2022 – 2021 BULLETIN BULLETIN

Columbia | Engineering 2021 –2022 500 West 120th Street 120th West 500 NY 10027 York, New Academic Calendar 2021–2022 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 2021 SPRING TERM 2022

August January 24–26; Sept. 2–6 Registration by appointment (undergraduate) 4–7, 10–14 Registration by appointment (undergraduate and 27–Sept. 10 Graduate orientation and graduate department graduate) orientations TBA Graduate orientation 29–Sept. 8 New student orientation program 17 Birthday of Martin Luther King Jr., 31–Sept. 2 Registration by appointment (graduate) University holiday 18 First day of classes September 18–31 Change of program by appointment (weekdays) 1 Last Day to apply for October degrees 22 Deadline to add spring courses 6 Labor Day, University holiday UNDERGRADUATE ADMISSIONS Need more information? 9 First day of classes February Office of Undergraduate Admissions You can find the contact information 9–21 Change of program by appointment (weekdays) 9 February degrees conferred 212 Hamilton Hall, Mail Code 2807 in the Resource List 21 Last day to (1) register for academic credit, (2) change course programs, (3) submit written March 1130 Amsterdam Avenue on pages 226–228 or visit the Columbia Engineering 7 Midterm date 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 14–18 Spring recess Phone: 212-854-2522 special fees, (4) drop Core Curriculum classes. No 24 Last day to drop Engineering courses without For the most current information, visit our online Fax: 212-854-3393 adjustment of fees for individual courses dropped academic penalty. Last day to change grading bulletin at bulletin.engineering.columbia.edu. [email protected] after this date. option 30 Last day to confirm, update, or request a waiver from undergrad.admissions.columbia.edu the Student Medical Insurance Plan. April Photography: TBA Registration by appointment for fall 2022 GRADUATE ADMISSIONS Monolayer WSe2 hosting “composite fermions,” a October 20 October degrees conferred May Graduate Admissions quasi-particle that forms due to strong interactions 21 Midterm date 2 Last day of spring classes 1220 S. W. Mudd, Mail Code 4708 between electrons and is responsible for the 3–5 Study days 500 West 120th Street sequence of fractional quantum Hall states. From November 5 Last day for continuing students to apply New York, NY 10027 the lab of Wang-Fong Jen Professor of Mechanical 1 Last day to apply for February degrees for financial aid for the 2022–2023 academic year. 212-854-4688 Engineering James Hone. 1 Academic holiday 6–13 Final exam period for spring courses 16–18 Class Day and University Commencement will [email protected] 2 Election Day. University holiday 15–19 Registration by appointment for spring 2022 take place during this week (specific dates to be gradengineering.columbia.edu Superimposed over this image is the emblem of the (undergraduate) announced). School’s vision, Columbia Engineering for Humanity. 18 Last day to drop Engineering courses without FINANCIAL AID academic penalty. Last day to change a grading option. Office of Financial Aid and Educational Financing 22–24 Registration by appointment (graduate) Office: 618 Lerner Hall 24 Academic holiday Mailing: 100 Hamilton Hall, Mail Code 2802 25–26 Thanksgiving holiday 1130 Amsterdam Avenue December New York, NY 10027 1 Last day to apply for May degrees Phone: 212-854-3711 13 Last day of classes Fax: 212-854-5353 14–15 Study days [email protected] 16–23 Final examinations cc-seas.financialaid.columbia.edu 24–Jan. 17 Winter recess BULLETIN 2021– 2022 Mission The mission of Columbia Engineering (The Fu Foundation School of Engineering and Applied Science) is to expand knowledge and advance technology through research, while educating students to become leaders and innovators informed by an engineering foundation. Enriched with the intellectual resources of a global university in the City of New York, we push disciplinary frontiers, confront complex issues, and engineer innovative solutions to address the grand challenges of our time. We create a collaborative environment that embraces interdisciplinary thought, 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 2021–2022 A MESSAGE FROM THE DEAN

elcome to Columbia University’s Our school vision—Columbia Engineering for Fu Foundation School of Humanity—encapsulates our efforts to make Engineering and Applied Science. a positive impact on society. It highlights the WTogether with a talented group of students innovative and interdisciplinary work that from around the world, you are embarking on a our faculty and students are engaged in to course of study that will enable you to become create a more sustainable, healthy, secure, the next generation of leaders—leaders with connected, creative, and equitable world. a foundational degree in engineering that As you prepare for a new academic year, will prepare you for a wealth of pursuits in we urge you to reflect on this vision and engineering and applied science, as well as embrace the many opportunities afforded to many other fields and industries. you by a world-class university. Our community has a long history of There has never been a better time to be scientific and engineering breakthroughs a Columbia Engineer. I encourage you to seek that have impacted our world. From the out the exceptional opportunities for learning School’s beginning in 1864 through today, and advancement that await you here. the work of faculty, alumni, and students has pushed disciplinary frontiers to create, invent, and innovate devices, materials, tools, and With best wishes for the academic year, processes to make life better. Our first dean, Charles Frederick Chandler, Shih-Fu Chang served as president of ’s Interim Dean, Columbia Engineering Metropolitan Board of Health. In this role, he Richard Dicker Professor of Electrical crusaded to ensure the purity of food and Engineering and drugs, the safety of milk, the availability of clean water in the city, and the introduction of building codes. Today, we continue to be a school embedded in our community while cultivating a global mindset that is mindful of the ways in which we are all connected. Our faculty and students continue to bring their curiosity, creative drive, and entrepreneurial spirit to some of the biggest challenges of our time.

ENGINEERING 2021–2022 TABLE OF CONTENTS­

About the School and 1 Financing Graduate Education 32 MECHANICAL ENGINEERING 186 University Instructions for Financial Aid 32 COLUMBIA ENGINEERING—­ 2 Applicants Undergraduate Minors 203 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 Policy on Degree Requirements 9 Employment 34 ENGINEERING COURSES 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 Programs in Preparation for 16 University and School 213 45 Other Professions Academic Departments Policies, Procedures, and Joint Programs 17 and Programs Regulations Undergraduate Admissions 17 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 63 ACADEMIC INTEGRITY AND 221 UNDERGRADUATE STUDY DISCIPLINE CHEMICAL ENGINEERING 78

Graduate Studies 21 CIVIL ENGINEERING AND 88 Directory of University 225 THE GRADUATE PROGRAMS 22 ENGINEERING MECHANICS Resources The Master of Science Degree 22 COMPUTER ENGINEERING 102 COLUMBIA UNIVERSITY 226 Doctoral Degrees: Eng.Sc.D. 24 PROGRAM RESOURCE LIST and Ph.D. Nondegree Students 25 COMPUTER SCIENCE 107 MAPS 230 Office of Graduate Student Affairs 25 EARTH AND ENVIRONMENTAL 123 INDEX 232 COLUMBIA VIDEO NETWORK 26 ENGINEERING Academic Calendar (see inside back GRADUATE ADMISSIONS 28 ELECTRICAL ENGINEERING 136 cover)

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

FINANCIAL AID FOR GRADUATE 32 MATERIALS SCIENCE AND 177 STUDY ENGINEERING PROGRAM About the School and University 2 COLUMBIA ENGINEERING–YESTERDAY AND TODAY

A COLONIAL CHARTER A MODERN SCHOOL and detect the frequencies of enemy Since its founding in 1754, as King’s FOR MODERN TIMES aircraft ignition systems. After the war, College, Columbia University has always The School of Mines became the Armstrong improved his method of been an institution both of and for the School of Mines, Engineering, and frequency modulation (FM), and by City of New York. And it has always Chemistry in 1896, and its professors 1931, had both eliminated the static been an institution of and for engineers. included Michael Idvorsky Pupin, a and improved the fidelity of radio In its original charter, the College stated graduate of the Columbia College Class broadcasting forever. The historic that it would teach, among other things, of 1883. As a professor at Columbia, significance of Armstrong’s contributions “the arts of Number and Measuring, Pupin did pioneering work in carrier- was recognized by the U.S. government of Surveying and Navigation, . . . the wave detection and current analysis, when the laboratory knowledge of . . . Meteors, Stones, with important applications in radio was designated a National Historic Mines and Minerals, Plants and Animals, broadcasting. He is perhaps most Landmark in 2003. and everything useful for the Comfort, famous for having invented the “Pupin As the United States evolved into the Convenience and Elegance of Life.” coil,” which extended the range of long- a major twentieth-century political distance telephones. power, the University continued to build An early student of Pupin’s was onto its undergraduate curriculum the THE GILDED AGE Irving Langmuir. Langmuir, Class of 1903, broad range of influential graduate As the city grew, so did the School. enjoyed a long career at the General and professional schools that define it King’s College was rechartered as Electric research laboratory. There he today. Renamed once again in 1926, Columbia College in 1784 and relocated invented a gas-filled tungsten lamp, the School of Engineering prepared from the Wall Street area to what is contributed to the development of students for careers not only as now Midtown in 1857. Students began the radio vacuum tube, and extended engineers of nuclear-age technology, entering the new School of Mines in Gilbert Lewis's work on electron but as leaders engaged with the far- 1864. Trained in mining, mineralogy, bonding and atomic structure. His reaching political implications of that and engineering, Columbia graduates research in monolayering and surface technology as well. continued to make their mark both at chemistry led to a Nobel Prize in After receiving a master’s degree home and abroad. Chemistry in 1932. from the School in 1929, Admiral Hyman Working around the globe, William But early work on radio vacuum George Rickover served during the Barclay Parsons, Class of 1882, was an tubes was not restricted to private Second World War as head of the engineer on the Chinese railway and industry. Working with Pupin, an electrical section of the Navy’s Bureau the Cape Cod and Canals. engineering student named Edwin of Ships. A proponent of nuclear sea Most important for New York, he was Howard Armstrong was conducting power, Rickover directed the planning chief engineer of the city’s first subway. experiments with the Audion tube and construction of the world’s first Opened in 1904, the subway’s electric in the basement of Philosophy Hall nuclear submarine, the 300-foot-long cars took passengers from City Hall when he discovered how to amplify Nautilus, launched in 1954. to Brooklyn, the Bronx, and the newly radio signals through regenerative renamed and relocated Columbia circuits. Armstrong, Class of 1913, was TECHNOLOGY AND BEYOND University in Morningside Heights. stationed in France during the First Today, The Fu Foundation School of World War, where he invented the Engineering and Applied Science, as superheterodyne circuit to tune in it was named in 1997, continues to

ENGINEERING 2021–2022 3

provide leadership for scientific and of Physicians and Surgeons, the university actively participating in a educational advances. Even Joseph Graduate School of Journalism, Lamont- broad range of standards-based patent Engelberger, Class of 1946, the father Doherty Earth Observatory, The Earth pools, including AVC (Advanced Video of modern robotics, could not have Institute, Teachers College, Columbia Coding), the world standard for audio/ anticipated the revolutionary speed with Business School, and the Graduate video compression that is now one of which cumbersome and expensive “big School of Architecture, Planning and the most commonly used HD formats science” computers would shrink to the Preservation. The transforming gift of and most commonly employed in size of a wallet. The Fu Foundation has catapulted the streaming media; and ATSC, a standard No one could have imagined the School into the forefront of collaborative developed by the Advanced Television explosive growth of technology and research and teaching and has given Systems Committee for digital television its interdisciplinary impact. Columbia students the opportunity to work with transmission. It is now the U.S. standard Engineering is in a unique position to prize-winning academicians, including for recording and retrieval of data and take advantage of the research facilities Nobel laureates from many disciplines. HD audio-visual media. In addition to and talents housed at Columbia to form the standards, Columbia Engineering relationships among and between other faculty have patents in areas as diverse NEW RESEARCH FRONTIERS schools and departments within the as modular cameras, carbon capture, Columbia’s technology transfer office, University. Biomedical Engineering, with a search engine that matches facial Columbia Technology Ventures, works close ties to the Medical School, is but features, and even methods to combat with faculty inventors to commercialize one example. Interdisciplinary centers virtual reality sickness. ideas and brings in millions in licensing are the norm, with cross-disciplinary Increasingly, the inventions emerging revenue annually. Columbia Engineering research going on in biomedical from Columbia Engineering are faculty have been instrumental in imaging, environmental chemistry, developed in collaboration with other developing some of the most successful materials science, nanotechnology, researchers, expanding the potential inventions in consumer electronics, as digital, and new media technologies. applications for their important work. well as establishing many of the widely The School and its departments Programs such as the Columbia accepted global standards for storage have links to the Departments of Biomedical Technology Accelerator and transmission of high-quality audio Physics, Chemistry, Earth Science, and (BiomedX), PowerBridgeNY, the and video data. Columbia is the only Mathematics, as well as the College NYC Media Lab Combine program,

ENGINEERING 2021–2022 4 the COSMOS Wireless Testbed, A FORWARD-LOOKING TRADITION from small Chelsea galleries to major the Columbia IBM-Center for But, for all its change, there is still a museums; music from Harlem jazz clubs Blockchain and Data Transparency, continuous educational thread that to the Metropolitan Opera; theater from and the Columbia Electrochemical remains the same. Committed to the performance art in the East Village Energy Center are strengthening educational philosophy that a broad, to musicals on Broadway; food from interdisciplinary capacity and fostering rigorous exposure to the liberal arts around the world; and every sport an entrepreneurial and inventive energy provides the surest chart with which imaginable, New York is the cultural within the School. Some of these an engineer can navigate the future, crossroads of the world. programs and centers have helped all undergraduates must complete a New York is also a major player in prepare ideas for commercialization, modified but equally rigorous version high-tech research and development, including personalized robotics for of Columbia College’s celebrated where Fortune 500 companies traded use in physical rehabilitation and an Core Curriculum. It is these selected on Wall Street seek partnerships with implantable device that acts as a courses in contemporary civilization in high-tech startups in Tribeca and minimally-invasive glucose sensor for the West and other global cultures that Brooklyn. As part of the research diabetic patients. best prepare a student for advanced community themselves, Columbia coursework; a wide range of eventual students have exceptional opportunities for contact with industry both on and ENTREPRENEURSHIP professions; and a continuing, life-long pursuit of knowledge, understanding, off campus. Senior representatives of Throughout the academic year, the and social perspective. It is also these companies often visit Columbia to School hosts many activities and these Core courses that most closely lecture as adjunct faculty members or networking events to support its tie today’s student to the alumni of as guest speakers, and undergraduate active startup community, including centuries past. Through a shared and graduate students frequently the Columbia Engineering Fast Pitch exposure to the nontechnical areas, all undertake research or internships with Competition, Columbia Venture Columbia Engineering students—past, these and other companies, oftentimes Competition, Design Challenges, present, and future—gain the humanistic leading to offers of full-time employment Hackathons, and the Ignition Grants tools needed to build lives not solely as after graduation. program, which funds ventures started technical innovators, but as social and In addition to its ties to private by current students. political ones as well. industry, Columbia also has a historically An exciting way the School fosters close relationship with the public sector entrepreneurship is with its BiomedX of New York, stretching back to the Program. A major goal of the program A COLLEGE WITHIN THE eighteenth century. No other city in is to educate researchers, clinicians, UNIVERSITY the world offers as many impressive and students about the many aspects Combining the advantages of a small examples of the built environment— involved in commercializing biomedical college with the extensive resources the world’s most famous collection innovation. of a major research university, students of skyscrapers, long-span bridges, Entrepreneurship remains an at Columbia Engineering pursue their road and railroad tunnels, and one important central educational theme academic interests under the guidance of the world’s largest subway and at Columbia Engineering. The School of outstanding senior faculty members water supply systems. Involved in offers a range of programs and a who teach both undergraduate and all aspects of the city’s growth and 15-credit, interdisciplinary minor in graduate-level courses. Encouraged by capital improvements over the years, entrepreneurship made up of both the faculty to undertake research at all Columbia engineers have been Engineering and Business School levels, students at the School receive responsible for the design, analysis, and courses. The School also provides a the kind of personal attention that only maintenance of New York’s enormous four-year entrepreneurship experience Columbia’s exceptionally high faculty- infrastructure of municipal services and for all interested Columbia Engineering student ratio affords. communications links, as well as its students, regardless of major. great buildings, bridges, tunnels, and And for alumni, entrepreneurial monuments. support continues. The Columbia THE NEW YORK ADVANTAGE Startup Lab, a coworking facility located Besides the faculty, the single greatest in SoHo, provides subsidized space resource for students is without doubt THE UNIVERSITY AT LARGE for Columbia alumni entrepreneurs the City of New York. Within easy reach Columbia University occupies three to house and nurture their fledgling by walking, bus, subway, or taxi, New major campuses, as well as additional ventures. The Lab is the result of a York’s broad range of social, cultural, special-purpose facilities throughout unique partnership between the deans and business communities offer an the area. The main campus is located of Columbia College and the Schools unparalleled opportunity for students on the Upper West Side in Morningside of Business, Engineering, Law, and to expand their horizons or deepen Heights, and the Manhattanville International and Public Affairs. their understanding of almost any campus is the newest addition to human endeavor imaginable. With art Columbia University. This open and

ENGINEERING 2021–2022 environmentally sustainable campus architecture, business, the fine arts, and the Columbia Nano Initiative, 5 will grow over the next decade to journalism, law, and many other fields. established to serve as the hub for encompass more than 17 acres. Further multidisciplinary and collaborative uptown in Washington Heights is the research programs in nanoscale MANHATTANVILLE CAMPUS Columbia University Irving Medical science and engineering. Shared From Broadway and 125th Street West Center (CUIMC), which includes facilities and equipment to support nano to a revitalized Hudson River waterfront, Columbia’s College of Physicians and research at the Engineering School Columbia's 17-acre Manhattanville Surgeons, the Mailman School of Public include a state-of-the-art clean room campus is a welcoming environment of Health, the New York State Psychiatric in the Schapiro Center for Engineering publicly accessible open space, tree- Institute, College of Dental Medicine, and Physical Science Research (CEPSR) lined streets, neighborhood-friendly and School of Nursing. CUIMC is and a Transmission Electron Microscope retail, and innovative academic buildings the world’s first academic medical (TEM) Laboratory on the first floor of that invite community engagement. center, and opened in 1928 when Havemeyer. It is home to the Jerome L. Greene Columbia’s health-related schools and Founded in 2012 by Columbia Science Center, Columbia's Mortimer Presbyterian Hospital (now New York- Engineering, the Data Science Institute B. Zuckerman Mind Brain Behavior Presbyterian Hospital) moved to the also sits on the Morningside campus as Institute, the Lenfest Center for the Arts, Washington Heights location. Columbia a University-wide resource that spans and the University Forum, an event and Engineering’s Biomedical Engineering nine schools, including Journalism, the meeting space. Columbia Business Department has offices on both the Graduate School of Arts and Sciences, School is relocating to this campus, and Morningside campus and CUIMC. and the Columbia University Irving plans are underway to develop a new Beyond its schools and programs, Medical Center. The mission of the Data building here for Columbia Engineering, the measure of Columbia’s true breadth Science Institute is to train data science as well. These spaces house cutting- and depth must take into account its innovators and develop ideas for the edge research and teaching in brain internationally recognized centers and social good. science, an art gallery, screening room, institutions for specialized research. Details about specific programs’ and performance spaces, and space for These centers study everything from laboratories and equipment can be active community engagement. human rights to molecular recognition found in the sections describing those and hold close affiliations with Teachers programs. College, , the Juilliard COLUMBIA ENGINEERING School, and both the Jewish and Union Columbia Engineering (The Fu Columbia Engineering Computing Theological Seminaries. Columbia also Foundation School of Engineering Facilities maintains major off-campus facilities and Applied Science) occupies four The Botwinick Multimedia Learning such as the Lamont-Doherty Earth laboratory and classroom buildings Laboratory at Columbia University Observatory in Palisades, NY, and at the north end of the Morningside has redefined the way engineers are the in Irvington, campus, including the Northwest educated here. NY. Involved in many cooperative Corner Science and Engineering Designed with both education and ventures, Columbia also conducts Building, an interdisciplinary teaching interaction in mind, the lab provides ongoing research at such facilities as and research building. In this building students and instructors with: Brookhaven National Laboratory in researchers from across the University Upton, NY, and the NASA Goddard work together to create new areas • 48 desktops Institute for Space Studies located just of knowledge, in fields where the • A full set of professional-grade off the Morningside campus. biological, physical, and digital worlds engineering software tools fuse. This pandisciplinary frontier will • A collaborative classroom learning THE MORNINGSIDE HEIGHTS advance some of modern society’s environment CAMPUS most challenging problems in a wide range of sectors, from health to Columbia Engineering is located on The lab is utilized in some of the cybersecurity, from smart infrastructure Columbia’s Morningside campus. One School’s introductory first-year to the environment. of the handsomest urban institutions in engineering projects, as well as Supporting multiple programs the country, the 13.1 million gross square advanced classes in modeling and of study, the School's facilities are feet (gsf) of the Morningside campus animation, technology and society, designed and equipped to meet the comprise more than 200 buildings and entrepreneurship. laboratory and research needs of of housing; off-campus apartments both undergraduate and graduate and commercial buildings; recreation The Makerspace students. The School is also the site of and research facilities; centers for Columbia Engineering’s Makerspace an almost overwhelming array of basic the humanities and social and pure provides students with a dedicated and advanced research installations, sciences; and professional schools in place to collaborate, learn, explore, such as the Columbia Genome Center experiment, and create prototypes.

ENGINEERING 2021–2022 6 Students can utilize the space to work Commons and Blue Java Café comprise on a variety of innovative projects, 3,200 square feet with seating for including independent or group design 160 and areas for casual meetings, projects, product development, and individual and group work, and quiet new venture plans. This facility fosters study. Carleton Commons gives student creativity by bringing together students a dedicated and comfortable the workspace and tools for computer- space to gather, relax between classes, aided design, physical prototyping, or meet and work with one another fabric arts, woodworking, electronics, on problem sets or projects. The and software. new design also enables flexible and reconfigurable use of the space for Carleton Commons larger gatherings and special events. Located on the fourth floor (campus level) of the Mudd Building, Carleton

ENGINEERING 2021–2022 Undergraduate Studies 8 THE UNDERGRADUATE PROGRAMS

he undergraduate programs at While pursuing their own • provides information on Columbia Engineering not only interests, undergraduate students are preprofessional studies, major are academically exciting and encouraged to participate in a broad declaration, and completion of the Ttechnically innovative but also lead range of ongoing faculty research degree, as well as various leadership, into a wide range of career paths for projects encompassed by the Student career, graduate school, and research the educated citizen of the twenty-first Research Program. Students can apply opportunities century. Whether you want to become a for available research positions in • interprets and disseminates professional engineer, work in industry or Columbia Labs through the website at information regarding University government, or plan to pursue a career studentresearch.engineering.columbia. policies, procedures, resources, and in the physical and social sciences, edu. programs medicine, law, business, or education, In addition to in-depth exploration • educates and empowers students to Columbia Engineering will provide you of engineering and applied science, take responsibility in making informed with an unparalleled education. Columbia Engineering undergraduates decisions The School firmly believes explore the humanities and social • refers students to additional campus that students gain the most when sciences with Columbia College resources engineering is brought up front, early students through intellectually in the four-year curriculum. Therefore, challenging Core Curriculum courses Every undergraduate is assigned each first-year student takes the Art taught by the Faculty of Arts and an adviser from the Berick Center for of Engineering, which addresses the Sciences. These courses in art, Student Advising for the duration of his fundamental concepts of math and literature, music, major cultures, and or her undergraduate career. Generally, science in an engineering context, economics, among others, provide each matriculating student is assigned as well as nontechnical issues in students with a broad, intellectually to an advising dean, who is a liaison to professional engineering practice such disciplined, cultural perspective on the the department the student indicated as ethics and project management. times they live in and the work they do. as his or her first intended major on the Students in the Art of Engineering Columbia application. When a student choose a half-semester, hands-on James H. and Christine Turk Berick declares a major, a faculty member is project in one of the School’s nine Center for Student Advising also appointed to advise him or her undergraduate engineering disciplines, 403 Lerner Hall, MC 1201 for the next two years. Depending on followed by a half-semester general 212-854-6378 their chosen major, students may be project that changes each year. [email protected] assigned to a new advising dean who Depending on the project chosen, cc-seas.columbia.edu/csa is a CSA liaison to their department. students will solder, 3D print, laser Advising deans regularly refer students cut, simulate, design websites, and The James H. and Christine Turk to their academic departments to much more. These skills are further Berick Center for Student Advising receive expert advice about their developed as students progress toward (CSA) guides and supports engineering course selections. their senior year projects. Since the fall undergraduates at Columbia College of 2014, Columbia Engineering students and Columbia Engineering as they Preprofessional Advising have been able to utilize the School’s navigate their educations and lives at Preprofessional Advising is a brand new Makerspace, a collaborative Columbia University. Individually and specialized advising unit within the environment where students can collaboratively, each advising dean: James H. and Christine Turk Berick learn, explore, experiment, and create • provides individual and group Center for Student Advising. It is prototypes. academic advisement and counseling dedicated to providing information

ENGINEERING 2021–2022 and guidance to students who plan a Liberal Arts Core for global-core-requirement/) for a letter 9 career in law or the health professions, Columbia Engineering Students: grade. through individual advising, workshops, 27-Point Nontechnical Requirement 3. One of the following two courses: and other events related to professions This requirement provides a broad HUMA UN1121: Masterpieces of of law and health. Preprofessional liberal arts component that enhances Western art, or HUMA UN1123: advisers work closely with other CSA the Engineering professional curriculum Masterpieces of Western music (3 advisers to support students during their to help students meet the challenges points) undergraduate program of study. They of the twenty-first century. Our also provide extensive individualized students are destined to be leaders 4. ECON UN1105: Principles of econom- support to students and alumni through in their professions and will require ics. (This course can be satisfied their application process to professional sophisticated communication, planning, through Advanced Placement; see the schools. and management skills. The Committee Advanced Placement chart on page on Instruction established the School’s 12.) Note: Engineering students may not nontechnical requirement so that take any Barnard class as a substitute POLICY ON DEGREE for ECON UN1105. (4 points) REQUIREMENTS students would learn perspectives and principles of the humanities and social The Committee on Instruction and B. Elective Nontechnical Courses sciences as part of a well-rounded and faculty of The Fu Foundation School (9–11 points of credit) multiperspective education. Through of Engineering and Applied Science The following course listing by discussion, debate, and writing, review degree requirements and department specifies the Columbia students improve their abilities to curricula matters each year, and College, Barnard, or Columbia engage in ethical, analytic, discursive, the bulletin reflects these faculty Engineering courses that either fulfill and imaginative thinking that will prove recommendations and curricular or do not fulfill the nontechnical indispensable later in life. changes in its yearly reprinting. School requirement. policy requires students to fulfill all • Engineering students must take 16 to (Professional, workshop, lab, project, general degree requirements as stated 18 points of credit of required courses scientific, studio, music instruction, and in the bulletin of the first year of their in list A and 9 to 11 elective points master’s-level professional courses do matriculation into the School. Students chosen from the approved courses not satisfy the 27-point nontechnical declare their major during the first in list B. The total combined number requirement.) semester of their sophomore year. of nontechnical points (from lists A AFRICAN-AMERICAN STUDIES: All Requirements for the major or minor are and B, below) must add up to at least courses in accordance with the bulletin during 27. Neither list can be modified by AMERICAN STUDIES: All courses the year in which the student declares advising deans or faculty advisers. the major or minor. • Advanced Placement (AP) credit in ANCIENT STUDIES: All courses appropriate subject areas can be ANTHROPOLOGY: All courses in socio- THE FIRST-YEAR/SOPHOMORE applied toward the 9-point elective cultural anthropology PROGRAM nontechnical requirement and for All courses in archaeology except Principles of Economics. fieldwork Students entering Columbia Engineering No courses in biological/physical anthro- are encouraged to consider the wide A. Required Nontechnical Courses pology [UN1010, UN1011, UN3204, range of possibilities open to them, (16–18 points of credit) UN3940, GU4147-GU4148, GU4200, both academically and professionally. These courses must be taken at GU4700] To this end, the first and second Columbia. ARCHITECTURE: No courses years of the four-year undergraduate program comprise approximately half 1. ENGL CC1010: University writing (3 ART HISTORY AND ARCHEOLOGY: the total number of credits required for points) All courses the degree that expose students to a 2. One of the following two-semester ASIAN AMERICAN STUDIES: All courses cross-fertilization of ideas from different sequences: HUMA CC1001-CC1002: ASTRONOMY: No courses disciplines within the University. The Masterpieces of Western literature and sequence of study proceeds from an philosophy (All students registering for BIOLOGICAL SCIENCES: No courses engagement with engineering and this course should be prepared to dis- BUSINESS: No courses scientific fundamentals, along with cuss books 1–12 of the Iliad on the first CHEMISTRY: No courses humanities and social sciences, toward day of class) or COCI CC1101-CC1102: an increasingly focused training in the Introduction to contemporary civiliza- CLASSICS: All courses third and fourth years designed to give tion in the West or Global Core: Any COLLOQUIA: All courses students mastery of certain principles two courses from approved list (6–8 and arts central to engineering and points) If electing Global Core, students COMPARATIVE ETHNIC STUDIES: All courses applied science. must take two courses from the List of Approved Courses (bulletin.columbia. COMPARATIVE LITERATURE AND edu/columbia-college/core-curriculum/ SOCIETY: All courses

ENGINEERING 2021–2022 10 COMPUTER SCIENCE: No courses EEHS E3900 History of telecommunica- research tions GU4700 Math methods for political sci- CREATIVE WRITING: All courses ence (This is an exception to the workshop ENGLISH AND COMPARATIVE GU4765 Design and analysis of sample rule.) LITERATURE: All courses surveys DANCE: All courses except performance FILM STUDIES: All courses except lab GU4768 Experimental research: design, classes courses, and analysis, and interpretation UN3920 Senior seminar in screenwriting GU4710 Principles of quantitative political DRAMA AND THEATRE ARTS: All UN2400 The film medium: script analysis research courses except workshops, rehearsal, GU4711 Analysis of political data or performance classes, THTR BC2120 FRENCH AND ROMANCE PHILOLOGY: GU4712 Multivariate political analysis Technical production, THTR BC3135 All courses Set design, and THTR BC3134 Lighting PSYCHOLOGY: Only design GERMANIC LANGUAGES: All courses UN1001 The science of psychology GREEK: All courses UN2280 Introduction to developmental EARTH AND ENVIRONMENTAL psychology SCIENCES: No courses HISTORY: All courses All courses on perception, attention, EAST ASIAN LANGUAGES AND HISTORY AND PHILOSOPHY OF and cognition topics numbered 2200s, CULTURE: All courses SCIENCE: All courses 3200s, or 4200s can be taken as non- tech electives except for PSYC UN2235 ECOLOGY, EVOLUTION, AND HUMAN RIGHTS: All courses and UN4289. ENVIRONMENTAL BIOLOGY: No cours- All courses on social, personality, and ITALIAN: All courses es except EEEB GU4321 or GU4700 abnormal numbered 2600s, 3600s, or ECONOMICS: All courses except JAZZ STUDIES: All courses 4600s can be taken as nontech elec- tives. UN3025 Financial economics LATIN: All courses UN3211 Intermediate microeconomics RELIGION: All courses UN3213 Intermediate macroeconomics LATINO STUDIES: All courses SLAVIC LANGUAGES: All courses UN3412 Introduction to econometrics LINGUISTICS: All courses except CLLN UN3981 Applied econometrics GU4202 SOCIOLOGY: All courses except GU4020 Economics of uncertainty and SOCI UN3020 Social statistics information MATHEMATICS: No courses GU4211 Advanced microeconomics SPANISH AND PORTUGUESE: All MEDIEVAL AND RENAISSANCE GU4213 Advanced macroeconomics courses STUDIES: GU4251 Industrial organization All courses SPEECH: No courses GU4260 Marketing design GU4280 Corporate finance MIDDLE EASTERN AND ASIAN STATISTICS: No courses GU4301 Economic growth and develop- LANGUAGE AND CULTURES: All SUSTAINABLE DEVELOPMENT: No ment courses GU4412 Advanced econometrics courses MUSIC: All courses except performance GU4413 Econometrics of time series and URBAN STUDIES: All courses forecasting courses, instrument instruction courses, GU4415 Game theory and workshops VISUAL ARTS: No more than one course, which must be at the 3000 level or GU4505 International macroeconomics PHILOSOPHY: All courses except higher (This is an exception to the work- GU4526 Transition reforms, globalization, UN1401 Introduction to logic shop rule.) and financial crisis UN3411 Symbolic logic GU4911 Seminar in microeconomics GU4137 Nonclassical logics WOMEN AND GENDER STUDIES: All GU4913 Seminar in macroeconomics GU4431 Introduction to set theory courses GU4918 Seminar in econometrics GU4424 Modal logic BC1003 Introduction to economic CSPH GU4801 Mathematical logic I Music Instruction Courses reasoning (equivalent to ECON UN1105) CSPH GU4802 Incompleteness results BC1007 Mathematical methods for in logic Music instruction and performance economics GU4810 Lattices and Boolean algebras courses do not count toward the 128 BC2411 Statistics for economics Courses in logic points of credit required for a B.S. BC3014 Entrepreneurship degree. Please note that this includes PHYSICAL EDUCATION: No courses BC3018 Econometrics courses taken at Teachers College, BC3033 Intermediate macroeconomic PHYSICS: No courses Columbia College, and the School of theory BC3035 Intermediate microeconomic POLITICAL SCIENCE: All courses except the Arts. theory UN3220 Logic of collective choice BC3038 International money and finance UN3704 Data analysis and statistics for Visual Arts Courses political science research Students are allowed to take courses in EDUCATION: All courses UN3720 Scope and methods the Visual Arts Department for general GU4730 Game theory and political theory ENGINEERING: Only credit to be applied toward the B.S. BMEN E4010 Ethics for biomedical engi- GU4732 Research topics in game theory degree. However, no more than one neers GU4791 Advanced topics in quantitative CHEN E4020 Protection of industrial and research visual arts course, which must be taken intellectual property GU4792 Advanced topics in quantitative at the 3000 level or higher, may

ENGINEERING 2021–2022 count toward the nontechnical elective the diagnosis and treatment of disease. Medical (MEMS) and nanotechnology. The physical con- 11 requirement. This 3000 course is an imaging, medical devices: diagnostic and surgical cepts that govern the operation of these technolo- exception to the rule that no workshop instruments, drug delivery systems, prostheses, gies will be developed from basic principles and classes can fulfill the nontech elective artificial organs. Medical informatics and organiza- then applied in simple design problems. Students tion of the healthcare system. Current trends in will also be exposed to state-of-the art innova- requirement. biomedical engineering research. tions in each case study.

Technical Course Requirements CHEN E2100x Introduction to chemical engineering Professional Development and The prescribed First Year–Sophomore Serves as an introduction to the chemical engi- Leadership Program Program curriculum requires students neering profession. Students are exposed to The Professional Development and to complete a program of technical concepts used in the analysis of chemical engi- Leadership (PDL) program educates coursework introducing them to neering problems. Rigorous analysis of material students to maximize performance and five major areas of technical inquiry: and energy balances on open and closed systems achieve their full potential to become is emphasized. An introduction to important pro- engineering, mathematics, physics, engineering leaders. Core sessions chemistry, and computer science. cesses in the chemical and biochemical industries is provided. focus on development of skills and All first-year Engineering perspectives needed to compete and undergraduate students take ENGI CIEN E3000y The art of structural design succeed in a fast-changing technical E1102: The art of engineering (4 Basic scientific and engineering principles used climate. Topics include professional for the design of buildings, bridges, and other points). In this course, students see portfolio (resume, cover letter, business parts of the built infrastructure. Application of how their high school science and writing, social media presence), math knowledge can be applied in these principles to the analysis and design of a number of actual large-scale structures. History communication skills, leadership, ethics, an engineering context to solve real- of major structural design innovations and the life management (stress, sleep, and world problems through classroom engineers who introduced them. Critical examina- time management), and more. Elective presentations and participation in an tion of the unique aesthetic/artistic perspectives sessions include effective presentations, in-depth, hands-on project. Along inherent in structural design. Management, emotional intelligence, data the way, guest lecturers discuss socioeconomic, and ethical issues involved in the visualization, and interview preparation. social implications of technology, design and construction of large-scale structures. entrepreneurship, project management, Recent developments in sustainable engineering, Physical Education and other important nontechnical issues including green building design and adaptable structural systems. Two terms of physical education affecting the practicing engineer. (PHED UN1001 or PHED UN1002) are While students need not officially EAEE E2100x A better planet by design a degree requirement for Columbia commit to a particular branch of Introduction to design for a sustainable planet. Engineering students. No more than 4 engineering until the third semester, Scientific understanding of the challenges. points of physical education courses most programs recommend, and in Innovative technologies for water, energy, food, materials provision. Multiscale modeling may be counted toward the degree. some cases may require, that particular and conceptual framework for understanding The physical education requirement courses be taken earlier for maximum environmental, resource, human ecological, can be fulfilled with Barnard dance efficiency in program planning. and economic impacts and design performance, studio/technique courses. A student For information concerning these evaluation. Focus on linkages between planetary, who intends to participate in an requirements, students should turn to regional, and urban waste, energy, mineral, food, intercollegiate sport should register the individual program sections in this climate, economic, and ecological cycles. Solution for the appropriate section of PHED bulletin. strategies for developed and developing country settings. UN1005: Intercollegiate athletics. Intercollegiate athletes who attend ELEN E1201x and y Introduction to electrical Professional Development regularly receive 1 point of credit up to Professional-Level Courses engineering Basic concepts of electrical engineering. a maximum of 4. Student-athletes who The courses listed below may be Exploration of selected topics and their applica- leave the team in mid-term but still wish taken by first- and second-year tion. Electrical variables, circuit laws, nonlinear to receive academic credit must notify students. Some departments require and linear elements, ideal and real sources, trans- the Physical Education Office and be one of these courses; please consult ducers, operational amplifiers in simple circuits, placed in another physical education with departmental charts for more external behavior of diodes and transistors, first activity to complete the attendance information. order RC and RL circuits. Digital representation of requirement. Students who are advised a signal, digital logic gates, flip-flops. A lab is an Each course serves as an to follow a restricted or adapted activity integral part of the course. introduction to the area of study and is program should contact the Director taught by department faculty. MECE E1001x Mechanical engineering: of Physical Education and Recreation. The courses are: micro-machines to jumbo jets The physical education program offers Not offered in 2021–2022. a variety of activities in the areas of BMEN E1001x Engineering in medicine The role of mechanical engineering in developing aquatics, fitness, martial arts, individual Not offered in 2021–2022. many of the fundamental technological advances The present and historical role of engineering in on which today’s society depends. Topics include and dual sports, team sports, and medicine and healthcare delivery. Engineering airplanes, automobiles, robots, and modern outdoor education. Most activities are approaches to understanding organismic and manufacturing methods, as well as the emerg- designed for the introductory/beginner cellular function in living systems. Engineering in ing fields of micro-electro-mechanical machines levels. Intermediate/advanced courses

ENGINEERING 2021–2022 12 Advanced Placement Credit Chart In order to receive AP credit, students must be in possession of appropriate transcripts or scores and send official score reports to Columbia. The CEEB code is 2116. AP AP Subject Score Credit Requirements or Placement Status Credit Art History 5 3 No exemption from HUMA UN1121 Biology 5 3 No exemption Chemistry 4 or 5 3 Requires completion of CHEM UN1604 with grade of or better 4 or 5 6 Requires completion of CHEM UN2045-UN2046 with grade of C or better Computer Science A 4 or 5 3 Exemption from COMS W1004 Principles 4 or 5 3 Exemption from COMS W1001 Economics Micro & Macro 5 and 4 4* Exemption from ECON UN1105. Exams must be taken in both micro and macro, with a score of 5 in one and at least a 4 in the other. English Language and Composition 5 3 No exemption Literature and Composition 5 3 No exemption French Language 4 or 5 3 Literature 4 or 5 3 German Language 4 or 5 3 Government and Politics United States 5 4* Exemption from POLS UN1201. Comparative 5 4* Exemption from POLS UN1501. History European 5 3 United States 5 3 Italian Language 4 or 5 3 Latin Literature 5 3 Mathematics Calculus AB 4 or 5 3 Requires completion of MATH UN1102 with a grade of C or better. Credit is reduced to 0 if MATH UN1101 is taken. Calculus BC 4 3 Requires completion of MATH UN1102 with a grade of C or better. Credit is reduced to 0 if MATH UN1101 is taken. Calculus BC 5 6 Requires completion of APMA E2000 with a grade of C or better. Credit is reduced to 0 if MATH UN1101 is taken, or to 3 if MATH 1102 is taken. Physics Maximum of six credits. 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 is taken and the final grade is C- or lower. 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 is taken and the final grade is C- or lower. Physics 1 and 2 4 or 5 3 No exemption. Both AP Physics 1 and 2 must be taken to receive credit. Spanish Language 4 or 5 3 Literature 4 or 5 3 *AP credits may be applied toward minor requirements depending on the specific rules of the minor. When the rules of the minor allow AP credit to fulfill a requirement, then only one course for a minor may be replaced by advanced placement credit. **Columbia Engineering students with a 4 or 5 on Calculus AB or a 4 on Calculus BC must begin with MATH UN1101 (Calculus I) or MATH UN1102 (Calculus II). If a Columbia Engineering student with these scores goes directly into APMA E2000 (Multivariable Calculus), he or she will have to go back and complete MATH UN1102 (Calculus II). Students with A-level or IB calculus credit must start with MATH UN1102 (Calculus II).

ENGINEERING 2021–2022 are indicated on the schedule. British Advanced Level Examinations choose technical electives or courses in 13 The majority of the activities are Students with grades of A or B on their major. offered in ten time preferences. British Advanced Level examinations It is essential that students begin Additionally, there are early-morning may be granted 6 points of credit if the planning as early as possible. Students conditioning activities, Friday-only examinations were taken in disciplines are encouraged to meet with advisers classes at Baker Athletics Complex, and offered as undergraduate programs at in the Center for Undergraduate Global special courses that utilize off-campus Columbia University. The appropriate Engagement to review possible global facilities during weekends and vacation transcript should be submitted to the opportunities. Students must obtain periods. The courses offered by the James H. and Christine Turk Berick approval from their departmental department for each term are included Center for Student Advising, 403 Lerner. advisers to ensure that their work in the online Directory of Classes, and abroad meets the requirements of their a description of the scheduled activities Other National Systems majors, as well as clearance from their Advising Dean in the James H. and for each time preference is posted on Students whose secondary school work Christine Turk Berick Center for Student perec.columbia.edu. Students may only was in other national systems, such Advising. register for one section of physical as the French Baccalauréat, may be education each term. granted credit in certain disciplines for sufficiently high scores. The appropriate Eligibility Requirements Advanced Placement transcript should be submitted to the In order to participate in a semester- Prior to entering Columbia, students James H. and Christine Turk Berick long or yearlong study-abroad program, may have taken Advanced Placement Center for Student Advising, 403 Lerner. students must: examinations through the College • Be an enrolled student in good Entrance Examination Board (CEEB) in academic and disciplinary standing a number of technical and nontechnical STUDY ABROAD • Have at least a 3.0 GPA areas. A maximum of 16 points may Engineering today is a global • Be making adequate progress toward be applied. Students may be assigned profession. Study abroad allows finishing the first and second year to an advanced-level course in engineering students to discover requirements mathematics or physics based on their the field through the perspective • Have declared a major AP scores. of engineers working in a different In the required pure science areas, language and culture, enabling them Finances the number of advanced placement to learn the relationship of culture • Fall/spring (academic year) academic credits awarded to students to science and develop the range • Billed by Columbia: tuition and of engineering and applied science of transferable skills that employers health insurance varies from the levels awarded for are seeking today. Study abroad will • Billed by abroad institution/external liberal arts programs, notably in help students develop intellectually, vendors: room, board, living and mathematics, physics, chemistry, and emotionally, culturally, and socially. travel expenses computer science. The benefit of Columbia Engineering • Still eligible for financial aid advanced placement is acceleration undergraduate students can study • Summer through certain First Year–Sophomore abroad for either a semester (fall, spring, • Student pays most expenses Program requirements and thus the or summer) or, exceptionally, for a full directly to the program and opportunity of taking specialized academic year. Students from every external vendors courses earlier. engineering major have studied abroad, • Not eligible for financial aid Each year the School reviews the and most do so in the spring semester of their sophomore year or in their CEEB advanced placement curriculum Academic Credit junior year. Although not a requirement, and makes determinations as to • Students in Columbia-sponsored appropriate placements, credit, and/or students are encouraged to have some foreign language skills in order to programs receive direct Columbia exemption. Please see the Advanced credit, and the courses and grades Placement Credit Chart on p. 12. enhance their cultural competency and their overall study abroad experience. appear on students' academic The Center for Undergraduate transcripts. International Baccalaureate (IB) Global Engagement will help students • Credit from approved programs Entering students may be granted 6 identify the appropriate choice for their that are not Columbia sponsored is points of credit for each score of 6 or 7 country of interest and their major. certified as transfer credit toward the on IB Higher Level Examinations if taken Undergraduate Student Affairs advisers Columbia degree upon successful in disciplines offered as undergraduate and departmental advisers will help completion of the program verifiable programs at Columbia. Students should students with their course equivalencies by academic transcript. Students consult their adviser at the James H. for approved programs so they can must earn a grade of C or better in and Christine Turk Berick Center for graduate on time. Students can take order for credits to be transferred. Student Advising for further clarification. nontechnical electives overseas, or Course titles and grades for approved with departmental permission, they may programs do not appear on the Columbia transcript, and grades are

ENGINEERING 2021–2022 14 not factored into students' GPAs. college before entering the School THE JUNIOR-SENIOR • Faculty from the Columbia of Engineering and Applied Science. PROGRAMS Engineering academic departments They then must complete all the Students may review degree progress have the responsibility to assess requirements for the B.S. degree within via DARS (Degree Audit Reporting all work completed abroad and four consecutive semesters. System) as presented on Student make decisions about how these Services Online. Required courses courses fit into major requirements. The Combined Plan Program within that are not completed are detailed as It is imperative that students gain Columbia University deficiencies and must be completed course-by-course approval from their Under this plan, the pre-engineering during summer session or carried as department prior to departure on a student studies in Columbia College, overload courses in later semesters. study-abroad program. Barnard College, or the School of Having chosen their program General Studies for three or four years, major in the second semester of Deadlines then attends The Fu Foundation School their sophomore year, students are • Early October: to study abroad during of Engineering and Applied Science for assigned to a faculty adviser in the the spring semester two years, and is awarded the Bachelor department in which the program is • Early to mid-March: to study abroad of Arts degree and the Bachelor of offered. In addition to the courses during the fall semester or for year- Science degree in engineering upon required by their program, students long trips completion of the fifth or sixth year. This must continue to satisfy certain • Early May: to study abroad during the program is optional at Columbia, but the distributive requirements, choosing summer term School recommends it to all students elective courses that provide sufficient who wish greater enrichment in the content in engineering sciences For more information on study liberal arts and pure sciences. and engineering design. The order abroad, students should contact: and distribution of the prescribed coursework may be changed with the Center for Undergraduate Global The Combined Plan with Other adviser’s approval. Specific questions Engagement Affiliated Colleges concerning course requirements should 606 Kent Hall, MC 3948 There are more than one hundred be addressed to the appropriate 1140 Amsterdam Avenue affiliated liberal arts colleges, including department or division. The Vice Dean’s New York, NY 10027 those at Columbia, in which a student concurrent approval is required for all 212-854-2559 can enroll in a Combined Plan program waivers and substitutions. [email protected] leading to two degrees. Each college uge.columbia.edu requires the completion of a specified curriculum, including major and Double Major SEAS Undergraduate Student Affairs degree requirements, to qualify for Students who wish to apply for a [email protected] the baccalaureate from that institution. second major must consult their Every affiliated school has a liaison advising dean about next steps. A officer who coordinates the program proposal to double major must be COMBINED PLAN PROGRAMS at his or her home institution. Students approved by both departments and Undergraduate Admissions interested in this program should inform then forwarded to the Vice Dean for 212 Hamilton Hall, MC 2807 the liaison officer as early as possible, Undergraduate Programs for a final 1130 Amsterdam Avenue preferably in the first year, in order to decision. New York, NY 10027 receive guidance about completing Courses cannot be cross-counted 212-854-2522 program requirements. Applicants from between dual majors. Please consult [email protected] nonaffiliated schools are welcome to with an adviser and the respective undergrad.admissions.columbia.edu/ apply. departments to find alternative courses apply/combined-plan Visit the Undergraduate Admissions for duplicate requirements. website for a complete list of affiliated 3-2 students are not eligible to have Columbia Engineering maintains schools, admission application a second major because of the time cooperative program relationships with instructions, information on financial constraints of their program. institutions nationwide and with other aid, and curriculum requirements for Columbia University undergraduate Combined Plan program admission. Beta Pi divisions. The Combined Plan programs Please note that no change of major is Tau Beta Pi is the nation’s second- (3-2 and 4-2) allow students to receive allowed after an admission decision has oldest honor society, founded at a degree both in the liberal arts been rendered. Lehigh University in 1885. With the and in engineering. Combined Plan See page 23 for information on the creed “Integrity and excellence in students complete the requirements 4-2 Master of Science Program, which engineering,” it is the only engineering for the liberal arts degree along with is administered through the Office of honor society representing the entire required prerequisite coursework for Graduate Student Affairs. engineering profession. Columbia’s their studies in engineering during the chapter, New York Alpha, is the ninth three or four years at their liberal arts oldest and was founded in 1902. Many

ENGINEERING 2021–2022 15

Columbia buildings have been named subject to the following conditions: (1) requirements by taking at least 60 for some of the more prominent chapter the course must be accepted as part points of credit while enrolled in The Fu alumni: Charles Fredrick Chandler, of an approved graduate program of Foundation School of Engineering and Michael Idvorsky Pupin, Augustus study; (2) the course must not have Applied Science. Courses may not be Schermerhorn, and, of course, Harvey been used to fulfill a requirement repeated for credit unless it is stated Seeley Mudd. for the B.S. degree and must be so otherwise in the course description. Undergraduate students whose certified by the Dean; and (3) the The bachelor’s degree in scholarship places them in the top amount of graduate credit earned by engineering and applied science eighth of their class in their next-to-last an undergraduate cannot exceed 15 earned at Columbia University prepares year or in the top fifth of their class points. Undergraduates may not take students to enter a wide range of in their last college year are eligible CVN courses. professions. Students are, however, for membership consideration. These encouraged to consider graduate scholastically eligible students are The Bachelor of Science Degree work, at least to the master’s degree further considered on the basis of Students who complete a four-year level, which is increasingly considered personal integrity, breadth of interest sequence of prescribed study are necessary for many professional both inside and outside engineering, awarded the Bachelor of Science careers. adaptability, and unselfish activity. degree. The general requirement for The Engineering Accreditation Benefits of membership include the Bachelor of Science degree is Commission (EAC) of ABET, an exclusive scholarships and fellowships. the completion of a minimum of 128 organization formed by the major Many networking opportunities for jobs academic credits with a minimum engineering professional societies, and internships are also available, with cumulative grade-point average (GPA) accredits university engineering 230 collegiate chapters and more than of 2.0 (C) at the time of graduation. programs on a nationwide basis. 500,000 members in Tau Beta Pi. The program requirements, specified Completion of an accredited program elsewhere in this bulletin, include of study is usually the first step toward Taking Graduate Courses as an the first-year–sophomore course a professional engineering license. Undergraduate requirements, the major departmental Advanced study in engineering With the faculty adviser’s approval, a requirements, and technical and at a graduate school sometimes student may take graduate courses nontechnical elective requirements. presupposes the completion of an while still an undergraduate in the Students who wish to transfer points accredited program of undergraduate School. Such work may be credited of credit may count no more than 68 study. toward one of the graduate degrees transfer points toward the degree and The following undergraduate offered by the Engineering Faculty, must satisfy the University’s residence programs are accredited by the EAC

ENGINEERING 2021–2022 16 of ABET: biomedical engineering, of most professional schools. • One year of organic chemistry and chemical engineering, civil engineering, Undergraduate students should, organic chemistry lab earth and environmental engineering, however, make careful inquiry into the • One year of introductory biology and electrical engineering, and mechanical kinds of specific preparatory work that biology lab engineering. may be required for admission into • One semester of biochemistry highly specialized programs such as • One year of general physics and Minors medicine. physics lab Columbia Engineering undergraduates • One semester of introductory may choose to add minors to their Premed psychology programs. This choice should be made Medical, dental, and other health in the fall of their sophomore year, when professional schools prefer that As you prepare for this path, you they also decide on a major. undergraduates complete a four-year should consult regularly with both In considering a minor, students program of study toward the bachelor's your assigned adviser and one of must understand that not all minors are degree. All health professional schools the premedical advisers in the James available to all students. In addition, require prerequisite coursework, but H. Christine Turk Berick Center for the School cannot guarantee that a they do not prefer one type of major or Student Advising. These individuals selected minor can be completed within scholarly concentration. Students with will help to guide you in your course the usual residence period needed all types of engineering backgrounds selection and planning, and introduce for a major. Indeed, students choosing are highly valued. you to extracurricular and research minors should expect to encounter It is important to note, however, opportunities related to your interests scheduling difficulties. The potential for that each medical school in the in health and medicine. Preprofessional the successful completion of a minor United States and Canada individually Advising maintains an online list of many depends on the student’s major and determines its own entrance different clinical volunteer and research the minor chosen, as well as the course requirements, including prerequisite opportunities across New York City and schedules and availability, which may coursework and/or competencies. beyond. Exploration of the career and change from year to year. The list of Each medical school also sets its own sustained interactions with patients is minors, as well as their requirements, rules regarding acceptable courses viewed by many medical schools as appear on pages 203–208. or course equivalents. It is therefore essential preparation, and therefore essential that students plan early and students are strongly encouraged to confirm the premedical requirements spend time volunteering/working in PROGRAMS IN PREPARATION for those schools to which they intend clinical and research environments FOR OTHER PROFESSIONS to apply. The Engineering curriculum before applying to medical school. James H. and Christine Turk Berick covers many of the prerequisite Students must apply for admission Center for Student Advising courses required by medical schools; to health professional schools more 403 Lerner Hall, MC 1201 however, in addition to completing the than one year in advance of the entry 212-854-6378 mathematics, chemistry, and physics date. Students who are interested in [email protected] courses required by the First Year– going directly on to health professional cc-seas.columbia.edu/preprofessional/ Sophomore Program, most schools ask schools following graduation should for a full year of organic chemistry, a full complete all prerequisite courses The Fu Foundation School of year of biology, a full year of English, a required for the MCAT by the end of Engineering and Applied Science semester of statistics, and a semester the junior year. It is entirely acceptable prepares its students to enter any of biochemistry. Advanced Placement (and most common) for students to number of graduate programs and credit is accepted in fulfillment of these take time between undergraduate and professions outside of what is generally requirements by some schools but health professional school and thus thought of as the engineering field. In not all. Students are responsible for delay application to these schools for an increasingly technological society, monitoring the requirements of each one or more years. Students planning where the line between humanities school to which they intend to apply. to apply to medical or dental school and technology is becoming blurred, Generally, students with Advanced should be evaluated by the Premedical individuals with a thorough grounding Placement credit are strongly advised to Advisory Committee prior to application. in applied mathematics and the take further courses in the field in which A Premedical Advisory Committee physical and engineering sciences they have received such credit. application is made available each year find themselves highly sought after as In addition to medical school in December. For more information professionals in practically all fields of requirements, all medical schools regarding this process and other endeavor. currently require applicants to sit for premedical-related questions, please Engineering students interested in the Medical College Admissions Test consult with a premedical adviser in pursuing graduate work in such areas (MCAT). The recommended preparation the Berick Center for Student Advising as architecture, business, education, for this exam is: or peruse its website: www.cc-seas. journalism, or law will find themselves • One year of general chemistry and columbia.edu/preprofessional/health/. well prepared to meet the generally general chemistry lab flexible admissions requirements

ENGINEERING 2021–2022 Prelaw in the area of the certification sought: courses; and the successful completion 17 Students fulfilling the School of chemistry, biology, physics, or earth of any prerequisites for the College Engineering and Applied Science’s science. major or concentration. Students apply curriculum are well prepared to apply The deadline for application, at the end of their junior year at the to and enter professional schools of which includes an essay and letters of School; to be admitted to the program, law, which generally do not require any recommendation, is the first Monday in the student needs to have a plan in specific prelaw coursework. Schools of March of the student’s sophomore year. place to complete the College major or law encourage undergraduate students This allows program faculty to support concentration by the end of their fifth to complete a curriculum characterized students through program planning year. by rigorous intellectual training involving to ensure that students can meet the Interested students should relational, syntactical, and abstract requirements for certification. However, contact their advising dean for further thinking. While selecting courses, keep when space allows, applications will information. in mind the need to hone your writing be considered through the fall of the junior year. Applications from juniors skills, your communication skills, and School of International and Public are due no later than the first Monday your capacity for logical analysis. Affairs While engineering students may find in October. Students who plan to The Fu Foundation School of interests in many areas of the law, for study abroad during the spring of their Engineering and Applied Science and intellectual property and patent law, a junior year should apply during the the School of International and Public science and technology background will fall semester of their sophomore year. Affairs offer a joint program enabling a be greatly valued, if not essential. Students should decide on their interest in teacher certification by the end of the small number of students to complete the requirements for the degrees of Urban Teaching: New York State first year in order to start coursework in the sophomore year. Bachelor of Science and Master of Initial Certification in Adolescence International Affairs in five years instead Education Grades 7–12 for Teachers of six. Not only an excellent academic of Mathematics and the Sciences or JOINT PROGRAMS record but also maturity, fluency in in Elementary Education Grades 1–6 The 4-1 Program at Columbia an appropriate foreign language, and Barnard College Education Program College pertinent experience will determine 335-336 Milbank Hall admission to this program. For more Students who are admitted as first-year 3009 Broadway information, please contact your students to the School of Engineering New York, NY 10027 advising dean. and Applied Science and subsequently 212-854-7072 complete the four-year program for education.barnard.edu the Bachelor of Science degree have UNDERGRADUATE ADMISSIONS the opportunity to apply for admission The Barnard Education Program Undergraduate Admissions to either Columbia College or Barnard provides courses leading to certification 212 Hamilton Hall, MC 2807 College and, after one additional to teach in New York State (with 1130 Amsterdam Avenue year of study, receive the Bachelor reciprocal agreements with 41 other New York, NY 10027 of Arts degree. The fifth year of study states) at either the elementary 212-854-2522 commences in the fall semester, and or secondary level. Students gain [email protected] students are required to conclude their experience and develop skills in undergrad.admissions.columbia.edu studies while enrolled for two full-time urban school classrooms. Required semesters. coursework includes psychology and For information about undergraduate The program is selective, and education, a practicum, and student admissions, please visit the admission is based on the following teaching, totaling 23–26 points of credit Undergraduate Admissions website or factors: granting of the B.S. at Columbia depending on the level of certification contact the office by phone or email. Engineering at the end of the fourth sought. year; fulfillment of the College Core Certification to teach mathematics requirements by the end of the fourth requires 36 points in mathematics. Pure year at the School; a minimum GPA science courses required are: 36 points of 3.0 in the College Core and other in the sciences, of which 18 must be

ENGINEERING 2021–2022 18 UNDERGRADUATE TUITION, FEES, AND PAYMENTS

he 2021–2022 tuition and fees TUITION HEALTH INSURANCE are estimated. Tuition and fees Undergraduate students enrolled in The Columbia University offers the Student are prescribed by statute and are Fu Foundation School of Engineering Medical Insurance Plan, which provides subjectT to change at the discretion of and Applied Science pay a flat tuition both Basic and Comprehensive levels the Trustees. charge of $30,257 per term, regardless of coverage. Full-time students are University charges such as tuition, of the number of course credits taken. automatically enrolled in the Basic fees, and residence hall and meal plans Postgraduate special students and level of the Plan and billed for the are billed in the first Student Account degree candidates enrolled for a insurance premium in addition to the Statement of the term, which is sent ninth term are billed according to the Health Service fee. Visit the Columbia out in July and December of each year per-point system; the per-point cost is Health website at health.columbia. for the upcoming term. This account is $2,022. edu for detailed information about payable and due in full on or before the medical insurance coverage options payment due date announced in the and directions for making confirmation, MANDATORY FEES Statement, typically at the end of August enrollment, or waiver requests. or early January before the beginning Orientation fee: $485 (one-time charge of the billed term. Any student who in the first term of registration) does not receive the first Student Student Life fee: $843 fall / $927 spring PERSONAL EXPENSES Account Statement is expected to pay Health and Related Services fee: Students should expect to incur at registration. $623 per term miscellaneous personal expenses for If the University does not receive International Services charge: such items as clothing, linen, laundry, the full amount due for the term on or $120 per term (international students dry cleaning, and so forth. Students before the payment due date of the only) should also add to the above expenses first Statement, a late payment charge Document fee: $105 (one-time charge) the cost of two round trips between of $150 will be assessed. An additional home and the University to cover travel during the summer and the month-long, charge of 1.5 percent per billing cycle OTHER FEES may be imposed on any amount past midyear break. Application and late fees: The University advises students to due thereafter. • Application for undergraduate Students with an overdue account open a local bank account upon arrival admission: $85 in New York City. Since it often takes as balance may be prohibited from • Application for undergraduate transfer registering, changing programs, or long as three weeks for the first deposit admission: $85 to clear, students should plan to cover obtaining a diploma or transcripts. In • Late registration fee during late the case of persistently delinquent immediate expenses using either a registration: $50; credit card, traveler’s checks, or cash accounts, the University may utilize the after late registration: $100 services of an attorney and/or collection draft drawn on a local bank. Students agent to collect any amount past due. are urged not to arrive in New York Books and course materials: Depends without sufficient start-up funds. If a student’s account is referred for upon course collection, the student may be charged an additional amount equal to the cost Laboratory fees: See course listings LABORATORY CHARGES of collection, including reasonable Students may need to add another attorney’s fees and expenses incurred Room and board (estimated): $15,450 $100 to $300 for drafting materials or by the University. laboratory fees in certain courses. Each student taking laboratory courses must

ENGINEERING 2021–2022 furnish, at his or her own expense, the TUITION AND FEE REFUNDS Refunds will be credited in the following 19 necessary notebooks, blank forms, and Students who make a complete order: similar supplies. In some laboratory withdrawal from a term are assessed Federal Unsubsidized Stafford Loans courses, a fee is charged to cover a withdrawal fee of $75. Late fees, Federal Stafford Loans expendable materials and equipment application fees, withdrawal fees, tuition Federal Perkins Loans maintenance. Students engaged in deposits, special fees, computer fees, Federal PLUS Loans (when disbursed special tests, investigations, theses, or special examination fees, and transcript through the University) research work are required to meet fees are not refundable. Federal Pell Grants the costs of expendable materials as The Health Service Fee, Health Federal Supplemental Educational may be necessary for this work and in Insurance Premium, University facilities Opportunity Grants accordance with such arrangements as fees, and student activity fees are not Other Title IV funds may be made between the student and refundable. the department immediately concerned. Students who withdraw within the Withdrawing students should be first 60 percent of the academic period aware that they will not be entitled to any portion of a refund until all DAMAGES are subject to a refund calculation, which refunds a portion of tuition Title IV programs are credited and all All students will be charged for damage based on the percentage of the term outstanding charges have been paid. to instruments or apparatus caused by remaining after the time of withdrawal. their carelessness. The amount of the This calculation is made from the charge will be the actual cost of repair, date the student’s written notice of and, if the damage results in total loss of withdrawal is received by the Dean’s the apparatus, adjustment will be made Office. in the charge for age or condition. To ensure that there may be no question as to the liability for damage, students Percentage Refund for Withdrawal should note whether the apparatus is during First Nine Weeks of Term in good condition before use and, in Prorated for calendars of a different case of difficulty, request instruction in duration: its proper operation. Where there is 1st week 100% danger of costly damage, an instructor 2nd week 100% should be requested to inspect the 3rd week 90% apparatus. Liability for breakage will be 4th week 80% decided by the instructor in charge of 5th week 70% the course. 6th week 60% When the laboratory work is done 7th week 50% by a group, charges for breakage will 8th week 40% be divided among the members of the 9th week and after 0% group. The students responsible for any damage will be notified that a charge is For students receiving federal student being made against them. The amount aid, refunds will be made to the federal of the charge will be stated at that time aid programs in accordance with or as soon as it can be determined. Department of Education regulations.

ENGINEERING 2021–2022 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 federal SAP regulations. To be eligible 2920 Broadway visas by the United States, or who are for Federal Student Aid (Federal Pell Mailing: 100 Hamilton Hall, MC 2802 undocumented students in the United Grant, Federal SEOG, Federal Work- 1130 Amsterdam Avenue States are considered for admission in 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 student must meet or exceed the SAP not apply for financial aid in their standards set by his or her school or Phone: 212-854-3711 first year are not eligible to apply for program at the time SAP is assessed. Fax: 212-854-5353 financial aid in any subsequent years. The SAP policy may be found online at [email protected] Foreign transfer candidates applying sfs.columbia.edu/central-sap-policy. cc-seas.financialaid.columbia.edu for aid must understand that such aid is awarded on an extremely limited Columbia is committed to meeting basis. Columbia does not give any the full demonstrated financial need scholarships for academic, athletic, or for all applicants admitted as first-year artistic merit. students or transfer students pursuing Please visit the Financial Aid website their first degree. Financial aid is at cc-seas.financialaid.columbia.edu/ available for all four undergraduate for more information on financial aid, years, provided that students continue including requirements and application to demonstrate financial need. instructions.

ENGINEERING 2021–2022 Graduate Studies 22 THE GRADUATE PROGRAMS

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

ENGINEERING 2021–2022 subjects. Accordingly, Master of Science the development of academic, research, (FE) exam if their undergraduate degree 23 programs may include from 35 to 45 and professional skills. Students will also is not in engineering or a related points and may require three terms for have the opportunity to participate in field. Students should also check with completion. Doctoral research credits small group communication workshops individual state boards to determine cannot be used toward M.S. degree for doctoral students and individualized eligibility requirements for employment. requirements. coaching tailored to their specific goals. Please contact the Office of All degree requirements must be Doctoral students will be enrolled Graduate Student Affairs, The Fu completed within five years of the in ENGI E6001–6004 and should Foundation School of Engineering and beginning of graduate study. Under consult their program for specific PDL Applied Science, 530 S. W. Mudd, MC extraordinary circumstances, a written requirements. 4718, 500 West 120th Street, New York, request for an extension of this time NY 10027; you should also contact limit may be submitted to the student’s The 4-2 Master of Science Program your home institution’s Combined Plan department for approval by the The 4-2 Master of Science Program liaison for program information. You department chair and the Assistant provides the opportunity for students may, in addition, email questions to Dean. A minimum cumulative grade- holding bachelor’s degrees from [email protected]. point average of 2.5 is required for the affiliated liberal arts colleges (see the M.S. degree. A student who, at the end listing under the heading The Combined Dual Degree Program with the of any term, has not attained the grade- Plan Program with Other Affiliate School of Journalism in Computer point average required for the degree Colleges) with majors in mathematics, Science may be asked to withdraw. physics, chemistry, or certain other The Graduate School of Journalism and After the first semester of enrollment, physical sciences to receive the M.S. the Engineering School offer a dual an M.S. student may submit an degree after two years of study at degree program leading to the degrees application to apply and transfer to Columbia in the following fields of of Master of Science in Journalism and another academic program. If the engineering and applied science: the Master of Science in Computer student is not successful with the biomedical, chemical, civil, computer Science. (See Computer Science.) application process, then he or she science, earth and environmental, must make sure requirements for electrical, industrial, and mechanical Joint Program with the School of the original academic program are engineering; applied physics; applied Business in Industrial Engineering completed. mathematics; engineering mechanics; The Graduate School of Business operations research; and materials and the Engineering School offer a Professional Development science. joint program leading to the degrees Leadership M.S. Requirement Each applicant must produce of Master of Business Administration (ENGI E4000) evidence of an outstanding and Master of Science in Industrial The Professional Development and undergraduate record, including Engineering. (See Industrial Engineering Leadership (PDL) program educates superior performance in physics and Operations Research.) students to maximize performance and and mathematics through differential equations. The program of study will achieve their full potential to become Master of Science in Data Science engineering leaders. The core modules be individually designed in consultation Offered by the Engineering School focus on development of professional with a faculty adviser and will integrate (jointly between the Department of skills and perspectives needed to undergraduate work with the field of Computer Science and the Department succeed in a fast-changing technical engineering or applied science the of Industrial Engineering and Operations climate. student chooses to follow. During Research), in partnership with the M.S. students must complete the first year, the program will consist Graduate School of Arts and Sciences the professional development and primarily of basic undergraduate (the Department of Statistics), the M.S. in leadership course, ENGI E4000, as a courses; during the second year, of Data Science allows students to apply graduation requirement. graduate courses in the selected field. data science techniques to their field of The student must complete at least 30 interest. credits of graduate study to qualify for Professional Development Candidates for the Master of the degree. Leadership Doctoral Requirement Science in Data Science are required A student whose background may (ENGI E6001–6004) to complete a minimum of 30 graduate- require supplementary preparation in The Professional Development and level credits, which includes seven some specific area, or who has been Leadership (PDL) program educates required courses: Algorithms for Data out of school for a considerable period, students to maximize performance Science, Machine Learning for Data will have to carry a heavier than normal and achieve their full potential during Science, Exploratory Data Analysis and course load or extend the program and after the doctoral program. The Visualization, Probability and Statistics beyond two years. goal is to cultivate future scholars and for Data Science, Statistical Inference & Graduates of the 4-2 Master of leaders in their respective fields. The Modeling, Computer Systems for Data Science program may not be eligible to modules are tailored for each stage of Science, and Data Science Capstone take the Fundamentals of Engineering the doctoral program, with a focus on & Ethics. A minimum of 9 credits of

ENGINEERING 2021–2022 24 elective coursework are chosen in DOCTORAL DEGREES: a candidate for the Ph.D. degree. consultation with the student's adviser ENG.SC.D. AND PH.D. Application for admission as a doctoral and should be technical in nature and Two doctoral degrees in engineering candidate may be made while a student must be a 4000-level graduate course are offered by the University: the Doctor is enrolled as a master’s degree or higher that expands the student's of Engineering Science, administered candidate. Candidates for the Ph.D. expertise in data science. M.S. students by The Fu Foundation School of degree must register full time and must complete the professional Engineering and Applied Science, and complete six Residence Units. The development and leadership course, the , administered minimum requirement in coursework ENGI E4000, as a graduation by the Graduate School of Arts and for the doctoral degree is 60 points of requirement. Sciences. Both doctoral programs are credit beyond the bachelor’s degree. subject to review by the Committee A master’s degree from an accredited Certificate of Professional on Instruction of the School. Doctoral institution may be accepted in the form Achievement in Data Science students may submit a petition to the of advanced standing as the equivalent Graduate Online delivery is also Office of Graduate Student Affairs to of one year of residence (30 points of available for this program. Candidates change from the Eng.Sc.D. degree credit and two Residence Units). An for the Certification of Professional to the Ph.D. degree or from the Ph.D. application for advanced standing must Achievement in Data Science, a degree to the Eng.Sc.D. degree. The be completed during the first semester nondegree part-time program, are petition must be submitted within the of study. Ph.D. candidates will be required to complete a minimum of 12 first year of enrollment in the doctoral required to complete a minimum of 30 credits, including four required courses: program. Any petitions submitted after additional points of credit in residence Algorithms for Data Science, Probability this period will not be considered. for a letter grade beyond the M.S. and Statistics for Data Science, Doctoral degree status can be changed Ph.D. candidates should obtain a Machine Learning for Data Science, only once; students, therefore, must copy of the bulletin of the Graduate and Exploratory Data Analysis and determine which doctoral degree School of Arts and Sciences, in which Visualization. program is most appropriate for their are printed the requirements of the academic and professional endeavors. department of major interest. Master of Science Program Departmental requirements may in Management Science and include comprehensive written and oral For the Eng.Sc.D. Degree Engineering qualifying examinations. A student must A student must obtain the master’s have a satisfactory grade-point average degree (M.S.) before enrolling as a In collaboration with the Graduate to be admitted to the doctoral qualifying candidate for the Eng.Sc.D. degree. The School of Business's Decision, Risk examination. Thereafter, the student minimum requirement in coursework and Operations Division, the Industrial must write a dissertation embodying for the doctoral degree is 60 points of Engineering and Operations Research original research under the sponsorship credit beyond the bachelor’s degree. department offers a master’s degree of a member of his or her department Eng.Sc.D. candidates will be required program focused on management and and submit it to the department. If to complete a minimum of 30 additional engineering perspectives in solving the department recommends the points of credit in residence beyond problems of complex systems. (See dissertation for defense, the student the M.S. for a letter grade. A master’s Industrial Engineering and Operations applies for final examination, which is degree from an accredited institution Research.) held before an examining committee may be accepted in the form of approved by the appropriate Dean’s advanced standing as the equivalent of Master of Science Program in Office. This application must be made at 30 points of credit. Candidates for the Business Analytics least three weeks before the date of the Eng.Sc.D. degree must, in addition to In partnership with the Graduate final examination. the 60-point requirement, accumulate School of Business's Decision, Risk The defense of the dissertation 12 points of credit in the departmental and Operations Division and Marketing constitutes the final test of the course E9800: Doctoral research Division, the Industrial Engineering and candidate’s qualifications. It must be instruction (see below). The candidate Operations Research department offers demonstrated that the candidate has for the degree of Doctor of Engineering a master’s degree program designed made a contribution to knowledge in a Science must submit evidence that his for those who want to focus on learning chosen area. In content the dissertation or her dissertation has been filed in the modeling techniques and data should, therefore, be a distinctly original compliance with requirements set by science tools that help businesses use contribution in the selected field of the faculty of Engineering and Applied data to make better decisions. (See study. In form it must show the mastery Science. Industrial Engineering and Operations of written English, which is expected of Research.) a university graduate. Doctoral Research Instruction An Eng.Sc.D. candidate is required to For the Ph.D. Degree complete 12 credits in the departmental A student must obtain the master’s course E9800: Doctoral research degree (M.S.) before enrolling as instruction in accordance with the

ENGINEERING 2021–2022 following guidelines: completion together with the sponsor’s coursework completed as a nondegree 25 1. After obtaining a master’s degree or recommendation to the department student may be counted toward a advanced standing, at which time the chair. graduate degree. student begins doctoral research, Please contact the Office of For additional information and the student is eligible to register for Graduate Student Affairs for more regulations pertaining to nondegree E9800 (3, 6, 9, or 12 points of credit information. students, see Graduate Admissions. per term). 2. Registration for E9800 at a time other NONDEGREE STUDENTS OFFICE OF GRADUATE than that prescribed above is not Qualified persons who are not STUDENT AFFAIRS permitted, except by written interested in a degree program but who permission of the Dean. The Office of Graduate Student wish only to take certain courses may 3. The 12 points of E9800 required for Affairs at The Fu Foundation School be permitted to register as nondegree the Eng.Sc.D. degree do not count of Engineering and Applied Science students, provided facilities are toward the minimum residence is integral to the School’s teaching, available. requirements, e.g., 30 points beyond research, and service mission and Many graduate courses in The Fu the master’s degree or 60 points works to enhance the educational Foundation School of Engineering and beyond the bachelor’s degree. opportunities available to students. Applied Science are offered in the 4. If a student is required to take This office provides leadership for the late afternoon and evening in order coursework beyond the minimum integration of educational programs to make them available to working residence requirements, the 12 points and services that enhance recruitment, individuals who wish to further their of doctoral research instruction retention, and quality of campus life knowledge in the areas of engineering must still be taken in addition to the for graduate students at Columbia and applied science. Individuals who required coursework. Engineering. It strives to demonstrate find it difficult or impossible to attend 5. A student must register continuously sensitivity and concern in addressing classes on the Columbia campus may through the fall and the spring terms. the needs of the School’s population. be able to receive instruction from the This requirement does not include The office is dedicated to providing School through the Columbia Video the summer session. service to prospective, new, and Network without leaving their worksites. continuing students pursuing a graduate Individuals interested in this program education in engineering or applied Completion of Requirements should read the section describing science. The requirements for the Eng.Sc.D. the distance learning Columbia Video degree must be completed in no more Network (CVN), which follows in this than seven years. The seven-year time bulletin. period begins at the time of enrollment Nondegree students receive and extends to the date on which the grades and must maintain satisfactory dissertation defense is held. attendance and performance in classes Extension of the time allowed for or laboratories and will be subject to completion of the degree may be the same rules as degree candidates. granted on recommendation of the Should a nondegree student decide student’s sponsor and the department to pursue a degree program, work chair to the Dean when special completed as a nondegree student circumstances warrant. Such extensions may be considered for advanced are initiated by submitting a statement standing, but no more than 15 points of of work in progress and a schedule for

ENGINEERING 2021–2022 26 COLUMBIA VIDEO NETWORK

Columbia Video Network CVN graduates earn the same • Computer Science (9 tracks) 540 S. W. Mudd, MC 4719 degrees as on-campus students. – Computational Biology 500 West 120th Street CVN’s administrative staff is available to – Computer Security New York, NY 10027 assist with registration procedures and – Foundations of Computer Science technical queries. Students pursuing their – Machine Learning 212-854-6447 M.S. and DES are assigned an academic – Natural Language Processing [email protected] adviser. – Network Systems cvn.columbia.edu – Personalized Track – Software Systems BACKGROUND PROGRAMS OF STUDY – Vision Graphics, Interactions, Columbia University’s Fu Foundation CVN offers part-time online graduate and Robotics School of Engineering and Applied degree, certificate, and nondegree • Earth and Environmental Engineering Science established the Columbia programs. CVN students may enroll • Electrical Engineering Video Network (CVN) in 1986 to meet in select SEAS graduate courses in • Industrial Engineering: Systems a growing need within the engineering fall, spring, and summer terms. CVN Engineering community for a graduate distance administrators work closely with faculty • Materials Science and Engineering education program. More than 30 years members from each department to • Mechanical Engineering later, our part-time fully online programs select courses that best fit the needs of • Operations Research: Methods provide working professionals high our students. in Finance quality graduate engineering education in a convenient and flexible format. Master of Science (M.S.) M.S. Application Degree Programs The M.S. application requires a PROGRAM BENEFITS The M.S. is a coursework-based minimum cumulative undergraduate At CVN, the #1 ranked Best Graduate master's, which requires 30 credits of GPA of 3.0, a resume/CV, a 250-word Online Engineering Program by the online coursework. The M.S. must be personal/professional statement, 2021 U.S. News & World Report, completed within five years. Students an unofficial transcript for each students can enroll in online courses are required to maintain continuous university attended, three letters of and earn graduate engineering degrees enrollment, which is a minimum of two recommendation, self-reported GRE without ever having to set foot on classes per year, one in the fall and one General Test scores (GRE scores are campus. CVN courses are taught by in the spring semesters. valid for five years), TOEFL/IELTS scores Columbia University faculty, offering (if applicable), and a $150 application students flexibility coupled with the Fields of Study: fee. Applications are reviewed on a high-caliber teaching, resources, • Applied Mathematics rolling basis, and decisions are issued and standards inherent in The Fu • Applied Physics four to six weeks after submission. Foundation School of Engineering and • Biomedical Engineering Applications must be submitted via the Applied Science. • Chemical Engineering application portal on cvn.columbia.edu. CVN students view the same lectures • Civil Engineering Accepted students can begin and complete the same homework, coursework up to one year after projects, and exams as those offered to admission into CVN. students enrolled in on-campus SEAS courses. Students have access to online University resources and are a part of the Columbia community.

ENGINEERING 2021–2022 Doctor of Engineering Science (DES) Achievement programs in various personal/professional statement, 27 Degree Programs fields for those who desire graduate- an unofficial transcript for each The DES can be completed partially level coursework for professional university attended, three letters online. Students in the program can advancement. Up to six credits earned of recommendation, and a $150 complete some of their courses in the Certification of Professional application fee. Applications are online. Students also perform Achievement program can be applied reviewed on a rolling basis, and research on campus with a faculty towards an M.S. degree at CVN. decisions are issued within a week adviser. Applicants must already Students enrolled in the certificate of submission. Applications must be have an M.S. in a related field prior program must complete the program submitted via the application portal on to applying to the DES program. The within two years and earn a GPA of 3.0 cvn.columbia.edu. DES must be completed within seven or higher. years. Applicants must select their Fields of Study: Nondegree Courses faculty advisers prior to submitting Students who have earned an their applications. • Applied Mathematics undergraduate degree in engineering, • Business and Technology mathematics, or a related field may take Fields of Study: • Civil Engineering one or two courses as a nondegree • Earth and Environmental Engineering • Construction Management student. Any of the CVN courses listed • Electrical Engineering • Data Science on the CVN website may be taken as • Mechanical Engineering • Earth and Environmental a nondegree course, provided that the Engineering student has met the prerequisites for DES Application • Electrical Engineering that course. The DES application requires a • Financial Engineering Up to six credits earned as a non- minimum cumulative undergraduate • Industrial Engineering degree student may be applied GPA of 3.0, an M.S. in a related field, • Information Systems towards the M.S. course requirements. a resume/CV, a 250-word personal/ • Low Carbon and Efficiency Earning credit as a nondegree student professional statement, an unofficial Technology does not guarantee acceptance into a transcript for each university attended, • Manufacturing Engineering degree program. three letters of recommendation, self- • Materials Science Nondegree Application reported GRE General Test scores • Multimedia Networking The application requires a minimum (GRE scores are valid for five years), • Nanotechnology cumulative undergraduate GPA of 3.0, TOEFL/IELTS scores (if applicable), a • Networking and Systems a resume/CV, a 250-word personal/ $150 application fee, and the name of a • New Media Engineering professional statement, and unofficial prospective faculty adviser. Applications • Operations Research transcripts from every university must be submitted via the application • Sustainable Energy attended. There is no application fee. portal on cvn.columbia.edu. Applications • Systems Engineering Applications are reviewed on a rolling are reviewed on a rolling basis, and • Telecommunications basis, and decisions are issued within a decisions are issued four to six weeks • Wireless and Mobile week of submission. Applications must after submission. Communications be submitted via the application portal on cvn.columbia.edu. Certification of Professional Certification Application Achievement Programs The certification application requires a minimum cumulative undergraduate CVN offers 12-credit, four-course GPA of 3.0, a resume/CV, a 250-word Certification of Professional

ENGINEERING 2021–2022 28 GRADUATE ADMISSIONS

Office of Graduate Admissions of the Graduate School of Arts and APPLICATION REQUIREMENTS 1220 S. W. Mudd, MC 4708 Sciences), or nondegree student (not Applicants can only apply to one 500 West 120th Street a degree candidate). Note: Not more degree program per admission term. New York, NY 10027 than 15 points of credit completed as Applicants must submit an online a nondegree student may be counted application and required supplemental 212-854-4688 toward a degree. materials, as described below. [email protected] The applicant must submit all An official transcript from each gradengineering.columbia.edu/ materials directly, not through an agent postsecondary institution attended, admissions or third-party vendor, with the sole personal statement, and resume or exception of submissions by the U.S. curriculum vitae must be submitted. The basic requirement for admission Department of State's Fulbright Program Consideration for admission will be as a graduate student is a bachelor’s and its three partner agencies: IIE, based not only on the completion degree received from an institution of LASPAU and AMIDEAST, and by the of an earlier course of study, but acceptable standing. Ordinarily, the Danish-American Fulbright Commission also upon the quality of the record applicant will have majored in the field (DAF), Deutscher Akademischer presented and upon such evidence in which graduate study is intended, but Austauschdienst (DAAD), and Vietnam as can be obtained concerning the in certain programs, preparation in a Education Fund (VEF). In addition, the applicant’s personal fitness to pursue related field of engineering or science applicant will be required to attest to professional work. is acceptable. The applicant will be the accuracy and authenticity of all Additionally, applicants must provide admitted only if the undergraduate information and documents submitted three letters of recommendation and the record shows promise of productive to Columbia. If you have any questions results of required standardized exams. and effective graduate work. about this requirement, please contact The Graduate Record Examination Students who hold an appropriate the admissions office at seasgradmit@ (general) is required for all candidates. degree in engineering may apply columbia.edu. Applicants to the doctoral program in for admission to study for the Ph.D. Academic integrity is the applied physics are also required to degree. However, students are required cornerstone of a university education. submit official GRE Physics Test scores. to obtain the master’s degree first. Failure to submit complete, accurate, GRE general and subject test scores Students currently enrolled in the and authentic application documents are valid for five years from the test School's M.S. program may apply for consistent with these instructions administration date according to the admission to the doctoral program after may result in denial or revocation of Educational Testing Service (ETS). English completing 15 points of coursework. admission, cancellation of academic language test scores are required of all Completion of a relevant master's credit, suspension, expulsion, or applicants who received their bachelor's degree is required prior to entry into the eventual revocation of degree. degree in a country in which English Ph.D. program. Applicants may be required to assist is not the official and widely spoken Students may be admitted in one admissions staff and faculty involved in language. The Test of English as a of the following five classifications: admission reviews in the verification of Foreign Language (TOEFL), International candidate for the M.S. degree, all documents and statements made in English Language Testing System (IELTS), candidate for the M.S. degree leading documents submitted by students as or Pearson Test of English (PTE) scores to the Ph.D. degree, candidate for part of the application review process. satisfy the test requirement and are the Doctor of Engineering Science valid for two years according to the test degree, candidate for the Doctor of organizations. Philosophy degree (see also the bulletin

ENGINEERING 2021–2022 Applicants may be asked to GRADUATE ADMISSION ONE-TERM NONDEGREE 29 participate in an interview as part of the CALENDAR STUDENT STATUS application process. Applicants are admitted twice yearly, for Individuals who meet the eligibility the fall and spring semesters. requirements, who are U.S. citizens, ENGLISH PROFICIENCY • Fall admission application deadlines: U.S. permanent residents, or hold December 15 for Ph.D., Eng.Sc.D., an appropriate visa, and who wish The Office of Graduate Student and M.S. leading to Ph.D. programs to take courses for enrichment, may Affairs no longer requires students to and February 15 for most M.S. only secure faculty approval to take up to demonstrate English proficiency as and nondegree applicants. Please two graduate-level courses for one a graduation requirement at The Fu visit the Office of Graduate Student term only as a one-term nondegree Foundation School of Engineering and Affairs website for specific M.S. only student. This option is also appropriate Applied Science. Regardless of TOEFL, program deadlines. for individuals who missed application IELTS, or PTE scores submitted for • Spring admission application deadline: deadlines. Applications for the one-term admission, students should continue to October 1 for all departments and nondegree student status are available work on maintaining adequate verbal degree levels. at the Office of Graduate Student Affairs and/or written abilities for successful and must be submitted during the first integration within their classes and Applicants who wish to be considered week of the fall or spring semester. future professional endeavors. for scholarships, fellowships, and If a one-term nondegree student Students are highly encouraged to assistantships should file complete subsequently wishes either to continue be proactive about addressing their applications for fall admission. taking classes the following term or to English proficiency by utilizing the many become a degree candidate, a formal resources available within Columbia application must be made through the University and throughout New York EXPRESS APPLICATION Office of Graduate Student Affairs. City. Columbia Engineering, Columbia Students have the option of College, General Studies, and Barnard enrolling in communication courses seniors as well as alumni from the TRANSFER APPLICANTS offered through Columbia Engineering's same schools, who have graduated Master's degree students are not Professional Development and within three years, may be eligible to eligible for transfer credits. Leadership courses (noncredit, tuition apply to a master's program using the Students admitted to the doctoral free) and the American Language express application process. A minimum program who have been conferred Program (ALP) at Columbia University cumulative GPA of 3.50 in an approved an appropriate M.S. degree may be (credited). Course credits earned undergraduate program is required to awarded two residence units toward through ALP, however, do not count be eligible to submit an M.S. Express their Ph.D., as well as 30 points of toward the minimum engineering application. For more information about advanced standing toward their Ph.D. academic coursework requirements. eligibility, visit the Office of Graduate or Eng.Sc.D., with approval from the Enrollment in ALP courses is solely the Student Affairs website. academic department and the Office financial responsibility of the student. The M.S. Express online application, of Graduate Student Affairs. As a rule, ISSO will not permit students which waives the submission of GRE to drop courses or fall below full-time scores, letters of recommendation, registration for language proficiency and official transcripts, streamlines and deficiencies. simplifies the application process for graduate study. Contact your academic department or the Office of Graduate APPLICATION FEE Student Affairs for further details. The nonrefundable application fee for all graduate degree and nondegree programs is $85.

ENGINEERING 2021–2022 30 GRADUATE TUITION, FEES, AND PAYMENTS

he 2021–2022 tuition and fees TUITION • Health and Related Services fee: are estimated. Tuition and fees Graduate students enrolled in M.S. and $623 per term are prescribed by statute and are Eng.Sc.D. programs pay $2,272 per • International Services charge: subjectT to change at the discretion of $120 per term (international credit, except when a special fee is the Trustees. fixed. Graduate tuition for Ph.D. students students only) University charges such as tuition, is $25,248 per Residence Unit. The • Document fee: $105 (one-time charge) fees, and residence hall and meal plans Residence Unit, full-time registration for are billed in the first Student Account one semester rather than for individual OTHER FEES Statement of the term, which is sent courses (whether or not the student is Activities fees for master's programs: out in July and December of each year taking courses), provides the basis for • First year full-time students (12 or more for the upcoming term. This account tuition charges. Ph.D. students should credits): $300 is payable and due in full on or before consult the bulletin for the Graduate • Continuing full-time students (12 or the payment due date announced in School of Arts and Sciences. more credits): $300 the Statement, typically at the end of • First year part-time students (less than August or early January before the 12 credits): $150 beginning of the billed term. Any student COMPREHENSIVE FEE/ • Continuing part-time students (less who does not receive the first Student MATRICULATION AND than 12 credits): $150 Account Statement is expected to pay at FACILITIES registration. Eng.Sc.D. candidates engaged only All full-time and part-time M.S.-Ph.D. If the University does not receive in research, and who have completed track and Ph.D. students shall be the full amount due for the term on or their twelve (12) credits of Doctoral charged, per term, a student activities before the payment due date of the Research Instruction (see “The Graduate fee of $25. first Statement, a late payment charge Programs” in this bulletin), are assessed

of $150 will be assessed. An additional a Comprehensive Fee of $2,414 per Application and late fees: charge of 1.5 percent per billing cycle term by The Fu Foundation School of • Application for graduate admission: may be imposed on any amount past Engineering and Applied Science. $85 due thereafter. Ph.D. candidates engaged only in • Late registration fee: Students with an overdue account research are assessed $2,414 per term - during late registration: $50 balance may be prohibited from for Matriculation and Facilities by the - after late registration: $100 registering, changing programs, or Graduate School of Arts and Sciences. obtaining a diploma or transcripts. In Books and course materials: the case of persistently delinquent MANDATORY FEES • Depends upon course accounts, the University may utilize the University services and support fee: services of an attorney and/or collection Laboratory fees: See course listings • Full-time master's programs: agent to collect any amount past due. $504 fall / $588 spring IEOR master’s program fee: If a student’s account is referred for • Part-time master's programs: • Full-time master’s program: $1,000 collection, the student may be charged $372 fall / $456 spring • Part-time master’s program: $500 an additional amount equal to the cost • All other full-time programs: of collection, including reasonable $459 fall / $543 spring attorney’s fees and expenses incurred • All other part-time programs: by the University. $327 fall / $411 spring

ENGINEERING 2021–2022 HEALTH INSURANCE the apparatus, adjustment will be made 8th week 40% 31 Columbia University offers the Student in the charge for age or condition. To 9th week and after 0% Medical Insurance Plan, which provides ensure that there may be no question both Basic and Comprehensive levels as to the liability for damage, students Refund Policy When Dropping of coverage. Full-time students are should note whether the apparatus is Individual Courses automatically enrolled in the Basic in good condition before use and, in Tuition for courses dropped by the last level of the Plan and billed for the case of difficulty, request instruction in day of the Change-of-Program period insurance premium in addition to the its proper operation. Where there is is refunded in full. There is no refund of Health Service fee. Visit the Columbia danger of costly damage, an instructor tuition for individual courses dropped Health website at health.columbia. should be requested to inspect the after the last day of the Change-of- edu for detailed information about apparatus. Liability for breakage will be Program period. The Change-of- medical insurance coverage options decided by the instructor in charge of Program period is usually the first two and directions for making confirmation, the course. weeks of the fall or spring semesters enrollment, or waiver requests. When the laboratory work is done by (please note that the first week of the a group, charges for breakage will be semester usually begins on a Tuesday). divided among the members of the Please note: PERSONAL EXPENSES The prorated schedule group. The students responsible for any above does not pertain to individual Students should expect to incur damage will be notified that a charge is classes dropped (unless your entire miscellaneous personal expenses for being made against them. The amount schedule consists of only one class). such items as food, clothing, linen, of the charge will be stated at that time The prorated schedule pertains to laundry, dry cleaning, and so forth. or as soon as it can be determined. withdrawals. Withdrawal is defined as The University advises students to dropping one’s entire program. open a local bank account upon arrival For students receiving federal in New York City. Since it often takes as TUITION AND FEE REFUNDS student aid, refunds will be made long as three weeks for the first deposit Students who make a complete to the federal aid programs in to clear, students should plan to cover withdrawal from a term, including the accordance with Department of immediate expenses using either a summer, are assessed a withdrawal Education regulations. Refunds will be credit card, traveler’s checks, or cash fee of $75. Late fees, application credited in the following order: draft drawn on a local bank. Students fees, withdrawal fees, tuition deposits, are urged not to arrive in New York special fees, computer fees, special Federal Unsubsidized Stafford Loans without sufficient start-up funds. examination fees, and transcript fees are not refundable. Federal Stafford Loans The Health Service Fee, Health Federal Perkins Loans LABORATORY CHARGES Insurance Premium, University Federal PLUS Loans (when disbursed Students may need to add another facilities fees, and student activity through the University) $100 to $300 for drafting materials or fees are not refundable. Federal Pell Grants laboratory fees in certain courses. Each Students who withdraw within Federal Supplemental Educational student taking laboratory courses must the first 60 percent of the academic Opportunity Grants furnish, at his or her own expense, the period are subject to a pro rata refund Other Title IV funds necessary notebooks, blank forms, and calculation, which refunds a portion Withdrawing students should be similar supplies. In some laboratory of tuition based on the percentage of aware that they will not be entitled courses, a fee is charged to cover the term remaining after the time of to any portion of a refund until all expendable materials and equipment withdrawal. This calculation is made Title IV programs are credited and all maintenance; the amount of the fee from the date the student’s written outstanding charges have been paid. is shown with the descriptions in the notice of withdrawal is received by the course listings. Students engaged in Office of Graduate Student Affairs. special tests, investigations, theses, or research work are required to meet Percentage Refund for Withdrawal the costs of expendable materials as during First Nine Weeks of Term may be necessary for this work and in Prorated for calendars of a different accordance with such arrangements as duration, if the entire program is may be made between the student and dropped: the department immediately concerned. 1st week 100% DAMAGES 2nd week 100% All students will be charged for damage 3rd week 90% to instruments or apparatus caused by 4th week 80% their carelessness. The amount of the 5th week 70% charge will be the actual cost of repair, 6th week 60% and, if the damage results in total loss of 7th week 50%

ENGINEERING 2021–2022 32 FINANCIAL AID FOR GRADUATE STUDY

FINANCING GRADUATE INSTRUCTIONS FOR order to be considered for all forms of EDUCATION FINANCIAL AID APPLICANTS graduate financing (both departmentally- The academic departments of Deadlines administered and financial aid– Columbia Engineering and the Apply for financial aid at the same administered funds). The application Office of Student Financial Planning time that you apply for admission. for admission to Columbia Engineering seek to ensure that all academically Your admissions application must graduate programs is also used to qualified students have enough be received by the December 15 apply for departmental funding. Outside financial support to enable them to deadline to be eligible for The Fu scholarships for which you qualify must be reported to your department and the work toward their degree. Possible Foundation School of Engineering and Office of Student Financial Planning. forms of support for tuition, fees, Applied Science departmental funding The School reserves the right to adjust books, and living expenses are: (institutional grants, fellowships, and your institutional award if you hold an institutional grants, fellowships, teaching and research assistantships). outside scholarship, fellowship, or other teaching and research assistantships, Spring admissions applicants will not be outside funding. on- or off-campus employment, and considered for departmental funding. student loans. The Office of Student Incoming applicants and continuing Institutional Grants Financial Planning assists students students should complete the FAFSA (studentaid.gov/h/apply-for-aid/fafsa) for with developing financing plans for Institutional grants are awarded to fall enrollment. graduate students on the basis of completing a degree. Guidelines for continuing students academic merit. Recipients must Columbia University graduate are available from departmental maintain satisfactory academic standing. funds are administered by two advisers in advance of the established separate branches of the University, deadline. All continuing supported and the application materials Fellowships students must preregister for classes required by the two branches differ. Fellowships are financial and intellectual during the preregistration period. Institutional grants, fellowships, and awards for academic merit that provide teaching and research assistantships stipends to be used by fellows to further are all departmentally-administered GRADUATE SCHOOL their research. If you are awarded a fellowship, you are expected to devote funds. Questions regarding these DEPARTMENTAL FUNDING time to your own work, and you are not awards should be directed to your The graduate departments of Columbia required to render any service to the academic department. Federal Engineering offer an extensive array University or donor. You may publish Student Loans (Unsubsidized and of funding. Funding decisions, based research produced by your fellowship Graduate PLUS) and private student solely on merit, and contingent upon work. As a fellow, you may not engage loans are administered by the Office making satisfactory academic progress, in remunerative employment without of Student Financial Planning. are made by the departments. All consent of the Dean. Applicants should Questions about loans should be applicants for admission and continuing students maintaining satisfactory contact the department directly for directed to the financial aid office via information. email at [email protected] or phone academic standing will be considered at 212-854-7040. for departmental funds. Applicants Assistantships Further information can be found at should contact their department directly Teaching and research assistantships, sfs.columbia.edu/sfp-grad-engin. for information. Columbia Engineering prospective and continuing graduate available to doctoral students in all students must complete their FAFSA in departments, provide tuition exemption

ENGINEERING 2021–2022 and a living stipend. Duties may include considered for departmental funding. request form, your loan eligibility may 33 teaching, laboratory supervision, Continuing international students must be reduced. participation in faculty research, and preregister for classes during the The FAFSA, planned enrollment other related activities. Teaching and preregistration period and complete an form, and the loan request form must research assistantships require up to enrollment status form to be considered be completed each academic year, and 20 hours of work per week. If you are for departmental funding. you must maintain satisfactory academic participating in faculty research that Most private student loan programs progress as defined in “The Graduate fulfills degree requirements, you may are restricted to U.S. citizens and Programs” section in order to remain 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 a The U.S. Department of Veterans ALTERNATIVE FUNDING 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 for one or more of these programs. through open competition, applicants under those visas. Before making plans Many benefits are available to advance are encouraged to consider major for employment in the United States, the education and skills of veterans national and international fellowship international students should consult and service members. Spouses and opportunities. It is important that with the International Students and family members may also be eligible prospective graduate students explore Scholars Office (ISSO), located at 524 for education and training assistance. every available source of funding for Riverside Drive, Suite 200; 212-854- Please visit Vets.gov to apply for graduate study. 3587. Its website is isso.columbia.edu. education benefits. In researching outside funding you To qualify for deferred tuition may look to faculty advisers, career OTHER FINANCIAL AID— payments, please provide a copy of services offices, deans of students, and FEDERAL AND PRIVATE your Certificate of Eligibility and DD-214 offices of financial aid where frequently PROGRAMS (please note the DD-214 is not required you may find resource materials, books, U.S. citizens and permanent residents for dependents) to the Columbia Office and grant applications for a wide variety enrolled at least half-time in a of Military & Veterans Affairs (OMVA). of funding sources. You must notify both degree-granting program are eligible your Columbia Engineering academic to apply for federal student loans. • In person to 202 Kent Hall department and the Office of Student To apply for federal student loans, • Scan and email to veterans@ Financial Planning of any outside students should complete the Free columbia.edu awards that you will be receiving. Application for Federal Student Aid • Fax to 212-854-2818 (FAFSA) using Columbia University’s Funding for International Students school code 002707 by May 5 for fall For assistance with utilizing your enrollment. benefits as well as understanding the To secure a visa, international students Several private student loan timeline of payments, please contact a must demonstrate that they have programs are available to both U.S. School Certifying Official at 212-854-3161 sufficient funding to complete the citizens and international students. or [email protected]. degree. Many international students These loans require that you have a For questions related to the status obtain support for their educational good credit standing. International of the VA application or entitlement expenses from their government, a students may be eligible for a private eligibility, contact the Department of foundation, or a private agency. loan with a creditworthy U.S. citizen Veterans Affairs at 1-888-442-4551. International students who apply or permanent resident cosigner. Additional resources and veterans to doctoral programs of study by Detailed information and news can be found at sfs.columbia.edu/ the December 15 deadline and are application instructions for student departments/veterans-service. admitted to a Columbia Engineering loans may be found at the Office of doctoral program are automatically Student Financial Planning website at considered for departmental funding Veterans Benefits and Transition Act sfs.columbia.edu/sfp-grad-engin. (institutional grants, fellowships, and of 2018 Determination of your eligibility teaching and research assistantships), In accordance with Title 38 US Code for financial aid is based in part on upon completion of the required 3679 subsection (e), this school adopts the number of courses for which you financial aid forms referred to above. the following additional provisions for register. If you enroll in fewer courses Spring admissions applicants will not be any students using U.S. Department of than you initially reported on the loan Veterans Affairs (VA) Post 9/11 G.I. Bill®

ENGINEERING 2021–2022 34 (Ch. 33) or Vocational Rehabilitation Off-Campus Employment in Template_2019_Engineer_of_Mines. and Employment (Ch. 31) benefits, while New York City pdf and essential-policies.columbia. payment to the institution is pending One of the nation’s largest urban edu/files_facets/imce_shared/sure_ from the VA. This school will not: areas, the city offers a wide variety CU_Template_2019_Metallurgical_ • Prevent or delay the student's of opportunities for part-time work. Engineer.pdf. enrollment; Many students gain significant • Assess a late penalty fee to the experience in fields related to CONTACT INFORMATION student; their research and study while they For questions about institutional grants, • Require the student to secure meet a portion of their educational fellowships, and teaching and research alternative or additional funding; expenses. assistantships, contact your academic • Deny the student access to any department. resources available to other Gainful Employment Disclosures For questions about on- or off- students who have satisfied their Programs: Engineer of Mines and campus non-need-based employment, tuition and fee bills to the institution, Metallurgical Engineer contact: including, but not limited to, access These programs are designed to be to classes, libraries, or other completed in 32 weeks. Graduate Career Placement Center institutional facilities. These programs will cost $71,998 Phone: 646-832-5941 if completed within the normal time. [email protected] However, to qualify for this provision, There may be additional costs for career.engineering.columbia.edu. such students may be required to: living expenses. These costs were accurate at the time of the posting For questions about student loans, • Produce the Certificate of Eligibility but may have changed. contact: by the first day of class; Fewer than 10 students completed • Provide written request to be this program within the normal time. This Office of Student Financial Planning certified; number has been withheld to preserve 202 Kent Hall, MC 9205 • Provide additional information the confidentiality of the students. 1140 Amsterdam Avenue needed to properly certify the The following states/territories do New York, NY 10027 enrollment as described in other not have licensure requirements for this institutional policies. profession: Alabama, Alaska, American Phone: 212-854-7040 Samoa, Arizona, Arkansas, California, Fax: 212-854-2818 Further information can be found at Colorado, Connecticut, Delaware, [email protected] sfs.columbia.edu/content/information. District of Columbia, Federated States sfs.columbia.edu/sfp-grad-engin of Micronesia, Florida, Georgia, EMPLOYMENT Guam, Hawaii, Idaho, Illinois, Indiana, Students on fellowship support must Iowa, Kansas, Kentucky, Louisiana, obtain the permission of the Dean Maine, Marshall Islands, Maryland, before accepting remunerative Massachusetts, Michigan, Minnesota, employment. Mississippi, Missouri, Montana, Students who study at Columbia Nebraska, Nevada, New Hampshire, Engineering on temporary visas New Jersey, New Mexico, New should fully understand the regulations York, North Carolina, North Dakota, concerning possible employment Northern Marianas, Ohio, Oklahoma, under those visas. Before making plans Oregon, Palau, Pennsylvania, Puerto for employment in the United States, Rico, Rhode Island, South Carolina, international students should consult South Dakota, Tennessee, Texas, with the International Students and Utah, Vermont, Virgin Islands, Virginia, Scholars Office (ISSO) located at 524 Washington, West Virginia, Wisconsin, Riverside Drive, Suite 200; 212-854- and Wyoming. 3587. Its website is isso.columbia.edu. For more information about graduation rates, loan repayment rates, On-Campus Employment and post-enrollment earnings about The Graduate Career Placement Center this institution and other postsecondary maintains an extensive listing of student institutions, please read further on employment opportunities. Many collegescorecard.ed.gov. resources are available to Columbia For the specific Columbia Gainful engineers and scientists in their job Employment Disclosures, please search and career exploration. For more review them both at essential- information, visit: career.engineering. policies.columbia.edu/files_facets/ columbia.edu imce_shared/isclosure_CU_

ENGINEERING 2021–2022 Faculty and Administration 36 FACULTY AND ADMINISTRATION

OFFICERS Elias Bareinboim Mary C. Boyce Lee C. Bollinger, J.D. Assistant Professor of Computer Morris A. and Alma Schapiro Professor President of the University Science and Professor of Mechanical Engineering Mary C. Boyce, Ph.D. Katayun Barmak Vaziri Provost of the University Philips Electronics Professor of Applied Robert G. Bozic Physics and Applied Mathematics Lecturer in Chemical Engineering Shih-Fu Chang, Ph.D. Interim Dean Daniel Bauer Michael P. Burke Lecturer in Computer Science Assistant Professor of Mechanical Andrew Laine, D.Sc. Engineering Secretary Peter N. Belhumeur Professor of Computer Science Adam Cannon Senior Lecturer in Machine Learning FACULTY Steven M. Bellovin (Computer Science) Perry K. and Vida L. W. Hudson Shipra Agrawal Professor of Computer Science Agostino Capponi Assistant Professor of Industrial Assistant Professor of Industrial Engineering and Operations Research Keren Bergman Engineering and Operations Research Charles Batchelor Professor of Electrical Sunil Agrawal Engineering Luca Carloni Professor of Mechanical Engineering Professor of Computer Science Raimondo Betti Peter K. Allen Professor of Civil Engineering and Augustin Chaintreau Professor of Computer Science Engineering Mechanics Associate Professor of Computer Science Dimitris Anastassiou Daniel Bienstock Charles Batchelor Professor of Electrical Liu Family Professor of Industrial Siu-Wai Chan Engineering Engineering and Operations Research Professor of Materials Science (Henry and Professor of Applied Physics and Krumb School of Mines) and of Applied James Anderson Applied Mathematics Physics and Applied Mathematics Assistant Professor of Electrical Engineering Simon J. L. Billinge Kartik Chandran Professor of Earth and Environmental Professor of Materials Science and of Alexandr Andoni Engineering (Henry Krumb School of Applied Physics and Applied Mathematics Associate Professor of Computer Science Mines) Kyle J. M. Bishop Gerard A. Ateshian Julius Chang Associate Professor of Chemical Andrew Walz Professor of Mechanical Lecturer in Civil Engineering and Engineering Engineering and Professor of Engineering Mechanics Biomedical Engineering Paul Blaer Shih-Fu Chang Senior Lecturer in Computer Science The Richard Dicker Professor of Elham Azizi Telecommunications (Electrical Assistant Professor of Biomedical David M. Blei Engineering) and Professor of Computer Engineering Professor of Computer Science and of Science Statistics (Arts and Sciences) William E. Bailey Jingguang G. Chen Associate Professor of Materials Allen H. Boozer Thayer Lindsley Professor of Science (Henry Krumb School of Mines) Professor of Applied Physics Engineering (Chemical Engineering) and of Applied Physics and Applied Mathematics Athanasios Bourtsalas Xi Chen Lecturer in Earth and Environmental Associate Professor of Computer Eric Balkanski Engineering Science Assistant Professor of Industrial Engineering and Operations Research Christopher Boyce Xi Chen Assistant Professor of Chemical Professor of Earth and Environmental Scott A. Banta Engineering Engineering (Henry Krumb School of Professor of Chemical Engineering Mines)

ENGINEERING 2021–2022 Lydia Chilton Daniel Esposito X. Edward Guo 37 Assistant Professor of Computer Associate Professor of Chemical Stanley Dicker Professor of Biomedical Science Engineering Engineering

Asaf Cidon Yuri Faenza Christine P. Hendon Assistant Professor of Electrical Assistant Professor of Industrial Associate Professor of Electrical Engineering Engineering and Operations Research Engineering

Matei T. Ciocarlie Raymond Farinato Irving P. Herman Associate Professor of Mechanical Professor of Professional Practice of Edward Howard Armstrong Professor of Engineering Earth and Environmental Engineering Applied Physics

