural systems. design for shear, short columns, slender columns. prevention and control of pollution. Fundamentals transportation topics in risk-based insurance, case studies AISC/ASCE NSSBC design project: design of material and energy balances and reaction and of combined systems, such as CIEN E3010y Introduction to construction: 3 pts. Lect: 3. Professor Di. involving civil infrastructure systems, environmental of a steel bridge in accordance with National kinetics. Analysis of engineered systems to fluid-structure interaction; active, case studies Prerequisite: ENME E3105 or instructor's systems, mechanical and aerospace systems. Not Student Steel Bridge Competition rules; computer address environmental problems, including solid passive, and hybrid control systems 3 pts. Lect: 3. Professor Odeh. permission. Major elements of transportation open to undergraduate students. simulation and design by using SAP2000. and hazardous waste, and air, water, soil and Prerequisite: Instructor's permission. Introduces analytics. Develop basic skills in applying for structures under seismic loading; noise pollution. Life cycle assessments and CIEE E4116y Energy harvesting basic principles of how builders construct different CIEN E3128y Design projects fundamentals of data analytics to transportation dynamic soil-structure interaction emerging technologies. 3 pts. Lect: 3. Not offered in 2020–2021. types of projects. Shows detailed weekly cases on effects on the seismic response of 4 pts. Lect: 4. Professor Panayotidi. data analysis. Apply coding languages (e.g., Prerequisite: ENME E3114 or equivalent, or construction processes for infrastructure as well as Prerequisites: CIEN E3125 and E3126. CIEE E3260y Engineering for developing MATLAB, Python) and visualization tools instructor’s permission. Criterion of energy structures building projects. Cases show major differences Capstone design project in civil engineering. communities (e.g., Excel, Carto, R, Processing) to analyze harvesting, identification of energy sources. • Random processes and reliability: in constructing different types of projects and This project integrates structural, geotechnical 3 pts. Lect: 3. Professor Sisul. transportation data. Infer policy implications from Theory of vibrations of discrete and continuous problems in design against failure highlight challenges/solutions faced by project and environmental/water resources design Introduction to engineering problems faced analytics results. system, measurement and analysis. Selection under earthquake, wind, and wave team during construction phase. Projects problems with construction management tasks by developing communities and exploration of CIEN E4021x Elastic and plastic analysis of of materials for energy conversion, piezoelectric, loadings; noise, and turbulent flows; covered include: Tunnels, Bridges, Skyscrapers, and sustainability, legal and other social issues. design solutions in the context of a real project structures electromagnetic, thermoelectric, photovoltaic, Neighborhood Development, Mega Programs, Project is completed in teams, and communication with a community client. Emphasis is on the analysis of structures with random 3 pts. Lect: 3. Professor Kawashima. etc. Design and characterization, modeling and Airports, and Education. Detailed examples of real skills are stressed. Outside lecturers will address design of sustainable solutions that take account properties Prerequisite: CIEN E3121 or the equivalent. fabrication of vibration, motion, wind, wave, case studies of iconic national and international important current issues in engineering practice. of social, economical, and governance issues, • Fluid mechanics: turbulent flows, Overview of classical indeterminate structural thermal gradient, and light energy harvesters; projects. Includes site visits to active construction Every student in the course will be exposed with and that can be implemented now or in the near analysis methods (force and displacement methods), resonance phenomenon, power electronics and two-phase flows, fluid-structure projects. equal emphasis to issues related to geotechnical future. The course is open to all undergraduate approximate methods of analysis, plastic analysis energy storage and management. Applications to interaction, fluid-soil interaction, flow in engineering, water resources/environmental engineering students. Multidisciplinary teamwork CIEN E3111x Uncertainty and risk in civil methods, collapse analysis, shakedown theorem, buildings, geothermal systems, and transportation. porous media, computational methods engineering, structural engineering, and and approaches are stressed. Outside infrastructure systems structural optimization. To alternate with ENME E4115. construction engineering and management. lecturers are used to address issues specific for flow and transport processes, and 3.5 pts. Lect: 3. Professor Deodatis. to developing communities and the particular CIEN E4128y Civil engineering management flow and transport in fractured rock Prerequisite: Working knowledge of calculus. CIEN E3129x Project management for CIEN E4022y Bridge design and management project under consideration. 3 pts. Lect: 3. Professor Yanev. 3 pts. Not offered in 2020–2021. under mechanical loading Introduction to basic probability; hazard construction Prerequisite: CIEN E3125 or the equivalent. Bridge Principles of engineering management with a • Computational mechanics: finite function; reliability function; stochastic models 3 pts. Lect: 3. Professor Chang. CIEN E3303x and y Independent studies in design history, methods of analysis, loads: static, strong emphasis on planning of infrastructure element and boundary element of natural and technological hazards; extreme Prerequisite: Senior standing in Civil Engineering civil engineering for juniors live, dynamic. Design: allowable stress, ultimate systems. The course stresses leadership, creativity, value distributions; statistical inference or instructor’s permission. Introduction to 1–3 pts. By conference. Members of the faculty. techniques, symbolic computation, strength, load resistance factor, supply/demand. and management analysis. Program planning with methods; Monte Carlo simulation techniques; Project Management for design and construction A project on civil engineering subjects approved and bioengineering applications. Steel and concrete superstructures: suspension, optimization under financial and environmental fundamentals of integrated risk assessment processes. Elements of planning, estimating, by the chairman of the department. cable stayed, prestressed, arches. Management constraints; project planning and scheduling using and risk management; topics in risk-based scheduling, bidding, and contractual relationships. of the assets, life-cycle cost, expected useful life, deterministic and stochastic network theories; A flight structures program is insurance; case studies involving civil Computer scheduling and cost control. Critical CIEN E3304x and y Independent studies in inspection, maintenance, repair, reconstruction. production rate development and control using designed to meet the needs of industry infrastructure systems, environmental systems, path method. Design and construction activities. civil engineering for seniors Bridge inventories, condition assessments, data statistical, heuristic, simulation, and queuing in the fields of high-speed and space mechanical and aerospace systems, construction Field supervision. 1–3 pts. By conference. Members of the faculty. theory approaches. Students prepare and formally flight. The emphasis is on mechanics, management. A project on civil engineering subjects approved by acquisition and analysis, forecasts. Selected case CIEN E3141y Soil mechanics the chairman of the department. histories and field visits. present term projects. mathematics, fluid dynamics, flight CIEN E3121y Structural analysis 4 pts. Lect: 3. Lab 3. Professor Sun. CIEN E4100y Earthquake and wind CIEN E4129x and y Managing engineering and structures, and control. The program 3 pts. Lect: 3. Professor Feng. Prerequisite: ENME E3113. Index properties CIEN E3999x, y or s Fieldwork construction processes is a part of the Guggenheim Institute Methods of structural analysis. Trusses, arches, and classification; compaction; permeability and 1–2 pts. Instructor to be announced. engineering 3 pts. Lect: 3. Professors Odeh and Nagaraja. of Flight Structures in the department. cables, frames; influence lines; deflections; seepage; effective stress and stress distribution; Prerequisites: Obtained internship and approval 3 pts. Lect: 3. Professors Ashrafi and Balsamo. from faculty adviser. CEEM undergraduate Prerequisite: ENME E3106 or the equivalent. Basic Prerequisite: Graduate standing in Civil Specific information regarding degree force method; displacement method; computer shear strength of soil; consolidation; slope stability. applications. students only. Written application must be made concepts of seismology. Earthquake characteristics, Engineering, or instructor’s permission. requirements is available in the CIEE E3250y Hydrosystems engineering prior to registration outlining proposed internship/ magnitude, response spectrum, dynamic response Introduction to the principles, methods and tools department office. CIEN E3125y Structural design 3 pts. Lect: 3. Instructor to be announced. study program. Final reports required. May not be of structures to ground motion. Base isolation necessary to manage design and construction 3 pts. Lect: 3. Professor Panayotidi. Prerequisites: CHEN E3110 or ENME E3161 or taken for pass/fail credit or audited. International and earthquake-resistant design. Wind loads and processes. Elements of planning, estimating, Prerequisite: ENME E3113. Design criteria for equivalent, SIEO W3600 or equivalent, or the students must also consult with the International aeroelastic instabilities. Extreme winds. Wind scheduling, bidding and contractual relationships. COURSES IN CIVIL varied structural applications, including buildings instructor’s permission. A quantitative introduction Students and Scholars Office. effects on structures and gust factors. Valuation of project cash flows. Critical path ENGINEERING and bridges; design of elements using steel, to hydrologic and hydraulic systems, with a method. Survey of construction procedures. Cost CIEN E4010x Transportation engineering ECIA W4100y Management and development See also Courses in Engineering concrete, masonry, wood, and other materials. focus on integrated modeling and analysis of the control and effectiveness. Field supervision. water cycle and associated mass transport for 3 pts. Lect: 3. Professor Peterson. of water systems Mechanics at the end of this section. CIEN E3126y Computer-aided structural water resources and environmental engineering. An overview of the planning, design, operation, 3 pts. Lect: 3. Professors Gentine and Lall. CIEN E4130x Design of construction systems design Coverage of unit hydrologic processes such and construction of urban highways and mass Decision analytic framework for operating, 3 pts. Lect: 3. Professor Tirolo. 1 pt. Lect: 1. Lab: 1. Instructor to be announced. as precipitation, evaporation, infiltration, transportation systems. Transportation planning managing, and planning water systems, Prerequisite: CIEN E3125 or the equivalent, or the

ENGINEERING 2020–2021 ENGINEERING 2020–2021 instructor’s permission. Introduction to the design CIEN E4136y Entrepreneurship in engineering CIEN E4140x Environmental, health, and treatment systems. Small community and CIEN E4232x Advanced design of concrete continuous beams; composite construction; 96 97 of systems that support construction activities and construction safety concepts in construction processes residential systems. structures prestressed slabs and columns. and operations. Determination of design loads 3 pts. Lect: 3. Professor Peña-Mora. 3 pts. Lect: 3. Professor Haining. 3 pts. Lect: 3. Professor Panayotidi. CIEN E4210x Forensic structural engineering CIEN E4237x Architectural design, during construction. Design of excavation support Prerequisite: Instructor's permission. Capstone Prerequisite: Graduate standing in Civil Prerequisite: CIEN E3125 or equivalent. Design 3 pts. Lect: 3. Not offered in 2020–2021. computation, and method systems, earth retaining systems, temporary practicum where teams develop strategies Engineering and Engineering Mechanics. A of concrete beams for combined torsion, shear Prerequisites: Working knowledge of structural 3 pts. Lect: 1.5. Lab: 1.5. Not offered in supports and underpinning, concrete formwork and and business plans for a new enterprise in definitive review of and comprehensive introduction and flexure; moment-curvature relation; bar analysis and design; graduate student standing 2020–2021. shoring systems. Cranes and erection systems. the engineering and construction industry. to construction industry best practices and cut-off locations; design of two-way slabs; strut- Prerequisites: CIEN E3121 or equivalent. CIEN Tunneling systems. Instrumentation and monitoring. Identification of attractive market segments and or instructor’s permission. Review of significant and-tie method for the design of deep beams and fundamental concepts of environmental health E3125 or equivalent. Integrated methods of design Students prepare and present term projects. locations; development of an entry strategy; failures, civil/structural engineering design and corbels; gravity and shear wall design; retaining and safety management systems (EH&S) for the and structural analysis between engineering and acquisition of financing, bonding, and insurance; construction practices, ethical standards and wall design. CIEN E4131x and y Principles of construction construction management field. How modern EH&S architecture. Lectures on historical precedents organizational design; plans for recruiting and the legal positions as necessary background to techniques management system techniques and theories not CIEN E4233x Design of large-scale bridges on material use, structural inventiveness, and retaining personnel; personnel compensation/ forensic engineering. Discussion of standard- 3 pts. Lect: 3. Professors Hart, McManus, and only result in improved safe work environments 3 pts. Lect: 3. Professor Zoli. social importance. Labs on drafting and modeling incentives. Invited industry speakers. Priority given of-care. Study of the process of engineering Odeh. but ultimately enhance operational processes and Prerequisites: CIEN E3121 or equivalent, and software; physical modeling techniques and virtual to graduate students in Construction Engineering evaluation of structural defects and failures Prerequisite: CIEN E4129 or equivalent. performance in construction projects. CIEN E3127 or equivalent. Design of large-scale reality visualization. and Management. in construction and in service. Examination Current methods of construction, cost-effective and complex bridges with emphasis on cable- CIEN E4141y Public-private partnerships in of the roles, activities, conduct and ethics of CIEN E4241x Geotechnical engineering designs, maintenance, safe work environment. CIEN E4137y Managing civil infrastructure supported structures. Static and dynamic loads, global infrastructure development the forensic consultant and expert witness. fundamentals Design functions, constructability, site and systems component design of towers, superstructures 3 pts. Professor Chang. Students are assigned projects of actual cases 3 pts. Lect: 3. Professor Ling. environmental issues. 3 pts. Lect: 3. Professor Chang. and cables; conceptual design of major bridge Graduate students only. Delivery of infrastructure of nonperformance or failure of steel, concrete, Prerequisite: CIEN E3141 or instructor’s permission. Prerequisites: IEOR E4003, CIEN E4133, or types including arches, cable stayed bridges and CIEN E4132x Prevention and resolution of assets through Public-Private Partnerships (PPP). masonry, geotechnical, and temporary structures, Bearing capacity and settlement of shallow equivalent. Examination of the fundamentals of suspension bridges. construction disputes Value for Money analysis. Project organization. in order to perform, discuss, and report their own and deep foundations; earth pressure theories; infrastructure planning and management, with a 3 pts. Lect: 3. Professor White. Infrastructure sector characterization. Risk investigations under the guidance of the instructor. CIEN E4234y Design of large-scale building retaining walls and reinforced soil retaining walls; focus on the application of rational methods that Prerequisite: CIEN E4129 or equivalent. analysis, allocation, and mitigation. Monte Carlo structures sheet pile walls; braced excavation; slope stability. support infrastructure decision-making. Institutional CIEN E4212y Structural failures: cases, Contractual relationships in the engineering and methods and Real Options. Project finance 3 pts. Lect: 3. Professors Gottieb, Malsch, and environment and issues. Decision-making under causes, lessons learned CIEN E4242y Geotechnical earthquake construction industry and the actions that result and financing instruments. Case studies from Tomasetti. certainty and uncertainty. Capital budgeting and 3 pts. Lect: 3. Not offered in 2020–2021. engineering in disputes. Emphasis on procedures required to transportation, water supply, and energy sectors. Prerequisites: CIEN E3121 and E3127. Modern financing. Group decision processes. Elements of Prerequisites: A course each in engineering 3 pts. Lect: 3. Professor Ling. prevent disputes and resolve them quickly and challenges in the design of large-scale building decision and finance theory. CIEN E4142x International construction materials, structural analysis, concrete design, Prerequisite: CIEN E3141 or equivalent. Seismicity, cost-effectively. Case studies requiring oral and structures will be studied. Tall buildings, large management: theory and practice steel design, soil mechanics and foundations, earthquake intensity, propagation of seismic written presentations. CIEN E4138y Real estate finance for convention centers, and major sports stadiums 3 pts. Lect: 3. Professor Odeh. and construction; graduate student standing or waves, design of earthquake motion, seismic site construction management present major opportunities for creative solutions CIEN E4133x Capital facility planning and Prerequisites: CIEN E4129 or instructor's instructor's permission. The nature and causes response analysis, in situ and laboratory evaluation 3 pts. Lect: 3. Professor Riordan. and leadership on the part of engineers. This financing permission. Complex global construction of structural failures and the lessons learned of dynamic soil properties, seismic performance of Prerequisites: IEOR E2261, CIEN E3129 or course is designed to expose the students to this 3 pts. Lect: 3. Professor Chang. industry environment. Social, cultural, from them; insight into failure investigation in the underground structures, seismic performance of permission of instructor. Introduction to financial environment by having them undertake the complete Prerequisite: CIEN E4129 or equivalent. Planning technological, and political risks; technical, practice of forensic structural engineering. Case port and harbor facilities, evaluation and mitigation mechanics of public and private real estate design of a large structure from initial design and financing of capital facilities with a strong financial, and contractual risk. Understanding of histories of actual failures of real-life structures of soil liquefaction and its consequences. Seismic development and management. Working from concepts on through all the major design decisions. emphasis upon civil infrastructure systems. successful global project delivery principals and earth pressures, slopes stability, safety of dams perspectives of developers, investors and during construction and in service are introduced, The students work as members of a design team to Project feasibility and evaluation. Design of skills for construction professionals. Industry and embankments, seismic code provisions and taxpayers, financing of several types of real examined, analyzed, and discussed. Students overcome the challenges inherent in major projects. project delivery systems to encourage best efforts and trends to support global operational practice. To alternate with E4244. estate and infrastructure projects are covered. are assigned documented cases of failures of Topics include overview of major projects, project value, innovation and private sector participation. mechanism. Global Case Studies. Engage with structures of various types and materials to Basics of real estate accounting and finance, criteria and interface with architecture, design CIEN E4243x Foundation engineering Fundamentals of engineering economy and industry expert professionals. Student group review, discuss, and, in some cases, to conduct followed by in-depth studies of private, public, of foundations and structural systems, design 3 pts. Lect: 3. Professor Yang. project finance. Elements of life cycle cost projects with active ongoing global initiatives. investigations of the causes and responsibilities. and public/private-partnership projects and their challenges in the post 9/11 environment, and roles, Prerequisite: CIEN E3141 or equivalent. estimation and decision analysis. Environmental, financial structures. Focused on U.S.-based Students are required to prepare written reports responsibilities, and legal issues. Conventional types of foundations and foundation institutional, social and political factors. Case CIEN E4144x Real estate land development financing, with some international practices and make oral presentations of selected cases. problems: subsurface exploration and testing. studies from transportation, water supply and engineering CIEN E4235x Multihazard design of structures introduced and explored. Financial risks and Performance of shallow and deep foundations and wastewater treatment. 3 pts. Lect: 3. Professors Leventis, O'Connor, CIEN E4213x Elastic and inelastic buckling of 3 pts. Lect: 3. Professors Daddazio and rewards, and pertinent capital markets and and Vitolano. structures Mosquera. evaluation by field measurements. Case histories their financing roles. Impacts and incentives of CIEN E4134y Construction industry law Comprehensive review of various engineering 3 pts. Lect: 3. Professor Valenti. Prerequisite: CIEN E3125 or E4232 or instructor’s to illustrate typical design and construction various government programs, such as LEED 3 pts. Lect: 3. Professors Charney and Rubin. disciplines in the process of real estate land Stability of framed structures in the elastic and permission. Fundamental considerations of wave problems. To alternate with CIEN E4246. Prerequisite: Graduate standing or the instructor’s certification and solar power tax credits. Case development. Engineering disciplines covered inelastic ranges. Lateral buckling of beams. mechanics; design philosophies; reliability and CIEN E4244y Geosynthetics and applications permission. Practical focus upon legal concepts studies provide opportunity to compare U.S. include civil, infrastructure, transportation planning, Torsional buckling of compression members. risk concepts; basics of fluid mechanics; design 3 pts. Lect: 3. Professor Ling. applicable to the construction industry. Provides practices to several international methods. environmental planning, permitting, environmental Buckling of plates of plate-stiffener combinations. of structures subjected to blast; elements of Prerequisite: CIEN E4241 or the equivalent. sufficient understanding to manage legal aspects, remediation, geotechnical, and waterfront/marine. CIEN E4139x Theory and practice of virtual Linear stability analysis of cylindrical shells and seismic design; elements of fire design; flood Properties of geosynthetics. Geosynthetic design instead of being managed by them. Topics include Overview of land use and environmental law, design and construction discussion of its limitations. Discussion of the considerations; advanced analysis in support of for soil reinforcement. Geosynthetic applications in contractual relationships, contract performance, architecture and urban planning, as related to land 3 pts. Lect: 3. Professors Belote and David. semiempirical nature of the elastoplastic relations structural design. solid waste containment system. contract flexibility and change orders, liability and Prerequisites: CIEN E4129 or instructor’s development. Discussion of how these subjects used in the case of plates and shells. negligence, dispute avoidance/resolution, surety CIEN E4236y Design of prestressed concrete permission. History and development of Building affect decisions — cost, schedule, programming — CIEN E4245x Tunnel design and construction bonds, insurance and site safety. CIEN E4226y Advanced design of steel structures Information Modeling (BIM), its uses in design and involved in real estate development. Note: Graduate 3 pts. Lect: 3. Not offered in 2020–2021. structures 3 pts. Lect: 3. Professor Panayotidi. construction, and introduction to the importance and senior undergraduate students only. Third year Engineering design and construction of different CIEN E4135y Strategic management in 3 pts. Lect: 3. Professors Aly and Mosquera. Prerequisite: CIEN E4232 or instructor's of planning in BIM implementation. Role of visual undergraduate students with instructor's permission. types of tunnel, including cut and cover tunnel, engineering and construction Prerequisite: CIEN E3125 or equivalent. Review of permission. Properties of materials used in design and construction concepts and methodologies, rock tunnel, soft ground tunnel, immersed tub 3 pts. Lect: 3. Professor Peña-Mora. CIEE E4163x Sustainable water treatment loads and structural design approaches. Material prestressed concrete; pretensioning versus including integrated project delivery form in tunnel, and jacked tunnel. The design for the liner, Core concepts of strategic planning, management and reuse considerations in structural steel design. Behavior posttensioning; loss of prestress due to elastic architecture, engineering, and construction excavation, and instrumentation are also covered. A and analysis within the construction industry. 3 pts. Lect: 3. Instructor to be announced. and design of rolled steel, welded, cold-formed shortening, friction, anchorage slip, shrinkage, industries from project design, cost estimating, field trip will be arranged to visit the tunneling site. Industry analysis, strategic planning models Prerequisites: Introductory chemistry (with light-gauge, and composite concrete/steel members. creep and relaxation; full versus partial scheduling, coordination, fabrication, installation, and industry trends. Strategies for information laboratory) and fluid mechanics. Fundamentals Design of multistory buildings and space structures. prestressing; design of beams for flexure, shear, CIEN E4246x Earth retaining structures and financing. technology, emerging markets and globalization. of water pollution and wastewater characteristics. and torsion; method of load balancing; anchorage 3 pts. Lect: 3. Not offered in 2020–2021. Case studies to demonstrate key concepts in real- Chemistry, microbiology, and reaction kinetics. zone design; calculation of deflection by the Prerequisite: CIEN E3141. Retaining structures, world environments. Design of primary, secondary, and advanced lump-sum and incremental time-step methods; bulkheads, cellular cofferdams, and braced

ENGINEERING 2020–2021 ENGINEERING 2020–2021 excavations. Construction dewatering and seepage flows, and soil-structure interaction; CIEN E6133y Advanced construction and be selected for supervised study. A term paper Pre- or corequisite: ENME E3105 or equivalent. ENME E4202y Advanced mechanics 98 99 underpinning. Instrumentation to monitor actual element and mesh instabilities. infrastructure risk management using real options is required. Stress and strain. Mechanical properties of 3 pts. Lect: 3. Professor Smyth. performances. Ground improvement techniques, 3 pts. Lect: 3. Not offered in 2020–2021. materials. Axial load, bending, shear, and torsion. Prerequisite: ENME E3105 or equivalent. CIEE E4257x Groundwater contaminant CIEN E9165x and y–S9165 Independent including earth reinforcement, geotextiles, and Prerequisite: CIEN E6131. Advanced concepts Stress transformation. Deflection of beams. Buckling Differentiation of vector functions. Review of transport and remediation studies in environmental engineering grouting. To alternate with CIEN E4243. of risk analysis and management applied to civil of columns. Combined loadings. Thermal stresses. kinematics. Generalized coordinates and constraint 3 pts. Lect: 3. Professors Mutch and Carbonaro. 4 pts. Not offered in 2020–2021. engineering systems. Identifying and valuing equations. Generalized forces. Lagrange’s CIEN E4247y Design of large-scale deep Prerequisites: ENME E3161 and CIEE E3250 Prerequisite: CIEE E4252 or the equivalent. ENME E3114y Experimental mechanics of flexibility in construction and operation. Tools equations. Impulsive forces. Collisions. or instructor's permission. Sources and types Emphasizes a one-on-one study approach to materials foundation systems to perform risk analysis in flexible civil Hamiltonian. Hamilton’s principle. of groundwater contamination. Groundwater specific environmental engineering problems. 4 pts. Lect: 2. Lab: 3. Professor Kawashima. 3 pts. Lect.: 3. Professors Frizzi, Gallagher, infrastructure systems. Valuation methods for real hydrology. Groundwater contaminant fate and Students develop papers or work on design Prerequisite: ENME E3113. Material behavior ENME E4214y Theory of plates and shells Leventis, and Poeppel. options. Risk flexibility analysis; integrating real transport. Flow and transport in the unsaturated problems pertaining to the treatment of solid and constitutive relations. Mechanical properties 3 pts. Lect: 3. Professor Dasgupta. Prerequisite: CIEN E3141. Focus on deep options analysis with quantitative risk analysis. zone. Nonaqueous phase liquids and multiphase and liquid waste, contaminant migration, of metals and cement composites. Structural Prerequisite: ENME E3113. Static flexural foundations in difficult conditions and Applications to case studies on construction flow. Physical and numerical models for and monitoring and sampling programs for materials. Modern construction materials. response of thin, elastic, rectangular, and circular constraints of designing foundations. Design management, life-cycle cost analysis for contaminant transport. Characterization and remediation design. Experimental investigation of material properties plates. Exact (series) and approximate (Ritz) process from the start of field investigations infrastructure assets, public-private partnerships assessments of contaminated sites. Groundwater and behavior of structural elements including solutions. Circular cylindrical shells. Axisymmetric through construction and the application of projects, real estate developments, and renewable CIEN E9201x and y–S9201 Civil engineering remediation alternatives. Regulations. fracture, fatigue, bending, torsion, buckling. and nonaxisymmetric membrane theory. Shells of deep foundations. energy infrastructure projects. reports arbitrary shape. CIEE E4260x Urban ecology studio 1–4 pts. Not offered in 2020–2021. ENME E3161x Fluid mechanics CIEE E4250x or y Hydrosystems CIEN E6232x Advanced topics in concrete 3 pts. Lect: 2.5. Lab 2.5. Not offered in 2020–2021. A project on some civil engineering subject 4 pts. Lect: 3. Lab: 3. Professor Giometto. ENME E4215x Theory of vibrations 3 pts. Lect: 3. Professor Gentine. engineering Prerequisites: Senior undergraduate or graduate approved by department chair. Prerequisites: ENME E3105 and ordinary 3 pts. Lect: 3. Professor Betti. Prerequisites: CHEN E3110 or ENME E3161 3 pts. Lect: 3. Not offered in 2020–2021. student standing and instructor’s permission. differential equations. Fluid statics. Fundamental Frequencies and modes of discrete and continuous or equivalent, or the instructor’s permission. Prerequisite: CIEN E3125 or the equivalent. CIEN E9500x and y Departmental seminar Conjoint studio run with the Graduate School of principles and concepts of flow analysis. Differential elastic systems. Forced vibrations-steady-state The hydrologic cycle and relevant atmospheric Behavior of concrete under general states of 0 pts. Professor Ling. Architecture, Planning and Preservation (GSAPP) and finite control volume approach to flow analysis. and transient motion. Effect of damping. Exact and processes; water and energy balance; radiation; stress, numerical modeling of steel and concrete, All doctoral students are required to attend that explores solutions to problems of urban density. Dimensional analysis. Application of flow analysis: approximate methods. Applications. boundary layer; precipitation formation; evapora- finite element analysis of reinforced concrete, the department seminar as long as they are in Engineering and GSAPP students will engage flow in pipes, external flow, flow in open channels. tion; vegetation transpiration; infiltration; storm design of slabs and their shell concrete structures. residence. No degree credit is granted. ENME E4332x Finite element analysis, I in a joint project that addresses habitability and runoff; snowmelt; and flood processes. Routing ENME E3332x A first course in finite elements 3 pts. Lect: 3. Professor Waisman. sustainability issues in an urban environment, and CIEN E6246y Advanced soil mechanics of runoff and floodwaters. Groundwater flow and CIEN E9800x and y–S9800 Doctoral research 3 pts. Lect: 3. Professor Fish. Prerequisites: Mechanics of solids, structural also provides community service. Emphasis will 3 pts. Lect: 3. Professor Ling. the hydraulics of wells. Probabilistic modeling, and instruction Prerequisite: Senior standing or instructor’s permission. analysis, elementary computer programming be on the integration of science, engineering and Prerequisite: CIEN E3141. Stress-dilatancy of extreme-value theory. 3–12 pts. May be taken for 3, 6, 9, or 12 points, Recommended corequisite: differential equations. (MATLAB) is recommended, linear algebra design within a social context. Interdisciplinary sand; failure criteria; critical state soil mechanics; dependent on instructor’s permission. Focus on formulation and application of the finite and ordinary differential equations. Direct CIEN E4250y Waste containment design and approaches and communication will be stressed. limit analysis; finite element method and case A candidate for the Eng.Sc.D. degree in civil element to engineering problems such as stress stiffness approach for trusses. Strong and practice histories of consolidation analysis. engineering must register for 12 points of doctoral CIEN E4300x Infrastructural materials: analysis, heat transfer, fluid flow, and electromagnetics. weak forms for one-dimensional problems. 3 pts. Lect: 3. Not offered in 2020–2021. research instruction. Registration in CIEN E9800 production, use, properties and performance CIEN E6248x Experimental soil mechanics Topics include finite element formulation for one- Galerkin finite element formulation, shape Prerequisites: ENME E3161 and CIEN E3141, may not be used to satisfy the minimum residence 3 pts. Lect: 3. Professor Wheeler. 3 pts. Lect: 3. Not offered in 2020–2021. dimensional problems, such as trusses, electrical functions, Gauss quadrature, convergence. or equivalents. Strategies for the containment requirement for the degree. Multidimensional scalar field problems (heat Basic concepts of materials science for civil Prerequisite: CIEN E3141. Advanced soil testing, and hydraulic systems; scalar field problems in two of buried wastes. Municipal and hazardous conduction), triangular and rectangular elements, infrastructure materials. Relate composition, including triaxial and plane strain compression CIEN E9900x and y–S9900 Doctoral dissertation dimensions, such as heat transfer; and vector field waste landfill design; bioreactor landfills; vertical Isoparametric formulation. Multidimensional structure, processing to engineering properties tests; small-strain measurement. Model testing; 0 pts. Members of the faculty. problems, such as elasticity and finally usage of the barriers, evapotranspiration barriers and capillary vector field problems (linear elasticity). Practical (e.g., strength, modulus, ductility-malleability, application (of test results) to design. A candidate for the doctorate may be required commercial finite element program. Students taking barriers; hydraulic containment; in situ stabilization FE modeling with commercial software (ABAQUS). to register for this course every term after the ENME E3332 cannot take ENME E4332. and solidification techniques; site investigation; durability). Materials covered include stone, CIEN E9101x and y–S9101 Civil engineering Computer implementation of the finite element student’s coursework has been completed and monitoring and stewardship of buried wastes; brick, terra cotta, concrete, cast stone, metals, research ENME E4113x Advanced mechanics of solids method. Advanced topics. Not open to until the dissertation has been accepted. options for land reuse/redevelopment. and wood. Overview of sourcing and production, 1–4 pts. Members of the faculty. 3 pts. Lect: 3. Professor Yin. undergraduate students. identification, fabrication, chemical, physical and Advanced study in a specialized field under the Stress and deformation formulation in two-and three- CIEE E4252x Foundations of environmental ENME E4363y Multiscale computational mechanical properties. supervision of a member of the department staff. dimensional solids; viscoelastic and plastic material engineering COURSES IN ENGINEERING science and engineering Before registering, the student must submit an in one and two dimension energy methods. 3 pts. Lect: 3. Professor Chandran. CIEN E4999x and y Fieldwork MECHANICS 3 pts. Lect: 3. Professor Fish. Prerequisites: CHEM UN1403 or equivalent; outline of the proposed work for approval of the 1–2 pts. Instructor to be announced. See also Courses in Civil Engineering at ENME E4114x Mechanics of fracture Prerequisites: ENME E4332, elementary ENME E3161 or the equivalent. Engineering Prerequisite: Instructor’s written approval. May supervisor and the department chair. and fatigue the beginning of this section. computer programming, linear algebra. aspects of problems involving human interaction be repeated for credit, but no more than 3 total CIEN E9120x and y–S9120 Independent 3 pts. Lect: 3. Not offered in 2020–2021. Introduction to multiscale analysis. Information- with the natural environment. Review of points may be used for degree credit. Only for studies in flight sciences ENME E3105x and y Mechanics Prerequisite: Undergraduate mechanics of solids passing bridging techniques: among them, fundamentals principles that underlie the discipline Civil Engineering and Engineering Mechanics 3 pts. Not offered in 2020–2021. 4 pts. Lect: 4. Professors Hone and course. Elastic stresses at a crack; energy and generalized mathematical homogenization of environmental engineering, i.e., constituent graduate students who include relevant off- Prerequisite: Instructor’s permission. Geared Kougioumtzoglou. stress intensity criteria for crack growth; effect theory, the heterogeneous multiscale method, transport and transformation processes in campus work experience as part of their toward students interested in flight sciences and Prerequisites: PHYS UN1401, MATH UN1101, of plastic zone at the crack; fracture testing variational multiscale method, the discontinuous environmental media such as water, air and approved program of study. Final report and flight structures. Topics related to aerodynamics, MATH UN1102, and MATH UN1201 or APMA applications. Fatigue characterization by stress-life Galerkin method and the kinetic Monte ecosystems. Engineering applications for letter of evaluation required. May not be taken propulsion, noise, structural dynamics, aeroelasticity, E2000. Elements of statics; dynamics of a particle and strain-life; damage index; crack propagation; Carlo–based methods. Concurrent multiscale addressing environmental problems such as water for pass/fail credit or audited. and structures may be selected for supervised and systems of particles. fail safe and safe life analysis. techniques: domain bridging, local enrichment, quality and treatment, air pollutant emissions, and and multigrid-based concurrent multiscale CIEN E6132y Leadership in engineering and study. A term paper is required. ENME E3106y Dynamics and vibrations hazardous waste remediation. Presented in the EMME E4115y Micromechanics of composite methods. Analysis of multiscale systems. context of current issues facing practicing engineers construction CIEN E9130x and y–S9130 Independent 3 pts. Lect: 2. Instructor to be announced. materials and government agencies, including legal and 3 pts. Lect: 3. Professor Peña-Mora. studies in construction Prerequisites: MATH UN1201 or APMA E2000, and 3 pts. Lect: 3. Professor Yin. ENME E6215x Principles and applications of regulatory framework, environmental impact Prerequisite: CIEN E4129 or the equivalent. 3 pts. Not offered in 2020–2021. APMA E2101. Corequisite: ENME E3105. Kinematics Prerequisite: ENME E4113 or instructor’s sensors for structural health monitoring assessments, and natural resource management. Introduces and employs various tools, concepts, Prerequisites: Permission by department chair of rigid bodies; momentum and energy methods; approval. An introduction to the constitutive 3 pts. Lect: 2.5. Lab: 0.5. Professor Feng. and analytical frameworks to enhance students' and instructor. Independent study of engineering vibrations of discrete and continuous systems; modeling of composite materials: Green’s Prerequisite: ENME E4215. Concepts, principles, CIEN E4253x Finite elements and plasticity in ability to define and analyze leadership problems. and construction industry problems. Topics eigenvalue problems, natural frequencies and modes. functions in heterogenous media, Eshelby’s and applications of various sensors for sensing geotechnical engineering In-depth analysis of leadership literature and related to capital planning and financing, project Basics of computer simulation of dynamics problems equivalent inclusion methods, eigenstrains, structural parameters and nondestructive 3 pts. Lect: 3. Not offered in 2020–2021. practical situational immersion using industry management, contracting strategies and risk using MATLAB. spherical and ellipsoidal inclusions, dislocations, evaluation techniques for subsurface inspection, Prerequisites: CIEN E3141 and ENME E4332. case studies. Term project exploring leadership homogenization of elastic fields, elastic, data acquisition, and signal processing allocation, dispute mitigation and resolution, and ENME E3113x Mechanics of solids State-of-the-art computer solutions in in engineering and construction industry, working viscoelastic and elastoplastic constitutive modeling, techniques. Lectures, demonstrations, and infrastructure assessment and management may 3 pts. Lect: 3. Professor Betti. geotechnical engineering; 3D consolidation, closely with industry leaders. micromechanics-based models. hands-on laboratory experiments.

ENGINEERING 2020–2021 ENGINEERING 2020–2021 ENME E6216y Structural health monitoring finite element models, explicit and implicit time in Cartesian coordinates; tensor calculus and 100 3 pts. Lect: 3. Professor Betti. integrators, and operator splitting techniques for the calculus of variation; large deformations in Prerequisites: ENME E4215 and ENME poromechanics problems. curvilinear coordinates; electricity problems and E4332. Principles of traditional and emerging applications. ENME E6333y Finite element analysis, II sensors, data acquisition and signal processing 3 pts. Lect: 3. Professor Waisman. techniques, experimental modal analysis (input- ENME E8320y Viscoelasticity and plasticity Prerequisite: ENME E4332. FE formulation output), operational modal analysis (output- 4 pts. Lect: 3. Professor Dasgupta. for beams and plates. Generalized eigenvalue only), model-based diagnostics of structural Prerequisite: ENME E6315 or equivalent, or problems (vibrations and buckling). FE integrity, long-term monitoring and intelligence instructor’s permission. Constitutive equations formulation for time-dependent parabolic and maintenance. Lectures and demonstrations, of viscoelastic and plastic bodies. Formulation hyperbolic problems. Nonlinear problems, hands-on laboratory experiments. and methods of solution of the boundary value, linearization, and solution algorithms. Geometric problems of viscoelasticity and plasticity. ENME E6220y Random processes in and material nonlinearities. Introduction to mechanics continuum mechanics. Total and updated ENME E8323y Nonlinear vibrations 3 pts. Lect: 3. Professor Kougioumtzoglou. Lagrangian formulations. Hyperelasticity and 3 pts. Lect: 3. Not offered in 2020–2021. Prerequisites: CIEN E4111 and ENME E4215 plasticity. Special topics: fracture and damage Prerequisite: ENME E4215 or equivalent. Free (or equivalent). Review of random variables. mechanics, extended finite element method. and forced motion of simple oscillators with Random process theory: stationary and ergodic nonlinear damping and stiffness. Exact, perturbation, ENME E6364x Nonlinear computational processes, correlation functions, power spectra. iteration, and graphical methods of solution. mechanics Nonstationary and non-Gaussian processes. Stability of motion. Chaotic vibrations. 3 pts. Lect: 3. Not offered in 2020–2021. Linear random vibration theory. Crossing rates, Prerequisites: ENME E4332 or equivalent, peak distributions, and response analysis of elementary computer programming, linear nonlinear structures to random loading. Major COURSES IN GRAPHICS algebra. The formulations and solution strategies emphasis on simulation of various types of for finite element analysis of nonlinear problems GRAP E2005y Computer-aided engineering random processes. Monte Carlo simulation. are developed. Topics include the sources of graphics ENME E6315x Theory of elasticity nonlinear behavior (geometric, constitutive, 3 pts. Lect: 1.5. Lab: 2.5. Not offered in 2020–2021. 3 pts. Lect: 3. Not offered in 2020–2021. boundary condition), derivation of the governing Prerequisite: MATH UN1101. Basic concepts Foundations of continuum mechanics. General discrete equations for nonlinear systems such needed to prepare and understand engineering theorems of elasticity. Application to stress analysis as large displacement, nonlinear elasticity, rate drawings and computer-aided representations: and wave propagation. independent and dependent plasticity and other preparation of sketches and drawings, nonlinear constitutive laws, solution strategies preparation and transmission of graphic ENME E6320x Computational poromechanics for nonlinear problems (e.g., incrementation, information. Lectures and demonstrations, hands- 3 pts. Lect: 3. Professor Sun. iteration), and computational procedures for large on computer-aided graphics laboratory work. Prerequisite: ENME E3332 or instructor’s systems of nonlinear algebraic equations. Term project. permission. A fluid infiltrating porous solid is a multiphase material whose mechanical behavior ENME E6370y Turbulence theory and GRAP E4005y Computer graphics in is significantly influenced by the pore fluid. modeling engineering Diffusion, advection, capillarity, heating, cooling, 3 pts. Lect: 3. Professor Giometto. 3 pts. Lect: 3. Professor Dasgupta. and freezing of pore fluid, buildup of pore Prerequisites: ENME E3161 or equivalent, Prerequisites: Any programming language and pressure, and mass exchanges among solid and Ordinary and partial differential equations. linear algebra. Numerical and symbolic (algebraic) fluid constituents all influence the stability and Turbulence phenomenology, spatial and temporal problem solving with Mathematica. Formulation integrity of the solid skeleton, causing shrinkage, scales in turbulent flows, statistical description, for graphics application in civil, mechanical, and swelling, fracture, or liquefaction. These filtering and Reynolds decomposition, equations bioengineering. Example of two-and three-dimen- coupling phenomena are important for numerous governing the resolved flow, fluctuations and their sional curve and surface objects in C++ disciplines, including geophysics, biomechanics, energetics, turbulence closure problem for RANS and Mathematica; special projects of interest to and material sciences. Fundamental principles of and LES, two-equation turbulence models, and electrical and computer science. poromechanics essential for engineering practice second-moment closures. and advanced study on porous media. Topics include balance principles, Biot’s poroelasticity, ENME E8310x Advanced continuum mixture theory, constitutive modeling of path mechanics independent and dependent multiphase 3 pts. Lect: 3. Professor Dasgupta. materials, numerical methods for parabolic and Prerequisites: MECE E6422 and E6423. Open to hyperbolic systems, inf-sup conditions, and Ph.D. students and to M.S. students with instruc- common stabilization procedures for mixed tor’s permission. Review of continuum mechanics

ENGINEERING 2020–2021 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 212-854-3105 compeng.columbia.edu

PROGRAM CHAIR Xiaofang Fred Jiang, Simha Sethumadhavan, Martha A. Kim Assistant Professor of Electrical Associate Professor of Computer Science 469 CSB Engineering Kenneth L. Shepard, Ethan Katz-Bassett, Professor of Electrical Engineering and COMPUTER ENGINEERING COMMITTEE Assistant Professor of Electrical Biomedical Engineering Luca Carloni, Engineering Stephen H. Unger, Professor of Computer Science Martha A. Kim, Professor Emeritus of Computer Science Asaf Cidon, Associate Professor of Computer Science and Electrical Engineering Assistant Professor of Electrical Vishal Misra, Charles A. Zukowski, Engineering Professor of Computer Science Professor of Electrical Engineering Stephen A. Edwards, Daniel Rubenstein, Gil Zussman, Associate Professor of Computer Science Associate Professor of Computer Science Professor of Electrical Engineering Mingoo Seok, Professor of Electrical Engineering

he computer engineering UNDERGRADUATE PROGRAM electrical engineering, or computer program is run jointly by the This undergraduate program engineering. For example, they could T Computer Science and Electrical incorporates most of the core curricula take more advanced courses in VLSI, Engineering departments. It offers both in both electrical engineering and communications theory, computer B.S. and M.S. degrees. computer science so that students architecture, electronic circuit theory, The program covers some of will be well prepared to work in the software engineering, or digital design. engineering’s most active, exciting, area of computer engineering, which Minors in electrical engineering and and critical areas, which lie at the substantially overlaps both fields. Both computer science are not open to interface between CS and EE. The hardware and software aspects of computer engineering majors, due to focus of the major is on computer computer science are included, and, excessive overlap. systems involving both digital in electrical engineering, students hardware and software. receive a solid grounding in circuit Technical Electives Some of the key topics covered theory and in electronic circuits. The The Computer Engineering Program are computer design (i.e., computer program includes several electrical includes 15 points of technical architecture); embedded systems (i.e., engineering laboratory courses as well electives. All must be 3000-level or the design of dedicated hardware/ as the Computer Science Department’s above, technical, and must not have software for cell phones, automobiles, advanced programming course. significant overlap with other courses robots, games, and aerospace); digital Detailed lists of requirements can be taken for the major. Adviser approval and VLSI circuit design; computer found at compeng.columbia.edu. of technical electives is required. networks; design automation (i.e., Students will be prepared to work Most courses at the 3000-level CAD); and parallel and distributed on all aspects of the design of digital or above offered by the Computer systems (including architectures, hardware, as well as on the associated Science and Electrical Engineering programming, and compilers). software that is now often an integral departments are eligible, and up to Students in the programs have two part of computer architecture. They will two from outside those departments “home” departments. The Electrical also be well equipped to work in the can be considered for approval as Engineering Department maintains growing field of telecommunications. well. If a department advertises student records and coordinates Students will have the prerequisites to that one of its courses can be used advising appointments. delve more deeply into either hardware as a technical elective that does or software areas, and enter graduate not necessarily mean it will be programs in computer science, approved as a technical elective in

ENGINEERING 2020–2021 102 103 COMPUTER ENGINEERING PROGRAM: FIRST AND SECOND YEARS COMPUTER ENGINEERING: THIRD AND FOURTH YEARS EARLY-STARTING STUDENTS EARLY-STARTING STUDENTS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

APMA E2000 (4) either semester ELEN E3331 (3)

1 Electronic circuits COMS W4118 (3) Operating systems MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) IEOR E3658 (3) Probability or APMA E2101 (3)1 COMS W3261 (3) COMS W4115 (3) Programming lang. Computer sci. theory CORE REQUIRED COMS W3157 (4) COURSES Advanced programming UN1401 (3) UN1402 (3) Lab UN1494 (3) or (Choose 3 of 6) chem. lab UN1500 (3) ELEN E3201 (3.5) CSEE W4119 (3) Computer networks, EECS E4321 (3) Digital VLSI circuits, CSEE Circuit analysis PHYSICS UN1601 (3.5) UN1602 (3.5) Lab UN1494 (3) or W4823 (3) Advanced logic design, CSEE W4824 (3) Computer architecture, CSEE (three tracks, W4840 (3) Embedded systems, CSEE W4868 (3) System-on-chip platforms choose one) chem. lab UN1500 (3)

UN2801 (4.5) UN2802 (4.5) Lab UN3081 (2) or chem. lab UN1500 (3) ELEN E3081 (1) ELEN E3083 (1) REQUIRED LABS Circuit analysis lab Electronic circuits lab

one-semester lecture (3–4) UN1403 or UN1404 or TECH2 15 points required; see details within the text UN2045 or UN1604 CHEMISTRY Lab UN1500 (3) either semester or Complete 27-point requirement; see page 9 (27-Point Nontechnical Requirement) NONTECH physics lab UN1493 (3) ELECTIVES or seas.columbia.edu for details (administered by the advising dean)

COMS W3134 (3) or TOTAL POINTS3 17.5 17 15 15­ W3137 (4) CORE REQUIRED ELEN E1201 (3.5) ELEN E3801 (3.5) Data structures COURSES Intro. to elec. eng. (either semester) Signals and systems For a discussion about programming languages used in the program, please see compeng.columbia.edu. CSEE W3827 (3) 1 Fund. of computer sys. SIEO W3600, STAT GU4203, and STAT GU4001 can be used instead of IEOR E3658, but W3600 and GU4001 may not provide enough probability background for elective courses such as ELEN E3701. Students completing an economics minor who want such a background can take IEOR E3658 and augment it with IEOR E4307. 2 ELEN E3084 (1) ELEN E3082 (1) The total points of technical electives is reduced to 12 if APMA E2101 has been replaced by MATH UN2030 (formerly MATH E1210) and either APMA REQUIRED LABS Signals and systems lab Digital systems lab E3101 or MATH UN2010, or COMS W3251. Combined-plan students with good grades in separate, advanced courses in linear algebra and ODEs can apply for this waiver, but the courses must have been at an advanced level for this to be considered. 3 “Total points” assumes that 20 points of nontechnical electives and other courses are included. UNIVERSITY CC1010 (3) either semester WRITING the computer engineering program. “early-starting” and “late-starting” engineering, computer science, or HUMA CC1001, HUMA CC1002, There must be sufficient technical programs, see the degree track charts. electrical engineering with at least a 3.2 COCI CC1101, COCI CC1102, content and computer engineering It must be emphasized that these GPA in technical courses. The Graduate REQUIRED or Global Core (3–4) or Global Core (3–4) NONTECHNICAL connection within the entire 15 points, charts present examples only; actual Record Examination (GRE), General Test ELECTIVES2 HUMA UN1121 or ECON UN1105 (4) and so approval of some courses may schedules may be customized in only, is required of all applicants. UN1123 (3) UN1155 recitation (0) depend on the other electives chosen. consultation with academic advisers. Students must take at least 30 points Economics courses cannot be used of courses at Columbia University at COMS W1004 (3) or COMS W3203 (3) as technical electives. COMS W3101 or above the 4000 level. These must COMPUTER ENGI E1006 (3) GRADUATE PROGRAM SCIENCE W1007 (3) Discrete math. /W3102 courses, and not-very- include at least 15 points from the The Computer Engineering Program technical courses within the school courses listed below that are deemed offers a course of study leading to the of engineering, cannot be used as core to computer engineering. Other PHYSICAL UN1001 (1) UN1002 (1) degree of Master of Science (M.S.). EDUCATION technical electives either. courses may be chosen with the prior The basic courses in the M.S. program approval of a faculty adviser in the come from the Electrical Engineering THE ART OF Computer Engineering Program. ENGI E1102 (4) either semester Starting Early and Computer Science Departments. ENGINEERING M.S. students must complete Students are strongly encouraged to Students completing the program are begin taking core computer engineering the professional development and 1 prepared to work (or study further) in APMA E2101 may be replaced by MATH UN2030 (formerly MATH E1210) and either APMA E3101, or MATH UN2010, or COMS W3251. courses as sophomores. They start leadership course, ENGI E4000, 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. such fields as digital computer design, as a graduation requirement. Ph.D. with ELEN E1201: Introduction to digital communications, and the design candidates are strongly encouraged to electrical engineering in the second of embedded computer systems. complete the course. semester of their first year and may Applicants are generally expected to continue with other core courses have a bachelor’s degree in computer one semester after that. For sample

ENGINEERING 2020–2021 ENGINEERING 2020–2021 104 105 COMPUTER ENGINEERING PROGRAM: FIRST AND SECOND YEARS COMPUTER ENGINEERING: THIRD AND FOURTH YEARS LATE-STARTING STUDENTS LATE-STARTING STUDENTS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

APMA E2000 (4) either semester COMS W4118 (3) Operating systems IEOR E3658 (3)1 COMS W3157 (4) MATH UN1101 (3) MATH UN1102 (3) Probability Advanced programming or MATHEMATICS COMS W4115 (3) Programming lang. APMA E2101 (3)1 COMS W3134 (3) or ELEN E3331 (3) W3137 (4) Electronic circuits Data structures UN1401 (3) UN1402 (3) Lab UN1494 (3) or CORE REQUIRED (Choose 3 of 6) COURSES COMS W3261 (3)2 CSEE W4119 (3) Computer networks, EECS E4321 chem. lab UN1500 (3) ELEN E3201 (3.5) Models of comp. (3) Digital VLSI circuits, CSEE W4823 (3) Advanced Circuit analysis PHYSICS logic design, CSEE W4824 (3) Computer architecture, UN1601 (3.5) UN1602 (3.5) Lab UN1494 (3) or CSEE W3827 (3) (three tracks, CSEE W4840 (3) Embedded systems, CSEE W4868 chem. lab UN1500 (3) ELEN E3801 (3.5) Fund. of computer choose one) (3) System-on-chip platforms Signals and systems systems UN2801 (4.5) UN2802 (4.5) Lab UN3081 (2) or chem. lab UN1500 (3)

ELEN E3081 (1)3 ELEN E3083 (1)3 one-semester lecture (3–4) Circuit analysis lab Electronic circuits lab UN1403 or UN1404 or REQUIRED LABS UN2045 or UN1604 ELEN E3084 (1)3 ELEN E3082 (1)3 CHEMISTRY Signals and systems lab Digital systems lab Lab UN1500 (3) either semester or physics lab UN1493 (3) TECH4 15 points required; see details within the text

2 CORE REQUIRED ELEN E1201 (3.5) COURSES Intro. to elec. eng. (either semester) Complete 27-point requirement; see page 9 (27-Point Nontechnical Requirement) NONTECH ELECTIVES or seas.columbia.edu for details (administered by the advising dean)

UNIVERSITY CC1010 (3) either semester WRITING 5 TOTAL POINTS 15 18 15 18­

HUMA CC1001, HUMA CC1002, COCI CC1101, COCI CC1102, For a discussion about programming languages used in the program, please see compeng.columbia.edu. REQUIRED or Global Core (3–4) or Global Core (3–4) 1 NONTECHNICAL SIEO W3600, STAT GU4203, and STAT GU4001 can be used instead of IEOR E3658, but W3600 and GU4001 may not provide enough probability background for ELECTIVES elective courses such as ELEN E3701. Students completing an economics minor who want such a background can take IEOR E3658 and augment it with IEOR HUMA UN1121 or ECON UN1105 (4) and E4307. UN1123 (3) UN1155 recitation (0) 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. COMS W1004 (3) or W3203 (3) 4 COMPUTER ENGI E1006 (3) The total points of technical electives is reduced to 12 if APMA E2101 has been replaced by MATH UN2030 (formerly MATH E1210) and either APMA E3101 or SCIENCE W1007 (3) Discrete math. MATH UN2010, or COMS W3251. Combined-plan students with good grades in separate, advanced courses in linear algebra and ODEs can apply for this waiver, but the courses must have been at an advanced level for this to be considered. 5 Assuming technical electives taken Semesters VII and VIII, and 9 points of nontechnical electives taken Semesters VI, VII, and VIII. PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

Core Computer Engineering Courses CSEE E6824: Parallel computer architecture at least 2.7 must be maintained, and all THE ART OF ENGI E1102 (4) either semester CSEE E6861: CAD of digital systems ENGINEERING CSEE W4119: Computer networks degree requirements must be completed CSEE E6863: Formal verification of hardware/ CSEE W4140: Networking laboratory within five years of the beginning of the EECS E4321: Digital VLSI circuits software systems 1 first course credited toward the degree. APMA E2101 may be replaced by MATH UN2030 (formerly MATH E1210) and either APMA E3101, or MATH UN2010, or COMS W3251. EECS E4750: Hybrid comp. for sig. & data proc. CSEE E6868: Embedded scalable platforms 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 EECS E4764: Iot—intelligent & connected sys. junior year. Note that this includes some background in discrete math (see COMS W3203) and electronic circuits (see ELEN E1201). Transfer and combined-plan CSEE W4823: Advanced logic design 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, The overall program must include at CSEE W4824: Computer architecture prerequisite constraints make it difficult to complete the remaining computer engineering program by the end of the senior year. least 12 points of 6000-level ELEN, CSEE W4840: Embedded systems EECS, CSEE, or COMS courses CSEE W4868: Systems-on-chip platforms (exclusive of seminars). No more than 9 EECS E4951: Wireless networks & systems EECS E6180: Modeling & performance eval points of research project may be taken EECS E6321: Adv. digital electronic circuits for credit. No more than 3 points of a EECS E6322: VLSI hard. arch. for sig. proc. & ml nontechnical elective (at or above the COMS E6424: Hardware security 4000 level and with adviser approval) EECS E6765: Internet of things—sys. & physical may be included. A minimum GPA of data analytics

ENGINEERING 2020–2021 ENGINEERING 2020–2021 106 in areas with an immediate relationship and the Quick Guide (cs.columbia.edu/ 6. MATH UN2010 or UN2020 or 107 COMPUTER SCIENCE to the computer, such as programming education/undergraduate/). APMA E2101 or E3101 (3) or 450 Computer Science, MC 0401 languages, operating systems, and COMS W3251 (4) 212-939-7000 computer architecture, and partially The CS Major Requirements 7. CSEE W3827 (3) cs.columbia.edu in theoretical computer science and The Undergraduate program consists 8. STAT GU4001 or IEOR E4150 (3) mathematics. Thus, students obtain of a minimum of 63 or 64 points and CHAIR PROFESSORS ASSOCIATE SENIOR LECTURERS Venkat the background to pursue their includes the following: ENGI E1006 Tracks Rocco A. Servedio Peter K. Allen PROFESSORS IN DISCIPLINE Venkatasubramanian interests both in applications and in 517 Computer Science Peter N. Belhumeur Alexandr Andoni Paul Blaer which is a prerequisite to the CS In addition, an advanced track is Rebecca Wright theoretical developments. 212-939-7004 Steven M. Bellovin Elias Bareinboim Adam Cannon Gil Zussman major, the CS Core consisting of 7-8 available by invitation for qualified David Blei Augustin Chaintreau Eleni Drinea Practical experience is an essential classes (24-25 points), 7 Track courses students who desire an extra VICE CHAIR Luca Carloni Xi Chen Ansaf Salleb-Aouissi SENIOR RESEARCH component of the computer science (21 points), and 15 points of general opportunity for advanced learning. Luca Carloni Stephen A. Edwards Jae Woo Lee SCIENTIST Michael J. Collins program. Undergraduate students technical electives. Any course exceptions to the track 466 Computer Science Steven K. Feiner Roxana Geambasu Gaston Ormazabal are often involved in advanced faculty 212-939-7043 Luis Gravano Eitan Grinspun LECTURERS IN Bjarne Stroustrup Note: All courses toward the CS requirements must be approved by Julia B. Hirschberg Daniel Hsu DISCIPLINE Arthur Werschulz research projects using state-of-the-art major must be taken for a letter grade. A the faculty adviser. All thesis, projects, DIRECTOR OF Gail E. Kaiser Suman Jana Daniel Bauer Moti Yung computing facilities. Qualified majors maximum of one course worth no more special topics, and general technical UNDERGRADUATE John R. Kender Martha Allen Kim Tony Dear sometimes serve as consultants than 4 points passed with a grade of D electives must also be approved by the STUDIES Tal Malkin Itsik Pe’er Nakul Verma ASSOCIATE RESEARCH at Columbia University Information Paul Blaer SCIENTISTS may be counted towards the major. faculty adviser. The 6 predefined tracks Kathleen R. McKeown Simha Sethumadhavan Technology (CUIT), which operates 703 CEPSR Vishal Misra Eugene Wu JOINT Yizheng Cheng Any course exceptions to the noted are as follows: 212-939-7034 Shree Kumar Nayar Junfeng Yang Shih-Fu Chang Giuseppe Di Guglielmo several computer labs at convenient requirements toward the CS major, all • Foundations of Computer Science Jason Nieh Changxi Zheng Clifford Stein Efsun Kayi locations on the campus. thesis, projects, special topics, and • Software Systems DIRECTOR OF Christos Papadimitriou Shanghack Lee Upper-level students in computer FINANCE AND AFFILIATES general technical electives must be • Digital Systems Kenneth A. Ross ASSISTANT Paolo Mantovani science may assist faculty members ADMINISTRATION PROFESSORS Shipra Agrawal Hiroshi Sasaki approved by the faculty adviser in writing. • Intelligent Systems Tim Roughgarden with research projects, particularly Maria Joanta Daniel S. Rubenstein Lydia Chilton Elham Azizi Eran Tromer • Applications 450 Computer Science Henning G. Schulzrinne Ronghui Gu Asaf Cidon in the development of software. Prerequisite to the CS Major • Vision, Graphics, Interactions, and 212-939-7020 Matei Ciocarlie EMERITUS Ongoing faculty projects include Rocco A. Servedio David Knowles ENGI E1006 Introduction to computing Robotics Salvatore J. Stolfo Baishakhi Ray Noemie Elhadad Alfred V. Aho algorithmic analysis, computational Xiaofan Jiang Edward G. Coffman Jr. for engineers and applied scientists. Vladimir Vapnik Brian Smith complexity, software tool design, Shuran Song Ethan Katz-Bassett Zvi Galil All CS majors are required to take this Undergraduate Thesis Jeannette Wing distributed computation, modeling and Mihalis Yannakakis Carl Vondrick Hod Lipson Jonathan L. Gross course and it is recommended that they A student may, with adviser approval, Liam Paninski performance evaluation, computer Omri Weinstein Steven M. Nowick do so in their first or second semester. choose to complete a thesis in place Feniosky Peña-Mora Stephen H. Unger networks, computer architecture, CAD of up to 6 points of track elective or Henryk Wozniakowski for digital systems, computer graphics, Yechiam Yemini The Computer Science Core general technical elective points. A programming environments, expert thesis consists of an independent systems, natural language processing, The core of the major consists of 7 or 8 theoretical or experimental investigation he function and influence of is available in such areas as artificial such as Baxter Research Robot, PR2 computer vision, robotics, computational courses plus one prerequisite course for of an appropriate problem in computer the computer is pervasive intelligence, machine learning, computer mobile robot manipulator, Staubli biology, computer security, a total of 8 or 9 courses. These courses science carried out under the in contemporary society. graphics, computer vision, robotics, RX-60L Robotic arm, Kinova, MICO multicomputer design, user interfaces, provide the foundation for the tracks and T advanced courses. Beginning with the supervision of a Computer Science Today’s computers process the daily computational complexity and the arm, custom-built overhead XYZ gantry VLSI applications, artificial intelligence, Department faculty member. A formal transactions of international banks, the analysis of algorithms, combinatorial robot, Toshiba RMA manipulator, Barrett combinatorial modeling, virtual class of 2023 the CS Core requirements written report is mandatory and an oral data from communications satellites, the methods, computer architecture, Technology robotic hand, 2 RWI Pioneer environments, and microprocessor will change as noted below. presentation may also be required. images in video games, and even the computer-aided digital design, mobile robots, 1 Evolution ER-1 robot, applications. Students are strongly fuel and ignition systems of automobiles. computer communications, databases, 1 RWI ATRV-2 mobile robot with RTK encouraged to arrange for participation The following are required courses General Technical Electives Computer software is as mathematical models for computation, GPS, Leica HDS-500 and HDS-3000 100 by consulting individual faculty members toward the CS Core for the class of commonplace in education and optimization, and software systems. meter range scanners, real-time Imaging and by attending the Computer Science 2023 and beyond: An additional 15 points of adviser recreation as it is in science and boards, a number of 3D printers (such as Research Fair held at the beginning of 1. COMS W1004 or W1007 (3) approved general technical electives at 2. COMS W3134 (3) or W3137 (4) the 3000 level or above are also required. business. There is virtually no field or Laboratory Facilities UPrint, Autodesk Ember) and professional each semester. 3. COMS W3157 (4) These general technical electives should profession that does not rely upon The department has well-equipped lab audio recording devices; a networking Most graduates of the computer 4. COMS W3203 (4) be in mathematics, science, engineering computer science for the problem- areas for research in computer graphics, testbed with Cisco backbone routers, science program at Columbia step 5. COMS W3251 (4) or closely related disciplines. solving skills and the production expertise computer-aided digital design, computer traffic generators; an IDS testbed with directly into career positions in computer 6. COMS W3261 (3) required in the efficient processing vision, databases and digital libraries, secured LAN, Cisco routers, EMC storage, science with industry or government, 7. CSEE W3827 (3) Advanced Placement of information. Computer scientists, data mining and knowledge discovery, and Linux servers; a simulation testbed or continue their education in graduate therefore, function in a wide variety of distributed systems, mobile and with several Linux servers and Cisco degree programs. Many choose to Students who pass the Computer The following are required courses roles, ranging from pure theory and wearable computing, natural-language Catalyst routers. The department uses a combine computer science with a Science Advanced Placement (AP) toward the CS Core for the class of design to programming and marketing. processing, networking, operating SIP IP phone system. The protocol was second career interest by taking Exam with a 4 or 5 will receive 3 points 2022 and earlier: The computer science curriculum systems, programming systems, developed in the department. additional programs in business of credit and an exemption from COMS 1. COMS W1004 or W1007 (3) at Columbia places strong emphasis robotics, user interfaces, real-time administration, medicine, or other W1004. 2. COMS W3134 (3) or W3137 (4) both on theoretical computer science multimedia, and speech research. professional studies. UNDERGRADUATE PROGRAM 3. COMS W3157 (4) and mathematics and on applied The labs for research in image For further information on the Track 1: Foundations of CS Track Computer science majors at Columbia 4. COMS W3203 (3) aspects of computer technology. A processing, vision, graphics, and undergraduate computer science The foundations track is suitable for study an integrated curriculum, partially 5. COMS W3261 (3) broad range of upper-level courses robotics contain specialized equipment program, please see the home page

ENGINEERING 2020–2021 ENGINEERING 2020–2021 108 109 COMPUTER SCIENCE PROGRAM: FIRST AND SECOND YEARS COMPUTER SCIENCE: THIRD AND FOURTH YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) APMA E2000 (4)1 CSEE W3827 (3) Fund. of comp. systems REQUIRED and COURSES PHYSICS UN1401 (3) UN1402 (3) COMS W3261 (3) (three tracks, UN1601 (3.5) UN1602 (3.5) Chemistry or physics lab: Computer sci. theory choose one) UN2801 (4.5) UN2802 (4.5) PHYS UN1494 (3) or PHYS UN3081 (2) or CHEM UN1500 (3) or NONTECH 3 points 6 points 3 points CHEMISTRY/ CHEM UN1403 (3) or higher or CHEM UN1507 (3) or BIOLOGY EEEB UN2001 (4) or UN2005 (4) or higher CHEM UN3085 (4) (choose one course) either semester TECH 6 points 12 points 9 points 9 points ELECTIVES

UNIVERSITY CC1010 (3) either semester WRITING TOTAL POINTS 15–16 15 15 12

ECON UN1105 (4) and UN1105 recitation (0) any semester Note: No more than 6 points of project/thesis Track 3: Intelligent Systems Track courses (COMS W3902, W3998, W4901) can courses (COMS W3902, W3998, W4901) can count toward the track. HUMA CC1002 or count toward the track. The intelligent systems track is for REQUIRED COCI CC1102 or students interested in machine learning, NONTECHNICAL HUMA CC1001 or Major Cultures (3–4) ELECTIVES Students who declared their Computer Science robots, and systems capable of Track 4: Applications Track COCI CC1101 or major prior to Fall 2016 may also count COMS The applications track is for students Major Cultures (3–4) exhibiting “human-like” intelligence. A W4241, W4205, W4281, W4444, W4771, and interested in the implementation of HUMA UN1121 or W4772 as elective courses. total of seven required breadth and UN1123 (3) elective courses are to be chosen from interactive multimedia applications for the following schedule. the internet and wireless networks. Track 2: Software Systems Track REQUIRED REQUIRED: 6 points ENGI E1006 Computing for EAS (3) either semester The software systems track is for REQUIRED: 9 Points from: TECH ELECTIVES COMS W4115: Programming languages and students interested in networks, COMS W4701: Artificial intelligence translators programming languages, operating COMS W4705: Natural language processing COMS W1004 (3) COMS W3134 (3) or COMS W3157 (4) COMS W4706: Spoken language processing COMS W4170: User interface design Intro. to computer science COMS W3137 (4) Adv. programming systems, software engineering, COMS W4731: Computer vision or Data structures and ELECTIVES: 15 points from the following list: COMPUTER databases, security, and distributed COMS W4733: Computational aspects of robotics SCIENCE COMS W1007 (3) and COMS W3251 (4) COMS W3902: Undergraduate thesis* systems. COMS W4771: Machine learning Object-oriented programming COMS W3203 (4) Computational COMS W3998: Undergraduate projects in computer either semester Discrete math linear algebra REQUIRED: 9 points ELECTIVES: 12 points required science* COMS W4115: Programming languages and Up to 12 points from the following list: Any COMS W41xx course translators Any COMS W47xx course PHYSICAL UN1001 (1) UN1002 (1) COMS W4165: Pixel processing EDUCATION COMS W4118: Operating systems COMS W4252: Computational learning theory COMS W4901: Projects in computer science* CSEE W4119: Computer networks Any COMS W47xx course if not used as a COMS W4995-W4996: Special topics in computer science, I and II (with adviser THE ART OF ENGI E1102 (4) either semester ELECTIVES: 12 points from the following list: required course ENGINEERING COMS W4995-W4996: Special topics in computer approval) COMS W3902: Undergraduate thesis* science, I and II (with adviser Any COMS E69xx course (with adviser approval) COMS W3998: Undergraduate projects in computer approval) COMS E6998-E6999: Topics in computer science, MATH GU4061: Introduction to modern analysis I Advanced cryptography science* students who are interested in algorithms, COMS E6261: Any COMS W67xx course I and II (with adviser approval)* MATH GU4155: Probability theory Scheduling: deterministic models Any COMS W41xx course computational complexity, and other IEOR E6400: COMS E6998-E6999: Topics in computer science, COMS W4252: Computational learning theory IEOR E6603: Combinatorial optimization COMS W4444: Programming and problem solving * With adviser approval, may be repeated for credit areas of theoretical Computer Science. I and II (with adviser approval)* COMS W4261: Introduction to cryptography IEOR E6606: Advanced topics in network flows Any COMS W48xx course Note: No more than 6 points of project/thesis REQUIRED: 6 points APMA E4300: Numerical methods IEOR E6608: Integer programming COMS W4901: Projects in computer science* Up to 6 points from the following list: courses (COMS W3902, W3998, W4901) can CSOR W4231: Analysis of algorithms IEOR E4407: Game theoretic models of operation IEOR E6610: Approximation algorithms COMS W4995-W4996: Special topics in computer COMS W3902: Undergraduate thesis* count toward the track. COMS W4236: Introduction to computational PHIL GU4431: Set theory EEOR E6616: Convex optimization science, I and II (with adviser COMS W3998: Undergraduate projects in computer complexity CSPH GU4801: Mathematical logic I IEOR E6613: Optimization I (4.5) approval) science* Track 5: Vision, Interaction, CSPH GU4802: Mathematical logic II: IEOR E6614: Optimization II (4.5) Any COMS E61xx or E68xx course (with adviser COMS W4901: Projects in computer science* ELECTIVES: 15 points from the following list: incompleteness IEOR E6711: Stochastic models I approval) Graphics, and Robotics Track MATH UN3020: Number theory and cryptography COMS W4901: Projects in computer science* IEOR E6712: Stochastic models II COMS E6998-E6999: Topics in computer science, Up to 3 points from the following list: The vision, interaction, graphics, MATH UN3025: Making, breaking codes COMS W4995-W4996: Special topics in computer ELEN E6717: Information theory I and II (with adviser approval)* COMS W4111: Database systems and robotics track focus on visual COMS W3902: Undergraduate thesis* COMS W4160: Computer graphics science, I and II (with adviser ELEN E6718: Algebraic coding theory * With adviser approval, may be repeated for credit information with topics in vision, COMS W3998: Projects in Computer Science* COMS W4170: User interface design approval) ELEN E6970: Resource allocation and networking graphics, human-computer interaction, COMS W4203: Graph theory COMS E6232: Analysis of algorithms, II games Note: No more than 6 points of project/thesis COMS W4999: Computing and the humanities MATH GU4032: Fourier analysis courses (COMS W3902, W3998, W4901) can count robotics, modeling, and learning. MATH GR6238: Enumerative combinatorics COMS E6998-E6999: Topics in computer science, * With adviser approval, may be repeated for credit MATH GU4041: Introduction to modern algebra I COMS E6253: Advanced topics in computational I and II (with adviser approval)* toward the track. Students learn about fundamental MATH GU4042: Introduction to modern algebra II learning theory Note: No more than 6 points of project/thesis ways in which visual information is * With adviser approval, may be repeated for credit

ENGINEERING 2020–2021 ENGINEERING 2020–2021 110 111 EFFECTIVE CLASS OF 2022 AND PRIOR EFFECTIVE CLASS OF 2022 AND PRIOR COMPUTER SCIENCE PROGRAM: FIRST AND SECOND YEARS COMPUTER SCIENCE: THIRD AND FOURTH YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) APMA E2000 (4) APMA E2101 (3) or MATH UN2010 (3) or COMS W3251 (4) PHYSICS UN1401 (3) UN1402 (3) and (three tracks, UN1601 (3.5) UN1602 (3.5) Chemistry or physics lab: REQUIRED COMS W3261 (3) choose one) UN2801 (4.5) UN2802 (4.5) PHYS UN1494 (3) or COURSES Computer sci. theory PHYS UN3081 (2) or and CHEM UN1500 (3) or STAT GU4001(3) or IEOR E4150 (3) CHEMISTRY/ CHEM UN1403 (3) or higher or CHEM UN1507 (3) or BIOLOGY EEEB UN2001 (4) or UN2005 (4) or higher CHEM UN3085 (4) Prob. and stat. (choose one course) either semester

NONTECH 3 points 6 points 3 points UNIVERSITY CC1010 (3) either semester WRITING

TECH 6 points 12 points 9 points 9 points ECON UN1105 (4) and UN1105 recitation (0) any semester ELECTIVES

15–16 15 15 12 HUMA CC1002 or TOTAL POINTS REQUIRED COCI CC1102 or NONTECHNICAL HUMA CC1001 or Major Cultures (3–4) ELECTIVES COCI CC1101 or 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 Major Cultures (3–4) for COMS W1004-W3134 and COMS W1007-3137 is Java. COMS W1004 may be waived for students who have scored 4 or 5 on the AP computer science A exam. HUMA UN1121 or UN1123 (3) Plus 3 points from: collective faculty invitation, (GRE) is required for admission to the COMS W4115: Programming languages and extended to students who have already department's graduate programs. translators completed the core courses and the Applicants for September admission REQUIRED ENGI E1006 Computing for EAS (3) either semester COMS W4118: Operating systems TECH ELECTIVES required courses for one of those tracks. should take the GREs by October of the COMS W4130: Parallel programming REQUIRED TRACK COURSES preceding year. Applicants for January ELECTIVES: 12 points from the following list: COMS W1004 (3) COMS W3134 (3) or COMS W3157 (4) A student designates one of the six other track admission should take these exams by Intro. to computer science COMS W3137 (4) Adv. programming COMS W3902: Undergraduate thesis* areas and completes the set of required track April of the preceding year. or Data structures and COMPUTER COMS E3998: Undergraduate projects in courses for that track, prior to entry into the M.S. students must complete the SCIENCE COMS W1007 (3) and CSEE W3827 (3) computer science* Object-oriented programming COMS W3203 (3) Fund. of computer Advanced Track. There are two or three courses, professional development and leadership Any COMS/CSEE W41xx course either semester Discrete math systems depending on the designated area. course, ENGI E4000, as a graduation Any COMS/CSEE W48xx course COMS E4901: Projects in computer science ELECTIVES requirement. Ph.D. candidates are strongly encouraged to complete PHYSICAL UN1001 (1) UN1002 (1) COMS W4995-W4996: Special topics in computer At least 6 points of 4000-level lecture courses EDUCATION science, I and II (with adviser from the menu for the designated track, plus 6 ENGI E6001–6004 and should consult approval) points of 6000-level courses in the designated their program for PDL requirements. THE ART OF ENGI E1102 (4) either semester CSEE E6824: Parallel computer architecture* track area. ENGINEERING CSEE E6847: Distributed embedded systems* M.S. in Computer Science Program CSEE E6861: CAD of digital systems** ​THESIS CSEE E6868: Embedded scalable platforms** There is a required 6-point senior thesis. The Master of Science (M.S.) COMS W4701: Artificial intelligence captured, manipulated, Track 6: Digital Systems Track COMS E6998-E6999: Topics in computer science, program is intended for students with COMS W4733: Computational aspects of robotics INVITATION and experienced. I and II (with adviser approval)* a bachelor's degree in Computer COMS W4735: Visual interfaces to computers The digital systems track is for students Only the top 20 percent of computer science Science or a strongly related field who REQUIRED: 6 points from: COMS W4771: Machine learning interested in working at the interface of * With adviser approval, may be repeated for credit majors in course performance in computer science COMS W4160: Computer graphics COMS W4901: Projects in computer science* hardware and software. Subjects include **With adviser approval. courses will be considered for invitation during the wish to broaden and deepen their COMS W4995-W4996: Special topics in computer junior year. (A student in the advanced track who understanding of computer science. COMS W4731: Computer vision digital design, computer architecture Note: No more than 6 points of project/thesis science, I and II (with adviser does not maintain this status may be required to Columbia University and the New York COMS W4167: Computer animation (both sequential and parallel) and courses (COMS W3902, W3998, W4901) can approval) return to his or her previously selected track area.) City environment provide excellent ELECTIVES: 15 points from the following list: embedded systems. count toward the track. Any COMS E691x course (with adviser approval) career opportunities with multiple COMS W3902: Undergraduate thesis* REQUIRED: 3 points COMS E6998-E6999: Topics in computer science, industries. The program provides a COMS W3998: Undergraduate projects in I and II (with adviser approval)* CSEE W4824: Computer architecture Track 7: Advanced GRADUATE PROGRAMS computer science* unique opportunity to develop leading- The advanced track of the B.S. in The Department of Computer Science COMS W4162: Advanced computer graphics * With adviser approval, may be repeated for credit Plus 3 points from: edge in-depth knowledge of specific Computer Science provides extra offers graduate programs leading to COMS W4165: Pixel processing Note: No more than 6 points of project/thesis CSEE W4823: Advanced logic design computer science disciplines. opportunity for advanced learning. COMS W4167: Computer animation courses (COMS W3902, W3998, W4901) can CSEE W4840: Embedded systems the degree of Master of Science and Students in the M.S. program must COMS W4170: User interface design count toward the track. CSEE E4868: System-on-chip platforms It comprises accelerated versions of the degree of Doctor of Philosophy. complete a total of 30 points with a COMS W4172: 3D user interface design the other six tracks. Entry is only by The Graduate Record Examination GPA of at least 2.7. Every student

ENGINEERING 2020–2021 ENGINEERING 2020–2021 COMS W1005x or y Introduction to computer three hours per week for the first third of the term, Corequisite: COMS W3203. An honors introduction 112 selects a track that focuses on a elsewhere, and the department does not flexibility for both scheduling and 113 particular field of computer science. consider admission of part-time Ph.D. the choice of courses depending science and programming in MATLAB or for two hours per week for the first six weeks. to data types and structures: arrays, stacks, singly 3 pts. Lect: 3. Professor Blaer. May be repeated for credit if different languages and doubly linked lists, queues, trees, sets, and There are currently eight predefined students. Further information is available on a student's prior experience and A general introduction to computer science are involved. graphs. Programming techniques for processing M.S. tracks: Computational Biology; at cs.columbia.edu/education/phd/. concurrent obligations. Students will also concepts, algorithmic problem-solving capabilities, such structures: sorting and searching, hashing, Computer Security; Foundations of COMS W3102x and y Development be closely advised during this process in and programming skills in MATLAB. Assumes garbage collection. Storage management. Design Computer Science; Machine Learning; technologies order to prepare for M.S. track selection. no prior programming background. Columbia and analysis of algorithms. Taught in Java. Note: Natural Language Processing; Network DUAL DEGREE PROGRAM IN 1–2 pts. Lect: 2. Lab: 0-2. Members of the Once the bridge is completed with an University students may receive credit for only one Due to significant overlap, students may receive JOURNALISM AND COMPUTER faculty. Systems; Software Systems; Vision, overall 3.3 GPA or higher, students are of the following two courses: W1004 or W1005. credit for only one of the following three courses: Graphics, Interaction, and Robotics. SCIENCE Prerequisite: Fluency in at least one then eligible for an automatic transfer COMS W3134, W3136, or W3137. Every track has a set of required The Graduate School of Journalism ENGI E1006x and y Introduction to computing programming language. Introduction to into the M.S. in Computer Science courses and a wide range of elective and the School of Engineering for engineers and applied scientists software development tools and environments. COMS W3157x and y Advanced programming program. Further information is available 3 pts. Lect: 3. Professor Salleb-Aouissi. Each section is devoted to a specific tool or 4 pts. Lect: 4. Professor Lee. courses that allow the students flexibility and Applied Science offer a dual at cs.columbia.edu/ms-bridge/. An interdisciplinary course in computing environment. One-point sections meet for two Prerequisite: Two terms of programming in designing their program according degree program leading to the M.S. to their interests, under the guidance intended for first year SEAS students. Introduces hours each week for half a semester, and two- experience. COMS W3134 or W3137. degree from the Graduate School of computational thinking, algorithmic problem point sections include an additional two-hour lab. Recommended: Data Structures. C programming of a faculty adviser. Besides the eight Journalism and the M.S. degree in COURSES IN COMPUTER solving and Python programming with applications language and Unix systems programming. Also predefined tracks, there is also the COMS W3107x Clean object-oriented design Computer Science from the School of SCIENCE in science and engineering. Assumes no prior covers Git, Make, TCP/IP networking basics, C++ option of a M.S. Personalized track for 3 pts. Lect: 3. Professor Kender. Engineering and Applied Science. In the listing below, the designator programming background. fundamentals. students who want to study an area of Prerequisites: COMS W1004 or instructor's Admitted students will enroll for COMS (Computer Science) is computer science that is not covered by COMS W1007x Honors introduction to permission. May not take for credit if already COMS W3203x and y Discrete structures in a total of four semesters consisting understood to precede all course one of the eight tracks, and the option computer science received credit for COMS W1007. A course in mathematics and probability of 27 points of Computer Science numbers for which no designator is of the M.S. Thesis track for students 3 pts. Lect: 3. Professor Kender. designing, documenting, coding, and testing robust 4 pts. Lect: 3. Professor Salleb-Aouissi. coursework in which an overall 2.7 indicated. NOTE: Students may receive computer software, according to object-oriented who want to do extensive research in Prerequisite: AP Computer Science with a grade Prerequisite: MATH UN1102 or UN1201 or GPA must be maintained in addition credit for only one of the following two of 4 or 5 or similar experience. An honors-level design patterns and clean coding practices. APMA E2000 and COMS W1002 or W1004 or a subfield and write an M.S. thesis, Taught in Java. Object-oriented design principles under the supervision of a faculty to the Journalism requirements. In courses: COMS W1004 and W1005. introduction to computer science, intended W1007 or ENGI E1006. Logic and formal proofs, primarily for students considering a major in include: use cases; CRC; UML; javadoc; patterns sets and relations, advanced proof techniques, member. Students in all the tracks are addition to taking classes already Likewise, students may receive credit for computer science. Computer science as a science (adapter, builder, command, composite, decorator, number theory and modular arithmetic, graph encouraged to pursue research if they offered at the journalism and only one of the following three courses: of abstraction. Creating models for reasoning facade, factory, iterator, lazy evaluation, observer, theory, counting and basic probability, conditional wish, and many participate in research engineering schools, students will COMS W3134, W3136, or W3137. singleton, strategy, template, visitor); design by about and solving problems. The basic elements of probability and Bayes rule, random variables, attend a seminar and workshop contract; loop invariants; interfaces and inheritance projects with the faculty. The faculty in COMS W1001x or y Introduction to computers and computer programs. Implementing expectation and variance, central limit theorem, hierarchies; anonymous classes and null objects; the department conduct research in all designed specifically for the joint information science abstractions using data structures and algorithms. probability distributions (Gaussians, binomial, and graphical widgets; events and listeners; Java's areas of computer science. For detailed program. The seminar will teach 3 pts. Lect: 3. Instructor to be announced. Taught in Java. geometric). Object class; generic types; reflection; timers, information on the M.S. program, please students about the impact of digital Basic Introduction to concepts and skills in threads, and locks. see cs.columbia.edu/education/ms/. techniques on journalism; the Information Sciences: human-computer interfaces, COMS W1404x and y Emerging scholars COMS W3210x or y Scientific computation program seminar 3 pts. Lect: 3. Instructor to be announced. emerging role of citizens in the news representing information digitally, organizing and COMS W3134x and y Data structures in Java 1 pt. Sem: 1. Professor Cannon. Prerequisites: Two terms of calculus. Introduction searching information on the internet, principles 3 pts. Lect: 3. Professor Blaer. Ph.D. in Computer Science process; the influence of social media; Corequisite: COMS W1004/1007 or ENGI E1006. to computation on digital computers. Design of algorithmic problem solving, introduction to Prerequisite: COMS W1004 or knowledge of Program and the changing business models Enrollment with instructor permission only. Peer-led and analysis of numerical algorithms. Numerical database concepts, introduction to programming Java. Data types and structures: arrays, stacks, The primary focus of the doctoral that will support newsgathering. In the weekly seminar intended for first- and second-year solution of equations, integration, recurrences, in Python. singly and doubly linked lists, queues, trees, workshop, students will use a hands- undergraduates considering a major in computer chaos, differential equations. Introduction to program is research, with the philosophy sets, and graphs. Programming techniques on approach to delve deeply into COMS W1002x Computing in context science. Pass/fail only. Monte Carlo methods. Properties of floating point that students learn best by doing— for processing such structures: sorting and 4 pts. Lect: 4. Professor Cannon. arithmetic. Applications to weather prediction, beginning as apprentices and becoming information design, focusing on how ECBM E3060x Introduction to genomic searching, hashing, garbage collection. Storage Introduction to elementary computing concepts computational finance, computational science, junior colleagues working with faculty on to build a site, section, or application information science and technology management. Rudiments of the analysis of and Python programming with domain-specific and computational engineering. scholarly research projects. The faculty from concept to development, 3 pts. Lect: 3. Professor Anastassiou. algorithms. Taught in Java. Note: Due to applications. Shared CS concepts and Python in the department conduct research ensuring the editorial goals are kept Introduction to the information system paradigm of significant overlap, students may receive credit COMS W3251x and y Computational linear programming lectures with track-specific sections. uppermost in mind. molecular biology. Representation, organization, for only one of the following three courses: algebra in all areas of computer science. The Track themes will vary but may include computing structure, function and manipulation of the COMS W3134, W3136, or W3137. 4 pts. Lect: 3. Professor Dear. degree of Doctor of Philosophy requires for the social sciences, computing for economics biomolecular sequences of nucleic acids and Prerequisites: MATH UN1102 or UN1201 or APMA a dissertation based on the candidate's COMS W3136y Data structures with C/C++ CS@CU MS BRIDGE PROGRAM and finance, digital humanities, and more. Intended proteins. The role of enzymes and gene regulatory E2000 and COMS W1002 or W1004 or W1007 original research, which is supervised by 4 pts. Lect: 3. Professor Lee. IN COMPUTER SCIENCE for nonmajors. Students may receive credit for only elements in natural biological functions as well or ENGI E1006. Functions and compositions. Prerequisite: COMS W1004, W1005, W1007, a faculty member, and all students in the one of the following two courses: ENGI E1006 or as in biotechnology and genetic engineering. Vectors and linear functions, matrices and linear The CS@CU MS Bridge Program in or ENGI E1006. A second programming course Ph.D. program are actively engaged in COMS W1002. Recombination and other macromolecular transforms, inverses and Gaussian elimination. Computer Science offers prospective intended for nonmajors with at least one semester research throughout the program. Ph.D. processes viewed as mathematical operations with Vector spaces, bases, subspaces, and dimension. applicants from non-computer science COMS W1004x and y Introduction to of introductory programming experience. Basic students spend at least half of their simulation and visualization using simple computer Inner products, norms, and orthogonal projections. backgrounds, including those without computer science and programming in Java elements of programming in C and C++, array- time on research under the direction of programming. Shares lectures with ECBM E4060, Eigenvectors and eigenvalues, spectral programming experience, the opportunity 3 pts. Lect: 3. Professor Cannon. based data structures, heaps, linked lists, C their faculty adviser from their first day but the work requirements differ somewhat. decomposition. Quadratic forms, and singular to acquire the knowledge and skills A general introduction to computer science for programming in UNIX environment, object-oriented in the program and devote themselves science and engineering students interested in value decomposition. Note: Previously offered for necessary to build careers in technology. COMS W3101x and y Programming languages programming in C++, trees, graphs, generic full time to research after coursework majoring in computer science or engineering. 3 points. Admitted students will first take a 1 pt. Lect: 1. Members of the faculty. programming, hash tables. Due to significant and other preliminaries have been Covers fundamental concepts of computer science, overlap, students may only receive credit for either COMS W3261x and y Computer science theory total of five undergraduate courses Prerequisite: Fluency in at least one programming completed. Ph.D. students are also algorithmic problem-solving capabilities, and language. Introduction to a programming language. COMS W3134, W3136, or W3137. 3 pts. Lect: 3. Professor Malkin. (the bridge curriculum) over two to introductory Java programming skills. Assumes Each section is devoted to a specific language. Prerequisite: COMS W3203. Corequisites: COMS expected to participate in departmental COMS W3137y Honors data structures and three semesters, which will build the no prior programming background. Columbia Intended only for those who are already fluent in W3134, W3136, or W3137. Regular languages: and laboratory activities full time on algorithms necessary foundation of programming University students may receive credit for only one at least one programming language. Sections may deterministic and nondeterministic finite automata, campus throughout the program, 4 pts. Lect: 3. Professor Blaer. and mathematical skills. There is of the following two courses: W1004 or W1005. meet for one hour per week for the whole term, for regular expressions. Context-free languages: except possibly for summer internships Prerequisite: COMS W1004 or W1007.