Rachel Cummings Robert J. Farrauto Henry S. Hess Assistant Professor of Industrial Professor of Professional Practice of Professor of Biomedical Engineering Engineering and Operations Research Earth and Environmental Engineering Elizabeth M. C. Hillman Tal Danino Steven K. Feiner Associate Professor of Biomedical Assistant Professor of Biomedical Professor of Computer Science Engineering and of Radiology (Physics) Engineering Maria Q. Feng Ali Hirsa Gautam Dasgupta Renwick Professor of Civil Engineering Professor of Practice Industrial Professor of Civil Engineering and and Engineering Mechanics Engineering and Operations Research Engineering Mechanics Jacob Fish Julia B. Hirschberg Tony Dear Robert A. W. and Christine S. Carleton Percy K. and Vida L. W. Hudson Lecturer in Computer Science Professor of Civil Engineering Professor of Computer Science

George Deodatis Alexander Gaeta James C. Hone The Santiago and Robertina Calatrava David M. Rickey Professor of Applied Wang Fong-Jen Professor of Mechanical Family Professor of Civil Engineering Physics and of Materials Science Engineering

Emanuel Derman Oleg Gang Daniel J. Hsu Professor of Professional Practice of Professor of Chemical Engineering Associate Professor of Computer Industrial Engineering and Operations Science Research Roxana Geambasu Associate Professor of Computer Science Clark T. Hung Xuan Sharon Di Professor of Biomedical Engineering Assistant Professor of Civil Engineering Pierre Gentine and Engineering Mechanics Associate Professor of Earth and James S. Im Environmental Engineering (Henry Professor of Materials Science (Henry Antonius Dieker Krumb School of Mines) Krumb School of Mines) and of Applied Associate Professor of Industrial Physics and Applied Mathematics Engineering and Operations Research Javad Ghaderi Dehkordi Garud N. Iyengar Associate Professor of Electrical Professor of Industrial Engineering and Chris Dolan Engineering Operations Research Lecturer in Industrial Engineering and Operations Research Marco Giometto Joshua Jacobs Assistant Professor of Civil Engineering Assistant Professor of Biomedical Eleni Drinea and Engineering Mechanics Engineering Lecturer in the Data Science Institute and in Computer Science Donald Goldfarb Suman Jana Alexander and Hermine Avanessians Assistant Professor of Computer Science Qiang Du Professor of Industrial Engineering and The Fu Foundation Professor of Applied Operations Research Predrag R. Jelenkovic Mathematics Professor of Electrical Engineering Vineet Goyal Associate Professor of Industrial Christopher J. Durning Xiaofan Fred Jiang Professor of Chemical Engineering Engineering and Operations Research Assistant Professor of Electrical Engineering Stephen A. Edwards Luis Gravano Associate Professor of Computer Science Professor of Computer Science Hardeep V. Johar Senior Lecturer in Industrial Engineering Adam Elmachtoub Ronghui Gu and Operations Research Assistant Professor of Industrial Assistant Professor of Computer Engineering and Operations Research Science

ENGINEERING 2021–2022 38 Cedric Josz Zoran Kostic Qiao Lin Assistant Professor of Industrial Associate Professor of Professional Professor of Mechanical Engineering Engineering and Operations Research Practice in Electrical Engineering Hoe I. Ling Jingyue Ju Ioannis A. Kougioumtzoglou Professor of Civil Engineering and Samuel Ruben–Peter G. Viele Professor Assistant Professor of Civil Engineering Engineering Mechanics of Engineering (Chemical Engineering) and Engineering Mechanics Hod Lipson Christoph W. Juchem Harish Krishnaswamy Professor of Mechanical Engineering Associate Professor of Biomedical Associate Professor of Electrical Engineering Engineering Michal Lipson Eugene Higgins Professor of Electrical Soulaymane Kachani Christian Kroer Engineering Professor of Professional Practice of Assistant Professor of Industrial Industrial Engineering and Operations Engineering and Operations Research Richard W. Longman Research Professor of Mechanical Engineering Sanat K. Kumar and of Civil Engineering and Gail E. Kaiser Bykhovsky Professor of Chemical Engineering Mechanics Professor of Computer Science Engineering Helen H. Lu Lance C. Kam Aaron M. Kyle Professor of Biomedical Engineering Professor of Biomedical Engineering Senior Lecturer in Biomedical Engineering Design Tal Malkin Karen Kasza Associate Professor of Computer Science Clare Boothe Luce Assistant Professor Ioannis Kymissis of Mechanical Engineering Professor of Electrical Engineering Kyle Mandli Assistant Professor of Applied Ethan Katz-Bassett Jeffrey W. Kysar Mathematics Associate Professor of Electrical Professor of Mechanical Engineering Engineering Lauren Marbella Daniel Lacker Assistant Professor of Chemical Shiho Kawashima Assistant Professor of Industrial Engineering Associate Professor of Civil Engineering Engineering and Operations Research and Engineering Mechanics Chris A. Marianetti Andrew F. Laine Associate Professor of Materials John R. Kender Percy K. and Vida L. W. Hudson Science (Henry Krumb School of Mines) Professor of Computer Science Professor of Biomedical Engineering and of Applied Physics and Applied and Professor of Radiology (Health Mathematics Dion Khodagholy Sciences) Assistant Professor of Electrical Mike Massimino Engineering Upmanu Lall Professor of Professional Practice of Alan and Carol Silberstein Professor of Addis Kidane Mechanical Engineering Earth and Environmental Engineering Associate Professor of Civil Engineering (Henry Krumb School of Mines) and of Civil and Engineering Mechanics Michael E. Mauel Engineering and Engineering Mechanics Professor of Applied Physics Martha A. Kim Kwai Hung Henry Lam Associate Professor of Computer José McFaline-Figueroa Associate Professor of Industrial Science Assistant Professor of Biomedical Engineering and Operations Research Engineering Peter R. Kinget Bernard J. Lechner Professor of Aurel A. Lazar Kathleen McKeown Electrical Engineering Professor of Electrical Engineering Henry and Gertrude Rothschild Professor of Computer Science David Knowles Jae Woo Lee Assistant Professor of Computer Senior Lecturer in Computer Science V. Faye McNeill Science Associate Professor of Chemical Sophia Hyoseon Lee Engineering Elisa E. Konofagou Lecturer in Discipline, English Robert and Margaret Hariri Professor of Proficiency Nima Mesgarani Biomedical Engineering and Professor Associate Professor of Electrical of Radiology (Health Sciences) Kam Leong Engineering Samuel Y. Sheng Professor of Biomedical Engineering

ENGINEERING 2021–2022 Vishal Misra John Paisley Amir Sagiv 39 Professor of Computer Science Associate Professor of Electrical Assistant Professor of Applied Physics Engineering and Applied Mathematics Debasis Mitra Professor of Electrical Engineering Thomas Panayotidi Paul Sajda Lecturer in Civil Engineering and Professor of Biomedical Engineering Vijay Modi Engineering Mechanics and of Electrical Engineering and of Professor of Mechanical Engineering Radiology (Health Sciences) Christos Papadimitriou Aaron Moment Donovan Family Professor of Computer Ansaf Salleb-Aouissi Professor of Practice in Chemical Science Lecturer in Computer Science Engineering Ah-Hyung Alissa Park P. James Schuck Barclay Morrison III Lenfest Earth Institute Associate Associate Professor of Mechanical Professor of Biomedical Engineering Professor in Climate Change (Earth and Engineering Environmental Engineering) Kristin M. Myers Henning G. Schulzrinne Associate Professor of Mechanical Carlos Paz-Soldan Julian Clarence Levi Professor of Engineering Associate Professor of Applied Physics Mathematical Methods and Computer and Applied Mathematics Science and Professor of Electrical D. R. Nagaraj Engineering Professor of Practice in Earth and Itsik Pe’er Environmental Engineering Associate Professor of Computer Science Mingoo Seok Associate Professor of Electrical Arvind Narayanaswamy Feniosky Peña-Mora Engineering Associate Professor of Mechanical Edwin Howard Armstrong Professor Engineering of Civil Engineering and Engineering Rocco A. Servedio Mechanics and Professor of Earth and Professor of Computer Science Gerald A. Navratil Environmental Engineering and of Thomas Alva Edison Professor Computer Science Simha Sethumadhavan of Applied Physics Associate Professor of Computer Science Aron Pinczuk Shree K. Nayar Professor of Applied Physics and of Jay Sethuraman T. C. Chang Professor of Computer Physics (Arts and Sciences) Professor of Industrial Engineering and Science Operations Research Lorenzo M. Polvani Nandan Nerurkar Professor of Applied Mathematics and Kenneth L. Shepard Assistant Professor of Biomedical of Earth and Environmental Sciences Lau Family Professor of Electrical Engineering (Arts and Sciences) Engineering and Professor of Biomedical Engineering Jason Nieh Matthias Preindl Professor of Computer Science Assistant Professor of Electrical Samuel K. Sia Engineering Professor of Biomedical Engineering Ismail Cevdet Noyan Professor of Materials Science (Henry Baishakhi Ray Karl Sigman Krumb School of Mines) and of Applied Assistant Professor of Computer Science Professor of Industrial Engineering and Physics and Applied Mathematics Operations Research Martin Reiman Allie C. Obermeyer Professor of Industrial Engineering and Mijo Simunovic Assistant Professor of Chemical Operations Research Assistant Professor of Chemical Engineering Engineering Kui Ren Ibrahim S. Odeh Professor of Applied Physics and Applied Brian Smith Senior Lecturer in Civil Engineering and Mathematics Assistant Professor of Computer Science Engineering Mechanics Kenneth A. Ross Andrew W. Smyth Elizabeth S. Olson Professor of Computer Science Professor of Civil Engineering and Professor of Biomedical Engineering Engineering Mechanics and Auditory Biophysics (in Timothy Roughgarden Otolaryngology/Head and Neck Professor of Computer Science Adam H. Sobel Surgery) Professor of Applied Physics and Applied Dan Rubenstein Mathematics and of Environmental Ben O’Shaughnessy Associate Professor of Computer Science Sciences (Arts and Sciences) Professor of Chemical Engineering

ENGINEERING 2021–2022 40 Ponisseril Somasundaran John T. Vaughan Alan C. West LaVon Duddleson Krumb Professor Professor of Biomedical Engineering in Samuel Ruben-Peter G. Viele Professor of Mineral Engineering (Earth and the Mortimer B. Zuckerman Mind Brain of Electrochemistry (Chemical Environmental Engineering) Behavior Institute Engineering)

Shuran Song Vijay Vedula Harry West Assistant Professor of Computer Science Assistant Professor of Mechanical Professor of Professional Practice in Engineering Industrial Engineering and Operations Marc W. Spiegelman Research Arthur D. Storke Memorial Professor of Latha Venkataraman Earth and Environmental Sciences (Arts Professor of Applied Physics and Chris H. Wiggins and Sciences) and Professor of Applied Chemistry Associate Professor of Applied Mathematics Physics and Applied Mathematics Venkat Venkatasubramanian Jeannette Wing Clifford Stein Samuel Ruben–Peter G. Viele Professor of Computer Science Professor of Industrial Engineering and Professor of Engineering (Chemical Operations Research and of Computer Engineering) John Wright Science Associate Professor of Electrical Nakul Verma Engineering Daniel Steingart Lecturer in Computer Science Stanley-Thompson Associate Professor of Eugene Wu Chemical Metallurgy Carl Vondrick Assistant Professor of Computer Science Assistant Professor of Computer Science Milan N. Stojanovic Cheng-Shie Wuu Professor of Biomedical Engineering Sinisa Vukelic Professor of Clinical Radiation Oncology, and of Medical Science (in Medicine) Lecturer in Mechanical Engineering and of Environmental Health Sciences, and of Applied Physics Fred R. Stolfi Gordana Vunjak-Novakovic Senior Lecturer in Mechanical University Professor and Mikati Bolun Xu Engineering Foundation Professor of Biomedical Assistant Professor of Earth and Engineering Environmental Engineering Salvatore J. Stolfo Professor of Computer Science Haim Waisman Junfeng Yang Associate Professor of Civil Engineering Associate Professor of Computer Science WaiChing Steve Sun and Engineering Mechanics Assistant Professor of Civil Engineering Yuan Yang and Engineering Mechanics Kaizheng Wang Assistant Professor of Applied Physics Assistant Professor of Industrial and Applied Mathematics Wenpin Tang Engineering and Operations Research Assistant Professor of Industrial Mihalis Yannakakis Engineering and Operations Research Qi Wang Percy K. and Vida L. W. Hudson Assistant Professor of Biomedical Professor of Computer Science Michael K. Tippett Engineering Associate Professor of Applied Physics David Da-Wei Yao and Applied Mathematics Wen I. Wang Piyasombatkul Family Professor of Thayer Lindsley Professor in the Faculty Industrial Engineering and Operations Van-Anh Truong of Engineering and Applied Science Research Associate Professor of Industrial (Electrical Engineering) and Professor of Engineering and Operations Research Applied Physics Y. Lawrence Yao Professor of Mechanical Engineering Yannis P. Tsividis Xiaodong Wang Edwin Howard Armstrong Professor of Professor of Electrical Engineering Yevgeniy Yesilevskiy Electrical Engineering Lecturer in Mechanical Engineering Michael I. Weinstein Alexander Urban-Artrith Professor of Applied Mathematics Huiming Yin Assistant Professor of Chemical Associate Professor of Civil Engineering Engineering Omri Weinstein and Engineering Mechanics Assistant Professor of Computer David G. Vallancourt Science Ngai Yin Yip Senior Lecturer in Circuits and Systems Assistant Professor of Earth and (Electrical Engineering) Renata Maria Mattosinho Wentzcovitch Environmental Engineering Professor of Materials Science and Vladimir Vapnik Applied Physics, and Earth and Professor of Computer Science Environmental Science

ENGINEERING 2021–2022 41

Drew Youngren FACULTY MEMBERS-AT-LARGE Daniel N. Beshers Lecturer in Applied Physics and Applied Carlos J. Alonso Professor Emeritus of Metallurgy (Earth Mathematics Dean, Graduate School of Arts and and Environmental Engineering) Sciences Nanfang Yu Mark A. Cane Associate Professor of Applied Physics Sidney R. Hemming G. Unger Vetlesen Professor Emeritus Chair, Department of Earth and of Earth and Climate Sciences and Zhou Yu Environmental Sciences Professor Emeritus of Applied Physics Assistant Professor of Computer and Applied Mathematics Science Liang Tong Chair, Department of Biological Huk Yuk Cheh Henry Yuen Sciences Samuel Ruben-Peter G. Viele Professor Assistant Professor of Computer Emeritus of Electrochemistry Science Costis Maglaras Dean, Rene Chevray Lu Zhang Professor Emeritus of Mechanical Assistant Professor of Applied Physics David Reichman Engineering and Applied Mathematics Chair, Department of Chemistry C. K. Chu Changxi Zheng Michael Thaddeus Fu Foundation Professor Emeritus Associate Professor of Computer Science Chair, Department of Mathematics of Applied Physics in the Faculty of Engineering and Applied Science Xunyu Zhou James J. Valentini Liu Family Professor of Industrial Dean, Columbia College Edward G. Coffman Engineering and Operations Research Professor Emeritus of Electrical Robert Mawhinney Engineering and of Computer Science Charles Zukowski Chair, Department of Physics Professor of Electrical Engineering Paul Diament EMERITI AND RETIRED OFFICERS Professor Emeritus of Electrical Gil Zussman Engineering (NOT IN RESIDENCE) Associate Professor of Electrical Engineering Frank L. DiMaggio Alfred V. Aho Robert A. W. and Christine S. Carleton Lawrence Gussman Professor Emeritus Professor Emeritus of Civil Engineering of Computer Science

ENGINEERING 2021–2022 42 Zvi Galil Michael P. Sheetz Katherine Briant Julian Clarence Leu Professor Emeritus William R. Kenan Jr. Professor Emeritus Manager of Operations and Enrollment of Mathematical Methods and of of Cell Biology and Professor Emeritus Services Computer Science and Dean Emeritus of Biomedical Engineering Yannick Brookes Jonathan L. Gross Jordan L. Spencer Assistant Dean of Graduate Student Professor Emeritus of Computer Science Professor Emeritus of Chemical Affairs Engineering Jeffrey T. Koberstein Leora Brovman Percy K. and Vida L. W. Hudson Thomas E. Stern Senior Associate Dean of Professor Emeritus of Chemical Dicker Professor Emeritus of Electrical Undergraduate and Graduate Student Engineering Engineering Affairs

John T. F. Kuo Horst Stormer Alexander Browne Maurice Ewing and J. Lamar Worzel I. I. Rabi Professor Emeritus of Physics Assistant Manager, CVN Production Professor Emeritus of Geophysics (Arts and Sciences) and Professor Emeritus of Applied Physics Cecily Castle W. Michael Lai Leadership Giving Officer Professor Emeritus of Mechanical Malvin Carl Teich Engineering and of Orthopedic Professor Emeritus of Engineering Nancy Cedeno Bioengineering (Orthopedic Surgery) Science Financial Coordinator

Eugene S. Machlin Rene B. Testa Andy Chae Henry Marion Howe Professor Emeritus Professor Emeritus of Civil Engineering Associate Director of Graduate Student of Metallurgy and Engineering Mechanics Life

Thomas C. Marshall Nickolas J. Themelis Jaclyn Chu Professor Emeritus of Applied Physics Professor Emeritus of Earth and Senior Major Gifts Officer Environmental Engineering Henry E. Meadows Jr. Brianne Cortese Professor Emeritus of Electrical Engineering Stephen H. Unger Assistant Director of Admissions and Professor Emeritus of Computer Science Academic Affairs Van C. Mow and of Electrical Engineering Stanley Dicker Professor Emeritus of Gerald Cotiangco Biomedical Engineering and Professor Rimas Vaicaitis Career Placement Officer, Business Emeritus of Orthopedic Engineering Renwick Professor Emeritus of Civil Analytics (Orthopedic Surgery) Engineering Rafael Cruz Steven M. Nowick Henryk Wozniakowski Assistant Director of Procurement and Professor of Computer Science and Professor Emeritus of Computer Science Compliance Electrical Engineering Edward S. Yang Perry D'Amelio Richard M. Osgood Jr. Professor Emeritus of Electrical Engineering Admissions Operations Officer Higgins Professor Emeritus of Electrical Engineering and Professor Emeritus Tuncel M. Yegulalp Ryan Day of Applied Physics and Applied Professor Emeritus of Mining (Earth Graduate Career Placement Manager Mathematics and Environmental Engineering, Henry Krumb School of Mines) Joshua DeJoy Enders Robinson Development Coordinator, Annual Maurice Ewing and J. Lamar Worzel Yechiam Yemini Giving Professor Emeritus of Applied Professor Emeritus of Computer Science Geophysics (Earth and Environmental Irina Dimitrov Engineering) Interim Director, Alumni Relations ADMINISTRATIVE OFFICERS AND Peter Schlosser STAFF Ervis Dinkel Maurice Ewing and J. Lamar Worzel Shih-Fu Chang Financial Business Manager Professor Emeritus of Geophysics Interim Dean and Professor Emeritus of Earth and Ivy Elkins Environmental Sciences Rumana Ashraf Career Placement Officer, Computer Manager, Grants and Contracts, Pre- Science Mischa Schwartz Award Charles Batchelor Professor Emeritus Allison Elliott of Electrical Engineering Mark Beer Communications Writer Systems Engineer

ENGINEERING 2021–2022 Karin Ente Garud Iyengar Jenny Mak 43 Assistant Director of Graduate Vice Dean of Research and Operations Executive Director, Graduate Admissions Research Career Placement and Professional Development and Leadership Holly Evarts Meaghan Jameyson Director, Strategic Communications Assistant Director of Graduate Jessica L. Marinaccio and Media Relations Admissions Dean of Undergraduate Admissions and Financial Aid Mindy Farabee Peter Janus Associate Director, Communications Admissions Operations Officer Liam Maserjian CVN Production Manager Jennifer Feierman de Lannoy Soulaymane Kachani Director of Development, Graduate Senior Vice Dean Janine Nadia Maslov Programs Graduate Admissions Officer Asha Kaufman Samantha Fellers Director of Annual Giving Betty Matias Hsu Development Coordinator, Major Gifts, Associate Director of Graduate Student SEAS Lauren Kopac Services Institutional Research Analyst David Fitzgerald Bianca Matthew Career Placement Officer, Operations Mercedes Kriesel Student Services Officer Research Career Placement Officer, Financial Engineering Neil McClure Rachel Fitzgerald Senior Associate Dean of Faculty Affairs Facilities Specialist Bennett Kushnick and Chief Administrative Officer Development Assistant Genevieve Fleming Emily Anne McCormack Senior Manager - Special Projects Jackson Lau Associate Director, Career Placement, System Administrator Civil Engineering and Mechanical Gabrielle Gannon Engineering Director of Graduate Admissions Abby Lee Video Producer, Columbia Video Joan McDowell Libby Goss Network Associate Director of Human Resources Program Manager, Artificial Intelligence Technology Jennifer Lee Theresa A. McKenzie Career Placement Officer, Electrical Executive Director of Budget and Julie Han Engineering Finance Admissions Operations Officer Logan Lee Ryan Michels Nolan Harpp Alumni Programs Coordinator Institutional Research Analyst, Academic Instructional Media Specialist Programs Mindi Levinson Keely Henderson Director of Career Placement, Alexis Moore Senior Associate Dean of Advancement, Management Science and Engineering, Associate Director of Operations and SEAS Industrial Engineering Enrollment Services

Kristen Henlin Raaya Lewis Jordan Moore Career Placement Officer, Applied Recruitment and Marketing Manager Assistant Director for Donor Relations Physics and Applied Mathematics and and Stewardship Gabriella Lilienthal Biomedical Engineering Program Manager, Professional Mairead Moore Development and Leadership Shavonna Hinton Director of Alumni Relations Assistant Dean of Diversity, Equity, and Alan Lin Inclusion Flatra Morina Financial Analyst Business Service Administrator Michele Hoos Christina Liu Executive Director of Communications Barclay Morrison Reunion Coordinator Vice Dean of Undergraduate Programs Shu-Yi Hsu Helen Lu Assistant Director, Online Learning Jane Nisselson Vice Dean of Faculty Affairs and Associate Director, Multimedia Advancement John Hyde Communications Assistant Director of Career Development and Alumni Services, Data Science

ENGINEERING 2021–2022 44 Quy O Ivy Schultz Alex J. Vervoort Associate Director of Technology Director of Entrepreneurship Programs Associate Director of Alumni Relations Services Esther Schwartz Eric Vieira Kwame Osei-Sarfo Executive Assistant to the Dean Director of Strategic Collaborations Director, Bridge to the Ph.D. Program Dempsey Simonis Kamille Way Timur Pakay Assistant Director for Annual Giving, Instructional Designer, CVN Associate Director of Executive SEAS Education Programs Emma Williams David Simpson Assistant Director of Alumni Relations Dylan Pappas Administrative Assistant Senior Analyst, Budget and Finance Nancy Wong Michelle R. Stevenson Marketing and Strategic Planning Jade Quintero Coordinator, Columbia Video Network Officer, Annual Giving, SEAS Admissions Operations Officer Elizabeth Strauss Sofia Yagaeva Madeline Ramos Director of Professional Development Assistant Director, Columbia Video Faculty Affairs Officer and Leadership and Graduate Career Network Placement Raina Ranaghan William Yandolino Career Placement Officer, Chemical Maura Swisher Executive Director of Finance and Engineering and Earth and Senior Analyst, Budget and Finance Operations Environmental Engineering Malcom Thaxton Marina Zamalin Adrieanna Reyes Financial Coordinator Executive Director of Online Learning Undergraduate Student Affairs Program Officer Randy Torres Associate Director, Faculty Affairs Stan Sakry Director of Facilities and Space Planning Dario Vasquez Program Specialist Anthony Schmitt Manager, Grants and Contracts, Pre- Tania Velimirovici Award Academic Programs and Special Projects Manager

ENGINEERING 2021–2022 Academic Departments and Programs 46 KEY TO COURSE LISTINGS

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

ENGINEERING 2021–2022 ELEN Electrical Engineering MUSI Music Arts and Sciences 47 ENGI Engineering ORCA Operations Research, Computer CC Columbia College Science and Applied Mathematics ENGL English UN Undergraduate PHED Physical Education EMME Engineering Mechanics GU Undergraduate, Graduate and Mechanical Engineering PHIL Philosophy GR Graduate Only ENME Engineering Mechanics PHYS Physics FINC Finance PLAN Planning The first digit indicates the level of the course, as follows: FREN French POLS Political Science 0 Course that cannot be credited GERM German PSLG Physiology toward any degree PSYC Psychology GRAP Graphics 1 Undergraduate course RELI Religion HIST History 2 Undergraduate course, intermediate SCNC Science HSAM History and Applied Mathematics 3 Undergraduate course, advanced SIEO Statistics and Industrial Engineering HUMA Humanities 4 Graduate course that is open to qualified and Operations Research IEME Industrial Engineering and undergraduates SOCI Sociology Mechanical Engineering 6 Graduate course SPAN Spanish IEOR Industrial Engineering and 8 Graduate course, advanced Operations Research STAT Statistics 9 Graduate research course or seminar INAF International Affairs STCS Statistics and Computer Science INTA Earth and Environmental Engineering, URBS Urban Studies An x following the course number Civil Engineering, and means that the course meets in the fall International and Public Affairs VIAR Visual Arts semester; y indicates the spring semester. MATH Mathematics HOW COURSES ARE NUMBERED MEBM Mechanical Engineering and DIRECTORY OF CLASSES Biomedical Engineering The course number that follows each Room assignments, days and hours, and designator consists of one or two course changes for all courses are avail- MECE Mechanical Engineering capital letters followed by four digits. able online at columbia.edu/cu/ MECH Mechanical Engineering and The capital letter indicates the University bulletin/uwb. Chemical Engineering division or affiliate offering the course: The School reserves the right to MECS Mechanical Engineering and B Business withdraw or modify the courses of Computer Science instruction or to change the instructors E Engineering and Applied Science at any time. MEEM Mechanical Engineering and Engineering Mechanics P Mailman School of Public Health MEIE Mechanical Engineering and S Summer Session Industrial Engineering U International and Public Affairs MSAE Materials Science and Engineering W Interfaculty course MSIE Management Science and Industrial Z American Language Program Engineering and Operations Research

ENGINEERING 2021–2022 48 APPLIED PHYSICS AND APPLIED MATHEMATICS 200 S. W. Mudd, MC 4701 212-854-4457 Applied Physics and Applied Mathematics: apam.columbia.edu/ Materials Science and Engineering: matsci.apam.columbia.edu

CHAIR Christopher H. Scholz, ADJUNCT PROFESSORS John Marshall POSTDOCTORAL Marc W. Spiegelman Professor Emeritus, Vittorio M. Canuto Patricia Mooney RESEARCH SCIENTISTS 208 S. W. Mudd Earth and Environmental Peter F. Caracappa David Yuen Zhengqian Cheng Sciences Barbara E. Carlson Bithi De DEPARTMENT Adam Sobel C. Julian Chen RESEARCH Veronika Klevarova ADMINISTRATOR Marc W. Spiegelman David E. Keyes SCIENTISTS Vladimir Kobzar Stella M. Lau Latha Venkataraman Ron L. Miller Jacek Chowdhary Joseph Kraisler Wen I. Wang, Electrical Stephen L. Ostrow Igor Geogdzhayev Zachary S. McGraw PROFESSORS Engineering Thomas S. Pedersen Jeffrey Levesque James M. Scott Katayun Barmak Michael I. Weinstein Lawrence N. Rothenberg Catherine Naud Sandra H. Skjaervoe Daniel Bienstock, Renata M. Wentzcovitch Stephen A. Sabbagh Yoshitomo Okawachi Boyuan Zhang Industrial Engineering Cheng-Shie Wuu, George Tselioudis and Operations Radiation Oncology Marco Zaider ASSOCIATE RESEARCH POSTDOCTORAL Research Pat Zanzonico SCIENTISTS RESEARCH FELLOWS Simon J. L. Billinge ASSOCIATE Mikhail Alexandrov Miriam Blau Allen H. Boozer PROFESSORS ADJUNCT ASSOCIATE Michael Bauer Kevin DallaSanta Mark A. Cane, Professor William E. Bailey PROFESSORS Gregory Elsaesser Emeritus, Earth Kyle Mandli Brian Cairns Robert Field SPECIAL LECTURERS and Environmental Chris A. Marianetti Yuan He Jeremy Hanson Daniel N. Beshers Sciences Carlos Paz-Soldan Clara Orbe Jae Kyung Jang C. K. Chu Siu-Wai Chan Michael K. Tippett Anastasia Romanou Yanzheng Jiang Monique C. Katz Qiang Du Chris H. Wiggins Anna Rozenshtein Paul Lerner Alexander Gaeta Yuan Yang Li Liu SPECIAL RESEARCH Oleg Gang Nanfang Yu ADJUNCT ASSISTANT Young Seok Park SCIENTIST Irving P. Herman PROFESSORS Yang Sun Shalom J. Wind James S. Im ASSISTANT PROFESSORS Dorian Goldman Francesca Turco Michal Lipson, Electrical Amir Sagiv Jacob Hofman Inigo Urteaga Engineering Lu Zhang Shuguang Wang Michael E. Mauel SENIOR RESEARCH Jingbo Wu Gerald A. Navratil AFFILIATED FACULTY SCIENTISTS Ismail C. Noyan John Wright, Electrical John Berkery ADJUNCT ASSOCIATE Richard M. Osgood Jr., Engineering James Bialek RESEARCH SCIENTISTS Professor Emeritus, Thomas C. Marshall Emmanouil Electrical Engineering LECTURER IN Steven A. Sabbagh Antonogiannakis Aron Pinczuk DISCIPLINE Thomas A. Caswell Lorenzo M. Polvani Drew Youngren ADJUNCT SENIOR Gabriel Chiodo Kui Ren RESEARCH SCIENTISTS Lingjie Du C. Julian Chen Chris Hansen Yigal Komem

he Department of Applied Physics described on pages 181–183. techniques; and (5) the development of and Applied Mathematics new plasma measurement techniques. includes undergraduate Current Research Activities in The results from our fusion science andT graduate studies in the experiments are used as a basis Applied Physics and Applied fields of applied physics, applied Mathematics for collaboration with large national mathematics, and materials science Applied Physics. and international experiments. For and engineering. The graduate Plasma physics and fusion energy. example, methods of active feedback program in applied physics includes In experimental plasma physics, research control of plasma instability developed plasma physics and controlled fusion; is being conducted on (1) equilibrium, at Columbia University are guiding solid-state physics; optical and stability, and transport in fusion research on NSTX at the Princeton laser physics and medical physics. plasmas: high-beta tokamaks, spherical Plasma Physics Laboratory, on the The graduate program in applied tokamaks, and levitated dipoles; (2) DIII-D tokamak at General Atomics, and mathematics includes research in magnetospheric physics: trapped for the design of the next-generation applied analysis, data science, and particle instabilities and stochastic burning plasma experiment, ITER. In atmospheric, oceanic, and earth particle motion; (3) confinement theoretical plasma physics, research physics. The graduate programs in of toroidal nonneutral plasmas; (4) is conducted in the theory of plasma materials science and engineering are plasma source operation and heating equilibrium and stability, active control

ENGINEERING 2021–2022 of MHD instabilities, the kinetic theory the Department of Systems Biology, and microwave heating, and microwave 49 of turbulence and transport, and the the Department of Statistics. Extensive diagnostics of neutral stellarator development of techniques based on collaborations exist with national climate plasmas. Two smaller devices the theory of general coordinates and research centers (the Geophysical Fluid investigate, respectively, an innovative dynamical systems. The work is applied Dynamics Laboratory and the National tokamak-stellarator hybrid plasma to magnetic fusion, nonneutral and Center for Atmospheric Research) and confinement concept and the use of space plasmas. with national laboratories of the U.S. toroidal electron-heated plasmas as Department of Energy, custodians of the sources of ions for accelerators. The Optical and laser physics. Active nation’s most powerful supercomputers. Columbia Linear Machine (CLM) is a areas of research include inelastic light continuously operating, linear mirror scattering in nanomaterials, optical Atmospheric, oceanic, and earth device for the study of collisionless diagnostics of film processing, flat physics. Current research focuses on plasma instabilities, plasma, transport, optics, metasurfaces, nonlinear optics, the dynamics of the atmosphere and the and feedback stabilization. Columbia’s ultrafast optoelectronics, photonic ocean, climate modeling, cloud physics, Collisionless Terrella Experiment switching, optical physics of surfaces, radiation transfer, remote sensing, investigates plasma transport in laser-induced crystallization, and photon geophysical/geological fluid dynamics, magnetospheric geometry and the integrated circuits. and geochemistry. The department generation of strong plasma flow from engages in ongoing research with nonlinear electrostatic potentials. Solid-state physics. Research in solid- the NASA Goddard Institute for Space Experimental research in solid- state physics covers nanoscience and Studies and the Lamont-Doherty Earth state physics and laser physics is nanoparticles, electronic transport Observatory. Seven faculty members conducted within the department and and inelastic light scattering in low- share appointments with the Department also in association with the Columbia dimensional correlated electron of Earth and Environmental Sciences. Nano Initiative. Facilities include systems, heterostructure physics and In addition to the faculty and laser processing and spectroscopic applications, grain boundaries and graduate students, many others apparatus, ultrahigh vacuum chambers interfaces, nucleation in thin films, participate in these projects, including for surface analysis, picosecond and molecular electronics, nanostructure full-time research faculty, faculty and femtosecond lasers, and a clean room analysis, and electronic structure students from other departments, and that includes photo-lithography and calculations. visiting scientists. thin film fabrication systems. Within this Applied physics is part of the field, the Laser Diagnostics and Solid- Columbia Quantum Initiative. Research Laboratory and Computational State Physics Laboratory conducts opportunities also exist within the Facilities in Applied Physics and studies in laser spectroscopy of Columbia Nano Initiative (CNI), including Applied Mathematics nanomaterials and semiconductor thin the NSF Materials Research Science and films, and laser diagnostics of thin film The Plasma Physics Laboratory, Engineering Center, which focuses on processing. The Laser Lab focuses founded in 1961, is one of the leading low dimensional materials. on the study of laser surface chemical university laboratories for the study of processing and new semiconductor plasma physics in the United States. Applied mathematics. Current research structures. Research is also conducted There are four experimental facilities. encompasses analytical and numerical in the shared characterization The Columbia High-Beta Tokamak analysis of deterministic and stochastic laboratories and clean room operated (HBT-EP) supports the national program partial differential equations, large-scale by CNI. to develop controlled fusion energy. scientific computation, fluid dynamics, The department maintains an It utilizes high voltage, pulsed power dynamical systems and chaos, inverse extensive network of computing systems, and laser and magnetic problems, algorithms for data and clusters and desktop computers. The diagnostics to study the properties learning, as well as applications research of the Plasma Lab is supported of high-beta plasmas and the use of to various fields of physical and by a dedicated data acquisition/data feedback stabilization to increase biological sciences. The applications to analysis system. The department has the achievable beta. A collaborative physical science include quantum and a leadership role in development and program with the Princeton Plasma condensed-matter physics, materials support of Columbia Shared Computing Physics Laboratory and the DIII-D science, electromagnetics, optics, resources and has access to multiple tokamak group at General Atomics HPC clusters. Researchers in the photonics, plasma physics, medical is studying the properties of high- department are additionally using imaging, and the earth sciences, notably beta plasmas in order to maximize supercomputing facilities at the National atmospheric, oceanic, and climate fusion power production in these Center for Atmospheric Research; science, and solid earth geophysics large, neutral beam-heated tokamaks the San Diego Supercomputing (see below). Other applications include and spherical tori. The stellarator Center; the National Energy Research machine learning and biophysical known as Columbia Nonneutral Supercomputer Center in Berkeley, modeling, e.g., collaborations with Torus (CNT) conducts research on California; the National Leadership Columbia’s Data Science Institute (DSI), the magnetohydrodynamic stability, Class Facility at Oak Ridge, Tennessee;

ENGINEERING 2021–2022 50 APPLIED PHYSICS PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

APMA E2000 (4) and E2001 (0) either semester MATHEMATICS1 MATH UN1101 (3) MATH UN1102 (3) and ODE (3)2

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

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

UNIVERSITY CC1010 (3) either semester WRITING

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

REQUIRED (3) Student’s choice TECH ELECTIVES

COMPUTER ENGI E1006 (3)3 any semester SCIENCE

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 Students with advanced standing may start the calculus sequence at a higher level (see page 12 of the Bulletin for placement), in which case students are suggested to add linear algebra in the first two years. 2 Applied physics majors should satisfy their ODE requirement with the Mathematics Department (ordinarily MATH UN2030). Students who take APMA E2101 prior to declaring their major in applied physics may use this course to satisfy their ODE requirement with the permission of the faculty adviser. 3 With permission of faculty adviser, students demonstrating familiarity with computational mathematics using Python may waive course requirement and use 3 credits for another technical course. various allocations via XSEDE; and science. The materials science program technical electives are normally at the others. The Amazon Elastic Compute is described on pages 178–181. 3000 level or above. Cloud (EC2) is also utilized to The applied physics and applied supplement computing resources in mathematics programs provide an UNDERGRADUATE PROGRAM IN times of high demand. excellent preparation for graduate study APPLIED PHYSICS or for careers in which mathematical and The applied physics program stresses Current Research Activities and technical sophistication are important. the basic physics that underlies most Laboratory Facilities in Materials Using the large number of electives in developments in engineering and the Science and Engineering these programs, students can tailor their mathematical tools that are important to programs to fit their personal and career See pages 177–178. both physicists and engineers. Since the interests. By focusing their technical advances in most branches of technology electives, students can obtain a strong lead to rapid changes in state-of-the-art UNDERGRADUATE PROGRAMS base of knowledge in a specialized techniques, the applied physics program The Department of Applied Physics area. In addition to formal minors, some provides the student with a broad base and Applied Mathematics offers three areas of specialization that are available of fundamental science and mathematics undergraduate programs: applied phys- are described on pages 53–54. All ics, applied mathematics, and materials while retaining the opportunity for

ENGINEERING 2021–2022 51 APPLIED PHYSICS: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

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

TECH1 3 points 3 points 2 points 9 points

NONTECH 3 points 3 points 3 points 3 points

ELECTIVES OR TECH

TOTAL POINTS 16 15 16 17

1 They must include at least 2 points of laboratory courses. If PHYS UN3081 is taken as part of the first two years of the program, these technical electives need not include laboratory courses. Technical electives must be at the 3000 level or above unless prior approval is obtained. specialization through technical electives. physics students participate in an informal laboratory in addition to APPH E4018. The applied physics curriculum undergraduate seminar to study current Technical electives must be at the 3000 offers students the skills, experience, and practical problems in applied physics level or above unless prior approval is and preparation necessary for several and obtain hands-on experience in at obtained from the department. A number career options, including opportunities least two advanced laboratory courses. of approved technical electives are to minor in economics and to take Majors are introduced to two areas listed in the section on specialty areas. business-related courses. In recent years, of application of applied physics (AP) by The remaining points of electives are applied physics graduates have entered a course in each of two areas. Approved intended primarily as an opportunity to graduate programs in many areas of areas and courses are complete the absolutely mandatory four- applied physics or physics, enrolled year, 27-point nontechnical requirement in medical school, or been employed DYNAMICAL SYSTEMS: for the B.S. degree, but if this 27-point APMA E4101 or PHYS GU4003 in various technical or financial areas nontechnical requirement has been met immediately after receiving the B.S. OPTICAL OR LASER PHYSICS: already, then any type of coursework can degree. APPH E4110 or E4112 satisfy these elective points. Opportunities for undergraduate NUCLEAR SCIENCE: APPH E4010 research exist in the many research PLASMA PHYSICS: APPH E4301 UNDERGRADUATE PROGRAM IN programs in applied physics. These APPLIED MATHEMATICS include fusion and space plasma physics, PHYSICS OF FLUIDS: APPH E4200 The applied mathematics program is optical and laser physics, and condensed SOLID STATE/CONDENSED MATTER PHYSICS: flexible and intensive. A student must matter physics. Undergraduate students PHYS GU4018 take the required courses listed below, can receive course credit for research BIOPHYSICAL MODELING: APMA E4400 or prove equivalent standing, and or an independent project with a faculty In addition to these courses, courses then may elect the other courses from member. Opportunities also exist for listed in the Specialty Areas in Applied mathematics, computer science, physics, undergraduate students in the applied Physics can be used to satisfy this earth and environmental sciences, physics program to participate in this requirement with preapproval of the biophysics, economics, business and research through part-time employment applied physics adviser. finance, or other application fields. during the academic year and full-time All students must take 30 points of Each student tailors his or her own employment during the summer, either electives in the third and fourth years, program in close collaboration with an at Columbia or as part of the NSF REU of which 17 points must be technical adviser and should confer with their program nationwide. Practical research courses approved by the adviser. The 17 adviser on a regular basis to make experience is a valuable supplement to points include 2 points of an advanced sure they are on track for graduation. the formal course of instruction. Applied

ENGINEERING 2021–2022 52 APPLIED MATHEMATICS PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

APMA E2000 (4) and E2001 (0) either semester MATHEMATICS1 MATH UN1101 (3) MATH UN1102 (3) and ODE (3)2

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

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

UNIVERSITY CC1010 (3) either semester WRITING

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

REQUIRED (3) Student’s choice TECH ELECTIVES

COMPUTER ENGI E1006 (3) any semester SCIENCE

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF E1102 (4) either semester ENGINEERING

1 Students with advanced standing may start the calculus sequence at a higher level (see page 12 of the Bulletin for placement), in which case students are suggested to add linear algebra in the first two years. 2 Applied mathematics majors should satisfy their ODE requirement with the Mathematics Department (ordinarily MATH UN2030). Students who take APMA E2101 prior to declaring their major in applied mathematics may use this course to satisfy their ODE requirement with the permission of the faculty adviser. 3 Transfer students who have not fulfilled the physics requirement prior to enrolling at Columbia may substitute this course with PHYS BC3001. 4 Or a lab course in Astronomy, Astrophysics, Biology, or Chemistry.

In particular, all required courses listed find employment directly in industry, approval of the applied mathematics in the table must be taken to graduate, government, education, or other fields. program chair. however, the specific sequence in which Of the 27 points of elective content they are taken may depend somewhat in the third and fourth years, at least 15 UNDERGRADUATE DOUBLE on the student's area of specialization. points of technical courses approved MAJOR IN APPLIED PHYSICS In general, each student should always by the adviser must be taken. The AND APPLIED MATHEMATICS check with their adviser. He or she must remaining points of electives are also register for the applied mathematics intended primarily as an opportunity to Students satisfy all requirements for seminar during both the junior and senior complete the absolutely mandatory four- both majors, except for the seminar years. During the junior year, the student year, 27-point nontechnical requirement requirements. They are required to take attends the seminar lectures for 0 points; for the B.S. degree, but if this 27-point both senior seminars, APMA E4903 and during the senior year, he or she attends nontechnical requirement has been met APPH E4903 (taking one in the junior the seminar lectures as well as tutorial already, then any type of coursework year and one in the senior year, due problem sessions for 3 or 4 points. can satisfy these elective points. to timing conflicts), but not the junior While it is common for students Transfers into the applied seminars, APMA E4901 and APPH in the program to go on to graduate mathematics program from other majors E4901. A single foundational course may school, many graduating seniors will require a GPA of 3.0 or above, and the be used to fulfill a requirement in both majors. Students must maintain a GPA at

ENGINEERING 2021–2022 53 APPLIED MATHEMATICS: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

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

TECH4 3 points 3 points 3 points 6 points

NONTECH 3 points 3 points 3 points 3 points ELECTIVES

TOTAL POINTS 15 15 16 15

1 MATH UN2010 or COMS W3561 may be substituted for APMA E3101; MATH UN3028 may be substituted for APMA E3102; MATH UN3007 may be substituted for APMA E4204; MATH UN2500 may be substituted for MATH GU4061. 2 One course from Group A (Probability) and one course from Group B (Applied Probability/Statistics) required for graduation. Group A: IEOR E3658: Probability for engineers or IEOR E4150: Introduction to probability and statistics; STAT GU4203: Probability theory; MATH W4155: Probability theory. Group B: IEOR E3106: Stochastic systems and applications; IEOR E4106: Stochastic models; STAT GU4204: Statistical inference; STAT GU4207: Elementary stochastic processes; COMS W4771: Machine learning. 3 With an adviser’s permission, an approved technical elective may be substituted. 4 Any course in science, math, 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. Elective courses may be chosen from other departments in SEAS and Arts and Sciences, e.g., the Departments of Mechanical Engineering, Electrical Engineering, Mathematics, and Statistics. or above 3.75, and must graduate with and interests. Some specialties are given • Earth and Atmospheric Sciences at least 143 points, 15 above the regular below, but this is not an exclusive list, and The earth sciences provide a wide 128-point requirement. These extra 15 others can be worked out in coordination range of problems of interest to points should be technical electives with the student’s adviser. The courses that physicists and mathematicians ranging appropriate for one or both majors. are often taken, or in some cases need to from the dynamics of Earth’s climate be taken, in the junior year are denoted to earthquake physics to dynamics To apply, a student first obtains with a “J.” of Earth’s deep interior. The Lamont- the approval of both the general Doherty Earth Observatory, which is undergraduate Applied Physics adviser Technical Electives part of Columbia University, provides and the general undergraduate Applied • Applications of Physics enormous resources for students Mathematics adviser, and then the Courses that will give a student a broad interested in this area. approval of the Dean. background in applications of physics: ATMOSPHERE, OCEANS, AND CLIMATE ELEN E3000x: Circuits, systems, and APAM E3109: Climate physics SPECIALTY AREAS IN APAM electronics (J) EESC GU4008: Intro to atmospheric science Both applied physics and applied math- MSAE E3010x: Introduction to materials APPH E4200: Physics of fluids science, I ematics students can focus their technical APPH E4210: Geophysical fluid dynamics APPH E4010x: Intro to nuclear science EESC GU4925: Principles of physical electives and develop a strong base of PHYS GU4018y: Solid-state physics oceanography knowledge in a specialty area. There is APMA E4101x: Intro to dynamical systems EESC GU4930: Earth’s oceans and no requirement to focus electives, so APPH E4110y: Modern optics atmosphere students may take as many or as few of APPH E4112x: Laser physics the recommended courses in a specialty APPH E4200x: Physics of fluids SOLID EARTH GEOPHYSICS Intro to plasma physics area as is appropriate to their schedules APPH E4301y: EESC UN3201: Solid earth dynamics EESC GU4085: Geodynamics

ENGINEERING 2021–2022 54 EESC GU4113: Intro to mineralogy • Fundamental Mathematics in Applied The second term of biology will be EESC GU4300: Earth's deep interior Mathematics considered a technical elective if a EESC GU4701: Intro to igneous petrology This specialization is intended for student has credits from at least two Introduction to seismology EESC GU4949: students who desire a more solid other of the recommended courses in (See also courses listed under foundation in the mathematical quantitative biology at the 3000 level Scientific Computation and Computer methods and underlying theory. For or above. Science below.) example, this specialization could be • Scientific Computation and Computer followed by students with an interest in Science • Basic Physics and Astrophysics graduate work in applied mathematics. Advanced computation has become Fundamental physics and astrophysics a core tool in science, engineering, can be emphasized. Not only is MATH UN3386x: Differential geometry APMA E4101x: Intro to dynamical systems and mathematics and provides astrophysics providing a deeper APMA E4150x: Applied functional analysis challenges for both physicists understanding of the universe, but it is MATH GU4032x: Fourier analysis and mathematicians. Courses also testing the fundamental principles MATH GU4062y: Modern analysis, II that build on both practical and of physics. STAT GU4001x, y: Intro to probability and theoretical aspects of computing and statistics (J) PHYS UN3002y: From quarks to the cosmos: computation include: Geometrical applications of modern PHYS GU4386x-GU4387y: concepts in physics MATH UN3020x: Number theory and physics cryptography (J) ASTR UN3601x: General relativity, black holes, COMS W3137x,y: Data structures and and cosmology (J) • Quantitative Biology algorithms (or COMS W3139y: ASTR UN3602y: Physical cosmology (J) Traditionally biology was considered a Honors data structures and ASTR GU4001y: Astrophysics, I descriptive science in contrast to the algorithms) (J) APMA E4101x: Intro to dynamical systems quantitative sciences that are based COMS W3157x,y: Advanced programming (J) on mathematics, such as physics. This COMS W3203x,y: Discrete mathematics: intro • Business and Finance view no longer coincides with reality. to combinatorics and graph The knowledge of physics and math- Researchers from biology as well as theory (J) ematics that is gained in the applied from the physical sciences, applied COMS W4203y: Graph theory physics and applied mathematics APMA E4300x: Intro to numerical methods mathematics, and computer science programs is a strong base for a career APMA E4301y: Numerical methods for partial are rapidly building a quantitative base in business or finance. differential equations of biological knowledge. Students can APMA E4302x: Methods in computational science ECONOMICS acquire a strong base of knowledge in quantitative biology, both biophysics COMS W4701x,y: Artificial intelligence ECON UN3211x,y: Intermed microeconomics (J) COMS W4771y: Machine learning ECON UN3213x,y: Intermed macroeconomics(J) and computational biology, while completing the applied physics or INDUSTRIAL ENGINEERING • Solid-State Physics applied mathematics programs. AND OPERATIONS RESEARCH Much of modern technology is based IEOR E4003x: Industrial economics RECOMMENDED: on solid-state physics, the study of IEOR E4201x: The eng of management, I BIOL UN2005x-UN2006y: Intro biology, I solids and liquids. Courses that will IEOR E4202y: The eng of management, II and II build a strong base for a career in this APPH E3400y: Physics of the human body area are FINANCE APMA E4400y: Intro to biophysical modeling MATH GU4071x: Mathematics of finance PHYS UN3083y: Electronics laboratory (J) IEOR E4106y: Intro to operations research: OTHER TECHNICAL ELECTIVES (A COURSE IN MSAE E3110x: Introduction to materials stochastic models (J) AT LEAST TWO AREAS RECOMMENDED): science, I STAT GU4001x,y: Probability and statistics (J) ELEN E3106x: Solid-state devices and BIOLOGICAL MATERIALS ECON GU4280x,y: Corporate finance materials (J) IEOR E4700x: Intro to financial engineering BIOL GU4070x: The biology and physics of MSAE E4100x: Crystallography single molecules PHYS GU4018y: Solid-state physics • Mathematics Applicable to Physics CHEN E4650x: Biopolymers MSAE E4206x: Electronic and magnetic properties of solids Applied physics students can specialize BIOMECHANICS in the mathematics that is applicable BMEN E3320y: Fluid biomechanics (J) to physics. This specialization is BMEN E4300y: Solid biomechanics (J) UNDERGRADUATE PROGRAM IN particularly useful for students MATERIALS SCIENCE interested in theoretical physics. GENOMICS AND BIOINFORMATICS See page 178. MATH UN3386x: Differential geometry BIOL UN3037y: Whole genome bioinformatics Intro to dynamical systems (J) APMA E4101x: GRADUATE PROGRAMS APMA E4301y: Numerical methods for partial ECBM E3060x: Intro to genomic information differential equations science and technology (J) Financial aid is available for students APMA E4302x: Methods in computational CBMF W4761y: Computational genomics pursuing a doctorate. Fellowships, science scholarships, teaching assistantships, PHYS GU4019y: Mathematical methods of NEUROBIOLOGY and graduate research assistantships physics BIOL UN3004x: Neurobiology, I (J) are awarded on a competitive basis. Neurobiology, II (J) BIOL UN3005y: The Aptitude Test of the Graduate Computational neuroscience ELEN E4011x: Record Examination is required of

ENGINEERING 2021–2022 candidates for admission to the must complete five of the following nine Other elective courses may be 55 department and for financial aid; the courses: chosen from other departments in Advanced Tests are recommended. SEAS and Arts and Sciences, e.g., M.S. students must complete APMA E4101: Intro to dynamical systems the Departments of Mechanical the professional development and APMA E4150: Applied functional analysis APMA E4200: Partial differential equations Engineering, Electrical Engineering, leadership course, ENGI E4000, as APMA E4204: Functions of a complex variable Mathematics, and Statistics. a graduation requirement. Doctoral APMA E4300: Intro to numerical methods students will be enrolled in ENGI E6001– APMA E4301: Numerical methods for partial M.S. Program in Materials Science 6004 and should consult their program differential equations and Engineering for specific PDL requirements. APMA E6301: Analytic methods for partial See page 181. Ethics training is required of all differential equations students pursuing a doctorate. APMA E6302: Numerical analysis for partial differential equations M.S. Program in Medical Physics M.S. Program in Applied Physics This CAMPEP-approved 36-point Students must also take a required program in medical physics leads to the This 30-point program of study leading Research Seminar course, APMA E6100 M.S. degree. It is administered by faculty to the degree of Master of Science, x or y from the School of Engineering and while emphasizing continued work in Applied Science in collaboration with basic physics, permits many options in A student must select five elective faculty from the College of Physicians several applied physics specialties. The courses from those listed below (or any and Surgeons and the Mailman School program may be considered simply as of those not used to satisfy the core of Public Health. It provides preparation additional education in areas beyond requirements from the list above) for toward certification by the American the bachelor’s level, or as preparatory to a total of 15 points of graduate credit. Board of Radiology. The program doctoral studies in the applied physics Additional courses not listed below consists of a core curriculum of medical fields of plasma physics, laser physics, can be applied toward the elective and nuclear physics courses, anatomy, or solid-state physics. Specific course requirements, subject to the approval of lab, seminar, a tutorial, one elective, requirements for the master’s degree the faculty adviser*. and two practicums. Specific course are determined in consultation with the requirements are APPH E4010, E4330, program adviser, but must include four *Courses from the Department of E4710, E4500, E4550, E4600, E6319, of the six core courses listed below. Economics, School of Business, School E6330, E6335, and APBM E4650. The core courses provide a of International and Public Affairs, or Approved electives include APPH E4711, student with a solid foundation in the quantitative courses offered by the APPH E6336, APAM E6650, and a third fundamentals of applied physics, but School of Professional Studies may not practicum. Up to 6 points of this 36-point with the approval of the faculty adviser, be counted as electives toward the program may be waived based on prior other graduate-level courses with APPH degree. equivalent academic work. A student designators not listed below may also Computer science elective courses who enters the 36-point M.S. Program. count as core courses. include: in Medical Physics, having satisfactorily completed, prior to beginning the APPH E4100: Quantum physics of matter CSOR W4231: Analysis of algorithms, I APPH E4110: Modern optics COMS W4236: Intro to computational complexity Program, a course determined by the APPH E4112: Laser physics COMS W4241: Numerical algorithms and faculty to be equivalent in content to APPH E4200: Physics of fluids complexity a required course within the Program, APPH E4300: Applied electrodynamics COMS W4252: Computational learning theory may be considered to have satisfied that APPH E4301: Introduction to plasma physics content requirement, may be allowed Industrial engineering/operations to have that requirement waived, and M.S. Program in Applied Mathematics research elective courses include**: may be permitted to graduate from the This 30-point program leads to a M.S. Program in Medical Physics with Industrial economics Master of Science degree. Students IEOR E4003: fewer than 36 points, but not fewer IEOR E4004: Intro to operations research: than the 30-point minimum required by must complete five core courses and deterministic models the School of Engineering and Applied five electives. All degree requirements IEOR E4007: Optimization: models and must be completed within five years. A methods Science. Evaluation of prior coursework candidate is required to maintain at least IEOR E4106:  Stochastic models may include review of syllabi, a 2.5 grade point average. If a student STAT GU4001: Intro to probability and statistics comparison of textbooks, consultation admitted to the Applied Mathematics IEOR E4403:  Advanced engineering and with instructors, and/or written or M.S. only program is interested in the corporate economics oral examination administered by Ph.D. program, the student must reapply IEOR E4407:  Game theoretic models of Program faculty. A passing grade on a operations for admission. The core courses provide comprehensive examination is required STAT GU4606: Elementary stochastic processes for graduation. This examination, on a student with a foundation in the IEOR E4700: Intro to financial engineering fundamentals of applied mathematics subjects covered in the curriculum, is and contribute 15 points of graduate **Please check IEOR website for registration taken after two terms of study. credit toward the degree. Students procedures required of non-IEOR students.

ENGINEERING 2021–2022 56 Certification of Professional is more interested in problems coming MATH GU4032: Fourier analysis Achievement in Medical Physics from other fields. Compared with the This graduate program of instruction engineer and the physical scientist, the Materials Science leads to the Certification of Professional applied mathematician is more concerned and Engineering Program Achievement and requires satisfactory with the formulation of problems and See page 181. completion of six of the following courses: the nature of solutions. Compared with the computer scientist, the applied Applied Physics APPH E4330: Radiobiology mathematician is more concerned with This doctoral program has three APPH E4500: Health physics the accuracy of approximations and the APPH E4600: Dosimetry interpretation of results. Needless to specialties. APPH E4018 Applied physics APBM E4650: Anatomy for physicists and say, even in this age of specialization, laboratory is required for each of the engineers the work of mathematicians, scientists, three specialties in the first year of APPH E6319: Clinical nuclear medicine physics and engineers frequently overlaps. the doctoral program, in addition to Diagnostic radiology physics or APPH E6330: Applied mathematics, by its very nature, any specific courses required of each APPH E6335: Radiation therapy physics has occupied a central position in this specialty. or APPH E6336: Advanced topics in radiation therapy interplay and has remained a field of fascination and excitement for active Plasma Physics This is a part-time nondegree program. minds. This graduate specialty is designed to Students are admitted to the department The Applied Analysis specialty emphasize preparation for professional as certificate-track students. includes research on analytical and careers in plasma research, controlled numerical partial differential equations; fusion, and space research. This PH.D. AND ENG.SC.D. PROGRAMS mathematical foundations of data includes basic training in relevant areas analytics, uncertainty quantification, of applied physics, with emphasis After completing the M.S. program, stochastic analysis; large-scale scientific on plasma physics and related areas doctoral students specialize in one area computation; fluid dynamics and of their programs. Some specializations leading to extensive experimental and continuum mechanics; dynamical systems have specific course requirements for theoretical research in the Columbia and chaos; and applications to various the doctorate; elective courses are University Plasma Physics Laboratory. fields of data and physical and life determined in consultation with the Specific course requirements for the sciences. program adviser. Successful completion plasma physics doctoral program The Atmospheric, Oceanic, and Earth of an approved 30-point program of are APPH E4018, E4200, E4300, Physics specialty includes research on study is required in addition to successful E6101, E6102, and E9142 or E9143, or dynamics of the atmosphere and the completion of a written qualifying equivalents taken at another university. ocean; climate modeling; cloud physics; examination taken after two semesters radiation transfer; remote sensing; of graduate study. An oral examination, Optical and Laser Physics geophysical/geological fluid dynamics; taken within one year after the written This graduate specialty involves a basic and geochemistry. qualifying examination, and a thesis training in relevant areas of applied proposal examination, taken within physics, with emphasis in quantum Courses: two years after the written qualifying mechanics, quantum electronics, and APMA E4101: Intro to dynamical systems examination, are required of all doctoral APMA E4150: Applied functional analysis related areas of specialization. Some candidates, as is training in research and APMA E4200: Partial differential equations active areas of research in which professional ethics in the first two years APMA E4204: Functions of a complex variable the student may concentrate are of the doctoral program. APMA E4300: Intro to numerical methods laser modification of surfaces, optical APMA E4301: Numerical methods for partial diagnostics of film processing, inelastic differential equations Applied Mathematics light scattering in nanomaterials, Applied mathematics deals with APMA E4302: Intro to computational science APMA E4400: Intro to biophysical modeling nonlinear optics, ultrafast optoelectronics mathematical concepts and techniques APMA E6301: Analytic methods for partial photonic switching, optical physics used in various fields of science and differential equations of surfaces, and photon integrated engineering. Historically, mathematics APMA E6302: Numerical analysis for partial circuits. Specific course requirements was first applied with great success differential equations for the optical and laser physics doctoral in astronomy and mechanics. Then it specialization are set with the academic developed into a main tool for physics, Related courses of specialization: other physical science, and engineering. APMA E6901: Special topics in applied mathematics adviser. It is now becoming important in the APMA E8308: Asymptotic methods in applied biological, geological, economics, mathematics Solid-State Physics business, etc. With the coming of age APPH E4210: Geophysical fluid dynamics This graduate specialty encompasses APMA E9815: Geophysical fluid dynamics of the computer, applied mathematics the study of the electrical, optical, seminar transcended its traditional style and now COMS E4205: Combinatorial theory magnetic, thermal, high-pressure, and assumes an even greater importance COMS E4241: Numerical algorithms and ultrafast dynamical properties of solids, and a new vitality. complexity with an aim to understanding them Compared with the pure EESC GU4008: Introduction to atmospheric in terms of the atomic and electronic mathematician, the applied mathematician science structure. The field emphasizes the PHYS GU4019: Mathematical methods in physics

ENGINEERING 2021–2022 formation, processing, and properties of Prerequisite(s): PHYS UN1201 or UN1401, and APPH E4018y Applied physics laboratory 57 thin films, low-dimensional structures— Calculus I. Corequisites: PHYS UN1202 or UN1402, 2 pts. Lab: 4. Professor Mauel. such as one- and two-dimensional and Calculus II. This introductory course analyzes Prerequisite(s): APPH E3300 or ELEN E3401 or electron gases, nanocrystals, surfaces the human body from the basic principles of equivalent. Typical experiments are in the areas physics. Topics covered include the energy bal- of plasma physics, microwaves, laser applications, of electronic and optoelectronic ance in the body, the mechanics of motion, fluid optical spectroscopy physics, and superconduc- interest, and molecules. Facilities dynamics of the heart and circulation, vibrations tivity. include a microelectronics laboratory, in speaking and hearing, muscle mechanics, gas high-pressure diamond anvil cells, exchange and transport in the lungs, vision, struc- APCH E4080x Soft condensed matter a molecular beam epitaxy machine, tural properties and limits, electrical properties 3 pts. Lect: 3. Professor Gang. and the development and sensing of magnetic Prerequisite(s): MSAE E3111, CHEE E3010, or CHEN ultrahigh vacuum systems, lasers, E3120 or equivalent. Course is aimed at senior equipment for the study of optical fields, and basics of equilibrium and regulatory control. In each case, a simple model of the body undergraduate and graduate students. Introduces properties and transport on the organ, property, or function will be derived and fundamental ideas, concepts, and approaches nanoscale, and the instruments in then applied. in soft condensed matter with emphasis on bio- the shared facilities overseen by the molecular systems. Covers the broad range of Columbia Nano Initiative (CNI). There APPH E3900x and y Undergraduate research molecular, nanoscale, and colloidal phenomena are also significant resources for in applied physics with revealing their mechanisms and physical 0–4 pts. Members of the faculty. foundations. The relationship between molecular electrical and optical experimentation Prerequisite(s): Written permission from instructor architecture and interactions and macroscopic at low temperatures and high magnetic and approval from adviser. May be repeated for behavior are discussed for the broad range of soft fields. Specific course requirements credit, but no more than 6 points may be counted and biological matter systems, from surfactants for the solid-state physics doctoral toward the satisfaction of the B.S. degree require- and liquid crystals to polymers, nanoparticles, and specialization are set with the academic ments. Candidates for the B.S. degree may con- biomolecules. Modern characterization methods adviser, in consultation with the duct an investigation in applied physics or carry for soft materials, including X-ray scattering, Committee on Materials Science and out a special project under the supervision of the molecular force probing, and electron microcopy staff. Credit for course is contingent upon the sub- are reviewed. Example problems, drawn from Engineering/Solid-State Science and mission of an acceptable thesis or final report. the recent scientific literature, link the studied Engineering. materials to the actively developed research APAM E3999x, y or s Undergraduate areas. Course grade based on midterm and final fieldwork exams, weekly homework assignments, and final COURSES IN APPLIED PHYSICS 1–2 pts. Members of the faculty. individual/team project. Prerequisite(s): Obtained internship and approval APPH E3100y Introduction to quantum from adviser. Restricted to ENAPMA, ENAPPH, APPH E4090y Nanotechnology mechanics ENMSAE. May be repeated for credit, but no 3 pts. Lect: 3. Not offered in 2021–2022. 3 pts. Lect: 3. Professor Herman. more than 3 total points may be used toward the Prerequisite(s): APPH E3100 and MSAE E3010 or Prerequisite(s): PHYS UN1403 or equivalent, and 128-credit degree requirement. Only for APAM their equivalents with instructor’s permission. The differential and integral calculus. Corequisites: undergraduate students who include relevant science and engineering of creating materials, APMA E3101 or equivalent. Basic concepts off-campus work experience as part of their functional structures and devices on the nano- and assumptions of quantum mechanics, approved program of study. Final report and letter meter scale. Carbon nanotubes, nanocrystals, Schrodinger’s equation, solutions for one- of evaluation required. Fieldwork credits may not quantum dots, size dependent, properties, self- dimensional problems, including square wells, count toward any major core, technical, elective, assembly, nanostructured materials. Devices and barriers, and the harmonic oscillator, introduction or nontechnical requirements. May not be taken applications, nanofabrication. Molecular engineer- to the hydrogen atom, atomic physics and X-rays, for pass/fail credit or audited. ing, bionanotechnology. Imaging and manipulat- electron spin. ing at the atomic scale. Nanotechnology in society APPH E4008x Introduction to atmospheric and industry. APPH E3200x Mechanics: fundamentals and science applications 3 pts. Lect: 3. Professor Polvani. APPH E4100x Quantum physics of matter 3 pts. Lect: 3. Professor Mauel. Prerequisite(s): Advanced calculus and general 3 pts. Lect: 3. Professor Venkataraman. Prerequisite(s): PHYS UN1402, MATH UN2030, physics, or instructor’s permission. Basic physi- Prerequisite(s): APPH E3100. Corequisite: APMA or equivalent. Basic non-Euclidean coordinate cal processes controlling atmospheric structure: E3102 or equivalent. Basic theory of quantum systems, Newtonian mechanics, oscillations, thermodynamics; radiation physics and radiative mechanics, well and barrier problems, the har- Green’s functions, Newtonian gravitation, transfer; principles of atmospheric dynamics; monic oscillator, angular momentum identical Lagrangian mechanics, central force motion, cloud processes; applications to Earth’s atmo- particles, quantum statistics, perturbation theory two-body collisions, noninertial reference frames, spheric general circulation, climatic variations, and applications to the quantum physics of atoms, rigid body dynamics. Applications, including GPS and the atmospheres of the other planets. molecules, and solids. and feedback control systems, are emphasized APPH E4110y Modern optics throughout. APPH E4010x Introduction to nuclear science 3 pts. Lect: 3. Professor Ostrow. 3 pts. Lect: 3. Professor Yu. APPH E3300y Applied electromagnetism Prerequisite(s): MATH UN1202 or APMA E2000, Prerequisite(s): APPH E3300. Ray optics, matrix 3 pts. Lect: 3. Professor Navratil. and UN2030 and PHYS UN1403 or equivalents. formulation, wave effects, interference, Gaussian Corequisite: APMA E3102. Vector analysis, elec- Introductory course for individuals with an interest beams, Fourier optics, diffraction, image forma- trostatic fields, Laplace’s equation, multipole in medical physics and other branches of radiation tion, electromagnetic theory of light, polarization expansions, electric fields in matter: dielectrics, science. Topics include basic concepts, nuclear and crystal optics, coherence, guided wave and magnetostatic fields, magnetic materials, and models, semiempirical mass formula, interac- fiber optics, optical elements, photons, selected superconductors. Applications of electromag- tion of radiation with matter, nuclear detectors, topics in nonlinear optics. netism to devices and research areas in applied nuclear structure and instability, radioactive decay APPH E4112x Laser physics physics. process and radiation, particle accelerators, and 3 pts. Lect: 3. Professor Yu. fission and fusion processes and technologies. APPH E3400y Physics of the human body Recommended but not required: APPH E3100 3 pts. Lect: 3. Not offered in 2021–2022. and E3300 or their equivalents. Optical resona-

ENGINEERING 2021–2022 58 tors, interaction of radiation and atomic systems, experimental demonstrations of catalysis in APPH E4500x Health physics theory of laser oscillation, specific laser systems, electric fields. Each topic will draw on elements 3 pts. Lect: 3. Professor Caracappa. rate processes, modulation, detection, harmonic of organometallic/organic catalysis, quantum Prerequisite(s): APPH E4600 or Corequisite: APPH generation, and applications. mechanics, enzymatic catalysis, and nano elec- E4600. Fundamental principles and objectives of tronics to form the basis for understanding this health physics (radiation protection), quantities of APPH E4114y Quantum and nonlinear new branch of catalytic science. radiation dosimetry (the absorbed dose, equiva- photonics lent dose, and effective dose) used to evaluate 3 pts. Lect: 3. Professor Gaeta. APPH E4200x Physics of fluids human radiation risks, elementary shielding Prerequisite(s): APPH E3300 and PHYS UN3008. 3 pts. Lect: 3. Not offered in 2021–2022. calculations and protection measures for clinical Advanced senior-level/M.S./Ph.D. course cover- Prerequisite(s): APMA E3102 or equivalent; PHYS environments, characterization and proper use of ing interaction of laser light with matter in both UN1401 or UN1601 or equivalent. An introduction health physics instrumentation, and regulatory classical and quantum domains. First half intro- to the physical behavior of fluids for science and and administrative requirements of health physics duces microscopic origin of optical nonlinearities engineering students. Derivation of basic equa- programs in general and as applied to clinical through formal derivation of nonlinear susceptibil- tions of fluid dynamics: conservation of mass, activities. ities, emphasis on second- and third-order optical momentum, and energy. Dimensional analysis. processes. Topics include Maxwell's wave equa- Vorticity. Laminar boundary layers. Potential APPH E4550y Medical physics seminar tion, and nonlinear optical processes such as sec- flow. Effects of compressibility, stratification, and 0 pts. Lect: 1. Professor Wuu. ond-harmonic, difference-frequency generation, rotation. Waves on a free surface; shallow water Required for all graduate students in the Medical four-wave mixing, and self-phase modulation, equations. Turbulence. Physics Program. Practicing professionals and including various applications of processes such faculty in the field present selected topics in as frequency conversion, and optical parametric APPH E4210y Geophysical fluid dynamics medical physics. amplifiers and oscillators. Second half describes 3 pts. Lect: 3. Professor Polvani. two-level atomic systems and quantization of Prerequisite(s): APMA E3101, E3102 (or equiva- APPH E4600x Fundamentals of radiological electromagnetic field. Descriptions of coherent, lents) and APPH E4200 (or equivalent), or permis- physics and radiation dosimetry Fock, and squeezed states of light discussed and sion from instructor. Fundamental concepts in the 3 pts. Lect: 3. Members of the faculty. techniques to generate such states outlined. dynamics of rotating, stratified flows. Geostrophic Prerequisite(s): APPH E4010 or equivalent or and hydrostatic balances, potential vorticity, f and Corequisite: APPH E4010. Basic radiation physics: CHAP E4120y Statistical mechanics beta plane approximations, gravity and Rossby radioactive decay, radiation producing devices, 3 pts. Lect: 3. Professor O’Shaughnessy. waves, geostrophic adjustment and quasigeo- characteristics of the different types of radiation Prerequisite(s): CHEN E3210 or equivalent strophy, baroclinic and barotropic instabilities, (photons, charged and uncharged particles) and thermodynamics course, or instructor’s permis- Sverdrup balance, boundary currents, Ekman mechanisms of their interactions with materials. sion. Fundamental principles and underlying layers. Essentials of the determination, by measurement assumptions of statistical mechanics. Boltzmann’s and calculation, of absorbed doses from ionizing APPH E4300x Applied electrodynamics entropy hypothesis and its restatement in terms radiation sources used in medical physics (clinical) 3 pts. Lect: 3. Professor Gaeta. of Helmholtz and Gibbs free energies and for situations and for health physics purposes. open systems. Correlation times and lengths. Prerequisite(s): APPH E3300. Overview of proper- Exploration of phase space and observation time ties and interactions of static electric and magnet- APBM E4650x Anatomy for physicists and scale. Correlation functions. Fermi-Dirac and ic fields. Study of phenomena of time dependent engineers Bose-Einstein statistics. Fluctuation-response the- electric and magnetic fields including induction, 3 pts. Lect: 3. Professors Rozenshtein and Katz. ory. Applications to ideal gases, interfaces, liquid waves, and radiation as well as special relativity. Prerequisite(s): Engineering or physics back- crystals, microemulsions and other complex fluids, Applications are emphasized. ground. Systemic approach to the study of the human body from a medical imaging point of polymers, Coulomb gas, interactions between APPH E4301y Introduction to plasma physics view: skeletal, respiratory, cardiovascular, diges- charged polymers and charged interfaces, order- 3 pts. Lect: 3. Not offered in 2021–2022. tive, and urinary systems, breast and women’s ing transitions. Prerequisite(s): PHYS UN3008 or APPH E3300. issues, head and neck, and central nervous Definition of a plasma. Plasmas in laboratories APPH E4130x Physics of solar energy system. Lectures are reinforced by examples from and nature, plasma production. Motion of charged 3 pts. Lect: 3. Professor Chen. clinical two- and three-dimensional and functional particles in electric and magnetic fields, adiabatic Prerequisite(s): General physics (PHYS UN1403 or imaging (CT, MRI, PET, SPECT, U/S, etc.). UN1602) and mathematics, including ordinary dif- invariants. Heuristic treatment of collisions, dif- ferential equations and complex numbers (such as fusion, transport, and resistivity. Plasma as a APPH E4710x Radiation instrumentation and MATH UN1202 or UN2030) or instructor’s permis- conducting fluid. Electrostatic and magnetostatic measurement laboratory, I sion. The physics of solar energy including solar equilibria of plasmas. Waves in cold plasmas. 3 pts. Lect: 1. Lab: 4. Professors Ostrow and radiation, the analemma, atmospheric efforts, Demonstration of laboratory plasma behavior, Zaider. thermodynamics of solar energy, physics of solar measurement of plasma properties. Illustrative Prerequisite or corequisite: APPH E4010. Lab fee: cells, energy storage and transmission, and phys- problems in fusion, space, and nonneutral or $50. Theory and use of alpha, beta, gamma, and ics and economics in the solar era. beam plasmas. X-ray detectors and associated electronics for counting, energy spectroscopy, and dosimetry; APPH E4330y Radiobiology for medical APPH E4164x Electric field effects in catalysis radiation safety; counting statistics and error physicists 3 pts. Lect: 2.5. Professors Berkelbach, propagation; mechanisms of radiation emission 3 pts. Lect: 3. Professor Zaider. Nuckolls, Rovis, Roy, and Venkatataman. and interaction. (Topic coverage may be revised.) Prerequisite(s): physical chemistry or equivalent. Prerequisite(s): APPH E4010 or equivalent or Real-time exposition of an emerging area of study Corequisite: APPH E4010. Interface between clini- APPH E4711x or y Radiation instrumentation at the interface between chemistry, physics, engi- cal practice and quantitative radiation biology. and measurement laboratory, II neering, and biology to understand and control Microdosimetry, dose-rate effects and biological 3 pts. Lect: 1. Lab: 4. Not offered in 2021–2022. how electric fields can be used to catalyze chemi- effectiveness thereof; radiation biology data, Prerequisite(s): APPH E4710. Lab fee: $50. cal transformations. Taught by a cross-disciplinary radiation action at the cellular and tissue level; Additional detector types; applications and sys- group of faculty. Topics covered: (1) theoretical radiation effects on human populations, carci- tems including coincidence, low-level, and liquid underpinnings for catalysis in nanoscale electri- nogenesis, genetic effects; radiation protection; scintillation counting; neutron activation; TLD cal environments, (2) experimental tools used tumor control, normal-tissue complication prob- dosimetry, gamma camera imaging. (Topic cover- to study these chemical transformations, (3) abilities; treatment plan optimization. age may be revised.)

ENGINEERING 2021–2022 APPH E4901x Seminar: problems in applied APPH E6091y Magnetism and magnetic and requires a laboratory report. Two areas are 59 physics materials emphasized: 1. computer-assisted treatment plan- 1 pt. Lect: 1. Professor Mauel. 3 pts. Lect. 3. Not offered in 2021–2022. ning (design of typical treatment plans for various Required for, and can be taken only by, all Prerequisite(s): MSAE E4206, APPH E6081, or treatment sites including prostate, breast, head applied physics majors and minors in the junior equivalent. Types of magnetism. Band theory of and neck, lung, brain, esophagus, and cervix) year. Discussion of specific and self-contained ferromagnetism. Magnetic metals, insulators, and and 2. clinical dosimetry and calibrations (radia- problems in areas such as applied electrodynam- semiconductors. Magnetic nanostructures: ultra- tion measurements for both photon and electron ics, physics of solids, and plasma physics. Topics thin films, superlattices, and particles. Surface beams, as well as daily, monthly, and part of change yearly. magnetism and spectroscopies. High speed mag- annual QA). netization dynamics. Spin electronics. APPH E4903x Seminar: problems in applied APPH E6335y Radiation therapy physics physics APPH E6101x Plasma physics, I 3 pts. Lect: 3. Professors Wuu and Hamacher. 2 pts. Lect: 1. Tutorial: 1. Professor Mauel. 3 pts. Lect: 3. Professor Navratil. Prerequisite(s): APPH E4600; APPH E4330 Required for, and can be taken only by, all applied Prerequisite(s): APPH E4300. Debye screen- recommended. Review of X-ray production and physics majors in the senior year. Discussion of ing. Motion of charged particles in space- and fundamentals of nuclear physics and radioactiv- specific and self-contained problems in areas time-varying electromagnetic fields. Two-fluid ity. Detailed analysis of radiation absorption and such as applied electrodynamics, physics of sol- description of plasmas. Linear electrostatic and interactions in biological materials as specifically ids, and plasma physics. Formal presentation of a electromagnetic waves in unmagnetized and related to radiation therapy and radiation therapy term paper required. Topics change yearly. magnetized plasmas. The magnetohydrodynamic dosimetry. Surveys of use of teletherapy isotopes (MHD) model, including MHD equilibrium, stability, and X-ray generators in radiation therapy plus APPH E4990x and y Special topics in applied and MHD waves in simple geometries. the clinical use of interstitial and intracavitary physics isotopes. Principles of radiation therapy treatment 1–3 pts. Members of the faculty. APPH E6102y Plasma physics, II planning and isodose calculations. Problem sets Prerequisite(s): Instructor’s permission. May be 3 pts. Lect: 3. Professor Paz-Soldan. taken from actual clinical examples are assigned. repeated for credit. Topics and instructors change Prerequisite(s): APPH E6101. Magnetic coordi- from year to year. For advanced undergraduate nates. Equilibrium, stability, and transport of APPH E6336x Advanced topics in radiation students and graduate students in engineering, toroidal plasmas. Ballooning and tearing instabili- therapy physical sciences, and other fields. ties. Kinetic theory, including Vlasov equation, 3 pts. Lect: 3. Professor Wuu. Fokker-Planck equation, Landau damping, kinetic Prerequisite(s): APPH E6335. Advanced technol- APAM E4999x and y–S4999 Supervised transport theory. Drift instabilities. ogy applications in radiation therapy physics, internship including intensity modulated, image guided, 1–3 pts. Members of the faculty. APPH E6110x Laser interactions with matter stereotactic, and hypofractionated radiation Prerequisite(s): Obtained internship and approval 3 pts. Lect: 3. Not offered in 2021–2022. therapy. Emphasis on advanced technological, from adviser. Only for master’s students in the Prerequisite(s): APPH E4112 or equivalent, and engineering, clinical and quality assurance issues Department of Applied Physics and Applied quantum mechanics. Principles and applications associated with high-technology radiation therapy Mathematics who may need relevant work expe- of laser-matter coupling, nonlinear optics, three- and the special role of the medical physicist in the rience as part of their program of study. Final and four-wave mixing, harmonic generation, laser safe clinical application of these tools. report required. May not be taken for pass/fail or processing of surfaces, laser probing of materials, audited. spontaneous and stimulated light scattering, satu- APPH E6340x or y Diagnostic radiology ration spectroscopy, multiphoton excitation, laser practicum APPH E6081x Solid state physics, I isotope separation, transient optical effects. 3 pts. Lab: 6. Professor Jambawalikar. 3 pts. Lect: 3. Professor Pinczuk. Prerequisite(s): Grade of B+ or better in APPH Prerequisite(s): APPH E3100 or the equivalent. APPH E6319y Clinical nuclear medicine E6330 and instructor’s permission. Practical Knowledge of statistical physics on the level of physics applications of diagnostic radiology for various MSAE E3111 or PHYS GU4023 strongly recom- 3 pts. Lect: 3. Professor Zanzonico. measurements and equipment assessments. mended. Crystal structure, reciprocal lattices, Prerequisite(s): APPH E4010 or equivalent Instruction and supervised practice in radiation classification of solids, lattice dynamics, anhar- recommended. Introduction to the instrumenta- safety procedures, image quality assessments, monic effects in crystals, classical electron models tion and physics used in clinical nuclear medicine regulatory compliance, radiation dose evaluations of metals, electron band structure, and low- and PET with an emphasis on detector systems, and calibration of equipment. Students participate dimensional electron structures. tomography and quality control. Problem sets, in clinical QC of the following imaging equipment: papers, and term project. APPH E6082y Solid state physics, II radiologic units (mobile and fixed), fluoroscopy 3 pts. Lect: 3. Professor Pasupathy. APPH E6330y Diagnostic radiology physics units (mobile and fixed), angiography units, Prerequisite(s): APPH E6081 or instructor’s per- 3 pts. Lect: 3. Professor Jambawalikar. mammography units, CT scanners, MRI units and mission. Semiclassical and quantum mechanical Prerequisite(s): APPH E4600. Physics of medical ultrasound units. The objective is familiarization electron dynamics and conduction, dielectric imaging. Imaging techniques: radiography, fluo- in routine operation of test instrumentation and properties of insulators, semiconductors, defects, roscopy, computed tomography, mammography, QC measurements utilized in diagnostic medical magnetism, superconductivity, low-dimensional ultrasound, magnetic resonance. Includes con- physics. Students are required to submit QC forms structures, and soft matter. ceptual, mathematical/theoretical, and practical with data on three different types of radiology clinical physics aspects. imaging equipment. MSAE E6085y Computing the electronic APPH E6365x or y Nuclear medicine structure of complex materials APPH E6333x or y Radiation therapy physics 3 pts. Lect: 3. Professor Wentzcovitch. practicum practicum Prerequisite(s): APPH E3100 or equivalent. 3 pts. Lab: 6. Professor Wuu. 3 pts. Lab: 6. Professor Hamacher. Basics of density functional theory (DFT) and its Prerequisite(s): Grade of B+ or better in APPH Prerequisite(s): Grade of B+ or better in APPH application to complex materials. Computation of E6335 and instructor’s permission. Students E6319 and instructor’s permission. Practical electronics and mechanical properties of materi- spend two to four days per week studying the applications of nuclear medicine theory and als. Group theory, numerical methods, basis sets, clinical aspects of radiation therapy physics. application for processing and analysis of clinical computing, and running open source DFT codes. Projects on the application of medical physics in images and radiation safety and quality assurance Problem sets and a small project. cancer therapy within a hospital environment are programs. Topics may include tomography, instru- assigned; each entails one or two weeks of work mentation, and functional imaging. Reports.

ENGINEERING 2021–2022 60 APPH E6380x or y Health physics practicum variables. Topics include partial differentiation; ment of climate system physics and mechanisms 3 pts. Lab: 6. Professor Caracappa optimization of functions of several variables; of anthropogenic climate change. Topics include: Prerequisite(s): Grade of B+ or better in APPH line, area, volume, and surface integrals; vector how solar radiation and rotating fluid dynamics E4500 and instructor’s permission or Corequisite: functions and vector calculus; theorems of Green, determine basic climate state, mechanisms of APPH E4500 and permission of the instructor. Gauss, and Stokes; applications to selected prob- natural variability and change in climate, why Radiation protection practices and procedures for lems in engineering and applied science. anthropogenic climate change is occurring, and clinical and biomedical research environments. which scientific uncertainties are most important Includes design, radiation safety surveys of diag- APMA E2001x and y Multivariable calculus for to estimates of 21st century change. Designed for nostic and therapeutic machine source facilities, engineers and applied scientists undergraduate students seeking qualitative intro- the design and radiation protection protocols for 0 pts. Professors Youngren and Sagiv. duction to climate and climate change science. facilities using unsealed sources of radioactiv- Required recitation session for students enrolled Note: EESC UN2100 can only be taken for credit ity—nuclear medicine suites and sealed sources— in APMA E2000. prior to APAM EESC E3109. brachytherapy suites. Also includes radiation pro- APMA E2101y Introduction to applied tection procedures for biomedical research facili- APMA E3900x and y Undergraduate research mathematics in applied mathematics ties and the administration of programs for com- 3 pts. Lect: 3. Professor He. pliance to professional health physics standards 0–4 pts. Members of the faculty. Prerequisite(s): Calculus III. A unified, single- Prerequisite(s): Written permission from instructor and federal and state regulatory requirements for semester introduction to differential equations the possession and use of radioactive materials and approval from adviser. May be repeated for and linear algebra with emphases on (1) elemen- credit, but no more than 6 points may be counted and machine sources of ionizing and nonionizing tary analytical and numerical technique and (2) radiations in clinical situations. Individual topics toward the satisfaction of the B.S. degree require- discovering the analogs on the continuous and ments. Candidates for the B.S. degree may con- are decided by the student and the collaborating discrete sides of the mathematics of linear opera- duct an investigation in applied mathematics Clinical Radiation Safety Officer. tors: superposition, diagonalization, fundamental or carry out a special project under the supervi- solutions. Concepts are illustrated with applica- APAM E6650x and y–S6650 Research project sion of the staff. Credit for the course is contin- tions using the language of engineering, the natu- 1–6 pts. Members of the faculty. gent upon the submission of an acceptable thesis ral sciences, and the social sciences. Students Prerequisite(s): Written permission from instruc- or final report. tor and approval from adviser. May be repeated execute scripts in Mathematica and MATLAB (or for credit. A special investigation of a problem the like) to illustrate and visualize course concepts APMA E4007x Applied linear algebra in nuclear engineering, medical physics, applied (programming not required). 3 pts. Lect: 3. Professor Tippett. Prerequisite(s): Course cannot be taken together mathematics, applied physics, and/or plasma APAM - HSAM W2901y Data: past, present physics consisting of independent work on the with APMA E3101. and future part of the student and embodied in a formal Fundamentals of linear algebra, including vector 3 pts. Lect: 1.5. Lab: 1.5. Professors Wiggins report. and Matrix algebra, solution of linear systems, and Jones. existence and uniqueness, gaussian elimination, Prerequisite(s): Instructor's permission. Critical APPH E9142x-E9143y Applied physics Gauss-Jordan elimination, the matrix inverse, thinking and practice regarding the past, pres- seminar elementary matrices and the LU factorization, ent, and future of data. Readings covering how 3 pts. Sem: 3. Not offered in 2021–2022. computational cost of solutions. Vector spaces students, scholars, and citizens can make sense These courses may be repeated for credit. and subspaces, linear independence, basis and of data in science, public policy, and our personal Selected topics in applied physics. Topics and dimension. The four fundamental subspaces of lives. Labs covering descriptive, predictive, and instructors change from year to year. a matrix. Orthogonal projection onto a subspace prescriptive modeling of data. and solution of Linear Least Squares problems, APAM E9301x and y–S9301 Doctoral research unitary matrices, inner products, orthogonaliza- 0–15 pts. Members of the faculty. APMA E3101x Linear algebra tion algorithms and QR factorization, applications. Prerequisite(s): Qualifying examination for the 3 pts. Lect: 3. Professor He. Determinants and applications. Eigen problems, doctorate. Required of doctoral candidates. Matrix algebra, elementary matrices, inverses, rank, determinants. Computational aspects of including diagonalization, symmetric matrices, APAM E9800x and y–S9800 Doctoral solving systems of linear equations: existence- positive-definite systems, eigen factorization and research instruction uniqueness of solutions, Gaussian elimina- applications to dynamical systems and iterative 3, 6, 9, or 12 pts. Members of the faculty. tion, scaling, ill-conditioned systems, iterative maps. Introduction to singular value decomposi- A candidate for the Eng.Sc.D. degree must regis- techniques. Vector spaces, bases, dimension. tion and its applications. ter for 12 points of doctoral research instruction. Eigenvalue problems, diagonalization, inner prod- APMA E4008y Advanced linear algebra Registration for APAM E9800 may not be used to ucts, unitary matrices. 3 pts. Lect: 3. Members of the faculty. satisfy the minimum residence requirement for Prerequisite(s): APMA E3101 or E4007. the degree. APMA E3102y Partial differential equations 3 pts. Lect: 3. Professor Tippett. Advanced topics in linear algebra with applica- APAM E9900x and y–S9900 Doctoral Prerequisite(s): MATH UN2030 or equivalent. tions to data analysis, algorithms, dynamics and dissertation Introduction to partial differential equations; differential equations, and more. (1) General 0 pts. Members of the faculty. integral theorems of vector calculus. Partial dif- vector spaces, linear transformations, spaces iso- A candidate for the doctorate may be required ferential equations of engineering in rectangular, morphisms; (2) spectral theory - normal matrices to register for this course every term after the cylindrical, and spherical coordinates. Separation and their spectral properties, Rayleigh quotient, coursework has been completed, and until the of the variables. Characteristic-value problems. Courant-Fischer Theorem, Jordan forms, eigen- dissertation has been accepted. Bessel functions, Legendre polynomials, other value perturbations; (3) least square problem and orthogonal functions; their use in boundary value Gauss-Markov Theorem; (4) singular value decom- problems. Illustrative examples from the fields of position, its approximation properties, matrix COURSES IN APPLIED electromagnetic theory, vibrations, heat flow, and norms, PCA and CCA. MATHEMATICS fluid mechanics. APMA E4101y Introduction to dynamical APMA E2000x and y Multivariable calculus APAM / EESC E3109x Climate physics systems for engineers and applied scientists 3 pts. Lect: 3. Professor Sobel. 3 pts. Lect: 3. Professor Sagiv. 4 pts. Lect: 3. Professors Youngren and Sagiv. Prerequisite(s): Full year of calculus-based physics Prerequisite(s): APMA E3101 or MATH UN2010 Differential and integral calculus of multiple and multivariable calculus. Calculus-based treat- (Linear Algebra), and MATH UN2030 (ODE), or

ENGINEERING 2021–2022 their equivalents, or instructor’s permission. advanced courses in scientific computing and APMA E4903x Seminar: problems in applied 61 An introduction to the analytic and geometric numerical methods for PDEs (e.g., APMA E4301, mathematics theory of dynamical systems; basic existence, APMA E4302). Topics include numerical solutions 3–4 pts. Lect: 1. Tutorial: 2. Professor Wiggins. uniqueness and parameter dependence of solu- of algebraic systems, linear least-squares, eigen- Required for all applied mathematics majors in tions to ordinary differential equations; constant value problems, solution of nonlinear systems, the senior year. Term paper required. Examples of coefficient and parametrically forced systems; optimization, interpolation, numerical integration problem areas are nonlinear dynamics, asymptot- Fundamental solutions; resonance; limit points, and differentiation, initial value problems, and ics, approximation theory, numerical methods, etc. limit cycles and classification of flows in the plane boundary value problems for systems of ODE’s. Approximately three problem areas are studied (Poincare-Bendixson Theorem); conservative and All programming exercises will be in Python. per term. dissipative systems; linear and nonlinear stabil- ity analysis of equilibria and periodic solutions; APMA E4301y Numerical methods for partial APMA E4990x and y Special topics in applied stable and unstable manifolds; bifurcations, e.g., differential equations mathematics Andronov-Hopf; sensitive dependence and cha- 3 pts. Lect: 3. Professor Mandli. 1–3 pts. Lect: 3. Members of the faculty. otic dynamics; selected applications. Prerequisite(s): APMA E4300 and APMA E3102 Prerequisite(s): Advanced calculus and junior year or APMA E4200 or equivalents. Numerical solu- applied mathematics, or their equivalents. May be APMA E4150y Applied functional analysis tion of differential equations, in particular partial repeated for credit. Topics and instructors from 3 pts. Lect: 3. Professor Weinstein. differential equations arising in various fields of the Applied Mathematics Program and the staff Prerequisite(s): Advanced calculus and course application. Presentation emphasizes finite differ- change from year to year. For advanced under- in basic analysis, or instructor’s permission. ence approaches to present theory on stability, graduate students and graduate students in engi- Introduction to modern tools in functional analysis accuracy, and convergence with minimal coverage neering, physical sciences, biological sciences, that are used in the analysis of deterministic and of alternate approaches (left for other courses). and other fields. Examples of topics include multi- stochastic partial differential equations and in Method coverage includes explicit and implicit scale analysis and Applied Harmonic Analysis. the analysis of numerical methods: metric and time-stepping methods, direct and iterative solv- normed spaces, Banach space of continuous ers for boundary-value problems. APMA E6100x or y Research Seminar functions, measurable spaces, the contraction 0 pts. Lect: 1. Professor Du. mapping theorem, Banach and Hilbert spaces APMA E4302x Methods in computational Prerequisite(s): MATH UN3027 or APMA E4101, bounded linear operators on Hilbert spaces and science MATH UN3028 or APMA E4200, MATH UN2010 or their spectral decomposition, and time permitting 3 pts. Lect: 3. Professor Mandli. APMA E3101 or their equivalents. An M.S. degree distributions and Fourier transforms. Prerequisite(s): APMA E4300, application and requirement. Students attend at least three knowledge in C, Fortran or similar compiled Applied Mathematics research seminars within APMA E4200x and y Partial differential language. Introduction to the key concepts and the Department of Applied Physics and Applied equations issues in computational science aimed at getting Mathematics and submit reports on each. 3 pts. Lect: 3. Professor Du and Members of students to a basic level of understanding where the faculty. they can run simulations on machines aimed at APMA E6209x Approximation theory Prerequisite(s): Course in ordinary differential a range of applications and sizes from a single 3 pts. Lect: 2. Not offered in 2021–2022. equations. Techniques of solution of partial dif- workstation to modern super-computer hard- Prerequisite(s): MATH GU4061 or some knowledge ferential equations. Separation of the variables. ware. Topics include but are not limited to basic of modern analysis. Theory and application of Orthogonality and characteristic functions, knowledge of unix shells, version control systems, approximate methods of analysis from the view- nonhomogeneous boundary value problems. reproducibility, OpenMP, MPI, and many-core point of functional analysis. Approximate numeri- Solutions in orthogonal curvilinear coordinate technologies. Applications will be used through- cal and analytical treatment of linear and nonlin- systems. Applications of Fourier integrals, Fourier out to demonstrate the various use cases and ear algebraic, differential, and integral equations. and Laplace transforms. Problems from the fields pitfalls of using the latest computing hardware. Topics include function spaces, operators in of vibrations, heat conduction, electricity, fluid normed and metric spaces, fixed point theorems dynamics, and wave propagation are considered. APMA E4400y Introduction to biophysical and their applications. modeling APMA E4204x Functions of a complex 3 pts. Lect: 3. Not offered in 2021–2022. APMA E6301x Analytic methods for partial variable Prerequisite(s): PHYS UN1401 or equivalent, and differential equations 3 pts. Lect. 3. Professor Ren. APMA E2101 or MATH UN2030 or equivalent. 3 pts. Lect: 2. Professor Weinstein. Prerequisite(s): MATH UN1202 or APMA E2000 or Introduction to physical and mathematical models Prerequisite(s): Advanced calculus, basic concepts equivalent. Complex numbers, functions of a com- of cellular and molecular biology. Physics at the in analysis, APMA E3101 or E4200 or their equiva- plex variable, differentiation and integration in the cellular scale (viscosity, heat, diffusion, statistical lents, or instructor’s permission. Introduction complex plane. Analytic functions, Cauchy integral mechanics). RNA transcription and regulation to analytic theory of PDEs of fundamental and theorem and formula, Taylor and Laurent series, of genetic expression. Genetic and biochemical applied science; wave (hyperbolic), Laplace and poles and residues, branch points, evaluation of networks. Bioinformatics as applied to reverse- Poisson equations (elliptic), heat (parabolic) and contour integrals. Conformal mapping. Schwarz- engineering of naturally-occurring networks and Schroedinger (dispersive) equations; fundamental Christoffel transformation. Applications to to forward-engineering of synthetic biological solutions, Green’s functions, weak/distribution physical problems. networks. Mathematical and physical aspects of solutions, maximum principle, energy estimates, functional genomics. variational methods, method of characteristics; APMA E4300x and y Computational math: elementary functional analysis and applications introduction to numerical methods APMA E4901x Seminar: problems in applied to PDEs; introduction to nonlinear PDEs, shocks; 3 pts. Lect: 3. Professor Spiegelman. mathematics selected applications. Prerequisite(s): MATH UN1201 or APMA E2000, 0 pts. Lect: 1. Professor Wiggins. UN2030, and APMA E3101 and ENGI E1006 or Required for, and can be taken only by, all APMA E6302y Numerical analysis of partial their equivalents. Programming experience in applied mathematics majors in the junior year. differential equations Python extremely useful. Introduction to fun- Introductory seminars on problems and tech- 3 pts. Lect: 2. Professor Zhang. damental algorithms and analysis of numerical niques in applied mathematics. Typical topics Prerequisite(s): APMA E3102 or E4200. Numerical methods commonly used by scientists, math- are nonlinear dynamics, scientific computation, analysis of initial and boundary value problems for ematicians, and engineers. Designed to give a economics, operations research, etc. partial differential equations. Convergence and fundamental understanding of the building blocks stability of the finite difference method, the of scientific computing that will be used in more

ENGINEERING 2021–2022 62 spectral method, the finite element method and Asymptotic treatment of ordinary and partial dif- COURSES IN MATERIALS applications to elliptic, parabolic, and hyperbolic ferential equations in problems arising in applied SCIENCE AND ENGINEERING equations. mathematics. Asymptotic series. Asymptotic evaluation of integrals. Expansion of solutions See page 183. APMA E6304y Integral transforms of ordinary differential equations: connection 3 pts. Lect: 2. Not offered in 2021–2022. problem and turning points. Stoke’s phenomenon. Prerequisite(s): APMA E4204 and MATH UN2030, Differential equations with a parameter: “bound- or their equivalents. Laplace, Fourier, Hankel, and ary layer” phenomenon. Application to partial dif- Mellin transforms. Selection of suitable transform ferential equations: problems from fluid dynamics, for a given partial differential equation boundary wave propagation theory, electromagnetic theory. value problem. Operational properties of trans- forms. Inversion theorems. Approximate evalu- APMA E9101x-E9102y Research ation of inversion integrals for small and large 1–4 pts. Members of the faculty. values of parameter. Application to the solution of Prerequisite(s): Permission of the supervising fac- integral equations. ulty member. May be repeated. Advanced study in a special area. APMA E6901x and y–E6901y Special topics in applied mathematics APMA E9810x or y SEAS colloquium in climate 3 pts. Lect: 3. Members of the faculty. science Prerequisite(s): Advanced calculus and junior year 0 pts. Lect: 1. Professors Polvani and Sobel. applied mathematics, or their equivalents. May be Prerequisite(s): Instructor’s permission. Current repeated for credit. Topics and instructors from research in problems at the interface between the Applied Mathematics Program and the staff applied mathematics and earth and environmental change from year to year. For students in engi- sciences. neering, physical sciences, biological sciences, and other fields. Examples of topics include APMA E9815x or y Geophysical fluid uncertainty quantification. dynamics seminar 1–3 pts. May be repeated for up to 10 points of APMA E8308y Asymptotic methods in applied credit. Not offered in 2021–2022. mathematics Prerequisite(s): Instructor’s permission. Problems 3 pts. Lect: 2. Not offered in 2021–2022. in the dynamics of geophysical fluid flows. Prerequisite(s): APMA E4204 or equivalent.

ENGINEERING 2021–2022 BIOMEDICAL ENGINEERING 63 351 Engineering Terrace, MC 8904 212-854-4460 [email protected] bme.columbia.edu

CHAIR COMMUNICATIONS AND Helen H. Lu, SENIOR LECTURER EMERITUS FACULTY X. Edward Guo EVENTS MANAGER Percy K. and Vida Aaron M. Kyle Van C. Mow, Alexis M. Newman L. W. Hudson Stanley Dicker VICE CHAIR Professor of JOINT FACULTY Professor Emeritus Paul Sajda GRANTS MANAGER Biomedical Gerard A. Ateshian, of Biomedical Monica Ionescu-Albu Engineering Andrew Walz Engineering CHAIR OF Kam W. Leong, Samuel Professor of UNDERGRADUATE GRANTS ANALYST Y. Sheng Professor Mechanical ADJUNCT PROFESSORS STUDIES TBA of Biomedical Engineering Hariklia Deligianni Lance C. Kam Engineering Shunichi Homma, David Elad FINANCIAL ASSISTANT Barclay Morrison III Margaret Miliken Ernest Feleppa CHAIR OF GRADUATE Michelle Cintron Paul Sajda Hatch Professor of Mark Gelfand STUDIES Karen Evans Samuel K. Sia Medicine Howard Levin Henry S. Hess J. Thomas Vaughan Sachin Jambawalikar PROFESSORS Gordana Vunjak- Gerard Karsenty, Paul ADJUNCT ASSOCIATE DIRECTOR OF FINANCE X. Edward Guo, Stanley Novakovic, University A. Marks Professor PROFESSOR AND ADMINISTRATION Dicker Professor Professor and the of Genetics and Alayar Kangarlu Mindaugas Paunksnis of Biomedical Mikati Foundation Development Engineering Professor of Edward F. Leonard AFFILIATES BUSINESS MANAGER Henry S. Hess Biomedical Andrew Marks, Clyde Sunil Agrawal Maria Leah Kim Elizabeth M. C. Hillman, Engineering '56 and Helen Wu Nadeen Chahine Herbert and Florence Professor of Molecular Anthony Fitzpatrick STUDENT AFFAIRS Irving Professor ASSOCIATE Cardiology (in Jennifer Gelinas MANAGER Clark T. Hung PROFESSORS Medicine) Christine Hendon Helen Cen Lance C. Kam Tal Danino Elizabeth S. Olson Chi-Min Ho Elisa E. Konofagou, Joshua Jacobs Kenneth L. Shepard, Lau Karen Kasza STUDENT AFFAIRS Robert and Margaret Christoph Juchem Family Professor of Wei Min SPECIALIST Hariri Professor Qi Wang Electrical Engineering Kristin Myers Jocelyn McArthur of Biomedical Milan N. Stojanovic Raju Tomer Engineering and ASSISTANT Stavros Thomopoulos, Stephen Tsang LABORATORY MANAGER Radiology PROFESSORS Robert E. Carroll Binsheng Zhao TBA Andrew F. Laine, Elham Azizi and Jane Chace Percy K. and Vida Jose L. McFaline- Carroll Professor of CAREER PLACEMENT L. W. Hudson Figueroa Biomechanics OFFICER Professor of Nandan Nerurkar Kristen Henlin Biomedical Engineering

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

ENGINEERING 2021–2022 64 center and enjoys a basic commitment to provides exceptional access to current as follows: interdisciplinary research is important to practices in biomedical engineering 1. Professional employment in areas the quality and strength of the program. and related sciences. such as the medical device industry, Educational programs at all levels Research facilities of the Biomedical engineering consulting, and are based on engineering and biological Engineering faculty include the biotechnology; fundamentals. From this basis, the Computational Cancer Biology Laboratory 2. Graduate studies in biomedical program branches into concentrations of (Professor Azizi), the Synthetic Biological engineering or related fields; contemporary biomedical engineering Systems Laboratory (Professor Danino), 3. Attendance at medical, dental, or other fields. The intrinsic breadth of these the Heffner Biomedical Imaging professional schools. concentrations, and a substantial elective Laboratory (Professor Laine), the content, prepare bachelor’s and master’s Laboratory for Intelligent Imaging and The undergraduate program in students to commence professional Neural Computing (Professor Sajda), biomedical engineering will prepare activity in any area of biomedical the Bone Bioengineering Laboratory graduates who will have: engineering or to go on to graduate (Professor Guo), the Cellular Engineering school for further studies in related fields. Laboratory (Professor Hung), the 1. an ability to identify, formulate, and The program also provides excellent Biomaterial and Interface Tissue solve complex engineering problems preparation for the health sciences and Engineering Laboratory (Professor Lu), by applying principles of engineering, the study of medicine. Graduates of the Neurotrauma and Repair Laboratory science, and mathematics the doctoral program are prepared for (Professor Morrison), the Laboratory 2. an ability to apply engineering design research activities at the highest level. for Stem Cells and Tissue Engineering to produce solutions that meet Areas of particular interest to Columbia (Professor Vunjak-Novakovic), the specified needs with consideration faculty include biomechanics (Professors Ultrasound and Elasticity Imaging of public health, safety, and welfare, Ateshian, Guo, Hess, Morrison, Mow, and Laboratory (Professor Konofagou), as well as global, cultural, social, Nerurkar), cellular and tissue engineering the Magnetic Resonance Scientific environmental, and economic factors (Professors Danino, Hung, Kam, Leonard, Engineering for Clinical Excellence 3. an ability to communicate effectively Leong, Lu, Morrison, Sia, and Vunjak- Laboratory (Professor Juchem), the with a range of audiences Novakovic), auditory biophysics (Professor Microscale Biocomplexity Laboratory 4. an ability to recognize ethical and Olson), biomaterials (Professors Danino, (Professor Kam), the Molecular and professional responsibilities in Hess, Kam, Leong, Lu, Sia, and Vunjak- Microscale Bioengineering Laboratory engineering situations and make informed judgments, which must Novakovic), biosignals and biomedical (Professor Sia), the Laboratory for consider the impact of engineering imaging (Professors Guo, Hillman, Jacobs, Functional Optical Imaging (Professor solutions in global, economic, Juchem, Konofagou, Laine, Sajda, Hillman), the Cognitive Electrophysiology environmental, and societal contexts Vaughan, and Wang), neuroengineering Laboratory (Professor J. Jacobs), the 5. an ability to function effectively on (Professors Hillman, Jacobs, Konofagou, Nanobiotechnology and Synthetic Biology teams whose members together Laine, Morrison, Sajda, and Wang) and Laboratory (Professor Hess), the Raymond provide leadership, create a machine learning (Azizi, Laine, Sajda). and Beverly Sackler Laboratory for Neural collaborative and inclusive Engineering and Control (Professor Wang), environment, establish goals, plan the Morphogenesis and Developmental Facilities tasks, and meet objectives The Department of Biomedical Biomechanics Lab (Professor Nerurkar), 6. an ability to develop and conduct Engineering has been supported and the Laboratory for Nanomedicine and appropriate experimentation, by grants obtained from NIH, NSF, Regenerative Medicine (Professor Leong). analyze and interpret data, and DoT, DoD, New York State, numerous These laboratories are supplemented use engineering judgment to draw research foundations, and University with core facilities, including a tissue conclusions funding. The extensive facilities that are culture facility, a histology facility, a 7. an ability to acquire and apply at the Medical Center, Manhattanville, confocal microscope, an atomic force new knowledge as needed, using and Morningside campuses include microscope, a 2-photon microscope, appropriate learning strategies. teaching and research laboratories epifluorescence microscopes, a freezer that provide students with unusual room, biomechanics facilities, a machine The undergraduate curriculum is access to contemporary research shop, and a specimen preparation room. designed to provide broad knowledge equipment specially selected of the physical and engineering for its relevance to biomedical UNDERGRADUATE PROGRAM sciences and their application to the engineering. Another addition is an The program in biomedical engineering solution of biological and medical undergraduate wet laboratory devoted leading to the B.S. degree is accredited problems. Students are strongly to biomechanics and cell and tissue by the Engineering Accreditation encouraged to take courses in the engineering, together with a biosignals Commission of ABET, http://www.abet. order specified in the course tables; and biomedical imaging and data org. deviations must be discussed with a processing laboratory. Each laboratory The objectives of the undergraduate departmental adviser and approved incorporates equipment normally program in biomedical engineering are by the department before registration. reserved for advanced research and The first two years provides a strong

ENGINEERING 2021–2022 grounding in the physical and chemical First and Second Years Beginning in junior year, all students 65 sciences, engineering fundamentals, As outlined in this bulletin, in the take the two-semester sequence mathematics, and modern biology. first two years, all engineering Biomedical engineering laboratory, I ­­ This background is used to provide a students are expected to complete a & II (BMEN E3810, E3820). In this two- unique physical approach to the study sequence of courses in mathematics, semester series, students learn through of biological systems. The last two years physics, chemistry, computer science, hands-on experience the principles and of the undergraduate program provide engineering, modern biology, English methods of biomedical engineering substantial exposure to fundamentals in composition, and physical education, as experimentation, measurement biomedical engineering with emphasis well as nontechnical electives including techniques, quantitative theories of biomedical engineering, data analysis, on the integration of principles of the humanities. For most of these and independent design of biomedical biomedical engineering, quantitative sequences, the students may choose engineering experiments, in parallel to analysis of physiology, and experimental from two or more tracks. If there is a the Biomedical engineering I & II and quantification and measurements of question regarding the acceptability Quantitative physiology I & II courses. In biomedical systems. of a course as a nontechnical elective, addition, all students must take BMEN The common core biomedical please consult the approved listing of E4110: Biostatistics for engineers. In the engineering curriculum provides courses beginning on page 9 or contact senior year, students are required to a broad yet solid foundation in your advising dean for clarification. take a two-semester capstone design biomedical engineering. The flexible Please see the charts in this course, Biomedical engineering design choice of technical electives in section for a specific description of (BMEN E3910 and E3920), in which the Department of Biomedical course requirements. students work within a team to tackle Engineering, other departments in For students who are interested an open-ended design project in the Engineering School, as well as in the biomedical engineering major, biomedical engineering. The underlying in other departments in the arts and they must take E1201: Introduction to philosophy of these core requirements sciences allows students to broaden electrical engineering. For the computer is to provide our biomedical engineering their biomedical engineering education science requirement, students must students with a broad knowledge and to their individualized interests for take ENGI E1006. They must take understanding of topics in the field of a personalized curriculum. These the two-semester BIOL UN2005 and biomedical engineering. qualities allow the faculty to prepare UN2006: Introduction to Biology I & II in Parallel to these studies in core cours- students for activity in all contemporary the second year, which gives students es, students are required to take flexible areas of biomedical engineering. a comprehensive overview of modern technical elective courses (21 points) Graduates of the program are equipped biology from molecular to organ system to obtain an in-depth understanding of for employment in the large industrial levels. In addition, all students must take their chosen interests. A technical elec- sector devoted to health care, which APMA E2101: Introduction to applied tive is defined as a 3000-level or above includes pharmaceuticals, medical mathematics in their second year. course taught in SEAS or 3000-level or devices, artificial organs, prosthetics above courses in biology, chemistry, bio- and sensory aids, diagnostics, medical Third and Fourth Years chemistry, or biotechnology. Exceptions instrumentation, and medical imaging. The biomedical engineering programs include organic chemistry lecture courses Graduates also accept employment at Columbia are based on engineering and laboratory (which are 2000-level in oversight organizations (FDA, NIH, and biological fundamentals. This is courses). At least 15 points (five courses) OSHA, and others), medical centers, emphasized in our core requirements, of these technical electives must have and research institutes. They are which cannot be waived nor substituted. engineering content, while at least two prepared for graduate study in All students must take the two-semester of the five courses have to be from the biomedical engineering and several introduction to biomedical engineering Department of Biomedical Engineering. related areas of engineering and the courses, BMEN E3010 and E3020: The curriculum prepares students who health sciences. Students can meet Biomedical engineering I & II, which wish to pursue careers in medicine entrance requirements for graduate provide a broad yet solid foundation in by satisfying most requirements in the training in the various allied health the biomedical engineering discipline. premedical programs with no more than professions. No more than three In parallel, all students take the two- three additional courses. Some of these additional courses are required to semester Quantitative physiology, I and additional courses may also be counted satisfy entrance requirements for II sequence (BMEN E4001-E4002), which as nonengineering technical electives. most U.S. medical schools. is taught by biomedical engineering Please see the course tables for sched- faculty and emphasizes quantitative All biomedical engineering ules leading to a bachelor’s degree in applications of engineering principles in students are expected to register for biomedical engineering. understanding biological systems and nontechnical electives, both those It is strongly advised that students phenomena from molecular to organ specifically required by the School of take required courses during the system levels. In the fields of biomedical Engineering and Applied Science and specific term that they are designated engineering, experimental techniques those needed to meet the 27-point total in the course tables, as scheduling and principles are fundamental skills that of nontechnical electives required for conflicts may arise if courses are taken good biomedical engineers must master. graduation. out of sequence.

ENGINEERING 2021–2022 66 BIOMEDICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

MATHEMATICS MATH UN1102 (3) APMA E2000 (4) and E2001 (0) either semester

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

UN1403 (4) UN1404 (4) CHEMISTRY UN1500 (3) (or semester 1) (three tracks, choose one) UN1604 (4) UN1507 (3) UN2045 (4) UN2046 (4), UN1507 (3)

UNIVERSITY CC1010 (3) either semester WRITING

COMPUTER ENGI E1006 (3) SCIENCE (or semester II)

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION1

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

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

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

TOTAL POINTS 202 192 14.52 152

1 Students can mix these requirements according to what is available. 2 Estimations

Technical Elective Requirements 1. Technical elective courses with in the Department of Mechanical Students are required to take at least sufficient engineering content that Engineering, except MECE 48 points of engineering content can count toward the 48 units of E4007: Creative engineering and coursework toward their degree. engineering courses required for entrepreneurship The 48-point requirement is a ABET accreditation: c. All 3000-level or higher courses criterion established by ABET. Taking a. All 3000-level or higher courses in the Department of Chemical into consideration the number of in the Department of Biomedical Engineering, except CHEN E4020: engineering content points conferred Engineering, except BMEN E4010, Safeguarding intellectual and by the required courses of the BME E4103, E4104, E4105, E4106, E4107, business property curriculum, a portion of technical E4108, and E6510; additionally, d. All 3000-level or higher courses electives must be clearly engineering in BMEN E4000 001 in fall 2019. (Note in the Department of Electrical nature (Engineering Content Technical that only 3 points of BMEN E3998 Engineering, except EEHS E3900: Electives), specifically as defined below: may be counted toward technical History of telecommunications: elective degree requirements.) from the telegraph to the internet b. All 3000-level or higher courses e. All 3000-level or higher courses

ENGINEERING 2021–2022 67 BIOMEDICAL ENGINEERING: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

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

NONTECH 3 points 3 points 3 points ELECTIVES

TOTAL POINTS 16 15 16 13

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

in the Civil Engineering and For example, APBM E4560 Anatomy engineering courses. B.S. students Engineering Mechanics program, for physicists & engineers does not can also declare a concentration in except CIEN E4128, E4129, E4130, count as engineering content technical one of the areas listed below. To earn E4131, E4132, E4133, E4134, E4135, elective, since the course is owned this designation a student must take E4136, E4138, and E4140 by Applied Physics (and cross-listed at least four of the courses listed for f. All 3000-level or higher courses with Biomedical Engineering). BMCH that concentration, and at least two of in the Earth and Environmental E4810 Artificial organs is counted as an those must be biomedical engineering Engineering program engineering content technical elective, courses. as the course is owned by Biomedical BIOFABRICATION & NANOTECHNOLOGY 2. Courses from the following Engineering (and cross listed with MECE E3100: Introduction to mechanics of fluids (3) departments are not allowed to Chemical Engineering). MECE E3113: Mechanics of solids (3) count toward the required 48 units of Based on the above for Engineering MSAE E4090: Nanotechnology (3) engineering courses: Technical Electives, a cross-listed course MECE E4212: Microelectromechanical systems (3) a. Department of Applied Physics and that is greater than or equal to 3000 BMEN E4550: Micro- and nanostructures in cellular engineering (3) Applied Mathematics level and with BMEN as its starting call b. Department of Computer Science BMEN E4580: Foundations of nanobiotechnology letters will qualify as a BME Engineering and nanobioscience (3) c. Department of Industrial Technical Elective. BMEN E4590: BioMems: cellular and molecular Engineering and Operations The accompanying charts describe applications (3) Research the eight-semester degree program BIOINFORMATICS & MACHINE LEARNING d. Program of Materials Science and schedule of courses leading to the Engineering BIOL UN3041: Cell biology (3) bachelor’s degree in biomedical COMS W3101: Programming languages (1) engineering. COMS W3137: Data structures and algorithms (4) Once 48 points of engineering The undergraduate Biomedical BINF G4006: Translational bioinformatics (3) content are satisfied, students may Engineering program is designed to BINF G4015: Computational systems biology: proteins, networks, function (3) choose any course above the 3000 provide a solid biomedical engineering level in Columbia Engineering as well ECBM E4040: Neural networks and deep curriculum through its core requirements learning (3) as biology, chemistry, biochemistry, and while providing flexibility to meet the ECBM E4060: Introduction to genomic biotechnology as technical electives. individualized interests of the students. information science and If the 3000-level course is greater All students are encouraged to design technology (3) than or equal to the course cross their own educational paths through STAT GU4241: Statistical machine learning (3) COMS W4252: Introduction to computational listed, its eligibility as an engineering technical electives while meeting the content technical elective is determined learning theory (3) following requirements: (1) courses BMEN E4420: Biomedical signal processing and by the call letters of the first (owning) must be at the 3000-level or above; (2) signal modeling (3) department in the course name five of the seven electives must meet BMEN E4460: Deep learning in biomedical designation. The department owning the above criteria to be considered imaging (3) Deep learning in biomedical the course must be ABET accredited to engineering content; and (3) two of the BMEN E4470: be considered engineering. signal processing (3) seven electives must be biomedical COMS W4701: Artificial intelligence (3)

ENGINEERING 2021–2022 68 CBMF W4761: Computational genomics (3) GENOMICS AND SYSTEMS BIOLOGY DUAL DEGREE PROGRAMS COMS W4771: Machine learning (3) CHBM E4321: The genome and the cell (3) BMEN E4895: Analysis and quantification of APMA E4400: Introduction to biological Integrated B.S./M.S. Program in medical images (3) modeling (3) Biomedical Engineering BMEN E4420: Biosignal process and modeling (3) BIOMATERIALS The B.S./M.S. degree program is open to BMEN E4520: Synthetic biology: principles of MSAE E3010: Introduction to materials science (3) a select group of Columbia juniors and genetic circuits (3) makes possible the earning of both the BMEN E4501: Biomaterials (3) BMEN E4530: Drug and gene delivery (3) BMEN E4510: Tissue engineering (3) BMEN E4590: BioMems: cellular and molecular B.S. and M.S. degrees in an integrated BMEN E4520: Synthetic biology: principles of applications (3) fashion. Benefits of this program include genetic circuits (3) CHEN E4700: Principles of genomic technologies the matching of graduate courses BMEN E4530: Drug and gene delivery (3) (3) with the corresponding prerequisites, BMEN E4590: BioMems: cellular and molecular CHEN E4760: Genomics sequence laboratory (3) a greater ability to plan ahead for applications (3) CHEN E4800: Protein engineering (3) MEBM E4710: Morphogenesis shape and optimal course planning, and a structure in biological materials (3) NEURAL ENGINEERING simplified application process with no CHEN E4800: Protein engineering (3) ELEN E3810:  Signals and systems (3.5) GRE required. Up to 6 points from the BMEB W4020: Computational neuroscience: B.S. degree requirements, specifically BIOMECHANICS circuits in the brain (3) BMEN E4001 and E4002, will also count MECE E3100: Introduction to mechanics of fluids (3) BMEE E4030: Neural control engineering (3) toward fulfilling the M.S. degree course ENME E3105: Mechanics (4) BMEN E4050: Electrophysiology of human MECE E3113: Mechanics of solids (3) memory and navigation (0) requirements. To qualify for this program, MECE E3301: Thermodynamics (3) BMEN E4310: Solid biomechanics (3) students must have a cumulative GPA BMEN E4301: Structure, mechanics and BMEN E4420: Biosignal process and modeling (3) of at least 3.4 and should apply for the adaptation of bone (3) BMEN E4430: Principles of MRI (3) program by April 30 in their junior year. BMEN E4302: Biomechanics of soft tissue (3) ELEN E4810: Digital signal processing (3) For more information on requirements BMEN E4310: Solid biomechanics (3) BMEN E4894: Biomedical imaging (3) BMEN E4320: Fluid biomechanics (3) and application process, please visit BMEN E4340: Biomechanics of cells (3) PREMED AND PRE-HEALTH PROFESSIONAL bme.columbia.edu. MEBM E4710: Morphogenesis shape and CHEM UN2443: Organic chemistry I (3.5) structure in biological materials (3) CHEM UN2444: Organic chemistry II (3.5) M.D./M.S. Program in Biomedical Sound and hearing (3) Organic chemistry lab BMEN E4750: CHEM UN2493:  Engineering (techniques) (0) BIOSIGNALS & BIOMEDICAL IMAGING CHEM UN2494: Organic chemistry lab (synthesis) The Doctor of Medicine/Master of ELEN E3810: Signals and systems (3.5) (0) Science in Biomedical Engineering BMEN E4410: Ultrasound in diagnostic imaging BIOC UN3300: Biochemistry (4) (M.D./M.S.) program is an integrated (3) BMEN E4320: Fluid biomechanics (3) program offered between The Fu BMEN E4420: Biomedical signal process and BMEN E4410: Ultrasound in diagnostic imaging Foundation School of Engineering and signal modeling (3) (3) Applied Science and the College of BMEN E4430: Principles of MRI (3) BMEN E4530: Drug and gene delivery (3) BMEE E4740: Bioinstrumentation (3) Physicians and Surgeons at Columbia ELEN E4810: Digital signal processing (3) ROBOTICS AND CONTROL OF BIOLOGICAL University. The purpose of this program BMEN E4894: Biomedical imaging (3) SYSTEMS is to supplement the current training BMEN E4898: Biophotonics (3) MECE E3100: Introduction to mechanics of of medical students with world-class fluids (3) training in biomedical engineering at CELL AND TISSUE ENGINEERING ENME E3105: Mechanics (4) the graduate-level. This interdisciplinary CHEM UN2443: Organic chemistry I (3.5) MECE E3113: Mechanics of solids (3) CHEM UN2444: Organics chemistry II (3.5) BMEE E4030: Neural control engineering (3) educational experience will prepare BMEN E4210: Driving forces of biological systems BMEN E4050: Electrophysiology of human students to become innovative leaders (3) memory and navigation (3) in science, engineering, and medicine. BMEN E4310: Solid biomechanics (3) MEBM E4439: Modeling and identification of The program is open to a select group BMEN E4501: Biomaterials (3) dynamic systems (3) of Columbia medical students and BMEN E4510: Tissue engineering (3) MECE E4602: Introduction to robotics (3) makes possible the earning of both BMEN E4550: Micro- and nanostructures in BMEE E4740: Bioinstrumentation (3) cellular engineering (3) the M.D. and M.S. degree in 5 years (4 years for the M.D. program, 1 year for To meet entrance requirements DESIGN INNOVATION AND ENTREPRENEURSHIP the M.S. program). Six points from the of most U.S. medical schools, stu- MECE E3408: Computer graphics and design (3) M.D. degree, through completion of Research to Revenue (3) dents will need to take BIOC UN3501 ENGI W4100: anatomy coursework, will also count BIOT GU4160: Biotechnology Law (3) Biochemistry: Structure and metabolism toward the Master of Science degree. BIOT GU4161: Ethics in Biopharmaceutical Patent (4), CHEM UN2545 Organic chem- Students must apply separately to the and Regulatory Law (3) istry laboratory (3), PHYS UN1493: BIOT GU4200: Biopharmaceutical Development & Department of Biomedical Engineering. Introduction to experimental physics (3), Regulation (3) For more information on requirements and PSYC UN1001: The science of psy- BIOT GU4201: Biotechnology Development and and application process, please visit Regulatory Issues (3) chology (3) as well. bme.columbia.edu. BMEE E4740: Bioinstrumentation (3) CHEN E4920: Pharmaceutical industry for engineers (3)

ENGINEERING 2021–2022 GRADUATE PROGRAMS requirements of the degree program. of the standard track (including BMEN 69 The graduate curriculum in biomedical Columbia Engineering does not admit 6003, Applied Math, BMEN 9700, four engineering is track-free at the master’s students holding the bachelor’s degree BMEN courses, three SEAS courses, level while at the doctoral level, it directly to doctoral studies; admission and one 3 credit SEAS/non-SEAS consists of three tracks: biomechanics, is offered either to the M.S. program or course), with one exception: students cell and tissue engineering, and to the M.S. program/doctoral track. The must take at least 12 credits from a list biosignals and biomedical imaging. Department of Biomedical Engineering of courses. also admits students into the 4-2 Initial graduate study in biomedical BIOINFORMATICS AND MACHINE LEARNING program, which provides the opportunity engineering is designed to expand the BINF G4006: Translational bioinformatics (3) student’s undergraduate preparation for students holding a bachelor’s BINF G4015: Computational systems biology: in the direction of the concentration degree from certain physical sciences to proteins, networks, functions (3) of interest. In addition, sufficient receive the M.S. degree after two years ECBM E4040: Neural networks and deep knowledge is acquired in other areas of study at Columbia. learning (3) to facilitate broad appreciation of M.S. students must complete the STAT GU4241: Statistical machine learning (3) COMS W4252: Introduction to computational problems and effective collaboration professional development and leadership course, ENGI E4000, as a graduation learning theory (3) with specialists from other scientific, BMEN E4420: Biomedical signal processing and medical, and engineering disciplines. requirement. Doctoral students will signal modeling (3) The Department of Biomedical be enrolled in ENGI E6001–6004 and BMEN E4520: Synthetic biology: principles of Engineering offers a graduate program should consult their program for specific genetic circuits (3) leading to the Master of Science degree PDL requirements. BMEN E4460: Deep learning in biomedical (M.S.), the Doctor of Philosophy degree imaging (3) COMS W4701: Artificial intelligence (3) (Ph.D.), and the Doctor of Engineering CURRICULUM AND EXAM CBMF W4761: Computational genomics (3) Science degree (Eng.Sc.D.). Applicants REQUIREMENTS COMS W4771: Machine learning (3) who have a Master of Science degree COMS W4772 (E6772): Advanced machine or equivalent may apply directly to the learning (3) Master’s Degree doctoral degree program. All applicants BMEN E4895: Analysis and quantification of are expected to have earned the In consultation with an appointed faculty medical images (3) Master's research (3) bachelor’s degree in engineering or adviser, M.S. students should select BMEN E9100: in a cognate scientific program. The a program of 30 points of credit of BIOMATERIALS AND TISSUE ENGINEERING graduate courses (4000 level or above) Graduate Record Examination (General BMEN E4210: Driving forces of biological Test only) is required of all applicants. appropriate to their career goals. This systems (3) Students whose bachelor’s degree was program must include the course in BMCH E4500: Biological transport and rate not earned in a country where English computational modeling of physiological processes (3) BMEN E4501: Biomaterials (3) is the dominant spoken language are systems (BMEN E6003); two semesters of BMEN E9700: Biomedical BMEN E4510: Tissue engineering (3) required to take the TOEFL test. In Drug and gene delivery (3) engineering seminar; at least four other BMEN E4530: addition, for the doctoral program, the BMEN E4550: Micro- and nanostructures in individual tracks require applicants to biomedical engineering courses where cellular engineering (3) have taken the following foundation BME is the course's owning department; BMEN E4580: Fundamentals of nanobioscience and at least one graduate-level course courses: and nanobiotechnology (3) BMEN E4590: BioMems: cellular and molecular • Biomechanics: One year of biology in the Applied Mathematics department. applications (3) and/or physiology, solid mechanics, Up to 6 credits of Master’s Research BMEN E9100 may be taken to fulfill BMEN E6001: Current topics in nanbiotechnology statics and dynamics, fluid mechanics, and synthetic biology (3) degree requirements. Up to 3 credits of ordinary differential equations. BMEN E6500: Tissue and molecular engineering • Cell and Tissue Engineering: One coursework outside of SEAS may count laboratory (4) year of biology and/or physiology, towards the MS degree. Students with BMEN E6505: Advanced biomaterials and tissue one year of organic chemistry or deficiency in physiology coursework are engineering (3) BMEN E9100: Master's research (3) biochemistry with laboratory, fluid required to take the BMEN E4001-E4002 mechanics, rate processes, ordinary sequence before taking BMEN E6003. BIOMECHANICS differential equations. Candidates must achieve a minimum MECE E4100: Mechanics of fluids (3) • Biosignals and Biomedical grade-point average of 2.5. A thesis BMEN E4301: Structure, mechanics, and Imaging: One year of biology and/ based on experimental, computational, adaptation of bone (3) Biomechanics of musculoskeletal or physiology and/or biochemistry. or analytical research is optional. BMEN E4302: soft tissues (3) Linear algebra, Students wishing to pursue the Master’s Thesis option should register for BMEN BMEN E4305: Cardiac mechanics (3) ordinary differential equations, Fourier BMEN E4310: Solid biomechanics (3) E9100 Master’s Research and consult analysis, digital signal processing. BMEN E4570: Science and engineering of body with their BME faculty adviser. fluids (3) Applicants lacking some of these M.S. students can also declare BMME E4702: Advanced musculoskeletal courses may be considered for a concentration listed below. The biomechanics (3) MEBM E4703: Molecular mechanics in biology (3) admission with stipulated deficiencies requirements for these elective that must be satisfied in addition to the concentrations are identical to those

ENGINEERING 2021–2022 70 MEBM E4710: Morphogenesis: shape and ROBOTICS AND CONTROL OF BIOLOGICAL in teaching (one semester for M.D./Ph.D. structure in biological materials (3) SYSTEMS students). This may include supervising BMEN E4750: Sound and hearing (3) BMEE E4030: Neural control engineering (3) and assisting undergraduate students Advanced mechanics of fluids (3) MECE E6100: MECE E4058: Mechatronics and embedded in laboratory experiments, grading, and BMEN E6301: Modeling of biological tissues with microcomputer control (3) preparing lecture materials to support finite elements (3) BMEN E4420: Biomedical signal processing and the teaching mission of the department. MEBM E6310-E6311: Mixture theories for signal modeling (3) biological tissues, I and II (3) MEBM E4439: Modeling and identification of The requirement must be completed by MECE E6422-E6423: Introduction to the theory dynamic systems (3) the 3rd year of graduate studies. The of elasticity, I and II (3) EEME E4601: Digital control systems (3) Department of Biomedical Engineering MECE E8501: Advanced continuum biomechanics MECE E4602: Introduction to robotics (3) is the only engineering department (3) MECS E4603: Applied robotics: algorithms and that offers Ph.D. training to M.D./Ph.D. BMEN E9100: Master's research (3) software (3) students. These candidates are expected MECE E4606: Digital manufacturing (3) BIOMEDICAL IMAGING to complete their Ph.D. program within BMME E4702: Advanced musculoskeletal BMEN E4410: Ultrasound in diagnostic imaging (3) biomechanics (3) 3.5 years, with otherwise the same BMEN E4420: Biomedical signal processing and BMEE E4740: Bioinstrumentation (3) requirements as those outlined for the signal modeling (3) MECE E6400: Advanced machine dynamics (3) Doctoral Degree program. BMEN E4430: Principles of magnetic resonance EEME E6601: Introduction to control theory (3) imaging (3) EEME E6602: Modern control theory (3) Doctoral Qualifying Examination BMEE E4740: Bioinstrumentation (3) EEME E6610: Optimal control theory (3) ELEN E4810: Digital signal processing (3) MECE E6614: Advanced topics in robotics and Doctoral candidates are required to BMEN E4840: Functional imaging for the brain(3) mechanism synthesis (3) pass a qualifying examination. This BMEN E4894: Biomedical imaging (3) MECE E6615: Robotic manipulation (3) examination is given once a year, and BMEN E4895: Analysis and quantification of Master's research (3) it should be taken after the student has medical images (3) BMEN E9100: BMEN E4898: Biophotonics (3) completed 30 points of graduate study. BMEN E6410 : Principles and practices of in vivo Doctoral Degree The qualifying examination consists of magnetic resonance spectroscopy (3) Doctoral students must complete an oral exam during which the student Master's research (3) BMEN E9100: a program of 30 points of credit presents an analysis of assigned NEURAL ENGINEERING beyond the M.S. degree. The core scientific papers, as well as answers to BMEB W4020: Computational neuroscience: course requirements (9 credits) for questions in topics covering applied circuits in the brain (3) the doctoral program include the mathematics, quantitative biology and BMEE E4030: Neural control engineering (3) course in computational modeling of physiology, and track-specific material. BMEN E4050: Electrophysiology of human physiological systems (BMEN E6003), The committee consists of the thesis memory and navigation (3) plus at least one graduate-level adviser and two BME core faculty BMEN E4420: Biomedical signal processing and members approved by the graduate signal modeling (3) course from the Applied Mathematics studies committee. A written analysis of BMEN E4430: Principles of magnetic resonance department and one graduate-level imaging (3) course in the following departments: the assigned scientific papers must ELEN E4810: Digital signal processing (3) Statistics, Applied Mathematics, or a be submitted prior to the oral exam. BMEN E4894: Biomedical imaging (3) graduate-level Biostatistics course such A minimum cumulative grade-point BMEN E9070: Massively parallel neural as BMEN E4110. If BMEN E6003 has average of 3.2 without research computation (3) already been taken for the master’s credit grades is required to register BMEN E9100: Master's research (3) degree, a technical elective can be for this examination. DESIGN, INNOVATION, AND used to complete the core course ENTREPRENEURSHIP requirement. If one or both graduate Doctoral Committee and Thesis ENGI W4100: Research to revenue (3) level applied mathematics courses have Students who pass the qualifying BIOT GU4180: Entrepreneurship in biotechnology been taken for the master's degree, examination must have a core BME (3) technical elective(s) can be used as a BIOT W4200: Biopharmaceutical development faculty member who will serve as their and regulation (3) substitution. Students must register for primary research adviser or co-adviser. IEME E4200: Intro to human centered design BMEN E9700: Biomedical engineering Each student is expected to submit (3) seminar and for research credits during a research proposal and present it IEME E4310: Manufacturing enterprise (3) the first two semesters of doctoral study. to a committee that consists of three MECE E4604: Product design for Remaining courses should be selected manufacturability (3) BME faculty members (two must be in consultation with the student’s faculty MECE E4610: Advanced manufacturing core BME faculty members, including processes (3) adviser to prepare for the doctoral research adviser) before the end of IEOR E4570: Entrepreneurship bootcamp (1.5) qualifying examination and to develop year 4. The committee considers the BMEE E4740: Bioinstrumentation (3) expertise in a clearly identified area scope of the proposed research, its Biomedical innovation I (3) BMEN E6005: of biomedical engineering. Students suitability for doctoral research and BMEN E6006: Biomedical innovation II (3) should not receive more than two "C" or the appropriateness of the research BMEN E6007: Lab-to-market: commercializing below letter grades. biomedical innovations (3) plan. The committee may approve All graduate students admitted to the the proposal without reservation or doctoral degree program must satisfy the may recommend modifications. In equivalent of two semesters’ experience

ENGINEERING 2021–2022 general, the student is expected to with simulation and visualization using simple required. Fieldwork credits may not count toward 71 submit his/her research proposal after computer programming. Shares lectures with any major core, technical, elective, and nontechni- five semesters of doctoral studies. ECBM E4060, but the work requirements differ cal requirements. May not be taken for pass/fail somewhat. credit or audited. In accordance with regulations of the Graduate School of Arts and BMEN E3810x Biomedical engineering BMEN E4000x or y Special topics Sciences, each student is expected to laboratory, I 3 pts. Lect: 3. Members of the faculty. submit a thesis and defend it before a 3 pts. Lab: 4. Professor Kyle. Current topics in biomedical engineering. committee of five faculty, one of whom Fundamental considerations of wave mechanics; Subject matter will vary by year. Instructors design philosophies; reliability and risk concepts; may impose prerequisites depending on the holds primary appointment in another basics of fluid mechanics; design of structures topic. department or school or university. subjected to blast; elements of seismic design; Every doctoral candidate is required to elements of fire design; flood considerations; BMEN E4001x Quantitative physiology, I: cells have had at least one first-author full- advanced analysis in support of structural design. and molecules length paper accepted for publication 3 pts Lect: 3. Professor Kam. BMEN E3820y Biomedical engineering Prerequisite(s): BIOL UN2005 and UN2006. in a peer-reviewed journal prior to laboratory, II Corequisites: BMEN E3010 and E3810. recommendation for award of the 3 pts. Lab: 4. Professor Hung. Physiological systems at the cellular and molecu- degree. Biomedical experimental design and hypothesis lar level are examined in a highly quantitative testing. Statistical analysis of experimental mea- context. Topics include chemical kinetics, molecu- COURSES IN BIOMEDICAL surements. Analysis of variance, post hoc testing. lar binding and enzymatic processes, molecular Fluid shear and cell adhesion, neuro-electrophysi- motors, biological membranes, and muscles. ENGINEERING ology, soft tissue biomechanics, biomedical imag- BMEN E4002y Quantitative physiology, II: BMEN E1001x Engineering in medicine ing and ultrasound, characterization of excitable tissues, microfluidics. organ systems 3 pts. Lect: 3. Not offered in 2021–2022. 3 pts. Lect: 3. Professor Morrison. The present and historical role of engineering in BMEN E3910x-E3920y Biomedical Prerequisite(s): BIOL UN2005 and UN2006. medicine and health care delivery. Engineering engineering design, I and II Corequisites: BMEN E3020, E3820. Students approaches to understanding organismic and 4 pts. Lect: 1. Lab: 3. Professors Hillman and are introduced to a quantitative, engineering cellular function in living systems. Engineering in Sajda. approach to cellular biology and mammalian the diagnosis and treatment of disease. Medical A two-semester design sequence to be taken in physiology. Beginning with biological issues imaging, medical devices: diagnostic and surgical the senior year. Elements of the design process, related to the cell, the course progresses to instruments, drug delivery systems, prostheses, with specific applications to biomedical engineer- considerations of the major physiological systems artificial organs. Medical informatics and organiza- ing: concept formulation, systems synthesis, of the human body (nervous, circulatory, respira- tion of the health care system. Current trends in design analysis, optimization, biocompatibility, tory, renal). biomedical engineering research. impact on patient health and comfort, health care costs, regulatory issues, and medical ethics. BMEN E4010y Ethics for biomedical engineers BMEN E3010x Biomedical engineering, I 2 pts. Lect: 2. Not offered in 2021–2022. 3 pts. Lect: 3. Professor Wang. Selection and execution of a project involving the design of an actual engineering device or system. Prerequisite(s): senior status in biomedical engi- Prerequisite(s): BIOL UN2005 and UN2006, or neering or the instructor’s permission. Covers a instructor’s permission. Corequisites: BMEN Introduction to entrepreneurship, biomedical start-ups, and venture capital. Semester I: statisti- wide range of ethical issues expected to confront E4001, BMEN E3810. Various concepts within graduates as they enter the biotechnology indus- the field of biomedical engineering, foundational cal analysis of detection/classification systems (receiver operation characteristic analysis, logistic try, research, or medical careers. Topics vary knowledge of engineering methodology applied and incorporate guest speakers from Physicians to biological and/or medical problems through regression), development of design prototype, need, approach, benefits and competition analy- and Surgeons, , Columbia modules in biomechanics, biomaterials, and cell College, and local industry. and tissue engineering. sis. Semester II: spiral develop process and test- ing, iteration and refinement of the initial design/ BMEB W4020x Computational neuroscience: BMEN E3020y Biomedical engineering, II prototype, and business plan development. A lab circuits in the brain 3 pts. Lect: 3. Professor Lu. fee of $100 each is collected. 3 pts. Lect: 3. Professor Lazar. Prerequisite(s): BIOL UN2005 and UN2006, or Prerequisite(s): ELEN E3801 or BIOL UN3004. The instructor’s permission. Corequisites: BMEN BMEN E3998x or y Projects in biomedical engineering biophysics of computation: modeling biological E4002, BMEN E3820. Various concepts within neurons, the Hodgkin-Huxley neuron, modeling the field of biomedical engineering, foundational 1–3 pts. Hours to be arranged. Members of the faculty. channel conductances and synapses as memris- knowledge of engineering methodology applied tive systems, bursting neurons and central pattern to biological and/or medical problems through Independent projects involving experimental, theoretical, computational, or engineering design generators, I/O equivalence and spiking neuron modules in biomechanics, bioinstrumentation, and models. Information representation and neural biomedical imaging. work. May be repeated, but no more than 3 points of this or any other projects or research course encoding: stimulus representation with time ECBM E3060x Introduction to genomic may be counted toward the technical elective encoding machines, the geometry of time encod- information science and technology degree requirements as engineering technical ing, encoding with neural circuits with feedback, 3 pts. Lect: 3. Professor Varadan. electives. population time encoding machines. Dendritic Introduction to the information system paradigm computation: elements of spike processing and of molecular biology. Representation, organiza- BMEN E3999x, y or s Fieldwork neural computation, synaptic plasticity and learn- tion, structure, function and manipulation of the 1–2 pts. Professor Kam. ing algorithms, unsupervised learning and spike biomolecular sequences of nucleic acids and Prerequisite(s): Obtained internship and approval time-dependent plasticity, basic dendritic integra- proteins. The role of enzymes and gene regula- from faculty adviser. BMEN undergraduate stu- tion. Projects in MATLAB. dents only. May be used toward the 128-credit tory elements in natural biological functions as BMEE E4030x Neural control engineering well as in biotechnology and genetic engineer- degree requirement. Only for BMEN undergradu- ate students who include relevant off-campus 3 pts. Lect: 3. Professor Wang. ing. Recombination and other macromolecular Prerequisite(s): ELEN E3801. Topics include basic processes viewed as mathematical operations work experience as part of their approved pro- gram of study. Final report and letter of evaluation cell biophysics, active conductance and the

ENGINEERING 2021–2022 72 Hodgkin-Huxley model, simple neuron models, mushroom body and the lateral horn. Canonical Engineering graduate student interested in acquir- ion channel models and synaptic models, statisti- circuits for associative learning and innate memo- ing in-depth knowledge of anatomy relevant to cal models of spike generation, Wilson-Cowan ry. Projects in Python. his/her doctoral research. Lectures and tutorial model of cortex, large-scale electrophysiological sessions may be taken with or without the associ- recording methods, sensorimotor integration and ECBM E4090x or y Brain computer interfaces ated laboratory (BMEN E4108). optimal state estimation, operant conditioning (BCI) laboratory of neural activity, nonlinear modeling of neural 3 pts. Lect: 2. Lab: 3. Professor Mesgarani. BMEN E4108x Anatomy laboratory: head and systems, sensory systems: visual pathway and Prerequisite(s): ELEN E3801. Hands-on experi- neck somatosensory pathway, neural encoding model: ence with basic neural interface technologies. 2 pts. Lab: 2. Not offered in 2021–2022. spike triggered average (STA) and spike triggered Recording EEG (electroencephalogram) signals Prerequisite(s): Graduate standing in Biomedical covariance (STC) analysis, neuronal response to using data acquisition systems (noninvasive scalp Engineering. Corequisites: BMEN E4107. recordings). Real-time analysis and monitoring of electrical micro-stimulation, DBS for Parkinson’s BMEN E4110x Biostatistics for engineers disease treatment, motor neural prostheses, and brain responses. Analysis of intention and percep- tion of external visual and audio signals. 4 pts. Lect: 4. Professor Jacobs. sensory neural prostheses. Prerequisite(s): MATH UN1202 or APMA E2000 ECBM E4040x or y Neural networks and deep BMEN E4100 BMakE—Biomedical device and APMA E2101. Fundamental concepts of prob- learning design & fabrication ability and statistics applied to biology and medi- 3 pts. Lect: 3. Professor Kostic. 3 pts. Lect: 3. Professor Kyle. cine. Probability distributions, hypothesis testing Prerequisite(s): BMEB W4020 or BMEE E4030 or Recommended: Coursework in statics and/or and inference, summarizing data and testing for ECBM E4090 or ELEN E4750 or COMS W4771 or dynamics, basic electrical principles, and basic trends. Signal detection theory and the receiver an equivalent. Developing features and internal computer programming. Hands-on course. operator characteristic. Lectures accompanied by representations of the world, artificial neural Covers medical device design to develop basic data analysis assignments using MATLAB and R as networks, classifying handwritten digits with fabrication skills. Includes central project theme, well as discussion of bioethics and case studies logistics regression, feedforward deep networks, i.e., through individual modules, students create in biomedicine. different components of a biomedical device. back propagation in multilayer perceptrons, BMEN E4150x The cell as a machine First offering focuses on creation of a device regularization of deep or distributed models, opti- 3 pts. Lect: 3. Not offered in 2021–2022. pertinent for COVID-19: a mechanical ventilator. mization for training deep models, convolutional Prerequisite(s): MATH UN1101 or equivalent. The mechanical ventilator combines physics neural networks, recurrent and recursive neural Corequisites: One semester of BIOL UN2005 (fluid dynamics, pressure-flow relationships) with networks, deep learning in speech, and object or BIOC UN3501, and one semester of PHYS recognition. fabrication, (bio)materials, sensing, signal acquisi- tion and processing, and controls. As a highly UN1401 or equivalent. Cells as complex micron- BMEN E4050x or y Electrophysiology of advanced, life-supporting device, its functional sized machines, basic physical aspects of cell human memory and navigation aspects can be decomposed into modules of this components (diffusion, mechanics, electrostatics, 3 pts. Lect: 3. Professor Jacobs. course to create a benchtop ventilator. hydrophobicity), energy transduction (motors, Prerequisite(s): Instructor's permission. Human transporters, chaperones, synthesis complexes), memory, including working, episodic, and pro- BMEN E4103x Anatomy of the thorax and basic cell functions. Biophysical principles, feed- cedural memory. Electrophysiology of cognition, abdomen back controls for robust cell function, adaptation noninvasive and invasive recordings. Neural basis 2 pts. Lect: 2. Not offered in 2021–2022. to environmental perturbations. Prerequisite(s): Graduate standing in Biomedical of spatial navigation, with links to spatial and epi- BMEN E4210y Driving forces of biological Engineering. Designed for the Biomedical sodic memory. Computational models of memory, systems Engineering graduate student interested in acquir- brain stimulation, lesion studies. 4 pts. Lect: 4. Professor Sia. ing in-depth knowledge of anatomy relevant to Prerequisite(s): CHEM UN1404 and MATH UN1202 ECBM E4060x Introduction to genomic his/her doctoral research. Lectures and tutorial or AMPA E2000. Corequisite: BIOL UN2005 or information sessions may be taken with or without the associ- equivalent. Introduction to the statistical mechan- 3 pts. Lect: 3. Professor Anastassiou. ated laboratory (BMEN E4104). Prerequisite(s): None. Introduction to the infor- ics and thermodynamics of biological systems, mation system paradigm of molecular biology. BMEN E4104x Anatomy laboratory: thorax with a focus on connecting microscopic molecular Representation, organization, structure, function and abdomen properties to macroscopic states. Both classical and manipulation of the biomolecular sequence 2 pts. Lect: 2. Not offered in 2021–2022. and statistical thermodynamics will be applied of nucleic acids and proteins. The role of enzymes Prerequisite(s): Graduate standing in Biomedical to biological systems; phase equilibria, chemical and gene regulatory elements in natural biological Engineering. Corequisite: BMEN E4103. reactions, and colligative properties. Topics in modern biology, macromolecular behavior in solu- functions as well as in biotechnology and genetic BMEN E4105x Anatomy of the extremities engineering. Recombination and other macro- tions and interfaces, protein-ligand binding, and 2 pts. Lect: 2. Not offered in 2021–2022. the hydrophobic effect. molecular processes viewed as mathematical Prerequisite(s): Graduate standing in Biomedical operations with simulation and visualization using Engineering. Designed for the Biomedical BMEN E4301x Structure, mechanics, and simple computer programming. Engineering graduate student interested in acquir- adaptation of bone ECBM E4070y Computing with brain circuits ing in-depth knowledge of anatomy relevant to 3 pts. Lect: 3. Not offered in 2021–2022. of model organisms his/her doctoral research. Lectures and tutorial Introduction to structure, physiology, and biome- 3 pts. Lect: 3. Professor Lazar. sessions may be taken with or without the associ- chanics of bone. Structure, function, and physiol- Prerequisite(s): ELEN E3801 or BIOL W3004, and ated laboratory (BMEN E4106). ogy of skeletal bones; linear elastic properties of cortical and trabecular bone; anisotropy and Python programming experience, or instruc- BMEN E4106x Anatomy laboratory: tor's permission. Building the functional map of constitutive models of bone tissue; failure and extremities damage mechanics of bone; bone adaptation and the fruit fly brain. Molecular transduction and 2 pts. Lab: 2. Not offered in 2021–2022. spatio-temporal encoding in the early visual sys- fracture healing; experimental determination of Prerequisite(s): Graduate standing in Biomedical bone properties; and morphological analysis of tem. Predictive coding in the Drosophila retina. Engineering. Corequisites: BMEN E4105. Canonical circuits in motion detection. Canonical bone microstructure. navigation circuits in the central complex. BMEN E4107x Anatomy of the head and neck BMEN E4302x Biomechanics of Molecular transduction and combinatorial encod- 2 pts. Lect: 2. Not offered in 2021–2022. musculoskeletal soft tissues ing in the early olfactory system. Predictive coding Prerequisite(s): Graduate standing in Biomedical 3 pts. Lect: 3. TBA. in the antennal lobe. The functional role of the Engineering. Designed for the Biomedical

ENGINEERING 2021–2022 Prerequisite(s): ENME E3113 or equivalent. transient and permanent gene activation, and cell harmonic imaging; acoustic output of ultrasound 73 Restricted to seniors and graduate students. commitment, development, and death. systems; biological effects of ultrasound. Biomechanics of orthopaedic soft tissues (carti- lage, tendon, ligament, meniscus, etc.). Basic and BMEN E4350y Biomechanics of BMEN E4420y Biomedical signal processing advanced viscoelasticity applied to the musculo- developmental biology and signal modeling skeletal system. Topics include mechanical prop- 3 pts. Lect: 3. Professor Nerurkar. 3 pts. Lect: 3. Not offered in 2021–2022. erties, applied viscoelasticity theory, and biology Prerequisite(s): Undergraduate-level course in Prerequisite(s): ELEN E3801 and either APMA of orthopaedic soft tissues. mechanics (e.g. MECE E3113, BMEN E4310) and E2101 or E3101 or instructor’s permission. cell biology (e.g. BIOL UN2005/6) or by instruc- Fundamental concepts of signal processing in lin- BMEN E4305y Cardiac mechanics tor's permission. Biophysical mechanisms of tis- ear systems and stochastic processes. Estimation, 3 pts. Lect: 3. Not offered in 2021–2022. sue organization during embryonic development: detection, and filtering methods applied to Prerequisite(s): BMEN E4310 and BMEN E4320 or conservation laws, reaction-diffusion, finite elas- biomedical signals. Harmonic analysis, auto- equivalents. Cardiac anatomy, passive myocar- ticity, and fluid mechanics reviewed and applied regressive model, Wiener and Matched filters, dial constitutive properties, electrical activation, to topics in developmental biology, from early linear discriminants, and independent compo- ventricular pump function, ventricular-vascular development to later organogenesis of the central nents. Methods are developed to answer concrete coupling, invasive and noninvasive measures of nervous, cardiovascular, musculoskeletal, respira- questions on specific data sets in modalities such regional and global function, models for predict- tory, and gastrointestinal systems. Subdivided into as ECG, EEG, MEG, ultrasound. Lectures accompa- ing ventricular wall stress. Alterations in muscle modules on patterning (conversion of diffusible nied by data analysis assignments using MATLAB. properties and ventricular function resulting from cues into cell fates) and morphogenesis (shaping myocardial infarction, heart failure, and left ven- of tissues). Includes lectures, problem sets, read- BMEN E4430x Principles of magnetic tricular assist. ing of primary literature, and a final project. resonance imaging 3 pts. Lect: 3. Professor Juchem. BMEN E4310x or y Solid biomechanics BMEN E4340x Biomechanics of cells Prerequisite(s): PHYS UN1403 and APMA E2101, 3 pts. Lect: 3. Professor Guo. 3 pts. Lect: 3. Not offered in 2021–2022. or instructor’s permission. Fundamental principles Prerequisite(s): ENME E3105 and ENME E3113. Prerequisite(s): BMEN E3320 and BMEN E4300 of Magnetic Resonance Imaging (MRI), including Applications of continuum mechanics to the or equivalents. Survey of experiments and the underlying spin physics and mathematics of understanding of various biological tissues prop- theoretical analyses of the mechanical behavior image formation with an emphasis on the applica- erties. The structure, function, and mechanical of individual living nonmuscle cells. Emphasis tion of MRI to neuroimaging, both anatomical and properties of various tissues in biological systems, on quantitative analytic description using con- functional. The course examines both theory and such as blood vessels, muscle, skin, brain tis- tinuum mechanics and molecular level theory experimental design techniques. sue, bone, tendon, cartilage, ligaments, etc., are from the standpoint of statistical mechanics and examined. The establishment of basic governing mechanical models. Mechanics of erythrocytes, MEBM E4439x Modeling and identification of mechanical principles and constitutive relations leukocytes, endothelial cells, and fibroblasts; dynamic systems for each tissue. Experimental determination of models of aggregation, adhesion, locomotion, 3 pts. Lect: 3. Professor Chbat. various tissue properties. Medical and clinical amoeba motility, cell division and morphogenesis; Prerequisite(s): APMA E2101, ELEN E3801 or implications of tissue mechanical behavior. molecular level models of actin, myosin, microtu- corequisite EEME E3601, or instructor’s permis- bules, and intermediate filaments and relation to sion. Generalized dynamic system modeling and BMEN E4320x or y Fluid biomechanics mechanical properties of cells and cytoskeleton. simulation. Fluid, thermal, mechanical, diffusive, 3 pts. Lect: 3. Professor Guo. Alternative models of cytoskeletal mechanics, electrical, and hybrid systems are considered. Prerequisite(s): APMA E2101, ENME E3105, foam theory, tensegrity. Analysis of experimental Nonlinear and high order systems. System identifi- and MECE E4100. The principles of continuum techniques including micropipette studies, optical cation problem and Linear Least Squares method. mechanics as applied to biological fluid flows and and magnetic cytometry, and nanoindentation. State-space and noise representation. Kalman transport. Continuum formulations of basic con- Filter. Parameter estimation via prediction-error servation laws, Navier-Stokes equations, mechan- BMEE E4400x Wavelet applications in and subspace approaches. Iterative and bootstrap ics of arterial and venous blood flow, blood biomedical image and signal processing methods. Fit criteria. Wide applicability: medical, rheology and non-Newtonian properties, flow and 3 pts. Lect: 3. Not offered in 2021–2022. energy, others. MATLAB and Simulink environ- transport in the microcirculation, oxygen diffusion, Prerequisite(s): APMA E2101 or E3101 or equiva- ments. capillary filtration. lent. An introduction to methods of wavelet analysis and processing techniques for the quan- BMEN E4440y Physiological control systems CHBM E4321y The genome and the cell tification of biomedical images and signals. Topics 3 pts. Lect: 3. Professor Chbat. 3 pts. Lect: 3. Not offered in 2021–2022. include frames and overcomplete representations, Prerequisite(s): MEBM E4439 and APMA E2101, Prerequisite(s): BIOL UN2005 and MATH UN2030. multiresolution algorithms for denoising and or instructor’s permission. Fundamentals of The utility of genomic information lies in its image restoration, multiscale texture segmenta- time and frequency domains analyses and capacity to predict the behavior of living cells in tion and classification methods for computer stability. Frequency domain controller design. physiological, developmental, and pathological aided diagnosis. Cardiovascular and respiratory systems - situations. The effect of variations in genome tion. Endogenous control systems: baroreflex, structure between individuals within a species, BMEN E4410x Ultrasound in diagnostic chemoreflex, thermoregulation, pupillary light including those deemed healthy or diseased, imaging reflex. Open and closed loop physiological sys- and among species, can be inferred statistically 3 pts. Lect: 3. Professor Konofagou. tems. Exogenous control systems: ventilators, by comparisons of sequences with behaviors Prerequisite(s): MATH UN1202 or APMA E2000 or infusion pumps. Nonlinear actuators and delayed and mechanistically, by studying the action of equivalent. Fourier analysis. Physics of diagnostic feedback systems. Acute disease simulation and molecules whose structure is encoded within ultrasound and principles of ultrasound imaging clinical decision support in the intensive care unit. the genome. Examines known mechanisms that instrumentation. Propagation of plane waves in MATLAB and Simulink environments utilized. elucidate the combined effect of environmental lossless medium; ultrasound propagation through stimulation and genetic makeup on the behavior biological tissues; single-element and array trans- BMEN E4450y Dental and craniofacial tissue of cells in homeostasis, disease states, and during ducer design; pulse-echo and Doppler ultrasound engineering development, and includes assessments of the instrumentation, performance evaluation of ultra- 3 pts. Lect: 3. Not offered in 2021–2022. probable effect of these behaviors on the whole sound imaging systems using tissue-mimicking Prerequisite(s): MSAE E3103, BMEN E4210, E4501, organism. Quantitative models of gene translation phantoms, ultrasound tissue characterization; or equivalent. Principles of dental and craniofacial and intracellular signal transduction will be used ultrasound nonlinearity and bubble activity; bioengineering, periodontal tissue engineering: to illustrate switching of intracellular processes, beyond guided tissue regeneration, craniofacial

ENGINEERING 2021–2022 74 regeneration by stem cells and engineered scaf- troscopy (MRS) with focus on the brain. Covers all include textbook chapters and journal papers. folds, biomaterials: Engineering approaches in tis- aspects of in vivo MRS from theory to experiment, Homework assignments take format of assay sue regeneration, bone biology and development: from data acquisition to derivation of metabolic responding to open-ended question. Term paper instructive cues for tissue engineers. signatures, and from study design to clinical inter- and 30-minute PowerPoint presentation required pretation. Includes theoretical concepts, hands-on at end of semester. BMEN E4460y Deep learning in biomedical training in MRS data literacy, and direct experi- imaging mental experience using a 3T MR scanner. BMEN E4540y Bioelectrochemistry 3 pts. Lect: 3. Professor Laine. 3 pts. Lect: 3. Not offered in 2021–2022. Prerequisite(s): MATH UN1202 or APMA E2000 BMCH E4500x or y Biological transport and Prerequisite(s): CHEM UN3079 and UN2443 or and APMA E2101. Recommended: background in rate processes equivalent. Application of electrochemical kinetics Python programming. Introduction to methods 3 pts. Lect: 3. Not offered in 2021–2022. to interfacial processes occurring in biomedical deep learning, with focus on applications to Prerequisite(s): CHEM UN2443, APMA E2101. systems. Basics of electrochemistry, electro- quantitative problems in biomedical imaging and Corequisites: BIOL UN2005. Convective and dif- chemical instrumentation, and relevant cell and Artificial Intelligence (AI) in medicine. Network fusive movement and reaction of molecules in electrophysiology reviewed. Applications to inter- models: Deep feedforward networks, convo- biological systems. Kinetics of homogeneous and pretation of excitable and nonexcitable membrane lutional neural networks and recurrent neural heterogeneous reactions in biological environ- phenomena, with emphasis on heterogeneous networks. Deep autoencoders for denoising. ments. Mechanisms and models of transport mechanistic steps. Examples of therapeutic Segmentation and classification of biological tis- across membranes. Convective diffusion with and devices created as a result of bioelectrochemical sues and biomarker of disease. Theory and meth- without chemical reaction. Diffusion in restricted studies. ods lectures will be accompanied with examples spaces. Irreversible thermodynamic approaches from biomedical image including analysis of neu- to transport and reaction in biological systems. BMEN E4550y Micro- and nanostructures in rological images of the brain (MRI), CT images of cellular engineering the lung for cancer and COPD, cardiac ultrasound. BMEN E4501x Biomaterials 3 pts. Lect: 3. Professor Kam. Programming assignments will use tensorflow/ 3 pts. Lect: 3. Not offered in 2021–2022. Prerequisite(s): BIOL UN2005 and UN2006 or Pytorch and Jupyter Notebook. Examinations and Prerequisite(s): BIOL UN2005, UN2006, BMEN equivalent. Design, fabrication, and application of a final project will also be required. E4001, and E4002. An introduction to the strate- micro-/nanostructured systems for cell engineer- gies and fundamental bioengineering design ing. Recognition and response of cells to spatial BMEN E4470x Deep learning for biomedical criteria in the development of biomaterials and aspects of their extracellular environment. Focus signal processing tissue engineered grafts. Materials structural- on neural, cardiac, coculture, and stem cell sys- 3 pts. Lect: 3. Professor Sajda. functional relationships, biocompatibility in terms tems. Molecular complexes at the nanoscale. Prerequisite(s): MATH UN1202 or APMA E2000 of material and host responses. Through discus- and APMA E2101. Recommended: background in sions, readings, and a group design project, BMEN E4560y Dynamics of biological Python programming. Introduction to methods in students acquire an understanding of cell-material membranes deep learning, focus on applications to biomedi- interactions and identify the parameters critical 3 pts. Lect: 3. Not offered in 2021–2022. cal signals and sequences. Review of traditional in the design and selection of biomaterials for Prerequisite(s): BIOL UN2005, BMEN E4001, or methods for analysis of signals and sequences. biomedical applications. equivalent. The structure and dynamics of bio- Temporal convolutional neural networks and logical (cellular) membranes are discussed, with recurrent neural networks. Long-short term mem- BMEN E4510x or y Tissue engineering an emphasis on biophysical properties. Topics ory (LSTM) models and deep state-space models. 3 pts. Lect: 3. Professor Hung. include membrane composition, fluidity, lipid Theory and methods lectures accompanied with Prerequisite(s): BIOL UN2005, UN2006, BMEN asymmetry, lipid-protein interactions, membrane examples from biomedical signal and sequence E4001, E4002. An introduction to the strategies turnover, membrane fusion, transport, lipid phase analysis, including analysis of electroencepha- and fundamental bioengineering design criteria behavior. In the second half of the semester, logram (EEG), electrocardiogram (ECG/EKG), and behind the development of cell-based tissue sub- students will lead discussions of recent journal genomics. Programming assignments use tensor- stitutes. Topics include biocompatibility, biological articles. grafts, gene therapy-transfer, and bioreactors. flow/keras. Exams and final project required. BMEN E4570x Science and engineering of BMEN E4480x Statistical machine learning BMEN E4520x Synthetic biology: principles of body fluids for genomics genetic circuits 3 pts. Lect: 3. Not offered in 2021–2022. 3 pts. Lect: 3. Professor Azizi. 3 pts. Lect: 3. Professor Danino. Prerequisite(s): General chemistry, organic chem- Prerequisite(s): APMA E2101, MATH UN1202, Basic principles of synthetic biology and survey istry, and basic calculus. Body fluids as a dilute MATH UN2010, Proficiency in Python/R program- of the field. Fundamentals of biological circuits, solution of polyelectrolyte molecules in water. ming, and background in probability/statistics. including circuit design, modern techniques for Study of physical behavior as affected by the Recommended: COMS W4771. Introduction to DNA assembly, quantitative characterization of presence of ions in surrounding environments. statistical machine learning methods using appli- genetic circuits, and ODE modeling of biological The physics of covalent, ionic, and hydrogen cations in genomic data and in particular high- circuits with MATLAB. Knowledge of biology, ordi- bonds are reviewed, in relation to the structure/ dimensional single-cell data. Concepts of molecu- nary differential equations, and MATLAB will be properties of the body fluid. Selected physiologi- lar biology relevant to genomic technologies, assumed. Intended for advanced undergraduate cal processes are examined in physical-chemical challenges of high-dimensional genomic data and graduate students. terms for polymers. analysis, bioinformatics preprocessing pipelines, BMEN E4530x Drug and gene delivery BMEN E4580y Foundations of nanobioscience dimensionality reduction, unsupervised learning, 3 pts. Lect: 3. Professor Leong. and nanobiotechnology clustering, probabilistic modeling, hidden Markov Prerequisite(s): BMEN E3010. Application of 3 pts. Lect: 3. Professor Hess. models, Gibbs sampling, deep neural networks, polymers and other materials in drug and gene Prerequisite(s): BIOL UN2005, UN2006, BMEN gene regulation, Programming assignments and delivery, with focus on recent advances in field. E4001-E4002 or instructor's permission. final project will be required. Basic polymer science, pharmacokinetics, and Fundamentals of nanobioscience and nanobio- BMEN E4490x Magnetic resonance biomaterials, cell-substrate interactions, drug technology, scientific foundations, engineering spectroscopy: a window to the living brain delivery system fabrication from nanoparticles principles, current and envisioned applications. 3 pts. Lect: 3. Professors Juchem and Kegeles. to microparticles and electrospun fibrous mem- Includes discussion of intermolecular forces and Corequisite: Quantitative Physiology I or II. branes. Applications include cancer therapy, bonding, of kinetics and thermodynamics of Introduction to use of magnetic resonance spec- immunotherapy, gene therapy, tissue engineer- self-assembly, of nanoscale transport processes ing, and regenerative medicine. Course readings arising from actions of biomolecular motors, com-

ENGINEERING 2021–2022 putation and control in biomolecular systems, and MEBM E4710x or y Morphogenesis: shape and ear, and the mechanical processing of sound 75 of mitochondrium as an example of nanoscale structure in biological materials within the inner ear. factory. 3 pts. Lect: 3. Not offered in 2021–2022. CBMF W4761y Computational genomics Prerequisite(s): Courses in mechanics, thermody- BMEN E4590x BioMems: cellular and 3 pts. Lect: 3. Professor Pe’er. namics, and ordinary differential equations at the Prerequisite(s): Working knowledge of at least one molecular applications undergraduate level or instructor's permission. programming language, and some background 3 pts. Lect: 3. Professor Sia. Introduction to how shape and structure are gen- - Prerequisite(s): Chemistry, CHEM UN2443, or erated in biological materials using engineering in probability and statistics. Computational tech niques for analyzing and understanding genomic CHEM UN3545 or equivalent, MATH UN1201 or approach emphasizing application of fundamental data, including DNA, RNA, protein and gene APMA E2000, BIOL UN2005, and UN2006. Topics physical concepts to a diverse set of problems. expression data. Basic concepts in molecular include biomicroelectromechanical, microfluidic, Mechanisms of pattern formation, self-assembly, biology relevant to these analyses. Emphasis on and lab-on-a-chip systems in biomedical engi- and self-organization in biological materials, techniques from artificial intelligence and machine neering, with a focus on cellular and molecular including intracellular structures, cells, tissues, learning. String-matching algorithms, dynamic applications. Microfabrication techniques, bio- and developing embryos. Structure, mechanical programming, hidden Markov models, expecta- compatibility, miniaturization of analytical and properties, and dynamic behavior of these materi- tion-maximization, neural networks, clustering diagnostic devices, high-throughput cellular stud- als. Discussion of experimental approaches and algorithms, support vector machines. Students ies, microfabrication for tissue engineering, and modeling. Course uses textbook materials as well with life sciences backgrounds who satisfy the in vivo devices. as collection of research papers. prerequisites are encouraged to enroll. BMEN E4601y Cellular electricity BMEN E4737x Computer control of medical BMCH E4810y Artificial organs 3 pts. Lect: 2. Lab: 1. Not offered in instrumentation 3 pts. Lect: 3. Not offered in 2021–2022. 2021–2022. 3 pts. Lect: 2. Lab: 1. Not offered in 2021–2022. Analysis and design of replacements for the heart, Bioelectricity of the cell membrane. Basis of cell Prerequisite(s): Basic knowledge of the C pro- kidneys, and lungs. Specification and realization resting voltage, voltage changes that lead to the gramming language. Acquisition and presentation of structures for artificial organ systems. action potential and electrical oscillations used of data for medical interpretation. Operating in sensing systems. Laboratory includes building principles of medical devices: technology of BMEN E4840y Functional imaging for the electronic circuits to measure capacitance of medical sensors, algorithms for signal analysis, brain artificial membranes and ion pumping in frog skin. computer interfacing and programming, interface Lab required. 3 pts. Lect: 3. Not offered in 2021–2022. design. Laboratory assignments cover basic Prerequisite(s): APMA E2101, APMA E4200, ELEN APBM E4650x Anatomy for physicists and measurement technology, interfacing techniques, E3801, or instructor’s permission. Fundamentals engineers use of Labview software instrument interrogation of modern medical functional imaging. In-depth 3 pts. Lect: 3. Professors Katz and Rozenshtein. and control, automated ECG analysis, ultrasonic exploration of functional magnetic resonance Prerequisite(s): Engineering or physics back- measurements, image processing applied to X-ray imaging (fMRI), arterial spin labeling (ASL), and ground. A systemic approach to the study of the images and CAT scans. positron emission tomography (PET). Human - human body from a medical imaging point of BMEN E4738y Transduction and acquisition of brain anatomy, physiology, and neurophysiologi cal bases underlying each functional imaging. view: skeletal, respiratory, cardiovascular, diges- biomedical data Statistical and digital signal processing methods tive, and urinary systems, breast and women’s 3 pts. Lect: 2. Lab: 1. Not offered in 2021–2022. specific for functional image analysis. Final cumu- issues, head and neck, and central nervous Data transduction and acquisition systems used in lative project requiring coding in MATLAB, Python, system. Lectures are reinforced by examples from biomedicine. Assembly of biotransducers and the R, or C. clinical two- and three-dimensional and functional analog/digital circuitry for acquiring electrocardio- imaging (CT, MRI, PET, SPECT, U/S, etc.). gram, electromyogram, and blood pressure sig- BMEN E4894x Biomedical imaging BMME E4702x Advanced musculoskeletal nals. Each small group will develop and construct 3 pts. Lect: 3. Not offered in 2021–2022. biomechanics a working data acquisition board, which will be Covers image formation, methods of analysis, 3 pts. Lect: 2.5. Lab: 0.5. Not offered in interfaced with a signal generator to elucidate the and representation of digital images. Measures of 2021–2022. dynamics of timing constraints during retrieval of qualitative performance in the context of clinical Advanced analysis and modeling of the muscu- biodata. Lab required. imaging. Algorithms fundamental to the construc- tion of medical images via methods of computed loskeletal system. Topics include advanced con- BMEE E4740y Bioinstrumentation tomography, magnetic resonance, and ultrasound. cepts of 3D segmental kinematics, musculoskele- 3 pts. Lect: 3. Not offered in 2021–2022. tal dynamics, experimental measurements of joint Algorithms and methods for the enhancement and Prerequisite(s): ELEN E1201, COMS W1005. Hands- kinematics and anatomy, modeling of muscles quantification of specific features of clinical impor- on experience designing, building, and testing and locomotion, multibody joint modeling, intro- tance in each of these modalities. the various components of a benchtop cardiac duction to musculoskeletal surgical simulations. pacemaker. Design instrumentation to measure BMEN E4895x or y Analysis and MEBM E4703y Molecular mechanics in biomedical signals as well as to actuate living tis- quantification of medical images biology sues. Transducers, signal conditioning electronics, 3 pts. Lect: 3. Not offered in 2021–2022. 3 pts. Lect: 3. Professor Chbat. data acquisition boards, the Arduino microproces- Prerequisite(s): BMEN E4894. Corequisite: BMEN Prerequisite(s): ENME E3105, APMA E2101, or sor, and data acquisition and processing using E4894. Novel methods of mathematical analysis applied to problems in medical imaging. Design instructor’s permission. Mechanical understanding MATLAB will be covered. Various devices will be requirements for screening protocols, treatment of biological structures including proteins, DNA discussed throughout the course, with laboratory therapies, and surgical planning. Sensitivity and and RNA in cells and tissues. Force response of work focusing on building an emulated version of proteins and DNA, mechanics of membranes, specificity in screening mammography and chest a cardiac pacemaker. biophysics of molecular motors, mechanics of radiographs, computer-aided diagnosis systems, protein-protein interactions. Introduction to BMEN E4750y Sound and hearing surgical planning in orthopaedics, quantitative modeling and simulation techniques, and modern 3 pts. Lect: 3. Not offered in 2021–2022. analysis of cardiac performance, functional biophysical techniques such as single molecule Prerequisite(s): PHYS UN1401 and MATH UN1105- magnetic resonance imaging, positron emission FRET, optical traps, AFM, and superresolution MATH UN1106. Introductory acoustics, basics of tomography, and echocardiography data. imaging for understanding molecular mechanics waves and discrete mechanical systems. The BMEN E4898y Biophotonics and dynamics. mechanics of hearing—how sound is transmitted 3 pts. Lect: 3. Not offered in 2021–2022. through the external and middle ear to the inner

ENGINEERING 2021–2022 76 Prerequisite(s): BMEN E4894 Biomedical imaging, ence for graduate students. Elements of design to year, and different topics rotate through the PHYS UN1403 Classical and quantum waves, or process, with focus on skills development, proto- course numbers 6090-6099. instructor’s permission. Provides a broad-based type development and testing, and business plan- introduction into the field of Biophotonics. ning. Real-world training in biomedical design, BMEN E6301y Modeling of biological tissues Fundamental concepts of optical, thermal, and innovation, and entrepreneurship. with finite elements chemical aspects of the light-tissue interactions 3 pts. Lect: 3. Not offered in 2021–2022. will be presented. The application of these con- BMEN E6007y Lab-to-market: Prerequisite(s): MECE E6422, or ENME E6315, cepts for medical therapy and diagnostics will be commercializing biomedical innovations or equivalent. Structure-function relations and discussed. The course includes theoretical model- 3 pts. Lect: 3. TBA. linear/nonlinear constitutive models of biologi- ing of light-tissue interactions as well as optical Introduction to and application of commercializa- cal tissues: anisotropic elasticity, viscoelasticity, medical instrument design and methods of clinical tion of biomedical innovations. Topics include porous media theories, mechano-electrochemical data interpretation. needs clarification, stakeholder analysis, market models, infinitesimal and large deformations. analysis, value proposition, business models, Emphasis on the application and implementation BMEN E4999x and y Graduate fieldwork intellectual property, regulatory, and reimburse- of constitutive models for biological tissues into 1–2 pts. Professor Hung. ment. Development of path-to-market strategy existing finite element software packages. Model Prerequisite(s): Obtained internship and and pitch techniques. generation from biomedical images by extraction approval from faculty adviser. BMEN graduate of tissue geometry, inhomogeneity and anisot- students only. Only for BMEN graduate students EEBM E6020y Methods of computational ropy. Element-by-element finite element solver who need relevant work experience as part of neuroscience for large-scale image based models of trabecular their program of study. Final reports required. 4.5 pts. Lect: 3. Not offered in 2021–2022. bone. Implementation of tissue remodeling simu- May not be taken for pass/fail credit or audits. Prerequisite(s): BMEB W4020. Formal methods in lations in finite element models. computational neuroscience including methods of BMEN E6000x and y Graduate special topics signal processing, communications theory, infor- MEBM E6310x-E6311y Mixture theories for in biomedical engineering mation theory, systems and control, system iden- biological tissues, I and II 3 pts. Lect: 3. Members of the faculty. tification and machine learning. Molecular models 3 pts. Lect: 3. Not offered in 2021–2022. Current topics in biomedical engineering. Subject of transduction pathways. Robust adaptation Prerequisite(s): MECE E6422 and APMA E4200, or matter will vary by year. Instructors may impose and integral feedback. Stimulus representation equivalent Development of governing equations prerequisites depending on the topic. and groups. Stochastic and dynamical systems for mixtures with solid matrix, interstitial fluid, models of spike generation. Neural diversity and and ion constituents. Formulation of constitu- BMEN E6001x Current topics in ensemble encoding. Time encoding machines and tive models for biological tissues. Linear and nanobiotechnology and synthetic biology neural codes. Stimulus recovery with time decod- nonlinear models of fibrillar and viscoelastic 3 pts. Lect: 3. Professor Hess. ing machines. MIMO models of neural computa- porous matrices. Solutions to special problems, Targeted toward graduate students; undergradu- tion. Synaptic plasticity and learning algorithms. such as confined and unconfined compression, ate students may participate with permission Major project(s) in MATLAB. permeation, indentation and contact, and swelling of the instructor. Review and critical discussion experiments. of recent literature in nanobiotechnology and BMEE E6030x Neural modeling and synthetic biology. Experimental and theoretical neuroengineering BMEN E6400x Analysis and quantification of techniques, critical advances. Quality judgments 3 pts. Lect: 3. Not offered in 2021–2022. medical images of scientific impact and technical accuracy. Styles Prerequisite(s): ELEN E3801, and either APMA 3 pts. Lect: 3. Not offered in 2021–2022. of written and graphical communication, the peer E2101 or E3101, or equivalent, or instructor’s Novel methods of mathematical analysis review process. permission. Engineering perspective on the study applied to problems in medical imaging. Design of multiple levels of brain organization, from requirements for screening protocols, treatment BMEN E6003y Computational modeling of single neurons to cortical modules and systems. therapies, and surgical planning. Sensitivity and physiological systems Mathematical models of spiking neurons, neural specificity in screening mammography and chest 3 pts. Lect: 3. TBA. dynamics, neural coding, and biologically-based radiographs, computer aided diagnosis systems, Prerequisite(s): BMEN E4001 and E4002 or equiv- computational learning. Architectures and learn- surgical planning in orthopaedics, quantitative alent, and APMA E4200 or equivalent. Advanced ing principles underlying both artificial and analysis of cardiac performance, functional computational modeling and quantitative analysis biological neural networks. Computational models magnetic resonance imaging, positron emission of selected physiological systems from molecules of cortical processing, with an emphasis on the tomography, and echocardiography data. to organs. Selected systems are analyzed in depth visual system. Applications of principles in neu- with an emphasis on modeling methods and roengineering; neural prostheses, neuromorphic BMEN E6500x Tissue and molecular quantitative analysis. Topics may include cell sig- systems and biomimetics. Course includes a com- engineering laboratory naling, molecular transport, excitable membranes, puter simulation laboratory. Lab required. 4 pts. Lect: 1. Lab: 4. TBA. respiratory physiology, nerve transmission, circu- Prerequisite(s): Biology BIOL UN2005 and BIOL latory control, auditory signal processing, muscle ECBM E6070-6079x or y Topics in UN2006 or permission of instructor. Hands-on physiology, data collection and analysis. neuroscience and deep learning experiments in molecular and cellular techniques, 3 pts. Lect: 2. Members of the faculty. including fabrication of living engineered tissues. BMEN E6005x Biomedical innovation I Prerequisite(s): the instructor's permission. Covers sterile technique, culture of mammalian 3 pts. Lect: 3. TBA. Selected advanced topics in neuroscience and cells, microscopy, basic subcloning and gel elec- Master's students only. Project-based design deep learning. Content varies from year to year, trophoresis, creation of cell-seeded scaffolds, and experience for graduate students. Elements of and different topics rotate through the course the effects of mechanical loading on the metabo- design process, including need identification, numbers 6070 to 6079. lism of living cells or tissues. Theory, background, concept generation, concept selection, and imple- and practical demonstration for each technique EEBM E6090-6099x or y Topics in mentation. Development of design prototype and will be presented. Lab required. introduction to entrepreneurship and implementa- computational neuroscience and tion strategies. Real-world training in biomedical neuroengineering BMEN E6505x or y Advanced biomaterials & design and innovation. 3 pts. Lect: 2. Professor Sajda. tissue engineering Prerequisite(s): Instructor’s permission. Selected 3 pts. Lect: 2.5. Lab: 0.5. Professor Lu. BMEN E6006y Biomedical innovation II advanced topics in computational neuroscience Prerequisite(s): BMEN E4501 or equivalent. 3 pts. Lect 3. TBA. and neuroengineering. Content varies from year Corequisites: BMEN E4001 or E4002. Advanced Second semester of project-based design experi- biomaterial selection and biomimetic scaffold

ENGINEERING 2021–2022 design for tissue engineering and regenerative EEBM E9070y Massively parallel neural BMEN E9700x or y Biomedical engineering 77 medicine. Formulation of bio-inspired design computation seminar criteria, scaffold characterization and testing, 3 pts. Lect: 3. Professor Mesgarani. 0 pts. Sem: 1. Professors Danino, Juchem, and and applications on forming complex tissues or Prerequisite(s): BMEB W4020 or permission of Olson. organogenesis. Laboratory component includes instructor. Drosophila connectomics. Detailed All matriculated graduate students are required basic scaffold fabrication, characterization and in description of the fruit fly’s olfactory and vision to attend the seminar as long as they are in resi- vitro evaluation of biocompatibility. Group projects systems. Parallel processing on GPSs. dence. No degree credit is granted. The seminar target the design of scaffolds for select tissue is the principal medium of communication among engineering applications. BMEN E9100x or y Master’s research those with biomedical engineering interests 1–6 pts. Members of the faculty. within the University. Guest speakers from other BMEN E6510y Stem cell, genome Candidates for the M.S. degree may conduct institutions, Columbia faculty, and students within engineering, and regenerative medicine an investigation of some problem in biomedical the department who are advanced in their studies 3 pts. Lect: 3. Professors Tsang, Egli, and engineering culminating in a thesis describing the frequently offer sessions. Vunjak-Novakovic. results of their work. No more than 6 points may Prerequisite(s): Biology, Cell Biology, BMEN E4001 be counted for graduate credit, and this credit is BMEN E9800x or y Doctoral research or BMEN E4002. General lectures on stem cell contingent upon the submission of an acceptable instruction biology followed by student presentations and thesis. 3–12 pts. Members of the faculty. discussion of primary literature. Themes pre- A candidate for the Eng.Sc.D. degree in biomedi- BMEN E9500x or y Doctoral research sented include: basic stem cell concepts; basic cal engineering must register for 12 points of doc- cell and molecular biological characterization 1–6 pts. Members of the faculty. toral research instruction. Registration may not be of endogenous stem cell populations; concepts Doctoral candidates are required to make an used to satisfy the minimum residence require- related to reprogramming; directed differentia- original investigation of a problem in biomedical ment for the degree. tion of stem cell populations; use of stem cells in engineering, the results of which are presented in disease modeling or tissue replacement/repair; the dissertation. BMEN E9900x or y Doctoral dissertation clinical translation of stem cell research. 0 pts. Members of the faculty. A candidate for the doctorate in biomedical engineering or applied biology may be required to register for this course in every term after the student’s coursework has been completed and until the dissertation has been accepted.

ENGINEERING 2021–2022 78 CHEMICAL ENGINEERING 801 S. W. Mudd, MC 4721 212-854-2965 cheme.columbia.edu

CHAIR Jingguang G. Chen, V. Faye McNeill ASSOCIATE PROFESSOR EMERITUS FACULTY Jingguang Chen Thayer Lindsley Ben O’Shaughnessy Daniel Esposito Edward F. Leonard Professor of Chemical Ah-Hyung (Alissa) Park VICE CHAIR Engineering Daniel Steingart ASSISTANT ADJUNCT PROFESSORS Scott A. Banta Christopher J. Durning Venkat PROFESSORS Christopher Chen Oleg Gang Venkatasubramanian, Christopher Boyce Elias Mattas DIRECTOR OF FINANCE Jingyue Ju, Samuel Ruben–Peter Lauren Marbella Kenneth Spall AND ADMINISTRATION Samuel Ruben–Peter G. Viele Professor of Allie Obermeyer Kathy Marte-Garcia G. Viele Professor of Engineering Mijo Simunovic ADJUNCT ASSOCIATE Engineering Alan C. West, Samuel Alexander Urban PROFESSORS PROFESSORS Sanat K. Kumar, Ruben–Peter G. Aghavni Bedrossian- Scott A. Banta Bykhovsky Professor Viele Professor of LECTURERS Omer Kyle Bishop of Chemical Electrochemistry Robert Bozic Hartoun Hartounian Engineering Aaron Moment Gregory Hounsell

hemical engineering is a unique properties. Examples include involves analytical mathematical physics, highly interdisciplinary field, environmental technologies, emerging numerical simulations, and data science. focused on the study and biotechnologies of major medical Interested students will have the Cdesign of chemical systems from the importance employing DNA- or protein- opportunity to conduct research in molecular to the process, system, based chemical sensors, controlled- these and other areas. The Department and global scales. Practicing chemical release drugs, new agricultural of Chemical Engineering at Columbia engineers are the experts in charge products, nanoparticle-based materials, is committed to a leadership role in of the development and production bio-nanoparticle conjugates, and many research and education in frontier of diverse materials and processes others. areas of research and technology in traditional chemical industries as Driven by this diversity of where progress derives from the well as many emerging new areas. applications, chemical engineering is conjunction of many different traditional Chemical engineers in industry guide perhaps the broadest of all engineering research disciplines. Increasingly, the passage of the product from the disciplines, drawing upon physics, new technologies and fundamental laboratory to the marketplace, from chemistry, biology, mathematics and research questions demand this type of ideas and prototypes to functioning data science, and design. Some of the interdisciplinary approach. articles and processes, from theory to areas under active investigation are The undergraduate program reality. Chemical engineering research protein engineering, fundamentals and provides a chemical engineering degree is broader still, applying the principles engineering of polymers, biopolymers, that is a passport to many careers in of chemical engineering to the study and other soft materials, colloidal directly related industries as diverse as and design of systems in biochemistry machines, atmospheric chemistry and air biochemical engineering, environmental or environmental science, energy, quality, fundamentals and applications management, and pharmaceuticals. advanced materials, and more. of electrochemistry for energy storage The degree is also used by many The expertise of chemical engineers and manufacturing, multiphase students as a springboard from which is essential to production, marketing, flows, carbon capture and utilization, to launch careers in medicine, law, and application in such areas as catalysis, and electrocatalysis, solar consulting, management, finance, renewable energy, pharmaceuticals, fuels, embryogenesis, the engineering and so on. For those interested in the high-performance materials in the and biochemistry of sequencing the fundamentals, a career of research and aerospace and automotive industries, human genome, emergent phenomena teaching is a natural continuation of biotechnologies, semiconductors in in complex and dynamical systems, their undergraduate studies. Whichever the electronics industry, paints and the biophysics of cellular processes path the student may choose after plastics, synthetic fibers, artificial organs, in living organisms, and DNA-guided graduation, the program offers a deep biocompatible implants and prosthetics assembly of inorganic and biological understanding of the physical and and numerous others. Increasingly, nanoscale objects. Diverse experimental chemical nature of things and provides chemical engineers are involved in new approaches are employed, from NMR, an insight into an exploding variety technologies employing highly novel to urban field measurements using of new technologies that are rapidly materials, whose unusual response at sensor networks, to synchrotron reshaping the society in which we live. the molecular level endows them with techniques, and the theoretical work

ENGINEERING 2021–2022 Facilities for Teaching and Research and service within their chosen in term III, taught by the Chemical 79 The Department of Chemical profession. Engineering Department. This course Engineering provides access to state- is a requirement for the chemical of-the-art research instrumentation Upon graduation, we expect our engineering major. It can also possibly and computational facilities for its students to have: serve as a technical elective for other undergraduate and graduate students, engineering majors. Those wishing to postdoctoral associates, and faculty. 1. an ability to identify, formulate, and major in chemical engineering should The recently renovated chemical solve complex engineering problems also take ENGI E1006 Introduction engineering undergraduate laboratory by applying principles of engineering, to computing for engineering and features equipment including a science, and mathematics applied scientists in term II. Chemical Waters HPLC system, a SpectraMax 2. an ability to apply engineering design engineering majors receive additional spectrophotometer, a rotating disk to produce solutions that meet instruction in their junior year on the electrode and potentiostat, a fixed specified needs with consideration use of computational methods to solve bed adsorption unit, a solar cell/ of public health, safety, and welfare, chemical engineering problems. electrolyzer/fuel cell apparatus, flow as well as global, cultural, social, In the junior-senior sequence one and temperature control equipment, environmental, and economic factors specializes in the chemical engineering an IR camera, two PhyMetrix Bench- 3. an ability to communicate effectively major. The table on page 80 spells top Moisture Analyzer units, and 15 with a range of audiences out the core course requirements, computer work stations. 4. an ability to recognize ethical and which are split between courses State-of-the-art specialized research professional responsibilities in emphasizing engineering science and equipment are housed within individual engineering situations and make those emphasizing practical and/or faculty laboratories. Shared research informed judgments, which must professional aspects of the discipline. laboratory facilities exist in the Columbia consider the impact of engineering Throughout, skills required of practicing Electrochemical Energy Center, the Soft solutions in global, economic, engineers are developed (e.g., writing Materials laboratory, and the Columbia environmental, and societal contexts and presentation skills, competency Genome Center. 5. an ability to function effectively on with computers). Chemical engineering students, teams whose members together The table also shows that a faculty, and research staff also provide leadership, create a significant fraction of the junior-senior have access to shared NMR, MRI, collaborative and inclusive program is reserved for electives, photochemical, spectroscopic, and mass environment, establish goals, plan both technical and nontechnical. spectrometry facilities in the Department tasks, and meet objectives Nontechnical electives are courses of Chemistry. 6. an ability to develop and conduct that are not quantitative, such as appropriate experimentation, those taught in the humanities and UNDERGRADUATE PROGRAM analyze and interpret data, and social sciences. These provide an use engineering judgment to draw opportunity to pursue interests in areas conclusions other than engineering. A crucial part Chemical Engineering 7. an ability to acquire and apply of the junior-senior program is the Graduates of the Chemical Engineering new knowledge as needed, using 21-point (7 courses) technical elective Program achieve success in one or appropriate learning strategies. requirement. Technical electives are more of the following within a few years science and/or technology based and of graduation: Columbia’s program in chemical feature quantitative analysis. Generally, 1. Careers in industries that require engineering leading to the B.S. degree technical electives must be 3000 level technical expertise in chemical is accredited by the Engineering or above but there are a few exceptions engineering. Accreditation Commission of ABET, including: PHYS UN1403, PHYS UN2601, 2. Leadership positions in industries http://www.abet.org. BIOL UN2005, BIOL UN2006, BIOL that require technical expertise in The first and sophomore years of UN2501, and CHEM UN2444. The chemical engineering. study introduce general principles technical electives are subject to the 3. Graduate-level studies in chemical of science and engineering and following constraints: engineering and related technical include a broad range of subjects in • Of the seven elective courses, at least or scientific fields (e.g. biomedical or the humanities and social sciences. five must be within SEAS. Among environmental engineering, materials Although the program for all those courses, at least four must have science). engineering students in these first two significant engineering content (i.e. 4. Careers outside of engineering that years is to some extent similar, there are not mathematical or computational take advantage of an engineering are a few important differences for in nature). At least two must be within education, such as business, chemical engineering majors. Those chemical engineering (e.g., with the management, finance, law, medicine, wishing to learn about, or major in, designator BMCH, CHEN, CHEE, or education. chemical engineering should take the CHAP, or MECH). At least one must be 5. A commitment to life-long learning professional elective CHEN E2100 Introduction to chemical engineering outside chemical engineering.

ENGINEERING 2021–2022 80 CHEMICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

APMA E2000 (4) and E2001 (0) either semester

MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) MATH UN2030 (3) ODE MATH elective (3)4 or APMA E2101 (3)

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

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

UNIVERSITY CC1010 (3) either semester WRITING

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

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

COMPUTER SCIENCE ENGI E1006 (3)

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

TOTAL POINTS3 17 18 16.5 18

1 Four core humanities electives should be taken as follows: In Semester III, HUMA CC1001or COCI CC1101 (4) or any initial course in one of the Global Core 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 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 Should be taken in Semester III, but may be moved upon adviser’s approval to Semester V if CHEM UN2543: Organic chemistry lab is taken in Semester III. This course fulfills the SEAS professional engineering elective requirement. 3 Taking the first track in each row and E1102 in Semester II. 4 Elective options include APMA E3101, MATH UN2010, APMA E3102, APMA E4150, APMA E4300, STAT GU4001, or another course approved by the major adviser.

• The remaining technical elective new, interesting areas beyond the core toward the technical elective courses must contain "advanced requirements of the degree. Often, content. (Note that if more than 3 science" coursework, which includes students satisfy the technical electives points of research are pursued, an the natural sciences and certain by taking courses from another SEAS undergraduate thesis is required.) engineering coursework. At least one department in order to obtain a minor The program details discussed of these courses must be taken outside from that department. Alternately, you above apply to undergraduates who of SEAS (e.g., in a science department may wish to take courses in several are enrolled at Columbia as first-years at Columbia). Qualifying engineering new areas, or perhaps to explore and declare the chemical engineering courses are determined by Chemical familiar subjects in greater depth, or major in the sophomore year. Engineering department advisers. you may wish to gain experience in However, the chemical engineering actual laboratory research. Up to 6 program is designed to be readily The junior-senior technical electives points of CHEN E3900: Undergraduate accessible to participants in any of provide the opportunity to explore research project may be counted Columbia’s Combined Plans and to

ENGINEERING 2021–2022 81 CHEMICAL ENGINEERING: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

CHEN E3110 (3) CHEN E3120 (3) Transp. phenomena, I Transp. phenomena, II CHEN E4500 (4) Process and product CHEE E3010 (3) CHEN E3210 (3) design, I REQUIRED Principles of chem. Chem. eng. COURSES eng. thermodynamics thermodynamics CHEE E4140 (3) Eng. separations CHEN E3020 (3) CHEN E3230 (3) processes Analysis of Reaction kinetics and chem. eng. problems, I reactor design

CHEM UN2495 (1.5)1 CHEM UN2496 (1.5)1 CHEN E4300 (3) CHEN E3810 (3) REQUIRED LABS Org. chem. lab I Org. chem. lab II Chem. eng. control Chem. eng. lab and CHEM UN2493 (0) and CHEM UN2494 (0)

NONTECH 3 points 3 points 3 points

TECH2 3 points 3 points 3 points 12 points REQUIRED ELECTIVES

TOTAL POINTS (normal track) 16.5 16.5 16 15

1 May be taken in Semester III and IV with adviser’s permission. Additional option is that Intensive organic chemistry lab course UN2545 (3) can count in place of UN2495 and UN2496. 2 The total of 21 points (7 courses) of required technical electives must include five engineering courses, two of which must be in chemical engineering and one must be outside chemical engineering, and 6 points (2 courses) of "advanced science" (i.e., courses in chemistry, physics, biology, and certain engineering courses, one of which must be outside engineering). transfer students. In such cases, the the professional development and fields may enroll in the scientist-to- guidance of one of the departmental leadership course, ENGI E4000, as engineer (S2E) program that leads advisers in planning your program is a graduation requirement. Doctoral to the master’s degree in chemical required (contact information for the students will be enrolled in ENGI E6001– engineering. This program requires departmental UG advisers is listed 6004 and should consult their program an extra 6 credits associated with two on the department’s website: for specific PDL requirements. mandatory Essentials classes (CHEN cheme.columbia.edu). E4001 and E4002) that are used to ease M.S. Degree the transition into chemical engineering. Requirements for a Minor in The requirements are (1) the core Chemical Engineering courses: (i) math core: Mathematical Doctoral Degrees See page 205. methods in chemical engineering The Ph.D. and D.E.S. degrees have (CHEN E4010), (ii) transport core: essentially the same requirements. All Transport phenomena, III (CHEN E4110) students in a doctoral program must GRADUATE PROGRAMS or Transport in fluid mixtures (CHEN (1) earn satisfactory grades in the four The graduate program in chemical E4112), (iii) kinetics core: Advanced core courses (CHEN E4010, E4110, engineering, with its large proportion chemical kinetics (CHEN E4130) or E4330, E4130/CHAP E4120); (2) pass a of elective courses and independent Surface reactions and kinetics (CHEN qualifying exam; (3) defend a proposal research, offers experience in any E4235), and (iv) thermo core: Advanced of research within 12 months of of the fields of departmental activity chemical engineering thermodynamics passing the qualifying exam; (4) defend mentioned in previous sections. For (CHEN E4130) or Statistical mechanics their thesis; and (5) satisfy course both chemical engineers and those (CHAP E4120); and (2) 18 points requirements beyond the four core with undergraduate educations in other of 4000-level or higher courses, courses. For detailed requirements, related fields such as physics, chemistry, approved by the graduate coordinator please consult the departmental office and biochemistry, the Ph.D. program or research adviser, of which up to or graduate coordinator. Students provides the opportunity to become 6 may be Master’s research (CHEN with degrees in related fields such as expert in research fields central to 9400). Students with undergraduate physics, chemistry, biochemistry, and modern technology and science. preparation in physics, chemistry, others are encouraged to apply to this M.S. students must complete biochemistry, pharmacy, and related highly interdisciplinary program.

ENGINEERING 2021–2022 Reynolds stress, the Reynolds analogy, continuum investigation of some problem in chemical engi- 82 COURSES IN CHEMICAL ENGINEERING modeling of turbulent flows and heat transfer neering or applied chemistry or carry out a special processes, friction factor, and Nusselt number project under the supervision of the staff. Credit Note: Check the department website correlations for turbulent conditions. Then, mac- for the course is contingent upon the submission for the most current course offerings roscopic (system-level) mass, momentum, and of an acceptable thesis or final report. No more and descriptions. energy balances for one-component systems than 6 points may be counted toward the satisfac- are developed and applied to complex flows and tion of the B.S. degree requirements. CHEN E2100x Introduction to chemical heat exchange processes. The final part focuses engineering on mass transport in mixtures of simple fluids: CHEN E3999x, y, or s Undergraduate 3 pts. Lect: 3. Professor Banta. Molecular-level origins of diffusion phenomena, fieldwork Prerequisite(s): First-year chemistry and phys- Fick’s law and its multicomponent generalizations, 1–2 pts. Members of the faculty. ics, or equivalent. Serves as an introduction to continuum-level framework for mixtures and its Prerequisite(s): Obtained internship and approval the chemical engineering profession. Students application to diffusion dominated processes, from adviser. Restricted to CHEN undergraduate are exposed to concepts used in the analysis of diffusion with chemical reaction, and forced/free students. Provides work experience on chemi- chemical engineering problems. Rigorous analysis convection mass transport. cal engineering in relevant intern or fieldwork of material and energy balances on open and experience as part of their program of study as closed systems is emphasized. An introduction CHEN E3210y Chemical engineering determined by the instructor. Written application to important processes in the chemical and bio- thermodynamics must be made prior to registration outlining pro- chemical industries is provided. 3 pts. Lect: 3. Professor Obermeyer. posed internship/study program. A written report Prerequisite(s): CHEE E3010 and CHEN E2100. describing the experience and how it relates CHEE E3010x Principles of chemical Corequisite: CHEN E3220. Deals with fundamental to the chemical engineering core curriculum is engineering thermodynamics and applied thermodynamic principles that form required. Employer feedback on student perfor- 3 pts. Lect: 3. Professor Kumar. the basis of chemical engineering practice. Topics mance and the quality of the report are the basis Prerequisite(s): CHEM UN1403. Corequisite: include phase equilibria, methods to treat ideal of the grade. May not be taken for pass/fail or CHEN E3020. Introduction to thermodynam- and nonideal mixtures, and estimation of proper- audited. May not be used as a technical or non- ics. Fundamentals are emphasized: the laws of ties using computer-based methods. technical elective. May be repeated for credit, but thermodynamics are derived and their meaning no more than 3 points total of CHEN E3999 may explained and elucidated by applications to BMCH E3500y Transport in biological systems be used for degree credit. engineering problems. Pure systems are treated, 3 pts. Lect: 3. Not offered in 2021–2022. followed by an introduction to mixtures and phase Prerequisite(s): CHEM UN2443 and MATH CHEN E4001x Essentials of chemical equilibrium. UN2030. Corequisite: BIOL UN2005. Convective engineering—A and diffusive movement and reaction of mol- 3 pts. Lect: 3. Professor Banta. CHEN E3020x Analysis of chemical ecules in biological systems. Kinetics of homoge- Prerequisite(s): First-year chemistry and physics, engineering problems neous and heterogeneous reactions in biological vector calculus, ordinary differential equations, 3 pts. Lect: 1.5. Lab: 1.5. Professor West. environments. Mechanisms arid models of and the instructor’s permission. Part of an accel- Prerequisite(s): Vector calculus, ordinary differen- transport across membranes. Convective diffusion erated consideration of the essential chemical tial equations. Corequisites: CHEE E3010, CHEN with and without chemical reaction. Diffusion in engineering principles from the undergraduate E3110. Computational solutions of chemical engi- restricted spaces. Irreversible thermodynamic program, including topics from Mass and Energy neering problems in thermodynamics, transport approaches to transport and reaction in biological balances, Process Control, and Transport I and II. phenomena, and reaction design. systems. While required for all M.S. students with Scientist to Engineer status, the credits from this course CHEN E3110x Transport phenomena, I CHEN E3810y Chemical engineering 3 pts. Lect: 3. Professor McNeill. may not be applied toward any chemical engi- laboratory neering degree. Prerequisite(s): mechanics, vector calculus, ordi- 3 pts. Lab: 3. Professors Ju and Bedrossian. nary differential equations. Corequisite: CHEN Prerequisite(s): Completion of core chemical CHEN E4002x Essentials of chemical E3020. Analysis of momentum and energy trans- engineering curricula through the fall semester of engineering—B port processes at molecular, continuum, and sys- senior year (includes: CHEN E3110, E3120, E4230, 3 pts. Lect: 3. Professor Banta. tem scales for systems of simple fluids (gases and E2100, E3210, E4140, E4500, CHEE E3010), Prerequisite(s): First-year chemistry and physics, low-molecular-weight liquids). Molecular-level ori- or instructor’s permission. Emphasizes active, vector calculus, ordinary differential equations, gins of fluid viscosity, continuum fluid mechanics experiment-based resolution of open-ended and the instructor’s permission. Part of an accel- analysis of laminar flows, and the resulting dimen- problems involving use, design, and optimiza- erated consideration of the essential chemical sionless correlations of kinematic and mechanical tion of equipment, products, or materials. Under engineering principles from the undergradu- characteristics of a system needed for engineer- faculty guidance students formulate, carry out, ate program, including topics from Chemical ing design (e.g., friction factor vs. Reynolds validate, and refine experimental procedures, and Engineering Thermodynamics, I and II, Chemical number correlations). Molecular origins of fluid present results in oral and written form. Develops and Biochemical Separations. Reaction Kinetics conductivity, continuum heat transfer analysis, analytical, communications, and cooperative and Reactor Design. While required for all M.S. and the resulting correlations of a system’s ther- problem-solving skills in the context of problems students with Scientist to Engineer status, the mal characteristics useful in engineering design that span from traditional, large scale separations credits from this course may not be applied (e.g., Nusselt number correlations). Examples are and processing operations to molecular level toward any chemical engineering degree. reviewed of analyses typical in chemical engineer- design of materials or products. Sample projects ing technologies. Essential mathematical methods include scale up of apparatus, process control, CHEN E4010x Mathematical methods are reviewed or introduced in context. chemical separations, microfluidics, surface in chemical engineering engineering, molecular sensing, and alternative 3 pts. Lect: 3. Professor Bozic. CHEN E3120y Transport phenomena, II Prerequisite(s): CHEN E3120 and E4230, or equiv- 3 pts. Lect: 3. Professor Durning. energy sources. Safety awareness is integrated throughout the course. alent, or instructor’s permission. Mathematical Prerequisite(s): CHEN E3110. Corequisite: CHEN description of chemical engineering problems E3220. Developments in Transport I are extended CHEN E3900x and y Undergraduate research and the application of selected methods for their to handle turbulence. Topics include turbulent project solution. General modeling principles, including energy cascade, wall-bounded turbulent shear 1–6 pts. Members of the faculty. model hierarchies. Linear and nonlinear ordinary flow, time-averaging of the equations of change, Candidates for the B.S. degree may conduct an differential equations and their systems, including Prandtl’s mixing length hypothesis for the

ENGINEERING 2021–2022 those with variable coefficients. Partial differential CHEN E4112y Transport phenomena in fluids unit operations employed in chemical engineering 83 equations in Cartesian and curvilinear coordinates and mixtures separations. Fundamental aspects of single and for the solution of chemical engineering problems. 3 pts. Lect: 3. Professor Durning. multistaged operations using both equilibrium and Prerequisite(s): CHEN E3110 and E3120 or rate-based methods. Examples include distillation, CHEN E4020y Protection of industrial and equivalent. Develops and applies nonequilib- absorption and stripping, extraction, membranes, intellectual property rium thermodynamics for modeling of trans- crystallization, bioseparations, and environmental 3 pts. Lect: 3. Professor Spall. port phenomena in fluids and their mixtures. applications. To expose engineers, scientists and technology Continuum balances of mass, energy, and CHEN E4150y Computational fluid dynamics managers to areas of the law they are most likely momentum for pure fluids; nonequilibrium to be in contact with during their career. Principles thermodynamic development of Newton's law in chemical engineering are illustrated with various case studies together of viscosity and Fourier's law; applications 3 pts. Lect: 3. Professor Boyce. with active student participation. (conduction dominated energy transport, Fundamentals of numerical algorithms for forced and free convection energy transport modeling dynamics of fluid flow computation- CHEE E4050y Principles of industrial ally. Includes various approaches to discretize electrochemistry in fluids); balance laws for fluid mixtures; nonequilibrium thermodynamic development time and space on structured and unstructured 3 pts. Lect: 3. Not offered in 2021–2022. grids with a variety of boundary conditions. Prerequisite(s): CHEE E3010 or equivalent. A pre- of Fick's law; applications (diffusion-reaction problems, analogy between energy and mass Involves programming of basic CFD codes in sentation of the basic principle underlying electro- MATLAB or Python to test example problems chemical processes. Thermodynamics, electrode transport process, transport in electrolyte solutions, sedimentation). in fluid mechanics with different discretization kinetics, and ionic mass transport. Examples of schemes. Uses open-source software OpenFOAM industrial and environmental applications illus- CHEN E4115y Topics in transport phenomena to investigate more complex geometries and trated by means of laboratory experiments: elec- 3 pts. Instructor to be announced. numerical approaches. Introduction to simula- troplating, refining, and winning in aqueous solu- Prerequisite(s): Undergraduate fluid mechanics, or tion of multiphase flow. Course grade based on tions and in molten salts; electrolytic treatment of transport phenomena, or instructor’s permission. homework assignments and final project report wastes; primary, secondary, and fuel cells. Self-contained treatments of selected topics in and presentation. APCH E4080x Soft condensed matter transport phenomena (e.g., rheology, nonequi- librium thermodynamics, molecular-level aspects CHEN E4201x Engineering applications of 3 pts. Lect: 3. Professor Gang. electrochemistry Prerequisite(s): MSAE E3111, CHEE E3010, or CHEN of transport turbulence). Topics and instructor may change from year to year. Intended for junior/ 3 pts. Lect: 3. Professor West. E3120 or equivalent. Course is aimed at senior Prerequisite(s): Physical chemistry and a course undergraduate and graduate students. Introduces senior level undergraduates and graduate stu- dents in engineering and the physical sciences. in transport phenomena. Engineering analysis fundamental ideas, concepts, and approaches of electrochemical systems, including electrode in soft condensed matter with emphasis on bio- CHAP E4120y Statistical mechanics kinetics, transport phenomena, mathematical molecular systems. Covers the broad range of 3 pts. Lect: 3. Professor O’Shaughnessy. modeling, and thermodynamics. Common experi- molecular, nanoscale, and colloidal phenomena Prerequisite(s): CHEE E3010 or equivalent mental methods are discussed. Examples from with revealing their mechanisms and physical thermodynamics course, or instructor’s permis- common applications in energy conversion and foundations. The relationship between molecular sion. Fundamental principles and underlying metallization are presented. architecture and interactions and macroscopic assumptions of statistical mechanics. Boltzmann’s behavior are discussed for the broad range of soft entropy hypothesis and its restatement in terms CHEN E4231x Solar fuels and biological matter systems, from surfactants of Helmholtz and Gibbs free energies and for 3 pts. Lect: 3. Professors Esposito and West. and liquid crystals to polymers, nanoparticles, and open systems. Correlation times and lengths. Prerequisite(s): Graduate standing or CHEN biomolecules. Modern characterization methods Exploration of phase space and observation E4230. Fundamentals and applications of solar for soft materials, including X-ray scattering, timescale. Correlation functions. Fermi-Dirac and energy conversion, especially technologies for molecular force probing, and electron microcopy Bose-Einstein statistics. Fluctuation-response the- conversion of sunlight into storable chemical are reviewed. Example problems, drawn from ory. Applications to ideal gases, interfaces, liquid energy or solar fuels. Topics include fundamentals the recent scientific literature, link the studied crystals, microemulsions and other complex fluids, of photoelectrochemistry, kinetics of solar fuels materials to the actively developed research polymers, Coulomb gas, interactions between production, solar harvesting technologies, solar areas. Course grade based on midterm and final charged polymers and charged interfaces, order- reactors, and solar thermal production of solar exams, weekly homework assignments, and final ing transitions. fuels. Applications include solar fuels technology individual/team project. for grid-scale energy storage, chemical industry, CHEN E4130x Advanced chemical engineering manufacturing, environmental remediation. CHEN E4110y Mechanisms of transport thermodynamics phenomena in fluids 3 pts. Lect: 3. Professor O'Shaughnessy. CHEN E4235x Surface reactions and kinetics 3 pts. Lect: 3. Professor Durning. Prerequisite(s): Successful completion of an 3 pts. Lect: 3. Professor Chen. Prerequisite(s): CHEN E3110 and E3120 or undergraduate thermodynamics course. The Fundamental concepts and techniques to equivalent. Continuum framework for modeling course provides a rigorous and advanced founda- describe electronic, structural, chemical, non-equilibrium phenomena in fluids with clear tion in chemical engineering thermodynamics and catalytic properties of surfaces. Kinetics connections to molecular/microscopic mecha- suitable for chemical engineering Ph.D. students and thermodynamics in adsorption, reaction, nisms for "conductive" transport. Continuum expected to undertake diverse research projects. desorption, and diffusion processes on surfaces. balances of mass and momentum; continuum- Topics include intermolecular interactions, nonide- Effects of transport in modifying surface level development of conductive momentum flux al systems, mixtures, phase equilibria and phase reaction kinetics. Applies basic concepts in the (stress tensor) for simple fluids; applications of transitions and interfacial thermodynamics. chemical engineering curriculum (mathematical continuum framework for simple fluids (lubrication modeling, reaction kinetics, thermodynamics, flows, creeping flows). Microscopic developments CHEN E4140x Engineering separations transport) to surface reactions. of stress for simple and/or complex fluids; kinetic processes theory and/or liquid state models for transport 3 pts. Lect: 3. Professor Durning. CHEE E4252x Introduction to surface and coefficients in simple fluids; Langevin/Fokker- Prerequisite(s): CHEN E2100, E3120, and E3210 or colloid chemistry Plank/Smoluchowski framework for stress in com- permission of instructor. Design and analysis of 3 pts. Lect: 3. Professors Farinato and plex fluids; stress in active matter; applications for Somasundaran. complex fluids. Prerequisite(s): Elemental physical chemistry. The

ENGINEERING 2021–2022 84 principles of surfaces and colloid chemistry critical molecules relevant in biotechnology. The unit classroom experience on chemical engineering to range of technologies indispensable to modern operations used in recovery and purification of process safety as well as Safety in Chemical life. Surface and colloid chemistry has significance biological molecules. Theory and design of filtra- Engineering certification. Process safety and to life sciences, pharmaceuticals, agriculture, tion, microfiltration, centrifugation, cell disruption, process control emphasized. Application of basic environmental remediation and waste manage- extraction, adsorption, chromatography, precipita- chemical engineering concepts to chemical ment, earth resources recovery, electronics, tions, ultrafiltration, crystallization, and drying. reactivity hazards, industrial hygiene, risk assess- advanced materials, enhanced oil recovery, and Students will have an understanding of basic ment, inherently safer design, hazard operability emerging extraterrestrial mining. Topics include: principles of downstream processing, design analysis, and engineering ethics. Application of thermodynamics of surfaces, properties of sur- and operations of various unit operations used in safety to full spectrum of chemical engineering factant solutions and surface films, electrokinetic recovery of biological products, examining tradi- operations. phenomena at interfaces, principles of adsorption tional unit operations, as well as new concepts and mass transfer and modern experimental and emerging technologies that are likely to ben- CHEN E4510y Process and product design, II techniques. Leads to deeper understanding of efit biochemical product recovery in the future. 4 pts. Lect: 4. Professor Venkatasubramanian. interfacial engineering, particulate dispersions, Prerequisite(s): CHEN E4500. Students carry out a emulsions, foams, aerosols, polymers in solution, CHEN E4330y Advanced chemical kinetics semester long process or product design course and soft matter topics. 3 pts. Lect: 3. Professor Esposito. with significant industrial involvement. The project Prerequisite(s): CHEN E4230 or instructor’s per- culminates with a formal written design report CHEN E4300x Chemical process control and mission. Complex reactive systems, molecular and a public presentation. Recitation section process safety view of reaction kinetics, reactions in liquid, required. 3 pts. Lect: 1. Lab: 2. Professor McNeill. reactions at surfaces, diffusion-reaction systems. Prerequisite(s): Material and energy balances. Applications to the design of batch and continu- CHEE E4530y Corrosion of metals Ordinary differential equations including Laplace ous reactors. 3 pts. Lect: 3. transforms. Reactor Design. An introduction to Prerequisite(s): CHEE E3010 or equivalent. The process control applied to chemical engineering CHEN E4400x Chemical process development theory of electrochemical corrosion, corrosion through lecture and laboratory. Concepts include 3 pts. Lect: 3. Professor Mattas. tendency, rates, and passivity. Application to vari- the dynamic behavior of chemical engineering Prerequisite(s): CHEM UN2443 or equivalent or ous environments. Cathodic protection and coat- systems, feedback control, controller tuning, and instructor’s permission. Process development ings. Corrosion testing. for new compounds, including fine and specialty process stability. Introduction to the fundamentals CHEN E4580x Artificial intelligence in of process safety and hazard analysis. chemicals, pharmaceuticals, biologicals, and agro- chemicals. Experimental strategy and methods Chemical Engineering CHEN E4320y Molecular phenomena in for process scale-up from bench to pilot plant. 3 pts. Lect: 3. Professor Venkatasubramanian. chemical engineering Evaluation of process economics. Hazard and Prerequisite(s): Background in chemical engi- 3 pts. Lect: 3. Not offered in 2021–2022. risk evaluation for environmental and industrial neering and Python/MATLAB. Introduction to AI Prerequisite(s): CHEN E3120 or instructor’s per- hygiene safety. Capture and use of process methods including knowledge-based systems mission. Introduces a molecular-level understand- know-how for process and plant design, regula- and deep learning in the context of chemical ing of topics in modern chemical engineering. It tory approvals, and technology transfer to first engineering applications. Topics include chemical builds upon and validates the concepts presented manufacture. engineering modeling approaches, knowledge in the rest of the chemical engineering curriculum representation, symbolic reasoning and inference, CHEN E4410x Environmental control via a molecular perspective. knowledge-based systems, statistical data analy- technology sis, and machine learning methods such as clus- CHBM E4321x The genome and the cell 3 pts. Lect: 3. Not offered in 2021–2022. tering, neural networks, random forests, Bayesian 3 pts. Lect: 3. Not offered in 2021–2022. Prerequisite(s): CHEN E3010 or the equivalent. networks, and directed evolution. Chemical engi- Prerequisite(s): BIOL UN2005, MATH UN2030. Causes of pollution and effect on life. Legal neering case studies in process monitoring, diag- The utility of genomic information lies in its aspects, OSHA and EPA rules. Pollution at home nosis, and control, process/product design, sched- capacity to predict the behavior of living cells in and at work; radon, fumes, and dust; ventilation, uling, and process hazards analysis. Development physiological, developmental, and pathological dust collection, carbon adsorption. Fuel and acid of hybrid models that combine first-principles situations. The effect of variations in genome gases, smog and dispersion. Treatment of ground, knowledge of the underlying physics and chemis- structure between individuals within a species, saline, and wastewater. Primary and secondary try with data-driven techniques and the develop- including those deemed healthy or diseased, (biological) treatment. Tertiary water treatment ment of causal mechanism-based models. and among species, can be inferred statistically with membranes, ion exchange, carbon, and by comparisons of sequences with behaviors, sieves. Solid hazardous waste. Visit New York City CHEN E4600x Aerosols and mechanistically, by studying the action of wastewater treatment plant. 3 pts. Lect: 3. Professor McNeill. molecules whose structure is encoded within Prerequisite(s): CHEN E3120 or instructor’s permis- the genome. Examines known mechanisms that CHEN E4500x Process and product design, I sion. Aerosol impacts on indoor and outdoor air elucidate the combined effect of environmental 4 pts. Lect: 4. Professor Bozic. quality, health, and climate. Major topics include stimulation and genetic makeup on the behavior Prerequisite(s): CHEN E2100, CHEN E4140. The aerosol sources, physics, and chemistry; field and of cells in homeostasis, disease states, and during practical application of chemical engineering laboratory techniques for aerosol characteriza- development, and includes assessments of the principles for the design and economic evaluation tion; aerosol direct and indirect effects on climate; probable effect of these behaviors on the whole of chemical processes and plants. Use of ASPEN aerosols in biogeochemical cycles and climate organism. Quantitative models of gene translation Plus for complex material and energy balances of engineering; health impacts, including exposure and intracellular signal transduction will be used real processes. Students are expected to build on to ambient aerosols and transmission of respira- to illustrate switching of intracellular processes, previous coursework to identify creative solutions tory disease. to two design projects of increasing complexity. transient and permanent gene activation, and cell CHEN E4610y Chemical product design commitment, development, and death. Each design project culminates in an oral presen- tation, and in the case of the second project, a 3 pts. Lect: 3. Instructor to be announced. CHEN E4325y Bioseparations written report. Prerequisite(s): CHEN E3210 and CHEM UN2443 3 pts. Lect: 3. Professor Hartounian. or equivalent, or instructor’s permission. Prerequisite(s): CHEN E2100 or CHEN E3230, CHEN E4501y Chemical engineering process Application of chemical and engineering knowl- or equivalent. Design and analysis of the con- safety edge to the design of new chemical products. centration, recovery, and isolation of biological 3 pts. Lect.: 3. Professor Bozic. Relationships between composition and physical Aimed at seniors and graduate students. Provides properties. Strategies for achieving desired volu-

ENGINEERING 2021–2022 metric, rheological, phase equilibrium, thermal, and experimental design. Advanced topics such CHEN E4780x or y Quantitative methods in 85 and environmental behavior. Case studies, includ- as nonparametric estimation and Markov chain cell biology ing separation solvents, blood substitutes, refrig- Monte Carlo (MEME) techniques are introduced. 3 pts. Lect: 3. Professor O’Shaughnessy. erants, and aircraft deicing fluids. Example problems and case studies drawn Prerequisite(s): Elementary calculus, physics and from chemical engineering practice are used to biology, or instructor’s permission. Quantitative CHEN E4620y Introduction to polymers and highlight the practical relevance of the material. statistical analysis and mathematical model- soft materials Theory reduced to practice through programming ing in cell biology for an audience with diverse 3 pts. Lect: 3. Not offered in 2021–2022. in Mathematica. Course grade based on midterm backgrounds. The course presents quantitative Prerequisite(s): An elementary course in physical and final exams, biweekly homework assign- methods needed to analyze complex cell biologi- chemistry or thermodynamics. Organic chemistry, ments, and final team project. cal experimental data and to interpret the analysis statistics, calculus and mechanics are helpful, but in terms of the underlying cellular mechanisms. not essential. An introduction to the chemistry and CHOR E4690y Managing systemic risk in Optical and electrical experimental methods to physics of soft material systems (polymers, col- complex systems study cells and basic image analysis techniques loids, organized surfactant systems and others), 3 pts. Lect: 3. Professor Venkatasubramanian. are described. Methods of statistical analysis of emphasizing the connection between microscopic Prerequisite(s): Senior or graduate standing experimental data and techniques to test and structure and macroscopic physical properties. To in SEAS or instructor's permission. Course will compare mathematical models against measured develop an understanding of each system, illus- introduce systems engineering concepts and statistical properties will be introduced. Concepts trative experimental studies are discussed along tools such as digraphs, fault trees, probabilistic and techniques of mathematical modeling will with basic theoretical treatments. High molecular risk assessment, HAZOP, FMEA, etc., for model- be illustrated by applications to mechanosensing weight organic polymers are discussed first (basic ing enterprise-wide risk in complex systems. in cells, the mechanics of cytokinesis during cell notions, synthesis, properties of single polymer Important industrial accidents will be discussed as division and synaptic transmission in the nervous molecules, polymer solution and blend thermo- case studies. system. Image analysis, statistical analysis, and dynamics, rubber and gels). Colloidal systems are CHEN E4700x Principles of genomic model assessment will be illustrated for these treated next (dominant forces in colloidal systems, systems. flocculation, preparation and manipulation of technologies colloidal systems) followed by a discussion of 3 pts. Lect: 3. Professor Ju. CHEN E4800x Protein engineering self-organizing surfactant systems (architecture of Prerequisite(s): Undergraduate-level biology, 3 pts. Lect: 3. Professor Banta. surfactants, micelles and surfactant membranes, organic chemistry, and instructor’s permission. Prerequisite(s): CHEN E4230, may be taken phase behavior). Chemical and physical aspects of genome concurrently, or the instructor’s permission. structure and organization, genetic information Fundamental tools and techniques currently used CHEN E4630y Topics in soft materials flow from DNA to RNA to protein. Nucleic acid to engineer protein molecules. Methods used to 3 pts. Instructor to be announced. hybridization and sequence complexity of DNA analyze the impact of these alterations on differ- Prerequisite(s): Physical chemistry or instructor’s and RNA. Genome mapping and sequencing ent protein functions with specific emphasis on permission. Self-contained treatments of selected methods. The engineering of DNA polymerase for enzymatic catalysis. Case studies reinforce con- topics in soft materials (e.g., polymers, colloids, DNA sequencing and polymerase chain reaction. cepts covered, and demonstrate the wide impact amphiphiles, liquid crystals, glasses, powders). Fluorescent DNA sequencing and high-throughput of protein engineering research. Application of Topics and instructor may change from year to DNA sequencer development. Construction of basic concepts in the chemical engineering cur- year. Intended for junior/senior level undergradu- gene chip and micro array for gene expression riculum (reaction kinetics, mathematical modeling, ates and graduate students in engineering and analysis. Technology and biochemical approach thermodynamics) to specific approaches utilized the physical sciences. for functional genomics analysis. Gene discovery in protein engineering. and genetics database search method. The appli- CHEN E4650y Polymer physics cation of genetic database for new therapeutics BMCH E4810y Artificial organs 3 pts. Lect.: 3. Professor Kumar. discovery. 3 pts. Lect: 3. Professor Leonard. Prerequisite(s): CHEN E3110, CHEN E3120 and Analysis and design of replacements for the heart, E4620. Senior undergraduate/first-year graduate CHEN E4740x Biological transport and rate kidneys, and lungs. Specification and realization course on the physics of polymer systems. Topics phenomena, II of structures for artificial organ systems. include scaling behavior of chains under different 3 pts. Lect: 3. Not offered in 2021–2022. conditions, mixing thermodynamics, networks Prerequisite(s): Any two of the following: CHEN CHEN E4850x or y Contaminated site cleanup and generation, polymer dynamics, including E3110; BIOL UN2005; CHEN E3210 or BMCH 3 pts. Lect: 3. Professor Tsiamis. reptation and entanglements. Special topics: E3500. Analysis of transport and rate phenomena Aimed at senior undergraduate and graduate nanocomposites. in biological systems and in the design of biomi- students. Introduces the science fundamentals metic transport-reaction systems for technologi- and the policies and regulations that govern the CHEN E4660x Biochemical engineering cal and therapeutic applications. Modeling of cleanup of sites contaminated with hazardous 3 pts. Lect.: 3. Professor Obermeyer. homogeneous and heterogeneous biochemical materials and discusses the processes used for Prerequisite(s): CHEN E4320 or instructor’s reactions. The Bases of biological transport: roles their treatment and safe disposal. Covers the permission. Engineering of biochemical and of convection, ordinary diffusion, forced diffusion. methods used to investigate the extent of con- microbiological reaction systems. Kinetics, reactor Systems where reaction and transport interact tamination in soil, groundwater, and sediment. analysis, and design of batch and continuous fer- strongly. Applications to natural and artificial tis- Uses case studies to illustrate the application of mentation and enzyme processes. Recovery and sue beds, tumor modeling, controlled release, technologies used to address different categories separations in biochemical engineering systems. natural and artificial organ function. of contaminants (metals, volatile and semivolatile CHEN E4670x Chemical engineering data organics). Applies basic concepts in the chemical CHEN E4760y Genomics sequencing analysis engineering curriculum to specific approaches laboratory 3 pts. Lect: 3. Professor Bishop. utilized in characterizing the fate and transport of 3 pts. Lect: 1. Lab: 2. Not offered in 2021–2022. Prerequisite(s): CHEN E4230, CHEN E3120, and contaminants and for designing the engineering Prerequisite(s): Undergraduate level biology, CHEN E3210 or equivalents. Course is aimed at processes utilized for their treatment. organic chemistry, and instructor’s permis- senior undergraduate and graduate students. sion. The chemical, biological and engineering CHEN E4860x NMR for bio, soft, and energy Introduces fundamental concepts of Bayesian principles involved in the genomics sequencing materials data analysis as applied to chemical engineering process will be illustrated throughout the course 3 pts. Lect: 3. Professor Marbella. problems. Covers basic elements of probability for engineering students to develop the hands-on Prerequisite(s): PHYS UN1401, CHEE E3010, theory, parameter estimation, model selection, skills in conducting genomics research. or instructor’s permission. Note: junior/senior

ENGINEERING 2021–2022 86 undergraduates and graduate (M.S.) students CHEN E4900x or y Topics in chemical work experience as part of their program of study only. Course focuses on the fundamentals of engineering as determined by the instructor. A written report nuclear magnetic resonance (NMR) spectroscopy 3 pts. Members of the faculty. describing their experience and how it relates and imaging in fields ranging from biomedical Prerequisite(s): Instructor's permission. Additional to the chemical engineering core curriculum is engineering to electrochemical energy storage. current topics in chemical engineering taught by required. Employer feedback on student perfor- Covers basic NMR theory, instrumentation (includ- regular or visiting faculty. Special topics arranged mance and the quality of the report are the basis ing in situ/operando setup), data interpretation, as the need and availability arise. Topics usually of the grade. May not be taken for pass/fail credit and experimental design to couple with other offered on a one-time basis. Since the content of or audited. Only 3 points of CHEN E4999 can be materials characterization strategies. Course this course changes each time it is offered, it may credited toward the M.S. degree. Furthermore, grade based on problem sets, quizzes, and final be repeated for credit. students who take CHEN E4999 can use only a project presentation. maximum of 3 points of CHEN E 9400 in fulfill- CHEN E4910x and y Solid state chemistry in ment of the M.S. degree. CHEN E4870y Synthetic organogenesis pharmaceutical development 3 pts. Lect: 3. Professor Simunovic. 3 pts. Lect: 3. Not offered in 2021–2022. CHEN E6050x Advanced electrochemistry Prerequisite(s): Any quantitative undergradu- Prerequisite(s): Thermodynamics (any) or General 3 pts. Lect: 3. Not offered in 2021–2022. ate course with elements of biology, such as Chemistry. Fundamentals of solid state as related Prerequisite(s): Instructor’s permission. An Chemistry, Biochemical Engineering/Biochemistry, to pharmaceutical development, and is intended advanced overview of the fundamentals of elec- Biophysics, or at the instructor's permission. for junior and senior undergraduates and gradu- trochemistry, with examples taken from modern Synthetic organogenesis to use stem cells to ate students. Theoretical and practical aspects applications. An emphasis is placed on mass reconstitute aspects of embryo development and are covered, including segments on thermal and transfer and scaling phenomena. Principles are organ formation in vitro. Examines the molecular spectroscopic analytical instrumentation. Topics reinforced through the development of math- basis of human embryogenesis. Introduces syn- include crystal structure, polymorphism, crystal- ematical models of electrochemical systems. thetic organogenesis as an interdisciplinary field. lization processes, pharmaceutical properties, Course projects will require computer simulations. Students learn to recognize generic molecular amorphous solids, solid state reactions, stability The course is intended for advanced graduate mechanisms behind signaling and cell lineage testing, solid oral formulation, particle size con- students, conducting research involving electro- specification. Covers recent advances in applying trol, and dissolution testing. Connections between chemical technologies. engineering and contemporary biology to creat- molecular structure, physical structure (e.g., par- EACH E6181x Advanced electrochemical ing organoids and organs on chips using human ticle size distribution), and product performance energy storage stem cells. will be focus of class. 3 pts. Lect: 3. Professor Steingart. CHEN E4880x or y Atomistic simulations for CHEN E4920x and y Pharmaceutical industry Prerequisite(s): EAEE E4180, EAEE E4002. Most science and engineering for engineers modern commercial implementations of elec- 3 pts. Lect: 3. Not offered in 2021–2022. 3 pts. Lect: 3. Not offered in 2021–2022. trochemical energy storage are not fully deter- Prerequisite(s): statistical mechanics or thermody- Prerequisite(s): General Chemistry and Organic ministic: provides context and best-hypotheses namics or instructor's permission. Aimed at senior Chemistry. Overview of biopharmaceutical design, for modern challenges. Topics include current undergraduates and graduate students. Covers development, manufacturing, and regulatory understanding of Lithium/Lithium Anode Solid- atomistic simulation techniques for applications requirements from an engineering perspective. Electrolyte-Interphase, Reversible and Irreversible at interface of chemical engineering and materi- Unit operations, equipment selection, and process Side Reactions in Redox flow systems, electro- als science. Theoretical background of various development associated with small molecule, chemically correlated mechanical fracture at simulation techniques ranging from empirical to biologics, and vaccine manufacturing illustrated multiple scales, relationships between electrolyte first-principles approaches and hands-on experi- through examples, and quantitative engineering solvation and electrode insertion, roughening, ence in using state-of-the-art (free and open approaches applied as appropriate. Small mole- smoothing, and detachment behavior of metal source) simulation software. Practical examples cules, biologics, vaccines, solid oral formulations, anodes, best practices in structural, chemical, and focus on inorganic materials mostly in crystalline sterile processing, and design of experiments microscopic characterization, morphological vs. solids, though methods taught are transferable to (DoE) treated along with a module on regulatory macro-homogenous transport models, particle to other materials classes. Course grades based on requirements. electrode to cell nonlinearity. reports for practical assignments. CHEN E4930y Biopharmaceutical process CHEE E6201x or y Topics in electrochemical CHEN E4890x or y Biopharmaceuticals, laboratory energy storage and conversion entrepreneurship, and chemical engineering 3 pts. Lect: 3. Professor Moment. 3 pts. Lect: 3. Professor West. 3 pts. Lect: 3. Professor Hartounian. Prerequisite(s): Organic Chemistry Lab I, Prerequisite(s): CHEN E4201 or instructor’s permis- Aimed at graduate students of Chemical Undergraduate organic Chemistry. Laboratory- sion. Selected topics in electrochemical energy Engineering. Examines the application of based course intended for junior and senior storage and/or conversion. Experimental, theoreti- Chemical Engineering fundamentals and entrepre- undergraduate and graduate students interested cal, technological topics vary. Critical analysis neurship in starting up a biopharmaceutical com- in gaining hands-on experience in biopharma- of scientific and engineering literature. Team pany and in developing a biopharmaceutical prod- ceutical industry, including tableting, dissolution, projects and student-led discussions. Topics and uct. Serves as a description of the major stages of disintegration, fermentation, chromatography, tan- instructor may change from year to year. Note: developing a biopharmaceutical product. Topics gential flow filtration, mixing, and crystallization. recommended for Ph.D. students. presented will include drug discovery, preclinical Connections between process parameters, chemi- CHEE E6220y Equilibria and kinetics in and clinical development, IP, manufacturing, and cal and molecular properties, process parameters, hydrometallurgical systems regulatory process. In addition, implementation of chemical and molecular properties, process 3 pts. Lect: 3. Not offered in 2021–2022. the lean startup methodology, business valuation, performance, and product attributes illustrated Prerequisite(s): Instructor’s permission. An and financial considerations for a biopharma- through combination of lectures (given during lab advanced overview of the fundamentals of elec- ceutical startup will be offered. Basic topics in time) experiments, and report writing. the chemical engineering curriculum (reaction trochemistry, with examples taken from modern kinetics, mathematical modeling, unit operations, CHEN E4999x and y Fieldwork applications. An emphasis is placed on mass thermodynamics), as well as specific topics in 1.5–3 pts. Lect: 3. Members of the faculty. transfer and scaling phenomena. Principles are developing biopharmaceuticals will be discussed Prerequisite(s): M.S. student. Intended only for reinforced through the development of math- in this course. M.S. students. Provides work experience on ematical models of electrochemical systems. chemical engineering in relevant intern or field- Course projects will require computer simulations.