ENGINEERING 2020–2021 ENGINEERING 2020–2021 context-free grammars, push-down automata. report and letter of evaluation may be required. systems, replication, consistency models, fault Prerequisites: Background in Computer System Significant implementation is required: the final Firewalls, virtual private networks, viruses. Mobile 114 115 Turing machines, the Chomsky hierarchy, and the May not be used as a technical or nontechnical tolerance, distributed transactions, agreement Organization and good working knowledge of C/ project involves writing an interactive 3D video and app security. Usable security. Church-Turing thesis. Introduction to complexity elective. May not be taken for pass/fail credit or and commitment, Paxos-based consensus, C++. Corequisites: CSOR W4246, STAT GU4203, game in OpenGL. Note: May not earn credit for both W4181 and theory and NP-completeness. audited. MapReduce infrastructures, scalable distributed or equivalent approved by faculty adviser. W4180 or W4187. COMS W4162x or y Advanced computer databases. Combines concepts and algorithms Introduction to computer distributed systems with COMS W3410y Computers and society ECBM E4060x Introduction to genomic graphics COMS W4182y Security II with descriptions of real-world implementations emphasis on warehouse scale computing systems. 3 pts. Lect: 3. Professor Bellovin. information 3 pts. Lect: 3. Professor Zheng. 3 pts. Lect: 3. Professor Bellovin. at Google, Facebook, Yahoo, Microsoft, Topics include fundamental tradeoffs in computer Broader impact of computers. Social networks 3 pts. Lect: 3. Professor Anastassiou. Prerequisite: COMS W4160 or equivalent, or Prerequisites: COMS W4181, COMS W4118, Linkedin, etc. systems, hardware and software techniques for and privacy. Employment, intellectual property, Introduction to the information system paradigm of exploiting instruction-level parallelism, data-level instructor’s permission. A second course in computer CSEE W4119. Advanced security. Centralized, and the media. Science and engineering ethics. molecular biology. Representation, organization, COMS W4115x and y Programming languages parallelism and task level parallelism, scheduling, graphics covering more advanced topics including distributed, and cloud system security. Suitable for nonmajors. structure, function, and manipulation of the and translators caching, prefetching, network and memory image and signal processing, geometric modeling Cryptographic protocol design choices. Hardware biomolecular sequences of nucleic acids and with meshes, advanced image synthesis including and software security techniques. Security testing CSEE W3827x and y Fundamentals of 3 pts. Lect: 3. Professor Edwards or Ray. architecture, latency and throughput optimizations, proteins. The role of enzymes and gene regulatory ray tracing and global illumination, and other and fuzzing. Blockchain. Human security issues. computer systems Prerequisites: COMS W3134, W3136, or W3137 specializations, and introduction to programming elements in natural biological functions as well data center computers. topics as time permits. Emphasis will be placed Note: May not earn credit for both W4182 and 3 pts. Lect: 3. Professor Kim or Rubenstein. (or equivalent), W3261, and CSEE W3827, or as in biotechnology and genetic engineering. both on implementation of systems and important W4180 or W4187. Prerequisite: An introductory programming course. instructor’s permission. Modern programming Recombination and other macromolecular COMS W4130x Principles and practice of mathematical and geometric concepts such as Fundamentals of computer organization and digital languages and compiler design. Imperative, object- COMS W4186x Malware analysis and reverse processes viewed as mathematical operations with parallel programming Fourier analysis, mesh algorithms and subdivision, logic. Boolean algebra, Karnaugh maps, basic gates oriented, declarative, functional, and scripting engineering simulation and visualization using simple computer 3 pts. Lect: 2.5. Professor Kim. and Monte Carlo sampling for rendering. Note: and components, flip-flops and latches, counters languages. Language syntax, control structures, 3 pts. Lect: 3. Lab 3. Professor Sikorski. programming. Shares lectures with ECBM E3060, Prerequisites: Experience in Java, basic Course will be taught every two years. and state machines, basics of combinational and but the work requirements differ somewhat. data types, procedures and parameters, binding, understanding of analysis of algorithms. COMS Prerequisites: COMS W3157 or equivalent; CSEE sequential digital design. Assembly language, scope, run-time organization, and exception COMS W4167x or y Computer animation W3827. Hands-on analysis of malware. How COMS W4111x and y Introduction to databases W3134, W3136, or W3137 (or equivalent). instruction sets, ALUs, single-cycle and multi- handling. Implementation of language translation 3 pts. Lect: 3. Professor Grinspun. hackers package and hide malware and viruses to 3 pts. Lect: 3. Professor Gravano. Principles of parallel software design. Topics include cycle processor design, introduction to pipelined tools including compilers and interpreters. Lexical, Prerequisite: Multivariable calculus, linear algebra, evade analysis. Disassemblers, debuggers, and Prerequisites: COMS W3134, W3136, or W3137, task and data decomposition, load-balancing, processors, caches, and virtual memory. C++ programming proficiency. COMS W4156 other tools for reverse engineering. Deep study of or instructor’s permission. Covers definition of syntactic, and semantic analysis; code generation; reasoning about correctness, determinacy, safety, recommended. Theory and practice of physics- Windows Internals and x86 assembly. COMS W3902x and y Undergraduate thesis database systems, effective design of databases, introduction to code optimization. Teams implement and deadlock-freedom. Application of techniques based animation algorithms, including animated 1–6 pts. Members of the faculty. querying databases, and developing applications a language and its compiler. through semester-long design project implementing COMS W4203y Graph theory Prerequisite: Agreement by faculty member to clothing, hair, smoke, water, collisions, impact, using databases. Includes: entity-relationship performant, parallel application in a modern parallel 3 pts. Lect: 3. Instructor to be announced. COMS W4117x or y Compilers and interpreters and kitchen sinks. Topics covered: integration serve as thesis adviser. An independent theoretical modeling, logical design of relational databases, 3 pts. Lect: 3. programming language. Prerequisite: COMS W3203. General introduction or experimental investigation by an undergraduate relational algebra, SQL, database security, of ordinary differential equations, formulation Prerequisite: COMS W4115 or instructor’s to graph theory. Isomorphism testing, algebraic major of an appropriate problem in computer and an overview of query optimization and CSEE W4140x or y Networking laboratory of physical models, treatment of discontinuities permission. Continuation of COMS W4115, specification, symmetries, spanning trees, science carried out under the supervision of transaction processing. Additional topics: NoSQL, 3 pts. Lect: 3. Professor Zussman. including collisions/contact, animation control, with broader and deeper investigation into the traversability, planarity, drawings on higher-order a faculty member. A formal written report is graph, object-relational, cloud databases, data Prerequisite: CSEE W4119 or equivalent. constrained Lagrangian Mechanics, friction/ design and implementation of contemporary surfaces, colorings, extremal graphs, random mandatory and an oral presentation may also preparation, and cleaning of real-world data. Students will learn how to put “principles into dissipation, continuum mechanics, finite elements, language translators, be they compilers or graphs, graphical measurement, directed graphs, be required. May be taken over more than one Offers both programming and non-programming practice,” in a hands-on networking lab course. rigid bodies, thin shells, discretization of Navier- interpreters. Topics include parsing, semantic Burnside-Polya counting, voltage graph theory. term, in which case the grade is deferred until homework and projects, to accommodate different The course will cover the technologies and Stokes equations. General education requirement: analysis, code generation and optimization, run- all 6 points have been completed. Consult the programming skills and backgrounds. protocols of the internet using equipment quantitative and deductive reasoning (QUA). CSOR W4231x Analysis of algorithms, I time environments, and compiler-compilers. A department for section assignment. currently available to large internet service programming project is required. 3 pts. Lect: 3. Professor Yannakakis, Drinea, COMS W4112y Database system providers such as CISCO routers and end COMS W4170x or y User interface design COMS W3995x or y Special topics in or Andoni. implementation systems. A set of laboratory experiments provides 3 pts. Lect: 3. Professor Chilton or Feiner. computer science COMS W4118x and y Operating systems, I Prerequisites: COMS W3134, W3136 or W3137, 3 pts. Lect: 2.5. Professor Ross. hands-on experience with engineering wide- Prerequisite: COMS W3134, W3136, or W3137. 3 pts. Lect: 3. 3 pts. Lect: 3. Professor Lee or Nieh. and W3203. Introduction to the design and Prerequisites: COMS W4111; fluency in Java area networks and will familiarize students with Introduction to the theory and practice of computer Prerequisite: Instructor’s permission. Consult the Prerequisites: CSEE W3827 and knowledge of analysis of efficient algorithms. Topics include or C++. CSEE W3827 is recommended. The the Internet Protocol (IP), Address Resolution user interface design, emphasizing the software department for section assignment. Special topics C and programming tools as covered in W3136, models of computation, efficient sorting and principles and practice of building large-scale Protocol (ARP), Internet Control Message design of graphical user interfaces. Topics include arranged as the need and availability arise. Topics W3157, or W3101, or instructor’s permission. searching, algorithms for algebraic problems, database management systems. Storage methods Protocol (ICMP), User Datagram Protocol (UDP) basic interaction devices and techniques, human are usually offered on a one-time basis. Since Design and implementation of operating systems. graph algorithms, dynamic programming, and indexing, query processing and optimization, and Transmission Control Protocol (TCP), the factors, interaction styles, dialogue design, and the content of this course changes each time it is probabilistic methods, approximation algorithms, materialized views, transaction processing and Topics include process management, process Domain Name System (DNS), routing protocols software infrastructure. Design and programming offered, it may be repeated for credit. and NP-completeness. recovery, object-relational databases, parallel and synchronization and interprocess communication, (RIP, OSPF, BGP), network management projects are required. distributed databases, performance considerations. memory management, virtual memory, interrupt protocols (SNMP, and application-level protocols COMS W4232y Advanced algorithms COMS W3998x and y Undergraduate projects COMS W4172y 3D user interfaces and Programming projects are required. handling, processor scheduling, device management, (FTP, TELNET, SMTP). 3 pts. Lect: 3. Professor Andoni. in computer science augmented reality I/O, and file systems. Case study of the UNIX Prerequisite: COMS W4231. Introduces classic 1–3 pts. Members of the faculty. COMS W4113x Fundamentals of large-scale COMS W4156x Advanced software engineering 3 pts. Lect: 3. Professor Feiner. Prerequisite: Approval by a faculty member who operating system. A programming project is required. and modern algorithmic ideas central to many distributed systems 3 pts. Lect: 3. Professor Kaiser. Prerequisite: COMS W4160 or W4170 or agrees to supervise the work. Independent project areas of Computer Science. Focus on most 3 pts. Lect: 3. Professor Geambasu. CSEE W4119x and y Computer networks Prerequisite: COMS W3157 or equivalent. instructor’s permission. Design, development, involving laboratory work, computer programming, powerful paradigms and techniques of how to Prerequisites: COMS W3134, W3136, or 3 pts. Lect: 3. Professor Katz-Bassett. Software lifecycle using frameworks, libraries, and evaluation of 3D user interfaces. Interaction analytical investigation, or engineering design. design and measure efficiency of algorithms. W3137. COMS W3157 or good working Prerequisites: Comfort with basic probability and and services. Major emphasis on software techniques and metaphors, from desktop to May be repeated for credit, but not for a total of Broad intent, covering diverse algorithmic knowledge of C and C++. COMS W4118 or programming fluency in Python, C++, Java, or testing. Centers on a team project. immersive. Selection and manipulation. Travel more than 3 points of degree credit. Consult the techniques. Covered topics are implemented CSEE W4119. Design and implementation Ruby. Introduction to computer networks and the and navigation. Symbolic, menu, gestural, and department for section assignment. COMS W4160y Computer graphics and used in industry. Topics include: hashing, of large-scale distributed and cloud systems. technical foundations of the internet, including multimodal interaction. Dialogue design. 3D 3 pts. Lect: 3. Professor Reed. sketching/streaming, nearest neighbor search, COMS E3999x, y or s Fieldwork Abstractions, design, and implementation applications, protocols, local area networks, software support. 3D interaction devices and Prerequisite: COMS W3134, W3136, or W3137; graph algorithms, spectral graph theory, linear 1–2 pts. Members of the faculty. techniques that enable the building of fast, algorithms for routing and congestion control, displays. Virtual and augmented reality. Tangible W4156 is recommended. Strong programming programming, models for large-scale computation, Prerequisites: Obtained internship and approval security, elementary performance evaluation. user interfaces. Review of relevant 3D math. scalable, fault-tolerant distributed systems. background and some mathematical familiarity from a faculty adviser. May be repeated for credit, Several written and programming assignments and other related topics. Topics include distributed communication including linear algebra is required. Introduction but no more than 3 total points may be used required. COMS W4181x Security I models (e.g., sockets, remote procedure to computer graphics. Topics include 3D viewing COMS W4236y Introduction to computational toward the 128-credit degree requirement. Only for 3 pts. Lect: 3. Professor Jana. calls, distributed shared memory), distributed CSEE W4121y Computer systems for data and projections, geometric modeling using spline complexity SEAS computer science undergraduate students Prerequisites: COMS W3157 or equivalent. synchronization (clock synchronization, logical science curves, graphics systems such as OpenGL, 3 pts. Lect: 3. Professor Chen. who include relevant off-campus work experience Introduction to security. Threat models. Operating clocks, distributed mutex), distributed file 3 pts. Lect: 3. Professor Cidon. lighting and shading, and global illumination. Prerequisite: COMS W3261. Develops a as part of their approved program of study. Final system security features. Vulnerabilities and tools.

ENGINEERING 2020–2021 ENGINEERING 2020–2021 quantitative theory of the computational not required although helpful. Introduction to MECS E4510x Evolutionary computation and Representation, Propositional logic, Predicate COMS W4733x or y Computational aspects covers sequence analysis algorithms, dynamic 116 117 difficulty of problems in terms of the resources quantum computing. Shor’s factoring algorithm, design automation Calculus (first order logic), Reasoning under of robotics programming, hidden Markov models, phylogenetic (e.g., time, space) needed to solve them. Grover’s database search algorithm, the quantum 3 pts. Lect: 3. Professor Lipson. uncertainty, Machine Learning, and other topics in 3 pts. Lect: 3. Professor Allen. analysis, Bayesian network techniques, neural Classification of problems into complexity summation algorithm. Relationship between Prerequisite: Basic programming experience in AI (including vision, natural language processing, Prerequisite: COMS W3134, W3136, or W3137. networks, clustering algorithms, support vector classes, reductions and completeness. Power classical and quantum computing. Potential power any language. Fundamental and advanced topics and robotics) as time permits. Introduction to robotics from a computer science machines, Boolean models of regulatory networks, and limitations of different modes of computation of quantum computers. in evolutionary algorithms and their application perspective. Topics include coordinate frames and flux based analysis of metabolic networks and COMS W4705x Natural language processing such as nondeterminism, randomization, to open-ended optimization and computational kinematics, computer architectures for robotics, scale-free network models. The course provides EECS E4340x Computer hardware design 3 pts. Lect: 3. Professor Collins or McKeown. interaction and parallelism. design. Covers genetic algorithms, genetic integration and use of sensors, world modeling self-contained introduction to relevant biological 3 pts. Lect: 2. Lab: 3. Professor Sethumadhavan. programming, and evolutionary strategies, as Prerequisite: COMS W3134, W3136, or W3137 systems, design and use of robotic programming mechanisms and methods. COMS W4241y Numerical algorithms and Prerequisites: ELEN E3331 and CSEE W3827. well as governing dynamic of coevolution and (or equivalent), or instructor’s permission. languages, and applications of artificial intelligence COMS W4762x Machine learning for complexity Practical aspects of computer hardware design symbiosis. Includes discussions of problem Computational approaches to natural language for planning, assembly, and manipulation. functional genomics 3 pts. Lect: 3. Instructor to be announced. through the implementation, simulation, and representations and applications to design generation and understanding. Recommended 3 pts. Lect: 3. Professor Knowles. Prerequisite: Knowledge of a programming prototyping of a PDP-8 processor. High-level problems in a variety of domains including preparation: Some previous or concurrent COMS W4735x or y Visual interfaces to Prerequisites: Proficiency in a high-level language. Some knowledge of scientific computation and assembly languages, I/O, interrupts, software, electronics, and mechanics. exposure to AI or machine learning. Topics computers programming language (Python/R/Julia). is desirable. Modern theory and practice of datapath and control design, pipelining, include information extraction, summarization, 3 pts. Lect: 3. Professor Kender. COMS W4560x Introduction to computer Recommended: introductory machine learning computation on digital computers. Introduction to busses, memory architecture. Programmable machine translation, dialogue systems, and Prerequisite: COMS W3134, W3136, or W3137. applications in health care and biomedicine class (such as COMS W4771). Introduces modern concepts of computational complexity. Design and logic and hardware prototyping with FPGAs. emotional speech. Particular attention is Visual input as data and for control of computer 3 pts. Lect: 3. probabilistic machine learning methods using analysis of numerical algorithms. Applications to Fundamentals of VHDL for register-transfer given to robust techniques that can handle systems. Survey and analysis of architecture, Prerequisites: Experience with computers and algorithms, and underlying assumptions applications in data analysis tasks from functional computational finance, computational science, and level design. Testing and validation of hardware. understanding and generation for the large a passing familiarity with medicine and biology. of commercial and research systems that genomics, where massively-parallel sequencing computational engineering. Hands-on use of industry CAD tools for amounts of text on the web or in other large Undergraduates in their senior or junior years recognize and interpret human gestures, is used to measure the state of cells, e.g., what simulation and synthesis. corpora. Programming exercises in several of STCS W4242x or y Introduction to data science may take this course only if they have adequate analyze imagery such as fingerprint or iris genes are being expressed, what regions of DNA these areas. ("chromatin") are active ("open") or bound by 3 pts. Lect: 3. Professor Salleb-Aouissi. COMS W4419x or y Internet, technology, background in mathematics and receive permission patterns, generate natural language descriptions specific proteins. Practical techniques for working with large-scale economics, and policy from the instructor. An overview of the field of COMS W4706y Spoken language processing of medical or map imagery. Explores foundations data. Topics include statistical modeling and 3 pts. Lect: 3. Professor Schulzrinne. biomedical informatics, combining perspectives 3 pts. Lect: 3. Professor Hirschberg. in human psychophysics, cognitive science, and COMS W4771y Machine learning machine learning, data pipelines, programming Technology, economics, and policy aspects of from medicine, computer science, and social Prerequisite: COMS W3134, W3136, or W3137 artificial intelligence. 3 pts. Lect: 3. Professor Hsu or Verma. languages, “big data” tools, and real-world science. Use of computers and information in (or equivalent), or instructor’s permission. the internet. Summarizes how the internet works COMS W4737x or y Biometrics Prerequisites: Any introductory course in linear topics and case studies. Statistical and data health care and the biomedical sciences, covering Computational approaches to speech technically, including protocols, standards, radio 3 pts. Lect: 3. Professor Belhumeur. algebra and any introductory course in statistics manipulation software required. Intended for specific applications and general methods, current generation and understanding. Topics include spectrum, global infrastructure and interconnection. Prerequisite: A background at the sophomore level are both required. Highly recommended: COMS issues, capabilities and limitations of biomedical speech recognition and understanding, speech nonquantitative graduate-level disciplines. Micro-economics with a focus on media and in computer science, engineering, or like discipline. W4701 or knowledge of artificial intelligence. telecommunication economic concerns, including informatics. Biomedical Informatics studies the analysis for computational linguistics research, Topics from generative and discriminative machine COMS W4252x or y Introduction to We will explore the latest advances in biometrics competition and monopolies, platforms, and organization of medical information, the effective and speech synthesis. Speech applications learning including least squares methods, computational learning theory as well as the machine learning techniques behind behavioral economics. U.S. constitution, freedom management of information using computer including dialogue systems, data mining, support vector machines, kernel methods, 3 pts. Lect: 3. Professor Servedio. them. Students will learn how these technologies of speech, administrative procedures act and technology, and the impact of such technology summarization, and translation. Exercises neural networks, Gaussian distributions, linear Prerequisites: CSOR W4231 or COMS W4236 work and how they are sometimes defeated. regulatory process, universal service, role of FFC. on medical research, education, and patient involve data analysis and building a small text- classification, linear regression, maximum or W3203 and instructor’s permission or Grading will be based on homework assignments Not a substitute for CSEE W4119. Suitable for care. The field explores techniques for assessing to-speech system. likelihood, exponential family distributions, COMS W3261 and instructor’s permission. and a final project. There will be no midterm or non-majors. May not be used as a track elective current information practices, determining the final exam. Shares lectures with COMS E6737. Bayesian networks, Bayesian inference, mixture Possibilities and limitations of performing COMS W4725x or y Knowledge representation for computer science major. information needs of health care providers and Students taking COMS E6737 are required to models, the EM algorithm, graphical models and learning by computational agents. Topics include and reasoning patients, developing interventions using computer complete additional homework problems and hidden Markov models. Algorithms implemented computational models of learning, polynomial time COMS W4444x Programming and problem 3 pts. Lect: 3. technology, and evaluating the impact of those undertake a more rigorous final project. Students in MATLAB. learnability, learning from examples and learning Prerequisite: COMS W4701. General aspects solving interventions. will only be allowed to earn credit for COMS from queries to oracles. Computational and of knowledge representation (KR). The two 3 pts. Lect: 3. Professor Ross. W4737 or COMS E6737 but not both. COMS W4772x Advanced machine learning statistical limitations of learning. Applications to Prerequisites: COMS W3134, W3136, or W3137, MECS E4603x Applied robotics: algorithms fundamental paradigms (semantic networks and 3 pts. Lect: 3. Professor Hsu. Boolean functions, geometric functions, automata. and CSEE W3827. Hands-on introduction to and software frames) and illustrative systems. Topics include EECS E4750x or y Heterogeneous computing Prerequisites: COMS W4771 or instructor’s solving open-ended computational problems. 3 pts. Lect: 3. Professor Ciocarlie. hybrid systems, time, action/plans, defaults, for signal and data processing permission; knowledge of linear algebra and COMS W4261x or y Introduction to Emphasis on creativity, cooperation, and Prerequisites: Fundamental programming skills abduction, and case-based reasoning. Throughout 3 pts. Lect: 2. Professor Marianetti. introductory probability or statistics is required. cryptography collaboration. Projects spanning a variety (e.g., COMS W1002, W1004, W1005, ENGI E1006, the course particular attention is paid to design Prerequisites: ELEN E3801 and COMS An exploration of advanced machine learning 3 pts. Lect: 2.5. Professor Malkin. of areas within computer science, typically or equivalent). Science and systems aspects of trade-offs between language expressiveness and W3134 or similar, recommended. Methods for tools for perception and behavior learning. Prerequisites: Comfort with basic discrete math and requiring the development of computer programs. Robotics from applied perspective, focusing on reasoning complexity, and issues relating to the deploying signal and data processing algorithms How can machines perceive, learn from, and probability. Recommended: COMS W3261 or CSOR Generalization of solutions to broader problems, algorithms and software tools. Spatial reasoning; use of KR systems in larger applications. on contemporary general purpose graphics classify human activity computationally? Topics W4231. An introduction to modern cryptography, and specialization of complex problems to make tools for manipulating and visualizing spatial processing units (GPGPUs) and heterogeneous include appearance-based models, principal and focusing on the complexity-theoretic foundations relationships. Analysis of robotic manipulators; COMS W4731x or y Computer vision them manageable. Team-oriented projects, student computing infrastructures. Using programming independent components analysis, dimensionality of secure computation and communication in numerical methods for kinematic analysis. Motion 3 pts. Lect: 3. Professor Nayar. presentations, and in-class participation required. languages such as OpenCL and CUDA for reduction, kernel methods, manifold learning, adversarial environments; a rigorous approach, planning, search-based and stochastic approaches. Prerequisites: The fundamentals of calculus, linear computational speedup in audio, image, and latent models, regression, classification, Bayesian based on precise definitions and provably secure COMS W4460y Principles of innovation and Applications for force and impedance control. algebra, and C programming. Students without any video processing and computational data methods, maximum entropy methods, real-time protocols. Topics include private and public entrepreneurship Grading based on combination of exams and of these prerequisites are advised to contact the analysis. Significant design project. tracking, extended Kalman filters, time series key encryption schemes, digital signatures, 3 pts. Lect: 3. projects implemented using Robot Operating instructor prior to taking the course. Introductory prediction, hidden Markov models, factorial authentication, pseudorandom generators and Prerequisites: COMS W3134, W3136, or W3137 System (ROS) software framework and executed course in computer vision. Topics include image CBMF W4761x or y Computational genomics HMMs, input-output HMMs, Markov random fields, functions, one-way functions, trapdoor functions, (or equivalent), or instructor’s permission. Team on real and simulated robotic manipulators. formation and optics, image sensing, binary 3 pts. Lect: 3. Professor Pe’er. variational methods, dynamic Bayesian networks, number theory and computational hardness, project-centered course focused on principles images, image processing and filtering, edge Prerequisites: Introductory probability and COMS W4701x or y Artificial intelligence and Gaussian/Dirichlet processes. Links to identification and zero knowledge protocols. of planning, creating, and growing a technology extraction and boundary detection, region growing statistics and basic programming skills. Provides 3 pts. Lect: 3. Professor Salleb-Aouissi or Dear. cognitive science. venture. Topics include identifying and analyzing and segmentation, pattern classification methods, comprehensive introduction to computational COMS W4281x or y Introduction to quantum Prerequisite: COMS W3134, W3136, or W3137 opportunities created by technology paradigm brightness and reflectance, shape from shading techniques for analyzing genomic data including COMS W4773y Machine learning theory computing and any course on probability. Recommended: shifts, designing innovative products, protecting and photometric stereo, texture, binocular stereo, DNA, RNA and protein structures; microarrays; 3 pts. Lect: 3. Professor Hsu. 3 pts. Lect: 3. Instructor to be announced. Prior knowledge of Python. Overview of intellectual property, engineering innovative optical flow and motion, 2D and 3D object transcription and regulation; regulatory, metabolic Prerequisite: COMS W4771. Theoretical study Prerequisite: Knowledge of linear algebra. Artificial Intelligence (AI) covering Search, business models. representation, object recognition, vision systems and protein interaction networks. The course of algorithms for machine learning and high- Prior knowledge of quantum mechanics is Problem Solving, Game Playing, Knowledge and applications.

ENGINEERING 2020–2021 ENGINEERING 2020–2021 dimensional data analysis. Topics include high- synthesis (Mealy and Moore machines); adders the content of this course changes each time it is COMS E6121x Reliable software COMS E6160x or y Topics in computer the fundamental aspects of security, including 118 119 dimensional probability, theory of generalization and multipliers; structured logic blocks (PLDs, offered, it may be repeated for credit. Consult the 3 pts. Lect: 3. Professor Yang. graphics authentication, authorization, access control, and statistical learning, online learning and PALs, ROMs); iterative circuits. Modern design department for section assignment. Prerequisite: at least one of COMS W4118, 3 pts. Lect: 2. Professor Belhumeur. confidentiality, privacy, integrity, and availability. optimization, spectral analysis. methodology: register transfer level modeling W4115, or W4117, or significant software Prerequisite: COMS W4160 or instructor’s Review security techniques and tools, and their COMS W4996x or y Special topics in (RTL); algorithmic state machines (ASMs); development experiences. Topics include permission. An advanced graduate course, applications in various problem areas. Study COMS W4774y Unsupervised learning computer science, II introduction to hardware description languages automated debugging, automated software involving study of an advanced research topic the state of the art in research. A programming 3 pts. Lect: 3. Professor Verma. 3 pts. Lect: 3. (VHDL or Verilog); system-level modeling and repair, concurrent software reliability, software in Computer Graphics. Content varies between project is required. Prerequisites: COMS W4771 and background Prerequisite: Instructor’s permission. A continuation simulation; design examples. offerings, and the course may be repeated of COMS W4995 when the special topic extends error detection, and more. in probability and statistics, linear algebra, and for credit. Recent offerings have included COMS E6184y Seminar on anonymity and multivariate calculus. Ability to program in a CSEE W4824x Computer architecture over two terms. COMS E6123x or y Programming appearance models in graphics, and high quality privacy high-level language, and familiarity with basic 3 pts. Lect: 3. Professor Sethumadhavan. COMS E6111y Advanced database systems environments and software tools (PEST) real-time rendering. 3 pts. Lect: 3. algorithm design and coding principles. Core topics Prerequisite: CSEE W3827 or equivalent. Focuses Prerequisite: COMS W4261 or W4180 or CSEE 3 pts. Lect: 2. Professor Gravano. 3 pts. Lect: 2. Professor Kaiser. on advanced topics in computer architecture, COMS E6174y Interaction design: a from unsupervised learning such as clustering, Prerequisites: COMS W4111 and knowledge Prerequisite: COMS W4156 or equivalent. W4119 or instructor’s permission. Covers the illustrated by case studies from classic and perceptual approach dimensionality reduction and density estimation. of Java or instructor’s permission. Continuation Software methodologies and technologies following topics: Legal and social framework for modern processors. Fundamentals of quantitative 3 pts. Lect: 3. Topics in clustering: k-means clustering, of COMS W4111, covers latest trends in both concerned with development and operation of privacy. Data mining and databases. Anonymous analysis. Pipelining. Memory hierarchy design. Prerequisite: COMS W4170 or instructor’s hierarchical clustering, spectral clustering, database research and industry: information today’s software systems. Reliability, security, commerce and internet usage. Traffic analysis. Instruction-level and thread-level parallelism. Data- permission. Design methodology for special- clustering with various forms of feedback, retrieval, web search, data mining, data systems management and societal issues. Policy and national security considerations. level parallelism and graphics processing units. purpose user interfaces. Emphasis on how good initialization techniques and convergence warehousing, OLAP, decision support, multimedia Emerging software architectures such as Classes are seminars with students presenting Multiprocessors. Cache coherence. Interconnection psychology and perception inform good design. analysis of various clustering procedures. Topics databases, and XML and databases. Programming enterprise and grid computing. Term paper and papers and discussing them. Seminar focus networks. Multi-core processors and systems-on- Interviewing and task modeling, participatory in dimensionality reductions: linear techniques projects required. programming project. Seminar focus changes changes frequently to remain timely. design, and low-fidelity prototyping. Applications of such as PCA, ICA, Factor Analysis, Random chip. Platform architectures for embedded, mobile, frequently to remain timely. brain research, graphic design and art to develop COMS E6185x or y Intrusion and anomaly Projections, non-linear techniques such as LLE, and cloud computing. COMS E6113y Topics In database systems 3 pts. Lect: 2. COMS E6124x Hardware security custom user interfaces components, screen detection systems ISOMap, Laplacian Eigenmaps, tSNE, and study of CSEE W4840y Embedded systems Prerequisite: COMS W4111. Concentration on 3 pts. Lect: 3. Professor Sethumadhavan. layouts, and interaction techniques for application- 3 pts. Lect: 2. Professor Stolfo. embeddings of general metric spaces, what sorts 3 pts. Lect: 3. Professor Edwards. some database paradigm, such as deductive, Prerequisites: CSEE W3827 and COMS W3157. specific systems. Pre- or corequisite: COMS W4180 Network of theoretical guarantees can one provide about Prerequisite: CSEE W4823. Embedded system heterogeneous, or object-oriented, and/or Recommended: CSEE W4824 and COMS security. The state of threats against computers, such techniques. Miscellaneous topics: design design and implementation combining hardware COMS E6176x or y User interfaces for mobile some database issue, such as data modeling, W4187. Techniques for securing the foundational and networked systems. An overview of and analysis of data structures for fast Nearest and software. I/O, interfacing, and peripherals. and wearable computing distribution, query processing, semantics, or aspects of all computing devices and systems. computer security solutions and why they fail. Neighbor search such as Cover Trees and LSH. Weekly laboratory sessions and term project on 3 pts. Lect: 2. Professor Feiner. transaction management. A substantial project is Topics include: hardware-up security, hardware Provides a detailed treatment for network and Algorithms will be implemented in either Matlab design of a microprocessor-based embedded Prerequisite: COMS W4170 or instructor’s typically required. May be repeated for credit with supply chain trust and security, storing secrets in host-based intrusion detection and intrusion or Python. system including at least one custom peripheral. permission. Introduction to research on user instructor’s permission. hardware, boot time trust and security, side channel prevention systems. Considerable depth is Knowledge of C programming and digital logic interfaces for mobile and wearable computing COMS W4775y Causal inference attacks and defenses, hardware support for provided on anomaly detection systems to required. Lab required. COMS E6114y Advanced distributed systems compartmentalization, fault attacks and defenses, through lectures, invited talks, student-led 3 pts. Lect: 3. Professor Bareinboim. detect new attacks. Covers issues and problems 3 pts. Lect: 2. Professor Geambasu. hardware support to strengthen software: memory discussions of important papers, and programming Prerequisites: Discrete Math, Calculus, Statistics CSEE E4868x or y System-on-chip platforms in e-mail (spam, and viruses) and insider attacks Prerequisites: COMS W4113 and W4118. Reviews safety, control flow integrity, information flow projects. Designing and authoring for mobility (basic probability, modeling, experimental design), 3 pts. Lect: 3. Professor Carloni. (masquerading and impersonation). influential research that provides the basis of most tracking, diversity, obfuscation, anomaly detection. and wearability. Ubiquitous/pervasive computing. some programming experience. Causal Inference Prerequisites: COMS W3157 and CSEE W3827 large-scale, cloud infrastructures today. Students Hardware support for accelerating cryptography Collaboration with other users. Display, COMS E6232x or y Analysis of algorithms, theory and applications. Theoretical topics Design and programming of System-on-Chip read, present, and discuss papers. Topics include and applied cryptography. interaction, and communication technologies. (SoC) platforms. Topics include overview of II include 3-layer causal hierarchy, causal bayesian distributed consensus, consistency models and Sensors for tracking position, orientation, motion, technology and economic trends, methodologies 3 pts. Lect: 2. networks, structural learning, identification problem algorithms, service-oriented architectures, large- COMS E6125y Web-enhanced information environmental context, and personal context. and supporting CAD tools for system-level Prerequisites: CSOR W4231. Continuation of and do-calculus, linear identifiability, bounding, scale data storage, distributed transactions, big- management (WHIM) Applications and social consequences. design; models of computation, the SystemC CSOR W4231. and counterfactual analysis. Applied topics include data processing frameworks, distributed systems 3 pts. Lect: 2. Professor Kaiser. language, transaction-level modeling, hardware- CSEE E6180x or y Modeling and performance intersection with statistics, empirical-data sciences security. Reviews established results and state-of- Prerequisites: At least one COMS W41xx or COMS COMS E6253y Advanced topics in software partitioning, high-level synthesis, system 3 pts. Lect: 2. Professor Misra. (social and health), and AI and ML. the-art research. E61xx course and/or COMS W4444, or instructor’s computational learning theory programming, on-chip communication, memory Prerequisites: COMS W4118 and STAT GU4001. permission. Strongly recommended: COMS 3 pts. Lect: 3. Professor Servedio. COMS W4776x Machine learning for data organization, power management and optimization, COMS E6117x or y Topics in programming Introduction to queuing analysis and simulation W4111. History of hypertext, markup languages, Prerequisite: CSOR W4231 or equivalent; science integration of programmable processor cores and languages and translators techniques. Evaluation of time-sharing and groupware and the web. Evolving web protocols, COMS W4252 or W4236 helpful but not 3 pts. Lect: 3. Members of the faculty. specialized accelerators. Case studies of modern 3 pts. Lect: 2. multiprocessor systems. Topics include priority formats and computation paradigms such as required. In-depth study of inherent abilities Prerequisites: IEOR E4150 or STAT GU4001 SoC platforms for various classes of applications. Prerequisite: COMS W4115 or instructor’s permission. queuing, buffer storage, and disk access, HTTP, XML and Web Services. Novel application and limitations of computationally efficient or equivalent, COMS W3251 or equivalent. Concentration on the design and implementation interference and bus contention problems, and COMS W4901x and y Projects in computer domains enabled by the web and societal issues. learning algorithms. Algorithms for learning rich Introduction to machine learning, emphasis on of programming languages, and tools focused on modeling of program behaviors. science Term paper and programming project. Seminar Boolean function classes in online, Probably data science. Topics include least square methods, advanced applications in new areas in software focus changes frequently to remain timely. 1–3 pts. Members of the faculty. COMS E6181x or y Advanced internet Approximately Correct, and exact learning Gaussian distributions, linear classification, linear verification, distributed systems, programming in the Prerequisite: Approval by a faculty member who services models. Connections with computational regression, maximum likelihood, exponential large, and web computing. A substantial project is COMS E6156y Topics in software engineering agrees to supervise the work. A second-level 3 pts. Lect: 2. Professor Schulzrinne. complexity theory emphasized. Substantial family distributions, Bayesian networks, Bayesian typically required. May be repeated for credit. 3 pts. Lect: 2. Professor Kaiser. independent project involving laboratory work, In-depth survey of protocols and algorithms course project or term paper required. inference, mixture models, the EM algorithm, Topics in software engineering arranged as the computer programming, analytical investigation, COMS E6118y Operating systems, II need and availability arises, usually offered on a needed to transport multimedia information graphical models, hidden Markov models, support COMS E6261x or y Advanced cryptography or engineering design. May be repeated for 3 pts. Lect: 2. Professor Nieh. one-time basis. Since the content of this course across the internet, including audio and video vector machines kernel methods. Emphasizes 3 pts. Lect: 3. Professor Malkin. credit, but not for a total of more than 3 points of Prerequisite: COMS W4118. Corequisite: CSEE changes, it may be repeated for credit with encoding, multicast, quality-of-service, voice- methods and problems relevant to big data. Prerequisite: COMS W4261. A study of degree credit. Consult the department for section W4119. Continuation of COMS W4118, with over IP, streaming media and peer-to-peer instructor approval. Consult the department for advanced cryptographic research topics such Students may not receive credit for both COMS assignment. emphasis on distributed operating systems. Topics multimedia systems. Includes a semester-long section assignment. Software methodologies and as: secure computation, zero knowledge, W4771 and W4776. include interfaces to network protocols, distributed programming project. COMS W4995x or y Special topics in technologies concerned with development and privacy, anonymity, cryptographic protocols. run-time binding, advanced virtual memory issues, CSEE W4823x or y Advanced logic design computer science, I operation of today’s software systems. Reliability, COMS E6183x or y Advanced topics in Concentration on theoretical foundations, advanced means of interprocess communication, 3 pts. Lect: 3. Professor Nowick. 3 pts. Lect: 3. Members of the faculty. security, privacy, sustainability, and societal network security rigorous approach, and provable security. file system design, design for extensibility, security Prerequisite: CSEE W3827, or a half-semester Prerequisite: Instructor’s permission. Special topics issues. Emerging software architectures such as 3 pts. Lect: 3. Professor Jana. Content varies between offerings. May be in a distributed environment. Investigation is introduction to digital logic, or equivalent. An arranged as the need and availability arises. Topics microservices, serverless, and deep learning. Term Prerequisites: COMS W4180, CSEE W4119 repeated for credit. deeper and more hands-on than in COMS W4118. introduction to modern digital system design. are usually offered on a one-time basis. Since paper and programming project. and COMS W4261 recommended. Review Advanced topics in digital logic: controller A programming project is required.

ENGINEERING 2020–2021 ENGINEERING 2020–2021 COMS E6291x or y Theoretical topics in write software to analyze data. Knowledge of COMS E6735y Visual databases and security. The course requires substantial transducers, and language modeling. Selected COMS E9800x and y Directed research in 120 121 computer science programming language for statistics and machine 3 pts. Lect: 3. Professor Kender. reading, class participation and a research project. advanced topics will be covered in more depth. computer science 3 pts. Lect: 3. Professor Servedio. learning, such as R or Python. PhD-level course Prerequisite: COMS W3134, W3136, or W3137 1–15 pts. Members of the faculty. CSEE E6861y Computer-aided design of COMS E6900x and y Tutorial in computer Prerequisite: Instructor’s permission. Concentration on development and use of probability models. (or equivalent). COMS W4731 and W4735 helpful Prerequisites: Submission of outline of proposed digital systems science on some theoretical aspect of computer science. Covers mathematical properties, algorithms, but not required. Contact instructor if uncertain. research for approval by faculty member who 3 pts. Lect: 2. Professor Nowick. 1–3 pts. Members of the faculty. Content varies from year to year. May be repeated and their application to real problems. In-depth The analysis and retrieval of large collections will supervise. The department must approve the Prerequisites: (i) one semester of advanced Prerequisite: Instructor’s permission. A reading for credit. understanding of cutting-edge modern probabilistic of image and video data, with emphasis on number of points. May be repeated for credit. Only digital logic (CSEE W4823 or equivalent, or course in an advanced topic for a small number of modeling. Weekly papers, assignments, and final visual semantics, human psychology, and user for Eng.Sc.D. candidates. EECS E6321y Advanced digital electronic instructor’s permission); and (ii) a basic course students, under faculty supervision. project required. interfaces. Low-level processing: features circuits in data structures and algorithms COMS W3134, COMS E9910x and y Graduate research, I and similarity measures; shot detection; key COMS E6901x Projects in computer science 3 pts. Lect: 2. Professor Seok. COMS E6731y Humanoid robots W3136, W3137, W3157, or equivalent, and 1–6 pts. Members of the faculty. frame selection; machine learning methods 1–12 pts. Members of the faculty. Prerequisite: EECS E4321. Advanced topics in familiarity with programming. Introduction to Prerequisites: Submission of an outline of the 3 pts. Lect: 2. Professor Allen. for classification. Middle-level processing: Prerequisite: Instructor’s permission. Software or the design of digital integrated circuits. Clocked modern digital CAD synthesis and optimization proposed research for approval by the faculty Prerequisite: A course in at least one of the organizational rules for videos, including unedited hardware projects in computer science. Before techniques. Topics include modern digital member who will supervise. The department must and nonclocked combinational logic styles. Timing following: AI, robotics, computer graphics, or (home, educational), semiedited (sports, talk registering, the student must submit a written system design (high-level synthesis, register- approve the number of credits. May be repeated circuits: latches and flip-flops, phase-locked computer vision. Seminar on humanoid robots. shows), edited (news, drama); human memory proposal to the instructor for review. The proposal transfer level modeling, algorithmic state for credit. Only for M.S. candidates holding GRA loops, delay-locked loops. SRAM and DRAM Analysis of existing hardware and software limits; progressive refinement; visualization should give a brief outline of the project, estimated machines, optimal scheduling algorithms, or TA appointments. Note: It is NOT required that memory circuits. Modeling and analysis of on-chip platforms. Programming of multi-degree-of- techniques; incorporation of audio and text. High- schedule of completion, and computer resources resource allocation and binding, retiming), a student take Graduate research, I prior to taking interconnect. Power distribution and power-supply freedom robots. Understanding sensor feedback in level processing: extraction of thematic structures; needed. Oral and written reports are required. controller synthesis and optimization, exact and Graduate research, II. Consult the department for noise. Clocking, timing, and synchronization perceive-act-sense control paradigms. Task-level ontologies, semantic filters, and learning; May be taken over more than one semester, in heuristic two-level logic minimization, advanced section assignment. issues. Circuits for chip-to-chip electrical planning and reasoning. Final project includes personalization of summaries and interfaces; which case the grade will be deferred until all 12 implementing a humanoid robot task on either a detection of pacing and emotions. Examples and multilevel logic optimization, optimal technology communication. Advanced technology issues that mapping to library cells (for delay, power and points have been completed. No more than 12 COMS E9911x and y Graduate research, II affect circuit design. The class may include a team simulated or physical robot. demonstrations from commercial and research points of COMS E6901 may be taken. Consult the 1-15 pts. Members of the faculty. systems throughout. Substantial course project or area minimization), advanced data structures circuit design project. COMS E6732x or y Computational imaging (binary decision diagrams), SAT solvers and department for section assignment. Prerequisites: Submission of an outline of the term paper required. proposed research for approval by the faculty 3 pts. Lect: 3. Professor Nayar. their applications, static timing analysis, and COMS E6902x and y Thesis COMS E6424x Hardware security member who will supervise. The department Prerequisite: COMS W4731 or instructor’s COMS E6737x or y Biometrics introduction to testability. Includes hands-on 1–9 pts. Members of the faculty. 3 pts. Lect: 2. Professor Sethumadhavan. must approve the number of points. May be permission. Computational imaging uses a 3 pts. Lect: 3. Professor Belhumeur. small design projects using and creating CAD Available to M.S. candidates. An independent Prerequisite: CSEE W3827 and COMS W3157; repeated for credit. Only for M.S./Ph.D. track and combination of novel imaging optics and a Prerequisite: Background at the sophomore level tools. investigation of an appropriate problem in Recommended: CSEE W4824 and COMS Ph.D. students. Note: It is NOT required that a computational module to produce new forms of in computer science, engineering, or like discipline. computer science carried out under the supervision W4187. Techniques for securing the foundational CSEE E6863x Formal verification of student take Graduate research, I prior to taking visual information. Survey of the state-of-the- Corequisites: None. We will explore the latest of a faculty member. A formal written report is aspects of all computing devices and systems. hardware and software systems Graduate research, II. Consult the department for art in computational imaging. Review of recent advances in biometrics as well as the machine essential and an oral presentation may also Topics include hardware-up security, hardware 3 pts. Lect: 2. Professor Theobald or Ivancic. section assignment. papers on omnidirectional and panoramic imaging, learning techniques behind them. Students will be required. May be taken over more than one supply chain trust and security, storing secrets in Prerequisite: COMS W3134, W3136, or catadioptric imaging, high dynamic range imaging, learn how these technologies work and how they semester, in which case the grade will be deferred hardware, boot time trust and security, side channel W3137 and COMS W3261. Introduction to mosaicing and superresolution. Classes are are sometimes defeated. Grading will be based on until all 9 points have been completed. No more attacks and defenses, hardware support for the theory and practice of formal methods for seminars with the instructor, guest speakers, and homework assignments and a final project. There than 9 points of COMS E6902 may be taken. compartmentalization, fault attacks and defenses, the design and analysis of correct (i.e., bug- students presenting papers and discussing them. will be no midterm or final exam. Shares lectures Consult the department for section assignment. hardware support to strengthen software: memory free) concurrent and embedded hardware/ safety, control flow integrity, information flow with COMS W4737. Students taking COMS E6737 COMS E6733x or y 3D photography software systems. Topics include temporal COMS E6910x and y Fieldwork tracking, diversity, obfuscation, anomaly detection. are required to complete additional homework 3 pts. Lect: 2. Professor Allen. logics; model checking; deadlock and liveness 1 pt. Members of the faculty. Hardware support for accelerating cryptography problems and undertake a more rigorous final Prerequisite: Experience with at least one of the issues; fairness; satisfiability (SAT) checkers; Prerequisites: Obtained internship and approval and applied cryptography. project. Students will only be allowed to earn credit following topics: Computer graphics, computer for COMS W4737 or COMS E6737 but not both. binary decision diagrams (BDDs); abstraction from faculty adviser. Only for M.S. students in the CSEE W6600x or y From data to solutions vision, pixel processing, robotics or computer-aided techniques; introduction to commercial formal Computer Science Department who need relevant CSEE E6824y Parallel computer architecture 3 pts. Lect: 3. Professor Hirschberg or Chang. design, or permission of instructor. Programming verification tools. Industrial state-of-the-art, work experience as part of their program of study. 3 pts. Lect: 2. Professor Sethumadhavan. Prerequisites: Familiarity with common data proficiency in C, C++, or JAVA. 3D Photography— case studies, and experiences: software Final report required. May not be taken for pass/fail the process of automatically creating 3D, Prerequisite: CSEE W4824. Parallel computer science methods and tools. Must be able to write analysis (C/C++/Java), hardware verification credit or audited. texture-mapped models of objects in detail. principles, machine organization and design of coherent weekly summary. Intended for students (RTL). Applications include robotics, medicine, graphics, parallel systems including parallelism detection COMS E6915y Technical writing for computer interested in data science and interdisciplinary virtual reality, entertainment and digital movies methods, synchronization, data coherence and CSEE E6868x or y Embedded scalable scientists and engineers research. Covers problems in medical research, etc. Topics include 3D data acquisition devices, interconnection networks. Performance analysis platforms 1 pt. Members of the faculty. journalism, history, economics, business, English, 3D modeling systems and algorithms to acquire, and special purpose parallel machines. 3 pts. Lect: 2. Professor Carloni. Available to M.S. or Ph.D. candidates in CS/ psychology, and other areas amenable to create, augment, manipulate, render, animate and Prerequisites: CSEE W4868 or instructor's CE. Topics to help CS/CE graduate students’ CSEE E6847y Distributed embedded systems computational approaches. physically build such models. permission. Interdisciplinary graduate-level communication skills. Emphasis on writing, 3 pts. Lect: 2. seminar on design and programming of presenting clear, concise proposals, journal Prerequisite: Any COMS W411X, CSEE W48XX, articles, conference papers, theses, and technical EECS E6690-6699x or y Topics in data driven embedded scalable platforms. Content varies COMS E6734y Computational photography or ELEN E43XX course, or instructor’s permission. presentations. May be repeated for credit. Credit analysis and computation between offerings to cover timely relevant 3 pts. Lect: 3. Professor Belhumeur. An interdisciplinary graduate-level seminar on issues and latest advances in system-on-chip may not be used to satisfy degree requirements. 3 pts. Lect: 2. Members of the faculty. the design of distributed embedded systems. Prerequisites: COMS W4160, W4731, or a working design, embedded software programming, Prerequisite: the instructor's permission. Selected System robustness in the presence of highly COMS E6998x and y Topics in computer knowledge of photography are recommended. and electronic design automation. Requires advanced topics in data-driven analysis and Students should have knowledge in any of three variable communication delays and heterogeneous science substantial reading of research papers, class computation. Content varies from year to year, and core areas: computer vision, computer graphics, component behaviors. The study of the enabling 3 pts. Members of the faculty. participation, and semester-long project. different topics rotate through the course numbers or photography. Computational techniques are technologies (VLSI circuits, communication Prerequisite: Instructor’s permission. Selected 6690 to 6699. used to produce a new level of images and visual protocols, embedded processors, RTOSs), models EECS E6870x or y Speech recognition topics in computer science. Content varies from year to year. May be repeated for credit. STCS GU6701x or y Foundations of graphical representations. Topics include HDR imaging, of computation, and design methods. The analysis 3 pts. Lect: 3. Members of the faculty. of modern domain-specific applications including models feature matching using RANSAC, image mosaics, Prerequisites: Basic probability and statistics. COMS E6999x and y Topics in computer image-based rendering, motion magnification, on-chip micro-networks, multiprocessor systems, 3 pts. Lect: 3. Professor Blei. Theory and practice of contemporary science, II camera lens arrays, programmable lighting, face fault-tolerant architectures, and robust deployment Prerequisites: Basic probability and statistics, automatic speech recognition. Gaussian 3 pts. detection, single and multiview geometry, and more. of embedded software. Research challenges such calculus, and some optimization. Ability to mixture distributions, hidden Markov models, Prerequisite: COMS E6998. Continuation of as design complexity, reliability, scalability, safety, pronunciation modeling, decision trees, finite-state COMS E6998.

ENGINEERING 2020–2021 ENGINEERING 2020–2021 122 EARTH AND ENVIRONMENTAL ENGINEERING program in Materials Science and resources, and the recycling or disposal water use, reclamation and recycling in 123 Engineering (matsci.columbia. of used materials. EEE offers the natural resource processing industries, and on the use of environmental microbiology Henry Krumb School of Mines OUR MISSION edu) (MSE) is the successor of the Bachelor of Science (B.S.) in Earth and Earth and Environmental Engineering at the Henry Krumb HKSM traditional physical metallurgy Environmental Engineering, the Master of for wastewater treatment and energy 918 S. W. Mudd, MC 4711 School of Mines fosters excellence in education and research program and focuses on the design Science (M.S.) in Earth and Environmental conversion. State-of-the-art methods from 212-854-2905 for the development and application of science and technology molecular genomics are being developed eee.columbia.edu to maximize the quality of life for all, through the sustainable of advanced materials and the effects Engineering, and the doctorate degrees use and responsible management of Earth’s resources. of composition and processing on (Ph.D., Eng.Sc.D.) in EEE. and used to address nitrification and material properties. This program, The EEE program welcomes denitrification in wastewater treatment and administered by the Department Combined Plan students. An EEE minor energy production. of Applied Physics and Applied is offered to all Columbia engineering Center for Advanced Materials for students who want to enrich their DEPARTMENT CHAIR PROFESSOR OF LECTURER SENIOR RESEARCH Mathematics, is described on page Energy and Environment. The Center Upmanu Lall PROFESSIONAL A.C. (Thanos) Bourtsalas SCIENTIST academic record by concentrating some 177. develops advanced materials to address PRACTICE Vasilis M. Fthenakis • The Earth Engineering Center of their technical electives on Earth/ DIRECTOR OF FINANCE Raymond S. Farinato ADJUNCT PROFESSORS challenges for closing the energy (seas.columbia.edu/earth) is Environment subjects. There is close AND ADMINISTRATION Robert Farrauto Vasilis M. Fthenakis ASSOCIATE RESEARCH collaboration between EEE and the loop, carbon loop, and water loop. Muamer Lihic D. R. Nagaraj Yuri Gorokhovich SCIENTISTS the engineering unit of The Earth Departments of Civil Engineering and Using material genomics, the Center Paul Knowles Partha Patra institute and is dedicated to directing Earth and Environmental Sciences, designs and synthesize various novel PROFESSORS ASSOCIATE Eric Rosenberg engineering research toward the Kartik Chandran PROFESSORS including several joint appointments. 2D, nano-structured, and functional reconfiguring of industrial activities Xi Chen Pierre Gentine LAMONT ASSOCIATE materials and structures with intriguing George Deodatis Ah-Hyung (Alissa) Park RESEARCH PROFESSOR with full understanding of their physical, chemical, and mechanical Upmanu Lall Daniel Steingart Wade McGillis environmental impacts. Several RESEARCH CENTERS properties, with applications from Vjay Modi faculty of the HKSM are associated ASSOCIATED WITH EARTH Ismail C. Noyan ASSISTANT SPECIAL RESEARCH cradle to grave of the energy and Ponisseril Somasundaran PROFESSORS SCIENTIST with the Earth Engineering Center. AND ENVIRONMENTAL environmental resources. Major areas Alan West Ngai Yin Yip Nickolas J. Themelis ENGINEERING include (a) negative emission, through Bolun Xu As a result of the vast developments Columbia Water Center. The Center scalable and low-cost materials for in the technologies and fields of was established in 2008 to address direct air capture of carbon dioxide, environmental management, in 1996 issues of Global Water Security. It and seamless integration with efficient EARTH RESOURCES AND THE and Mineral Engineering. However, the within the department of Earth and and 1998 respectively, the engineering currently has 3 major initiatives: chemical and biological pathways of ENVIRONMENT title "School of Mines" was retained Environmental Engineering. school created the M.S. program in The Global Water Sustainability carbon conversion into useful products; Initiative is focused on an assessment The Earth and Environmental by Columbia University honoris causa. In 1986, HKSM was designated by Earth Resources Engineering and the (b) energy storage, through the of global water scarcity and risk, and Engineering program fosters education You can see the bronze statue of The Governor Cuomo as the mining and B.S. program in Earth and Environmental development of compatible, low-cost, innovations across scales, from farmer’s and research in the development Metallurgist (Le Marteleur) in front of Mineral Resources Research Institute of Engineering to meet the needs of a and scalable flexible batteries, structural field to reservoir optimization to national and application of technology for the Columbia's Mudd Hall that was named the State of New York. changed society. Students interested batteries, and recyclable batteries that policy modifications to international sustainable development, use, and after an alumnus of the School of Mines. The Henry Krumb School of Mines in the traditional disciplines of mining, are of high energy and power densities; trade, to develop real world solutions to One century after its formation, the within The Fu Foundation School of mineral engineering and metallurgy (c) novel material structures for water integrated management of Earth’s an impending global water crisis. School of Mines was renamed Henry Engineering and Applied Science (SEAS) continue to study these fields through collection, desalination, catalysis, robotic resources. Resources are identified The Global Flood Initiative recognizes Krumb School of Mines (HKSM) in has three units: the Earth and Environmental Engineering functions, cosmetic and biomedical as minerals, energy, water, air, and that of all natural hazards, floods are honor of the generous alumnus of the department course offerings as well as applications, etc. land, as well as the physical, chemical, responsible for the largest average and biological components of the School of Mines and his wife, Lavon • The Department of Earth and the course offerings through the Material annual loss of property and life. They Center for Life Cycle Analysis (CLCA). environment. There is close collaboration Duddleson Krumb. HKSM has been Environmental Engineering Science and Engineering program. are also a significant contributor to The Center for Life Cycle Analysis with other engineering disciplines, the a leader in mining and metallurgy (eee.columbia.edu) (EEE): The B.S. program in Earth and pollutant loading and environmental (CLCA) provides a framework for research and education, including the With the creation of the Earth Environmental Engineering was initiated Lamont-Doherty Earth Observatory, impact in water bodies. In a globalized quantifying the potential environmental first mining handbook by Professor Institute at Columbia University, in the fall of 1998 to replace the mining/ the International Research Institute society the disruption of food, energy, impacts of material and energy inputs Peel, the first mineral processing a major initiative in the study of mineral/extractive metallurgy programs of for Climate Prediction, the Center and manufactured goods supply chains and outputs of a process or product handbook by Professor Taggart, Earth, its environment and society, HKSM and is now accredited by ABET. for Environmental Research and by floods has also emerged as an issue. from “cradle to grave.” The mission and other pioneering work in mineral the traditional programs of HKSM The initiative is developing state-of-the- Conservation, and other Columbia Earth of the Center is to guide technology benefaction, chemical thermodynamics, in mining, mineral processing, and art climate analyses for global flood Institute units. EARTH AND ENVIRONMENTAL and energy policy decisions with data- kinetics, transport phenomena in mineral extractive metallurgy were expanded risk projection, its mapping onto supply ENGINEERING (EEE) based, well-balanced, and transparent extraction and processing, ecological in the late nineties to encompass chains, and risk management using Starting in 1996, the educational descriptions of the environmental profiles THE HENRY KRUMB SCHOOL and environmentally responsible mining, environmental concerns related to the novel structural and financial tools. programs of Columbia University in of energy generation and storage OF MINES AT COLUMBIA and pursuit of state-of-the-art research use of materials, energy and water America’s Water is the third mining and mineral engineering were systems in current and future electricity UNIVERSITY advancing responsible use of our earth resources, and to reflect one of nine major initiative. It is driven by the transformed into the present program grids. Current research thrusts include: The School of Mines of Columbia goal of developing sustainable water resources. The Henry Krumb School departments of SEAS with a focus in Earth and Environmental Engineering University was the first mining and management and infrastructure design of Mines located in The Fu Foundation on the development and application (EEE). This program is concerned with • Solar energy grid integration: metallurgy school in the U.S. (1864). It paradigms for the 21st century, recognizing School of Engineering and Applied of technology for the sustainable the environmentally sound extraction became the foundation for Columbia’s the linkages between urban functioning, The CLCA is engaged in model Science offers students interested in development, use and integrated and processing of primary materials development and technical and School of Engineering and Applied food, water, energy, and climate. mining and metallurgy the opportunity management of Earth's resources. (minerals, fuels, water), the management environmental systems analyses of Science and later the home of the In addition, the department has active to focus their studies in these fields • Columbia’s interdepartmental and development of land and water renewable energy integration into Department of Mining, Metallurgical research on improving the efficiency of

ENGINEERING 2020–2021 ENGINEERING 2020–2021 124 125 EARTH AND ENVIRONMENTAL ENGINEERING PROGRAM: EARTH AND ENVIRONMENTAL ENGINEERING: FIRST AND SECOND YEARS THIRD AND FOURTH YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

MATH UN1101 (3) MATH UN1102 (3) APMA E2000 (4) APMA E2101 (3) CIEE E3255 (3) EAEE E3103 (3) EAEE E3998 (2) EAEE E3999 (2) Environmental control and Energy, minerals, and Undergraduate Undergraduate MATHEMATICS MATH UN1207 (4) MATH UN1208 (4) MATH UN2030 (3) pollution reduction or material systems design project design project ODE systems

UN1401 (3) UN1402 (3) CIEE E4252 (3) CIEE E3250 (3) EAEE E4003 (3) Environmental engineering Hydrosystems engineering Aquatic chemistry PHYSICS or UN1601 (3.5) UN1602 (3.5) CHEM UN2443 (3.5) or UN2801 (4.5) UN2802 (4.5) EAEE E3200 (3) or EAEE E4160 (3) EAEE E3801 (2) Applied transport PHYS UN1403 (3) REQUIRED Solid and hazardous Earth and environmental and chemical rate or COURSES waste management engineering lab, II UN1403 (3.5) UN1404 (3.5) phenomena PHYS UN2601 (3.5) and Lab UN1500 (3) either semester or BIOL UN2005 (4) CHEMISTRY or UN1604 (3.5) UN1507 (3) EAEE E3800 (2) Earth and environmental or UN2045 (3.5) UN2046 (3.5) and CHEE E3010 (3) engineering lab, I Lab UN1507 (3) Principles of chemical engineering thermodynamics EAEE E3901 (3) HUMA CC1002, Environmental COCI CC1102, microbiology or Global Core (3–4)

HUMA CC1001, REQUIRED ENGL CC1010 (3) TECHNICAL 3 points 6 points 9 points NONTECHNICAL COCI CC1101, ECON UN1105 (4) and ELECTIVES ELECTIVES or Global Core (3–4) UN1155 recitation (0)

NONTECHNICAL 3 points 3 points 6 points ELECTIVES HUMA UN1121 or UN1123 (3) TOTAL POINTS 15 17 16 17

EESC GU4001 (4) or EESC UN2100 (4.5) REQUIRED or EESC UN2200 (4.5) Brookhaven National Laboratory and Mexico, and the U.K. EEC conducts a The goals of CPaSS are to perform PROFESSIONAL STAT GU4001 (3) AND TECHNICAL several European, South American, biannual survey of waste management industrially relevant research to ELECTIVES EEAE E2100 (3) and Asian institutions. in the 50 states of the Union. address the technological needs in A better planet by design commercial surfactant and polymer Earth Engineering Center (EEC). Industry/University Cooperative systems, develop new and more EEC has concentrated on advancing Research Center for Particulate and efficient surface-active reagents for COMPUTER ENGI E1006 (3) any semester SCIENCE the goals of sustainable waste Surfactant Systems (CPaSS). CPaSS specific applications in the industry management in the U.S. and globally. was established in 1998 by the Henry and methodologies for optimizing Economic development has resulted Krumb School of Mines, Department of PHYSICAL UN1001 (1) UN1002 (1) their performance, promote the use EDUCATION in the generation of billions of tons Chemical Engineering, and Department of environmentally benign surfactants of used materials that can be a of Chemistry at Columbia University. The in a wide array of technological THE ART OF ENGI E1102 (4) either semester considerable resource, but when Center encompasses detailed structure- ENGINEERING processes, and build a resource not managed properly, constitute a property assessment of several classes center to perform and provide state- major environmental problem both in of surface-active molecules, including of-the-art facilities for characterization electricity grids. It is developing to compensate for solar and wind end-of-life photovoltaic systems and developed and developing nations. In oligomeric, polymeric, and biomolecules. of surface-active reagents. models for evaluating and optimizing variability in large-scale penetrations. infrastructures for their collection. 2003, in collaboration with the Energy The aim of CPaSS is to develop and energy storage units for ramping • Resource assessment and recycling • Life-cycle environmental and Recovery Council of the U.S., EEC characterize novel surfactants for International Research Institute for rate control in photovoltaic power of critical energy materials variability: environmental health and safety founded the Waste to Energy Research industrial applications such as coatings, Climate Prediction (IRI). The IRI is plants, optimizing penetration of The CLCA, together with the (EH&S) risk assessment: Risk- and and Technology Council (WTERT). As of dispersions, deposition, gas hydrate the world’s leading institute for the solar and wind resources, and Brookhaven National Laboratory are CLCA-based comparisons of solar 2013, the Global WTERT Council control, personal care products, soil development and application of seasonal unit commitment and economic developing technologies for optimizing electric and conventional energy (www.wtert.org) has sister organizations decontamination, waste treatment, to interannual climate forecasts. The dispatch of conventional generators recycling of various elements from technologies in collaboration with in 14 countries including Canada, corrosion prevention, flotation, and mission of the IRI is to enhance society’s China, Germany, Greece, India, Italy, controlled chemical reactions. capability to understand, anticipate, and

ENGINEERING 2020–2021 ENGINEERING 2020–2021 126 manage the impacts of seasonal climate to work together and encourage the flows through the environment; of the program consist of a group of billion. Sustainable development and of water resource systems, and 127 fluctuations, in order to improve human effective, rapid transfer of knowledge assessment of environmental impact required courses in engineering science environmental quality has become a top related sectors such as energy, health, welfare and the environment, especially between participating members of of past, present, and future industrial and a broad selection of technical priority of government and industry in the agriculture, ecological resources, in developing countries. This mission various fields and global communities. activities; and analysis and design of electives organized into three distinct United States and many other nations. and natural hazards control. Climatic is to be conducted through strategic For more information: processes for remediation, recycling, concentrations, representing major areas This M.S. program is offered in uncertainties can be broadly classified and applied research, education and energy.columbia.edu. and disposal of used materials. of focus within the department. collaboration with the Departments into two areas: (1) those related to capacity building, and provision of 4. Graduates will practice their Several Columbia departments, of Civil Engineering and Earth and anthropogenic climate change; (2) forecast and information products, with profession with excellent written such as Civil Engineering, Mechanical Environmental Sciences. Many of those related to seasonal- to century- SCHOLARSHIPS, FELLOWSHIPS, an emphasis on practical and verifiable and communication skills and Engineering, and Earth and the teaching faculty are affiliated with scale natural variations. The climate AND INTERNSHIPS utility and partnerships. with professional ethics and Environmental Sciences (Lamont- Columbia’s Earth Engineering Center. change issues impact the design The department arranges for responsibilities. Doherty Earth Observatory), as well as For students with a B.S. in of physical, social, and financial undergraduate summer internships Langmuir Center for Colloids the Mailman School of Public Health, engineering, at least 30 points (ten infrastructure systems to support after the sophomore and junior years. and Interfaces (LCCI). This Center Undergraduate Student Outcomes contribute courses to the EEE program. courses) are required. For students the sectors listed above. The climate Undergraduates can also participate in brings together experts from mineral 1. an ability to identify, formulate, and EEE students are strongly encouraged with a nonengineering B.S. or a B.A., variability and predictability issues graduate research projects under the engineering, applied chemistry, chemical solve complex engineering problems to work as summer interns in industry preferably with a science major, up to 48 impact systems operation, and work-study program. Graduate research engineering, biological sciences, and by applying principles of engineering, or agencies on projects related to Earth points (total of sixteen courses) may be hence design. The goal of the M.S. and teaching assistantships, as well as chemistry to probe complex interactions science, and mathematics and Environmental Engineering. The required for makeup courses. Students concentration in water resources and fellowships funded by the Department, of colloids and interfaces with 2. an ability to apply engineering design department helps students get summer may carry out a research project and climate risks is to provide (1) a capacity are available to qualified graduate surfactants and macromolecules. LCCI to produce solutions that meet internships. write a thesis worth 3–6 points. A for understanding and quantifying the students. GRE scores are required of all activities involve significant interaction specified needs with consideration number of areas of study are available projections for climate change and applicants for graduate studies. with industrial sponsors and adopt of public health, safety, and welfare, for the M.S.-EEE, and students may GRADUATE PROGRAMS variability in the context of decisions an interdisciplinary approach toward as well as global, cultural, social, choose courses that match their interest M.S. students must complete the for water resources and related sectors state-of-the-art research on interfacial environmental, and economic factors and career plans. The areas of study UNDERGRADUATE PROGRAM professional development and leadership of impact; and (2) skills for integrated phenomena. Major areas of research include: The Bachelor of Science (B.S.) degree 3. an ability to communicate effectively course, ENGI E4000, as a graduation risk assessment and management at LCCI are thin films, surfactant and in Earth and Environmental Engineering with a range of audiences requirement. Ph.D. candidates are for operations and design, as well polymer adsorption, environmental • Alternative energy and carbon prepares students for careers in the 4. an ability to recognize ethical and strongly encouraged to complete as for regional policy analysis and management problems, enhanced oil recovery, public and private sector concerned with professional responsibilities in ENGI E6001–6004 and should consult management. Specific areas of interest engineering situations and make • Climate risk assessment and computer tomography, corrosion and primary materials (minerals, fuels, water) their program for PDL requirements. include: management catalysis mechanisms, membrane and the environment. Graduates are informed judgments, which must • Numerical and statistical modeling of • Environmental health engineering technology, novel separations of also prepared to continue with further consider the impact of engineering global and regional climate systems solutions in global, economic, M.S. in Earth and Environmental • Sustainable waste management minerals, biocolloids, microbial surfaces, studies in Earth/Environmental sciences and attendant uncertainties environmental, and societal contexts Engineering (M.S.-EEE) • Natural and mineral resource and interfacial spectroscopy. and engineering, business, public policy, • Methods for forecasting seasonal to 5. an ability to function effectively The M.S.-EEE program is designed development and management international studies, law, and medicine. interannual climate variations and Lenfest Center for Sustainable on teams whose members for engineers and scientists who plan • Novel technologies: surficial and The EEE program is accredited as an their sectoral impacts Energy. The mission of the Lenfest together provide leadership, create to pursue, or are already engaged in, colloidal chemistry and environmental engineering program • Models for design and operation of Center for Sustainable Energy (LCSE) a collaborative and inclusive environmental management/development nanotechnology by the Engineering Accreditation water resource systems, considering is to advance science and develop environment, establish goals, plan careers. The focus of the program is • Urban environments and spatial analysis Commission of ABET, www.abet.org. climate and other uncertainties innovative technologies that provide tasks, and meet objectives the environmentally sound mining and • Water quality engineering, including • Integrated risk assessment and sustainable energy for all humanity while 6. an ability to develop and conduct processing of primary materials (minerals, drinking water purification, desalination management across water resources maintaining the stability of the Earth's Undergraduate Program Objectives appropriate experimentation, energy, and water) and the recycling or and wastewater treatment. and related sectors natural systems. The development of 1. Graduates equipped with the analyze and interpret data, and proper disposal of used materials. The necessary tools (mathematics, novel energy conversion pathways use engineering judgment to draw program also includes technologies for Additionally, there are three optional chemistry, physics, Earth sciences, and technologies—particularly with conclusions assessment and remediation of past concentrations in the program, in Sustainable Energy and engineering science) will reduced environmental footprints (i.e., 7. an ability to acquire and apply damage to the environment. Students each of which there are a number of Building and shaping the energy understand and implement the CO emission and water usage)—is new knowledge as needed, using can choose a pace that allows them to required specific core courses and infrastructure of the twenty-first century 2 underlying principles used in the one of the greatest challenges faced by appropriate learning strategies. complete the M.S.-EEE requirements electives. The concentrations are is one of the central tasks for modern engineering of processes and systems. humanity that cannot be overcome by while being employed. described briefly below; details and the engineering. The purpose of the 2. Graduates will be able to pursue lists of specific courses for each track simply employing traditional scientific or The Curriculum M.S.-EEE graduates are specially sustainable energy concentration is careers in industry, government are available from the department. engineering approaches. more than ever, The first two years of the EEE program qualified to work for engineering, to expose students to modern energy agencies, and other organizations Students interested in a specific focus the development and implementation of are similar to those of other engineering financial, and operating companies technologies and infrastructures and to concerned with the environment in Mining Engineering or related fields sustainable energy technologies require programs. Students are provided with a engaged in mineral processing ventures, the associated environmental, health, and the provision of primary and should consult their faculty adviser for cross-cutting collaborations between strong foundation in basic sciences and the environmental industry, environmental and resource limitations. Emphasis secondary materials and energy, relevant course listings. natural science. engineering and social mathematics, as well as the liberal arts groups in all industries, and for city, state, will be on energy generation and use as well as continue their education science disciplines. Furthermore, the core. Specific to the EEE program is an and federal agencies responsible for technologies that aim to overcome the as graduate students in related development of viable policy frameworks early and sustained introduction to Earth the environment and energy/resource Water Resources and limits to growth that are experienced disciplines. and market structures are also science and environmental engineering, conservation. At the present time, the Climate Risks today. Energy and economic well-being 3. Graduates will possess the basic skills important for the significant reduction and options for a number of science U.S. environmental industry comprises Climate-induced risk is a significant are tightly coupled. Fossil fuel resources needed for the practice of Earth and of anthropogenic carbon emissions. To courses to meet the specific interests of nearly 30,000 big and small businesses component of decision making for are still plentiful, but access to energy is Environmental Engineering, including each student. The junior and senior years with total revenues of more than $150 the planning, design, and operation limited by environmental and economic achieve this ambitious goal, we need measurement and control of material