ENGINEERING 2021–2022 The course is intended for advanced graduate and textbook materials providing overviews to CHEN E9600x and y Advanced research 87 students, conducting research involving electro- various biological areas including: evolution, problems chemical technologies. immune system, development and cell special- 2–10 pts. Members of the faculty. ization, the cytoskeleton and cell motility, DNA Prerequisite(s): Recommendation of the professor CHEE E6252y Applied surface and colloid transcription in gene circuits, protein networks, concerned and approval of the master’s research chemistry recombinant DNA technology, aging, and gene department. For postdoctoral students and other 3 pts. Lect: 2. Lab: 3. Professors Somasundaran therapy. qualified special students who wish to pursue and Farinato. research under the guidance of members of the CHEN E9000x and y Chemical engineering Prerequisite(s): CHEE E4252. Applications of sur- department. Not open to undergraduates or to face chemistry principles to wetting, flocculation, colloquium candidates for the degrees of Ch.E., M.S., Ph.D., flotation, separation techniques, catalysis, mass 0 pts. Col: 1. Professor Esposito. or Eng.Sc.D. transfer, emulsions, foams, aerosols, membranes, Graduate students on the Ph.D. track are required biological surfactant systems, microbial surfaces, to attend the department colloquium as long as CHEN E9800x and y Doctoral research enhanced oil recovery, and pollution problems. they are in residence. No degree credit is granted. instruction Appropriate individual experiments and projects. 3, 6, 9, or 12 pts. Members of the faculty. CHEN E9001x M.S. Chemical engineering Lab required. A candidate for the Eng.Sc.D. degree in chemical colloquium engineering must register for 12 points of doctoral CHEN E6543x Chemical engineering research 0 pts. Lect.: 1. Professor Bozic. research instruction. Registration in CHEN E9800 methodology Required for all M.S. students in residence in may not be used to satisfy the minimum residence 1 pts. Professor Bishop. their first semester. Topics related to professional requirement for the degree. For first year graduate students entering the development and the practice of chemical engi- Ph.D. program. Serves as a "survival skills" course neering. No degree credits granted. Intended for CHEN E9900x and y–S9900 Doctoral to familiarize students with graduate studies, M.S. students only. dissertation research, technical writing, and professional- 0 pts. Members of the faculty. CHEN E9400x and y Master’s research ism. Covers manuscript preparation, proposal Open only to certified doctoral candidates. A 1–6 pts. Members of the faculty. preparation, protection of intellectual property, candidate for the doctorate in chemical engineer- Prescribed for M.S. and Ch.E. candidates; elective professional ethics, etc. Topics include: (1) labora- ing may be required to register for this course in for others with the approval of the Department. tory safe practices including rules administered by every term after the student’s coursework has Degree candidates are required to conduct an EHRS and preparation for obtaining the required been completed, and until the dissertation has investigation of some problem in chemical engi- NYFD Certificate of Fitness, (2) expectations and been accepted. responsibilities of teaching assistants (TAs) and neering or applied chemistry and to submit a the- (3) rules, milestones, and assessment of prog- sis describing the results of their work. No more ress within the Chemical Engineering graduate than 6 points may be counted for graduate credit, program. and this credit is contingent upon the submission of an acceptable thesis. CHEN E8100y Topics in biology 3 pts. Lect: 3. Professor O’Shaughnessy. CHEN E9500x and y–S9500 Doctoral Prerequisite(s): Instructor’s permission. This research research seminar introduces topics at the 1–15 pts. Members of the faculty. forefront of biological research in a format and Prerequisite(s): The qualifying examinations for language accessible to quantitative scientists and the doctorate. Open only to certified candidates engineers lacking biological training. Conceptual for the Ph.D. and Eng.Sc.D. degrees. Doctoral and technical frameworks from both biological candidates in chemical engineering are required and physical science disciplines are utilized. The to make an original investigation of a problem in objective is to reveal to graduate students where chemical engineering or applied chemistry, the potential lies to apply techniques from their own results of which are presented in their disserta- disciplines to address pertinent biological ques- tions. No more than 15 points of credit toward the tions in their research. Classes entail reading, degree may be granted when the dissertation is criticism and group discussion of research papers accepted by the department.

ENGINEERING 2021–2022 88 CIVIL ENGINEERING AND ENGINEERING MECHANICS 610 S. W. Mudd, MC 4709 212-854-3143 civil.columbia.edu

CHAIR PROFESSORS LECTURERS IN Daniel Peterson ASSOCIATE MANAGER, Jacob Fish Raimondo Betti DISCIPLINE Alan Poeppel CARLETON LABORATORY Gautam Dasgupta Julius Chang Kevin Riordan TBA DEPARTMENT George Deodatis Ibrahim Odeh Robert A. Rubin ADMINISTRATOR Maria Q. Feng Thomas Panayotidi Vincent Tirolo MANAGER, CENTRIFUGE Alma Levin Jacob Fish Richard L. Tomasetti LABORATORY Upmanu Lall, Earth ADJUNCT FACULTY Mario Valenti Liming Li GRADUATE ADMISSIONS and Environmental Amr Aly Christopher Vitolano AND STUDENT AFFAIRS Engineering Ali Ashrafi George Wheeler SENIOR LABORATORY OFFICER Hoe I. Ling Luciana Balsamo Bojidar Yanev TECHNICIAN Scott Kelly Richard W. Longman, Emily Belote Songtao Yang TBA Mechanical Adrian Brügger Theodore P. Zoli ASSOCIATE DIRECTOR, Engineering Richard F. Carbonaro SENIOR LABORATORY CAREER PLACEMENT Feniosky Peña-Mora Steven Charney DIRECTOR, CARLETON ENGINEER Emily-Anne McCormack Andrew Smyth Raymond Daddazio LABORATORY Freddie E. Wheeler Jonathan David Adrian Brügger FINANCIAL ANALYST ASSOCIATE PROFESSORS Rudolph Frizzi Laura Lichtblau Shiho Kawashima Marc Gallagher FACULTY DIRECTOR, Ioannis Eli B. Gottlieb CARLETON LABORATORY SYSTEM ADMINISTRATOR Kougioumtzoglou Paul Haining Andrew Smyth Michael Smith WaiChing Sun George Leventis Haim Waisman Elisabeth Malsch MANAGER, CARLETON Huiming Yin ADMINISTRATIVE Tim McManus LABORATORY ASSISTANT Virginia Mosquera William A. Hunnicutt Nathalie Benitez ASSISTANT PROFESSORS Sharon (Xuan) Di Robert D. Mutch Marco Giometto Mysore Nagaraja Michele O'Connor

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

ENGINEERING 2021–2022 fluid dynamics and thermodynamics, advanced cement/concrete placement indicators of infrastructure performance 89 turbulence and turbulent mixing, processes. and service; market analysis. boundary-layer flow, urban and Computational mechanics: aimed at vegetation canopy flow, particle-laden understanding and solving problems in FACILITIES flow, wind loading, flow through porous science and engineering, topics include The offices and laboratories of the media, and flow and transport in multiscale methods in space and time department are in the S. W. Mudd fractured rock. (e.g., homogenization and multigrid Building and the Engineering Terrace. Environmental engineering/water methods); multiphysics modeling; resources: modeling of flow and material and geometric nonlinearities; Computing pollutant transport in surface and strong and weak discontinuities (e.g., The department manages a substantial subsurface waters, unsaturated cracks and inclusions); discretization computing facility of its own in addition zone hydrology, geoenvironmental techniques (e.g., extended finite element to being networked to all the systems containment systems, analysis of methods and mixed formulations); operated by the University. The depart- watershed flows including reservoir verification and validation (e.g., error ment facility enables its users to perform simulation. analysis); software development and symbolic and numeric computation, parallel computing. Structures: dynamics, stability, and three-dimensional graphics, and expert design of structures, structural failure Multiscale mechanics: solving various systems development. Connections and damage detection, fluid and soil engineering problems that have to wide-area networks allow the facil- structure interaction, ocean structures important features at multiple spatial ity’s users to communicate with centers subjected to wind-induced waves, and temporal scales, such as predicting throughout the world. All faculty and inelastic dynamic response of reinforced material properties or system behavior student offices and department labora- concrete structures, earthquake-resistant based on information from finer tories are hardwired to the computing design of structures. scales; focus on information reduction facility, which is also accessible remotely methods that provide balance between to users. Numerous personal computers Geotechnical engineering: soil behavior, computational feasibility and accuracy. and graphics terminals exist throughout constitutive modeling, reinforced soil the department, and a PC lab is available structures, geotechnical earthquake Transportation engineering: to students in the department in addition engineering, liquefaction and numerical understanding and modeling to the larger school-wide facility. analysis of geotechnical systems. transportation systems that are radically evolving due to emerging Structural materials: cement-based Laboratories communication and sensing materials, micro- and macromodels of technologies; leveraging large data Robert A. W. Carleton Strength of fiber-reinforced cement composites, collected from various traffic sensors Materials Laboratory utilization of industrial by-products to understand transformation in travel The Carleton Laboratory serves as the and waste materials, beneficiation of behavior patterns; modeling travel central laboratory for all experimental dredged material. behavior using a game theory approach work performed in the Department Earthquake engineering: response of to help decision-makers understand of Civil Engineering and Engineering structures to seismic loading, seismic upcoming changes and prepare for Mechanics. It is the largest laboratory risk analysis, active and passive control effective planning and management of at Columbia University’s Morningside of structures subject to earthquake next generation transportation systems. campus and is equipped for teaching excitation, seismic analysis of long-span and research in all types of engineer- Construction engineering and cable-supported bridges. ing materials and structural elements, management: contracting strategies; as well as damage detection, fatigue, Flight structures: composite materials, alternative project delivery systems; vibrations, and sensor networks. The smart and multifunctional structures, minimizing project delays and disputes; Laboratory has a full-time staff who multiscale and failure analysis, vibration advanced technologies to enhance provide assistance in teaching and control, computational mechanics and productivity and efficiency; strategic research. The Laboratory is equipped finite element analysis, fluid-structure decisions in global engineering and with a strong floor that allows for the interaction, aeroelasticity, optimal construction markets; industry trends testing of full-scale structural compo- design, and environmental degradation and challenges. nents such as bridge decks, beams, and of structures. Infrastructure delivery and columns. Furthermore, it is equipped Advanced materials: multifunctional management: decision support systems with universal testing machines ranging engineering materials, advanced for infrastructure asset management; in capacity from 150 kN (30,000 lbs.) to energy materials, durable infrastructure assessing and managing infrastructure 3 MN (600,000 lbs.). The seamless inte- materials, new concretes/composites assets and systems; capital budgeting gration of both research and teaching in using nanotubes, nanoparticles, and processes and decisions; innovative the same shared space allows civil engi- other additives with alternative binders, financing methods; procurement neering students of all degree tracks to sustainable manufacturing technologies, strategies and processes; data gain a unique appreciation of modern rheological characterization for management practices and systems; experimental approaches to material sci-

ENGINEERING 2021–2022 90 CIVIL ENGINEERING PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

APMA E2000 (4) and APMA E2101 (3) MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) E2001 (0) Intro. to applied math.

UN1401 (3) UN1402 (3) Lab UN1494 (3) PHYSICS or chem. lab (three tracks, choose one) UN1601 (3.5) UN1602 (3.5) UN2801 (4.5) UN2802 (4.5) Lab UN3081 (2)

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

GEOLOGY EESC UN1011 (4), UN2100 (4), UN2200 (4), UN2300 (4), or equivalent

MECHANICS ENME E3105 (4) either semester

CIEE E3260 (3) CIVIL ENGINEERING CIEN E3000 (3) (Spring semester; recommended but not required) Eng for dev communities

UNIVERSITY CC1010 (3) either semester WRITING

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

COMPUTER Computer Language: ENGI E1006 (3) or equivalent (any semester) SCIENCE

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

ence and engineering mechanics. Machine Shop’s machine tool pool is conditions, direct sheer device for mini- The Carleton Laboratory serves as state-of-the-art, either of the latest gen- mum compliance, and a unique sand the hub of instruction for classes offered eration or recently rebuilt and modern- hopper which prepares foundations and by the Department of Civil Engineering ized. The machine shop is open for use slopes for small scale model testing. The and Engineering Mechanics, most by undergraduate students performing Laboratory has established a link and prominently ENME E3114 Experimental independent research and is supported cooperation for large-scale testing for Mechanics of Materials, ENME E3106 by the Lab’s senior lab technician. earthquake and geosynthetic applica- Dynamics and Vibrations, and CIEN tions with NRIAE, the centrifuge facilities E3141 Soil Mechanics. The Laboratory The Donald M. Burmister Soil at the Rensselaer Polytechnic Institute also hosts and advises the AISC Steel Mechanics Laboratory and the Tokyo Institute of Technology. Bridge Team in the design, fabrication, The Burmister Laboratory contains and construction phases of their bridge, equipment and workspace to carry out The Heffner Hydrologic Research which goes to regional and national all basic soil mechanics testing for our Laboratory competition annually. undergraduate and graduate programs. The Heffner Laboratory is a facility for Additionally, the Carleton Laboratory Several unique apparatuses have been both undergraduate instruction and has a fully outfitted machine shop acquired or fabricated for advanced soil research in aspects of fluid mechanics, capable of machining parts, fittings, and testing and research: automated plain environmental applications, and water testing enclosures in steel, nonferrous strain/triaxial apparatus for stress path resources. The Heffner Laboratory hous- metals, acrylic, and wood. The Carleton testing at both drained and undrained es the facilities for teaching the labora-

ENGINEERING 2021–2022 91 CIVIL ENGINEERING: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

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

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

TECH 3 points 3 points 9 points ELECTIVES

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

TECH 6 points 3 points 6 points ELECTIVES

CIEE E3255 (3) Environ. control / pollution CIEE E4163 (3) Sust. water treat. / reuse CIEE E4257 (3) WATER RES./ CIEE E3250 (3) ENVIRON. Ground contam. transport Hydrosystems eng. EAEE E4006 (3) ENG. / remed. Field methods for CIEN E3303 (1) environ. eng. Independent studies

TECH 6 points 3 points 6 points ELECTIVES

NONTECH 3 points 3 points 3 points ELECTIVES

TOTAL POINTS 13 21 18.5 13

ENGINEERING 2021–2022 92 ENGINEERING MECHANICS PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

APMA E2000 (4) and APMA E2101 (3) MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) E2001 (0) Intro. to applied math.

UN1401 (3) UN1402 (3) Lab UN1494 (3) PHYSICS or chem. lab (three tracks, choose one) UN1601 (3.5) UN1602 (3.5) UN2801 (4.5) UN2802 (4.5) Lab UN3081 (2)

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

MECHANICS ENME E3105 (4) any semester

UNIVERSITY CC1010 (3) either semester WRITING

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

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

COMPUTER Computer Language: ENGI E1006 (3) or equivalent (any semester) SCIENCE

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

tory component of the ENME E3161 Fluid nondestructive structural health monitoring of civil engineering, deals with the Mechanics course and includes multiple facility, allowing the conduct of research in planning, design, construction, and hydraulic benches with a full array of the assessment of our nation’s degrading maintenance of structures and the experimental modules. civil infrastructure. infrastructure. These include buildings, foundations, bridges, transportation The Eugene Mindlin Laboratory for The Institute of Flight Structures facilities, nuclear and conventional Structural Deterioration Research The Institute of Flight Structures was power plants, hydraulic structures, and The Mindlin Laboratory has been devel- established within the department other facilities essential to society. The oped for teaching and research dedicated through a grant by the Daniel and second is the science of mechanics and to all facets of the assessment of structures, Florence Guggenheim Foundation. It its applications to various engineering deterioration of structural performance provides a base for graduate training disciplines. Frequently referred to as and surface coatings, dynamic testing for in aerospace and aeronautical related applied mechanics, it includes the earthquakes, and other applications. The applications of structural analysis and study of the mechanical properties of commissioning of a state-of-the-art 150 kN design. materials, stress analysis of stationary Instron universal testing machine, a QUV and movable structures, the dynamics ultraviolet spray corrosion system, and vibrations of complex structures, a freeze-thaw tester, a Keyence optical UNDERGRADUATE PROGRAMS aero- and hydrodynamics, micro- and microscope and surface analyzer have The Department of Civil Engineering nanomechanics, and the mechanics of further expanded the Mindlin Laboratory’s and Engineering Mechanics focuses biological and energy systems. capabilities in material testing and char- on two broad areas of instruction and acterization. The Mindlin Laboratory also research. The first, the classical field serves as a state-of-the-art medium scale

ENGINEERING 2021–2022 93 ENGINEERING MECHANICS: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

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

TECH 3 points 6 points 6 points 9 points

ELECTIVES NONTECH 3 points 3 points

TOTAL POINTS 13 19 18 15

Program Objectives as well as global, cultural, social, Civil Engineering 1. Graduates with a broad and funda- environmental, and economic factors The prerequisites for this program mental technical base will be able to 3. an ability to communicate effectively are the courses listed in the First enter the professional civil engineer- with a range of audiences and Second Years Program (see ing workforce either with a B.S. to 4. an ability to recognize ethical and above) or their equivalents. The civil develop specialized expertise by professional responsibilities in engineering program offers three areas way of apprenticeship or through the engineering situations and make of concentration: civil engineering and increasingly common path of a spe- informed judgments, which must construction management, geotechnical cialized M.S. consider the impact of engineering engineering or structural engineering, solutions in global, economic, 2. Graduates with a firm foundation in and water resources/environmental environmental, and societal contexts the basic math, science, and engi- engineering. In the junior and senior 5. an ability to function effectively on neering science that underlie all years, 15 credits of technical electives are teams whose members together technological development will be allocated. provide leadership, create a well equipped to adapt to changing Columbia’s program in civil collaborative and inclusive technology in the profession. engineering leading to the B.S. degree environment, establish goals, plan 3. Graduates equipped with a broad is accredited by the Engineering tasks, and meet objectives technical background will be able to Accreditation Commission of ABET, 6. an ability to develop and conduct follow other technical or nontechnical http://www.abet.org. appropriate experimentation, career paths. analyze and interpret data, and 4. Graduates will practice their profes- use engineering judgment to draw Minor in Architecture sion with effective writing and com- conclusions Civil engineering program students may munication skills, with professional 7. an ability to acquire and apply want to consider a minor in architecture ethics, as well as with awareness of new knowledge as needed, using (see page 204). societal issues. appropriate learning strategies. GRADUATE PROGRAMS Student Outcomes Engineering Mechanics M.S. students must complete the 1. an ability to identify, formulate, and The prerequisites for this program professional development and solve complex engineering problems are the courses listed in the First and leadership course, ENGI E4000, as by applying principles of engineering, Second Years Program (page 92) or a graduation requirement. Doctoral science, and mathematics their equivalents, with the provision students will be enrolled in ENGI E6001– 2. an ability to apply engineering design that ENME E3105: Mechanics be taken 6004 and should consult their program to produce solutions that meet in the sophomore year and that the for specific PDL requirements. specified needs with consideration student have obtained a grade of B of public health, safety, and welfare, or better.

ENGINEERING 2021–2022 94 Master of Science Degree Program Philosophy (Ph.D.), administered by the • Environmental Engineering and The Department of Civil Engineering Graduate School of Arts and Science. Water Resources: transport of and Engineering Mechanics offers The Eng.Sc.D. and Ph.D. programs have water-borne substances, hydrology, a graduate program leading to the nearly identical academic requirements sediment transport, hydrogeology, degree of Master of Science (M.S.) with regard to courses, qualifying and geoenvironmental design of in Civil Engineering and Engineering examinations, and the dissertation, but containment systems Mechanics. The Master of Science differ in residence requirements and in • Geotechnical Engineering: soil degree is awarded upon the satisfactory certain administrative details. A student mechanics, foundation engineering, completion of a minimum of 30 points must obtain the master's degree (M.S.) earth-retaining structures, slopes, and of credit of approved graduate study before enrolling as a candidate for geotechnical earthquake engineering extending over at least two semesters. either the Ph.D. or Eng.Sc.D. degree. • Forensic (Structural) Engineering: The M.S. program is very flexible In conjunction with their faculty investigation and determination and includes minimal core course adviser, doctoral degree students of the causes of structural failures requirements. Every student is plan an appropriate course of study of buildings, bridges, and other assigned a faculty member as an related to their area of focus within the constructed facilities academic adviser. Student and adviser department. Doctoral degree students • Structural Engineering: applications to meet regularly and plan together the must complete a minimum of 30 credits steel and concrete buildings, bridges, sequence of courses that best fit the of graduate-level coursework beyond and other structures student's interests. While a suitable the M.S. degree. Candidates for the Eng. M.S. program will necessarily entail Sc.D. degree must also accumulate 12 Engineering Mechanics some degree of specialization, the credits in the departmental course CIEN Programs in engineering mechanics program of study established between E9800 Doctoral Research Instruction. In offer comprehensive training in the the student and the adviser should be addition to coursework requirements, principles of applied mathematics well balanced, including basic subjects doctoral degree students must write a and continuum mechanics and in the of broad importance as well as theory dissertation embodying original research application of these principles to the and applications. Students may take under the sponsorship of their faculty solution of engineering problems. The graduate-level courses from across adviser. emphasis is on basic principles, enabling various concentrations within the Major research thrusts for the students to choose from among a wide department and may complete multiple doctoral degree programs include: range of technical areas. Students may concentrations. Computational mechanics work on problems in such disciplines as The Master of Science Multiscale mechanics systems analysis, acoustics, and stress concentrations are: Poromechanics analysis, and in fields as diverse as • Advanced Infrastructure Materials Dynamics and vibrations transportation, environmental, structural, • Computational and Data-Driven Infrastructure monitoring nuclear, and aerospace engineering. Engineering Mechanics Cementitious materials and concrete Program areas include: • Construction Engineering and Advanced infrastructure materials Management Structural safety and reliability • Continuum mechanics: solid and • Construction Strategic Management, Probabilistic mechanics fluid mechanics, theories of elastic Entrepreneurship, and Leadership Sustainable/green infrastructure and inelastic behavior, and damage • Engineering Mechanics Geomechanics mechanics • Environmental Engineering and Water Fluid mechanics • Vibrations: nonlinear and random Resources Autonomous transportation vibrations; dynamics of continuous • Forensic (Structural) Engineering Disasters and natural hazards media, of structures and rigid bodies, • Geotechnical Engineering and of combined systems, such as • Infrastructure Engineering Civil Engineering fluid-structure interaction; active, passive, and hybrid control systems • Real Estate Development, By selecting technical electives, for structures under seismic loading; Construction, and Finance students may focus on one of several dynamic soil-structure interaction • Smart and Sustainable Cities areas of concentration or prepare for effects on the seismic response of • Structural Engineering future endeavors such as architecture. structures • Transportation Engineering • Construction Engineering and • Random processes and reliability: Management: capital facility planning problems in design against failure Doctoral Degree Programs and financing, strategic management, under earthquake, wind, and wave Two doctoral degrees in engineering managing engineering and loadings; noise, and turbulent flows; are offered within the department: construction processes, construction analysis of structures with random the Doctor of Engineering science industry law, construction techniques, properties (Eng.Sc.D.), administered by The Fu managing civil infrastructure systems, • Fluid mechanics: turbulent flows, two- Foundation School of Engineering and civil engineering and construction phase flows, fluid-structure interaction, Applied Science, and the Doctor of entrepreneurship 

ENGINEERING 2021–2022 fluid-soil interaction, flow in porous Introduction to basic probability; hazard function; Engineering or instructor’s permission. 95 media, computational methods for reliability function; stochastic models of natural Introduction to Project Management for design flow and transport processes, and and technological hazards; extreme value distribu- and construction processes. Elements of planning, tions; statistical inference methods; Monte Carlo estimating, scheduling, bidding, and contractual flow and transport in fractured rock simulation techniques; fundamentals of integrated relationships. Computer scheduling and cost con- under mechanical loading risk assessment and risk management; topics in trol. Critical path method. Design and construction • Computational mechanics: finite risk-based insurance; case studies involving civil activities. Field supervision. element and boundary element infrastructure systems, environmental systems, CIEN E3141y Soil mechanics techniques, symbolic computation, mechanical and aerospace systems, construction management. 4 pts. Lect: 3. Lab 3. Professor Sun. and bioengineering applications. Prerequisite(s): ENME E3113. Index properties and CIEN E3121y Structural analysis classification; compaction; permeability and seep- A flight structures program is 3 pts. Lect: 3. Professor Feng. age; effective stress and stress distribution; shear designed to meet the needs of industry Methods of structural analysis. Trusses, arches, strength of soil; consolidation; slope stability. cables, frames; influence lines; deflections; force in the fields of high-speed and space method; displacement method; computer applica- CIEE E3250y Hydrosystems engineering flight. The emphasis is on mechanics, tions. 3 pts. Lect: 3. Instructor to be announced. mathematics, fluid dynamics, flight Prerequisite(s): CHEN E3110 or ENME E3161 or structures, and control. The program CIEN E3125y Structural design equivalent, SIEO W3600 or equivalent, or the 3 pts. Lect: 3. Professor Panayotidi. instructor’s permission. A quantitative introduc- is a part of the Guggenheim Institute Prerequisite(s): ENME E3113. Design criteria for tion to hydrologic and hydraulic systems, with a of Flight Structures in the department. varied structural applications, including buildings focus on integrated modeling and analysis of the Specific information regarding degree and bridges; design of elements using steel, con- water cycle and associated mass transport for requirements is available in the crete, masonry, wood, and other materials. water resources and environmental engineering. department office. Coverage of unit hydrologic processes such as CIEN E3126y Computer-aided structural precipitation, evaporation, infiltration, runoff gen- design eration, open channel and pipe flow, subsurface 1 pt. Lect: 1. Lab: 1. Instructor to be announced. COURSES IN CIVIL ENGINEERING flow and well hydraulics in the context of example Corequisite: CIEN E3125. Introduction to soft- watersheds and specific integrative problems See also Courses in Engineering ware for structural analysis and design with lab. such as risk-based design for flood control, provi- Mechanics at the end of this section. Applications to the design of structural elements sion of water, and assessment of environmental and connections. Lab required. CIEN E3000y The art of structural design impact or potential for nonpoint source pollution. 3 pts. Lect: 3. Professor Deodatis. CIEN E3127x Structural design projects Spatial hydrologic analysis using GIS and water- Basic scientific and engineering principles for the 3 pts. Lect: 3. Professor Panayotidi. shed models. Note: This course is to be joint listed design of buildings, bridges, and other parts of Prerequisite(s): CIEN E3125 and E3126 or the with CIEN and replaces the previous CIEN 3250. the built infrastructure. Application of principles instructor’s permission. Design of steel members CIEE E3255y Environmental control and to analysis and design of actual large-scale struc- in accordance with AISC 360: moment redistribu- pollution reduction systems tures. Coverage of the history of major structural tion in beams; plastic analysis; bearing plates; 3 pts. Lect: 3. Professor Farrauto. design innovations and of the engineers who beam-columns: exact and approximate second- Prerequisite(s): EAEE E3200 or ENME E3161 or introduced them. Critical examination of the order analysis; design by the Effective Length MECE E3100. Review of engineered systems for unique aesthetic/artistic perspectives inherent in method and the Direct Analysis method. Design prevention and control of pollution. Fundamentals structural design. Consideration of management, of concrete members in accordance with ACI 318: of material and energy balances and reaction socioeconomic, and ethical issues involved in bar anchorage and development length, bar splic- kinetics. Analysis of engineered systems to design and construction of large-scale structures. es, design for shear, short columns, slender col- address environmental problems, including Introduction to recent developments in sustain- umns. AISC/ASCE NSSBC design project: design solid and hazardous waste, and air, water, soil able engineering, including green building design of a steel bridge in accordance with National and noise pollution. Life cycle assessments and and adaptable structural systems. Student Steel Bridge Competition rules; computer emerging technologies. simulation and design by using SAP2000. CIEN E3010y Introduction to construction: CIEE E3260y Engineering for developing case studies CIEN E3128y Design projects communities 3 pts. Lect: 3. Professor Odeh. 4 pts. Lect: 4. Professor Panayotidi. 3 pts. Lect: 3. Professor Sisul. Prerequisite(s): Instructor's permission. Introduces Prerequisite(s): CIEN E3125 and E3126. Capstone Introduction to engineering problems faced basic principles of how builders construct dif- design project in civil engineering. This project by developing communities and exploration of ferent types of projects. Shows detailed weekly integrates structural, geotechnical and environ- design solutions in the context of a real project cases on construction processes for infrastructure mental/water resources design problems with with a community client. Emphasis is on the as well as building projects. Cases show major construction management tasks and sustainability, design of sustainable solutions that take account differences in constructing different types of proj- legal and other social issues. Project is completed of social, economic, and governance issues, ects and highlight challenges/solutions faced by in teams, and communication skills are stressed. and that can be implemented now or in the near project team during construction phase. Projects Outside lecturers will address important current future. The course is open to all undergraduate covered include: Tunnels, Bridges, Skyscrapers, issues in engineering practice. Every student in engineering students. Multidisciplinary teamwork Neighborhood Development, Mega Programs, the course will be exposed with equal emphasis and approaches are stressed. Outside lecturers Airports, and Education. Detailed examples of real to issues related to geotechnical engineering, are used to address issues specific to develop- case studies of iconic national and international water resources/environmental engineering, ing communities and the particular project under projects. Includes site visits to active construction structural engineering, and construction engineer- consideration. projects. ing and management. CIEN E3303x and y Independent studies in CIEN E3129x Project management for CIEN E3111x Uncertainty and risk in civil civil engineering for juniors infrastructure systems construction 1–3 pts. By conference. Members of the faculty. 3.5 pts. Lect: 3. Professor Deodatis. 3 pts. Lect: 3. Professor Chang. A project on civil engineering subjects approved Prerequisite(s): Working knowledge of calculus. Prerequisite(s): Senior standing in Civil by the chair of the department.

ENGINEERING 2021–2022 96 CIEN E3304x and y Independent studies in tion assessments, data acquisition and analysis, CIEN E4129x and y Managing engineering civil engineering for seniors forecasts. Selected case histories and field visits. and construction processes 1–3 pts. By conference. Members of the faculty. 3 pts. Lect: 3. Professors Odeh and Nagaraja. CIEN E4100y Earthquake and wind A project on civil engineering subjects approved Prerequisite(s): Graduate standing in Civil by the chair of the department. engineering Engineering, or instructor’s permission. 3 pts. Lect: 3. Professors Ashrafi and Balsamo. Introduction to the principles, methods and tools CIEN E3999x, y or s Fieldwork Prerequisite(s): ENME E3106 or the equivalent. necessary to manage design and construction 1–2 pts. Instructor to be announced. Basic concepts of seismology. Earthquake charac- processes. Elements of planning, estimating, Prerequisite(s): Obtained internship and approval teristics, magnitude, response spectrum, dynamic scheduling, bidding and contractual relationships. from faculty adviser. CEEM undergraduate stu- response of structures to ground motion. Base Valuation of project cash flows. Critical path dents only. Written application must be made isolation and earthquake-resistant design. Wind method. Survey of construction procedures. Cost prior to registration outlining proposed internship/ loads and aeroelastic instabilities. Extreme winds. control and effectiveness. Field supervision. study program. Final reports required. May not be Wind effects on structures and gust factors. taken for pass/fail credit or audited. International CIEN E4130x Design of construction systems students must also consult with the International ECIA W4100y Management and development 3 pts. Lect: 3. Professor Tirolo. Students and Scholars Office. of water systems Prerequisite(s): CIEN E3125 or the equivalent, 3 pts. Lect: 3. Professors Gentine and Lall. or the instructor’s permission. Introduction to CIEN E4010x Transportation engineering Decision analytic framework for operating, man- the design of systems that support construction 3 pts. Lect: 3. Professor Peterson. aging, and planning water systems, considering activities and operations. Determination of design An overview of the planning, design, operation, changing climate, values, and needs. Public and loads during construction. Design of excava- and construction of urban highways and mass private sector models explored through U.S.- tion support systems, earth retaining systems, transportation systems. Transportation planning international case studies on topics ranging from temporary supports and underpinning, concrete and traffic studies; traffic and highway engineer- integrated watershed management to the analysis formwork and shoring systems. Cranes and erec- ing; rapid transit and railroad engineering. of specific projects for flood mitigation, water tion systems. Tunneling systems. Instrumentation and wastewater treatment, or distribution system and monitoring. Students prepare and present CEOR E4011y Infrastructure systems evaluation and improvement. optimization term projects. 3 pts. Lect: 3. Not offered in 2021–2022. CIEN E4111x Uncertainty and risk in CIEN E4131x and y Principles of construction Prerequisite(s): Basic linear algebra. Basic prob- infrastructure systems techniques ability and statistics. Engineering economic 3 pts. Lect: 3. Professor Deodatis. 3 pts. Lect: 3. Professors McManus and Odeh. concepts. Basic spreadsheet analysis and pro- Introduction to basic probability, hazard function, Prerequisite(s): CIEN E4129 or equivalent. Current gramming skills. Subject to instructor's permis- reliability function, stochastic models of natural methods of construction, cost-effective designs, sion. Infrastructure design and systems concepts, and technological hazards, extreme value distri- maintenance, safe work environment. Design analysis, and design under competing/conflicting butions, Monte Carlo simulation techniques, fun- functions, constructability, site and environmental objectives, transportation network models, traf- damentals of integrated risk assessment and risk issues. fic assignments, optimization, and the simplex management, topics in risk-based insurance, case algorithm. studies involving civil infrastructure systems, envi- CIEN E4132x Prevention and resolution of ronmental systems, mechanical and aerospace construction disputes CIEN E4011y Big data analytics in systems. Not open to undergraduate students. 3 pts. Lect: 3. Professor White. transportation Prerequisite(s): CIEN E4129 or equivalent. CIEE E4116y Energy harvesting 3 pts. Lect: 3. Professor Di. Contractual relationships in the engineering and 3 pts. Lect: 3. Not offered in 2021–2022. Prerequisite(s): ENME E3105 or instructor's per- construction industry and the actions that result Prerequisite(s): ENME E3114 or equivalent, or mission. Major elements of transportation analyt- in disputes. Emphasis on procedures required to instructor’s permission. Criterion of energy har- ics. Develop basic skills in applying fundamentals prevent disputes and resolve them quickly and vesting, identification of energy sources. Theory of data analytics to transportation data analysis. cost-effectively. Case studies requiring oral and of vibrations of discrete and continuous system, Apply coding languages (e.g., MATLAB, Python) written presentations. and visualization tools (e.g., Excel, Carto, R, measurement and analysis. Selection of materials Processing) to analyze transportation data. Infer for energy conversion, piezoelectric, electromag- CIEN E4133x Capital facility planning and policy implications from analytics results. netic, thermoelectric, photovoltaic, etc. Design financing and characterization, modeling and fabrication of 3 pts. Lect: 3. Professor Chang. CIEN E4021x Elastic and plastic analysis of vibration, motion, wind, wave, thermal gradient, Prerequisite(s): CIEN E4129 or equivalent. structures and light energy harvesters; resonance phenom- Planning and financing of capital facilities with 3 pts. Lect: 3. Not offered in 2021–2022. enon, power electronics and energy storage and a strong emphasis upon civil infrastructure sys- Prerequisite(s): CIEN E3121 or the equivalent. management. Applications to buildings, geother- tems. Project feasibility and evaluation. Design Overview of classical indeterminate structural mal systems, and transportation. To alternate with of project delivery systems to encourage best analysis methods (force and displacement meth- ENME E4115. value, innovation and private sector participation. ods), approximate methods of analysis, plastic Fundamentals of engineering economy and proj- CIEN E4128y Civil engineering management analysis methods, collapse analysis, shakedown ect finance. Elements of life cycle cost estimation 3 pts. Not offered in 2021–2022. theorem, structural optimization. and decision analysis. Environmental, institutional, Principles of engineering management with a social and political factors. Case studies from CIEN E4022y Bridge design and management strong emphasis on planning of infrastructure sys- transportation, water supply and wastewater 3 pts. Lect: 3. Professor Yanev. tems. The course stresses leadership, creativity, treatment. Prerequisite(s): CIEN E3125 or the equivalent. and management analysis. Program planning with Bridge design history, methods of analysis, loads: optimization under financial and environmental CIEN E4134y Construction industry law static, live, dynamic. Design: allowable stress, constraints; project planning and scheduling using 3 pts. Lect: 3. Professors Charney and Rubin. ultimate strength, load resistance factor, supply/ deterministic and stochastic network theories; Prerequisite(s): Graduate standing or the instruc- demand. Steel and concrete superstructures: production rate development and control using tor’s permission. Practical focus upon legal suspension, cable stayed, prestressed, arches. statistical, heuristic, simulation, and queuing concepts applicable to the construction industry. Management of the assets, life-cycle cost, theory approaches. Students prepare and formally Provides sufficient understanding to manage expected useful life, inspection, maintenance, present term projects. legal aspects, instead of being managed by them. repair, reconstruction. Bridge inventories, condi- Topics include contractual relationships, contract

ENGINEERING 2021–2022 performance, contract flexibility and change Prerequisite(s): CIEN E4129 or instructor’s per- Third-year undergraduate students with instruc- 97 orders, liability and negligence, dispute avoid- mission. History and development of Building tor's permission. ance/resolution, surety bonds, insurance and site Information Modeling (BIM), its uses in design and safety. construction, and introduction to the importance CIEN E4145x Applied use of AEC data of planning in BIM implementation. Role of visual 3 pts. Lect: 2.5. Professors Diaz-Gonzalez and CIEN E4135y Strategic management in design and construction concepts and methodolo- Jeon. engineering and construction gies, including integrated project delivery form Digital transformation optimizes day-to-day 3 pts. Lect: 3. Professor Peña-Mora. in architecture, engineering, and construction operations to provide maximum performance in Core concepts of strategic planning, management industries from project design, cost estimating, Architecture, Engineering, and Construction (AEC) and analysis within the construction industry. scheduling, coordination, fabrication, installation, workflows. Focuses on broadening knowledge Industry analysis, strategic planning models and and financing. of AEC data leading to building data manage- industry trends. Strategies for information technol- ment. Use of open data sets from the design, ogy, emerging markets and globalization. Case CIEN E4140x Environmental, health, and construction, and operations of buildings to learn studies to demonstrate key concepts in real-world safety concepts in construction processes and practice data management and its applied environments. 3 pts. Lect: 3. Professor Haining. use. Major technical topics include Project Prerequisite(s): Graduate standing in Civil Management Information System (PMIS) and CIEN E4136y Entrepreneurship in engineering Engineering and Engineering Mechanics. A defini- Facility Management (FM), leading to Digital Twin and construction tive review of and comprehensive introduction data management, data processing, and data 3 pts. Lect: 3. Professor Peña-Mora. to construction industry best practices and fun- visualization. Prerequisite(s): Instructor's permission. Capstone damental concepts of environmental health and practicum where teams develop strategies and safety management systems (EH&S) for the con- CIEE E4163y Sustainable water treatment business plans for a new enterprise in the engi- struction management field. How modern EH&S and reuse neering and construction industry. Identification management system techniques and theories not 3 pts. Lect: 3. Instructor to be announced. of attractive market segments and locations; only result in improved safe work environments Prerequisite(s): Introductory chemistry (with development of an entry strategy; acquisition but ultimately enhance operational processes and laboratory) and fluid mechanics. Fundamentals of of financing, bonding, and insurance; organiza- performance in construction projects. water pollution and wastewater characteristics. tional design; plans for recruiting and retaining Chemistry, microbiology, and reaction kinetics. personnel; personnel compensation/incentives. CIEN E4141y Public-private partnerships in Design of primary, secondary, and advanced treat- Invited industry speakers. Priority given to gradu- global infrastructure development ment systems. Small community and residential ate students in Construction Engineering and 3 pts. Professor Chang. systems. Management. Graduate students only. Delivery of infrastructure assets through Public-Private Partnerships (PPP). CIEN E4210x Forensic structural engineering CIEN E4137y Managing civil infrastructure Value for Money analysis. Project organization. 3 pts. Lect: 3. Not offered in 2021–2022. systems Infrastructure sector characterization. Risk analy- Prerequisite(s): Working knowledge of structural 3 pts. Lect: 3. Professor Chang. sis, allocation, and mitigation. Monte Carlo meth- analysis and design; graduate student standing Prerequisite(s): IEOR E4003, CIEN E4133, or equiv- ods and Real Options. Project finance and financ- or instructor’s permission. Review of significant alent. Examination of the fundamentals of infra- ing instruments. Case studies from transportation, failures, civil/structural engineering design and structure planning and management, with a focus water supply, and energy sectors. construction practices, ethical standards and the on the application of rational methods that sup- legal positions as necessary background to foren- port infrastructure decision-making. Institutional CIEN E4142x International construction sic engineering. Discussion of standard-of-care. environment and issues. Decision-making under management: theory and practice Study of the process of engineering evaluation certainty and uncertainty. Capital budgeting and 3 pts. Lect: 3. Professor Odeh. of structural defects and failures in construction financing. Group decision processes. Elements of Prerequisite(s): CIEN E4129 or instructor's per- and in service. Examination of the roles, activities, decision and finance theory. mission. Complex global construction industry conduct and ethics of the forensic consultant and environment. Social, cultural, technological, and expert witness. Students are assigned projects of CIEN E4138y Real estate finance for political risks; technical, financial, and contractual actual cases of nonperformance or failure of steel, construction management risk. Understanding of successful global project concrete, masonry, geotechnical, and temporary 3 pts. Lect: 3. Professor Riordan. delivery principals and skills for construction structures, in order to perform, discuss, and Prerequisite(s): IEOR E2261, CIEN E3129 or per- professionals. Industry efforts and trends to sup- report their own investigations under the guid- mission of instructor. Introduction to financial port global operational mechanism. Global Case ance of the instructor. mechanics of public and private real estate Studies. Engage with industry expert profession- CIEN E4212y Structural failures: cases, development and management. Working from als. Student group projects with active ongoing perspectives of developers, investors and taxpay- global initiatives. causes, lessons learned ers, financing of several types of real estate and 3 pts. Lect: 3. Not offered in 2021–2022. infrastructure projects are covered. Basics of CIEN E4144x Real estate land development Prerequisite(s): A course each in engineering real estate accounting and finance, followed by engineering materials, structural analysis, concrete design, in-depth studies of private, public, and public/ 3 pts. Lect: 3. Professors Leventis, O'Connor, steel design, soil mechanics and foundations, private-partnership projects and their financial and Vitolano. and construction; graduate student standing or structures. Focused on U.S.-based financing, Comprehensive review of various engineering dis- instructor's permission. The nature and causes with some international practices introduced ciplines in the process of real estate land devel- of structural failures and the lessons learned and explored. Financial risks and rewards, and opment. Engineering disciplines covered include from them; insight into failure investigation in the pertinent capital markets and their financing civil, infrastructure, transportation planning, envi- practice of forensic structural engineering. Case roles. Impacts and incentives of various govern- ronmental planning, permitting, environmental histories of actual failures of real-life structures ment programs, such as LEED certification and remediation, geotechnical, and waterfront/marine. during construction and in service are introduced, solar power tax credits. Case studies provide Overview of land use and environmental law, examined, analyzed, and discussed. Students are opportunity to compare U.S. practices to several architecture and urban planning, as related to assigned documented cases of failures of struc- international methods. land development. Discussion of how these sub- tures of various types and materials to review, jects affect decisions—cost, schedule, program- discuss, and, in some cases, to conduct investiga- CIEN E4139x Theory and practice of virtual ming—involved in real estate development. Note: tions of the causes and responsibilities. Students design and construction Graduate and senior undergraduate students only. 3 pts. Lect: 3. Professors Belote and David.

ENGINEERING 2021–2022 98 are required to prepare written reports and make CIEN E4235x Multihazard design of structures and evaluation by field measurements. Case his- oral presentations of selected cases. 3 pts. Lect: 3. Professors Daddazio and tories to illustrate typical design and construction Mosquera. problems. To alternate with CIEN E4246. CIEN E4213x Elastic and inelastic buckling of Prerequisite(s): CIEN E3125 or E4232 or instruc- CIEN E4244y Geosynthetics and applications structures tor’s permission. Fundamental considerations of 3 pts. Lect: 3. Professor Ling. 3 pts. Lect: 3. Professor Valenti. wave mechanics; design philosophies; reliability Prerequisite(s): CIEN E4241 or the equivalent. Stability of framed structures in the elastic and and risk concepts; basics of fluid mechanics; Properties of geosynthetics. Geosynthetic design inelastic ranges. Lateral buckling of beams. design of structures subjected to blast; elements for soil reinforcement. Geosynthetic applications Torsional buckling of compression members. of seismic design; elements of fire design; flood in solid waste containment system. Buckling of plates of plate-stiffener combinations. considerations; advanced analysis in support of Linear stability analysis of cylindrical shells and structural design. CIEN E4245x Tunnel design and construction discussion of its limitations. Discussion of the 3 pts. Lect: 3. Not offered in 2021–2022. semiempirical nature of the elastoplastic relations CIEN E4236y Design of prestressed concrete Engineering design and construction of different used in the case of plates and shells. structures types of tunnel, including cut and cover tunnel, 3 pts. Lect: 3. Professor Panayotidi. rock tunnel, soft ground tunnel, immersed tub CIEN E4226y Advanced design of steel Prerequisite(s): CIEN E4232 or instructor's permis- tunnel, and jacked tunnel. The design for the structures sion. Properties of materials used in prestressed liner, excavation, and instrumentation are also 3 pts. Lect: 3. Professors Aly and Mosquera. concrete; pretensioning versus posttensioning; covered. A field trip will be arranged to visit the Prerequisite(s): CIEN E3125 or equivalent. Review loss of prestress due to elastic shortening, friction, tunneling site. of loads and structural design approaches. anchorage slip, shrinkage, creep and relaxation; Material considerations in structural steel design. full versus partial prestressing; design of beams CIEN E4246x Earth retaining structures Behavior and design of rolled steel, welded, for flexure, shear, and torsion; method of load 3 pts. Lect: 3. Not offered in 2021–2022. cold-formed light-gauge, and composite concrete/ balancing; anchorage zone design; calculation Prerequisite(s): CIEN E3141. Retaining structures, steel members. Design of multistory buildings and of deflection by the lump-sum and incremental bulkheads, cellular cofferdams, and braced space structures. time-step methods; continuous beams; composite excavations. Construction dewatering and CIEN E4232x Advanced design of concrete construction; prestressed slabs and columns. underpinning. Instrumentation to monitor actual performances. Ground improvement techniques, structures CIEN E4237x Architectural design, including earth reinforcement, geotextiles, and 3 pts. Lect: 3. Professor Panayotidi. computation, and method grouting. To alternate with CIEN E4243. Prerequisite(s): CIEN E3125 or equivalent. Design 3 pts. Lect: 1.5. Lab: 1.5. Not offered in of concrete beams for combined torsion, shear 2021–2022. CIEN E4247y Design of large-scale deep and flexure; moment-curvature relation; bar Prerequisite(s): CIEN E3121 or equivalent. CIEN foundation systems cut-off locations; design of two-way slabs; strut- E3125 or equivalent. Integrated methods of 3 pts. Lect.: 3. Professors Frizzi, Gallagher, and-tie method for the design of deep beams and design and structural analysis between engi- Leventis, and Poeppel. corbels; gravity and shear wall design; retaining neering and architecture. Lectures on historical Prerequisite(s): CIEN E3141. Focus on deep foun- wall design. precedents on material use, structural inventive- dations in difficult conditions and constraints of CIEN E4233x Design of large-scale bridges ness, and social importance. Labs on drafting and designing foundations. Design process from the 3 pts. Lect: 3. Professor Zoli. modeling software; physical modeling techniques start of field investigations through construction Prerequisite(s): CIEN E3121 or equivalent, and and virtual reality visualization. and the application of deep foundations. CIEN E3127 or equivalent. Design of large-scale CIEN E4241x Geotechnical engineering CIEE E4250x or y Hydrosystems and complex bridges with emphasis on cable- fundamentals 3 pts. Lect: 3. Professor Gentine. supported structures. Static and dynamic loads, 3 pts. Lect: 3. Professor Ling. Prerequisite(s): CHEN E3110 or ENME E3161 or component design of towers, superstructures Prerequisite(s): CIEN E3141 or instructor’s permis- equivalent, or the instructor’s permission. The and cables; conceptual design of major bridge sion. Bearing capacity and settlement of shallow hydrologic cycle and relevant atmospheric pro- types including arches, cable stayed bridges and and deep foundations; earth pressure theories; cesses; water and energy balance; radiation; suspension bridges. retaining walls and reinforced soil retaining walls; boundary layer; precipitation formation; evapora- CIEN E4234y Design of large-scale building sheet pile walls; braced excavation; slope stability. tion; vegetation transpiration; infiltration; storm runoff; snowmelt; and flood processes. Routing of structures CIEN E4242y Geotechnical earthquake runoff and floodwaters. Groundwater flow and the 3 pts. Lect: 3. Professors Gottlieb, Malsch, and engineering hydraulics of wells. Probabilistic modeling, and Tomasetti. 3 pts. Lect: 3. Professor Ling. extreme-value theory. Prerequisite(s): CIEN E3121 and E3127. Modern Prerequisite(s): CIEN E3141 or equivalent. challenges in the design of large-scale building Seismicity, earthquake intensity, propagation of CIEN E4250y Waste containment design and structures will be studied. Tall buildings, large seismic waves, design of earthquake motion, practice convention centers, and major sports stadiums seismic site response analysis, in situ and labora- 3 pts. Lect: 3. Not offered in 2021–2022. present major opportunities for creative solutions tory evaluation of dynamic soil properties, seismic Prerequisite(s): ENME E3161 and CIEN E3141, or and leadership on the part of engineers. This performance of underground structures, seismic equivalents. Strategies for the containment of course is designed to expose the students to performance of port and harbor facilities, evalu- buried wastes. Municipal and hazardous waste this environment by having them undertake the ation and mitigation of soil liquefaction and its landfill design; bioreactor landfills; vertical barri- complete design of a large structure from initial consequences. Seismic earth pressures, slopes ers, evapotranspiration barriers and capillary bar- design concepts on through all the major design stability, safety of dams and embankments, seis- riers; hydraulic containment; in situ stabilization decisions. The students work as members of a mic code provisions and practice. To alternate and solidification techniques; site investigation; design team to overcome the challenges inher- with E4244. monitoring and stewardship of buried wastes; ent in major projects. Topics include overview options for land reuse/redevelopment. of major projects, project criteria and interface CIEN E4243x Foundation engineering with architecture, design of foundations and 3 pts. Lect: 3. Professor Yang. CIEE E4252x Foundations of environmental structural systems, design challenges in the post Prerequisite(s): CIEN E3141 or equivalent. engineering 9/11 environment, and roles, responsibilities, and Conventional types of foundations and foundation 3 pts. Lect: 3. Professor Chandran. legal issues. problems: subsurface exploration and testing. Prerequisite(s): CHEM UN1403 or equivalent; Performance of shallow and deep foundations ENME E3161 or the equivalent. Engineering

ENGINEERING 2021–2022 aspects of problems involving human interaction Civil Engineering and Engineering Mechanics CIEN E9120x and y–S9120 Independent 99 with the natural environment. Review of funda- graduate students who include relevant off- studies in flight sciences mentals principles that underlie the discipline campus work experience as part of their approved 3 pts. Not offered in 2021–2022. of environmental engineering, i.e., constituent program of study. Final report and letter of evalu- Prerequisite(s): Instructor’s permission. Geared transport and transformation processes in envi- ation required. May not be taken for pass/fail toward students interested in flight sciences and ronmental media such as water, air and ecosys- credit or audited. flight structures. Topics related to aerodynamics, tems. Engineering applications for addressing propulsion, noise, structural dynamics, aeroelas- CIEN E6132y Leadership in engineering and environmental problems such as water quality and ticity, and structures may be selected for super- treatment, air pollutant emissions, and hazardous construction vised study. A term paper is required. waste remediation. Presented in the context of 3 pts. Lect: 3. Professor Peña-Mora. current issues facing practicing engineers and Prerequisite(s): CIEN E4129 or the equivalent. CIEN E9130x and y–S9130 Independent government agencies, including legal and regula- Introduces and employs various tools, concepts, studies in construction tory framework, environmental impact assess- and analytical frameworks to enhance students' 3 pts. Not offered in 2021–2022. ments, and natural resource management. ability to define and analyze leadership problems. Prerequisite(s): Permission by department chair In-depth analysis of leadership literature and and instructor. Independent study of engineer- CIEN E4253x Finite elements and plasticity in practical situational immersion using industry case ing and construction industry problems. Topics geotechnical engineering studies. Term project exploring leadership in engi- related to capital planning and financing, project 3 pts. Lect: 3. Professor Sun. neering and construction industry, working closely management, contracting strategies and risk Prerequisite(s): CIEN E3141 and ENME E4332. with industry leaders. allocation, dispute mitigation and resolution, and State-of-the-art computer solutions in geotechni- infrastructure assessment and management may CIEN E6133y Advanced construction and cal engineering; 3D consolidation, seepage flows, be selected for supervised study. A term paper and soil-structure interaction; element and mesh infrastructure risk management using real is required. instabilities. options 3 pts. Lect: 3. Not offered in 2021–2022. CIEN E9165x and y–S9165 Independent CIEE E4257x Groundwater contaminant Prerequisite(s): CIEN E6131. Advanced concepts studies in environmental engineering transport and remediation of risk analysis and management applied to civil 4 pts. Not offered in 2021–2022. 3 pts. Lect: 3. Professors Mutch and Carbonaro. engineering systems. Identifying and valuing Prerequisite(s): CIEE E4252 or the equivalent. Prerequisite(s): ENME E3161 and CIEE E3250 or flexibility in construction and operation. Tools to Emphasizes a one-on-one study approach to instructor's permission. Sources and types of perform risk analysis in flexible civil infrastructure specific environmental engineering problems. groundwater contamination. Groundwater hydrol- systems. Valuation methods for real options. Risk Students develop papers or work on design prob- ogy. Groundwater contaminant fate and transport. flexibility analysis; integrating real options analy- lems pertaining to the treatment of solid and liq- Flow and transport in the unsaturated zone. sis with quantitative risk analysis. Applications uid waste, contaminant migration, and monitoring Nonaqueous phase liquids and multiphase flow. to case studies on construction management, and sampling programs for remediation design. Physical and numerical models for contaminant life-cycle cost analysis for infrastructure assets, transport. Characterization and assessments of public-private partnerships projects, real estate CIEN E9201x and y–S9201 Civil engineering contaminated sites. Groundwater remediation developments, and renewable energy infrastruc- reports alternatives. Regulations. ture projects. 1–4 pts. Not offered in 2021–2022. A project on some civil engineering subject CIEE E4260x Urban ecology studio CIEN E6232x Advanced topics in concrete approved by department chair. 3 pts. Lect: 2.5. Lab 2.5. Not offered in engineering 2021–2022. 3 pts. Lect: 3. Not offered in 2021–2022. CIEN E9500x and y Departmental seminar Prerequisite(s): Senior undergraduate or gradu- Prerequisite(s): CIEN E3125 or the equivalent. 0 pts. Professor Ling. ate student standing and instructor’s permission. Behavior of concrete under general states of All doctoral students are required to attend the Conjoint studio run with the Graduate School of stress, numerical modeling of steel and concrete, department seminar as long as they are in resi- Architecture, Planning and Preservation (GSAPP) finite element analysis of reinforced concrete, dence. No degree credit is granted. that explores solutions to problems of urban den- design of slabs and their shell concrete structures. CIEN E9800x and y–S9800 Doctoral research sity. Engineering and GSAPP students will engage CIEN E6246y Advanced soil mechanics instruction in a joint project that addresses habitability and 3–12 pts. May be taken for 3, 6, 9, or 12 points, sustainability issues in an urban environment, and 3 pts. Lect: 3. Professor Ling. dependent on instructor’s permission. also provides community service. Emphasis will Prerequisite(s): CIEN E3141. Stress-dilatancy of A candidate for the Eng.Sc.D. degree in civil be on the integration of science, engineering and sand; failure criteria; critical state soil mechanics; engineering must register for 12 points of doctoral design within a social context. Interdisciplinary limit analysis; finite element method and case research instruction. Registration in CIEN E9800 approaches and communication will be stressed. histories of consolidation analysis. may not be used to satisfy the minimum residence CIEN E4300x Infrastructural materials CIEN E6248x Experimental soil mechanics requirement for the degree. 3 pts. Lect: 3. Professor Wheeler. 3 pts. Lect: 3. Not offered in 2021–2022. CIEN E9900x and y–S9900 Doctoral Basic concepts of materials science for civil Prerequisite(s): CIEN E3141. Advanced soil testing, dissertation infrastructure materials. Relate composition, struc- including triaxial and plane strain compression 0 pts. Members of the faculty. ture, processing to engineering properties (e.g., tests; small-strain measurement. Model testing; A candidate for the doctorate may be required to strength, modulus, ductility-malleability, durabil- application (of test results) to design. register for this course every term after the stu- ity). Materials covered include stone, brick, terra CIEN E9101x and y–S9101 Civil engineering dent’s coursework has been completed and until cotta, concrete, cast stone, metals, and wood. research the dissertation has been accepted. Overview of sourcing and production, identifica- 1–4 pts. Members of the faculty. tion, fabrication, chemical, physical and mechani- Advanced study in a specialized field under the cal properties. supervision of a member of the department staff. COURSES IN ENGINEERING CIEN E4999x and y Fieldwork Before registering, the student must submit an MECHANICS outline of the proposed work for approval of the 1–2 pts. Instructor to be announced. See also Courses in Civil Engineering at supervisor and the department chair. Prerequisite(s): Instructor’s written approval. May the beginning of this section. be repeated for credit, but no more than 3 total points may be used for degree credit. Only for

ENGINEERING 2021–2022 100 ENME E3105x and y Mechanics ENME E4114x Mechanics of fracture puter programming, linear algebra. Introduction to 4 pts. Lect: 4. Professors Hone and and fatigue multiscale analysis. Information-passing bridging Kougioumtzoglou. 3 pts. Lect: 3. Professor Brügger. techniques: among them, generalized mathemati- Prerequisite(s): PHYS UN1401, MATH UN1101, Prerequisite(s): Undergraduate mechanics of sol- cal homogenization theory, the heterogeneous MATH UN1102, and MATH UN1201 or APMA ids course. Elastic stresses at a crack; energy and multiscale method, variational multiscale method, E2000. Elements of statics; dynamics of a particle stress intensity criteria for crack growth; effect of the discontinuous Galerkin method and the kinetic and systems of particles. plastic zone at the crack; fracture testing applica- Monte Carlo–based methods. Concurrent multi- tions. Fatigue characterization by stress-life and scale techniques: domain bridging, local enrich- ENME E3106y Dynamics and vibrations strain-life; damage index; crack propagation; fail ment, and multigrid-based concurrent multiscale 3 pts. Lect: 2. Professor Smyth. safe and safe life analysis. methods. Analysis of multiscale systems. Prerequisite(s): MATH UN1201 or APMA E2000, and APMA E2101. Corequisite: ENME E3105. EMME E4115y Micromechanics of composite ENME E6215x Principles and applications of Kinematics of rigid bodies; momentum and energy materials sensors for structural health monitoring methods; vibrations of discrete and continuous 3 pts. Lect: 3. Professor Yin. 3 pts. Lect: 2.5. Lab: 0.5. Professor Feng. systems; eigenvalue problems, natural frequen- Prerequisite(s): ENME E4113 or instructor’s approv- Prerequisite(s): ENME E4215. Concepts, principles, cies and modes. Basics of computer simulation of al. An introduction to the constitutive modeling and applications of various sensors for sensing dynamics problems using MATLAB. of composite materials: Green’s functions in het- structural parameters and nondestructive evalu- erogenous media, Eshelby’s equivalent inclusion ation techniques for subsurface inspection, data ENME E3113x Mechanics of solids methods, eigenstrains, spherical and ellipsoidal acquisition, and signal processing techniques. 3 pts. Lect: 3. Professor Betti. inclusions, dislocations, homogenization of elas- Lectures, demonstrations, and hands-on labora- Pre- or corequisite: ENME E3105 or equivalent. tic fields, elastic, viscoelastic and elastoplastic tory experiments. Stress and strain. Mechanical properties of materi- constitutive modeling, micromechanics-based ENME E6216y Structural health monitoring als. Axial load, bending, shear, and torsion. Stress models. transformation. Deflection of beams. Buckling of 3 pts. Lect: 3. Professor Betti. columns. Combined loadings. Thermal stresses. ENME E4202y Advanced mechanics Prerequisite(s): ENME E4215 and ENME E4332. 3 pts. Lect: 3. Professor Smyth. Principles of traditional and emerging sensors, ENME E3114y Experimental mechanics of Prerequisite(s): ENME E3105 or equivalent. data acquisition and signal processing techniques, materials Differentiation of vector functions. Review of kine- experimental modal analysis (input-output), opera- 4 pts. Lect: 2. Lab: 3. Professor Kawashima. matics. Generalized coordinates and constraint tional modal analysis (output-only), model-based Prerequisite(s): ENME E3113. Material behavior equations. Generalized forces. Lagrange’s equa- diagnostics of structural integrity, long-term moni- and constitutive relations. Mechanical properties tions. Impulsive forces. Collisions. Hamiltonian. toring and intelligence maintenance. Lectures and of metals and cement composites. Structural Hamilton’s principle. demonstrations, hands-on laboratory experiments. materials. Modern construction materials. Experimental investigation of material properties ENME E4214y Theory of plates and shells ENME E6220y Random processes in and behavior of structural elements including frac- 3 pts. Lect: 3. Professor Dasgupta. mechanics ture, fatigue, bending, torsion, buckling. Prerequisite(s): ENME E3113. Static flexural 3 pts. Lect: 3. Professor Kougioumtzoglou. response of thin, elastic, rectangular, and circular Prerequisite(s): CIEN E4111 and ENME E4215 ENME E3161x Fluid mechanics plates. Exact (series) and approximate (Ritz) solu- (or equivalent). Review of random variables. 4 pts. Lect: 3. Lab: 3. Professor Giometto. tions. Circular cylindrical shells. Axisymmetric Random process theory: stationary and ergodic Prerequisite(s): ENME E3105 and ordinary dif- and nonaxisymmetric membrane theory. Shells of processes, correlation functions, power spectra. ferential equations. Fluid statics. Fundamental arbitrary shape. Nonstationary and non-Gaussian processes. principles and concepts of flow analysis. Linear random vibration theory. Crossing rates, Differential and finite control volume approach to ENME E4215x Theory of vibrations peak distributions, and response analysis of flow analysis. Dimensional analysis. Application of 3 pts. Lect: 3. Professor Betti. nonlinear structures to random loading. Major flow analysis: flow in pipes, external flow, flow in Frequencies and modes of discrete and continu- emphasis on simulation of various types of ran- open channels. ous elastic systems. Forced vibrations-steady- dom processes. Monte Carlo simulation. state and transient motion. Effect of damping. ENME E3332x A first course in finite elements Exact and approximate methods. Applications. ENME E6315x Theory of elasticity 3 pts. Lect: 3. Professor Fish. 3 pts. Lect: 3. Not offered in 2021–2022. Prerequisite(s): Senior standing or instructor’s per- ENME E4332x Finite element analysis, I Foundations of continuum mechanics. General mission. Recommended corequisite: differential 3 pts. Lect: 3. Professor Waisman. theorems of elasticity. Application to stress analy- equations. Focus on formulation and application Prerequisite(s): Mechanics of solids, structural sis and wave propagation. of the finite element to engineering problems analysis, elementary computer programming such as stress analysis, heat transfer, fluid flow, (MATLAB) is recommended, linear algebra and ENME E6320x Computational poromechanics and electromagnetics. Topics include finite ele- ordinary differential equations. Direct stiffness 3 pts. Lect: 3. Not offered in 2021–2022. ment formulation for one-dimensional problems, approach for trusses. Strong and weak forms Prerequisite(s): ENME E3332 or instructor’s such as trusses, electrical and hydraulic systems; for one-dimensional problems. Galerkin finite permission. A fluid infiltrating porous solid is a scalar field problems in two dimensions, such element formulation, shape functions, Gauss multiphase material whose mechanical behav- as heat transfer; and vector field problems, such quadrature, convergence. Multidimensional scalar ior is significantly influenced by the pore fluid. as elasticity and finally usage of the commercial field problems (heat conduction), triangular and Diffusion, advection, capillarity, heating, cooling, finite element program. Students taking ENME rectangular elements, Isoparametric formulation. and freezing of pore fluid, buildup of pore pres- E3332 cannot take ENME E4332. Multidimensional vector field problems (linear sure, and mass exchanges among solid and fluid elasticity). Practical FE modeling with commercial constituents all influence the stability and integrity ENME E4113x Advanced mechanics of solids software (ABAQUS). Computer implementation of of the solid skeleton, causing shrinkage, swelling, 3 pts. Lect: 3. Professor Yin. the finite element method. Advanced topics. Not fracture, or liquefaction. These coupling phe- Stress and deformation formulation in two-and open to undergraduate students. nomena are important for numerous disciplines, three-dimensional solids; viscoelastic and plas- including geophysics, biomechanics, and material tic material in one and two dimension energy ENME E4363y Multiscale computational sciences. Fundamental principles of porome- methods. science and engineering chanics essential for engineering practice and 3 pts. Lect: 3. Professor Fish. advanced study on porous media. Topics include Prerequisite(s): ENME E4332, elementary com- balance principles, Biot’s poroelasticity, mixture

ENGINEERING 2021–2022 theory, constitutive modeling of path independent ENME E6370y Turbulence theory and COURSES IN GRAPHICS 101 and dependent multiphase materials, numerical modeling methods for parabolic and hyperbolic systems, 3 pts. Lect: 3. Professor Giometto. GRAP E2005y Computer-aided engineering inf-sup conditions, and common stabilization pro- Prerequisite(s): ENME E3161 or equivalent, graphics cedures for mixed finite element models, explicit Ordinary and partial differential equations. 3 pts. Lect: 1.5. Lab: 2.5. Not offered in and implicit time integrators, and operator split- Turbulence phenomenology, spatial and temporal 2021–2022. ting techniques for poromechanics problems. scales in turbulent flows, statistical description, Prerequisite(s): MATH UN1101. Basic concepts filtering and Reynolds decomposition, equations needed to prepare and understand engineering ENME E6333y Finite element analysis, II governing the resolved flow, fluctuations and their drawings and computer-aided representations: 3 pts. Lect: 3. Professor Waisman. energetics, turbulence closure problem for RANS preparation of sketches and drawings, prepara- Prerequisite(s): ENME E4332. FE formulation and LES, two-equation turbulence models, and tion and transmission of graphic information. for beams and plates. Generalized eigenvalue second-moment closures. Lectures and demonstrations, hands-on computer- problems (vibrations and buckling). FE formula- aided graphics laboratory work. Term project. tion for time-dependent parabolic and hyperbolic ENME E8310x Advanced continuum problems. Nonlinear problems, linearization, mechanics GRAP E4005y Computer graphics in and solution algorithms. Geometric and material 3 pts. Lect: 3. Professor Dasgupta. engineering nonlinearities. Introduction to continuum mechan- Prerequisite(s): MECE E6422 and E6423. Open to 3 pts. Lect: 3. Professor Dasgupta. ics. Total and updated Lagrangian formulations. Ph.D. students and to M.S. students with instruc- Prerequisite(s): Any programming language and Hyperelasticity and plasticity. Special topics: tor’s permission. Review of continuum mechanics linear algebra. Numerical and symbolic (algebraic) fracture and damage mechanics, extended finite in Cartesian coordinates; tensor calculus and problem solving with Mathematica. Formulation element method. the calculus of variation; large deformations in for graphics application in civil, mechanical, and curvilinear coordinates; electricity problems and bioengineering. Example of two-and three-dimen- ENME E6364x Nonlinear computational applications. sional curve and surface objects in C++ mechanics and Mathematica; special projects of interest to 3 pts. Lect: 3. Not offered in 2021–2022. ENME E8320x Viscoelasticity and plasticity electrical and computer science. Prerequisite(s): ENME E4332 or equivalent, 4 pts. Lect: 3. Professor Dasgupta. elementary computer programming, linear alge- Prerequisite(s): ENME E6315 or equivalent, or bra. The formulations and solution strategies for instructor’s permission. Constitutive equations of finite element analysis of nonlinear problems are viscoelastic and plastic bodies. Formulation and developed. Topics include the sources of nonlin- methods of solution of the boundary value, prob- ear behavior (geometric, constitutive, boundary lems of viscoelasticity and plasticity. condition), derivation of the governing discrete equations for nonlinear systems such as large ENME E8323y Nonlinear vibrations displacement, nonlinear elasticity, rate indepen- 3 pts. Lect: 3. Not offered in 2021–2022. dent and dependent plasticity and other nonlinear Prerequisite(s): ENME E4215 or equivalent. Free constitutive laws, solution strategies for nonlinear and forced motion of simple oscillators with problems (e.g., incrementation, iteration), and nonlinear damping and stiffness. Exact, perturba- computational procedures for large systems of tion, iteration, and graphical methods of solution. nonlinear algebraic equations. Stability of motion. Chaotic vibrations.

ENGINEERING 2021–2022 102 COMPUTER ENGINEERING PROGRAM Administered by both the Electrical Engineering and Computer Science Departments through a joint Computer Engineering Committee. Student records are kept in the Electrical Engineering Department.

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

PROGRAM CHAIR Xiaofang Fred Jiang, Mingoo Seok, Martha A. Kim Associate Professor of Electrical Associate Professor of Electrical 469 CSB Engineering Engineering Ethan Katz-Bassett, Simha Sethumadhavan, COMPUTER ENGINEERING COMMITTEE Associate Professor of Electrical Associate Professor of Computer Science Luca Carloni, Engineering Kenneth L. Shepard, Professor of Computer Science Martha A. Kim, Professor of Electrical Engineering and Asaf Cidon, Associate Professor of Computer Science Biomedical 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

he computer engineering UNDERGRADUATE PROGRAM electrical engineering, or computer program is run jointly by the This undergraduate program engineering. For example, they could Computer Science and Electrical incorporates most of the core curricula take more advanced courses in VLSI, EngineeringT departments. It offers both communications theory, computer in both electrical engineering and 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 critical areas, which lie at the substantially overlaps both fields. Both and 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., CAD); Students will be prepared to work Most courses at the 3000-level and parallel and distributed systems on all aspects of the design of digital or above offered by the Computer (including architectures, programming, hardware, as well as on the associated Science and Electrical Engineering 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 Engineering Department maintains growing field of telecommunications. as well. If a department advertises student records and coordinates Students will have the prerequisites that one of its courses can be used advising appointments. to delve more deeply into either as a technical elective that does hardware or software areas, and enter not necessarily mean it will be graduate programs in computer science, approved as a technical elective in

ENGINEERING 2021–2022 103 COMPUTER ENGINEERING PROGRAM: FIRST AND SECOND YEARS EARLY-STARTING STUDENTS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

APMA E2000 (4) and E2001 (0) either semester MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) APMA E2101 (3)1

UN1401 (3) UN1402 (3) Lab UN1494 (3) or chem. lab UN1500 (3)

PHYSICS UN1601 (3.5) UN1602 (3.5) Lab UN1494 (3) or (three tracks, choose one) chem. lab UN1500 (3) UN2801 (4.5) UN2802 (4.5) Lab UN3081 (2) or chem. lab UN1500 (3)

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

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

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

UNIVERSITY CC1010 (3) either semester WRITING

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

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

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

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

ENGINEERING 2021–2022 104 COMPUTER ENGINEERING: THIRD AND FOURTH YEARS EARLY-STARTING STUDENTS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

ELEN E3331 (3) Electronic circuits COMS W4118 (3) Operating systems IEOR E3658 (3)1 or Probability COMS W3261 (3) COMS W4115 (3) Programming lang. Computer sci. theory CORE REQUIRED COMS W3157 (4) COURSES Advanced programming (Choose 3 of 6) ELEN E3201 (3.5) CSEE W4119 (3) Computer networks, EECS E4321 (3) Digital VLSI circuits, CSEE Circuit analysis W4823 (3) Advanced logic design, CSEE W4824 (3) Computer architecture, CSEE W4840 (3) Embedded systems, CSEE W4868 (3) System-on-chip platforms

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

TECH2 15 points required; see details within the text

Complete 27-point requirement; see page 9 (27-Point Nontechnical Requirement) NONTECH

ELECTIVES or seas.columbia.edu for details (administered by the advising dean)

TOTAL POINTS3 17.5 17 15 15­

For a discussion about programming languages used in the program, please see compeng.columbia.edu. 1 SIEO W3600, STAT GU4203, and STAT GU4001 can be used instead of IEOR E3658, but W3600 and GU4001 may not provide enough probability background for elective courses such as ELEN E3701. Students completing an economics minor who want such a background can take IEOR E3658 and augment it with IEOR E4307. 2 The total points of technical electives is reduced to 12 if APMA E2101 has been replaced by MATH UN2030 (formerly MATH E1210) and either APMA E3101 or MATH UN2010, or COMS W3251. 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.

the computer engineering program. one semester after that. For sample have a bachelor’s degree in computer There must be sufficient technical “early-starting” and “late-starting” engineering, computer science, or content and computer engineering programs, see the degree track charts. electrical engineering with at least a 3.2 connection within the entire 15 It must be emphasized that these GPA in technical courses. The Graduate points, so approval of some courses charts present examples only; actual Record Examination (GRE), General Test may depend on the other electives schedules may be customized in only, is required of all applicants. chosen. Economics courses cannot consultation with academic advisers. Students must take at least 30 points be used as technical electives. COMS of courses at Columbia University at W3101 /W3102 courses, and not-very- or above the 4000 level. These must GRADUATE PROGRAM technical courses within the school include at least 15 points from the The Computer Engineering Program of engineering, cannot be used as courses listed below that are deemed offers a course of study leading to the technical electives either. core to computer engineering. Other degree of Master of Science (M.S.). courses may be chosen with the prior The basic courses in the M.S. program Starting Early approval of a faculty adviser in the come from the Electrical Engineering Computer Engineering Program. Students are strongly encouraged and Computer Science Departments. to begin taking core computer M.S. students must complete Students completing the program are the professional development and engineering courses as sophomores. prepared to work (or study further) in They start with ELEN E1201: leadership course, ENGI E4000, as such fields as digital computer design, a graduation requirement. Doctoral Introduction to electrical engineering digital communications, and the design students will be enrolled in ENGI E6001– in the second semester of their first of embedded computer systems. 6004 and should consult their program year and may continue with other core Applicants are generally expected to for specific PDL requirements. courses

ENGINEERING 2021–2022 105 COMPUTER ENGINEERING PROGRAM: FIRST AND SECOND YEARS LATE-STARTING STUDENTS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

APMA E2000 (4) and E2001 (0) either semester MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) APMA E2101 (3)1

UN1401 (3) UN1402 (3) Lab UN1494 (3) or chem. lab UN1500 (3)

PHYSICS UN1601 (3.5) UN1602 (3.5) Lab UN1494 (3) or (three tracks, choose one) chem. lab UN1500 (3) UN2801 (4.5) UN2802 (4.5) Lab UN3081 (2) or chem. lab UN1500 (3)

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

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

UNIVERSITY CC1010 (3) either semester WRITING

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

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

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

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

ENGINEERING 2021–2022 106 COMPUTER ENGINEERING: THIRD AND FOURTH YEARS LATE-STARTING STUDENTS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

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

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

TECH4 15 points required; see details within the text

Complete 27-point requirement; see page 9 (27-Point Nontechnical Requirement) NONTECH

ELECTIVES or seas.columbia.edu for details (administered by the advising dean)

TOTAL POINTS5 15 18 15 18­

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

Core Computer Engineering Courses CSEE E6824: Parallel computer architecture of at least 2.7 must be maintained, CSEE W4119: Computer networks CSEE E6861: CAD of digital systems and all degree requirements must CSEE W4140: Networking laboratory CSEE E6863: Formal verification of hardware/ be completed within five years of the software systems EECS E4321: Digital VLSI circuits beginning of the first course credited CSEE E6868: Embedded scalable platforms EECS E4750: Hybrid comp. for sig. & data proc. toward the degree. EECS E4764: Iot—intelligent & connected sys. CSEE W4823: Advanced logic design The overall program must include at CSEE W4824: Computer architecture 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 points of research project may be taken EECS E6180: Modeling & performance eval 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 data analytics

ENGINEERING 2021–2022 COMPUTER SCIENCE 107 450 Computer Science, MC 0401 212-853-8400 cs.columbia.edu

CHAIR Gail E. Kaiser Martha Allen Kim LECTURERS IN SENIOR RESEARCH Luca Carloni John R. Kender Itsik Pe’er DISCIPLINE SCIENTISTS 466 Computer Science Tal Malkin Simha Sethumadhavan Daniel Bauer Gaston Ormazabal 212-853-8425 Kathleen R. McKeown Eugene Wu Tony Dear Bjarne Stroustrup Vishal Misra Junfeng Yang Nakul Verma Arthur Werschulz VICE CHAIR Shree Kumar Nayar Changxi Zheng Moti Yung Itsik Pe'er Jason Nieh JOINT 505 Computer Science Christos Papadimitriou ASSISTANT Andrew Blumberg ASSOCIATE RESEARCH Toniann Pitassi PROFESSORS Shih-Fu Chang SCIENTISTS DIRECTOR OF Kenneth A. Ross Josh Alman Feniosky Peña-Mora Yizheng Cheng UNDERGRADUATE Lydia Chilton Clifford Stein Giuseppe Di Guglielmo STUDIES Daniel S. Rubenstein Ronghui Gu Efsun Kayi Paul Blaer Henning G. Schulzrinne David Knowles AFFILIATES Shanghack Lee 703 CEPSR Rocco A. Servedio Baishakhi Ray Shipra Agrawal Paolo Mantovani 212-853-8441 Salvatore J. Stolfo Brian Smith Elham Azizi Hiroshi Sasaki Vladimir Vapnik Shuran Song Paolo Blikstein Eran Tromer DIRECTOR OF FINANCE Jeannette Wing Carl Vondrick Asaf Cidon AND ADMINISTRATION Mihalis Yannakakis Omri Weinstein Matei Ciocarlie EMERITUS TBA Richard Zemei Zhou Yu Noemie Elhadad Alfred V. Aho 450 Computer Science Henry Yuen Xiaofan Jiang Peter K. Allen 212-853-8401 ASSOCIATE Ethan Katz-Bassett Edward G. Coffman Jr. PROFESSORS SENIOR LECTURERS IN Hod Lipson Zvi Galil PROFESSORS Alexandr Andoni DISCIPLINE Liam Paninski Jonathan L. Gross Peter N. Belhumeur Elias Bareinboim Paul Blaer Barbara Tversky Steven M. Nowick Steven M. Bellovin Augustin Chaintreau Adam Cannon Venkat Stephen H. Unger David Blei Xi Chen Eleni Drinea Venkatasubramanian Henryk Wozniakowski Luca Carloni Stephen A. Edwards Ansaf Salleb-Aouissi Rebecca Wright Yechiam Yemini Steven K. Feiner Roxana Geambasu Jae Woo Lee Gil Zussman Luis Gravano Daniel Hsu Julia B. Hirschberg Suman Jana

he function and influence of is available in such areas as artificial systems. It houses several computer the computer is pervasive in intelligence, machine learning, computer clusters for research and student contemporary society. Today’s graphics, computer vision, robotics, use and several hundred research computersT process the daily transactions computational complexity and the systems, all supported by more than a of international banks, the data from analysis of algorithms, combinatorial petabyte of storage. Services offered to communications satellites, the images methods, computer architecture, the department utilize virtual machines in video games, and even the fuel and computer-aided digital design, (VMWare supporting more than 500 ignition systems of automobiles. computer communications, databases, instances) and containerization (100 Computer software is as mathematical models for computation, Docker containers). commonplace in education and optimization, and software systems. In addition, the department has recreation as it is in science and numerous individual laboratories with business. There is virtually no field or Laboratory Facilities specialized hardware dedicated to profession that does not rely upon The department has a dedicated particular research areas, including, but computer science for the problem-solving computing work space for students not limited to, robotics, computer vision, skills and the production expertise with dedicated workstations as well computer networks, computer security, required in the efficient processing as audiovisual equipment for group computer architecture, speech processing, of information. Computer scientists, meetings, specialized office hours, and machine learning, and natural language therefore, function in a wide variety of small seminars. The department also has processing. roles, ranging from pure theory and its own 120-seat lecture hall featuring design to programming and marketing. flexible seating, a dedicated podium UNDERGRADUATE PROGRAM The computer science curriculum computer, and presentation equipment, Computer science majors at Columbia at Columbia places strong emphasis as well as video conferencing study an integrated curriculum, both on theoretical computer science capabilities. partially in areas with an immediate and mathematics and on applied The department maintains its own relationship to the computer, such as aspects of computer technology. A dedicated Data Center for computational programming languages, operating broad range of upper-level courses research, storage, and administrative

ENGINEERING 2021–2022 108 COMPUTER SCIENCE PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

APMA E2000 (4) and MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) E2001 (0)

PHYSICS UN1401 (3) UN1402 (3) (three tracks, UN1601 (3.5) UN1602 (3.5) Chemistry or physics lab: choose one) UN2801 (4.5) UN2802 (4.5) PHYS UN1494 (3) or PHYS UN3081 (2) or CHEM UN1500 (3) or CHEMISTRY/ CHEM UN1403 (3) or higher or CHEM UN1507 (3) or BIOLOGY EEEB UN2001 (4) or UN2005 (4) or higher CHEM UN3085 (4) (choose one course) either semester

UNIVERSITY CC1010 (3) either semester WRITING

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

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

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

COMS W1004 (3) COMS W3134 (3) or COMS W3157 (4) Intro. to computer science COMS W3137 (4) Adv. programming COMPUTER or Data structures and SCIENCE COMS W1007 (3) and COMS W3251 (4) Object-oriented programming COMS W3203 (4) Computational either semester Discrete math linear algebra

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

systems, and computer architecture, at Columbia University Information strongly encouraged to arrange for partially in artificial intelligence and Technology (CUIT), which operates participation by consulting individual associated application areas such several computer labs at convenient faculty members and by attending the as computational biology, machine locations on the campus. Computer Science Research Fair held at learning, and robotics, and partially Upper-level students in computer the beginning of each semester. in theoretical computer science and science may assist faculty members Most graduates of the computer mathematics. Thus, students obtain the with research projects, particularly in science program at Columbia step background to pursue their interests the development of software. Ongoing directly into career positions in both in applications and in theoretical faculty projects span a wide range of computer science with industry or developments. research areas including computer government, or continue their education Practical experience is an essential science theory, graphics and user in graduate degree programs. Many component of the computer science interfaces, natural language processing choose to combine computer science program. Undergraduate students are and speech, security and privacy, with a second career interest by often involved in advanced faculty computational biology, software systems, taking additional programs in business research projects using state-of-the-art computer engineering, networking, administration, medicine, or other computing facilities. Qualified majors vision and robotics, machine learning, professional studies. sometimes serve as consultants and artificial intelligence. Students are For further information on the

ENGINEERING 2021–2022 109 COMPUTER SCIENCE: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

CSEE W3827 (3) Fund. of comp. systems REQUIRED COURSES and COMS W3261 (3) Computer sci. theory

NONTECH 3 points 6 points 3 points

TECH 6 points 12 points 9 points 9 points ELECTIVES

TOTAL POINTS 15–16 15 15 12 undergraduate computer science requirements will change as noted • Foundations of Computer Science program, please see the home page below. • Software Systems and the Quick Guide (cs.columbia.edu/ • Digital Systems education/undergraduate/). The following are required courses • Intelligent Systems toward the CS Core for the class of • Applications The CS Major Requirements 2023 and beyond: • Vision, Graphics, Interactions, and The Undergraduate program consists 1. COMS W1004 or W1007 (3) Robotics of a minimum of 63 or 64 points and 2. COMS W3134 (3) or W3137 (4) includes the following: ENGI E1006 3. COMS W3157 (4) Undergraduate Thesis which is a prerequisite to the CS 4. COMS W3203 (4) A student may, with adviser approval, major, the CS Core consisting of 7-8 5. COMS W3251 (4) choose to complete a thesis in place classes (24-25 points), 7 Track courses 6. COMS W3261 (3) of up to 6 points of track elective or (21 points), and 15 points of general 7. CSEE W3827 (3) general technical elective points. A technical electives. thesis consists of an independent Note: All courses toward the CS The following are required courses theoretical or experimental investigation major must be taken for a letter grade. A toward the CS Core for the class of of an appropriate problem in computer maximum of one course worth no more 2022 and earlier: science carried out under the than 4 points passed with a grade of D 1. COMS W1004 or W1007 (3) supervision of a Computer Science may be counted towards the major. 2. COMS W3134 (3) or W3137 (4) Department faculty member. A formal Any course exceptions to the noted 3. COMS W3157 (4) written report is mandatory and an oral requirements toward the CS major, 4. COMS W3203 (3) presentation may also be required. all thesis, projects, special topics, and 5. COMS W3261 (3) general technical electives must be 6. MATH UN2010 or UN2020 or General Technical Electives APMA E2101 or E3101 (3) or COMS approved by the faculty adviser in writing. An additional 15 points of adviser W3251 (4) approved general technical electives 7. CSEE W3827 (3) Prerequisite to the CS Major at the 3000 level or above are also 8. STAT GU4001 or IEOR E4150 (3) ENGI E1006 Introduction to computing required. These general technical for engineers and applied scientists. electives should be in mathematics, All CS majors are required to take this Tracks science, engineering, or closely related course and it is recommended that they In addition, an advanced track is disciplines and should be approved by do so in their first or second semester. available by invitation for qualified your faculty adviser. students who desire an extra The Computer Science Core opportunity for advanced learning. Advanced Placement Any course exceptions to the track The core of the major consists of 7 or Students who pass the Computer requirements must be approved by 8 courses plus one prerequisite course Science Advanced Placement (AP) Exam the faculty adviser. All thesis, projects, for a total of 8 or 9 courses. These with a 4 or 5 will receive 3 points of special topics, and general technical courses provide the foundation for the credit and an exemption from COMS electives must also be approved by the tracks and advanced courses. Beginning W1004. faculty adviser. The 6 predefined tracks with the class of 2023 the CS Core are as follows:

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

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

APMA E2000 (4) and MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) E2001 (0)

PHYSICS UN1401 (3) UN1402 (3) (three tracks, UN1601 (3.5) UN1602 (3.5) Chemistry or physics lab: choose one) UN2801 (4.5) UN2802 (4.5) PHYS UN1494 (3) or PHYS UN3081 (2) or CHEM UN1500 (3) or CHEMISTRY/ CHEM UN1403 (3) or higher or CHEM UN1507 (3) or BIOLOGY EEEB UN2001 (4) or UN2005 (4) or higher CHEM UN3085 (4) (choose one course) either semester

UNIVERSITY CC1010 (3) either semester WRITING

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

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

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

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

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

Track 1: Foundations of CS Track COMS W4203: Graph theory COMS E6232: Analysis of algorithms, II The foundations track is suitable MATH GU4032: Fourier analysis MATH GR6238: Enumerative combinatorics MATH GU4041: Introduction to modern algebra I COMS E6253: Advanced topics in computational for students who are interested in MATH GU4042: Introduction to modern algebra II learning theory algorithms, computational complexity, MATH GU4061: Introduction to modern analysis I COMS E6261: Advanced cryptography and other areas of theoretical Computer MATH GU4155: Probability theory IEOR E6400: Scheduling: deterministic models Science. COMS W4252: Computational learning theory IEOR E6603: Combinatorial optimization COMS W4261: Introduction to cryptography IEOR E6606: Advanced topics in network flows REQUIRED: 6 points APMA E4300: Numerical methods IEOR E6608: Integer programming CSOR W4231: Analysis of algorithms IEOR E4407: Game theoretic models of operation IEOR E6610: Approximation algorithms COMS W4236: Introduction to computational PHIL GU4431: Set theory EEOR E6616: Convex optimization complexity CSPH GU4801: Mathematical logic I IEOR E6613: Optimization I (4.5) ELECTIVES: 15 points from the following list: CSPH GU4802: Mathematical logic II: IEOR E6614: Optimization II (4.5) incompleteness Stochastic models I Any COMS BC3xxx course (with adviser approval) IEOR E6711: Projects in computer science* Stochastic models II MATH UN3020: Number theory and cryptography COMS W4901: IEOR E6712: Special topics in Information theory MATH UN3025: Making, breaking codes COMS W4995-W4996: ELEN E6717: computer science, I and II (with Algebraic coding theory COMS W3902: Undergraduate thesis* ELEN E6718: adviser approval) COMS W3998: Projects in Computer Science*

ENGINEERING 2021–2022 111 EFFECTIVE CLASS OF 2022 AND PRIOR COMPUTER SCIENCE: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

APMA E2101 (3) or MATH UN2010 (3) or COMS W3251 (4) and REQUIRED COMS W3261 (3) COURSES Computer sci. theory and STAT GU4001(3) or IEOR E4150 (3) Prob. and stat.

NONTECH 3 points 6 points 3 points

TECH 6 points 12 points 9 points 9 points ELECTIVES

TOTAL POINTS 15–16 15 15 12

The primary programming languages for the undergraduate major are Python, C, and Java, and students are expected to learn all three at an early stage. The language for COMS W1004-W3134 and COMS W1007-3137 is Java. COMS W1004 may be waived for students who have scored 4 or 5 on the AP computer science A exam.