ENGINEERING 2020–2021 ENGINEERING 2020–2021 to environmental engineering projects. The aim 128 constraints. A future world population address these serious challenges. The Coursework includes four core faculty members. The adviser of the • Sensing and remediation: 129 of 10 billion people trying to approach overall goal of industry to develop and required courses and six elective courses student will be a member of the exam understanding of transport processes at is to provide a broad background for earth and environmental engineers in careers involving the standard of living of the developed implement technologies for sensible from a pre-approved list of choices. committee but may not be the chair. different scales and in different media; minerals and industrial, large-scale environmental nations cannot rely on today’s energy and sustainable use of earth resources Core courses: The students will be examined in their containment systems; modeling flow projects. technologies and infrastructures without is part of a "mines of the future" understanding of fundamentals as they and transport in surface and subsurface severe environmental impacts. Concerns paradigm, which encompasses topics • EAEE E4001 Industrial ecology of earth apply in the areas of research of the systems; soil/water decontamination EAEE E3103x Energy, minerals, and materials systems over climate change and changes in such as mine-to-metal integration, resources department: water resources, materials and bioremediation. 3 pts. Lect: 3. Professor Park. ocean chemistry require reductions in modular processing, digital optimization, • EAEE E4009 Geographic information processing, energy, and chemical and Prerequisites: MSAE E3111 or MECE E3301 carbon dioxide emissions, but most machine learning and AI, sensors systems (GIS) for resource, biochemical processes. It is expected COURSES IN EARTH and ENME E3161 or MECE E3100 or equivalent alternatives to conventional fossil and chemometrics, benign process environmental and infrastructure that each question period will last about Corequisites: MSAE E3111 or MECE E3301 and AND ENVIRONMENTAL fuels, including nuclear energy, are too chemicals, and a host of other forward- management 20 minutes, of which 15 minutes will ENME E3161 or MECE E3100 or equivalent. expensive to fill the gap. Yet access looking concepts. A similar effort and • EAEE E4006 Field methods for be led by the faculty member from the ENGINEERING Overview of energy resources, resource to clean, cheap energy is critical for outlook exists for urban mining and environmental engineering area and the remaining 5 minutes will be EAEE E2002x Alternative energy resources management from extraction and processing to providing minimal resources: water, recycling. The transformation of waste open for questions by all faculty present 3 pts. Lect: 3. Professor Steingart. recycling and final disposal of wastes. Resources availability and resource processing in the food, housing, and transportation. to energy and the recovery of minerals Elective courses must be six courses at the exam. There will be a final period Unconventional, alternative energy resources. context of the global natural and anthropogenic Concentration-specific classes will from recycling streams are examples of at the 4000 or higher level from within of 20 minutes for general questions. Technological options and their role in the world energy markets. Comparison of conventional and material cycles; thermodynamic and chemical sketch out the availability of resources, these areas that EEE is a world leader the Earth and Environmental Engineering All graduate students are expected unconventional, renewable and nonrenewable conditions including nonequilibrium effects that their geographic distribution, the in. The EEE program in Sustainable Department, the Chemical Engineering to have a background equivalent to energy resources and analysis of the shape the resource base; extractive technologies economic and environmental cost of Mining and Materials integrates Department, or others as approved by the required core of our undergraduate consequences of various technological choices and their impact on the environment and the resource extraction, and avenues for foundational engineering principles and the adviser. These include but are not program. They have, of course, an and constraints. Economic considerations, energy biogeochemical cycles; chemical extraction from increasing energy utilization efficiency, processes with the transformational limited to: EAEE E4900, CHEE E4252, opportunity to make up for any deficiency availability, and the environmental consequences mineral ores, and metallurgical processes for extraction of metals. In analogy to metallurgical such as cogeneration, district heating, innovations under development in the CIEE E4252, EAEE E4257, ELEN E4004, in their master’s program. In order to be of large-scale, widespread use of each particular processing, power generation and the refining and distributed generation of energy. earth resources management sector. EAEE E4160, EAEE E4300, EAEE E6132, prepared for the exam, students can technology. Introduction to carbon dioxide capture and carbon dioxide disposal as a means of of fuels are treated as extraction and refining Classes will discuss technologies EAEE E6140, EAEE E6150, EAEE E6212. take at least one course in each core sustaining the fossil fuel option. processes. Large scale of power generation for efficiency improvement in the M.S. in Carbon Management Although not required, interested students area during their first two semesters at and a discussion of its impact on the global EAEE E2100x A better planet by design generation and consumption sector; Interdisciplinary training with a core may choose to complete up to six credits Columbia (see website for up-to-date biogeochemical cycles. 3 pts. Lect: 3. Professor Lall. energy recovery from solid wastes; curriculum in engineering, ecology, in EAEE E9309. course listing). In case the student declares Introduction to design for a sustainable planet. EAEE E3112y Introduction to rock mechanics alternatives to fossil fuels, including an explicit minor in another department, decision science, business, and law Scientific understanding of the challenges. 3 pts. Lect: 3. Not offered in 2020–2021. solar and wind energy, energy storage; and policy. Courses that individually Doctoral Programs the qualifying exam requirements will be Innovative technologies for water, energy, Prerequisites: EAEE E3101 and ENME 3111, and technologies for addressing the embody the interdisciplinary nature of EEE offers two doctoral degrees: modified in consultation with the graduate food, materials provision. Multiscale modeling or their equivalents. Rock as an engineering environmental concerns over the use of carbon management, from science to (1) the Eng.Sc.D. degree, administered by committee. The minor has to be approved and conceptual framework for understanding material, geometry and strength of rock joints, geotechnical classification of rock masses, fossil fuels. Classes on climate change, engineering, to business, law, policy, and Columbia Engineering; and (2) the Ph.D. by both departments. environmental, resource, human, ecological, air quality, and health impacts focus on The engineering objectives of EEE and economic impacts and design performance strength and failure of rock, field investigations psychology. Preparation of well-rounded degree, administered by the Graduate prior to excavation in rock, rock reinforcement, the consequences of energy use. Policy research and education include: evaluation. Focus on the linkages between professionals with an understanding School of Arts and Sciences. analysis and support of rock slopes and tunnels, and its interactions with environmental planetary, regional, and urban water, energy, of the science of climate change and mineral, food, climate, economic, and ecological and case histories. sciences and energy engineering will • Provision and disposal of materials: carbon management, as well as their Doctoral Qualifying Examination and cycles. Solution strategies for developed and be another aspect of the concentration. environmentally sustainable MSAE E3141y Processing of metals and economic, financial, political, and societal Research Proposal developing country settings. semiconductors Additional specialization may consider extraction and processing of primary implications. Graduates may serve as Before the end of the first semester in 3 pts. Lect: 3. Instructor to be announced. region-specific energy development. materials; manufacturing of derivative CHEE E3010x Principles of chemical consultants, carbon market specialists, the doctoral program, the student and engineering thermodynamics Prerequisite: MSAE E3103 or equivalent. products; recycling of used materials; REDD program developers, financial her/his adviser will set up an advisory 3 pts. Lect: 3. Professor Moment. Synthesis and production of metals and management of industrial residues Sustainable Mining and Materials planners, or policy staff, to name a few. committee of two or three faculty Prerequisite: CHEM UN1403. Corequisite: CHEN semiconductors with engineered microstructures and used products; materials-related for desired properties. Includes high-temperature, Earth mineral and metal resources are members. This committee will meet E3030. Introduction to thermodynamics. the backbone of civilization and are application of industrial ecology. Fundamentals are emphasized: the laws of aqueous, and electrochemical processing; thermal Professional Degree; Engineer at least once a semester to assess and mechanical processing of metals and alloys; critical to economic development and • Management of water resources: thermodynamics are derived and their meaning of Mines academic and research progress casting and solidification; diffusion, microstructural meeting the demands of a growing understanding, prediction, and explained and elucidated by applications to The program is designed for engineers of the student and to recommend engineering problems. Pure systems are treated, evolution, and phase transformations; modification population. their development today management of the processes that who wish to do advanced work beyond corrective action in case of emerging with an emphasis on phase equilibrium. and processing of surfaces and interfaces; govern the quantity and quality of faces several big challenges: (i) declining the level of the M.S. degree but who or existing deficiencies. deposition and removal of thin films. Processing water resources, including the role EAEE E3101y Earth resource value content in the available ore bodies do not desire to emphasize research. Doctoral students are required to of Si and other materials for elemental and of climate; development/operation of production systems compound semiconductor-based electronic, and poor quality of the resources; (ii) Admissions requirements include pass a qualifying exam within their increasing focus on safety and health water resource facilities; management of 3 pts. Lect: 3. Not offered in 2020–2021. magnetic, and optical devices. Undergraduate engineering degree, first year into the program. They will Technologies and equipment common to a wide risks, and environmental impacts; (iii) water-related hazards. minimum 3.0 GPA, and GRE. submit and defend their research range of surface and subsurface engineering EAEE E3185y Summer fieldwork for Earth and • Energy resources and carbon inefficient and high energy and water Candidates must complete at least 30 proposal approximately one year after activities: mine reclamation, hazardous waste environmental engineers management: mitigation of consumption; (iv) huge risks associated credits of graduate work beyond the M.S., successful completion of the qualifying remediation, discovering and operating surface 0.5 pt. Not offered in 2020–2021. environmental impacts of energy Undergraduates in Earth and environmental with waste generation and management. or 60 points of graduate work beyond exam. Submission of the dissertation and underground mines, detection and removal It is well recognized in the earth production; energy recovery from of hidden underground objects, waste disposal, engineering may spend up to 3 weeks in the field the B.S. No thesis is required. All degree and thesis defense will follow general under staff direction. The course consists of mine, resource development industry that waste materials; advancement of dredging and harbor rehabilitation, and tunneling requirements must be completed within 5 University rules. landfill, plant, and major excavation site visits the traditional processing paradigm energy efficient systems; new energy for transportation or water distribution systems. years of the beginning of the first course The qualifying examination will be These methods and equipment are examined and brief instruction of surveying methods. A final is no longer sustainable and cannot sources; development of carbon credited toward the degree. an oral exam administered by three as they apply across the spectrum from mining report is required. sequestration strategies.

ENGINEERING 2020–2021 ENGINEERING 2020–2021 EAEE E3200x Applied transport and chemical processes: energy generation, analysis and environmental engineering, and design of an factors. Laboratory demonstrations and a field trip New York City and other standard databases. Term Theory of vibrations of discrete and continuous 130 131 rate phenomena purification of water, environmental biology, and engineering solution including technical, economic, will be included. projects emphasize information synthesis toward system, measurement and analysis. Selection 3 pts. Lect: 3. Professor Chen. biochemical treatment of wastes. Students will environmental, ethical, health and safety, social the solution of a specific problem. of materials for energy conversion, piezoelectric, EAEE E4005x Near-surface engineering Prerequisite: APMA E2101. Fluid statics. Basics learn the laboratory procedures and use analytical issues. Use of software for design, visualization, electromagnetic, thermoelectric, photovoltaic, geophysics EAEE E4010y Remote sensing and of flow analysis. Dimensional analysis. Pipe flow. equipment firsthand, hence demonstrating economic analysis, and report preparation. etc. Design and characterization, modeling and 3 pts. Lect: 3. Not offered in 2020–2021. environmental change Fluid dynamics, heat and mass transfer. Effects of experimentally the theoretical concepts learned Students may work in teams. Presentation of fabrication of vibration, motion, wind, wave, Geophysical methods as applicable to engineering 3 pts. Lect: 3. Not offered in 2020–2021. velocity, temperature, and concentration gradients in class. results in a formal report and public presentation. thermal gradient, and light energy harvesters; problems. Principles of geophysics and noninvasive Prerequisite: EAEE E4009 or EESC GU4050 or and material properties on fluid flow, heat and resonance phenomenon, power electronics and EAEE E3801x Earth and environmental EAEE E4000x Machine learning for imaging techniques (inversion technology) and instructor’s permission. Practical and theoretical mass transfer. Applications to environmental energy storage and management. Applications to engineering laboratory, II environmental engineering and science benefits and pitfalls of geophysics vs. direct imaging foundations for the application of remote sensing engineering problems. buildings, geothermal systems, and transportation. 2 pts. Lect: 1. Lab: 3. Professor Bourtsalas. 3 pts. Lect: 2.5. Professor Gentine. methods. Discussion of theory of each method. techniques to identification and monitoring of EAEE E3221x Environmental geophysics Prerequisite: EAEE E3800. Corequisite: EAEE Prerequisites: Computer language (Python Discussion of data acquisition, processing and environmental change. Designing and applying CHEE E4140x Engineering separations 3 pts. Lect: 3. Not offered in 2020–2021. E4003. A continuation of EAEE E3800, with or Julia), some linear algebra and machine interpretation for each method. Treatment of several spectral indices for assessment and monitoring, processes Introduction to applied and environmental emphasis on the principles underlying water learning. Aimed at understanding and testing case studies. Class-wide planning and execution of time series analysis of remote sensing data for 3 pts. Lect: 3. Professor Durning. geophysics methods. Overview of principles of analysis for inorganic, organic, and bacterial state-of-the-art methods in machine learning small-scale geophysical survey. analyzing environmental problems. Discussions Prerequisites: CHEN E3100, E3120, and geophysics, geophysical methods and techniques contaminants. Lab required. applied to environmental sciences and of published literature relevant to the central topic E3210 or permission of instructor. Design EAEE E4006y Field methods for (seismic, ground penetrating radar, resistivity, engineering problems. Potential applications covered in class. Analysis of remote sensing data and analysis of unit operations employed in EAEE E3900x and y–S3900 Undergraduate environmental engineering frequency em, and magnetics), and theory and include but are not limited to remote sensing, using IRI data library. chemical engineering separations. Fundamental research in Earth and environmental 3 pts. Lect: 1.5. Lab: 2. Professor McGillis. practical aspects of data processing and inversion. and environmental and geophysical fluid aspects of single and multistaged operations engineering Prerequisite: ENME E3161 or equivalent or EAEE E4011y Industrial ecology for Examination of geophysical case studies for dynamics. Includes testing "vanilla" ML instructor’s permission Principles and methods for manufacturing using both equilibrium and rate-based methods. engineering and environmental purposes. 0–3 pts. Directed study. Members of the faculty. algorithms, feedforward neural networks, This course may be repeated for credit, but designing, building and testing systems to sense 3 pts. Lect: 3. Not offered in 2020–2021. Examples include distillation, absorption and random forests, shallow vs deep networks, and stripping, extraction, membranes, crystallization, CIEE E3250y Hydrosystems engineering no more than 3 points of this course may be the details of machine learning techniques. the environment. Monitoring the atmosphere, water Prerequisite: EAEE E4001 or instructor's 3 pts. Lect: 3. Professor Gentine. counted toward the satisfaction of the B.S. degree bodies and boundary interfaces between the two. permission. Application of industrial ecology to bioseparations, and environmental applications. EAEE E4001x Industrial ecology of earth Prerequisites: CHEN E3110 or ENME E3161 requirements. Candidates for the B.S. degree may Sensor systems for monitoring heat and mass Design for Environment (DFE) of processes and EAEE E4150y Air pollution prevention and resources or equivalent, or instructor’s permission. A conduct an investigation in Earth and Environmental flows, chemicals, and biota. Measurements of products using environmental indices of resources control quantitative introduction to hydrologic and hydraulic 3 pts. Lect: 3. Professor Bourtsalas. velocity, temperature, flux and concentration in the consumption and pollution loads. Introduction of Engineering, or carry out a special project under the 3 pts. Lect: 3. Professor Fthenakis. systems, with a focus on integrated modeling and Industrial ecology examines how to reconfigure field. The class will involve planning and execution methodology for Life Cycle Assessment (LCA) of supervision of EAEE faculty. Credit for the course Adverse effects of air pollution, sources and analysis of the water cycle and associated mass industrial activities so as to minimize the adverse of a study to sense a local environmental system. manufactured products. Analysis of several DFE is contingent on the submission of an acceptable transport media, monitoring and modeling of transport for water resources and environmental thesis or final report. This course cannot substitute environmental and material resource effects and LCA case studies. Term project required on EAEE E4007y Environmental geophysics field air quality, collection and treatment techniques, engineering. Coverage of unit hydrologic on the planet. Engineering applications of use of DFE/LCA on a specific product/process: for the Undergraduate design project (EAEE E3999 pollution prevention through waste minimalization processes such as precipitation, evaporation, methodology of industrial ecology in the analysis studies (a) product design complete with materials and or EAEE E3999). and clean technologies, laws, regulations, infiltration, runoff generation, open channel and of current processes and products and the 3 pts. Lect: 3. Not offered in 2020–2021. process selection, energy consumption, and standards, and guidelines. pipe flow, subsurface flow and well hydraulics in EAEE E3901y Environmental microbiology selection or design of environmentally superior Application of geophysical methods to noninvasive waste loadings; (b) LCA of an existing industrial the context of example watersheds and specific 3 pts. Lect: 3. Professor Chandran. alternatives. Home assignments of illustrative assessment of the near surface. First part consists or consumer product using a commercially EAEE E4160y Solid and hazardous waste integrative problems such as risk-based design for Prerequisite: CHEM UN1404 or equivalent. quantitative problems. of series of two-hour lectures of physics and established method. management Fundamentals of microbiology, genetics and math involved in instrumental methods and data flood control, provision of water, and assessment 3 pts. Lect: 3. Professor Bourtsalas. molecular biology, principles of microbial nutrition, EAEE E4003x Aquatic chemistry acquisition and processing. The field (nine field CHEE E4050x Industrial and environmental of environmental impact or potential for non-point Generation, composition, collection, transport, energetics and kinetics, application of novel and 3 pts. Lect: 3. Professor Yip. days) students plan surveys; collect and analyze electrochemistry source pollution. Spatial hydrologic analysis using storage and disposal of solid and hazardous state-of-the-art techniques in monitoring the Prerequisite: CHEE E3010. Principles of geophysical data in teams; learn how to integrate 3 pts. Lect: 3. Not offered in 2020–2021. GIS and watershed models. waste. Impact on the environment and public structure and function of microbial communities physical chemistry applied to equilibria and geophysical data with invasive data, hydrological, Prerequisite: CHEN E3010 or equivalent. A health. Government regulations. Recycling and CIEE E3255y Environmental control and in the environment, engineered processes for kinetics of aqueous solutions in contact with geological, engineering, and contaminant transport presentation of the basic principle underlying resource recovery. pollution reduction systems biochemical waste treatment and bioremediation, minerals and anthropogenic residues. The models; and develop a comprehensive and electrochemical processes. Thermodynamics, 3 pts. Lect: 3. Professor Farrauto. microorganisms and public health, global microbial scientific background for addressing problems justifiable model of the subsurface. Geophysical electrode kinetics, and ionic mass transport. CIEE E4163y Sustainable water treatment Prerequisite: EAEE E3200 or ENME E3161 elemental cycles. of aqueous pollution, water treatment, and methods include GPR (Ground Penetrating Examples of industrial and environmental and reuse or MECE E3100. Sources of solid/gaseous air sustainable production of materials with minimum Radar), conductivity, and magnetic and seismic applications illustrated by means of laboratory 3 pts. Lect: 3. Professor Knowles. EAEE E3995x, y, and s Fieldwork pollution and the technologies used for modern environmental impact. Hydrolysis, oxidation- methods. Field applications include infrastructure/ experiments: electroplating, refining, and Prerequisites: Introductory chemistry (with lab) 1 pt. Members of the faculty. methods of abatement. Air pollution and its reduction, complex formation, dissolution and environmental assessment, archeological studies, winning in aqueous solutions and in molten and fluid mechanics, or the equivalent. Theory Prerequisite: Instructor's permission. Obtained abatement from combustion of coal, oil, and precipitation, predominance diagrams; examples and high resolution geology. salts; electrolytic treatment of wastes; primary, and application of the physical and chemical internship and approval from faculty adviser. natural gas and the thermodynamics of heat of natural water systems, processes for water secondary, and fuel cells. processes for treating potable water and reusing Written application must be made prior to EAEE E4009x Geographic information engines in power generation. Catalytic emission treatment and for the production of inorganic wastewater. Disinfection/oxidation, coagulation registration outlining proposed internship and systems (GIS) for resource, environmental ECIA W4100y Management and development control is contrasted to thermal processes for materials from minerals. and flocculation, clarification, filtration, ion study program. Final reports required. May not and infrastructure management of water systems abating carbon monoxide, hydrocarbons, oxides exchange, adsorption, membrane processes, be taken for pass/fail credit or audited. Fieldwork EAEE E4004x Physical processing and 3 pts. Lect: 3. Not offered in 2020–2021. of nitrogen and sulfur from vehicles and stationary 3 pts. Lect: 3. Professor Gorokhovich. advanced oxidation processes, activated sludge, credits may not count toward any major core, recovery of solids Decision analytic framework for operating, sources. Processing of petroleum for generating Prerequisite: Permission of the instructor. Basic and anaerobic sludge digestion. fuels. Technological challenges of controlling technical elective, and nontechnical requirements. 3 pts. Lect: 3. Not offered in 2020–2021. concepts of geomatics, spatial data representation managing, and planning water systems, greenhouse gas emissions. Biomass and the International students must also consult with the Generalized treatment of processes for solids and organization, and analytical tools that considering changing climate, values and needs. EAEE E4180y Electrochemical energy storage hydrogen economy coupled with fuel cells as future International Students and Scholars Office. Note: separation. Applications to materials processing comprise GIS are introduced and applied to a Public and private sector models explored through systems sources of energy. only for EAEE undergraduate students who need and handling; mining; solid waste, recycling, and variety of problems including watershed protection, U.S.-international case studies on topics ranging 3 pts. Lect: 3. Professor Steingart. relevant off-campus work experience as a part of resource recovery; construction materials and environmental risk assessment, material mass from integrated watershed management to the Prerequisites: CHEM UN1403-1404 or equivalent, EAEE E3800y Earth and environmental their program of study as determined by instructor. debris; scrap materials, yard and park wastes. balance, flooding, asset management, and analysis of specific projects for flood mitigation, MECE E3301 or equivalent, PHYS UN1402 or engineering laboratory, I Economic considerations and context. Relevant emergency response to natural or man-made water and wastewater treatment, or distribution equivalent. Corequisites: CHEN E4201, EAEE EAEE E3998x-E3999y Undergraduate design 2 pts. Lect: 1. Lab: 3. Professor Bourtsalas. materials properties and bulk materials analyses. hazards. Technical content includes geography and system evaluation and improvement. E3103. Survey course on electrochemical project Prerequisite: CHEE E3010. Corequisite: CIEE Process system flow-sheets and analysis. Solid/ map projections, spatial statistics, database design energy storage with a focus on closed-form 2 pts. (each semester). Lect: 1. Lab: 2. CIEE E4116x Energy harvesting E3255. Experiments on fundamental aspects solid, solid/liquid, and solid/gas separation and use, interpolation and visualization of spatial cells. Fundamentals of thermodynamics will be Professor Farrauto. 3 pts. Lect: 3. Professor Yin. of Earth and environmental engineering with process. Liberation, concentration, and auxiliary surfaces and volumes from irregularly spaced data, reviewed and fundamentals of electrochemistry Prerequisite: senior standing. Students must enroll Prerequisite: ENME E3114 or equivalent, or emphasis on the applications of chemistry, processes. Design of separation machines: types and decision analysis in an applied setting. Taught introduced. Application of fundamentals to for both 3998x and 3999y during their senior instructor’s permission. Criterion of energy biology and thermodynamics to environmental and intensities of force involved; scaling-up in a laboratory setting using ArcGIS. Access to devices such as batteries, flow batteries, and fuel year. Selection of an actual problem in Earth and harvesting, identification of energy sources.

ENGINEERING 2020–2021 ENGINEERING 2020–2021 cells. Device optimization with respect to energy combustion or gasification of wastes. Application Prerequisites: CHEN E3110 or ENME E3161 CIEE E4257y Groundwater contaminant science or instructor’s permission. Major recovery, shale fracking, photo and electrochemical 132 133 density, power density, cycle life, and capital cost of thermal conversion technologies, ranging or equivalent, or the instructor’s permission. transport and remediation technologies to store carbon dioxide, geological, conversion of CO2 to chemical and fuels, and will be considered. from combustion to gasification and pyrolysis. The hydrologic cycle and relevant atmospheric 3 pts. Lect: 3. Professors Mutch and Carbonaro. ocean, and in the carbon chemical pool. Carbon formation of solid carbonates and their various Quantitative description of the dominant waste processes; water and energy balance; radiation; Prerequisite: CIEE E3250 or equivalent. Sources dioxide transport technologies also covered. uses. Life cycle analyses of potential products EAEE E4190x Photovoltaic systems to energy processes used worldwide, including boundary layer; precipitation formation; and types of groundwater contamination. In addition to basic science and engineering and utilization schemes will also be discussed, engineering and sustainability feedstock preparation, moving grate and fluid bed evaporation; vegetation transpiration; infiltration; Groundwater hydrology. Groundwater contaminant challenges of each technology, full spectrum as well as the use of renewable energy for CO 3 pts. Lect: 3. Not offered in 2020–2021. 2 combustion, heat transfer from combustion gases storm runoff; snowmelt; and flood processes. rate and transport. Flow and transport in the of economic, environmental, regulatory, and conversion. Prerequisite: Senior standing or instructor’s to steam, mitigation of high-temperature corrosion, Routing of runoff and floodwaters. Groundwater unsaturated zone. Nonaqueous phase liquids and political/policy aspects, and their implication permission. A systems approach for intermittent EAEE E4350x Planning and management of electricity generation, district heating, metal flow and the hydraulics of wells. Probabilistic multiphase flow. Physical and numerical models for regional and global carbon management renewable energy involving the study of resources, urban hydrologic systems recovery, emission control, and beneficial use of modeling, and extreme-value theory. for contaminant transport. Characterization and strategies of the future. Combination of lectures, generation, demand, storage, transmission, 3 pts. Lect: 3. Professor Rosenberg ash residues. assessment of contaminated sites. Groundwater class debates and breakout groups, student economics and politics. Study of current and EACH E4252x Introduction to surface and Prerequisite: ENME E3161 or equivalent. remediation alternatives. Regulations. presentations, and independent final projects. emerging photovoltaic technologies, with focus on EAEE E4220x Energy system economics and colloid chemistry Introduction to runoff and drainage systems in an basic sustainability metrics (e.g., cost, resource optimization 3 pts. Lect: 3. Professors Farinato and EAEE E4257y Environmental data analysis and EAEE E4303x or y Carbon measurement and urban setting, including hydrologic and hydraulic availability, and life-cycle environmental impacts). 3 pts. Lect: 3. Professor Xu. Somasundaran. modeling monitoring analyses, flow and water quality monitoring, The status and potential of first- and second- Prerequisites: Basic linear algebra, basic Prerequisite: Elemental physical chemistry. The 3 pts. Lect: 3. Professor Xu. 3 pts. Lect: 3. Not offered in 2020–2021. common regulatory issues, and mathematical generation photovoltaic technologies (e.g., probability and statistics, and basic programming principles of surfaces and colloid chemistry Prerequisite: STAT GU4250 or equivalent. Statistical Prerequisites: Undergraduate level math and modeling. Applications to problems of climate crystalline and amorphous Si, CdTe, CIGS) and skills. Transitioning into a sustainable energy critical to range of technologies indispensable to methods for the analysis of the space and time science or instructor permission. Sources of variation, land use changes, infrastructure emerging third-generation ones. Storage options system is not only a technical challenge but modern life. Surface and colloid chemistry has structure in environmental data. Application various GHGs (whether fossil/industrial or operation and receiving water quality, developed to overcome the intermittency constraint. Large also an economical one. Teaches students significance to life sciences, pharmaceuticals, to problems of climate variation and change; biogenic), their chemical behavior, interactions, using statistical packages, public-domain models, scales of renewable energy technologies and fundamentals of power system economics over agriculture, environmental remediation and hydrology; air, water and soil pollution dynamics; and global warming potential once airborne; and Geographical Information Systems (GIS). plug-in hybrid electric cars. which current electricity markets are designed. waste management, earth resources recovery, disease propagation; ecological change; and available measurement, monitoring, and detection Team projects that can lead to publication quality Also examines challenges and opportunities electronics, advanced materials, enhanced oil resource assessment. Applications are developed analyses in relevant fields of interest. Emphasis on EAEE E4200y Introduction to sustainable technologies to track gas emissions, including in future sustainable energy systems such as recovery, and emerging extraterrestrial mining. using the ArcView Geographical Information System the unique technical, regulatory, fiscal, policy, and production of earth mineral & metal resources leakage from storage sites. Carbon accounting carbon tax, renewable energy, demand response, Topics include: thermodynamics of surfaces, (GIS), integrated with currently available statistical other interdisciplinary issues that pose a challenge 3 pts. Lect: 3. Professors Farinato and Nagaraj. and reporting methodologies such as life cycle and energy storage. Covers mixed-integer linear properties of surfactant solutions and surface packages. Team projects that lead to publication- to effective planning and management of urban Prerequisites: EAEE E3103 and undergraduate analysis, and corporate carbon footprinting. programming and demonstrates how mathematical films, electrokinetic phenomena at interfaces, quality analyses of data in various environmental hydrologic systems. level courses in chemistry (especially inorganic, In addition to basic science and engineering optimizations are integrated into energy system principles of adsorption and mass transfer and fields of interest. An interdisciplinary perspective is physical and organic). Introductory course focused challenges of each technology, full spectrum of EAEE E4361y Economics of Earth resource operations. Provides overview of current energy modern experimental techniques. Leads to deeper emphasized in this applications-oriented class. economic, environmental, regulatory, and political/ industries on engineering principles and unit operations system research topics. Includes a project using understanding of interfacial engineering, particulate policy aspects, and their implication for regional involved in sustainable processing of primary and mathematical tools to solve real-world problems in dispersions, emulsions, foams, aerosols, polymers EAEE E4300x or y Introduction to carbon 3 pts. Lect: 3. Not offered in 2020–2021. and global carbon management strategies of the secondary earth mineral and metal resources. the energy system. in solution, and soft matter topics. management Prerequisite: EAEE E3103 or instructor’s Covers entire value chain, viz, aspects of 3 pts. Lect: 3. Not offered in 2020–2021. future. Combination of lectures, class debates permission. Definition of terms. Survey of economic resource deposits, mining, fundamental EAEE E4228y Separation science and CIEE E4252y Foundations of environmental Prerequisites: Undergraduate level mathematics and breakout groups, student presentations, and Earth resource industries: resources, reserves, principles and processes for size reduction, technology in sustainable earth resources engineering and science, or instructor’s permission. independent final projects. production, global trade, consumption of mineral separations based on physical and chemical development 3 pts. Lect: 3. Professor Chandran. Introduction to natural and anthropogenic carbon commodities and fuels. Economics of recycling properties of minerals and metals, solid-liquid 3 pts. Lect: 3. Professors Farunato and Nagaraj. Prerequisites: CHEM UN1403, or equivalent; cycle, and carbon and climate. Rationale and need EAEE E4304x Closing the carbon cycle and substitution. Methods of project evaluation: separation, waste and pollution management, Prerequisites: EAEE E3103 and undergraduate ENME E3161 or equivalent. Engineering aspects to manage carbon and tools with which to do so 3 pts. Lect: 3. Professor Eisenberger. estimation of operating costs and capital water and energy efficiency and management, level courses in chemistry (especially inorganic, of problems involving human interaction with (basic science, psychology, economics and policy Prerequisites: Calculus, basic inorganic requirements, project feasibility, risk assessment, safety and health, environmental impact physical and organic). Recommended: EAEE the natural environment. Review of fundamental background, negotiations and society; emphasis chemistry, and basic physics, including and environmental compliance. Cost estimation assessment and control, and economic efficiency. E4252, EAEE E4003, and EAEE E4200. Detailed principles that underlie the discipline of on interdisciplinary and inter-dependent approach). thermodynamics, or instructor’s permission. for reclamation/remediation projects. Financing of Special emphasis on concepts and practical study of the chemical and physicochemical environmental engineering, i.e., constituent Simple carbon emission model to estimate the Introduction to complex systems, their impact on reclamation costs at abandoned mine sites and applications within "mines of the future" framework principles underlying separations in development transport and transformation processes in impacts of a specific intervention with regard to our understanding and predictability of the carbon waste-disposal postclosure liability. to highlight innovations and transformational of earth resources in a safe and sustainable environmental media such as water, air, and national, per capita, and global emissions. Student- cycle, the use of systems analysis and modeling CHEE E4530y Corrosion of metals technological changes in progress. manner. Covers wide-range of solid-solid, ecosystems. Engineering applications for led case studies (e.g., reforestation, biofuels, tools, as well as Bayesian statistics and decision 3 pts. Lect: 3. Instructor to be announced. solid-liquid and liquid-liquid separations used addressing environmental problems such as water CCS, efficiency, alternative energy) to illustrate theory for evaluating various solutions to close EAIA W4200y Alternative energy resources Prerequisite: CHEN E3010 or equivalent. The in processing of mineral resources. Interfacial quality and treatment, air pollution emissions, necessary systems approach required to tackle the carbon cycle, a detailed examination of the 3 pts. Lect: 3. Professor Steingart. theory of electrochemical corrosion, corrosion science and engineering principles of important and hazardous waste remediation. Presented in global challenges. geochemical carbon cycle, major conceptual Unconventional, alternative energy resources. tendency, rates, and passivity. Application to industrial processes of flotation, flocculation, the context of current issues facing the practicing models that couple its changes to climate Technological options and their role in the world various environments. Cathodic protection and dewatering, interfacial transport, magnetic/gravity/ engineers and government agencies, including EAEE E4301y Carbon storage change, analysis of the anthropogenic carbon energy markets. Comparison of conventional and coatings. Corrosion testing. electrostatic separations, solvent extraction, legal and regulatory framework, environmental 3 pts. Lect: 3. Not offered in 2020–2021. sources and sinks and role of carbon in energy unconventional, renewable and nonrenewable, Prerequisites: Undergraduate level mathematics production, closing the carbon cycle impacts solid-support extraction, crystallization and impact assessments, and natural resource EAEE E4550x Catalysis for emissions control energy resources and analysis of the and science, or instructor’s permission. Major on energy security, economic development and precipitation. Emphasis on concepts in interfacial management. 3 pts. Lect: 3. Professor Farrauto. consequences of various technological choices technologies to capture carbon dioxide via new or climate change protection, analysis of solutions to chemistry and concepts associated with 'mines of Prerequisite: One year of general college and constraints. Economic considerations, energy EAEE E4255x River and coastal retrofitted power plant designs, during industrial close the carbon cycle. the future' framework. chemistry. Fundamentals of heterogeneous availability, and the environmental consequences hyrdrodynamics processes, and from ambient air. In addition EAEE E4305y Carbon utilization and catalysis including modern catalytic preparation of large-scale, widespread use of each particular EAEE E4241x Solids handling and transport 3 pts. Lect: 3. Not offered in 2020–2021. to basic science and engineering challenges techniques. Analysis and design of catalytic technology. Introduction to carbon dioxide disposal systems Prerequisites: CHEN E3110 or ENME E3161 or the of each technology, full spectrum of economic, conversion emissions control systems. Introduction to current as a means of sustaining the fossil fuel option. 3 pts. Lect: 3. Not offered in 2020–2021. equivalent. Dynamics of flow and waves in rivers environmental, regulatory, and political/policy 3 pts. Lect: 3. Not offered in 2020–2021. industrial catalytic solutions for controlling gaseous Recitation section required. Analysis and design of transportation systems and coastal settings, with applications to flooding aspects, and their implication for regional and Prerequisites: Undergraduate level emissions. Introduction to future catalytically for bulk solids in tunnels, mines, and large and mixing of saline and fresh waters, sediment global carbon management strategies of the thermodynamics or instructor's permission. EAEE E4210x Thermal treatment of waste and Introduction to various CO utilization and enabled control technologies. excavations. Design of hoisting, cable transport, transport. Integrative hydrodynamics modeling future. Combination of lectures, class debates 2 biomass materials conversion technologies that can reduce the rail and trackless haulage systems, conveyor experience using numerical and analytical tools and breakout groups, student presentations, and EAEE E4560y Particle technology 3 pts. Lect: 3. Professor Bourtsalas. overall carbon footprint of commodity chemicals belts, selection of loaders, excavators, off-highway applied to complex real world setting, including independent final projects. 3 pts. Lect: 3. Not offered in 2020–2021. Prerequisite: CHEE E3010 or the equivalent and materials. Fundamentals of thermodynamics, trucks, and draglines for large excavations. concerns of anthropogenic change in rivers and Prerequisites: ENME E3161 and MSAE E3111 or instructor’s permission. Origins, quantities EAEE E4302x or y Carbon capture fluid mechanics, reaction kinetics, catalysis estuaries and sea level fluctuations at the river- or equivalent. Introduction to engineering generated, and characterization of solid wastes. CIEE E4250x or y Hydrosystems 3 pts. Lect: 3. Not offered in 2020–2021. and reactor design will be discussed using estuary boundary. processes involving particulates and powders. Chemical and physical phenomena in the 3 pts. Lect: 3. Professor Gentine. Prerequisites: Undergraduate level math and technological examples such as enhanced oil The fundamentals of particle characterization,

ENGINEERING 2020–2021 ENGINEERING 2020–2021 multiphase flow behavior, particle formation, impact on modern urban environmental quality, EACH E6181x Advanced electrochemical CHEE E6252y Advanced surface and current research and literature in the field of EAEE E9305x and y–S9305 Earth and 134 135 processing and utilization of particles in various natural resources, and government, municipal, and energy storage colloid chemistry hydrometallurgy, electrometallurgy, and corrosion. environmental engineering research engineering applications with examples in social planning and management programs. Strong 3 pts. Lect: 3. Professor Steingart. 3 pts. Lect: 2. Lab: 3. Professors Somasundaran Topics will be selected by the instructor to 0–12 pts. Members of the faculty. energy and environment related technologies. emphasis on current and twentieth-century waste Prerequisites: EAEE E4180, EAEE E4002. and Farinato. illustrate the application of thermodynamics and Graduate research directed toward solution of a Engineering of functionalized particles and management in New York City. Most modern commercial implementations Prerequisite: CHEE E4252. Applications of surface rate phenomena to the design and control of problem in mineral processing or chemical metallurgy. design of multiphase reactors and processing of electrochemical energy storage are not chemistry principles to wetting, flocculation, electrochemical engineering processes. EAEE E4999x and y Fieldwork EAEE E9800x and y–S9800 Doctoral research units with emphasis on fluidization technology. fully deterministic: provides context and best- flotation, separation techniques, catalysis, mass 1 pt. Members of faculty. EAEE E8233x and y Research topics in instruction Particle technology is an interdisciplinary field. hypotheses for modern challenges. Topics transfer, emulsions, foams, aerosols, membranes, Prerequisite: Instructor’s written permission. Only particle processing 3, 6, 9, or 12 pts. Members of the faculty. Due to the complexity of particulate systems, include: current understanding of lithium/lithium biological surfactant systems, microbial surfaces, EAEE graduate students who need relevant off- 0 pts. Professor Somasundaran. A candidate for the Eng.Sc.D. degree in mineral particle technology is often treated as art rather anode solid-electrolyte-interphase, reversible enhanced oil recovery, and pollution problems. campus work experience as part of their program Emergent findings in the interactions of particles engineering must register for 12 points of doctoral than science. In this course, the fundamental and irreversible side reactions in redox flow Appropriate individual experiments and projects. of study as determined by the instructor. Written with reagents and solutions, especially inorganics, research instruction. Registration in EAEE E9800 principles governing the key aspects of particle systems, electrochemically coorelated mechanical Lab required. application must be made prior to registration surfactants, and polymers in solution, and may not be used to satisfy the minimum residence science and technology are introduced along with fracture at multiple scales, relationships between outlining proposed study program. Final reports EAEE E6255x-E6256y Methods and their role in grinding, flotation, agglomeration, requirement for the degree. various industrial examples. electrolyte solvation and electrode insertion, required. This course may not be taken for pass/ applications of analytical decision making in filtration, enhanced oil recovery, and other mineral roughening, smoothing, and detachment behavior EAEE E9900x and y–S9900 Doctoral EAEE E4901y Environmental microbiology fail credit or audited. International students must mineral industries processing operations. of metal anodes, best practices in structural, dissertation 3 pts. Lect: 3. Professor Chandran. also consult with the International Students and 3 pts. Lect: 3. Not offered in 2020–2021. chemical, and microscopic characterization, EAEE E8273x-E8274y Mining engineering 0 pts. Members of the faculty. Basic microbiological principles; microbial Scholars Office. Prerequisites: Instructor’s permission. morphological vs. macro-homogenous transport reports A candidate for the doctorate may be required metabolism; identification and interactions Advanced study of decision-making problems EAEE E6132y Numerical methods in models, particle to electrode to cell non-linearity. 0–4 pts. Not offered in 2020–2021. to register for this course every term after the of microbial populations responsible for the with critical survey and applications of geomechanics May substitute for formal thesis, EAEE E9271, student’s coursework has been completed, and biotransformation of pollutants; mathematical EAIA W6201x or y Complexity science quantitative decision-making techniques in 3 pts. Lect: 3. Professor Chen. upon recommendation of the student’s adviser. until the dissertation has been accepted. modeling of microbially mediated processes; mineral industries. Systematic development Prerequisites: EAEE E3112 and CIEN E4241 4 pts. Lect: 4. Professors Castner, Dumas, Lall, biotechnology and engineering applications using of methods of the formulation, analysis, and or instructor’s permission. A detailed survey Mutter, and Rising. EAEE E9271x and y–S9271 Earth and microbial systems for pollution control. resolution of these problems. of numerical methods used in geomechanics, Prerequisites: Graduate standing and instructor’s environmental engineering thesis EAEE E4950x Environmental biochemical emphasizing the Finite Element Method (FEM). permission. Survey of techniques, applications, and EAEE P6329x or y Water, sanitation, and 0–6 pts. Members of the faculty. processes Review of the behavior of geological materials. implications of complexity science and complex human health Research work culminating in a creditable dissertation on a problem of a fundamental nature 3 pts. Lect: 3. Professor Chandran. Offered only Water and heat flow problems. FEM techniques systems. Topics include systems dynamics, chaos, 3 pts. Lect: 3. Professor Shaman. selected in conference between student and in odd years. for solving nonlinear problems, and simulating scaling, fat-tailed distributions, fractals, information Prerequisite: Instructor’s permission. In-depth adviser. Wide latitude is permitted in choice of a Prerequisite: EAEE E4901, E4003, CIEE E4252, or incremental excavation and loading on the surface theory, emergence, criticality, agent-based models, analysis of issues relating to water, sanitation, and subject, but independent work of distinctly graduate instructor’s approval. Qualitative and quantitative and underground. graph theory, and social networks. Applications hygiene in both the developed and developing considerations in engineered environmental will cover climate science, ecology, conflict, character is required in its handling. EAEE E6140y Environmental physicochemical worlds. Hydrologic cycle, major causes of enteric biochemical processes. Characterization of hydrology, geomorphology, physics, social theory, processes morbidity and mortality, and design, financing and EAEE E9273x-E9274y Earth and multiple microbial reactions in a community and epidemiology, and governance. implementation of sanitation systems. For both 3 pts. Lect: 3. Professor Yip. environmental engineering reports techniques for determining associated kinetic and engineering and public health students; intended to Prerequisites: CIEE E4252 and CIEE E4163 or EAEE E6212y Carbon sequestration 0–4 pts. stoichiometric parameters. Engineering design foster dialog between the two communities. the equivalent, or the instructor's permission. 3 pts. Lect: 3. Professor Park. May substitute for the formal master’s thesis, of several bioreactor configurations employed Fundamentals and applications of key Prerequisite: EAEE E3200 or equivalent or EAEE E9271, upon recommendation of for biochemical waste treatment. Mathematical EAEE E8229x Selected topics in processing physicochemical processes relevant to water instructor’s permission. New technologies for the department. modeling of engineered biological reactors using minerals and wastes quality engineering (such as water treatment, capturing carbon dioxide and disposing of it away state-of-the-art simulation packages. 3 pts. Lect: 2. Lab: 3. Not offered in 2020–2021. EAEE E9280x and y Earth and environmental waste water treatment/reuse/recycling, from the atmosphere. Detailed discussion of the Prerequisite: CHEE E4252 or instructor’s engineering colloquium EAEE E4951x Engineering systems for water desalination) and the natural environment (e.g., extent of the human modifications to the natural permission. Critical discussion of current research 0 pts. Lect: 1.5. Professor Yip. treatment and reuse lakes, rivers, groundwater). carbon cycle, the motivation and scope of future topics and publications in the area of flotation, All graduate students are required to attend the 3 pts. Lect: 3. Not offered in 2020–2021. carbon management strategies and the role of EAEE E6150y Industrial catalysis flocculation, and other mineral processing departmental colloquium as long as they are in Prerequisites: CIEE E4163 and EAEE E3901, carbon sequestration. Introduction of several 3 pts. Lect: 3. Professor Farrauto. residence. Advanced doctoral students may be or the instructor’s permission. Application of carbon sequestration technologies that allow for techniques, particularly mechanisms of adsorption, Prerequisite: EAEE E4550 or equivalent, or excused after three years of residence. No degree fundamental principles to designing water the capture and permanent disposal of carbon interactions of particles in solution, thinning of instructor’s permission. Fundamental principles credit is granted. treatment and reuse plants. Development of dioxide. Engineering issues in their implementation, liquid films, and optimization techniques. of kinetics, characterization and preparation of process designs for a potable water treatment economic impacts, and the environmental issues EAEE E9302x and y Mining engineering catalysts for production of petroleum products EAEE E8231y Selected topics in hydro- and plant, a biological wastewater treatment plant, or raised by the various methods. research for conventional transportation fuels, specialty electrometallurgy a water reclamation and reuse facility by students 0–4 pts. Not offered in 2020–2021. chemicals, polymers, food products, hydrogen CHEE E6220y Equilibria and kinetics in 3 pts. Lect: 3. Instructor to be announced. working in teams. Student work in evaluation Graduate research directed toward solution of and fuel cells and the application of catalysis hydrometallurgical systems Prerequisites: EAEE E4003 and CHEE of water quality and pilot plant data, screening technicoscientific problems in mining. in biomass conversion to fuel. Update of the 3 pts. Lect: 3. Not offered in 2020–2021. E4050, or instructor’s permission. Review of process alternatives, conducting regulatory reviews ever changing demands and challenges in Prerequisite: CHEE E4050 or EAEE E4003. and recommending a process for implementation, environmental applications, focusing on advanced Detailed examination of chemical equilibria supported by engineering drawings and capital catalytic applications as described in modern in hydrometallurgical systems. Kinetics and operating costs. Periodic oral progress reports literature and patents. mechanisms of homogeneous and heterogeneous and a full engineering report are required. reactions in aqueous solutions. Presentations by practicing engineers, utility EAEE E6151y Applied geophysics personnel, and regulators; and field trips to water, 3 pts. Lect: 3. Not offered in 2020–2021. EAEE E6228y Theory of flotation wastewater, and water reuse facilities. Potential field data, prospecting, wave equations. 3 pts. Lect: 3. Not offered in 2020–2021. Huygens’ principle, Green’s functions, Kirchoff Prerequisite: CHEE E4252 or instructor’s EAEE E4980 Urban environmental technology equation, WKB approximation, ray tracing. Wave permission. A detailed study of the and policy propagation, parameters. Computer applications. physicochemical principles of the flotation process. 3 pts. Lect: 3. Not offered in 2020–2021. Wavelet processing, filters and seismic data. Progress of urban pollution engineering via Stratified Earth model, seismic processing and contaminant abatement technology, government profiling. Radon transform and Fourier migration. policy, and public action in urban pollution. Pollutant Multidimensional geological interpretation.

ENGINEERING 2020–2021 ENGINEERING 2020–2021 136 of future technology, that will affect analog,mixed-mode, (sub) mm-wave, Laboratory for Unconventional 137 ELECTRICAL ENGINEERING almost every aspect of society: signals, RF, power, and digital circuits, and Electronics, Advanced Semiconductor 1300 S. W. Mudd, MC 4712 information, and data; networking and their applications from computation Device Laboratory, Motor Drives and 212-854-3105 communications; nanoscale structures and sensing to cyber-physical and Power Electronics Laboratory, Intelligent ee.columbia.edu and integrated solid-state devices; implantable biomedical systems. and Connected Systems Laboratory, Columbia Integrated Systems Laboratory ACTING CHAIR Paul Sajda, Biomedical ASSOCIATE ADJUNCT ASSISTANT POSTDOCTORAL nanoelectronics and nanophotonics; The area of Nanoscale Structures Ioannis Kymissis Engineering PROFESSOR OF PROFESSORS RESEARCH integrated circuits and systems; systems and Integrated Devices applies (CISL), Analog & RF IC Design Laboratory, 1013 CEPSR Henning G. Schulzrinne, PROFESSIONAL Wei-Yi Cheng SCIENTISTS biology; neuroengineering; and smart fundamental physical principles to VLSI Design Laboratory, High Speed Computer Science PRACTICE Guido Hugo Jajamovich Filipe Arroyo Cardoso electric energy. Details on all of develop revolutionary new electronic, and mmWave IC Laboratory, Analog and VICE CHAIR Zoran Kostic Wooram Lee Tianwei Deng Kenneth L. Shepard these areas can be found at photonic, and optical devices made from Mixed Signal IC Laboratory, Bioelectronics Gil Zussman Yannis P. Tsividis Chong Li Jason Fabbri 809 CEPSR Wen I. Wang SENIOR LECTURER Xiang Meng Guangxing Han ee.columbia.edu/research. conventional and emerging materials, Laboratory, Lightwave Laboratory, and Xiaodang Wang David Vallancourt Jose Ramirez Bjoern David The Signals, Information including graphene, 2D semiconductors, Nano Photonics Laboratory. DIRECTOR OF Charles A. Zukowski Bodhisatwa Sadhu Hellenkamp and Data area concerns the and organic semiconductors. Laboratory instruction is provided in a ADJUNCT FINANCE AND Gil Zussman Damian F. Sciano Linbi Hong PROFESSORS representation, processing, analysis, Research includes nanofabrication, suite of newly-renovated facilities on the ADMINISTRATION Shahriar Shahramian Jakub Piotr Jadwiszczak Yves Baeyens and communication of information characterization, and electromagnetic twelfth floor of the S. W. Mudd Building. Wendy Villa ASSOCIATE Lei Zhang Ahmed Kord Doru Calin 1303 S. W. Mudd PROFESSORS Yang Liu embedded in signals and datasets design of quantum device structures These teaching laboratories are used for Timothy Dickson Javad Ghaderi Dehkordi ADJUNCT SENIOR Sajjad Moazeni arising in a wide range of application and complex silicon photonic circuits circuit prototyping, device measurement, Irving Kalet PROFESSORS Christine P. Hendon RESEARCH Victoria Andino Ching-Yung Lin areas, including audio, video, images, that impact numerous fields from VLSI design, embedded systems Dimitris Anastassiou Xiaofan Fred Jiang SCIENTIST Pavlovsky Debasis Mitra Reuven Opher communications, and biology. Research Lidar and optogenetics to low-energy design, as well as computer engineering Keren Bergman Ethan Katz-Bassett Abhinav Parihar Shih-Fu Chang Krishan Sabnani interests include the development of computation and flexible electronics. and Internet-of-Things experiments. Harish Krishnaswamy SENIOR RESEARCH Mohit Sharma Alexander Gaeta, Jacob Sharony Nima Mesgarani SCIENTIST George Spyropoulos models, algorithms and analyses for The smart electric energy area Applied Physics and Deepak Turaga John Paisley Debasis Mitra Ilke Uguz sensing, detection and estimation, focuses on the optimization of the Materials Science Anwar Walid UNDERGRADUATE PROGRAM Mingoo Seok Maria Vomero Hoots statistical and machine learning, and generation, conversion, distribution, and Andreas H. Hielscher, Thomas Woo Bo Wu The educational objective of the John Wright ASSOCIATE RESEARCH the recognition, organization, and consumption of electric energy as well Biomedical Engineering Zifang Zhao ADJUNCT ASSOCIATE SCIENTISTS Electrical Engineering program, in Predrag Jelenkovic ASSISTANT understanding of the information content as the electrification of energy systems. PROFESSOR Andreas Hartel support of the mission of the School, is Peter Kinget PROFESSORS POSTDOCTORAL of signals and data. Research spans the analysis, design, Alexei Ashikhmin Erik F. Young to prepare graduates to achieve success Ioannis (John) Kymissis James Anderson RESEARCH FELLOW Ori Shental Yiyin Zhou The Networking and Communications and control of power electronics, motor Aurel A. Lazar Dion Khodagholy Araghy Jakob Kiliam Buchheim in one or more of the following within a Jacob Trevino area focuses on the design drive, and energy storage systems, Michal Lipson Asaf Cidon few years after graduation: George Tulevski Vishal Misra, Matthias Preindl and performance evaluation of grid resilience and security, and Computer Science communication systems and data Internet-of-Things. Applications include James Teherani A. Graduate or professional studies—as networks of all kinds, including wireless/ transportation electrification, smart grid, evidenced by admission to a top-tier cellular, optical, ultra-low power, vehicular, renewable energy, and smart building ontemporary electrical handling systems of the future. activities by participating in a program program, attainment of advanced mobile, wearable, data center networks, systems. engineering is a broad discipline Innovations in electrical engineering have of undergraduate research projects with degrees, research contributions, or cyber physical systems, and the that encompasses a wide range had a dramatic impact on the way in the faculty. professional recognition. C internet. Methods range from analyzing of activities. A common theme is the which we work and live: the transistor, A master’s level program in electrical Laboratory Facilities B. Engineering practice—as evidenced and refining existing approaches to use of electrical and electromagnetic integrated circuits, computers, radio and engineering permits graduate students Current research activities are fully by entrepreneurship; employment in the development of new and evolving signals for the generation, transmission, television, satellite transmission systems, to further specialize their knowledge and supported by more than a dozen industry, government, academia, or networking techniques and systems. processing, storage, conversion, and lasers, fiber optic transmission systems, skills within a wide range of disciplines. well-equipped research laboratories nonprofit organizations in engineering; The Systems Biology and control of information and energy. An and medical electronics. For those who are interested in pursuing run by the department faculty. In patents; or professional recognition. Neuroengineering area aims to equally important aspect is the human The faculty of the Electrical a career in teaching, research, or addition, faculty and students have C. Careers outside of engineering that understand and analyze biological interface and the role of individuals Engineering Department at Columbia advanced development, our Ph.D. access to a clean room for micro- take advantage of an engineering systems within the living cell and as the sources and recipients of University is dedicated to the continued program offers the opportunity to conduct and nanofabrication, a materials- education—as evidenced by in the brain. Examples of related information. The rates at which development of further innovations research under faculty supervision at the characterization facility, and an contributions appropriate to the information is transmitted today range through its program of academic leading edge of technology and applied tasks are biomolecular data analysis electron-microscopy facility, managed chosen field. from megabits per second to gigabits instruction and research. Our science. Seminars are offered in all for medical applications, synthetic by the Columbia Nano Initiative. per second and in some cases, as high undergraduate program in electrical research areas. biology, establishing the principles Faculty laboratories include Digital The Electrical Engineering program will as terabits per second. The range of engineering is designed to prepare The Electrical Engineering of neuroinformation processing Video and Multimedia Networking prepare its undergraduates to attain frequencies over which these processes students for a career in industry, research, Department, along with the Computer in the brain for developing robust Laboratory, Wireless and Mobile the following: are studied extends from direct current or business by providing them with a Science Department, also offers B.S. sensory processing and motor control Networking Laboratory, Network 1. an ability to identify, formulate, and (i.e., zero frequency), to microwave and thorough foundation of the fundamental and M.S. programs in computer algorithms, accelerating the clinical Algorithms Laboratory, Genomic solve complex engineering problems optical frequencies. concepts and analytical tools of engineering. Details on those programs translation of devices that make contact Information Systems Laboratory, by applying principles of engineering, The need for increasingly faster and contemporary electrical engineering. A can be found in the Computer with neurons, and building massively Structure-Function Imaging Laboratory, science, and mathematics more sophisticated methods of handling wide range of elective courses permits Engineering section in this bulletin. parallel brain-computer interfaces. Neural Acoustic Processing 2. an ability to apply engineering design information poses a major challenge to the student to emphasize specific The Integrated Circuits and Systems Laboratory, Signal Processing and to produce solutions that meet area focuses on the integration of the electrical engineer. New materials, disciplines such as communications, Research Activities Communication Laboratory, Translational specified needs with consideration circuits and systems on semiconductor of public health, safety, and welfare, devices, systems, and network concepts devices, circuits, or signal processing. The research interests of the faculty Neuroelectronics Laboratory, Bionet platforms. Research spans the analysis, as well as global, cultural, social, are needed to build the advanced Undergraduates have an opportunity encompass a number of rapidly Laboratory, Molecular Beam Epitaxy design, simulation, and validation of environmental, and economic factors communications and information to learn firsthand about current research growing areas, vital to the development Laboratory, Surface Analysis Laboratory,

ENGINEERING 2020–2021 ENGINEERING 2020–2021 138 139 ELECTRICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS ELECTRICAL ENGINEERING: THIRD AND FOURTH YEARS EARLY-STARTING STUDENTS EARLY-STARTING STUDENTS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

APMA E2000 (4) either semester UN1403 (3) Lab UN1494 (3)1 PHYSICS UN2601 (3.5) Lab UN2699 (3) MATH UN1101 (3) MATH UN1102 (3) MATHEMATICS (tracks continued) Lab W3081 (2) and APMA E2101 (3)1

ELEN E3401 (4) PHYSICS UN1401 (3) UN1402 (3) Electromagnetics (three tracks, UN1601 (3.5) UN1602 (3.5) 2 choose one) UN2801 (4.5) UN2802 (4.5) EE CORE ELEN E3106 (3.5) ELEN E3701 (3) REQUIRED Solid-state devices and Intro. to COURSES materials communication systems one-semester lecture or (3–4) CSEE W4119 (3)2 CHEMISTRY UN1403 or UN1404 or Computer networks UN2045 or UN1604 ELEN E3043 (3) Solid state, microwave, ELEN E3201 (3.5) ELEN E3331 (3) ELEN E3390 (3)3 ELEN E1201 (3.5) Circuit analysis Electronic circuts and fiber optics lab CORE REQUIRED EE REQUIRED LABS Capstone design Introduction to electrical engineering course COURSES (either semester) ELEN E3801 (3.5) CSEE E3827 (3) ELEN E3399 (1) Signals and systems Fund. of computer sys. EE practice

ELEN E3081 (1)2 ELEN E3083 (1)2 IEOR E3658 or STAT GU42034; and COMS W3136 (or W3134 or W3137)5 OTHER REQUIRED (Some of these courses are not offered both semesters. Students with an adequate Circuit analysis lab Electronic circuits lab COURSES REQUIRED LABS background can take some of these courses in the sophomore year) ELEN E3084 (1)2 ELEN E3082 (1)2 Signals and systems lab Digital systems lab 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; UNIVERSITY CC1010 (3) either semester TECH (c) signals and systems; and (d) communications and networking WRITING (For details, see ee.columbia.edu)

HUMA CC1001, COCI CC1101, Global Core (3–4); HUMA UN1121 UN1123 (3); HUMA CC1002, COCI REQUIRED or or (at least 6 points total) CC1102, Global Core (3–4); ECON UN1105 (4) UN1155 recitation (0); some of these courses can be NONTECHNICAL or and At least two technical electives outside the chosen depth area; must be courses with significant ELECTIVES postponed to the junior or senior year, to make room for taking the above electrical engineering courses. BREADTH TECH engineering content (see ee.columbia.edu)

3 COMPUTER ENGI E1006 (3) either semester ELECTIVES SCIENCE OTHER Additional technical electives (consisting of more depth or breadth courses, or further options listed at TECH ee.columbia.edu/ee-undergraduate-program) as required to bring the total points of technical electives to 186 PHYSICAL UN1001 (1) UN1002 (1) EDUCATION Complete 27-point requirement; see page 9 (27-Point Nontechnical Requirement) NONTECH THE ART OF ENGI E1102 (4) either semester or seas.columbia.edu for details (administered by the advising dean) ENGINEERING

1 APMA E2101 may be replaced by MATH UN2030 (formerly MATH E1210) and either APMA E3101 or MATH UN2010. TOTAL POINTS7 16.5 17 16 18 2 If possible, these labs should be taken along with their corresponding lecture courses. 3 ENGI E1006 may not be offered every semester. See ee.columbia.edu for more discussion about the Computer Science sequences. 1 Chemistry lab (CHEM UN1500) may be substituted for physics lab, although this is not generally recommended. 3. an ability to communicate effectively on teams whose members 7. an ability to acquire and apply 2 These courses can be taken in the sophomore year if the prerequisites/corequisites are satisfied. with a range of audiences together provide leadership, create new knowledge as needed, using 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 4. an ability to recognize ethical and a collaborative and inclusive appropriate learning strategies. 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. professional responsibilities in environment, establish goals, plan 4 SIEO W3600 and STAT GU4001 cannot generally be used to replace IEOR E3658 or STAT GU4203. engineering situations and make tasks, and meet objectives The B.S. program in electrical 5 Students who plan to minor in Computer Science should choose COMS W3134 or W3137. informed judgments, which must 6. an ability to develop and conduct engineering at Columbia University seeks 6 The total points of technical electives is reduced to 15 if APMA E2101 has been replaced by MATH UN2030 (formerly MATH E1210) and either APMA E3101 or consider the impact of engineering appropriate experimentation, to provide a broad and solid foundation MATH UN2010. Combined-plan students with good grades in separate, advanced courses in linear algebra and ODEs can also apply for this waiver, but the courses must have been at an advanced level for this to be considered. solutions in global, economic, analyze and interpret data, and in the current theory and practice of 7 “Total points” assumes that 20 points of nontechnical electives and other courses are included. environmental, and societal contexts use engineering judgment to draw electrical engineering, including familiarity 5. an ability to function effectively conclusions with basic tools of math and science,

ENGINEERING 2020–2021 ENGINEERING 2020–2021 140 141 ELECTRICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS ELECTRICAL ENGINEERING: THIRD AND FOURTH YEARS LATE-STARTING STUDENTS LATE-STARTING STUDENTS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

APMA E2000 (4) either semester CSEE W3827(3) Fund. of computer sys. MATHEMATICS MATH UN1101(3) MATH UN1102 (3) and APMA E2101 (3)1 ELEN E3106 (3.5) ELEN E3331 (3) Solid-state devices and Electronic circuits materials UN1401 (3) UN1402 (3) UN1403 (3) EE CORE ELEN E3401 (4) PHYSICS Lab UN1494 (3)2 (three tracks, UN1601 (3.5) UN1602 (3.5) UN2601 (3.5) REQUIRED ELEN E3201 (3.5) Electromagnetics choose one) UN2801 (4.5) UN2802 (4.5) Lab UN3081 (2) COURSES Circuit analysis ELEN E3701 (3) ELEN E3801 (3.5) Intro. to Signals and systems communication systems one-semester lecture or (3–4) CSEE W4119 (3) CHEMISTRY UN1403 or UN1404 or Computer networks UN2045 or UN1604

ELEN E3043 (3) ELECTRICAL 3 ELEN E3081 (1)1 ELEN E3083 (1)1 ELEN E1201 (3.5) either semester Solid state, microwave, ENGINEERING 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 UNIVERSITY CC1010 (3) either semester ELEN E3399 (1) WRITING Signals and systems lab Digital systems lab EE practice

HUMA CC1001, HUMA CC1002, COCI CC1101, COCI CC1102, OTHER REQUIRED IEOR E3658 or STAT GU42033; and COMS W3136 (or W3134 or W3137)4 REQUIRED or Global Core (3–4) or Global Core (3–4) COURSES (Some of these courses are not offered both semesters) NONTECHNICAL ELECTIVES HUMA UN1121 or ECON UN1105 (4) and UN1123 (3) UN1155 recitation (0) 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. COMPUTER ENGI E1006 (3) any semester4 (For details, see ee.columbia.edu.) SCIENCE

PHYSICAL UN1001 (1) UN1002 (1) (at least 6 points total) EDUCATION BREADTH At least two technical electives outside the chosen depth area; must be courses with significant engineering TECH content (see ee.columbia.edu)

THE ART OF ENGI E1102 (4) either semester ENGINEERING ELECTIVES OTHER Additional technical electives (consisting of more depth or breadth courses, or further options listed at TECH ee.columbia.edu/ee-undergraduate-program) as required to bring the total points of technical electives to 185 1 APMA E2101 may be replaced by MATH UN2030 (formerly MATH E1210) and either APMA E3101 or MATH UN2010. 2 Chemistry lab (CHEM UN1500) may be substituted for physics lab, although this is not generally recommended. 3 Transfer students and 3-2 Combined Plan students who have not taken ELEN E1201 prior to the junior year are expected to have taken a roughly equivalent course Complete 27-point requirement; see page 9 (27-Point Nontechnical Requirement) when they start ELEN E3201. NONTECH or seas.columbia.edu for details (administered by the advising dean) 4 ENGI E1006 may not be offered every semester. See ee.columbia.edu for more discussion about the Computer Science sequences.

an ability to communicate ideas, and Required science courses cover courses on circuit theory and electronic TOTAL POINTS6 15.5 18 16 18 a humanities background sufficient to basic chemistry and physics, whereas circuits, one course on semiconductor understand the social implications of math requirements cover calculus, devices, one on electromagnetics, one 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 engineering practice. Graduates should differential equations, probability, on signals and systems, one on digital a recommended earlier start. be qualified to enter the profession and linear algebra. Basic computer systems, and one on communications 1 If possible, these labs should be taken along with their corresponding lecture courses. of engineering, to continue toward a knowledge is also included, with or networking. Engineering practice is 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 career in engineering research, or to an introductory course on using developed further through a sequence 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. enter other fields in which engineering engineering workstations and two of laboratory courses, starting with a 3 SIEO W3600 and STAT GU4001 cannot generally be used to replace IEOR E3658 or STAT GU4203. knowledge is essential. Required rigorous introductory computer science first-year course to introduce hands- 4 Students who plan to minor in Computer Science should choose COMS W3134 or W3137. nontechnical courses cover civilization courses. Core electrical engineering on experience early and to motivate 5 The total points of technical electives is reduced to 15 if APMA E2101 has been replaced by MATH UN2030 (formerly MATH E1210) and either APMA E3101 or and culture, philosophy, economics, courses cover the main components theoretical work. Simple creative design MATH UN2010. Combined-plan students with good grades in separate, advanced courses in linear algebra and ODEs can also apply for this waiver, but the courses must have been at an advanced level for this to be considered. and a number of additional electives. of modern electrical engineering and experiences start immediately in this 6 “Total points” assumes that 9 points of nontechnical electives are included. English communication skills are an illustrate basic engineering principles. first-year course. Following this is a important aspect of these courses. Topics include a sequence of two sequence of lab courses that parallel

ENGINEERING 2020–2021 ENGINEERING 2020–2021 142 the core lecture courses. Opportunities engineering courses in one of four advanced math and physics concepts, students. This double degree program Graduate course charts for original research, conducted under the 143 for exploring design can be found defined areas: (a) photonics, solid- and motivates the study of such makes possible the earning of both several focus areas can be found at supervision of a faculty member. The both within these lab courses and state devices, and electromagnetics; concepts. Finally, it allows more time for the Bachelor of Science and Master ee.columbia.edu. work may be theoretical or experimental in the parallel lecture courses, often (b) circuits and electronics; (c) signals students to take classes in a chosen of Science degrees in an integrated M.S. students must complete the or both. coupled with experimentation and and systems; and (d) communications depth area, or gives them more time to fashion. Up to 6 points may be credited professional development and leadership Students who wish to become computer simulation, respectively. The and networking. The depth requirement explore before choosing a depth area. to both degrees, and some graduate course, ENGI E4000, as a graduation candidates for the doctoral degree in culmination of the laboratory sequence provides an opportunity to pursue Students can start with ELEN E1201: classes taken in the senior year may requirement. Ph.D. candidates are electrical engineering have the option of and the design experiences introduced particular interests and exposure to Introduction to electrical engineering count toward the M.S. degree. Interested strongly encouraged to complete the applying for admission to the Eng.Sc.D. throughout earlier courses is a senior the process of exploring a discipline in in the second semester of their first students can find further information ENGI E6001–6004 and should consult program or the Ph.D. program. Students design course (capstone design course), depth—an essential process that can be year, and can continue with other core at ee.columbia.edu and can discuss their program for PDL requirements. who elect the Eng.Sc.D. degree register which includes a significant design applied later to other disciplines, if desired. courses one semester after that, as options directly with their faculty adviser. in the School of Engineering and Applied project that ties together the core The breadth component must shown in the “early-starting students” Students must be admitted prior to Master of Science Degree Science; those who elect the Ph.D. program, encourages creativity, explores consist of at least 6 additional points chart. It is emphasized that both the the start of their seventh semester at Candidates for the M.S. degree in degree register in the Graduate School practical aspects of engineering of courses that are outside of the early- and late-starting sample programs Columbia Engineering. Students in the electrical engineering must complete 30 of Arts and Sciences. practice, and provides additional chosen depth area and have significant shown in the charts are examples only; 3-2 Combined Plan undergraduate points of credit beyond the bachelor’s Doctoral candidates must obtain experience with communication skills in engineering content. These courses schedules may vary depending on program are not eligible for admission to degree. A minimum of 15 points of credit a minimum of 60 points of formal an engineering context. Finally, several can be from other departments within student preparation and interests. this program. must be at the 6000 level or higher. No course credit beyond the bachelor’s technical electives are required, chosen the School. The breadth requirement credit will be allowed for undergraduate degree. A master’s degree from an to provide both breadth and depth in a precludes overspecialization. Breadth courses (3000 or lower). At least 15 accredited institution may be accepted Transfer Students GRADUATE PROGRAMS specific area of interest. More detailed is particularly important today, as points must be in electrical engineering, as equivalent to 30 points. A minimum Transfer students coming to The Department of Electrical Engineering program objectives and outcomes are innovation requires more and more of an defined as including all courses with an of 30 points beyond the master’s degree Columbia as juniors with sufficient offers graduate programs leading to the posted at ee.columbia.edu. interdisciplinary approach, and exposure ELEN designator or a joint designator must be earned while in residence in the general background can complete all degree of Master of Science (M.S.) and The program in electrical engineering to other fields is known to help one’s containing electrical engineering as a doctoral program. requirements for the B.S. degree in the degrees of Doctor of Engineering leading to the B.S. degree is accredited creativity in one’s own main field. member, e.g., EECS, CSEE, EEME, More detailed information regarding electrical engineering. Such students fall Science (Eng.Sc.D.) and Doctor of by the Engineering Accreditation Breadth also reduces the chance of ECBM, etc. And it is expected that at the requirements for the doctoral degree into one of two categories: Philosophy (Ph.D.). The Graduate Commission of ABET, www.abet.org. obsolescence as technology changes. least 12 of the first 24 points taken will be may be obtained in the department Plan 1: Students coming to Columbia Record Examination (General Test only) There is a strong interaction Any remaining technical elective in electrical engineering. office and at ee.columbia.edu. without having taken the equivalent of is required of all applicants except between the Department of Electrical courses, beyond the minimum 12 points Not all technical courses can be ELEN E1201 must take this course in special students. An undergraduate Engineering and the Departments of of depth and breadth, do not have to be applied toward the M.S. degree, and Optional M.S. Specializations their junior year. This requires postponing grade-point average equivalent to B or Computer Science, Applied Physics engineering courses (except for students some have restrictions. Up to 6 points Students in the electrical engineering the core courses in circuits and better from an institution comparable to and Applied Mathematics, Industrial without ELEN E1201 or approved transfer of research (such as ELEN E4998, M.S. program often choose to use some electronics until the senior year, and thus Columbia is expected. Engineering and Operations Research, credit for ELEN E1201) but must be ELEN E6001, and ELEN E6002) can be of their electives to focus on a particular does not allow taking electives in that Applicants who, for good reasons, Physics, and Chemistry. technical. Generally, math and science applied. Up to 1.5 points of fieldwork are unable to submit GRE test results field. Students may pick one of a courses that do not overlap with courses area; thus, such students cannot choose (ELEN E6999) can be used. No more by the deadline date but whose number of optional, formal specialization used to fill other requirements are allowed. circuits and electronics as a depth area. than 3 points of courses that do not EE Core Curriculum undergraduate record is clearly superior templates or design their own M.S. If another department advertises contain primarily engineering, math, or All electrical engineering (EE) students Plan 2: This plan is for students who may file an application without the GRE program in consultation with an adviser. that one of their courses can be used science content can be used, subject must take a set of core courses, which have taken a course equivalent to ELEN scores. An explanatory note should be These specializations are not degree as a technical elective, that does not to the written pre-approval of the collectively provide the student with E1201 at their school of origin, including added to ensure that the application will requirements. They represent suggestions necessarily mean it will be approved department. Any course that is not on fundamental skills, expose him/her a laboratory component. See the bulletin be processed even while incomplete. If from the faculty as to how one might as a technical elective in the electrical the list of standard courses specified to the breadth of EE, and serve as a for a description of this course. Many the candidate’s admissibility is clear, the fill one’s programs so as to focus on a engineering program. Which courses are at ee.columbia.edu/masters-program springboard for more advanced work, or pre-engineering programs and physics decision may be made without the GRE particular area of interest. Students may approved depends on other electives requires prior written department for work in areas not covered in the core. departments at four-year colleges offer scores; otherwise, it may be deferred wish to follow these suggestions, but chosen due to the depth and breadth approval, including during the summer These courses are shown on the charts such courses. Such students can start until the scores are received. they need not. The degree requirements restrictions, and the need for sufficient session. in Undergraduate Degree Tracks. A full taking circuits at Columbia immediately, There are no prescribed course are quite flexible and are listed in the engineering and technical content within The general school requirements curriculum checklist is also posted at and thus can choose circuits and requirements in any of the regular Master of Science Degree section, the entire 18 points. Electrical engineering listed earlier in this bulletin, such as ee.columbia.edu. electronics as a depth area. graduate degree programs. Students, in above. All students, whether following technical electives must also be 3000- minimum GPA, must also be satisfied. a formal specialization template or not, It is stressed that ELEN E1201 or consultation with their faculty advisers, level or above and must not have All degree requirements must be are expected to include breadth in their Technical Electives its equivalent is a key part of the EE design their own programs, focusing on significant overlap with other courses completed within five years of the program. Not all of the elective courses The 18-point technical elective requirement curriculum. The preparation provided by particular fields of electrical engineering. taken for the major. beginning of the first course credited listed here are offered every year. For the for the electrical engineering program this course is essential for a number of Among the fields of graduate study toward the degree. latest information on available courses, consists of three components: depth, other core courses. are Communications, Networking, More details and a requirements Starting Early visit the Electrical Engineering home page breadth, and other. A general outline is Sample programs for both Plan 1 Internet & Internet of Things; Computer checklist for approvals can be found at The EE curriculum is designed to allow at ee.columbia.edu. provided here, and more specific course and Plan 2 transfer students can be Engineering; Integrated Circuits and ee.columbia.edu/masters-program. restrictions can be found at ee.columbia. students to start their study of EE in found at ee.columbia.edu. Systems & Electronics; Integrated edu. For any course not clearly listed there, their first year. This motivates students Devices & Photonics; Signals, Specialization in Data-Driven Doctoral Degree adviser approval is necessary. early and allows them to spread Information, Data, Learning & Control; Analysis and Computation B.S./M.S. Program The requirements for the Ph.D. and Eng. The depth component must nontechnical requirements more evenly. Smart Electric Energy; and Systems Advisers: Professors Dimitris The B.S./M.S. degree program is open Sc.D. degrees are identical. Both require consist of at least 6 points of electrical It also makes evident the need for Biology and Neuroengineering. Anastassiou, Shih-Fu Chang, Pedrag to a select group of undergraduate a dissertation based on the candidate’s