ELEN E6970: Resource allocation and networking COMS W3998: Undergraduate projects in COMS W4733: Computational aspects of robotics games computer science* COMS W4771: Machine learning COMS E6998-E6999: Topics in computer Any COMS W41xx course ELECTIVES: 12 points required science, I and II (with adviser COMS W4444: Programming and problem solving approval)* Any COMS W48xx course Up to 12 points from the following list: COMS W4901: Projects in computer science* Any COMS BC3xxx course (with adviser approval) * With adviser approval, may be repeated for COMS W4995-W4996: Special topics in COMS W4165: Pixel processing credit computer science, I and II (with COMS W4252: Computational learning theory Note: No more than 6 points of project/thesis adviser approval) Any COMS W47xx course if not used as a courses (COMS W3902, W3998, W4901) can Any COMS E61xx course (with adviser approval required course count toward the track. Any COMS E68xx course (with adviser approval) COMS W4995-W4996: Special topics in COMS E6998-E6999: Topics in computer computer science, I and II (with Students who declared their Computer Science science, I and II (with adviser adviser approval) major prior to Fall 2016 may also count COMS approval)* Any COMS W67xx course W4241, W4205, W4281, W4444, W4771, and COMS E6998-E6999: Topics in computer W4772 as elective courses. * With adviser approval, may be repeated for science, I and II (with adviser credit approval)* Track 2: Software Systems Track Note: No more than 6 points of project/thesis Up to 6 points from the following list: courses (COMS W3902, W3998, W4901) can The software systems track is for COMS W3902: Undergraduate thesis* count toward the track. students interested in networks, COMS W3998: Undergraduate projects in programming languages, operating computer science* systems, software engineering, Track 3: Intelligent Systems Track COMS W4901: Projects in computer science* The intelligent systems track is for databases, security, and distributed Up to 3 points from the following list: systems. students interested in machine COMS W4111: Database systems learning, robots, and systems capable REQUIRED: 9 points COMS W4160: Computer graphics of exhibiting “human-like” intelligence. COMS W4115: Programming languages and COMS W4170: User interface design translators A total of seven required breadth and COMS W4999: Computing and the humanities COMS W4118: Operating systems elective courses are to be chosen from * With adviser approval, may be repeated for CSEE W4119: Computer networks the following schedule. credit ELECTIVES: 12 points from the following list: REQUIRED: 9 Points from: Note: No more than 6 points of project/thesis COMS W3107: Clean object-oriented design COMS W4701: Artificial intelligence courses (COMS W3902, W3998, W4901) can Any COMS BC3xxx course (with adviser approval) COMS W4705: Natural language processing count toward the track. COMS W3902: Undergraduate thesis* COMS W4706: Spoken language processing COMS BC3930: Creative embedded systems COMS W4731: Computer vision I: first principles

ENGINEERING 2021–2022 112 Track 4: Applications Track COMS W4771: Machine learning Track 7: Advanced The applications track is for students COMS W4901: Projects in computer science* The advanced track of the B.S. in COMS W4995-W4996: Special topics in interested in the implementation of Computer Science provides extra computer science, I and II (with interactive multimedia applications for adviser approval) opportunity for advanced learning. the internet and wireless networks. COMS W4995: Special topics in CS (video game It comprises accelerated versions of the other six tracks. Entry is only by REQUIRED: 6 points technology) Any COMS E691x course (with adviser approval) collective faculty invitation, extended to COMS W4115: Programming languages and COMS E6998-E6999: Topics in computer translators students who have already completed science, I and II (with adviser COMS W4170: User interface design the core courses and the required approval)* courses for one of those tracks. ELECTIVES: 15 points from the following list: * With adviser approval, may be repeated for REQUIRED TRACK COURSES COMS W3107: Clean object-oriented design credit Any COMS BC3xxx course (with adviser approval) A student designates one of the six other track COMS BC3420: Privacy in a networked world Note: No more than 6 points of project/thesis areas and completes the set of required track COMS BC3430: Computational sound courses (COMS W3902, W3998, W4901) can courses for that track, prior to entry into the COMS BC3930: Creative embedded systems count toward the track. Advanced Track. There are two or three courses, COMS W3902: Undergraduate thesis* depending on the designated area. COMS W3998: Undergraduate projects in Track 6: Digital Systems Track ELECTIVES computer science* The digital systems track is for students Any COMS W41xx course At least 6 points of 4000-level lecture courses interested in working at the interface of Any COMS W47xx course from the menu for the designated track, plus 6 COMS W4901: Projects in computer science* hardware and software. Subjects include points of 6000-level courses in the designated COMS W4995-W4996: Special topics in digital design, computer architecture track area. computer science, I and II (with (both sequential and parallel) and ​THESIS adviser approval) embedded systems. There is a required 6-point senior thesis. Any COMS E69xx course (with adviser approval) COMS E6998-E6999: Topics in computer REQUIRED: 3 points INVITATION science, I and II (with adviser CSEE W4824: Computer architecture Only the top 20 percent of computer science approval)* Plus 3 points from: majors in course performance in computer science courses will be considered for invitation * With adviser approval, may be repeated for CSEE W4823: Advanced logic design during the junior year. (A student in the advanced credit CSEE W4840: Embedded systems track who does not maintain this status may be CSEE E4868: System-on-chip platforms Note: No more than 6 points of project/thesis required to return to his or her previously selected courses (COMS W3902, W3998, W4901) can Plus 3 points from: track area.) count toward the track. COMS W4115: Programming languages and translators Track 5: Vision, Interaction, Graphics, COMS W4118: Operating systems GRADUATE PROGRAMS and Robotics Track COMS W4130: Parallel programming The Department of Computer Science The vision, interaction, graphics, ELECTIVES: 12 points from the following list: offers graduate programs leading to the degree of Master of Science and and robotics track focus on visual Any COMS BC3xxx course (with adviser approval) information with topics in vision, COMS BC3930: Creative embedded systems the degree of Doctor of Philosophy. graphics, human-computer interaction, COMS W3902: Undergraduate thesis* The Graduate Record Examination robotics, modeling, and learning. COMS E3998: Undergraduate projects in (GRE) is required for admission to Students learn about fundamental ways computer science* the department's graduate programs. Any COMS/CSEE W41xx course in which visual information is captured, Applicants for September admission Any COMS/CSEE W48xx course should take the GREs by October of the manipulated, and experienced. COMS E4901: Projects in computer science preceding year. Applicants for January REQUIRED: 6 points from: COMS W4995-W4996: Special topics in computer science, I and II (with admission should take these exams by COMS W4160: Computer graphics adviser approval) April of the preceding year. COMS W4731: Computer vision I: first principles CSEE E6824: Parallel computer architecture* COMS W4167: Computer animation M.S. students must complete CSEE E6847: Distributed embedded systems* the professional development and ELECTIVES: 15 points from the following list: CSEE E6861: CAD of digital systems** leadership course, ENGI E4000, as Any COMS BC3xxx course (with adviser approval) CSEE E6868: Embedded scalable platforms** a graduation requirement. Doctoral COMS E6998-E6999: Topics in computer COMS W3902: Undergraduate thesis* students will be enrolled in ENGI E6001– Undergraduate projects in science, I and II (with adviser COMS W3998:  6004 and should consult their program computer science* approval)* for specific PDL requirements. COMS W4162: Advanced computer graphics * With adviser approval, may be repeated for COMS W4165: Pixel processing credit COMS W4167: Computer animation **With adviser approval. M.S. in Computer Science Program COMS W4170: User interface design The Master of Science (M.S.) program Note: No more than 6 points of project/thesis COMS W4172: 3D user interface design is intended for students with a COMS W4701: Artificial intelligence courses (COMS W3902, W3998, W4901) can bachelor's degree in Computer COMS W4733: Computational aspects of robotics count toward the track. COMS W4735: Visual interfaces to computers Science or a strongly related field who

ENGINEERING 2021–2022 wish to broaden and deepen their Ph.D. students spend at least half of their backgrounds, including those without 113 understanding of computer science. time on research under the direction of programming experience, the opportunity Columbia University and the New York their faculty adviser from their first day to acquire the knowledge and skills City environment provide excellent in the program and devote themselves necessary to build careers in technology. career opportunities with multiple full time to research after coursework Admitted students will first take a industries. The program provides a and other preliminaries have been total of five undergraduate courses unique opportunity to develop leading- completed. Ph.D. students are also (the bridge curriculum) over two to edge in-depth knowledge of specific expected to participate in departmental three semesters, which will build the computer science disciplines. and laboratory activities full time on necessary foundation of programming Students in the M.S. program must campus throughout the program, and mathematical skills. There is complete a total of 30 points with except possibly for summer internships flexibility for both scheduling and a GPA of at least 2.7. Every student elsewhere, and the department does not the choice of courses depending selects a track that focuses on a consider admission of part-time Ph.D. on a student's prior experience and particular field of computer science. students. Further information is available concurrent obligations. Students will also There are currently eight predefined at cs.columbia.edu/education/phd/. be closely advised during this process in M.S. tracks: Computational Biology; order to prepare for M.S. track selection. Computer Security; Foundations of Once the bridge is completed with an Computer Science; Machine Learning; DUAL DEGREE PROGRAM IN overall 3.3 GPA or higher, students are Natural Language Processing; Network JOURNALISM AND COMPUTER then eligible for an automatic transfer Systems; Software Systems; Vision, SCIENCE into the M.S. in Computer Science Graphics, Interaction, and Robotics. The Graduate School of Journalism program. Further information is available Every track has a set of required and the School of Engineering and at cs.columbia.edu/ms-bridge/. courses and a wide range of elective Applied Science offer a dual degree courses that allow the students flexibility program leading to the M.S. degree in in designing their program according Journalism from the Graduate School COURSES IN COMPUTER to their interests, under the guidance of Journalism and the M.S. degree in SCIENCE of a faculty adviser. Besides the eight Computer Science from the School of In the listing below, the designator predefined tracks, there is also the Engineering and Applied Science. COMS (Computer Science) is option of a M.S. Personalized track for Admitted students enroll for a students who want to study an area of understood to precede all course computer science that is not covered by total of four semesters consisting numbers for which no designator is one of the eight tracks, and the option of 27 points of Computer Science indicated. NOTE: Students may receive of the M.S. Thesis track for students coursework in which an overall 2.7 credit for only one of the following two who want to do extensive research GPA must be maintained and of 37 courses: COMS W1004 and W1005. in a subfield and write an M.S. thesis, points of Journalism coursework. In Likewise, students may receive credit for under the supervision of a faculty addition to taking classes already only one of the following three courses: member. Students in all the tracks are offered at the two schools, students COMS W3134, W3136, or W3137. encouraged to pursue research if they will take Frontiers of computational COMS W1001x or y Introduction to wish, and many participate in research journalism, a course designed information science projects with the faculty. The faculty in specifically for the dual program. 3 pts. Lect: 3. Instructor to be announced. the department conduct research in all The course will teach students about Basic Introduction to concepts and skills in areas of computer science. For detailed the impact of digital techniques on Information Sciences: human-computer interfaces, information on the M.S. program, please journalism; the emerging role of representing information digitally, organizing and searching information on the internet, principles see cs.columbia.edu/education/ms/. citizens in the news process; the of algorithmic problem solving, introduction to influence of social media; and the database concepts, introduction to programming Ph.D. in Computer Science Program changing business models that will in Python. The primary focus of the doctoral support newsgathering. Students COMS W1002x Computing in context program is research, with the philosophy will use a hands-on approach to 4 pts. Lect: 4. Professor Cannon. that students learn best by doing— delve deeply into information design, Introduction to elementary computing concepts beginning as apprentices and becoming focusing on how to build a site, and Python programming with domain-specific junior colleagues working with faculty on section, or application from concept applications. Shared CS concepts and Python scholarly research projects. The faculty to development, ensuring the editorial programming lectures with track-specific sections. Track themes will vary but may include computing in the department conduct research goals are kept uppermost in mind. for the social sciences, computing for economics in all areas of computer science. The and finance, digital humanities, and more. degree of Doctor of Philosophy requires Intended for nonmajors. Students may receive CS@CU MS BRIDGE PROGRAM IN a dissertation based on the candidate's credit for only one of the following two courses: COMPUTER SCIENCE original research, which is supervised ENGI E1006 or COMS W1002. by a faculty member, and all students in The CS@CU MS Bridge Program in the Ph.D. program are actively engaged Computer Science offers prospective in research throughout the program. applicants from noncomputer science

ENGINEERING 2021–2022 114 COMS W1004x and y Introduction to visualization using simple computer programming. linked lists, C programming in UNIX environment, computer science and programming in Java Shares lectures with ECBM E4060, but the work object-oriented programming in C++, trees, 3 pts. Lect: 3. Professor Cannon. requirements differ somewhat. graphs, , hash tables. Due A general introduction to computer science for to significant overlap, students may only receive science and engineering students interested in COMS W3101x and y Programming languages credit for either COMS W3134, W3136, or W3137. majoring in computer science or engineering. 1 pt. Lect: 1. Members of the faculty. Covers fundamental concepts of computer Prerequisite(s): Fluency in at least one COMS W3137y Honors data structures and science, algorithmic problem-solving capabilities, programming language. Introduction to a algorithms and introductory Java programming skills. programming language. Each section is 4 pts. Lect: 3. Professor Blaer. Assumes no prior programming background. devoted to a specific language. Intended only Prerequisite(s): COMS W1004 or W1007. Columbia University students may receive credit for those who are already fluent in at least one Corequisite: COMS W3203. An honors for only one of the following two courses: W1004 programming language. Sections may meet for introduction to data types and structures: arrays, or W1005. one hour per week for the whole term, for three stacks, singly and doubly linked lists, queues, hours per week for the first third of the term, or trees, sets, and graphs. Programming techniques COMS W1005x or y Introduction to computer for two hours per week for the first six weeks. for processing such structures: sorting and science and programming in MATLAB May be repeated for credit if different languages searching, hashing, garbage collection. Storage 3 pts. Lect: 3. Professor Blaer. are involved. management. Design and analysis of algorithms. A general introduction to computer science Taught in Java. Note: Due to significant overlap, COMS W3102x and y Development concepts, algorithmic problem-solving students may receive credit for only one of the capabilities, and programming skills in MATLAB. technologies following three courses: COMS W3134, W3136, Assumes no prior programming background. 1–2 pts. Lect: 2. Lab: 0-2. Members of the or W3137. Columbia University students may receive credit faculty. for only one of the following two courses: W1004 Prerequisite(s): Fluency in at least one COMS W3157x and y Advanced programming or W1005. programming language. Introduction to 4 pts. Lect: 4. Professor Lee. software development tools and environments. Prerequisite(s): Two terms of programming ENGI E1006x and y Introduction to computing Each section is devoted to a specific tool or experience. COMS W3134 or W3137. for engineers and applied scientists environment. One-point sections meet for two Recommended: Data Structures. C programming 3 pts. Lect: 3. Professor Salleb-Aouissi. hours each week for half a semester, and two- language and Unix systems programming. Also An interdisciplinary course in computing point sections include an additional two-hour lab. covers Git, Make, TCP/IP networking basics, C++ intended for first year SEAS students. Introduces fundamentals. computational thinking, algorithmic problem COMS W3107x Clean object-oriented design COMS W3203x and y Discrete structures in solving and Python programming with 3 pts. Lect: 3. Professor Kender. applications in science and engineering. Assumes Prerequisite(s): COMS W1004 or instructor's mathematics and probability no prior programming background. permission. May not take for credit if already 4 pts. Lect: 3. Professor Salleb-Aouissi. received credit for COMS W1007. A course in Prerequisite(s): MATH UN1102 or UN1201 or COMS W1007x Honors introduction to designing, documenting, coding, and testing robust APMA E2000 and COMS W1002 or W1004 or computer science computer software, according to object-oriented W1007 or ENGI E1006. Logic and formal proofs, 3 pts. Lect: 3. Professor Kender. design patterns and clean coding practices. sets and relations, advanced proof techniques, Prerequisite(s): AP Computer Science with Taught in Java. Object-oriented design principles number theory and modular arithmetic, graph a grade of 4 or 5 or similar experience. An include: use cases; CRC; UML; javadoc; patterns theory, counting and basic probability, conditional honors-level introduction to computer science, (adapter, builder, command, composite, decorator, probability and Bayes rule, random variables, intended primarily for students considering a facade, factory, iterator, lazy evaluation, observer, expectation and variance, central limit theorem, major in computer science. Computer science singleton, strategy, template, visitor); design by probability distributions (Gaussians, binomial, and as a science of abstraction. Creating models for contract; loop invariants; interfaces and inheritance geometric). reasoning about and solving problems. The basic hierarchies; anonymous classes and null objects; COMS W3210x or y Scientific computation elements of computers and computer programs. graphical widgets; events and listeners; Java's 3 pts. Lect: 3. Instructor to be announced. Implementing abstractions using data structures Object class; generic types; reflection; timers, Prerequisite(s): Two terms of calculus. Introduction and algorithms. Taught in Java. threads, and locks. to computation on digital computers. Design COMS W1404x and y Emerging scholars COMS W3134x and y Data structures in Java and analysis of numerical algorithms. Numerical program seminar 3 pts. Lect: 3. Professor Blaer. solution of equations, integration, recurrences, 1 pt. Sem: 1. Professor Cannon. Prerequisite(s): COMS W1004 or knowledge of chaos, differential equations. Introduction to Corequisite: COMS W1004/1007 or ENGI E1006. Java. Data types and structures: arrays, stacks, Monte Carlo methods. Properties of floating point Enrollment with instructor permission only. singly and doubly linked lists, queues, trees, arithmetic. Applications to weather prediction, Peer-led weekly seminar intended for first- and sets, and graphs. Programming techniques computational finance, computational science, second-year undergraduates considering a major for processing such structures: sorting and and computational engineering. in computer science. Pass/fail only. searching, hashing, garbage collection. Storage management. Rudiments of the analysis of COMS W3251x and y Computational linear ECBM E3060x Introduction to genomic algorithms. Taught in Java. Note: Due to algebra information science and technology significant overlap, students may receive credit 4 pts. Lect: 3. Professor Dear. 3 pts. Lect: 3. Professor Anastassiou. for only one of the following three courses: COMS Prerequisite(s): MATH UN1102 or UN1201 or APMA Introduction to the information system W3134, W3136, or W3137. E2000 and COMS W1002 or W1004 or W1007 paradigm of molecular biology. Representation, or ENGI E1006. Functions and compositions. organization, structure, function and manipulation COMS W3136y Data structures with C/C++ Vectors and linear functions, matrices and linear of the biomolecular sequences of nucleic 4 pts. Lect: 3. Professor Lee. transforms, inverses and Gaussian elimination. acids and proteins. The role of enzymes and Prerequisite(s): COMS W1004, W1005, W1007, Vector spaces, bases, subspaces, and dimension. gene regulatory elements in natural biological or ENGI E1006. A second programming Inner products, norms, and orthogonal functions as well as in biotechnology and course intended for nonmajors with at least projections. Eigenvectors and eigenvalues, genetic engineering. Recombination and one semester of introductory programming spectral decomposition. Quadratic forms, and other macromolecular processes viewed as experience. Basic elements of programming in singular value decomposition. Note: Previously mathematical operations with simulation and C and C++, array-based data structures, heaps, offered for 3 points.

ENGINEERING 2021–2022 COMS W3261x and y Computer science COMS E3999x, y or s Fieldwork and cloud systems. Abstractions, design, 115 theory 1–2 pts. Members of the faculty. and implementation techniques that enable 3 pts. Lect: 3. Professor Malkin. Prerequisite(s): Obtained internship and approval the building of fast, scalable, fault-tolerant Prerequisite(s): COMS W3203. Corequisites: from a faculty adviser. May be repeated for distributed systems. Topics include distributed COMS W3134, W3136, or W3137. Regular credit, but no more than 3 total points may be communication models (e.g., sockets, remote languages: deterministic and nondeterministic used toward the 128-credit degree requirement. procedure calls, distributed shared memory), finite automata, regular expressions. Context- Only for SEAS computer science undergraduate distributed synchronization (clock synchronization, free languages: context-free grammars, students who include relevant off-campus work logical clocks, distributed mutex), distributed file push-down automata. Turing machines, the experience as part of their approved program of systems, replication, consistency models, fault Chomsky hierarchy, and the Church-Turing study. Final report and letter of evaluation may tolerance, distributed transactions, agreement thesis. Introduction to complexity theory and be required. May not be used as a technical or and commitment, Paxos-based consensus, NP-completeness. nontechnical elective. May not be taken for pass/ MapReduce infrastructures, scalable distributed fail credit or audited. databases. Combines concepts and algorithms COMS W3410y Computers and society with descriptions of real-world implementations at 3 pts. Lect: 3. Professor Bellovin. ECBM E4060x Introduction to genomic Google, Facebook, Yahoo, Microsoft, LinkedIn etc. Broader impact of computers. Social networks information and privacy. Employment, intellectual property, 3 pts. Lect: 3. Professor Anastassiou. COMS W4115x and y Programming languages and the media. Science and engineering ethics. Introduction to the information system and translators Suitable for nonmajors. paradigm of molecular biology. Representation, 3 pts. Lect: 3. Professor Edwards or Ray. organization, structure, function, and manipulation Prerequisite(s): COMS W3134, W3136, or W3137 CSEE W3827x and y Fundamentals of of the biomolecular sequences of nucleic (or equivalent), W3261, and CSEE W3827, or computer systems acids and proteins. The role of enzymes and instructor’s permission. Modern programming 3 pts. Lect: 3. Professor Kim or Rubenstein. gene regulatory elements in natural biological languages and compiler design. Imperative, Prerequisite(s): An introductory programming functions as well as in biotechnology and object-oriented, declarative, functional, course. Fundamentals of computer organization genetic engineering. Recombination and and scripting languages. Language syntax, and digital logic. Boolean algebra, Karnaugh other macromolecular processes viewed as control structures, data types, procedures maps, basic gates and components, flip-flops mathematical operations with simulation and and parameters, binding, scope, run-time and latches, counters and state machines, basics visualization using simple computer programming. organization, and . of combinational and sequential digital design. Shares lectures with ECBM E3060, but the work Implementation of language translation tools Assembly language, instruction sets, ALUs, requirements differ somewhat. including compilers and interpreters. Lexical, single-cycle and multi-cycle processor design, syntactic, and semantic analysis; code generation; introduction to pipelined processors, caches, and COMS W4111x and y Introduction to introduction to code optimization. Teams virtual memory. databases implement a language and its compiler. 3 pts. Lect: 3. Professor Gravano. COMS W3902x and y Undergraduate thesis Prerequisite(s): COMS W3134, W3136, or W3137, COMS W4117x or y Compilers and interpreters 1–6 pts. Members of the faculty. or instructor’s permission. Covers definition of 3 pts. Lect: 3. Prerequisite(s): Agreement by faculty member database systems, effective design of databases, Prerequisite(s): COMS W4115 or instructor’s to serve as thesis adviser. An independent querying databases, and developing applications permission. Continuation of COMS W4115, with theoretical or experimental investigation by an using databases. Includes: entity-relationship broader and deeper investigation into the undergraduate major of an appropriate problem modeling, logical design of relational databases, design and implementation of contemporary in computer science carried out under the relational algebra, SQL, database security, language translators, be they compilers or supervision of a faculty member. A formal written and an overview of query optimization and interpreters. Topics include parsing, semantic report is mandatory and an oral presentation may transaction processing. Additional topics: NoSQL, analysis, code generation and optimization, run- also be required. May be taken over more than graph, object-relational, cloud databases, data time environments, and compiler-compilers. A one term, in which case the grade is deferred preparation, and cleaning of real-world data. programming project is required. until all 6 points have been completed. Consult Offers both programming and non-programming the department for section assignment. homework and projects, to accommodate COMS W4118x and y Operating systems, I different programming skills and backgrounds. 3 pts. Lect: 3. Professor Lee or Nieh. COMS W3995x or y Special topics in Prerequisite(s): CSEE W3827 and knowledge of computer science COMS W4112y Database system C and programming tools as covered in W3136, 3 pts. Lect: 3. implementation W3157, or W3101, or instructor’s permission. Prerequisite(s): Instructor’s permission. Consult 3 pts. Lect: 2.5. Professor Ross. Design and implementation of operating systems. the department for section assignment. Special Prerequisite(s): COMS W4111; fluency in Java or Topics include process management, process topics arranged as the need and availability arise. C++. CSEE W3827 is recommended. The principles synchronization and interprocess communication, Topics are usually offered on a one-time basis. and practice of building large-scale database memory management, virtual memory, interrupt Since the content of this course changes each management systems. Storage methods and handling, processor scheduling, device time it is offered, it may be repeated for credit. indexing, query processing and optimization, management, I/O, and file systems. Case study COMS W3998x and y Undergraduate projects materialized views, transaction processing of the UNIX operating system. A programming in computer science and recovery, object-relational databases, project is required. parallel and distributed databases, performance 1–3 pts. Members of the faculty. CSEE W4119x and y Computer networks considerations. Programming projects are Prerequisite(s): Approval by a faculty member 3 pts. Lect: 3. Professor Katz-Bassett. required. who agrees to supervise the work. Independent Prerequisite(s): Comfort with basic probability project involving laboratory work, computer COMS W4113x Fundamentals of large-scale and programming fluency in Python, C++, Java, or programming, analytical investigation, or distributed systems Ruby. Introduction to computer networks and the engineering design. May be repeated for credit, 3 pts. Lect: 3. Professor Geambasu. technical foundations of the internet, including but not for a total of more than 3 points of Prerequisite(s): COMS W3134, W3136, or W3137. applications, protocols, local area networks, degree credit. Consult the department for section COMS W3157 or good working knowledge of C algorithms for routing and congestion control, assignment. and C++. COMS W4118 or CSEE W4119. Design security, elementary performance evaluation. and implementation of large-scale distributed Several written and programming assignments required.

ENGINEERING 2021–2022 116 CSEE W4121y Computer systems for data spline curves, graphics systems such as OpenGL, Firewalls, virtual private networks, viruses. Mobile science lighting and shading, and global illumination. and app security. Usable security. 3 pts. Lect: 3. Professor Cidon. Significant implementation is required: the final Note: May not earn credit for both W4181 and Prerequisite(s): Background in Computer System project involves writing an interactive 3D video W4180 or W4187. Organization and good working knowledge of C/ game in OpenGL. C++. Corequisites: CSOR W4246, STAT GU4203, COMS W4182y Security II or equivalent approved by faculty adviser. COMS W4162x or y Advanced computer 3 pts. Lect: 3. Professor Bellovin. Introduction to computer distributed systems graphics Prerequisite(s): COMS W4181, COMS W4118, with emphasis on warehouse scale computing 3 pts. Lect: 3. Professor Zheng. CSEE W4119. Advanced security. Centralized, systems. Topics include fundamental tradeoffs Prerequisite(s): COMS W4160 or equivalent, distributed, and cloud system security. in computer systems, hardware and software or instructor’s permission. A second course in design choices. Hardware techniques for exploiting instruction-level computer graphics covering more advanced and software security techniques. Security testing parallelism, data-level parallelism and task level topics including image and signal processing, and fuzzing. Blockchain. Human security issues. parallelism, scheduling, caching, prefetching, geometric modeling with meshes, advanced Note: May not earn credit for both W4182 and network and memory architecture, latency image synthesis including ray tracing and global W4180 or W4187. and throughput optimizations, specializations, illumination, and other topics as time permits. Emphasis will be placed both on implementation COMS W4186x Malware analysis and reverse and introduction to programming data center engineering computers. of systems and important mathematical and geometric concepts such as Fourier analysis, 3 pts. Lect: 3. Lab 3. Professor Sikorski. COMS W4130x Principles and practice of mesh algorithms and subdivision, and Monte Prerequisite(s): COMS W3157 or equivalent; CSEE parallel programming Carlo sampling for rendering. Note: Course will be W3827. Hands-on analysis of malware. How 3 pts. Lect: 2.5. Professor Kim. taught every two years. hackers package and hide malware and viruses Prerequisite(s): Experience in Java, basic to evade analysis. Disassemblers, debuggers, and understanding of analysis of algorithms. COMS COMS W4167x or y Computer animation other tools for reverse engineering. Deep study of W3134, W3136, or W3137 (or equivalent). 3 pts. Lect: 3. Members of the faculty. Windows Internals and x86 assembly. Prerequisite(s): Multivariable calculus, linear Principles of parallel software design. Topics COMS W4203y Graph theory include task and data decomposition, load- algebra, C++ programming proficiency. COMS W4156 recommended. Theory and practice of 3 pts. Lect: 3. Instructor to be announced. balancing, reasoning about correctness, Prerequisite(s): COMS W3203. General determinacy, safety, and deadlock-freedom. physics-based animation algorithms, including animated clothing, hair, smoke, water, collisions, introduction to graph theory. Isomorphism testing, Application of techniques through semester-long algebraic specification, symmetries, spanning design project implementing performant, parallel impact, and kitchen sinks. Topics covered: integration of ordinary differential equations, trees, traversability, planarity, drawings on application in a modern parallel programming higher-order surfaces, colorings, extremal graphs, language. formulation of physical models, treatment of discontinuities including collisions/contact, random graphs, graphical measurement, directed CSEE W4140x or y Networking laboratory animation control, constrained Lagrangian graphs, Burnside-Polya counting, voltage graph 3 pts. Lect: 3. Professor Zussman. Mechanics, friction/dissipation, continuum theory. Prerequisite(s): CSEE W4119 or equivalent. mechanics, finite elements, rigid bodies, thin CSOR W4231x Analysis of algorithms I Students will learn how to put “principles shells, discretization of Navier-Stokes equations. 3 pts. Lect: 3. Professor Yannakakis, Drinea, or into practice,” in a hands-on networking lab General education requirement: quantitative and Andoni. course. The course will cover the technologies deductive reasoning (QUA). Prerequisite(s): COMS W3134, W3136 or W3137, and protocols of the internet using equipment and W3203. Introduction to the design and currently available to large internet service COMS W4170x or y User interface design 3 pts. Lect: 3. Professor Chilton or Feiner. analysis of efficient algorithms. Topics include providers such as CISCO routers and end models of computation, efficient sorting and systems. A set of laboratory experiments provides Prerequisite(s): COMS W3134, W3136, or W3137. Introduction to the theory and practice of searching, algorithms for algebraic problems, hands-on experience with engineering wide-area graph algorithms, dynamic programming, networks and will familiarize students with the computer user interface design, emphasizing the software design of graphical user interfaces. probabilistic methods, approximation algorithms, Internet Protocol (IP), Address Resolution Protocol and NP-completeness. (ARP), Internet Control Message Protocol (ICMP), Topics include basic interaction devices and User Datagram Protocol (UDP) and Transmission techniques, human factors, interaction styles, COMS W4232y Advanced algorithms Control Protocol (TCP), the Domain Name System dialogue design, and software infrastructure. 3 pts. Lect: 3. Professor Andoni. (DNS), routing protocols (RIP, OSPF, BGP), network Design and programming projects are required. Prerequisite(s): COMS W4231. Introduces classic management protocols (SNMP, and application- COMS W4172y 3D user interfaces and and modern algorithmic ideas central to many level protocols (FTP, TELNET, SMTP). augmented reality areas of Computer Science. Focus on most powerful paradigms and techniques of how to COMS W4156x Advanced software 3 pts. Lect: 3. Professor Feiner. Prerequisite(s): COMS W4160 or W4170 or design and measure efficiency of algorithms. engineering Broad intent, covering diverse algorithmic 3 pts. Lect: 3. Professor Kaiser. instructor’s permission. Design, development, and evaluation of 3D user interfaces. Interaction techniques. Covered topics are implemented Prerequisite(s): COMS W3157 or equivalent. and used in industry. Topics include: hashing, Software lifecycle using frameworks, libraries, techniques and metaphors, from desktop to immersive. Selection and manipulation. Travel sketching/streaming, nearest neighbor search, and services. Major emphasis on software testing. graph algorithms, spectral graph theory, Centers on a team project. and navigation. Symbolic, menu, gestural, and multimodal interaction. Dialogue design. 3D linear programming, models for large-scale COMS W4160y Computer graphics software support. 3D interaction devices and computation, and other related topics. 3 pts. Lect: 3. Professor Reed. displays. Virtual and augmented reality. Tangible COMS W4236y Introduction to computational Prerequisite(s): COMS W3134, W3136, or W3137; user interfaces. Review of relevant 3D math. complexity W4156 is recommended. Strong programming COMS W4181x Security I 3 pts. Lect: 3. Professor Chen. background and some mathematical familiarity Prerequisite(s): COMS W3261. Develops a including linear algebra is required. Introduction 3 pts. Lect: 3. Professor Jana. Prerequisite(s): COMS W3157 or equivalent. quantitative theory of the computational difficulty to computer graphics. Topics include 3D viewing of problems in terms of the resources (e.g., time, and projections, geometric modeling using Introduction to security. Threat models. Operating system security features. Vulnerabilities and tools. space) needed to solve them. Classification of

ENGINEERING 2021–2022 problems into complexity classes, reductions and classical and quantum computing. Potential power programming, and evolutionary strategies, as 117 completeness. Power and limitations of different of quantum computers. well as governing dynamic of coevolution and modes of computation such as nondeterminism, symbiosis. Includes discussions of problem randomization, interaction and parallelism. EECS E4340x Computer hardware design representations and applications to design 3 pts. Lect: 2. Lab: 3. Professor Sethumadhavan. problems in a variety of domains including COMS W4241y Numerical algorithms and Prerequisite(s): ELEN E3331 and CSEE W3827. software, electronics, and mechanics. complexity Practical aspects of computer hardware design 3 pts. Lect: 3. Instructor to be announced. through the implementation, simulation, and COMS W4560x Introduction to computer Prerequisite(s): Knowledge of a programming prototyping of a PDP-8 processor. High-level and applications in healthcare and biomedicine language. Some knowledge of scientific assembly languages, I/O, interrupts, datapath 3 pts. Lect: 3. computation is desirable. Modern theory and and control design, pipelining, busses, memory Prerequisite(s): Experience with computers and practice of computation on digital computers. architecture. Programmable logic and hardware a passing familiarity with medicine and biology. Introduction to concepts of computational prototyping with FPGAs. Fundamentals of VHDL Undergraduates in their senior or junior years complexity. Design and analysis of numerical for register-transfer level design. Testing and may take this course only if they have adequate algorithms. Applications to computational finance, validation of hardware. Hands-on use of industry background in mathematics and receive computational science, and computational CAD tools for simulation and synthesis. permission from the instructor. An overview of engineering. the field of biomedical informatics, combining COMS W4419x or y Internet, technology, perspectives from medicine, computer science, STCS W4242x or y Introduction to data economics, and policy and social science. Use of computers and science 3 pts. Lect: 3. Professor Schulzrinne. information in healthcare and the biomedical 3 pts. Lect: 3. Professor Salleb-Aouissi. Technology, economics, and policy aspects sciences, covering specific applications and Practical techniques for working with large-scale of the internet. Summarizes how the internet general methods, current issues, capabilities and data. Topics include statistical modeling and works technically, including protocols, standards, limitations of biomedical informatics. Biomedical machine learning, data pipelines, programming radio spectrum, global infrastructure and Informatics studies the organization of medical languages, “big data” tools, and real-world interconnection. Micro-economics with a focus information, the effective management of topics and case studies. Statistical and data on media and telecommunication economic information using computer technology, and the manipulation software required. Intended for concerns, including competition and monopolies, impact of such technology on medical research, nonquantitative graduate-level disciplines. platforms, and behavioral economics. U.S. education, and patient care. The field explores constitution, freedom of speech, administrative COMS W4252x or y Introduction to techniques for assessing current information procedures act and regulatory process, universal practices, determining the information needs of computational learning theory service, role of FFC. Not a substitute for CSEE 3 pts. Lect: 3. Professor Servedio. healthcare providers and patients, developing W4119. Suitable for nonmajors. May not be used interventions using computer technology, and Prerequisite(s): CSOR W4231 or COMS W4236 as a track elective for computer science major. or W3203 and instructor’s permission or evaluating the impact of those interventions. COMS W3261 and instructor’s permission. COMS W4444x Programming and problem MECS E4603x Applied robotics: algorithms Possibilities and limitations of performing solving and software learning by computational agents. Topics include 3 pts. Lect: 3. Professor Ross. 3 pts. Lect: 3. Professor Ciocarlie. computational models of learning, polynomial Prerequisite(s): COMS W3134, W3136, or W3137, Prerequisite(s): Fundamental programming skills time learnability, learning from examples and and CSEE W3827. Hands-on introduction to (e.g., COMS W1002, W1004, W1005, ENGI E1006, learning from queries to oracles. Computational solving open-ended computational problems. or equivalent). Science and systems aspects of and statistical limitations of learning. Applications Emphasis on creativity, cooperation, and Robotics from applied perspective, focusing on to Boolean functions, geometric functions, collaboration. Projects spanning a variety of algorithms and software tools. Spatial reasoning; automata. areas within computer science, typically requiring tools for manipulating and visualizing spatial the development of computer programs. relationships. Analysis of robotic manipulators; COMS W4261x or y Introduction to Generalization of solutions to broader problems, cryptography numerical methods for kinematic analysis. and specialization of complex problems to make Motion planning, search-based and stochastic 3 pts. Lect: 2.5. Professor Malkin. them manageable. Team-oriented projects, Prerequisite(s): Comfort with basic discrete math approaches. Applications for force and impedance student presentations, and in-class participation control. Grading based on combination of exams and probability. Recommended: COMS W3261 required. or CSOR W4231. An introduction to modern and projects implemented using Robot Operating cryptography, focusing on the complexity- COMS W4460y Principles of innovation and System (ROS) software framework and executed theoretic foundations of secure computation and entrepreneurship on real and simulated robotic manipulators. communication in adversarial environments; a 3 pts. Lect: 3. COMS W4701x or y Artificial intelligence rigorous approach, based on precise definitions Prerequisite(s): COMS W3134, W3136, or W3137 3 pts. Lect: 3. Professor Salleb-Aouissi or Dear. and provably secure protocols. Topics include (or equivalent), or instructor’s permission. Team Prerequisite(s): COMS W3134, W3136, or W3137 private and public key schemes, project-centered course focused on principles and any course on probability. Recommended: digital signatures, authentication, pseudorandom of planning, creating, and growing a technology Prior knowledge of Python. Overview of Artificial generators and functions, one-way functions, venture. Topics include identifying and analyzing Intelligence (AI) covering Search, Problem Solving, trapdoor functions, number theory and opportunities created by technology paradigm Game Playing, Knowledge Representation, computational hardness, identification and zero shifts, designing innovative products, protecting Propositional logic, Predicate Calculus (first order knowledge protocols. intellectual property, engineering innovative logic), Reasoning under uncertainty, Machine business models. COMS W4281x or y Introduction to quantum Learning, and other topics in AI (including vision, computing MECS E4510x Evolutionary computation and natural language processing, and robotics) as 3 pts. Lect: 3. Instructor to be announced. design automation time permits. Prerequisite(s): Knowledge of linear algebra. 3 pts. Lect: 3. Professor Lipson. Prior knowledge of quantum mechanics is Prerequisite(s): Basic programming experience in not required although helpful. Introduction to any language. Fundamental and advanced topics quantum computing. Shor’s factoring algorithm, in evolutionary algorithms and their application Grover’s database search algorithm, the quantum to open-ended optimization and computational summation algorithm. Relationship between design. Covers genetic algorithms, genetic

ENGINEERING 2021–2022 118 COMS W4705x Natural language processing and few-shot learning, image synthesis and techniques for analyzing genomic data 3 pts. Lect: 3. Professor McKeown. generative models, object tracking, vision and including DNA, RNA and protein structures; Prerequisite(s): COMS W3134, W3136, or W3137 language, vision and audio, 3D representation, microarrays; transcription and regulation; (or equivalent), or instructor’s permission. interpretability, and bias, ethics, and media regulatory, metabolic and protein interaction Computational approaches to natural language deception. networks. The course covers sequence analysis generation and understanding. Recommended algorithms, dynamic programming, hidden preparation: Some previous or concurrent COMS W4733x or y Computational aspects Markov models, phylogenetic analysis, Bayesian exposure to AI or machine learning. Topics include of robotics network techniques, neural networks, clustering information extraction, summarization, machine 3 pts. Lect: 3. Professors Dear or Song. algorithms, support vector machines, Boolean translation, dialogue systems, and emotional Prerequisite(s): COMS W3134, W3136, or W3137. models of regulatory networks, flux based speech. Particular attention is given to robust Introduction to robotics from a computer science analysis of metabolic networks and scale-free techniques that can handle understanding and perspective. Topics include coordinate frames network models. The course provides self- generation for the large amounts of text on the and kinematics, computer architectures for contained introduction to relevant biological web or in other large corpora. Programming robotics, integration and use of sensors, world mechanisms and methods. exercises in several of these areas. modeling systems, design and use of robotic programming languages, and applications of COMS W4762x Machine learning for COMS W4706y Spoken language processing artificial intelligence for planning, assembly, and functional genomics 3 pts. Lect: 3. Professor Hirschberg. manipulation. 3 pts. Lect: 3. Professor Knowles. Prerequisite(s): COMS W3134, W3136, or W3137 Prerequisite(s): Proficiency in a high-level (or equivalent), or instructor’s permission. COMS W4735x or y Visual interfaces to programming language (Python/R/Julia). Computational approaches to speech generation computers Recommended: introductory machine learning and understanding. Topics include speech 3 pts. Lect: 3. Professor Kender. class (such as COMS W4771). Introduces modern recognition and understanding, speech analysis Prerequisite(s): COMS W3134, W3136, or W3137. probabilistic machine learning methods using for computational linguistics research, and speech Visual input as data and for control of computer applications in data analysis tasks from functional synthesis. Speech applications including dialogue systems. Survey and analysis of architecture, genomics, where massively-parallel sequencing systems, data mining, summarization, and algorithms, and underlying assumptions of is used to measure the state of cells, e.g., what translation. Exercises involve data analysis and commercial and research systems that recognize genes are being expressed, what regions of DNA building a small text-to-speech system. and interpret human gestures, analyze imagery ("chromatin") are active ("open") or bound by such as fingerprint or iris patterns, generate specific proteins. COMS W4725x or y Knowledge natural language descriptions of medical or representation and reasoning map imagery. Explores foundations in human COMS W4771y Machine learning 3 pts. Lect: 3. psychophysics, cognitive science, and artificial 3 pts. Lect: 3. Professor Hsu or Verma. Prerequisite(s): COMS W4701. General aspects intelligence. Prerequisite(s): Any introductory course in linear of knowledge representation (KR). The two algebra and any introductory course in statistics fundamental paradigms (semantic networks and COMS W4737x or y Biometrics are both required. Highly recommended: COMS frames) and illustrative systems. Topics include 3 pts. Lect: 3. Professor Belhumeur. W4701 or knowledge of artificial intelligence. hybrid systems, time, action/plans, defaults, Prerequisite(s): A background at the sophomore Topics from generative and discriminative abduction, and case-based reasoning. Throughout level in computer science, engineering, or like machine learning including least squares the course particular attention is paid to design discipline. We will explore the latest advances methods, support vector machines, kernel trade-offs between language expressiveness and in biometrics as well as the machine learning methods, neural networks, Gaussian distributions, reasoning complexity, and issues relating to the techniques behind them. Students will learn linear classification, linear regression, maximum use of KR systems in larger applications. how these technologies work and how they are likelihood, exponential family distributions, sometimes defeated. Grading will be based on Bayesian networks, Bayesian inference, mixture COMS W4731x or y Computer vision I: first homework assignments and a final project. There models, the EM algorithm, graphical models and principles will be no midterm or final exam. Shares lectures hidden Markov models. Algorithms implemented 3 pts. Lect: 3. Professor Nayar. with COMS E6737. Students taking COMS E6737 in MATLAB. Prerequisite(s): Fundamentals of calculus, are required to complete additional homework linear algebra, and C programming. Students problems and undertake a more rigorous final COMS W4772x Advanced machine learning without any of these prerequisites are advised project. Students will only be allowed to earn 3 pts. Lect: 3. Professor Hsu. to contact the instructor prior to taking the credit for COMS W4737 or COMS E6737 but not Prerequisite(s): COMS W4771 or instructor’s course. Introductory course in computer vision. both. permission; knowledge of linear algebra and Topics include image formation and optics, introductory probability or statistics is required. image sensing, binary images, image processing EECS E4750x or y Heterogeneous computing An exploration of advanced machine learning and filtering, edge extraction and boundary for signal and data processing tools for perception and behavior learning. detection, region growing and segmentation, 3 pts. Lect: 2. Professor Marianetti. How can machines perceive, learn from, and pattern classification methods, brightness and Prerequisite(s): ELEN E3801 and COMS W3134 or classify human activity computationally? Topics reflectance, shape from shading and photometric similar, recommended. Methods for deploying include appearance-based models, principal and stereo, texture, binocular stereo, optical flow and signal and data processing algorithms on independent components analysis, dimensionality motion, 2D and 3D object representation, object contemporary general purpose graphics reduction, kernel methods, manifold learning, recognition, vision systems and applications. processing units (GPGPUs) and heterogeneous latent models, regression, classification, Bayesian computing infrastructures. Using programming methods, maximum entropy methods, real-time COMS W4732y Computer vision II: learning languages such as OpenCL and CUDA for tracking, extended Kalman filters, time series 3 pts. Lect: 3. Professor Vondrick. computational speedup in audio, image, and prediction, hidden Markov models, factorial Prerequisite(s): Fundamentals of calculus, linear video processing and computational data HMMs, input-output HMMs, Markov random algebra, and C programming. Students without analysis. Significant design project. fields, variational methods, dynamic Bayesian any of these prerequisites are advised to contact CBMF W4761x or y Computational genomics networks, and Gaussian/Dirichlet processes. Links the instructor prior to taking the course. Advanced to cognitive science. course in computer vision. Topics include 3 pts. Lect: 3. Professor Pe’er. convolutional networks and back-propagation, Prerequisite(s): Introductory probability and object and action recognition, self-supervised statistics and basic programming skills. Provides comprehensive introduction to computational

ENGINEERING 2021–2022 COMS W4773y Machine learning theory CSEE W4823x or y Advanced logic design COMS W4995x or y Special topics in 119 3 pts. Lect: 3. Professor Hsu. 3 pts. Lect: 3. Professor Nowick. computer science, I Prerequisite(s): COMS W4771. Theoretical study Prerequisite(s): CSEE W3827, or a half-semester 3 pts. Lect: 3. Members of the faculty. of algorithms for machine learning and high- introduction to digital logic, or equivalent. An Prerequisite(s): Instructor’s permission. Special dimensional data analysis. Topics include high- introduction to modern digital system design. topics arranged as the need and availability dimensional probability, theory of generalization Advanced topics in digital logic: controller arises. Topics are usually offered on a one-time and statistical learning, online learning and synthesis (Mealy and Moore machines); adders basis. Since the content of this course changes optimization, spectral analysis. and multipliers; structured logic blocks (PLDs, each time it is offered, it may be repeated PALs, ROMs); iterative circuits. Modern design for credit. Consult the department for section COMS W4774y Unsupervised learning methodology: register transfer level modeling assignment. 3 pts. Lect: 3. Professor Verma. (RTL); algorithmic state machines (ASMs); Prerequisite(s): COMS W4771 and background introduction to hardware description languages COMS W4996x or y Special topics in in probability and statistics, linear algebra, (VHDL or Verilog); system-level modeling and computer science, II and multivariate calculus. Ability to program simulation; design examples. 3 pts. Lect: 3. in a high-level language, and familiarity with Prerequisite(s): Instructor’s permission. A basic algorithm design and coding principles. CSEE W4824x Computer architecture continuation of COMS W4995 when the special Core topics from unsupervised learning such 3 pts. Lect: 3. Professor Sethumadhavan. topic extends over two terms. as clustering, dimensionality reduction and Prerequisite(s): CSEE W3827 or equivalent. density estimation. Topics in clustering: k-means Focuses on advanced topics in computer COMS E6111y Advanced database systems clustering, hierarchical clustering, spectral architecture, illustrated by case studies from 3 pts. Lect: 2. Professor Gravano. clustering, clustering with various forms of classic and modern processors. Fundamentals Prerequisite(s): COMS W4111 and knowledge of feedback, good initialization techniques and of quantitative analysis. Pipelining. Memory Java or instructor’s permission. Continuation convergence analysis of various clustering hierarchy design. Instruction-level and thread- of COMS W4111, covers latest trends in both procedures. Topics in dimensionality reductions: level parallelism. Data-level parallelism and database research and industry: information linear techniques such as PCA, ICA, Factor graphics processing units. Multiprocessors. Cache retrieval, web search, data mining, data Analysis, Random Projections, non-linear coherence. Interconnection networks. Multi- warehousing, OLAP, decision support, multimedia techniques such as LLE, ISOMap, Laplacian core processors and systems-on-chip. Platform databases, and XML and databases. Programming Eigenmaps, tSNE, and study of embeddings of architectures for embedded, mobile, and cloud projects required. general metric spaces, what sorts of theoretical computing. COMS E6113y Topics In database systems guarantees can one provide about such 3 pts. Lect: 2. techniques. Miscellaneous topics: design and CSEE W4840y Embedded systems 3 pts. Lect: 3. Professor Edwards. Prerequisite(s): COMS W4111. Concentration on analysis of data structures for fast Nearest some database paradigm, such as deductive, Neighbor search such as Cover Trees and LSH. Prerequisite(s): CSEE W4823. Embedded system design and implementation combining hardware heterogeneous, or object-oriented, and/or Algorithms will be implemented in either Matlab some database issue, such as data modeling, or Python. and software. I/O, interfacing, and peripherals. Weekly laboratory sessions and term project on distribution, query processing, semantics, or COMS W4775y Causal inference design of a microprocessor-based embedded transaction management. A substantial project is 3 pts. Lect: 3. Professor Bareinboim. system including at least one custom peripheral. typically required. May be repeated for credit with Prerequisite(s): Discrete Math, Calculus, Statistics Knowledge of C programming and digital logic instructor’s permission. (basic probability, modeling, experimental design), required. Lab required. COMS E6114y Advanced distributed systems some programming experience. Causal Inference CSEE E4868x or y System-on-chip platforms 3 pts. Lect: 2. Professor Geambasu. theory and applications. Theoretical topics Prerequisite(s): COMS W4113 and W4118. Reviews include 3-layer causal hierarchy, causal bayesian 3 pts. Lect: 3. Professor Carloni. Prerequisite(s): COMS W3157 and CSEE W3827 influential research that provides the basis of networks, structural learning, identification most large-scale, cloud infrastructures today. problem and do-calculus, linear identifiability, Design and programming of System-on-Chip (SoC) platforms. Topics include overview of Students read, present, and discuss papers. bounding, and counterfactual analysis. Applied Topics include distributed consensus, consistency topics include intersection with statistics, technology and economic trends, methodologies and supporting CAD tools for system-level models and algorithms, service-oriented empirical-data sciences (social and health), and architectures, large-scale data storage, distributed AI and ML. design; models of computation, the SystemC language, transaction-level modeling, hardware- transactions, big-data processing frameworks, COMS W4776x Machine learning for data software partitioning, high-level synthesis, distributed systems security. Reviews established science system programming, on-chip communication, results and state-of-the-art research. 3 pts. Lect: 3. Members of the faculty. memory organization, power management COMS E6117x or y Topics in programming and optimization, integration of programmable Prerequisite(s): IEOR E4150 or STAT GU4001 languages and translators processor cores and specialized accelerators. or equivalent, COMS W3251 or equivalent. 3 pts. Lect: 2. Case studies of modern SoC platforms for various Introduction to machine learning, emphasis Prerequisite(s): COMS W4115 or instructor’s classes of applications. on data science. Topics include least square permission. Concentration on the design and methods, Gaussian distributions, linear COMS W4901x and y Projects in computer implementation of programming languages, and classification, linear regression, maximum tools focused on advanced applications in new likelihood, exponential family distributions, science 1–3 pts. Members of the faculty. areas in software verification, distributed systems, Bayesian networks, Bayesian inference, mixture programming in the large, and web computing. models, the EM algorithm, graphical models, Prerequisite(s): Approval by a faculty member who agrees to supervise the work. A second-level A substantial project is typically required. May be hidden Markov models, support vector machines repeated for credit. kernel methods. Emphasizes methods and independent project involving laboratory work, problems relevant to big data. Students may not computer programming, analytical investigation, COMS E6118y Operating systems, II receive credit for both COMS W4771 and W4776. or engineering design. May be repeated for 3 pts. Lect: 2. Professor Nieh. credit, but not for a total of more than 3 points of Prerequisite(s): COMS W4118. Corequisite: degree credit. Consult the department for section CSEE W4119. Continuation of COMS W4118, with assignment. emphasis on distributed operating systems. Topics include interfaces to network protocols,

ENGINEERING 2021–2022 120 distributed run-time binding, advanced virtual operation of today’s software systems. Reliability, COMS E6181x or y Advanced internet services memory issues, advanced means of interprocess security, privacy, sustainability, and societal 3 pts. Lect: 2. Professor Schulzrinne. communication, file system design, design for issues. Emerging software architectures such as In-depth survey of protocols and algorithms extensibility, security in a distributed environment. microservices, serverless, and deep learning. needed to transport multimedia information Investigation is deeper and more hands-on than in Term paper and programming project. across the internet, including audio and video COMS W4118. A programming project is required. encoding, multicast, quality-of-service, voice-over COMS E6160x or y Topics in computer IP, streaming media and peer-to-peer multimedia COMS E6121x Reliable software graphics systems. Includes a semester-long programming 3 pts. Lect: 3. Professor Yang. 3 pts. Lect: 2. Professor Belhumeur. project. Prerequisite(s): at least one of COMS W4118, Prerequisite(s): COMS W4160 or instructor’s W4115, or W4117, or significant software permission. An advanced graduate course, COMS E6183x or y Advanced topics in development experiences. Topics include involving study of an advanced research topic network security automated debugging, automated software repair, in Computer Graphics. Content varies between 3 pts. Lect: 3. Professor Jana. concurrent software reliability, software error offerings, and the course may be repeated for Prerequisite(s): COMS W4180, CSEE W4119 detection, and more. credit. Recent offerings have included appearance and COMS W4261 recommended. Review the models in graphics, and high quality real-time fundamental aspects of security, including COMS E6123x or y Programming rendering. authentication, authorization, access control, environments and software tools (PEST) confidentiality, privacy, integrity, and availability. 3 pts. Lect: 2. Professor Kaiser. COMS E6174y Interaction design: a Review security techniques and tools, and their Prerequisite(s): COMS W4156 or equivalent. perceptual approach applications in various problem areas. Study Software methodologies and technologies 3 pts. Lect: 3. the state of the art in research. A programming concerned with development and operation of Prerequisite(s): COMS W4170 or instructor’s project is required. today’s software systems. Reliability, security, permission. Design methodology for special- systems management and societal issues. purpose user interfaces. Emphasis on how COMS E6184y Seminar on anonymity and Emerging software architectures such as psychology and perception inform good design. privacy enterprise and grid computing. Term paper and Interviewing and task modeling, participatory 3 pts. Lect: 3. programming project. Seminar focus changes design, and low-fidelity prototyping. Applications Prerequisite(s): COMS W4261 or W4180 or CSEE frequently to remain timely. of brain research, graphic design and art to W4119 or instructor’s permission. Covers the develop custom user interfaces components, following topics: Legal and social framework for COMS E6124x Hardware security screen layouts, and interaction techniques for privacy. Data mining and databases. Anonymous 3 pts. Lect: 3. Professor Sethumadhavan. application-specific systems. commerce and internet usage. Traffic analysis. Prerequisite(s): CSEE W3827 and COMS W3157. Policy and national security considerations. Recommended: CSEE W4824 and COMS W4187. COMS E6176x or y User interfaces for mobile Classes are seminars with students presenting Techniques for securing the foundational and wearable computing papers and discussing them. Seminar focus aspects of all computing devices and systems. 3 pts. Lect: 2. Professor Feiner. changes frequently to remain timely. Topics include: hardware-up security, hardware Prerequisite(s): COMS W4170 or instructor’s supply chain trust and security, storing secrets permission. Introduction to research on user COMS E6185x or y Intrusion and anomaly in hardware, boot time trust and security, interfaces for mobile and wearable computing detection systems side channel attacks and defenses, hardware through lectures, invited talks, student-led 3 pts. Lect: 2. Professor Stolfo. support for compartmentalization, fault attacks discussions of important papers, and programming Pre- or corequisite: COMS W4180 Network and defenses, hardware support to strengthen projects. Designing and authoring for mobility security. The state of threats against computers, software: memory safety, control flow integrity, and wearability. Ubiquitous/pervasive computing. and networked systems. An overview of computer information flow tracking, diversity, obfuscation, Collaboration with other users. Display, security solutions and why they fail. Provides a anomaly detection. Hardware support for interaction, and communication technologies. detailed treatment for network and host-based accelerating cryptography and applied Sensors for tracking position, orientation, motion, intrusion detection and intrusion prevention cryptography. environmental context, and personal context. systems. Considerable depth is provided on Applications and social consequences. anomaly detection systems to detect new attacks. COMS E6125y Web-enhanced information Covers issues and problems in e-mail (spam, and management (WHIM) – COMS E6178y Human computer interaction viruses) and insider attacks (masquerading and 3 pts. Lect: 2. Professor Kaiser. seminar impersonation). Prerequisite(s): At least one COMS W41xx or 3 pts. Lect: 2.5. Professor Smith. COMS E61xx course and/or COMS W4444, or Prerequisite(s): COMS W4170. Human–computer COMS E6232x or y Analysis of algorithms, II instructor’s permission. Strongly recommended: interaction (HCI) studies (1) what computers are 3 pts. Lect: 2. COMS W4111. History of hypertext, markup used for, (2) how people interact with computers, Prerequisite(s): CSOR W4231. Continuation of languages, groupware and the web. Evolving web and (3) how either of those should change in CSOR W4231. protocols, formats and computation paradigms the future. Topics include ubiquitous computing, such as HTTP, XML and Web Services. Novel mobile health, interaction techniques, social COMS E6253y Advanced topics in application domains enabled by the web and computing, mixed reality, accessibility, and ethics. computational learning theory societal issues. Term paper and programming Activities include readings, presentations, and 3 pts. Lect: 3. Professor Servedio. project. Seminar focus changes frequently to discussions of research papers. Substantial HCI Prerequisite(s): CSOR W4231 or equivalent; remain timely. research project required. COMS W4252 or W4236 helpful but not required. In-depth study of inherent abilities and limitations COMS E6156y Topics in software engineering CSEE E6180x or y Modeling and performance of computationally efficient learning algorithms. 3 pts. Lect: 2. Professor Kaiser. 3 pts. Lect: 2. Professor Misra. Algorithms for learning rich Boolean function Topics in software engineering arranged as the Prerequisite(s): COMS W4118 and STAT GU4001. classes in online, Probably Approximately Correct, need and availability arises, usually offered on a Introduction to queuing analysis and simulation and exact learning models. Connections with one-time basis. Since the content of this course techniques. Evaluation of time-sharing and computational complexity theory emphasized. changes, it may be repeated for credit with multiprocessor systems. Topics include priority Substantial course project or term paper required. instructor approval. Consult the department for queuing, buffer storage, and disk access, section assignment. Software methodologies and interference and bus contention problems, and technologies concerned with development and modeling of program behaviors.

ENGINEERING 2021–2022 COMS E6261x or y Advanced cryptography STCS GU6701x or y Foundations of graphical camera lens arrays, programmable lighting, face 121 3 pts. Lect: 3. Professor Malkin. models detection, single and multiview geometry, and Prerequisite(s): COMS W4261. A study of 3 pts. Lect: 3. Professor Blei. more. advanced cryptographic research topics such as: Prerequisite(s): Basic probability and statistics, secure computation, zero knowledge, privacy, calculus, and some optimization. Ability to COMS E6735y Visual databases anonymity, cryptographic protocols. Concentration write software to analyze data. Knowledge 3 pts. Lect: 3. Professor Kender. on theoretical foundations, rigorous approach, of programming language for statistics and Prerequisite(s): COMS W3134, W3136, or W3137 and provable security. Content varies between machine learning, such as R or Python. PhD-level (or equivalent). COMS W4731 and W4735 helpful offerings. May be repeated for credit. course on development and use of probability but not required. Contact instructor if uncertain. models. Covers mathematical properties, The analysis and retrieval of large collections COMS E6291x or y Theoretical topics in algorithms, and their application to real of image and video data, with emphasis on computer science problems. In-depth understanding of cutting-edge visual semantics, human psychology, and user 3 pts. Lect: 3. Professor Servedio. modern probabilistic modeling. Weekly papers, interfaces. Low-level processing: features Prerequisite(s): Instructor’s permission. assignments, and final project required. and similarity measures; shot detection; key Concentration on some theoretical aspect of frame selection; machine learning methods computer science. Content varies from year to COMS E6731y Humanoid robots for classification. Middle-level processing: year. May be repeated for credit. 3 pts. Lect: 2. Members of the faculty. organizational rules for videos, including unedited Prerequisite(s): A course in at least one of the (home, educational), semiedited (sports, talk EECS E6321y Advanced digital electronic following: AI, robotics, computer graphics, or shows), edited (news, drama); human memory circuits computer vision. Seminar on humanoid robots. limits; progressive refinement; visualization 3 pts. Lect: 2. Professor Seok. Analysis of existing hardware and software techniques; incorporation of audio and text. High- Prerequisite(s): EECS E4321. Advanced topics in platforms. Programming of multi-degree-of- level processing: extraction of thematic structures; the design of digital integrated circuits. Clocked freedom robots. Understanding sensor feedback ontologies, semantic filters, and learning; and nonclocked combinational logic styles. in perceive-act-sense control paradigms. Task- personalization of summaries and interfaces; Timing circuits: latches and flip-flops, phase- level planning and reasoning. Final project detection of pacing and emotions. Examples and locked loops, delay-locked loops. SRAM and includes implementing a humanoid robot task on demonstrations from commercial and research DRAM memory circuits. Modeling and analysis either a simulated or physical robot. systems throughout. Substantial course project or of on-chip interconnect. Power distribution term paper required. and power-supply noise. Clocking, timing, and COMS E6732x or y Computational imaging synchronization issues. Circuits for chip-to-chip 3 pts. Lect: 3. Professor Nayar. COMS E6737x or y Biometrics electrical communication. Advanced technology Prerequisite(s): COMS W4731 or instructor’s 3 pts. Lect: 3. Professor Belhumeur. issues that affect circuit design. The class may permission. Computational imaging uses a Prerequisite(s): Background at the sophomore include a team circuit design project. combination of novel imaging optics and a level in computer science, engineering, or like computational module to produce new forms of discipline. Corequisites: None. We will explore COMS E6424x Hardware security visual information. Survey of the state-of-the-art in the latest advances in biometrics as well as 3 pts. Lect: 2. Professor Sethumadhavan. computational imaging. Review of recent papers the machine learning techniques behind them. Prerequisite(s): CSEE W3827 and COMS W3157; on omnidirectional and panoramic imaging, Students will learn how these technologies work Recommended: CSEE W4824 and COMS W4187. catadioptric imaging, high dynamic range and how they are sometimes defeated. Grading Techniques for securing the foundational imaging, mosaicing and superresolution. Classes will be based on homework assignments and aspects of all computing devices and systems. are seminars with the instructor, guest speakers, a final project. There will be no midterm or Topics include hardware-up security, hardware and students presenting papers and discussing final exam. Shares lectures with COMS W4737. supply chain trust and security, storing secrets them. Students taking COMS E6737 are required to in hardware, boot time trust and security, complete additional homework problems and side channel attacks and defenses, hardware COMS E6733x or y 3D photography undertake a more rigorous final project. Students support for compartmentalization, fault attacks 3 pts. Lect: 2. Members of the faculty. will only be allowed to earn credit for COMS and defenses, hardware support to strengthen Prerequisite(s): Experience with at least one of the W4737 or COMS E6737 but not both. software: memory safety, control flow integrity, following topics: Computer graphics, computer information flow tracking, diversity, obfuscation, vision, pixel processing, robotics or computer- CSEE E6824y Parallel computer architecture anomaly detection. Hardware support for aided design, or permission of instructor. 3 pts. Lect: 2. Professor Sethumadhavan. accelerating cryptography and applied Programming proficiency in C, C++, or JAVA. Prerequisite(s): CSEE W4824. Parallel computer cryptography. 3D Photography—the process of automatically principles, machine organization and design of creating 3D, texture-mapped models of objects parallel systems including parallelism detection CSEE W6600x or y From data to solutions in detail. Applications include robotics, medicine, methods, synchronization, data coherence and 3 pts. Lect: 3. Professor Hirschberg or Chang. graphics, virtual reality, entertainment and digital interconnection networks. Performance analysis Prerequisite(s): Familiarity with common data movies etc. Topics include 3D data acquisition and special purpose parallel machines. science methods and tools. Must be able to write devices, 3D modeling systems and algorithms coherent weekly summary. Intended for students to acquire, create, augment, manipulate, render, CSEE E6847y Distributed embedded systems interested in data science and interdisciplinary animate and physically build such models. 3 pts. Lect: 2. research. Covers problems in medical research, Prerequisite(s): Any COMS W411X, CSEE W48XX, journalism, history, economics, business, English, COMS E6734y Computational photography or ELEN E43XX course, or instructor’s permission. psychology, and other areas amenable to 3 pts. Lect: 3. Professor Belhumeur. An interdisciplinary graduate-level seminar on the computational approaches. Prerequisite(s): COMS W4160, W4731, or a working design of distributed embedded systems. System knowledge of photography are recommended. robustness in the presence of highly variable EECS E6690-6699x or y Topics in data driven Students should have knowledge in any of three communication delays and heterogeneous analysis and computation core areas: computer vision, computer graphics, component behaviors. The study of the enabling 3 pts. Lect: 2. Members of the faculty. or photography. Computational techniques are technologies (VLSI circuits, communication Prerequisite(s): the instructor's permission. used to produce a new level of images and visual protocols, embedded processors, RTOSs), Selected advanced topics in data-driven analysis representations. Topics include HDR imaging, models of computation, and design methods. The and computation. Content varies from year to feature matching using RANSAC, image mosaics, analysis of modern domain-specific applications year, and different topics rotate through the image-based rendering, motion magnification, including on-chip micro-networks, multiprocessor course numbers 6690 to 6699. systems, fault-tolerant architectures, and robust

ENGINEERING 2021–2022 122 deployment of embedded software. Research design automation. Requires substantial reading COMS E6915y Technical writing for computer challenges such as design complexity, reliability, of research papers, class participation, and scientists and engineers scalability, safety, and security. The course semester-long project. 1 pt. Members of the faculty. requires substantial reading, class participation Available to M.S. or Ph.D. candidates in CS/ EECS E6870x or y Speech recognition and a research project. CE. Topics to help CS/CE graduate students’ 3 pts. Lect: 3. Members of the faculty. communication skills. Emphasis on writing, CSEE E6861y Computer-aided design of Prerequisite(s): Basic probability and statistics. presenting clear, concise proposals, journal Theory and practice of contemporary digital systems articles, conference papers, theses, and technical automatic speech recognition. Gaussian 3 pts. Lect: 2. Professor Nowick. presentations. May be repeated for credit. Credit mixture distributions, hidden Markov models, Prerequisite(s): (i) one semester of advanced may not be used to satisfy degree requirements. digital logic (CSEE W4823 or equivalent, or pronunciation modeling, decision trees, finite- instructor’s permission); and (ii) a basic course state transducers, and language modeling. COMS E6998x and y Topics in computer in data structures and algorithms COMS W3134, Selected advanced topics will be covered in more science W3136, W3137, W3157, or equivalent, and depth. 3 pts. Members of the faculty. familiarity with programming. Introduction to Prerequisite(s): Instructor’s permission. Selected COMS E6900x and y Tutorial in computer modern digital CAD synthesis and optimization topics in computer science. Content varies from science techniques. Topics include modern digital year to year. May be repeated for credit. system design (high-level synthesis, register- 1–3 pts. Members of the faculty. transfer level modeling, algorithmic state Prerequisite(s): Instructor’s permission. A reading COMS E6999x and y Topics in computer machines, optimal scheduling algorithms, course in an advanced topic for a small number of science, II resource allocation and binding, retiming), students, under faculty supervision. 3 pts. Prerequisite(s): COMS E6998. Continuation of controller synthesis and optimization, exact COMS E6901x Projects in computer science COMS E6998. and heuristic two-level logic minimization, 1–12 pts. Members of the faculty. advanced multilevel logic optimization, optimal Prerequisite(s): Instructor’s permission. Software COMS E9800x and y Directed research in technology mapping to library cells (for delay, or hardware projects in computer science. computer science power and area minimization), advanced Before registering, the student must submit a 1–15 pts. Members of the faculty. data structures (binary decision diagrams), written proposal to the instructor for review. The Prerequisite(s): Submission of outline of proposed SAT solvers and their applications, static proposal should give a brief outline of the project, research for approval by faculty member who timing analysis, and introduction to testability. estimated schedule of completion, and computer will supervise. The department must approve the Includes hands-on small design projects using resources needed. Oral and written reports number of points. May be repeated for credit. and creating CAD tools. are required. May be taken over more than Only for Eng.Sc.D. candidates. CSEE E6863x Formal verification of hardware one semester, in which case the grade will be COMS E9910x and y Graduate research, I and software systems deferred until all 12 points have been completed. No more than 12 points of COMS E6901 may 1–6 pts. Members of the faculty. 3 pts. Lect: 2. Professor Theobald or Ivancic. Prerequisite(s): Submission of an outline of the Prerequisite(s): COMS W3134, W3136, or be taken. Consult the department for section assignment. proposed research for approval by the faculty W3137 and COMS W3261. Introduction to the member who will supervise. The department must theory and practice of formal methods for the COMS E6902x and y Thesis approve the number of credits. May be repeated design and analysis of correct (i.e., bug-free) 1–9 pts. Members of the faculty. for credit. Only for M.S. candidates holding GRA concurrent and embedded hardware/software Available to M.S. candidates. An independent or TA appointments. Note: It is NOT required that systems. Topics include temporal logics; model investigation of an appropriate problem a student take Graduate research, I prior to taking checking; deadlock and liveness issues; fairness; in computer science carried out under the Graduate research, II. Consult the department for satisfiability (SAT) checkers; binary decision supervision of a faculty member. A formal written section assignment. diagrams (BDDs); abstraction techniques; report is essential and an oral presentation may introduction to commercial formal verification also be required. May be taken over more than COMS E9911x and y Graduate research, II tools. Industrial state-of-the-art, case studies, one semester, in which case the grade will be 1-15 pts. Members of the faculty. and experiences: software analysis (C/C++/Java), deferred until all 9 points have been completed. Prerequisite(s): Submission of an outline of the hardware verification (RTL). No more than 9 points of COMS E6902 may proposed research for approval by the faculty member who will supervise. The department must CSEE E6868x or y Embedded scalable be taken. Consult the department for section assignment. approve the number of points. May be repeated platforms for credit. Only for M.S./Ph.D. track and Ph.D. 3 pts. Lect: 2. Professor Carloni. COMS E6910x and y Fieldwork students. Note: It is NOT required that a student Prerequisite(s): CSEE W4868 or instructor's 1 pt. Members of the faculty. take Graduate research, I prior to taking Graduate permission. Interdisciplinary graduate-level Prerequisite(s): Obtained internship and approval research, II. Consult the department for section seminar on design and programming of from faculty adviser. Only for M.S. students in the assignment. embedded scalable platforms. Content varies Computer Science Department who need relevant between offerings to cover timely relevant issues work experience as part of their program of study. and latest advances in system-on-chip design, Final report required. May not be taken for pass/ embedded software programming, and electronic fail credit or audited.

ENGINEERING 2021–2022 EARTH AND ENVIRONMENTAL ENGINEERING 123

Henry Krumb School of Mines OUR MISSION Earth and Environmental Engineering at the Henry Krumb School of Mines fosters excellence in 918 S. W. Mudd, MC 4711 education and research for the development and application of science and technology to maximize 212-854-2905 the quality of life for all, through the sustainable use and responsible management of Earth’s eee.columbia.edu resources. The department strives to provide education and carry out research that underpins the sustainable and equitable utilization of Earth's material, water, and energy resources at a scale that is beneficial to society. By leveraging cross-disciplinary opportunities afforded by the range of academic work in the department and the University, we tackle complex challenges that exist across the natural materials-water-energy-climate network of interdependencies.

DEPARTMENT CHAIR Ponisseril Somasundaran LECTURER SENIOR RESEARCH Ah-Hyung (Alissa) Park Alan West A. C. (Thanos) Bourtsalas SCIENTIST Vasilis M. Fthenakis DIRECTOR OF FINANCE PROFESSOR OF ADJUNCT PROFESSORS AND ADMINISTRATION PROFESSIONAL PRACTICE Vasilis M. Fthenakis ASSOCIATE RESEARCH Muamer Lihic Raymond S. Farinato Yuri Gorokhovich SCIENTISTS Robert Farrauto Paul Knowles Partha Patra PROFESSORS D. R. Nagaraj Eric Rosenberg Kartik Chandran Xi Chen ASSOCIATE PROFESSOR LAMONT ASSOCIATE George Deodatis Daniel Steingart RESEARCH PROFESSOR Pierre Gentine Wade McGillis Upmanu Lall ASSISTANT PROFESSORS Vjay Modi Ngai Yin Yip SPECIAL RESEARCH Ismail C. Noyan Bolun Xu SCIENTIST Ah-Hyung (Alissa) Park Nickolas J. Themelis

EARTH RESOURCES AND THE the Department of Mining, Metallurgical within the department of Earth and ENVIRONMENT and Mineral Engineering. However, the Environmental Engineering. The Earth and Environmental title "School of Mines" was retained In 1986, HKSM was designated by Engineering program fosters education by Columbia University honoris causa. Governor Cuomo as the mining and and research in the development You can see the bronze statue of The Mineral Resources Research Institute of and application of technology for Metallurgist (Le Marteleur) in front of the State of New York. the sustainable development, use, Columbia's Mudd Hall that was named after an alumnus of the School of Mines. and integrated management of EARTH AND ENVIRONMENTAL One century after its formation, the Earth’s resources. Resources are ENGINEERING (EEE) identified as minerals, energy, water, School of Mines was renamed Henry With the creation of air, and land, as well as the physical, Krumb School of Mines (HKSM) in at Columbia University, a major chemical, and biological components honor of the generous alumnus of the initiative in the study of Earth, its of the environment. There is close School of Mines and his wife, Lavon environment and society, the traditional collaboration with other engineering Duddleson Krumb. HKSM has been programs of HKSM in mining, mineral disciplines, the Lamont-Doherty Earth a leader in mining and metallurgy processing, and extractive metallurgy Observatory, the International Research research and education, including the were expanded in the late nineties to Institute for Climate Prediction, the first mining handbook by Professor encompass environmental concerns Center for Environmental Research and Peel, the first mineral processing related to the use of materials, energy Conservation, and other Columbia Earth handbook by Professor Taggart, and and water resources, and to reflect Institute units. other pioneering work in mineral one of nine departments of SEAS benefaction, chemical thermodynamics, with a focus on the development kinetics, transport phenomena in mineral THE HENRY KRUMB SCHOOL and application of technology for the extraction and processing, ecological OF MINES AT COLUMBIA sustainable development, use and and environmentally responsible mining, UNIVERSITY integrated management of Earth's and pursuit of state-of-the-art research resources. The department is the direct lineage advancing responsible use of Earth's As a result of the vast developments of the School of Mines of Columbia resources. The Henry Krumb School in the technologies and fields of University, which was the first mining of Mines located in The Fu Foundation environmental management, in 1996 and metallurgy school in the U.S. School of Engineering and Applied and 1998, respectively, the engineering (1864). It became the foundation for Science offers students interested in school created the M.S. program in Columbia’s School of Engineering and mining and metallurgy the opportunity Earth Resources Engineering and the Applied Science and later the home of to focus their studies in these fields

ENGINEERING 2021–2022 124 EARTH AND ENVIRONMENTAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

APMA E2000 (4) MATH UN1101 (3) MATH UN1102 (3) APMA E2101 (3) and E2001 (0) MATHEMATICS or MATH UN1207 (4) MATH UN1208 (4) MATH UN2030 (3) ODE

UN1401 (3) UN1402 (3)

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

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

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

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

HUMA UN1121 or UN1123 (3)

EESC GU4001 (4) or EESC UN2100 (4.5) REQUIRED or EESC UN2200 (4.5) PROFESSIONAL STAT GU4001 (3) AND TECHNICAL ELECTIVES EEAE E2100 (3) A better planet by design

COMPUTER ENGI E1006 (3) any semester SCIENCE

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

ENGINEERING 2021–2022 125 EARTH AND ENVIRONMENTAL ENGINEERING: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

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

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

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

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

TECHNICAL 3 points 6 points 9 points ELECTIVES

NONTECHNICAL 3 points 3 points 6 points ELECTIVES

TOTAL POINTS 15 17 16 17

B.S. program in Earth and Environmental • climate change mitigation RESEARCH CENTERS Engineering to meet the needs of a • minerals, metals, and materials ASSOCIATED WITH EARTH AND changed society. Students interested processing, extraction, and reuse ENVIRONMENTAL ENGINEERING in the traditional disciplines of mining, • waste and pollution prevention, Center for Advanced Materials for mineral engineering and metallurgy mitigation and management Energy and Environment. The Center continue to study these fields through • renewable energy and carbon develops advanced materials to address the Earth and Environmental Engineering management challenges for closing the energy loop, department course offerings as well as carbon loop, and water loop. By bridging engineering scales the course offerings through the Material from colloidal interfaces to resource Science and Engineering program. Center for Life Cycle Analysis (CLCA). distribution, the department now The B.S. program in Earth and The Center for Life Cycle Analysis considers resource development both Environmental Engineering was initiated (CLCA) provides a framework for on Earth and off, with a new effort in in the fall of 1998 to replace the mining/ quantifying the potential environmental space mining. mineral/extractive metallurgy programs impacts of material and energy inputs The EEE program warmly welcomes of HKSM and is now accredited by ABET. and outputs of a process or product Combined Plan students. An EEE minor The department builds upon this from “cradle to grave.” For more is offered to all Columbia engineering legacy every year through its core class information: clca.columbia.edu. students who wish to enrich their and unofficial motto, "A Better Planet By academic record by concentrating some . For more Design," bringing together of their technical electives on Earth/ information: climate.columbia.edu. Environment subjects. • water conservation, allocation, and Columbia Electrochemical Energy decontamination Center (CEEC). For more information:

ENGINEERING 2021–2022 126 ceec.engineering.columbia.edu. SCHOLARSHIPS, FELLOWSHIPS, assessment of environmental impact AND INTERNSHIPS of past, present, and future industrial . The Center The department arranges for activities; and analysis and design of was established in 2008 to address undergraduate summer internships processes for remediation, recycling, issues of Global Water Security. For after the sophomore and junior years. and disposal of used materials. more information: water.columbia.edu. Undergraduates can also participate in 4. Graduates will practice their profession with excellent written Earth Engineering Center (EEC). graduate research projects under the and communication skills and EEC has concentrated on advancing work-study program. Graduate research with professional ethics and the goals of sustainable waste and teaching assistantships, as well as responsibilities. management in the U.S. and fellowships funded by the Department, globally. For more information: earth. are available to qualified graduate engineering.columbia.edu. students. GRE scores are required of all Undergraduate Student Outcomes applicants for graduate studies. 1. an ability to identify, formulate, and Industry/University Cooperative solve complex engineering problems Research Center for Particulate and by applying principles of engineering, UNDERGRADUATE PROGRAM Surfactant Systems (CPaSS). The goals science, and mathematics The Bachelor of Science (B.S.) degree of CPaSS are to perform industrially 2. an ability to apply engineering design in Earth and Environmental Engineering relevant research to address the to produce solutions that meet prepares students for careers in the technological needs in commercial specified needs with consideration public and private sector concerned with surfactant and polymer systems, of public health, safety, and welfare, primary materials (minerals, fuels, water) develop new and more efficient as well as global, cultural, social, and the environment. Graduates are surface-active reagents for specific environmental, and economic factors also prepared to continue with further applications in the industry and 3. an ability to communicate effectively studies in Earth/Environmental sciences methodologies for optimizing their with a range of audiences and engineering, business, public policy, performance, promote the use of 4. an ability to recognize ethical and international studies, law, and medicine. environmentally benign surfactants professional responsibilities in The EEE program is accredited as an in a wide array of technological engineering situations and make environmental engineering program processes, and build a resource informed judgments, which must by the Engineering Accreditation consider the impact of engineering center to perform and provide state- Commission of ABET, http://www.abet. of-the-art facilities for characterization solutions in global, economic, org. Practice and theory are both environmental, and societal contexts of surface-active reagents. For more critical to the advancement of earth 5. an ability to function effectively on information: blogs.cuit.columbia.edu/ and environmental engineering; the teams whose members together iucrc/. department works actively with students provide leadership, create a to reach their learning outcomes and Langmuir Center for Colloids and collaborative and inclusive research and career goals. Interfaces (LCCI). This center brings environment, establish goals, plan together experts from mineral tasks, and meet objectives engineering, applied chemistry, chemical Undergraduate Program Objectives 6. an ability to develop and conduct engineering, biological sciences, and 1. Graduates equipped with the appropriate experimentation, chemistry to probe complex interactions necessary tools (mathematics, analyze and interpret data, and of colloids and interfaces with chemistry, physics, earth sciences, and use engineering judgment to draw surfactants and macromolecules. engineering science) will understand conclusions and implement the underlying 7. an ability to acquire and apply Lamont-Doherty Earth Observatory principles used in the engineering of new knowledge as needed, using (LCCI). For more information: ldeo. processes and systems. appropriate learning strategies. columbia.edu. 2. Graduates will be able to pursue careers in industry, government The Curriculum Lenfest Center for Sustainable Energy. agencies, and other organizations The first two years of the EEE program The mission of the Lenfest Center concerned with the environment are similar to those of other engineering for Sustainable Energy (LCSE) is to and the provision of primary and programs. Students are provided with a advance science and develop innovative secondary materials and energy, strong foundation in basic sciences and technologies that provide sustainable as well as continue their education mathematics, as well as the liberal arts energy for all humanity while maintaining as graduate students in related core. Specific to the EEE program is an the stability of Earth's natural systems. For disciplines. early and sustained introduction to earth more information: 3. Graduates will possess the basic skills science and environmental engineering, energy.columbia.edu. needed for the practice of Earth and and options for a number of science Environmental Engineering, including courses to meet the specific interests The Earth Institute. For more measurement and control of material information: earth.columbia.edu. of each student. The junior and senior flows through the environment; years of the program consist of a group

ENGINEERING 2021–2022 of required courses in engineering industry comprises nearly 30,000 big projections for climate change and 127 science and a broad selection of and small businesses with total revenues variability in the context of decisions technical electives organized. The of more than $150 billion. Sustainable for water resources and related sectors department website (eee.columbia.edu) development, climate change adaptation of impact; and (2) skills for integrated details the required courses and other and mitigation, as well as environmental risk assessment and management information. quality have become top priorities of for operations and design, as well Several Columbia departments, government and industries in the United as for regional policy analysis and such as Civil Engineering, Mechanical States and many other nations. management. Required classes include: Engineering, and Earth and This M.S. program is offered in • CIEE E4250 Hydrosystems Environmental Sciences (Lamont- collaboration with the Departments • CIEE E4163 Sustainable water Doherty Earth Observatory), as well as of Civil Engineering and Earth and treatment and reuse the Mailman School of Public Health, Environmental Sciences. Many of the • EAEE E4257 Environmental data contribute courses to the EEE program. teaching faculty are affiliated with analysis and modeling EEE students are strongly encouraged Columbia’s Earth Engineering Center. to work as summer interns in industry For students with a B.S. in engineering, Sustainable Energy or agencies on projects related to Earth at least 30 points (ten courses) are Building and shaping the energy and Environmental Engineering. required. Students may carry out a infrastructure of the twenty-first century research project (3 credits) or write a is one of the central tasks for modern thesis worth 6 points. A number of areas GRADUATE PROGRAMS engineering. The purpose of the of study are available for the M.S.-EEE, M.S. students must complete the sustainable energy concentration is and students may choose courses that professional development and to expose students to modern energy match their interest and career plans. leadership course, ENGI E4000, as technologies and infrastructures and to Additionally, there are three a graduation requirement. Doctoral the associated environmental, health, optional concentrations in the students will be enrolled in ENGI E6001– and resource limitations. Emphasis program, in each of which there 6004 and should consult their program will be on energy generation and use are a number of required specific for specific PDL requirements. technologies that aim to overcome the core courses and electives. The limits to growth that are experienced concentrations are described briefly M.S. in Earth and Environmental below; details and the lists of specific today. Energy and economic well- Engineering (M.S.-EEE) courses for each track are available being are tightly coupled. Fossil fuel The M.S.-EEE program is designed from the department. Students resources are still plentiful, but access for engineers and scientists who plan interested in a specific focus in to energy is limited by environmental to pursue, or are already engaged Mining Engineering or related fields and economic constraints. A future in, environmental management/ should consult their faculty adviser for world population of 10 billion people development careers. The focus of the relevant course listings. trying to approach the standard of program is the environmentally sound living of the developed nations cannot rely on today’s energy technologies mining and processing of primary Water Resources and and infrastructures without severe materials (minerals, energy, and water) Climate Risks to the recycling and proper disposal environmental impacts. Concerns over Climate-induced risk is a significant of used materials. The program also climate change and changes in ocean component of decision making for includes technologies for assessment chemistry require reductions in carbon the planning, design, and operation and remediation of damages to the dioxide emissions, but most alternatives of water resource systems, and environment including water treatment, to conventional fossil fuels, including related sectors such as energy, health, processing of mine tailings, and carbon nuclear energy, are too expensive to agriculture, ecological resources, capture, utilization and storage. Students fill the gap. Yet access to clean, cheap and natural hazards control. Climatic can choose a pace that allows them to energy is critical for providing minimal uncertainties can be broadly classified complete the M.S.-EEE requirements resources: water, food, housing, and into two areas: (1) those related to while being employed. transportation. anthropogenic climate change; (2) M.S.-EEE graduates are specially Concentration-specific classes will those related to seasonal- to century- qualified to work for engineering, sketch out the availability of resources, scale natural variations. Climate change financial startup, and operating their geographic distribution, the impacts the design of physical, social, companies engaged in the earth economic and environmental cost of and financial infrastructure systems to resources development and resource extraction, and avenues for support the sectors listed above. The environmental industries and increasing energy utilization efficiency, climate variability and predictability technologies, environmental groups in all such as cogeneration, district heating, issues impact systems operation, and industries, and for city, state, and federal and distributed generation of energy. hence design. The goal of the M.S. agencies responsible for the environment Classes will discuss technologies concentration in water resources and and energy/resource conservation. At for efficiency improvement in the climate risks is to provide (1) a capacity the present time, the U.S. environmental generation and consumption sector; for understanding and quantifying the energy recovery from solid wastes;

ENGINEERING 2021–2022 128 alternatives to fossil fuels, including earth resources management sector. required courses and six elective courses solar and wind energy, energy storage; Core classes include: from a pre-approved list of choices. and technologies for addressing the • EAEE E4160 Solid and hazardous Core courses: environmental concerns over the use of waste management • EAEE E4001 Industrial ecology of earth fossil fuels. Classes on climate change, • EAEE E4200 Introduction to resources air quality, and health impacts focus on sustainable production of earth • EAEE E4009 Geographic information the consequences of energy use. Policy mineral & metal resources systems (GIS) for resource, and its interactions with environmental • EAEE E4228 Separation science environmental and infrastructure sciences and energy engineering will and technology in sustainable earth management be another aspect of the concentration. resources development • EAEE E4006 Field methods for Additional specialization may consider environmental engineering region-specific energy development. M.S. in Carbon Management (MCM) Required classes include: The program is designed to prepare Elective courses must be six courses • EAEE E4002 Alternative energy students to create and implement multi- at the 4000 or higher level from within resources faceted solutions to the carbon problem the Earth and Environmental Engineering • EAEE E4220 Energy system with an in-depth understanding of the Department, the Chemical Engineering economics and optimization complexity and multidisciplinary nature of Department, or others as approved by the issues. the adviser. These include but are not Sustainable Mining and Materials Coursework includes 30 credits limited to: EAEE E4900, CHEE E4252, Earth mineral and metal resources are of graduate coursework. Depending CIEE E4252, EAEE E4257, ELEN E4004, the backbone of civilization and are on student's backgrounds, some EAEE E4160, EAEE E4300, EAEE E6132, critical to economic development and undergraduate level science courses EAEE E6140, EAEE E6150, EAEE E6212. meeting the demands of a growing may be required. Each student will Although not required, interested students population. their development today develop an academic plan with the may choose to complete up to six credits faces several big challenges: (i) program director. There are three in EAEE E9309. declining value content in the available options for completing the 30 credits: ore bodies and poor quality of the • 30 credits of lecture courses Doctoral Programs resources; (ii) increasing focus on safety • 24 credits of lecture courses and 6 EEE offers two doctoral degrees: and health risks, and environmental credits of research with a culminating (1) the Eng.Sc.D. degree, administered by impacts; (iii) inefficient and high energy Master's Thesis Columbia Engineering; and (2) the Ph.D. and water consumption; (iv) huge risks • 27 credits of lecture courses and 3 degree, administered by the Graduate associated with waste generation and credits of research with a concluding School of Arts and Sciences. management. report It is well recognized in the earth Core courses: Doctoral Qualifying Examination and resource development industry that • EAEE E4300/E6212 Introduction to Research Proposal the traditional processing paradigm carbon management Before the end of the first semester in is no longer sustainable and cannot • EAEE E4302 Carbon capture the doctoral program, the student and address these serious challenges. The • EAEE E4301 Carbon storage her/his adviser will set up an advisory overall goal of industry to develop and • EAEE E4305 CO2 utilization and committee of two or three faculty implement technologies for sensible conversion members. This committee will meet and sustainable use of earth resources at least once a semester to assess is part of a "mines of the future" Professional Degree; Engineer academic and research progress paradigm, which encompasses topics of Mines of the student and to recommend such as mine-to-metal integration, The program is designed for engineers corrective action in case of emerging modular processing, digital optimization, who wish to do advanced work beyond or existing deficiencies. machine learning and AI, sensors the level of the M.S. degree but who Doctoral students are required to and chemometrics, benign process do not desire to emphasize research. pass a qualifying exam within their chemicals, and a host of other forward- Admissions requirements include first year into the program. They will looking concepts. A similar effort and Undergraduate engineering degree, submit and defend their research outlook exists for urban mining and minimum 3.0 GPA, and GRE. proposal approximately one year after recycling. The transformation of waste Candidates must complete at least 30 successful completion of the qualifying to energy and the recovery of minerals credits of graduate work beyond the M.S., exam. Submission of the dissertation from recycling streams are examples of or 60 points of graduate work beyond and thesis defense will follow general these areas that EEE is a world leader the B.S. No thesis is required. All degree University rules. in. The EEE program in Sustainable requirements must be completed within 5 The qualifying examination will be Mining and Materials integrates years of the beginning of the first course an oral exam administered by three foundational engineering principles and credited toward the degree. faculty members. The adviser of the processes with the transformational Coursework includes four core student will be a member of the exam innovations under development in the

ENGINEERING 2021–2022 committee but may not be the chair. different scales and in different media; EAEE E3103x Energy, minerals, and materials 129 The students will be examined in their containment systems; modeling flow systems understanding of fundamentals as they and transport in surface and subsurface 3 pts. Lect: 3. Professor Park. Prerequisite(s): MSAE E3111 or MECE E3301 apply in the areas of research of the systems; soil/water decontamination and ENME E3161 or MECE E3100 or equivalent department: water resources, materials and bioremediation. Corequisites: MSAE E3111 or MECE E3301 and processing, energy, and chemical and ENME E3161 or MECE E3100 or equivalent. biochemical processes. It is expected Overview of energy resources, resource COURSES IN EARTH AND that each question period will last about management from extraction and processing to ENVIRONMENTAL ENGINEERING 20 minutes, of which 15 minutes will be recycling and final disposal of wastes. Resources availability and resource processing in the led by the faculty member from the area EAEE E2002x Alternative energy resources context of the global natural and anthropogenic 3 pts. Lect: 3. Professor Steingart. and the remaining 5 minutes will be material cycles; thermodynamic and chemical Unconventional, alternative energy resources. open for questions by all faculty present conditions including nonequilibrium effects that Technological options and their role in the world at the exam. There will be a final period shape the resource base; extractive technologies energy markets. Comparison of conventional and and their impact on the environment and the of 20 minutes for general questions. unconventional, renewable and nonrenewable biogeochemical cycles; chemical extraction from All graduate students are expected energy resources and analysis of the mineral ores, and metallurgical processes for consequences of various technological choices to have a background equivalent to the extraction of metals. In analogy to metallurgical and constraints. Economic considerations, energy required core of our undergraduate processing, power generation and the refining availability, and the environmental consequences program. They have, of course, an of fuels are treated as extraction and refining of large-scale, widespread use of each particular processes. Large scale of power generation opportunity to make up for any deficiency technology. Introduction to carbon dioxide and a discussion of its impact on the global in their master’s program. In order to be capture and carbon dioxide disposal as a means biogeochemical cycles. prepared for the exam, students can of sustaining the fossil fuel option. take at least one course in each core EAEE E3112y Introduction to rock mechanics EAEE E2100x A better planet by design 3 pts. Lect: 3. Not offered in 2021–2022. area during their first two semesters at 3 pts. Lect: 3. Professor Lall. Prerequisite(s): EAEE E3101 and ENME 3111, Columbia (see website for up-to-date Introduction to design for a sustainable planet. or their equivalents. Rock as an engineering Scientific understanding of the challenges. course listing). In case the student declares material, geometry and strength of rock joints, Innovative technologies for water, energy, an explicit minor in another department, geotechnical classification of rock masses, food, materials provision. Multiscale modeling the qualifying exam requirements will be strength and failure of rock, field investigations and conceptual framework for understanding modified in consultation with the graduate prior to excavation in rock, rock reinforcement, environmental, resource, human, ecological, analysis and support of rock slopes and tunnels, committee. The minor has to be approved and economic impacts and design performance and case histories. by both departments. evaluation. Focus on the linkages between The engineering objectives of EEE planetary, regional, and urban water, energy, MSAE E3141y Processing of metals and research and education include: mineral, food, climate, economic, and ecological semiconductors cycles. Solution strategies for developed and 3 pts. Lect: 3. Instructor to be announced. developing country settings. Prerequisite(s): MSAE E3103 or equivalent. • Provision and disposal of materials: Synthesis and production of metals and CHEE E3010x Principles of chemical environmentally sustainable semiconductors with engineered microstructures engineering thermodynamics extraction and processing of primary for desired properties. Includes high- 3 pts. Lect: 3. Professor Moment. materials; manufacturing of derivative temperature, aqueous, and electrochemical Prerequisite(s): CHEM UN1403. Corequisite: CHEN processing; thermal and mechanical processing products; recycling of used materials; E3030. Introduction to thermodynamics. of metals and alloys; casting and solidification; management of industrial residues Fundamentals are emphasized: the laws of diffusion, microstructural evolution, and phase and used products; materials-related thermodynamics are derived and their meaning transformations; modification and processing of explained and elucidated by applications to application of industrial ecology. surfaces and interfaces; deposition and removal engineering problems. Pure systems are treated, • Management of water resources: of thin films. Processing of Si and other materials with an emphasis on phase equilibrium. understanding, prediction, and for elemental and compound semiconductor- management of the processes that EAEE E3101y Earth resource based electronic, magnetic, and optical devices. production systems govern the quantity and quality of EAEE E3185y Summer fieldwork for earth and 3 pts. Lect: 3. Not offered in 2021–2022. water resources, including the role environmental engineers Technologies and equipment common to a wide 0.5 pt. Not offered in 2021–2022. of climate; development/operation of range of surface and subsurface engineering Undergraduates in earth and environmental water resource facilities; management activities: mine reclamation, hazardous waste engineering may spend up to three weeks in the of water-related hazards. remediation, discovering and operating surface field under staff direction. The course consists and underground mines, detection and removal • Energy resources and carbon of mine, landfill, plant, and major excavation site of hidden underground objects, waste disposal, management: mitigation of visits and brief instruction of surveying methods. dredging and harbor rehabilitation, and tunneling environmental impacts of energy A final report is required. for transportation or water distribution systems. production; energy recovery from These methods and equipment are examined EAEE E3200x Applied transport and chemical waste materials; advancement of as they apply across the spectrum from mining rate phenomena energy efficient systems; new energy to environmental engineering projects. The aim 3 pts. Lect: 3. Professor Chen. sources; development of carbon is to provide a broad background for earth and Prerequisite(s): APMA E2101. Fluid statics. Basics sequestration strategies. environmental engineers in careers involving of flow analysis. Dimensional analysis. Pipe flow. minerals and industrial, large-scale environmental • Sensing and remediation: Fluid dynamics, heat and mass transfer. Effects of projects. velocity, temperature, and concentration gradients understanding of transport processes at

ENGINEERING 2021–2022 130 and material properties on fluid flow, heat and EAEE E3801x Earth and environmental EAEE E4000x Machine learning for mass transfer. Applications to environmental engineering laboratory, II environmental engineering and science engineering problems. 2 pts. Lect: 1. Lab: 3. Professor Bourtsalas. 3 pts. Lect: 2.5. Professor Gentine. Prerequisite(s): EAEE E3800. Corequisite: EAEE Prerequisite(s): Computer language (Python or EAEE E3221x Environmental geophysics E4003. A continuation of EAEE E3800, with Julia), some linear algebra and machine learning. 3 pts. Lect: 3. Not offered in 2021–2022. emphasis on the principles underlying water Aimed at understanding and testing state-of- Introduction to applied and environmental analysis for inorganic, organic, and bacterial the-art methods in machine learning applied geophysics methods. Overview of principles contaminants. Lab required. to environmental sciences and engineering of geophysics, geophysical methods and problems. Potential applications include but are techniques (seismic, ground penetrating radar, EAEE E3900x and y–S3900 Undergraduate not limited to remote sensing, and environmental resistivity, frequency em, and magnetics), and research in earth and environmental and geophysical fluid dynamics. Includes testing theory and practical aspects of data processing engineering "vanilla" ML algorithms, feedforward neural and inversion. Examination of geophysical case 0–3 pts. Directed study. Members of the faculty. networks, random forests, shallow vs deep studies for engineering and environmental This course may be repeated for credit, but networks, and the details of machine learning purposes. no more than 3 points of this course may be techniques. counted toward the satisfaction of the B.S. CIEE E3250y Hydrosystems engineering degree requirements. Candidates for the B.S. EAEE E4001x Industrial ecology of earth 3 pts. Lect: 3. Professor Gentine. degree may conduct an investigation in Earth resources Prerequisite(s): CHEN E3110 or ENME E3161 and Environmental Engineering, or carry out a 3 pts. Lect: 3. Professor Bourtsalas. or equivalent, or instructor’s permission. A special project under the supervision of EAEE Industrial ecology examines how to reconfigure quantitative introduction to hydrologic and faculty. Credit for the course is contingent on industrial activities so as to minimize the adverse hydraulic systems, with a focus on integrated the submission of an acceptable thesis or final environmental and material resource effects modeling and analysis of the water cycle and report. This course cannot substitute for the on the planet. Engineering applications of associated mass transport for water resources Undergraduate design project (EAEE E3999 or methodology of industrial ecology in the analysis and environmental engineering. Coverage of EAEE E3999). of current processes and products and the unit hydrologic processes such as precipitation, selection or design of environmentally superior evaporation, infiltration, runoff generation, open EAEE E3901y Environmental microbiology alternatives. Home assignments of illustrative channel and pipe flow, subsurface flow and well 3 pts. Lect: 3. Professor Chandran. quantitative problems. hydraulics in the context of example watersheds Prerequisite(s): CHEM UN1404 or equivalent. and specific integrative problems such as risk- Fundamentals of microbiology, genetics and EAEE E4003x Aquatic chemistry based design for flood control, provision of water, molecular biology, principles of microbial 3 pts. Lect: 3. Professor Yip. and assessment of environmental impact or nutrition, energetics and kinetics, application Prerequisite(s): CHEE E3010. Principles of physical potential for non-point source pollution. Spatial of novel and state-of-the-art techniques in chemistry applied to equilibria and kinetics of hydrologic analysis using GIS and watershed monitoring the structure and function of microbial aqueous solutions in contact with minerals and models. communities in the environment, engineered anthropogenic residues. The scientific background processes for biochemical waste treatment and for addressing problems of aqueous pollution, CIEE E3255y Environmental control and bioremediation, microorganisms and public water treatment, and sustainable production pollution reduction systems health, global microbial elemental cycles. of materials with minimum environmental 3 pts. Lect: 3. Professor Farrauto. impact. Hydrolysis, oxidation-reduction, complex Prerequisite(s): EAEE E3200 or ENME E3161 EAEE E3995x, y, and s Fieldwork formation, dissolution and precipitation, or MECE E3100. Sources of solid/gaseous air 1 pt. Members of the faculty. predominance diagrams; examples of natural pollution and the technologies used for modern Prerequisite(s): Instructor's permission. Obtained water systems, processes for water treatment methods of abatement. Air pollution and its internship and approval from faculty adviser. and for the production of inorganic materials from abatement from combustion of coal, oil, and Written application must be made prior to minerals. natural gas and the thermodynamics of heat registration outlining proposed internship and engines in power generation. Catalytic emission study program. Final reports required. May not EAEE E4004x Physical processing and control is contrasted to thermal processes for be taken for pass/fail credit or audited. Fieldwork recovery of solids abating carbon monoxide, hydrocarbons, oxides credits may not count toward any major core, 3 pts. Lect: 3. Not offered in 2021–2022. of nitrogen and sulfur from vehicles and stationary technical elective, and nontechnical requirements. Generalized treatment of processes for solids sources. Processing of petroleum for generating International students must also consult with separation. Applications to materials processing fuels. Technological challenges of controlling the International Students and Scholars Office. and handling; mining; solid waste, recycling, and greenhouse gas emissions. Biomass and the Note: only for EAEE undergraduate students who resource recovery; construction materials and hydrogen economy coupled with fuel cells as need relevant off-campus work experience as a debris; scrap materials, yard and park wastes. future sources of energy. part of their program of study as determined by Economic considerations and context. Relevant instructor. materials properties and bulk materials analyses. EAEE E3800y Earth and environmental Process system flow-sheets and analysis. Solid/ engineering laboratory, I EAEE E3998x-E3999y Undergraduate design solid, solid/liquid, and solid/gas separation 2 pts. Lect: 1. Lab: 3. Professor Bourtsalas. project process. Liberation, concentration, and auxiliary Prerequisite(s): CHEE E3010. Corequisite: CIEE 2 pts. (each semester). Lect: 1. Lab: 2. processes. Design of separation machines: types E3255. Experiments on fundamental aspects Professor Farrauto. and intensities of force involved; scaling-up of earth and environmental engineering with Prerequisite(s): senior standing. Students must factors. Laboratory demonstrations and a field trip emphasis on the applications of chemistry, enroll for both 3998x and 3999y during their will be included. biology and thermodynamics to environmental senior year. Selection of an actual problem in earth processes: energy generation, analysis and and environmental engineering, and design of an EAEE E4005x Near-surface engineering purification of water, environmental biology, and engineering solution including technical, economic, geophysics biochemical treatment of wastes. Students will environmental, ethical, health and safety, social 3 pts. Lect: 3. Not offered in 2021–2022. learn the laboratory procedures and use analytical issues. Use of software for design, visualization, Geophysical methods as applicable to equipment firsthand, hence demonstrating economic analysis, and report preparation. engineering problems. Principles of geophysics experimentally the theoretical concepts learned Students may work in teams. Presentation of and noninvasive imaging techniques (inversion in class. results in a formal report and public presentation. technology) and benefits and pitfalls of

ENGINEERING 2021–2022 geophysics vs. direct imaging methods. EAEE E4010y Remote sensing and fabrication of vibration, motion, wind, wave, 131 Discussion of theory of each method. Discussion environmental change thermal gradient, and light energy harvesters; of data acquisition, processing and interpretation 3 pts. Lect: 3. Not offered in 2021–2022. resonance phenomenon, power electronics and for each method. Treatment of several case Prerequisite(s): EAEE E4009 or EESC GU4050 or energy storage and management. Applications studies. Class-wide planning and execution of instructor’s permission. Practical and theoretical to buildings, geothermal systems, and small-scale geophysical survey. foundations for the application of remote sensing transportation. techniques to identification and monitoring of EAEE E4006y Field methods for environmental change. Designing and applying CHEE E4140x Engineering separations environmental engineering spectral indices for assessment and monitoring, processes 3 pts. Lect: 1.5. Lab: 2. Professor McGillis. time series analysis of remote sensing data for 3 pts. Lect: 3. Professor Durning. Prerequisite(s): ENME E3161 or equivalent or analyzing environmental problems. Discussions of Prerequisite(s): CHEN E3100, E3120, and E3210 or instructor’s permission Principles and methods for published literature relevant to the central topic permission of instructor. Design and analysis of designing, building and testing systems to sense covered in class. Analysis of remote sensing data unit operations employed in chemical engineering the environment. Monitoring the atmosphere, using IRI data library. separations. Fundamental aspects of single and water bodies and boundary interfaces between multistaged operations using both equilibrium and the two. Sensor systems for monitoring heat and EAEE E4011y Industrial ecology for rate-based methods. Examples include distillation, mass flows, chemicals, and biota. Measurements manufacturing absorption and stripping, extraction, membranes, of velocity, temperature, flux and concentration 3 pts. Lect: 3. Not offered in 2021–2022. crystallization, bioseparations, and environmental in the field. The class will involve planning Prerequisite(s): EAEE E4001 or instructor's applications. and execution of a study to sense a local permission. Application of industrial ecology to environmental system. Design for Environment (DFE) of processes and EAEE E4150y Air pollution prevention and products using environmental indices of resources control EAEE E4007y Environmental geophysics field consumption and pollution loads. Introduction of 3 pts. Lect: 3. Professor Fthenakis. studies methodology for Life Cycle Assessment (LCA) of Adverse effects of air pollution, sources and 3 pts. Lect: 3. Not offered in 2021–2022. manufactured products. Analysis of several DFE transport media, monitoring and modeling of Application of geophysical methods to and LCA case studies. Term project required on air quality, collection and treatment techniques, noninvasive assessment of the near surface. use of DFE/LCA on a specific product/process: pollution prevention through waste minimalization First part consists of series of two-hour lectures (a) product design complete with materials and and clean technologies, laws, regulations, of physics and math involved in instrumental process selection, energy consumption, and standards, and guidelines. methods and data acquisition and processing. waste loadings; (b) LCA of an existing industrial The field (nine field days) students plan surveys; EAEE E4160y Solid and hazardous waste or consumer product using a commercially management collect and analyze geophysical data in teams; established method. learn how to integrate geophysical data 3 pts. Lect: 3. Professor Bourtsalas. with invasive data, hydrological, geological, CHEE E4050x Industrial and environmental Generation, composition, collection, transport, engineering, and contaminant transport models; electrochemistry storage and disposal of solid and hazardous and develop a comprehensive and justifiable 3 pts. Lect: 3. Not offered in 2021–2022. waste. Impact on the environment and public model of the subsurface. Geophysical methods Prerequisite(s): CHEN E3010 or equivalent. A health. Government regulations. Recycling and include GPR (Ground Penetrating Radar), presentation of the basic principle underlying resource recovery. conductivity, and magnetic and seismic methods. electrochemical processes. Thermodynamics, CIEE E4163y Sustainable water treatment Field applications include infrastructure/ electrode kinetics, and ionic mass transport. and reuse environmental assessment, archeological studies, Examples of industrial and environmental 3 pts. Lect: 3. Professor Knowles. and high resolution geology. applications illustrated by means of laboratory Prerequisite(s): Introductory chemistry (with lab) experiments: electroplating, refining, and EAEE E4009x Geographic information and fluid mechanics, or the equivalent. Theory winning in aqueous solutions and in molten systems (GIS) for resource, environmental and application of the physical and chemical salts; electrolytic treatment of wastes; primary, processes for treating potable water and reusing and infrastructure management secondary, and fuel cells. 3 pts. Lect: 3. Professor Gorokhovich. wastewater. Disinfection/oxidation, coagulation Prerequisite(s): Permission of the instructor. ECIA W4100y Management and development and flocculation, clarification, filtration, ion Basic concepts of geomatics, spatial data of water systems exchange, adsorption, membrane processes, representation and organization, and analytical 3 pts. Lect: 3. Not offered in 2021–2022. advanced oxidation processes, activated sludge, tools that comprise GIS are introduced and Decision analytic framework for operating, and anaerobic sludge digestion. applied to a variety of problems including managing, and planning water systems, EAEE E4180y Electrochemical energy storage watershed protection, environmental risk considering changing climate, values and needs. systems assessment, material mass balance, flooding, Public and private sector models explored through 3 pts. Lect: 3. Professor Steingart. asset management, and emergency response U.S.-international case studies on topics ranging Prerequisite(s): CHEM UN1403-1404 or equivalent, to natural or man-made hazards. Technical from integrated watershed management to the MECE E3301 or equivalent, PHYS UN1402 or content includes geography and map analysis of specific projects for flood mitigation, equivalent. Corequisites: CHEN E4201, EAEE projections, spatial statistics, database design water and wastewater treatment, or distribution E3103. Survey course on electrochemical and use, interpolation and visualization of system evaluation and improvement. energy storage with a focus on closed-form spatial surfaces and volumes from irregularly CIEE E4116x Energy harvesting cells. Fundamentals of thermodynamics will be spaced data, and decision analysis in an reviewed and fundamentals of electrochemistry applied setting. Taught in a laboratory setting 3 pts. Lect: 3. Professor Yin. Prerequisite(s): ENME E3114 or equivalent, or introduced. Application of fundamentals to using ArcGIS. Access to New York City and devices such as batteries, flow batteries, and fuel other standard databases. Term projects instructor’s permission. Criterion of energy harvesting, identification of energy sources. cells. Device optimization with respect to energy emphasize information synthesis toward the density, power density, cycle life, and capital cost solution of a specific problem. Theory of vibrations of discrete and continuous system, measurement and analysis. Selection of will be considered. materials for energy conversion, piezoelectric, EAEE E4190x Photovoltaic systems electromagnetic, thermoelectric, photovoltaic, engineering and sustainability etc. Design and characterization, modeling and 3 pts. Lect: 3. Not offered in 2021–2022.

ENGINEERING 2021–2022 132 Prerequisite(s): Senior standing or instructor’s corrosion, electricity generation, district heating, EAEE E4241x Solids handling and transport permission. A systems approach for intermittent metal recovery, emission control, and beneficial systems renewable energy involving the study of use of ash residues. 3 pts. Lect: 3. Not offered in 2021–2022. resources, generation, demand, storage, Analysis and design of transportation systems EAEE E4220x Energy system economics and transmission, economics and politics. Study of for bulk solids in tunnels, mines, and large current and emerging photovoltaic technologies, optimization excavations. Design of hoisting, cable transport, with focus on basic sustainability metrics 3 pts. Lect: 3. Professor Xu. rail and trackless haulage systems, conveyor (e.g., cost, resource availability, and life-cycle Prerequisite(s): Basic linear algebra, basic belts, selection of loaders, excavators, off- environmental impacts). The status and potential probability and statistics, and basic programming highway trucks, and draglines for large of first- and second-generation photovoltaic skills. Transitioning into a sustainable energy excavations. technologies (e.g., crystalline and amorphous Si, system is not only a technical challenge but CdTe, CIGS) and emerging third-generation ones. also an economical one. Teaches students CIEE E4250x or y Hydrosystems Storage options to overcome the intermittency fundamentals of power system economics over 3 pts. Lect: 3. Professor Gentine. constraint. Large scales of renewable energy which current electricity markets are designed. Prerequisite(s): CHEN E3110 or ENME E3161 technologies and plug-in hybrid electric cars. Also examines challenges and opportunities or equivalent, or the instructor’s permission. in future sustainable energy systems such as The hydrologic cycle and relevant atmospheric EAEE E4200y Introduction to sustainable carbon tax, renewable energy, demand response, processes; water and energy balance; radiation; production of earth mineral & metal resources and energy storage. Covers mixed-integer boundary layer; precipitation formation; 3 pts. Lect: 3. Professors Farinato and Nagaraj. linear programming and demonstrates how evaporation; vegetation transpiration; infiltration; Prerequisite(s): EAEE E3103 and undergraduate mathematical optimizations are integrated into storm runoff; snowmelt; and flood processes. level courses in chemistry (especially inorganic, energy system operations. Provides overview of Routing of runoff and floodwaters. Groundwater physical and organic). Introductory course current energy system research topics. Includes flow and the hydraulics of wells. Probabilistic focused on engineering principles and unit a project using mathematical tools to solve real- modeling, and extreme-value theory. operations involved in sustainable processing world problems in the energy system. of primary and secondary earth mineral and CHEE E4252x Introduction to surface and metal resources. Covers entire value chain, viz, EAEE E4222y Interfacial engineering for colloid chemistry aspects of economic resource deposits, mining, sustainable energy and materials 3 pts. Lect: 3. Professors Farinato and fundamental principles and processes for size 3 pts. Lect: 3. Professor Farinoto. Somasundaran. reduction, separations based on physical and Prerequisite(s): EAEE E3103 or equivalent or Prerequisite(s): Elemental physical chemistry. chemical properties of minerals and metals, instructor's permission. Materials and systems in The principles of surfaces and colloid chemistry solid-liquid separation, waste and pollution sustainable energy and material science sectors critical to range of technologies indispensable to management, water and energy efficiency and depend on properly engineering surfaces and modern life. Surface and colloid chemistry has management, safety and health, environmental interfaces within. Interfacial junctions can be significance to life sciences, pharmaceuticals, impact assessment and control, and economic bottlenecks for transport processes, chemical agriculture, environmental remediation and efficiency. Special emphasis on concepts and reactions, and stress transfer. Principles of waste management, earth resources recovery, practical applications within "mines of the surface science form the basis for addressing electronics, advanced materials, enhanced oil future" framework to highlight innovations issues and problems in interfacial engineering. recovery, and emerging extraterrestrial mining. and transformational technological changes in Fundamentals of interfacial engineering Topics include: thermodynamics of surfaces, progress. are illustrated via a wide variety of practical properties of surfactant solutions and surface technological examples related to sustainable films, electrokinetic phenomena at interfaces, EAIA W4200y Alternative energy resources energy (material acquisition and processing, principles of adsorption and mass transfer and 3 pts. Lect: 3. Professor Steingart. waste management, device manufacture) and modern experimental techniques. Leads to Unconventional, alternative energy resources. material science (composites, coatings, ceramics, deeper understanding of interfacial engineering, Technological options and their role in the world membranes, biomaterials, microelectronics). particulate dispersions, emulsions, foams, energy markets. Comparison of conventional and Interfacial engineering is inherently cross- aerosols, polymers in solution, and soft matter unconventional, renewable and nonrenewable, disciplinary, and underlying concepts are topics. energy resources and analysis of the applicable. consequences of various technological choices CIEE E4252y Foundations of environmental and constraints. Economic considerations, energy EAEE E4228y Separation science and engineering availability, and the environmental consequences technology in sustainable earth resources 3 pts. Lect: 3. Professor Chandran. of large-scale, widespread use of each particular development Prerequisite(s): CHEM UN1403, or equivalent; technology. Introduction to carbon dioxide 3 pts. Lect: 3. Professors Farunato and Nagaraj. ENME E3161 or equivalent. Engineering aspects disposal as a means of sustaining the fossil fuel Prerequisite(s): EAEE E3103 and undergraduate of problems involving human interaction with option. Recitation section required. level courses in chemistry (especially inorganic, the natural environment. Review of fundamental physical and organic). Recommended: EAEE principles that underlie the discipline of EAEE E4210x Thermal treatment of waste and E4252, EAEE E4003, and EAEE E4200. Detailed environmental engineering, i.e., constituent biomass materials study of the chemical and physicochemical transport and transformation processes in 3 pts. Lect: 3. Professor Bourtsalas. principles underlying separations in development environmental media such as water, air, and Prerequisite(s): CHEE E3010 or the equivalent of earth resources in a safe and sustainable ecosystems. Engineering applications for or instructor’s permission. Origins, quantities manner. Covers wide-range of solid-solid, addressing environmental problems such as water generated, and characterization of solid wastes. solid-liquid and liquid-liquid separations used quality and treatment, air pollution emissions, Chemical and physical phenomena in the in processing of mineral resources. Interfacial and hazardous waste remediation. Presented in combustion or gasification of wastes. Application science and engineering principles of important the context of current issues facing the practicing of thermal conversion technologies, ranging industrial processes of flotation, flocculation, engineers and government agencies, including from combustion to gasification and pyrolysis. dewatering, interfacial transport, magnetic/ legal and regulatory framework, environmental Quantitative description of the dominant waste gravity/electrostatic separations, solvent impact assessments, and natural resource to energy processes used worldwide, including extraction, solid-support extraction, crystallization management. feedstock preparation, moving grate and fluid and precipitation. Emphasis on concepts in bed combustion, heat transfer from combustion interfacial chemistry and concepts associated with gases to steam, mitigation of high-temperature 'mines of the future' framework.