ENGINEERING 2020–2021 ENGINEERING 2020–2021 144 Jelenkovic, Zoran Kostic, Aurel A. Lazar, 4. Three courses from the following list signal processing; ELEN E6950: E4510: Solar energy and smart grid Computational neuroscience, circuits of solar energy; APPH E6081: Solid 145 Nima Mesgarani, John Paisley, John (courses cannot be used to fulfill both Wireless and mobile networking, I; power systems. in the brain state physics, I; APPH E6082: Solid Wright, Xiaofan (Fred) Jiang this requirement and any of the above EECS E4951: Wireless network and 3. Take at least one control or 3. Take at least one course from BMEE state physics, II; APPH E6091: requirements): ELEN E6488: Optical systems; ELEN E6761: Computer optimization course from: EEME E4030: Neural control engineering; Magnetism and magnetic materials; 1. Satisfy M.S. degree requirements. interconnects and interconnection communication networks, I; ELEN E4601: Digital control systems; EEME ECBM E4040: Neural networks and APPH E6110: Laser interactions 2. Take at least two courses from ECBM networks; ELEN E6761: Computer E6712: Communication theory; ELEN E6601: Introduction to control theory; deep learning; ECBM E4070; ECBM with matter; MSAE E4202: E4040: Neural networks and deep communication networks I; ELEN E6713: Topics in communications; EEME E6602: Modern control theory; E4090: Brain computer interfaces Thermodynamics and reactions in learning; EECS E4764: Internet of E6767: internet economics, energy, ELEN E6717: Information ELEN E6873: Detection and estimation (BCI) laboratory; CBMF W4761: solids; MSAE E4206: Electronic things—intelligent and connected and society; ELEN E6770: Topic: next theory; ELEN E677x: Topics in theory; EEOR E4650: Convex Computational genomics; ELEN and magnetic properties of solids; systems; ELEN E4810: Digital signal generation networks; ELEN E6772: telecommunication networks. optimization for electrical engineering; E6010: Systems biology: design MSAE E4207: Lattice vibrations processing; ELEN E4720: Machine Topic: network algorithms; ELEN 4. At least two additional approved EEOR E6616: Convex optimization; principles for biological circuits; EEBM and crystal defects; MSAE E6120: learning for signals, information, E6775: Topic: computer networks: courses in wireless communications or EECS E4764: IoT—intelligent and E6020: Methods in computational Grain boundaries and interfaces; and data; EEOR E6616: Convex a systems approach; ELENE E6776: a related area. connected systems; CSEE W4840: neuroscience; BMEE E6030: Neural MSAE E6220: Crystal physics; optimization; EECS E6893: Topic: big Topic: content distribution networks; Embedded system Design. modeling and neuroengineering. MSAE E6229: Energy and particle data analytics. ELEN E6950: Wireless and mobile Specialization in Integrated Circuits 4. Take at least one nonelectric energy 4. Take at least one course from ECBM beam processing of materials; MSAE 3. Take at least one courses from networking I; EEOR E4650: Convex and Systems class course from: MECE E4210: E6040: Neural networks and deep E6225: Techniques in X-ray and ECBM E6040: Neural networks optimization for EE; EEOR E6616: Advisers: Professors Peter Kinget, Energy infrastructure planning; learning research; ECBM E607x: neutron diffraction. and deep learning research; EECS Convex optimization; CSEE E4140: Harish Krishnaswamy, Mingoo Seok, MECE E4320: Intro to combustion; Topics in neuroscience and deep E6720: Bayesian models for machine Networking laboratory; EECS Kenneth Shepard, Yannis Tsividis, MECE E4211: Energy: sources and learning; ELEN E608x: Topics in Specialization in Microelectronic learning; EECS E6765: Internet of E4951: Wireless networks and Charles Zukowski conversions; MECE E4302: Advanced systems biology; EEBM E609x: Devices things—systems and physical data systems; CSEE E6180: Modeling thermodynamics; EAEE E4190: Topics in computational neuroscience Advisers: Professors Dion Khodagholy, analytics; EECS E6895: Topic: and Performance Evaluation; 1. Satisfy M.S. degree requirements. Photovoltaic systems engineering and neuroengineering; ELEN E6261: Ioannis (John) Kymissis, Michal Lipson, advanced big data analytics. COMS W4180: Network security; 2. One digital course from: EECS E4321: and sustainability; EAEE E4257: Computational methods of circuit James Teherani, Wen Wang 4. Take a second course from #3 or COMS W4995: Internet technology, Digital VLSI circuits or EECS E6321: Environmental data analysis and analysis ELEN E6717: Information one course from ECBM E4060: economics, and policy, COMS Advanced digital electronic circuits. modeling; EAEE E4301: Carbon theory; ELEN E6860: Advanced digital 1. Satisfy M.S. degree requirements. Introduction to genomic information E6181: Advanced internet services; 3. One analog course from ELEN storage; EAEE E4302: Carbon signal processing. 2. One basic course such as: ELEN science and technology; ECBM COMS E6998: Cloud computing and E4312: Analog electronic circuits; capture; EAEE E4304: Closing the E4301: Introduction to semiconductor E4070; ECBM: E607x: Topics in big data; IEOR E6704: Queueing ELEN E6312: Advanced analog carbon cycle. Specialization in Lightwave devices or ELEN E4411: neuroscience and deep learning; theory; IEOR E4106: Stochastic integrated circuits; ELEN E6316: 5. Not required, but consider taking (Photonics) Engineering Fundamentals of photonics. ELEN E6690: Topics in data-driven models; with adviser approval, other Analog digital interfaces in VLSI; one of the following energy policy Advisers: Professors Keren Bergman, 3. One advanced course such as: ELEN analysis and computation; ELEN relevant advanced topic courses on ELEN E4314: Communication or market nontechnical elective Ioannis (John) Kymissis, Michal Lipson E4193: Modern display science E6876: Sparse and low-dimensional networking topics from ELEN E677x, circuits; ELEN E6314: Advanced courses (this course will fill the quota and technology; ELEN E4944: models for high-dimensional data; COMS W4995, COMS E6998, or communication circuits; ELEN E6320: of nontechnical courses on the M.S. 1. Satisfy M.S. degree requirements. Principles of device microfabrication; ELEN E9601: Seminar in data-driven other course numbers may be used Millimeter-wave IC design. Checklist): EAEE E4001: Industrial 2. Take both ELEN E4411: ELEN E4503: Sensors, actuators, analysis and computation. to fulfill this requirement. 4. Two additional courses such as other ecology of earth resources; EAIA Fundamentals of photonics and ELEN and electromechanical systems; 5. At least two of the four courses used courses from no. 2 and 3; ELEN W4200: Alternative energy resources; E6412: Lightware devices (or an ELEN E6151: Surface physics and Specialization in Networking to fulfill requirements 3 and 4 must E6350: VLSI design laboratory; ELEN INAF U6057 Electricity markets; E&M course, such as APPH E4300: analysis of electronic materials; ELEN Advisers: Professors Predrag Jelenkovic, be 6000-level ELEN, EECS, CSEE, or E6304: Topics in electronic circuits; INAF U6072: Energy systems Applied electrodynamics or PHYS E6331: Principles of semiconductor Javad Ghaderi, Ethan Katz-Bassett, EEOR courses. ELEN E6318: Microwave circuit fundamentals; SUMA K4135: Energy GR6092: Electromagnetic theory). physics, I; ELEN E6332: Principles Debasis Mitra, Gil Zussman, Xiaofan design; ELEN E9303: Seminar in analysis for energy efficiency; INAF 3. One more device/circuits/photonics of semiconductor physics, II; ELEN (Fred) Jiang Specialization in Wireless and electronic circuits. U6065: The economics of energy; course such as: ELEN E6413: E6333: Semiconductor device Mobile Communications 5. At least one additional approved INAF U6061: Global energy policy; Lightwave systems; ELEN E6414: physics; ELEN E6945: Nanoscale 1. Satisfy M.S. degree requirements. Adviser: Professors Gil Zussman, course in integrated circuits and INAF U6242: Energy policy; INAF Photonic integrated circuits; ELEN fabrication and devices. 2. One basic networking course from Predrag Jelenkovic, Xiaodong Wang systems or a related area. U6135: Renewable energy markets E4314: Communication circuits; 4. At least two other approved courses the following: ELEN E6761: Computer and policy. ELEN E4488: Optical systems; ELEN in devices or a related area. Options communication networks I, CSEE 1. Satisfy M.S. degree requirements. Specialization in Smart Electric E6488: Optical interconnects and also include courses outside EE such W4119: Computer networks. 2. One basic circuits course such as: Energy Specialization in Systems Biology interconnection networks; ELEN as APPH E4090: Nanotechnology; 3. One basic systems or analytical ELEN E4312: Analog electric circuits; Advisers: Professors Matthias Preindl, and Neuroengineering E4193: Modern display science and APPH E4100: Quantum physics of course from the following: Systems ELEN E4314: Communication Xiaofan (Fred) Jiang, Gil Zussman, Advisers: Professors Dimitris technology. matter; APPH E4110: Modern optics; courses: CSEE E4140: Networking circuits; ELEN E6314: Advanced Kenneth Shepard, Xiaodong Wang Anastassiou, Christine Hendon, 4. At least two additional approved CHAP E4120: Statistical mechanics; laboratory; COMS W4113: communication circuits; ELEN E6312: Pedrag Jelenkovic, Aurel A. Lazar, courses in photonics or a related APPH E4112: Laser physics; APPH Fundamentals of large-scale Advanced analog ICs. 1. Satisfy M.S. degree requirements. Nima Mesgarani, Kenneth Shepard, area. Options also include courses E4130: Physics of solar energy; distributed systems; COMS W4118: 3. Two communications or networking 2. Take at least two power conversion Xiaodong Wang outside EE such as APPH E4090: APPH E6081: Solid state physics, Operating systems I; Analytical courses such as: CSEE W4119: or power systems courses from: Nanotechnology; APPH E4100: courses: ELEN E6772: Topic: Computer networks; ELEN E4702: ELEN E4361: Power electronics; 1. Satisfy M.S. degree requirements. Quantum physics of matter; APPH I; APPH E6082: Solid state physics, network algorithms; ELEN E6950: Digital communications; ELEN ELEN E6902 Renewable power 2. Take both ECBM E4060: Introduction E4110: Modern optics; CHAP E4120: II; APPH E6091: Magnetism and Wireless and mobile networking, E4703: Wireless communications; systems; ELEN E6904: Motor drive to genomic information science Statistical mechanics; APPH E4112: magnetic materials; APPH E6110: I; CSEE E6180: Modeling and ELEN E6711: Stochastic signals systems; ELEN E4511: Power and technology and BMEB W4020: Laser physics; APPH E4130: Physics Laser interactions with matter; performance evaluation. and noise; ELEN E4810: Digital systems analysis and control; ELEN

ENGINEERING 2020–2021 ENGINEERING 2020–2021 Corequisite: CSEE W3827. Recommended techniques. Small-signal models. Single-stage and systems. Continuous-time systems. Time Prerequisite: ELEN E3801. Topics include basic ECBM E4090x or y Brain computer interfaces 146 MSAE E4202: Thermodynamics and 147 reactions in solids; MSAE E4206: preparation: ELEN E1201 or equivalent. transistor amplifiers. Analysis and design of domain analysis, convolution. Frequency domain cell biophysics, active conductance and the (BCI) laboratory CMOS logic gates. A/D and D/A converters. 3 pts. Lect: 2. Lab: 3. Professor Mesgarani. Electronic and magnetic properties Companion lab course for CSEE W3827. analysis, transfer functions. Fourier series. Fourier Hodgkin-Huxley model, simple neuron models, ion Experiments cover such topics as logic gates; and Laplace transforms. Discrete-time systems channel models and synaptic models, statistical Prerequisites: ELEN E3801. Hands-on of solids; MSAE E4207: Lattice ELEN E3390y Electrical engineering senior flip-flops; shift registers; counters; combinational and the Z transform. models of spike generation, Wilson-Cowan experience with basic neural interface vibrations and crystal defects; design project logic circuits; sequential logic circuits; model of cortex, large-scale electrophysiological technologies. Recording EEG 3 pts. Lab: 6. Professor Vallancourt. CSEE W3827x and y Fundamentals of MSAE E6120: Grain boundaries and programmable logic devices. The lab generally recording methods, sensorimotor integration and (electroencephalogram) signals using data Prerequisites: ELEN E3399 and completion of computer systems interfaces; MSAE E6220: Crystal meets on alternate weeks. optimal state estimation, operant conditioning acquisition systems (noninvasive, scalp most other required EE courses. Students work 3 pts. Lect: 3. Professor Kim. physics; MSAE E6229: Energy and of neural activity, nonlinear modeling of neural recordings). Real-time analysis and monitoring ELEN E3083y Electronic circuits laboratory in teams to specify, design, implement and test Prerequisites: An introductory programming particle beam processing of materials; systems, sensory systems: visual pathway and of brain responses. Analysis of intention and 1 pt. Lab: 3. Professor Kostic. an engineering prototype. Involves technical as course. Fundamentals of computer organization MSAE E6225: Techniques in X-ray somatosensory pathway, neural encoding model: perception of external visual and audio signals. Prerequisite: ELEN E3081. Corequisite: ELEN and digital logic. Boolean algebra, Karnaugh and neutron diffraction. well as non-technical considerations, such as spike triggered average (STA) and spike triggered E3331. Companion lab course for ELEN maps, basic gates and components, flip-flops CSEE W4119x and y Computer networks manufacturability, impact on the environment, covariance (STC) analysis, neuronal response to E3331. Experiments cover such topics as and latches, counters and state machines, basics 3 pts. Lect: 3. Professor Rubenstein. economics, engineering standards, and other real- electrical micro-stimulation, DBS for Parkinson’s macromodeling of nonidealities of opamps of combinational and sequential digital design. Corequisite: IEOR E3658 or SIEO W3600 or COURSES IN ELECTRICAL world constraints. Projects are presented publicly disease treatment, motor neural prostheses, and using SPICE; Schmitt triggers and astable Assembly language, instruction sets, ALUs, equivalents. Introduction to computer networks ENGINEERING by each design team in a school-wide expo. sensory neural prostheses. multivibrations using opamps and diodes; logic single-cycle and multicycle processor design, and the technical foundations of the internet, ELEN E1101x or y The digital information age inverters and amplifiers using bipolar junction ELEN E3399x Electrical engineering practice introduction to pipelined processors, caches, and ECBM E4040x or y Neural networks and deep including applications, protocols, local area 3 pts. Lect: 3. Professor Vallancourt. transistors; logic inverters and ring oscillators 1 pt. Professor Vallancourt. virtual memory. learning networks, algorithms for routing and congestion An introduction to information transmission and using MOSFETs; filter design using opamps. The Design project planning, written and oral 3 pts. Lect: 3. Professor Kostic. control, security, elementary performance ELEN E3990x, y or s Fieldwork storage, including technological issues. Binary lab generally meets on alternate weeks. technical communication, the origin and role Prerequisites: BMEB W4020 or BMEE E4030 evaluation. Several written and programming 1–2 pts. Members of the faculty. numbers; elementary computer logic; digital of standards, engineering ethics, and practical or ECBM E4090 or ELEN E4750 or COMS assignments required. ELEN E3084x Signals and systems laboratory Prerequisites: Obtained internship and approval speech and image coding; basics of compact aspects of engineering as a profession, such W4771 or an equivalent. Developing features from a faculty adviser. May be repeated for credit, CSEE W4121y Computer systems for data disks, telephones, modems, faxes, UPC bar 1 pt. Lab: 3. Professor X. Wang. and internal representations of the world, as career development and societal and but no more than 3 total points may be used for science codes, and the World Wide Web. Projects include Corequisite: ELEN E3801. Companion lab artificial neural networks, classifying handwritten environmental impact. Generally taken senior degree credit. Only for Electrical Engineering and 3 pts. Lect: 3. Professor Cidon. course for ELEN E3801. Experiments cover digits with logistics regression, feedforward implementing simple digital logic systems and Web year just before ELEN E3390. Computer Engineering undergraduate students Prerequisites: Background in Computer System topics such as: introduction and use of MATLAB deep networks, back propagation in multilayer pages. Intended primarily for students outside who include relevant off-campus work experience Organization and good working knowledge of C/ for numerical and symbolic calculations; ELEN E3401y Electromagnetics perceptrons, regularization of deep or distributed the School of Engineering and Applied Science. as part of their approved program of study. Final C++. Corequisites: CSOR W4246, STAT GU4203, linearity and time invariance; continuous-time 4 pts. Lect: 3. Professor Kash. The only prerequisite is a working knowledge of report and letter of evaluation required. May not models, optimization for training deep models, or equivalent approved by faculty adviser. convolution; Fourier-series expansion and signal Prerequisite: MATH UN1201 or APMA E2000, elementary algebra. be used as technical or nontechnical electives convolutional neural networks, recurrent and Introduction to computer distributed systems with reconstruction; impulse response and transfer PHYS UN1402 or PHYS UN1602, or equivalents. or to satisfy any other Electrical Engineering or recursive neural networks, deep learning in emphasis on warehouse scale computing systems. ELEN E1201x and y Introduction to electrical function; forced response. The lab generally Basic field concepts. Interaction of time-varying Computer Engineering major requirements. May speech, and object recognition. Topics include fundamental tradeoffs in computer engineering meets on alternate weeks. electromagnetic fields. Field calculation of not be taken for pass/fail credit or audited. systems, hardware and software techniques for 3.5 pts. Lect: 3. Lab:1. Professor Vallancourt. ECBM E4060x Introduction to genomic ELEN E3106x Solid-state devices and lumped circuit parameters. Transition from information science and technology exploiting instruction-level parallelism, data-level Prerequisite: MATH UN1101. Basic concepts of ELEN E3998x and y Projects in electrical parallelism and task level parallelism, scheduling, materials electrostatic to quasistatic and electromagnetic 3 pts. Lect: 3. Professor Anastassiou. electrical engineering. Exploration of selected engineering caching, prefetching, network and memory 3.5 pts. Lect: 3. Recit: 1. Professor Kymissis. regimes. Transmission lines. Energy transfer, Introduction to the information system topics and their application. Electrical variables, 0 to 3 pts. Members of faculty. architecture, latency and throughput optimizations, Prerequisite: MATH UN1201 or APMA E2000 dissipation, and storage. Waveguides. Radiation. paradigm of molecular biology. Representation, circuit laws, nonlinear and linear elements, Prerequisite: Requires approval by a faculty specializations, and introduction to programming or equivalent. Corequisite: PHYS UN1403 or organization, structure, function and manipulation ideal and real sources, transducers, operational EEME E3601x Classical control systems member who agrees to supervise the work. May be data center computers. amplifiers in simple circuits, external behavior PHYS UN2601 or equivalent. Crystal structure 3 pts. Lect: 3. Professor Longman. repeated for credit, but no more than 3 total points of the biomolecular sequences of nucleic and energy band theory of solids. Carrier of diodes and transistors, first order RC and RL Prerequisite: MATH UN2030. Analysis and may be used for degree credit. Independent project acids and proteins. The role of enzymes and CSEE W4140x or y Networking laboratory concentration and transport in semiconductors. 3 pts. Lect: 3. Professor Zussman. circuits. Digital representation of a signal, digital design of feedback control systems. Transfer involving laboratory work, computer programming, gene regulatory elements in natural biological P-n junction and junction transistors. Prerequisite: CSEE W4119 or equivalent. In this logic gates, flip-flops. A lab is an integral part of functions; block diagrams; proportional, rate, and analytical investigation, or engineering design. functions as well as in biotechnology and Semiconductor surface and MOS transistors. genetic engineering. Recombination and course, students learn how to put “principles the course. Required of electrical engineering and integral controllers; hardware; implementation. Optical effects and optoelectronic devices. BMEB W4020x Computational neuroscience: other macromolecular processes viewed as into practice,” in a hands-on-networking lab computer engineering majors. Routh stability criterion, root locus, Bode and Fabrication of devices and the effect of process circuits in the brain mathematical operations with simulation and course. The technologies and protocols of the Nyquist plots, compensation techniques. ELEN E3043x Solid state, microwave, and variation and distribution statistics on device and 3 pts. Lect: 3. Professor Lazar. visualization using simple computer programming. internet are covered, using equipment currently fiber optics laboratory circuit performance. ELEN E3701y Introduction to communication Prerequisite: ELEN E3801 or BIOL UN3004. This course shares lectures with ECBM E3060, available to large internet service providers 3 pts. Lect: 1. Lab: 6. Professor W. Wang. systems The biophysics of computation: modeling but the work requirements differ somewhat. such as CISCO routers and end-systems. A set ELEN E3201x Circuit analysis Prerequisites: ELEN E3106 and ELEN E3401. 3 pts. Lect: 3. Professor Kalet. biological neurons, the Hodgkin-Huxley neuron, of laboratory experiments provides hands-on 3.5 pts. Lect: 3. Recit: 1. Professor Zukowski. ECBM E4070y Computing with brain circuits Optical electronics and communications. Prerequisite: ELEN E3801. Corequisite: IEOR modeling channel conductances and synapses experience with engineering wide-area networks Prerequisite: ELEN E1201 or equivalent. of model organisms Microwave circuits. Physical electronics. E3658. A basic course in communication theory, as memristive systems, bursting neurons and and familiarizes students with the Internet Corequisite: MATH UN1201 or APMA E2000. A 3 pts. Lect: 3. Professor Lazar. central pattern generators, I/O equivalence and Protocol (IP), Address Resolution Protocol ELEN E3081x Circuit analysis laboratory course on analysis of linear and nonlinear circuits stressing modern digital communication systems. Prerequisites: ELEN E3801 or BIOL W3004, and spiking neuron models. Information representation (ARP), Internet Control Message Protocol 1 pt. Lab: 3. Professor Zukowski. and their applications. Formulation of circuit Nyquist sampling, PAM and PCM/DPCM systems, Python programming experience, or instructor's and neural encoding: stimulus representation (ICMP), User Datagram Protocol (UDP) and Prerequisite: ELEN E1201 or equivalent. time division multiplexing, high frequency digital permission. Building the functional map of the fruit equations. Network theorems. Transient response with time encoding machines, the geometry of Corequisite: ELEN E3201. Companion lab course (ASK, OOK, FSK, PSK) systems, and AM and fly brain. Molecular transduction and spatio-temporal Transmission Control Protocol (TCP), the of first and second order circuits. Sinusoidal time encoding, encoding with neural circuits with for ELEN E3201. Experiments cover such topics FM systems. An introduction to noise processes, encoding in the early visual system. Predictive Domain Name System (DNS), routing protocols steady state-analysis. Frequency response of feedback, population time encoding machines. as: use of measurement instruments; HSPICE detecting signals in the presence of noise, coding in the Drosophila retina. Canonical circuits (RIP, OSPF, BGP), network management linear circuits. Poles and zeros. Bode plots. Two- Dendritic computation: elements of spike simulation; basic network theorems; linearization of Shannon’s theorem on channel capacity, and in motion detection. Canonical navigation circuits protocols (SNMP), and application-level protocols port networks. processing and neural computation, synaptic nonlinear circuits using negative feedback; op-amp elements of coding theory. in the central complex. Molecular transduction (FTP, TELNET, SMTP). ELEN E3331y Electronic circuits plasticity and learning algorithms, unsupervised and combinatorial encoding in the early olfactory circuits; integrators; second order RLC circuits. ELEN E4193x or y Modern display science 3 pts. Lect: 3. Professor Kostic. ELEN E3801x Signals and systems learning and spike time-dependent plasticity, basic system. Predictive coding in the antennal lobe. The The lab generally meets on alternate weeks. and technology Prerequisites: ELEN E3201. Operational 3.5 pts. Lect: 3. Professor X. Wang. dendritic integration. Projects in MATLAB. functional role of the mushroom body and the lateral 3 pts. Lect: 3. Professor Kymissis. ELEN E3082y Digital systems laboratory amplifier circuits. Diodes and diode circuits. Corequisite: MATH UN1201 or APMA E2000. horn. Canonical circuits for associative learning and BMEE E4030y Neural control engineering Prerequisites: Linear algebra, differential 1 pt. Lab: 3. Professor Shepard. Modeling, description, and classification of signals innate memory. Projects in Python. MOS and bipolar junction transistors. Biasing 3 pts. Lect: 3. Not offered in 2020–2021.

ENGINEERING 2020–2021 ENGINEERING 2020–2021 equations, and basic semiconductor physics. prototyping of a PDP-8 processor. High-level semiconductors: generation, recombination, and modern-based digital control laws. Digital system Prerequisites: ELEN E3801 and COMS representations. Applications to circuits and devices, 148 149 Introduction to modern display systems in and assembly languages, I/O, interrupts, injection; heterostructures; absorption and gain identification. W3134 or similar, recommended. Methods for to communication, control, filtering, and prediction. an engineering context. The basis for visual datapath and control design, pipelining, coefficients. Semiconductor photon sources: LEDs; deploying signal and data processing algorithms EEOR E4650x or y Convex optimization for CSEE W4823x or y Advanced logic design perception, image representation, color busses, memory architecture. Programmable semiconductor optical amplifiers; homojunction on contemporary general purpose graphics electrical engineering 3 pts. Lect: 3. Professor Nowick. space, metrics of illumination. Physics of logic and hardware prototyping with FPGAs. and heterojunction laser diodes. Semiconductor processing units (GPGPUs) and heterogeneous 3 pts. Lect: 3. Prerequisite: CSEE W3827 or equivalent. An luminescence, propagation and manipulation Fundamentals of VHDL for register-transfer photon detectors: p-n, p-i-n, and heterostructure computing infrastructures. Using programming Prerequisite: ELEN E3801 or instructor’s introduction to modern digital system design. of light in anisotropic media, emissive displays, level design. Testing and validation of hardware. photo diodes; avalanche photodiodes. languages such as OpenCL and CUDA for and spatial light modulators. Fundamentals Hands-on use of industry CAD tools for permission. Theory of convex optimization; computational speedup in audio, image, and Advanced topics in digital logic: controller of display addressing, the Alt-Pleshko simulation and synthesis. ELEN E4488x Optical systems numerical algorithms; applications in circuits, video processing and computational data synthesis (Mealy and Moore machines); adders theorem, multiple line addressing. Large area 3 pts. Lect: 3. Professor Hendon. communications, control, signal processing and analysis. Significant design project. and multipliers; structured logic blocks (PLDs, ELEN E4361x or y Power electronics electronics, fabrication, and device integration of Prerequisite: ELEN E3401 or equivalent. power systems. PALs, ROMs); iterative circuits. Modern design 3 pts. Lect: 3. Professor Preindl. Introduction to optical systems based on physical EECS E4764 Internet of things—intelligent methodology: register transfer level modeling commercially important display types. A series of ELEN E4702x or y Digital communications Prerequisites: ELEN E3801 and E3331. design and engineering principles. Fundamental and connected systems (RTL); algorithmic state machines (ASMs); short laboratories will reinforce material from the 3 pts. Lect: 3. Professor Raghavan. Introduction to power electronics; power geometrical and wave optics with specific 3 pts. Lect 3. Professor Jiang. introduction to hardware description languages lectures. Enrollment may be limited. semiconductor devices: power diodes, thyristors, Prerequisite: ELEN E3701 or equivalent. Digital Prerequisite: Knowledge of programming emphasis on developing analytical and numerical (VHDL or Verilog); system-level modeling and commutation techniques, power transistors, communications for both point-to-point and or instructor's permission. Recommended: ELEN E4301y Introduction to semiconductor tools used in optical engineering design. Focus simulation; design examples. power MOSFETs, Triac, IGBTs, etc., and switch switched applications is further developed. Optimum ELEN E4703, CSEE W4119, CSEE W4840, devices on applications that employ optical systems and 3 pts. Lect: 3. Professor Laibowitz or Teherani. selection; nonsinusoidal power definitions and receiver structures and transmitter signal shaping or related courses. Cyber-physical systems CSEE W4824x or y Computer architecture networks, including examples in holographic Prerequisite: ELEN E3106 or equivalent. computations, modeling, and simulation; half- for both binary and M-ary signal transmission. An and Internet of Things. Various sensors and 3 pts. Lect: 3. Professor Sethumadhavan. imaging, tomography, Fourier imaging, confocal Semiconductor physics. Carrier injection and wave rectifiers; single-phase, full-wave rectifiers; introduction to block codes and convolutional codes, actuators, communication with devices through Prerequisite: CSEE W3827 or equivalent. microscopy, optical signal processing, fiber optic recombination. P-n junction and diodes: Schottky three-phase rectifiers; AC voltage controllers; with application to space communications. serial protocols and buses, embedded hardware, Focuses on advanced topics in modern DC/DC buck, boost, and buck-boost converters; communication systems, optical interconnects wired and wireless networks, embedded platforms barrier and heterojunctions, solar cells and light- ELEN E4703y Wireless communications computer architecture, illustrated by recent case discontinuous conduction mode of operation; and networks. such as Arduino and smartphones, web services emitting diodes. Junction and MOS field-effect 3 pts. Lect: 3. Professor Samardzia. studies. Fundamentals of quantitative analysis. DC power supplies: flyback, forward converter; on end devices and in the cloud, visualization transistors, bipolar transistors. Tunneling and ELEN E4510x or y Solar energy and smart Prerequisite: ELEN E3701 or equivalent. Pipelined, out-of-order, and speculative DC/AC inverters, PWM techniques; three-phase and analytics on sensor data, end-to-end IoT charge-transfer devices. grid power systems Wireless communication systems. System design execution. Superscalar, VLIW and vector inverters. applications. Group projects to create working 3 pts. Lect: 3. Professors Kymissis and Schwartz. processors. Embedded processors. Memory ELEN E4312x Analog electronic circuits fundamentals. Trunking theory. Mobile radio CPS/IoT system. BMEE E4400x Wavelet applications in Prerequisite: Background in circuits. Inorganic hierarchy design. Multiprocessors and thread- 3 pts. Lect: 3. Professor Dickson. propagation. Reflection of radio waves. Fading biomedical image and signal processing solar cell semiconductor physics. Single and EECS E4766 Internet of things—engineering level parallelism. Synchronization and cache Prerequisites: ELEN E3331 and E3801. and multipath. Modulation techniques; signal 3 pts. Lect: 3. innovations and commercialization coherence protocols. Interconnection networks. Differential and multistage amplifiers; small- tandem junction design. Measures of spectral space; probability of error, spread spectrum. Prerequisites: APMA E2101 or E3101 or 3 pts. Lect: 3. Professor Kostic. signal analysis; biasing techniques; frequency and energy efficiency. Introduction to organic Diversity. Multiple access. equivalent. An introduction to methods of Prerequisites: Basic programming and instructor’s ELEN E4830y Digital image processing response; negative feedback; stability criteria; solar cells and thin film inorganic cells. wavelet analysis and processing techniques ELEN E4720x or y Machine learning for permission. Deep dive into a couple of selected 3 pts. Lect: 3. Professor Hendon. frequency compensation techniques. Analog Batteries and other energy storage systems. for the quantification of biomedical images and signals, information, and data topics/use-cases from the area of Internet of Introduction to the mathematical tools and layout techniques. An extensive design project is Introduction to legacy power networks: Single signals. Topics include frames and overcomplete 3 pts. Lect: 3. Professor Paisley. Things. Coverage of the topic from device algorithmic implementation for representation and an integral part of the course. phase equivalents to three-phase networks. Prerequisites: Basic linear algebra and calculus. representations, multiresolution algorithms for to the cloud, with focus on practical aspects. processing of digital pictures, videos, and visual Reactive and real power. Equivalent circuits Intro-level courses in probability and statistics. ELEN E4314y Communication circuits denoising and image restoration, multiscale Innovative product definition, product development, sensory data. Image representation, filtering, of synchronous machines, transformers, and Programming. Introduction to supervised and 3 pts. Lect: 3. Professor Tsividis. texture segmentation and classification methods marketing, commercialization, and monetization. transform, quality enhancement, restoration, transmission lines. Smart grid technology: unsupervised techniques for machine learning. Cross-disciplinary coverage: EE, MechE, CS, feature extraction, object segmentation, Prerequisite: ELEN E4312. Principles of for computer-aided diagnosis. Control and management of distributed solar Probabilistic and non-probabilistic approaches. electronic circuits used in the generation, Bioengineering, marketing, business, design. motion analysis, classification, and coding for ELEN E4401x Wave transmission and fiber energy and other intermittent renewable power Focus on classification and regression models, transmission, and reception of signal waveforms, Building products and startups in the IoT data compression. A series of programming optics sources connected to legacy power networks. clustering methods, matrix factorization and domain. Collaboration between the Engineering as used in analog and digital communication sequential models. Linear and logistic regression, assignments reinforces material from the lectures. 3 pts. Lect: 3. Professor Diament. Microgrid concept. “Small world” networks and School, Business School, industry experts, and systems. Nonlinearity and distortion; power support vector machines, boosting, K-means Prerequisite: ELEN E3401 or equivalent. Waves fault management. Communication over power engagement in IoT activities in NYC. Collaborative ELEN E4835 Introduction to adaptive signal amplifiers; tuned amplifiers; oscillators; clustering, mixture models, expectation- and Maxwell’s equations. Field energetics, lines. Smart metering. project by groups of students from different representations multipliers and mixers; modulators and maximization algorithm, and hidden Markov disciplines. This course shares lectures with E6766, 3 pts. Lect: 2. Professor Wright. demodulators; phase-locked loops. An extensive dispersion, complex power. Waves in dielectrics ELEN E4511x or y Power systems analysis models. Algorithmic techniques for optimization, but the expected project complexity is lower. Prerequisites: Linear algebra (APMA E3101, MATH design project is an integral part of the course. and in conductors. Reflection and refraction. and control such as gradient and coordinate descent methods. UN2010, or equivalent), probability (IEOR E3658 Oblique incidence and total internal reflection. 3 pts. Lect: 3. ELEN E4810x Digital signal processing EECS E4321x Digital VLSI circuits BMEE E4740y Bioinstrumentation or equivalent), and signals and systems (ELEN Transmission lines and conducting waveguides. Prerequisites: ELEN E3201 and E3401, or 3 pts. Lect: 3. Professor Wright. 3 pts. Lect: 3. Professor Shepard. 3 pts. Lect: 1. Lab: 3. Professor Kyle. E3801), or instructor’s permission. Introduces Planar and circular dielectric waveguides; equivalents, or instructor’s permission. Modeling Prerequisite: ELEN E3801. Digital filtering in Recommended preparation: ELEN E3106, Prerequisites: COMS W1005, ELEN E1201. numerical tools for adaptive processing of signals. integrated optics and optical fibers. Hybrid and of power networks, steady-state and transient time and frequency domain, including properties E3331, and CSEE W3827. Design and analysis Hands-on experience designing, building, and LP modes. Graded-index fibers. Mode coupling; of discrete-time signals and systems, sampling Signal representations, sparsity in overcomplete of high speed logic and memory. Digital CMOS behaviors, control and optimization, electricity testing the various components of a benchtop wave launching. theory, transform analysis, system structures, bases. Techniques for sparse recovery, and BiCMOS device modeling. Integrated circuit market, and smart grid. cardiac pacemaker. Design instrumentation to IIR and FIR filter design techniques, the discrete applications to inpainting and denoising. Adaptive fabrication and layout. Interconnect and parasitic ELEN E4411x Fundamentals of photonics measure biomedical signals as well as to actuate EEME E4601y Digital control systems Fourier transform, fast Fourier transforms. representations: principal component analysis, elements. Static and dynamic techniques. 3 pts. Lect: 3. Professor Lipson. 3 pts. Lect: 3. Professor Longman. living tissues. Transducers, signal conditioning clustering and vector quantization, dictionary Worst-case design. Heat removal and I/O. Yield Prerequisite: ELEN E3401 or equivalent. Planar Prerequisite: ELEN E3801 or EEME E3601, electronics, data acquisition boards, the Arduino ELEN E4815y Random signals and noise learning. Source separation: independent and circuit reliability. Logic gates, pass logic, resonators. Photons and photon streams. or equivalent. Real-time control using digital microprocessor, and data acquisition and processing 3 pts. Lect: 3. Professor Kalet. component analysis and matrix factorizations. latches, PLAs, ROMs, RAMs, receivers, drivers, Photons and atoms: energy levels and band computers. Solving scalar and state-space using MATLAB will be covered. Various devices will Prerequisite: IEOR E3658 or equivalent. Signal classification: support vector machines repeaters, sense amplifiers. structure; interactions of photons with matter; difference equations. Discrete equivalents of be discussed throughout the course, with laboratory Characterization of stochastic processes as and boosting, learning with invariances. Hashing absorption, stimulated and spontaneous work focusing on building an emulated version of a models of signals and noise; stationarity, ergodicity, EECS E4340x Computer hardware design continuous systems fed by holds. Z-transfer and signal retrieval. Case studies from image emission; thermal light, luminescence light. cardiac pacemaker. Lab required. 3 pts. Lect: 2. Lab: 3. Professor Sethumadhavan. functions. Creating closed-loop difference correlation functions, and power spectra. Gaussian processing, audio, multimedia. Laser amplifiers: gain, saturation, and phase equation models by Z-transform and state processes as models of noise in linear and nonlinear Prerequisites: ELEN E3331 and CSEE W3827. EECS E4750x or y Heterogeneous computing CSEE W4840y Embedded systems shift; rate equations; pumping. Lasers: theory of variable approaches. The Nyquist frequency systems; linear and nonlinear transformations Practical aspects of computer hardware design for signal and data processing 3 pts. Lect: 3. Professor Edwards. oscillation; laser output characteristics. Photons in of random processes; orthogonal series through the implementation, simulation, and and sample rate selection. Classical- and 3 pts. Lect: 2. Professor Marianetti. Prerequisite: CSEE W4823 or equivalent.

ENGINEERING 2020–2021 ENGINEERING 2020–2021 Embedded system design and implementation permission. Various topics in the area of gene circuit design. Rules for gene regulation. learning. Content varies from year to year, and frequency compensation techniques; noise and non-clocked combinational logic styles. 150 151 combining hardware and software. I/O, interfacing, wireless and mobile networks and systems. Random networks and multiple time scales. different topics rotate through the course numbers in circuits and low-noise design; mismatch in Timing circuits: latches and flip-flops, phase- and peripherals. Weekly laboratory sessions and Functionalities in the layers above the physical Biological information processing. Numerical 6070 to 6079. circuits and low-offset design. Computer-aided locked loops, delay-locked loops. SRAM and layer. The latest wireless networking design analysis techniques are used in homework or a DRAM memory circuits. Modeling and analysis term project on design of a microprocessor-based and simulation techniques. Major project(s) in ELEN E6080–6089x or y Topics in systems design project. of on-chip interconnect. Power distribution embedded system including at least one custom challenges, protocols, proposed algorithms, MATLAB. biology peripheral. Knowledge of C programming and and applications. Includes several hands-on and power-supply noise. Clocking, timing, and 3 pts. Lect: 2. Members of the faculty. ELEN E6314x Advanced communication experiments as well as a final project. EEBM E6020y Methods of computational synchronization issues. Circuits for chip-to-chip digital logic required. Prerequisite: Instructor’s permission. Selected circuits neuroscience electrical communication. Advanced technology CSEE E4868x or y System-on-chip platforms ELEN E4998x or y Intermediate projects in advanced topics in systems biology. Content 3 pts. Lect: 2. 4.5 pts. Lect: 3. issues that affect circuit design. The class may 3 pts. Lect: 3. Professor Carloni. electrical engineering varies from year to year, and different topics Prerequisites: ELEN E4314 and E6312. Prerequisite: BMEB W4020 or instructor’s include a team circuit design project. Prerequisites: COMS W3157 and CSEE W3827 0–3 pts. Members of the faculty. permission. Formal methods in computational rotate through the course numbers 6080 to 6089. Overview of communication systems, modulation Design and programming of System-on-Chip and detection schemes. Receiver and transmitter EECS E6322x VLSI Hardware architecture for Prerequisite: Requires approval by a faculty neuroscience including methods of signal EEBM E6090–6099x or y Topics in computational (SoC) platforms. Topics include overview of architectures. Noise, sensitivity, and dynamic signal processing and machine learning member who agrees to supervise the work. processing, communications theory, information neuroscience and neuroengineering technology and economic trends, methodologies range. Nonlinearity and distortion. Low-noise 3 pts. Lect: 3. Professor Seok. May be repeated for credit, but no more than theory, systems and control, system identification 3 pts. Lect: 2. Members of the faculty. and supporting CAD tools for system-level RF amplifiers, mixers, and oscillators. Phase- Prerequisites: CSEE W3827 and ELEN E3801. 3 total points may be used for degree credit. and machine learning. Molecular models of Prerequisite: Instructor’s permission. Selected design; models of computation, the SystemC locked loops and frequency synthesizers. Recommended: ELEN E4810. Design of Substantial independent project involving transduction pathways. Robust adaptation and advanced topics in computational neuroscience language, transaction-level modeling, hardware- Typical applications discussed include wireless digital VLSI hardware for various digital signal laboratory work, computer programming, integral feedback. Stimulus representation and and neuroengineering. Content varies from year software partitioning, high-level synthesis, system RF transceivers or data links. Computer-aided processing and machine learning algorithms. analytical investigation, or engineering design. groups. Stochastic and dynamical systems to year, and different topics rotate through the programming, on-chip communication, memory analysis techniques are used in homework(s) or Data flow graphs, iteration bounds, pipelining, organization, power management and optimization, models of spike generation. Neural diversity and course numbers 6090 to 6099. ELEN E6001x-E6002y Advanced projects in a design project. parallel architectures, retiming, unfolding/ ensemble encoding. Time encoding machines integration of programmable processor cores and electrical engineering CSEE E6180x or y Modeling and performance folding, systolic architectures, bit-level specialized accelerators. Case studies of modern 1–4 pts. Members of the faculty. and neural codes. Stimulus recovery with time evaluation ELEN E6316y Analog-digital interfaces in arithmetic, numerical and algorithmic strength SoC platforms for various classes of applications. VLSI Prerequisite: Requires approval by a faculty decoding machines. MIMO models of neural 3 pts. Lect: 2. Professor Misra. reductions, CORDIC, distributed arithmetic, FFT, computation. Synaptic plasticity and learning 3 pts. Lect: 3. Professor Dickson. ELEN E4896y Music signal processing member who agrees to supervise the work. Prerequisites: COMS W4118 and STAT GU4001 or neural network hardware, vector processors, algorithms. Major project(s) in MATLAB. Prerequisite: ELEN E4312 or equivalent. subwordparallel architecture, and SIMD. May 3 pts. Lect: 3. Professor Ellis. May be repeated for up to 6 points of credit. permission of the instructor. Introduction to queuing analysis and simulation techniques. Evaluation of Analog-to-digital and digital-to-analog conversion include a team circuit design project. Prerequisite: ELEN E3801, E4810, or the Graduate-level projects in various areas of BMEE E6030x Neural modeling and time-sharing and multiprocessor systems. Topics techniques for very large scale integrated circuits equivalent. An investigation of the applications electrical engineering and computer science. neuroengineering ELEN E6324x or y Principles of RF and include priority queuing, buffer storage, and disk and systems. Precision sampling; quantization; of signal processing to music audio, spanning In consultation with an instructor, each student 3 pts. Lect: 3. Professor Sajda. microwave measurement access, interference and bus contention problems, A/D and D/A converter architectures and the synthesis of musical sounds (including designs his or her project depending on the 3 pts. Lect: 3. Professor Shahramian. Prerequisites: ELEN E3801 and either APMA and modeling of program behaviors. metrics; Nyquist architectures; oversampling frequency modulation [FM], additive sinusoidal student’s previous training and experience. Prerequisite: ELEN E4314 or equivalent, or E2101 or E3101, or equivalent, or instructor’s architectures; correction techniques; system synthesis, and linear predictive coding Students should consult with a professor in their ELEN E6201x Linear system theory instructor's permission. Principles behind, permission. Engineering perspective on the considerations. A design project is an integral [LPC]), the modification of real and synthetic area for detailed arrangements no later than the 3 pts. Lect: 3. Professor Sun. and techniques related to, RF and microwave study of multiple levels of brain organization, part of this course. sounds (including reverberation and time/ last day of registration. from single neurons to cortical modules and Prerequisites: ELEN E3801 and APMA E3101, simulation and measurements. S parameters; pitch scaling), and the analysis of music or equivalents. Abstract objects, the concepts of ELEN E6318x or y Microwave circuit design simulations and measurements for small-signal ELEN E6003x and y Master's thesis systems. Mathematical models of spiking audio to extract musical information (including state. Definition and properties of linear systems. 3 pts. Lect: 3. Professor Baeyens. and large signal / nonlinear circuits in the time 3 pts. Members of the faculty. neurons, neural dynamics, neural coding, Characterization of linear continuous-time and Prerequisites: ELEN E3331 and E3401, and frequency domains; noise. pitch tracking, chord transcription, and music Prerequisites: A minimum of 3 points of credit in and biologically based computational learning. discrete-time, fixed, and time-varying systems. or equivalents. Introduction to microwave matching). Emphasis on practical, hands-on ELEN E6001 or E6002 advanced projects with Architectures and learning principles underlying ELEN E6331y Principles of semiconductor engineering and microwave circuit design. Review experimentation, with a wide range of software the same instructor, instructor's permission, and both artificial and biological neural networks. State-space description; fundamental matrix, physics, I implementations introduced and modified within completion of at least 12 points of credit in MS Computational models of cortical processing, calculation by computer and matrix methods. of transmission lines. Smith chart, S-parameters, 3 pts. Lect: 2. Professor Wang. the class. program with GPA of at least 3.5. Research in with an emphasis on the visual system. Modes in linear systems. Adjoint systems. microwave impedance matching, transformation Prerequisite: ELEN E4301. Designed for area of Electrical Engineering culminating in a Controllability and observability. Canonical and power combining networks, active and students interested in research in semiconductor ELEN E4900-4909x or y Topics in electrical Applications of principles in neuroengineering; verbal presentation and a written thesis document neural prostheses, neuromorphic systems and forms and decompositions. State estimators. passive microwave devices, S-parameter- materials and devices. Topics include energy and computer engineering approved by thesis instructor. Must obtain biomimetics. Course will include a computer Lyapunov’s method and stability. based design of RF and microwave amplifiers. bands: nearly free electron and tight-binding 3 pts. Lect: 2. Members of the faculty. permission from thesis instructor to enroll. Thesis simulation laboratory. A microwave circuit design project (using approximations, the k.p. method, quantitative Prerequisite: Instructor’s permission. Selected ELEN E6302x or y MOS transistors projects span at least two terms: ELEN E6001 microwave CAD) is an integral part of the course. calculation of band structures and their topics in electrical and computer engineering. ECBM E6040y Neural networks and deep 3 pts. Lect: 2. Professor Tsividis. or E6002 Advanced Project followed by E6003 applications to quantum structure transistors, Content varies from year to year, and different learning research. Prerequisite: ELEN E3106 or equivalent. ELEN E6320x or y Millimeter-wave IC design Master's Thesis with same instructor. Students photodetectors, and lasers; semiconductor topics rotate through the course numbers 4900 must use department recommended format for 3 pts. Lect: 3. Professor Lazar. Operation and modeling of MOS transistors. 3 pts. Lect: 3. Professor Krishnaswamy. statistics, Boltzmann transport equation, to 4909. thesis writing. Counts towards total amount of Prerequisite: ECBM E4040 or the equivalent. MOS two- and three-terminal structures. The Prerequisites: ELEN E3401 or equivalent, scattering processes, quantum effect in transport research credit in MS program. Regularized autoencoders, sparse coding and MOS transistor as a four-terminal device; general ELEN E4314 and E6312. Principles behind the ELEN E4944x or y Principles of device phenomena, properties of heterostructures. predictive sparse decomposition, denoising charge-sheet modeling; strong, moderate, and implementation of millimeter-wave (30GHz- microfabrication ELEN E6010y Systems biology: design Quantum mechanical treatment throughout. autoencoders, representation learning, manifold weak inversion models; short-and-narrow- 300GHz) wireless circuits and systems in 3 pts. Lect: 3. Professor Trevino. principles for biological circuits perspective on representation learning, channel effects; ion-implanted devices; scaling silicon-based technologies. Silicon-based ELEN E6332y Principles of semiconductor Science and technology of conventional and 4.5 pts. Lect: 3. Professor Jelenkovic. structured probabilistic models for deep considerations in VLSI; charge modeling; large- active and passive devices for millimeter- physics, II advanced microfabrication techniques for Prerequisite: ECBM E4060 or instructor’s learning, Monte Carlo methods, training and signal transient and small-signal modeling for wave operation, millimeter-wave low-noise 3 pts. Lect: 2. electronics, integrated and discrete components. permission. Beyond bioinformatics, cells as evaluating models with intractable partition quasistatic and nonquasistatic operation. amplifiers, power amplifiers, oscillators and Prerequisites: ELEN E3106 or ELEN E6331. Topics include diffusion; ion implantation, systems. Metabolic networks, transcription VCOs, oscillator phase noise theory, mixers and functions, restricted Boltzmann machines, ELEN E6312y Advanced analog integrated Optical properties including absorption thin-film growth including oxides and metals, regulatory networks, signaling networks. frequency dividers for PLLs. A design project is approximate inference, deep belief networks, circuits and emission of radiation, electron-phonon molecular beam and liquid-phase epitaxy; Deterministic and stochastic kinetics. an integral part of the course. deep learning in speech, and object recognition. 3 pts. Lect: 2. Professor Krishnaswamy. interactions, radiative and phonon-mediated optical and advanced lithography; and plasma Mathematical representation of reconstructed processes, excitons, plasmons, polaritons, carrier ECBM E6070-6079x or y Topics in Prerequisite: ELEN E4312. Integrated circuit EECS E6321y Advanced digital electronic and wet etching. networks. Network motifs. Signal transduction recombination and generation, and related optical neuroscience and deep learning device characteristics and models; temperature- circuits and neuronal networks. Robustness. devices, tunneling phenomena, superconductivity. EECS E4951y Wireless networks and systems 3 pts. Lect: 2. Members of the faculty. and supply-independent biasing; IC operational 3 pts. Lect: 2. Professor Seok. Bacterial chemotaxis and patterning in fruit fly Quantum mechanical treatment throughout, heavy 3 pts. Lect: 3. Professor Zussman. Prerequisites: the instructor's permission. Selected amplifier analysis and design and their Prerequisite: EECS E4321. Advanced topics in development. Kinetic proofreading. Optimal use of perturbation theory. Prerequisite: CSEE W4119 or instructor’s advanced topics in neuroscience and deep applications; feedback amplifiers, stability and the design of digital integrated circuits. Clocked

ENGINEERING 2020–2021 ENGINEERING 2020–2021 ELEN E6333y Semiconductor device physics Discussion of numerical techniques for modeling EEOR E6616x or y Convex optimization Bhattacharya bounds, convolutional codes, and the Things. Coverage of the topic from device W48XX, or ELEN E43XX course, or instructor’s 152 153 3 pts. Lect: 2. circuits, including beam propagation and finite 3 pts. Lect: 3. Professor Iyengar. Viterbi algorithm. to the cloud, with focus on practical aspects. permission. An interdisciplinary graduate-level Prerequisites: ELEN E3106 or ELEN E4301 difference codes, and design of other devices: Prerequisites: IEOR E6613 and EEOR E4650. Innovative product definition, product development, seminar on the design of distributed embedded ELEN E6718y Error correcting codes: or equivalent. Physics and properties of optical isolators, demultiplexers. marketing, commercialization, and monetization. Convex sets and functions, and operations classical and modern systems. System robustness in the presence semiconductors. Transport and recombination preserving convexity. Convex optimization Cross-disciplinary coverage: EE, MechE, CS, ELEN E6430x or y Applied quantum optics 3 pts. Lect: 2. Professor Ashikhmin. of highly variable communication delays and of excess carriers. Schottky, P-N, MOS, problems. Convex duality. Applications of convex Bioengineering, marketing, business, design. heterogeneous component behaviors. The 3 pts. Lect: 2. Prerequisite: IEOR E3658. Main concepts Building products and start-ups in the IoT and heterojunction diodes. Field effect and optimization problems ranging from signal study of the enabling technologies (VLSI Prerequisites: Background in electromagnetism of error control codes. Linear block codes. domain. Collaboration between the Engineering bipolar junction transistors. Dielectric and processing and information theory to revenue circuits, communication protocols, embedded (ELEN E3401, E4401, E4411, or PHYS GR6092) Elements of algebra: Galois fields. BCH and School, Business School, industry experts, and optical properties. Optical devices including management. Convex optimization in Banach processors, RTOSs), models of computation, and quantum mechanics (APPH E3100, Reed Solomon codes. Convolutional Codes. engagement in IoT activities in NYC. Collaborative semiconductor lamps, lasers, and detectors. spaces. Algorithms for solving constrained convex E4100, or PHYS GU402x). An introduction to Modern, capacity-achieving codes: Low Density project by groups of students from different and design methods. The analysis of modern ELEN E6350y VLSI design laboratory fundamental concepts of quantum optics and optimization problems. Parity Check codes, TURBO codes, and Polar disciplines. This course shares lectures with domain-specific applications including on-chip micro-networks, multiprocessor systems, fault- 3 pts. Lab: 3. Professor Kinget. quantum electrodynamics with an emphasis EECS E6690-6699x or y Topics in data-driven codes. EXIT Charts analysis. E4766, but a more complex project is expected. Prerequisites: ELEN E4321 and E4312, or on applications in nanophotonic devices. tolerant architectures, and robust deployment analysis and computation EECS E6720 Bayesian models for machine ELEN E6767x or y Internet economics, instructor’s permission. Design of a CMOS The quantization of the electromagnetic of embedded software. Research challenges 3 pts. Lect: 2. Members of the faculty. learning engineering, and the implications for society mixed-signal integrated circuit. The class divides field; coherent and squeezed states of light; such as design complexity, reliability, scalability, Prerequisite: the instructor's permission. Selected 3 pts. Lect: 3. Professor Paisley. 3 pts. Lect: 2. Professor Mitra. up into teams to work on mixed-signal integrated interaction between light and electrons in the advanced topics in data-driven analysis and safety, and security. The course requires Prerequisites: Basic calculus, linear algebra, Prerequisites: CSEE W4119 or ELEN E6761 circuit designs. The chips are fabricated to be language of quantum electrodynamics (QED); computation. Content varies from year to year, and substantial reading, class participation and a probability, and programming. Basic statistics recommended, and ability to comprehend and tested the following term. Lectures cover use optical resonators and cavity QED; low-threshold different topics rotate through the course numbers research project. and machine learning strongly recommended. track development of sophisticated models. of computer-aided design tools, design issues lasers; and entangled states of light. 6690 to 6699. Bayesian approaches to machine learning. Topics Mathematical models, analyses of economics ELEN E6850x Visual information systems specific to the projects, and chip integration ELEN E6488y Optical interconnects and ELEN E6711x Stochastic models in include mixed-membership models, latent factor and networking interdependencies in the internet. 3 pts. Lect: 2. issues. This course shares lectures with E4350, models, Bayesian nonparametric methods, probit interconnection networks information systems Topics include microeconomics of pricing and Prerequisite: ELEN E4830 or instructor’s but the complexity requirements of integrated classification, hidden Markov models, Gaussian 3 pts. Lect: 2. Professor Bergman. 4.5 pts. Lect: 3. Professor Baryshnikov. regulations in communications industry, game permission. Introduction to critical image circuits are higher. mixture models, model learning with mean-field Prerequisite: ELEN E4411 or E4488 or an Prerequisite: IEOR E3658. Foundations: theory in revenue allocations, ISP settlements, technologies in advanced visual information variational inference, scalable inference for Big ELEN E6412y Lightwave devices equivalent photonics course. Introduction to optical probability review, Poisson processes, discrete- network externalities, two-sided markets. Economic systems, such as content-based image Data. Applications include image processing, 3 pts. Lect: 2. Professor Woodward. interconnects and interconnection networks for time Markov models, continuous-time Markov principles in networking and network design, topic modeling, collaborative filtering, and databases, video servers, and desktop video Prerequisites: ELEN E4411. Electro-optics: digital systems. Fundamental optical interconnects decentralized vs. centralized resource allocation, models, stationarity, and ergodicity. The course recommendation systems. editors. Intended for graduate students. principles; electro-optics of liquid crystals and technologies, optical interconnection network presents a sample-path (time domain) treatment “price of anarchy,” congestion control. Case studies Topics include visual data representation and design, characterization, and performance photo-refractive materials. Nonlinear optics: of stochastic models arising in information ELEN E6761x Computer communication of topical internet issues. Societal and industry compression, content-based visual indexing and evaluation. Enabling photonic technologies second-order nonlinear optics; third-order systems, including at least one of the following networks I implications of internet evolution. retrieval, storage system design (data placement, nonlinear optics; pulse propagation and solitons. including free-space structures, hybrid and 3 pts. Lect: 3. Professor Ghaderi. areas: communications networks (queueing ELEN E6770–6779x or y Topics in networking scheduling, and admission control), compressed Acousto-optics: interaction of light and sound; monolithic integration platforms for photonic Prerequisites: IEOR E3658 or equivalent, or systems), biological networks (hidden Markov 3 pts. Lect: 2. Members of the faculty. video editing, and synchronization issues of acousto-optic devices. Photonic switching on-chip, chip-to-chip, backplane, and node-to- instructor’s permission. Recommended: CSEE models), Bayesian restoration of images (Gibbs Further study of areas such as communication stored video/audio signals. Programming projects and computing: photonic switches; all-optical node interconnects, as well as photonic networks W4119. Analytical approach to the design of fields), and electric networks (random walks). protocols and architectures, flow and congestion and final presentations are required. switches; bistable optical devices. Introduction on-chip. (data) communication networks. Necessary tools to fiber-optic communications: components of ELEN E6712x Communication theory control in data networks, performance evaluation ELEN E6860y Advanced digital signal EEME E6601x Introduction to control theory for performance analysis and design of network the fiber-optic link; modulation, multiplexing 3 pts. Lect: 3. in integrated networks. Content varies from year processing 3 pts. Lect: 3. Professor Longman. protocols and algorithms. Practical engineering and coupling; system performance; receiver Prerequisite: ELEN E4815, or equivalent, or to year, and different topics rotate through the 3 pts. Lect: 2. Professor Nguyen. Prerequisite: MATH UN2030. A graduate-level applications in layered internet protocols in sensitivity; coherent optical communications. instructor’s permission. Representation of course numbers 6770 to 6779. Prerequisite: ELEN E4810. This course is introduction to classical and modern feedback Data link layer, Network layer, and Transport bandlimited signals and systems. Coherent designed as an extension to ELEN E4810, ELEN E6413y Lightwave systems control that does not presume an undergraduate layer. Review of relevant aspects of stochastic ELEN E6820y Speech and audio processing and incoherent communications over Gaussian with emphasis on emerging techniques in the 3 pts. Lect: 2. Professor Feuer. background in control. Scalar and matrix processes, control, and optimization. and recognition channels. Basic digital modulation schemes. area of digital signal processing. Topics include Prerequisites: ELEN E4411. Recommended differential equation models, and solutions in 3 pts. Lect: 2. Professor Mesgarani. Intersymbol inference channels. Fading multipath EECS E6765 Internet of things—systems and multirate signal processing, multidimensional preparation: ELEN E6412. Fiber optics. Guiding, terms of state transition matrices. Transfer Prerequisite: ELEN E4810 or instructor’s channels. Carrier and clock synchronization. physical data analytics signal processing, short-time Fourier transform, dispersion, attenuation, and nonlinear properties functions and transfer function matrices, block 3 pts. Lect: 3. Professor Kostic. permission. Fundamentals of digital speech signal expansion in discrete and continuous time, of fibers. Optical modulation schemes. Photonic diagram manipulations, closed-loop response. ELEN E6713y Topics in communications Prerequisites: Knowledge of programming; ELEN processing and audio signals. Acoustic and filter banks, multiresolution analysis, wavelets, components, optical amplifiers. Semiconductor Proportional, rate, and integral controllers, 3 pts. Lect: 3. E4703 or related; or CSEE W4119; or instructor's perceptual basics of audio. Short-time Fourier and their applications to image compression and laser transmitters. Receiver design. Fiber optic and compensators. Design by root locus and Prerequisite: ELEN E6712 or E4702 or E4703 or permission. Internet of Things from the point analysis. Analysis and filter bank models. Speech telecommunication links. Nonregenerative frequency response. Controllability, observability. equivalent, or instructor’s permission. Advanced of view of data. Methods for data analytics to and audio coding, compression, and reconstruction. understanding. Other topics may be included to transmission using erbium-doped fiber amplifier Luenberger observers, pole placement, and topics in communications, such as turbo codes, understand trade-offs and partitioning between Acoustic feature extraction and classification. reflect developments in the field. LDPC codes, multiuser communications, network chains. Coherent detection. Local area networks. linear-quadratic cost controllers. cloud-based data-analytics and physical-device Recognition techniques for speech and other CSEE E6861y Computer-aided design of coding, cross-layer optimization, cognitive radio. Advanced topics in light wave networks. data analytics. Two-way interaction between sounds, including hidden Markov models. digital systems EEME E6602y Modern control theory Content may vary from year to year to reflect the data and physical devices to support a truly ELEN E6414y Photonic integrated circuits 3 pts. Lect: 2. Professor Nowick. 3 pts. Lect: 3. latest development in the field. ubiquitous, networked, and autonomous cyber- CSEE E6824y Parallel computer architecture 3 pts. Lect: 3. Prerequisites: (i) one semester of advanced Prerequisite: EEME E6601 or E4601 or ELEN physical ecosystem. System-focused design of 3 pts. Lect: 2. Photonic integrated circuits are important ELEN E6717x Information theory digital logic (CSEE W4823 or equivalent, or E6201, or instructor’s permission. Singular value architectures, algorithms, networks, protocols, Prerequisite: CSEE W4824. Parallel computer 3 pts. Lect: 2. Professor Wang. instructor’s permission); and (ii) a basic course subsystem components for telecommunications, decomposition. ARX model and state-space communications, power, security, and standards. principles, machine organization and design of Prerequisite: IEOR E3658 or a course in in data structures and algorithms (COMS optically controlled radar, optical signal model system identification. Recursive least Focus on a significant design project. parallel systems including parallelism detection stochastic processes. Corequisite: ELEN E4815. W3133, W3134, W3137, W3139 or W3157, or processing, and photonic local area networks. squares filters and Kalman filters. LQR, H, linear methods, synchronization, data coherence and Mutual information and entropy. The source coding EECS E6766x Internet of things—engineering equivalent, and familiarity with programming. An introduction to the devices and the design of robust control, predictive control. Learning control, interconnection networks. Performance analysis theorem. The capacity of discrete memoryless innovations and commercialization Introduction to modern digital CAD synthesis these circuits. Principle and modeling of dielectric repetitive control, adaptive control. Liapunov and special purpose parallel machines. waveguides (including silica on silicon and InP channels and the noisy channel coding theorem. 3 pts. Lect: 3. Professor Kostic. and optimization techniques. Topics include and Popov stability. Nonlinear adaptive control, CSEE E6847y Distributed embedded systems based materials), waveguide devices (simple and The rate distortion function. Discrete memoryless Prerequisites: Basic programming and instructor’s modern digital system design (high-level nonlinear robust control, sliding mode control. 3 pts. Lect: 2. star couplers), and surface diffractive elements. sources and single-letter distortion measures. permission. Deep dive into a couple of selected synthesis, register-transfer level modeling, topics/use-cases from the area of Internet of Prerequisite: Any COMS W411X, CSEE algorithmic state machines, optimal scheduling

ENGINEERING 2020–2021 ENGINEERING 2020–2021 algorithms, resource allocation and binding, ELEN E6876x or y Sparse and low- course provides an understanding of the methods of doctoral research instruction. Registration for credit, but no more than 3 total points may be ELEN E4501x Electromagnetic devices and 154 155 retiming), controller synthesis and optimization, dimensional models for high-dimensional data used for structuring matter on the nanometer in ELEN E9800 may not be used to satisfy the used for degree credit. Short-term design project energy conversion exact and heuristic two-level logic minimization, 3 pts. Lect: 3. Professor Wright. length: thin-film technology; lithographic patterning minimum residence requirement for the degree. organized as a faculty-led team competition. 3 pts. Lect: 3. Professor Sen. advanced multi-level logic optimization, optimal Prerequisites: ELEN E4815 or equivalent and and technologies including photon, electron, ion Particular design targets are set that vary by Prerequisite: ELEN E3401. Linear and nonlinear ELEN E9900x, y and s Doctoral dissertation technology mapping to library cells (for delay, linear algebra. Recommended: ELEN E4810 or and atom, scanning probe, soft lithography, and semester. A set of hardware and software magnetic circuits. Electric and magnetic energy 0 pts. Members of the faculty. power and area minimization), advanced data equivalent. Overview of theory, computation and nanoimprinting; pattern transfer; self-assembly; constraints is specified. The project takes place A candidate for the doctorate may be required storage, loss, and transfer. Circuit behavior of structures (binary decision diagrams), SAT applications for sparse and low-dimensional data process integration; and applications. over an advertised subset of the semester, to register for this course every term after the energy storage and transfer devices. Field theory solvers and their applications, static timing modeling. Recoverability of sparse and low-rank beginning around the third week. ELEN E6950x Wireless and mobile networking, I student’s coursework has been completed, and of moving bodies. Dynamical equations of an analysis, and introduction to testability. Includes models. Optimization methods for low-dim data 4.5 pts. Lect: 2. Lab: 1. Professor Jelenkovic. until the dissertation has been accepted. ELEN E4215y Analog filter synthesis electromechanical system. Electromechanical hands-on small design projects using and modeling. Applications to imaging, neuroscience, Corequisite: ELEN E6761 or instructor’s and design and thermo-electric sensors and actuators. creating CAD tools. communications, web data. permission. Overview of mobile and wireless 3 pts. Lect: 3. Rotating electric energy converters. CSEE E6863 Formal verification of hardware ELEN E6880-6889x or y Topics in signal networking. Fundamental concepts in mobile COURSES IN ELECTRICAL Prerequisites: ELEN E3201 and ELEN E3801, Superconductivity and applications. and software systems processing wireless systems: propagation and fading, cellular ENGINEERING OFFERED or equivalent. Approximation techniques for 3 pts. Lect: 2. Members of the faculty. ELEN E4503x Sensors, actuators, and 3 pts. Lect: 2. Professor Theobald and Ivancic. systems, channel assignment, power control, OCCASIONALLY magnitude, phase, and delay specifications, electromechanical systems Prerequisite: COMS W3134, W3136, or W3137 Prerequisite: ELEN E4810. Advanced topics handoff. Examples of second-generation circuits- transfer function realization sensitivity, passive LC ECBM E3060x Introduction to genomic 3 pts. Lect: 3. and COMS W3261. Introduction to the theory in signal processing, such as multidimensional switched systems and standards. Quantitative filters, active RC filters, MOSFET-C filters, Gm-C information science and technology Prerequisites: ELEN E3201 and E3401, and practice of formal methods for the design signal processing, image feature extraction, homework assignments may require use of a filters, switched-capacitor filters, automatic tuning 3 pts. Lect: 3. Professor Anastassiou. or equivalents. Electromagnetic energy and analysis of correct (i.e., bug-free) concurrent image/video editing and indexing, advanced mathematical software package. techniques for integrated filters. Filter noise. A Introduction to the information system storage, loss, and transfer. Dynamics of and embedded hardware/software systems. digital filter design, multirate signal processing, design project is an integral part of the course. Topics include temporal logics; model checking; adaptive signal processing, and wave-form ELEN E6999x, y, or s Fieldwork paradigm of molecular biology. Representation, electromechanical systems. Linearization deadlock and liveness issues; fairness; coding of signals. Content varies from year to 0.5–1.5 pts. Members of the faculty. organization, structure, function, and manipulation ELEN E4302x or y Magnetic sensors and of nonlinear coupled dynamical equations satisfiability (SAT) checkers; binary decision year, and different topics rotate through the Prerequisites: Obtained internship and approval of the biomolecular sequences of nucleic instruments for medical imaging and equivalent circuits. Electromechanical diagrams (BDDs); abstraction techniques; course numbers 6880 to 6889. from a faculty adviser. May be repeated for acids and proteins. The role of enzymes and 3 pts. Lect: 2.5, Lab: 0.5. actuators: acoustic, IC-processed introduction to commercial formal verification credit, but no more than 3 total points may gene regulatory elements in natural biological Prerequisite: ELEN E3106, ELEN E3401, or micromachines. Electromechanical sensors: EECS E6890-6899x or y Topics in information tools. Industrial state-of-the-art, case studies and be used for degree credit. Only for electrical functions as well as in biotechnology and instructor’s permission. Physics of nuclear acoustic, pressure, and acceleration. Thermal processing experiences: software analysis (C/C++/Java), engineering and computer engineering graduate genetic engineering. Recombination and magnetic resonance (NMR) and superconducting sensors: polysilicon thermopiles and bipolar 3 pts. Lect: 2. Members of the faculty. hardware verification (RTL). students who include relevant off-campus work other macromolecular processes viewed as quantum interference device (SQUID). Design transistor temperature sensors. Electro-optic Advanced topics spanning electrical experience as part of their approved program of mathematical operations with simulation and and operation of superconducting DC magnet, sensors: visible light, infrared, and X-ray. CSEE E6868x or y Embedded scalable engineering and computer science such as study. Final report required. May not be taken for visualization using simple computer programming. RF receiver, Josephson junction, and integrated platforms ELEN E6151y Surface physics and analysis of speech processing and recognition, image and pass/fail credit or audited. This course shares lectures with ECBM E4060, SQUID. Principles of biomedical sensoring systems 3 pts. Lect: 2. Professor Carloni. electronic materials multimedia content analysis, and other areas but the work requirements differ somewhat. including Magnetic Resonance Imaging (MRI), Prerequisites: CSEE W4868 or instructor's EEME E8601y Advanced topics in control 3 pts. Lect: 2. drawing on signal processing, information theory, SQUID magnetometer, and NMR spectroscopy. permission. Inter-disciplinary graduate-level theory EEHS E3900y History of telecommunications: Prerequisite: Instructor’s permission. Basic machine learning, pattern recognition, and Medical image formation and processing. seminar on design and programming of related topics. Content varies from year to year, 3 pts. Lect: 3. Members of the faculty. from the telegraph to the internet physical principles of methods of surface embedded scalable platforms. Content varies and different topics rotate through the course See entry under “Courses in Mechanical 3 pts. Lect: 3. ELEN E4350y VLSI design laboratory analysis, surfaces of electronic materials between offerings to cover timely relevant issues numbers 6890 to 6899. Engineering” for description. Historical development of telecommunications 3 pts. Lab: 3. including structure and optical properties (auger and latest advances in system-on-chip design, from the telegraphy of the mid-1800s to Prerequisites: EECS E4321 and ELEN E4312, or electron spectroscopy, X-ray photoemission, ELEN E6900–6909x or y Topics in electrical ELEN E9001x and y–E9002 Research embedded software programming and electronic the internet at present. Included are the instructor’s permission. Design of a CMOS mixed- ultraviolet photoelectron spectroscopy, and computer engineering 0–6 pts. Members of the faculty. design automation. Requires substantial reading technologies of telephony, radio, and computer signal integrated circuit. The class divides up into electron energy loss spectroscopy, inverse 3 pts. Lect: 2. Members of the faculty. Prerequisite: Requires approval by a faculty of research papers, class participation, and communications. The coverage includes both teams to work on mixed-signal integrated circuit photoemission, photo stimulated desorption, semester-long project. Prerequisite: Instructor’s permission. Selected member who agrees to supervise the work. the technologies themselves and the historical designs. The chips are fabricated to be tested the and low energy electron diffraction), physical topics in electrical and computer engineering. Points of credit to be approved by the EECS E6870x or y Speech recognition events that shaped, and in turn were shaped by, following term. Lectures cover use of computer- principles of each approach. Content varies from year to year, and different department. Requires submission of an outline 3 pts. Lect: 2. the technologies. The historical development, aided design tools, design issues specific to the topics rotate through the course numbers 6900 of the proposed research for approval by the ELEN E6211x or y Circuit theory Prerequisites: Basic probability and statistics. both the general context and the particular projects, and chip integration issues. This course to 6909. faculty member who is to supervise the work 3 pts. Lect: 3. Theory and practice of contemporary events concerning communications, is presented shares lectures with E6350, but the complexity of the student. The research facilities of the Prerequisites: ELEN E3331 and ELEN E3801. automatic speech recognition. Gaussian ELEN E6910-6919x or y Topics in technical chronologically. The social needs that elicited requirements of integrated circuits are lower. department are available to qualified students An axiomatic development of circuit theory. Circuit mixture distributions, hidden Markov models, writing and presentation for electrical new technologies and the consequences of their interested in advanced study. ELEN E4420x Topics in electromagnetics theorems, circuit topology, general methods of pronunciation modeling, decision trees, finite- engineers adoption are examined. Throughout the course, 3 pts. Lect: 3. circuit analysis. Normal form characterizations. state transducers, and language modeling. 1 pt. Professor Kayfetz. ELEN E9011x and y–E9012 Doctoral research relevant scientific and engineering principles Prerequisites: Undergraduate electromagnetic Scattering characterization and sensitivity Selected advanced topics will be covered in Open to M.S. and Ph.D. students in EE/CE 0–6 pts. Members of the faculty. are explained as needed. These include, theory. Selected topics in the theory and practice function. Basic network synthesis methods: more depth. with instructor's permission. Topics to help EE/ Prerequisite: Requires approval by a faculty among others, the concept and effective use of electromagnetics, varying from year to year. immittance and transfer function realization, CE graduate students' communication skills. member who agrees to supervise the work. Points of spectrum, multiplexing to improve capacity, Topic for current term will be available in the multiport realization, approximation techniques. ELEN E6873x or y Detection and estimation Emphasis on writing clear, concise proposals, of credit to be approved by the department. Open digital coding, and networking principles. There theory department office one month before registration. journal articles, conference papers, and theses, only to doctoral students who have passed the are no prerequisites, and no prior scientific or ELEN E6261y Computational methods of circuit 3 pts. Lect: 2. This course may be taken more than once when and on preparing clear technical presentations. qualifying examinations. Requires submission engineering knowledge is required. Engineering analysis Prerequisite: ELEN E4815. Introduction to topics are different. Possible topics: microwave Different topics rotate through the course of an outline of the proposed research for the students may not count this course as a 3 pts. Lect: 3. the fundamental principles of statistical signal theory and design (generalized waveguides, numbers 6910 to 6919. May be repeated for approval of the faculty member who is to supervise technical elective. The course shares lectures Prerequisites: ELEN E3331 and APMA E3101. processing related to detection and estimation. excitation and coupling of waveguides, junctions, credit. Credit may not be used to satisfy degree the work of the student. with EEHS E4900, but the work requirements Computational algorithms for DC, transient, and Hypothesis testing, signal detection, parameter microwave networks, periodic structures, optical requirements. differ somewhat. frequency analysis of linear and nonlinear circuits. estimation, signal estimation, and selected ELEN E9800x and y Doctoral research fibers); antennas (filamentary antennas, arrays, Formulation of equations: state equations, hybrid advanced topics. Suitable for students doing ELEN E6945x or y Device nanofabrication instruction ELEN E3999x or y Electrical engineering aperture radiation, system properties, pattern equations, sparse tableaux. Solution techniques: research in communications, control, signal 3 pts. Lect: 3. 3, 6, 9 or 12 pts. Professor Kinget. design challenge synthesis); electrodynamics (special relativity, iterative methods to solve nonlinear algebraic processing, and related areas. Prerequisites: ELEN E3106 and E3401, or A candidate for the Eng.Sc.D. degree in 1 pt. radiation by charged particles, relativistic beams, equations; piecewise linear methods; sparse matrix equivalents. Recommended: ELEN E4944. This electrical engineering must register for 12 points Prerequisite: Approval by a faculty member who free electron lasers). agrees to supervise the work. May be repeated techniques; numerical integration of stiff, nonlinear

ENGINEERING 2020–2021 ENGINEERING 2020–2021 differential equations, companion network models; ELEN E9101x or y Seminar in physical ELEN E9501x or y Seminar in electrical power 156 waveform relaxation. electronics networks 3 pts. Lect: 2. 3 pts. Lect: 2. ELEN E6304x or y Topics in electronic circuits Prerequisites: Quantum electronics and ELEN Prerequisites: Open to doctoral candidates, and 3 pts. Lect: 3. E4944, or instructor’s permission. Advanced topics to qualified M.S. candidates with the instructor’s Prerequisite: Instructor’s permission. State-of-the- in classical and quantum phenomena that are permission. Recent developments in control & art techniques in integrated circuits. Topics may based on ion and electron beams, gas discharges, optimization for power systems, design of smart change from year to year. and related excitation sources. Application to new grid, and related topics. EEME E6610x Optimal control theory laser sources and microelectronic fabrication. EECS E9601x or y Seminar in data-driven 3 pts. Lect: 3. ELEN E9201x or y Seminar in circuit theory analysis and computation Prerequisite: ELEN E6201 or EEME E6601. 3 pts. Lect: 2. 3 pts. Lect: 2. Instructor to be announced. Objectives of optimal control. Continuous and Open to doctoral candidates, and to qualified M.S. Prerequisite: Open to doctoral candidates and discrete control problems. Calculus of variations: candidates with instructor’s permission. Study qualified M.S. candidates with the instructor's Mayer and Bolza; Pontryagin’s maximum principle. of recent developments in linear, nonlinear, and permission. Advanced topics and recent Bang-bang and singular controls. Existence distributed circuit theory and analysis techniques developments in mathematical techniques of optimal control. Hamilton-Jacobi theory and important to the design of very large scale and computational tools for data science and dynamic programming. Numerical methods. integrated circuits. engineering problems. Optimal feedback control regulatory problems. ELEN E9701x or y Seminar in information and Linear-quadratic-Gaussian estimation. Applications. ELEN E9301x or y Seminar in electronic devices communication theories ELEN E6762y Computer communication 3 pts. Lect: 2. Professor Kymissis. 3 pts. Lect: 2. networks, II Open to doctoral candidates, and to qualified M.S. Open to doctoral candidates, and to qualified M.S. 3 pts. Lect: 2. candidates with instructor’s permission. Theoretical candidates with instructor’s permission. Recent Prerequisite: ELEN E6761. Broadband and experimental studies of semiconductor developments in telecommunication networks, ISDN, services and protocols; ATM. Traffic physics, devices, and technology. information and communication theories, and characterization and modeling: Markov-modulated related topics. Poisson and Fluid Flow processes; application ELEN E9303x or y Seminar in electronic ELEN E9705x or y Seminar in cyber-physical to voice, video, and images. Traffic Management circuits systems in ATM networks: admission and access control, 3 pts. Lect: 2. 3 pts. Professor Jiang. flow control. ATM switch architectures; input/output Open to doctoral candidates, and to qualified M.S. Open to doctoral candidates and to qualified M.S. queueing. Quality of service (QoS) concepts. candidates with instructor’s permission. Study of recent developments in electronic circuits. candidates with instructor's permission. Advanced ELEN E6781y Topics in modeling and analysis topics in recent developments in research on of random phenomena ELEN E9402x or y Seminar in quantum cyber-physical systems (CPS) and related topics. 3 pts. Lect: 3. electronics ELEN E9801x or y Seminar in signal Prerequisite: ELEN E6711. Recommended 3 pts. Lect: 2. processing preparation: a course on real analysis and Open to doctoral candidates, and to qualified M.S. 3 pts. Lect: 2. advanced probability theory. Current methodology candidates with instructor’s permission. Recent Open to doctoral candidates, and to qualified in research in stochastic processes applied to experimental and theoretical developments in M.S. candidates with instructor’s approval. Recent communication, control, and signal processing. various areas of quantum electronics research. developments in theory and applications of signal Topics vary from year to year to reflect student Examples of topics that may be treated processing, machine learning, content analysis, interest and current developments in the field. include novel nonlinear optics, lasers, transient phenomena, and detectors. and related topics. ELEN E6920x or y Topics in VLSI systems design ELEN E9403x or y Seminar in photonics 3 pts. Lect: 2. 3 pts. Lect: 2. Prerequisite: ELEN E4321. Design automation: Prerequisite: ELEN E4411. Open to doctoral layout, placement, and routing. Circuit simulation candidates, and to qualified M.S. candidates with algorithms and optimization of performance instructor’s permission. Recent experimental and area. Multiprocessor computing systems. and theoretical developments in various areas of Verification of testing. Topics may change from photonics research. Examples of topics that may year to year. be treated include squeezed-light generation, quantum optics, photon detection, nonlinear optical ELEN E9060x or y Seminar in systems biology effects, and ultrafast optics. 3 pts. Lect: 2. Open to doctoral candidates, and to qualified M.S. ELEN E9404x or y Seminar in lightwave candidates with instructor’s permission. Study of communications recent developments in the field of systems biology. 3 pts. Lect: 2. Open to doctoral candidates, and to qualified EEBM E9070x or y Seminar in computational M.S. candidates with instructor’s approval. Recent neuroscience and neuroengineering theoretical and experimental developments in 3 pts. Lect: 2. Professor Mesgarani. light wave communications research. Examples Open to doctoral candidates and qualified of topics that may be treated include information M.S. candidates with instructor’s permission. capacity of light wave channels, photonic Study of recent developments in computational switching, novel light wave network architectures, neuroscience and neuroengineering. and optical neural networks.