ENGINEERING 2021–2022 EAEE E4255x River and coastal approach). Simple carbon emission model to tools, as well as Bayesian statistics and decision 133 hyrdrodynamics estimate the impacts of a specific intervention theory for evaluating various solutions to close 3 pts. Lect: 3. Not offered in 2021–2022. with regard to national, per capita, and global the carbon cycle, a detailed examination of the Prerequisite(s): CHEN E3110 or ENME E3161 or the emissions. Student-led case studies (e.g., geochemical carbon cycle, major conceptual equivalent. Dynamics of flow and waves in rivers reforestation, biofuels, CCS, efficiency, alternative models that couple its changes to climate change, and coastal settings, with applications to flooding energy) to illustrate necessary systems approach analysis of the anthropogenic carbon sources and and mixing of saline and fresh waters, sediment required to tackle global challenges. sinks and role of carbon in energy production, transport. Integrative hydrodynamics modeling closing the carbon cycle impacts on energy experience using numerical and analytical tools EAEE E4301y Carbon storage security, economic development and climate applied to complex real world setting, including 3 pts. Lect: 3. Not offered in 2021–2022. change protection, analysis of solutions to close concerns of anthropogenic change in rivers and Prerequisite(s): Undergraduate level mathematics the carbon cycle. estuaries and sea level fluctuations at the river- and science, or instructor’s permission. Major estuary boundary. technologies to capture carbon dioxide via new or EAEE E4305y Carbon utilization and retrofitted power plant designs, during industrial conversion CIEE E4257y Groundwater contaminant processes, and from ambient air. In addition to 3 pts. Lect: 3. Not offered in 2021–2022. transport and remediation basic science and engineering challenges of Prerequisite(s): Undergraduate level 3 pts. Lect: 3. Professors Mutch and Carbonaro. each technology, full spectrum of economic, thermodynamics or instructor's permission.

Prerequisite(s): CIEE E3250 or equivalent. environmental, regulatory, and political/policy Introduction to various CO2 utilization and Sources and types of groundwater contamination. aspects, and their implication for regional and conversion technologies that can reduce Groundwater hydrology. Groundwater global carbon management strategies of the the overall carbon footprint of commodity contaminant rate and transport. Flow and future. Combination of lectures, class debates chemicals and materials. Fundamentals of transport in the unsaturated zone. Nonaqueous and breakout groups, student presentations, and thermodynamics, fluid mechanics, reaction phase liquids and multiphase flow. Physical and independent final projects. kinetics, catalysis and reactor design will be numerical models for contaminant transport. discussed using technological examples such as EAEE E4302x or y Carbon capture Characterization and assessment of contaminated enhanced oil recovery, shale fracking, photo and 3 pts. Lect: 3. Not offered in 2021–2022. sites. Groundwater remediation alternatives. electrochemical conversion of CO to chemical Prerequisite(s): Undergraduate level math 2 Regulations. and fuels, and formation of solid carbonates and and science or instructor’s permission. Major their various uses. Life cycle analyses of potential EAEE E4257y Environmental data analysis technologies to store carbon dioxide, geological, products and utilization schemes will also be and modeling ocean, and in the carbon chemical pool. Carbon discussed, as well as the use of renewable energy 3 pts. Lect: 3. Professor Xu. dioxide transport technologies also covered. for CO conversion. Prerequisite(s): IEOR E3658, E4150, or STAT In addition to basic science and engineering 2 GU4001 or equivalent; some exposure to linear challenges of each technology, full spectrum EAEE E4350x Planning and management of algebra; basic programming experiences. of economic, environmental, regulatory, and urban hydrologic systems Introduction parametric and nonparametric political/policy aspects, and their implication 3 pts. Lect: 3. Professor Rosenberg statistical models applied to climate and for regional and global carbon management Prerequisite(s): ENME E3161 or equivalent. environmental data analysis. Time and space strategies of the future. Combination of lectures, Introduction to runoff and drainage systems in an data analysis methods will be focused, including class debates and breakout groups, student urban setting, including hydrologic and hydraulic clustering, autoregressive models, trend analysis, presentations, and independent final projects. analyses, flow and water quality monitoring, Bayesian analysis, missing data imputation, common regulatory issues, and mathematical EAEE E4303x or y Carbon measurement and geostatistics, and principal components modeling. Applications to problems of climate analysis. Application to problems of climate monitoring variation, land use changes, infrastructure variation and change; hydrology; air, water and 3 pts. Lect: 3. Not offered in 2021–2022. operation and receiving water quality, developed soil pollution dynamics; disease propagation; Prerequisite(s): Undergraduate level math using statistical packages, public-domain models, ecological change; and resource assessment. and science or instructor permission. Sources and Geographical Information Systems (GIS). The class requires the use of R with hands-on of various GHGs (whether fossil/industrial or Team projects that can lead to publication quality programmings and a term project applied to a biogenic), their chemical behavior, interactions, analyses in relevant fields of interest. Emphasis current environmental data analysis problem. and global warming potential once airborne; on the unique technical, regulatory, fiscal, policy, available measurement, monitoring, and detection and other interdisciplinary issues that pose a EAEE E4262y Space exploration and mining technologies to track gas emissions, including challenge to effective planning and management 3 pts. Lect: 3. Professors Bourtsalas and leakage from storage sites. Carbon accounting of urban hydrologic systems. Somasundaran. and reporting methodologies such as life cycle Needs and opportunities for space exploration analysis, and corporate carbon footprinting. EAEE E4361y Economics of earth resource and mining, resources in planets and asteroids, In addition to basic science and engineering industries history of human colonization, terraforming Mars, challenges of each technology, full spectrum 3 pts. Lect: 3. Not offered in 2021–2022. Titan, and the moon, safety and health issues, of economic, environmental, regulatory, and Prerequisite(s): EAEE E3103 or instructor’s benign mining, space junk extraction, microbial political/policy aspects, and their implication permission. Definition of terms. Survey of mining. for regional and global carbon management earth resource industries: resources, reserves, strategies of the future. Combination of lectures, production, global trade, consumption of mineral EAEE E4300x or y Introduction to carbon class debates and breakout groups, student commodities and fuels. Economics of recycling management presentations, and independent final projects. and substitution. Methods of project evaluation: 3 pts. Lect: 3. Not offered in 2021–2022. estimation of operating costs and capital Prerequisite(s): Undergraduate level mathematics EAEE E4304x Closing the carbon cycle requirements, project feasibility, risk assessment, and science, or instructor’s permission. 3 pts. Lect: 3. Professor Eisenberger. and environmental compliance. Cost estimation Introduction to natural and anthropogenic carbon Prerequisite(s): Calculus, basic inorganic for reclamation/remediation projects. Financing cycle, and carbon and climate. Rationale and chemistry, and basic physics, including of reclamation costs at abandoned mine sites and need to manage carbon and tools with which thermodynamics, or instructor’s permission. waste-disposal postclosure liability. to do so (basic science, psychology, economics Introduction to complex systems, their impact on and policy background, negotiations and society; our understanding and predictability of the carbon emphasis on interdisciplinary and inter-dependent cycle, the use of systems analysis and modeling

ENGINEERING 2021–2022 134 CHEE E4530y Corrosion of metals or the instructor’s permission. Application of Prerequisite(s): EAEE E4550 or equivalent, or 3 pts. Lect: 3. Instructor to be announced. fundamental principles to designing water instructor’s permission. Fundamental principles Prerequisite(s): CHEN E3010 or equivalent. The treatment and reuse plants. Development of of kinetics, characterization and preparation of theory of electrochemical corrosion, corrosion process designs for a potable water treatment catalysts for production of petroleum products tendency, rates, and passivity. Application to plant, a biological wastewater treatment plant, for conventional transportation fuels, specialty various environments. Cathodic protection and or a water reclamation and reuse facility by chemicals, polymers, food products, hydrogen coatings. Corrosion testing. students working in teams. Student work in and fuel cells and the application of catalysis evaluation of water quality and pilot plant data, in biomass conversion to fuel. Update of the EAEE E4550x Catalysis for emissions control screening process alternatives, conducting ever changing demands and challenges in 3 pts. Lect: 3. Professor Farrauto. regulatory reviews and recommending a process environmental applications, focusing on advanced Prerequisite(s): One year of general college for implementation, supported by engineering catalytic applications as described in modern chemistry. Fundamentals of heterogeneous drawings and capital operating costs. Periodic literature and patents. catalysis including modern catalytic preparation oral progress reports and a full engineering techniques. Analysis and design of catalytic report are required. Presentations by practicing EAEE E6151y Applied geophysics emissions control systems. Introduction to current engineers, utility personnel, and regulators; and 3 pts. Lect: 3. Not offered in 2021–2022. industrial catalytic solutions for controlling field trips to water, wastewater, and water reuse Potential field data, prospecting, wave equations. gaseous emissions. Introduction to future facilities. Huygens’ principle, Green’s functions, Kirchoff catalytically enabled control technologies. equation, WKB approximation, ray tracing. Wave EAEE E4980 Urban environmental technology propagation, parameters. Computer applications. EAEE E4560y Particle technology and policy Wavelet processing, filters and seismic data. 3 pts. Lect: 3. Not offered in 2021–2022. 3 pts. Lect: 3. Not offered in 2021–2022. Stratified Earth model, seismic processing and Prerequisite(s): ENME E3161 and MSAE E3111 Progress of urban pollution engineering via profiling. Radon transform and Fourier migration. or equivalent. Introduction to engineering contaminant abatement technology, government Multidimensional geological interpretation. processes involving particulates and powders. policy, and public action in urban pollution. The fundamentals of particle characterization, Pollutant impact on modern urban environmental EACH E6181x Advanced electrochemical multiphase flow behavior, particle formation, quality, natural resources, and government, energy storage processing and utilization of particles in various municipal, and social planning and management 3 pts. Lect: 3. Professor Steingart. engineering applications with examples in programs. Strong emphasis on current and Prerequisite(s): EAEE E4180, EAEE E4002. energy and environment related technologies. twentieth-century waste management in New Most modern commercial implementations Engineering of functionalized particles and design York City. of electrochemical energy storage are not of multiphase reactors and processing units with fully deterministic: provides context and best- emphasis on fluidization technology. Particle EAEE E4999x and y Fieldwork hypotheses for modern challenges. Topics technology is an interdisciplinary field. Due to 1 pt. Members of faculty. include: current understanding of lithium/lithium the complexity of particulate systems, particle Prerequisite(s): Instructor’s written permission. anode solid-electrolyte-interphase, reversible technology is often treated as art rather than Only EAEE graduate students who need relevant and irreversible side reactions in redox flow science. In this course, the fundamental principles off- campus work experience as part of their systems, electrochemically correlated mechanical governing the key aspects of particle science and program of study as determined by the instructor. fracture at multiple scales, relationships between technology are introduced along with various Written application must be made prior to electrolyte solvation and electrode insertion, industrial examples. registration outlining proposed study program. roughening, smoothing, and detachment behavior Final reports required. This course may not be of metal anodes, best practices in structural, EAEE E4901y Environmental microbiology taken for pass/fail credit or audited. International chemical, and microscopic characterization, 3 pts. Lect: 3. Professor Chandran. students must also consult with the International morphological vs. macro-homogenous transport Basic microbiological principles; microbial Students and Scholars Office. models, particle to electrode to cell non-linearity. metabolism; identification and interactions of microbial populations responsible for the EAEE E6132y Numerical methods in EAIA W6201x or y Complexity science biotransformation of pollutants; mathematical geomechanics 4 pts. Lect: 4. Professors Castner, Dumas, Lall, modeling of microbially mediated processes; 3 pts. Lect: 3. Professor Chen. Mutter, and Rising. biotechnology and engineering applications using Prerequisite(s): EAEE E3112 and CIEN E4241 Prerequisite(s): Graduate standing and instructor’s microbial systems for pollution control. or instructor’s permission. A detailed survey permission. Survey of techniques, applications, of numerical methods used in geomechanics, and implications of complexity science and EAEE E4950x Environmental biochemical emphasizing the Finite Element Method (FEM). complex systems. Topics include systems processes Review of the behavior of geological materials. dynamics, chaos, scaling, fat-tailed distributions, 3 pts. Lect: 3. Professor Chandran. Offered only Water and heat flow problems. FEM techniques fractals, information theory, emergence, criticality, in odd years. for solving nonlinear problems, and simulating agent-based models, graph theory, and social Prerequisite(s): EAEE E4901, E4003, CIEE incremental excavation and loading on the surface networks. Applications will cover climate science, E4252, or instructor’s approval. Qualitative and underground. ecology, conflict, hydrology, geomorphology, and quantitative considerations in engineered physics, social theory, epidemiology, and environmental biochemical processes. EAEE E6140y Environmental physicochemical governance. Characterization of multiple microbial reactions processes in a community and techniques for determining 3 pts. Lect: 3. Professor Yip. EAEE E6212y Carbon sequestration associated kinetic and stoichiometric parameters. Prerequisite(s): CIEE E4252 and CIEE E4163 or 3 pts. Lect: 3. Professor Park. Engineering design of several bioreactor the equivalent, or the instructor's permission. Prerequisite(s): EAEE E3200 or equivalent or configurations employed for biochemical waste Fundamentals and applications of key instructor’s permission. New technologies for treatment. Mathematical modeling of engineered physicochemical processes relevant to water capturing carbon dioxide and disposing of it biological reactors using state-of-the-art quality engineering (such as water treatment, away from the atmosphere. Detailed discussion simulation packages. waste water treatment/reuse/recycling, of the extent of the human modifications to the desalination) and the natural environment (e.g., natural carbon cycle, the motivation and scope EAEE E4951x Engineering systems for water lakes, rivers, groundwater). of future carbon management strategies and treatment and reuse the role of carbon sequestration. Introduction of 3 pts. Lect: 3. Not offered in 2021–2022. EAEE E6150y Industrial catalysis several carbon sequestration technologies that Prerequisite(s): CIEE E4163 and EAEE E3901, 3 pts. Lect: 3. Professor Farrauto.

ENGINEERING 2021–2022 allow for the capture and permanent disposal EAEE E8229x Selected topics in processing EAEE E9280x and y Earth and environmental 135 of carbon dioxide. Engineering issues in their minerals and wastes engineering colloquium implementation, economic impacts, and the 3 pts. Lect: 2. Lab: 3. Not offered in 2021–2022. 0 pts. Lect: 1.5. Professor Yip. environmental issues raised by the various Prerequisite(s): CHEE E4252 or instructor’s All graduate students are required to attend the methods. permission. Critical discussion of current departmental colloquium as long as they are in research topics and publications in the area residence. Advanced doctoral students may be CHEE E6220y Equilibria and kinetics in of flotation, flocculation, and other mineral excused after three years of residence. No degree hydrometallurgical systems processing techniques, particularly mechanisms credit is granted. 3 pts. Lect: 3. Not offered in 2021–2022. of adsorption, interactions of particles in Prerequisite(s): CHEE E4050 or EAEE E4003. solution, thinning of liquid films, and optimization EAEE E9302x and y Mining engineering Detailed examination of chemical equilibria techniques. research in hydrometallurgical systems. Kinetics and 0–4 pts. Not offered in 2021–2022. mechanisms of homogeneous and heterogeneous EAEE E8231y Selected topics in hydro- and Graduate research directed toward solution of reactions in aqueous solutions. electrometallurgy technicoscientific problems in mining. 3 pts. Lect: 3. Instructor to be announced. EAEE E6228y Theory of flotation Prerequisite(s): EAEE E4003 and CHEE EAEE E9305x and y–S9305 Earth and 3 pts. Lect: 3. Not offered in 2021–2022. E4050, or instructor’s permission. Review of environmental engineering research Prerequisite(s): CHEE E4252 or instructor’s current research and literature in the field of 0–12 pts. Members of the faculty. permission. A detailed study of the hydrometallurgy, electrometallurgy, and corrosion. Graduate research directed toward solution of physicochemical principles of the flotation Topics will be selected by the instructor to a problem in mineral processing or chemical process. illustrate the application of thermodynamics and metallurgy. CHEE E6252y Advanced surface and rate phenomena to the design and control of EAEE E9800x and y–S9800 Doctoral research colloid chemistry electrochemical engineering processes. instruction 3 pts. Lect: 2. Lab: 3. Professors Somasundaran EAEE E8233x and y Research topics in 3, 6, 9, or 12 pts. Members of the faculty. and Farinato. particle processing A candidate for the Eng.Sc.D. degree in mineral Prerequisite(s): CHEE E4252. Applications 0 pts. Professor Somasundaran. engineering must register for 12 points of doctoral of surface chemistry principles to wetting, Emergent findings in the interactions of particles research instruction. Registration in EAEE E9800 flocculation, flotation, separation techniques, with reagents and solutions, especially inorganics, may not be used to satisfy the minimum residence catalysis, mass transfer, emulsions, foams, surfactants, and polymers in solution, and requirement for the degree. aerosols, membranes, biological surfactant their role in grinding, flotation, agglomeration, systems, microbial surfaces, enhanced oil EAEE E9900x and y–S9900 Doctoral filtration, enhanced oil recovery, and other dissertation recovery, and pollution problems. Appropriate mineral processing operations. individual experiments and projects. Lab required. 0 pts. Members of the faculty. EAEE E8273x-E8274y Mining engineering A candidate for the doctorate may be required EAEE E6255x-E6256y Methods and reports to register for this course every term after the applications of analytical decision making in 0–4 pts. Not offered in 2021–2022. student’s coursework has been completed, and mineral industries May substitute for formal thesis, EAEE E9271, until the dissertation has been accepted. 3 pts. Lect: 3. Not offered in 2021–2022. upon recommendation of the student’s adviser. Prerequisite(s): Instructor’s permission. Advanced study of decision-making problems with critical EAEE E9271x and y–S9271 Earth and survey and applications of quantitative decision- environmental engineering thesis making techniques in mineral industries. 0–6 pts. Members of the faculty. Systematic development of methods of the Research work culminating in a creditable formulation, analysis, and resolution of these dissertation on a problem of a fundamental problems. nature selected in conference between student and adviser. Wide latitude is permitted in choice EAEE P6329x or y Water, sanitation, and of a subject, but independent work of distinctly human health graduate character is required in its handling. 3 pts. Lect: 3. Professor Shaman. Prerequisite(s): Instructor’s permission. In-depth EAEE E9273x-E9274y Earth and analysis of issues relating to water, sanitation, and environmental engineering reports hygiene in both the developed and developing 0–4 pts. worlds. Hydrologic cycle, major causes of enteric May substitute for the formal master’s thesis, morbidity and mortality, and design, financing and EAEE E9271, upon recommendation of implementation of sanitation systems. For both the department. engineering and public health students; intended to foster dialog between the two communities.

ENGINEERING 2021–2022 136 ELECTRICAL ENGINEERING 1300 S. W. Mudd, MC 4712 212-854-3105 ee.columbia.edu

CHAIR Henning G. Schulzrinne, PROFESSOR OF ADJUNCT ASSISTANT Linbi Hong Ioannis Kymissis Computer Science PROFESSIONAL PROFESSORS Jakub Piotr Jadwiszczak 1013 CEPSR Kenneth L. Shepard PRACTICE Guido Hugo Jajamovich Igor Kadota Yannis P. Tsividis Zoran Kostic Wooram Lee David Lynall VICE CHAIR Wen I. Wang Xiang Meng Victoria Andino Gil Zussman Xiaodang Wang SENIOR LECTURER Damian F. Sciano Pavlovsky 809 CEPSR Charles A. Zukowski David Vallancourt Sichao Yang Abhinav Parihar Gil Zussman Lei Zhang Mohit Sharma DIRECTOR OF FINANCE ADJUNCT PROFESSORS Christopher Thomas Alexei Ashikhmin SENIOR RESEARCH AND ADMINISTRATION ASSOCIATE Ilke Uguz Yves Baeyens SCIENTIST Wendy Villa PROFESSORS Kevin Vermeulen Doru Calin Debasis Mitra 1303 S. W. Mudd Javad Ghaderi Dehkordi Maria Vomero Hoots Timothy Dickson Christine P. Hendon Heyu Yin Irving Kalet ASSOCIATE RESEARCH PROFESSORS Xiaofan Fred Jiang Zifang Zhao SCIENTISTS Dimitris Anastassiou Ethan Katz-Bassett Ching-Yung Lin Jakob Kiliam Buchheim Keren Bergman Harish Krishnaswamy Debasis Mitra STAFF ASSOCIATES Andreas Hartel Shih-Fu Chang Nima Mesgarani Krishan Sabnani Adam Banees Yiyin Zhou Alexander Gaeta, John W. Paisley Jacob Sharony Lovish Chum Applied Physics and Matthias Preindl Deepak Turaga POSTDOCTORAL Materials Science Mingoo Seok Anwar Walid RESEARCH SCIENTISTS Predrag Jelenkovic John N. Wright Thomas Woo Peter Kinget Filipe Arroyo Cardoso ADJUNCT ASSOCIATE Long Chen Ioannis (John) Kymissis ASSISTANT Min-Seong Choo Aurel A. Lazar PROFESSORS PROFESSORS Jason Fabbri Michal Lipson James Anderson Wei-Yi Cheng Guangxing Han Paul Sajda, Biomedical Dion Khodagholy Chong Li Bjoern David Engineering Araghy Shahriar Shahramian Hellenkamp Asaf Cidon

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

ENGINEERING 2021–2022 and integrated solid-state devices; and Integrated Devices applies (CISL), Analog & RF IC Design Laboratory, 137 nanoelectronics and nanophotonics; fundamental physical principles to VLSI Design Laboratory, High Speed integrated circuits and systems; systems develop revolutionary new electronic, and mmWave IC Laboratory, Analog and biology; neuroengineering; and smart photonic, and optical devices made from Mixed Signal IC Laboratory, Bioelectronics electric energy. Details on all of conventional and emerging materials, Laboratory, Lightwave Laboratory, and these areas can be found at including graphene, 2D semiconductors, Nano Photonics Laboratory. ee.columbia.edu/research. and organic semiconductors. Laboratory instruction is provided The Signals, Information and Data Research includes nanofabrication, in a suite of newly-renovated facilities area concerns the representation, characterization, and electromagnetic on the twelfth floor of the S. W. Mudd processing, analysis, and communication design of quantum device structures Building. These teaching laboratories of information embedded in signals and complex silicon photonic circuits are used for circuit prototyping, device and datasets arising in a wide range that impact numerous fields from measurement, VLSI design, embedded of application areas, including audio, Lidar and optogenetics to low-energy systems design, as well as computer video, images, communications, computation and flexible electronics. engineering and Internet-of-Things and biology. Research interests The smart electric energy area experiments. include the development of models, focuses on the optimization of the algorithms and analyses for sensing, generation, conversion, distribution, and UNDERGRADUATE PROGRAM detection and estimation, statistical and consumption of electric energy as well The educational objective of the machine learning, and the recognition, as the electrification of energy systems. Electrical Engineering program, in organization, and understanding of the Research spans the analysis, design, support of the mission of the School, information content of signals and data. and control of power electronics, motor is to prepare graduates to achieve The Networking and Communications drive, and energy storage systems, success in one or more of the following area focuses on the design grid resilience and security, and within a few years after graduation: and performance evaluation of Internet-of-Things. Applications include communication systems and data transportation electrification, smart grid, A. Graduate or professional studies—as networks of all kinds, including wireless/ renewable energy, and smart building evidenced by admission to a top-tier cellular, optical, ultra-low power, vehicular, systems. program, attainment of advanced mobile, wearable, data center networks, degrees, research contributions, or cyber physical systems, and the internet. Laboratory Facilities professional recognition. Methods range from analyzing and Current research activities are fully B. Engineering practice—as evidenced refining existing approaches to the supported by more than a dozen by entrepreneurship; employment development of new and evolving well-equipped research laboratories in industry, government, academia, networking techniques and systems. run by the department faculty. In or nonprofit organizations in The Systems Biology and addition, faculty and students have engineering; patents; or professional Neuroengineering area aims to access to a clean room for micro- recognition. understand and analyze biological and nanofabrication, a materials- C. Careers outside of engineering that systems within the living cell and characterization facility, and an take advantage of an engineering in the brain. Examples of related electron-microscopy facility, managed education—as evidenced by tasks are biomolecular data analysis by the Columbia Nano Initiative. contributions appropriate to the for medical applications, synthetic Faculty laboratories include Digital chosen field. biology, establishing the principles Video and Multimedia Networking of neuroinformation processing Laboratory, Wireless and Mobile The Electrical Engineering program will in the brain for developing robust Networking Laboratory, Network prepare its undergraduates to attain sensory processing and motor control Algorithms Laboratory, Genomic the following: algorithms, accelerating the clinical Information Systems Laboratory, 1. an ability to identify, formulate, and translation of devices that make contact Structure-Function Imaging Laboratory, solve complex engineering problems with neurons, and building massively Neural Acoustic Processing by applying principles of engineering, parallel brain-computer interfaces. Laboratory, Signal Processing and science, and mathematics The Integrated Circuits and Systems Communication Laboratory, Translational 2. an ability to apply engineering design area focuses on the integration of Neuroelectronics Laboratory, Bionet to produce solutions that meet circuits and systems on semiconductor Laboratory, Molecular Beam Epitaxy specified needs with consideration platforms. Research spans the analysis, Laboratory, Surface Analysis Laboratory, of public health, safety, and welfare, design, simulation, and validation of Laboratory for Unconventional as well as global, cultural, social, analog, mixed-mode, (sub) mm-wave, Electronics, Advanced Semiconductor environmental, and economic factors RF, power, and digital circuits, and Device Laboratory, Motor Drives and 3. an ability to communicate effectively their applications from computation Power Electronics Laboratory, Intelligent with a range of audiences and sensing to cyber-physical and and Connected Systems Laboratory, 4. an ability to recognize ethical and implantable biomedical systems. Columbia Integrated Systems Laboratory professional responsibilities in The area of Nanoscale Structures engineering situations and make

ENGINEERING 2021–2022 138 ELECTRICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS EARLY-STARTING STUDENTS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

APMA E2000 (4) and E2001 (0) either semester MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) and APMA E2101 (3)1

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

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

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

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

UNIVERSITY CC1010 (3) either semester WRITING

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

COMPUTER ENGI E1006 (3) either semester3 SCIENCE

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 APMA E2101 may be replaced by MATH UN2030 (formerly MATH E1210) and either APMA E3101 or MATH UN2010. 2 If possible, these labs should be taken along with their corresponding lecture courses. 3 ENGI E1006 may not be offered every semester. See ee.columbia.edu for more discussion about the Computer Science sequences.

informed judgments, which must 6. an ability to develop and conduct engineering at Columbia University consider the impact of engineering appropriate experimentation, seeks to provide a broad and solid solutions in global, economic, analyze and interpret data, and foundation in the current theory and environmental, and societal contexts use engineering judgment to draw practice of electrical engineering, 5. an ability to function effectively on conclusions including familiarity with basic tools teams whose members together 7. an ability to acquire and apply of math and science, an ability to provide leadership, create a new knowledge as needed, using communicate ideas, and a humanities collaborative and inclusive appropriate learning strategies. background sufficient to understand environment, establish goals, plan the social implications of engineering tasks, and meet objectives The B.S. program in electrical practice. Graduates should be

ENGINEERING 2021–2022 139 ELECTRICAL ENGINEERING: THIRD AND FOURTH YEARS EARLY-STARTING STUDENTS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

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

ELEN E3401 (4) Electromagnetics

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

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

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

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

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

Complete 27-point requirement; see page 9 (27-Point Nontechnical Requirement) NONTECH or seas.columbia.edu for details (administered by the advising dean)

TOTAL POINTS7 16.5 17 16 18

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

ENGINEERING 2021–2022 140 ELECTRICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS LATE-STARTING STUDENTS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

APMA E2000 (4) and E2001 (0) either semester MATHEMATICS MATH UN1101(3) MATH UN1102 (3) and APMA E2101 (3)1

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

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

ELECTRICAL ELEN E1201 (3.5) either semester3 ENGINEERING

UNIVERSITY CC1010 (3) either semester WRITING

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

COMPUTER ENGI E1006 (3) any semester4 SCIENCE

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

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

qualified to enter the profession of and linear algebra. Basic computer systems, and one on communications engineering, to continue toward a knowledge is also included, with or networking. Engineering practice is career in engineering research, or to an introductory course on using developed further through a sequence enter other fields in which engineering engineering workstations and two of laboratory courses, starting with a knowledge is essential. Required rigorous introductory computer science first-year course to introduce hands- nontechnical courses cover civilization courses. Core electrical engineering on experience early and to motivate and culture, philosophy, economics, courses cover the main components theoretical work. Simple creative design and a number of additional electives. of modern electrical engineering and experiences start immediately in this 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 Required science courses cover courses on circuit theory and electronic the core lecture courses. Opportunities basic chemistry and physics, whereas circuits, one course on semiconductor for exploring design can be found math requirements cover calculus, devices, one on electromagnetics, one both within these lab courses and differential equations, probability, on signals and systems, one on digital in the parallel lecture courses, often

ENGINEERING 2021–2022 141 ELECTRICAL ENGINEERING: THIRD AND FOURTH YEARS LATE-STARTING STUDENTS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

CSEE W3827(3) Fund. of computer sys.

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

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

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

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

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

Complete 27-point requirement; see page 9 (27-Point Nontechnical Requirement) NONTECH or seas.columbia.edu for details (administered by the advising dean)

TOTAL POINTS6 15.5 18 16 18

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

ENGINEERING 2021–2022 142 coupled with experimentation and electronics; (c) signals and systems; allows more time for students to take computer simulation, respectively. The and (d) communications and networking. classes in a chosen depth area, or culmination of the laboratory sequence The depth requirement provides an gives them more time to explore before and the design experiences introduced opportunity to pursue particular interests choosing a depth area. Students can throughout earlier courses is a senior and exposure to the process of exploring start with ELEN E1201: Introduction to design course (capstone design course), a discipline in depth—an essential electrical engineering in the second which includes a significant design process that can be applied later to other semester of their first year, and can project that ties together the core disciplines, if desired. continue with other core courses one program, encourages creativity, explores The breadth component must consist semester after that, as shown in the practical aspects of engineering of at least 6 additional points of courses “early-starting students” chart. It is practice, and provides additional that are outside of the chosen depth emphasized that both the early- and experience with communication skills in area and have significant engineering late-starting sample programs shown in an engineering context. Finally, several content. These courses can be from the charts are examples only; schedules technical electives are required, chosen other departments within the School. may vary depending on student to provide both breadth and depth in a The breadth requirement precludes preparation and interests. specific area of interest. More detailed overspecialization. Breadth is particularly program objectives and outcomes are important today, as innovation requires Transfer Students posted at ee.columbia.edu. more and more of an interdisciplinary Transfer students coming to Columbia The program in electrical approach, and exposure to other fields as juniors with sufficient general engineering leading to the B.S. degree is known to help one’s creativity in one’s background can complete all is accredited by the Engineering own main field. Breadth also reduces the requirements for the B.S. degree in Accreditation Commission of ABET, chance of obsolescence as technology electrical engineering. Such students fall http://www.abet.org. changes. into one of two categories: There is a strong interaction Any remaining technical elective Plan 1: Students coming to Columbia between the Department of Electrical courses, beyond the minimum 12 points without having taken the equivalent of Engineering and the Departments of of depth and breadth, do not have to be ELEN E1201 must take this course in their Computer Science, Applied Physics engineering courses (except for students junior year. This requires postponing the and Applied Mathematics, Industrial without ELEN E1201 or approved transfer core courses in circuits and electronics Engineering and Operations Research, credit for ELEN E1201) but must be until the senior year, and thus does not Physics, and Chemistry. technical. Generally, math and science courses that do not overlap with courses allow taking electives in that area; thus, such students cannot choose circuits EE Core Curriculum used to fill other requirements are and electronics as a depth area. All electrical engineering (EE) students allowed. must take a set of core courses, which If another department advertises Plan 2: This plan is for students who collectively provide the student with that one of their courses can be used have taken a course equivalent to fundamental skills, expose him/her as a technical elective, that does not ELEN E1201 at their school of origin, to the breadth of EE, and serve as a necessarily mean it will be approved including a laboratory component. springboard for more advanced work, or as a technical elective in the electrical See the bulletin for a description of for work in areas not covered in the core. engineering program. Which courses are this course. Many pre-engineering These courses are shown on the charts approved depends on other electives programs and physics departments at in Undergraduate Degree Tracks. A full chosen due to the depth and breadth four-year colleges offer such courses. curriculum checklist is also posted at restrictions, and the need for sufficient Such students can start taking circuits ee.columbia.edu. engineering and technical content within at Columbia immediately, and thus can the entire 18 points. Electrical engineering choose circuits and electronics as a technical electives must also be 3000- Technical Electives depth area. level or above and must not have The 18-point technical elective requirement significant overlap with other courses It is stressed that ELEN E1201 or for the electrical engineering program its equivalent is a key part of the EE taken for the major. consists of three components: depth, curriculum. The preparation provided by breadth, and other. A general outline is this course is essential for a number of Starting Early provided here, and more specific course other core courses. The EE curriculum is designed to allow restrictions can be found at ee.columbia. Sample programs for both Plan 1 and students to start their study of EE in their edu. For any course not clearly listed Plan 2 transfer students can be found at first year. This motivates students early there, adviser approval is necessary. ee.columbia.edu. The depth component must consist of and allows them to spread nontechnical requirements more evenly. It also makes at least 6 points of electrical engineering B.S./M.S. Program evident the need for advanced math courses in one of four defined areas: The B.S./M.S. degree program is open and physics concepts, and motivates (a) photonics, solid-state devices, to a select group of undergraduate the study of such concepts. Finally, it and electromagnetics; (b) circuits and students. This double degree program

ENGINEERING 2021–2022 makes possible the earning of both Graduate course charts for original research, conducted under the 143 the Bachelor of Science and Master several focus areas can be found at supervision of a faculty member. The of Science degrees in an integrated ee.columbia.edu. work may be theoretical or experimental fashion. Up to 6 points may be credited M.S. students must complete or both. to both degrees, and some graduate the professional development and Students who wish to become classes taken in the senior year may leadership course, ENGI E4000, as candidates for the doctoral degree in count toward the M.S. degree. Interested a graduation requirement. Doctoral electrical engineering have the option of students can find further information students will be enrolled in ENGI E6001– applying for admission to the Eng.Sc.D. at ee.columbia.edu and can discuss 6004 and should consult their program program or the Ph.D. program. Students options directly with their faculty adviser. for specific PDL requirements. who elect the Eng.Sc.D. degree register Students must be admitted prior to in the School of Engineering and the start of their seventh semester at Master of Science Degree Applied Science; those who elect the Columbia Engineering. Students in the Candidates for the M.S. degree in Ph.D. degree register in the Graduate 3-2 Combined Plan undergraduate electrical engineering must complete 30 School of Arts and Sciences. program are not eligible for admission to points of credit beyond the bachelor’s Doctoral candidates must obtain a this program. degree. A minimum of 15 points of credit minimum of 60 points of formal course must be at the 6000 level or higher. No credit beyond the bachelor’s degree. credit will be allowed for undergraduate A master’s degree from an accredited GRADUATE PROGRAMS courses (3000 or lower). At least 15 institution may be accepted as The Department of Electrical points must be in electrical engineering, equivalent to 30 points. A minimum of Engineering offers graduate programs defined as including all courses with an 30 points beyond the master’s degree leading to the degree of Master of ELEN designator or a joint designator must be earned while in residence in Science (M.S.) and the degrees of containing electrical engineering as a the doctoral program. Doctor of Engineering Science (Eng. member, e.g., EECS, CSEE, EEME, ECBM, More detailed information regarding Sc.D.) and Doctor of Philosophy (Ph.D.). etc. And it is expected that at least 12 the requirements for the doctoral The Graduate Record Examination of the first 24 points taken will be in degree may be obtained in the (General Test only) is required of all electrical engineering. department office and at ee.columbia. applicants except special students. An Not all technical courses can be edu. undergraduate grade-point average applied toward the M.S. degree, and equivalent to B or better from an some have restrictions. Up to 6 points Optional M.S. Specializations institution comparable to Columbia is of research (such as ELEN E4998, Students in the electrical engineering expected. ELEN E6001, and ELEN E6002) can be Applicants who, for good reasons, M.S. program often choose to use applied. Up to 1.5 points of fieldwork some of their electives to focus on are unable to submit GRE test results (ELEN E6999) can be used. No more by the deadline date but whose a particular field. Students may pick than 3 points of courses that do not one of a number of optional, formal undergraduate record is clearly superior contain primarily engineering, math, or may file an application without the GRE specialization templates or design their science content can be used, subject own M.S. program in consultation with scores. An explanatory note should be to the written pre-approval of the added to ensure that the application will an adviser. These specializations are not department. Any course that is not on degree requirements. They represent be processed even while incomplete. If the list of standard courses specified the candidate’s admissibility is clear, the suggestions from the faculty as to how at ee.columbia.edu/masters-program one might fill one’s programs so as to decision may be made without the GRE requires prior written department scores; otherwise, it may be deferred focus on a particular area of interest. approval, including during the summer Students may wish to follow these until the scores are received. session. There are no prescribed course suggestions, but they need not. The The general school requirements degree requirements are quite flexible requirements in any of the regular listed earlier in this bulletin, such as graduate degree programs. Students, in and are listed in the Master of Science minimum GPA, must also be satisfied. Degree section, above. All students, consultation with their faculty advisers, All degree requirements must be design their own programs, focusing on whether following a formal specialization completed within five years of the template or not, are expected to include particular fields of electrical engineering. beginning of the first course credited Among the fields of graduate study are breadth in their program. Not all of the toward the degree. elective courses listed here are offered Communications, Networking, Internet More details and a requirements and Internet of Things; Computer every year. For the latest information checklist for approvals can be found at on available courses, visit the Electrical Engineering; Integrated Circuits and ee.columbia.edu/masters-program. Systems and Electronics; Integrated Engineering home page at ee.columbia. edu. Devices and Photonics; Signals, Doctoral Degree Information, Data, Learning and Control; The requirements for the Ph.D. and Eng. Smart Electric Energy; and Systems Sc.D. degrees are identical. Both require Biology and Neuroengineering. a dissertation based on the candidate’s

ENGINEERING 2021–2022 144 Specialization in Data-Driven algorithms; ELEN E6950: Wireless Computer networks; ELEN E4702: Analysis and Computation and mobile networking, I; CSEE Digital communications; ELEN Advisers: Professors Dimitris E6180: Modeling and performance E4703: Wireless communications; Anastassiou, Shih-Fu Chang, Pedrag evaluation. ELEN E6711: Stochastic signals Jelenkovic, Zoran Kostic, Aurel A. Lazar, 4. Three courses from the following and noise; ELEN E4810: Digital Nima Mesgarani, John Paisley, John list (courses cannot be used to signal processing; ELEN E6950: Wright, Xiaofan (Fred) Jiang fulfill both this requirement and any Wireless and mobile networking, I; of the above requirements): ELEN EECS E4951: Wireless network and 1. Satisfy M.S. degree requirements. E6488: Optical interconnects and systems; ELEN E6761: Computer 2. Take at least two courses from ECBM interconnection networks; ELEN communication networks, I; ELEN E4040: Neural networks and deep E6761: Computer communication E6712: Communication theory; ELEN learning; EECS E4764: Internet of networks I; ELEN E6767: internet E6713: Topics in communications; things—intelligent and connected economics, energy, and society; ELEN E6717: Information theory; ELEN systems; ELEN E4810: Digital signal ELEN E6770: Topic: next generation E677x: Topics in telecommunication processing; ELEN E4720: Machine networks; ELEN E6772: Topic: networks. learning for signals, information, network algorithms; ELEN E6775: 4. At least two additional approved and data; EEOR E6616: Convex Topic: computer networks: a courses in wireless communications or optimization; EECS E6893: Topic: big systems approach; ELENE E6776: a related area. data analytics. Topic: content distribution networks; 3. Take at least one courses from ELEN E6950: Wireless and mobile Specialization in Integrated Circuits ECBM E6040: Neural networks networking I; EEOR E4650: Convex and Systems and deep learning research; EECS optimization for EE; EEOR E6616: Advisers: Professors Peter Kinget, E6720: Bayesian models for machine Convex optimization; CSEE E4140: Harish Krishnaswamy, Mingoo Seok, learning; EECS E6765: Internet Networking laboratory; EECS Kenneth Shepard, Yannis Tsividis, of things—systems and physical E4951: Wireless networks and Charles Zukowski data analytics; EECS E6895: Topic: systems; CSEE E6180: Modeling advanced big data analytics. and Performance Evaluation; 1. Satisfy M.S. degree requirements. 4. Take a second course from #3 or COMS W4180: Network security; 2. One digital course from: EECS E4321: one course from ECBM E4060: COMS W4995: Internet technology, Digital VLSI circuits or EECS E6321: Introduction to genomic information economics, and policy, COMS Advanced digital electronic circuits. science and technology; ECBM E6181: Advanced internet services; 3. One analog course from ELEN E4312: E4070; ECBM: E607x: Topics in COMS E6998: Cloud computing and Analog electronic circuits; ELEN neuroscience and deep learning; big data; IEOR E6704: Queueing E6312: Advanced analog integrated ELEN E6690: Topics in data-driven theory; IEOR E4106: Stochastic circuits; ELEN E6316: Analog digital analysis and computation; ELEN models; with adviser approval, other interfaces in VLSI; ELEN E4314: E6876: Sparse and low-dimensional relevant advanced topic courses on Communication circuits; ELEN E6314: models for high-dimensional data; networking topics from ELEN E677x, Advanced communication circuits; ELEN E9601: Seminar in data-driven COMS W4995, COMS E6998, or ELEN E6320: Millimeter-wave IC analysis and computation. other course numbers may be used design. to fulfill this requirement. 4. Two additional courses such as other Specialization in Networking 5. At least two of the four courses used courses from no. 2 and 3; ELEN to fulfill requirements 3 and 4 must Advisers: Professors Predrag Jelenkovic, E6350: VLSI design laboratory; ELEN be 6000-level ELEN, EECS, CSEE, or Javad Ghaderi, Ethan Katz-Bassett, E6304: Topics in electronic circuits; EEOR courses. Debasis Mitra, Gil Zussman, Xiaofan ELEN E6318: Microwave circuit (Fred) Jiang design; ELEN E9303: Seminar in Specialization in Wireless and Mobile electronic circuits. 1. Satisfy M.S. degree requirements. Communications 5. At least one additional approved 2. One basic networking course from Advisers: Professors Gil Zussman, course in integrated circuits and the following: ELEN E6761: Computer Predrag Jelenkovic, Xiaodong Wang systems or a related area. communication networks I, CSEE W4119: Computer networks. 1. Satisfy M.S. degree requirements. Specialization in Smart Electric 3. One basic systems or analytical 2. One basic circuits course such Energy course from the following: as: ELEN E4312: Analog electric Advisers: Professors Matthias Preindl, Systems courses: CSEE E4140: circuits; ELEN E4314: Communication Xiaofan (Fred) Jiang, Gil Zussman, Networking laboratory; COMS circuits; ELEN E6314: Advanced Kenneth Shepard, Xiaodong Wang W4113: Fundamentals of large-scale communication circuits; ELEN E6312: distributed systems; COMS W4118: Advanced analog ICs. 1. Satisfy M.S. degree requirements. Operating systems I; Analytical 3. Two communications or networking 2. Take at least two power conversion courses: ELEN E6772: Topic: network courses such as: CSEE W4119: or power systems courses from:

ENGINEERING 2021–2022 ELEN E4361: Power electronics; 1. Satisfy M.S. degree requirements. Quantum physics of matter; APPH 145 ELEN E6902 Renewable power 2. Take both ECBM E4060: Introduction E4110: Modern optics; CHAP E4120: systems; ELEN E6904: Motor drive to genomic information science Statistical mechanics; APPH E4112: systems; ELEN E4511: Power systems and technology and BMEB W4020: Laser physics; APPH E4130: Physics analysis and control; ELEN E4510: Computational neuroscience, circuits of solar energy; APPH E6081: Solid Solar energy and smart grid power in the brain state physics, I; APPH E6082: systems. 3. Take at least one course from BMEE Solid state physics, II; APPH E6091: 3. Take at least one control or E4030: Neural control engineering; Magnetism and magnetic materials; optimization course from: EEME ECBM E4040: Neural networks and APPH E6110: Laser interactions E4601: Digital control systems; EEME deep learning; ECBM E4070; ECBM with matter; MSAE E4202: E6601: Introduction to control theory; E4090: Brain computer interfaces Thermodynamics and reactions EEME E6602: Modern control theory; (BCI) laboratory; CBMF W4761: in solids; MSAE E4206: Electronic ELEN E6873: Detection and estimation Computational genomics; ELEN and magnetic properties of solids; theory; EEOR E4650: Convex E6010: Systems biology: design MSAE E4207: Lattice vibrations and optimization for electrical engineering; principles for biological circuits; EEBM crystal defects; MSAE E6120: Grain EEOR E6616: Convex optimization; E6020: Methods in computational boundaries and interfaces; MSAE EECS E4764: IoT—intelligent and neuroscience; BMEE E6030: Neural E6220: Crystal physics; MSAE E6229: connected systems; CSEE W4840: modeling and neuroengineering. Energy and particle beam processing Embedded system Design. 4. Take at least one course from ECBM of materials; MSAE E6225: 4. Take at least one nonelectric energy E6040: Neural networks and deep Techniques in X-ray and neutron class course from: MECE E4210: learning research; ECBM E607x: diffraction. Energy infrastructure planning; Topics in neuroscience and deep MECE E4320: Intro to combustion; learning; ELEN E608x: Topics in Specialization in Microelectronic MECE E4211: Energy: sources and systems biology; EEBM E609x: Topics Devices conversions; MECE E4302: Advanced in computational neuroscience and Advisers: Professors Dion Khodagholy, thermodynamics; EAEE E4190: neuroengineering; ELEN E6261: Ioannis (John) Kymissis, Michal Lipson, Photovoltaic systems engineering Computational methods of circuit James Teherani, Wen Wang and sustainability; EAEE E4257: analysis ELEN E6717: Information Environmental data analysis and theory; ELEN E6860: Advanced 1. Satisfy M.S. degree requirements. modeling; EAEE E4301: Carbon digital signal processing. 2. One basic course such as: ELEN storage; EAEE E4302: Carbon E4301: Introduction to semiconductor capture; EAEE E4304: Closing the Specialization in Lightwave devices or ELEN E4411: Fundamentals carbon cycle. (Photonics) Engineering of photonics. 5. Not required, but consider taking Advisers: Professors Keren Bergman, 3. One advanced course such as: ELEN one of the following energy policy Ioannis (John) Kymissis, Michal Lipson E4193: Modern display science and or market nontechnical elective technology; ELEN E4944: Principles courses (this course will fill the quota 1. Satisfy M.S. degree requirements. of device microfabrication; ELEN of nontechnical courses on the M.S. 2. Take both ELEN E4411: Fundamentals E4503: Sensors, actuators, and Checklist): EAEE E4001: Industrial of photonics and ELEN E6412: electromechanical systems; ELEN ecology of earth resources; EAIA Lightware devices (or an E&M course, E6151: Surface physics and analysis W4200: Alternative energy resources; such as APPH E4300: Applied of electronic materials; ELEN INAF U6057 Electricity markets; electrodynamics or PHYS GR6092: E6331: Principles of semiconductor INAF U6072: Energy systems Electromagnetic theory). physics, I; ELEN E6332: Principles fundamentals; SUMA K4135: Energy 3. One more device/circuits/photonics of semiconductor physics, II; ELEN analysis for energy efficiency; INAF course such as: ELEN E6413: E6333: Semiconductor device U6065: The economics of energy; Lightwave systems; ELEN E6414: physics; ELEN E6945: Nanoscale INAF U6061: Global energy policy; Photonic integrated circuits; ELEN fabrication and devices. INAF U6242: Energy policy; INAF E4314: Communication circuits; 4. At least two other approved courses U6135: Renewable energy markets ELEN E4488: Optical systems; ELEN in devices or a related area. Options and policy. E6488: Optical interconnects and also include courses outside EE such interconnection networks; ELEN as APPH E4090: Nanotechnology; Specialization in Systems Biology E4193: Modern display science and APPH E4100: Quantum physics of and Neuroengineering technology. matter; APPH E4110: Modern optics; Advisers: Professors Dimitris 4. At least two additional approved CHAP E4120: Statistical mechanics; Anastassiou, Christine Hendon, courses in photonics or a related APPH E4112: Laser physics; APPH Pedrag Jelenkovic, Aurel A. Lazar, area. Options also include courses E4130: Physics of solar energy; APPH Nima Mesgarani, Kenneth Shepard, outside EE such as APPH E4090: E6081: Solid state physics, Xiaodong Wang Nanotechnology; APPH E4100:

ENGINEERING 2021–2022 146 I; APPH E6082: Solid state physics, ELEN E3082y Digital systems laboratory ELEN E3390y Electrical engineering senior II; APPH E6091: Magnetism and 1 pt. Lab: 3. Professor Shepard. design project magnetic materials; APPH E6110: Corequisite: CSEE W3827. Recommended 3 pts. Lab: 6. Professor Vallancourt. preparation: ELEN E1201 or equivalent. Prerequisite(s): ELEN E3399 and completion of Laser interactions with matter; Companion lab course for CSEE W3827. most other required EE courses. Students work MSAE E4202: Thermodynamics and Experiments cover such topics as logic gates; in teams to specify, design, implement and test reactions in solids; MSAE E4206: flip-flops; shift registers; counters; combinational an engineering prototype. Involves technical as Electronic and magnetic properties logic circuits; sequential logic circuits; well as non-technical considerations, such as of solids; MSAE E4207: Lattice programmable logic devices. The lab generally manufacturability, impact on the environment, vibrations and crystal defects; meets on alternate weeks. economics, engineering standards, and other real-world constraints. Projects are presented MSAE E6120: Grain boundaries and ELEN E3083y Electronic circuits laboratory publicly by each design team in a school-wide interfaces; MSAE E6220: Crystal 1 pt. Lab: 3. Professor Kostic. expo. physics; MSAE E6229: Energy Prerequisite(s): ELEN E3081. Corequisite: ELEN E3331. Companion lab course for ELEN E3331. and particle beam processing of ELEN E3399x Electrical engineering practice Experiments cover such topics as macromodeling 1 pt. Professor Vallancourt. materials; MSAE E6225: Techniques of nonidealities of opamps using SPICE; Schmitt Design project planning, written and oral in X-ray and neutron diffraction. triggers and astable multivibrations using opamps technical communication, the origin and role and diodes; logic inverters and amplifiers using of standards, engineering ethics, and practical bipolar junction transistors; logic inverters and aspects of engineering as a profession, such COURSES IN ELECTRICAL ring oscillators using MOSFETs; filter design using as career development and societal and ENGINEERING opamps. The lab generally meets on alternate environmental impact. Generally taken senior weeks. year just before ELEN E3390. ELEN E1101x or y The digital information age 3 pts. Lect: 3. Professor Vallancourt. ELEN E3084x Signals and systems laboratory ELEN E3401y Electromagnetics An introduction to information transmission and 1 pt. Lab: 3. Professor X. Wang. 4 pts. Lect: 3. Professor Kash. storage, including technological issues. Binary Corequisite: ELEN E3801. Companion lab course Prerequisite(s): MATH UN1201 or APMA E2000, numbers; elementary computer logic; digital for ELEN E3801. Experiments cover topics such PHYS UN1402 or PHYS UN1602, or equivalents. speech and image coding; basics of compact as: introduction and use of MATLAB for numerical Basic field concepts. Interaction of time-varying disks, telephones, modems, faxes, UPC bar and symbolic calculations; linearity and time electromagnetic fields. Field calculation of codes, and the World Wide Web. Projects include invariance; continuous-time convolution; Fourier- lumped circuit parameters. Transition from implementing simple digital logic systems and series expansion and signal reconstruction; electrostatic to quasistatic and electromagnetic Web pages. Intended primarily for students impulse response and transfer function; forced regimes. Transmission lines. Energy transfer, outside the School of Engineering and Applied response. The lab generally meets on alternate dissipation, and storage. Waveguides. Radiation. Science. The only prerequisite is a working weeks. knowledge of elementary algebra. EEME E3601x Classical control systems ELEN E3106x Solid-state devices and 3 pts. Lect: 3. Professor Longman. ELEN E1201x and y Introduction to electrical materials Prerequisite(s): MATH UN2030. Analysis and engineering 3.5 pts. Lect: 3. Recit: 1. Professor Kymissis. design of feedback control systems. Transfer 3.5 pts. Lect: 3. Lab:1. Professor Vallancourt. Prerequisite(s): MATH UN1201 or APMA E2000 functions; block diagrams; proportional, rate, and Prerequisite(s): MATH UN1101. Basic concepts of or equivalent. Corequisite: PHYS UN1403 or integral controllers; hardware; implementation. electrical engineering. Exploration of selected PHYS UN2601 or equivalent. Crystal structure Routh stability criterion, root locus, Bode and topics and their application. Electrical variables, and energy band theory of solids. Carrier Nyquist plots, compensation techniques. circuit laws, nonlinear and linear elements, concentration and transport in semiconductors. ELEN E3701y Introduction to communication ideal and real sources, transducers, operational P-n junction and junction transistors. amplifiers in simple circuits, external behavior Semiconductor surface and MOS transistors. systems of diodes and transistors, first order RC and RL Optical effects and optoelectronic devices. 3 pts. Lect: 3. Professor Kalet. circuits. Digital representation of a signal, digital Fabrication of devices and the effect of process Prerequisite(s): ELEN E3801. Corequisite: IEOR logic gates, flip-flops. A lab is an integral part of variation and distribution statistics on device and E3658. A basic course in communication theory, the course. Required of electrical engineering and circuit performance. stressing modern digital communication systems. computer engineering majors. Nyquist sampling, PAM and PCM/DPCM systems, ELEN E3201x Circuit analysis time division multiplexing, high frequency digital ELEN E3043x Solid state, microwave, and 3.5 pts. Lect: 3. Recit: 1. Professor Zukowski. (ASK, OOK, FSK, PSK) systems, and AM and FM fiber optics laboratory Prerequisite(s): ELEN E1201 or equivalent. systems. An introduction to noise processes, 3 pts. Lect: 1. Lab: 6. Professor W. Wang. Corequisite: MATH UN1201 or APMA E2000. A detecting signals in the presence of noise, Prerequisite(s): ELEN E3106 and ELEN E3401. course on analysis of linear and nonlinear circuits Shannon’s theorem on channel capacity, and Optical electronics and communications. and their applications. Formulation of circuit elements of coding theory. Microwave circuits. Physical electronics. equations. Network theorems. Transient response of first and second order circuits. Sinusoidal ELEN E3801x Signals and systems ELEN E3081x Circuit analysis laboratory steady state-analysis. Frequency response of 3.5 pts. Lect: 3. Professor X. Wang. 1 pt. Lab: 3. Professor Zukowski. linear circuits. Poles and zeros. Bode plots. Two- Corequisite: MATH UN1201 or APMA E2000. Prerequisite(s): ELEN E1201 or equivalent. port networks. Modeling, description, and classification of signals Corequisite: ELEN E3201. Companion lab course and systems. Continuous-time systems. Time for ELEN E3201. Experiments cover such topics ELEN E3331y Electronic circuits domain analysis, convolution. Frequency domain as: use of measurement instruments; HSPICE 3 pts. Lect: 3. Professor Kostic. analysis, transfer functions. Fourier series. Fourier simulation; basic network theorems; linearization Prerequisite(s): ELEN E3201. Operational amplifier and Laplace transforms. Discrete-time systems of nonlinear circuits using negative feedback; circuits. Diodes and diode circuits. MOS and and the Z transform. op-amp circuits; integrators; second order RLC bipolar junction transistors. Biasing techniques. circuits. The lab generally meets on alternate Small-signal models. Single-stage transistor weeks. amplifiers. Analysis and design of CMOS logic gates. A/D and D/A converters.

ENGINEERING 2021–2022 CSEE W3827x and y Fundamentals of of neural activity, nonlinear modeling of neural ELEN E4106x Advanced solid state devices 147 computer systems systems, sensory systems: visual pathway and and materials 3 pts. Lect: 3. Professor Kim. somatosensory pathway, neural encoding model: 3 pts. Lect: 2.5. Lab: 1. Professor Kymissis. Prerequisite(s): An introductory programming spike triggered average (STA) and spike triggered Prerequisite(s): APMA E2000 and Math UN1201. course. Fundamentals of computer organization covariance (STC) analysis, neuronal response to Corequisties: PHYS UN1403 and UN2601. and digital logic. Boolean algebra, Karnaugh electrical micro-stimulation, DBS for Parkinson’s Crystal structure and energy band theory of maps, basic gates and components, flip-flops disease treatment, motor neural prostheses, and solids. Carrier concentration and transport and latches, counters and state machines, basics sensory neural prostheses. in semiconductors. P-n junction and junction of combinational and sequential digital design. transistors. Semiconductor surface and MOS ECBM E4040x or y Neural networks and deep Assembly language, instruction sets, ALUs, transistors. Optical effects and optoelectronic single-cycle and multicycle processor design, learning devices. Fabrication of devices and the effect introduction to pipelined processors, caches, and 3 pts. Lect: 3. Professor Kostic. of process variation and distribution statistics virtual memory. Prerequisite(s): BMEB W4020 or BMEE E4030 on device and circuit performance. Course or ECBM E4090 or ELEN E4750 or COMS W4771 shares lectures with ELEN E3106, but the work ELEN E3990x, y or s Fieldwork or an equivalent. Developing features and requirements differ. Undergraduate students are 1–2 pts. Members of the faculty. internal representations of the world, artificial not eligible to register. Prerequisite(s): Obtained internship and approval neural networks, classifying handwritten digits from a faculty adviser. May be repeated for credit, with logistics regression, feedforward deep CSEE W4119x and y Computer networks but no more than 3 total points may be used for networks, back propagation in multilayer 3 pts. Lect: 3. Professor Rubenstein. degree credit. Only for Electrical Engineering and perceptrons, regularization of deep or distributed Corequisite: IEOR E3658 or SIEO W3600 or Computer Engineering undergraduate students models, optimization for training deep models, equivalents. Introduction to computer networks who include relevant off-campus work experience convolutional neural networks, recurrent and and the technical foundations of the internet, as part of their approved program of study. Final recursive neural networks, deep learning in including applications, protocols, local area report and letter of evaluation required. May not speech, and object recognition. networks, algorithms for routing and congestion be used as technical or nontechnical electives control, security, elementary performance or to satisfy any other Electrical Engineering or ECBM E4060x Introduction to genomic evaluation. Several written and programming Computer Engineering major requirements. May information science and technology assignments required. not be taken for pass/fail credit or audited. 3 pts. Lect: 3. Professor Anastassiou. Introduction to the information system CSEE W4121y Computer systems for data ELEN E3998x and y Projects in electrical paradigm of molecular biology. Representation, science engineering organization, structure, function and manipulation 3 pts. Lect: 3. Professor Cidon. 0 to 3 pts. Members of the faculty. of the biomolecular sequences of nucleic Prerequisite(s): Background in Computer System Prerequisite(s): Requires approval by a faculty acids and proteins. The role of enzymes and Organization and good working knowledge of C/ member who agrees to supervise the work. gene regulatory elements in natural biological C++. Corequisites: CSOR W4246, STAT GU4203, May be repeated for credit, but no more than functions as well as in biotechnology and or equivalent approved by faculty adviser. 3 total points may be used for degree credit. genetic engineering. Recombination and Introduction to computer distributed systems Independent project involving laboratory work, other macromolecular processes viewed as with emphasis on warehouse scale computing computer programming, analytical investigation, mathematical operations with simulation and systems. Topics include fundamental tradeoffs or engineering design. visualization using simple computer programming. in computer systems, hardware and software This course shares lectures with ECBM E3060, but techniques for exploiting instruction-level BMEB W4020x Computational neuroscience: the work requirements differ somewhat. parallelism, data-level parallelism and task level circuits in the brain parallelism, scheduling, caching, prefetching, 3 pts. Lect: 3. Professor Lazar. ECBM E4070y Computing with brain circuits network and memory architecture, latency Prerequisite(s): ELEN E3801 or BIOL UN3004. of model organisms and throughput optimizations, specializations, The biophysics of computation: modeling 3 pts. Lect: 3. Professor Lazar. and introduction to programming data center biological neurons, the Hodgkin-Huxley neuron, Prerequisite(s): ELEN E3801 or BIOL W3004, and computers. modeling channel conductances and synapses as Python programming experience, or instructor's memristive systems, bursting neurons and central permission. Building the functional map of the CSEE W4140x or y Networking laboratory pattern generators, I/O equivalence and spiking fruit fly brain. Molecular transduction and spatio- 3 pts. Lect: 3. Professor Zussman. neuron models. Information representation and temporal encoding in the early visual system. Prerequisite(s): CSEE W4119 or equivalent. In this neural encoding: stimulus representation with Predictive coding in the Drosophila retina. course, students learn how to put “principles into time encoding machines, the geometry of time Canonical circuits in motion detection. Canonical practice,” in a hands-on-networking lab course. encoding, encoding with neural circuits with navigation circuits in the central complex. The technologies and protocols of the internet feedback, population time encoding machines. Molecular transduction and combinatorial are covered, using equipment currently available Dendritic computation: elements of spike encoding in the early olfactory system. Predictive to large internet service providers such as CISCO processing and neural computation, synaptic coding in the antennal lobe. The functional role routers and end-systems. A set of laboratory plasticity and learning algorithms, unsupervised of the mushroom body and the lateral horn. experiments provides hands-on experience with learning and spike time-dependent plasticity, Canonical circuits for associative learning and engineering wide-area networks and familiarizes basic dendritic integration. Projects in MATLAB. innate memory. Projects in Python. students with the Internet Protocol (IP), Address Resolution Protocol (ARP), Internet Control BMEE E4030y Neural control engineering ECBM E4090x or y Brain computer interfaces Message Protocol (ICMP), User Datagram Protocol 3 pts. Lect: 3. Not offered in 2021–2022. (BCI) laboratory (UDP) and Transmission Control Protocol (TCP), Prerequisite(s): ELEN E3801. Topics include basic 3 pts. Lect: 2. Lab: 3. Professor Mesgarani. the Domain Name System (DNS), routing protocols cell biophysics, active conductance and the Prerequisite(s): ELEN E3801. Hands-on experience (RIP, OSPF, BGP), network management protocols Hodgkin-Huxley model, simple neuron models, ion with basic neural interface technologies. (SNMP), and application-level protocols (FTP, channel models and synaptic models, statistical Recording EEG (electroencephalogram) signals TELNET, SMTP). models of spike generation, Wilson-Cowan using data acquisition systems (noninvasive, scalp model of cortex, large-scale electrophysiological recordings). Real-time analysis and monitoring ELEN E4193x or y Modern display science and recording methods, sensorimotor integration and of brain responses. Analysis of intention and technology optimal state estimation, operant conditioning perception of external visual and audio signals. 3 pts. Lect: 3. Professor Kymissis.

ENGINEERING 2021–2022 148 Prerequisite(s): Linear algebra, differential architecture. Programmable logic and hardware ELEN E4488x Optical systems equations, and basic semiconductor physics. prototyping with FPGAs. Fundamentals of VHDL 3 pts. Lect: 3. Professor Hendon. Introduction to modern display systems in for register-transfer level design. Testing and Prerequisite(s): ELEN E3401 or equivalent. an engineering context. The basis for visual validation of hardware. Hands-on use of industry Introduction to optical systems based on physical perception, image representation, color space, CAD tools for simulation and synthesis. design and engineering principles. Fundamental metrics of illumination. Physics of luminescence, geometrical and wave optics with specific propagation and manipulation of light in ELEN E4361x or y Power electronics emphasis on developing analytical and numerical anisotropic media, emissive displays, and spatial 3 pts. Lect: 3. Professor Preindl. tools used in optical engineering design. Focus light modulators. Fundamentals of display Prerequisite(s): ELEN E3801 and E3331. on applications that employ optical systems and addressing, the Alt-Pleshko theorem, multiple line Introduction to power electronics; power networks, including examples in holographic addressing. Large area electronics, fabrication, semiconductor devices: power diodes, thyristors, imaging, tomography, Fourier imaging, confocal and device integration of commercially important commutation techniques, power transistors, microscopy, optical signal processing, fiber optic display types. A series of short laboratories will power MOSFETs, Triac, IGBTs, etc., and switch communication systems, optical interconnects reinforce material from the lectures. Enrollment selection; nonsinusoidal power definitions and and networks. may be limited. computations, modeling, and simulation; half- wave rectifiers; single-phase, full-wave rectifiers; ELEN E4510x or y Solar energy and smart ELEN E4301y Introduction to semiconductor three-phase rectifiers; AC voltage controllers; grid power systems devices DC/DC buck, boost, and buck-boost converters; 3 pts. Lect: 3. Professors Kymissis and 3 pts. Lect: 3. Professor Laibowitz or Teherani. discontinuous conduction mode of operation; Schwartz. Prerequisite(s): ELEN E3106 or equivalent. DC power supplies: flyback, forward converter; Prerequisite(s): Background in circuits. Inorganic Semiconductor physics. Carrier injection and DC/AC inverters, PWM techniques; three-phase solar cell semiconductor physics. Single and recombination. P-n junction and diodes: Schottky inverters. tandem junction design. Measures of spectral and barrier and heterojunctions, solar cells and light- energy efficiency. Introduction to organic solar BMEE E4400x Wavelet applications in emitting diodes. Junction and MOS field-effect cells and thin film inorganic cells. Batteries and biomedical image and signal processing transistors, bipolar transistors. Tunneling and other energy storage systems. Introduction to 3 pts. Lect: 3. charge-transfer devices. legacy power networks: Single phase equivalents Prerequisite(s): APMA E2101 or E3101 or to three-phase networks. Reactive and real ELEN E4312x Analog electronic circuits equivalent. An introduction to methods of power. Equivalent circuits of synchronous 3 pts. Lect: 3. Professor Dickson. wavelet analysis and processing techniques machines, transformers, and transmission lines. Prerequisite(s): ELEN E3331 and E3801. for the quantification of biomedical images and Smart grid technology: Control and management Differential and multistage amplifiers; small- signals. Topics include frames and overcomplete of distributed solar energy and other intermittent signal analysis; biasing techniques; frequency representations, multiresolution algorithms for renewable power sources connected to legacy response; negative feedback; stability criteria; denoising and image restoration, multiscale power networks. Microgrid concept. “Small frequency compensation techniques. Analog texture segmentation and classification methods world” networks and fault management. layout techniques. An extensive design project is for computer-aided diagnosis. Communication over power lines. Smart metering. an integral part of the course. ELEN E4401x Wave transmission and fiber ELEN E4511x or y Power systems analysis ELEN E4314y Communication circuits optics and control 3 pts. Lect: 3. Professor Tsividis. 3 pts. Lect: 3. Professor Diament. 3 pts. Lect: 3. Prerequisite(s): ELEN E4312. Principles of Prerequisite(s): ELEN E3401 or equivalent. Waves Prerequisite(s): ELEN E3201 and E3401, or electronic circuits used in the generation, and Maxwell’s equations. Field energetics, equivalents, or instructor’s permission. Modeling transmission, and reception of signal waveforms, dispersion, complex power. Waves in dielectrics of power networks, steady-state and transient as used in analog and digital communication and in conductors. Reflection and refraction. behaviors, control and optimization, electricity systems. Nonlinearity and distortion; power Oblique incidence and total internal reflection. market, and smart grid. amplifiers; tuned amplifiers; oscillators; multipliers Transmission lines and conducting waveguides. and mixers; modulators and demodulators; Planar and circular dielectric waveguides; EEME E4601y Digital control systems phase-locked loops. An extensive design project integrated optics and optical fibers. Hybrid and 3 pts. Lect: 3. Professor Longman. is an integral part of the course. LP modes. Graded-index fibers. Mode coupling; Prerequisite(s): ELEN E3801 or EEME E3601, wave launching. or equivalent. Real-time control using digital EECS E4321x Digital VLSI circuits computers. Solving scalar and state-space 3 pts. Lect: 3. Professor Shepard. ELEN E4411x Fundamentals of photonics difference equations. Discrete equivalents of Recommended preparation: ELEN E3106, E3331, 3 pts. Lect: 3. Professor Lipson. continuous systems fed by holds. Z-transfer and CSEE W3827. Design and analysis of high Prerequisite(s): ELEN E3401 or equivalent. functions. Creating closed-loop difference speed logic and memory. Digital CMOS and Planar resonators. Photons and photon streams. equation models by Z-transform and state BiCMOS device modeling. Integrated circuit Photons and atoms: energy levels and band variable approaches. The Nyquist frequency and fabrication and layout. Interconnect and parasitic structure; interactions of photons with matter; sample rate selection. Classical- and modern- elements. Static and dynamic techniques. Worst- absorption, stimulated and spontaneous based digital control laws. Digital system case design. Heat removal and I/O. Yield and emission; thermal light, luminescence light. identification. circuit reliability. Logic gates, pass logic, latches, Laser amplifiers: gain, saturation, and phase PLAs, ROMs, RAMs, receivers, drivers, repeaters, shift; rate equations; pumping. Lasers: theory of EEOR E4650x or y Convex optimization for sense amplifiers. oscillation; laser output characteristics. Photons electrical engineering in semiconductors: generation, recombination, 3 pts. Lect: 3. EECS E4340x Computer hardware design and injection; heterostructures; absorption Prerequisite(s): ELEN E3801 or instructor’s 3 pts. Lect: 2. Lab: 3. Professor and gain coefficients. Semiconductor photon permission. Theory of convex optimization; Sethumadhavan. sources: LEDs; semiconductor optical amplifiers; numerical algorithms; applications in circuits, Prerequisite(s): ELEN E3331 and CSEE W3827. homojunction and heterojunction laser diodes. communications, control, signal processing and Practical aspects of computer hardware design Semiconductor photon detectors: p-n, p-i-n, power systems. through the implementation, simulation, and and heterostructure photodiodes; avalanche prototyping of a PDP-8 processor. High-level and photodiodes. ELEN E4702x or y Digital communications assembly languages, I/O, interrupts, datapath 3 pts. Lect: 3. Professor Raghavan. and control design, pipelining, busses, memory Prerequisite(s): ELEN E3701 or equivalent.

ENGINEERING 2021–2022 Digital communications for both point-to-point E4703, CSEE W4119, CSEE W4840, or related CSEE W4824x or y Computer architecture 149 and switched applications is further developed. courses. Cyber-physical systems and Internet 3 pts. Lect: 3. Professor Sethumadhavan. Optimum receiver structures and transmitter of Things. Various sensors and actuators, Prerequisite(s): CSEE W3827 or equivalent. signal shaping for both binary and M-ary signal communication with devices through serial Focuses on advanced topics in modern computer transmission. An introduction to block codes and protocols and buses, embedded hardware, wired architecture, illustrated by recent case studies. convolutional codes, with application to space and wireless networks, embedded platforms Fundamentals of quantitative analysis. Pipelined, communications. such as Arduino and smartphones, web services out-of-order, and speculative execution. on end devices and in the cloud, visualization Superscalar, VLIW and vector processors. ELEN E4703y Wireless communications and analytics on sensor data, end-to-end IoT Embedded processors. Memory hierarchy design. 3 pts. Lect: 3. Professor Samardzia. applications. Group projects to create working Multiprocessors and thread-level parallelism. Prerequisite(s): ELEN E3701 or equivalent. CPS/IoT system. Synchronization and cache coherence protocols. Wireless communication systems. System design Interconnection networks. fundamentals. Trunking theory. Mobile radio EECS E4766 Internet of things—engineering propagation. Reflection of radio waves. Fading innovations and commercialization ELEN E4830y Digital image processing and multipath. Modulation techniques; signal 3 pts. Lect: 3. Professor Kostic. 3 pts. Lect: 3. Professor Hendon. space; probability of error, spread spectrum. Prerequisite(s): Basic programming and Introduction to the mathematical tools and Diversity. Multiple access. instructor’s permission. Deep dive into a couple algorithmic implementation for representation and of selected topics/use-cases from the area of processing of digital pictures, videos, and visual ELEN E4720x or y Machine learning for Internet of Things. Coverage of the topic from sensory data. Image representation, filtering, signals, information, and data device to the cloud, with focus on practical transform, quality enhancement, restoration, 3 pts. Lect: 3. Professor Paisley. aspects. Innovative product definition, product feature extraction, object segmentation, Prerequisite(s): Basic linear algebra and calculus. development, marketing, commercialization, motion analysis, classification, and coding for Intro-level courses in probability and statistics. and monetization. Cross-disciplinary coverage: data compression. A series of programming Programming. Introduction to supervised and EE, MechE, CS, Bioengineering, marketing, assignments reinforces material from the lectures. unsupervised techniques for machine learning. business, design. Building products and startups Probabilistic and non-probabilistic approaches. in the IoT domain. Collaboration between the ELEN E4835 Introduction to adaptive signal Focus on classification and regression models, Engineering School, Business School, industry representations clustering methods, matrix factorization and experts, and engagement in IoT activities in NYC. 3 pts. Lect: 2. Professor Wright. sequential models. Linear and logistic regression, Collaborative project by groups of students from Prerequisite(s): Linear algebra (APMA E3101, MATH support vector machines, boosting, K-means different disciplines. This course shares lectures UN2010, or equivalent), probability (IEOR E3658 clustering, mixture models, expectation- with E6766, but the expected project complexity or equivalent), and signals and systems (ELEN maximization algorithm, and hidden Markov is lower. E3801), or instructor’s permission. Introduces models. Algorithmic techniques for optimization, numerical tools for adaptive processing of signals. such as gradient and coordinate descent ELEN E4810x Digital signal processing Signal representations, sparsity in overcomplete methods. 3 pts. Lect: 3. Professor Wright. bases. Techniques for sparse recovery, Prerequisite(s): ELEN E3801. Digital filtering in applications to inpainting and denoising. Adaptive BMEE E4740y Bioinstrumentation time and frequency domain, including properties representations: principal component analysis, 3 pts. Lect: 1. Lab: 3. Professor Kyle. of discrete-time signals and systems, sampling clustering and vector quantization, dictionary Prerequisite(s): COMS W1005, ELEN E1201. theory, transform analysis, system structures, learning. Source separation: independent Hands-on experience designing, building, and IIR and FIR filter design techniques, the discrete component analysis and matrix factorizations. testing the various components of a benchtop Fourier transform, fast Fourier transforms. Signal classification: support vector machines cardiac pacemaker. Design instrumentation to and boosting, learning with invariances. Hashing measure biomedical signals as well as to actuate ELEN E4815y Random signals and noise and signal retrieval. Case studies from image living tissues. Transducers, signal conditioning 3 pts. Lect: 3. Professor Kalet. processing, audio, multimedia. electronics, data acquisition boards, the Arduino Prerequisite(s): IEOR E3658 or equivalent. microprocessor, and data acquisition and Characterization of stochastic processes as CSEE W4840y Embedded systems processing using MATLAB will be covered. Various models of signals and noise; stationarity, 3 pts. Lect: 3. Professor Edwards. devices will be discussed throughout the course, ergodicity, correlation functions, and power Prerequisite(s): CSEE W4823 or equivalent. with laboratory work focusing on building an spectra. Gaussian processes as models of noise in Embedded system design and implementation emulated version of a cardiac pacemaker. Lab linear and nonlinear systems; linear and nonlinear combining hardware and software. I/O, required. transformations of random processes; orthogonal interfacing, and peripherals. Weekly laboratory series representations. Applications to circuits and sessions and term project on design of a EECS E4750x or y Heterogeneous computing devices, to communication, control, filtering, and microprocessor-based embedded system for signal and data processing prediction. including at least one custom peripheral. 3 pts. Lect: 2. Professor Marianetti. Knowledge of C programming and digital logic Prerequisite(s): ELEN E3801 and COMS W3134 or CSEE W4823x or y Advanced logic design required. similar, recommended. Methods for deploying 3 pts. Lect: 3. Professor Nowick. signal and data processing algorithms on Prerequisite(s): CSEE W3827 or equivalent. An CSEE E4868x or y System-on-chip platforms contemporary general purpose graphics introduction to modern digital system design. 3 pts. Lect: 3. Professor Carloni. processing units (GPGPUs) and heterogeneous Advanced topics in digital logic: controller Prerequisite(s): COMS W3157 and CSEE W3827 computing infrastructures. Using programming synthesis (Mealy and Moore machines); adders Design and programming of System-on-Chip languages such as OpenCL and CUDA for and multipliers; structured logic blocks (PLDs, (SoC) platforms. Topics include overview of computational speedup in audio, image, and PALs, ROMs); iterative circuits. Modern design technology and economic trends, methodologies video processing and computational data methodology: register transfer level modeling and supporting CAD tools for system-level analysis. Significant design project. (RTL); algorithmic state machines (ASMs); design; models of computation, the SystemC introduction to hardware description languages language, transaction-level modeling, hardware- EECS E4764 Internet of things—intelligent (VHDL or Verilog); system-level modeling and software partitioning, high-level synthesis, and connected systems simulation; design examples. system programming, on-chip communication, 3 pts. Lect 3. Professor Jiang. memory organization, power management Prerequisite(s): Knowledge of programming or and optimization, integration of programmable instructor's permission. Recommended: ELEN

ENGINEERING 2021–2022 150 processor cores and specialized accelerators. electrical engineering and computer science. single neurons to cortical modules and systems. Case studies of modern SoC platforms for various In consultation with an instructor, each student Mathematical models of spiking neurons, neural classes of applications. designs his or her project depending on the dynamics, neural coding, and biologically student’s previous training and experience. based computational learning. Architectures ELEN E4896y Music signal processing Students should consult with a professor in their and learning principles underlying both artificial 3 pts. Lect: 3. Professor Ellis. area for detailed arrangements no later than the and biological neural networks. Computational Prerequisite(s): ELEN E3801, E4810, or the last day of registration. models of cortical processing, with an emphasis equivalent. An investigation of the applications on the visual system. Applications of principles of signal processing to music audio, spanning ELEN E6003x and y Master's thesis in neuroengineering; neural prostheses, the synthesis of musical sounds (including 3 pts. Members of the faculty. neuromorphic systems and biomimetics. Course frequency modulation [FM], additive sinusoidal Prerequisite(s): A minimum of 3 points of credit will include a computer simulation laboratory. synthesis, and linear predictive coding [LPC]), in ELEN E6001 or E6002 advanced projects with the modification of real and synthetic sounds the same instructor, instructor's permission, ECBM E6040y Neural networks and deep (including reverberation and time/pitch scaling), and completion of at least 12 points of credit in learning research. and the analysis of music audio to extract musical MS program with GPA of at least 3.5. Research 3 pts. Lect: 3. Professor Lazar. information (including pitch tracking, chord in area of Electrical Engineering culminating Prerequisite(s): ECBM E4040 or the equivalent. transcription, and music matching). Emphasis on in a verbal presentation and a written thesis Regularized autoencoders, sparse coding and practical, hands-on experimentation, with a wide document approved by thesis instructor. Must predictive sparse decomposition, denoising range of software implementations introduced obtain permission from thesis instructor to enroll. autoencoders, representation learning, manifold and modified within the class. Thesis projects span at least two terms: ELEN perspective on representation learning, structured E6001 or E6002 Advanced Project followed by probabilistic models for deep learning, Monte ELEN E4900-4909x or y Topics in electrical E6003 Master's Thesis with same instructor. Carlo methods, training and evaluating models and computer engineering Students must use department recommended with intractable partition functions, restricted 3 pts. Lect: 2. Members of the faculty. format for thesis writing. Counts towards total Boltzmann machines, approximate inference, Prerequisite(s): Instructor’s permission. Selected amount of research credit in M.S. program. deep belief networks, deep learning in speech, topics in electrical and computer engineering. and object recognition. Content varies from year to year, and different ELEN E6010y Systems biology: design topics rotate through the course numbers 4900 principles for biological circuits ECBM E6070-6079x or y Topics in to 4909. 4.5 pts. Lect: 3. Professor Jelenkovic. neuroscience and deep learning Prerequisite(s): ECBM E4060 or instructor’s 3 pts. Lect: 2. Members of the faculty. ELEN E4944x or y Principles of device permission. Beyond bioinformatics, cells as Prerequisite(s): the instructor's permission. microfabrication systems. Metabolic networks, transcription Selected advanced topics in neuroscience and 3 pts. Lect: 3. Professor Trevino. regulatory networks, signaling networks. deep learning. Content varies from year to year, Science and technology of conventional and Deterministic and stochastic kinetics. and different topics rotate through the course advanced microfabrication techniques for Mathematical representation of reconstructed numbers 6070 to 6079. electronics, integrated and discrete components. networks. Network motifs. Signal transduction Topics include diffusion; ion implantation, thin-film and neuronal networks. Robustness. Bacterial ELEN E6080–6089x or y Topics in systems growth including oxides and metals, molecular chemotaxis and patterning in fruit fly biology beam and liquid-phase epitaxy; optical and development. Kinetic proofreading. Optimal gene 3 pts. Lect: 2. Members of the faculty. advanced lithography; and plasma and wet circuit design. Rules for gene regulation. Random Prerequisite(s): Instructor’s permission. Selected etching. networks and multiple time scales. Biological advanced topics in systems biology. Content information processing. Numerical and simulation varies from year to year, and different topics EECS E4951y Wireless networks and systems rotate through the course numbers 6080 to 6089. 3 pts. Lect: 3. Professor Zussman. techniques. Major project(s) in MATLAB. Prerequisite(s): CSEE W4119 or instructor’s EEBM E6020y Methods of computational EEBM E6090–6099x or y Topics in permission. Various topics in the area of wireless neuroscience computational neuroscience and and mobile networks and systems. Functionalities 4.5 pts. Lect: 3. neuroengineering in the layers above the physical layer. The latest Prerequisite(s): BMEB W4020 or instructor’s 3 pts. Lect: 2. Members of the faculty. wireless networking design challenges, protocols, permission. Formal methods in computational Prerequisite(s): Instructor’s permission. Selected proposed algorithms, and applications. Includes neuroscience including methods of signal advanced topics in computational neuroscience several hands-on experiments as well as a final processing, communications theory, information and neuroengineering. Content varies from year project. theory, systems and control, system identification to year, and different topics rotate through the course numbers 6090 to 6099. ELEN E4998x or y Intermediate projects in and machine learning. Molecular models of electrical engineering transduction pathways. Robust adaptation and CSEE E6180x or y Modeling and performance integral feedback. Stimulus representation 0–3 pts. Members of the faculty. evaluation and groups. Stochastic and dynamical systems Prerequisite(s): Requires approval by a faculty 3 pts. Lect: 2. Professor Misra. models of spike generation. Neural diversity and member who agrees to supervise the work. May Prerequisite(s): COMS W4118 and STAT GU4001 ensemble encoding. Time encoding machines be repeated for credit, but no more than 3 total or permission of the instructor. Introduction to and neural codes. Stimulus recovery with time points may be used for degree credit. Substantial queuing analysis and simulation techniques. decoding machines. MIMO models of neural independent project involving laboratory work, Evaluation of time-sharing and multiprocessor computation. Synaptic plasticity and learning computer programming, analytical investigation, systems. Topics include priority queuing, buffer algorithms. Major project(s) in MATLAB. or engineering design. storage, and disk access, interference and bus contention problems, and modeling of program ELEN E6001x-E6002y Advanced projects in BMEE E6030x Neural modeling and behaviors. electrical engineering neuroengineering 1–4 pts. Members of the faculty. 3 pts. Lect: 3. Professor Sajda. ELEN E6201x Linear system theory Prerequisite(s): Requires approval by a faculty Prerequisite(s): ELEN E3801 and either APMA 3 pts. Lect: 3. Professor Sun. member who agrees to supervise the work. E2101 or E3101, or equivalent, or instructor’s Prerequisite(s): ELEN E3801 and APMA E3101, or May be repeated for up to 6 points of credit. permission. Engineering perspective on the study equivalents. Abstract objects, the concepts of Graduate-level projects in various areas of of multiple levels of brain organization, from state. Definition and properties of linear systems.

ENGINEERING 2021–2022 Characterization of linear continuous-time and design of RF and microwave amplifiers. A statistics, Boltzmann transport equation, 151 discrete-time, fixed, and time-varying systems. microwave circuit design project (using microwave scattering processes, quantum effect in transport State-space description; fundamental matrix, CAD) is an integral part of the course. phenomena, properties of heterostructures. calculation by computer and matrix methods. Quantum mechanical treatment throughout. Modes in linear systems. Adjoint systems. ELEN E6320x or y Millimeter-wave IC design Controllability and observability. Canonical forms 3 pts. Lect: 3. Professor Krishnaswamy. ELEN E6332y Principles of semiconductor and decompositions. State estimators. Lyapunov’s Prerequisite(s): ELEN E3401 or equivalent, physics, II method and stability. ELEN E4314 and E6312. Principles behind the 3 pts. Lect: 2. implementation of millimeter-wave (30GHz- Prerequisite(s): ELEN E3106 or ELEN E6331. ELEN E6302x or y MOS transistors 300GHz) wireless circuits and systems in silicon- Optical properties including absorption 3 pts. Lect: 2. Professor Tsividis. based technologies. Silicon-based active and and emission of radiation, electron-phonon Prerequisite(s): ELEN E3106 or equivalent. passive devices for millimeter-wave operation, interactions, radiative and phonon-mediated Operation and modeling of MOS transistors. millimeter-wave low-noise amplifiers, power processes, excitons, plasmons, polaritons, carrier MOS two- and three-terminal structures. The amplifiers, oscillators and VCOs, oscillator phase recombination and generation, and related optical MOS transistor as a four-terminal device; general noise theory, mixers and frequency dividers for devices, tunneling phenomena, superconductivity. charge-sheet modeling; strong, moderate, and PLLs. A design project is an integral part of the Quantum mechanical treatment throughout, heavy weak inversion models; short-and-narrow- course. use of perturbation theory. channel effects; ion-implanted devices; scaling considerations in VLSI; charge modeling; large- EECS E6321y Advanced digital electronic ELEN E6333y Semiconductor device physics signal transient and small-signal modeling for circuits 3 pts. Lect: 2. quasistatic and nonquasistatic operation. 3 pts. Lect: 2. Professor Seok. Prerequisite(s): ELEN E3106 or ELEN E4301 Prerequisite(s): EECS E4321. Advanced topics in or equivalent. Physics and properties of ELEN E6312y Advanced analog integrated the design of digital integrated circuits. Clocked semiconductors. Transport and recombination circuits and non-clocked combinational logic styles. of excess carriers. Schottky, P-N, MOS, and 3 pts. Lect: 2. Professor Krishnaswamy. Timing circuits: latches and flip-flops, phase- heterojunction diodes. Field effect and Prerequisite(s): ELEN E4312. Integrated circuit locked loops, delay-locked loops. SRAM and bipolar junction transistors. Dielectric and device characteristics and models; temperature- DRAM memory circuits. Modeling and analysis optical properties. Optical devices including and supply-independent biasing; IC operational of on-chip interconnect. Power distribution semiconductor lamps, lasers, and detectors. amplifier analysis and design and their and power-supply noise. Clocking, timing, and applications; feedback amplifiers, stability and synchronization issues. Circuits for chip-to-chip ELEN E6350y VLSI design laboratory frequency compensation techniques; noise in electrical communication. Advanced technology 3 pts. Lab: 3. Professor Kinget. circuits and low-noise design; mismatch in circuits issues that affect circuit design. The class may Prerequisite(s): ELEN E4321 and E4312, or and low-offset design. Computer-aided analysis include a team circuit design project. instructor’s permission. Design of a CMOS mixed- techniques are used in homework or a design signal integrated circuit. The class divides up into project. EECS E6322x VLSI Hardware architecture for teams to work on mixed-signal integrated circuit signal processing and machine learning designs. The chips are fabricated to be tested the ELEN E6314x Advanced communication 3 pts. Lect: 3. Professor Seok. following term. Lectures cover use of computer- circuits Prerequisite(s): CSEE W3827 and ELEN E3801. aided design tools, design issues specific to the 3 pts. Lect: 2. Recommended: ELEN E4810. Design of digital VLSI projects, and chip integration issues. This course Prerequisite(s): ELEN E4314 and E6312. Overview hardware for various digital signal processing and shares lectures with E4350, but the complexity of communication systems, modulation and machine learning algorithms. Data flow graphs, requirements of integrated circuits are higher. detection schemes. Receiver and transmitter iteration bounds, pipelining, parallel architectures, architectures. Noise, sensitivity, and dynamic retiming, unfolding/folding, systolic architectures, ELEN E6412y Lightwave devices range. Nonlinearity and distortion. Low-noise bit-level arithmetic, numerical and algorithmic 3 pts. Lect: 2. Professor Woodward. RF amplifiers, mixers, and oscillators. Phase- strength reductions, CORDIC, distributed Prerequisite(s): ELEN E4411. Electro-optics: locked loops and frequency synthesizers. arithmetic, FFT, neural network hardware, vector principles; electro-optics of liquid crystals and Typical applications discussed include wireless processors, subwordparallel architecture, and photo-refractive materials. Nonlinear optics: RF transceivers or data links. Computer-aided SIMD. May include a team circuit design project. second-order nonlinear optics; third-order analysis techniques are used in homework(s) or a nonlinear optics; pulse propagation and solitons. design project. ELEN E6324x or y Principles of RF and Acousto-optics: interaction of light and sound; microwave measurement acousto-optic devices. Photonic switching ELEN E6316y Analog-digital interfaces in VLSI 3 pts. Lect: 3. Professor Shahramian. and computing: photonic switches; all-optical 3 pts. Lect: 3. Professor Dickson. Prerequisite(s): ELEN E4314 or equivalent, switches; bistable optical devices. Introduction Prerequisite(s): ELEN E4312 or equivalent. or instructor's permission. Principles behind, to fiber-optic communications: components of Analog-to-digital and digital-to-analog conversion and techniques related to, RF and microwave the fiber-optic link; modulation, multiplexing techniques for very large scale integrated circuits simulation and measurements. S parameters; and coupling; system performance; receiver and systems. Precision sampling; quantization; simulations and measurements for small-signal sensitivity; coherent optical communications. A/D and D/A converter architectures and metrics; and large signal / nonlinear circuits in the time Nyquist architectures; oversampling architectures; and frequency domains; noise. ELEN E6413y Lightwave systems correction techniques; system considerations. A 3 pts. Lect: 2. Professor Feuer. design project is an integral part of this course. ELEN E6331y Principles of semiconductor Prerequisite(s): ELEN E4411. Recommended physics, I preparation: ELEN E6412. Fiber optics. Guiding, ELEN E6318x or y Microwave circuit design 3 pts. Lect: 2. Professor Wang. dispersion, attenuation, and nonlinear properties 3 pts. Lect: 3. Professor Baeyens. Prerequisite(s): ELEN E4301. Designed for of fibers. Optical modulation schemes. Photonic Prerequisite(s): ELEN E3331 and E3401, students interested in research in semiconductor components, optical amplifiers. Semiconductor or equivalents. Introduction to microwave materials and devices. Topics include energy laser transmitters. Receiver design. Fiber optic engineering and microwave circuit design. Review bands: nearly free electron and tight-binding telecommunication links. Nonregenerative of transmission lines. Smith chart, S-parameters, approximations, the k.p. method, quantitative transmission using erbium-doped fiber amplifier microwave impedance matching, transformation calculation of band structures and their chains. Coherent detection. Local area networks. and power combining networks, active and applications to quantum structure transistors, Advanced topics in light wave networks. passive microwave devices, S-parameter-based photodetectors, and lasers; semiconductor

ENGINEERING 2021–2022 152 ELEN E6414y Photonic integrated circuits squares filters and Kalman filters. LQR, H, linear coding theorem. The rate distortion function. 3 pts. Lect: 3. robust control, predictive control. Learning Discrete memoryless sources and single-letter Photonic integrated circuits are important control, repetitive control, adaptive control. distortion measures. Bhattacharya bounds, subsystem components for telecommunications, Liapunov and Popov stability. Nonlinear adaptive convolutional codes, and the Viterbi algorithm. optically controlled radar, optical signal control, nonlinear robust control, sliding mode processing, and photonic local area networks. control. ELEN E6718y Error correcting codes: classical An introduction to the devices and the design of and modern these circuits. Principle and modeling of dielectric EEOR E6616x or y Convex optimization 3 pts. Lect: 2. Professor Ashikhmin. waveguides (including silica on silicon and InP 3 pts. Lect: 3. Professor Iyengar. Prerequisite(s): IEOR E3658. Main concepts of based materials), waveguide devices (simple and Prerequisite(s): IEOR E6613 and EEOR E4650. error control codes. Linear block codes. Elements star couplers), and surface diffractive elements. Convex sets and functions, and operations of algebra: Galois fields. BCH and Reed Solomon Discussion of numerical techniques for modeling preserving convexity. Convex optimization codes. Convolutional Codes. Modern, capacity- circuits, including beam propagation and finite problems. Convex duality. Applications of convex achieving codes: Low Density Parity Check codes, difference codes, and design of other devices: optimization problems ranging from signal TURBO codes, and Polar codes. EXIT Charts optical isolators, demultiplexers. processing and information theory to revenue analysis. management. Convex optimization in Banach ELEN E6430x or y Applied quantum optics spaces. Algorithms for solving constrained convex EECS E6720 Bayesian models for machine 3 pts. Lect: 2. optimization problems. learning Prerequisite(s): Background in electromagnetism 3 pts. Lect: 3. Professor Paisley. (ELEN E3401, E4401, E4411, or PHYS GR6092) EECS E6690-6699x or y Topics in data-driven Prerequisite(s): Basic calculus, linear algebra, and quantum mechanics (APPH E3100, E4100, or analysis and computation probability, and programming. Basic statistics PHYS GU402x). An introduction to fundamental 3 pts. Lect: 2. Members of the faculty. and machine learning strongly recommended. concepts of quantum optics and quantum Prerequisite(s): the instructor's permission. Bayesian approaches to machine learning. Topics electrodynamics with an emphasis on applications Selected advanced topics in data-driven analysis include mixed-membership models, latent factor in nanophotonic devices. The quantization and computation. Content varies from year to models, Bayesian nonparametric methods, probit of the electromagnetic field; coherent and year, and different topics rotate through the classification, hidden Markov models, Gaussian squeezed states of light; interaction between course numbers 6690 to 6699. mixture models, model learning with mean-field light and electrons in the language of quantum variational inference, scalable inference for Big ELEN E6711x Stochastic models in Data. Applications include image processing, electrodynamics (QED); optical resonators and information systems cavity QED; low-threshold lasers; and entangled topic modeling, collaborative filtering, and 4.5 pts. Lect: 3. Professor Baryshnikov. recommendation systems. states of light. Prerequisite(s): IEOR E3658. Foundations: ELEN E6488y Optical interconnects and probability review, Poisson processes, discrete- ELEN E6761x Computer communication interconnection networks time Markov models, continuous-time Markov networks I 3 pts. Lect: 2. Professor Bergman. models, stationarity, and ergodicity. The course 3 pts. Lect: 3. Professor Ghaderi. Prerequisite(s): ELEN E4411 or E4488 or an presents a sample-path (time domain) treatment Prerequisite(s): IEOR E3658 or equivalent, or equivalent photonics course. Introduction to of stochastic models arising in information instructor’s permission. Recommended: CSEE optical interconnects and interconnection systems, including at least one of the following W4119. Analytical approach to the design of (data) networks for digital systems. Fundamental areas: communications networks (queueing communication networks. Necessary tools for optical interconnects technologies, optical systems), biological networks (hidden Markov performance analysis and design of network interconnection network design, characterization, models), Bayesian restoration of images (Gibbs protocols and algorithms. Practical engineering and performance evaluation. Enabling photonic fields), and electric networks (random walks). applications in layered internet protocols in Data link layer, Network layer, and Transport technologies including free-space structures, ELEN E6712x Communication theory hybrid and monolithic integration platforms for layer. Review of relevant aspects of stochastic 3 pts. Lect: 3. processes, control, and optimization. photonic on-chip, chip-to-chip, backplane, and Prerequisite(s): ELEN E4815, or equivalent, node-to-node interconnects, as well as photonic or instructor’s permission. Representation of EECS E6765 Internet of things—systems and networks on-chip. bandlimited signals and systems. Coherent physical data analytics EEME E6601x Introduction to control theory and incoherent communications over Gaussian 3 pts. Lect: 3. Professor Kostic. 3 pts. Lect: 3. Professor Longman. channels. Basic digital modulation schemes. Prerequisite(s): Knowledge of programming; ELEN Prerequisite(s): MATH UN2030. A graduate-level Intersymbol inference channels. Fading multipath E4703 or related; or CSEE W4119; or instructor's introduction to classical and modern feedback channels. Carrier and clock synchronization. permission. Internet of Things from the point of view of data. Methods for data analytics to control that does not presume an undergraduate ELEN E6713y Topics in communications understand trade-offs and partitioning between background in control. Scalar and matrix 3 pts. Lect: 3. cloud-based data-analytics and physical-device differential equation models, and solutions Prerequisite(s): ELEN E6712 or E4702 or E4703 or data analytics. Two-way interaction between in terms of state transition matrices. Transfer equivalent, or instructor’s permission. Advanced data and physical devices to support a truly functions and transfer function matrices, block topics in communications, such as turbo codes, ubiquitous, networked, and autonomous cyber- diagram manipulations, closed-loop response. LDPC codes, multiuser communications, network physical ecosystem. System-focused design of Proportional, rate, and integral controllers, coding, cross-layer optimization, cognitive radio. architectures, algorithms, networks, protocols, and compensators. Design by root locus and Content may vary from year to year to reflect the communications, power, security, and standards. frequency response. Controllability, observability. latest development in the field. Luenberger observers, pole placement, and Focus on a significant design project. ELEN E6717x Information theory linear-quadratic cost controllers. EECS E6766x Internet of things—engineering 3 pts. Lect: 2. Professor Wang. innovations and commercialization EEME E6602y Modern control theory Prerequisite(s): IEOR E3658 or a course in 3 pts. Lect: 3. Professor Kostic. 3 pts. Lect: 3. stochastic processes. Corequisite: ELEN E4815. Prerequisite(s): Basic programming and Prerequisite(s): EEME E6601 or E4601 or ELEN Mutual information and entropy. The source instructor’s permission. Deep dive into a couple E6201, or instructor’s permission. Singular value coding theorem. The capacity of discrete of selected topics/use-cases from the area of decomposition. ARX model and state-space memoryless channels and the noisy channel model system identification. Recursive least Internet of Things. Coverage of the topic from

ENGINEERING 2021–2022 device to the cloud, with focus on practical component behaviors. The study of the enabling CSEE E6863 Formal verification of hardware 153 aspects. Innovative product definition, product technologies (VLSI circuits, communication and software systems development, marketing, commercialization, and protocols, embedded processors, RTOSs), 3 pts. Lect: 2. Professor Theobald and Ivancic. monetization. Cross-disciplinary coverage: EE, models of computation, and design methods. The Prerequisite(s): COMS W3134, W3136, or MechE, CS, Bioengineering, marketing, business, analysis of modern domain-specific applications W3137 and COMS W3261. Introduction to the design. Building products and start-ups in the IoT including on-chip micro-networks, multiprocessor theory and practice of formal methods for the domain. Collaboration between the Engineering systems, fault-tolerant architectures, and robust design and analysis of correct (i.e., bug-free) School, Business School, industry experts, and deployment of embedded software. Research concurrent and embedded hardware/software engagement in IoT activities in NYC. Collaborative challenges such as design complexity, reliability, systems. Topics include temporal logics; model project by groups of students from different scalability, safety, and security. The course checking; deadlock and liveness issues; fairness; disciplines. This course shares lectures with requires substantial reading, class participation satisfiability (SAT) checkers; binary decision E4766, but a more complex project is expected. and a research project. diagrams (BDDs); abstraction techniques; introduction to commercial formal verification ELEN E6767x or y Internet economics, ELEN E6850x Visual information systems tools. Industrial state-of-the-art, case studies 3 pts. Lect: 2. engineering, and the implications for society and experiences: software analysis (C/C++/Java), Prerequisite(s): ELEN E4830 or instructor’s 3 pts. Lect: 2. Professor Mitra. hardware verification (RTL). Prerequisite(s): CSEE W4119 or ELEN E6761 permission. Introduction to critical image recommended, and ability to comprehend and technologies in advanced visual information CSEE E6868x or y Embedded scalable track development of sophisticated models. systems, such as content-based image databases, platforms Mathematical models, analyses of economics and video servers, and desktop video editors. 3 pts. Lect: 2. Professor Carloni. networking interdependencies in the internet. Intended for graduate students. Topics include Prerequisite(s): CSEE W4868 or instructor's Topics include microeconomics of pricing and visual data representation and compression, permission. Inter-disciplinary graduate-level regulations in communications industry, game content-based visual indexing and retrieval, seminar on design and programming of theory in revenue allocations, ISP settlements, storage system design (data placement, embedded scalable platforms. Content varies network externalities, two-sided markets. scheduling, and admission control), compressed between offerings to cover timely relevant issues Economic principles in networking and network video editing, and synchronization issues of and latest advances in system-on-chip design, design, decentralized vs. centralized resource stored video/audio signals. Programming projects embedded software programming and electronic allocation, “price of anarchy,” congestion control. and final presentations are required. design automation. Requires substantial reading Case studies of topical internet issues. Societal of research papers, class participation, and ELEN E6860y Advanced digital signal and industry implications of internet evolution. semester-long project. processing ELEN E6770–6779x or y Topics in networking 3 pts. Lect: 2. Professor Nguyen. EECS E6870x or y Speech recognition 3 pts. Lect: 2. Members of the faculty. Prerequisite(s): ELEN E4810. This course is 3 pts. Lect: 2. Further study of areas such as communication designed as an extension to ELEN E4810, with Prerequisite(s): Basic probability and statistics. protocols and architectures, flow and congestion emphasis on emerging techniques in the area Theory and practice of contemporary control in data networks, performance evaluation of digital signal processing. Topics include automatic speech recognition. Gaussian in integrated networks. Content varies from year multirate signal processing, multidimensional mixture distributions, hidden Markov models, to year, and different topics rotate through the signal processing, short-time Fourier transform, pronunciation modeling, decision trees, finite- course numbers 6770 to 6779. signal expansion in discrete and continuous time, state transducers, and language modeling. filter banks, multiresolution analysis, wavelets, Selected advanced topics will be covered in more ELEN E6820y Speech and audio processing and their applications to image compression and depth. and recognition understanding. Other topics may be included to 3 pts. Lect: 2. Professor Mesgarani. reflect developments in the field. ELEN E6873x or y Detection and estimation Prerequisite(s): ELEN E4810 or instructor’s theory permission. Fundamentals of digital speech CSEE E6861y Computer-aided design of 3 pts. Lect: 2. processing and audio signals. Acoustic and digital systems Prerequisite(s): ELEN E4815. Introduction to perceptual basics of audio. Short-time Fourier 3 pts. Lect: 2. Professor Nowick. the fundamental principles of statistical signal analysis. Analysis and filter bank models. Prerequisite(s): (i) one semester of advanced processing related to detection and estimation. Speech and audio coding, compression, and digital logic (CSEE W4823 or equivalent, or Hypothesis testing, signal detection, parameter reconstruction. Acoustic feature extraction and instructor’s permission); and (ii) a basic course estimation, signal estimation, and selected classification. Recognition techniques for speech in data structures and algorithms (COMS W3133, advanced topics. Suitable for students doing and other sounds, including hidden Markov W3134, W3137, W3139 or W3157, or equivalent, research in communications, control, signal models. and familiarity with programming. Introduction to processing, and related areas. modern digital CAD synthesis and optimization CSEE E6824y Parallel computer architecture techniques. Topics include modern digital system ELEN E6876x or y Sparse and low- 3 pts. Lect: 2. design (high-level synthesis, register-transfer dimensional models for high-dimensional Prerequisite(s): CSEE W4824. Parallel computer level modeling, algorithmic state machines, data principles, machine organization and design of optimal scheduling algorithms, resource 3 pts. Lect: 3. Professor Wright. parallel systems including parallelism detection allocation and binding, retiming), controller Prerequisite(s): ELEN E4815 or equivalent and methods, synchronization, data coherence and synthesis and optimization, exact and heuristic linear algebra. Recommended: ELEN E4810 or interconnection networks. Performance analysis two-level logic minimization, advanced multi- equivalent. Overview of theory, computation and and special purpose parallel machines. level logic optimization, optimal technology applications for sparse and low-dimensional data modeling. Recoverability of sparse and low-rank CSEE E6847y Distributed embedded systems mapping to library cells (for delay, power and models. Optimization methods for low-dim data 3 pts. Lect: 2. area minimization), advanced data structures modeling. Applications to imaging, neuroscience, Prerequisite(s): Any COMS W411X, CSEE W48XX, (binary decision diagrams), SAT solvers and communications, web data. or ELEN E43XX course, or instructor’s permission. their applications, static timing analysis, and An interdisciplinary graduate-level seminar on the introduction to testability. Includes hands-on small design of distributed embedded systems. System design projects using and creating CAD tools. robustness in the presence of highly variable communication delays and heterogeneous

ENGINEERING 2021–2022 154 ELEN E6880-6889x or y Topics in signal switched systems and standards. Quantitative organization, structure, function, and processing homework assignments may require use of a manipulation of the biomolecular sequences of 3 pts. Lect: 2. Members of the faculty. mathematical software package. nucleic acids and proteins. The role of enzymes Prerequisite(s): ELEN E4810. Advanced topics and gene regulatory elements in natural in signal processing, such as multidimensional ELEN E6999x, y, or s Fieldwork biological functions as well as in biotechnology signal processing, image feature extraction, 0.5–1.5 pts. Members of the faculty. and genetic engineering. Recombination image/video editing and indexing, advanced Prerequisite(s): Obtained internship and approval and other macromolecular processes viewed digital filter design, multirate signal processing, from a faculty adviser. May be repeated for credit, as mathematical operations with simulation adaptive signal processing, and wave-form but no more than 3 total points may be used for and visualization using simple computer coding of signals. Content varies from year to degree credit. Only for electrical engineering and programming. This course shares lectures with year, and different topics rotate through the computer engineering graduate students who ECBM E4060, but the work requirements differ course numbers 6880 to 6889. include relevant off-campus work experience as somewhat. part of their approved program of study. Final EECS E6890-6899x or y Topics in information report required. May not be taken for pass/fail EEHS E3900y History of telecommunications: processing credit or audited. from the telegraph to the internet 3 pts. Lect: 2. Members of the faculty. 3 pts. Lect: 3. EEME E8601y Advanced topics in control Advanced topics spanning electrical engineering Historical development of telecommunications and computer science such as speech processing theory from the telegraphy of the mid-1800s to and recognition, image and multimedia content 3 pts. Lect: 3. Members of the faculty. the internet at present. Included are the analysis, and other areas drawing on signal See entry under “Courses in Mechanical technologies of telephony, radio, and computer processing, information theory, machine learning, Engineering” for description. communications. The coverage includes both pattern recognition, and related topics. Content ELEN E9001x and y–E9002 Research the technologies themselves and the historical varies from year to year, and different topics 0–6 pts. Members of the faculty. events that shaped, and in turn were shaped by, rotate through the course numbers 6890 to 6899. Prerequisite(s): Requires approval by a the technologies. The historical development, both the general context and the particular ELEN E6900–6909x or y Topics in electrical faculty member who agrees to supervise the work. Points of credit to be approved by the events concerning communications, is presented and computer engineering department. Requires submission of an outline of chronologically. The social needs that elicited 3 pts. Lect: 2. Members of the faculty. the proposed research for approval by the faculty new technologies and the consequences of their Prerequisite(s): Instructor’s permission. Selected member who is to supervise the work of the adoption are examined. Throughout the course, topics in electrical and computer engineering. student. The research facilities of the department relevant scientific and engineering principles Content varies from year to year, and different are available to qualified students interested in are explained as needed. These include, topics rotate through the course numbers 6900 advanced study. among others, the concept and effective use to 6909. of spectrum, multiplexing to improve capacity, ELEN E9011x and y–E9012 Doctoral research ELEN E6910-6919x or y Topics in technical digital coding, and networking principles. There 0–6 pts. Members of the faculty. are no prerequisites, and no prior scientific or writing and presentation for electrical Prerequisite(s): Requires approval by a faculty engineering knowledge is required. Engineering engineers member who agrees to supervise the work. Points students may not count this course as a technical 1 pt. Professor Kayfetz. of credit to be approved by the department. Open elective. The course shares lectures with Open to M.S. and Ph.D. students in EE/CE only to doctoral students who have passed the EEHS E4900, but the work requirements differ with instructor's permission. Topics to help EE/ qualifying examinations. Requires submission somewhat. CE graduate students' communication skills. of an outline of the proposed research for Emphasis on writing clear, concise proposals, the approval of the faculty member who is to ELEN E3999x or y Electrical engineering journal articles, conference papers, and theses, supervise the work of the student. design challenge and on preparing clear technical presentations. 1 pt. Different topics rotate through the course ELEN E9800x and y Doctoral research Prerequisite(s): Approval by a faculty member numbers 6910 to 6919. May be repeated for instruction who agrees to supervise the work. May be credit. Credit may not be used to satisfy degree 3, 6, 9 or 12 pts. Professor Kinget. repeated for credit, but no more than 3 total requirements. A candidate for the Eng.Sc.D. degree in electrical points may be used for degree credit. Short-term engineering must register for 12 points of design project organized as a faculty-led team ELEN E6945x or y Device nanofabrication doctoral research instruction. Registration in ELEN competition. Particular design targets are set that 3 pts. Lect: 3. E9800 may not be used to satisfy the minimum vary by semester. A set of hardware and software Prerequisite(s): ELEN E3106 and E3401, or residence requirement for the degree. constraints is specified. The project takes place equivalents. Recommended: ELEN E4944. This over an advertised subset of the semester, course provides an understanding of the methods ELEN E9900x, y and s Doctoral dissertation beginning around the third week. used for structuring matter on the nanometer 0 pts. Members of the faculty. length: thin-film technology; lithographic A candidate for the doctorate may be required ELEN E4215y Analog filter synthesis patterning and technologies including photon, to register for this course every term after the and design electron, ion and atom, scanning probe, soft student’s coursework has been completed, and 3 pts. Lect: 3. lithography, and nanoimprinting; pattern until the dissertation has been accepted. Prerequisite(s): ELEN E3201 and ELEN E3801, transfer; self-assembly; process integration; and or equivalent. Approximation techniques for applications. magnitude, phase, and delay specifications, COURSES IN ELECTRICAL ELEN E6950x Wireless and mobile transfer function realization sensitivity, passive LC ENGINEERING OFFERED filters, active RC filters, MOSFET-C filters, Gm-C networking, I filters, switched-capacitor filters, automatic tuning 4.5 pts. Lect: 2. Lab: 1. Professor Jelenkovic. OCCASIONALLY techniques for integrated filters. Filter noise. A Corequisite: ELEN E6761 or instructor’s ECBM E3060x Introduction to genomic design project is an integral part of the course. permission. Overview of mobile and wireless networking. Fundamental concepts in mobile information science and technology wireless systems: propagation and fading, cellular 3 pts. Lect: 3. Professor Anastassiou. systems, channel assignment, power control, Introduction to the information system handoff. Examples of second-generation circuits- paradigm of molecular biology. Representation,

ENGINEERING 2021–2022 ELEN E4302x or y Magnetic sensors and bipolar transistor temperature sensors. Electro- ELEN E6781y Topics in modeling and analysis 155 instruments for medical imaging optic sensors: visible light, infrared, and X-ray. of random phenomena 3 pts. Lect: 2.5, Lab: 0.5. 3 pts. Lect: 3. ELEN E6151y Surface physics and analysis of Prerequisite(s): ELEN E3106, ELEN E3401, or Prerequisite(s): ELEN E6711. Recommended instructor’s permission. Physics of nuclear electronic materials preparation: a course on real analysis and magnetic resonance (NMR) and superconducting 3 pts. Lect: 2. advanced probability theory. Current methodology quantum interference device (SQUID). Design Prerequisite(s): Instructor’s permission. Basic in research in stochastic processes applied to and operation of superconducting DC magnet, physical principles of methods of surface analysis, communication, control, and signal processing. RF receiver, Josephson junction, and integrated surfaces of electronic materials including Topics vary from year to year to reflect student SQUID. Principles of biomedical sensoring structure and optical properties (auger electron interest and current developments in the field. systems including Magnetic Resonance spectroscopy, X-ray photoemission, ultraviolet Imaging (MRI), SQUID magnetometer, and NMR photoelectron spectroscopy, electron energy ELEN E6920x or y Topics in VLSI systems spectroscopy. Medical image formation and loss spectroscopy, inverse photoemission, photo design processing. stimulated desorption, and low energy electron 3 pts. Lect: 2. diffraction), physical principles of each approach. Prerequisite(s): ELEN E4321. Design automation: ELEN E4350y VLSI design laboratory layout, placement, and routing. Circuit simulation ELEN E6211x or y Circuit theory 3 pts. Lab: 3. algorithms and optimization of performance 3 pts. Lect: 3. Prerequisite(s): EECS E4321 and ELEN E4312, or and area. Multiprocessor computing systems. Prerequisite(s): ELEN E3331 and ELEN E3801. An instructor’s permission. Design of a CMOS mixed- Verification of testing. Topics may change from axiomatic development of circuit theory. Circuit signal integrated circuit. The class divides up into year to year. teams to work on mixed-signal integrated circuit theorems, circuit topology, general methods of designs. The chips are fabricated to be tested the circuit analysis. Normal form characterizations. ELEN E9060x or y Seminar in systems biology following term. Lectures cover use of computer- Scattering characterization and sensitivity 3 pts. Lect: 2. aided design tools, design issues specific to the function. Basic network synthesis methods: Open to doctoral candidates, and to qualified M.S. projects, and chip integration issues. This course immittance and transfer function realization, candidates with instructor’s permission. Study shares lectures with E6350, but the complexity multiport realization, approximation techniques. of recent developments in the field of systems biology. requirements of integrated circuits are lower. ELEN E6261y Computational methods of ELEN E4420x Topics in electromagnetics circuit analysis EEBM E9070x or y Seminar in computational 3 pts. Lect: 3. 3 pts. Lect: 3. neuroscience and neuroengineering Prerequisite(s): Undergraduate electromagnetic Prerequisite(s): ELEN E3331 and APMA E3101. 3 pts. Lect: 2. Professor Mesgarani. theory. Selected topics in the theory and practice Computational algorithms for DC, transient, and Open to doctoral candidates and qualified of electromagnetics, varying from year to year. frequency analysis of linear and nonlinear circuits. M.S. candidates with instructor’s permission. Topic for current term will be available in the Formulation of equations: state equations, hybrid Study of recent developments in computational department office one month before registration. equations, sparse tableaux. Solution techniques: neuroscience and neuroengineering. iterative methods to solve nonlinear algebraic This course may be taken more than once when ELEN E9101x or y Seminar in physical topics are different. Possible topics: microwave equations; piecewise linear methods; sparse matrix techniques; numerical integration of stiff, electronics theory and design (generalized waveguides, 3 pts. Lect: 2. excitation and coupling of waveguides, junctions, nonlinear differential equations, companion network models; waveform relaxation. Prerequisite(s): Quantum electronics and ELEN microwave networks, periodic structures, optical E4944, or instructor’s permission. Advanced topics fibers); antennas (filamentary antennas, arrays, ELEN E6304x or y Topics in electronic circuits in classical and quantum phenomena that are aperture radiation, system properties, pattern 3 pts. Lect: 3. based on ion and electron beams, gas discharges, synthesis); electrodynamics (special relativity, Prerequisite(s): Instructor’s permission. State-of- and related excitation sources. Application to new radiation by charged particles, relativistic beams, the-art techniques in integrated circuits. Topics laser sources and microelectronic fabrication. free electron lasers). may change from year to year. ELEN E9201x or y Seminar in circuit theory ELEN E4501x Electromagnetic devices and EEME E6610x Optimal control theory 3 pts. Lect: 2. energy conversion 3 pts. Lect: 3. Open to doctoral candidates, and to qualified M.S. 3 pts. Lect: 3. Professor Sen. Prerequisite(s): ELEN E6201 or EEME E6601. candidates with instructor’s permission. Study Prerequisite(s): ELEN E3401. Linear and nonlinear Objectives of optimal control. Continuous and of recent developments in linear, nonlinear, and magnetic circuits. Electric and magnetic energy discrete control problems. Calculus of variations: distributed circuit theory and analysis techniques storage, loss, and transfer. Circuit behavior of Mayer and Bolza; Pontryagin’s maximum important to the design of very large scale energy storage and transfer devices. Field theory principle. Bang-bang and singular controls. integrated circuits. of moving bodies. Dynamical equations of an Existence of optimal control. Hamilton-Jacobi electromechanical system. Electromechanical and theory and dynamic programming. Numerical ELEN E9301x or y Seminar in electronic thermo-electric sensors and actuators. Rotating methods. Optimal feedback control regulatory devices electric energy converters. Superconductivity and problems. Linear-quadratic-Gaussian estimation. 3 pts. Lect: 2. Professor Kymissis. applications. Applications. Open to doctoral candidates, and to qualified M.S. candidates with instructor’s permission. ELEN E4503x Sensors, actuators, and ELEN E6762y Computer communication Theoretical and experimental studies of electromechanical systems networks, II semiconductor physics, devices, and technology. 3 pts. Lect: 3. 3 pts. Lect: 2. Prerequisite(s): ELEN E3201 and E3401, or Prerequisite(s): ELEN E6761. Broadband ELEN E9303x or y Seminar in electronic equivalents. Electromagnetic energy storage, ISDN, services and protocols; ATM. Traffic circuits loss, and transfer. Dynamics of electromechanical characterization and modeling: Markov-modulated 3 pts. Lect: 2. systems. Linearization of nonlinear coupled Poisson and Fluid Flow processes; application to Open to doctoral candidates, and to qualified M.S. dynamical equations and equivalent circuits. voice, video, and images. Traffic Management in candidates with instructor’s permission. Study of Electromechanical actuators: acoustic, ATM networks: admission and access control, flow recent developments in electronic circuits. IC-processed micromachines. Electromechanical control. ATM switch architectures; input/output sensors: acoustic, pressure, and acceleration. queueing. Quality of service (QoS) concepts. Thermal sensors: polysilicon thermopiles and

ENGINEERING 2021–2022 156 ELEN E9402x or y Seminar in quantum ELEN E9501x or y Seminar in electrical power ELEN E9801x or y Seminar in signal electronics networks processing 3 pts. Lect: 2. 3 pts. Lect: 2. 3 pts. Lect: 2. Open to doctoral candidates, and to qualified Prerequisite(s): Open to doctoral candidates, and Open to doctoral candidates, and to qualified M.S. candidates with instructor’s permission. to qualified M.S. candidates with the instructor’s M.S. candidates with instructor’s approval. Recent Recent experimental and theoretical permission. Recent developments in control & developments in theory and applications of signal developments in various areas of quantum optimization for power systems, design of smart processing, machine learning, content analysis, electronics research. Examples of topics that may grid, and related topics. and related topics. be treated include novel nonlinear optics, lasers, transient phenomena, and detectors. EECS E9601x or y Seminar in data-driven analysis and computation ELEN E9403x or y Seminar in photonics 3 pts. Lect: 2. Instructor to be announced. 3 pts. Lect: 2. Prerequisite(s): Open to doctoral candidates and Prerequisite(s): ELEN E4411. Open to doctoral qualified M.S. candidates with the instructor's candidates, and to qualified M.S. candidates with permission. Advanced topics and recent instructor’s permission. Recent experimental and developments in mathematical techniques theoretical developments in various areas of and computational tools for data science and photonics research. Examples of topics that may engineering problems. be treated include squeezed-light generation, quantum optics, photon detection, nonlinear ELEN E9701x or y Seminar in information and optical effects, and ultrafast optics. communication theories 3 pts. Lect: 2. ELEN E9404x or y Seminar in lightwave Open to doctoral candidates, and to qualified communications M.S. candidates with instructor’s permission. 3 pts. Lect: 2. Recent developments in telecommunication Open to doctoral candidates, and to qualified networks, information and communication M.S. candidates with instructor’s approval. Recent theories, and related topics. theoretical and experimental developments in light wave communications research. Examples ELEN E9705x or y Seminar in cyber-physical of topics that may be treated include information systems capacity of light wave channels, photonic 3 pts. Professor Jiang. switching, novel light wave network architectures, Open to doctoral candidates and to qualified M.S. and optical neural networks. candidates with instructor's permission. Advanced topics in recent developments in research on cyber-physical systems (CPS) and related topics.