ENGINEERING 2020–2021 INDUSTRIAL ENGINEERING AND OPERATIONS RESEARCH 157 315 S. W. Mudd, MC 4704 212-854-2941 ieor.columbia.edu

CHAIR PROFESSORS PROFESSORS OF SENIOR LECTURER Jay Sethuraman Daniel Bienstock PROFESSIONAL IN DISCIPLINE 326 S. W. Mudd Mark Broadie, PRACTICE Hardeep Johar Business School Emanuel Derman EXECUTIVE DIRECTOR Awi Federgruen, Ali Hirsa ASSOCIATES Jenny S. Mak Business School Soulaymane Kachani IN DISCIPLINE 324 S. W. Mudd Donald Goldfarb Harry West Uday Menon Garud Iyengar Yi Zhang DIRECTOR OF FINANCE Kamel Jedidi, Business ASSOCIATE AND ADMINISTRATION School PROFESSORS ADJUNCT FACULTY Shi Yee Lee Evan Picoult, Agostino Capponi Krzysztof Choromanski 309 S. W. Mudd Business School Ton Dieker Siddhartha Dastidar Jay Sethuraman Vineet Goyal Kosrow Dehnad David DeRosa DIRECTOR: Karl Sigman Henry Lam Sebastien Donadio UNDERGRADUATE Medini Singh, Van Anh Truong Tony Effik PROGRAMS Business School Leon S. Gold Van Anh Truong Clifford Stein ASSISTANT David Gulley Yi Zhang Harborne Stuart, PROFESSORS Shipra Agrawal Sufian Ikhmeis Business School DIRECTOR: FINANCIAL Eric Balkanski Ebad Jahangir Olivier Toubia, Business ENGINEERING Adam Elmachtoub Alireza Javaheri School Emanuel Derman Yuri Faenza Paul Logston Ward Whitt Ali Hirsa Cédric Josz Allan Malz David D. Yao Christian Kroer Michael Miller Xunyu Zhou DIRECTOR: DOCTORAL Daniel Lacker Gerard Neumann PROGRAMS Dylan Possamaï Moshe Rosenwein Vineet Goyal WenPin Tang Ali Sadighian Kaizheng Wang Maya Waisman DIRECTOR: EXECUTIVE Nadejda Zaets EDUCATION Soulaymane Kachani

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

ENGINEERING 2020–2021 158 Current Research Activities the dissemination of research done by provides a broad foundation in the 159 In industrial engineering, research is members of the Center. current ideas, models, and methods of INDUSTRIAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS conducted in the area of logistics, The Computational Optimization industrial engineering. It also includes a SEMESTER I SEMESTER II SEMESTER III SEMESTER IV routing, scheduling, production and Research Center (CORC) at Columbia substantial component in the humanities University is an interdisciplinary group and social sciences to help students supply chain management, inventory MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) APMA E2000 (4) Linear algebra (3)1 control, revenue management, and of researchers from a variety of understand the societal implications of

quality control. departments on the Columbia campus. their work. Chemistry or physics lab: PHYS UN1494 (3) or Its permanent members are Professors The industrial engineering program UN1401 (3) UN1402 (3) In operations research, new PHYSICS PHYS UN3081 (2) or UN1601 (3.5) UN1602 (3.5) (three tracks, CHEM UN1500 (3) or developments are being explored Daniel Bienstock, Don Goldfarb, Garud objectives are: UN2801 (4.5) UN2802 (4.5) choose one) CHEM UN1507 (3) or in mathematical programming, Iyengar, Jay Sethuraman, and Cliff CHEM UN3085 (4) or combinatorial optimization, stochastic Stein, from the Industrial Engineering 1. To provide students with the requisite modeling, computational and and Operations Research Department, analytical and computational skills CHEMISTRY UN1403 (3) or UN1404 (3) or (choose one course) UN1604 (3.5) or UN2045 (3.5) mathematical finance, queueing and Professor David Bayer, from the to assess practical situations and theory, reliability, simulation, and both Department of Mathematics at Barnard academic problems, formulate UNIVERSITY WRITING CC1010 (3) either semester deterministic and stochastic College. Researchers at CORC specialize models of the problems represented network flows. in the design and implementation of or embedded therein, design HUMA CC1001, HUMA CC1002, In engineering and management state-of-the-art algorithms for the solution potential solutions, and evaluate their COCI CC1101, COCI CC1102, or Global core (3–4) or Global core (3–4) systems, research is conducted in of large-scale optimization problems impact; REQUIRED ECON UN1105 (4) and UN1155 recitation (0) NONTECHNICAL either semester the areas of logistics, supply chain arising from a wide variety of industrial 2. To prepare students for the workplace ELECTIVES HUMA UN1121 or UN1123 (3) optimization, and revenue and risk and commercial applications. by fostering their ability to participate either semester management. The FDT Center for Intelligent in teams, understand and practice In financial engineering, research Asset Management is led by interpersonal and organizational FIRST- AND SECOND- YEAR DEPT. IEOR E3658 (3) either semester is being carried out in portfolio Professor Xunyu Zhou at Columbia behaviors, and communicate their REQUIREMENTS management; option pricing, including University. The Center will focus solutions and recommendations COMPUTER 1. COMS W1004 (3) and COMS W3134 (3) exotic and real options; computational on the exploration of theoretical effectively through written, oral, and SCIENCE or (two tracks, 2. COMS W1007 (3) and COMS W3137 (4)2 finance, such as Monte Carlo simulation underpinnings and modeling strategies electronic presentations; choose one) and numerical methods; as well as data for financial portfolio management 3. To familiarize students with the PHYSICAL UN1001 (1) UN1002 (1) mining and risk management. through the introduction of big data historical development of industrial EDUCATION Projects are sponsored and analytical techniques. The Center's engineering tools and techniques and THE ART OF ENGI E1102 (4) either semester supported by leading private firms research will combine modern portfolio with the contemporary state of the ENGINEERING and government agencies. In addition, theory, behavioral finance, machine art, and to instill the need for lifelong our students and faculty are involved learning, and data science to study learning within their profession; and 1 The linear algebra requirement may be filled by either MATH UN2010 or APMA E3101. in the work of four research and core problems including optimal asset 4. To instill in our students an 2 The department encourages students to select sequence 1 or 2. ENGI E1006 (3) and COMS W3136 (3) may be substituted in place of sequence 1 or 2. educational centers: the Center for allocation and risk management; and understanding of ethical issues Applied Probability (CAP), the Center the research of the Center sits at the and professional and managerial for Financial Engineering (CFE), the crossroads of financial engineering, responsibilities. Computational and Optimization computer science, statistics, and INDUSTRIAL ENGINEERING: THIRD AND FOURTH YEARS Research Center (CORC), and the FDT finance, aiming at providing innovative Operations Research Center for Intelligent Asset Management. and intelligent investment solutions. The operations research program SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII The Center for Applied Probability is one of several applied science (CAP) is a cooperative center involving programs offered at the School. At BACHELOR OF SCIENCE IEOR E3402 (4) IEOR E3106 (3) IEOR E4003 (3) IEOR E4405 (3) the School of Engineering and Applied the undergraduate level, it offers Production & inventory planning PROGRAMS Stochastic systems and Corporate finance for eng. Scheduling Science, several departments in the basic courses in probability, statistics, applications IEOR E3404 (4) IEOR E4207 (3) IEOR E4510 (3) Graduate School of Arts and Sciences, applied mathematics, simulation, Simulation Human factors Project management Industrial Engineering IEOR E3608 (3) REQUIRED Foundations of optimization and the Graduate School of Business. and optimization as well as more 1 IEOR E3609 (3) The undergraduate program is COURSES Advanced optimization Its interests are in four applied areas: professionally oriented operations IEOR E4307 (3) Statistics and data analysis designed to develop the technical IEOR E4412 (3) mathematical and computational finance, Choose One: research courses. The curriculum is well Quality control and skills and intellectual discipline needed COMS W4111(3) IEOR E4505 (3) OR in public policy stochastic networks, logistics and suited for students with an aptitude for management by our graduates to become leaders Database systems IEOR E4506 (3) Designing digital operating models distribution, and population dynamics. mathematics applications. IEOR E4650 (3) Business analytics in industrial engineering and related The Center for Financial Engineering It prepares graduates for professional professions. The program is distinctive (CFE) at Columbia University encourages employment as operations research in its emphasis on quantitative, NONTECH 3 3 3 interdisciplinary research in financial analysts, e.g., with management engineering and mathematical modeling economic, computer-aided approaches consultant and financial service INDUSTRIAL to production and service management ELECTIVES 2 6 3 in finance and promoting collaboration organizations, as well as for graduate ENGINEERING problems. It is focused on providing between Columbia faculty and financial studies in operations research or an experimental and mathematical 15 14 15 15 institutions, through the organization of business. It is flexible enough to be TOTAL POINTS problem-formulating and problem- research seminars, workshops, and adapted to the needs of future medical solving framework for industrial and law students. 1 Taking required courses later than the prescribed semester is not permitted. engineering work. The curriculum 2 9 points total. Complete list is available at ieor.columbia.edu.

ENGINEERING 2020–2021 ENGINEERING 2020–2021 160 161 OPERATIONS RESEARCH PROGRAM: FIRST AND SECOND YEARS OPERATIONS RESEARCH PROGRAM: ANALYTICS: FIRST AND SECOND YEARS SEMESTER I SEMESTER II SEMESTER III SEMESTER IV SEMESTER I SEMESTER II SEMESTER III SEMESTER IV MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) APMA E2000 (4) Linear algebra (3)1 MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) APMA E2000 (4) Linear algebra (3)1

Chemistry or physics lab: PHYS UN1494 (3) or UN1401 (3) UN1402 (3) PHYSICS PHYS UN3081 (2) or Chemistry or physics lab: (three tracks, UN1601 (3.5) UN1602 (3.5) PHYS UN1494 (3) or CHEM UN1500 (3) or UN1401 (3) UN1402 (3) choose one) UN2801 (4.5) UN2802 (4.5) PHYSICS PHYS UN3081 (2) or CHEM UN1507 (3) or (three tracks, UN1601 (3.5) UN1602 (3.5) CHEM UN1500 (3) or CHEM UN3085 (4) or choose one) UN2801 (4.5) UN2802 (4.5) CHEM UN1507 (3) or CHEM UN3085 (4) or

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

UNIVERSITY WRITING CC1010 (3) either semester UNIVERSITY WRITING CC1010 (3) either semester

HUMA CC1001, HUMA CC1002, COCI CC1101, COCI CC1102, or Global Core (3–4) or Global Core (3–4) HUMA CC1001, HUMA CC1002, REQUIRED ECON UN1105 (4) and UN1155 recitation (0) COCI CC1101, COCI CC1102, NONTECHNICAL either semester or Global Core (3–4) or Global Core (3–4) ELECTIVES REQUIRED ECON UN1105 (4) and UN1155 recitation (0) NONTECHNICAL HUMA UN1121 or UN1123 (3) either semester ELECTIVES either semester HUMA UN1121 or UN1123 (3) either semester FIRST- AND SECOND- YEAR DEPT. IEOR E3658 (3) either semester REQUIREMENTS FIRST- AND SECOND- YEAR DEPT. IEOR E3658 (3) either semester REQUIREMENTS COMPUTER 1. COMS W1004 (3) and COMS W3134 (3) SCIENCE or COMPUTER (two tracks, 2. COMS W1007 (3) and COMS W3137 (4)2 1. COMS W1004 (3) and COMS W3134 (3) choose one) SCIENCE or (two tracks, 2. COMS W1007 (3) and COMS W3137 (4)2 choose one) PHYSICAL UN1001 (1) UN1002 (1) EDUCATION PHYSICAL UN1001 (1) UN1002 (1) EDUCATION THE ART OF ENGI E1102 (4) either semester ENGINEERING THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 The linear algebra requirement may be filled by either MATH UN2010 or APMA E3101.

2 The department encourages students to select sequence 1 or 2. ENGI E1006 (3) and COMS W3136 (3) may be substituted in place of sequence 1 or 2. 1 The linear algebra requirement may be filled by either MATH UN2010 or APMA E3101. 2 The department encourages students to select sequence 1 or 2. ENGI E1006 (3) and COMS W3136 (3) may be substituted in place of sequence 1 or 2.

OPERATIONS RESEARCH: THIRD AND FOURTH YEARS OPERATIONS RESEARCH: ANALYTICS: THIRD AND FOURTH YEARS SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII IEOR E4003 (3) IEOR E3106 (3) Corporate finance for eng. Stochastic systems and IEOR E4405 (3) applications IEOR E3402 (4) IEOR E4407 (3) Scheduling IEOR E3106 (3) IEOR E4003 (3) IEOR E4650 (3) Production & inventory planning Game theoretic models of Stochastic systems and Corporate finance for eng. Business analytics IEOR E3608 (3) operations applications IEOR E3402 (4) REQUIRED Foundation of optimization IEOR E3404 (4) Production & inventory planning IEOR E4407 (3) Choose one: COURSES1 Simulation IEOR E3608 (3) Game theoretic models of IEOR E4405 (3) IEOR E4307 (3) Foundation of optimization IEOR E3404 (4) operations Scheduling Statistics and data analysis IEOR E3609 (3) Choose one: Simulation or Advanced optimization REQUIRED IEOR E4307 (3)7 IEOR E4601 (3) IEOR E4505 Operations research for public policy 1 COMS W4111(3) COURSES IEOR E4507 Healthcare operations management Statistics and data analysis IEOR E3609 (3) Dynamic pricing & revenue Database systems IEOR E4650 Business analytics Advanced optimization management IEOR E4700 Introduction to FE IEOR E4212 (3) Data analytics & python for OR IEOR E4418 (3) Transportation analytics & logistics COMS W4111(3) NONTECH 3 3 3 Database systems

OPERATIONS 6 6 ELECTIVES RESEARCH2 NONTECH 3 3 3

TOTAL POINTS 12 14 15 15

2

ELECTIVES ANALYTICS 6 6

1 Taking required courses later than the prescribed semester is not permitted. 2 12 points total. At least two technical electives must be chosen from IEOR; the complete list is available at ieor.columbia.edu. TOTAL POINTS 15 17 15 15

1 Taking required courses later than the prescribed semester is not permitted. 2 12 points total. At least two technical electives must be chosen from IEOR; the complete list is available at ieor.columbia.edu. ENGINEERING 2020–2021 ENGINEERING 2020–2021 162 163 OPERATIONS RESEARCH: ENGINEERING MANAGEMENT SYSTEMS: OPERATIONS RESEARCH: FINANCIAL ENGINEERING: FIRST AND SECOND YEARS FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

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

Chemistry or physics lab: Physics or chemistry lab: PHYS UN1494 (3) or UN1401 (3) UN1402 (3) PHYS UN1494 (3) or PHYSICS PHYS UN3081 (2) or UN1401 (3) UN1402 (3) (three tracks, UN1601 (3.5) UN1602 (3.5) PHYSICS PHYS UN3081 (2) or CHEM UN1500 (3) or (three tracks, UN1601 (3.5) UN1602 (3.5) choose one) UN2801 (4.5) UN2802 (4.5) CHEM UN1500 (3) or CHEM UN1507 (3) or choose one) UN2801 (4.5) UN2802 (4.5) CHEM UN1507 (3) or CHEM UN3085 (4) or CHEM UN3085 (4) or

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

UNIVERSITY WRITING CC1010 (3) either semester UNIVERSITY WRITING CC1010 (3) either semester

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

FIRST- AND SECOND- FIRST- AND SECOND- YEAR DEPT. IEOR E3658 (3) either semester YEAR DEPT. IEOR E3658 (3) either semester REQUIREMENTS REQUIREMENTS

COMPUTER 1. COMS W1004 (3) and COMS W3134 (3) COMPUTER SCIENCE 1. COMS W1004 (3) and COMS W3134 (3) or SCIENCE or (two tracks, 2 2. COMS W1007 (3) and COMS W3137 (4) (two tracks, 2. COMS W1007 (3) and COMS W3137 (4)2 choose one) choose one)

PHYSICAL UN1001 (1) UN1002 (1) PHYSICAL UN1001 (1) UN1002 (1) EDUCATION EDUCATION

THE ART OF ENGI E1102 (4) either semester THE ART OF ENGI E1102 (4) either semester ENGINEERING ENGINEERING

1 The linear algebra requirement may be filled by either MATH UN2010 or APMA E3101. 2 The department encourages students to select sequence 1 or 2. ENGI E1006 (3) and COMS W3136 (3) may be substituted in place of sequence 1 or 2. 1 The linear algebra requirement may be filled by either MATH UN2010 or APMA E3101. 2 The department encourages students to select sequence 1 or 2. ENGI E1006 (3) and COMS W3136 (3) may be substituted in place of sequence 1 or 2.

OPERATIONS RESEARCH: ENGINEERING MANAGEMENT SYSTEMS: THIRD AND FOURTH YEARS OPERATIONS RESEARCH: FINANCIAL ENGINEERING: THIRD AND FOURTH YEARS SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII IEOR E4003 (3) ECON UN3211 (4) Corporate finance for eng. ECON UN3213 (4) Microeconomics IEOR E3106 (3) ECON 3213 (4) Choose one: Choose one: Stochastic systems and Macroeconomics Macroeconomics IEOR E3106 (3) IEOR E4550 (3) IEOR E4211 (3) applications ECON UN3211 (4) IEOR E4407 (3) IEOR E3402 (4) Stochastic systems and Entrepreneurial business Applied consulting Microeconomics IEOR E3402 (4) Game theoretic models Production & inventory applications creation IEOR E3608 (3) Production & inventory Foundations of optimization IEOR E3404 (4) of operations planning planning REQUIRED IEOR E3608 (3) IEOR E4998 (3) Simulation 1 REQUIRED IEOR E4500 (3) IEOR E4630 (3) COURSES Managing technological 1 IEOR E4003 (3) Foundations of optimization COURSES IEOR E3404 (4) innovations Corporate finance for eng IEOR E3609 (3) Applications prog. for FE Asset allocation Simulation IEOR E4307 (3) Advanced optimization IEOR E4620 (3) Statistics and data analysis IEOR E4307 (3) IEOR E3609 (3) Statistics and data analysis IEOR E4700 (3) Pricing models for FE Choose One: Advanced optimization Intro. to FE COMS W4111(3) IEOR E4510 (3) Project management COMS W4111(3) Database systems IEOR E4506 (3) Designing digital operating models Database systems IEOR E4650 (3) Business analytics ECON E3412 (4) Intro. to econometrics either semester

NONTECH 6 3 NONTECH 3 3 3

TECH2 3 3 6 FINANCIAL 3 6 ELECTIVES ENGINEERING2 ELECTIVES MANAGEMENT3 3 6 TOTAL POINTS 18 17 16 20

TOTAL POINTS 16 18 18 18 1 Taking required courses later than the prescribed semester is not permitted. 2 9 points total. The complete list is available at ieor.columbia.edu. 1 Taking required courses later than the prescribed semester is not permitted. 2 12 points total. At least two technical electives must be chosen from IEOR; the complete list is available at ieor.columbia.edu. 3 9 points total. ENGINEERING 2020–2021 ENGINEERING 2020–2021 164 Operations Research: Engineering of the application of engineering and industrial engineering majors may in completing the program. As a result, 165 Management Systems methodologies and quantitative elect to minor in operations research. Business Analytics (36 points) students failing to meet this criterion This operations research option is methods to finance. Financial The department does not offer a may be asked to withdraw. minor in engineering management Required Core Courses IEOR E4004 Optimization models and methods (first fall semester) designed to provide students with engineering is a multidisciplinary (18 points) IEOR E4101 Probability, statistics and simulation (first fall semester) Courses taken at the School field integrating financial theory with systems or financial engineering. IEOR E4502 Python for analytics (0 pt) (first fall semester) of Professional Studies will not be an understanding of contemporary IEOR E4523 Data analytics (fall or spring semester) technology and management. It is economics, methods of engineering, ENGI E4000 Professional development (0 pt) (first fall semester, yearl long) counted toward the M.S. degree in tools of mathematics, and practice of IEOR E4650 Business analytics (spring semester) the IEOR Department (e.g., courses for students who are interested in a GRADUATE PROGRAMS IEOR E4524 Analytics in practice (spring semester) technical-management background programming. Students graduating with M.S. students must complete the pro- IEOR E4599 MSBA quantitative bootcamp (0 pt) with the following prefixes: ACTU, rather than one in a traditional this concentration are prepared to enter fessional development and leadership Concentration Courses (Financial Analytics & Financial Technology (FinTech), Marketing Analytics, Healthcare Analytics, and BUSI, COPR, IKNS, SUMA, FUND, Analytics Algorithms & Methodology) engineering field. It consists of required careers in securities, banking, financial course, ENGI E4000, as a graduation and more). Please consult with your courses in industrial engineering and management, and consulting industries, requirement. Ph.D. candidates are Financial Analytics & IEOR E4106 Stochastic models academic adviser regarding electives Financial Technology IEOR E4500 Applications programming for Financial Engineering operations research, economics, and fill quantitative roles in corporate strongly encouraged to complete ENGI (FinTech) (9 points) IEOR E4525 Machine learning for OR & FE offered in other departments and business, and computer science, treasury and finance departments of E6001–6004 and should consult their IEOR E4574 Technology innovation in financial services (1.5) schools, prior to registration. IEOR E4742 Deep learning for OR & FE intended to provide a foundation general manufacturing and service firms. program for PDL requirements. IEOR E4725 Big data in finance for dealing with engineering and Students who are interested in MRKT B8649 Pricing strategies Business Analytics DROM B8106 Operations strategy management systems problems. pursuing the rigorous concentration MASTER OF SCIENCE DROM B8116 Risk management The M.S. program in Business Analytics Elective courses are generally intended in financial engineering must DROM/MGMT B8510 Managerial negotiations (MSBA) offered by the IEOR Department PROGRAMS MRKT B8776 Foundations of innovation to provide a substantive core in at least demonstrate proficiency in calculus, in partnership with Columbia Business The Department of Industrial DROM B8816 Quantitative pricing and revenue analytics one technology area and at least one computer programming, linear DROM B9122 Computing for business research School. This program is formed and algebra, ordinary differential equations, Engineering and Operations Research management area. Marketing Analytics IEOR E4407 Game theoretic models of operations structured following many interactions offers courses and M.S. programs in (9 points) Due to the flexibility of this option, it probability, and statistics. IEOR E4506 Designing digital operating models with corporations, alumni, and students. (1) financial engineering on a full-time can incorporate the varied educational IEOR E4312 Application of OR & AI techniques in marketing (1.5) It emphasizes on developing new basis only; (2) management science IEOR E4562 Innovate using design thinking (Blockweek) needs of preprofessional students Undergraduate Advanced Track IEOR E4601 Dynamic pricing and revenue management insights and understanding of business and engineering on a full-time basis interested in law, medicine, business, The undergraduate advanced DROM B8122 Game-theoretic business strategy performance using data, statistical and only; (3) business analytics on a full-time DROM B8123 Demand and supply analytics and finance. In addition, most students track is designed for advanced quantitative analysis, and explanatory basis only; (4) industrial engineering on DROM E8131 Sports analytics are encouraged to add a minor in undergraduate students with the desire DROM/MRKT B8510 Managerial negotiations and predictive modeling to help make either a full- or part-time basis; and (5) MRKT B8607 Strategic consumer insights economics or computer science to their to pursue further higher education actionable decisions and to improve operations research on either a full- or MRKT B8608 New product development standard course schedules. after graduation. Students with a MRKT B8617 Marketing research and analytics business operations. Students pursuing part-time basis. Both the Department’s MRKT B8623 Intro to product management (1.5) minimum cumulative GPA of 3.4 and this degree program are provided M.S. programs in Business Analytics MRKT B8625 Winning strategic capabilities Operations Research: Analytics faculty approval have the opportunity MRKT B8679 Digital marketing with rigorous exposure to optimization and Management Science and to participate. Students are invited to MRKT B8681 Advanced marketing strategy and stochastic modeling, and a deep The analytics concentration within the Engineering is offered in conjunction MRKT B8683 Marketing models operations research program seeks to apply to the track upon the completion DROM B9122 Computing for business research coverage of applications in the areas with the Columbia Graduate School of DROM B9127 Online marketplaces train students to leverage advanced of their sophomore year. Advanced of analytics. The role of analytics has Business. Lastly, the Department and MRKT B9613 Mathematical models in marketing track students are required to take grown increasingly critical in business, quantitative models, algorithms, and the Graduate School of Business offer a MRKT B9651 Marketing analytics higher-level IEOR courses, including the MRKT B9656 Customer management: concepts and tools (1.5) health care, government, and many data for making actionable decisions to combined M.S./M.B.A. degree program improve business operations. Examples following: Healthcare Analytics IEOR E4108/DROM 8108 Supply chain analytics other sectors of the economy. in industrial engineering. (9 points) include staffing and scheduling at IEOR E4405 Scheduling It is a 36-credit degree STEM- IEOR E4004 instead of IEOR E3608 All degree program applicants are IEOR E4505 Operations research in public policy designated program (equivalent of hospitals, ride matching and pricing for IEOR E4106 instead of IEOR E3106 required to take the Aptitude Tests IEOR E4507 Health care operations management IEOR E4520 Applied systems engineering 12 three-credit courses), assuming on-demand car services, personalized IEOR E4403 instead of IEOR E4003 of the Graduate Record Examination IEOR E4521 Systems engineering tools and methods (OR) adequate preparation in probability promotions in online retail, and smarter IEOR E4404 instead of IEOR E3404 (GRE). M.S./M.B.A. candidates are IEOR E4540 Data mining for engineers and statistics, with students taking at energy consumption. Students are and MATH UN2500 also required to take the Graduate DROM B8105 Healthcare analytics (1.5) provided with a rigorous exposure to DROM B8107 Service operations least six courses (18 credits) within Management Admissions Test (GMAT). DROM B8128 Healthcare investment and entrepreneurship HCIT and services Students successfully completing the IEOR Department, and four to six optimization and stochastic modeling, A minimum grade-point average of 3.0 DROM B8132 Digital health care systems as well as machine learning and data the requirements of the undergraduate DROM/MGMT B8510 Managerial negotiations courses (12–18 credits) at the Business (B) or its equivalent in an undergraduate MRKT B8692 Pharmaceutical drug commercialization: strategy & practice (1.5) advanced track will receive recognition School. The remaining courses, if analysis tools for predictive modeling engineering program is required for DROM B8832 U.S. health care system on their academic record. MRKT B9656 Customer management: concepts and tools (1.5) any, can be taken at the School of and prescriptive analytics. Elective in admission to the M.S. programs. At a Analytics Algorithms & IEOR E4008 Computational discrete optimization Engineering, the School of International the areas of healthcare, marketing, minimum, students are expected, on Minors Methodology COMS W4111 Introduction to databases and Public Affairs, the Law School, transportation, deep learning, and many entry, to have completed courses in (9 points) CSOR W4231 Analysis of algorithms A number of minors are available for IEOR E4407 Game theoretic models of operations or the Departments of Economics, others further enrich students with ordinary differential equations, linear students wishing to add them to their IEOR E4418 Transportation analytics & logistics Mathematics, and Statistics. Additional domain expertise, and provide many algebra, probability, and a programming IEOR E4525 Machine learning for FE and Operations programs. These minors are described IEOR E4526 Analytics on the cloud details are available on the MSBA opportunities to work directly with data language such as C, Java, or Python. starting on page 204 of this bulletin. IEOR E4540 Data mining for engineers website: msba.engineering.columbia. on real-world problems. The Department requires that M.S. DROM B8110 Business analytics strategy IEOR program students may want DROM B8111 Analytics for business research edu/content/curriculum. students achieve grades of B– or to consider minors in economics DROM B8127 Big immersion seminar—big data (1.5 pts) Operations Research: Financial higher in each of the fundamental DROM B8130 Applied statistics and data analytics or computer science. In addition, MRKT B9160 Applied multivariate statistics Financial Engineering Engineering core courses in the discipline of study. operations research and engineering MRKT B9608 Experimental design & analysis for behavioral research The operations research concentration Poor performance in core courses is MRKT B9616 Bayesian modeling & computation The M.S. program in Financial and management systems majors may MRKT B9652 MS marketing models in financial engineering is designed to indicative of inadequate preparation and Engineering is offered on a full time basis elect to minor in industrial engineering, MRKT B9653 MS machine learning (1.5) provide students with an understanding is very likely to lead to serious problems MRKT B9654 MS artificial intelligence only. Financial Engineering is intended to

ENGINEERING 2020–2021 ENGINEERING 2020–2021 166 provide a unique technical background 3-point courses (36 points). 167 for students interested in pursuing Financial Engineering (36 points)1 Management Science and Engineering (36 points) Students must take at least six career opportunities in financial analysis courses (18 points) within the IEOR and risk management. In addition to the Fall Semester Required core courses: Required Core IEOR E4004 Optimization models and methods (first fall semester) Department, three to six courses at the (9 points)2 IEOR E4007 Optimization models and methods Courses (12 points) basic requirements for graduate study, IEOR E4101 Probability, statistics, and simulation (first fall semester) Business School, and the remaining IEOR E4701 Stochastic models IEOR E4102 Stochastic models (spring semester) students are expected, on entry, to have courses (if any) within the School of IEOR E4706 Foundations of financial engineering IEOR E4111 Operations consulting (starts first fall semester, year-long course) attained a high level of mathematical IEOR E4798 Financial engineering seminar (0 pt) DROM B8000 Optimization and simulation bootcamp (0 pt) Engineering, the School of International and computer programming skills, IEOR E4799 MSFE quantitative & computational bootcamp (0 pt) and Public Affairs, the Law School, Plus Financial Engineering electives, 3–6 points 3 particularly in probability, statistics, linear Semi-Core Courses (DRO, Analysis, and Management Electives 18 points) or the Departments of Economics, algebra, and the use of a programming Spring Semester Required core courses: Mathematics, and Statistics. Students (9 points)2 IEOR E4703 Monte Carlo simulation language such as C, Python or JAVA. in residence during the summer IEOR E4707 Continuous time finance Decision, Risk, and IEOR E4650 Business analysis Previous professional experience is IEOR E4709 Statistical analysis and time series Operations Electives DROM B8101 Business analytics II (1.5 pt) term can take two to four Business highly desirable but not required. Plus Financial Engineering electives, 3–6 points 3 (9 points) DROM B8105 Healthcare analytics (1.5) School courses in the third (summer) Graduate studies in Financial DROM B8106 Operations strategy (1.5 pt) semester in order to complete their Summer and/or CSOR W4231 Analysis of algorithms I DROM B8107 Service operations program. Additional details regarding Engineering consists of 36 points (12 Fall Semester IEOR E4311 Derivatives marketing & structuring (1.5) DROM B8110 Business analytics strategy courses), starting the fall semester. (For remaining IEOR E4500 Applications programming for financial engineers DROM B8116 Risk management these electives are available in the credits)2 IEOR E4525 Machine learning for FE & OR Students may complete the program DROM B8123 Demand & supply analytics Departmental office and on the MS&E IEOR E4602 Quantitative risk management DROM B8131 Sports analytics in May, August, or December of the IEOR E4630 Asset allocation website: mse.ieor.columbia.edu. following year. The requirements include IEOR E4710 Term structure modeling DROM B8510 Managerial negotiations six required core courses and additional IEOR E4718 Beyond Black-Scholes: the implied volatility smile Industrial Engineering IEOR E4722 Stochastic control & financial applications elective courses chosen from a variety of Analysis and Management Electives (9 points minimum) IEOR E4723 Blockchain & cryptocurrency investing (1.5) Graduate studies in Industrial Engineering departments or schools at Columbia. The IEOR E4726 Applied financial risk management enable students with industrial six required core courses for Financial IEOR E4729 Algorithmic trading Analysis Group IEOR E4008 Computational discrete optimization At least one of the CSOR W4231 Analysis of algorithms I engineering bachelor’s degrees to Engineering are IEOR E4007, E4701, IEOR E4731 Credit risk modeling and derivatives IEOR E4732 Computational methods in finance following: IEOR E4405 Scheduling enhance their undergraduate training E4703, E4706, E4707, and E4709. In IEOR E4734 Foreign exchange and related derivatives instruments (1.5) IEOR E4407 Game theoretic models of operations with studies in special fields such as addition, students are required to attend IEOR E4735 Introduction to structured and hybrid products IEOR E4418 Transportation analytics and logistics production planning, inventory control, IEOR E4798 Financial Engineering IEOR E4741 Programming for financial engineering IEOR E4501 Tools for analytics scheduling, and industrial economics. IEOR E4742 Deep learning for OR & FE Seminar and submit learning journals. IEOR E4507 Healthcare operations management However, the department also offers a Financial Engineering has seven Additional Financial Engineering electives will be offered 3 IEOR E4523 Data analytics broader master’s program for engineers concentrations: (1) Asset Management; IEOR E4525 Machine learning for financial engineering & operations research whose undergraduate training is not in IEOR E4526 Analytics on the cloud (2) Computation and Programming; 1 industrial engineering. Students may Students may conclude the program in May, August, or December 2020. Please visit the departmental IEOR E4540 Data mining for engineering (3) Computational Finance and website (ieor.columbia.edu/masters-financial-engineering) for more information. complete the studies on a full-time (12 IEOR E4572 Visualization & storytelling with data (1.5) Trading Systems; (4) Derivatives; (5) 2 All courses listed are for 3 points, unless stated otherwise. points per term) or part-time basis. 3 IEOR E4573 Performance, objectives & results using data analytics (1.5) Finance and Economics; (6) Financial The list of Financial Engineering electives can be found at ieor.columbia.edu/masters-financial-engineering/ IEOR E4601 Dynamic pricing and revenue optimization Industrial Engineers are required Technology; and (7) Machine Learning curriculum. IEOR E4742 Deep learning for operations research & financial engineering to satisfy a core program of graduate for Financial Engineering. A sample DROM B8108 Supply chain analytics courses in production management, Operations (DRO) Division at the content/mse-concentrations. schedule is available in the Department probability theory, statistics, simulation, Business School. Coursework emphasize Graduates of this program are office and on the IEOR website: ieor. Management Group and operations research. Students with both management and engineering expected to assume positions as IEOR E4412 Quality control and management columbia.edu. Students select electives At least one of the B.S. degrees in industrial engineering will perspectives in solving problems, analysts and associates in consulting IEOR E4505 Operations research in public policy from a group of specialized offerings following: usually have satisfied this core in their making decisions, and managing risks firms, business analysts in logistics, IEOR E4506 Designing digital operating models in both the fall and spring terms. They undergraduate programs. All students in complex systems. Students pursuing supply chain, operations, or revenue IEOR E4510 Project management may select from a variety of approved IEOR E4550 Entrepreneurial business creation for engineers must take at least 18 points of graduate this specialization are provided with management departments of large electives from the Department, the IEOR E4560 Lean launchpad (weeklong course in mid-January, by work in industrial engineering and at a rigorous exposure to optimization corporations, and as financial School of Business, and the Graduate application only) least 30 points of graduate studies at and stochastic modeling, and a deep analysts in various functions (e.g., risk School of Arts and Sciences. IEOR E4561 Launch your startup: tech Columbia. Industrial Engineering may coverage of applications in the areas of management) of investment banks, IEOR E4562 Innovate using design thinking (weeklong course in mid-January, by include concentrations in: (1) Healthcare operations engineering and management. hedge funds, credit-card companies, application only) Management Science and Management; (2) Regulated Industries; In addition to the core and semi- and insurance firms. IEOR E4570 Entrepreneurship bootcamp for engineers (3-day long course fall or Engineering spring semester, by application only) and (3) Systems Engineering. Additional core requirements, Management Management Science and Management Science and Engineering IEOR E4711 Global capital markets details regarding these concentrations Science and Engineering has six Engineering (36 points) can be completed (MS&E), offered by the IEOR Department IEOR E4998 Managing technological innovation and entrepreneurship and electives are available in the concentrations: (1) Operations and in a single calendar year, in three in partnership with Columbia Business FINC B8307 Advanced corporate finance Departmental office and on the IEOR Analytics; (2) Pricing and Revenue semesters. Students enter in the fall term School, is the first such program website: ieor.columbia.edu. Management; (3) Entrepreneurship and and can either finish their coursework between Columbia Engineering and Innovation; (4) Logistics and Supply at the end of the following August, or Breadth Electives: Columbia Business School. It reflects The breadth electives can be selected from the Business School, the School of Engineering, the School of Operations Research Chain Management; (5) Financial alternatively, have the option to take the the next logical step in the long- International and Public Affairs, the Law School, or the Departments of Economics, Mathematics, and Statistics. Technology (Fin Tech); and (6) Healthcare summer term off (e.g., for an internship) Graduate studies in Operations Research standing close collaboration between Management. Additional details regarding and complete their coursework by the enables students to concentrate their the IEOR Department at the Engineering these concentrations are available on the end of the following fall term. Students studies in methodological areas such as School and the Decision, Risk, and MS&E website: mse.ieor.columbia.edu/ are required to take the equivalent of 12 mathematical programming, stochastic

ENGINEERING 2020–2021 ENGINEERING 2020–2021 168 and investors. Key topics covered include GU4001, and knowledge of a programming IEOR E3900x and y Undergraduate research 169 Operations Research (30 points) principles of accrual accounting; recognizing and language such as Python, C, C++ or Matlab. or project recording accounting transactions; preparation and It is strongly advised that Stochastic modeling 1–3 pts. Members of the faculty. Required Core Courses IEOR E4150 Intro to probability and statistics (or STAT GU4001 for spring intake only)1 analysis of financial statements; ratio analysis; pro- (IEOR E3106 or IEOR E4106) be taken before Prerequisite: Approval by a faculty member who (12 points) IEOR E4004 Optimization models and methods forma projections; time value of money (present this course. This is an introductory course to agrees to supervise the work. Independent work IEOR E4106 Stochastic models values, future values and interest/discount rates); simulation, a statistical sampling technique that involving experiments, computer programming, inflation; discounted-cash-flow (DCF) project uses the power of computers to study complex analytical investigation, or engineering design. IEOR E4404 Simulation evaluation methods; deterministic and probabilistic stochastic systems when analytical or numerical IEOR E3999x, y or s Fieldwork Concentrations measures of risk; capital budgeting. techniques do not suffice. The course focuses on 1–1.5 pts. (up to 2 pts, summer only) The department Analytics Healthcare Management discrete-event simulation, a general technique ORCA E2500y Foundations of data science Prerequisites: Obtained internship and approval recommends taking Decision, Risk, and Analysis Logistics and Supply Chain Management used to analyze a model over time and determine 3 pts. Lect: 3. from faculty adviser. Only for IEOR undergraduate three to five elective Entrepreneurship and Innovation Machine Learning and Artificial Intelligence the relevant quantities of interest. Topics covered Prerequisites: Calculus I and II, some familiarity students who need relevant work experience as part courses, depending on the in the course include the generation of random Finance and Management Optimization with programming. Designed to provide an of their program of study. Final reports are required. concentration. numbers, sampling from given distributions, introduction to data science for sophomore SEAS May not be taken for pass/fail credit or audited. simulation of discrete-event systems, output 1 majors. Combines three perspectives: inferential STAT GU4001 will not count towards the 18 IEOR point requirement. analysis, variance reduction techniques, goodness IEOR E4003x Corporate finance for engineers thinking, computational thinking, and real-world of fit tests, and the selection of input distributions. 3 pts. Lect: 3. applications. Given data arising from some real- The first half of the course is oriented toward the Prerequisites or corequisites: Probability theory and world phenomenon, how does one analyze that their first year of study. If a substantial design and implementation of algorithms, while the linear programming. Required for all undergraduate models, and simulation. Students may (2) and (3), they may be asked to data so as to understand that phenomenon? second half is more theoretical in nature and relies students majoring in IE, OR:EMS, OR:FE, and OR. complete the studies on a full time (12 equivalent has been completed during withdraw from the program at the end of Teaches critical concepts and skills in computer heavily on material covered in prior probability Introduction to the economic evaluation of industrial points per term) or part time basis. undergraduate studies, students should the second year. programming, statistical inference, and machine courses. The teaching methodology consists of projects. Economic equivalence and criteria. Operations Research has eight areas consult with a faculty adviser in order to Doctoral students are also required learning, in conjunction with hands-on analysis lectures, recitations, weekly homework, and both Deterministic approaches to economic analysis. obtain exemption from a required course. of real-world datasets such as economic data, of concentrations, including: (1) Analytics; to take 4 additional Ph.D. courses in-class and take-home exams. Homework almost Multiple projects and constraints. Analysis and document collections, geographical data, and (2) Decision, Risk, and Analysis; (3) (possibly in other departments) during always includes a programming component for choice under risk and uncertainty. social networks. At least one project will address a Entrepreneurship and Innovation; (4) PH.D. PROGRAM the course of the Ph.D. Research which students are encouraged to work in teams. problem relevant to New York City. IEOR E4004x and y Optimization models and Finance and Management; (5) Healthcare The IEOR Department offers two Ph.D. credits (IEOR E9101) do not count IEOR E3608x Foundations of optimization methods Management; (6) Logistics and Supply towards this requirement. It is important IEOR E3106x Stochastic systems and programs in (1) Industrial Engineering; 3 pts. Lect: 3. 3 pts. Lect: 3. applications Chain Management; (7) Machine and (2) Operations Research. The to select courses you find interesting Prerequisite: MATH UN2010. Corequisite: Data A graduate course only for MS&E, IE, and OR 3 pts. Lect: 3. Learning and Artificial Intelligence; and requirements for the Ph.D. in industrial while considering your background structures. This first course in optimization focuses Prerequisite: IEOR E3658. For undergraduates students. This is also required for students in the (8) Optimization. Students may select engineering and operations research and in consultation with your academic on theory and applications of linear optimization, only. Required for all undergraduate students Undergraduate Advanced Track. For students who from a variety of approved electives from network optimization, and dynamic programming. are identical. Both programs require adviser. Students can consider courses majoring in IE, OR:EMS, OR:FE, and OR. have not studied linear programming. Some of the the Department, the School of Business, the student to complete the qualifying from other departments including Must be taken during (or before) the fifth semester. IEOR E3609y Advanced optimization main methods used in IEOR applications involving and the Graduate School of Arts and procedure and submit and defend a Mathematics, Computer Science, Some of the main stochastic models used in 3 pts. Lect: 3. deterministic models: linear programming, the Sciences. Additional details regarding dissertation based on the candidate's Statistics, Economics, and Decision Risk engineering and operations research applications: Prerequisite: IEOR E3608. For undergraduates simplex method, nonlinear, integer and dynamic programming. these concentrations and electives are original research, conducted under and Operations. Doctoral candidates discrete-time Markov chains, Poisson processes, only. Required for all undergraduate students available in the Departmental office and the supervision of the faculty. The must obtain a minimum of 60 points birth and death processes and other continuous majoring in IE, OR:EMS, OR:FE, and OR. This IEOR E4007x Optimization models and on IEOR's website: ieor.columbia.edu. dissertation work may be theoretical or of formal course credit beyond the Markov chains, renewal reward processes. is a follow-up to IEOR E3608 and will cover methods for financial engineering Applications: queueing, reliability, inventory, advanced topics in optimization, including computational or both. bachelor’s degree. A master’s degree 3 pts. Lect: 3. and finance. IEOR E3106 must be completed integer optimization, convex optimization, and The qualifying procedure consists from an accredited institution may be Prerequisite: Linear algebra. This graduate course JOINT M.S. AND M.B.A. by the fifth term. Only students with special optimization under uncertainty, with a strong focus is only for M.S. Program in Financial Engineering of three components, including: (1) accepted as equivalent to 30 points. The department and the Graduate academic circumstances may be allowed to take on modeling, formulations, and applications. students. Linear, quadratic, nonlinear, dynamic, complete the four core courses during A minimum of 30 points beyond the these courses in alternative semesters with the School of Business offer a joint IEOR E3658x and y Probability for engineers and stochastic programming. Some discrete the first year with an average grade master’s degree must be earned while consultation of CSA and Departmental advisers. M.S. master's program in Industrial 3 pts. Lect: 3. optimization techniques will also be introduced. of (A-) or above; (2) conduct research in residence in the doctoral program. Engineering. Prospective students for this IEOR E3402y Production and inventory Prerequisite: Calculus. For undergraduates The theory underlying the various optimization special program must submit separate during the first summer (ideally starting Detailed information regarding the planning only. Required for OR:FE concentration. Must be methods is covered. The emphasis is on modeling applications to Columbia Engineering and in Spring or earlier) and present it in a requirements for the doctoral degree 4 pts. Lect: 3. Recit: 1. taken during or before third semester. Students and the choice of appropriate optimization methods. the Graduate School of Business and be department seminar at the beginning may be obtained in the Department Prerequisites: IEOR E3608 and E3658. who take IEOR E3658 may not take W4150 Applications from financial engineering are discussed. admitted to both schools for entrance of the third semester; and (3) submit a office and on IEOR website: ieor. For undergraduates only. Required for all due to significant overlap. Recommended: IEOR E4008x or y Computational discrete undergraduate students majoring in IE, OR:EMS, strong mathematical skills. Introductory course into the joint program. research report (paper) at the end of the columbia.edu. optimization OR:FE, and OR. Must be taken during (or before) to probability theory and does not assume any third semester. Students will be reviewed 3 pts. Lect: 3. Admissions requirements are the the sixth semester. Inventory management and after each component. A student who prior knowledge of subject. Teaches foundations Prerequisites: Linear programming, basic prob- same as those for the regular M.S. COURSES IN INDUSTRIAL production planning. Continuous and periodic required to use probability in applications, but fails to complete component (1) may be ability theory. Discrete optimization problems. program in Industrial Engineering and ENGINEERING AND review models: optimal policies and heuristic course itself is theoretical in nature. Basic asked to withdraw from the program at Mathematical techniques and testing strengths for the M.B.A. This joint program is OPERATIONS RESEARCH solutions, deterministic and probabilistic demands. definitions and axioms of probability and notions the end of the first year. and limits in practice on relevant applications. coordinated so that both degrees can For up-to-date course offerings, please Material requirements planning. Aggregate of independence and conditional probability Transportation (travelling salesman and vehicle A student who successfully planning of production, inventory, and work force. introduced. Focus on random variables, both be obtained after five terms of full-time visit ieor.columbia.edu. routing) and matching (online advertisement and completes component (1) will typically Multi-echelon integrated production-inventory continuous and discrete, and covers topics of study (30 points in two terms while school allocation) problems. move on to do summer research, IEOR E2261x and y Accounting and finance systems. Production scheduling. Term project. expectation, variance, conditional distributions, registered in Columbia Engineering and advised by a faculty member in the 3 pts. Lect: 3. Recitation section required. conditional expectation and variance, and moment IEOR E4009x or y Nonlinear optimization 45 points in three terms while registered Prerequisite: ECON UN1105 Principles of generating functions. Also Central Limit Theorem 3 pts. Lect: 3. Not offered in 2020–2021. IEOR Department. In the rare instance IEOR E3404y Simulation modeling and analysis in the Graduate School of Business). economics. For undergraduates only. Examines the for sums of random variables. Consists of lectures, Prerequisites: A course on optimization models the Ph.D. committee is dissatisfied with 4 pts. Lect: 4. Students in the joint program must fundamental concepts of financial accounting and recitations, weekly homework, and in-class exams. and methods (at the level of IEOR E4004) and a a student's performance in components Prerequisites: IEOR E3658 and E4307 or STAT complete certain courses by the end of finance, from the perspective of both managers course on linear algebra. Unconstrained and con-

ENGINEERING 2020–2021 ENGINEERING 2020–2021 170 strained nonlinear optimization involving continu- processes and other continuous Markov chains, tion to human-centered design. Students learn enterprise, the technology and methodology IEOR E4403x Quantitative corporate finance concave returns; equitable resource allocation; 171 ous functions. Additionally, fundamental concepts renewal reward processes. Applications: queueing, the vocabulary of design methods, understanding needed for manufacturing and product 3 pts. Lect: 3. lexicographic minmax/maxmin optimization; such as optimality conditions and convergence, reliability, inventory, and finance. of design process. Small group projects to create development, and strategic planning as currently Prerequisites: Probability theory and linear extensions to substitutable resources; multiperiod principle focus on practical optimization methods. prototypes. Design of simple product, more com- practiced in industry. programming Required for students in resource allocation; equitable allocation in IEOR E4108/DROM B8108x or y Supply chain plex systems of products and services, and design the Undergraduate Advanced Track. Key multicommodity network flow models; equitable CSOR E4010y Graph theory: a combinatorial view IEOR E4311x Derivatives marketing & analytics of business. measures and analytical tools to assess the content distribution in networks; equitable resource structuring 3 pts. Lect: 3. Not offered in 2020–2021. 3 pts. Lect: 2.5. financial performance of a firm and perform allocation with discrete decision variables. Prerequisites: Linear algebra, or instructor’s Prerequisite: IEOR E3402 or instructor's IEOR E4206x or y Intellectual property for 1.5 pts. Lect: 1.5. the economic evaluation of industrial projects. permission. An introductory course in graph theory permission. MS IEOR students only. Supply engineers Prerequisites: IEOR E3402, IEOR E4000, Deterministic mathematical programming IEOR E4412y Quality control and with emphasis on its combinatorial aspects. Basic chain management, model design of a supply 0 pts. or instructor's permission. Covers topics in models for capital budgeting. Concepts in management definitions, and some fundamental topics in graph chain network, inventories, stock systems, Intellectual property (patents, copyrights, trade- Accounting, relationships among different utility theory, game theory and real options 3 pts. Lect: 3. theory and its applications. Topics include trees commonly used inventory models, supply marks) are an increasingly critical part of almost elements of financial statements, short- term analysis. Prerequisite: IEOR E3658 and working knowledge and forests graph coloring, connectivity, matching contracts, value of information and information any business, at almost any stage of growth. and long-term financing alternatives, using of statistics. Required for undergraduate students IEOR E4404x and y Simulation theory and others. sharing, risk pooling, design for postponement, Provides the aspiring business executive, tech swaps, cap, and floors to manage interest rate majoring in IE. Statistical methods for quality 4 pts. Lect: 3. Recit: 1. managing product variety, information entrepreneur, or engineer with an overview of risk, hedging interest risk of corporate finance, control and improvement: graphical methods, IEOR E4100x Statistics and simulation Prerequisites: IEOR E3658 and E4307 or STAT technology and supply chain management; commercial opportunities and risks associated using options as cheapeners, structured introduction to experimental design and reliability 1.5 pts. Lect: 1.5. GU4001, computer programming. Corequisite: international and environmental issues. Note: with intellectual property, with a particular focus swaps, accounting treatment of derivatives, engineering and the relationships between quality Prerequisites: Understanding of single- and on technology patents. While legal principles will IEOR E3106 or IEOR E4106. Required for all replaces IEOR E4000 beginning in fall 2018. cash flow hedging, accrual accounting, and productivity. Contemporary methods used by multivariable calculus. Probability and simulation. be addressed, the primary focus is on leveraging hedging issuance of a bond using treasuries, undergraduate students majoring in IE, OR:EMS, manufacturing and service organizations in product Statistics building on knowledge in probability and IEOR E4111x and y Operations consulting intellectual property to create financial returns. hedging employee stock options, preferred OR:FE, and OR. Also required for MSOR. and process design, production and delivery of simulation. Point and interval estimation, hypothesis 3 pts. Lect: 3. shares and their use in corporate treasury, FX Generation of random numbers from given products and services. IEOR E4207x Human factors: performance testing, and regression. A specialized version of Prerequisites: Probability and statistics at risk and FX translation, commodities hedging, distributions; variance reduction; statistical output 3 pts. Lect: 3. IEOR E4418x or y Transportation analytics IEOR E4150 for MSE and MSBA students who are the level of IEOR E3658 and E4307 or STAT operating lease vs capital lease, credit risk, analysis; introduction to simulation languages; Required for undergraduate students majoring and logistics exempt from the first half of IEOR E4101. Must GU4001, and Deterministic Models at the level and cred spread and funding. Note: restricted application to financial, telecommunications, in IE. Sensory and cognitive (brain) processing 3 pts. Lect: 3. obtain waiver for E4101. of IEOR E3608 or IEOR E4004, or instructor to IEOR MS students. computer, and production systems. Graduate considerations in the design, development, and Prerequisite: IEOR E3608 or E4404 or permission permission. For MS-MS&E students only. students must register for 3 points. Undergraduate operations of systems, products, and tools. User or IEOR E4312y Application of OR & AI of instructor. Introduces quantitative techniques IEOR E4101x Probability, statistics and Aims to develop and harness the modeling, students must register for 4 points. NOTE: operator limits and potential in sensing, perceiving techniques in marketing and state-of-the-art practice of operations simulation analytical, and managerial skills of engineering Students who have taken IEOR E4703 Monte decision making, movement coordination, memory, 1.5 pts. Lect: 1.5. research relevant to the design and both the 3 pts. Lect: 3. students and apply them to improve the Carlo simulation may not register for this course for and motivation. Prerequisites: working knowledge of Excel, tactical and strategic management of logistical Prerequisites: Understanding of single- and operations of both service and manufacturing credit. Recitation section required. multivariable calculus. MSE and MSBA high level language (such as Python, R, and transportation systems. Discusses a wide firms. Structured as a hands-on laboratory in IEOR E4208y Seminar in human factors design MATLAB, or VBA), and intro course in IEOR E4405y Scheduling variety of passenger and freight systems, students only. Basic probability theory, including which students "learn by doing" on real-world 3 pts. Lect: 3. probability and statistics. Covers working 3 pts. Lect: 3. including air, urban and highway traffic, rail, independence and conditioning, discrete and consulting projects (October to May). The Prerequisite: IEOR E4207 or instructor’s knowledge of quantitative methods and data Prerequisites: IEOR E3608 and E3658. Computer and maritime systems. Explores the practice continuous random variable, law of large numbers, student teams focus on identifying, modeling, permission. An elective for undergraduate students mining techniques applied to marketing and programming. Required for undergraduate students of revenue management and dynamic pricing. central limit theorem, and stochastic simulation, and testing (and sometimes implementing) majoring in IE. An in-depth exploration of the customer relationship management. Topics majoring in IE and OR. Job shop scheduling: Through case studies, analyzes successes and basic statistics, including point and interval operational improvements and innovations with application potential of human factor principles for include clustering methods, conjoint analysis parallel machines, machines in series; arbitrary failures in third-party logistics, postal, truck and estimation, hypothesis testing, and regression; high potential to enhance the profitability and/or the design of products and processes. Applications and customer preferences, forecasting, job shops. Algorithms, complexity, and worst- rail pickup and delivery systems. Investigates examples from business applications such as achieve sustainable competitive advantage for to industrial products, tools, layouts, workplaces, market share, product life cycle, new product, case analysis. Effects of randomness: machine large-scale integrated logistics and transportation inventory management, medical treatments, and their sponsor companies. The course is targeted and computer displays. Consideration to nearest neighbor, discriminant analysis, breakdowns, random processing time. Term systems and studies the underlying principles finance. A specialized version of IEOR E4150 for toward students planning careers in technical environmental factors, training and documentation. decision tree, revenue management, price project. governing transportation planning, investment and MSE and MSBA students. consulting (including operations consulting) Term project. and advertising elasticity, resource allocation operations. and management consulting, or pursuing IEOR E4407x Game theoretic models of IEOR E4102y Stochastic models for MSE IEOR E4212x Data analytics for OR and return on investment (ROI), economic positions as business analysts in operations, operations IEOR E4500x Applications programming for 3 pts. Lect: 3. 3 pts. Lect: 3. analysis of a network and its formation, and logistics, supply chain and revenue management 3 pts. Lect: 3. financial engineering Prerequisite: IEOR E4101. Introduction to sto- Surveys tools available in Python for getting, networked markets. Note: restricted to IEOR functions, positions in general management, and Prerequisites: IEOR E4004 (or E3608), IEOR 3 pts. Lect: 3. chastic processes and models, with emphasis cleaning, and analyzing data. Data from files MS students. future entrepreneurs. E4106 (or E3106), familiarity with differential Prerequisite: Computer programming or (csv, html, json, xml) and databases (Mysql, on applications to engineering and management; IEOR E4402x Corporate finance, accounting, equations and computer programming; instructor’s approval. Required for undergraduate PostgreSQL, NoSQL), covers rudiments of data random walks, gambler’s ruin problem, Markov IEOR E4150x Introduction to probability and & investment banking or instructor’s permission. Required for students majoring in OR:FE. We will take a hands- cleaning, and examine data analysis, machine chains in both discrete and continuous time, statistics 3 pts. Lect: 3. undergraduate students majoring in OR:FE on approach to developing computer applications learning (regression, decision trees, clustering) Poisson processes, renewal processes, stopping 3 pts. Lect: 3. Prerequisite: Covers primary financial theories and and OR. A mathematically rigorous study for Financial Engineering. Special focus will be data visualization packages (NumPy, Pandas, times, Wald’s equation, binomial lattice model Prerequisite: Calculus, including multiple alternative theories underlying Corporate Finance, of game theory and auctions, and their placed on high-performance numerical applications Scikit-learn Bokeh, available in Python. Note: for pricing risky assets, simple option pricing; integration. Covers the following topics: such as CAPM, Miller Modigliani, Fama French application to operations management. that interact with a graphical interface. In the IEOR students only. simulation of simple stochastic processes, fundamentals of probability theory and statistical factors, Smart Beta, etc. Interpret financial state- Topics include introductory game theory, course of developing such applications we will Brownian motion, and geometric Brownian inference used in engineering and applied science; IEOR E4307x Statistics and data analysis ments, build cash flow models, value projects, private value auction, revenue equivalence, learn how to create DLLs, how to integrate motion. A specialized version of IEOR E4106 for Probabilistic models, random variables, useful 3 pts. Lect: 3. value companies, and make Coporate Finance mechanism design, optimal auction, multiple- VBA with C/C++ programs, and how to write MSE students. distributions, expectations, law of large numbers, Prerequisites: probability, linear algebra. decisions. Additional topics include: cost of capi- unit auctions, combinatorial auctions, multithreaded programs. Examples of problems central limit theorem; Statistical inference: pint and Descriptive statistics, central limit theorem, incentives, and supply chain coordination with settings that we consider include simulation of IEOR E4106x and y Stochastic models tal, dividend policy, debt policy, impact of taxes, confidence interval estimation, hypothesis tests, parameter estimation, sufficient statistics, contracts. No previous knowledge of game stock price evolution, tracking, evaluation and 3 pts. Lect: 3. Shareholder/Debtholder agency costs, dual-class linear regression. For IEOR graduate students. hypothesis testing, regression, logistic regression, theory is required. optimization of a stock portfolio; optimal trade Prerequisites: STAT GU4001 or probability theory shares, using option pricing theory to analyze goodness-of-fit tests, applications to operations execution. In the course of developing these IEME E4200x or y Human-centered design & management behavior, investment banking activi- IEOR E4408x Resource allocation: models, or IEOR E4150. This graduate course is only for research models. applications, we review topics of interest to OR:FE ties, including equity underwriting, syndicated lend- algorithms, and applications IE and OR students. Also required for students in innovation in a holistic fashion. the Undergraduate Advanced Track. Some of the 3 pts. Lect: 2.5. IEME E4310x The manufacturing enterprise ing, venture capital, private equity investing and 3 pts. Lect: 3. Not offered in 2020–2021. main stochastic models used in engineering and Prerequisite: Instructor's permission. Open to 3 pts. Lect: 3. Not offered in 2020–2021. private equity secondaries. Application of theory in Prerequisites: Linear programming (IEOR E3608 ORCA E4500x or y Foundations of data operations research applications: discrete-time SEAS graduate and advanced undergraduate The strategies and technologies of global real-world situations: analyzing financial activities or E4004), basic knowledge of nonlinear and science Markov chains, Poisson processes, birth and death students, Business School, and GSAPP. Students manufacturing and service enterprises. of companies such as General Electric, Google, integer programming. Overview of resource 3 pts. Lect: 3. from other schools may apply. Fast-paced introduc- Connections between the needs of a global Snapchat, Spotify, and Tesla. allocation models. Single resource allocation with Prerequisites: Calculus I and II, some familiar-

ENGINEERING 2020–2021 ENGINEERING 2020–2021 172 ity with programming. Designed to provide an analytical, and managerial skills of engineering IEOR E4524y Analytics in practice world in creating, funding, investing in, relating Primer on quantitative and mathematical concepts. horizons, and pricing of fixed-income derivatives 173 introduction to data science for sophomore SEAS and health care management students. Enables 3 pts. Lect: 3. to, and operating entrepreneurial ventures. Required for all incoming MSBA students. (Ho-Lee, Black-Derman-Toy, Heath-Jarrow- majors. Combines three perspectives: inferential students to master an array of fundamental Prerequisites: IEOR E4522 or E4501 and IEOR The first half of the course focuses on the Morton interest rate model). IEOR E4601y Dynamic pricing and revenue thinking, computational thinking, and real-world operations management tools adapted to the E4523. MSOR students only. Groups of students underpinning principles and skills required in management IEOR E4650x and y Business analytics applications. Given data arising from some real- management of health care systems. Through real- will work on real world projects in analytics, focus- recognizing, analyzing, evaluating, and nurturing 3 pts. Lect: 3. 3 pts. Lect 3. Recit: 1. world phenomenon, how does one analyze that world business cases, students learn to identify, ing on three aspects: identifying client analytical a business idea. The second half focuses on Prerequisites: STAT GU4001 and IEOR E4004. Prerequisite: STAT GU4001 or IEOR E4150. data so as to understand that phenomenon? model, and analyze operational improvements and requirements; assembling, cleaning, and organizing basic legal knowledge necessary in creating a Focus on capacity allocation, dynamic pricing and Prepares students to gather, describe, and Teaches critical concepts and skills in computer innovations in a range of health care contexts. data; identifying and implementing analytical tech- business entity, defending your business assets, revenue management. Perishable and/or limited analyze data, using advanced statistical tools programming, statistical inference, and machine niques (statistics, OR, machine learning); and deliv- and in promoting effective interaction with other IEOR E4510y Project management product and pricing implications. Applications to to support operations, risk management, and learning, in conjunction with hands-on analysis ering results in a client-friendly format. Each project individuals and organizations. 3 pts. Lect: 3. various industries including service, airlines, hotel, response to disruptions. Analysis is done by of real-world datasets such as economic data, has a well-defined goal, comes with sources of data Prerequisites: IEOR E4004 (or IEOR E3608). IEOR E4555x or y Design and agile project resource rentals, etc. targeting economic and financial decisions in document collections, geographical data, and preidentified, and has been structured so that it can Management of complex projects and the tools management engineering lab complex systems that involve multiple partners. social networks. be completed in one semester. Client-facing class IEOR E4602y Quantitative risk management that are available to assist managers with 3 pts. Lect: 3. Not offered in 2020–2021. with numerous on-site client visits; students should 3 pts. Lect: 3. Topics include probability, statistics, hypothesis such projects. Topics include project selection, Intensive, team-, and project-based seminar IEOR E4501x and y Tools for analytics keep Fridays clear for this purpose. Prerequisites: STAT GU4001 and IEOR E4106. testing, experimentation, and forecasting. project teams and organizational issues, project covering multidisciplinary approach to evidence- 3 pts. Lect: 3. Risk management models and tools; measure risk monitoring and control, project risk management, IEOR E4525x and y Machine learning for based product design; agile project planning and IEOR E4700x and y Introduction to financial MS IEOR students only. Introduction programming using statistical and stochastic methods, hedging project resource management, and managing financial engineering and operations execution; rapid MVP prototyping; and launch engineering in Python, tools with the programmer's ecosystem. and diversification. Examples include insurance multiple projects. 3 pts. Lect: 3. strategy formulation and implementation. Focuses 3 pts. Lect: 3. Python, Data Analysis tools in Python (NumPy, risk, financial risk, and operational risk. Topics Prerequisites: Optimization, applied probability, on practical use of design thinking, design stu- Prerequisite: IEOR E4106 or E3106. Required pandas, bokeh), GIT, Bash, SQL, VIM, Linux/ IEOR 4520x Applied systems engineering covered include VaR, estimating rare events, statistics or simulation. MS IEOR students only. dio, and iterative design sprint methodologies. for undergraduate students majoring in OR:FE. Debia, SSH. 3 pts. Lect: 3. Introduction to machine learning, practical imple- Systematic approaches to Lean User Research, extreme value analysis, time series estimation of Introduction to investment and financial Prerequisites: B.S. in engineering or applied IEOR E4502x Python for analytics mentation ML algorithms and applications to User Experience (UX), and User Interface (UI) extremal events; axioms of risk measures, hedging instruments via portfolio theory and derivative sciences; professional experience recommended; 0 pts. Lect: 1. financial engineering and operations. Probabilistic design and deployment are integral components using financial options, credit risk modeling, and securities, using basic operations research/ calculus, probability and statistics, linear algebra. Zero-credit course. Primer on Python for analytics tools of machine learning, learning theory, clas- of course curriculum. Mix of startup and enter- various insurance risk models. engineering methodology. Portfolio theory, Introduction to fundamental methods used in concepts. Required for MSBA students. sification, resampling methods and regularization, prise projects, including application drive, data- arbitrage; Markowitz model, market equilibrium, systems engineering. Rigorous process that IEOR E4615y Service engineering support vector machines (SVMs), unsupervised driven, or combination of both. Teams are fully IEOR E4505y Operations research in public translates customer needs into a structured set 3 pts. Lect: 3. Not offered in 2020–2021. and the capital asset pricing model. General learning, dimensionality reduction and clustering supported in devising prototypes and actualizing policy of specific requirements; synthesizes a system Prerequisites: Introductory courses in probability models for asset price fluctuations in discrete algorithms, EM algorithm, and neural networks and proposed solutions. 3 pts. Lect: 3. architecture that satisfies those requirements and statistics such as IEOR E3658 and E4307, and continuous time. Elementary introduction to deep learning. Prerequisites: IEOR E3608 or IEOR E4004, and allocates them in a physical system, meeting IEOR E4561x or y Launch your startup: tech and introductory courses in stochastic processes Brownian motion and geometric Brownian motion. IEOR E3106 or IEOR E4106. Aims to give cost, schedule, and performance objectives IEOR E4526x or y Analytics on the cloud 3 pts. Lect: 3. such as IEOR E3106 or IEOR E4106. Focus on Option theory; Black-Scholes equation and call the student a broad overview of the role of throughout the product life-cycle. Sophisticated 3 pts. Lect: 3. Tools and knowledge to develop a comprehensive service systems viewed as stochastic networks, option formula. Computational methods such as Operations Research in public policy. The modeling of requirements optimization and Prerequisites: IEOR E4501 and E4523. To new venture that is scalable, repeatable, and capi- exploiting the theoretical framework of queueing Monte Carlo simulation. dependencies, risk management, probabilistic theory. Includes multidisciplinary perspectives specific areas covered include voting theory, introduce students to programming issues around tal efficient. Covers customer discovery, market IEOR E4701x Stochastic models for financial scenario scheduling, verification matrices, and involving Statistics, Psychology, and Marketing. apportionment, deployment of emergency working with clouds for data analytics. Class will sizing, pricing, competition, distribution, funding, engineering systems-of-systems constructs are synthesized Significant emphasis on data analysis, exploiting units, location of hazardous facilities, health learn how to work with infrastructure of cloud plat- developing a minimal viable product, and other fac- 3 pts. Lect: 3. to define the meta-workflow at the top of every data from banks, hospitals, and call centers to care, organ allocation, management of natural forms, and discussion about distributed computing, ets of creating new ventures. A company blueprint Prerequisite: STAT GU4001. This graduate course resources, energy policy, and aviation security. major engineering project. focus of course is on programming. Topics covered and final investor pitch are deliverables. demonstrate the use of decision support tools. Analytical models, flow models of service networks, is only for M.S. Program in Financial Engineering Draws on a variety techniques such as linear and include MapReduce, parallelism, rewriting of IEOR 4521y Systems engineering tools and IEOR E4562x, y, or s Innovate using design Little’s law, measuring methods in face-to-face students, offered during the summer session. integer programming, statistical and probabilistic algorithms (statistical, OR, and machine learning) methods thinking and computerized systems, forecasting methods, Review of elements of probability theory, Poisson methods, decision analysis, risk analysis, and for the cloud, and basics of porting applications so 3 pts. Lect: 3. 3 pts. Lect: 3. stability of service systems, operational quality processes, exponential distribution, renewal theory, analysis and control of dynamic systems. that they run on the cloud. Prerequisites: B.S. in engineering or applied How Design Thinking can enhance innovation of service, economies of scale, staffing, complex Wald’s equation. Introduction to discrete-time IEOR E4506x Designing digital operating sciences; probability and statistics, optimization, IEOR E4540x and y Data mining for engineers activities, market impact, value creation, and service networks, skill-based routing. Markov chains and applications to queueing theory, models linear algebra, and basic economics. Applications 3 pts. Lect: 3. speed. Topics include: conceptual and practi- inventory models, branching processes. IEOR E4620x Pricing models for financial of SE tools and methods in various settings. Prerequisites: Linear Algebra, Calculus, Probability, 3 pts. Lect: 3. cal understanding of design thinking, creative IEOR E4703y Monte Carlo simulation and some basic programming. Course covers major engineering IEOR students only. Understand digital businesses, Encompasses modern complex system solutions, develop robust practices to lead inter- 3 pts. Lect: 3. statistical learning methods for data mining under 3 pts. Lect: 3. apply scientific, engineering thinking to digital development environments, including aerospace and disciplinary teams. Course aims to strengthen Prerequisite: IEOR E4701. This graduate course both supervised and unsupervised settings. Topics Prerequisite: IEOR E4700. Required for economy. Data-driven digital strategies and defense, transportation, energy, communications, individuals and collaborative capabilities to is only for M.S. Program in Financial Engineering covered include linear regression and classification, undergraduate students majoring in OR:FE. operating models. Sectors: ecommerce, advertising and modern software-intensive systems. identify customer needs, indirect and qualitative students. Multivariate random number generation, model selection and regularization, tree-based Characteristics of commodities or credit technology, and marketing technology. Automation research, create concept hypotheses, develop bootstrapping, Monte Carlo simulation, efficiency IEOR E4523x and y Data analytics methods, support vector machines, and unsuper- derivatives. Case study and pricing of structures of the marketing, sales, and advertising functions. prototype, defined opportunities into actionable improvement techniques. Simulation output 3 pts. Lect: 3. vised learning. Students learn about principles and products. Topics covered include swaps, Algorithms, patents, and business models. innovation possibilities, and recommendations for analysis, Markov-chain Monte Carlo. Applications Corequisite: IEOR E4522 or E4501. IEOR stu- underlying each method, how to determine which credit derivatives, single tranche CDO, hedging, Business side of the digital ecosytem and the client organizations. to financial engineering. Introduction to financial dents only; priority to MSBA students. Survey methods are most suited to applied settings, con- convertible arbitrage, FX, leverage leases, debt digital economy. engineering simulation software and exposure to tools available in Python for getting, cleaning, and cepts behind model fitting and parameter tuning, markets, and commodities. modeling with real financial data. NOTE: Students IEOR E4507x or y Healthcare operations analyzing data. Obtain data from files (csv, html, and how to apply methods in practice and assess IEOR E4570-4579x and y Topics in operations IEOR E4630y Asset allocation who have taken IEOR E4404 Simulation may not management json, xml) and databases (Mysql, PostgreSQL, their performance. Emphasizes roles of statistical research 3 pts. Lect: 3. register for this course for credit. 3 pts. Lect: 3. NoSQL), cover the rudiments of data cleaning, modeling and optimization in data mining. 1.5–3 pts. Lect: 1.5–3. Members of the faculty. Prerequisite: IEOR E4700. Models for pricing Prerequisites: for senior undergraduate and examine data analysis, machine learning, Prerequisites: IEOR E4150, E4004, and E4106, or IEOR E4706x Foundations of financial IEOR E4550x Entrepreneurial business creation and hedging equity, fixed-income, credit- Engineering students: IEOR E3608, E3658, and and data visualization packages (NumPy, pandas, instructor's permission. Each offering of this course engineering for engineers derivative securities, standard tools for hedging E4307; for Engineering graduate students (M.S. Scikit-lern, bokeh) available in Python. Brief is devoted to a particular sector of Operations 3 pts. Lect: 3. 3 pts. Lect: 3. and risk management, models and theoretical or Ph.D.): Probability and statistics at the level overview of natural language processing, network Research and its contemporary research, practice, Prerequisites: IEOR E4701, E4702, and linear Prerequisite: IEOR E2261. Required for foundations for pricing equity options (standard of IEOR E4150, and deterministic models at the analysis, and big data tools available in Python. and approaches. If topics are different, then course algebra. This graduate course is only for M.S. undergraduate students majoring in OR:EMS. European, American equity options, Asian level of IEOR E4004; for health care management Contains a group project component that will can be taken more than once for credit. Program in Financial Engineering students, offered Introduces the basic concepts and methodologies options), standard Black-Scholes model (with students: P8529 Analytical methods for health require students to gather, store, and analyze a during the summer session. Discrete-time models that are used by the nonengineering part of the IEOR E4599x MSBA quantitative bootcamp multiasset extension), asset allocation, portfolio services management. Develops modeling, data set of their choosing. of equity, bond, credit, and foreign-exchange 0 pts. Lect: 3. optimization, investments over longtime

ENGINEERING 2020–2021 ENGINEERING 2020–2021 174 markets. Introduction to derivative markets. Pricing utility theory and on systematic biases against in Java, mortgage-backed securities, numerical ideal platform for derivatives. The emphasis is quantitative finance applications. Note: restricted to IEOR E4900s, x and y Master’s research or 175 and hedging of derivative securities. Complete rational beliefs such as Bayesian rule. solutions of partial differential equations, quantitative on familiarizing the student with the nature of the IEOR MS FE students only. project and incomplete markets. Introduction to portfolio portfolio management, risk management, trade and foreign exchange market and those factors that 1–3 pts. Members of the faculty. IEOR E4714x Risk management, financial IEOR E4742x and y Deep learning and its optimization and the capital asset pricing model. technology in financial markets. make it special among financial markets, enabling Prerequisite: Approval by a faculty member who system and financial crisis applications in FE and OR the student to gain a deeper understanding of the agrees to supervise the work. Independent work IEOR E4707y Financial engineering: 1.5 pts. Not offered in 2020–2021. IEOR E4731x Credit risk modeling and related market for derivatives on foreign exchange. 3 pts. Lect: 3. involving experiments, computer programming, continuous-time asset pricing Risk-taking and risk management are at the heart derivatives Selected topics of interest in area of quantitative analytical investigation, or engineering design. 3 pts. Lect: 3. of the financial system, and of the current financial 3 pts. Lect: 3. IEOR E4735y Structured and hybrid products finance. Some topics include energy derivatives, Prerequisites: IEOR E4701. This graduate crisis. An introduction to risk management both Prerequisites: IEOR E4701 and E4707. 3 pts. Lect: 3. experimental finance, foreign exchange IEOR E4998y Managing technological course is only for MS program in FE students. from an individual financial firm’s and from a public Introduction to quantitative modeling of credit risk, Prerequisite: IEOR E4700. Conceptual and and related derivative instruments, inflation innovation and entrepreneurship Modeling, analysis, and computation of derivative policy viewpoint. Overview of the contemporary with a focus on the pricing of credit derivatives. practical understanding of structured and derivatives, hedge fund management, modeling 3 pts. Lect: 3. securities. Applications of stochastic calculus financial system, focusing on innovations of the Focus on the pricing of single-name credit hybrid products from the standpoint of relevant equity derivatives in Java, mortgage-backed A required course for undergraduate students and stochastic differential equations. Numerical past few decades that have changed how financial derivatives (credit default swaps) and collateralized risk factors, design goals and characteristics, securities, numerical solutions of partial differential majoring in OR:EMS. Focus on the management techniques: finite-difference, binomial method, risk is generated and distributed among market debt obligations (CDOs). Detail topics include pricing, hedging, and risk management. equations, quantitative portfolio management, risk and consequences of technology-based and Monte Carlo. participants, such as the growth of non-bank default and credit risk, multiname default barrier Detailed analysis of the underlying cash-flows, management, trade and technology in financial innovation. Explores how new industries financial intermediaries, the increased prevalence models and multiname reduced form models. embedded derivative instruments, and various markets. Note: open to IEOR students only. IEOR E4708y Seminar on important papers in are created, how existing industries can be of leverage and liquidity risk, and the development structural features of these transactions, both transformed by new technologies, the linkages financial engineering IEOR E4732x Computational methods in IEOR E4743s Financial correlations— of structured credit products. Introduction to the from the investor and issuer perspectives, and 3 pts. Lect: 3. Not offered in 2020–2021. modeling, trading, risk management &AI between technological development and basic quantitative tools used in market, credit, and finance analysis of the impact of the prevailing market Prerequisites: IEOR E4703, E4706, probability 3 pts. Lect: 3. the creation of wealth and the management liquidity risk management. The two strands of the 3 pts. Lect: 3. conditions and parameters on their pricing and statistics. Selected topics of special interest to Introduction to math finance, knowledge of challenges of pursuing strategic innovation. course are brought together to help understand Prerequisite: IEOR E4700. MS IEOR students only. and risk characteristics. Numerical methods M.S. students in financial engineering. If topics are working as a "Quant" in investment banking, how the financial crisis arose and is playing Application of various computational methods/ for valuing and managing risk of structured/ IEOR E4999s, x and y Fieldwork different then this course can be taken more than hedge funds, algo shop, HFT firm, Fed, Exchange, out, examining the mechanics of runs and the techniques in quantitative/computational finance. hybrid products and their embedded derivatives 1–1.5 pts (up to 2 pts, summer only). once for credit. SEC, IMF, back office, mutual fund, as a trader in behavior of asset prices during crises. Attempt to Transform techniques: fast Fourier transform and their application to equity, interest rates, Prerequisites: Obtained internship and approval for data de-noising and pricing, finite difference risk management, product development, model IEOR E4709y Statistical analysis and time understand the emergency programs deployed by commodities and currencies, inflation, and from faculty adviser. Only for IEOR graduate methods for partial differential equations (PDE), validation, compliance, reporting, academia. Open series central bankers and other policy makers to address credit-related products. Conceptual and students who need relevant work experience partial integro-differential equations (PIDE), only to master's students in IEOR department. 3 pts. Lect: 3. crises historically and today. mathematical principles underlying these as part of their program of study. Final reports Monte-Carlo simulation techniques in finance, and Prerequisites: Probability and IEOR E4702. techniques, and practical issues that arise in IEOR E4744s Modeling & market making in required. May not be taken for pass/fail credit IEOR E4715x, s Commodity derivatives calibration techniques, filtering and parameter Corequisites: IEOR E4706, E4707. This graduate their implementations in the Microsoft Excel/VBA foreign exchange or audited. 1.5 pts. Not offered in 2020–2021. estimation techniques. Computational platform will course is only for M.S. Program in Financial and other programming environments. Special 1.5 pts. Lect: 1.5. Commodities markets have been much in the be C++/Java/Python/Matlab/R. MSIE W6408y Inventory theory Engineering students. Empirical analysis of asset contractual provisions encountered in structured Introduction to topics in modeling and market public eye recently as volatility has increased and 3 pts. Lect: 3. Not offered in 2020–2021. prices: heavy tails, test of the predictability of stock IEOR E4733x or y Algorithmic trading and hybrid transactions, and incorporation of making in foreign exchange, such as spots they changed from markets dominated by physical Prerequisites: Probability theory, dynamic returns. Financial time series: ARMA, stochastic 3 pts. Lect: 3. Not offered in 2020–2021. yield curves, volatility smile, and other features markets, forward markets, vanilla option markets, participants to ones which have a significant programming. Construction and analysis of volatility, and GARCH models. Regression models: Prerequisite: IEOR E4700. Large and amorphous of the underlying processes into pricing and exotic derivative markets, and algorithmic index investor component. The largest banks either mathematical models used in the design and linear regression and test of CAPM, nonlinear collection of subjects ranging from the study implementation framework for these products. markets. Open only to master's students in IEOR already have profitable commodities franchises or regression and fitting of term structures. of market microstructure, to the analysis of analysis of inventory systems. Deterministic and are actively building them, and money managers IEOR E4738x Programming for FE 1: tools for department. optimal trading strategies, to the development of stochastic demands and lead times. Optimality IEOR E4710x Fixed income and term structure and funds are increasingly including these assets building financial data and risk systems IEOR E4745x Applied financial risk computerized, high-frequency trading strategies. of (s, S) policies. Multiproduct and multiechelon modeling in their portfolio mix. The end result is a dramatic 3 pts. Lect: 3. Not offered in 2020–2021. Analysis of these subjects, the scientific and management systems. Computational methods. 3 pts. Lect: 3. Not offered in 2020–2021. increase in focus on these markets from all Prerequisite: Familiarity with object-oriented practical issues they involve, and the extensive 3 pts. Lect: 3. Prerequisites: IEOR E4706, E4707, and computer aspects of the financial markets, including the programming. Object-oriented programming and IEOR E6602y Nonlinear and convex body of academic literature they have spawned. Prerequisites: courses in probability and statistics, programming. Interest rate models and numerical quantitative end. database development for building financial data programming Attempt to understand and uncover the economic instruments of the financial markets, and asset techniques for pricing and hedging interest rate and risk systems; Python and Python's scientific 3 pts. Lect: 3. Not offered in 2020–2021. IEOR E4718x or y Beyond Black-Scholes: the and financial mechanisms that drive and ultimately pricing models. Introduces risk management contracts and fixed income securities. Prerequisite: Ph.D.-level linear programming. implied volatility smile relate them. libraries; basic database theory, querying and principles, practical implementation and constructing databases; basic risk management applications, standard market, liquidity, and Convex sets and functions, convex duality and IEOR E4711x Global capital markets 3 pts. Lect: 3. IEOR E4734y Foreign exchange and related and design of risk systems. credit risk measurement techniques, and their optimality conditions. Computational methods: 3 pts. Lect: 3. Prerequisites: IEOR E4706, knowledge of derivatives instruments drawbacks and limitations. Note: restricted to steepest descent, Newton and quasi-Newton Prerequisites: Refer to course syllabus. An derivatives valuation models. During the past 15 1.5 pts. Lect: 1.5. IEOR E4739y Programming for FE 2: IEOR students only. methods for unconstrained problems, active set, introduction to capital markets and investments years the behavior of market options prices have Prerequisite: IEOR E4700. Foreign exchange implementing high-performance financial penalty set, interior point, augmented Lagrangian providing an overview of financial markets and shown systematic deviations from the classic market and its related derivative instruments—the systems IEOR E4798x Financial Engineering and sequential quadratic programming methods tools for asset valuation. Topics covered include Black-Scholes model. Examines the empirical latter being forward contracts, futures, options, 3 pts. Lect: 3. Not offered in 2020–2021. practitioners seminar series for constrained problems. Introduction to the pricing of fixed-income securities (treasury behavior of implied volatilities, in particular the 0 pts. Lect: 1.5. and exotic options. What is unusual about foreign Prerequisites: IEOR E4738 and instructor’s nondifferentiable optimization and bundle methods. markets, interest rate swaps futures, etc.), volatility smile that now characterizes most exchange is that although it can rightfully claim to permission. Developing effective software Degree requirement for all MSFE first-year discussions on topics in credit, foreign exchange, markets, the mathematics and intuition behind be the largest of all financial markets, it remains implementations in C programming language; students. Topics in Financial Engineering. IEOR E6613x Optimization, I sovereign ad securitized markets—private equity new models that can account for the smile, and an area where very few have any meaningful modeling of portfolio optimization; modeling Past seminar topics include Evolving Financial 4.5 pts. Lect: 3. and hedge funds, etc. their consequences for hedging and valuation. Intermediation, Measuring and Using Trading experience. Virtually everyone has traded stocks, of price impact trading models; review of Prerequisite: Linear algebra. Theory and Algorithms Effectively, Path-Dependent Volatility, geometry of linear programming. The simplex IEOR E4712x Behavioral finance IEOR E4720x and y–E4729 Topics in bonds, and mutual funds. Comparatively few synchronization of programs using the file system; Artificial Intelligence and Data Science in modern method. Duality theory, sensitivity analysis, 1.5 pts. Lect: 3. Not offered in 2020–2021. quantitative finance individuals have ever traded foreign exchange. review of synchronization of programs using financial decision making, Risk-Based Performance column generation and decomposition. Interior Prerequisite: IEOR E4700. Behavioral finance 1.5–3 pts. Lect: 2–2.5. Members of the faculty. In part that is because foreign exchange is an threads; review of synchronization of programs Attribution, and Financial Machine Learning. Meets point methods. Introduction to nonlinear is the application of behavioral psychology to Prerequisites: IEOR E4700; additional interbank market. Ironically the foreign exchange using sockets; implementation of high-performance select Monday evenings. optimization: convexity, optimality conditions, financial decision making. Focuses on the portfolio prerequisites will be announced depending on markets may be the best place to trade derivatives simulations in finance. steepest descent, and Newton’s method, active aspect of behavioral finance and briefly touches offering. Selected topics of interest in the area and to invent new derivatives—given the massive IEOR E4799x MSFE quantitative and IEOR E4741x Programming for Financial set, and barrier methods. on other aspects. Compared with classical theory of quantitative finance. Offerings vary each two-way flow of trading that goes through bank computational bootcamp of portfolio choice, behavioral portfolio choice dealing rooms virtually twenty-four hours a day. Engineering year; some topics include energy derivatives, 0 pts. Lect: 3. IEOR E6614y Optimization, II features human being’s psychological biases. It And most of that is transacted at razor-thin 3 pts. Lect: 3. experimental finance, foreign exchange and related Primer on quantitative and mathematical concepts. 4.5 pts. Lect: 3. margins, at least comparatively speaking, a fact Covers C++ programming language, applications, builds both on behavioral preference structures derivative instruments, inflation derivatives, hedge Required of all incoming MSFE students. that makes the foreign exchange market an and features for financial engineering, and Prerequisite: Linear algebra. An introduction to different from mean variance theory and expected fund management, modeling equity derivatives

ENGINEERING 2020–2021 ENGINEERING 2020–2021 176 combinatorial optimization, network flows and Jump diffusion models. Applications, including Prerequisite: Faculty adviser’s permission. 177 discrete algorithms. Shortest path problems, pricing of real and electricity options and hedging Selected topics of current research interest. May MATERIALS SCIENCE AND ENGINEERING PROGRAM maximum flow problems. Matching problems, of real options. be taken more than once for credit. Program in the Department of Applied Physics and Applied Mathematics, bipartite and cardinality nonbipartite. Introduction IEOR E6711x Stochastic models, I IEOR E9101s, x and y Research sharing teaching and research with the faculty of the Henry Krumb School of Mines. to discrete algorithms and complexity theory: 4.5 pts. Lect: 3. 1–6 pts. Members of the faculty. NP-completeness and approximation algorithms. Prerequisite: STAT GU4001 or equivalent. Before registering, the student must submit an 200 S. W. Mudd, MC 4701 IEOR E6617x Machine learning and high- Advanced treatment of stochastic modeling in the outline of the proposed work for approval by 212-854-4457 dimensional data analysis in operations context of queueing, reliability, manufacturing, the supervisor and the chair of the Department. apam.columbia.edu research insurance risk, financial engineering and other Advanced study in a specialized field under the matsci.apam.columbia.edu 3 pts. Lect: 3. engineering applications. Review of elements of supervision of a member of the department staff. Discusses recent advances in fields of machine probability theory; exponential distribution; renewal May be repeated for credit. learning: kernel methods, neural networks theory; Wald’s equation; Poisson processes. PROGRAM CHAIR COMMITTEE ON Science Ismail C. Noyan Yuan Yang (various generative adversarial net architectures), Introduction to both discrete and continuous-time Professor William E. MATERIALS SCIENCE Siu-Wai Chan Professor of Materials Associate Professor of and reinforcement learning (with applications Bailey AND ENGINEERING/ Professor of Materials Science Materials Science Markov chains; introduction to Brownian motion. SOLID-STATE SCIENCE in robotics). Quasi Monte Carlo methods in 1140 S. W. Mudd Science Aron Pinczuk Nanfang Yu AND ENGINEERING the context of approximating RBF kernels via IEOR E6712y Stochastic models, II Irving P. Herman Professor of Applied Associate Professor of IN CHARGE OF SOLID- William E. Bailey orthogonal transforms (instances of the structured 4.5 pts. Lect: 3. Professor of Applied Physics and Physics Applied Physics STATE SCIENCE AND Associate Professor of technique). Will discuss techniques such as TD(0), Prerequisite: IEOR E6711 or equivalent. Physics Renata Wentzcovitch ENGINEERING Materials Science James S. Im Professor of Materials TD(λ), LSTDQ, LSPI, DQN. Continuation of IEOR E6711, covering further Professor Irving P. Katayun Barmak topics in stochastic modeling in the context of Professor of Materials Science and Applied Herman Professor of Materials Science Physics, and Earth and IEOR E6703y Advanced financial engineering queueing, reliability, manufacturing, insurance 905 CEPSR Science Chris A. Marianetti Environmental Science 3 pts. Lect: 2. Not offered in 2020–2021. risk, financial engineering, and other engineering Simon J. Billinge Prerequisites: Probability theory and advanced Associate Professor of applications. Topics from among generalized Professor of Materials Materials Science stochastic models at the SIEO GR6501 level. semi-Markov processes; processes with a Review of basic mathematics, including renewal nondiscrete state space; point processes; theory and stochastic calculus. Martingale stochastic comparisons; martingales; introduction Physics and Applied Mathematics. and computers have intensified the approach to Black-Scholes formula. Optimal to stochastic calculus. aterials Science and stopping and American options. Pricing of Engineering (MSE) focuses on Those interested in the solid-state demand for a systematic approach IEOR E8100x and y Advanced topics in IEOR continuous and discrete exotic options. Term understanding, designing, and science and engineering specialty enroll to the problem of relating properties structure models and pricing of bond options. 1–3 pts. Members of the faculty. M producing technology-enabling materials in the doctoral program within Applied to structure and have necessitated a by analyzing the relationships among the Physics and Applied Mathematics or multidisciplinary approach. synthesis and processing of materials, Electrical Engineering. The faculty listed Materials science and solid-state their properties, and their detailed above constitute but a small fraction of science use techniques such as transport structure. This includes a wide range those participating in materials research. measurements, X-ray photoelectron of materials such as metals, polymers, Materials science and engineering spectroscopy, ferromagnetic resonance, ceramics, and semiconductors. Solid- uses optical, electron, and scanning inelastic light scattering, luminescence, state science and engineering focuses probe microscopy and diffraction and nonlinear optics to understand on understanding and modifying the techniques to reveal details of structure, electrical, optical, and magnetic properties properties of solids from the viewpoint ranging from the atomic to the on a quantum mechanical level. Such of the fundamental physics of the macroscopic scale—details essential to methods are used to investigate exciting atomic and electronic structure. understanding the relationship between new types of structures, such as epitaxial The undergraduate and graduate materials synthesis and processing metals, two-dimensional transition metal programs in materials science and materials properties, including dichalcogenides, superconductors, and and engineering are coordinated electronic, magnetic, mechanical, semiconductor surfaces and nanocrystals. through the MSE Program in the optical, and thermal properties. These Department of Applied Physics and studies also give insight into problems Current Research Activities Applied Mathematics. This program of the deterioration of materials in Current research activities in the materials promotes the interdepartmental service, enabling designers to prolong science and engineering program at nature of the discipline and involves the useful life of their products. Materials Columbia focus on thin films, electronic the Departments of Applied Physics science and engineering also focuses and magnetic materials, materials at and Applied Mathematics, Chemical on new ways to synthesize and process high pressures, materials for advanced Engineering and Applied Chemistry, materials, from bulk samples to ultrathin batteries, and the structure of materials. Electrical Engineering, and Earth and films to epitaxial heterostructures to Specific topics under investigation Environmental Engineering in the Henry nanocrystals. This involves techniques include interfaces, stresses, and grain Krumb School of Mines (HKSM) with such as UHV sputtering; molecular boundaries in thin films; lattice defects advisory input from the Departments of beam epitaxy; plasma etching; laser and electrical properties of metals and Chemistry and Physics. ablation, chemistry, and recrystallization; semiconductors; laser processing and Students interested in materials and other nonequilibrium processes. ultrarapid solidification of thin films; science and engineering enroll in the The widespread use of new materials nucleation in condensed systems; materials science and engineering and the new uses of existing materials magnetic and electrical properties of program in the Department of Applied in electronics, communications, semiconductors and metals; synthesis of

ENGINEERING 2020–2021 ENGINEERING 2020–2021 178 nanocrystals, two-dimensional materials, other disciplines to provide a coherent Required Materials Science Courses 179 and nanotechnology-related materials; background for immediate application in Students are required to take 13 MATERIALS SCIENCE PROGRAM: FIRST AND SECOND YEARS deposition, in situ characterization, engineering or for subsequent advanced Materials Science courses for a total electronic testing, and ultrafast study. The emphasis is on fundamentals of 37 points. The required courses are SEMESTER I SEMESTER II SEMESTER III SEMESTER IV spectroscopy of magnetoelectronic relating atomic-to-microscopic-scale MSAE E3010, E3012, E3013, E3156, ultrathin films and heterostructures. phenomena to materials properties E3157, E4100, E4102, E4200, E4201, APMA E2000 (4) either semester In addition, there is research in and processing, including design and E4202, E4206, E4215, and E4250. MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) control of industrially important materials first-principles electronic structure and APMA E2101 (3) computation. processes. Core courses and electives Technical Elective Requirements The research activities in solid-state combine rigor with flexibility and provide Students are required to take nine UN1401 (3) UN1402 (3) PHYSICS UN1403 (3) science and engineering are described opportunities for focusing on such areas (three tracks, UN1601 (3.5) UN1602 (3.5) technical electives (27 points) from the UN2601 (3.5) later in this section. as nanomaterials, materials for green choose one) UN2801 (4.5) UN2802 (4.5) list given below, which offers significant energy, materials for infrastructure and flexibility in allowing students to tailor manufacturing, materials for health and LABORATORY FACILITIES their degree program to their interests. biotechnology, and materials for next UN1403 (4) or UN1404 (4) or UN2045 (4) CHEMISTRY Facilities exist within the Materials generation electronics. or UN1604 (4) a. All 3000-level or higher courses in Science Laboratory, which also The unifying theme of understanding the Materials Science program of the serves as shared facilities for and interrelating materials synthesis, Materials Structural and Mechanical Department of Applied Physics and processing, structure, and properties PHYS UN1493 (3) or UN3081 (2) or Applied Mathematics, except those REQUIRED LAB Characterization. Facilities and research forms the basis of our program CHEM UN1500 (3) or UN1507 (3) or UN3085 (4) MSAE courses that are required. opportunities also exist within the inter- and is evident in the undergraduate b. All 3000-level or higher courses in departmental Columbia Nanotechnology curriculum and in faculty research Applied Physics or Applied Math Initiative (CNI). Modern clean room activities. These activities include work UNIVERSITY CC1010 (3) either semester Programs of the Department WRITING facilities with optical and e-beam lithog- on polycrystalline silicon for flat panel of Applied Physics and Applied raphy, thin film deposition, and surface displays; semiconductors for lasers Mathematics. analytical probes (STM, SPM, XPS) as and solar cell applications, magnetic HUMA CC1001, COCI CC1101, c. All 3000-level or higher courses well as electron microscopes (SEM, S/ heterostructures for information storage NONTECHNICAL or Global Core (3–4); HUMA UN1121 (3) in the Department of Biomedical REQUIREMENTS1 or UN1123 (3); HUMA CC1002, COCI CC1102, TEM) are available. More specialized and novel computation architectures; Engineering, Civil Engineering or Global Core (3–4); ECON UN1105 (4) and UN1155 recitation (0) equipment exists in individual research electronic ceramics for batteries, gas and Engineering Mechanics pro- groups in solid state engineering and sensors and fuel cells; electrodeposition gram, Department of Chemical PHYSICAL UN1001 (1) UN1002 (1) materials science and engineering. The and corrosion of metals; and the EDUCATION Engineering, Department of Computer research facilities in solid-state science analysis and design of high-temperature Science, Department of Earth and engineering are listed in the sections reactors and first principles calculations. THE ART OF ENGI E1102 (4) either semester and Environmental Engineering, ENGINEERING for each host department. Through involvement with our research Department of Electrical Engineering, groups, students gain valuable hands- Department of Industrial Engineering COMPUTER ENGI E1006 (3) any semester on experience and are often engaged SCIENCE UNDERGRADUATE PROGRAM and Operations Research, and in joint projects with industrial and IN MATERIALS SCIENCE Department of Mechanical government laboratories. MSAE E3010 (3) The objectives of the undergraduate Engineering, except for courses that TECHNICAL Foundations of materials Students are strongly encouraged REQUIREMENTS program in the Materials Science require graduate standing. science to take courses in the order specified Program of the Department of Applied d. ORCA E2500 Foundations of data in the course tables; implications of Physics and Applied Mathematics are as science 1 Some of nontech courses can be postponed to junior or senior year, so lab courses MSAE E3012 and MSAE E3013 can be taken along with MSAE E3010. deviations should be discussed with a follows: e. Courses in the Department of departmental adviser before registration. 1. Professional employment in industry, Chemistry listed in the Focus BMEN E4550y: Micro- and nanostructures in CHEE E4050x: Industrial and environmental MECE E3610y: Materials and processes in The first two years provide a strong cellular engineering electrochemistry manufacturing including materials production, auto- Areas below. motive, aerospace, microelectronics, grounding in the physical and chemical ELEN E4944x: Principles of device CHEM GU4071x: Inorganic chemistry ENME E4113x: Advanced mechanics of solids sciences, materials fundamentals, and microfabrication APPH E4130: Physics of solar energy ENME E4114y: Mechanics of fracture and fatigue information storage, medical devices, Focus Areas for technical electives mathematics. This background is used EAEE E4190x: Photovoltaic systems engineering ENME E4115y: Micromechanics of composite energy production, storage and con- are listed below. Students may choose MATERIALS FOR NEXT GENERATION and sustainability materials to provide a unique physical approach version, and in engineering consulting from any one area if they so choose. ELECTRONICS EAIA E4200y: Alternative energy resources CIEN E4226y: Advanced design of steel structures to the study of materials. The last two firms. They are not required to do so. APPH E3100y: Intro to quantum mechanics MECE E4210x: Energy infrastructure planning CHEE E4530x: Corrosion of metals 2. Graduate studies in materials science years of the undergraduate program ELEN E3106x: Solid state devices-materials MECE E4211y: Energy: sources and conversion and engineering or related fields. provide substantial exposure to modern NANOMATERIALS APPH E4100x: Quantum physics of matter EAEE E4550x: Catalysis for emissions control MATERIALS FOR HEALTH AND materials science and include courses APPH E3100y: Intro to quantum mechanics ELEN E4301y: Intro to semiconductor devices BIOTECHNOLOGY ELEN E4944x: Principles of device MATERIALS FOR 21ST CENTURY CHEM UN2443x-UN2444y: Organic chemistry The undergraduate curriculum in processing, structure and properties CHEM GU4071x: Inorganic chemistry of materials that extend the work of MSAE E4090y: Nanotechnology microfabrication INFRASTRUCTURE AND MANUFACTURING APPH E3400y: Physics of the human body is designed to provide the basis CHEM GU4168x: Materials chemistry, I the first two years. Graduates of the APPH E4100x: Quantum physics of matter CIEE E3255y: Environmental control and pollution for developing, improving, and MATERIALS FOR GREEN ENERGY reduction systems BMEN E4210y: Thermodynamics of biological program are equipped for employment CHEM GU4168x: Materials chemistry, I understanding materials and processes EAEE E3103x: Energy, minerals, materials CIEE E3260y: Engineering for developing systems in industry. Graduates are prepared for ELEN E4193x: Modern display technology for application in engineered systems. MECE E4212x or y: Microelectromechanical systems communities BMEN E4301x: Structure, mechanics, and graduate study in materials science and It draws from physics, chemistry and systems EAEE E4004x: Physical processing and recovery ENME E3114y: Experimental mechanics of adaptation of bone engineering and related fields. of solids materials BMEN E4310x or y: Solid biomechanics

ENGINEERING 2020–2021 ENGINEERING 2020–2021 180 BMEN E4450y: Dental and craniofacial tissue strongly encouraged to complete ENGI MSAE E6085: Computing the electronic structure 181 engineering E6001–6004 and should consult their of complex materials BMEN E4501x: Tissue engineering, I: biomaterials MSAE E6091: Magnetism and magnetic materials MATERIALS SCIENCE PROGRAM: THIRD AND FOURTH YEARS program for PDL requirements. and scaffold design MSAE E6225: T echniques in X-ray and neutron CHEE E4530y: Corrosion of metals diffraction SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII BMEN E4550x: Micro- and nanostructures in Master of Science Degree MSAE E6229: Energy and particle beam cellular engineering Candidates for the Master of Science processing of materials MSAE E3156 (2) MSAE E3157 (2) MSAE E3012 (3)1 MSAE E3013 (3)1 degree in Materials Science and MSAE E6230: Kinetics of phase transformations Design project Design project * Note that BIOL UN2005x: Introductory biology, MSAE E6251: Thin films and layers Laboratory in mat. sci. I Laboratory in mat. sci. II Engineering will follow a program of MSAE E4200 (3) MSAE E4202 (3) I and BIOL UN2006y: Introductory biology, II are MSAE E6273: Materials science reports MSAE E4100 (3) MSAE E4201 (3) study formulated in consultation with Theory of crystalline Kinetics of transformations prerequisites for a number of courses in this track. MSAE E8235: Selected topics in materials science REQUIRED Crystallography Materials thermodynamics and approved by a faculty adviser. COURSES materials in materials MSAE E4000-, 6000- or 8000-level courses not and phase diagrams MATERIALS CHEMISTRY/SOFT MATERIALS Thirty points of credit are required listed here, except MSAE E6100. MSAE E4102 (3) MSAE E4206 (3) MSAE E4215 (3) Synthesis and processing MSAE E4250 (3) CHEM UN2443x-UN2444y: Organic chemistry at a minimum. Students interested APCH E4080: Soft condensed matter Electronic and magnetic Mechanical behavior of materials Ceramics and composites CHEN E4201: Applications of electrochemistry in a specific focus in metallurgy or APMA E4101: Dynamical systems properties of solids of materials CHEE E4252: Intro surface & colloid chemistry other areas in materials science and APMA E4200: Partial differential equations CHEN E4620: Intro polymers / soft materials APMA E4204: Functions of a complex variable engineering should consult their faculty CHEN E4640: Polymer surfaces and interfaces APMA E4300: Computational mathematics: intro TECHNICAL Students must complete 27 units of Technical Electives. ELECTIVES adviser for relevant course listings. to numerical methods The following six courses (18 points) Nontechnical Elective Requirements APPH E4100: Quantum physics of matter NONTECHNICAL Students must complete the 27-point requirement.2 are required for the degree. Students APPH E4110: Modern optics ELECTIVES All materials science students must take a minimum of two of the six APPH E4112: Laser physics are also expected to register for required courses, one of which must be APPH E4200: Physics of fluids 1 Motivated students are highly encouraged to take the materials science laboratory I and II courses in the sophomore year to obtain practical understanding of nontechnical electives, both those MSAE E4100 Crystallography, in their APPH E4300: Applied electrodynamics material covered in the junior and senior years. specifically required by the School of first semester. APPH E4990: Special topics in applied physics 2 See page 9 or seas.columbia.edu for details (administered by the advising dean). Engineering and Applied Science and APPH E6081: Solid state physics those needed to meet the 27-point BMEN E4300: Solid biomechanics 18 points: BMEN E4580: Foundations of nanobioscience and total of nontechnical electives required MSAE E4100: Crystallography nanobiotechnology for graduation. MSAE E4200: Theory of crystalline materials: CEEM E4113: Advanced mechanics of solids phonons CEEM E4114: Mechanics of fracture and fatigue Transfer Students MSAE E4201: Materials thermodynamics and CIEN E4021: Elastic and plastic analysis of MATERIALS SCIENCE PROGRAM: THIRD AND FOURTH YEARS phase diagrams Combined Plan 3-2/Transfer structures (TRANSFER STUDENTS) MSAE E4202: Kinetics of transformations in CHEN E4201: Engineering applications of students and students transferring materials electrochemistry from another SEAS department into MSAE E4206: Electronic and magnetic properties SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII CHEN E4630: T opics in soft materials the Materials Science Program in of solids CHEN E4880: Atomistic simulations for science the junior year (upon approval of the MSAE E4215: Mechanical behavior of structural and engineering MSAE E3156 (2) materials MSAE E3010 (3) Design project Materials Science Undergraduate EAEE E4252: Introduction to surface and colloidal MSAE E3013 (3) Foundations of materials MSAE E3157 (2) chemistry Laboratory in materials Transfer Committee) will take the If a candidate has already taken science and engineering MSAE E4100 (3) Design project ELEN E4193: Modern display science and science, II following courses to satisfy the degree one or more of these courses at Crystallography technology MSAE E3012 (3) MSAE E4202 (3) requirements: The required courses are Columbia University, substitutions from MSAE E4201 (3) ELEN E4411: Fundamentals of photonics Laboratory in materials MSAE E4200 (3) Kinetics of transformations MSAE E3010, E3012, E3013, E3156, REQUIRED Materials thermodynamics the Electives list must be approved by ELEN E4944: Principles of device microfabrication science, I Theory of crystalline in materials COURSES and phase diagrams E3157, E4100, E4102, E4200, E4201, consultation with their faculty adviser ELEN E6331/6333: Semiconductor device physics materials MSAE E4215 (3) E4202, E4206, E4215, and E4250. and approval of the program committee. IEOR E4150: Introduction to probability and MSAE E4250 (3) MSAE E4102 (3) MSAE E4206 (3) Mechanical behavior of Combined Plan 3-2/Transfer The remaining 12 points will be statistics Ceramics and composites Synthesis and processing Electronic and magnetic materials Students will be guided by their chosen from elective courses. MECE E4212: Microelectromechanical systems of materials properties of solids academic advisers to avoid duplication MECE E4213: BioMEMS: design, fabrication, and analysis of courses previously taken. The Electives: MECE E4214: MEMS production and packaging course tables describe the four- MECE E4610: Advanced manufacturing processes TECHNICAL Students must complete 27 or 24 units of Technical Electives.1 semester program schedule of courses MSAE E4090: Nanotechnology ELECTIVES MSAE E4101: Structural analysis of materials MECE E6137: Nanoscale actuation and sensing leading to the bachelor’s degree in MSAE E4102: Synthesis and processing of STAT GU4001: Introduction to probability and NONTECHNICAL Students must complete the 27-point requirement.2 the Materials Science Program of the materials statistics ELECTIVES Department of Applied Physics and MSAE E4105: Ceramic nanomaterials All degree requirements must be Applied Mathematics. MSAE E4132: Fundamentals of polymers and completed within five years. A candidate 1 Students transferring from another SEAS department into the Materials Science program in the junior year must complete the 27 units of technical elective ceramics is required to maintain at least a 2.5 requirement; Combined Plan 3/2 transfer students must complete 24 units of technical electives. MSAE E4203: Theory of crystalline materials: GPA. Applicants for admission are 2 Students transferring from another SEAS department into the Materials Science program in the junior year must complete the 27-point requirement; see page 9 or GRADUATE PROGRAMS IN electrons required to take the Graduate Record seas.columbia.edu for details (administered by the advising dean). Combined Plan 3/2 transfer students do not need nontechnical electives; see page 14 or MATERIALS SCIENCE AND MSAE E4250: Ceramics and composites seas.columbia.edu. Examinations. ENGINEERING MSAE E4260: Electrochemical materials and M.S. students must complete the devices: from structure to performance Professional Degree; Metallurgical professional development and leadership MSAE E4301: Materials science laboratory course, ENGI E4000, as a graduation MSAE E4990: Special topics in materials science Engineer and engineering requirement. Ph.D. candidates are The program is designed for engineers

ENGINEERING 2020–2021 ENGINEERING 2020–2021 182 who wish to do advanced work beyond Candidates must submit a written sputtering, electrodeposition, and technology, e.g., for computers and for solid-state science and engineering. metallography, hardness and tensile testing, plastic 183 the level of the M.S. degree but who proposal and defend it orally before a plasma and laser processing. For energy production and utilization. The following are regarded as core deformation, annealing, phase diagrams, brittle fracture of glass, temperature and strain-rate do not desire to emphasize research. Thesis Proposal Defense Committee analyzing materials structures and courses of the specialty: dependent deformation of polymers; written and Admissions requirements include the consisting of three members of the properties, faculty and students employ Areas of Research APPH E4100: Quantum physics of matter oral reports. This is the second of a two-semester undergraduate engineering degree, mini- faculty, including the adviser in the spring electron microscopy, scanning probe The graduate specialty in solid-state APPH E4110: Modern optics sequence materials laboratory course. mum 3.0 GPA, and GRE. semester of their third year. Doctoral microscopy, photoluminescence, science and engineering includes APPH E4112: Laser physics MSAE E3111x Thermodynamics, kinetic Candidates must complete at least 30 candidates must submit a thesis to magnetotransport measurements, and research programs in metamaterials APPH E6081: Solid state physics theory and statistical mechanics credits of graduate work beyond the M.S., be defended before a Dissertation X-ray diffraction techniques. Faculty CHEM GU4230: Statistical thermodynamics and infrared optoelectronic devices 3 pts. Lect: 3. Professor Herman. or 60 points of graduate work beyond Defense Committee consisting of members have research collaborations (Professor Yu, Applied Physics and or An introduction to the basic thermodynamics the B.S. No thesis is required. All degree five faculty members, including two with IBM, and other New York area Applied Mathematics); and inelastic CHAP E4120: Statistical mechanics of systems, including concepts of equilibrium, requirements must be completed within professors from outside the doctoral research and manufacturing centers, light scattering in low-dimensional ELEN E4301: Intro to semiconductor devices entropy, thermodynamic functions, and phase five years of the beginning of the first program. Requirements for the Eng. as well as major international research electron gases within semiconductors ELEN E4944: Principles of device microfabrication changes. Basic kinetic theory and statistical course credited toward the degree. Sc.D. (administered by the School of centers. Scientists and engineers from (Professor Pinczuk, Applied Physics ELEN E6331-E6332: Principles of semiconductor mechanics, including diffusion processes, concept physics Coursework includes five core required Engineering and Applied Science) and these institutions also serve as adjunct and Applied Mathematics/Physics); of phase space, classical and quantum statistics, ELEN E6403: Classical electromagnetic theory courses and five elective courses from a the Ph.D. (administered by the Graduate faculty members at Columbia. The large-area electronics and thin-film and applications thereof. or pre-approved list of choices. School of Arts and Sciences) are listed National Synchrotron Light Source at transistors (Professor Im, Henry Krumb MSAE E3141y Processing of metals and PHYS GR6092: Electromagnetic theory, I Core courses: elsewhere in this bulletin. Brookhaven National Laboratory is used School of Mines/Applied Physics semiconductors MSAE E4100: Crystallography for high-resolution X-ray diffraction and 3 pts. Lect: 3. Not offered in 2020–2021. and Applied Mathematics); structural MSAE E4206: Electronic and magnetic properties • EAEE E4001 Industrial ecology of earth Areas of Research absorption measurements. Prerequisite: MSAE E3011 or equivalent. analysis and high Tc superconductors of solids resources Materials science and engineering is Entering students typically have (Professor Chan, Henry Krumb School PHYS GR6018: Physics of the solid state Synthesis and production of metals and • EAEE E4009 Geographic information concerned with synthesis, processing, undergraduate degrees in materials of Mines/Applied Physics and Applied PHYS GR6037: Quantum mechanics semiconductors with engineered microstructures systems (GIS) for resource, environmen- structure, and properties of metals, science, metallurgy, physics, chemistry, Mathematics); X-ray microdiffraction for desired properties. Includes high- temperature, aqueous, and electrochemical tal and infrastructure management ceramics, and other materials, or other science and engineering and stresses (Professor Noyan, Henry COURSES IN MATERIALS processing; thermal and mechanical processing • EAEE E4160 Solid and hazardous disciplines. First-year graduate courses Krumb School of Mines/Applied Physics with emphasis on understanding of metals and alloys; casting and solidification; waste materials provide a common base of knowledge SCIENCE AND ENGINEERING and exploiting relationships among and Applied Mathematics); electronic diffusion, microstructural evolution, and phase • EAEE E4900 Applied transport/chemical and technical skills for more advanced For related courses, see also Applied structure, properties, and applications and magnetic metal thin films (Professor transformations; modification and processing Physics and Applied Mathematics, rate phenomena requirements. Our graduate research courses and for research. In addition Barmak, Applied Physics and Applied of surfaces and interfaces; deposition and • EAEE E6255-6 Methods and applica- programs encompass research areas to coursework, students usually Mathematics); magnetic properties of Chemical Engineering, Earth and removal of thin films. Processing of Si and tions of analytical decision making in as diverse as polycrystalline silicon, begin an association with a research thin films (Professor Bailey, Applied Environmental Engineering, Electrical other materials for elemental and compound mineral industries electronic ceramics grain boundaries group, individual laboratory work, and Physics and Applied Mathematics); the Engineering, and Mechanical Engineering. semiconductor-based electronic, magnetic, and and interfaces, microstructure and participation in graduate seminars structure of nanomaterials (Professor MSAE E3010x Foundations of materials optical devices. Elective courses must be five courses during their first year. stresses in microelectronics thin films, Billinge, Applied Physics and Applied science MSAE E3142y Processing of ceramics and at the 4000 or higher level from within oxide thin films for novel sensors and Mathematics); and electronic structure 3 pts. Lect: 3. Professor Billinge. polymers the Earth and Environmental Engineering Prerequisites: CHEM UN1404 and PHYS UN1011. fuel cells, optical diagnostics of thin-film GRADUATE SPECIALTY IN calculations of materials (Professors 3 pts. Lect: 3. Not offered in 2020–2021. Department, the Chemical Engineering processing, ceramic nanocomposites, Marianetti and Wentzcovitch, Applied Introduction to quantum mechanics: atoms, Prerequisite: MSAE E3011 or equivalent. SOLID-STATE SCIENCE AND electron shells, bands, bonding; introduction Department, Materials Science Program, electrodeposition and corrosion Physics and Applied Mathematics). Established and novel methods involved in ENGINEERING or others as approved by the adviser. to group theory: crystal structures, symmetry, the processing of polymers and ceramics. processes, structure, properties, and crystallography; introduction to materials classes: These include but are not limited to: Solid-state science and engineering The fundamental aspects of the structure and transmission electron microscopy Program of Study metals, ceramics, polymers, liquid crystals, EAEE E4150, CHEE E4252, CIEE E4252, is an interdepartmental graduate properties of polymers and ceramic materials; and crystal orientation mapping, nanomaterials; introduction to polycrystals specialty that provides coverage of an The applicant for the graduate specialty strategy in the preparatory, synthesis, and EAEE E4256, EAEE E4257, EAEE E6208. magnetic thin films for spintronic and disordered materials; noncrystalline and important area of modern technology must be admitted to one of the processing methods for obtaining them. Although it is not required, interested stu- applications, chemical synthesis of amorphous structures; grain boundary structures, that no single department can provide. It participating programs: applied physics Topics include polymer synthesis, elastomers, dents may choose to complete up to six nanoscale materials, nanocrystals, two- diffusion; phase transformations; phase encompasses the study of the full range and applied mathematics, or electrical thermoplastics, thermoset materials, design credits in MSAE E9259-60. diagrams, time-temperature-transformation dimensional materials, nanostructure engineering. A strong undergraduate and molding processes. Ceramics: inorganic of properties of solid materials, with diagrams; properties of single crystals: optical analysis using X-ray and neutron glasses and composites, materials production special emphasis on electrical, magnetic, background in physics or chemistry and properties, electrical properties, magnetic Doctoral Program diffraction techniques, and electronic and principle inorganic chemistry. Processing optical, and thermal properties. The in mathematics is important. properties, thermal properties, mechanical At the end of the first year of graduate structure calculation of materials using methodology, conditioning, drying, forming, science of solids is concerned with The doctoral student must meet the properties, and failure of polycrystalline and sintering, and microstructure development. study in the doctoral program, density functional and dynamical formal requirements for the Eng. Sc.D. amorphous materials. understanding these properties in Relevant aspects of transport phenomena, candidates are required to take a mean-field theories. Application targets or Ph.D. degree set by the department terms of the atomic and electronic MSAE E3012x Laboratory in materials science, I colloid and sol-gel science, contemporary issues comprehensive written qualifying for polycrystalline silicon are thin film in which he or she is registered. structure of the materials in question. 3 pts. Lect: 3. Professor Noyan. in modern polymer and ceramic processing. examination, which is designed to test transistors for active matrix displays Insulators (dielectrics), semiconductors, However, the bulk of the program for the Pre/Corequisite: MSAE E3010. Measurement of the ability of the candidate to apply and silicon-on-insulator structures for MSAE E3156x-E3157y Design project ceramics, and metallic materials are all specialty will be arranged in consultation electrical, thermal, and magnetic properties of coursework in problem solving and ULSI devices. Novel applications are 2 pts (each semester). Lect.: 3. studied from this viewpoint. Quantum with a member of the interdepartmental single crystals. Single crystal diffraction analysis, creative thinking. The standard is first- being developed for oxide thin films, Committee on Materials Science and polarized light microscopy, and infrared microscopy Professor Billinge. and statistical mechanics are key Prerequisite: Senior standing. Written permission year graduate level. There are two four- including uncooled IR focal plane arrays Engineering/ Solid-State Science and in Si single crystals, written and oral reports. background subjects. The engineering from instructor and approval from adviser. hour examinations over a two-day period. and integrated fuel cells for portable Engineering. At the end of the first year aspects deal with the design of materials MSAE E3013y Laboratory in materials science, II E3156: A design problem in materials science Candidates in the program must equipment. to achieve desired properties and the of graduate study, doctoral candidates 3 pts. Lect: 3. Professor Noyan. or metallurgical engineering selected jointly by take the oral examination in the Thin film synthesis and processing assembling of materials into systems to are required to take a comprehensive Prerequisite: MSAE E3012. Metallographic sample the student and a professor in the department. spring semester of their second year. in this program include evaporation, produce devices of interest to modern written examination concentrating on preparation, optical microscopy, quantitative The project requires research by the student,

ENGINEERING 2020–2021 ENGINEERING 2020–2021 184 directed reading, and regular conferences with applications; surface energy, surface tension Pre/Corequisite: MSAE E4201. Review of or instructor’s permission. Will cover some of and mechanical properties of materials. Group mechanical properties, adhesion, interconnects, 185 the professor in charge. E3157: Completion of and surface stress; effect of ligands, surfactants, thermodynamics, irreversible thermodynamics, the fundamental processes of atomic diffusion, theory, numerical methods, basis sets, computing, and electromigration. the research, directed reading, and conferences, adsorbents, isoelectric point, and surface diffusion in crystals and noncrystalline materials, sintering and microstructural evolution, defect and running open source DFT codes. Problem sets MSAE E6273x and y–S6273 Materials science culminating in a written report and an oral charges; supersaturation and homogenous phase transformations via nucleation and chemistry, ionic transport, and electrical properties and a small project. reports presentation to the department. nucleation for monodispersity. growth, overall transformation analysis and time- of ceramic materials. Following this, we will MSAE E6091y Magnetism and magnetic 0 to 6 pts. Members of the faculty. temperature-transformation (TTT) diagrams, examine applications of ceramic materials, MSAE E3900x and y Undergraduate research MSAE E4132y Fundamentals of polymers and materials Prerequisite: Written permission from instructor and precipitation, grain growth, solidification, specifically, ceramic thick and thin film materials in materials science ceramics 3 pts. Lect. 3. Not offered in 2020–2021. approval from adviser. Formal written reports and spinodal and order-disorder transformations, in the areas of sensors and energy conversion/ 0–4 pts. Members of the faculty. 3 pts. Lect: 3. Not offered in 2020–2021. Prerequisite: MSAE E4206, APPH E6081, or conferences with the appropriate member of the martensitic transformation. storage devices such as fuel cells, and batteries. Prerequisite: Written permission from instructor Prerequisite: MSAE E3010 or instructor’s equivalent. Types of magnetism. Band theory faculty on a subject of special interest to the student The coursework level assumes that the and approval from adviser. May be repeated permission. The science and engineering of MSAE E4203y Theory of crystalline materials: of ferromagnetism. Magnetic metals, insulators, but not covered in the other course offerings. student has already taken basic courses in the for credit, but no more than 6 points may be polymer, ceramic and composite inorganic electrons and semiconductors. Magnetic nanostructures: thermodynamics of materials, diffusion in materials, MSAE E8235x and y Selected topics in counted toward the satisfaction of the B.S. degree materials. Fundamental aspects of structure, 3 pts. Lect: 3. Professor Marianetti. ultrathin films, superlattices, and particles. Surface and crystal structures of materials. materials science requirements. Candidates for the B.S. degree may processing and properties. Polymers: Prerequisite: MSAE E4200 or instructor's magnetism and spectroscopies. High speed 3 pts. Lect: 3. Not offered in 2020–2021. conduct an investigation in materials science or classification, synthesis, elastomers, permission. Phenomenological theoretical MSAE E4260y Electrochemical materials and magnetization dynamics. Spin electronics. May be repeated for credit. Selected topics in carry out a special project under the supervision of thermoplastics, thermosets; ceramics: understanding of electrons in crystalline devices: from structure to performance MSAE E6100y Transmission electron materials science. Topics and instructors change the staff. Credit is contingent upon the submission Crystal structure, morphology, classification, materials. Both translational and point symmetry 3 pts. Lect: 3. Professor Yang. microscopy from year to year. For students in engineering, of an acceptable thesis or final report. oxides, nitrides, carbides, silicates. Electrical, employed to block diagonalize the Schrödinger Prerequisites: CHEM UN1403, MSAE E3010, 3 pts. Lect: 3. Not offered in 2020–2021. physical sciences, biological sciences, and mechanical, thermal and optical properties. equation and compute observables related to equivalents, or instructor's permission. Overview MSAE E4090y Nanotechnology Prerequisite: permission of the instructor. Theory related fields. Common and advanced technological electrons. Topics include nearly free electrons, of electrochemical processes and applications 3 pts. Lect: 3. Not offered in 2020–2021. and practice of transmission electron microscopy applications, electrical/optical devices, catalytic tight-binding, electron-electron interactions, from perspectives of materials and devices. MSAE E9000x and y Materials science and Prerequisites: APPH E3100 and MSAE E3010 (TEM): principles of electron scattering, diffraction, and environmental applications. transport, magnetism, optical properties, Thermodynamics and principles of electrochem- engineering colloquium or their equivalents with instructor’s permission. and microscopy; analytical techniques used to topological insulators, spin-orbit coupling, and istry, methods to characterize electrochemical 0 pt. Professor Yang. The science and engineering of creating MSAE E4200x Theory of crystalline materials: determine local chemistry; introduction to sample superconductivity. Illustrated using both minimal processes, application of electrochemical materials Speakers from universities, national laboratories, and materials, functional structures and devices phonons preparation; laboratory and in-class remote model Hamiltonians in addition to accurate and devices, including batteries, supercapacitors, industry are invited to speak on the recent impact of on the nanometer scale. Carbon nanotubes, 3 pts. Lect: 3. Professor Marianetti. fuel cells, electrochemical sensor, focus on link access demonstrations, several hours of hands-on Hamiltonians for real materials. materials science and engineering innovations. nanocrystals, quantum dots, size dependent Pre/Corequisite: MSAE E4100 or instructor’s between material structure, composition, and prop- laboratory operation of the microscope; the use of properties, self-assembly, nanostructured permission. Phenomenological theoretical MSAE E4206x Electronic and magnetic erties with electrochemical performance. simulation and analysis software; guest lectures MSAE E9259x-E9260y Research topics materials. Devices and applications, understanding of vibrational behavior of crystalline properties of solids on cryomicroscopy for life sciences and high in materials science and metallurgical MSAE E4301x Materials science laboratory nanofabrication. Molecular engineering, materials; introducing all key concepts at classical 3 pts. Lect: 3. Professor Bailey. resolution transmission electron microscopy for engineering 3 pts. Professor Yang. bionanotechnology. Imaging and manipulating at level before quantizing the Hamiltonian. Basic Prerequisite: PHYS UN1401-3 or equivalent. A physical sciences; and, time permitting, a visit to 1 pt. Lect: 1. Members of the faculty. Prerequisites: Introductory materials course or the atomic scale. Nanotechnology in society and notions of Group Theory introduced and exploited: survey course on the electronic and magnetic the electron microscopy facility in the Center for Discussion of a group of technical papers related equivalent and instructor’s permission. General industry. Offered in alternate years. irreducible representations, Great Orthogonality properties of materials, oriented toward Functional Nanomaterials (CFN) at the Brookhaven to a topic of current research interest. experimental techniques in materials science, Theorem, character tables, degeneration, product materials for solid state devices. Dielectric National Laboratory (BNL). MSAE E4100x Crystallography including X-ray diffraction, scanning electron MSAE E9301x-S9301 Doctoral research groups, selection rules, etc. Both translational and and magnetic properties, ferroelectrics 3 pts. Lect: 3. Professor Barmak. microscopies, atomic force microscopy, materials MSAE E6229y Energy and particle beam 0–15 pts. Members of the faculty. point symmetry employed to block diagonalize the and ferromagnets. Conductivity and Prerequisites: CHEM UN1403, PHYS UN1403, synthesis and thermodynamics, characterization of processing of materials Prerequisite: Qualifying examination for doctorate. Hamiltonian and compute observables related to superconductivity. Electronic band theory of APMA E2101, or equivalent. A first course on material properties (mechanical, electrochemical, 3 pts. Lect: 3. Not offered in 2020–2021. Required of doctoral candidates. vibrations/phonons. Topics include band structures, solids: classification of metals, insulators, crystallography. Crystal symmetry, Bravais magnetic, electronic). Additional experiments at Prerequisites: MSAE E4202 or instructor’s density of states, band gap formation, nonlinear and semiconductors. Materials in devices: MSAE E9309x and y–S9309 Proposal of lattices, point groups, space groups. Diffraction discretion of instructor. permission. Laser-, electron-, and ion-beam (anharmonic) phenomena, elasticity, thermal examples from semiconductor lasers, cellular Research for the Doctorate and diffracted intensities. Exposition of typical modification of materials to achieve unique conductivity, heat capacity, optical properties, telephones, integrated circuits, and magnetic MSAE E4990x and y Special topics in 0–3 pts. Members of the faculty. crystal structures in engineering materials, microstructures and metastable phases ferroelectricty. Illustrated using both minimal model storage devices. Topics from physics are materials science and engineering A written report prepared by the prospective including metals, ceramics, and semiconductors. for electronic and structural applications. Hamiltonians in addition to accurate Hamiltonians introduced as necessary. 1–3 pts. Members of the faculty. doctoral candidate defining the proposed Crystalline anisotropy. Fundamentals of energy deposition and heat for real materials (e.g., Graphene). Prerequisite: Instructor’s permission. May be research for the dissertation, and oral defense of MSAE E4215y Mechanical behavior of flow during laser- and electron-beam irradiation. MSAE E4102x Synthesis and processing repeated for credit. Topics and instructors change the proposal. MSAE E4201y Materials thermodynamics and structural materials Atomic displacement processes in ion-irradiated of materials from year to year. For advanced undergraduate phase diagrams 3 pts. Lect: 3. Professor Bailey. materials. Beam-induced microstructural evolution, MSAE E9800x and y–S9800 Doctoral research 3 pts. Lect: 3. Professor Im. students and graduate students in engineering, 3 pts. Lect: 3. Professor Barmak. Prerequisite: MSAE E3010. Recommended crystallization, surface alloying, rapid solidification, instruction Prerequisite: MSAE E3010 or equivalent or physical sciences, and other fields. Prerequisite: MSAE E3010 or equivalent or preparation: A course in mechanics of materials. and metastable phase formation. Review of current 3, 6, 9, or 12 pts. Members of the faculty. instructor’s permission. A course on synthesis and instructor’s permission. Review of laws of Review of states of stress and strain and MSAE E4999x or y–S4999 Supervised industrial applications. A candidate for the Eng.Sc.D. degree must processing of engineering materials. Established thermodynamics, thermodynamic variables their relations in elastic, plastic, and viscous internship register for 12 points of doctoral research and novel methods to produce all types of MSAE E6230y Kinetics of phase and relations, free energies and equilibrium materials. Dislocation and elastic-plastic concepts 1–3 pts. Members of the faculty. instruction. Registration in MSAE E9800 may materials (including metals, semiconductors, transformations in thermodynamic systems, statistical introduced to explain work hardening, various Prerequisite: Internship and approval from adviser not be used to satisfy the minimum residence ceramics, polymers, and composites). 3 pts. Lect: 3. Not offered in 2020–2021. thermodynamics. Unary, binary, and ternary materials-strengthening mechanisms, ductility, must be obtained in advance. Only for master’s requirement for the degree. Fundamental and applied topics relevant to Prerequisite: MSAE E4202 or instructor’s phase diagrams, compounds and of surfaces and materials devices, material reliability and fracture, students in the Department of Applied Physics optimizing the microstructure of the materials with permission. Principles of nonequilibrium MSAE E9900x and y–S9900 Doctoral interfaces, effect of particle size, intermediate and toughness. Macroscopic and microstructural and Applied Mathematics who may need relevant desired properties. Synthesis and processing of thermodynamics; stochastic equations; nucleation, dissertation phases, solid solutions and Hume-Rothery aspects of brittle and ductile fracture mechanics, work experience as part of their program of study. bulk, thin-film, and nano materials for various growth, and coarsening reactions in solids; 0 pts. Members of the faculty. rules, relationship between phase diagrams and creep and fatigue phenomena. Case studies Final report required. May not be taken for pass/ mechanical and electronic applications. spinodal decomposition; eutectic and eutectoid A candidate for the doctorate may be required metastability, defects in crystals. Thermodynamics used throughout, including flow and fracture of fail or audited. transformations. to register for this course every term after the MSAE E4105x Ceramic nanomaterials of surfaces and interfaces, effect of particle size structural alloys, polymers, hybrid materials, MSAE E6085y Computing the electronic coursework has been completed and until the on phase equilibria, adsorption isotherms, grain composite materials, ceramics, and electronic MSAE E6251y Thin films and layers 3 pts. Lect: 3. Not offered in 2020–2021. structure of complex materials dissertation has been accepted. boundaries, surface energy, electrochemistry. prevention emphasized. 3 pts. Lect: 3. Professor Chan. Prerequisite: CHEM UN1404 or equivalent 3 pts. Lect: 3. Professor Wentzcovitch. undergraduate thermodynamics. Ceramic Vacuum basics, deposition methods, nucleation MSAE E4202y Kinetics of transformation in MSAE E4250y Ceramics and composites Prerequisite: APPH E3100 or equivalent. Basics of nanomaterials and nanostructures: synthesis, and growth, epitaxy, critical thickness, defects materials 3 pts. Lect: 3. Professor Chan. density functional theory (DFT) and its application characterization, size-dependent properties, and properties, effect of deposition procedure, 3 pts. Lect: 3. Professor Im. Pre/Corequisites: MSAE E3010 and E3013, to complex materials. Computation of electronics

ENGINEERING 2020–2021 ENGINEERING 2020–2021 186 with the application of continuum emphasizes iterative learning control and mobile manipulation in unstructured 187 MECHANICAL ENGINEERING theories of mixtures to problems of (ILC) and repetitive control (RC). ILC environments. (Ciocarlie) 220 S. W. Mudd, MC 4703 electromechanical behavior of soft creates controllers that learn from At the Creative Machines Lab 212-854-0661 biological tissues, contact mechanics, previous experience performing a (CreativeMachines.org) we are interested me.columbia.edu lubrication of diarthrodial joints, and specific command, such as robots in robots that create and robots that cartilage tissue engineering. (Ateshian) on an assembly line, aiming for high- are themselves creative. We develop The Kysar group studies the precision mechanical motions. RC learns novel autonomous systems that can CHAIR PROFESSORS Matei Ciocarlie Harry West J. P. Hilton mechanics and mechanical properties to cancel repetitive disturbances, such design and make other machines— Jeffrey W. Kysar Sunil Agrawal Kristin Myers Peter LeVoci of small-scale structures and materials. as precision motion through gearing, automatically. We are working on a 248 S. W. Mudd Gerard A. Ateshian LECTURER IN Arvind Narayanaswamy Kerwin Low Examples of material systems include machining, satellite precision pointing, self-replicating robots, self-aware robots, Mary C. Boyce P. James Schuck DISCIPLINE Mohammad H. N. DIRECTOR OF James Hone Sinisa Vukelic Naraghi two-dimensional materials such as particle accelerators, etc. Time optimal robots that improve themselves over FINANCE AND Jeffrey W. Kysar ASSISTANT Yevgeniy Yesilevskiy Alexander Staroselsky graphene, nanoporous metal thin films, control of robots is being studied for time, and robots that compete and ADMINISTRATION Qiao Lin PROFESSORS Graham Walker metallic and polymeric composites increased productivity on assembly cooperate with other robots. We build Milko Milkov Hod Lipson Karen Kasza ADJUNCT FACULTY Enrico Zordan containing nanoscale strengthening lines through dynamic motion planning. robots that paint art, cook food, build 220 S. W. Mudd Richard W. Longman Vijay Vedula Homayoon Beigi agents, single crystal metals, and the Research is also being conducted on bridges and fabricate other robots. Vijay Modi Matthew Bilson MANAGER OF Y. Lawrence Yao PROFESSOR OF Sean Bradshaw INSTRUCTIONAL ear's round Window Membrane, among improved system identification, making Our work is inspired from biology, ASSOCIATE PROFESSIONAL Joshua Browne LABORATORIES several others. The work is experimental, mathematical models from input-output as we seek new biological concepts PROFESSORS PRACTICE Nicholas Chbat Robert G. Stark theoretical, and computational in nature. data. The results can be the starting for engineering and new engineering Michael P. Burke Michael J. Massimino Dustin Demetriou The ultimate goal is to understand and point for designing controllers, but they insights into biology. (Lipson) predict the mechanical behavior based are also studied as a means of assessing In the area of advanced on fundamental physics and chemistry damage in civil engineering structures manufacturing processes and systems, echanical engineering is a (implants, prosthetic devices, The breadth of the mechanical through the development of multiple from earthquake data. (Longman) current research concentrates on laser diverse subject that derives fluidic systems for pharmaceutical engineering discipline allows students length scale models. Robotics research focuses on materials processing. Investigations its breadth from the need to industries); computers and electronics a variety of career options beyond M At the Kasza Living Materials Lab design of novel rehabilitation machines are being carried out in laser design and manufacture everything from (disk drives, printers, cooling some of the industries listed above. we are interested in how cells self- and training algorithms for functional micromachining; laser forming of sheet small individual parts/devices (e.g., micro- systems, semiconductor tools); Regardless of the particular future path organize to build tissues and organs with rehabilitation of neural impaired adults metal; microscale laser shock-peening, scale sensors, inkjet printer nozzles) microelectromechanical systems, or they envision for themselves after they mechanical properties that are required and children. The research also aims material processing using improved to large systems (e.g., spacecraft and MEMS (sensors, actuators, micro power graduate, their education would have for proper function. A major focus is to to design intelligent machines using laser-beam quality. Both numerical and machine tools). The role of a mechanical generation); energy conversion (gas provided them with the creative thinking uncover fundamental mechanical and nonlinear system theoretic principles, experimental work is conducted using engineer is to take a product from an turbines, wind turbines, solar energy, fuel that allows them to design an exciting biological mechanisms that coordinate the computational algorithms for planning, state-of-the-art equipment, instruments, idea to the marketplace. In order to cells); environmental control (HVAC, air- product or system, the analytical tools behaviors of cells in developing tissues. and optimization. and computing facilities. Close ties accomplish this, a broad range of skills conditioning, refrigeration, compressors); to achieve their design goals, the ability To do this, we study morphogenesis in Robotic Systems Engineering (ROSE) with industry have been established for are needed. The particular skills in which automation (robots, data/image to meet several sometimes conflicting developing embryos of model organisms Lab develops technology capable collaborative efforts. (Yao) the mechanical engineer acquires deeper acquisition, recognition, and control); constraints, and the teamwork needed and combine approaches such as in vivo of solving difficult design problems, knowledge are the ability to understand manufacturing (machining, machine Energy, Fluid Mechanics, and to design, market, and produce a imaging, optogenetics, and biomechanical such as cable-actuated systems, the forces and the thermal environment tools, prototyping, microfabrication). Heat/Mass Transfer. In the area of system. These skills also prove to measurements. We are leveraging this under-actuated systems, and others. that a product, its parts, or its To put it simply, mechanical energy, one effort is in energy systems be valuable in other endeavors and knwledge to design and build novel cell- Robotics and Rehabilitation (ROAR) subsystems will encounter; design them engineering deals with anything with an eye towards cost-effective can launch a career in medicine, law, based tissue structures and systems. Our Lab focuses on developing new and for functionality, aesthetics, and the ability that moves. Mechanical engineers decarbonization using technologies consulting, management, banking, goals are to shed light on human health innovative technologies to improve the to withstand the forces and the thermal learn about materials, solid and fluid that are at hand or near-ready. The finance, and so on. and disease and learn how to better build quality of care and patient outcomes. environment they will be subjected to; mechanics, thermodynamics, heat interaction of the electric grid, with For those interested in applied functional tissues in the lab. The lab designs novel exoskeletons determine the best way to manufacture transfer, control, instrumentation, buildings, transportation, gas networks, scientific and mathematical aspects Other areas of biomechanics for upper and lower limbs training of them and ensure they will operate without design, and manufacturing to realize/ storage and electrofuels is being of the discipline, graduate study in include characterizing the structure- stroke patients, and mobile platforms failure. Perhaps the one skill that is the understand mechanical systems. studied. Another effort addresses the mechanical engineering can lead to a function behavior of the cervix during to improve socialization in physically mechanical engineer’s exclusive domain is Specialized mechanical engineering integration of thermal storage into HVAC career of research and teaching. the remodeling events of pregnancy impaired infants (Agrawal). the ability to analyze and design objects subjects include biomechanics, systems for efficient use of variable and characterizing the mechanical The Robotic Manipulation and and systems with motion. cartilage tissue engineering, energy renewable energy. The development of Current Research Activities properties of the eye-wall in relation to Mobility (ROAM) Lab focuses on versatile Since these skills are required conversion, laser-assisted materials measurement, monitoring and control Current research activities in the glaucoma. Research in our lab includes manipulation and mobility in robotics, for virtually everything that is made, processing, combustion, MEMS, systems using IoT devices for use in Department of Mechanical Engineering the mechanical testing of biological aiming for robotic applications pervasive mechanical engineering is perhaps microfluidic devices, fracture mechanics, micrositing and operation of microgrids are in the areas of controls and robotics, soft tissues, the biochemical analysis in everyday life. Research areas include the broadest and most diverse nanomechanics, mechanisms, and enabling flexibility or demand energy and micropower generation, of tissue microstructure, and material manipulation and grasping, interactive or of engineering disciplines. Hence micropower generation, tribology response of load. (Modi) fluid mechanics, heat/mass transfer, modeling based on structure-mechanical Human-in-the-Loop robotics, dynamic mechanical engineers play a central (friction and wear), and vibrations. In the area of energy, demand mechanics of materials, manufacturing, property relationships. In collaboration simulators and virtual environments, role in such industries as automotive The American Society of Mechanical estimation and prediction of interest material processing, MEMS, with clinicians, our goal is to understand machine perception and modeling, (from the car chassis to its every Engineers (ASME) currently lists thirty- using utility data, satellite imagery and nanotechnology, and biomechanics. the etiologies of tissue pathology and and many more. We are interested in subsystem—engine, transmission, six technical divisions, from advanced lean, robust field data capture. (Modi) disease. (Myers) application domains such as versatile sensors); aerospace (airplanes, aircraft energy systems and aerospace Biomechanics and Mechanics In the area of nanoscale thermal automation in manufacturing and engines, control systems for airplanes engineering to solid waste engineering of Materials. Some of the current Control, Robotics, Design, and transport, our research efforts center on logistics, assistive and rehabilitation and spacecraft); biotechnology and textile engineering. research in biomechanics is concerned Manufacturing. Control research the enhancement of thermal radiation robotics in health care, space robotics,

ENGINEERING 2020–2021 ENGINEERING 2020–2021 188 transport across interfaces separated by diseases. A few applications that we involve modeling and understanding the surroundings, a process that plays a Mass radiological triage is critical complexity from basic instrumentation 189 a nanoscale gap. The scaling behavior are particularly interested in include, physics of micro/ nanofluidic devices major role in maintaining healthy cellular after a large-scale radiological event and fundamental exercises to advanced of nanoscale radiation transport is myocardial infarction and heart failure, and systems, exploiting polymer and tissue function. (Hone) because of the need to identify experiments in such diverse areas as measured using a novel heat transfer valvular calcifications and repair, structures to enable micro/nanofluidic Microelectromechanical systems those individuals who will benefit automatic controls, heat transfer, fluid measurement technique based on remodeling and dysfunction in congenital manipulation, and integrating MEMS (MEMS) are being exploited to enable from medical intervention as soon as mechanics, stress analysis, vibrations, the deflection of a bimaterial atomic heart disease, aortic dissections and sensors with microfluidics for measuring and facilitate the characterization and possible. The goal of the ongoing NIH- microcomputer-based data acquisition, force microscope cantilever. Numerical repair, cardiomyopathies, etc. We are physical properties of biomolecules. (Lin) manipulation of biomolecules. MEMS funded research project is to design and control of mechanical systems. simulations are also performed to actively collaborating with cardiologists The Schuck group aims to technology allows biomolecules to a prototype of a fully automated, ultra Equipment includes microcomputers confirm these measurements. The and cardiothoracic surgeons for characterize, understand, and control be studied in well-controlled micro/ high throughput biodosimetry. This and microprocessors, analog-to-digital measurements are also used to infer understanding the unmet clinical needs nanoscale light-matter interactions, nanoenvironments of miniaturized, prototype is supposed to accommodate and digital-to-analog converters, extremely small variations of van der and thereby, provide engineering with a primary focus on sensing, integrated devices, and may enable multiple assay preparation protocols lasers and optics for holography Waals forces with temperature. This solutions with a goal to improve patient- engineering, and exploiting novel novel biomedical investigations not that allow the determination of the and interferometry, a laser-Doppler enhancement of radiative transfer will management and provide a better quality optoelectronic phenomena emerging attainable by conventional techniques. levels of radiation exposure that a velocimetry system, a particle image ultimately be used to improve the power of life. The techniques developed in our from nanostructures and interfaces. This The research interests center on the patient received. The input to this fully velocimetry system (PIV), a Schlieren density of thermophotovoltaic energy group could also find their utility in other offers unprecedented opportunities for development of MEMS devices and autonomous system is a large number system, dynamic strain indicators, a conversion devices. (Narayanaswamy) traditional mechanical and aerospace developing innovative devices that rely systems for label-free manipulation of capillaries filled with blood of patients servoelectric material testing machine, Also in the area of energy, research engineering applications. (Vedula) on the dynamic manipulation of single and interrogation of biomolecules. collected using finger sticks. These photoelasticity, Digital Image Correlation is being performed to improve the photons and charge carriers. We are Current research efforts primarily involve capillaries are processed by the system (DIC) capabilities, a dynamometer, MEMS and Nanotechnology. In these thermochemical models used in continuously developing new multimodal microfluidic devices that exploit specific to distill the micronucleus assay in supersonic de Laval nozzle and areas, research activities focus on power accelerating development of cleaner, and multidimensional spectroscopic and reversible, stimulus-dependent lymphocytes, with all the assays being subsonic wind tunnel, a cryogenic generation systems, nanostructures for more fuel-efficient engines through methods that provide unique access binding between biomolecules and carried out in situ in multiwell plates. apparatus, a coordinate measurement photonics, fuel cells and photovoltaics, computational design. In particular, to optical, electrical, and structural receptor molecules to enable selective The research effort on this project machine (CMM), and three-dimensional and microfabricated adaptive cooling skin data-driven approaches to creating properties at relevant length scales in purification, concentration, and involves the automation system design printers as well as laser cutters. A and sensors for flow, shear, and wind high-accuracy, uncertainty-quantified real environments encountered in energy label-free detection of nucleic acid, and integration including hierarchical CNC wire electrical discharge machine speed. Basic research in fluid dynamics thermochemicals models are being and biological applications. (Schuck) protein, and small molecule analytes; control algorithms, design and control (EDM) is also available for the use of and heat/mass transfer phenomena at developed that utilize both theoretical miniaturized instruments for label-free of custom built robotic devices, and specialized projects for students with small scales also support these activities. Biological Engineering and and experimental data. Special characterization of thermodynamic automated image acquisition and prior arrangement. The undergraduate (Hone, Kysar, Lin, Modi, Narayanaswamy) Biotechnology. Active areas of research emphasis is placed on the generation and other physical properties of processing for sample preparation and laboratory also houses experimental We study the dynamics of in the musculoskeletal biomechanics and analysis of data across the full biomolecules; and subcutaneously analysis. (Yao) setups for the understanding and microcantilevers and atomic force laboratory include theoretical and range of relevant scales—from the implantable MEMS affinity biosensors for A technology that couples the performance evaluation of a complete microscope cantilevers to use them experimental analysis of articular small-scale electronic behavior that continuous monitoring of glucose and power of multidimensional microscopy small steam power generation system, as microscale thermal sensors based cartilage mechanics; theoretical and governs molecular reactivity to the large- other metabolites. (Kysar, Lin) (three spatial dimensions, time, and a heat exchanger, a solar cell system, on the resonance frequency shifts experimental analysis of cartilage scale turbulent, reactive phenomena that The Kysar group has an NIH-funded multiple wavelengths) with that of a fuel cell system, a compressor, and of vibration modes of the cantilever. lubrication, cartilage tissue engineering, govern engine performance. (Burke) project to design and develop a method DNA array technology is investigated a torsional control system. Part of the Bimaterial microcantilever-based and bioreactor design; growth and The Vedula group aims to advance to deliver therapeutics into the inner ear in an NIH-funded project. Specifically, undergraduate laboratory is a staffed sensors are used to determine the remodeling of biological tissues; cell clinical management of cardiovascular through the Round Window Membrane a system is developed in which machine shop with machining tools such thermophysical properties of thin films. mechanics; and mixture theory for disease using computational modeling. (RWM) that serves as a portal for acoustic individual cells selected on the as CNC vertical milling machines, a CNC (Narayanaswamy) biological tissues with experiments and We are developing novel computational energy between the middle ear and basis of optically detectable multiple lathe, standard vertical milling machines, Research in the area of nanotechnology computational analysis (Ateshian). techniques for performing patient- inner ear. This involves the design and features at critical time points in engine and bench lathes, surface grinder, focuses on nanomaterials such as The Hone laboratory studies specific modeling of the cardiovascular fabrication of arrays of microneedles, the dynamic processes can be rapidly band saw, drill press, tool grinders, a nanotubes and nanowires and two-dimensional (2D) materials such system aimed at understanding the measurements of diffusive flux of chemical and robotically micromanipulated into horizontal bandsaw, several Othermills their applications, especially in as graphene, with efforts spanning role of biomechanical factors in disease species across a perforated RWM, and reaction chambers to permit amplified used for light machining and circuit board nanoelectromechanical systems (NEMS). synthesis of single crystals and thin and development, device design, and the design, delivery, and testing of surgical DNA synthesis and subsequent array fabrication. A laboratory is available for the synthesis films; device nanofabrication; and testing 'virtual' surgery planning. Computational tools, all in close collaboration with Anil analysis. Customized image processing A mechatronics laboratory affords of graphene and other two-dimensional of electronic, optical, mechanical, and modeling combined with machine K. Lalwani, M.D., at Columbia University and pattern recognition techniques the opportunity for hands-on experience materials using chemical vapor other properties. The group develops learning and data-mining strategies Medical Center. (Kysar) are developed, including Fisher’s with microcomputer-embedded control deposition (CVD) techniques and to build methods to combine 2D materials into provides unprecedented opportunities The Schuck group is involved in linear discriminant preprocessing with of electromechanical systems. Facilities devices using electron-beam lithography layered heterostructures, which are to not only examine acute response engineering novel near-infrared (NIR) neural net, a support vector machine for the construction and testing of and various etching techniques. This used to explore fundamental properties, to treatment, but also predict and risk upconverting nanoparticles (UCNPs) and with improved training, multiclass cell analog and digital electronic circuits effort will seek to optimize the fabrication, achieve new functionality, and enable stratify patients susceptible to long-term UCNP-based microdevices for large-scale detection with error correcting output aid the students in learning the basic readout, and sensitivity of these devices applications in electronics, photonics, remodeling and dysfunction. (Vedula) sensing applications, including deployment coding, and kernel principal component components of the microcomputer for numerous applications, such as sensing, and other areas. (Hone) The Vedula group is involved in in projects aimed at deep-tissue imaging analysis. (Yao) architecture. The laboratory is divided sensitive detection of mass, charge, and The Hone group uses developing multiscale-multiphysics and the control of neural function deep into work centers for two-person magnetic resonance. (Hone, Kysar, Modi) nanofabrication techniques to create models of the heart coupling cardiac within brain tissue. UCNPs have the Facilities for Teaching and Research student laboratory teams. Each work Research in BioMEMS aims to design tools for studying the role of mechanical electrophysiology, tissue mechanics, potential to overcome nearly all limitations center is equipped with a mixed signal and create MEMS and micro/nanofluidic forces and geometry in cellular biology. The undergraduate laboratories, blood flow and valvular interactions, of current optical probes and sensors, oscilloscope, several power supplies systems to control the motion and These investigations seek to understand occupying an area of approximately thereby creating an integrated heart which have run into fundamental chemical (for low-power electronics and higher measure the dynamic behavior of how cells sense the mechanical 6,000 square feet of floor space, are model, that could be used to study and photophysical incompatibilities with power control), a function generator, a biomolecules in solution. Current efforts properties or physical shape of their the site of experiments ranging in a variety of cardiac and valvular living systems. (Schuck) multimeter, a protoboard for building

ENGINEERING 2020–2021 ENGINEERING 2020–2021 190 MECHANICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS 191 MECHANICAL ENGINEERING: THIRD AND FOURTH YEARS STANDARD TRACK STANDARD TRACK SEMESTER I SEMESTER II SEMESTER III SEMESTER IV SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII APMA E2000 (4) and ORCA E2500 (3)6 either semester MECE E3028 (3) MECE E3018 (3) Lab II Lab I MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) 1 APMA E2101 (3) ENME E3106 (3) MECE E3100 (3) or Dynamics and vibrations Linear Algebra (3)2 Fluids I MECE E3409 (3) 3 Machine design and ODE (3) MECE E3311 (3) MECE E3301 (3) Heat transfer Thermodynamics MECE E3420 (3) MECE E3430 (3) 4 REQUIRED Engineering design: Engineering design: PHYSICS UN1401 (3) UN1402 (3) UN1403 (3) COURSES MECE E3610 (3) 4 MECE E3408 (3) concept creation (three tracks, UN1601 (3.5) UN1602 (3.5) UN2601 (3.5) Materials and processes choose one) Graphics and design UN2801 (4.5) UN2802 (4.5) in manufacturing EEME E3601 (3) ENME E3113 (3) Classical control sys. ELEN E1201 (3.5)1 one semester lecture (3–4) Mechanics of solids Intro. elec. eng. CHEMISTRY UN1403 or UN1404 or Lab UN1500 (3)5 UN2045 or UN1604 MECE E1008 (1) Intro to machining (either semester) UNIVERSITY CC1010 (3) either semester WRITING TECHNICAL 6 points 6 points ELECTIVES2 HUMA CC1001, HUMA CC1002, COCI CC1101, COCI CC1102, NONTECH Students must complete the 27-point requirement.4 REQUIRED or Global Core (3–4) or Global Core (3–4) ELECTIVES3 NONTECHNICAL COURSES HUMA UN1121 or ECON UN1105 (4) and TOTAL ESTIMATED 15–16 16.5–17.5 16 15 UN1123 (3) UN1155 recitation (0) POINTS5

REQUIRED 1 Strongly recommended to be taken in Semester III or IV. TECHNICAL ENME E3105 (4) 2 If APMA E2101 is taken instead of Linear algebra and ODE, students must complete an additional 3-point course in math or basic science with the following course COURSES designators: MATH, PHYS, CHEM, BIOL, STAT, APMA, or EEEB. One technical elective (3000–level or higher) may be substituted for this purpose. 3 Not required for Combined Plan students. COMPUTER Computer language: COMS W1004 or COMS W1005 (3) or ENGI E1006 (3) (in semester I or III) 4 See page 9; not required for Combined Plan students. SCIENCE 5 Students must complete a minimum of 128 points to graduate.

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION Through their participation in the NSF- and innovative efforts in science, environmental, and economic factors MRSEC center, the faculty also have engineering, and technology, as well 3. an ability to communicate effectively THE ART OF ENGI E1102 (4) either semester access to shared instrumentation and as other professional careers. with a range of audiences ENGINEERING the clean room located in the Schapiro 3. Conduct themselves in a responsible, 4. an ability to recognize ethical and Center for Engineering and Physical professional, and ethical manner. professional responsibilities in 1 Students who take APMA E2101 must complete an additional 3 point course in math or basic science with the following course designators: MATH, PHYS, CHEM, Science Research. Columbia University’s 4. Participate in activities that support engineering situations and make BIOL, STAT, APMA, or EEEB. One technical elective (3000–level or higher) may be substituted for this purpose. extensive library system has superb humanity and economic development informed judgments, which must 2 Linear algebra may be fulfilled by either APMA E3101 or MATH UN2010. consider the impact of engineering scientific and technical collections. nationally and globally, developing as 3 Ordinary differential equations may be fulfilled by either MATH UN2030 or MATH UN3027. solutions in global, economic, 4 May substitute EEEB UN2001, BIOL UN2005, or higher. Email and computing services are leaders in their fields of expertise. 5 environmental, and societal contexts May substitute Physics Lab UN1494 (3) or UN3081 (2). maintained by Columbia University As stated on the Mechanical 6 5. an ability to function effectively Offered in spring semester. Information Technology (CUIT) Engineering department website, on teams whose members (columbia.edu/cuit). circuits, a microcomputer circuit board simulator, debugger, and C compiler. stations with state-of-the-art design graduates of the Mechanical Engineering together provide leadership, create (which includes the microcomputer The laboratory is also equipped with software. The research facilities are program at Columbia University will a collaborative and inclusive and peripheral components), a a portable oscilloscope, an EPROM located within individual or group UNDERGRADUATE PROGRAM attain: environment, establish goals, plan microcomputer programmer, and a eraser (to erase microcomputer research laboratories in the department, The Mechanical Engineering 1. an ability to identify, formulate, and tasks, and meet objectives personal computer that contains a data programs from the erasable chips), and these facilities are being continually Undergraduate Program at Columbia solve complex engineering problems 6. an ability to develop and conduct acquisition board. The data acquisition a logic probe, and an analog filter upgraded. To view the current research University has the following Program by applying principles of engineering, appropriate experimentation, system serves as an oscilloscope, bank that the student teams share, as capabilities please visit the various Educational Objectives (PEOs) for its science, and mathematics analyze and interpret data, and additional function generator, and well as a stock of analog and digital laboratories within the research section graduates: 2. an ability to apply engineering design use engineering judgment to draw to produce solutions that meet spectrum analyzer for the student team. electronic components. of the department website. The students 1. Practice mechanical engineering in a conclusions specified needs with consideration The computer also contains a complete The department maintains a modern and staff of the department can, by broad range of industries. 7. an ability to acquire and apply of public health, safety, and welfare, microcomputer software development computer-aided design laboratory prior arrangement, use much of the 2. Pursue advanced education, research new knowledge as needed, using as well as global, cultural, social, system, including editor, assembler, equipped with thirty computer work equipment in these research facilities. and development, and other creative appropriate learning strategies.