ENGINEERING 2021–2022 INDUSTRIAL ENGINEERING AND OPERATIONS RESEARCH 157 315 S. W. Mudd, MC 4704 212-854-2941 ieor.columbia.edu

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

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

ENGINEERING 2021–2022 158 Current Research Activities The Computational Optimization current ideas, models, and methods of In industrial engineering, research Research Center (CORC) at Columbia industrial engineering. It also includes a is conducted in the area of logistics, University is an interdisciplinary group substantial component in the humanities routing, scheduling, production and of researchers from a variety of and social sciences to help students supply chain management, inventory departments on the Columbia campus. understand the societal implications of control, revenue management, and Its permanent members are Professors their work. quality control. Daniel Bienstock, Don Goldfarb, Garud The industrial engineering program In operations research, new Iyengar, Jay Sethuraman, and Cliff objectives are: developments are being explored Stein, from the Industrial Engineering in mathematical programming, and Operations Research Department, 1. To provide students with the requisite combinatorial optimization, stochastic and Professor David Bayer, from the analytical and computational skills modeling, computational and Department of Mathematics at Barnard to assess practical situations and mathematical finance, queueing College. Researchers at CORC specialize academic problems, formulate models theory, reliability, simulation, and both in the design and implementation of of the problems represented or deterministic and stochastic state-of-the-art algorithms for the solution embedded therein, design potential network flows. of large-scale optimization problems solutions, and evaluate their impact; In engineering and management arising from a wide variety of industrial 2. To prepare students for the systems, research is conducted in and commercial applications. workplace by fostering their ability the areas of logistics, supply chain The FDT Center for Intelligent to participate in teams, understand optimization, and revenue and risk Asset Management is led by and practice interpersonal and management. Professor Xunyu Zhou at Columbia organizational behaviors, and In financial engineering, research University. The Center will focus communicate their solutions and is being carried out in portfolio on the exploration of theoretical recommendations effectively management; option pricing, including underpinnings and modeling through written, oral, and electronic exotic and real options; computational strategies for financial portfolio presentations; finance, such as Monte Carlo simulation management through the introduction 3. To familiarize students with the and numerical methods; as well as data of big data analytical techniques. historical development of industrial mining and risk management. The Center's research will combine engineering tools and techniques and Projects are sponsored and modern portfolio theory, behavioral with the contemporary state of the supported by leading private firms and finance, machine learning, and data art, and to instill the need for lifelong government agencies. In addition, our science to study core problems learning within their profession; and students and faculty are involved in the including optimal asset allocation and 4. To instill in our students an work of four research and educational risk management; and the research understanding of ethical issues centers: the Center for Applied of the Center sits at the crossroads and professional and managerial Probability (CAP), the Center for Financial of financial engineering, computer responsibilities. Engineering (CFE), the Computational science, statistics, and finance, aiming and Optimization Research Center at providing innovative and intelligent Operations Research (CORC), and the FDT Center for investment solutions. The operations research program Intelligent Asset Management. is one of several applied science The Center for Applied Probability BACHELOR OF SCIENCE programs offered at the School. At (CAP) is a cooperative center involving PROGRAMS the undergraduate level, it offers the School of Engineering and Applied basic courses in probability, statistics, Science, several departments in the applied mathematics, simulation, Industrial Engineering Graduate School of Arts and Sciences, and optimization as well as more The undergraduate program is and the Graduate School of Business. professionally oriented operations designed to develop the technical Its interests are in four applied areas: research courses. The curriculum is well skills and intellectual discipline needed mathematical and computational finance, suited for students with an aptitude for by our graduates to become leaders stochastic networks, logistics and mathematics applications. in industrial engineering and related distribution, and population dynamics. It prepares graduates for professions. The program is distinctive The Center for Financial Engineering professional employment as in its emphasis on quantitative, (CFE) at Columbia University encourages operations research analysts, e.g., with economic, computer-aided approaches interdisciplinary research in financial management consultant and financial to production and service management engineering and mathematical modeling service organizations, as well as for problems. It is focused on providing in finance and promoting collaboration graduate studies in operations research an experimental and mathematical between Columbia faculty and financial or business. It is flexible enough to be problem-formulating and problem- institutions, through the organization of adapted to the needs of future medical solving framework for industrial research seminars, workshops, and and law students. the dissemination of research done by engineering work. The curriculum members of the Center. provides a broad foundation in the

ENGINEERING 2021–2022 159 INDUSTRIAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

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

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

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

UNIVERSITY WRITING CC1010 (3) either semester

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

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

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

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 The linear algebra requirement may be filled by either MATH UN2010 or APMA E3101. 2 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.

INDUSTRIAL ENGINEERING: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

IEOR E3402 (4) IEOR E3106 (3) Production & inventory IEOR E4003 (3) IEOR E4405 (3) Stochastic systems and planning Corporate finance for eng. Scheduling applications IEOR E3404 (4) IEOR E4207 (3) IEOR E4510 (3) IEOR E3608 (3) Simulation Human factors Project management REQUIRED Foundations of optimization COURSES1 IEOR E3609 (3) IEOR E4307 (3) Advanced optimization Statistics and data analysis IEOR E4412 (3) Choose One: COMS W4111(3) Quality control and IEOR E4505 (3) OR in public policy Database systems management IEOR E4506 (3) Designing digital operating models IEOR E4650 (3) Business analytics

NONTECH 3 3 3

INDUSTRIAL ELECTIVES 6 3 ENGINEERING2

TOTAL POINTS 15 14 15 15

1 Taking required courses later than the prescribed semester is not permitted. 2 9 points total. Complete list is available at ieor.columbia.edu.

ENGINEERING 2021–2022 160 OPERATIONS RESEARCH PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

APMA E2000 (4) MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) Linear algebra (3)1 and E2001 (0)

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

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

UNIVERSITY WRITING CC1010 (3) either semester

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

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

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

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 The linear algebra requirement may be filled by either MATH UN2010 or APMA E3101. 2 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

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

IEOR E4003 (3) IEOR E3106 (3) Corporate finance for eng. Stochastic systems and IEOR E3402 (4) IEOR E4405 (3) applications Production & inventory IEOR E4407 (3) Scheduling planning Game theoretic models of IEOR E3608 (3) operations REQUIRED Foundation of optimization IEOR E3404 (4) COURSES1 Simulation IEOR E4307 (3) Statistics and data analysis IEOR E3609 (3) Choose one: Advanced optimization IEOR E4505 Operations research for public policy COMS W4111(3) IEOR E4507 Healthcare operations management Database systems IEOR E4650 Business analytics IEOR E4700 Introduction to FE

NONTECH 3 3 3

OPERATIONS

ELECTIVES 6 6 RESEARCH2

TOTAL POINTS 12 14 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 2021–2022 161 OPERATIONS RESEARCH PROGRAM: ANALYTICS: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) APMA E2000 (4) and E2001 (0) Linear algebra (3)1

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

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

UNIVERSITY WRITING CC1010 (3) either semester

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

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

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

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 The linear algebra requirement may be filled by either MATH UN2010 or APMA E3101. 2 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: ANALYTICS: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

IEOR E3106 (3) IEOR E4003 (3) IEOR E4650 (3) Stochastic systems and Corporate finance for eng. Business analytics IEOR E3402 (4) applications Production & inventory IEOR E4407 (3) Choose one: planning IEOR E3608 (3) Game theoretic models of IEOR E4405 (3) Foundation of optimization operations Scheduling IEOR E3404 (4) or REQUIRED Simulation IEOR E4307 (3)7 IEOR E4601 (3) COURSES1 Statistics and data analysis Dynamic pricing & revenue IEOR E3609 (3) management Advanced optimization IEOR E4212 (3) Data analytics & python for OR IEOR E4418 (3) Transportation analytics & logistics COMS W4111(3) Database systems

NONTECH 3 3 3

2 ELECTIVES ANALYTICS 6 6

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 2021–2022 162 OPERATIONS RESEARCH: ENGINEERING MANAGEMENT SYSTEMS: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) APMA E2000 (4) and E2001 (0) Linear algebra (3)1

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

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

UNIVERSITY WRITING CC1010 (3) either semester

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

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

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

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 The linear algebra requirement may be filled by either MATH UN2010 or APMA E3101. 2 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

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

IEOR E4003 (3) ECON UN3211 (4) Corporate finance for eng. Microeconomics ECON 3213 (4) Choose one: Macroeconomics IEOR E3106 (3) IEOR E4550 (3) Stochastic systems and Entrepreneurial business IEOR E3402 (4) applications creation Production & inventory or REQUIRED planning IEOR E3608 (3) IEOR E4998 (3) COURSES1 Foundations of optimization Managing technological IEOR E3404 (4) innovations Simulation IEOR E4307 (3) Statistics and data analysis IEOR E3609 (3) Advanced optimization Choose one: COMS W4111(3) IEOR E4510 (3) Project management or Database systems IEOR E4506 (3) Designing digital operating models or IEOR E4650 (3) Business analytics

NONTECH 6 3

TECH2 3 3 6 ELECTIVES MANAGEMENT3 3 6

TOTAL POINTS 16 18 18 18

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 2021–2022 163 OPERATIONS RESEARCH: FINANCIAL ENGINEERING: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) APMA E2000 (4) and E2001 (0) Linear algebra (3)1

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

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

UNIVERSITY WRITING CC1010 (3) either semester

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

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

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

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 The linear algebra requirement may be filled by either MATH UN2010 or APMA E3101. 2 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: FINANCIAL ENGINEERING: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

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

IEOR E4307 (3) IEOR E3609 (3) IEOR E4620 (3) Statistics and data analysis Advanced optimization Pricing models for FE

COMS W4111(3) IEOR E4700 (3) Database systems Intro. to FE ECON E3412 (4) Intro. to econometrics either semester

NONTECH 3 3 3

FINANCIAL

ELECTIVES 3 6 ENGINEERING2

TOTAL POINTS 18 17 16 20

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.

ENGINEERING 2021–2022 164 Operations Research: Engineering of the application of engineering and industrial engineering majors may Management Systems methodologies and quantitative elect to minor in operations research. This operations research option is methods to finance. Financial The department does not offer a designed to provide students with engineering is a multidisciplinary minor in engineering management an understanding of contemporary field integrating financial theory with systems or financial engineering. technology and management. It is economics, methods of engineering, tools of mathematics, and practice of for students who are interested in a GRADUATE PROGRAMS programming. Students graduating with technical-management background M.S. students must complete the pro- this concentration are prepared to enter rather than one in a traditional fessional development and leadership careers in securities, banking, financial engineering field. It consists of required course, ENGI E4000, as a graduation management, and consulting industries, courses in industrial engineering and requirement. Doctoral students will and fill quantitative roles in corporate operations research, economics, be enrolled in ENGI E6001–6004 and treasury and finance departments of business, and computer science, should consult their program for specific general manufacturing and service firms. intended to provide a foundation PDL requirements. for dealing with engineering and Students who are interested in management systems problems. pursuing the rigorous concentration Elective courses are generally intended in financial engineering must MASTER OF SCIENCE PROGRAMS to provide a substantive core in at least demonstrate proficiency in calculus, The Department of Industrial one technology area and at least one computer programming, linear algebra, Engineering and Operations Research management area. ordinary differential equations, offers courses and M.S. programs in Due to the flexibility of this option, it probability, and statistics. (1) financial engineering on a full-time can incorporate the varied educational basis only; (2) management science needs of preprofessional students Undergraduate Advanced Track and engineering on a full-time basis interested in law, medicine, business, The undergraduate advanced track is only; (3) business analytics on a full-time and finance. In addition, most students designed for advanced undergraduate basis only; (4) industrial engineering on are encouraged to add a minor in students with the desire to pursue either a full- or part-time basis; and (5) economics or computer science to their further higher education after operations research on either a full- or standard course schedules. graduation. Students with a minimum part-time basis. Both the Department’s cumulative GPA of 3.4 and faculty M.S. programs in Business Analytics and Operations Research: Analytics approval have the opportunity to Management Science and Engineering is offered in conjunction with the The analytics concentration within the participate. Students are invited to Columbia Graduate School of Business. operations research program seeks to apply to the track upon the completion Lastly, the Department and the Graduate train students to leverage advanced of their sophomore year. Advanced School of Business offer a combined quantitative models, algorithms, and track students are required to take M.S./M.B.A. degree program in industrial data for making actionable decisions to higher-level IEOR courses, including the engineering. improve business operations. Examples following: All degree program applicants are include staffing and scheduling at IEOR E4004 instead of IEOR E3608 required to take the Aptitude Tests hospitals, ride matching and pricing for IEOR E4106 instead of IEOR E3106 of the Graduate Record Examination on-demand car services, personalized IEOR E4403 instead of IEOR E4003 (GRE). M.S./M.B.A. candidates are promotions in online retail, and smarter IEOR E4404 instead of IEOR E3404 also required to take the Graduate energy consumption. Students are and MATH UN2500 Management Admissions Test (GMAT). provided with a rigorous exposure to A minimum grade-point average of 3.0 optimization and stochastic modeling, Students successfully completing (B) or its equivalent in an undergraduate as well as machine learning and data the requirements of the undergraduate engineering program is required for analysis tools for predictive modeling advanced track will receive recognition admission to the M.S. programs. At a and prescriptive analytics. Elective in on their academic record. minimum, students are expected, on the areas of healthcare, marketing, entry, to have completed courses in transportation, deep learning, and many Minors ordinary differential equations, linear others further enrich students with A number of minors are available for algebra, probability, and a programming domain expertise, and provide many students wishing to add them to their language such as C, Java, or Python. opportunities to work directly with data programs. These minors are described The Department requires that M.S. on real-world problems. starting on page 204 of this bulletin. IEOR program students may want students achieve grades of B– or higher in each of the fundamental Operations Research: Financial to consider minors in economics core courses in the discipline of study. Engineering or computer science. In addition, operations research and engineering Poor performance in core courses is The operations research concentration indicative of inadequate preparation and in financial engineering is designed to and management systems majors may elect to minor in industrial engineering, is very likely to lead to serious problems provide students with an understanding in completing the program. As a result,

ENGINEERING 2021–2022 students failing to meet this criterion 165 Business Analytics (36 points) may be asked to withdraw. Courses taken at the School Required Core Courses IEOR E4004 Optimization models and methods (first fall semester) (18 points) IEOR E4101 Probability, statistics and simulation (first fall semester) of Professional Studies will not be IEOR E4502 Python for analytics (0 pt) (first fall semester) counted toward the M.S. degree in the IEOR E4523 Data analytics (fall semester) ENGI E4000 Professional development (0 pt) (first fall semester, yearl long) IEOR Department (e.g., courses with IEOR E4650 Business analytics (spring semester) the following prefixes: ACTU, BUSI, IEOR E4524 Analytics in practice (spring semester) IEOR E4599 MSBA quantitative bootcamp (0 pt) COPR, IKNS, SUMA, FUND, and more). MRKT B9651 Marketing analytics (first fall semester) Please consult with your academic Concentration Courses (Financial Analytics & Financial Technology (FinTech), Marketing Analytics, Healthcare Analytics, and adviser regarding electives offered in Analytics Algorithms & Methodology) other departments and schools, prior Financial Analytics & IEOR E4106 Stochastic models to registration. Financial Technology IEOR E4500 Applications programming for Financial Engineering (FinTech) (9 points) IEOR E4525 Machine learning for FE & OR IEOR E4574 Technology innovation in financial services (1.5) Business Analytics IEOR E4742 Deep learning for FE & OR IEOR E4725 Big data in finance The M.S. program in Business Analytics MRKT B8649 Pricing strategies DROM B8106 Operations strategy (MSBA) offered by the IEOR Department DROM B8116 Risk management in partnership with Columbia Business DROM/MGMT B8510 Managerial negotiations School. This program is formed and MRKT B8776 Foundations of innovation DROM B8816 Quantitative pricing and revenue analytics structured following many interactions DROM B9122 Computing for business research with corporations, alumni, and students. Marketing Analytics IEOR E4407 Game theoretic models of operations It emphasizes on developing new (9 points) IEOR E4506 Designing digital operating models insights and understanding of business IEOR E4312 Application of OR & AI techniques in marketing (1.5) IEOR E4562 Innovate using design thinking (Blockweek) performance using data, statistical and IEOR E4601 Dynamic pricing and revenue management quantitative analysis, and explanatory DROM B8122 Game-theoretic business strategy and predictive modeling to help make DROM B8123 Demand and supply analytics DROM E8131 Sports analytics actionable decisions and to improve DROM/MRKT B8510 Managerial negotiations business operations. Students pursuing MRKT B8607 Strategic consumer insights MRKT B8608 New product development this degree program are provided MRKT B8617 Marketing research and analytics with rigorous exposure to optimization MRKT B8623 Intro to product management (1.5) MRKT B8625 Winning strategic capabilities and stochastic modeling, and a deep MRKT B8679 Digital marketing coverage of applications in the areas MRKT B8681 Advanced marketing strategy MRKT B8683 Marketing models of analytics. The role of analytics has DROM B9122 Computing for business research grown increasingly critical in business, DROM B9127 Online marketplaces health care, government, and many MRKT B9613 Mathematical models in marketing MRKT B9656 Customer management: concepts and tools (1.5) other sectors of the economy. It is a 36-credit degree STEM- Healthcare Analytics IEOR E4108/DROM 8108 Supply chain analytics (9 points) IEOR E4405 Scheduling designated program (equivalent of IEOR E4505 Operations research in public policy 12 three-credit courses), assuming IEOR E4507 Health care operations management IEOR E4520 Applied systems engineering adequate preparation in probability and IEOR E4521 Systems engineering tools and methods (OR) statistics, with students taking at least IEOR E4540 Data mining for engineers six courses (18 credits) within the IEOR DROM B8105 Healthcare analytics (1.5) DROM B8107 Service operations Department, and four to six courses (12– DROM B8128 Healthcare investment and entrepreneurship HCIT and services 18 credits) at the Business School. The DROM B8132 Digital health care systems DROM/MGMT B8510 Managerial negotiations remaining courses, if any, can be taken MRKT B8692 Pharmaceutical drug commercialization: strategy & practice (1.5) at the School of Engineering, the School DROM B8832 U.S. health care system MRKT B9656 Customer management: concepts and tools (1.5) of International and Public Affairs, the Law School, or the Departments of Analytics Algorithms & IEOR E4008 Computational discrete optimization Methodology COMS W4111 Introduction to databases Economics, Mathematics, and Statistics. (9 points) CSOR W4231 Analysis of algorithms Additional details are available on the IEOR E4407 Game theoretic models of operations IEOR E4418 Transportation analytics & logistics MSBA website: msba.engineering. IEOR E4525 Machine learning for FE & OR columbia.edu/content/curriculum. IEOR E4526 Analytics on the cloud IEOR E4540 Data mining for engineers DROM B8110 Business analytics strategy Financial Engineering DROM B8111 Analytics for business research DROM B8127 Big immersion seminar—big data (1.5 pts) The M.S. program in Financial DROM B8130 Applied statistics and data analytics MRKT B9160 Applied multivariate statistics Engineering is offered on a full time MRKT B9608 Experimental design & analysis for behavioral research basis only. Financial Engineering is MRKT B9616 Bayesian modeling & computation MRKT B9652 MS marketing models intended to provide a unique technical MRKT B9653 MS machine learning (1.5) background for students interested MRKT B9654 MS artificial intelligence in pursuing career opportunities in

ENGINEERING 2021–2022 166 financial analysis and risk management. In addition to the basic requirements for Financial Engineering (36 points)1 graduate study, students are expected, on entry, to have attained a high Fall Semester Required core courses: 2 level of mathematical and computer (9 points) IEOR E4007 Optimization models and methods IEOR E4701 Stochastic models programming skills, particularly in IEOR E4706 Foundations of financial engineering probability, statistics, linear algebra, and IEOR E4798 Financial engineering seminar (0 pt) the use of a programming language IEOR E4799 MSFE quantitative & computational bootcamp (0 pt) Plus Financial Engineering electives, 3–6 points 3 such as C, Python or JAVA. Previous professional experience is highly Spring Semester Required core courses: 2 desirable but not required. (9 points) IEOR E4703 Monte Carlo simulation IEOR E4707 Continuous time finance Graduate studies in Financial IEOR E4709 Statistical analysis and time series Engineering consists of 36 points (12 Plus Financial Engineering electives, 3–6 points 3 courses), starting the fall semester. Summer and/or CSOR W4231 Analysis of algorithms I Students may complete the program Fall Semester IEOR E4311 Derivatives marketing & structuring (1.5) in May, August, or December of the (For remaining IEOR E4500 Applications programming for financial engineers following year. The requirements include credits)2 IEOR E4525 Machine learning for FE & OR IEOR E4602 Quantitative risk management six required core courses and additional IEOR E4630 Asset allocation elective courses chosen from a variety IEOR E4710 Term structure modeling of departments or schools at Columbia. IEOR E4718 Beyond Black-Scholes: the implied volatility smile The six required core courses for IEOR E4722 Stochastic control & financial applications IEOR E4723 Blockchain & investing (1.5) Financial Engineering are IEOR E4007, IEOR E4726 Applied financial risk management E4701, E4703, E4706, E4707, and E4709. IEOR E4729 Algorithmic trading In addition, students are required to IEOR E4731 Credit risk modeling and derivatives Computational methods in finance attend IEOR E4798 Financial Engineering IEOR E4732 IEOR E4734 Foreign exchange and related derivatives instruments (1.5) Seminar and submit learning journals. IEOR E4735 Introduction to structured and hybrid products Financial Engineering has seven IEOR E4741 Programming for financial engineering concentrations: (1) Asset Management; IEOR E4742 Deep learning for OR & FE (2) Computation and Programming; Additional Financial Engineering electives will be offered 3 (3) Computational Finance and

Trading Systems; (4) Derivatives; (5) 1 Students may conclude the program in May, August, or December 2020. Please visit the departmental Finance and Economics; (6) Financial website (ieor.columbia.edu/masters-financial-engineering) for more information.

Technology; and (7) Machine Learning 2 All courses listed are for 3 points, unless stated otherwise. for Financial Engineering. A sample 3 The list of Financial Engineering electives can be found at ieor.columbia.edu/masters-financial-engineering/ schedule is available in the Department curriculum. office and on the IEOR website: ieor. emphasize both management and columbia.edu. Students select electives Graduates of this program are engineering perspectives in solving from a group of specialized offerings expected to assume positions as problems, making decisions, and in both the fall and spring terms. They analysts and associates in consulting managing risks in complex systems. may select from a variety of approved firms, business analysts in logistics, Students pursuing this specialization are electives from the Department, the supply chain, operations, or revenue provided with a rigorous exposure to School of Business, and the Graduate management departments of large optimization and stochastic modeling, School of Arts and Sciences. corporations, and as financial analysts in and a deep coverage of applications in various functions (e.g., risk management) the areas of operations engineering and of investment banks, hedge funds, credit- Management Science and management. card companies, and insurance firms. Engineering In addition to the core and semi-core Management Science and Management Science and Engineering requirements, Management Science Engineering (36 points) can be (MS&E), offered by the IEOR Department and Engineering has six concentrations: completed in a single calendar year, in partnership with Columbia Business (1) Operations and Analytics; (2) in three semesters. Students enter in School, is the first such program Pricing and Revenue Management; (3) the fall term and can either finish their between Columbia Engineering Entrepreneurship and Innovation; (4) coursework at the end of the following and Columbia Business School. It Logistics and Supply Chain Management; August, or alternatively, have the option reflects the next logical step in the (5) Financial Technology (Fin Tech); and to take the summer term off (e.g., long-standing close collaboration (6) Healthcare Management. Additional for an internship) and complete their between the IEOR Department at the details regarding these concentrations coursework by the end of the following Engineering School and the Decision, are available on the MS&E website: fall term. Students are required to take Risk, and Operations (DRO) Division mse.ieor.columbia.edu/content/mse- the equivalent of 12 3-point courses (36 at the Business School. Coursework concentrations. points).

ENGINEERING 2021–2022 Students must take at least six 167 Management Science and Engineering (36 points) courses (18 points) within the IEOR Department, three to six courses at the Required Core IEOR E4004 Optimization models and methods (first fall semester) Business School, and the remaining Courses (12 points) IEOR E4101 Probability, statistics, and simulation (first fall semester) courses (if any) within the School of IEOR E4102 Stochastic models (spring semester) Engineering, the School of International IEOR E4111 Operations consulting (starts first fall semester, year-long course) and Public Affairs, the Law School, DROM B8000 Optimization and simulation bootcamp (0 pt) or the Departments of Economics, Mathematics, and Statistics. Students Semi-Core Courses (DRO, Analysis, and Management Electives 18 points) in residence during the summer term can take two to four Business Decision, Risk, and IEOR E4650 Business analysis Operations Electives DROM B8101 Business analytics II (1.5 pt) School courses in the third (summer) (9 points) DROM B8105 Healthcare analytics (1.5) semester in order to complete their DROM B8106 Operations strategy (1.5 pt) program. Additional details regarding DROM B8107 Service operations these electives are available in the DROM B8110 Business analytics strategy Departmental office and on the MS&E DROM B8116 Risk management website: mse.ieor.columbia.edu. DROM B8123 Demand & supply analytics DROM B8131 Sports analytics DROM B8510 Managerial negotiations Industrial Engineering Graduate studies in Industrial Engineering Analysis and Management Electives (9 points minimum) enable students with industrial engineering bachelor’s degrees to Analysis Group IEOR E4008 Computational discrete optimization enhance their undergraduate training At least one of the Analysis of algorithms I CSOR W4231 with studies in special fields such as following: IEOR E4405 Scheduling production planning, inventory control, IEOR E4407 Game theoretic models of operations scheduling, and industrial economics. IEOR E4418 Transportation analytics and logistics IEOR E4501 Tools for analytics However, the department also offers a IEOR E4507 Healthcare operations management broader master’s program for engineers IEOR E4523 Data analytics whose undergraduate training is not in IEOR E4525 Machine learning for financial engineering & operations research industrial engineering. Students may IEOR E4526 Analytics on the cloud complete the studies on a full-time (12 IEOR E4540 Data mining for engineering points per term) or part-time basis. IEOR E4572 Visualization & storytelling with data (1.5) Industrial Engineers are required IEOR E4573 Performance, objectives & results using data analytics (1.5) to satisfy a core program of graduate IEOR E4601 Dynamic pricing and revenue optimization courses in production management, IEOR E4742 Deep learning for operations research & financial engineering probability theory, statistics, simulation, DROM B8108 Supply chain analytics and operations research. Students with B.S. degrees in industrial engineering will Management Group IEOR E4412 Quality control and management At least one of the usually have satisfied this core in their following: IEOR E4505 Operations research in public policy undergraduate programs. All students Designing digital operating models IEOR E4506 must take at least 18 points of graduate IEOR E4510 Project management work in industrial engineering and at IEOR E4550 Entrepreneurial business creation for engineers IEOR E4560 Lean launchpad (weeklong course in mid-January, by least 30 points of graduate studies at application only) Columbia. Industrial Engineering may IEOR E4561 Launch your startup: tech include concentrations in: (1) Healthcare IEOR E4562 Innovate using design thinking (weeklong course in mid-January, by Management; (2) Regulated Industries; application only) and (3) Systems Engineering. Additional IEOR E4570 Entrepreneurship bootcamp for engineers (3-day long course fall or details regarding these concentrations spring semester, by application only) IEOR E4711 Global capital markets and electives are available in the IEOR E4998 Managing technological innovation and entrepreneurship Departmental office and on the IEOR FINC B8307 Advanced corporate finance website: ieor.columbia.edu.

Operations Research Breadth Electives: The breadth electives can be selected from the Business School, the School of Engineering, the School Graduate studies in Operations Research of International and Public Affairs, the Law School, or the Departments of Economics, Mathematics, and enables students to concentrate their Statistics. studies in methodological areas such as mathematical programming, stochastic models, and simulation. Students may

ENGINEERING 2021–2022 168 Operations Research (30 points)

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

Concentrations The department Analytics Healthcare Management recommends taking Decision, Risk, and Analysis Logistics and Supply Chain Management three to five elective Entrepreneurship and Innovation Machine Learning and Artificial Intelligence courses, depending on the Finance and Management Optimization concentration.

1 STAT GU4001 will not count toward the 18 IEOR point requirement.

complete the studies on a full time (12 equivalent has been completed during and (3), they may be asked to withdraw points per term) or part time basis. undergraduate studies, students should from the program at the end of the Operations Research has eight consult with a faculty adviser in order to second year. areas of concentrations, including: (1) obtain exemption from a required course. Doctoral students are also required Analytics; (2) Decision, Risk, and Analysis; to take 4 additional Ph.D. courses (3) Entrepreneurship and Innovation; (4) PH.D. PROGRAM (possibly in other departments) during Finance and Management; (5) Healthcare The IEOR Department offers two Ph.D. the course of the Ph.D. Research credits Management; (6) Logistics and Supply programs in (1) Industrial Engineering; (IEOR E9101) do not count towards this Chain Management; (7) Machine and (2) Operations Research. The requirement. It is important to select Learning and Artificial Intelligence; and requirements for the Ph.D. in industrial courses you find interesting while (8) Optimization. Students may select engineering and operations research considering your background and from a variety of approved electives from are identical. Both programs require in consultation with your academic the Department, the School of Business, the student to complete the qualifying adviser. Students can consider courses and the Graduate School of Arts and procedure and submit and defend a from other departments including Sciences. Additional details regarding dissertation based on the candidate's Mathematics, Computer Science, these concentrations and electives are original research, conducted under Statistics, Economics, and Decision Risk available in the Departmental office and the supervision of the faculty. The and Operations. Doctoral candidates on IEOR's website: ieor.columbia.edu. dissertation work may be theoretical or must obtain a minimum of 60 points computational or both. of formal course credit beyond the JOINT M.S. AND M.B.A. The qualifying procedure consists bachelor’s degree. A master’s degree The department and the Graduate of three components, including: (1) from an accredited institution may be School of Business offer a joint M.S. mas- complete the four core courses during accepted as equivalent to 30 points. ter's program in Industrial Engineering. the first year with an average grade A minimum of 30 points beyond the Prospective students for this special of (A-) or above; (2) conduct research master’s degree must be earned while program must submit separate applica- during the first summer (ideally starting in residence in the doctoral program. tions to Columbia Engineering and the in Spring or earlier) and present it in a Detailed information regarding the Graduate School of Business and be department seminar at the beginning requirements for the doctoral degree admitted to both schools for entrance of the third semester; and (3) submit may be obtained in the Department into the joint program. a research report (paper) at the end office and on IEOR website: ieor. columbia.edu. Admissions requirements are the of the third semester. Students will same as those for the regular M.S. be reviewed after each component. program in Industrial Engineering and A student who fails to complete COURSES IN INDUSTRIAL for the M.B.A. This joint program is component (1) may be asked to withdraw ENGINEERING AND coordinated so that both degrees can from the program at the end of the first OPERATIONS RESEARCH year. be obtained after five terms of full-time For up-to-date course offerings, please A student who successfully study (30 points in two terms while visit ieor.columbia.edu. registered in Columbia Engineering and completes component (1) will typically IEOR E1000x or y Frontiers in operations 45 points in three terms while registered move on to do summer research, advised by a faculty member in the IEOR research and data analytics in the Graduate School of Business). 1 pt. Lect: 1. Students in the joint program must Department. In the rare instance the Introductory course for overview of modern complete certain courses by the end Ph.D. committee is dissatisfied with a approaches and ideas of operations research and of their first year of study. If a substantial student's performance in components (2) data analytics. Through a series of interactive

ENGINEERING 2021–2022 sessions, students engage in activities exploring echelon integrated production-inventory systems. conditional distributions, conditional expectation 169 OR topics with various faculty members from the Production scheduling. Term project. Recitation and variance, and moment generating functions. IEOR department. section required. Also Central Limit Theorem for sums of random variables. Consists of lectures, recitations, weekly IEOR E2261x and y Accounting and finance IEOR E3404y Simulation modeling and homework, and in-class exams. 3 pts. Lect: 3. analysis Prerequisite(s): ECON UN1105 Principles of eco- 4 pts. Lect: 4. IEOR E3900x and y Undergraduate research nomics. For undergraduates only. Examines the Prerequisite(s): IEOR E3658 and E4307 or STAT or project fundamental concepts of financial accounting GU4001, and knowledge of a programming 1–3 pts. Members of the faculty. and finance, from the perspective of both manag- language such as Python, C, C++ or Matlab. It Prerequisite(s): Approval by a faculty member ers and investors. Key topics covered include is strongly advised that Stochastic modeling who agrees to supervise the work. Independent principles of accrual accounting; recognizing and (IEOR E3106 or IEOR E4106) be taken before work involving experiments, computer program- recording accounting transactions; preparation this course. This is an introductory course to ming, analytical investigation, or engineering and analysis of financial statements; ratio analy- simulation, a statistical sampling technique that design. sis; pro-forma projections; time value of money uses the power of computers to study complex (present values, future values and interest/dis- stochastic systems when analytical or numerical IEOR E3999x, y or s Fieldwork count rates); inflation; discounted-cash-flow (DCF) techniques do not suffice. The course focuses on 1–1.5 pts. (up to 2 pts, summer only) project evaluation methods; deterministic and discrete-event simulation, a general technique Prerequisite(s): Obtained internship and approval probabilistic measures of risk; capital budgeting. used to analyze a model over time and determine from faculty adviser. Only for IEOR undergraduate the relevant quantities of interest. Topics covered students who need relevant work experience as ORCA E2500y Foundations of data science in the course include the generation of random part of their program of study. Final reports are 3 pts. Lect: 3. numbers, sampling from given distributions, simu- required. May not be taken for pass/fail credit or Prerequisite(s): MATH UN1101 and UN1102. Some lation of discrete-event systems, output analysis, audited. familiarity with programming. Designed to provide variance reduction techniques, goodness of fit an introduction to data science for sophomore IEOR E4003x Corporate finance for engineers tests, and the selection of input distributions. 3 pts. Lect: 3. SEAS majors. Combines three perspectives: infer- The first half of the course is oriented toward the ential thinking, computational thinking, and real- Prerequisite(s) or corequisites: Probability theory design and implementation of algorithms, while and linear programming. Required for all under- world applications. Given data arising from some the second half is more theoretical in nature and real-world phenomenon, how does one analyze graduate students majoring in IE, OR:EMS, OR:FE, relies heavily on material covered in prior proba- and OR. Introduction to the economic evaluation that data so as to understand that phenomenon? bility courses. The teaching methodology consists Teaches critical concepts and skills in computer of industrial projects. Economic equivalence of lectures, recitations, weekly homework, and and criteria. Deterministic approaches to eco- programming, statistical inference, and machine both in-class and take-home exams. Homework learning, in conjunction with hands-on analysis nomic analysis. Multiple projects and constraints. almost always includes a programming compo- Analysis and choice under risk and uncertainty. of real-world datasets such as economic data, nent for which students are encouraged to work document collections, geographical data, and in teams. IEOR E4004x and y Optimization models and social networks. At least one project will address methods a problem relevant to New York City. IEOR E3608x Foundations of optimization 3 pts. Lect: 3. 3 pts. Lect: 3. A graduate course only for MS&E, IE, and OR IEOR E3106x Stochastic systems and Prerequisite(s): MATH UN2010. Corequisite: applications students. This is also required for students in the Data structures. This first course in optimization Undergraduate Advanced Track. For students 3 pts. Lect: 3. focuses on theory and applications of linear Prerequisite(s): IEOR E3658. For undergraduates who have not studied linear programming. Some optimization, network optimization, and dynamic of the main methods used in IEOR applications only. Required for all undergraduate students programming. majoring in IE, OR:EMS, OR:FE, and OR. involving deterministic models: linear program- Must be taken during (or before) the fifth semes- IEOR E3609y Advanced optimization ming, the simplex method, nonlinear, integer and ter. Some of the main stochastic models used in 3 pts. Lect: 3. dynamic programming. engineering and operations research applica- Prerequisite(s): IEOR E3608. For undergraduates IEOR E4007x Optimization models and tions: discrete-time Markov chains, Poisson only. Required for all undergraduate students methods for financial engineering processes, birth and death processes and other majoring in IE, OR:EMS, OR:FE, and OR. This is a 3 pts. Lect: 3. continuous Markov chains, renewal reward pro- follow-up to IEOR E3608 and will cover advanced Prerequisite(s): Linear algebra. This graduate cesses. Applications: queueing, reliability, inven- topics in optimization, including integer optimiza- course is only for M.S. Program in Financial tory, and finance. IEOR E3106 must be completed tion, convex optimization, and optimization under Engineering students. Linear, quadratic, nonlinear, by the fifth term. Only students with special uncertainty, with a strong focus on modeling, dynamic, and stochastic programming. Some academic circumstances may be allowed to take formulations, and applications. discrete optimization techniques will also be these courses in alternative semesters with the introduced. The theory underlying the various consultation of CSA and Departmental advisers. IEOR E3658x and y Probability for engineers 3 pts. Lect: 3. optimization methods is covered. The emphasis IEOR E3402y Production and inventory Prerequisite(s): Calculus. For undergraduates is on modeling and the choice of appropriate planning only. Required for OR:FE concentration. Must be optimization methods. Applications from financial 4 pts. Lect: 3. Recit: 1. taken during or before third semester. Students engineering are discussed. who take IEOR E3658 may not take W4150 due to Prerequisite(s): IEOR E3608 and E3658. For IEOR E4008x or y Computational discrete undergraduates only. Required for all undergradu- significant overlap. Recommended: strong math- optimization ate students majoring in IE, OR:EMS, OR:FE, and ematical skills. Introductory course to probability 3 pts. Lect: 3. OR. Must be taken during (or before) the sixth theory and does not assume any prior knowledge Prerequisite(s): Linear programming, basic prob- semester. Inventory management and produc- of subject. Teaches foundations required to use ability theory. Discrete optimization problems. tion planning. Continuous and periodic review probability in applications, but course itself is Mathematical techniques and testing strengths models: optimal policies and heuristic solutions, theoretical in nature. Basic definitions and axioms and limits in practice on relevant applications. deterministic and probabilistic demands. Material of probability and notions of independence and Transportation (travelling salesman and vehicle requirements planning. Aggregate planning of conditional probability introduced. Focus on routing) and matching (online advertisement and production, inventory, and work force. Multi- random variables, both continuous and discrete, school allocation) problems. and covers topics of expectation, variance,

ENGINEERING 2021–2022 170 IEOR E4009x or y Nonlinear optimization chains, renewal reward processes. Applications: guished panel of successful minds from across 3 pts. Lect: 3. Not offered in 2021–2022. queueing, reliability, inventory, and finance. the city. Prerequisite(s): A course on optimization models and methods (at the level of IEOR E4004) and a IEOR E4108/DROM B8108x or y Supply chain IEOR E4199y MSIEOR quantitative bootcamp course on linear algebra. Unconstrained and con- analytics 0 pt. Lect: 0. strained nonlinear optimization involving continu- 3 pts. Lect: 2.5. Zero-credit course. Primer on quantitative and ous functions. Additionally, fundamental concepts Prerequisite(s): IEOR E3402 or instructor's per- mathematical concepts. Required for all incoming such as optimality conditions and convergence, mission. MS IEOR students only. Supply chain MSOR and MSIE students. principle focus on practical optimization methods. management, model design of a supply chain network, inventories, stock systems, commonly IEME E4200x or y Human-centered design & CSOR E4010y Graph theory: a combinatorial used inventory models, supply contracts, value innovation view of information and information sharing, risk pool- 3 pts. Lect: 2.5. 3 pts. Lect: 3. Not offered in 2021–2022. ing, design for postponement, managing product Prerequisite(s): Instructor's permission. Open to Prerequisite(s): Linear algebra, or instructor’s per- variety, information technology and supply chain SEAS graduate and advanced undergraduate mission. An introductory course in graph theory management; international and environmental students, Business School, and GSAPP. Students with emphasis on its combinatorial aspects. Basic issues. Note: replaced IEOR E4000 beginning in from other schools may apply. Fast-paced intro- definitions, and some fundamental topics in graph fall 2018. duction to human-centered design. Students learn theory and its applications. Topics include trees the vocabulary of design methods, understanding and forests graph coloring, connectivity, matching IEOR E4111x and y Operations consulting of design process. Small group projects to cre- theory and others. 3 pts. Lect: 3. ate prototypes. Design of simple product, more Prerequisite(s): Probability and statistics at the complex systems of products and services, and IEOR E4100x Statistics and simulation level of IEOR E3658 and E4307 or STAT GU4001, design of business. 1.5 pts. Lect: 1.5. and Deterministic Models at the level of IEOR Prerequisite(s): Understanding of single- and E3608 or IEOR E4004, or instructor permission. IEOR E4206x or y Intellectual property for multivariable calculus. Probability and simulation. For MS-MS&E students only. Aims to develop and engineers Statistics building on knowledge in probability and harness the modeling, analytical, and managerial 0 pts. simulation. Point and interval estimation, hypoth- skills of engineering students and apply them Intellectual property (patents, copyrights, trade- esis testing, and regression. A specialized version to improve the operations of both service and marks) are an increasingly critical part of almost of IEOR E4150 for MSE and MSBA students who manufacturing firms. Structured as a hands-on any business, at almost any stage of growth. are exempt from the first half of IEOR E4101. Must laboratory in which students "learn by doing" on Provides the aspiring business executive, tech obtain waiver for E4101. real-world consulting projects (October to May). entrepreneur, or engineer with an overview of The student teams focus on identifying, model- commercial opportunities and risks associated IEOR E4101x Probability, statistics and ing, and testing (and sometimes implementing) with intellectual property, with a particular focus simulation operational improvements and innovations with on technology patents. While legal principles will 3 pts. Lect: 3. high potential to enhance the profitability and/ be addressed, the primary focus is on leveraging Prerequisite(s): Understanding of single- and mul- or achieve sustainable competitive advantage for intellectual property to create financial returns. tivariable calculus. MSE and MSBA students only. their sponsor companies. The course is targeted IEOR E4207x Human factors: performance Basic probability theory, including independence toward students planning careers in technical and conditioning, discrete and continuous random 3 pts. Lect: 3. consulting (including operations consulting) and Required for undergraduate students majoring variable, law of large numbers, central limit theo- management consulting, or pursuing positions rem, and stochastic simulation, basic statistics, in IE. Sensory and cognitive (brain) processing as business analysts in operations, logistics, sup- considerations in the design, development, and including point and interval estimation, hypothesis ply chain and revenue management functions, testing, and regression; examples from business operations of systems, products, and tools. User positions in general management, and future or operator limits and potential in sensing, per- applications such as inventory management, med- entrepreneurs. ical treatments, and finance. A specialized version ceiving decision making, movement coordination, of IEOR E4150 for MSE and MSBA students. IEOR E4150x Introduction to probability and memory, and motivation. statistics IEOR E4102y Stochastic models for MSE IEOR E4208y Seminar in human factors 3 pts. Lect: 3. design 3 pts. Lect: 3. Prerequisite(s): Calculus, including multiple inte- Prerequisite(s): IEOR E4101. Introduction to sto- 3 pts. Lect: 3. gration. Covers the following topics: fundamentals Prerequisite(s): IEOR E4207 or instructor’s chastic processes and models, with emphasis on of probability theory and statistical inference used applications to engineering and management; permission. An elective for undergraduate in engineering and applied science; Probabilistic students majoring in IE. An in-depth explora- random walks, gambler’s ruin problem, Markov models, random variables, useful distributions, chains in both discrete and continuous time, tion of the application potential of human factor expectations, law of large numbers, central limit principles for the design of products and pro- Poisson processes, renewal processes, stopping theorem; Statistical inference: pint and confidence times, Wald’s equation, binomial lattice model for cesses. Applications to industrial products, tools, interval estimation, hypothesis tests, linear regres- layouts, workplaces, and computer displays. pricing risky assets, simple option pricing; simula- sion. For IEOR graduate students. tion of simple stochastic processes, Brownian Consideration to environmental factors, training motion, and geometric Brownian motion. A spe- IEOR E4177y Think bigger and documentation. Term project. cialized version of IEOR E4106 for MSE students. 3 pts. Lect: 3. IEOR E4212x Data analytics for OR Innovative solutions to complex problems that 3 pts. Lect: 3. IEOR E4106x and y Stochastic models are both novel and useful. Focuses on The Think 3 pts. Lect: 3. Surveys tools available in Python for getting, Bigger Innovation Method, uses decision-making cleaning, and analyzing data. Data from files Prerequisite(s): STAT GU4001 or probability theory theory, cognitive science, and industry practice or IEOR E4150. This graduate course is only for (csv, html, json, xml) and databases (Mysql, to facilitate creativity and innovation. Designed PostgreSQL, NoSQL), covers rudiments of data IE and OR students. Also required for students in to foster new ideas during the beginning of the the Undergraduate Advanced Track. Some of the cleaning, and examine data analysis, machine semester that will then function as the seeds for learning (regression, decision trees, clustering) main stochastic models used in engineering and entrepreneurially minded. Culminates in a final operations research applications: discrete-time data visualization packages (NumPy, Pandas, project with presentation of formal and polished Scikit-learn Bokeh, available in Python. Note: Markov chains, Poisson processes, birth and pitch of an innovative idea in front of a distin- death processes and other continuous Markov IEOR students only.

ENGINEERING 2021–2022 IEOR E4307x Statistics and data analysis projects, value companies, and make Corporate IEOR E4408x Resource allocation: models, 171 3 pts. Lect: 3. Finance decisions. Additional topics include: cost algorithms, and applications Prerequisite(s): probability, linear algebra. of capital, dividend policy, debt policy, impact of 3 pts. Lect: 3. Not offered in 2021–2022. Descriptive statistics, central limit theorem, taxes, Shareholder/Debtholder agency costs, dual- Prerequisite(s): Linear programming (IEOR E3608 parameter estimation, sufficient statistics, class shares, using option pricing theory to ana- or E4004), basic knowledge of nonlinear and hypothesis testing, regression, logistic regression, lyze management behavior, investment banking integer programming. Overview of resource goodness-of-fit tests, applications to operations activities, including equity underwriting, syndicat- allocation models. Single resource allocation research models. ed lending, venture capital, private equity invest- with concave returns; equitable resource alloca- ing and private equity secondaries. Application of tion; lexicographic minmax/maxmin optimization; IEME E4310x The manufacturing enterprise theory in real-world situations: analyzing financial extensions to substitutable resources; multiperiod 3 pts. Lect: 3. Not offered in 2021–2022. activities of companies such as General Electric, resource allocation; equitable allocation in multi- The strategies and technologies of global manu- Google, Snapchat, Spotify, and Tesla. commodity network flow models; equitable con- facturing and service enterprises. Connections tent distribution in networks; equitable resource IEOR E4403x Quantitative corporate finance between the needs of a global enterprise, the allocation with discrete decision variables. technology and methodology needed for manu- 3 pts. Lect: 3. facturing and product development, and strategic Prerequisite(s): Probability theory and linear IEOR E4412y Quality control and planning as currently practiced in industry. programming Required for students in the management Undergraduate Advanced Track. Key measures 3 pts. Lect: 3. IEOR E4311x Derivatives marketing & and analytical tools to assess the financial per- Prerequisite(s): IEOR E3658 and working knowl- structuring formance of a firm and perform the economic edge of statistics. Required for undergraduate 1.5 pts. Lect: 1.5. evaluation of industrial projects. Deterministic students majoring in IE. Statistical methods for Prerequisite(s): IEOR E3402, IEOR E4000, mathematical programming models for capital quality control and improvement: graphical meth- or instructor's permission. Covers topics in budgeting. Concepts in utility theory, game theory ods, introduction to experimental design and reli- Accounting, relationships among different ele- and real options analysis. ability engineering and the relationships between ments of financial statements, short- term and quality and productivity. Contemporary methods IEOR E4404x and y Simulation long-term financing alternatives, using swaps, used by manufacturing and service organizations 4 pts. Lect: 3. Recit: 1. cap, and floors to manage interest rate risk, in product and process design, production and Prerequisite(s): IEOR E3658 and E4307 or STAT hedging interest risk of corporate finance, delivery of products and services. using options as cheapeners, structured swaps, GU4001, computer programming. Corequisite: accounting treatment of derivatives, cash flow IEOR E3106 or IEOR E4106. Required for all under- IEOR E4418x or y Transportation analytics hedging, accrual accounting, hedging issuance graduate students majoring in IE, OR:EMS, OR:FE, and logistics of a bond using treasuries, hedging employee and OR. Also required for MSOR. Generation 3 pts. Lect: 3. stock options, preferred shares and their use in of random numbers from given distributions; Prerequisite(s): IEOR E3608 or E4404 or permis- corporate treasury, FX risk and FX translation, variance reduction; statistical output analysis; sion of instructor. Introduces quantitative tech- commodities hedging, operating lease vs capital introduction to simulation languages; application niques and state-of-the-art practice of operations lease, credit risk, and cred spread and funding. to financial, telecommunications, computer, and research relevant to the design and both the tac- Note: restricted to IEOR MS students. production systems. Graduate students must reg- tical and strategic management of logistical and ister for 3 points. Undergraduate students must transportation systems. Discusses a wide variety IEOR E4312y Application of OR & AI register for 4 points. Note: Students who have of passenger and freight systems, including air, techniques in marketing taken IEOR E4703 Monte Carlo simulation may urban and highway traffic, rail, and maritime sys- 1.5 pts. Lect: 1.5. not register for this course for credit. Recitation tems. Explores the practice of revenue manage- Prerequisite(s): working knowledge of Excel, high section required. ment and dynamic pricing. Through case studies, level language (such as Python, R, MATLAB, or analyzes successes and failures in third-party IEOR E4405y Scheduling VBA), and intro course in probability and statis- logistics, postal, truck and rail pickup and deliv- 3 pts. Lect: 3. tics. Covers working knowledge of quantitative ery systems. Investigates large-scale integrated Prerequisite(s): IEOR E3608 and E3658. Computer methods and data mining techniques applied to logistics and transportation systems and studies programming. Required for undergraduate stu- marketing and customer relationship manage- the underlying principles governing transportation dents majoring in IE and OR. Job shop scheduling: ment. Topics include clustering methods, conjoint planning, investment and operations. analysis and customer preferences, forecasting, parallel machines, machines in series; arbitrary market share, product life cycle, new product, job shops. Algorithms, complexity, and worst-case IEOR E4500x Applications programming for nearest neighbor, discriminant analysis, decision analysis. Effects of randomness: machine break- financial engineering tree, revenue management, price and advertis- downs, random processing time. Term project. 3 pts. Lect: 3. ing elasticity, resource allocation and return on Prerequisite(s): Computer programming or IEOR E4407x Game theoretic models of investment (ROI), economic analysis of a network instructor’s approval. Required for undergraduate operations and its formation, and networked markets. Note: students majoring in OR:FE. We will take a hands- 3 pts. Lect: 3. restricted to IEOR MS students. on approach to developing computer applications Prerequisite(s): IEOR E4004 (or E3608), IEOR for Financial Engineering. Special focus will be IEOR E4399y MSE quantitative bootcamp E4106 (or E3106), familiarity with differential equa- placed on high-performance numerical applica- 0 pt. Lect: 0. tions and computer programming; or instructor’s tions that interact with a graphical interface. In Zero-credit course. Primer on quantitative and permission. Required for undergraduate students the course of developing such applications we mathematical concepts. Required for all incoming majoring in OR:FE and OR. A mathematically rigor- will learn how to create DLLs, how to integrate MSOR and MSIE students. ous study of game theory and auctions, and their VBA with C/C++ programs, and how to write application to operations management. Topics multithreaded programs. Examples of problems IEOR E4402x Corporate finance, accounting, include introductory game theory, private value settings that we consider include simulation of & investment banking auction, revenue equivalence, mechanism design, stock price evolution, tracking, evaluation and 3 pts. Lect: 3. optimal auction, multiple-unit auctions, combina- optimization of a stock portfolio; optimal trade Prerequisite(s): Covers primary financial theories torial auctions, incentives, and supply chain coor- execution. In the course of developing these and alternative theories underlying Corporate dination with contracts. No previous knowledge of applications, we review topics of interest to OR:FE Finance, such as CAPM, Miller Modigliani, Fama game theory is required. French factors, Smart Beta, etc. Interpret finan- in a holistic fashion. cial statements, build cash flow models, value

ENGINEERING 2021–2022 172 ORCA E4500x or y Foundations of data es management. Develops modeling, analytical, data. Obtain data from files (csv, html, json, xml) science and managerial skills of engineering and health and databases (Mysql, PostgreSQL, NoSQL), cover 3 pts. Lect: 3. care management students. Enables students to the rudiments of data cleaning, and examine data Prerequisite(s): MATH UN1101 and UN1102, some master an array of fundamental operations man- analysis, machine learning, and data visualization familiarity with programming. Designed to provide agement tools adapted to the management of packages (NumPy, pandas, Scikit-lern, bokeh) an introduction to data science for sophomore health care systems. Through real-world business available in Python. Brief overview of natural lan- SEAS majors. Combines three perspectives: infer- cases, students learn to identify, model, and ana- guage processing, network analysis, and big data ential thinking, computational thinking, and real- lyze operational improvements and innovations in tools available in Python. Contains a group project world applications. Given data arising from some a range of health care contexts. component that will require students to gather, real-world phenomenon, how does one analyze store, and analyze a data set of their choosing. IEOR E4510y Project management that data so as to understand that phenomenon? 3 pts. Lect: 3. IEOR E4524y Analytics in practice Teaches critical concepts and skills in computer Prerequisite(s): IEOR E4004 (or IEOR E3608). 3 pts. Lect: 3. programming, statistical inference, and machine Management of complex projects and the tools Prerequisite(s): IEOR E4522 or E4501 and IEOR learning, in conjunction with hands-on analysis of that are available to assist managers with such E4523. MSOR students only. Groups of students real-world datasets such as economic data, docu- projects. Topics include project selection, project will work on real world projects in analytics, ment collections, geographical data, and social teams and organizational issues, project monitor- focusing on three aspects: identifying client networks. ing and control, project risk management, project analytical requirements; assembling, cleaning, IEOR E4501x and y Tools for analytics resource management, and managing multiple and organizing data; identifying and implement- 3 pts. Lect: 3. projects. ing analytical techniques (statistics, OR, machine MS IEOR students only. Introduction program- learning); and delivering results in a client-friendly IEOR E4511x or y Industry projects in ming in Python, tools with the programmer's format. Each project has a well-defined goal, ecosystem. Python, Data Analysis tools in Python analytics and operations research comes with sources of data preidentified, and has (NumPy, pandas, bokeh), GIT, Bash, SQL, VIM, 3 pts. Lect: 3. been structured so that it can be completed in Linux/Debia, SSH. Teams of students work on real-world projects one semester. Client-facing class with numerous in analytics. Focus on three aspects of analytics: on-site client visits; students should keep Fridays IEOR E4502x Python for analytics identifying client analytical requirements; assem- clear for this purpose. 0 pts. Lect: 1. bling, cleaning and organizing data; identifying Zero-credit course. Primer on Python for analytics and implementing analytical techniques (e.g., IEOR E4525y Machine learning for financial concepts. Required for MSBA students. statistics and/or machine learning); and delivering engineering and operations research results in a client-friendly format. Each project 3 pts. Lect: 3. IEOR E4505y Operations research in public has a defined goal and pre-identified data to Prerequisite(s): Optimization, applied probability, policy analyze in one semester. Client facing class. Class statistics, and knowledge of (or experience in) 3 pts. Lect: 3. requires 10 hours of time per week and possible computer programming. MS IEOR students only. Prerequisite(s): IEOR E3608 or IEOR E4004, IEOR client visits on Fridays. Introduction to machine learning, practical use E3106 or IEOR E4106. Aims to give the student of ML algorithms and applications to financial a broad overview of the role of Operations IEOR 4520x Applied systems engineering engineering and operations. Supervised learning: Research in public policy. The specific areas 3 pts. Lect: 3. regression, classification, resampling methods, covered include voting theory, apportionment, Prerequisite(s): B.S. in engineering or applied regularization, support vector machines (SVMs), deployment of emergency units, location of sciences; professional experience recommended; and deep learning. Unsupervised learning: dimen- hazardous facilities, health care, organ allocation, calculus, probability and statistics, linear alge- sionality reduction, matrix decomposition, and management of natural resources, energy policy, bra. Introduction to fundamental methods used clustering algorithms. and aviation security. Draws on a variety tech- in systems engineering. Rigorous process that niques such as linear and integer programming, translates customer needs into a structured set IEOR E4526x or y Analytics on the cloud statistical and probabilistic methods, decision of specific requirements; synthesizes a system 3 pts. Lect: 3. analysis, risk analysis, and analysis and control of architecture that satisfies those requirements and Prerequisite(s): IEOR E4501 and E4523. To intro- dynamic systems. allocates them in a physical system, meeting cost, duce students to programming issues around schedule, and performance objectives throughout working with clouds for data analytics. Class will IEOR E4506x Designing digital operating the product life-cycle. Sophisticated modeling of learn how to work with infrastructure of cloud models requirements optimization and dependencies, risk platforms, and discussion about distributed com- 3 pts. Lect: 3. management, probabilistic scenario scheduling, puting, focus of course is on programming. Topics IEOR students only. Understand digital busi- verification matrices, and systems-of-systems con- covered include MapReduce, parallelism, rewrit- nesses, apply scientific, engineering thinking to structs are synthesized to define the meta-work- ing of algorithms (statistical, OR, and machine digital economy. Data-driven digital strategies flow at the top of every major engineering project. learning) for the cloud, and basics of porting and operating models. Sectors: ecommerce, applications so that they run on the cloud. advertising technology, and marketing technology. IEOR 4521y Systems engineering tools and Automation of the marketing, sales, and advertis- methods IEOR E4540x and y Data mining for engineers ing functions. Algorithms, patents, and business 3 pts. Lect: 3. 3 pts. Lect: 3. models. Business side of the digital ecosytem and Prerequisite(s): B.S. in engineering or applied Prerequisite(s): Linear Algebra, Calculus, the digital economy. sciences; probability and statistics, optimization, Probability, and some basic programming. Course linear algebra, and basic economics. Applications covers major statistical learning methods for data IEOR E4507x or y Healthcare operations of SE tools and methods in various settings. mining under both supervised and unsupervised management Encompasses modern complex system develop- settings. Topics covered include linear regression 3 pts. Lect: 3. ment environments, including aerospace and and classification, model selection and regu- Prerequisite(s): for senior undergraduate defense, transportation, energy, communications, larization, tree-based methods, support vector Engineering students: IEOR E3608, E3658, and and modern software-intensive systems. machines, and unsupervised learning. Students E4307; for Engineering graduate students (M.S. learn about principles underlying each method, or Ph.D.): Probability and statistics at the level of IEOR E4523x and y Data analytics how to determine which methods are most suited IEOR E4150, and deterministic models at the level 3 pts. Lect: 3. to applied settings, concepts behind model fitting of IEOR E4004; for healthcare management stu- Corequisite: IEOR E4522 or E4501. IEOR students and parameter tuning, and how to apply methods dents: P8529 Analytical methods for health servic- only; priority to MSBA students. Survey tools avail- in practice and assess their performance. able in Python for getting, cleaning, and analyzing

ENGINEERING 2021–2022 Emphasizes roles of statistical modeling and opti- this course is devoted to a particular sector management, models and theoretical foundations 173 mization in data mining. of Operations Research and its contemporary for pricing equity options (standard European, research, practice, and approaches. If topics are American equity options, Asian options), standard IEOR E4550x Entrepreneurial business different, then course can be taken more than Black-Scholes model (with multiasset extension), creation for engineers once for credit. asset allocation, portfolio optimization, invest- 3 pts. Lect: 3. ments over longtime horizons, and pricing of Prerequisite(s): IEOR E2261. Required for under- IEOR E4599x MSBA quantitative bootcamp fixed-income derivatives (Ho-Lee, Black-Derman- graduate students majoring in OR:EMS. Introduces 0 pts. Lect: 3. Toy, Heath-Jarrow-Morton interest rate model). the basic concepts and methodologies that are Primer on quantitative and mathematical con- used by the nonengineering part of the world in cepts. Required for all incoming MSBA students. IEOR E4650x and y Business analytics creating, funding, investing in, relating to, and 3 pts. Lect 3. Recit: 1. IEOR E4601y Dynamic pricing and revenue operating entrepreneurial ventures. The first Prerequisite(s): STAT GU4001 or IEOR E4150. half of the course focuses on the underpinning management Prepares students to gather, describe, and ana- principles and skills required in recognizing, ana- 3 pts. Lect: 3. lyze data, using advanced statistical tools to sup- lyzing, evaluating, and nurturing a business idea. Prerequisite(s): STAT GU4001 and IEOR E4004. port operations, risk management, and response The second half focuses on basic legal knowledge Focus on capacity allocation, dynamic pricing and to disruptions. Analysis is done by targeting necessary in creating a business entity, defending revenue management. Perishable and/or limited economic and financial decisions in complex your business assets, and in promoting effective product and pricing implications. Applications to systems that involve multiple partners. Topics interaction with other individuals and organiza- various industries including service, airlines, hotel, include probability, statistics, hypothesis testing, tions. resource rentals, etc. experimentation, and forecasting. IEOR E4555x or y Design and agile project IEOR E4602y Quantitative risk management IEOR E4700x and y Introduction to financial management engineering lab 3 pts. Lect: 3. engineering Prerequisite(s): STAT GU4001 and IEOR E4106. 3 pts. Lect: 3. Not offered in 2021–2022. 3 pts. Lect: 3. Risk management models and tools; measure risk Intensive, team-, and project-based seminar Prerequisite(s): IEOR E4106 or E3106. Required using statistical and stochastic methods, hedging covering multidisciplinary approach to evidence- for undergraduate students majoring in OR:FE. and diversification. Examples include insurance based product design; agile project planning and Introduction to investment and financial instru- execution; rapid MVP prototyping; and launch risk, financial risk, and operational risk. Topics ments via portfolio theory and derivative securi- strategy formulation and implementation. Focuses covered include VaR, estimating rare events, ties, using basic operations research/engineer- on practical use of design thinking, design stu- extreme value analysis, time series estimation of ing methodology. Portfolio theory, arbitrage; - dio, and iterative design sprint methodologies. extremal events; axioms of risk measures, hedg Markowitz model, market equilibrium, and the ing using financial options, credit risk modeling, Systematic approaches to Lean User Research, capital asset pricing model. General models for and various insurance risk models. User Experience (UX), and User Interface (UI) asset price fluctuations in discrete and continuous design and deployment are integral components IEOR E4615y Service engineering time. Elementary introduction to Brownian motion of course curriculum. Mix of startup and enter- 3 pts. Lect: 3. Not offered in 2021–2022. and geometric Brownian motion. Option theory; prise projects, including application drive, data- Prerequisite(s): Introductory courses in probability Black-Scholes equation and call option formula. driven, or combination of both. Teams are fully and statistics such as IEOR E3658 and E4307, and Computational methods such as Monte Carlo supported in devising prototypes and actualizing introductory courses in stochastic processes such simulation. proposed solutions. as IEOR E3106 or IEOR E4106. Focus on service IEOR E4701x Stochastic models for financial systems viewed as stochastic networks, exploiting IEOR E4561x or y Launch your startup: tech engineering the theoretical framework of queueing theory. 3 pts. Lect: 3. 3 pts. Lect: 3. Includes multidisciplinary perspectives involving Tools and knowledge to develop a comprehen- Prerequisite(s): STAT GU4001. This graduate Statistics, Psychology, and Marketing. Significant sive new venture that is scalable, repeatable, course is only for M.S. Program in Financial emphasis on data analysis, exploiting data from and capital efficient. Covers customer discovery, Engineering students, offered during the summer banks, hospitals, and call centers to demonstrate market sizing, pricing, competition, distribution, session. Review of elements of probability theory, the use of decision support tools. Analytical funding, developing a minimal viable product, and Poisson processes, exponential distribution, models, flow models of service networks, Little’s other facets of creating new ventures. A company renewal theory, Wald’s equation. Introduction to law, measuring methods in face-to-face and com- blueprint and final investor pitch are deliverables. discrete-time Markov chains and applications to puterized systems, forecasting methods, stability queueing theory, inventory models, branching IEOR E4562x, y, or s Innovate using design of service systems, operational quality of service, processes. thinking economies of scale, staffing, complex service 3 pts. Lect: 3. networks, skill-based routing. IEOR E4703y Monte Carlo simulation How Design Thinking can enhance innovation 3 pts. Lect: 3. IEOR E4620x Pricing models for financial activities, market impact, value creation, and Prerequisite(s): IEOR E4701. This graduate course engineering speed. Topics include: conceptual and practical is only for M.S. Program in Financial Engineering 3 pts. Lect: 3. understanding of design thinking, creative solu- students. Multivariate , Prerequisite(s): IEOR E4700. Required for tions, develop robust practices to lead interdis- bootstrapping, Monte Carlo simulation, efficiency undergraduate students majoring in OR:FE. ciplinary teams. Course aims to strengthen indi- improvement techniques. Simulation output Characteristics of commodities or credit deriva- viduals and collaborative capabilities to identify analysis, Markov-chain Monte Carlo. Applications tives. Case study and pricing of structures and customer needs, indirect and qualitative research, to financial engineering. Introduction to financial products. Topics covered include swaps, credit create concept hypotheses, develop prototype, engineering simulation software and exposure to derivatives, single tranche CDO, hedging, convert- defined opportunities into actionable innovation modeling with real financial data. Note: Students ible arbitrage, FX, leverage leases, debt markets, possibilities, and recommendations for client who have taken IEOR E4404 Simulation may not and commodities. organizations. register for this course for credit. IEOR E4630y Asset allocation IEOR E4570-4579x and y Topics in operations IEOR E4706x Foundations of financial 3 pts. Lect: 3. research engineering Prerequisite(s): IEOR E4700. Models for pricing 1.5–3 pts. Lect: 1.5–3. Members of the faculty. 3 pts. Lect: 3. and hedging equity, fixed-income, credit-deriva- Prerequisite(s): IEOR E4150, E4004, and E4106, Prerequisite(s): IEOR E4701, E4702, and linear tive securities, standard tools for hedging and risk or instructor's permission. Each offering of algebra. This graduate course is only for M.S.

ENGINEERING 2021–2022 174 Program in Financial Engineering students, builds both on behavioral preference structures Java, mortgage-backed securities, numerical solu- offered during the summer session. Discrete-time different from mean variance theory and expected tions of partial differential equations, quantitative models of equity, bond, credit, and foreign- utility theory and on systematic biases against portfolio management, risk management, trade exchange markets. Introduction to derivative mar- rational beliefs such as Bayesian rule. and technology in financial markets. kets. Pricing and hedging of derivative securities. Complete and incomplete markets. Introduction IEOR E4714x Risk management, financial IEOR E4731x Credit risk modeling and to portfolio optimization and the capital asset system and financial crisis derivatives pricing model. 1.5 pts. Not offered in 2021–2022. 3 pts. Lect: 3. Risk-taking and risk management are at the heart Prerequisite(s): IEOR E4701 and E4707. IEOR E4707y Financial engineering: of the financial system, and of the current finan- Introduction to quantitative modeling of credit continuous-time asset pricing cial crisis. An introduction to risk management risk, with a focus on the pricing of credit deriva- 3 pts. Lect: 3. both from an individual financial firm’s and from tives. Focus on the pricing of single-name credit Prerequisite(s): IEOR E4701. This graduate course a public policy viewpoint. Overview of the con- derivatives (credit default swaps) and collateral- is only for MS program in FE students. Modeling, temporary financial system, focusing on innova- ized debt obligations (CDOs). Detail topics include analysis, and computation of derivative securities. tions of the past few decades that have changed default and credit risk, multiname default barrier Applications of stochastic calculus and stochastic how financial risk is generated and distributed models and multiname reduced form models. differential equations. Numerical techniques: among market participants, such as the growth of finite-difference, binomial method, and Monte non-bank financial intermediaries, the increased IEOR E4732x Computational methods in Carlo. prevalence of leverage and liquidity risk, and finance the development of structured credit products. 3 pts. Lect: 3. IEOR E4708y Seminar on important papers in Introduction to the basic quantitative tools used in Prerequisite(s): IEOR E4700. MS IEOR students financial engineering market, credit, and liquidity risk management. The only. Application of various computational meth- 3 pts. Lect: 3. Not offered in 2021–2022. two strands of the course are brought together to ods/techniques in quantitative/computational Prerequisite(s): IEOR E4703, E4706, probability help understand how the financial crisis arose and finance. Transform techniques: fast Fourier trans- and statistics. Selected topics of special interest is playing out, examining the mechanics of runs form for data de-noising and pricing, finite differ- to M.S. students in financial engineering. If topics and the behavior of asset prices during crises. ence methods for partial differential equations are different then this course can be taken more Attempt to understand the emergency programs (PDE), partial integro-differential equations (PIDE), than once for credit. deployed by central bankers and other policy Monte-Carlo simulation techniques in finance, and makers to address crises historically and today. calibration techniques, filtering and parameter IEOR E4709y Statistical analysis and time estimation techniques. Computational platform series IEOR E4715x, s Commodity derivatives will be C++/Java/Python/Matlab/R. 3 pts. Lect: 3. 1.5 pts. Not offered in 2021–2022. Prerequisite(s): Probability and IEOR E4702. Commodities markets have been much in the IEOR E4733x or y Algorithmic trading Corequisites: IEOR E4706, E4707. This gradu- public eye recently as volatility has increased and 3 pts. Lect: 3. Not offered in 2021–2022. ate course is only for M.S. Program in Financial they changed from markets dominated by physi- Prerequisite(s): IEOR E4700. Large and amor- Engineering students. Empirical analysis of asset cal participants to ones which have a significant phous collection of subjects ranging from the prices: heavy tails, test of the predictability of investor component. The largest banks either study of market microstructure, to the analysis of stock returns. Financial time series: ARMA, sto- already have profitable commodities franchises optimal trading strategies, to the development chastic volatility, and GARCH models. Regression or are actively building them, and money manag- of computerized, high-frequency trading strate- models: linear regression and test of CAPM, non- ers and funds are increasingly including these gies. Analysis of these subjects, the scientific and linear regression and fitting of term structures. assets in their portfolio mix. The end result is a practical issues they involve, and the extensive dramatic increase in focus on these markets from body of academic literature they have spawned. IEOR E4710x Fixed income and term structure Attempt to understand and uncover the economic modeling all aspects of the financial markets, including the quantitative end. and financial mechanisms that drive and ulti- 3 pts. Lect: 3. Not offered in 2021–2022. mately relate them. Prerequisite(s): IEOR E4706, E4707, and computer IEOR E4718x or y Beyond Black-Scholes: the programming. Interest rate models and numerical implied volatility smile IEOR E4734y Foreign exchange and related techniques for pricing and hedging interest rate 3 pts. Lect: 3. derivatives instruments contracts and fixed income securities. Prerequisite(s): IEOR E4706, knowledge of deriva- 1.5 pts. Lect: 1.5. tives valuation models. During the past 15 years Prerequisite(s): IEOR E4700. Foreign exchange IEOR E4711x Global capital markets market and its related derivative instruments—the 3 pts. Lect: 3. the behavior of market options prices have shown systematic deviations from the classic Black- latter being forward contracts, futures, options, Prerequisite(s): Refer to course syllabus. An and exotic options. What is unusual about foreign introduction to capital markets and investments Scholes model. Examines the empirical behavior of implied volatilities, in particular the volatility exchange is that although it can rightfully claim to providing an overview of financial markets and be the largest of all financial markets, it remains tools for asset valuation. Topics covered include smile that now characterizes most markets, the mathematics and intuition behind new models an area where very few have any meaningful the pricing of fixed-income securities (treasury experience. Virtually everyone has traded stocks, markets, interest rate swaps futures, etc.), dis- that can account for the smile, and their conse- quences for hedging and valuation. bonds, and mutual funds. Comparatively few indi- cussions on topics in credit, foreign exchange, viduals have ever traded foreign exchange. In part sovereign ad securitized markets—private equity IEOR E4720x and y–E4729 Topics in that is because foreign exchange is an interbank and hedge funds, etc. quantitative finance market. Ironically the foreign exchange markets IEOR E4712x Behavioral finance 1.5–3 pts. Lect: 2–2.5. Members of the faculty. may be the best place to trade derivatives and 1.5 pts. Lect: 3. Not offered in 2021–2022. Prerequisite(s): IEOR E4700; additional to invent new derivatives—given the massive Prerequisite(s): IEOR E4700. Behavioral finance is Prerequisite(s) will be announced depending on two-way flow of trading that goes through bank the application of behavioral psychology to finan- offering. Selected topics of interest in the area dealing rooms virtually 24 hours a day. And most cial decision making. Focuses on the portfolio of quantitative finance. Offerings vary each year; of that is transacted at razor-thin margins, at least aspect of behavioral finance and briefly touches some topics include energy derivatives, experi- comparatively speaking, a fact that makes the on other aspects. Compared with classical theory mental finance, foreign exchange and related foreign exchange market an ideal platform for of portfolio choice, behavioral portfolio choice derivative instruments, inflation derivatives, hedge derivatives. The emphasis is on familiarizing the features human being’s psychological biases. It fund management, modeling equity derivatives in student with the nature of the foreign exchange

ENGINEERING 2021–2022 market and those factors that make it special finance. Some topics include energy derivatives, IEOR E4998y Managing technological 175 among financial markets, enabling the student to experimental finance, foreign exchange and innovation and entrepreneurship gain a deeper understanding of the related mar- related derivative instruments, inflation deriva- 3 pts. Lect: 3. ket for derivatives on foreign exchange. tives, hedge fund management, modeling equity A required course for undergraduate students derivatives in Java, mortgage-backed securities, majoring in OR:EMS. Focus on the management IEOR E4735y Structured and hybrid products numerical solutions of partial differential equa- and consequences of technology-based innova- 3 pts. Lect: 3. tions, quantitative portfolio management, risk tion. Explores how new industries are created, Prerequisite(s): IEOR E4700. Conceptual and management, trade and technology in financial how existing industries can be transformed by practical understanding of structured and hybrid markets. Note: open to IEOR students only. new technologies, the linkages between techno- products from the standpoint of relevant risk logical development and the creation of wealth factors, design goals and characteristics, pricing, IEOR E4743s Financial correlations— and the management challenges of pursuing hedging, and risk management. Detailed analysis modeling, trading, risk management &AI strategic innovation. of the underlying cash-flows, embedded deriva- 3 pts. Lect: 3. tive instruments, and various structural features Introduction to math finance, knowledge of work- IEOR E4999s, x and y Fieldwork of these transactions, both from the investor and ing as a "Quant" in investment banking, hedge 1–1.5 pts (up to 2 pts, summer only). issuer perspectives, and analysis of the impact funds, algo shop, HFT firm, Fed, Exchange, SEC, Prerequisite(s): Obtained internship and approval of the prevailing market conditions and param- IMF, back office, mutual fund, as a trader in risk from faculty adviser. Only for IEOR graduate stu- eters on their pricing and risk characteristics. management, product development, model vali- dents who need relevant work experience as part Numerical methods for valuing and managing risk dation, compliance, reporting, academia. Open of their program of study. Final reports required. of structured/hybrid products and their embedded only to master's students in IEOR department. May not be taken for pass/fail credit or audited. derivatives and their application to equity, interest rates, commodities and currencies, inflation, and IEOR E4744s Modeling & market making in MSIE W6408y Inventory theory credit-related products. Conceptual and math- foreign exchange 3 pts. Lect: 3. Not offered in 2021–2022. ematical principles underlying these techniques, 1.5 pts. Lect: 1.5. Prerequisite(s): Probability theory, dynamic and practical issues that arise in their imple- Introduction to topics in modeling and market programming. Construction and analysis of math- mentations in the Microsoft Excel/VBA and other making in foreign exchange, such as spots mar- ematical models used in the design and analysis programming environments. Special contractual kets, forward markets, vanilla option markets, of inventory systems. Deterministic and stochastic provisions encountered in structured and hybrid exotic derivative markets, and algorithmic index demands and lead times. Optimality of (s, S) transactions, and incorporation of yield curves, markets. Open only to master's students in IEOR policies. Multiproduct and multiechelon systems. volatility smile, and other features of the underly- department. Computational methods. ing processes into pricing and implementation IEOR E4745x Applied financial risk IEOR E6602y Nonlinear and convex framework for these products. management programming IEOR E4738x Programming for FE 1: tools for 3 pts. Lect: 3. 3 pts. Lect: 3. Not offered in 2021–2022. building financial data and risk systems Prerequisite(s): courses in probability and sta- Prerequisite(s): Ph.D.-level linear programming. 3 pts. Lect: 3. Not offered in 2021–2022. tistics, instruments of the financial markets, and Convex sets and functions, convex duality and Prerequisite(s): Familiarity with object-oriented asset pricing models. Introduces risk management optimality conditions. Computational methods: programming. Object-oriented programming and principles, practical implementation and applica- steepest descent, Newton and quasi-Newton database development for building financial data tions, standard market, liquidity, and methods for unconstrained problems, active set, and risk systems; Python and Python's scientific credit risk measurement techniques, and their penalty set, interior point, augmented Lagrangian libraries; basic database theory, querying and drawbacks and limitations. Note: restricted to and sequential quadratic programming methods constructing databases; basic risk management IEOR students only. for constrained problems. Introduction to nondif- and design of risk systems. ferentiable optimization and bundle methods. IEOR E4798x Financial Engineering IEOR E4739y Programming for FE 2: practitioners seminar series IEOR E6613x Optimization, I implementing high-performance financial 0 pts. Lect: 1.5. 4.5 pts. Lect: 3. systems Degree requirement for all MSFE first-year Prerequisite(s): Linear algebra. Theory and 3 pts. Lect: 3. Not offered in 2021–2022. students. Topics in Financial Engineering. geometry of linear programming. The simplex Prerequisite(s): IEOR E4738 and instructor’s Past seminar topics include Evolving Financial method. Duality theory, sensitivity analysis, col- permission. Developing effective software imple- Intermediation, Measuring and Using Trading umn generation and decomposition. Interior point mentations in C programming language; model- Algorithms Effectively, Path-Dependent Volatility, methods. Introduction to nonlinear optimization: ing of portfolio optimization; modeling of price Artificial Intelligence and Data Science in convexity, optimality conditions, steepest descent, impact trading models; review of synchronization modern financial decision making, Risk-Based and Newton’s method, active set, and barrier of programs using the file system; review of syn- Performance Attribution, and Financial Machine methods. Learning. Meets select Monday evenings. chronization of programs using threads; review IEOR E6614y Optimization, II of synchronization of programs using sockets; IEOR E4799x MSFE quantitative and 4.5 pts. Lect: 3. implementation of high-performance simulations computational bootcamp Prerequisite(s): Linear algebra. An introduction in finance. 0 pts. Lect: 3. to combinatorial optimization, network flows IEOR E4741x Programming for Financial Primer on quantitative and mathematical con- and discrete algorithms. Shortest path problems, Engineering cepts. Required of all incoming MSFE students. maximum flow problems. Matching problems, bipartite and cardinality nonbipartite. Introduction 3 pts. Lect: 3. IEOR E4900s, x and y Master’s research or Covers C++ programming language, applications, to discrete algorithms and complexity theory: project and features for financial engineering, and quan- NP-completeness and approximation algorithms. 1–3 pts. Members of the faculty. titative finance applications. Note: restricted to Prerequisite(s): Approval by a faculty member who IEOR E6617x Machine learning and high- IEOR MS FE students only. agrees to supervise the work. Independent work dimensional data analysis in operations IEOR E4742x and y Deep learning and its involving experiments, computer programming, research applications in FE and OR analytical investigation, or engineering design. 3 pts. Lect: 3. 3 pts. Lect: 3. Discusses recent advances in fields of machine Selected topics of interest in area of quantitative learning: kernel methods, neural networks (vari-

ENGINEERING 2021–2022 176 ous generative adversarial net architectures), and continuous-time Markov chains; introduction to reinforcement learning (with applications in robot- Brownian motion. ics). Quasi Monte Carlo methods in the context of approximating RBF kernels via orthogonal trans- IEOR E6712y Stochastic models, II forms (instances of the structured technique). Will 4.5 pts. Lect: 3. discuss techniques such as TD(0), TD(λ), LSTDQ, Prerequisite(s): IEOR E6711 or equivalent. LSPI, DQN. Continuation of IEOR E6711, covering further topics in stochastic modeling in the context of IEOR E6703y Advanced financial engineering queueing, reliability, manufacturing, insurance 3 pts. Lect: 2. Not offered in 2021–2022. risk, financial engineering, and other engineer- Prerequisite(s): Probability theory and advanced ing applications. Topics from among generalized stochastic models at the SIEO GR6501 level. semi-Markov processes; processes with a non- Review of basic mathematics, including renewal discrete state space; point processes; stochastic theory and stochastic calculus. Martingale comparisons; martingales; introduction to sto- approach to Black-Scholes formula. Optimal stop- chastic calculus. ping and American options. Pricing of continuous and discrete exotic options. Term structure mod- IEOR E8100x and y Advanced topics in IEOR els and pricing of bond options. Jump diffusion 1–3 pts. Members of the faculty. models. Applications, including pricing of real and Prerequisite(s): Faculty adviser’s permission. electricity options and hedging of real options. Selected topics of current research interest. May be taken more than once for credit. IEOR E6711x Stochastic models, I 4.5 pts. Lect: 3. IEOR E9101s, x and y Research Prerequisite(s): STAT GU4001 or equivalent. 1–6 pts. Members of the faculty. Advanced treatment of stochastic modeling in the Before registering, the student must submit an context of queueing, reliability, manufacturing, outline of the proposed work for approval by insurance risk, financial engineering and other the supervisor and the chair of the Department. engineering applications. Review of elements Advanced study in a specialized field under the of probability theory; exponential distribu- supervision of a member of the department staff. tion; renewal theory; Wald’s equation; Poisson May be repeated for credit. processes. Introduction to both discrete and

ENGINEERING 2021–2022 MATERIALS SCIENCE AND ENGINEERING PROGRAM 177 Program in the Department of Applied Physics and Applied Mathematics, sharing teaching and research with the faculty of the Henry Krumb School of Mines.

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

PROGRAM CHAIR COMMITTEE ON Simon J. Billinge Chris A. Marianetti Renata Wentzcovitch Professor William E. MATERIALS SCIENCE AND Professor of Materials Associate Professor of Professor of Materials Bailey ENGINEERING/SOLID- Science Materials Science Science and Applied 1140 S. W. Mudd STATE SCIENCE AND Siu-Wai Chan Ismail C. Noyan Physics, and Earth and ENGINEERING Professor of Materials Professor of Materials Environmental Science IN CHARGE OF SOLID- William E. Bailey Science Science Yuan Yang STATE SCIENCE AND Associate Professor of Irving P. Herman Aron Pinczuk Associate Professor of ENGINEERING Materials Science Professor of Applied Professor of Applied Materials Science Professor Irving P. Katayun Barmak Physics Physics and Physics Nanfang Yu Herman Professor of Materials James S. Im Associate Professor of 905 CEPSR Science Professor of Materials Applied Physics Science

aterials Science and Physics and Applied Mathematics. demand for a systematic approach Engineering (MSE) focuses Those interested in the solid-state to the problem of relating properties on understanding, designing, science and engineering specialty enroll to structure and have necessitated a Mand producing technology-enabling in the doctoral program within Applied multidisciplinary approach. materials by analyzing the relationships Physics and Applied Mathematics or Materials science and solid-state among the synthesis and processing Electrical Engineering. The faculty listed science use techniques such as transport of materials, their properties, and above constitute but a small fraction of measurements, X-ray photoelectron their detailed structure. This includes those participating in materials research. spectroscopy, ferromagnetic resonance, a wide range of materials such as Materials science and engineering inelastic light scattering, luminescence, metals, polymers, ceramics, and uses optical, electron, and scanning and nonlinear optics to understand semiconductors. Solid-state science and probe microscopy and diffraction electrical, optical, and magnetic properties engineering focuses on understanding techniques to reveal details of structure, on a quantum mechanical level. Such and modifying the properties of solids ranging from the atomic to the methods are used to investigate exciting from the viewpoint of the fundamental macroscopic scale—details essential to new types of structures, such as epitaxial physics of the atomic and electronic understanding the relationship between metals, two-dimensional transition metal structure. materials synthesis and processing dichalcogenides, superconductors, and The undergraduate and graduate and materials properties, including semiconductor surfaces and nanocrystals. programs in materials science electronic, magnetic, mechanical, and engineering are coordinated optical, and thermal properties. These Current Research Activities through the MSE Program in the studies also give insight into problems Current research activities in the Department of Applied Physics and of the deterioration of materials in materials science and engineering Applied Mathematics. This program service, enabling designers to prolong program at Columbia focus on thin promotes the interdepartmental the useful life of their products. Materials films, electronic and magnetic materials, nature of the discipline and involves science and engineering also focuses materials at high pressures, materials for the Departments of Applied Physics on new ways to synthesize and process advanced batteries, and the structure and Applied Mathematics, Chemical materials, from bulk samples to ultrathin of materials. Specific topics under Engineering and Applied Chemistry, films to epitaxial heterostructures to investigation include interfaces, stresses, Electrical Engineering, and Earth and nanocrystals. This involves techniques and grain boundaries in thin films; Environmental Engineering in the Henry such as UHV sputtering; molecular lattice defects and electrical properties Krumb School of Mines (HKSM) with beam epitaxy; plasma etching; laser of metals and semiconductors; laser advisory input from the Departments of ablation, chemistry, and recrystallization; processing and ultrarapid solidification Chemistry and Physics. and other nonequilibrium processes. of thin films; nucleation in condensed Students interested in materials The widespread use of new materials systems; magnetic and electrical science and engineering enroll in the and the new uses of existing materials properties of semiconductors and materials science and engineering in electronics, communications, metals; synthesis of nanocrystals, program in the Department of Applied and computers have intensified the

ENGINEERING 2021–2022 178 two-dimensional materials, and background for immediate application in Required Materials Science Courses nanotechnology-related materials; engineering or for subsequent advanced Students are required to take 13 deposition, in situ characterization, study. The emphasis is on fundamentals Materials Science courses for a total electronic testing, and ultrafast relating atomic-to-microscopic-scale of 37 points. The required courses are spectroscopy of magnetoelectronic phenomena to materials properties MSAE E3010, E3012, E3013, E3156, E3157, ultrathin films and heterostructures. and processing, including design and E4100, E4102, E4200, E4201, E4202, In addition, there is research in control of industrially important materials E4206, E4215, and E4250. first-principles electronic structure processes. Core courses and electives computation. combine rigor with flexibility and provide Technical Elective Requirements The research activities in solid-state opportunities for focusing on such areas Students are required to take nine science and engineering are described as nanomaterials, materials for green technical electives (27 points) from the later in this section. energy, materials for infrastructure and list given below, which offers significant manufacturing, materials for health and flexibility in allowing students to tailor biotechnology, and materials for next LABORATORY FACILITIES their degree program to their interests. generation electronics. Facilities exist within the Materials The unifying theme of understanding Science Laboratory, which also a. All 3000-level or higher courses in and interrelating materials synthesis, serves as shared facilities for the Materials Science program of the processing, structure, and properties Materials Structural and Mechanical Department of Applied Physics and forms the basis of our program and Characterization. Facilities and research Applied Mathematics, except those is evident in the undergraduate opportunities also exist within the inter- MSAE courses that are required. curriculum and in faculty research departmental Columbia Nanotechnology b. All 3000-level or higher courses activities. These activities include work Initiative (CNI). Modern clean room facili- in Applied Physics or Applied on polycrystalline silicon for flat panel ties with optical and e-beam lithography, Math Programs of the Department displays; semiconductors for lasers thin film deposition, and surface analyti- of Applied Physics and Applied and solar cell applications, magnetic cal probes (STM, SPM, XPS) as well as Mathematics. heterostructures for information storage electron microscopes (SEM, S/TEM) are c. All 3000-level or higher courses and novel computation architectures; available. More specialized equipment in the Department of Biomedical electronic ceramics for batteries, gas exists in individual research groups in Engineering, Civil Engineering sensors and fuel cells; electrodeposition solid state engineering and materials and Engineering Mechanics pro- and corrosion of metals; and the science and engineering. The research gram, Department of Chemical analysis and design of high-temperature facilities in solid-state science and engi- Engineering, Department of reactors and first principles calculations. neering are listed in the sections for Computer Science, Department of Through involvement with our research each host department. Earth and Environmental Engineering, groups, students gain valuable hands- Department of Electrical Engineering, on experience and are often engaged Department of Industrial Engineering UNDERGRADUATE PROGRAM IN in joint projects with industrial and and Operations Research, and MATERIALS SCIENCE government laboratories. Department of Mechanical The objectives of the undergraduate Students are strongly encouraged Engineering, except for courses that program in the Materials Science to take courses in the order specified require graduate standing. Program of the Department of Applied in the course tables; implications of d. ORCA E2500 Foundations of data Physics and Applied Mathematics are as deviations should be discussed with a science follows: departmental adviser before registration. e. Courses in the Department of 1. Professional employment in industry, The first two years provide a strong Chemistry listed in the Focus including materials production, auto- grounding in the physical and chemical Areas below. motive, aerospace, microelectronics, sciences, materials fundamentals, and information storage, medical devices, mathematics. This background is used Focus Areas for technical electives energy production, storage and con- to provide a unique physical approach are listed below. Students may choose version, and in engineering consult- to the study of materials. The last two from any one area if they so choose. ing firms. years of the undergraduate program They are not required to do so. 2. Graduate studies in materials science provide substantial exposure to modern and engineering or related fields. materials science and include courses NANOMATERIALS in processing, structure and properties APPH E3100y: Intro to quantum mechanics The undergraduate curriculum of materials that extend the work of CHEM GU4071x: Inorganic chemistry MSAE E4090y: Nanotechnology is designed to provide the basis the first two years. Graduates of the APPH E4100x: Quantum physics of matter program are equipped for employment for developing, improving, and CHEM GU4168x: Materials chemistry, I understanding materials and processes in industry. Graduates are prepared for ELEN E4193x: Modern display technology for application in engineered systems. graduate study in materials science and MECE E4212x or y: Microelectromechanical It draws from physics, chemistry and engineering and related fields. systems other disciplines to provide a coherent

ENGINEERING 2021–2022 179 MATERIALS SCIENCE PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

APMA E2000 (4) and E2001 (0) either semester MATHEMATICS MATH UN1101 (3) MATH UN1102 (3) and APMA E2101 (3)

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

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

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

UNIVERSITY CC1010 (3) either semester WRITING

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

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

COMPUTER ENGI E1006 (3) any semester SCIENCE

MSAE E3010 (3) TECHNICAL Foundations of materials REQUIREMENTS 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.

BMEN E4550y: Micro- and nanostructures in CHEE E4050x: Industrial and environmental MECE E3610y: Materials and processes in cellular engineering electrochemistry manufacturing ELEN E4944x: Principles of device CHEM GU4071x: Inorganic chemistry ENME E4113x: Advanced mechanics of solids microfabrication APPH E4130: Physics of solar energy ENME E4114y: Mechanics of fracture and fatigue EAEE E4190x: Photovoltaic systems engineering ENME E4115y: Micromechanics of composite MATERIALS FOR NEXT GENERATION and sustainability materials ELECTRONICS EAIA E4200y: Alternative energy resources CIEN E4226y: Advanced design of steel APPH E3100y: Intro to quantum mechanics MECE E4210x: Energy infrastructure planning structures ELEN E3106x: Solid state devices-materials MECE E4211y: Energy: sources and conversion CHEE E4530x: Corrosion of metals APPH E4100x: Quantum physics of matter EAEE E4550x: Catalysis for emissions control ELEN E4301y: Intro to semiconductor devices MATERIALS FOR HEALTH AND ELEN E4944x: Principles of device MATERIALS FOR 21ST CENTURY BIOTECHNOLOGY microfabrication INFRASTRUCTURE AND MANUFACTURING CHEM UN2443x-UN2444y: Organic chemistry CIEE E3255y: Environmental control and pollution APPH E3400y: Physics of the human body MATERIALS FOR GREEN ENERGY reduction systems CHEM GU4168x: Materials chemistry, I EAEE E3103x: Energy, minerals, materials CIEE E3260y: Engineering for developing BMEN E4210y: Thermodynamics of biological systems communities systems EAEE E4004x: Physical processing and recovery ENME E3114y: Experimental mechanics of BMEN E4301x: Structure, mechanics, and of solids materials adaptation of bone

ENGINEERING 2021–2022 180 MATERIALS SCIENCE: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

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

TECHNICAL Students must complete 27 units of Technical Electives. ELECTIVES

NONTECHNICAL Students must complete the 27-point requirement.2 ELECTIVES

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 material covered in the junior and senior years. 2 See page 9 or seas.columbia.edu for details (administered by the advising dean).

MATERIALS SCIENCE: THIRD AND FOURTH YEARS (TRANSFER STUDENTS)

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

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

TECHNICAL Students must complete 27 or 24 units of Technical Electives.1 ELECTIVES

NONTECHNICAL Students must complete the 27-point requirement.2 ELECTIVES

1 Students transferring from another SEAS department into the Materials Science program in the junior year must complete the 27 units of technical elective requirement; Combined Plan 3/2 transfer students must complete 24 units of technical electives. 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 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 seas.columbia.edu.