ENGINEERING 2020–2021 ENGINEERING 2020–2021 192 193 MECHANICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS MECHANICAL ENGINEERING: THIRD AND FOURTH YEARS EARLY DECISION TRACK EARLY DECISION TRACK

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

APMA E2000 (4) ORCA E2500 (3)6 and MECE E3028 (3) either semester Lab II MECE E3018 (3) MATH UN1101 (3) MATH UN1102 (3) Lab I ENME E3106 (3) MATHEMATICS APMA E2101 (3)1 MECE E3409 (3) Dynamics and vibrations Machine design or MECE E3100 (3) Linear Algebra (3)2 Fluids I MECE E3311 (3) ODE (3)3 MECE E3420 (3) MECE E3430 (3) and REQUIRED Heat transfer Engineering design: Engineering design: COURSES MECE E3301 (3) concept creation 4 Thermodynamics MECE E3610 (3) PHYSICS UN1401 (3) UN1402 (3) UN1403 (3) (three tracks, UN1601 (3.5) UN1602 (3.5) UN2601 (3.5)4 Materials and processes EEME E3601 (3) choose one) UN2801 (4.5) UN2802 (4.5) in manufacturing Classical control systems

one semester lecture (3–4) MECE E1008 (1) Intro to machining (either semester) CHEMISTRY UN1403 or UN1404 or Lab UN1500 (3)5 UN2045 or UN1604 REQUIRED HUMA UN1121 or ECON UN1105 (4) and NONTECHNICAL UN1123 (3) UN1155 recitation (0) COURSES UNIVERSITY CC1010 (3) either semester WRITING TECHNICAL 6 points 6 points ELECTIVES1 REQUIRED HUMA CC1001, HUMA CC1002, NONTECHNICAL COCI CC1101, COCI CC1102, COURSES or Global Core (3–4) or Global Core (3–4) NONTECH Students must complete the 27-point requirement.3 ELECTIVES

ELEN E1201 (3.5) Intro. to elec. eng. TOTAL ESTIMATED 12 16 16 15 REQUIRED ENME E3105 (4) ENME E3113 (3) POINTS2 TECHNICAL Mechanics Mechanics of solids COURSES MECE E3408 (3) Graphics and design 1 If APMA E2101 is taken instead of Linear Algebra and ODE, students must complete an additional 3-point course in math or basic science with the following course designators: MATH, PHYS, CHEM, BIOL, STAT, APMA, or EEEB. One technical elective (3000–level or higher) may be substituted for this purpose. 2 COMPUTER Computer language: COMS W1004 or COMS W1005 (3) or ENGI E1006 (3) (in semester I and III) Students must complete a minimum of 128 points to graduate. SCIENCE 3 See page 9; not required for Combined Plan students.

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION the Mechanical Engineering Department. course in linear algebra (either APMA commitment to professionalism and Of the 18 points of elective content in E3101 or MATH UN2010) and a stand- an established record of abilities that THE ART OF ENGI E1102 (4) either semester the third and fourth years, at least 9 points alone course in ordinary differential will help a job candidate stand out in ENGINEERING of technical elective courses, including equations (either MATH UN2030 or the field. Ideally, the FE exam should at least 6 points from the Department of UN3027), instead of the combined be taken in the senior year while the 1 Students who take APMA E2101 must complete an additional 3 point course in math or basic science with the following course designators: MATH, PHYS, CHEM, Mechanical Engineering, must be taken. A topics course APMA E2101. In addition, technical material learned while pursuing BIOL, STAT, APMA, or EEEB. One technical elective (3000–level or higher) may be substituted for this purpose. technical elective can be any engineering such students are encouraged to take the undergraduate degree is still fresh in 2 Linear algebra may be fulfilled by either APMA E3101 or MATH UN2010. course offered in the SEAS bulletin that a course in partial differential equations the student’s mind. In addition to the FE 3 Ordinary differential equations may be fulfilled by either MATH UN2030 or MATH UN3027. is 3000 level or above. Those prior (APMA E3102 or E4200) as well as a exam, achieving P.E. licensure requires 4 May substitute EEEB UN2001, BIOL UN2005, or higher. 5 May substitute Physics Lab UN1494 (3) or UN3081 (2). remaining points of electives are intended course in numerical methods (APAM some years of experience and a second 6 Offered in spring semester. primarily as an opportunity to complete E3105 or APMA E4300) as technical examination, which tests knowledge the four-year, 27-point nontechnical electives. Ideally, planning for these gained in engineering practice. For more Highly qualified students are business, patent law, medicine, or Undergraduates who wish to declare requirement. Consistent with professional courses should start at the beginning of information, please see http://ncees.org permitted to pursue an honors course management. Thus, the department’s mechanical engineering as their major accreditation standards, courses in the sophomore year. /exams/fe-exam/. consisting of independent study under undergraduate program provides should do so prior to the start of their engineering science and courses in The Mechanical Engineering the guidance of a member of the faculty. a sound foundation for a variety of junior year. Students who declare in their design must have a combined credit Fundamentals of Engineering (FE) Department strongly encourages all Upon graduation the student may professional endeavors. first year should follow the Early Decision of 48 points. Students should see their Exam seniors to take this exam and offers a wish to enter employment in industry The program in mechanical Track. Students who declare in their advisers for details. The FE exam is a state licensing exam review course covering material relevant or government, or continue with engineering leading to the B.S. degree second year should follow the Standard Undergraduate students who and the first step toward becoming to the exam, including a practice exam graduate study. Alternatively, training is accredited by the Engineering Track. Students who wish to declare intend to pursue graduate studies in a Professional Engineer (P.E.). P.E. to simulate the testing experience. The in mechanical engineering may be Accreditation Commission of ABET, during or after the fall semester of their engineering are strongly encouraged to licensure is important for engineers FE exam is given in the fall and spring of viewed as a basis for a career in www.abet.org. junior year must first obtain approval from take the combination of a stand-alone to obtain—it shows a demonstrated each year. The review course is offered

ENGINEERING 2020–2021 ENGINEERING 2020–2021 194 in the spring semester, concluding Engineering offers two doctoral degrees: 2. Every program must contain at least MECE E4210: Energy infrastructure planning M.S. in Mechanical Engineering with EEME E4601: Digital control systems** 195 MECE E4211: Energy: sources and conversion before the spring exam. Doctor of Philosophy (Ph.D.) and Doctor one course in mathematics (APMA, Concentration in Robotics and Control BMME E4702: Advanced musculoskeletal MECE E4302: Advanced thermodynamics biomechanics of Engineering Science (Eng.Sc.D.), and MATH, STAT course designations) MECE E4304: Turbomachinery Advisers: Professors Sunil Agrawal, COMS W4731: Computer vision* Integrated B.S./M.S. Program the Master of Science degree. The Ph.D. covering material beyond what the MECE E4305: Mechanics and thermodynamics Matei Ciocarlie, Hod Lipson, and COMS W4733: Computational aspects of robotics* degree is conferred by the Graduate The Integrated B.S./M.S. degree program student has taken previously. It is propulsion Richard Longman ELEN E4810: Digital signal processing is open to a qualified group of Columbia School of Arts and Science, and the recommended to be taken early in the MECE E4312: Solar thermal engineering EEME E6601: Introduction to control theory** juniors and makes possible the earning Eng.Sc.D. degree is conferred by The Fu sequence, in order to serve as a basis MECE E4314: Energy dynamics of green buildings The field of robotics is seeing EEME E6602: Modern control theory** of both the B.S. and M.S. degree in an Foundation School of Engineering and for the technical coursework. MECH E4320: Intro to combustion unprecedented growth, in areas as EEME E6610: Optimal control theory** Applied Science. integrated fashion. Benefits of this program 3. Out-of-department study is MECE E4330: Thermofluid systems design diverse as manufacturing, logistics, COMS E6733: 3D photography* M.S. students must complete the MECE E6100: Advanced mechanics of fluids include optimal matching of graduate encouraged, must be taken in transportation, health care, space professional development and leadership MECE E6102: Computational heat transfer and *Registration restrictions may apply. courses with corresponding undergraduate consultation with adviser. exploration, and more. This program course, ENGI E4000, as a graduation fluid flow **Count as MECE. prerequisites, greater ability to plan ahead 4. At least five course must be in prepares students for a career in requirement. Ph.D. candidates are MECE E6103: Compressible flow Mechanical Engineering. robotics and its many applications in for most advantageous course planning, strongly encouraged to complete ENGI MECE E6104: Case studies in computational fluid Examples of suitable APMA courses opportunities to do research for credit dynamics society. Students perform in-depth study E6001–6004 and should consult their Rather than selecting the standard are: APMA E4001y Principles of during the summer after senior year, and MECE E6313: Advanced heat transfer of topics such as robotic manipulation, program for PDL requirements. option, students can select an elective applied mathematics; APMA E4300y, up to 6 points of 4000-level technical EAEE E6126: Carbon sequestration navigation, perception, human specialization in either energy systems, Introduction to numerical methods; electives from the B.S. requirement may interaction, medical robotics, assistance Master of Science Degree Program micro/nanoscale engineering, or robotics APMA E4301x Numerical methods for count toward the fulfillment of the point *One 3-point research course can be and rehabilitation. This specialization The program leading to the Master and control. The requirements for a partial differential equations; and APMA requirement of the M.S. degree. Additional counted toward the specialization if the is a suitable preparation for joining of Science degree in mechanical specialization are identical to those of E4204x Functions for complex variables. benefits include simplified application research is approved by the student's established companies, information-age engineering requires completion of a the standard track, with one exception: process, no GRE is required, and no adviser and is energy related. dominant players investing heavily in minimum of 30 points of approved students must take at least 15 points Doctoral Degree Program reference letters are required. To qualify this field, or the new wave of robotics coursework consisting of no fewer from a list determined by an adviser in All applications to the doctoral for this program, students must have M.S. in Mechanical Engineering with start-ups aiming to provide disruptive than ten courses. A thesis based on consultation with an advisory committee. program in mechanical engineering are a cumulative GPA of at least 3.5 and Concentration in Micro/Nanoscale innovations. Many of the acquired skills either experimental, computational, or The currently available elective administered by The Fu Foundation strong recommendations from within the Engineering can be applied in other fields as diverse analytical research is optional and may specializations are listed below. School of Engineering and Applied Department. Students should apply for Advisers: Professors James Hone and P. as automation, manufacturing, computer be counted in lieu of up to 6 points of Science. Students who matriculate into the program by April 30 in their junior year. James Schuck graphics or machine vision. This coursework. In general, attainment of the doctoral program without a master's For more information on requirements and M.S. in Mechanical Engineering with program can also be a foundation for a the degree requires one academic year The elective concentration in micro/ degree earn a Master of Science degree access to an application form, please visit Concentration in Energy Systems research career in robotics and related of full-time study, although it may also nanoscale engineering provides the M.S. while pursuing their doctoral degree. me.columbia.edu/integrated-bsms- Advisers: Professors Vijay Modi and areas, in both academia and industry. be undertaken on a part-time basis candidate with an understanding of Doctoral candidates are expected program. Arvind Narayanaswamy Candidates for the M.S. with over a correspondingly longer period. A engineering challenges and opportunities specialization in Robotics and Control to attain a level of mastery in an area The concentration in energy systems Express M.S. Application minimum grade-point average of 2.5 is in micro- and nanoscale systems. The should simultaneously satisfy these two of mechanical engineering and must provides the M.S. candidate with a The Express M.S. Application is offered required for graduation. curriculum addresses fundamental sets of requirements: therefore choose a field and take the global understanding of current energy to current seniors, including 3-2 students, The M.S. degree in mechanical issues of mechanics, fluid mechanics, Take at least five courses from the list most advanced courses offered in challenges. Advanced thermofluidic who are enrolled in the BS program. In engineering requires a student to take optics, heat transfer, and manufacturing below during their M.S. (courses taken that field. Candidates are assigned a knowledge is provided to design the Express M.S. Application, a master’s a sequence of courses that shows a at small-size scales. Application areas during undergraduate studies do not faculty adviser whose task is to help and optimize energy systems, with degree can be earned seamlessly. clearly discernible focus. In consultation include MEMS, bio-MEMS, microfluidics, count): choose a program of courses, provide with his/her adviser an M.S. student a strong emphasis on renewable thermal systems, and carbon general advice on academic matters, Graduate classes are available for Courses in the Mechanical Engineering energies. Courses related to energy nanostructures. seniors to apply toward their M.S. degree can develop a focus specifically tailored Department and monitor academic performance. and environmental policy, two strong Requirements: While satisfying and the advanced courses that will be to his/her interests and objectives, and MEBM E4439: Modeling & id of dynamic system Candidates also choose a faculty areas of Columbia as a global taken have been designed to have the we refer to this as the standard track. the general mechanical engineering MECE E4058: Mechanics and embedded member in the pertinent area of university, can be integrated into the exact prerequisites completed as an Alternatively, M.S. students can pick requirements, take at least five courses microcomputer control specialization to serve as their research course sequence. This specialization undergraduate. Other advantages include from a set of predefined tracks. from: MECE E4510: Geometrical modeling adviser. This adviser helps select a is a suitable preparation for careers MECE E4601: Digital control systems the opportunity for better course planning Typical choices in the standard track MECE E4212: Microelectromechanical systems research problem and supervises the MECE E4602: Intro to robotics include such subjects as mechanics of in energy production and energy MECE E4213: BioMEMS research, writing, and defense of the and creating a streamlined set of courses MECE E4603: Applied robotics: algorithm & software consultation. MECE E6105: T ransport phenomena in the dissertation. more possible. Additional benefits include solids and fluids, thermodynamics, heat MECE E4606: Digital manufacturing Requirements: 30 points of presence of interfaces simplified application process, no GRE transfer, manufacturing engineering, MECE E6400: Advanced machine dynamics graduate level coursework, i.e., courses MECE E6700: Carbon nanotubes robotics, kinematics, dynamics and MECE E6424: Vibrations in machine, I Program Requirements is required and no reference letters are MECE E6710: Nanofabrication laboratory vibrations, controls, and power numbered 4000-level or higher, at least MECE E6601: Intro to control theory • 30 credits beyond master's degree required. To qualify for this program, your MECE E6720: Nano/microscale thermal transport two of which must be a 6000-level, MECE E6602: Modern control theory cumulative GPA should be at least 3.5. generation. Nevertheless, the following processes • GPA of 3.2 or better in graduate chosen in consultation with an adviser MECE E6610: Optimal control theory For more information on requirements guidelines must be adhered to: MECE E8990: Small scale mechanical behavior courses MECE E6614: Advanced topics in robotics and (MECE E6100 Advanced mechanics of ELEN E4503: Sensors, actuators, and • 4 semesters of graduate seminar and access to an application, please mechanism synthesis 1. All courses must be at the graduate fluids and MECE E6313 Advanced heat electromechanical systems MECE E9500 visit me.columbia.edu/ms-express- MECE E6615: Robotic manipulation level, i.e., numbered 4000 or higher, transfer are strongly recommended). ELEN E6945: Device nanofabrication application-1. MECE E6620: Applied signal recognition • Completion of all milestones with at least two 6000-level courses, Furthermore, students must take one BMEN E4590: BioMEMS: cellular and molecular Courses in the Other Departments in the applications chosen in consultation with an adviser. course in statistics (STAT designations) School of Engineering and Applied Science See me.columbia.edu/doctoral- GRADUATE PROGRAMS At least one of the 6000-level courses and at least five courses from the MSAE E4090: Nanotechnology ELEN E4501: Sensors, actuators and program-0 for more information. The Department of Mechanical must be in Mechanical Engineering. following list*: electromechanical systems

ENGINEERING 2020–2021 ENGINEERING 2020–2021 deformable bodies. Computer-aided mechanical MECE E4058x and y Mechatronics and or new infrastructure. Special guest lectures 196 COURSES IN MECHANICAL MECE E3038x Mechanical engineering and numerical methods applied to the solution of 197 laboratory, III mechanical engineering design problems. engineering design using established software embedded microcomputer control on infrastructure finance, regulation and public- ENGINEERING 3 pts. Lect: 3. Not offered in 2020–2021. tools and verifications against analytical and 3 pts. Lect: 3. Professor Zordan. private partnerships. MECE E3409x Machine design MECE E1001x Mechanical engineering: Mechatronic control of mechanical and finite difference solutions. Prerequisite: ELEN E1201. Recommended: 3 pts. Lect: 3. Professor Yesilevskiy. MECE E4211x or y Energy: sources and micromachines to jumbo jets electromechanical systems. Control of various ELEN E3000. Enrollment limited to 12 students. Prerequisite: MECE E3408. Computer-aided EEME E3601x Classical control systems conversion 3 pts. Lect: 3. Not offered in 2020–2021. thermodynamic cycles, including internal Mechatronics is the application of electronics and analysis of general loading states and deformation 3 pts. Lect: 3. Professor Longman. 3 pts. Lect: 3. Professor Modi. Corequisite: MATH UN1101 Calculus I. This combustion engine (Otto cycle). Reverse microcomputers to control mechanical systems. of machine components using singularity functions Prerequisite: MATH UN2030. Analysis and design Prerequisite: MECE E3301. Energy sources such introductory course explores the role of engineering of an electromechanical product. Systems explored include on/off systems, and energy methods. Theoretical introduction to of feedback control systems. Transfer functions; as oil, gas, coal, gas hydrates, hydrogen, solar, Mechanical Engineering in developing many of solenoids, stepper motors, DC motors, thermal MECE E3100x Introduction to mechanics static failure theories, fracture mechanics, and block diagrams; proportional, rate, and integral and wind. Energy conversion systems for electrical the fundamental technological advances on which systems, magnetic levitation. Use of analog and of fluids fatigue failure theories. Introduction to conceptual controllers; hardware, implementation. Routh power generation, automobiles, propulsion and today’s society depends. Students will be exposed digital electronics and various sensors for control. 3 pts. Lect: 3. Professor Kasza. design and design optimization problems. Design stability criterion, root locus, Bode and Nyquist refrigeration. Engines, steam and gas turbines, to several mature and emerging technologies Programming microcomputers in Assembly and C. Prerequisite: ENME E3105. Basic continuum of machine components such as springs, shafts, plots, compensation techniques. wind turbines; devices such as fuel cells, through a series of case studies. Topics Lab required. concepts. Liquids and gases in static equilibrium. fasteners, lead screws, rivets, welds. Modeling, thermoelectric converters, and photovoltaic cells. include airplanes, automobiles, robots, modern MECE 3610y Materials and processes in Continuity equation. Two-dimensional kinematics. analysis, and testing of machine assemblies for MECE E4078x or y Internet of (Mechanical) Specialized topics may include carbon-dioxide manufacturing methods as well as the emerging manufacturing Equation of motion. Bernoulli’s equation and prescribed design problems. Problems will be Things fields of microelectromechanical machines (MEMS) 3 pts. Lect: 3. Professor Yao. sequestration, cogeneration, hybrid vehicles and applications. Equations of energy and angular drawn from statics, kinematics, dynamics, solid 3 pts. Lect: 3. Professor Fernandez. and nanotechnology. The physical concepts that Prerequisites: ENME E3113 or the equivalent. energy storage devices. momentum. Dimensional analysis. Two- modeling, stress analysis, and design optimization. Hands-on, project-oriented course covering govern the operation of these technologies will be Introduction to microstructures and properties dimensional laminar flow. Pipe flow, laminar, and foundations of Internet of Things (IoT) technologies MECE E4212x or y Microelectromechanical developed from basic principles and then applied MECE E3411y Fundamentals of engineering of metals, polymers, ceramics and composites; turbulent. Elements of compressible flow. systems in simple design problems. Students will also be 1 pt. Lect: 3. Professor Vukelic. typical manufacturing processes: material removal, as they relate to the physical world. Projects utilizing Arduino and Raspberry Pi platforms. 3 pts. Lect: 1.5. Lab: 3. Professor Schuck. exposed to state-of-the art innovations in each ENME E3105x and y Mechanics Prerequisite: Senior standing. Review of core shaping, joining, and property alteration; behavior End-to-end IoT including sensors, basic controls, MEMS markets and applications; scaling laws; case study. 4 pts. Lect: 4. Professor Hone. courses in mechanical engineering, including of engineering materials in the manufacturing silicon as a mechanical material; Sensors and Prerequisites: PHYS UN1401 and MATH UN1101, mechanics, strength of materials, fluid mechanics, processes. embedded systems programming, networking, MECE E1008x or y Introduction to machining actuators; micromechanical analysis and design; UN1102, and UN1201 or APMA E2000. Elements thermodynamics, heat transfer, materials and IoT protocols, power consumption/optimization, 1 pt. Professor Vukelic. MECE E3900x-E3901y Honors tutorial in substrate (bulk) and surface micromachining; of statics, dynamics of a particle, and systems of processing, control, and mechanical design and and cloud connectivity. Build real IoT devices and Introduction to the manual machine operation, CNC mechanical engineering computer aided design; packaging; testing and particles. analysis. Review of additional topics, including systems in two team-based projects. fabrication and usage of basic hand tools, band/ 3 pts. Lect: 3. Members of the faculty. characterization; microfluidics. engineering economics and ethics in engineering. hack saws, drill presses, grinders and sanders. Prerequisite: 3.2 or higher GPA. Individual study; MECE E4100y Mechanics of fluids ENME E3113x Mechanics of solids The course culminates with a comprehensive MECE E4213x or y Biomicroelectromechanical may be selected after the first term of the junior 3 pts. Lect: 3. Professor Kasza. 3 pts. Lect: 3. Professor Betti. examination, similar to the Fundamentals of systems (BioMEMS): design, fabrication, and MECE E1304x or y Naval ship systems, I year by students maintaining a 3.2 grade-point Prerequisite: MECE E3100 or equivalent. Fluid Pre- or corequisite: ENME E3105 or equivalent. Engineering examination. Meets the first 4.5 analysis 3 pts. Lect: 3. Not offered in 2020–2021. average. Course format may vary from individual dynamics and analyses for mechanical engineering Stress and strain. Mechanical properties of weeks only. 3 pts. Lect: 3. Professor Lin. Students are strongly advised to consult with tutorial to laboratory work to seminar instruction and aerospace applications: boundary layers the ME Department prior to registering for this materials. Axial load, bending, shear, and Prerequisites: MECE E3100 and E3311, course in MECE E3420x Engineering design—concept/ under faculty supervision. Written application must and lubrication, stability and turbulence, and course. A study of ship characteristics and types torsion. Stress transformation. Deflection of transport phenomena, or instructor’s permission. design generating be made prior to registration outlining proposed compressible flow. Turbomachinery as well as including ship design, hydrodynamic forces, beams. Buckling of columns. Combined loadings. Silicon and polymer micro/nanofabrication 3 pts. Lect: 3. Professor Yesilevskiy. study program. Projects requiring machine- additional selected topics. stability, compartmentation, propulsion, electrical Thermal stresses. techniques; hydrodynamic microfluidic control; Prerequisite: Senior standing. Corequisite: MECE shop use must be approved by the laboratory and auxiliary systems, interior communications, IEME E4200x or y Introduction to human- electrokinetic microfluidic control; microfluidic MECE E3301x Thermodynamics E3409. A preliminary design for an original project supervisor. Students may count up to 6 points ship control, and damage control; theory and centered design separation and detection; sample preparation; 3 pts. Lect: 3. Professor Narayanaswamy. is a prerequisite for the capstone design course. toward degree requirements. Students must submit design of steam, gas turbine, and nuclear 1.5 pts. Lect: 4.5. Professor West. micro bioreactors and temperature control; Classical thermodynamics. Basic properties and Will focus on the steps required for generating both a project outline prior to registration and a propulsion; shipboard safety and firefighting. This Prerequisite: Application to instructor for implantable MEMS, including sensors, actuators concepts, thermodynamic properties of pure a preliminary design concept. Included will be final project write up at the end of the semester. course is part of the Naval ROTC program at approval. Open to SEAS graduate and advanced substances, equation of state, work, heat, the first a brainstorming concept generation phase, and drug delivery devices. Columbia but will be taught at SUNY Maritime. MECE E3998x and y Projects in mechanical undergraduate students, Business School, and and second laws for flow and nonflow processes, a literature search, incorporation of multiple Enrollment may be limited; priority is given to engineering GSAPP. Students from other schools may apply. MECE E4214x or y MEMS production and energy equations, entropy, and irreversibility. constraints, adherence to appropriate engineering students participating in Naval ROTC. Will not 1–3 pts. Members of the faculty. Fast-paced introduction to human-centered design. packaging Introduction to power and refrigeration cycles. codes and standards, and the production of a count as a technical elective. Students should Prerequisite: Approval by faculty member who Students learn the vocabulary of design methods, 3 pts. Lect: 3. Professor Hilton. layout drawing of the proposed capstone design see a faculty adviser as well as Columbia MECE E3311y Heat transfer agrees to supervise the work. Independent project understanding of design process. Small group Prerequisite: MECE E4212. Applications-driven project in a Computer Aided Design (CAD) NROTC staff ([email protected]) for more 3 pts. Lect: 3. Professor Narayanaswamy. involving theoretical, computational, experimental, projects to create prototypes. Design of simple study of the packaging and manufacturing of software package. Note: MECE students only. information. Steady and unsteady heat conduction. Radiative or engineering design work. May be repeated, but product, more complex systems of products and MEMS devices. Covers underlying physical heat transfer. Internal and external forced and free MECE E3430y Engineering design no more than 3 points may be counted toward services, and design of business. phenomena such as fracture mechanics and MECE E3018x Mechanical engineering convective heat transfer. Change of phase. Heat 3 pts. Lect: 2. Lab: 4. Professor Yesilevskiy. degree requirements. Projects requiring machine- materials science topics relevant to MEMS laboratory, I MECE E4210x or y Energy infrastructure exchangers. Prerequisite: MECE E3420. Building on the shop use must be approved by the laboratory production. Packaging approaches such as 3 pts. Lect: 3. Professor Yesilevskiy. preliminary design concept, the detailed supervisor. Students must submit both a project planning glass-to-metal seals and CTE matching. Electrical Experiments in instrumentation and measurement: MECE E3401x Mechanics of machines elements of the design process are completed: outline prior to registration and a final project write- 3 pts. Lect: 3. Professor Modi. filtering and noise sources as relevant to the optical, pressure, fluid flow, temperature, stress, 3 pts. Lect: 3. Professor Agrawal. systems synthesis, design analysis optimization, up at the end of the semester. Prerequisites: One year each of college level transducer signal chain. Comparative MEMS and electricity; viscometry, cantilever beam, digital Prerequisites: ENME E3105 and MECE E3408. incorporation of multiple constraints, compliance physics, chemistry, and mathematics. Energy design as focused on a common example: data acquisition. Probability theory: distribution, Introduction to mechanisms and machines, MECE E3999x, y or s Fieldwork with appropriate engineering codes and standards, infrastructure planning with specific focus on pressure transducers. functions of random variables, tests of significance, analytical and graphical synthesis of mechanism, 1–2 pts. Professor Myers. and Computer Aided Design (CAD) component countries with rapidly growing infrastructure correlation, ANOVA, linear regression. displacement analysis, velocity analysis, Prerequisites: Obtained internship and approval MECE E4302y Advanced thermodynamics part drawings. Execution of a project involving the needs. Spatiotemporal characteristics, scale, and acceleration analysis of linkages, dynamics of from a faculty adviser. May be repeated for credit, 3 pts. Lect: 3. Professor Burke. MECE E3028y Mechanical engineering design, fabrication, and performance testing of an environmental footprints of energy resources, mechanism, cam design, gear and gear trains, and but no more than 3 total points may be used toward Prerequisite: MECE E3301. Advanced classical actual engineering device or system. power generation and storage, modeling demand laboratory, II computer-aided mechanism design. the 128-credit degree requirement. Only for MECE thermodynamics. Availability, irreversibility, 3 pts. Lect: 3. Professor Lin. growth, technology choices and learning for MECE E3450x or y Computer-aided design undergraduate students who include relevant on- generalized behavior, equations of state for Experiments in engineering and physical phenomena: MECE E3408x and y Computer graphics planning. Computer-assisted decision support and 3 pts. Lect: 3. Professor Ateshian. campus and off-campus work experience as part of nonideal gases, mixtures and solutions, phase and aerofoil lift and drag in wind tunnels, laser Doppler and design network design/optimization tools. Similarities, Prerequisites: ENME E3105, E3113, MECE their approved program of study. Final report and chemical behavior, combustion. Thermodynamic anemometry in immersed fluidic channels, supersonic 3 pts. Lect: 3. Professor Vukelic. differences and interactions among electricity, E3408, E3311. Introduction to numerical letter of evaluation required. Fieldwork credits may properties of ideal gases. Applications to flow and shock waves, Rankine thermodynamical Introduction to drafting, engineering graphics, gas, information, transportation and water methods and their applications to rigid body not count toward any major core, technical, elec- automotive and aircraft engines, refrigeration and cycle for power generation, and structural truss computer graphics, solid modeling, and mechanical distribution networks. Penetration of renewable mechanics for mechanisms and linkages. tive, and nontechnical requirements. May not be air conditioning, and biological systems. engineering design. Interactive computer graphics and/or decentralized technologies into existing mechanics and analysis. Introduction to finite element stress analysis for taken for pass/fail credit or audited.

ENGINEERING 2020–2021 ENGINEERING 2020–2021 198 MECE E4304x Turbomachinery MECE E4314y Energy dynamics of green fundamentals of vehicle dynamics. A systems- intersections; boundary representation and artificial intelligence; manipulator programming modification. Introduction to electrochemical 199 3 pts. Lect: 3. Not offered in 2020–2021. buildings based engineering approach to explore areas boundary evaluation; applied computational requirements and languages. machining, electrical discharge machining and Introduces the basics of theory, design, selection 3 pts. Lect: 3. Professor Naraghi. of: tire characteristics, aerodynamics, stability geometry; analysis of geometrical algorithms abrasive water jet machining. MECS E4603x Applied robotics: algorithms and applications of turbomachinery. Turbomachines Prerequisites: MECE E3301 and E3311. and control, wheel loads, ride and roll rates, and associated data structures; applications of and software MECE E4611x or y Robotics studio are widely used in many engineering applications Introduction to analysis and design of heating, suspension geometry, and dampers. A high- geometrical modeling in vision and robotics. 3 pts. Lect: 3. Not offered in 2020–2021. such as energy conversion, power plants, ventilating and air-conditioning systems. Heating performance vehicle (racecar) platform used as an 3 pts. Lect: 1. Lab: 4. Professor Lipson. MECE E4502x Computational geometry for Prerequisites: Fundamental programming skills air-conditioning, pumping, refrigeration and and cooling loads. Humidity control. Solar gain and example to review topics. Prerequisites: Knowledge of basic computer CAD/CAM (e.g., COMS W1002, W1004, W1005, ENGI vehicle engines, as there are pumps, blowers, passive solar design. Global energy implications. programming (e.g., Java, Matlab, Python) or MECE E4431x or y Space vehicle dynamics 3 pts. Lect: 3. Not offered in 2020–2021. E1006, or equivalent). Science and systems compressors, gas turbines, jet engines, wind Green buildings. Building-integrated photovoltaics. instructor's permission. Hands-on studio class 3 pts. Lect: 3. Professor Longman. Prerequisite: COMS W1005 FORTRAN or aspects of Robotics from applied perspective, turbines, etc. Applications are drawn from energy Roof-mounted gardens and greenhouses. Financial exposing students to practical aspects of the Prerequisite: ENME-MECE E3105; ENME E4202 PASCAL. Analysis of geometric problems and the focusing on algorithms and software tools. conversion technologies, HVAC and propulsion. assessment tools and case studies. Open to design, fabrication, and programming of physical recommended. Space vehicle dynamics and control, design of efficient methodologies to obtain solutions Spatial reasoning; tools for manipulating and Provides a basic understanding of the different Mechanical Engineering graduate students only. robotic systems. Students experience entire robot kinds of turbomachines. rocket equations, satellite orbits, initial trajectory to these problems. Algorithms to be studied include visualizing spatial relationships. Analysis of robotic creation process, covering conceptual design, geometric searching, convex hulls, triangulations, MECH E4320x Introduction to combustion designs from earth to other planets, satellite attitude manipulators; numerical methods for kinematic detailed design, simulation and modeling, digital MECE E4305y Mechanics and Voronoi diagrams, intersections, hidden surfaces. analysis. Motion planning, search-based and 3 pts. Lect: 3. Professor Burke. dynamics, gravity gradient stabilization of satellites, manufacturing, electronics and sensor design, and thermodynamics of propulsion spin-stabilized satellites, dual-spin satellites, satellite Emphasis will be on practical aspects of these stochastic approaches. Applications for force and Prerequisites: Introductory thermodynamics, fluid software programming. 3 pts. Lect: 3. Professor Bradshaw. dynamics, and heat transfer at the undergraduate attitude control, modeling, dynamics, and control of algorithms, and on applications of the solutions in impedance control. Grading based on combination Prerequisites: MECE E3301x Thermodynamics level or instructor’s permission. Thermodynamics large flexible spacecraft. computer-aided product design and manufacturing. of exams and projects implemented using Robot MECE E4612x or y Sustainable manufacturing and MECE E3311y Heat transfer; MECE Operating System (ROS) software framework 3 pts. Lect: 3. Professor Yao. and kinetics of reacting flows; chemical kinetic MEBM E4439x Modeling and identification of MECS E4510x Evolutionary computation and E4304x Turbomachinery (or instructor approval). and executed on real and simulated robotic Prerequisites: Introductory course in engineering mechanisms for fuel oxidation and pollutant dynamic systems design automation Principles of propulsion. Thermodynamic cycles manipulators. materials and manufacturing processes or formation; transport phenomena; conservation 3 pts. Lect: 3. Not offered in 2020–2021. 3 pts. Lect: 3. Professor Lipson. of air breathing propulsion systems including instructor's permission. Fundamentals of equations for reacting flows; laminar nonpremixed Prerequisite: APMA E2101, ELEN E3801, or Prerequisite: Basic programming experience in MECE E4604x Product design for ramjet, scramjet, turbojet, and turbofan engine flames (including droplet vaporization and burning); sustainable design and manufacturing, metrics and rocket propulsion system concepts. Turbine corequisite EEME E3601, or permission of any language. Fundamental and advanced topics manufacturability laminar premixed flames; flame stabilization, of sustainability, analytical tools, principles of life engine and rocket performance characteristics. instructor. Generalized dynamic system modeling in evolutionary algorithms and their application to 3 pts. Lect: 3. Professor Walker. quenching, ignition, extinction, and other limit cycle assessment, manufacturing tools, processes Component and cycle analysis of jet engines and and simulation. Fluid, thermal, mechanical, open-ended optimization and computational design. Prerequisites: Manufacturing process, computer phenomena; detonations; flame aerodynamics and and systems energy assessment and minimization turbomachinery. Advanced propulsion systems. diffusive, electrical, and hybrid systems are Covers genetic algorithms, genetic programming, graphics, engineering design, mechanical design. turbulent flames. in manufacturing, sustainable manufacturing Columbia Engineering interdisciplinary course. considered. Nonlinear and high order systems. and evolutionary strategies, as well as governing General review of product development process; automation, sustainable manufacturing systems, MECE E4330x Thermofluid systems design System identification problem and Linear dynamic of coevolution and symbiosis. Includes market analysis and product system design; MECE E4306x or y Introduction to remanufacturing, recycling and reuse. 3 pts. Lect: 3. Professor Bradshaw. Least Squares method. State-space and noise discussions of problem representations and principles of design for manufacturing; strategy aerodynamics Prerequisites: MECE E3100, E3301, E3311. representation. Kalman filter. Parameter estimation applications to design problems in a variety of for material selection and manufacturing process 3 pts. Lect: 3. Professor LeVoci. BMME E4702x Advanced musculoskeletal Theoretical and practical considerations, and design via prediction-error and subspace approaches. domains including software, electronics, and choice; component design for machining; casting; Principles of flight, incompressible flows, biomechanics principles, for modern thermofluids systems. Topics Iterative and bootstrap methods. Fit criteria. Wide mechanics. molding; sheet metal working and inspection; compressible regimes. Inviscid compressible 3 pts. Lect: 3. Not offered in 2020–2021. include boiling, condensation, phase change heat applicability: medical, energy, others. MATLAB and general assembly processes; product design aerodynamics in nozzles (wind tunnels, jet MECE E4520x or y Data science for Advanced analysis and modeling of the transfer, multimode heat transfer, heat exchangers, Simulink environments. for manual assembly; design for robotic and engines), around wings (aircraft, space shuttle) mechanical systems musculoskeletal system. Topics include and modeling of thermal transport systems. automatic assembly; case studies of product and around blunt bodies (rockets, reentry MECE E4440x or y Optimization of dynamic 3 pts. Lect: 3. Professor Browne. advanced concepts of 3D segmental kinematics, Emphasis on applications of thermodynamics, heat design and improvement. vehicles). Physics of normal shock waves, oblique systems Prerequisites: Knowledge of basic computer musculoskeletal dynamics, experimental transfer, and fluid mechanics to modeling actual shock waves, and explosion waves. 3 pts. Lect: 3. Professor Agrawal. programming (e.g., Java, Matlab, Python) or MECE E4606y Digital manufacturing measurements of joints kinematics and anatomy, physical systems. Term project on conceptual design Prerequisites: Course on linear and/or nonlinear instructor's permission. Introduction to practical 3 pts. Lect: 3. Professor Lipson. modeling of muscles and locomotion, multibody and presentation of a thermofluid system that meets IEME E4310x The manufacturing enterprise control theory, introduction to Robotics, or instruc- application of data science, machine learning, Prerequisite: Basic programming in any language. joint modeling, introduction to musculoskeletal specified criteria. 3 pts. Lect: 3. Not offered in 2020–2021. tor's permission. Fundamentals for optimizing and artificial intelligence and their application Additive manufacturing processes, CNC, Sheet surgical simulations. The strategies and technologies of global cutting processes, Numerical control, Generative MECE E4400x and y Computer laboratory access performance of dynamic systems described by a set in Mechanical Engineering. Review of relevant manufacturing and service enterprises. and algorithmic design. Social, economic, legal, MEBM E4703x Molecular mechanics in biology 0 pts. of ordinary differential equations based on theory of programming tools necessary for applying data Connections between the needs of a global and business implications. Course involves both 3 pts. Lect: 3. Not offered in 2020–2021. Sign up for this class to obtain a computer account variational calculus. Systematic methods to solve science is provided, as well as detailed review of enterprise, the technology and methodology theoretical exercises and a hands-on project. Prerequisite: ENME E3105, APMA E2101, or and access to the Department of Mechanical optimization problems using numerical methods. data infrastructure and database construction for needed for manufacturing and product instructor’s permission. Mechanical understanding Engineering Computer Laboratory. Topics include: Static Optimization of systems with data science. A series of industry case studies from MECE E4609y Computer-aided manufacturing development, and strategic planning as currently of biological structures including proteins, DNA and equality and inequality and inequality constraints, experts in the field of data science will be presented. 3 pts. Lect: 3. Professor Walker. practiced in industry. MECE E4404x or y Tribology: friction, RNA in cells and tissues. Force response of proteins Numerical methods to solve static optimization prob- Prerequisites: Introductory course on manufacturing lubrication, and wear EEME E4601y Digital control systems and DNA, mechanics of membranes, biophysics MECE E4312x Solar thermal engineering lems, Theory of calculus of variations, Application processes and knowledge of computer-aided design, 3 pts. Lect: 3. Not offered in 2020–2021. 3 pts. Lect: 3. Professor Beigi. of molecular motors, mechanics of protein-protein 3 pts. Lect: 3. Professor Naraghi. of calculus of variations to solve static optimization and mechanical design or instructor’s permission. Prerequisites: MECE E3100, E3311, and ENME Prerequisite: EEME E3601 or ELEN E3201. Real- interactions. Introduction to modeling and simulation Prerequisite: MECE E3311 (Heat transfer). problems with equality and inequality constraints, Computer-aided design, free-form surface modeling, E3113, or permission of the instructor. Friction, time control using digital computers. Solving scalar techniques, and modern biophysical techniques Fundamentals of solar energy transport: radiation numerical methods to solve static optimization prob- tooling and fixturing, computer numeric control, lubrication, and wear between sliding surfaces. and state-space difference equations. Discrete such as single molecule FRET, optical traps, AFM, heat transfer, convention, conduction and phase lems, theory of calculus variations to solve dynamic rapid prototyping, process engineering, fixed and Surface metrology, contact mechanics, and sliding equivalents of continuous systems fed by holds. and superresolution imaging, for understanding change processes. Heat exchangers and solar optimization problems with equality an dinequality programmable automation, industrial robotics. friction. Deformation, wear, and temperature rise of Z-transer functions. Creating closed-loop difference molecular mechanics and dynamics. collectors: basic methods of thermal design, flow constraints, direct and indirect numerical methods nonlubricated, liquid-lubricated, and solid-lubricated equation models by Z-transform and state variable MECE E4610x Advanced manufacturing arrangements, effects of variable conditions, rating to solve dynamic optimization problems, finite-time MEBM E4710x or y Morphogenesis: shape rolling and sliding materials. The theories of approaches. The Nyquist frequency and sample processes procedures. Solar energy concentration. Piping linear systems, steady state linear systems, multi and structure in biological materials boundary, elastohydrodynamic, hydrodynamic, rate selection. Classical and modern based digital 3 pts. Lect: 3. Professor Yao. Systems: series and parallel arrangements, fluid degree-of-freedom robotic systems. 3 pts. Lect: 3. Not offered in 2020–2021. hydrostatic, and solid-phase lubrication. Lubricant control laws. Digital system identification. Prerequisites: Introductory course on movers. Thermal response and management of Prerequisites: Courses in mechanics, flow and load-carrying capacity in bearings. Special MECE E4501y Geometrical modeling manufacturing processes, and heat transfer, photovoltaic energy conversion. Solar energy MECE E4602x Introduction to robotics thermodynamics, and ordinary differential applications such as geartrains, cam/tappets, and 3 pts. Lect: 3. Not offered in 2020–2021. knowledge of engineering materials, or storage. Solar cooling, solar thermal power and 3 pts. Lect: 3. Professor Ciocarlie. equations at the undergraduate level or instructor's micro- and nanoscale tribological interfaces. Prerequisite: COMS W1005. Relationship between instructor’s permission. Principles of nontraditional cogeneration. Applications to the design of solar Overview of robot applications and capabilities. permission. Introduction to how shape and 3D geometry and CAD/CAM; representations manufacturing, nontraditional transport and media. thermal engineering systems. MECE E4430x Automotive dynamics Linear algebra, kinematics, statics, and structure are generated in biological materials of solids; geometry as the basis of analysis, Emphasis on laser assisted materials processing, 3 pts. Lect: 3. Professor Browne. dynamics of robot manipulators. Survey of using engineering approach emphasizing design, and manufacturing; constructive solid laser material interactions with applications to Prerequisite: ENME 3105 or equivalent; sensor technology: force, proximity, vision, application of fundamental physical concepts to a geometry and the CSG tree; octree representation compliant manipulators. Motion planning and laser material removal, forming, and surface diverse set of problems. Mechanisms of pattern recommended: ENME 3106 or equivalent. Reviews and applications; surface representations and

ENGINEERING 2020–2021 ENGINEERING 2020–2021 200 formation, self-assembly, and self-organization MECE E4999x and y Fieldwork and colloid chemistry, or the equivalent, or the thermodynamics (e.g. MECE E4302), or introduction to classical and modern feedback research results in the field, participation in 201 in biological materials, including intracellular 1 pt. Professor Lipson. instructor’s permission. Surface energy and combustion (e.g. MECH E4320), or instructor's control that does not presume an undergraduate discussions, and course projects combining structures, cells, tissues, and developing embryos. Prerequisite: Instructor’s written permission. Only capillary phenomena. Wetting and spreading permission. Gaseous phenomena from a molecular background in control. Scalar and matrix simulation, processing of sensor data, planning Structure, mechanical properties, and dynamic for ME graduate students who need relevant off- of liquids, wetting line pinning and hysteresis, to macroscopic perspective. Quantum mechanics, differential equation models and solutions in terms for manipulation, design, and implementation on behavior of these materials. Discussion of campus work experience as part of their program dynamics of wetting. Surfactants. Bubbles: statistical thermodynamics, nonequilibrium of state transition matrices. Transfer functions real robot hands. experimental approaches and modeling. Course and transfer function matrices, block diagram of study as determined by the instructor. Written nucleation, stability, dynamics, microstreaming. statistical mechanics, reaction rate theories, master MECS E6616x or y Robot learning uses textbook materials as well as collection of manipulations, closed loop response. Proportional, application must be made prior to registration Jets and Drops: generation, dynamics, stability and equation, relaxation processes, kinetic theory, 3 pts. Lect: 3. Professor Ciocarlie. research papers. rate, and integral controllers, and compensators. outlining proposed study program. Final reports impact with surfaces. Measurement of transport equations of state, transport theories, and kinetic- Prerequisites: MECE E4602 or MECS E4603 required. May not be taken for pass/fail credit or phenomena involving interfaces. Interfacial transport transport equations. Applications to combustion, Design by root locus and frequency response. MEIE E4810y Introduction to human spaceflight or COMS W4733. Robots using machine Controllability and observability. Luenberger audited. International students must consult with phenomena involving thermal, chemical or electrical aerospace gas dynamics, and high-frequency learning to achieve high performance in 3 pts. Lect: 3. Professor Massimino. observers, pole placement, and linear-quadratic the International Students and Scholars Office. gradients. Applications in microfluidic systems. sound propagation. unscripted situations. Dimensionality reduction, Prerequisites: Department permission and knowledge cost controllers. of MATLAB or equivalent. Introduction to human MECE E6100x Advanced mechanics of fluids MECE E6137x or y Nanoscale actuation and MECE E6400y Advanced machine dynamics classification, and regression problems in spaceflight from a systems engineering perspective. 3 pts. Lect: 3. Professor Ateshian. sensing 3 pts. Lect: 3. Professor Chbat. EEME E6602y Modern control theory robotics. Deep Learning: Convolutional Neural Historical and current space programs and Prerequisites: MATH UN2030 and MECE E3100. 3 pts. Lect: 3. Professor Schuck. Prerequisite: MECE E3401. Review of classical 3 pts. Lect: 3. Not offered in 2020–2021. Networks for robot vision, Recurrent Neural spacecraft. Motivation, cost, and rationale for human Eulerian and Lagrangian descriptions of motion. Prerequisites: PHYS UN1402 or UN1602 or dynamics, including Lagrange’s equations. Analysis Prerequisite: EEME E6601 or E4601 or ELEN Networks, and sensorimotor robot control using space exploration. Overview of space environment Stress and strain rate tensors, vorticity, integral equivalent, or instructor's permission. Interaction of dynamic response of high-speed machine E6201, or instructor’s permission. Singular value neural networks. Model Predictive Control using decomposition. ARX model and state space needed to sustain human life and health, including and differential equations of mass, momentum, of light with nanoscale materials and structures elements and systems, including mass-spring learned dynamics models for legged robots model system identification. Recursive least physiological and psychological concerns in space and energy conservation. Potential flow. for purpose of inducing movement and detecting systems, cam-follower systems, and gearing; and manipulators. Reinforcement Learning in squares filters and Kalman filters. LQR, Hlinear robotics: model-based and model-free methods, habitat. Astronaut selection and training processes, small changes in strain, temperature, and shock isolation; introduction to gyrodynamics. spacewalking, robotics, mission operations, and future MECE E6102x or y Computational heat robust control, predictive control, adaptive control. deep reinforcement learning, sensorimotor chemistry within local environments. Methods for MECE E6422x–E6423y Introduction to the program directions. Systems integration for successful transfer and fluid flow Liapunov and Popov stability. Nonlinear adaptive control using reinforcement learning. concentrating and manipulating light at length theory of elasticity, I and II operation of a spacecraft. Highlights from current 3 pts. Lect: 3. Professor Demetriou. control, nonlinear robust control, sliding mode control. Prerequisites: MECE E3100 and E3311. scales below the diffraction limit. Plasmonics and 3 pts. Lect: 3. Professor Myers. MECE E6617y Advanced kinematics, events and space research, Space Shuttle, Hubble EEME E6610y Optimal control theory Mathematical description of pertinent physical metamaterials, as well as excitons, phonos, and Corequisite: APMA E4200. Analysis of stress dynamics and control in robotics Space Telescope, and International Space Station 3 pts. Lect: 3. Instructor to be announced. phenomena. Basics of finite-difference methods polaritons and their advantages for mechanical and and strain. Formulation of the problem of elastic 3 pts. Lect: 3. Professor Agrawal. (ISS). Includes a design project to assist International Prerequisite: EEME E6601 or E4601 or instructor’s of discretization, explicit and implicit schemes, chemical sensing, and controlling displacement equilibrium. Torsion and flexure of prismatic bars. Prerequisites: Course on linear and/or nonlinear Space Station astronauts. permission. Covers topics in calculus of variations, grid sizes, stability, and convergence. Solution of at nanometer length scales. Applications to Problems in stress concentration, rotating disks, control theory, Introduction to Robotics, or Pontryagin maximum principle, quadratic cost optimal MECE E4811x Aerospace human factors algebraic equations, relaxation. Heat conduction. nanophotonic devices and recently published shrink fits, and curved beams; pressure vessels, instructor's permission. Advanced topics in robotics control, predictive control, dynamic programming for engineering Incompressible fluid flow, stream function-vorticity progress in nanomechanics and related fields. contact and impact of elastic bodies, thermal using fundamentals of kinematics, dynamics, optimal control, Kalman filtering, numerical methods 3 pts. Lect: 2.5. Professor Massimino. formulation. Forced and natural convection. Use stresses, propagation of elastic waves. and control. Topics include: characterization of MECE E6200y Turbulence for solution. Some applications discussed include Prerequisite: Instructor's permission. Engineering of primitive variables, turbulence modeling, and orientation and angular velocity of rigid bodies, 3 pts. Lect: 3. Not offered in 2020–2021. MECE E6424x Vibrations in machines, I minimum energy subway operation (our solution fundamentals and experimental methods of human coordinate transformations. kinematic solutions of planar mechanisms, Prerequisite: MECE E6100. Introductory concepts 3 pts. Lect: 3. Instructor to be announced. saved 11% in tests on the Flushing Line, and the factors design and evaluation for spacecraft which dynamics of closed chains and free-floating and statistical description. Kinematics of random Prerequisite: MECE E3401. Review of vibration incorporate human-in-the-loop control. Develop MECE E6103x Compressible flow method was adopted by the transit authority, saving analysis of systems and mechanisms with one bodies, gravity balancing of mechanism, dynamics understanding of human factors specific to 3 pts. Lect: 3. Not offered in 2020–2021. velocity fields, dynamics of vorticity, and scalar many millions of dollars per year), minimum time degree of freedom. Natural frequencies. Forced and dependence of inertia redistribution, under- spacecraft design with human-in-the-loop control. Prerequisites: APMA E4200, MECE E3100 and quantities. Transport processes in a turbulent robot optimal control allowing one to run assembly vibrations. Effects of dry and viscous friction. actuation systems, feedback linearization of SISO Design of human factors experiments utilizing task E3301. Fundamental analysis of compressible medium. Turbulent shear flows: deterministic and lines faster for increased productivity. Energy methods of Rayleigh and Ritz. Suppression systems, feedback linearization of MIMO systems, analysis and user testing with quantitative evaluation flows and its applications for various sonic/ random structures. Experimental techniques, and elimination of vibration. Vibration isolation. MECE E6614x or y Advanced topics in design of under-actuated open-chain robots, metrics to develop a sate and high-performing supersonic elements including supersonic prediction methods, and simulation. Measuring instruments. Critical speeds in machinery. robotics and mechanism synthesis parallel-actuated robots. operational space system. Human-centered design, airfoils/projectiles, nozzles, and shock tubes. MEBM E6310x-E6311y Mixture theories for Synchronous whirl. Half-frequency whirl. Influence of 3 pts. Lect: 3. Professor Agrawal. functional allocation and automation, human Steady and unsteady shock/expansion waves, MECE E6620x or y Applied signal recognition biological tissues, I and II bearing characteristics on critical speeds. Effect of Prerequisites: APMA E2101, E3101, MECE E4602 sensory performance in the space environment, oblique shock waves. Shock reflections, methods and classification 3 pts. Lect: 3. Not offered in 2020–2021. gyroscopic moments. Systems with multiple degrees (or COMS W4733). Recommended: MECE E3401 task analysis, human factors experimental methods of characteristic. 3 pts. Lect: 3. Professor Beigi. Prerequisites: MECE E6422 and APMA E4200 or of freedom. Dynamic vibration absorbers. Self-tuning or instructor’s permission. Kinematic modeling and statistics, space vehicle displays and controls, Prerequisites: MATH UN2030, APMA E3101, MECE E6104x Case studies in computational equivalent. Development of governing equations absorbers of pendulum and roller types. Lagrangian methods for serial, parallel, redundant, wire- situation awareness, workload, usability, manual knowledge of a programming language, or fluid dynamics for mixtures with solid matrix, interstitial fluid, equations of motion as applied to vibrating systems. actuated robots and multifingered hands with piloting and handling qualities, human error analysis permission of instructor. Applied recognition and ion constituents. Formulation of constitutive General equations for transverse critical speeds of discussion of open research problems. Introduction and prevention, and anthropometrics. 3 pts. Lect: 3. Professor Bilson. and classification of signals using a selection models for biological tissues. Linear and nonlinear shafts. Surging of helical springs. to screw theory and line geometry tools for Prerequisites: APAM E4200 and MECE E6100. of tools borrowed from different disciplines. MECE E4990x or y Special topics in Corequisites: APAM E4300 and MECE E4400. models of fibrillar and viscoelastic porous matrices. kinematics. Applications of homotopy continuation MEEM E6432y Small-scale mechanical methods and symbolic-numerical methods for Applications include human biometrics, imaging, mechanical engineering Hands-on case studies in computational fluid Solutions to special problems, such as confined behavior direct kinematics of parallel robots and synthesis geophysics, machinery, electronics, networking, 3 pts. Lect: 3. Instructor to be announced. dynamics, including steady and transient flows, and unconfined compression, permeation, 3 pts. Lect: 3. Not offered in 2020–2021. languages, communications, and finance. Prerequisites: Permission of the instructor. Topics and indentation and contact, and swelling experiments. of mechanisms. Course uses textbook materials as heat and mass transfer, turbulence, compressible Prerequisites: ENME E3113 or equivalent; APMA Practical algorithms are covered in signal Instructors change from year to year. For advanced well as a collection of recent research papers. flow and multiphase flow. Identifying MECE E6313x Advanced heat transfer E4200 or equivalent. Mechanics of small-scale generation, modeling, feature extraction, metrics undergraduate students and graduate students in assumptions, computational domain selection, 3 pts. Lect: 3. Professor Narayanaswamy. materials and structures require nonlinear kinematics MECE E6615x or y Robotic manipulation: for comparison and classification, parameter engineering, physical sciences, and other fields. model creation and setup, boundary conditions, Prerequisites: MECE E3311. Corequisites: MECE and/or nonlinear stress vs. strain constitutive sensing, planning, design, and execution estimation, supervised, unsupervised and choice of convergence criteria, visualization and MECE E4998x and y M.S. projects in E6100. Application of analytical techniques to the relations to predict mechanical behavior. Topics 3 pts. Lect: 3. Professor Ciocarlie. hierarchical clustering and learning, optimization, interpretation of computed results. Taught in the solution of multidimensional steady and transient mechanical engineering include variational calculus, deformation and vibration Prerequisite: MECE E4602 or COMS W4733. scaling and alignment, signals as codes emitted Mechanical Engineering Computer Laboratory problems in heat conduction and convection. from natural sources, information, and extremely 1–3 pts. Members of the faculty. of beam, strings, plates, and membranes; fracture, Theory and mechanisms of robotic manipulation, with Computational Fluid Dynamics software. Lumped, integral, and differential formulations. large-scale search techniques. Prerequisite: Instructor's permission. Master's delamination, bulging, buckling of thin films, among from sensor data, reasoning, and planning to Topics include use of sources and sinks, laminar/ implementation and execution. Grasp quality level independent project involving theoretical, MECE E6105y Transport phenomena in the others. Thermodynamics of solids will be reviewed MECE E6700x Carbon nanotube science and turbulent forced convection, and natural convection measures and optimization; planning and computational, experimental, or engineering presence of interfaces to provide the basis for a detailed discussion of technology in internal and external geometries. execution for manipulation primitives; sensor design work. May be repeated, subject to Master's 3 pts. Lect: 3. Not offered in 2020–2021. nonlinear elastic behavior as well as the study of the 3 pts. Lect: 3. Professor Schuck. equilibrium and stability of surfaces. modalities: vision, touch, and proprioception; Program guidelines. Students must submit both Prerequisites: MECE E3301 Thermodynamics MECE E6320x or y Multiscale phenomena in Prerequisite: Knowledge of introductory solid simulation for manipulation planning; design a project outline prior to registration and a final and MECE E3311 Heat transfer; MECE E4100 gases EEME E6601x Introduction to control theory state physics (e.g., PHYS GU4018, APPH E6081, of robot manipulators. Grading based on a project write-up at the end of the semester. Mechanics of fluids, or equivalent or instructor’s 3 pts. Lect: 3. Not offered in 2020–2021. 3 pts. Lect: 3. Professor Longman. or MSAE E3103) or instructor’s permission. combination of class presentations of novel permission; CHEE E4252 Introduction to surface Prerequisites: Knowledge of advanced Prerequisite: MATH UN2030. A graduate-level Basic science of solid state systems. Crystal

ENGINEERING 2020–2021 ENGINEERING 2020–2021 202 structure, electronic and phonon band structures MECE E8100y Advanced topics in fluid MECE E9000x-E9001y and E9002s Graduate of nanotubes. Synthesis of nanotubes and other mechanics research and study nanomaterials. Experimental determination 3 pts. Lect: 3. Not offered in 2020–2021. 1–3 pts. Members of the faculty. of nanotube structures and techniques for Prerequisite: MECE E6100. May be taken more than Theoretical or experimental study or research in nanoscale imaging. Theory and measurement of once, since its content has minimal overlap between graduate areas in mechanical engineering and mechanical, thermal, and electronic properties of consecutive years. Selected topics from viscous engineering science. nanotubes and nanomaterials. Nanofabrication and flow, turbulence, compressible flow, rarefied gas nanoelectronic devices. Applications of nanotubes. dynamics, computational methods, and dynamical MECE E9500x and y Graduate seminar systems theory, non-Newtonian fluids, etc. 0 pts. Pass/fail only. Professor Schuck. MECE E6710y Nanofabrication laboratory All doctoral students are required to complete 3 pts. Lect: 3. Instructor to be announced. MECE E8501y Advanced continuum successfully four semesters of the mechanical Prerequisite: ELEN E6945 or instructor’s biomechanics engineering seminar MECE E9500. permission. Laboratory in techniques for 3 pts. Lect: 2. Professor Myers. MECE E9800x and y Doctoral research fabrication at the nanometer scale. Electron- Prerequisite: Instructor’s permission. The beam lithography. Plasma etching and 3D essentials of finite deformation theory of solids and instruction nanofabrication. Thin film deposition. Self- fluids needed to describe mechanical behavior of 3, 6, 9, or 12 pts. Members of the faculty. assembly and “bottom up” nanofabrication. biological tissue: kinematics of finite deformations, A candidate for the Eng.Sc.D. degree in Fabrication of and testing of complete balance laws, principle of material objectivity, mechanical engineering must register for 12 points nanodevices. A lab fee of $300 is required. theory of constitutive equations, concept of simple of doctoral research instruction. Registration in solids and simple fluids, approximate constitutive MECE E9800 may not be used to satisfy the MECE E6720x Nano/microscale thermal equations, some boundary-value problems. Topics minimum residence requirement for the degree. transport process include one- and two-point tensor components 3 pts. Lect: 3. Not offered in 2020–2021. MECE E9900x and y Doctoral dissertation with respect to generalized coordinates; finite Nano- and microscale origins of thermal 0 pts. Members of the faculty. deformation tensors, such as right and left Cauchy- transport phenomena by molecules, electrons, A candidate for the doctorate may be required Green tensors; rate of deformation tensors, such to register for this course every term after his/ Undergraduate Minors phonons, and photons. Quantum mechanics as Rivlin-Ericksen tensors; various forms of and statistical physics. Density of states. her coursework has been completed and until the objective time derivatives, such as corotational and Kinetic theory of gases. Boltzmann transport dissertation has been accepted. convected derivatives of tensors; viscometric flows equation (BTE), classical and quantum size of simple fluids; examples of rate and integral type effects. Landauer formalism for transport of constitutive equations. via nanostructures. Macroscopic constitutive equations from BTE. Application to electronics EEME E8601y Advanced topics in control theory cooling, thermoelectric and thermophotovoltaic 3 pts. Lect: 3. Not offered in 2020–2021. devices, and energy conversion. Prerequisites: EEME E6601 and E4601 or instructor’s permission. May be taken more than MECE E8020x or E8021y Master’s thesis once, since the content changes from year to year, 3–6 pts. Members of the faculty. electing different topics from control theory such Research in an area of mechanical engineering as learning and repetitive control, adaptive control, culminating in a verbal presentation and a written system identification, Kalman filtering, etc. thesis document approved by the thesis adviser. Must obtain permission from a thesis adviser to MECE E8990x and y Special topics in enroll. Recommended enrollment for two terms, mechanical engineering one of which can be the summer. A maximum 3 pts. Lect: 3. Instructor to be announced. of 6 points of master’s thesis may count toward Prerequisite: Instructor’s permission. May be taken an M.S. degree, and additional research points for credit more than once. The instructor from the cannot be counted. On completion of all master’s Mechanical Engineering Department and the topics thesis credits, the thesis adviser will assign a covered will vary from year to year. Intended for single grade. Students must use a department- students with graduate standing in Mechanical recommended format for thesis writing. Engineering and other engineering and applied sciences.

ENGINEERING 2020–2021 204 MINOR IN ART HISTORY 5. COMS W3261: Comp science theory (3) 205 2. ENME E3105: Mechanics (4) UNDERGRADUATE MINORS 6. CSEE W3827: Fund of computer systems (3) 1–7. Seven courses in art history, covering 3. ENME E3113: Mechanics of solids (3) or a 4000-level COMS technical elective four of the following areas: (a) ancient Mediterranean, (b) medieval Europe, 4–6. Electives: Three of the following courses: 7. APMA E2101 (or E3101): Intro to applied CIEN E3000: The art of structural design (3) (c) Renaissance and baroque, (d) 18th, mathematics (Applied math I: linear algebra) (3) ENME E3161: Fluid mechanics (4) or MATH UN2010 (or E2020): Linear 19th, and 20th century, and (e) non- ENME E3114: Exp mechanics of materials (4) algebra (3) Western ENME E3332: A first course in finite elements (3) or COMS W3251: Computational linear MECE E3414: Adv strength of materials (3) algebra (4) MINOR IN BIOMEDICAL CIEN E3125: Structural design (3) or STAT GU4001( or SIEO W3600): Intro to CIEN E4241: Geotech eng fundamentals (3) probability and statistics (3) ENGINEERING CIEE E3250: Hydrosystems engineering (3) The Biomedical Engineering program CIEE E4163: Environ eng: wastewater (3) offers a minor that consists of the CIEN E3129: Project mgmt for construction (3) MINOR IN DANCE following six courses. Participation in the CIEN E4131: Prin of construction tech (3) The dance minor consists of five minor is subject to the approval of the 3-point courses. Please note that no major program adviser. performance/choreography courses MINOR IN COMPUTER SCIENCE below count toward the nontech STAT, IEOR, or COMS that is approved by the Students who pass the Computer ndergraduate minors are Associate Dean of Undergraduate requirement for Engineering students. designed to allow engineering Student Affairs. applied mathematics program adviser. 1. BIOL UN2005: Introduction to biology, I (3) Science Advanced Placement Exam A 1–2. History/criticism: Two of the following: 2. BIOL UN2006: Introduction to biology, II (3) with a 4 or 5 will receive 3 points and and applied science students DNCE BC2565: World dance history (3) U exemption from COMS W1004. Taking to study, to a limited extent, a discipline MINOR IN APPLIED PHYSICS MINOR IN ANTHROPOLOGY 3. BMEN E3010: Biomedical engineering, I (3) DNCE BC2570: Dance in New York City (3) other than their major. Besides Prospective students should consult the COMS W1007 is recommended but not DNCE BC2575: Choreography for the 4. BMEN E3020: Biomedical engineering, II (3) engineering minors offered by Columbia 1. ANTH UN1002: The interpretation of culture (3) first- and second-year requirements for required for those students exempt from American musical (3) Engineering departments, liberal arts or ANTH UN1008: The rise of civilization (3) applied physics majors to ensure that 5. BMEN E4001: Quantitative physiology, I (3) COMS W1004. Participation in the minor DNCE BC3000: From the page to the is subject to the approval of the major dance stage (3) minors are also available. Note: UN1002 serves as a preview to prerequisites for the applied physics 6. BMEN E4002: Quantitative physiology, II (3) DNCE BC3001: Western theatrical dance A minor requires at least 15 points of sociocultural anthropology, while UN1008 minor are satisfied in the first two years. program adviser. For further information, from the Renaissance to the 1960s (3) serves as a preview to archaeology. Coursework counting toward the please see the QuickGuide at cs.columbia. credit, and no more than one course can DNCE BC3200: Dance in film (3) MINOR IN CHEMICAL edu/education/undergrad/seasguide. be taken outside of Columbia or met 2–5. Any four courses in the Anthropology applied physics minor may not include DNCE BC3567: Dance of India (3) through AP or IB credit. This includes department, in ethnomusicology, or taught advanced placement credits. ENGINEERING Beginning with the class of 2023, the DNCE BC3570: Latin American and CS core requirements will change as courses taken through study abroad. by an Anthropology instructor, regardless of 1. APPH E4901: Problems in applied physics (1) Of the six courses required, at least Caribbean dance (3) In Engineering departments with more department. No distribution requirement. three must have the CHEN, CHEE, or noted below. The following are required DNCE BC3576: Dance criticism (3) 2. APPH E3200: Mechanics (3) than one major program, a minor in the CHAP designator: courses toward the CS Core for the DNCE BC3577: Performing the political (3) second program may be permitted, if 3. APPH E3100: Intro to quantum mechanics (3) class of 2023 and beyond: DNCE BC3578: Traditions of African- MINOR IN APPLIED 1. CHEN E2100: Intro to chemical engineering (3) American dance (3) approved by the department. 1. COMS W1004: Intro to computer science and MATHEMATICS 4. APPH E3300: Applied electromagnetism (3) 2. CHEE E3010: Prin of chemical engineering No substitutions or changes of any programming in Java (3) 3–4. Performance/choreography: Two of the Prospective students should consult 5. MSAE E3111: Thermodynamics, kinetic theory, thermodynamics (3) kind from the approved minors are or COMS W1007: Honors intro to comp sci (3) following: ​ the first- and second-year requirements and statistical mechanics (3) or MSAE E3111: Thermodynamics, kinetic DNCE BC2563: Dance composition: form (3) permitted (see lists below). No appeal theory, and statistical mechanics (3) 2. COMS W3134: Data structures in Java (3) for applied mathematics majors to 6. Two of the following courses DNCE BC2564: Dance composition: content (3) for changes will be granted. Please note or MECE E3301: Thermodynamics (3) or COMS W3137: Honors data structures and ensure that prerequisites for the applied APPH E4010: Intro to nuclear science (3) DNCE BC2567: Music for dance (3) that the same courses may not be used or BMEN E4210: Thermodynamics of biological algorithms (4) mathematics minor are satisfied in the APPH E4100: Quantum physics of matter (3) DNCE BC2580: Tap as an American art to satisfy the requirements of more than systems (3) form (3) first two years. APPH E4110: Modern optics (3) 3. COMS W3157: Advanced programming (4) one minor. No courses taken for pass/fail APPH E4112: Laser physics (3) 3. CHEN E3110: Transport phenomena, I (3) DNCE BC3565: Composition: collaboration Coursework counting toward the 4. COMS W3203: Discrete mathematics (4) may be counted for a minor. Minimum APPH E4300: Applied electrodynamics (3) or EAEE E4900: Applied transport and and the creative process (3) applied mathematics minor may not GPA for the minor is 2.0. Departments APPH E4301: Intro to plasma physics (3) chemical rate phenomena (3) 5. COMS W3251: Computational linear algebra (4) DNCE BC3601-3604: Rehearsal and include advanced placement credits. or MECE E3100: Intro to mech of fluids (3) performance in dance (1–3) outside the Engineering School have no 6. COMS W3261: Comp science theory (3) Any substitutions for the courses listed or ENME E3161: Fluid mechanics (4) responsibility for nonengineering minors 5. One elective below require the approval of the applied MINOR IN ARCHITECTURE or BMEN E3220: Fluid biomechanics (4) 7. CSEE W3827: Fund of computer systems (3) offered by Engineering. mathematics program adviser. or a 4000-level COMS technical elective For a student to receive credit for 1. Studio: One of the following courses 4. CHEN E4230: Reaction kinetics and MINOR IN EARTH AND ARCH UN1020: Intro to architectural design and reactor design (3) a course taken while studying abroad, 1. APMA E3101: Linear algebra (3) ENVIRONMENTAL visual culture (3) The following are required courses the department offering the minor must or MATH UN2010: Linear algebra (3) 5–6. Two of the following courses: ARCH UN3101: Abstraction (4) towards the CS Core for the class of ENGINEERING approve the course in writing, ahead of 2. APMA E3102: Partial differential equations (3) Any 3000-level or higher CHEN or cross-listed ARCH UN3103: Perception (4) 2022 and earlier. 1–3. Three of the following courses: or MATH UN3028: Partial differential equations (CHAP, BMCH, CHEE, CHBM, CHOR, MECH) the student’s study abroad. EAEE E3103: Energy, minerals, and mat syst (3) (3) 2–4. History/theory courses (see Note below) course 1. COMS W1004: Intro to computer science and Students must expect a course load CIEE E3255: Environmental control and programming in Java (3) that is heavier than usual. In addition, 3–5. Three of the following courses: 5. Elective: must be either an approved second pollution reduction systems (3) or COMS W1007: Honors intro to comp sci (3) unforeseen course scheduling changes, APMA E4300: Intro to numerical methods (3) design studio or an additional history/theory MINOR IN CIVIL EAEE E4001: Industrial ecology of Earth res (3) APMA E4204: Func of complex variable (3) course 2. COMS W3134: Data structures in Java (3) EAEE E4003: Intro to aquatic chemistry (3) problems, and conflicts may occur. The ENGINEERING APMA E4101: Intro to dynamical systems (3) or COMS W3137: Honors data structures and EAEE E4004: Physical processing and recovery School cannot guarantee a satisfactory Note: A list of the approved history/theory MATH UN2500: Analysis and optimization (3) 1. CIEN E3121: Structural analysis (3) algorithms (4) of solids (3) completion of the minor. courses is available at the departmental STAT GU4001: Intro to probability and statistics (3) or ENME E3161: Fluid mechanics (4) EAEE E4006: Field methods for environ eng (3) 3. COMS W3157: Advanced programming (4) Students interested in establishing STAT GR5204: Statistical inference (3) office each semester. or MECE E3100: Intro to mech of fluids (3) EAEE E4009: GIS for resource, environment, a new minor should consult with the or any other course designated APMA, MATH, 4. COMS W3203: Discrete mathematics (4) and infrastructure management (3)

ENGINEERING 2020–2021 ENGINEERING 2020–2021 206 EAEE E4150: Air pollution prevention and 5–6. Electives: Two of the following courses: recommended that students take MINOR IN ENGLISH AND level German or CompLit-German courses excluding MSAE E4301 (Materials science 207 control (3) ECON UN2105: American economy (3) taught in German or English laboratory). UN3412 in the semester following the COMPARATIVE LITERATURE EAEE E4160: Solids and hazardous waste ECON UN2257: Global economy (3) statistics course. management (3) ECON UN3025: Financial economics (3) 1– 5. Any five courses in the English • Some courses done as part of the MINOR IN GREEK OR LATIN EAEE E4200: Prod of inorganic materials (3) ECON UN3265: Econ of money and economics minor may count toward Department with no distribution MINOR IN MECHANICAL EAEE E4257: Environ data analysis and banking (3) fulfilling the School’s nontechnical requirement. No speech courses, only one 1–4 . A minimum of 13 points in the chosen ENGINEERING modeling (3) ECON GU4020: Econ of uncertainty and requirements. However, other courses, writing course as above and excluding language at the 1200 level or higher 1–4. Four of the following courses: EAEE E4361: Econ of Earth res industries (3) info (3) such as UN3412: Intro to econometrics, ENGL CC1010, may be taken; total 15 5. 3 points in ancient history of the MECE E3100: Intro to mechanics of fluids (3) EACH E4560: Particle technology (3) ECON GU4211: Advanced microeconomics (3) may not be applied toward satisfaction points. ECON GU4213: Advanced macroeconomics (3) appropriate civilization or ENME E3161: Fluid mechanics (4) 4–6. Three of the following courses: of the nontechnical course requirements. ECON GU4228: Urban economics (3) or CHEN E3110: Transport phenomena, I (3) CHEE E3010: Prin of chemical engineering To determine which economic class ECON GU4230: Economics of NYC (3) MINOR IN ENTREPRENEURSHIP or EAEE E3200: App transport and thermodynamics (3) can count toward the nontech elective MINOR IN HISPANIC STUDIES ECON GU4235: Historical foundations of AND INNOVATION chemical rate phenomena (3) CHEE E3110: Transport phenomena, I (3) requirement, please consult the nontech modern economics (3) Minimum: 15 points 1. SPAN UN3300: Adv language through content (3) ENME E3105: Mechanics (4) CIEN E3141: Soil mechanics (3) elective section of this bulletin for further ECON GU4251: Industrial organization (3) ENME E3106: Dynamics and vibrations (3) CIEE E3250: Hydrosystems engineering (3) details. 1–2. Required courses: 2. SPAN UN3330: Intro to the study of Hispanic ECON GU4260: Market design (3) MECE E3301: Thermodynamics (3) ECIA W4100: Mgmt and dev of water systems (3) • Students with AP credit for economics IEOR E2261: Accounting and finance (3) cultures (3) ECON GU4280: Corporate finance (3) or CHEE E3010: Principles of chemical CIEE E4163: Environ eng: wastewater (3) and an exemption for UN1105 may use and IEOR E4998: Managing technological ECON GU4301: Economic growth and 3–4. SPAN UN3349 and UN3350: Hispanic engineering thermodynamics (3) EAEE E4190: Photovoltaic systems eng (3) the credit toward the minor. innovation and entrepreneurship (3) development (3) cultures, I and II (3, 3) or MSAE E3111: Thermodynamics, kinetic MECE E4211: Energy: sources and conv (3) • Transfer or study abroad credits may not ECON GU4321: Economic development (3) 3–5. Electives: Three of the following courses: theory, and statistical mechanics (3) CIEN E4250: Waste contain design and prac (3) be applied to fulfill the requirements of 5. One additional 3000-level elective course ECON GU4370: Political economy (3) BIOT GU4180: Entrepreneurship in biotech (3) ENME E3113: Mechanics of solids (3) CHEE E4252: Intro to surface and colloid the economics minor. in the Department of Latin American and ECON GU4400: Labor economics (3) BUSI W3021: Marketing management (3) MECE E3408: Comp graphics and design (3) chem (3) Iberian Cultures ECON GU4412: Advanced econometrics (3) CHEN E4020: Protection of industrial and MECE E3311: Heat transfer (3) CIEE E4252: Environmental engineering (3) ECON GU4415: Game theory (3) MINOR IN ELECTRICAL intellectual property (3) Note: Please see the director of MECE E3610: Materials and processes in CIEE E4257: Groundwater contaminant ECON GU4438: Economics of race in the CIEN E4136: Global entrepreneurship in civil undergraduate studies in the Department manufacturing (3) transport and remediation (3) ENGINEERING U.S. (3) engineering (3) of Latin American and Iberian Cultures for EEME E3601: Classical control systems (3) CHEN E4410: Environmental control 1. ELEN E1201: Intro to electrical eng (3.5) ECON GU4465: Public economics (3) COMS W4444: Program and problem solving (3) more information and to declare the minor. technology (3) (May be replaced by a similar course or roughly 5–6. Electives: Two additional mechanical ECON GU4480: Gender and applied COMS W4460: Principles of innovation in equivalent experience) engineering courses from either the above economics (3) biotechnology (3) MINOR IN HISTORY list or the following (not all courses in this MINOR IN EAST ASIAN ECON GU4500: International trade (3) 2. ELEN E3201: Circuit analysis (3.5) ECON GU4280: Corporate finance (3) list are given every year): ECON GU4505: Int’l monetary theory and IEOR E4003: Corporate finance for engineers (3) 1–5. Minimum 5 courses in the History STUDIES 3. CSEE W3827: Fund of computer systems (3) MECE E3401: Mechanics of machines (3) 1–5. Any two of the survey courses on policy (3) IEOR E4510: Project management (3) Department with no distribution or seminar MECE E3450: Computer-aided design (3) Chinese, Japanese, Korean, or ECON GU4615: Law and economics (3) 4. ELEN E3081 and ELEN E3082: IEOR E4550: Entrepreneurial business requirements. Transfer or study-abroad Any 3-credit 4000-level courses listed in the Tibetan civilization (ASCE UN1359, ECON GU4625: Economics of the Electrical engineering labs (2) creation for engineers (3) credits may not be applied. Mechanical Engineering Bulletin can also UN1361, UN1363, UN1365), plus three environment (3) IEOR E4560: Lean launchpad (3) 5. ELEN E3801: Signals and systems (3.5) be used to fulfill these additional course elective courses dealing with East ECON GU4700: Financial crises (3) (by application only with adviser approval) MINOR IN INDUSTRIAL requirements. Asia. The elective courses may be ECON GU4750: Globalization and its risks (3) 6. ELEN E3106: Solid-state dev and mat (3.5) ENGINEERING taken in departments outside of East ECON GU4850: Cognitive mechanisms and or ELEN E3401: Electromagnetics (4) Asian Languages and Cultures. The economic behavior (4) MINOR IN FRENCH 1. IEOR E3658: Probability for engineers (4) MINOR IN MIDDLE EASTERN, minor does not include a language Note: Not available to computer 1–2. FREN UN3333: Intro to literary study I (3) or STAT GU4001: Intro to probability and SOUTH ASIAN, AND AFRICAN requirement. However, one semester of engineering majors statistics (3) an East Asian language class may be Note: Electives may be taken only after and UN3334: Intro to literary study II (3) STUDIES the completion of both UN3211 and used to fulfill one of the three electives, 3–5. Three additional courses in French 2. IEOR E3608: Foundations of optimization (3) UN3213, with the exception of UN2257 MINOR IN ENGINEERING 1–5. Five courses, to be chosen with the as long as at least two semesters of that beyond satisfaction of the language 3. IEOR E3402: Production inventory planning and UN2105, which may be taken MECHANICS approval of the MESAAS Director of language have been taken. Placement requirement and control (4) after completion of UN1105. Some of Undergraduate Studies; no elementary or exams may not be used in place of these 1. ENME E3105: Mechanics (4) courses. the elective courses listed above have 4. IEOR E4003: Corporate finance for engineers (3) intermediate language courses may be additional prerequisites. Courses may 2. ENME E3113: Mechanics of solids (3) MINOR IN FRENCH AND 5–6. Electives: Two IEOR courses of interest counted. be taken only after the completion of all 3. ENME E3161: Fluid mechanics (4) FRANCOPHONE STUDIES and approved by a faculty adviser1 MINOR IN ECONOMICS prerequisites. Please see the Columbia Required: 15 points beyond second-year French or MECE E3100: Intro to mech of fluids (3) College bulletin for course descriptions and Note: In addition to the required courses, MINOR IN MUSIC 1. ECON UN1105: Principles of economics (4) 1–2. FREN UN3420 and UN3421: Intro to French complete lists of prerequisites. 4–6. Electives: Three of the following: students majoring in operations research and francophone studies, I and II (3, 3) 1. MUSI UN2318-2319: Music theory, I and II (3, 3) 2. ECON UN3211: Intermediate microeconomics ENME E3106: Dynamics and vibrations (3) and its concentrations (EMS or FE) (4) 7. Statistics: One of the following three ENME E3114: Exp mechanics of materials (4) 3–5. Three additional courses in French minoring in industrial engineering must take 2. MUSI UN1312-1313: Intro ear training (1) 3. ECON UN3213: Intermediate macroeconomics probability and statistics options (course or MECE E3414: Adv strength of materials (3) beyond satisfaction of the language three industrial engineering courses that 3. MUSI UN2314: Ear training, I (1) (4) or sequence): CIEN E3121: Structural analysis (3) requirement are not used to satisfy the requirements of a. SIEO W3600 (or STAT GU4001): Intro to ENME E4202: Advanced mechanics (3) their major. 4. One of the following courses: 4. ECON UN3412: Introduction to probability and statistics ENME E4113: Advanced mechanics of solids (3) MUSI UN3128: History of Western music, I (3) MINOR IN GERMAN 1 econometrics (4) b. IEOR E3658: Probability and ENME E4114: Mech of fracture and fatigue (3) Electives should be 3000-level or higher. MUSI UN3129: History of Western music, II (3) Required: 15 points beyond second-year German Note: UN1105 is a prerequisite for UN3211, E4307: Applied statistical models ENME E4214: Theory of plates and shells (3) 5–6. Any two electives at the 3000 or 4000 UN3213, and UN3412. Students must c. STAT UN4203 (or GR5203): Intro to ENME E4215: Theory of vibrations (3) 1. GERM UN3001 or 3002: Adv German, I or II (3) MINOR IN MATERIALS SCIENCE level. See also the Engineering-approved probability and statistics and STAT UN4204 MECE E3301: Thermodynamics (3) have completed Calculus I before taking 2. GERM UN3333: Intro to German literature (3) AND ENGINEERING nontechnical electives in music (page 10). UN3213, Calculus III before taking UN3211, (or GR5204): Statistical inference 3. One of the period survey courses in 1–5. Any five MSAE E3000 or MSAE E4000- Notes: and one of the introductory statistics Notes: German literature and culture, GERM level courses, excluding MSAE E3900 • Students must successfully place out of courses (see list) before taking UN3412. • The statistics course must be finished UN3442, UN3443, UN3444, UN3445 (Undergraduate research), and excluding MUSI UN1002: Fundamentals of music before taking UN3412, and it is MSAE E3156, E3157 (Design project), and (3.0 points). 4–5. Two courses taken from any 3000/4000-

ENGINEERING 2020–2021 ENGINEERING 2020–2021 208 • Steps 4 and 5 must be completed I. PERCEPTION AND COGNITION EAEE E2100: Better planet by design (3) to fulfill the nontechnical elective Courses numbered in the 2200s, 3200s, or CIEE E3250: Hydrosystems engineering (3) requirement for graduation. 4200s. CIEE E3260: Eng for developing comm (3) • Students are strongly encouraged to EAEE E3901: Environmental microbiology (3) II. PSYCHOBIOLOGY AND NEUROSCIENCE take HUMA UN1123: Masterpieces of EAEE E4001: Industrial ecology (3) PSYC UN1010: Mind, brain, and behavior (3) Western music (3.0 points) from the list ECIA W4100: Mgmt and dev of water systems (3) Courses numbered in the 2400s, 3400s, or APPH E4130: Physics of solar energy (3) of nontechnical electives. 4400s EAEE E4190: Photovoltaic systems eng and III. SOCIAL, PERSONALITY, AND ABNORMAL sustainability (3) MINOR IN OPERATIONS Courses numbered in the 2600s, 3600s, or MECE E4211: Energy sources and conversion (3) RESEARCH 4600s MECE E4312: Solar thermal engineering (3) 1. IEOR E3658: Probability for engineers (4) EAEE E4257: Environmental data analysis (3) MECE E4314: Dynamics of green buildings (3) or STAT GU4001: Intro to probability and MINOR IN RELIGION statistics (3) EESC GU4404: Regional climate and 1–5. Five courses (total 15 points), one of climate impacts (3) 2. IEOR E3106: Stochastic systems and which must be at the 2000 level 5. One of the following courses: Interdisciplinary Courses and applications (3) ECON UN2257: Global economy (3) 3. IEOR E3608: Foundations of optimization (4) MINOR IN SOCIOLOGY PLAN A4151: Found of urban economic 4. IEOR E3404: Simulation modeling and analysis analysis (3) 1. SOCI UN1000: The social world (3) (4) PLAN A4304: Intro to housing (3) Professional Development and 2. SOCI UN3000: Social theory (3) ECON UN4321: Economic development (3) 5–6. Electives: Two IEOR courses (6 pts) of ECON GU4527: Econ org and develop of interest and approved by a faculty adviser.1 3–5. Any two 2000-, 3000-, or 4000-level China (3) IEOR E3402: Production-inventory planning courses offered by the Department of PLAN A4579: Intro to environmental Leadership Program and control (3) is strongly recommended. Sociology; total 6 points planning (3) ECON GU4625: Economics of the Note: In addition to the required courses, environment (3) students majoring in industrial engineering MINOR IN STATISTICS must take three operations research 1. STAT UN1101: Intro to statistics 6. One of the following courses: courses that are not used to satisfy the (w/o calculus) (3) POLS UN3212: Environmental politics (3) requirements of their major. POLS UN3213: American urban politics (3) 2. STAT UN2102: App statistical computing (3) SOCI UN3235: Social movements (3) 1 Electives should be 3000-level or higher. 3. STAT UN2103: App linear regression SOCI UN3324: Global urbanism (3) analysis (3) MINOR IN PHILOSOPHY Note: If courses in Group 5 or 6 are not 4. STAT UN2104: App categorical data available, requesting approval for a similar 1–5. Any five courses in the Philosophy analysis (3) course from the groups "Economics" Department with no distribution 5. STAT UN3105: Appl. statistical methods (3) or "Law, Policy and Human Rights," requirement; total 15 points. See also respectively from the Columbia College the list of exceptions under Elective 6. STAT UN3106: Applied data mining (3) Sustainable Development course list Nontechnical Courses. is possible (bulletin.columbia.edu/ Notes: columbia-college/departments-instruction/ Note: Please be aware that some • The curriculum is designed for students sustainable-development/#coursestext) philosophy courses may not count as seeking practical training in applied nontechnical electives. statistics; students seeking a foundation for advanced work in probability and MINOR IN POLITICAL SCIENCE statistics should consider substituting UN3203, UN3204, UN3205, and 1–2. Two of the following courses: GR5207. POLS UN1201: Intro to American govt and • Students may, with permission of the politics (3) Director of Undergraduate Studies POLS UN1501: Intro to comparative politics (3) in Statistics, substitute for courses. POLS UN1601: International politics (3) Students may count up to two courses 3–5. Any three courses in the Political Science toward both the Statistics minor and Department with no distribution requirement; another Engineering major. total 9 points MINOR IN SUSTAINABLE MINOR IN PSYCHOLOGY ENGINEERING Minimum: 15 points Total of six courses from the following lists required with no substitutions 1. PSYC UN1001: The science of psychology (3) allowed: 2–5. Any four courses from, at a minimum, two 1–4. Four of the following courses: of the three groups below: EAEE E2002: Alternative energy sources (3)

ENGINEERING 2020–2021 210 INTERDISCIPLINARY ENGINEERING COURSES PROFESSIONAL DEVELOPMENT AND LEADERSHIP 211

f the following courses, some communications, is presented chronologically. ENGI E8000x, y, and s Doctoral fieldwork may be requirements for degree The social needs that elicited new technologies 1 pts. Professor Kachani and the consequences of their adoption are Fieldwork is integral to the academic preparation programs, and others may be O examined. Throughout the course, relevant and professional development of doctoral taken as electives. See your departmental scientific and engineering principles are explained students. This course provides the academic he Professional Development PROFESSIONAL DEVELOPMENT Columbia and doctoral studies, including teaching program of study or consult with an as needed. These include, among others, the framework for fieldwork experience required and Leadership (PDL) program and presentation skills (i.e., Microteaching, how to adviser for more information. concept and effective use of spectrum, multiplexing for the student’s program of study. Fieldwork AND LEADERSHIP CORE grade, hold office hours, conduct recitations, etc.); to improve capacity, digital coding, and networking documentation and faculty adviser approval is educates students to maximize FACULTY ENGI E1102x and y The art of engineering T cultivating relationships with mentors, faculty, and principles. There are no prerequisites, and no prior required prior to registration. A final written report performance and achieve their full Chuck Garcia: Communication 4 pts. Lect: 4. Professor Vallancourt. colleagues; inclusivity; managing your budget; well- scientific or engineering knowledge is required. must be submitted. This course will count toward potential to become engineering Helio Fred Garcia: Ethics and Integrity Core requirement for all entering SEAS students. A ness; research and academic integrity and ethics. Engineering students may not count this course as the degree program and cannot be taken for leaders. Core sessions focus on Holly Helstrom: Social Media bridge between the science-oriented, high school E6002x and y Professional development and a technical elective. pass/fail credit or audited. With approval from the development of skills and perspectives Tamar Hofer: Social Media way of thinking and the engineering point of view. leadership for second year Ph.D.'s department chair or the doctoral program director, Sophia Hyoseon Lee: Communication Fundamental concepts of math and science are ENGI W4100y Research to revenue needed to compete and succeed in a doctoral students can register for this course at 0 pts. The PDL Instructional Team. reviewed and reframed in an engineering context, fast-changing technical climate. Topics Paul Logston: Programming 3 pts. Lect: 3. Professors Sia and Toubia. most twice. In rare situations, exceptions may be For second year doctoral students, emphasizing with numerous examples of each concept drawn Jenny Mak: Resume An interschool course with Columbia Business granted by the Dean's Office to register for the include professional portfolio (resume, the skills needed for continued success in the from all disciplines of engineering represented at Raleigh Mayer: Executive Presence School that trains engineering and business course more than twice (e.g., doctoral students cover letter, business writing, social doctoral program, including presentation and Columbia. Nontechnical issues of importance in Elizabeth Strauss: Business Writing students to identify and pursue innovation funded by industrial grants who wish to perform media presence), communication skills, communication skills; academic writing skills; professional engineering practice such as ethics, opportunities that rely on intellectual property doctoral fieldwork for their corporate sponsor). leadership, ethics, life management academic conference preparation; resiliency and engineering project management, and societal coming out of academic research. Idea generation, The doctoral student must be registered for this (stress, sleep, and time management) project management skills. impact are addressed. Lab fee: $350. market research, product development, and PROFESSIONAL DEVELOPMENT course during the same term as the fieldwork and more. Elective sessions include E6003x and y Professional development and financing. Teams develop and present business experience. AND LEADERSHIP COURSES ORCA E2500x or y Foundations of data science effective presentations, Cloudproc/ leadership for third year Ph.D.'s 3 pts. Lect: 3. Professor Zhang. model for a technological invention. This course M.S. Course COSA E9800x and y Data Science Doctoral Pyspark, interview preparation. 0 pts. The PDL Instructional Team. Prerequisites: Calculus I and II, some familiarity has limited enrollment by application and is open Seminar ENGI E4000x and y Professional development For third year doctoral students to facilitate with programming. Designed to provide an to advanced undergraduate students and graduate M.S. students must complete the 1 pts. Professor Blei. and leadership for engineers and applied career exploration including teaching, presenta- introduction to data science for sophomore SEAS students. Consult with department for questions on professional development and leadership Prerequisite and Corequisite: Faculty approval. scientists tion and communication skills; public speaking majors. Combines three perspectives: inferential fulfillment of technical elective requirement. course, ENGI E4000, as a graduation Course required for all Data Science Doctoral 0 pts. The PDL Instructional Team. and facilitation; CV and resume writing; and thinking, computational thinking, and real-world requirement. Ph.D. candidates will be ORCA E4500x or y Foundations of data science students. Others by faculty approval. The Data The PDL course aims to enhance and expand Getting Things Done. applications. Given data arising from some real- 3 pts. Lect: 3. Professor Zhang. Science Doctoral Seminar is a 1-credit course that enrolled in ENGI E6001–6004 and Columbia Engineering graduate students' interper- world phenomenon, how does one analyze that E6004x and y Professional development and Prerequisites: Calculus I and II, some familiarity meets weekly. The purpose is to expose the doctoral should consult their program for specific sonal, professional, and leadership skills, through data so as to understand that phenomenon? leadership for fourth year Ph.D.'s with programming. Introduction to data science. students to a breadth of ideas in data science PDL requirements. Undergraduate six core sessions, covering (1) in-person com- Teaches critical concepts and skills in computer 0 pts. The PDL Instructional Team. Perspectives in inferential thinking, computational across disciplinary domains. The syllabus combines students are encouraged to participate munication skills; (2) resume; (3) business writing; programming, statistical inference and machine For fourth year doctoral students supporting job thinking, real-world applications. Given data arising guest lectures from academic data scientists in the in the professional development and (4) social media and the job search; (5) executive learning, in conjunction with hands-on analysis search and degree completion, including search- from some real-world phenomenon, analyze data greater NYC area and faculty at Columbia, along presence; and (6) academic and professional of real-world datasets such as economic data, leadership program. ing for job opportunities (Academia, Industry); to understand phenomenon. Critical concepts with a selection of related readings chosen by the ethics and integrity. ENGI E4000 also requires (4) document collections, geographical data, and interview preparation; creating an academic and skills in computer programming, statistical guest lecturers. As part of this seminar, students will elective sessions to further students development social networks. At least one project will address a portfolio; conducting a job talk; negotiation and inference and machine learning, hands-on analysis be expected to engage in active open discussion PROFESSIONAL DEVELOPMENT based on their personal interests. Students build problem relevant to New York City. mediation skills. of real-world datasets, economic data, document about the topics and readings covered in class, as AND LEADERSHIP STAFF upon and enhance interpersonal and intrapersonal EEHS E3900y History of telecommunications: collections, geographical data, social networks. well as discuss how such topics apply to their own Gabriella Lilienthal, Program Manager skills to further distinguish themselves in class- Note: for M.S. students only. from the telegraph to the internet respective research areas. Jenny Mak, Executive Director room and career. This course is offered at the Pass/D/Fail grading option. 3 pts. Lect: 3. ENGI E4990x and y Advanced master's Elizabeth Strauss, Associate Director Historical development of telecommunications from research For information on courses in other [email protected] Ph.D. Courses the telegraphy of the mid-1800s to the Internet 1–6 pts. divisions of the University, please consult pdl.engineering.columbia.edu at present. Included are the technologies of ENGI E6001x and y Professional development Advanced master's research for students the bulletins of Columbia College and the telephony, radio, and computer communications. and leadership for first year Ph.D.'s within departments that offer master's research Graduate School of Arts and Sciences. The coverage includes both the technologies specialization. Students may enroll for 1–6 credits 0 pts. The PDL Instructional Team. themselves and the historical events that shaped, per semester, for a maximum of 12 credits required For first year doctoral students, emphasizing the and in turn were shaped by, the technologies. skills needed for success in orienting them to for the master's program. Note: open to students in The historical development, both the general master's research only. context and the particular events concerning

ENGINEERING 2020–2021 ENGINEERING 2020–2021 212 GRADUATE CAREER ENGLISH COMMUNICATION ENGI E7102x and y Academic writing 0 pts. The PDL Instructional Team. Not offered PLACEMENT COURSES in 2020–2021. While enrolled in a graduate program at M.S. Courses Intensive analysis of principles of excellent writing Columbia Engineering you will also be coached for PhD students and scientists preparing a range by your dedicated Career Placement Officer. ENGI E5000x, y, and s Workplace of texts including research papers, conference communication in English We look forward to working with you on your posters, technical reports, research statements, E5001x, y, and s Professional presentation professional development and job search grant proposals, and other relevant texts. E5002x, y, and s Professional communication throughout your time at Columbia. in English ENGI E7103x and y Pronunciation of E5003x, y, and s Academic writing American English Gerald Contiangco E5009x, y, and s English communication 0 pts. The PDL Instructional Team. Not offered Industrial Engineering and Operations Research independent studies in 2020–2021. (BA) 0 pts. Lect: 1.7. Professor Lee. Workshop-style class focusing on specific areas English communication proficiency is important for improvement in pronunciation, stress, rhythm, Ivy Elkins for academic achievement and career success. In intonation, and fluency. Analyze, describe, and Computer Science small group settings, interactions with instructor practice articulation of vowels, consonants, and fellow students to improve communication and consonant clusters, important morpheme structures David Fitzgerald writing skills. Individual tutoring sessions offered. (final -ed, final -s). Discuss word stress, sentence Industrial Engineering and Operations Research Note: open only to Columbia Engineering Master's stress and rhythm, and intonation patterns across (OR) students. Grading is Pass/D/Fail. Course fee for a range of discourse functions including narration, ENGI E5000 is $350. description, process, and persuasion. Student Kristen Henlin Ph.D. Courses recitations of diagnostic passages recorded for Applied Physics, Applied Mathematics, Medical observation and feedback on progress. Physics, Material Science and Engineering; ENGI E7000x, y, and s English communication Biomedical Engineering E7001x, y, and s Professional presentation E7002x, y, and s Advanced academic writing John Hyde E7009x, y, and s English communication Data Science independent studies 0 pts. Lect: 1.7. Professor Lee. Mercedes Kriesel English communication proficiency is important Industrial Engineering and Operations research for academic achievement and career success. In (FE) small group settings, interactions with instructor and fellow students to improve communication and Jennifer Lee writing skills. Individual tutoring sessions offered. Electrical Engineering, Computer Engineering Note: open only to Columbia Engineering PhD and MS to PhD track students. Grading is Pass/D/Fail. Mindi Levinson ENGI E7101x and y Great presentations Industrial Engineering and Operations Research 0 pts. The PDL Instructional Team. Not offered (MSE & IE) in 2020–2021. Hands-on, practice intensive course focuses on Emily McCormack important elements of excellent formal presenta- Civil Engineering and Engineering Mechanics; tions. Fundamental principles discussed and Mechanical Engineering practiced in class can be applied in a variety of contexts including the short research talk, a Raina Ranaghan lab talk, the formal conference presentation, a Chemical Engineering; Earth and Environmental poster presentation, a job talk, an interview, a Engineering class presentation.

ENGINEERING 2020–2021 University and School Policies, Procedures, and Regulations 214 in eight academic terms. Full-time than 15 credits per term or 9 credits for of the semester. After these dates, 215 ACADEMIC PROCEDURES AND STANDARDS undergraduate registration is defined the last term. undergraduate students must petition as at least 12 semester credits per A graduate student who has the Committee on Academic Standing; term. However, in order to complete the matriculated in an M.S. program or graduate students must petition the degree, students must be averaging is a nondegree student is considered Office of Graduate Student Affairs. For 16 points per term. Students may not to be making normal progress if he courses dropped after these dates, no register for point loads greater than 21 or she has earned a cumulative GPA adjustment of fees will be made. Failure points per term without approval from of 2.5 or minimum GPA required by to attend a class will be indicated by a the Committee on Academic Standing. the academic department, whichever permanent unofficial withdrawal (UW) on To be eligible to receive the Bachelor is higher. Candidates in the Doctor of the transcript. of Science degree, a student must Engineering Science (Eng.Sc.D.) program complete the courses prescribed in a are expected to achieve a 3.0 GPA or Transfer Credits faculty-approved major/program (or minimum GPA required by the academic Undergraduate students may obtain faculty-authorized substitutions) and department, whichever is higher. academic credit toward the B.S. achieve a minimum cumulative grade- Graduate students (on-campus and degree by completing coursework at point average (GPA) of 2.0. Although online students) who do not meet the other accredited four-year institutions. the minimum number of academic minimum cumulative GPA of the school Normally, this credit is earned during REGISTRATION AND (212-854-3587), for further information. from any person who has outstanding credits is 128 for the B.S. degree, some and the department will be placed the summer. To count as credit toward ENROLLMENT Special billing authorization is financial, academic, or administrative programs of the School require a greater on academic probation. During the the degree, a course taken elsewhere Registration is the process that reserves required of all students whose bills obligations to the University. number of credits in order to complete probation period students must meet must have an equivalent at Columbia seats in particular classes for eligible are to be sent to a third party for Continuous registration until all the requirements. Undergraduate with their department to discuss and University and the student must achieve students. It is accomplished by following payment. Students who are not citizens completion of all requirements is engineering degrees are awarded only to develop an academic plan to improve a grade of at least B. An exception to the procedures announced in advance of the United States and who need obligatory for each degree. Students students who have completed at least their overall GPA. If the student does this policy is made for students enrolled of each term’s registration period. authorization for special billing of tuition are exempted from the requirement to 60 points of coursework at Columbia. No not meet the academic benchmarks in an approved study abroad program. Enrollment is the completion of the and/or fees to foreign institutions, register continuously only when granted credit is earned for duplicate courses or required by their department after the Students in an approved study abroad registration process and affords the full agencies, or sponsors should go a leave of absence by the Committee on for courses that are taken pass/fail and term in which they have been placed on program will receive transfer credit if they rights and privileges of student status. to the International Students and Academic Standing (for undergraduate the final grade is a P, with the exception probation, then they may be asked to earn a grade of C or higher. To transfer Enrollment is accomplished by the Scholars Office with two copies of the students) or the Office of Graduate of two nontechnical electives at the 3000 leave the School permanently. Degree credit, a student must obtain prior payment or other satisfaction of tuition sponsorship letter. Student Affairs (for graduate students). level or above, as noted below. requirements for master’s degrees approval from his or her CSA adviser and fees and by the satisfaction of other Undergraduates in the programs must be completed within five years; and the department before taking such obligations to the University. University Regulations Registration Instructions accredited by the Engineering those for the doctoral degrees must courses. A course description and Registration alone does not guarantee Each person whose enrollment has Registration instructions are announced Accreditation Commission of ABET be completed within seven years. A syllabus should be furnished as a part enrollment; nor does registration alone been completed is considered a student in advance of each registration period by (biomedical engineering, chemical minimum cumulative GPA of 2.5 (in all of the approval process. Courses taken guarantee the right to participate in class. of the University during the term for the Registrar. Students should consult engineering, civil engineering, earth courses taken as a degree candidate) is before the receipt of the high school In some cases, students will need to which he or she is enrolled unless his these instructions for the exact dates and environmental engineering, required for the M.S. degree; a minimum diploma may not be credited toward the obtain the approval of the instructor, or or her connection with the University and times of registration activities. electrical engineering, and mechanical GPA of 3.0 or minimum GPA required B.S. degree. A maximum of 6 credits of a representative of the department is officially severed by being withdrawn Students must be sure to obtain all engineering) satisfy ABET requirements by the academic department, whichever may be applied toward the degree for that offers a course, or permission of or for other reasons. No student necessary written course approvals and by taking the courses in prescribed is higher, is required for the Doctor of college courses taken following the the School offering the class. Students enrolled in any school or college of the advisers’ signatures before registering. programs, which have been designed Engineering Science (Eng.Sc.D.) and receipt of a high school diploma and should check this bulletin, their University shall at the same time be Undergraduate students who have not by the departments so as to meet the the Doctor of Philosophy degrees. The initial enrollment at Columbia University. registration instructions, the Directory of enrolled in any other school or college, registered for a full-time course load by ABET criteria. minimum residence requirement for each Master degree students are not Classes, and also with an adviser for all either of Columbia University or of any the end of the change of program period Columbia graduate degree is 30 points eligible for transfer credits. approvals that may be required. other institution, without the specific will be withdrawn, as will graduate Attendance of coursework completed at Columbia. Students possessing a conferred To comply with current and authorization of the dean or director of students who have not registered for Students are expected to attend M.S. degree upon entry into a Ph.D. anticipated Internal Revenue Service the school or college of the University in any coursework by the end of the their classes and laboratory periods. Changes in Registration program may be awarded 2 residence mandates, the University requires which he or she is first enrolled. change of program period. International Instructors may consider attendance in An undergraduate student who wishes units toward their Ph.D., as well all students who will be receiving The privileges of the University students enrolled in graduate degree assessing a student’s performance and to drop or add courses or to make as 30 points of advanced standing financial aid or payment through the are not available to any student until programs must maintain full-time status may require a certain level of attendance other changes in his or her program toward their Ph.D. or Eng.Sc.D. with University payroll system to report enrollment has been completed. until degree completion. for passing a course. of study after the change of program departmental approval. their Social Security number at the Students are not permitted to attend any period must obtain the approval of time of admission. Newly admitted University course for which they are not Graduate his or her CSA adviser. A student Examinations DEGREE REQUIREMENTS AND students who do not have a Social officially enrolled or for which they have Graduate students are required who wishes to drop or add a course Midterm examinations: Instructors SATISFACTORY PROGRESS Security number should obtain one not officially filed a program unless they to complete the School’s degree in his or her major must also obtain generally schedule these in late October well in advance of their first registration. have been granted auditing privileges. requirements as outlined on page 22 department approval. The deadline for and mid-March. Undergraduate International students should consult The University reserves the right to (The Graduate Programs). Full-time making program changes in each term Final examinations: These are given the International Students and Scholars withhold the privileges of registration and Undergraduate students are graduate registration is defined as at is shown in the Academic Calendar. at the end of each term. The Master Office, located at 524 Riverside Drive enrollment or any other University privilege required to complete the School’s least 12 credits per term. M.S. students Note: the drop-date for Columbia University Examination Schedule is degree requirements and graduate may not register for point loads greater Core courses is the second week available online and is confirmed by

ENGINEERING 2020–2021 ENGINEERING 2020–2021 216 November 1 for the fall term and April UW, and MU will not be included in the be automatically changed into an F or basis that may apply toward the 128 Name may be used in many University the instructions of the Dissertation 217 1 for the spring term. This schedule is computation of the grade-point average. the contingency grade. credits for the degree. Any course that is contexts, including SSOL, class rosters, Office, 107 Low Library. sent to all academic departments and The mark of R (registration credit; no The mark of YC (year course): a mark taken pass/fail does not count towards CourseWorks, and Canvas, and on ID General deadlines for applying for is available for viewing on the Columbia qualitative grade earned): not accepted given at the end of the first term of a the 128 credits an undergraduate needs Cards. For some other records, the graduation are November 1 for February, website. Students should consult with for degree credit in any program. R course in which the full year of work to complete to graduate unless the course University is legally required to use December 1 for May, and August 1 for their instructors for any changes to the credit is not available to undergraduate must be completed before a qualitative is taken for the nontechnical requirement a student's Legal Name. However, October. (When a deadline falls on a exam schedule. Examinations will not students for academic classes. In some grade is assigned. The grade given at (see restrictions above) or if the course is a whenever reasonably possible, a weekend or holiday, the deadline moves be rescheduled to accommodate divisions of the University, the instructor the end of the second term is the grade P.E. class. The P/F option does not count student's "Preferred Name" will be to the next business day.) Doctoral travel plans. may stipulate conditions for the grade for the entire course. toward degree requirements for graduate used. Please see registrar.columbia.edu/ students must deposit their dissertations Note: If a student has three final and report a failure if those conditions The mark of CP (credit pending): students and cannot be uncovered under content/name-and-address-changes for two days before the above conferral examinations scheduled during one are not satisfied. The R notation will given only in graduate research courses any circumstances. further details. dates in order to graduate. calendar day, as certified by the be given only to those students who in which student research projects The mark of W (official withdrawal): a Students may change their name of Students who fail to earn the degree Registrar, an arrangement may be made indicate, upon registration and to the regularly extend beyond the end of mark given to students who are granted record by submitting a name change by the conferral date for which they with one of the student’s instructors instructor, their intention to take the the term. Upon completion, a final a leave of absence after the drop affidavit to the Student Service Center. applied must file another application for to take that examination at another, course for R, or who, with the approval qualitative grade is then assigned and deadline for the semester. The grade Affidavits are available from this office or a later conferral date. mutually convenient time during the of the instructor, file written notice of credit allowed. The mark of CP implies of W, meaning “official withdrawal,” will online at registrar.columbia.edu. final examination period. This refers change of intention with the registrar satisfactory progress. be recorded as the official grade for Diplomas to a calendar day, not a 24-hour time not later than the last day for change of The mark of MU (make-up the course in lieu of a letter grade. The GRADUATION There is no charge for the preparation period. Undergraduate students unable program. Students wishing to change examination): given to a student who grade of W will zero out the credits for Columbia University awards degrees and conferral of an original diploma. to make suitable arrangements on their to R credit after this date are required has failed the final examination in a the class so the student’s GPA will not three times during the year: in February, If your diploma is lost or damaged, own should contact their CSA adviser. to submit written approval from the course but who has been granted the be affected. May, and October. There is one there will be a charge of $100 for Graduate students should contact the Office of Graduate Student Affairs and privilege of taking a second examination commencement ceremony in May. a replacement diploma. Note that Office of Graduate Student Affairs. the course instructor to the registrar. in an effort to improve his or her final Name Changes replacement diplomas carry the The request to change to R credit must grade. The privilege is granted only Columbia University recognizes that Application or Renewal of signatures of current University Transcripts and Certifications be made by the last day to change a when there is a wide discrepancy some students prefer to identify officials. Applications for replacement Application for the Degree For information on the Federal Family course grading option. A course that between the quality of the student’s themselves by a First Name and/or diplomas are available on our website: In general, students pick up and file an Education Rights and Privacy Act has been taken for R credit may not work during the term and his or her Middle Name, other than their Legal registrar.columbia.edu/registrar-forms/ application for a degree at their schools (FERPA) of 1974, please visit be repeated later for examination credit performance on the final examination, Name. For this reason, beginning application-replacement-diploma. or departments, but there are several facets.columbia.edu—Essential Policies and cannot be uncovered under any and when, in the instructor’s judgment, in the Spring 2016 semester, the Any questions regarding graduation exceptions. Candidates for Master of for the Columbia Community. Information circumstances. The mark of R does not the reasons justify a make-up University has enabled students to use or diploma processing should be Science degrees may pick up and file on obtaining University transcripts and count toward degree requirements for examination. A student may be granted a "Preferred Name" where possible in addressed to [email protected]. their application for the degree with certifications will be found as a subhead graduate students. The mark of R is the mark of MU in only two courses in the course of University business and the Diploma Division, 210 Kent Hall, under Essential Resources. automatically given in Doctoral Research one term, or, alternatively, in three or education. or through the registrar’s website: Instruction courses. more courses in one term if their total Under Columbia's Preferred Name registrar.columbia.edu/registrar-forms/ Report of Grades The mark of UW (unofficial point value is not more than 7 credits. policy, any student may choose to withdrawal): given to students who The student must remove MU by taking application-degree-or-certificate. Grades can be viewed by using the identify a Preferred First and/or Middle discontinue attendance in a course but a special examination administered as Candidates for doctoral and Master of Student Services Online feature located Name in addition to the Legal Name. are still officially registered for it, or who soon as the instructor can schedule it. Philosophy degrees should inquire at on the Student Services home page at Students may request this service via a fail to take a final examination without an The mark of P/F (pass/fail): their departments but must also follow columbia.edu/students. If you need an link on SSOL. The student's Preferred authorized excuse. Undergraduate students may take up to official printed report, you must request The mark of IN (incomplete): granted two courses of the 9-11 nontechnical a transcript (please see Transcripts and only in the case of incapacitating illness elective credit on a P/F basis. These Certifications above). as certified by the Health Services at courses must be at the 3000-level or All graduate students must have a Columbia, serious family emergency, or higher and must be courses that can current mailing address on file with the circumstances of comparable gravity. be taken P/F by students attending Registrar’s Office. Undergraduate students request an IN Columbia College (e.g., instruction by filling out the Incomplete Request classes in foreign language and core Transcript Notations Form with their CSA adviser prior to the curriculum classes are not eligible to be The grading system is as follows: A, final exam for the course in the semester taken pass/fail). These courses may not excellent; B, good; C, satisfactory; of enrollment. Students requesting an count toward the minor, and cannot be D, poor but passing; F, failure (a final IN must gain permission from both the uncovered under any circumstances. grade not subject to re-examination). Committee on Academic Standing (CAS) Students may take only one class P/F Occasionally, P (Pass) is the only passing and the instructor. Graduate students per semester to count toward the 128 option available. The grade-point should contact their instructor. If granted points, exclusive of physical education average is computed on the basis of the an IN, students must complete the credit and any other course that is following index: A=4, B=3, C=2, D=1, required work within a period of time taught only on a P/F basis. Please note F=0. Designations of + or – (used only stipulated by the instructor but not to that physical education classes are the with A, B, C) are equivalent to 0.33 (i.e., exceed one year. After a year, the IN will only courses taught solely on a P/F B+=3.33; B–=2.67). Grades of P, INC,

ENGINEERING 2020–2021 ENGINEERING 2020–2021 218218 The courses that the student medical leave, a student must submit sequence of courses as required for the 219219 ACADEMIC STANDING must take will be determined by proof of recovery from a physician or major and to meet all other graduation the Undergraduate Committee of counselor. Graduate students may also requirements by their eighth semester. Academic Standing and by the be required to meet with a medical The final decision regarding whether student’s departmental adviser when provider at Columbia. Doctoral students or not a student will be allowed to be the student has declared a major. All must have a faculty adviser and funding readmitted after a one-semester leave proposed courses will be reviewed from their faculty adviser and/or academic will be made by the Medical Leave by the appropriate faculty who teach department prior to and returning from an Readmission Committee. the equivalent classes at Columbia approved voluntary medical leave. Graduate students requesting University. All courses that are being A voluntary medical leave for an to return from VMLOA must submit taken to fulfill a major requirement or as undergraduate student is for a minimum supporting medical documentation and a technical elective must be approved of one year and cannot be longer than a personal statement that includes a by the student’s departmental adviser. two years. A voluntary medical leave for a well-developed plan to complete their Courses being taken to count as a graduate student is for a minimum of one degree. The deadlines for petitioning nontech elective or to count as general semester, up to two years. If the student a readmission are June 1 for the fall credit would only require the approval does not return within the two-year time semester and November 1 for the spring of the Undergraduate Committee frame, he or she will be permanently semester. The deadlines for petitioning a ACADEMIC HONORS uphold the policies and regulations courses for their major on Academic Standing. The existing withdrawn from the School. Students return from a voluntary medical leave for of the Committee on Instruction – not making significant progress procedures for the approval of outside may only return in the fall or spring term, graduate students after one semester Dean’s List and determine when circumstances toward the degree credit will be followed in these cases. not in summer sessions. are June 1 for the fall semester and Students must receive a grade of B or When a voluntary medical leave of November 1 for the spring semester. To be eligible for Dean’s List honors, an warrant exceptions to them. • Continued Probation: Students who better for the credit to be transferred. absence is granted during the course Students are not eligible to return from a undergraduate student must achieve a Academic performance is reviewed are already on probation and fail to The Office of Graduate Student of the semester, the fact that the medical leave during the summer. grade-point average of 3.5 or better and by advisers at the end of each semester. meet the minimum requirements as Affairs monitors the academic progress student was enrolled for the semester During the course of the leave, complete at least 15 graded credits with The Undergraduate Committee on stated in their sanction letter of graduate students in consultation and withdrew will be recorded on the students are not permitted to take any no unauthorized incompletes, UWs, or Academic Standing, in consultation • Strict Probation: Students who are with the departments. Students will student's transcript. The date of the courses for the purpose of transferring grades lower than C. with the departments, meets to review already on probation, fail to meet the undergraduate grades and progress minimum requirements as stated in be placed on Academic Probation withdrawal will also appear on the credit and are not permitted to be on toward the degree. Indicators of their sanction letter, and are far below if their cumulative GPA is below 2.5 transcript. If the leave begins prior to campus. For more information about Honors Awarded with the Degree academic well-being are grades that minimum expectations. This sanction or minimum GPA required by the the drop deadline, then the specific the voluntary medical leave of absence At the end of the academic year, a average above 2.0 each term, in a is typically applied when there are academic department, whichever is courses that the student is enrolled policy, consult your CSA adviser; select portion of the candidates for coordinated program of study, with no signs of severe academic difficulty. higher. Students who are on Academic in will be deleted from the student's graduate students should consult the the Bachelor of Science degree who incomplete grades. • Suspension and Dismissal: Students Probation and do not return to good record. If after the drop deadline, the Office of Graduate Student Affairs. have achieved the highest academic Possible academic sanctions include: who have been placed on academic standing after one semester may be course grades will normally be W (official cumulative grade-point average are probation and who fail to be restored dismissed from the program. withdrawal) in all courses. In certain accorded Latin honors. Latin honors are VOLUNTARY PERSONAL LEAVE • Warning: C– or below in any core to good academic standing in the circumstances, a student may qualify awarded in three categories (cum laude, OF ABSENCE science course or in a required course following semester can be considered for an incomplete, which would have to magna cum laude, and summa cum VOLUNTARY MEDICAL LEAVE A voluntary personal leave of absence for their major; low points toward either for suspension or dismissal by be completed by the first week of the laude) to no more than 25 percent of the OF ABSENCE (VPLOA) may be granted by the degree completion the Undergraduate Committee on semester in which the student returns graduating class, with no more than 5 A voluntary medical leave of absence Committee on Academic Standing to • Academic Probation: Students will be Academic Standing. The decision to to Columbia. If the Incomplete is not percent summa cum laude, 10 percent for an undergraduate student is granted undergraduate students who request placed on academic probation if they suspend or dismiss a student will be completed by that time, a W will be magna cum laude, and 10 percent by the James H. and Christine Turk a temporary withdrawal from Columbia meet any of the conditions below: made by the Committee on Academic inserted as the final grade. cum laude. Honors are awarded on the Berick Center for Student Advising to Engineering for a nonmedical reason. – fall below a 2.0 GPA in a given Standing in the Berick Center for In exceptional cases, an overall record of graduating seniors who an undergraduate student whose health Students considering a voluntary semester Student Advising and the Dean’s undergraduate student may apply will have completed a minimum of four prevents him or her from successfully personal leave must discuss this option – have not completed 12 points Office in close consultation with the for readmission following a one-term semesters at Columbia upon graduation. pursuing full-time study. Undergraduates in advance with their CSA adviser. successfully in a given semester student’s departmental adviser when voluntary medical leave of absence. Students who enter Columbia through who take a voluntary medical leave Voluntary leaves are granted for a – have not completed chemistry, the student has declared a major. In addition to providing a personal the Combined Plan program are eligible of absence are guaranteed housing period of one academic year only for physics, University Writing, The Art In cases of suspension, the student statement and supporting medical for honors based on three semesters at upon their return if they were already undergraduate students; VPLOAs of Engineering, and calculus during will be required to make up the documentation for the voluntary Columbia. Students may not apply for guaranteed housing prior to taking a will ordinarily not be granted for one the first year deficiencies in their academic record medical leave readmission committee honors. medical leave. semester, or for more than one year. – receive a D, F, UW, or unauthorized by taking appropriate courses at a to review, the student will also need A voluntary medical leave of absence Students must be in good academic Incomplete in any first-year/ four-year accredited institution in North to provide a well-developed academic for a graduate student is granted by the standing at the time of the leave and sophomore required courses America. Students must be able to plan that has been approved by the ACADEMIC MONITORING Office of Graduate Student Affairs, so must be able to complete their major – receive a D, F, UW, or unauthorized complete their degree requirements in departmental adviser and the Berick The SEAS Faculty Committee on please consult with this office for more and degree in eight semesters. Incomplete in any course required their eighth semester at Columbia after Center for Student Advising as part Instruction determines academic information. A voluntary personal leave of for the major readmission. If this is not achievable, of the readmission process. This plan policies and regulations for the Documentation from a physician absence for a graduate student is – receive straight C’s in the core then students should be considered for must demonstrate that his or her return School. or counselor must be provided before granted by the Office of Graduate science courses (chemistry, dismissal instead. to Columbia Engineering following a The Undergraduate Committee on such a leave is granted. In order to apply Student Affairs. A graduate student must calculus, physics) or in required one-semester leave of absence will Academic Standing is expected to for readmission following a voluntary be registered for at least one semester allow the student to properly follow the

ENGINEERING 2020–2021 ENGINEERING 2020–2021 220 and have a minimum cumulative 2.5 will review the student’s academic soon as possible, ideally by November 221 GPA to request a voluntary personal plan and request for readmission. The 1 for the spring semester and June 1 ACADEMIC INTEGRITY AND DISCIPLINE leave. Additionally, doctoral students deadlines for petitioning for readmission for the fall semester. Students must must have a faculty adviser and are June 1 for the fall semester and request readmission in writing and funding from their faculty adviser and/ November 1 for the spring semester. submit a statement describing their or academic department prior to and The deadlines for petitioning a return readiness to return. Once readmission returning from an approved voluntary from a voluntary personal leave for is granted, housing will be guaranteed. personal leave of absence. The deadline graduate students after one semester SEAS students may request permission to request a VPLOA for a given term is are June 1 for the fall semester and to return after one semester as long the last day to drop classes during that November 1 for the spring. as they can demonstrate that they term. VPLOA requests made after the Students may not take courses for can remain in sequence with their drop deadline will be denied. A graduate transferable credit while on leave. Finally, coursework and have the prior approval student may request to return from a students who choose to take voluntary of the departmental adviser. voluntary personal leave of absence for personal leaves are not guaranteed Students who decide not to return the fall, spring, or summer semester. A housing upon return to the University. must notify the James H. and Christine request to return must be made before International students should contact Turk Berick Center for Student Advising the semester starts. Please contact the the International Students and Scholars of their decision. The date of separation Office of Graduate Student Affairs for Office to ensure that a leave will not for the leave of absence will be the date ACADEMIC INTEGRITY circumstances should immediately Psychological Services (CPS), and more information. jeopardize their ability to return to of separation for withdrawal. Leaves Academic integrity defines a university contact their instructor and adviser Graduate Student Affairs, if feeling When a voluntary personal leave of Columbia Engineering. may not extend beyond four semesters. and is essential to the mission of for advice. overwhelmed, burdened or pressured. absence is granted during the course Students who do not notify the Berick education. At Columbia, you are For undergraduate students, another • Attend Academic Integrity workshops of the semester, the fact that the Center for Student Advising of their resource is the Academic section of the offered throughout the academic year. UNDERGRADUATE EMERGENCY expected to participate in an academic student was enrolled for the semester intentions by the end of the two-year Live Well | Learn Well site (wellbeing. • If you suspect that an academic FAMILY LEAVE OF ABSENCE community that honors intellectual work and withdrew will be recorded on the period will be permanently withdrawn. columbia.edu/resources) for Academic integrity violation may have occurred, Students who must leave the University and respects its origins. The abilities student's transcript. The date of the resources and support. know that you can talk to your for urgent family reasons that neces- to synthesize information and produce withdrawal will also appear on the The easiest way to avoid the instructor, Advising Dean, Director of sitate a semester-long absence (e.g., LEAVE FOR MILITARY DUTY original work are key components in the transcript. If the leave begins prior to temptation to cheat in the first place Academic Integrity, Office of Graduate family death or serious illness in the Please refer to Military Leave of learning process. As such, a violation the drop deadline, then the specific is to prepare yourself as best you can. Student Affairs, or the Student family) may request an emergency fam- Absence Policy in Essential Policies for of academic integrity is one of the most courses that the student is enrolled Here are some basic suggestions to Conduct and Community Standards ily leave of absence. Documentation the Columbia Community serious offenses that one can commit in will be deleted from the student's help you along the way: Office to report any allegations of of the serious nature of the emer- (facets.columbia.edu) for recent at Columbia. If found responsible, record. If after the drop deadline, the academic misconduct. gency must be provided. Students updates regarding leave for military duty. violations range from conditional course grades will normally be a W • Discuss with each of your faculty their must request an emergency family leave disciplinary probation to expulsion from (official withdrawal) in all courses. In expectations for maintaining academic Students found responsible for an of absence from their advising dean in the University. Compromising academic certain circumstances, a student may INVOLUNTARY LEAVE integrity. academic integrity violation may be the James H. and Christine Turk Berick integrity not only jeopardizes a student's qualify for an incomplete, which would OF ABSENCE POLICY • Understand that you have a student disqualified from receiving Latin Honors Center for Student Advising. academic, professional, and social have to be completed by the first week Please refer to Involuntary Leave of responsibility to uphold academic or other distinctions. When an emergency family leave of development; it violates the standards of of the semester in which the student Absence Policy in Essential Policies integrity based on the expectations absence is granted during the course our community. As a Columbia student, returns to Columbia. If the Incomplete is for the Columbia Community outlined in each of your course syllabi. Plagiarism and of the semester, the fact that the you are responsible for making informed not completed by that time, a W will be facets.columbia.edu). • Understand instructors' criteria for Acknowledgment of Sources student was enrolled for the semester choices with regard to academic inserted as the final grade. academic integrity and their policies and withdrew will be recorded on the integrity both inside and outside the Columbia has always believed that In exceptional cases, an on citation and group collaboration. student's transcript. The date of the classroom. writing effectively is one of the most undergraduate may apply for READMISSION • Clarify any questions or concerns withdrawal will also appear on the Students rarely set out with the important goals a college student can readmission following a one-term Students seeking readmission must about assignments with instructors as transcript. If the leave begins prior to intent of engaging in violations of achieve. Students will be asked to do voluntary personal leave of absence. submit evidence that they have early as possible. the drop deadline, then the specific academic integrity. But classes a great deal of written work while at The student will need to provide achieved the purposes for which they • Develop a timeline for drafts and courses that the student is enrolled are challenging at Columbia, and Columbia: term papers, seminar and to the Committee on Academic left. Consequently, specific readmission final edits of assignments and begin in will be deleted from the student's students may find themselves laboratory reports, and analytic essays Standing a well-developed academic procedures are determined by the preparation in advance. record. If after the drop deadline, the pressed for time, unprepared for of different lengths. These papers play plan that has been approved by the reasons for the withdrawal. Further • Avoid plagiarism: acknowledge course grades will normally be W (official an assignment or exam, or feeling a major role in course performance, departmental adviser and the Berick information for undergraduate students people’s opinions and theories by withdrawal) in all courses. In certain that the risk of earning a poor grade but more important, they play a Center for Student Advising as part of is available in the Berick Center for carefully citing their words and always circumstances, a student may qualify outweighs the need to be thorough. major role in intellectual development. the admission process. This plan must Student Advising. Graduate students indicating sources. for an incomplete, which would have to Such circumstances lead some Columbia's academic integrity policy demonstrate that his or her return to should see the Office of Graduate • Assume that collaboration in the be completed by the first week of the students to behave in a manner that in the Standards & Discipline defines Columbia Engineering following a one- Student Affairs. completion of assignments is semester in which the student returns compromises the integrity of the plagiarism as "the use of words, semester personal leave of absence will Students applying for readmission prohibited unless specified by the to Columbia. If the Incomplete is not academic community, disrespects phrases, or ideas belonging to the allow the student to properly follow the should complete all parts of the instructor. completed by that time, a W will be their instructors and classmates, and student, without properly citing or sequence of courses as required for the appropriate readmission procedures • Utilize the campus resources, inserted. deprives them of an opportunity to acknowledging the source, is prohibited. major and to meet all other graduation by June 1 for the autumn term or such as the Berick Center for To return, students must notify the learn. In short, they cheat. Students This may include, but is not limited to requirements by their eighth semester. November 1 for the spring term. Student Advising, Counseling and Berick Center for Student Advising as who find themselves in such copying computer programs for the The Committee on Academic Standing

ENGINEERING 2020–2021 ENGINEERING 2020–2021 222 purposes of completing assignments community at Columbia and severely is not limited to, using or consulting an instructor's express permission Office of Graduate Student Affairs is Confidentiality 223 for submission." Plagiarism, the use inhibits a student’s chance to grow unauthorized materials or using is prohibited. responsible for all disciplinary affairs Privacy and Reporting: Disciplinary pro- of words, phrases, or ideas belonging academically, professionally, and unauthorized equipment or devices • Plagiarism: the use of words, phrases, concerning graduate students that are ceedings conducted by the University to another, without properly citing or socially. As such, Columbia’s approach on tests, quizzes, assignments, or ideas belonging to another without not reserved to some other body. are subject to the Family Education acknowledging the source, is prohibited. to academic integrity is informed by or examinations, working on any properly citing or acknowledging Rights and Privacy Act ("FERPA," also This may include, but is not limited to, its explicit belief that students must examination, text, quiz, or assignment the source is prohibited. This may Dean’s Discipline Process for called "The Buckley Amendment"). copying computer programs for the take full responsibility for their actions, outside the time constraints imposed, include, but is not limited to, copying Undergraduate and Graduate There are several important exceptions purposes of completing assignments for meaning you will need to make the unauthorized use of prescription computer programs for the purposes Students to FERPA that will allow the University submission. informed choices inside and outside medication to enhance academic of completing assignments for It is expected that all students act in an to release information to third parties One of the most prevalent forms the classroom. Columbia offers a performance, and /or submitting an submission. honest way and respect the rights of without a student's consent. For exam- of plagiarism involves students using wealth of resources to help students altered examination or assignment to • Sabotage: inappropriately and others at all times. Dean's Discipline is ple, the release of student disciplinary information from the internet without make sound decisions regarding an instructor for regrading. deliberately harming someone else's the process utilized to investigate and records is permitted without prior stu- proper citation. While the internet academics, extracurricular activities, academic performance is prohibited. respond to allegations of behavioral dent consent to University officials with can provide a wealth of information, and personal issues. Undergraduate • Collaboration, Unauthorized: • Self-Plagiarism: using any material or academic misconduct. The Dean's a legitimate educational interest such sources obtained from the web must students should consult an advising collaborating on academic work portion of an assignment to fulfill the Discipline process is not meant to be as a student's academic adviser and to be properly cited just like any other dean or meet with the Director of without the instructor's permission is requirements of more than one course an adversarial or legal process, but Columbia Athletics if the student is an source. If you are uncertain how to Academic Integrity in Suite 601 of prohibited. This includes, but is not without the instructor's express instead aims to educate students about athlete. The University will also release properly cite a source of information Lerner Hall. Graduate students should limited to, unauthorized collaboration permission is prohibited. the impact their behavior may have on information when a student gives written that is not your own, whether from the consult or meet their assistant dean in on tests, quizzes, assignments, labs, • Test Conditions: violations of their own lives as well as on the greater permission for information to be shared. Internet or elsewhere, it is critical that the Office of Graduate Student Affairs and projects. compromising a testing environment community and, as a result, is not meant To obtain a FERPA waiver, please visit: you do not hand in your work until in Suite 530 in Mudd. • Dishonesty: falsification, forgery, or or violating specified testing to be an adversarial or legal process. columbia.edu/cu/studentconduct/ you have learned the proper way to misrepresentation of information conditions, to intentionally or The process is initiated when an documents/FerpaRelease.pdf. To read use in-text references, footnotes, and Academic Integrity Policies and to any University official in order to unintentionally create access to an allegation is reported that a student more about the exceptions that apply to bibliographies. Faculty members are Expectations gain an unfair academic advantage unfair advantage for oneself or others may have violated University policies. the disclosure of student records infor- available to help as questions arise Violations of policy may be intentional in coursework or lab work, on any is prohibited. Students may be subject to Dean's mation, please visit: essentialpolicies. about proper citations, references, and or unintentional and may include application, petition, or documents Discipline for any activity that occurs columbia.edu/policy-access-student- the appropriateness of group work submitted to this University is recordferpa. dishonesty in academic assignments DISCIPLINARY PROCEDURES on or off campus that impinges on the on assignments. Another option is prohibited. This includes, but is not Students found responsible for or in dealing with University officials, Many policy violations that occur in rights of other students and community to connect with Research Librarians limited to, falsifying information on a reportable violations of conduct, including faculty and staff members. the Residence Halls or within fraternity members. This also includes violations of for citation management workshops. resume, fabrication of credentials or including academic integrity violations, Moreover, dishonesty during the Dean’s and sorority housing are handled by local, state, or federal laws. Information on these workshops is academic records, misrepresenting may face reports of such offenses Discipline hearing process may result in Residential Life. Some serious offenses Student Conduct and Community posted online on the Columbia Libraries one's own research, providing false on future recommendations for law, more serious consequences. are referred directly to Student Conduct Standards is responsible for website. Or meet with the Director of or misleading information in order medical, or graduate school. Students Types of academic integrity violations: and Community Standards. Violations administering the Dean's Discipline Academic Integrity to review citation to be excused from classes or found responsible for any violations in University Apartment Housing are disciplinary process for all disciplinary styles at ugrad-integrity@columbia. assignments, and/or intentionally of conduct may be disqualified from • Academic Dishonesty, Facilitation of: handled by building managers and affairs concerning students that are not edu. Ignorance of proper citation underperforming on a placement receiving Latin Honors or other awards. assisting another student in a violation housing officials. Some incidents are reserved to some other body. methods does not exonerate one from exam. They may also be disqualified from of academic integrity is prohibited. referred directly to the School’s housing Students are expected to familiarize responsibility. • Ethics, Honor Codes, and participating in internships or other This may include but is not limited to liaison in the Office of Graduate Student themselves with the Standards For undergraduates only, students Professional Standards, Violation of: leadership roles. The parents or selling and/or providing notes, exams, Affairs. and Discipline handbook and the can also check with the Undergraduate any violation of published institutional guardians of undergraduate students and papers. In matters involving rallies, picketing, comprehensive list of policies and Writing Program or meet with the policies related to ethics, honor may also be notified. • Assistance, Unauthorized Giving: and other mass demonstrations, the expectations available on the Students Director of Academic Integrity to review codes, or professional standards unauthorized assistance to another Rules of University Conduct outlines Conduct and Community Standards citation styles at ugrad-integrity@ of a student's respective school is student or receiving unauthorized aid procedures. website (studentconduct.columbia.edu). columbia.edu. Ignorance of proper prohibited. from another person on tests, quizzes, Student Conduct and Community For more information about the citation methods does not exonerate • Failing to Safeguard Work: failure to assignments, or examinations without Standards is responsible for all discipline process for graduate students, one from responsibility. take precautions to safeguard one's the instructor's express permission is disciplinary affairs concerning please contact the Office of Graduate own work is prohibited. prohibited. undergraduate students that are not Student Affairs. Personal Responsibility, Finding • Giving or Taking Academic Materials, • Bribery: offering or giving any favor reserved to some other body. The Support, and More Information or thing of value for the purpose of Unauthorized: unauthorized A student’s education at Columbia improperly influencing a grade or other circulation or sharing of past or University is comprised of two evaluation of a student in an academic present course material(s) without complementary components: a program is prohibited. the instructor's express permission is mastery over intellectual material • Cheating: wrongfully using or prohibited. This includes, but is not within a discipline and the overall attempting to use unauthorized limited to, assignments, exams, lab development of moral character materials, information, study aids, reports, notebooks, and papers. and personal ethics. Participating or the ideas or work of another in • Obtaining Advanced Knowledge: in forms of academic dishonesty order to gain an unfair advantage is unauthorized advanced access to violates the standards of our prohibited. Cheating includes, but exams or other assignments without

ENGINEERING 2020–2021 ENGINEERING 2020–2021 Directory of University Resources 226 COLUMBIA UNIVERSITY RESOURCE LIST COMPUTING SUPPORT CENTER GLOBAL ENGAGEMENT HOUSING AND DINING 227 Client Services Help Desk Center for Undergraduate Global Columbia Housing 202 Philosophy, MC 4926 Engagement (UGE) 118 Hartley, MC 3003 212-854-1919 606 Kent Hall, MC 3948 212-854-2946 [email protected] 212-854-2559 [email protected] cuit.columbia.edu [email protected] facilities.columbia.edu/housing global.undergrad.columbia.edu Columbia Dining THE EARL HALL CENTER 118 Hartley, MC 3003 COLUMBIA HEALTH 212-854-4076 University Chaplain General Info: 212-854-2284 [email protected] Office: W710 Lerner [email protected] dining.columbia.edu Mailing: 202 Earl Hall, MC 2008 health.columbia.edu 212-854-6242, 212-854-1493 ouc.columbia.edu CU-EMS (Ambulance) INTERCOLLEGIATE ATHLETICS 212-854-5555 AND PHYSICAL EDUCATION

UNDERGRADUATE ADMISSIONS Student Engagement Undergraduate Writing Program EQUAL OPPORTUNITY AND Insurance and Immunization Dodge Physical Fitness Center 515 Lerner, MC 2601 310 Philosophy, MC 4995 Compliance Undergraduate Admissions AFFIRMATIVE ACTION 212-854-3439 212-854-3612 212-854-3886 John Jay, 3rd Floor, MC 3601 212 Hamilton, MC 2807 103 Low Library, MC 4333 cc-seas.columbia.edu/engagement [email protected] Insurance Office: 212-854-3286 212-854-2522 212-854-5511 INTERNATIONAL STUDENTS college.columbia.edu/core/uwp [email protected] [email protected] eoaa.columbia.edu AND SCHOLARS (ISSO) Immunization Compliance Office: undergrad.admissions.columbia.edu COLUMBIA COLLEGE Office: 524 Riverside Drive, Ground Floor GRADUATE STUDENT AFFAIRS 212-854-7210 208 Hamilton, MC 2805 Student Services for Gender-Based Mailing: 2960 Broadway, MC 5724 [email protected] UNDERGRADUATE ADVISING 212-854-2441 Graduate Student Affairs and Sexual Misconduct 212-854-3587 college.columbia.edu/ 530 S. W. Mudd, MC 4708 Wien Hall, Suite 108C [email protected] Student Health Insurance Plan James H. and Christine Turk Berick 212-854-6438 212-854-1717 isso.columbia.edu Administrators Center for Student Advising studentconduct.columbia.edu/gbm gradengineering.columbia.edu/ Aetna Student Health 403 Lerner Hall, MC 1201 CORE CURRICULUM PROGRAM 1-800-859-8471 LIBRARIES 212-854-6378 Center for the Core Curriculum Graduate Admissions FINANCIAL AID (UNDERGRADUATE) www.aetnastudenthealth.com/ [email protected] 202 Hamilton, MC 2811 530 S. W. Mudd, MC 4708 columbia Butler Library Information cc-seas.columbia.edu/csa 212-854-2453 212-854-6438 Undergraduate Financial Aid and 535 W. 114th Street Educational Financing Alice! Health Promotion college.columbia.edu/core gradengineering.columbia.edu/ 212-854-7309 UNDERGRADUATE STUDENT LIFE admissions Office: 618 Lerner John Jay, 3rd Floor, MC 3601 library.columbia.edu Mailing: 100 Hamilton, MC 2802 212-854-5453 505–515 Lerner, MC 2601 Art Humanities 212-854-3711 [email protected] 212-854-3612 826 Schermerhorn, MC 5517 Science & Engineering Library COLUMBIA VIDEO NETWORK [email protected] cc-seas.columbia.edu/studentlife 212-854-4505 Counseling and Psychological 401 Northwest Corner 540 S. W. Mudd, MC 4719 cc-seas.financialaid.columbia.edu arthum.college.columbia.edu/ Services 212-851-2950 212-854-6447 Multicultural Affairs Lerner, 8th floor, MC 2606 [email protected] 505 Lerner, MC 2607 Music Humanities 24/7 Support: 212-854-7878 MATH/SCIENCE DEPARTMENTS cvn.columbia.edu FINANCIAL AID (GRADUATE) 212-854-0720 621 Dodge, MC 1813 Disability Services Biological Sciences cc-seas.columbia.edu/OMA 212-854-3825 Federal Loans 108A Wien Hall, MC 3711 600 Fairchild, MC 2402 college.columbia.edu/core/classes/mh CENTER FOR CAREER EDUCATION Financial Aid and Educational Financing Intercultural Resource Center (IRC) Voice/TTY: 212-854-2388 212-854-4581 East Campus, Lower Level, MC 5727 615 Lerner, MC 2802 552 West 114th Street, MC 5755 [email protected] Contemporary Civilization 212-854-5609 212-854-3711 212-854-0720 Chemistry 514 Fayerweather, MC 2811 sfs.columbia.edu/financial-aid/graduate Medical Services cc-seas.columbia.edu/ [email protected] 344 Havemeyer, MC 3178 212-854-5682 John Jay Hall, 4th Floor multicultural/aboutus/irc.php careereducation.columbia.edu 212-854-2202 college.columbia.edu/core/conciv Institutional Financial Aid 212-854-6655 (Gay Health Advocacy (Grants, Fellowships, Assistantships) Project) Residential Life Earth and Environmental Sciences Literature Humanities Office of Graduate Student Affairs 24/7 Support: 212-854-7426 106 Geoscience, Lamont-Doherty 515 Lerner, MC 4205 202 Hamilton, 212-854-2453 530 S. W. Mudd, MC 4708 Earth Observatory, 845-365-8550 212-854-3612 Mail Code 2811 212-854-6438 Sexual Violence Response Lerner, 7th floor cc-seas.columbia.edu/reslife college.columbia.edu/lithum 24/7 Support: 212-854-HELP (4357) [email protected]

ENGINEERING 2020–2021 ENGINEERING 2020–2021 228 Mathematics PUBLIC SAFETY STUDENT SERVICE CENTER 229 410 Mathematics, MC 4426 111 Low Library, MC 4301 205 Kent, MC 9202 212-854-2432 212-854-2797 (24 hours a day) 212-854-4400 [email protected] [email protected] Physics publicsafety.columbia.edu ssc.columbia.edu 704 Pupin, Mail Code 5255 212-854-3348 Campus Emergencies: 212-854-5555 (4-5555) UNIVERSITY LIFE 212-854-0411 Statistics Escort Service: 1255 Amsterdam Avenue [email protected] 212-854-SAFE (4-7233) Room 1005 SSW, MC 4690 universitylife.columbia.edu 212-851-2132 REGISTRAR 210 Kent, MC 9202 OMBUDS OFFICE [email protected] 660 Schermerhorn Ext., MC 5558 registrar.columbia.edu 212-854-1234 [email protected] ombuds.columbia.edu/ STUDENT CONDUCT AND COMMUNITY STANDARDS On Wednesdays the Ombuds Officer is 800 Watson Hall at the Columbia Medical Center office: 612 West 115 Street, MC 2611 101 Bard Hall 212-854-6872 50 Haven Avenue [email protected] 212-304-7026 studentconduct.columbia.edu

ENGINEERING 2020–2021 ENGINEERING 2020–2021 230 COLUMBIA UNIVERSITY THE MORNINGSIDE HEIGHTS AREA OF NEW YORK CITY 231 THE MORNINGSIDE CAMPUS & ENVIRONS

ENGINEERING 2020–2021 ENGINEERING 2020–2021 232 undergraduate programs, 89–92 Counseling and Psychological Services Earth and Environmental Engineering, 233 INDEX classes (CPS), 221, 227 Department of, 122–135 attendance at, 215 courses graduate programs, 127–129 registration and enrollment in, 214 for pro­fessions other than research centers, 123–126 colleges and universities in Combined engineering, 16–17 scholarships, fellowships, and Plan program, 14 interdisciplinary engineering, 210 internships, 126 Columbia College, 226 key to listings, 46–47 undergraduate program, 126–127 Columbia Dining, 227 in Engineering School departments. See also Henry Krumb School of Columbia Genome Center (CGC), 78 See individual departments Mines Columbia Health, 227 credit, points of, required for degree Earth and Environmental Sciences, Columbia Housing, 227 graduate, 22–25, 215 Department of (Columbia College), Columbia University undergraduate, 8–13, 214–215 227 Columbia Engineering – Yesterday Earth Engineering Center, 123 and Today, 2–6 East Asian studies, D email addresses, list of, 226–228 minor in, 206 applications Botwinick Multimedia Learning A maps of campus, 230–231 damages, payment for, 19, 31 economics for degrees, 217 Laboratory, 5 academic advising. See James H. and policy, procedures, and regulations, dance, minor in, 205 minor in, 206 graduate, 28–29 Business, Graduate School of Christine Turk Berick Center for 214–223 Data-Driven Analysis, specialization electrical engineering undergraduate, 17 joint programs with, 23, 167 Student Advising Columbia University’s Health Promotion in, 144 courses in, 146–156 applied chemistry. See Chemical Butler Library, 227 academic calendar, inside back cover Program (Alice!), 227 Dean’s discipline, 223 minor in, 206 Engineering, Department of academic community, conduct Columbia Video Network (CVN), 26–27, Dean’s List, 218 Electrical Engineering, Department of, applied mathematics expected in, 221 C 226 Degree Audit Reporting System 136–156 courses in, 60–61 academic dishonesty, 222 application to, 26 (DARS), 14 B.S./M.S. program, 143 minor in, 204 academic honors, 218 calendar Columbia Water Center, 123 degrees specialization options in the M.S. applied physics academic integrity, 221–223 academic, inside back cover Combined Plan programs, 14 application for, 217 program, 143–146 courses in, 57–59 academic monitoring, 218 for graduate admissions, 29 commencement ceremony, 217 doctoral, requirements, 24–25, 215 graduate programs, 143–146 minor in, 204 academic procedures and standards, Carleton Commons, 6 Committee on Academic Standing, See also individual degrees laboratory facilities, 137 Applied Physics and Applied 214–217 Center for Applied Probability (CAP), 215–216, 218 diplomas, 217 research activities, 136–137 Mathematics, Department of, 48–61 academic progress, satisfactory, 20, 158 Committee on Instruction, 9, 24, 218 Disability Services, University Office undergraduate program, 137–143 current research activities, 48–49 214–217 Center for Career Education (CCE), 14, Computational and Optimization of, 227 email graduate programs, 54–57 academic standing, 218–220 34, 226 Research Center (CORC), 158 discipline, academic, 221–223 addresses of Columbia University laboratory facilities, 49–50 ABET, 15, 63, 65, 79, 92, 123, 126, Center for Financial Engineering, 158 Computer Engineering Program, 101–105 Dean’s, 223 resources and staff, 226–228 specialty areas, 53–54 142, 192 Center for Life Cycle Analysis (CLCA), graduate program, 103–105 procedures for administering, emeriti and retired officers, list of, undergraduate programs, 50–54 addresses of Columbia University 123–125 undergraduate program, 101–103 221–223 41–42 architecture, minor in, 92, 204 departments and resources, 226–228 Chaplain, University, Office of the, 227 computer science dishonesty, academic, 221–222 employment, student, 34 art history, minor in, 205 administrative officers, lists of, 36, chemical engineering courses in, 112–121 distance education. See Columbia Engineering Accreditation Commission assistantships, 32–33 42–44 courses in, 81–86 minor in, 205 Video Network (EAC), 15 athletic programs, 11, 13 admissions minor in, 80, 205 Computer Science, Department of, Doctor of Engineering Science (Eng. engineering courses, interdisciplinary, attendance, 215 graduate, 28–29, 226. See also Chemical Engineering, Department of, 106–121 Sc.D.), 24–25 210–212 Graduate Student Affairs 77–86 dual degree program, with School Doctor of Philosophy (Ph.D.), 24–25 Engineering Library, 227 facilities and laboratories, 78 undergraduate, 17, 226 B of Journalism, 23, 112 Dodge Physical Fitness Center, 227 engineering mechanics advanced placement, 9, 12, 13 graduate programs, 80–81 laboratory facilities, 106 dual degree courses in, 99–100 Bachelor of Science degree (B.S.), 15 advanced standing, of transfer undergraduate program, 79–80 graduate programs, 111–112 with the School of Journalism, in graduate program in, 93–94 Barnard Education Program, 17 students, 29 Chemistry, Department of, 227 undergraduate program, 106–111 computer science, 23, 112 minor in, 206 bioinductive and biomimetic materials, advising centers. See James H. and civil engineering Computing Support Center, 227 See also joint programs undergraduate program in, 90 program in, 66 Christine Turk Berick Center for courses in, 94–100 conduct See also Civil Engineering and Biological Sciences, Department of, 227 Student Advising minor in, 205 expected in the academic Engineering Mechanics, biomedical engineering E Alice! Columbia University’s Health Civil Engineering and Engineering community, 221 Department of courses in, 70–76 Promotion program, 227 Mechanics, Department of, unacceptable, subject to discipline, Earl Hall Center, 227 Engineering, School of minor in, 205 American Language Program (ALP), 29 87–100 221–223 Earth and environmental engineering courses. See individual departments Biomedical Engineering, Department anthropology, minor in, 204 current research activities, 87–88 Core Curriculum of Columbia courses in, 129–135 department and course codes, of, 62–76 facilities and laboratories, 88–89 program offices, 226 minor in, 205–206 46–47 graduate programs, 66–69 graduate programs, 92–94 departments and programs, 48–202 undergraduate program, 63–66

ENGINEERING 2020–2021 ENGINEERING 2020–2021 234 faculty and administration, 36–44 Fu Foundation School of Engineering undergraduate programs, 158–164 Library, Science & Engineering, 227 medical services and Columbia Health Physical Education, Intercollegiate 235 engineering students and Applied Science, The. See Industry/University Cooperative Libraries, Columbia University, 227 program, 227 Athletics and, Department of, 227 interdisciplinary courses for, 210– Engineering, School of Research Center for Particulate and lightwave (photonics) engineering, microelectronic devices, specialization Physics, Department of, 228 212 Fundamentals of Engineering (FE) Surfactant Systems (CPaSS), 125 specialization in, 145 in, 145 plagiarism, 221–222 See also students exam, 23, 193–194 Institute of Flight Structures, 90 loans, student, 33 Middle Eastern, South Asian, and plasma physics, graduate program English and comparative literature, institutional grants, 32 African Studies, minor in, 207 in, 56 minor in, 207 Insurance, Student Medical Plan, 18, military leave of absence, 220 Plasma Physics Laboratory, 49 G M enrollment, 214 30, 227 minors, academic, 15–16, 204–208 political science, minor in, 208 entrepreneurship and innovation, minor German, minor in, 207 integrated circuits and systems, Makerspace, 5–6 Morningside Heights campus, 5 prelaw program, 17 in, 207 grade-point average (GPA), 215 specialization in, 144 management science and engineering, maps of, 236–237 premed program, 16–17 Equal Opportunity and Affirmative grades, report of, 216 integrity, academic, 221–223 graduate program in, 166–167 Multicultural Affairs, 226 preprofessional advising, 9, 16–17 Action, Office of, 227 grading system, explained, 216–217 Intercultural Resource Center (IRC), maps of Columbia Morningside Heights music Professional Development and examinations, midterm and final, graduate courses, taking as an 226 campus, 230–231 instruction courses, 10 Leadership Program, 11, 23, 29, 215–216 undergraduate, 15 interdisciplinary engineering courses, marks. See grading system minor in, 207 54, 68, 78, 92, 102, 110, 127, 143, graduate programs, 22–25 210–212 Master of Science degree (M.S.), 164, 181, 195, 212 admission to, 28–29 International and Public Affairs, School 22–23 professions other than engineering, F N applying to, 28–29 of, joint programs with, 17 materials chemistry/soft materials, 179 Engineering programs in preparation faculty requirements, 22–25 International English Language Testing materials for green energy, 179 names, student, change of, 217 for, 16–17 lists of, 36–42 See also individual programs System (IELTS), 28 materials for health and biotechnology, nanomaterials, 178–179 psychological services, counseling and, members-at-large, list of, 41 Graduate Record Examination (GRE), 28 International Students and Scholars 179 networking, specialization in, 144 227 Family Educational Rights and Privacy Graduate Student Affairs, Office of, Office (ISSO), 227 materials for next generation New York City, 4 psychology, minor in, 208 Act (FERPA), 216, 223 28, 226 internships, 126 electronics, 179 New York State Public Safety, Office of, 228 federal financial aid, 20, 33, 227 graduate students materials science and engineering initial certification in adolescence fees degree requirements for, 215 courses in, 183–185 education, 17 J R graduate, 30–31 discipline process for, 221–223 minor in, 207 Nondegree students, 25, 29 refunds of, 19, 31 financial aid for, 32–34, 227 James H. and Christine Turk Berick Materials Science and Engineering nontechnical requirements, 9–13 readmission, 220 undergraduate, 18–19 tuition and fees, 30–31 Center for Student Advising, 8, 219, program (MSE), 55, 61, 123, refunds of tuition and fees, 19, 31 See also payments graduation, 217 226 177–186 registrar, 228 O fellowships, 32 graphics, courses in, 99 joint programs current research activities, 177–178 See also Student Service Center financial aid Greek or Latin, minor in, 207 with Data Science Institute, 23 graduate programs, 181–183 officers of Columbia Engineering registration, 214 eligibility for, 20 with the Graduate School of graduate specialty in solid-state list of, 36, 42–44 changes in, 215 employment and, 34 Business, in industrial engineering, science and engineering, 182–183 retired, list of, 41–42 religion, minor in, 208 H federal, 33 23, 167 interdepartmental committee and, 177 Ombuds Office, 228 report of grades, 216 to graduate students, 32–34, 227 health insurance, 18, 30–31 with the School of International and laboratory facilities, 178 operations research Residence Units, and the Ph.D., 24 how to apply for, 20 health service. See Columbia Health Public Affairs, 17 undergraduate program, 178–181 graduate program in, 158 resources, Columbia University, list of, private programs, 33 Henry Krumb School of Mines (HKSM), with School of Journalism, 23 Mathematics, Department of, 228 minor in, 208 226–228 to undergraduate students, 20, 227 122 See also dual degree mechanical engineering undergraduate programs in, 158–164 Rules of University Conduct, 221–223 financial engineering See also Earth and Environmental Junior-Senior programs, 14–16 courses in, 196–202 See also Industrial Engineering and graduate program in, 164 Engineering, Department of minor in, 207 Operations Research, Department S First Year–Sophomore Program course Hispanic studies, minor in, 207 Mechanical Engineering, Department of L requirements history, minor in, 207 of, 187–202 optical and laser physics, graduate sanctions, for academic dishonesty, nontechnical, 9–11 honors, academic, 218, 221 laboratory charges, 18–19, 31 current research activities, 186–189 program in, 56 218 professional-level, 11 Langmuir Center for Colloids and facilities for teaching and research, School of Engineering. See Engineering technical, 11 Interfaces (LCCI), 126 189–191 School I P 4-1 Combined Plan B.S. program, 17 Latin, Greek or, minor in, 207 graduate programs, 194–196 Science & Engineering Library, 227 4-2 Combined Plan M.S. program, 23 industrial engineering leave(s) of absence undergraduate program, 191–194 payments Sexual Violence Response, 227 Free Application for Federal Student courses in, 168–176 family, 220 medical care and insurance, 18, 30, timely and overdue, 18, 30 Social Security number, registration Aid (FAFSA), 32–33 minor in, 207 involuntary, 220 227 See also fees and, 214 French Industrial Engineering and Operations medical, 219 Medical College Admissions Test Pearson Test of English (PTE), 28 sociology, minor in, 208 and francophone studies, minor in, Research, Department of, 157–176 military, 220 (MCAT), 16 personal expenses of students, 18, 31 solid-state physics, graduate program 207 current research activities, 158 voluntary, personal, 219–220 medical leave of absence, 219 philosophy, minor in, 208 in, 56–57 minor in, 207 graduate programs, 164–168 Lenfest Center for Sustainable Energy, medical physics, graduate program physical education, 11, 13 solid-state science and engineering joint programs, 23, 168 126 in, 55 areas of research, 183 minors, 206–208 graduate specialty in, 182–183

ENGINEERING 2020–2021 ENGINEERING 2020–2021 236 sports, 11, 13 sustainable waste management, financial aid for, 20 Statistics, Department of, 227 127–128 minor programs for, 15–16, 204– statistics, minor in, 208 systems biology and neuroengineering, 208 Student Advising, Center for, 226 specialization in, 145 programs in Engineering School for, Student Conduct and Community 8–17 Standards, 228 tuition and fees of, 18–19 T Student Engagement, 226 See also students Student Financial Planning, Office of, Tau Beta Pi, 14 University Chaplain, Office of the, 227 32–34, 227 teacher certification, obtaining, 17 Student Financial Services. See telephone numbers of Columbia V Student Service Center University departments and student loans, 33 resources, 226–228 Veteran Affairs, Department of, 33 Student Medical Insurance Plan, 18, Test of English as a Foreign Language veterans, educational benefits for, 30–31, 227 (TOEFL), 28–29 33–34 student records, rights pertaining to, 3-2 Combined Plan B.A./B.S. program, visual arts courses, 10 223 14 Student Research Program, 8 transcripts, 216 W Student Service Center, 228 transfer credits, 215 students transfer students, 29 Waste to Energy Research and contributions of, to educational tuition Technology Council (WTERT), 125 costs, 18–19, 30–31 graduate, 30–31 water resources and climate risks, employment and earnings of, 33–34 refunds of, 18, 31 specialization in, 127 international, 33 undergraduate, 18–19 wireless and mobile communications, name changes of, 217 specialization in, 144 nondegree, status, 25, 29 U personal expenses of, 18, 31 transfer, 29 Undergraduate Financial Aid and See also engineering students; Educational Financing, 227 graduate students; undergraduates Undergraduate Global Engagement, study abroad, 13–14 Center of, 13–14, 227 Undergraduate Student Life, 226 sustainable energy undergraduates specialization in, 127–128 applications and admissions of, 17 sustainable engineering, minor in, 208 degree requirements for, 9, 214–217

ENGINEERING 2020–2021