ENGINEERING 2021–2022 BMEN E4310x or y: Solid biomechanics leadership course, ENGI E4000, as MSAE E4301: Materials science laboratory 181 BMEN E4450y: Dental and craniofacial tissue a graduation requirement. Doctoral MSAE E4990: Special topics in materials science engineering students will be enrolled in ENGI E6001– and engineering BMEN E4501x: Tissue engineering, I: biomaterials 6004 and should consult their program MSAE E6085: Computing the electronic structure and scaffold design of complex materials for specific PDL requirements. CHEE E4530y: Corrosion of metals MSAE E6091: Magnetism and magnetic materials BMEN E4550x: Micro- and nanostructures in MSAE E6225: Techniques in X-ray and neutron cellular engineering Master of Science Degree diffraction Candidates for the Master of Science MSAE E6229: Energy and particle beam * Note that BIOL UN2005x: Introductory biology, degree in Materials Science and processing of materials I and Introductory biology, II Kinetics of phase transformations BIOL UN2006y: Engineering will follow a program of MSAE E6230:  are prerequisites for a number of courses in this MSAE E6251: Thin films and layers study formulated in consultation with track. MSAE E6273: Materials science reports and approved by a faculty adviser. MSAE E8235: Selected topics in materials MATERIALS CHEMISTRY/SOFT MATERIALS Thirty points of credit are required science CHEM UN2443x-UN2444y: Organic chemistry at a minimum. Students interested MSAE E4000-, 6000- or 8000-level courses not CHEN E4201: Applications of electrochemistry in a specific focus in metallurgy or listed here, except MSAE E6100. CHEE E4252: Intro surface & colloid chemistry other areas in materials science and APCH E4080: Soft condensed matter CHEN E4620: Intro polymers / soft materials engineering should consult their faculty APMA E4101: Dynamical systems CHEN E4640: Polymer surfaces and interfaces APMA E4200: Partial differential equations adviser for relevant course listings. APMA E4204: Functions of a complex variable The following six courses (18 points) Nontechnical Elective Requirements APMA E4300: Computational mathematics: intro are required for the degree. Students to numerical methods All materials science students must take a minimum of two of the six APPH E4100: Quantum physics of matter are also expected to register for required courses, one of which must be APPH E4110: Modern optics nontechnical electives, both those MSAE E4100 Crystallography, in their APPH E4112: Laser physics specifically required by the School of first semester. APPH E4200: Physics of fluids Engineering and Applied Science and APPH E4300: Applied electrodynamics those needed to meet the 27-point APPH E4990: Special topics in applied physics 18 points: APPH E6081: Solid state physics total of nontechnical electives required MSAE E4100: Crystallography BMEN E4300: Solid biomechanics for graduation. MSAE E4200: Theory of crystalline materials: BMEN E4580: Foundations of nanobioscience phonons and nanobiotechnology Transfer Students MSAE E4201: Materials thermodynamics and CEEM E4113: Advanced mechanics of solids phase diagrams Combined Plan 3-2/Transfer CEEM E4114: Mechanics of fracture and fatigue MSAE E4202: Kinetics of transformations in students and students transferring CIEN E4021: Elastic and plastic analysis of materials structures from another SEAS department into MSAE E4206: Electronic and magnetic properties CHEN E4201: Engineering applications of the Materials Science Program in of solids electrochemistry the junior year (upon approval of the MSAE E4215: Mechanical behavior of structural CHEN E4630: Topics in soft materials Materials Science Undergraduate materials CHEN E4880: Atomistic simulations for science Transfer Committee) will take the If a candidate has already taken and engineering EAEE E4252: Introduction to surface and colloidal following courses to satisfy the degree one or more of these courses at requirements: The required courses chemistry Columbia University, substitutions from ELEN E4193: Modern display science and are MSAE E3010, E3012, E3013, E3156, the Electives list must be approved by technology E3157, E4100, E4102, E4200, E4201, consultation with their faculty adviser ELEN E4411: Fundamentals of photonics E4202, E4206, E4215, and E4250. and approval of the program committee. ELEN E4944: Principles of device microfabrication Combined Plan 3-2/Transfer The remaining 12 points will be ELEN E6331/6333: Semiconductor device physics Students will be guided by their chosen from elective courses. IEOR E4150: Introduction to probability and academic advisers to avoid duplication statistics of courses previously taken. The MECE E4212: Microelectromechanical systems Electives: MECE E4213: BioMEMS: design, fabrication, and course tables describe the four- analysis MSAE E4090: Nanotechnology semester program schedule of courses MECE E4214: MEMS production and packaging MSAE E4101: Structural analysis of materials leading to the bachelor’s degree in MECE E4610: Advanced manufacturing processes MSAE E4102: Synthesis and processing of the Materials Science Program of the MECE E6137: Nanoscale actuation and sensing materials Department of Applied Physics and STAT GU4001: Introduction to probability and MSAE E4105: Ceramic nanomaterials statistics Applied Mathematics. MSAE E4132: Fundamentals of polymers and ceramics All degree requirements must be MSAE E4203: Theory of crystalline materials: completed within five years. A candidate GRADUATE PROGRAMS IN electrons is required to maintain at least a 2.5 MATERIALS SCIENCE AND MSAE E4250: Ceramics and composites GPA. Applicants for admission are ENGINEERING MSAE E4260: Electrochemical materials required to take the Graduate Record M.S. students must complete the and devices: from structure to Examinations. professional development and performance

ENGINEERING 2021–2022 182 Professional Degree; Metallurgical Candidates in the program must Thin film synthesis and processing Engineer take the oral examination in the in this program include evaporation, The program is designed for engineers spring semester of their second year. sputtering, electrodeposition, and who wish to do advanced work beyond Candidates must submit a written plasma and laser processing. For the level of the M.S. degree but who proposal and defend it orally before a analyzing materials structures and do not desire to emphasize research. Thesis Proposal Defense Committee properties, faculty and students employ Admissions requirements include the consisting of three members of the electron microscopy, scanning probe undergraduate engineering degree, mini- faculty, including the adviser in the microscopy, photoluminescence, mum 3.0 GPA, and GRE. spring semester of their third year. magnetotransport measurements, and Candidates must complete at least 30 Doctoral candidates must submit a thesis X-ray diffraction techniques. Faculty credits of graduate work beyond the M.S., to be defended before a Dissertation members have research collaborations or 60 points of graduate work beyond Defense Committee consisting of with IBM, and other New York area the B.S. No thesis is required. All degree five faculty members, including two research and manufacturing centers, requirements must be completed within professors from outside the doctoral as well as major international research five years of the beginning of the first program. Requirements for the Eng. centers. Scientists and engineers from course credited toward the degree. Sc.D. (administered by the School of these institutions also serve as adjunct Coursework includes five core Engineering and Applied Science) and faculty members at Columbia. The required courses and five elective courses the Ph.D. (administered by the Graduate National Synchrotron Light Source at from a pre-approved list of choices. School of Arts and Sciences) are listed Brookhaven National Laboratory is used Core courses: elsewhere in this bulletin. for high-resolution X-ray diffraction and absorption measurements. • EAEE E4001 Industrial ecology of earth Areas of Research Entering students typically have resources Materials science and engineering is undergraduate degrees in materials • EAEE E4009 Geographic information concerned with synthesis, processing, science, metallurgy, physics, chemistry, systems (GIS) for resource, environmen- structure, and properties of metals, or other science and engineering tal and infrastructure management ceramics, and other materials, with disciplines. First-year graduate courses • EAEE E4160 Solid and hazardous waste emphasis on understanding and provide a common base of knowledge materials exploiting relationships among and technical skills for more advanced • EAEE E4900 Applied transport/chemical structure, properties, and applications courses and for research. In addition rate phenomena requirements. Our graduate research to coursework, students usually • EAEE E6255-6 Methods and applica- programs encompass research areas begin an association with a research tions of analytical decision making in as diverse as polycrystalline silicon, group, individual laboratory work, and mineral industries electronic ceramics grain boundaries participation in graduate seminars and interfaces, microstructure and during their first year. Elective courses must be five courses stresses in microelectronics thin films, at the 4000 or higher level from within oxide thin films for novel sensors and GRADUATE SPECIALTY IN the Earth and Environmental Engineering fuel cells, optical diagnostics of thin-film SOLID-STATE SCIENCE AND Department, the Chemical Engineering processing, ceramic nanocomposites, ENGINEERING Department, Materials Science Program, electrodeposition and corrosion Solid-state science and engineering or others as approved by the adviser. processes, structure, properties, and is an interdepartmental graduate These include but are not limited to: transmission electron microscopy and specialty that provides coverage of an EAEE E4150, CHEE E4252, CIEE E4252, crystal orientation mapping, magnetic important area of modern technology EAEE E4256, EAEE E4257, EAEE E6208. thin films for spintronic applications, that no single department can provide. It Although it is not required, interested stu- chemical synthesis of nanoscale encompasses the study of the full range dents may choose to complete up to six materials, nanocrystals, two-dimensional of properties of solid materials, with credits in MSAE E9259-60. materials, nanostructure analysis special emphasis on electrical, magnetic, using X-ray and neutron diffraction optical, and thermal properties. The techniques, and electronic structure Doctoral Program science of solids is concerned with calculation of materials using density At the end of the first year of graduate understanding these properties in functional and dynamical mean- study in the doctoral program, candidates terms of the atomic and electronic field theories. Application targets for are required to take a comprehensive structure of the materials in question. polycrystalline silicon are thin film written qualifying examination, which Insulators (dielectrics), semiconductors, transistors for active matrix displays is designed to test the ability of the ceramics, and metallic materials are all and silicon-on-insulator structures for candidate to apply coursework in studied from this viewpoint. Quantum ULSI devices. Novel applications are problem solving and creative thinking. and statistical mechanics are key being developed for oxide thin films, The standard is first-year graduate level. background subjects. The engineering including uncooled IR focal plane arrays There are two four-hour examinations aspects deal with the design of materials and integrated fuel cells for portable over a two-day period. to achieve desired properties and the equipment.

ENGINEERING 2021–2022 assembling of materials into systems to are required to take a comprehensive MSAE E3013y Laboratory in materials 183 produce devices of interest to modern written examination concentrating on science, II technology, e.g., for computers and for solid-state science and engineering. 3 pts. Lect: 3. Professor Noyan. Prerequisite(s): MSAE E3012. Metallographic energy production and utilization. The following are regarded as core sample preparation, optical microscopy, quantita- courses of the specialty: tive metallography, hardness and tensile testing, Areas of Research plastic deformation, annealing, phase diagrams, APPH E4100: Quantum physics of matter The graduate specialty in solid-state brittle fracture of glass, temperature and strain- APPH E4110: Modern optics rate dependent deformation of polymers; written science and engineering includes APPH E4112: Laser physics and oral reports. This is the second of a two- research programs in metamaterials APPH E6081: Solid state physics semester sequence materials laboratory course. and infrared optoelectronic devices CHEM GU4230: Statistical thermodynamics (Professor Yu, Applied Physics and MSAE E3111x Thermodynamics, kinetic theory or and statistical mechanics Applied Mathematics); and inelastic CHAP E4120: Statistical mechanics 3 pts. Lect: 3. Professor Herman. light scattering in low-dimensional ELEN E4301: Intro to semiconductor devices An introduction to the basic thermodynamics electron gases within semiconductors ELEN E4944: Principles of device microfabrication of systems, including concepts of equilibrium, (Professor Pinczuk, Applied Physics ELEN E6331-E6332: Principles of semiconductor entropy, thermodynamic functions, and phase and Applied Mathematics/Physics); physics changes. Basic kinetic theory and statistical large-area electronics and thin-film ELEN E6403: Classical electromagnetic theory mechanics, including diffusion processes, concept of phase space, classical and quantum statistics, transistors (Professor Im, Henry Krumb or and applications thereof. School of Mines/Applied Physics PHYS GR6092: Electromagnetic theory, I and Applied Mathematics); structural MSAE E4100: Crystallography MSAE E3141y Processing of metals and Electronic and magnetic properties analysis and high Tc superconductors MSAE E4206:  semiconductors of solids 3 pts. Lect: 3. Not offered in 2021–2022. (Professor Chan, Henry Krumb School PHYS GR6018: Physics of the solid state Prerequisite(s): MSAE E3011 or equivalent. of Mines/Applied Physics and Applied PHYS GR6037: Quantum mechanics Synthesis and production of metals and semi- Mathematics); X-ray microdiffraction conductors with engineered microstructures for and stresses (Professor Noyan, Henry desired properties. Includes high-temperature, Krumb School of Mines/Applied Physics COURSES IN MATERIALS aqueous, and electrochemical processing; thermal and mechanical processing of metals and alloys; and Applied Mathematics); electronic SCIENCE AND ENGINEERING For related courses, see also Applied casting and solidification; diffusion, microstruc- and magnetic metal thin films (Professor tural evolution, and phase transformations; modi- Barmak, Applied Physics and Applied Physics and Applied Mathematics, fication and processing of surfaces and interfaces; Mathematics); magnetic properties of Chemical Engineering, Earth and deposition and removal of thin films. Processing thin films (Professor Bailey, Applied Environmental Engineering, Electrical of Si and other materials for elemental and com- Physics and Applied Mathematics); the Engineering, and Mechanical pound semiconductor-based electronic, magnetic, and optical devices. structure of nanomaterials (Professor Engineering. Billinge, Applied Physics and Applied MSAE E3010x Foundations of materials MSAE E3142y Processing of ceramics and Mathematics); and electronic structure science polymers calculations of materials (Professors 3 pts. Lect: 3. Professor Billinge. 3 pts. Lect: 3. Not offered in 2021–2022. Prerequisite(s): CHEM UN1404 and PHYS UN1011. Prerequisite(s): MSAE E3011 or equivalent. Marianetti and Wentzcovitch, Applied Established and novel methods involved in the Physics and Applied Mathematics). Introduction to quantum mechanics: atoms, elec- tron shells, bands, bonding; introduction to group processing of polymers and ceramics. The fun- theory: crystal structures, symmetry, crystallog- damental aspects of the structure and properties Program of Study raphy; introduction to materials classes: metals, of polymers and ceramic materials; strategy in ceramics, polymers, liquid crystals, nanomaterials; the preparatory, synthesis, and processing meth- The applicant for the graduate specialty ods for obtaining them. Topics include polymer must be admitted to one of the introduction to polycrystals and disordered mate- rials; noncrystalline and amorphous structures; synthesis, elastomers, thermoplastics, thermo- participating programs: applied physics grain boundary structures, diffusion; phase trans- set materials, design and molding processes. and applied mathematics, or electrical formations; phase diagrams, time-temperature- Ceramics: inorganic glasses and composites, engineering. A strong undergraduate transformation diagrams; properties of single materials production and principle inorganic chemistry. Processing methodology, conditioning, background in physics or chemistry and crystals: optical properties, electrical properties, magnetic properties, thermal properties, mechani- drying, forming, sintering, and microstructure in mathematics is important. development. Relevant aspects of transport The doctoral student must meet the cal properties, and failure of polycrystalline and amorphous materials. phenomena, colloid and sol-gel science, contem- formal requirements for the Eng. Sc.D. or porary issues in modern polymer and ceramic Ph.D. degree set by the department in MSAE E3012x Laboratory in materials processing. which he or she is registered. However, science, I 3 pts. Lect: 3. Professor Noyan. MSAE E3156x-E3157y Design project the bulk of the program for the specialty Pre/Corequisite: MSAE E3010. Measurement of 2 pts (each semester). Lect.: 3. will be arranged in consultation with electrical, thermal, and magnetic properties of Professor Billinge. a member of the interdepartmental single crystals. Single crystal diffraction analysis, Prerequisite(s): Senior standing. Written permis- Committee on Materials Science and polarized light microscopy, and infrared micros- sion from instructor and approval from adviser. copy in Si single crystals, written and oral reports. E3156: A design problem in materials science or Engineering/ Solid-State Science and metallurgical engineering selected jointly by the Engineering. At the end of the first year student and a professor in the department. The of graduate study, doctoral candidates project requires research by the student, directed

ENGINEERING 2021–2022 184 reading, and regular conferences with the profes- MSAE E4132y Fundamentals of polymers and MSAE E4203y Theory of crystalline materials: sor in charge. E3157: Completion of the research, ceramics electrons directed reading, and conferences, culminating in 3 pts. Lect: 3. Not offered in 2021–2022. 3 pts. Lect: 3. Professor Marianetti. a written report and an oral presentation to the Prerequisite(s): MSAE E3010 or instructor’s per- Prerequisite(s): MSAE E4200 or instructor's department. mission. The science and engineering of polymer, permission. Phenomenological theoretical under- ceramic and composite inorganic materials. standing of electrons in crystalline materials. Both MSAE E3900x and y Undergraduate research Fundamental aspects of structure, processing and translational and point symmetry employed to in materials science properties. Polymers: classification, synthesis, block diagonalize the Schrödinger equation and 0–4 pts. Members of the faculty. elastomers, thermoplastics, thermosets; ceram- compute observables related to electrons. Topics Prerequisite(s): Written permission from instructor ics: Crystal structure, morphology, classification, include nearly free electrons, tight-binding, elec- and approval from adviser. May be repeated for oxides, nitrides, carbides, silicates. Electrical, tron-electron interactions, transport, magnetism, credit, but no more than 6 points may be counted mechanical, thermal and optical properties. optical properties, topological insulators, spin- toward the satisfaction of the B.S. degree require- Common and advanced technological applica- orbit coupling, and superconductivity. Illustrated ments. Candidates for the B.S. degree may con- tions, electrical/optical devices, catalytic and using both minimal model Hamiltonians in addi- duct an investigation in materials science or carry environmental applications. tion to accurate Hamiltonians for real materials. out a special project under the supervision of the staff. Credit is contingent upon the submission of MSAE E4200x Theory of crystalline materials: MSAE E4206x Electronic and magnetic an acceptable thesis or final report. phonons properties of solids 3 pts. Lect: 3. Professor Marianetti. 3 pts. Lect: 3. Professor Bailey. MSAE E4090y Nanotechnology Pre/Corequisite: MSAE E4100 or instructor’s Prerequisite(s): PHYS UN1401-3 or equivalent. A 3 pts. Lect: 3. Professor Yang. permission. Phenomenological theoretical under- survey course on the electronic and magnetic Prerequisite(s): APPH E3100 and MSAE E3010 or standing of vibrational behavior of crystalline properties of materials, oriented toward materials their equivalents with instructor’s permission. The materials; introducing all key concepts at classical for solid state devices. Dielectric and magnetic science and engineering of creating materials, level before quantizing the Hamiltonian. Basic properties, ferroelectrics and ferromagnets. functional structures and devices on the nano- notions of Group Theory introduced and exploited: Conductivity and superconductivity. Electronic meter scale. Carbon nanotubes, nanocrystals, irreducible representations, Great Orthogonality band theory of solids: classification of metals, quantum dots, size dependent properties, self- Theorem, character tables, degeneration, product insulators, and semiconductors. Materials in assembly, nanostructured materials. Devices and groups, selection rules, etc. Both translational devices: examples from semiconductor lasers, cel- applications, nanofabrication. Molecular engineer- and point symmetry employed to block diagonal- lular telephones, integrated circuits, and magnetic ing, bionanotechnology. Imaging and manipulat- ize the Hamiltonian and compute observables storage devices. Topics from physics are intro- ing at the atomic scale. Nanotechnology in society related to vibrations/phonons. Topics include band duced as necessary. and industry. Offered in alternate years. structures, density of states, band gap formation, MSAE E4215y Mechanical behavior of MSAE E4100x Crystallography nonlinear (anharmonic) phenomena, elasticity, structural materials 3 pts. Lect: 3. Professor Barmak. thermal conductivity, heat capacity, optical prop- 3 pts. Lect: 3. Professor Bailey. Prerequisite(s): CHEM UN1403, PHYS UN1403, erties, ferroelectricty. Illustrated using both mini- Prerequisite(s): MSAE E3010. Recommended APMA E2101, or equivalent. A first course on mal model Hamiltonians in addition to accurate preparation: A course in mechanics of materials. crystallography. Crystal symmetry, Bravais lat- Hamiltonians for real materials (e.g., Graphene). Review of states of stress and strain and their tices, point groups, space groups. Diffraction and MSAE E4201y Materials thermodynamics and relations in elastic, plastic, and viscous materi- diffracted intensities. Exposition of typical crystal phase diagrams als. Dislocation and elastic-plastic concepts structures in engineering materials, including 3 pts. Lect: 3. Professor Barmak. introduced to explain work hardening, various metals, ceramics, and semiconductors. Crystalline Prerequisite(s): MSAE E3010 or equivalent or materials-strengthening mechanisms, ductility, anisotropy. instructor’s permission. Review of laws of thermo- materials devices, material reliability and fracture, MSAE E4102x Synthesis and processing dynamics, thermodynamic variables and relations, and toughness. Macroscopic and microstructural of materials free energies and equilibrium in thermodynamic aspects of brittle and ductile fracture mechanics, 3 pts. Lect: 3. Professor Im. systems, statistical thermodynamics. Unary, creep and fatigue phenomena. Case studies used Prerequisite(s): MSAE E3010 or equivalent or binary, and ternary phase diagrams, compounds throughout, including flow and fracture of struc- instructor’s permission. A course on synthesis and and of surfaces and interfaces, effect of particle tural alloys, polymers, hybrid materials, composite processing of engineering materials. Established size, intermediate phases, solid solutions and materials, ceramics, and electronic prevention and novel methods to produce all types of materi- Hume-Rothery rules, relationship between phase emphasized. diagrams and metastability, defects in crystals. als (including metals, semiconductors, ceramics, MSAE E4250y Ceramics and composites polymers, and composites). Fundamental and Thermodynamics of surfaces and interfaces, effect 3 pts. Lect: 3. Professor Chan. applied topics relevant to optimizing the micro- of particle size on phase equilibria, adsorption Pre/Corequisites: MSAE E3010 and E3013, or structure of the materials with desired properties. isotherms, grain boundaries, surface energy, instructor’s permission. Will cover some of the Synthesis and processing of bulk, thin-film, and electrochemistry. fundamental processes of atomic diffusion, sinter- nano materials for various mechanical and elec- MSAE E4202y Kinetics of transformation in ing and microstructural evolution, defect chem- tronic applications. materials istry, ionic transport, and electrical properties of MSAE E4105x Ceramic nanomaterials 3 pts. Lect: 3. Professor Im. ceramic materials. Following this, we will examine 3 pts. Lect: 3. Professor Chan. Pre/Corequisite: MSAE E4201. Review of thermo- applications of ceramic materials, specifically, Prerequisite(s): CHEM UN1404 or equivalent dynamics, irreversible thermodynamics, diffusion ceramic thick and thin film materials in the areas undergraduate thermodynamics. Ceramic in crystals and noncrystalline materials, phase of sensors and energy conversion/storage devices nanomaterials and nanostructures: synthesis, transformations via nucleation and growth, overall such as fuel cells, and batteries. The coursework characterization, size-dependent properties, and transformation analysis and time-temperature- level assumes that the student has already taken applications; surface energy, surface tension transformation (TTT) diagrams, precipitation, grain basic courses in the thermodynamics of materials, and surface stress; effect of ligands, surfactants, growth, solidification, spinodal and order-disorder diffusion in materials, and crystal structures of adsorbents, isoelectric point, and surface charges; transformations, martensitic transformation. materials. supersaturation and homogenous nucleation for monodispersity.

ENGINEERING 2021–2022 MSAE E4260y Electrochemical materials and MSAE E6100y Transmission electron MSAE E8235x and y Selected topics in 185 devices: from structure to performance microscopy materials science 3 pts. Lect: 3. Professor Yang. 3 pts. Lect: 3. Not offered in 2021–2022. 3 pts. Lect: 3. Not offered in 2021–2022. Prerequisite(s): CHEM UN1403, MSAE E3010, Prerequisite(s): permission of the instructor. May be repeated for credit. Selected topics in equivalents, or instructor's permission. Overview Theory and practice of transmission electron materials science. Topics and instructors change of electrochemical processes and applications microscopy (TEM): principles of electron scat- from year to year. For students in engineering, from perspectives of materials and devices. tering, diffraction, and microscopy; analytical physical sciences, biological sciences, and related Thermodynamics and principles of electrochem- techniques used to determine local chemistry; fields. istry, methods to characterize electrochemical introduction to sample preparation; laboratory processes, application of electrochemical materi- and in-class remote access demonstrations, sev- MSAE E9000x and y Materials science and als and devices, including batteries, supercapaci- eral hours of hands-on laboratory operation of the engineering colloquium tors, fuel cells, electrochemical sensor, focus on microscope; the use of simulation and analysis 0 pt. Professor Yang. link between material structure, composition, and software; guest lectures on cryomicroscopy for Speakers from universities, national laboratories, properties with electrochemical performance. life sciences and high resolution transmission and industry are invited to speak on the recent electron microscopy for physical sciences; and, impact of materials science and engineering MSAE E4301x Materials science laboratory time permitting, a visit to the electron microscopy innovations. 3 pts. Professor Yang. facility in the Center for Functional Nanomaterials Prerequisite(s): Introductory materials course or MSAE E9259x-E9260y Research topics (CFN) at the Brookhaven National Laboratory in materials science and metallurgical equivalent and instructor’s permission. General (BNL). experimental techniques in materials science, engineering including X-ray diffraction, scanning electron MSAE E6229y Energy and particle beam 1 pt. Lect: 1. Members of the faculty. microscopies, atomic force microscopy, materials processing of materials Discussion of a group of technical papers related synthesis and thermodynamics, characterization 3 pts. Lect: 3. Not offered in 2021–2022. to a topic of current research interest. of material properties (mechanical, electrochemi- Prerequisite(s): MSAE E4202 or instructor’s MSAE E9301x-S9301 Doctoral research cal, magnetic, electronic). Additional experiments permission. Laser-, electron-, and ion-beam 0–15 pts. Members of the faculty. at discretion of instructor. modification of materials to achieve unique micro- Prerequisite(s): Qualifying examination for doctor- structures and metastable phases for electronic ate. Required of doctoral candidates. MSAE E4990x and y Special topics in and structural applications. Fundamentals of materials science and engineering energy deposition and heat flow during laser- and MSAE E9309x and y–S9309 Proposal of 1–3 pts. Members of the faculty. electron-beam irradiation. Atomic displacement Research for the Doctorate Prerequisite(s): Instructor’s permission. May be processes in ion-irradiated materials. Beam- 0–3 pts. Members of the faculty. repeated for credit. Topics and instructors change induced microstructural evolution, crystallization, A written report prepared by the prospective doc- from year to year. For advanced undergraduate surface alloying, rapid solidification, and metasta- toral candidate defining the proposed research students and graduate students in engineering, ble phase formation. Review of current industrial for the dissertation, and oral defense of the physical sciences, and other fields. applications. proposal. MSAE E4999x or y–S4999 Supervised MSAE E6230y Kinetics of phase MSAE E9800x and y–S9800 Doctoral internship transformations research instruction 1–3 pts. Members of the faculty. 3 pts. Lect: 3. Not offered in 2021–2022. 3, 6, 9, or 12 pts. Members of the faculty. Prerequisite(s): Internship and approval from Prerequisite(s): MSAE E4202 or instructor’s A candidate for the Eng.Sc.D. degree must regis- adviser must be obtained in advance. Only for permission. Principles of nonequilibrium ther- ter for 12 points of doctoral research instruction. master’s students in the Department of Applied modynamics; stochastic equations; nucleation, Registration in MSAE E9800 may not be used to Physics and Applied Mathematics who may need growth, and coarsening reactions in solids; satisfy the minimum residence requirement for relevant work experience as part of their program spinodal decomposition; eutectic and eutectoid the degree. of study. Final report required. May not be taken transformations. for pass/fail or audited. MSAE E9900x and y–S9900 Doctoral MSAE E6251y Thin films and layers dissertation MSAE E6085y Computing the electronic 3 pts. Lect: 3. Professor Chan. 0 pts. Members of the faculty. structure of complex materials Vacuum basics, deposition methods, nucleation A candidate for the doctorate may be required 3 pts. Lect: 3. Professor Wentzcovitch. and growth, epitaxy, critical thickness, defects to register for this course every term after the Prerequisite(s): APPH E3100 or equivalent. properties, effect of deposition procedure, coursework has been completed and until the dis- Basics of density functional theory (DFT) and its mechanical properties, adhesion, interconnects, sertation has been accepted. application to complex materials. Computation of and electromigration. electronics and mechanical properties of materi- als. Group theory, numerical methods, basis sets, MSAE E6273x and y–S6273 Materials science computing, and running open source DFT codes. reports Problem sets and a small project. 0 to 6 pts. Members of the faculty. Prerequisite(s): Written permission from instructor MSAE E6091y Magnetism and magnetic and approval from adviser. Formal written reports materials and conferences with the appropriate member 3 pts. Lect. 3. Not offered in 2021–2022. of the faculty on a subject of special interest to Prerequisite(s): MSAE E4206, APPH E6081, or the student but not covered in the other course equivalent. Types of magnetism. Band theory of offerings. ferromagnetism. Magnetic metals, insulators, and semiconductors. Magnetic nanostructures: ultra- thin films, superlattices, and particles. Surface magnetism and spectroscopies. High speed mag- netization dynamics. Spin electronics.

ENGINEERING 2021–2022 186 MECHANICAL ENGINEERING 220 S. W. Mudd, MC 4703 212-854-0661 me.columbia.edu

CHAIR PROFESSORS Matei Ciocarlie LECTURERS IN Kerwin Low James Hone Sunil Agrawal Kristin Myers DISCIPLINE Mohammad H. N. 248 S. W. Mudd Gerard A. Ateshian Arvind Narayanaswamy Sinisa Vukelic Naraghi Mary C. Boyce P. James Schuck Yevgeniy Yesilevskiy Alexander Staroselsky DIRECTOR OF FINANCE James Hone Graham Walker AND ADMINISTRATION Jeffrey W. Kysar ASSISTANT ADJUNCT FACULTY Enrico Zordan Milko Milkov Qiao Lin PROFESSORS Homayoon Beigi 220 S. W. Mudd Hod Lipson Karen Kasza Matthew Bilson MANAGER OF Richard W. Longman Vijay Vedula Sean Bradshaw INSTRUCTIONAL Vijay Modi Joshua Browne LABORATORIES Y. Lawrence Yao PROFESSORS OF Nicholas Chbat Robert G. Stark ASSOCIATE PROFESSIONAL PRACTICE Dustin Demetriou PROFESSORS Michael J. Massimino J. P. Hilton Michael P. Burke Harry West Peter LeVoci

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

ENGINEERING 2021–2022 is concerned with the application of valve device that can 'grow with the and optimization. 187 continuum theories of mixtures to child' would revolutionize current Robotic Systems Engineering (ROSE) problems of electromechanical behavior treatment for neonates born with valve Lab develops technology capable of soft biological tissues, contact disease. In close collaboration with Dr. of solving difficult design problems, mechanics, lubrication of diarthrodial David Kalfa, who is a pediatric heart such as cable-actuated systems, joints, and cartilage tissue engineering. surgeon at Columbia University Medical under-actuated systems, and others. (Ateshian) Center, and Dr. Haim Waisman from Robotics and Rehabilitation (ROAR) The Kysar group studies the the Civil Engineering department, the Lab focuses on developing new and mechanics and mechanical properties Kysar and Vedula groups are involved innovative technologies to improve the of small-scale structures and materials. in a multidisciplinary NIH-funded quality of care and patient outcomes. Examples of material systems include project to develop an expendable The lab designs novel exoskeletons two-dimensional materials such as biostable polymeric valved conduit. The for upper and lower limbs training of graphene, nanoporous metal thin films, device would be implanted surgically stroke patients, and mobile platforms metallic and polymeric composites to reconstruct the right ventricular to improve socialization in physically containing nanoscale strengthening outflow tract in neonates and then impaired infants (Agrawal). agents, single crystal metals, and expanded by successive transcatheter The Robotic Manipulation and the ear's round Window Membrane, procedures to reach the adult size. This Mobility (ROAM) Lab focuses on versatile among several others. The work project involves material design and manipulation and mobility in robotics, is experimental, theoretical, and characterization of the growth potential aiming for robotic applications pervasive computational in nature. The ultimate of a viscoplastic polymer, numerically in everyday life. Research areas include goal is to understand and predict model the fluid-structure interaction manipulation and grasping, interactive the mechanical behavior based on of the valved conduit, optimization or Human-in-the-Loop robotics, dynamic fundamental physics and chemistry for valve competence at every simulators and virtual environments, through the development of multiple stage of expansion, and assess the machine perception and modeling, length scale models. biocompatibility and durability in animal and many more. We are interested in At the Kasza Living Materials Lab models. (Kysar, Vedula) application domains such as versatile we are interested in how cells self- automation in manufacturing and Control, Robotics, Design, and organize to build tissues and organs with logistics, assistive and rehabilitation Manufacturing. Control research mechanical properties that are required robotics in healthcare, space robotics, emphasizes iterative learning control for proper function. A major focus is to and mobile manipulation in unstructured (ILC) and repetitive control (RC). ILC uncover fundamental mechanical and environments. (Ciocarlie) creates controllers that learn from biological mechanisms that coordinate the At the Creative Machines Lab previous experience performing a behaviors of cells in developing tissues. (CreativeMachines.org) we are specific command, such as robots To do this, we study morphogenesis in interested in robots that create and on an assembly line, aiming for high- developing embryos of model organisms robots that are themselves creative. We precision mechanical motions. RC learns and combine approaches such as in vivo develop novel autonomous systems that to cancel repetitive disturbances, such imaging, optogenetics, and biomechanical can design and make other machines— as precision motion through gearing, measurements. We are leveraging this automatically. We are working on a machining, satellite precision pointing, knowledge to design and build novel cell- self-replicating robots, self-aware robots, particle accelerators, etc. Time optimal based tissue structures and systems. Our robots that improve themselves over control of robots is being studied for goals are to shed light on human health time, and robots that compete and increased productivity on assembly and disease and learn how to better build cooperate with other robots. We build lines through dynamic motion planning. functional tissues in the lab. robots that paint art, cook food, build Research is also being conducted on Other areas of biomechanics bridges and fabricate other robots. improved system identification, making include characterizing the structure- Our work is inspired from biology, as mathematical models from input-output function behavior of the cervix during we seek new biological concepts for data. The results can be the starting the remodeling events of pregnancy engineering and new engineering point for designing controllers, but they and characterizing the mechanical insights into biology. (Lipson) are also studied as a means of assessing properties of the eye-wall in relation to In the area of advanced damage in civil engineering structures glaucoma. Research in our lab includes manufacturing processes and systems, from earthquake data. (Longman) the mechanical testing of biological current research concentrates on laser Robotics research focuses on soft tissues, the biochemical analysis materials processing. Investigations design of novel rehabilitation machines of tissue microstructure, and material are being carried out in laser and training algorithms for functional modeling based on structure-mechanical micromachining; laser forming of sheet rehabilitation of neural impaired adults property relationships. In collaboration metal; microscale laser shock-peening, and children. The research also aims with clinicians, our goal is to understand material processing using improved to design intelligent machines using the etiologies of tissue pathology and laser-beam quality. Both numerical and nonlinear system theoretic principles, disease. (Myers) experimental work is conducted using computational algorithms for planning, A surgically implantable pediatric state-of-the-art equipment, instruments,

ENGINEERING 2021–2022 188 and computing facilities. Close ties with scale electronic behavior that governs their applications, especially in industry have been established for molecular reactivity to the large-scale nanoelectromechanical systems (NEMS). collaborative efforts. (Yao) turbulent, reactive phenomena that A laboratory is available for the synthesis govern engine performance. (Burke) of graphene and other two-dimensional Energy, Fluid Mechanics, and Heat/ The Vedula group aims to advance materials using chemical vapor Mass Transfer. In the area of energy, clinical management of cardiovascular deposition (CVD) techniques and to build one effort is in energy systems disease using computational modeling. devices using electron-beam lithography with an eye toward cost-effective We are developing novel computational and various etching techniques. This decarbonization using technologies techniques for performing patient- effort will seek to optimize the fabrication, that are at hand or near-ready. The specific modeling of the cardiovascular readout, and sensitivity of these devices interaction of the electric grid, with system aimed at understanding the role for numerous applications, such as buildings, transportation, gas networks, of biomechanical factors in disease sensitive detection of mass, charge, and storage and electrofuels is being and development, device design, and magnetic resonance. (Hone, Kysar, Modi) studied. Another effort addresses the 'virtual' surgery planning. Computational Research in BioMEMS aims to design integration of thermal storage into HVAC modeling combined with machine and create MEMS and micro/nanofluidic systems for efficient use of variable learning and data-mining strategies systems to control the motion and renewable energy. The development of provides unprecedented opportunities measure the dynamic behavior of measurement, monitoring and control to not only examine acute response biomolecules in solution. Current efforts systems using IoT devices for use in to treatment, but also predict and risk involve modeling and understanding the micrositing and operation of microgrids stratify patients susceptible to long-term physics of micro/ nanofluidic devices and enabling flexibility or demand remodeling and dysfunction. (Vedula) and systems, exploiting polymer response of load. (Modi) The Vedula group is involved in structures to enable micro/nanofluidic In the area of energy, demand developing multiscale-multiphysics manipulation, and integrating MEMS estimation and prediction of interest models of the heart coupling cardiac sensors with microfluidics for measuring using utility data, satellite imagery and electrophysiology, tissue mechanics, physical properties of biomolecules. (Lin) lean, robust field data capture. (Modi) blood flow and valvular interactions, The Schuck group aims to In the area of nanoscale thermal thereby creating an integrated heart characterize, understand, and control transport, our research efforts center on model, that could be used to study a nanoscale light-matter interactions, the enhancement of thermal radiation variety of cardiac and valvular pediatric with a primary focus on sensing, transport across interfaces separated by and adult cardiovascular disease. A engineering, and exploiting novel a nanoscale gap. The scaling behavior few applications that we are particularly optoelectronic phenomena emerging of nanoscale radiation transport is interested in include cardiomyopathies, from nanostructures and interfaces. This measured using a novel heat transfer valvular calcifications and device offers unprecedented opportunities measurement technique based on design, remodeling and dysfunction in for developing innovative devices that the deflection of a bimaterial atomic congenital heart disease. (Vedula) rely on the dynamic manipulation of force microscope cantilever. Numerical single photons and charge carriers. simulations are also performed to MEMS and Nanotechnology. In these We are continuously developing new confirm these measurements. The areas, research activities focus on power multimodal and multidimensional measurements are also used to infer generation systems, nanostructures for spectroscopic methods that provide extremely small variations of van der photonics, fuel cells and photovoltaics, unique access to optical, electrical, and Waals forces with temperature. This and microfabricated adaptive cooling structural properties at relevant length enhancement of radiative transfer will skin and sensors for flow, shear, and wind scales in real environments encountered ultimately be used to improve the power speed. Basic research in fluid dynamics in energy and biological applications. density of thermophotovoltaic energy and heat/mass transfer phenomena at (Schuck) conversion devices. (Narayanaswamy) small scales also support these activities. Also in the area of energy, research (Hone, Kysar, Lin, Modi, Narayanaswamy) Biological Engineering and is being performed to improve the We study the dynamics of Biotechnology. Active areas of research thermochemical models used in microcantilevers and atomic force in the musculoskeletal biomechanics accelerating development of cleaner, microscope cantilevers to use them laboratory include theoretical and more fuel-efficient engines through as microscale thermal sensors based experimental analysis of articular computational design. In particular, on the resonance frequency shifts cartilage mechanics; theoretical and data-driven approaches to creating of vibration modes of the cantilever. experimental analysis of cartilage high-accuracy, uncertainty-quantified Bimaterial microcantilever-based lubrication, cartilage tissue engineering, thermochemicals models are being sensors are used to determine the and bioreactor design; growth and developed that utilize both theoretical thermophysical properties of thin films. remodeling of biological tissues; cell and experimental data. Special (Narayanaswamy) mechanics; and mixture theory for emphasis is placed on the generation Research in the area of nanotechnology biological tissues with experiments and and analysis of data across the full focuses on nanomaterials such as computational analysis (Ateshian). range of relevant scales—from the small- nanotubes and nanowires and The Hone laboratory studies

ENGINEERING 2021–2022 two-dimensional (2D) materials such the measurements of diffusive flux of dynamic processes can be rapidly 189 as graphene, with efforts spanning chemical species across a perforated and robotically micromanipulated into synthesis of single crystals and thin RWM, and the design, delivery, and reaction chambers to permit amplified films; device nanofabrication; and testing testing of surgical tools, all in close DNA synthesis and subsequent array of electronic, optical, mechanical, and collaboration with Anil K. Lalwani, M.D., analysis. Customized image processing other properties. The group develops at Columbia University Medical Center. and pattern recognition techniques methods to combine 2D materials into (Kysar) are developed, including Fisher’s layered heterostructures, which are The Schuck group is involved in linear discriminant preprocessing with used to explore fundamental properties, engineering novel near-infrared (NIR) neural net, a support vector machine achieve new functionality, and enable upconverting nanoparticles (UCNPs) and with improved training, multiclass cell applications in electronics, photonics, UCNP-based microdevices for large- detection with error correcting output sensing, and other areas. (Hone) scale sensing applications, including coding, and kernel principal component The Hone group uses deployment in projects aimed at deep- analysis. (Yao) nanofabrication techniques to create tissue imaging and the control of neural tools for studying the role of mechanical function deep within brain tissue. UCNPs Facilities for Teaching and Research forces and geometry in cellular have the potential to overcome nearly The undergraduate laboratories, biology. These investigations seek all limitations of current optical probes occupying an area of approximately to understand how cells sense the and sensors, which have run into 6,000 square feet of floor space, are mechanical properties or physical shape fundamental chemical and photophysical the site of experiments ranging in of their surroundings, a process that incompatibilities with living systems. complexity from basic instrumentation plays a major role in maintaining healthy (Schuck) and fundamental exercises to advanced cellular and tissue function. (Hone) Mass radiological triage is critical experiments in such diverse areas as Microelectromechanical systems after a large-scale radiological event automatic controls, heat transfer, fluid (MEMS) are being exploited to enable because of the need to identify mechanics, stress analysis, vibrations, and facilitate the characterization and those individuals who will benefit microcomputer-based data acquisition, manipulation of biomolecules. MEMS from medical intervention as soon as and control of mechanical systems. technology allows biomolecules to possible. The goal of the ongoing NIH- Equipment includes microcomputers be studied in well-controlled micro/ funded research project is to design and microprocessors, analog-to-digital nanoenvironments of miniaturized, a prototype of a fully automated, ultra and digital-to-analog converters, integrated devices, and may enable high throughput biodosimetry. This lasers and optics for holography novel biomedical investigations not prototype is supposed to accommodate and interferometry, a laser-Doppler attainable by conventional techniques. multiple assay preparation protocols velocimetry system, a particle image The research interests center on the that allow the determination of the velocimetry system (PIV), a Schlieren development of MEMS devices and levels of radiation exposure that a system, dynamic strain indicators, a systems for label-free manipulation patient received. The input to this fully servoelectric material testing machine, and interrogation of biomolecules. autonomous system is a large number photoelasticity, Digital Image Correlation Current research efforts primarily involve of capillaries filled with blood of patients (DIC) capabilities, a dynamometer, microfluidic devices that exploit specific collected using finger sticks. These supersonic de Laval nozzle and and reversible, stimulus-dependent capillaries are processed by the system subsonic wind tunnel, a cryogenic binding between biomolecules and to distill the micronucleus assay in apparatus, a coordinate measurement receptor molecules to enable selective lymphocytes, with all the assays being machine (CMM), and three-dimensional purification, concentration, and carried out in situ in multiwell plates. The printers as well as laser cutters. A label-free detection of nucleic acid, research effort on this project involves CNC wire electrical discharge machine protein, and small molecule analytes; the automation system design and (EDM) is also available for the use of miniaturized instruments for label-free integration including hierarchical control specialized projects for students with characterization of thermodynamic algorithms, design and control of custom prior arrangement. The undergraduate and other physical properties of built robotic devices, and automated laboratory also houses experimental biomolecules; and subcutaneously image acquisition and processing for setups for the understanding and implantable MEMS affinity biosensors for sample preparation and analysis. (Yao) performance evaluation of a complete continuous monitoring of glucose and A technology that couples the small steam power generation system, other metabolites. (Kysar, Lin) power of multidimensional microscopy a heat exchanger, a solar cell system, The Kysar group has a project to (three spatial dimensions, time, and a fuel cell system, a compressor, and design and develop a method to deliver multiple wavelengths) with that of a torsional control system. Part of the therapeutics into the inner ear through DNA array technology is investigated undergraduate laboratory is a staffed the Round Window Membrane (RWM) in an NIH-funded project. Specifically, machine shop with machining tools such that serves as a portal for acoustic a system is developed in which as CNC vertical milling machines, a CNC energy between the middle ear and individual cells selected on the lathe, standard vertical milling machines, inner ear. This involves the design and basis of optically detectable multiple engine and bench lathes, surface grinder, fabrication of arrays of microneedles, features at critical time points in

ENGINEERING 2021–2022 190 MECHANICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS STANDARD TRACK

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

APMA E2000 (4) and E2001 (0) and ORCA E2500 (3)6 either semester

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

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

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

UNIVERSITY CC1010 (3) either semester WRITING

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

REQUIRED TECHNICAL ENME E3105 (4) COURSES

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

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 Students who take APMA E2101 must complete an additional 3 point course in math or basic science with the following course designators: MATH, PHYS, CHEM, BIOL, STAT, APMA, or EEEB. One technical elective (3000–level or higher) may be substituted for this purpose. 2 Linear algebra may be fulfilled by either APMA E3101 or MATH UN2010. 3 Ordinary differential equations may be fulfilled by either MATH UN2030 or MATH UN3027. 4 May substitute EEEB UN2001, BIOL UN2005, or higher. 5 May substitute Physics Lab UN1494 (3) or UN3081 (2). 6 Offered in spring semester.

band saw, drill press, tool grinders, a architecture. The laboratory is divided personal computer that contains a data horizontal bandsaw, several Othermills into work centers for two-person acquisition board. The data acquisition used for light machining and circuit board student laboratory teams. Each work system serves as an oscilloscope, fabrication. center is equipped with a mixed signal additional function generator, and The Mech Tech laboratory affords oscilloscope, several power supplies spectrum analyzer for the student team. the opportunity for hands-on experience (for low-power electronics and higher The computer also contains a complete with microcomputer-embedded control power control), a function generator, a microcomputer software development of electromechanical systems. Facilities multimeter, a protoboard for building system, including editor, assembler, for the construction and testing of circuits, a microcomputer circuit board simulator, debugger, and C compiler. analog and digital electronic circuits (which includes the microcomputer The laboratory is also equipped with aid the students in learning the basic and peripheral components), a a portable oscilloscope, an EPROM components of the microcomputer microcomputer programmer, and a eraser (to erase microcomputer

ENGINEERING 2021–2022 191 MECHANICAL ENGINEERING: THIRD AND FOURTH YEARS STANDARD TRACK

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

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

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

TECHNICAL 9 points 4 ELECTIVES2

NONTECH Students must complete the 27-point requirement.5 ELECTIVES3

TOTAL ESTIMATED 15–16 16.5–17.5 16 15 POINTS6

1 Strongly recommended to be taken in Semester III or IV. 2 If APMA E2101 is taken instead of Linear algebra and ODE, students must complete an additional 3-point course in math or basic science with the following course designators: MATH, PHYS, CHEM, BIOL, STAT, APMA, or EEEB. One technical elective (3000–level or higher) may be substituted for this purpose. 3 Not required for Combined Plan students. 4 9 points required; 6 must be MECE courses. 5 See page 9; not required for Combined Plan students. 6 Students must complete a minimum of 128 points to graduate. programs from the erasable chips), the clean room located in the Schapiro 3. Conduct themselves in a responsible, a logic probe, and an analog filter Center for Engineering and Physical professional, and ethical manner. bank that the student teams share, as Science Research. Columbia University’s 4. Participate in activities that support well as a stock of analog and digital extensive library system has superb humanity and economic development electronic components. scientific and technical collections. nationally and globally, developing as The department maintains a modern Email and computing services are leaders in their fields of expertise. computer-aided design laboratory maintained by Columbia University As stated on the Mechanical equipped with thirty computer work Information Technology (CUIT) Engineering department website, stations with state-of-the-art design (columbia.edu/cuit). graduates of the Mechanical software. The research facilities are Engineering program at Columbia located within individual or group UNDERGRADUATE PROGRAM University will attain: research laboratories in the department, The Mechanical Engineering 1. an ability to identify, formulate, and and these facilities are being continually Undergraduate Program at Columbia solve complex engineering problems upgraded. To view the current research University has the following Program by applying principles of engineering, capabilities please visit the various Educational Objectives (PEOs) for its science, and mathematics laboratories within the research section graduates: 2. an ability to apply engineering design of the department website. The students to produce solutions that meet 1. Practice mechanical engineering in a and staff of the department can, by specified needs with consideration broad range of industries. prior arrangement, use much of the of public health, safety, and welfare, 2. Pursue advanced education, research equipment in these research facilities. as well as global, cultural, social, and development, and other creative Through their participation in the NSF- environmental, and economic factors and innovative efforts in science, MRSEC center, the faculty also have 3. an ability to communicate effectively engineering, and technology, as well access to shared instrumentation and with a range of audiences as other professional careers.

ENGINEERING 2021–2022 192 MECHANICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS EARLY DECISION TRACK

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

APMA E2000 (4) and E2001 (0) and ORCA E2500 (3)6 either semester

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

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

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

UNIVERSITY CC1010 (3) either semester WRITING

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

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

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

PHYSICAL UN1001 (1) UN1002 (1) EDUCATION

THE ART OF ENGI E1102 (4) either semester ENGINEERING

1 Students who take APMA E2101 must complete an additional 3 point course in math or basic science with the following course designators: MATH, PHYS, CHEM, BIOL, STAT, APMA, or EEEB. One technical elective (3000–level or higher) may be substituted for this purpose. 2 Linear algebra may be fulfilled by either APMA E3101 or MATH UN2010. 3 Ordinary differential equations may be fulfilled by either MATH UN2030 or MATH UN3027. 4 May substitute EEEB UN2001, BIOL UN2005, or higher. 5 May substitute Physics Lab UN1494 (3) or UN3081 (2). 6 Offered in spring semester.

4. an ability to recognize ethical and environment, establish goals, plan permitted to pursue an honors course professional responsibilities in tasks, and meet objectives consisting of independent study under engineering situations and make 6. an ability to develop and conduct the guidance of a member of the faculty. informed judgments, which must appropriate experimentation, Upon graduation the student may consider the impact of engineering analyze and interpret data, and wish to enter employment in industry solutions in global, economic, use engineering judgment to draw or government, or continue with environmental, and societal contexts conclusions graduate study. Alternatively, training 5. an ability to function effectively on 7. an ability to acquire and apply in mechanical engineering may be teams whose members together new knowledge as needed, using viewed as a basis for a career in provide leadership, create a appropriate learning strategies. business, patent law, medicine, or collaborative and inclusive Highly qualified students are management. Thus, the department’s

ENGINEERING 2021–2022 193 MECHANICAL ENGINEERING: THIRD AND FOURTH YEARS EARLY DECISION TRACK

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

MECE E3028 (3) Lab II MECE E3018 (3) Lab I ENME E3106 (3) MECE E3409 (3) Dynamics and vibrations Machine design MECE E3100 (3) Fluids I MECE E3311 (3) MECE E3420 (3) MECE E3430 (3) REQUIRED Engineering design: Engineering design: COURSES Heat transfer MECE E3301 (3) concept creation Thermodynamics MECE E3610 (3) Materials and processes EEME E3601 (3) in manufacturing Classical control systems

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

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

TECHNICAL 9 points 3 ELECTIVES1

NONTECH Students must complete the 27-point requirement.4 ELECTIVES

TOTAL ESTIMATED 12 16 16 15 POINTS2

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 Students must complete a minimum of 128 points to graduate. 3 9 points required; 6 must be MECE courses. 4 See page 9; not required for Combined Plan students. undergraduate program provides at least 6 points from the Department topics course APMA E2101. In addition, a sound foundation for a variety of of Mechanical Engineering, must be such students are encouraged to take professional endeavors. taken. A technical elective can be any a course in partial differential equations The program in mechanical engineering course offered in the SEAS (APMA E3102 or E4200) as well as a engineering leading to the B.S. degree bulletin that is 3000 level or above. Those course in numerical methods (APAM is accredited by the Engineering prior remaining points of electives are E3105 or APMA E4300) as technical Accreditation Commission of ABET, intended primarily as an opportunity electives. Ideally, planning for these http://www.abet.org. to complete the four-year, 27-point courses should start at the beginning of Undergraduates who wish to nontechnical requirement. Consistent the sophomore year. declare mechanical engineering as with professional accreditation standards, their major should do so prior to the courses in engineering science and Fundamentals of Engineering (FE) start of their junior year. Students who courses in design must have a combined Exam declare in their first year should follow credit of 48 points. Students should see The FE exam is a state licensing exam the Early Decision Track. Students who their advisers for details. and the first step toward becoming declare in their second year should Undergraduate students who a Professional Engineer (P.E.). P.E. follow the Standard Track. Students who intend to pursue graduate studies in licensure is important for engineers wish to declare during or after the fall engineering are strongly encouraged to to obtain—it shows a demonstrated semester of their junior year must first take the combination of a stand-alone commitment to professionalism and obtain approval from the Mechanical course in linear algebra (either APMA an established record of abilities that Engineering Department. E3101 or MATH UN2010) and a stand- will help a job candidate stand out in Of the 18 points of elective content in alone course in ordinary differential the field. Ideally, the FE exam should the third and fourth years, at least 9 points equations (either MATH UN2030 or be taken in the senior year while the of technical elective courses, including UN3027), instead of the combined

ENGINEERING 2021–2022 194 technical material learned while pursuing courses that will be taken have been than ten courses. A thesis based on the undergraduate degree is still fresh in designed to have the exact prerequisites either experimental, computational, or the student’s mind. In addition to the FE completed as an undergraduate. Other analytical research is optional and may exam, achieving P.E. licensure requires advantages include the opportunity for be counted in lieu of up to 6 points some years of experience and a second better course planning and creating of coursework. In general, attainment examination, which tests knowledge a streamlined set of courses more of the degree requires one academic gained in engineering practice. For possible. Additional benefits include year of full-time study, although it may more information, please see http:// simplified application process, no GRE also be undertaken on a part-time basis ncees.org/exams/fe-exam/. is required and no reference letters are over a correspondingly longer period. A The Mechanical Engineering required. To qualify for this program, your minimum grade-point average of 2.5 is Department strongly encourages all cumulative GPA should be at least 3.5. required for graduation. seniors to take this exam and offers a For more information on requirements The M.S. degree in mechanical review course covering material relevant and access to an application, please engineering requires a student to take to the exam, including a practice exam visit me.columbia.edu/ms-express- a sequence of courses that shows a to simulate the testing experience. The application-1. clearly discernible focus. In consultation FE exam is given in the fall and spring of with his/her adviser an M.S. student can each year. The review course is offered Barnard 4+1 Mechanical Engineering develop a focus specifically tailored to in the spring semester, concluding Pathways - Physics his/her interests and objectives, and before the spring exam. The Barnard 4+1 Pathway in Physics is we refer to this as the standard track. offered to current Barnard College juniors Alternatively, M.S. students can pick from Integrated B.S./M.S. Program with a GPA of 3.5 or higher to apply to a set of predefined tracks. The Integrated B.S./M.S. degree program Master's programs in Civil Engineering, Typical choices in the standard track is open to a qualified group of Columbia Electrical Engineering, and Mechanical include such subjects as mechanics of juniors and makes possible the earning Engineering. Students should inquire with solids and fluids, thermodynamics, heat of both the B.S. and M.S. degree in Beyond Barnard and plan on attending transfer, manufacturing engineering, an integrated fashion. Benefits of this an introductory information sessions for robotics, kinematics, dynamics and program include optimal matching of the unique 4+1 Pathway they may be vibrations, controls, and power graduate courses with corresponding interested in pursuing. generation. Nevertheless, the following undergraduate prerequisites, greater ability Faculty contact at Barnard: Professor guidelines must be adhered to: to plan ahead for most advantageous Reshmi Mukherjee [email protected] 1. All courses must be at the graduate course planning, opportunities to do at SEAS: Professor Gerard Ateshian level, i.e., numbered 4000 or higher, research for credit during the summer [email protected] with at least two 6000-level courses, after senior year, and up to 6 points of chosen in consultation with an adviser. 4000-level technical electives from the At least one of the 6000-level courses B.S. requirement may count toward the GRADUATE PROGRAMS must be in Mechanical Engineering. fulfillment of the point requirement of the The Department of Mechanical 2. Every program must contain at least M.S. degree. Additional benefits include Engineering offers two doctoral degrees: Doctor of Philosophy (Ph.D.) one course in mathematics (APMA, simplified application process, no GRE and Doctor of Engineering Science MATH, STAT course designations) is required, and no reference letters are (Eng.Sc.D.), and the Master of Science covering material beyond what the required. To qualify for this program, degree. The Ph.D. degree is conferred student has taken previously. It is students must have a cumulative GPA of by the Graduate School of Arts and recommended to be taken early in at least 3.5 and strong recommendations Science, and the Eng.Sc.D. degree is the sequence, in order to serve as a from within the Department. Students conferred by The Fu Foundation School basis for the technical coursework. should apply for the program by April 30 of Engineering and Applied Science. 3. Out-of-department study is in their junior year. For more information on M.S. students must complete encouraged, must be taken in requirements and access to an application the professional development and consultation with adviser. form, please visit leadership course, ENGI E4000, as 4. At least five courses must be in me.columbia.edu/integrated-bsms- a graduation requirement. Doctoral Mechanical Engineering. program. students will be enrolled in ENGI E6001– 6004 and should consult their program Rather than selecting the standard Express M.S. Application for specific PDL requirements. option, students can select a concentra- The Express M.S. Application is tion in either energy systems, micro/ offered to current seniors, including Master of Science Degree Program nanoscale engineering, or robotics and 3-2 students, who are enrolled in The program leading to the Master control. The requirements for a special- the BS program. In the Express M.S. of Science degree in mechanical ization are identical to those of the stan- Application, a master’s degree can be engineering requires completion of dard track, with one exception: students earned seamlessly. Graduate classes a minimum of 30 points of approved must take at least 15 points from a list are available for seniors to apply toward coursework consisting of no fewer determined by an adviser in consultation their M.S. degree and the advanced

ENGINEERING 2021–2022 with an advisory committee. The cur- M.S. in Mechanical Engineering with can be applied in other fields as diverse 195 rently available elective specializations Concentration in Micro/Nanoscale as automation, manufacturing, computer are listed below. Engineering graphics or machine vision. This Advisers: Professors James Hone and P. program can also be a foundation for a M.S. in Mechanical Engineering with James Schuck research career in robotics and related Concentration in Energy Systems areas, in both academia and industry. The concentration in micro/nanoscale Advisers: Professors Vijay Modi and While satisfying these requirements, engineering provides the M.S. candidate Arvind Narayanaswamy take at least five courses from: with an understanding of engineering The concentration in energy systems challenges and opportunities in micro- Courses in the Mechanical Engineering Department provides the M.S. candidate with a and nanoscale systems. The curriculum MEBM E4439: Modeling & id of dynamic system addresses fundamental issues of global understanding of current energy MECE E4058: Mechanics and embedded challenges. Advanced thermofluidic mechanics, fluid mechanics, optics, heat microcomputer control knowledge is provided to design transfer, and manufacturing at small- MECE E4510: Geometrical modeling and optimize energy systems, with size scales. Application areas include MECE E4601: Digital control systems a strong emphasis on renewable MEMS, bio-MEMS, microfluidics, thermal MECE E4602: Intro to robotics energies. Courses related to energy systems, and carbon nanostructures. MECE E4603: Applied robotics: algorithm & software and environmental policy, two strong Requirements: While satisfying MECE E4606: Digital manufacturing areas of Columbia as a global the general mechanical engineering MECE E6400: Advanced machine dynamics university, can be integrated into the requirements, take at least five courses MECE E6424: Vibrations in machine, I course sequence. This specialization from: MECE E6601: Intro to control theory is a suitable preparation for careers Modern control theory MECE E4212: Microelectromechanical systems MECE E6602: Optimal control theory in energy production and energy MECE E4213: BioMEMS MECE E6610: Advanced topics in robotics and consultation. MECE E6105: Transport phenomena in the MECE E6614: Requirements: 30 points of graduate presence of interfaces mechanism synthesis MECE E6615: Robotic manipulation level coursework, i.e., courses MECE E6700: Carbon nanotubes MECE E6620: Applied signal recognition numbered 4000-level or higher, at least MECE E6710: Nanofabrication laboratory Nano/microscale thermal transport two of which must be a 6000-level, MECE E6720: processes Courses in the Other Departments in the School chosen in consultation with an adviser MECE E8990: Small scale mechanical behavior of Engineering and Applied Science Sensors, actuators and (MECE E6100 Advanced mechanics of ELEN E4503: Sensors, actuators, and ELEN E4501: fluids and MECE E6313 Advanced heat electromechanical systems electromechanical systems Digital control systems** transfer are strongly recommended). ELEN E6945: Device nanofabrication EEME E4601: BMME E4702: Advanced musculoskeletal Furthermore, students must take one BMEN E4590: BioMEMS: cellular and molecular applications biomechanics course in statistics (STAT designations) COMS W4731: Computer vision* MSAE E4090: Nanotechnology and at least five courses from the COMS W4733: Computational aspects of following list*: robotics* M.S. in Mechanical Engineering with ELEN E4810: Digital signal processing MECE E4210: Energy infrastructure planning Concentration in Robotics and Control EEME E6601: Introduction to control theory** MECE E4211: Energy: sources and conversion EEME E6602: Modern control theory** MECE E4302: Advanced thermodynamics Advisers: Professors Sunil Agrawal, EEME E6610: Optimal control theory** MECE E4304: Turbomachinery Matei Ciocarlie, Hod Lipson, and Richard COMS E6733: 3D photography* MECE E4305: Mechanics and thermodynamics Longman propulsion *Registration restrictions may apply. MECE E4312: Solar thermal engineering The field of robotics is seeing **Count as MECE. MECE E4314: Energy dynamics of green buildings unprecedented growth, in areas as MECH E4320: Intro to combustion diverse as manufacturing, logistics, Examples of suitable APMA courses MECE E4330: Thermofluid systems design transportation, health care, space are: APMA E4001y Principles of MECE E6100: Advanced mechanics of fluids exploration, and more. This program MECE E6102: Computational heat transfer and applied mathematics; APMA E4300y, prepares students for a career in fluid flow Introduction to numerical methods; robotics and its many applications in MECE E6103: Compressible flow APMA E4301x Numerical methods for society. Students perform in-depth study MECE E6104: Case studies in computational fluid partial differential equations; and APMA of topics such as robotic manipulation, dynamics E4204x Functions for complex variables. MECE E6313: Advanced heat transfer navigation, perception, human EAEE E6126: Carbon sequestration interaction, medical robotics, assistance Doctoral Degree Program and rehabilitation. This specialization *One 3-point research course can be is a suitable preparation for joining All applications to the doctoral counted toward the specialization if the established companies, information-age program in mechanical engineering are research is approved by the student's dominant players investing heavily in administered by The Fu Foundation adviser and is energy related. this field, or the new wave of robotics School of Engineering and Applied start-ups aiming to provide disruptive Science. Students who matriculate into innovations. Many of the acquired skills the doctoral program without a master's

ENGINEERING 2021–2022 196 degree earn a Master of Science MECE E1304x or y Naval ship systems, I Stress and strain. Mechanical properties of materi- degree while pursuing their doctoral 3 pts. Lect: 3. Not offered in 2021–2022. als. Axial load, bending, shear, and torsion. Stress degree. Students are strongly advised to consult with the transformation. Deflection of beams. Buckling of ME Department prior to registering for this course. columns. Combined loadings. Thermal stresses. Doctoral candidates are expected A study of ship characteristics and types including to attain a level of mastery in an area ship design, hydrodynamic forces, stability, com- MECE E3301x Thermodynamics of mechanical engineering and must partmentation, propulsion, electrical and auxiliary 3 pts. Lect: 3. Professor Narayanaswamy. therefore choose a field and take the systems, interior communications, ship control, Classical thermodynamics. Basic properties and and damage control; theory and design of steam, concepts, thermodynamic properties of pure most advanced courses offered in substances, equation of state, work, heat, the first that field. Candidates are assigned a gas turbine, and nuclear propulsion; shipboard safety and firefighting. This course is part of the and second laws for flow and nonflow processes, faculty adviser whose task is to help Naval ROTC program at Columbia but will be energy equations, entropy, and irreversibility. choose a program of courses, provide taught at SUNY Maritime. Enrollment may be lim- Introduction to power and refrigeration cycles. general advice on academic matters, ited; priority is given to students participating in MECE E3311y Heat transfer and monitor academic performance. Naval ROTC. Will not count as a technical elective. 3 pts. Lect: 3. Professor Narayanaswamy. Candidates also choose a faculty Students should see a faculty adviser as well as Steady and unsteady heat conduction. Radiative Columbia NROTC staff ([email protected]) for member in the pertinent area of heat transfer. Internal and external forced and more information. specialization to serve as their research free convective heat transfer. Change of phase. Heat exchangers. adviser. This adviser helps select a MECE E3018x Mechanical engineering research problem and supervises the laboratory, I MECE E3401x Mechanics of machines 3 pts. Lect: 3. Professor Yesilevskiy. research, writing, and defense of the 3 pts. Lect: 3. Professor Agrawal. Experiments in instrumentation and measure- Prerequisite(s): ENME E3105 and MECE E3408. dissertation. ment: optical, pressure, fluid flow, temperature, Introduction to mechanisms and machines, ana- stress, and electricity; viscometry, cantilever lytical and graphical synthesis of mechanism, dis- Program Requirements beam, digital data acquisition. Probability theory: placement analysis, velocity analysis, acceleration • 30 credits beyond master's degree distribution, functions of random variables, tests analysis of linkages, dynamics of mechanism, cam • GPA of 3.2 or better in graduate of significance, correlation, ANOVA, linear regres- design, gear and gear trains, and computer-aided sion. courses mechanism design. • 4 semesters of graduate seminar MECE E3028y Mechanical engineering MECE E3408x and y Computer graphics MECE E9500 laboratory, II and design • Completion of all milestones 3 pts. Lect: 3. Professor Lin. 3 pts. Lect: 3. Professor Vukelic. Experiments in engineering and physical phenom- Introduction to drafting, engineering graphics, ena: aerofoil lift and drag in wind tunnels, laser computer graphics, solid modeling, and mechani- See www.me.columbia.edu/academics/ Doppler anemometry in immersed fluidic chan- cal engineering design. Interactive computer doctoral-program for more information. nels, supersonic flow and shock waves, Rankine graphics and numerical methods applied to thermodynamical cycle for power generation, and the solution of mechanical engineering design structural truss mechanics and analysis. problems. COURSES IN MECHANICAL ENGINEERING MECE E3038x Mechanical engineering MECE E3409x Machine design laboratory, III 3 pts. Lect: 3. Professor Yesilevskiy. MECE E1001x Mechanical engineering: 3 pts. Lect: 3. Not offered in 2021–2022. Prerequisite(s): MECE E3408. Computer-aided micromachines to jumbo jets Mechatronic control of mechanical and electro- analysis of general loading states and deforma- 3 pts. Lect: 3. Not offered in 2021–2022. mechanical systems. Control of various thermo- tion of machine components using singularity Corequisite: MATH UN1101 Calculus I. This intro- dynamic cycles, including internal combustion functions and energy methods. Theoretical intro- ductory course explores the role of Mechanical engine (Otto cycle). Reverse engineering of an duction to static failure theories, fracture mechan- Engineering in developing many of the funda- electromechanical product. ics, and fatigue failure theories. Introduction mental technological advances on which today’s to conceptual design and design optimization MECE E3100x Introduction to mechanics society depends. Students will be exposed to sev- problems. Design of machine components such of fluids eral mature and emerging technologies through as springs, shafts, fasteners, lead screws, rivets, 3 pts. Lect: 3. Professor Kasza. a series of case studies. Topics include airplanes, welds. Modeling, analysis, and testing of machine Prerequisite(s): ENME E3105. Basic continuum automobiles, robots, modern manufacturing assemblies for prescribed design problems. concepts. Liquids and gases in static equilibrium. methods as well as the emerging fields of micro- Problems will be drawn from statics, kinematics, Continuity equation. Two-dimensional kinemat- electromechanical machines (MEMS) and nano- dynamics, solid modeling, stress analysis, and ics. Equation of motion. Bernoulli’s equation technology. The physical concepts that govern the design optimization. and applications. Equations of energy and operation of these technologies will be developed angular momentum. Dimensional analysis. Two- from basic principles and then applied in simple MECE E3411y Fundamentals of engineering dimensional laminar flow. Pipe flow, laminar, and design problems. Students will also be exposed to 1 pt. Lect: 3. Professor Vukelic. turbulent. Elements of compressible flow. state-of-the art innovations in each case study. Prerequisite(s): Senior standing. Review of core courses in mechanical engineering, including ENME E3105x and y Mechanics MECE E1008x or y Introduction to machining mechanics, strength of materials, fluid mechan- 4 pts. Lect: 4. Professor Hone. 1 pt. Professor Vukelic. ics, thermodynamics, heat transfer, materials and Prerequisite(s): PHYS UN1401 and MATH UN1101, Introduction to the manual machine operation, processing, control, and mechanical design and UN1102, and UN1201 or APMA E2000. Elements CNC fabrication and usage of basic hand tools, analysis. Review of additional topics, including of statics, dynamics of a particle, and systems of band/hack saws, drill presses, grinders and engineering economics and ethics in engineer- particles. sanders. ing. The course culminates with a comprehensive ENME E3113x Mechanics of solids examination, similar to the Fundamentals of 3 pts. Lect: 3. Professor Betti. Engineering examination. Meets the first 4.5 Pre- or corequisite: ENME E3105 or equivalent. weeks only.

ENGINEERING 2021–2022 MECE E3420x Engineering design—concept/ to 6 points toward degree requirements. Students IEME E4200x or y Introduction to human- 197 design generating must submit both a project outline prior to regis- centered design 3 pts. Lect: 3. Professor Yesilevskiy. tration and a final project write up at the end of 1.5 pts. Lect: 4.5. Professor West. Prerequisite(s): Senior standing. Corequisite: the semester. Prerequisite(s): Application to instructor for MECE E3409. A preliminary design for an original approval. Open to SEAS graduate and advanced MECE E3998x and y Projects in mechanical project is a prerequisite for the capstone design undergraduate students, Business School, and course. Will focus on the steps required for gen- engineering GSAPP. Students from other schools may apply. erating a preliminary design concept. Included 1–3 pts. Members of the faculty. Fast-paced introduction to human-centered will be a brainstorming concept generation phase, Prerequisite(s): Approval by faculty member design. Students learn the vocabulary of design a literature search, incorporation of multiple who agrees to supervise the work. Independent methods, understanding of design process. Small constraints, adherence to appropriate engineer- project involving theoretical, computational, group projects to create prototypes. Design of ing codes and standards, and the production of a experimental, or engineering design work. May simple product, more complex systems of prod- layout drawing of the proposed capstone design be repeated, but no more than 3 points may be ucts and services, and design of business. project in a Computer Aided Design (CAD) soft- counted toward degree requirements. Projects ware package. Note: MECE students only. requiring machine-shop use must be approved by MECE E4210x or y Energy infrastructure the laboratory supervisor. Students must submit planning MECE E3430y Engineering design both a project outline prior to registration and a 3 pts. Lect: 3. Professor Modi. 3 pts. Lect: 2. Lab: 4. Professor Yesilevskiy. final project write-up at the end of the semester. Prerequisite(s): One year each of college level Prerequisite(s): MECE E3420. Building on the physics, chemistry, and mathematics. Energy MECE E3999x, y or s Fieldwork preliminary design concept, the detailed elements infrastructure planning with specific focus on 1–2 pts. Professor Myers. of the design process are completed: systems countries with rapidly growing infrastructure Prerequisite(s): Obtained internship and approval synthesis, design analysis optimization, incorpo- needs. Spatiotemporal characteristics, scale, and from a faculty adviser. May be repeated for credit, ration of multiple constraints, compliance with environmental footprints of energy resources, but no more than 3 total points may be used appropriate engineering codes and standards, power generation and storage, modeling demand toward the 128-credit degree requirement. Only and Computer Aided Design (CAD) component growth, technology choices and learning for plan- for MECE undergraduate students who include part drawings. Execution of a project involving the ning. Computer-assisted decision support and relevant on-campus and off-campus work experi- design, fabrication, and performance testing of an network design/optimization tools. Similarities, ence as part of their approved program of study. actual engineering device or system. differences and interactions among electricity, Final report and letter of evaluation required. gas, information, transportation and water distri- Fieldwork credits may not count toward any MECE E3450x or y Computer-aided design bution networks. Penetration of renewable and/ major core, technical, elective, and nontechni- 3 pts. Lect: 3. Professor Ateshian. or decentralized technologies into existing or new cal requirements. May not be taken for pass/fail Prerequisite(s): ENME E3105, E3113, MECE E3408, infrastructure. Special guest lectures on infra- credit or audited. E3311. Introduction to numerical methods and structure finance, regulation and public-private their applications to rigid body mechanics for MECE E4058x and y Mechatronics and partnerships. mechanisms and linkages. Introduction to finite embedded microcomputer control element stress analysis for deformable bodies. MECE E4211x or y Energy: sources and 3 pts. Lect: 3. Professor Zordan. Computer-aided mechanical engineering design conversion Prerequisite(s): ELEN E1201. Recommended: using established software tools and verifications 3 pts. Lect: 3. Professor Modi. ELEN E3000. Enrollment limited to 12 students. against analytical and finite difference solutions. Prerequisite(s): MECE E3301. Energy sources Mechatronics is the application of electronics such as oil, gas, coal, gas hydrates, hydrogen, EEME E3601x Classical control systems and microcomputers to control mechanical sys- solar, and wind. Energy conversion systems for tems. Systems explored include on/off systems, 3 pts. Lect: 3. Professor Longman. electrical power generation, automobiles, propul- solenoids, stepper motors, DC motors, thermal Prerequisite(s): MATH UN2030. Analysis and sion and refrigeration. Engines, steam and gas - systems, magnetic levitation. Use of analog and design of feedback control systems. Transfer func turbines, wind turbines; devices such as fuel cells, tions; block diagrams; proportional, rate, and inte- digital electronics and various sensors for control. thermoelectric converters, and photovoltaic cells. gral controllers; hardware, implementation. Routh Programming microcomputers in Assembly and C. Specialized topics may include carbon-dioxide stability criterion, root locus, Bode and Nyquist Lab required. sequestration, cogeneration, hybrid vehicles and plots, compensation techniques. MECE E4078x or y Internet of (Mechanical) energy storage devices. MECE 3610y Materials and processes in Things MECE E4212x or y Microelectromechanical manufacturing 3 pts. Lect: 3. Professor Fernandez. systems 3 pts. Lect: 3. Professor Yao. Hands-on, project-oriented course covering foun- 3 pts. Lect: 1.5. Lab: 3. Professor Schuck. Prerequisite(s): ENME E3113 or the equivalent. dations of Internet of Things (IoT) technologies as MEMS markets and applications; scaling laws; Introduction to microstructures and properties of they relate to the physical world. Projects utilizing silicon as a mechanical material; Sensors and metals, polymers, ceramics and composites; typi- Arduino and Raspberry Pi platforms. End-to-end actuators; micromechanical analysis and design; cal manufacturing processes: material removal, IoT including sensors, basic controls, embedded substrate (bulk) and surface micromachining; shaping, joining, and property alteration; behavior systems programming, networking, IoT protocols, computer aided design; packaging; testing and of engineering materials in the manufacturing power consumption/optimization, and cloud con- characterization; microfluidics. processes. nectivity. Build real IoT devices and systems in two team-based projects. MECE E4213x or y Biomicroelectromechanical MECE E3900x-E3901y Honors tutorial in systems (BioMEMS): design, fabrication, and mechanical engineering MECE E4100y Mechanics of fluids analysis 3 pts. Lect: 3. Members of the faculty. 3 pts. Lect: 3. Professor Kasza. 3 pts. Lect: 3. Professor Lin. Prerequisite(s): 3.2 or higher GPA. Individual Prerequisite(s): MECE E3100 or equivalent. Fluid Prerequisite(s): MECE E3100 and E3311, course study; may be selected after the first term of the dynamics and analyses for mechanical engineer- in transport phenomena, or instructor’s permis- junior year by students maintaining a 3.2 grade- ing and aerospace applications: boundary layers sion. Silicon and polymer micro/nanofabrication point average. Course format may vary from and lubrication, stability and turbulence, and techniques; hydrodynamic microfluidic control; individual tutorial to laboratory work to seminar compressible flow. Turbomachinery as well as electrokinetic microfluidic control; microfluidic instruction under faculty supervision. Projects additional selected topics. separation and detection; sample preparation; requiring machine-shop use must be approved by micro bioreactors and temperature control; the laboratory supervisor. Students may count up

ENGINEERING 2021–2022 198 implantable MEMS, including sensors, actuators facturing and service enterprises. Connections MECE E4404x or y Tribology: friction, and drug delivery devices. between the needs of a global enterprise, the lubrication, and wear technology and methodology needed for manu- 3 pts. Lect: 3. Not offered in 2021–2022. MECE E4214x or y MEMS production and facturing and product development, and strategic Prerequisite(s): MECE E3100, E3311, and ENME packaging planning as currently practiced in industry. E3113, or permission of the instructor. Friction, 3 pts. Lect: 3. Professor Hilton. lubrication, and wear between sliding surfaces. MECE E4312x Solar thermal engineering Prerequisite(s): MECE E4212. Applications-driven Surface metrology, contact mechanics, and slid- 3 pts. Lect: 3. Professor Naraghi. study of the packaging and manufacturing of ing friction. Deformation, wear, and temperature Prerequisite(s): MECE E3311 (Heat transfer). MEMS devices. Covers underlying physical phe- rise of nonlubricated, liquid-lubricated, and Fundamentals of solar energy transport: radiation nomena such as fracture mechanics and materials solid-lubricated rolling and sliding materials. The heat transfer, convention, conduction and phase science topics relevant to MEMS production. theories of boundary, elastohydrodynamic, hydro- change processes. Heat exchangers and solar Packaging approaches such as glass-to-metal dynamic, hydrostatic, and solid-phase lubrication. collectors: basic methods of thermal design, flow seals and CTE matching. Electrical filtering and Lubricant flow and load-carrying capacity in bear- arrangements, effects of variable conditions, noise sources as relevant to the transducer signal ings. Special applications such as geartrains, cam/ rating procedures. Solar energy concentration. chain. Comparative MEMS design as focused on a tappets, and micro- and nanoscale tribological Piping Systems: series and parallel arrangements, common example: pressure transducers. interfaces. fluid movers. Thermal response and management MECE E4302y Advanced thermodynamics of photovoltaic energy conversion. Solar energy MECE E4430x Automotive dynamics 3 pts. Lect: 3. Professor Burke. storage. Solar cooling, solar thermal power and 3 pts. Lect: 3. Professor Browne. Prerequisite(s): MECE E3301. Advanced classical cogeneration. Applications to the design of solar Prerequisite(s): ENME E3105 or equivalent; thermodynamics. Availability, irreversibility, gen- thermal engineering systems. Recommended: ENME E3100 or E3106. Reviews eralized behavior, equations of state for nonideal fundamentals of vehicle dynamics. A systems- MECE E4314y Energy dynamics of green gases, mixtures and solutions, phase and chemi- based engineering approach to explore areas of: cal behavior, combustion. Thermodynamic proper- buildings tire characteristics, aerodynamics, stability and ties of ideal gases. Applications to automotive and 3 pts. Lect: 3. Professor Naraghi. control, wheel loads, ride and roll rates, suspen- aircraft engines, refrigeration and air conditioning, Prerequisite(s): MECE E3301 and E3311. sion geometry, and dampers. A high-performance and biological systems. Introduction to analysis and design of heating, vehicle (racecar) platform used as an example to ventilating and air-conditioning systems. Heating review topics. MECE E4304x Turbomachinery and cooling loads. Humidity control. Solar gain 3 pts. Lect: 3. Not offered in 2021–2022. and passive solar design. Global energy implica- MECE E4431x or y Space vehicle dynamics Introduces the basics of theory, design, selec- tions. Green buildings. Building-integrated photo- 3 pts. Lect: 3. Professor Longman. tion and applications of turbomachinery. voltaics. Roof-mounted gardens and greenhouses. Prerequisite(s): ENME-MECE E3105; ENME E4202 Turbomachines are widely used in many engi- Financial assessment tools and case studies. recommended. Space vehicle dynamics and con- neering applications such as energy conversion, Open to Mechanical Engineering graduate stu- trol, rocket equations, satellite orbits, initial trajec- power plants, air-conditioning, pumping, refrig- dents only. tory designs from Earth to other planets, satellite eration and vehicle engines, as there are pumps, attitude dynamics, gravity gradient stabilization of blowers, compressors, gas turbines, jet engines, MECH E4320x Introduction to combustion satellites, spin-stabilized satellites, dual-spin sat- wind turbines, etc. Applications are drawn from 3 pts. Lect: 3. Professor Burke. ellites, satellite attitude control, modeling, dynam- energy conversion technologies, HVAC and pro- Prerequisite(s): Introductory thermodynamics, fluid ics, and control of large flexible spacecraft. pulsion. Provides a basic understanding of the dynamics, and heat transfer at the undergraduate different kinds of turbomachines. level or instructor’s permission. Thermodynamics MEBM E4439x Modeling and identification of and kinetics of reacting flows; chemical kinetic dynamic systems MECE E4305y Mechanics and mechanisms for fuel oxidation and pollutant 3 pts. Lect: 3. Not offered in 2021–2022. thermodynamics of propulsion formation; transport phenomena; conservation Prerequisite(s): APMA E2101, ELEN E3801, or 3 pts. Lect: 3. Professor Bradshaw. equations for reacting flows; laminar nonpremixed corequisite EEME E3601, or permission of instruc- Prerequisite(s): MECE E3301x Thermodynamics flames (including droplet vaporization and burn- tor. Generalized dynamic system modeling and and MECE E3311y Heat transfer; MECE E4304x ing); laminar premixed flames; flame stabilization, simulation. Fluid, thermal, mechanical, diffusive, Turbomachinery (or instructor approval). Principles quenching, ignition, extinction, and other limit electrical, and hybrid systems are considered. of propulsion. Thermodynamic cycles of air phenomena; detonations; flame aerodynamics Nonlinear and high order systems. System identifi- breathing propulsion systems including ramjet, and turbulent flames. cation problem and Linear Least Squares method. scramjet, turbojet, and turbofan engine and rocket State-space and noise representation. Kalman MECE E4330x Thermofluid systems design propulsion system concepts. Turbine engine and filter. Parameter estimation via prediction-error 3 pts. Lect: 3. Professor Bradshaw. rocket performance characteristics. Component and subspace approaches. Iterative and bootstrap Prerequisite(s): MECE E3100, E3301, E3311. and cycle analysis of jet engines and turboma- methods. Fit criteria. Wide applicability: medical, Theoretical and practical considerations, and chinery. Advanced propulsion systems. Columbia energy, others. MATLAB and Simulink environ- design principles, for modern thermofluids sys- Engineering interdisciplinary course. ments. tems. Topics include boiling, condensation, phase MECE E4306x or y Introduction to change heat transfer, multimode heat transfer, MECE E4440x or y Optimization of dynamic aerodynamics heat exchangers, and modeling of thermal trans- systems 3 pts. Lect: 3. Professor LeVoci. port systems. Emphasis on applications of ther- 3 pts. Lect: 3. Professor Agrawal. Principles of flight, incompressible flows, com- modynamics, heat transfer, and fluid mechanics to Prerequisite(s): Course on linear and/or nonlinear pressible regimes. Inviscid compressible aero- modeling actual physical systems. Term project on control theory, introduction to Robotics, or instruc- dynamics in nozzles (wind tunnels, jet engines), conceptual design and presentation of a thermo- tor's permission. Fundamentals for optimizing around wings (aircraft, space shuttle) and around fluid system that meets specified criteria. performance of dynamic systems described by blunt bodies (rockets, reentry vehicles). Physics of a set of ordinary differential equations based on MECE E4400x and y Computer laboratory normal shock waves, oblique shock waves, and theory of variational calculus. Systematic methods explosion waves. access to solve optimization problems using numerical 0 pts. methods. Topics include: Static Optimization of IEME E4310x The manufacturing enterprise Sign up for this class to obtain a computer 3 pts. Lect: 3. Not offered in 2021–2022. systems with equality and inequality and inequal- account and access to the Department of ity constraints, Numerical methods to solve static The strategies and technologies of global manu- Mechanical Engineering Computer Laboratory.

ENGINEERING 2021–2022 optimization problems, Theory of calculus of varia- EEME E4601y Digital control systems MECE E4609y Computer-aided manufacturing 199 tions, Application of calculus of variations to solve 3 pts. Lect: 3. Professor Beigi. 3 pts. Lect: 3. Professor Walker. static optimization problems with equality and Prerequisite(s): EEME E3601 or ELEN E3201. Prerequisite(s): Introductory course on manufac- inequality constraints, numerical methods to solve Real-time control using digital computers. Solving turing processes and knowledge of computer-aid- static optimization problems, theory of calculus scalar and state-space difference equations. ed design, and mechanical design or instructor’s variations to solve dynamic optimization problems Discrete equivalents of continuous systems fed by permission. Computer-aided design, free-form with equality and inequality constraints, direct holds. Z-transer functions. Creating closed-loop surface modeling, tooling and fixturing, computer and indirect numerical methods to solve dynamic difference equation models by Z-transform and numeric control, rapid prototyping, process engi- optimization problems, finite-time linear systems, state variable approaches. The Nyquist frequency neering, fixed and programmable automation, steady state linear systems, multi degree-of- and sample rate selection. Classical and modern industrial robotics. freedom robotic systems. based digital control laws. Digital system identi- fication. MECE E4610x Advanced manufacturing MECE E4501y Geometrical modeling processes 3 pts. Lect: 3. Not offered in 2021–2022. MECE E4602x Introduction to robotics 3 pts. Lect: 3. Professor Yao. Prerequisite(s): COMS W1005. Relationship 3 pts. Lect: 3. Professor Ciocarlie. Prerequisite(s): Introductory course on manufac- between 3D geometry and CAD/CAM; representa- Overview of robot applications and capabilities. turing processes, and heat transfer, knowledge of tions of solids; geometry as the basis of analysis, Linear algebra, kinematics, statics, and dynamics engineering materials, or instructor’s permission. design, and manufacturing; constructive solid of robot manipulators. Survey of sensor technol- Principles of nontraditional manufacturing, nontra- geometry and the CSG tree; octree representa- ogy: force, proximity, vision, compliant manipula- ditional transport and media. Emphasis on laser tion and applications; surface representations tors. Motion planning and artificial intelligence; assisted materials processing, laser material inter- and intersections; boundary representation and manipulator programming requirements and actions with applications to laser material remov- boundary evaluation; applied computational languages. al, forming, and surface modification. Introduction geometry; analysis of geometrical algorithms and to electrochemical machining, electrical discharge associated data structures; applications of geo- MECS E4603x Applied robotics: algorithms machining and abrasive water jet machining. metrical modeling in vision and robotics. and software 3 pts. Lect: 3. Not offered in 2021–2022. MECE E4611x or y Robotics studio MECE E4502x Computational geometry for Prerequisite(s): Fundamental programming skills 3 pts. Lect: 1. Lab: 4. Professor Lipson. CAD/CAM (e.g., COMS W1002, W1004, W1005, ENGI E1006, Prerequisite(s): Knowledge of basic computer 3 pts. Lect: 3. Not offered in 2021–2022. or equivalent). Science and systems aspects of programming (e.g., Java, Matlab, Python) or Prerequisite(s): COMS W1005 FORTRAN or Robotics from applied perspective, focusing on instructor's permission. Hands-on studio class PASCAL. Analysis of geometric problems and the algorithms and software tools. Spatial reason- exposing students to practical aspects of the design of efficient methodologies to obtain solu- ing; tools for manipulating and visualizing spatial design, fabrication, and programming of physical tions to these problems. Algorithms to be studied relationships. Analysis of robotic manipulators; robotic systems. Students experience entire robot include geometric searching, convex hulls, trian- numerical methods for kinematic analysis. Motion creation process, covering conceptual design, gulations, Voronoi diagrams, intersections, hidden planning, search-based and stochastic approach- detailed design, simulation and modeling, digital surfaces. Emphasis will be on practical aspects es. Applications for force and impedance control. manufacturing, electronics and sensor design, of these algorithms, and on applications of the Grading based on combination of exams and proj- and software programming. solutions in computer-aided product design and ects implemented using Robot Operating System manufacturing. (ROS) software framework and executed on real MECE E4612x or y Sustainable manufacturing and simulated robotic manipulators. 3 pts. Lect: 3. Professor Yao. MECS E4510x Evolutionary computation and Prerequisite(s): Introductory course in engineer- design automation MECE E4604x Product design for ing materials and manufacturing processes or 3 pts. Lect: 3. Professor Lipson. manufacturability instructor's permission. Fundamentals of sus- Prerequisite(s): Basic programming experience in 3 pts. Lect: 3. Professor Walker. tainable design and manufacturing, metrics of any language. Fundamental and advanced topics Prerequisite(s): Manufacturing process, computer sustainability, analytical tools, principles of life in evolutionary algorithms and their application graphics, engineering design, mechanical design. cycle assessment, manufacturing tools, processes to open-ended optimization and computational General review of product development process; and systems energy assessment and minimiza- design. Covers genetic algorithms, genetic pro- market analysis and product system design; tion in manufacturing, sustainable manufacturing gramming, and evolutionary strategies, as well as principles of design for manufacturing; strategy automation, sustainable manufacturing systems, governing dynamic of coevolution and symbiosis. for material selection and manufacturing process remanufacturing, recycling and reuse. Includes discussions of problem representations choice; component design for machining; casting; and applications to design problems in a variety molding; sheet metal working and inspection; BMME E4702x Advanced musculoskeletal of domains including software, electronics, and general assembly processes; product design for biomechanics mechanics. manual assembly; design for robotic and auto- 3 pts. Lect: 3. Not offered in 2021–2022. matic assembly; case studies of product design Advanced analysis and modeling of the mus- MECE E4520x or y Data science for and improvement. culoskeletal system. Topics include advanced mechanical systems concepts of 3D segmental kinematics, musculo- 3 pts. Lect: 3. Professor Browne. MECE E4606y Digital manufacturing skeletal dynamics, experimental measurements Prerequisite(s): Knowledge of basic computer 3 pts. Lect: 3. Professor Lipson. of joints kinematics and anatomy, modeling of programming (e.g., Java, Matlab, Python) or Prerequisite(s): Basic programming in any lan- muscles and locomotion, multibody joint model- instructor's permission. Introduction to practical guage. Additive manufacturing processes, CNC, ing, introduction to musculoskeletal surgical application of data science, machine learning, Sheet cutting processes, Numerical control, simulations. and artificial intelligence and their application Generative and algorithmic design. Social, eco- in Mechanical Engineering. Review of relevant nomic, legal, and business implications. Course MEBM E4703x Molecular mechanics in programming tools necessary for applying data involves both theoretical exercises and a hands- biology science is provided, as well as detailed review on project. 3 pts. Lect: 3. Not offered in 2021–2022. of data infrastructure and database construction Prerequisite(s): ENME E3105, APMA E2101, or for data science. A series of industry case studies instructor’s permission. Mechanical understanding from experts in the field of data science will be of biological structures including proteins, DNA presented. and RNA in cells and tissues. Force response of proteins and DNA, mechanics of membranes,

ENGINEERING 2021–2022 200 biophysics of molecular motors, mechanics of MECE E4990x or y Special topics in Hands-on case studies in computational fluid protein-protein interactions. Introduction to mechanical engineering dynamics, including steady and transient flows, modeling and simulation techniques, and modern 3 pts. Lect: 3. Instructor to be announced. heat and mass transfer, turbulence, compressible biophysical techniques such as single molecule Prerequisite(s): Permission of the instructor. Topics flow and multiphase flow. Identifying assump- FRET, optical traps, AFM, and superresolution and Instructors change from year to year. For tions, computational domain selection, model imaging, for understanding molecular mechanics advanced undergraduate students and graduate creation and setup, boundary conditions, choice and dynamics. students in engineering, physical sciences, and of convergence criteria, visualization and inter- other fields. pretation of computed results. Taught in the MEBM E4710x or y Morphogenesis: shape and Mechanical Engineering Computer Laboratory structure in biological materials MECE E4998x and y M.S. projects in with Computational Fluid Dynamics software. 3 pts. Lect: 3. Not offered in 2021–2022. mechanical engineering Prerequisite(s): Courses in mechanics, thermody- 1–3 pts. Members of the faculty. MECE E6105y Transport phenomena in the namics, and ordinary differential equations at the Prerequisite(s): Instructor's permission. Master's presence of interfaces undergraduate level or instructor's permission. level independent project involving theoretical, 3 pts. Lect: 3. Not offered in 2021–2022. Introduction to how shape and structure are gen- computational, experimental, or engineer- Prerequisite(s): MECE E3301 Thermodynamics erated in biological materials using engineering ing design work. May be repeated, subject to and MECE E3311 Heat transfer; MECE E4100 approach emphasizing application of fundamental Master's Program guidelines. Students must sub- Mechanics of fluids, or equivalent or instructor’s physical concepts to a diverse set of problems. mit both a project outline prior to registration and permission; CHEE E4252 Introduction to surface Mechanisms of pattern formation, self-assembly, a final project write-up at the end of the semester. and colloid chemistry, or the equivalent, or the and self-organization in biological materials, instructor’s permission. Surface energy and capil- including intracellular structures, cells, tissues, MECE E4999x and y Fieldwork lary phenomena. Wetting and spreading of liquids, and developing embryos. Structure, mechanical 1 pt. Professor Lipson. wetting line pinning and hysteresis, dynamics of properties, and dynamic behavior of these materi- Prerequisite(s): Instructor’s written permission. wetting. Surfactants. Bubbles: nucleation, stabil- als. Discussion of experimental approaches and Only for ME graduate students who need relevant ity, dynamics, microstreaming. Jets and Drops: modeling. Course uses textbook materials as well off-campus work experience as part of their generation, dynamics, stability and impact with as collection of research papers. program of study as determined by the instruc- surfaces. Measurement of transport phenomena tor. Written application must be made prior to involving interfaces. Interfacial transport phe- MEIE E4810y Introduction to human registration outlining proposed study program. nomena involving thermal, chemical or electrical spaceflight Final reports required. May not be taken for gradients. Applications in microfluidic systems. 3 pts. Lect: 3. Professor Massimino. pass/fail credit or audited. International students Prerequisite(s): Department permission and must consult with the International Students and MECE E6106x Finite element method for fluid knowledge of MATLAB or equivalent. Introduction Scholars Office. flow and fluid-structure interactions to human spaceflight from a systems engineer- 3 pts. Lect: 3. Professor Vedula. ing perspective. Historical and current space MECE E6100x Advanced mechanics of fluids Prerequisite(s): MECE E4100 or E6100, ENME programs and spacecraft. Motivation, cost, and 3 pts. Lect: 3. Professor Ateshian. E4332, or equivalents, or instructor's permission rationale for human space exploration. Overview Prerequisite(s): MATH UN2030 and MECE E3100. and high-level programming language (Fortran, of space environment needed to sustain human Eulerian and Lagrangian descriptions of motion. C, C++, Python, MATLAB, etc). Solving convection- life and health, including physiological and psy- Stress and strain rate tensors, vorticity, integral dominated phenomena using finite element chological concerns in space habitat. Astronaut and differential equations of mass, momentum, method (FEM), including convection-diffusion selection and training processes, spacewalking, and energy conservation. Potential flow. equation, Navier-Stokes, equation for incompress- robotics, mission operations, and future program MECE E6102x or y Computational heat ible viscous flows, and nonlinear fluid-structure directions. Systems integration for successful transfer and fluid flow interactions (FSI). Foundational concepts of FEM operation of a spacecraft. Highlights from cur- 3 pts. Lect: 3. Professor Demetriou. include function spaces, strong and weak forms, rent events and space research, Space Shuttle, Prerequisite(s): MECE E3100 and E3311. Galerkin FEM, isoparametric discretization, sta- Hubble Space Telescope, and International Space Mathematical description of pertinent physical bility analysis, and error estimates. Mixed FEM Station (ISS). Includes a design project to assist phenomena. Basics of finite-difference methods for Stokes flow, incompressibility and inf-sup International Space Station astronauts. of discretization, explicit and implicit schemes, conditions. Stabilization approaches, including grid sizes, stability, and convergence. Solution of residue-based variational multiscale methods. MECE E4811x Aerospace human factors Arbitrary Lagrangian-Eulerian (ALE) formulation engineering algebraic equations, relaxation. Heat conduction. Incompressible fluid flow, stream function-vorticity for nonlinear FSI, and selected advanced topics of 3 pts. Lect: 2.5. Professor Massimino. research interest. Prerequisite(s): Instructor's permission. formulation. Forced and natural convection. Use Engineering fundamentals and experimental of primitive variables, turbulence modeling, and MECE E6137x or y Nanoscale actuation and methods of human factors design and evalua- coordinate transformations. sensing tion for spacecraft which incorporate human- MECE E6103x Compressible flow 3 pts. Lect: 3. Professor Schuck. in-the-loop control. Develop understanding of 3 pts. Lect: 3. Not offered in 2021–2022. Prerequisite(s): PHYS UN1402 or UN1602 or human factors specific to spacecraft design with Prerequisite(s): APMA E4200, MECE E3100 and equivalent, or instructor's permission. Interaction human-in-the-loop control. Design of human fac- E3301. Fundamental analysis of compressible of light with nanoscale materials and structures tors experiments utilizing task analysis and user flows and its applications for various sonic/ for purpose of inducing movement and detect- testing with quantitative evaluation metrics to supersonic elements including supersonic airfoils/ ing small changes in strain, temperature, and develop a sate and high-performing operational projectiles, nozzles, and shock tubes. Steady chemistry within local environments. Methods for space system. Human-centered design, functional and unsteady shock/expansion waves, oblique concentrating and manipulating light at length allocation and automation, human sensory perfor- shock waves. Shock reflections, methods of scales below the diffraction limit. Plasmonics and mance in the space environment, task analysis, characteristic. metamaterials, as well as excitons, phonos, and human factors experimental methods and statis- polaritons and their advantages for mechanical tics, space vehicle displays and controls, situation MECE E6104x Case studies in computational and chemical sensing, and controlling displace- awareness, workload, usability, manual piloting fluid dynamics ment at nanometer length scales. Applications and handling qualities, human error analysis and 3 pts. Lect: 3. Professor Bilson. to nanophotonic devices and recently published prevention, and anthropometrics. Prerequisite(s): APAM E4200 and MECE E6100. progress in nanomechanics and related fields. Corequisites: APAM E4300 and MECE E4400.

ENGINEERING 2021–2022 MECE E6200y Turbulence MECE E6424x Vibrations in machines, I numerical methods for solution. Some applica- 201 3 pts. Lect: 3. Not offered in 2021–2022. 3 pts. Lect: 3. Instructor to be announced. tions discussed include minimum energy subway Prerequisite(s): MECE E6100. Introductory con- Prerequisite(s): MECE E3401. Review of vibration operation (our solution saved 11% in tests on the cepts and statistical description. Kinematics of analysis of systems and mechanisms with one Flushing Line, and the method was adopted by random velocity fields, dynamics of vorticity, and degree of freedom. Natural frequencies. Forced the transit authority, saving many millions of dol- scalar quantities. Transport processes in a turbu- vibrations. Effects of dry and viscous friction. lars per year), minimum time robot optimal control lent medium. Turbulent shear flows: deterministic Energy methods of Rayleigh and Ritz. Suppression allowing one to run assembly lines faster for and random structures. Experimental techniques, and elimination of vibration. Vibration isolation. increased productivity. prediction methods, and simulation. Measuring instruments. Critical speeds in machin- ery. Synchronous whirl. Half-frequency whirl. MECE E6614x or y Advanced topics in MEBM E6310x-E6311y Mixture theories for Influence of bearing characteristics on critical robotics and mechanism synthesis biological tissues, I and II speeds. Effect of gyroscopic moments. Systems 3 pts. Lect: 3. Professor Agrawal. 3 pts. Lect: 3. Not offered in 2021–2022. with multiple degrees of freedom. Dynamic vibra- Prerequisite(s): APMA E2101, E3101, MECE E4602 Prerequisite(s): MECE E6422 and APMA E4200 or tion absorbers. Self-tuning absorbers of pendulum (or COMS W4733). Recommended: MECE E3401 or equivalent. Development of governing equations and roller types. Lagrangian equations of motion instructor’s permission. Kinematic modeling meth- for mixtures with solid matrix, interstitial fluid, as applied to vibrating systems. General equa- ods for serial, parallel, redundant, wire-actuated and ion constituents. Formulation of constitu- tions for transverse critical speeds of shafts. robots and multifingered hands with discussion tive models for biological tissues. Linear and Surging of helical springs. of open research problems. Introduction to screw nonlinear models of fibrillar and viscoelastic theory and line geometry tools for kinematics. porous matrices. Solutions to special problems, MEEM E6432y Small-scale mechanical Applications of homotopy continuation methods such as confined and unconfined compression, behavior and symbolic-numerical methods for direct kine- permeation, indentation and contact, and swelling 3 pts. Lect: 3. Not offered in 2021–2022. matics of parallel robots and synthesis of mecha- experiments. Prerequisite(s): ENME E3113 or equivalent; APMA nisms. Course uses textbook materials as well as E4200 or equivalent. Mechanics of small-scale a collection of recent research papers. MECE E6313x Advanced heat transfer materials and structures require nonlinear kine- 3 pts. Lect: 3. Professor Narayanaswamy. matics and/or nonlinear stress vs. strain constitu- MECE E6615x or y Robotic manipulation: Prerequisite(s): MECE E3311. Corequisites: MECE tive relations to predict mechanical behavior. sensing, planning, design, and execution E6100. Application of analytical techniques to the Topics include variational calculus, deformation 3 pts. Lect: 3. Professor Ciocarlie. solution of multidimensional steady and transient and vibration of beam, strings, plates, and mem- Prerequisite(s): MECE E4602 or COMS W4733. problems in heat conduction and convection. branes; fracture, delamination, bulging, buckling Theory and mechanisms of robotic manipulation, Lumped, integral, and differential formulations. of thin films, among others. Thermodynamics of from sensor data, reasoning, and planning to Topics include use of sources and sinks, laminar/ solids will be reviewed to provide the basis for a implementation and execution. Grasp quality mea- turbulent forced convection, and natural convec- detailed discussion of nonlinear elastic behavior sures and optimization; planning and execution tion in internal and external geometries. as well as the study of the equilibrium and stabil- for manipulation primitives; sensor modalities: ity of surfaces. vision, touch, and proprioception; simulation for MECE E6320x or y Multiscale phenomena in manipulation planning; design of robot manipula- gases EEME E6601x Introduction to control theory tors. Grading based on a combination of class 3 pts. Lect: 3. Not offered in 2021–2022. 3 pts. Lect: 3. Professor Longman. presentations of novel research results in the Prerequisite(s): Knowledge of advanced thermo- Prerequisite(s): MATH UN2030. A graduate-level field, participation in discussions, and course dynamics (e.g., MECE E4302), or combustion (e.g., introduction to classical and modern feedback projects combining simulation, processing of sen- MECH E4320), or instructor's permission. Gaseous control that does not presume an undergraduate sor data, planning for manipulation, design, and phenomena from a molecular to macroscopic per- background in control. Scalar and matrix differ- implementation on real robot hands. spective. Quantum mechanics, statistical thermo- ential equation models and solutions in terms of dynamics, nonequilibrium statistical mechanics, state transition matrices. Transfer functions and MECS E6616x or y Robot learning reaction rate theories, master equation, relaxation transfer function matrices, block diagram manipu- 3 pts. Lect: 3. Professor Ciocarlie. processes, kinetic theory, equations of state, lations, closed loop response. Proportional, rate, Prerequisite(s): MECE E4602 or MECS E4603 transport theories, and kinetic-transport equa- and integral controllers, and compensators. or COMS W4733. Robots using machine learn- tions. Applications to combustion, aerospace gas Design by root locus and frequency response. ing to achieve high performance in unscripted dynamics, and high-frequency sound propagation. Controllability and observability. Luenberger situations. Dimensionality reduction, classifica- tion, and regression problems in robotics. Deep MECE E6400y Advanced machine dynamics observers, pole placement, and linear-quadratic cost controllers. Learning: Convolutional Neural Networks for 3 pts. Lect: 3. Professor Chbat. robot vision, Recurrent Neural Networks, and Prerequisite(s): MECE E3401. Review of classi- EEME E6602y Modern control theory sensorimotor robot control using neural networks. cal dynamics, including Lagrange’s equations. 3 pts. Lect: 3. Not offered in 2021–2022. Model Predictive Control using learned dynam- Analysis of dynamic response of high-speed Prerequisite(s): EEME E6601 or E4601 or ELEN ics models for legged robots and manipulators. machine elements and systems, including mass- E6201, or instructor’s permission. Singular value Reinforcement Learning in robotics: model-based spring systems, cam-follower systems, and gear- decomposition. ARX model and state space model and model-free methods, deep reinforcement ing; shock isolation; introduction to gyrodynamics. system identification. Recursive least squares learning, sensorimotor control using reinforce- MECE E6422x–E6423y Introduction to the filters and Kalman filters. LQR, Hlinear robust con- ment learning. trol, predictive control, adaptive control. Liapunov theory of elasticity, I and II MECE E6617y Advanced kinematics, dynamics 3 pts. Lect: 3. Professor Myers. and Popov stability. Nonlinear adaptive control, nonlinear robust control, sliding mode control. and control in robotics Corequisite: APMA E4200. Analysis of stress 3 pts. Lect: 3. Professor Agrawal. and strain. Formulation of the problem of elastic EEME E6610y Optimal control theory Prerequisite(s): Course on linear and/or nonlinear equilibrium. Torsion and flexure of prismatic bars. 3 pts. Lect: 3. Instructor to be announced. control theory, Introduction to Robotics, or instruc- Problems in stress concentration, rotating disks, Prerequisite(s): EEME E6601 or E4601 or instruc- tor's permission. Advanced topics in robotics shrink fits, and curved beams; pressure vessels, tor’s permission. Covers topics in calculus of vari- using fundamentals of kinematics, dynamics, and contact and impact of elastic bodies, thermal ations, Pontryagin maximum principle, quadratic control. Topics include: characterization of orien- stresses, propagation of elastic waves. cost optimal control, predictive control, dynamic tation and angular velocity of rigid bodies, kine- programming for optimal control, Kalman filtering, matic solutions of planar mechanisms, dynamics

ENGINEERING 2021–2022 202 of closed chains and free-floating bodies, gravity Boltzmann transport equation (BTE), classical electing different topics from control theory such balancing of mechanism, dynamics and depen- and quantum size effects. Landauer formalism as learning and repetitive control, adaptive con- dence of inertia redistribution, under-actuation for transport via nanostructures. Macroscopic trol, system identification, Kalman filtering, etc. systems, feedback linearization of SISO systems, constitutive equations from BTE. Application to feedback linearization of MIMO systems, design electronics cooling, thermoelectric and thermo- MECE E8990x and y Special topics in of under-actuated open-chain robots, parallel- photovoltaic devices, and energy conversion. mechanical engineering actuated robots. 3 pts. Lect: 3. Instructor to be announced. MECE E8020x or E8021y Master’s thesis Prerequisite(s): Instructor’s permission. May be MECE E6620x or y Applied signal recognition 3–6 pts. Members of the faculty. taken for credit more than once. The instructor and classification Research in an area of mechanical engineering from the Mechanical Engineering Department and 3 pts. Lect: 3. Professor Beigi. culminating in a verbal presentation and a written the topics covered will vary from year to year. Prerequisite(s): MATH UN2030, APMA E3101, thesis document approved by the thesis adviser. Intended for students with graduate standing in knowledge of a programming language, or Must obtain permission from a thesis adviser to Mechanical Engineering and other engineering permission of instructor. Applied recognition and enroll. Recommended enrollment for two terms, and applied sciences. classification of signals using a selection of tools one of which can be the summer. A maximum borrowed from different disciplines. Applications of 6 points of master’s thesis may count toward MECE E9000x-E9001y and E9002s Graduate include human biometrics, imaging, geophysics, an M.S. degree, and additional research points research and study machinery, electronics, networking, languages, cannot be counted. On completion of all master’s 1–3 pts. Members of the faculty. communications, and finance. Practical algorithms thesis credits, the thesis adviser will assign a Theoretical or experimental study or research in are covered in signal generation, modeling, fea- single grade. Students must use a department- graduate areas in mechanical engineering and ture extraction, metrics for comparison and classi- recommended format for thesis writing. engineering science. fication, parameter estimation, supervised, unsu- MECE E8100y Advanced topics in fluid MECE E9500x and y Graduate seminar pervised and hierarchical clustering and learning, 0 pts. Pass/fail only. Professor Schuck. optimization, scaling and alignment, signals as mechanics 3 pts. Lect: 3. Not offered in 2021–2022. All doctoral students are required to complete codes emitted from natural sources, information, successfully four semesters of the mechanical Undergraduate Minors and extremely large-scale search techniques. Prerequisite(s): MECE E6100. May be taken more than once, since its content has minimal overlap engineering seminar MECE E9500. MECE E6700x Carbon nanotube science and between consecutive years. Selected topics from MECE E9800x and y Doctoral research technology viscous flow, turbulence, compressible flow, instruction 3 pts. Lect: 3. Professor Schuck. rarefied gas dynamics, computational methods, 3, 6, 9, or 12 pts. Members of the faculty. Prerequisite(s): Knowledge of introductory solid and dynamical systems theory, non-Newtonian A candidate for the Eng.Sc.D. degree in mechani- state physics (e.g., PHYS GU4018, APPH E6081, fluids, etc. cal engineering must register for 12 points of doc- or MSAE E3103) or instructor’s permission. Basic toral research instruction. Registration in MECE science of solid state systems. Crystal structure, MECE E8501y Advanced continuum biomechanics E9800 may not be used to satisfy the minimum electronic and phonon band structures of nano- residence requirement for the degree. tubes. Synthesis of nanotubes and other nanoma- 3 pts. Lect: 2. Professor Myers. terials. Experimental determination of nanotube Prerequisite(s): Instructor’s permission. The essen- MECE E9900x and y Doctoral dissertation structures and techniques for nanoscale imaging. tials of finite deformation theory of solids and 0 pts. Members of the faculty. Theory and measurement of mechanical, thermal, fluids needed to describe mechanical behavior A candidate for the doctorate may be required to and electronic properties of nanotubes and nano- of biological tissue: kinematics of finite deforma- register for this course every term after his/her materials. Nanofabrication and nanoelectronic tions, balance laws, principle of material objec- coursework has been completed and until the dis- devices. Applications of nanotubes. tivity, theory of constitutive equations, concept sertation has been accepted. of simple solids and simple fluids, approximate MECE E6710y Nanofabrication laboratory constitutive equations, some boundary-value 3 pts. Lect: 3. Instructor to be announced. problems. Topics include one- and two-point Prerequisite(s): ELEN E6945 or instructor’s permis- tensor components with respect to generalized sion. Laboratory in techniques for fabrication at coordinates; finite deformation tensors, such as the nanometer scale. Electron-beam lithography. right and left Cauchy-Green tensors; rate of defor- Plasma etching and 3D nanofabrication. Thin film mation tensors, such as Rivlin-Ericksen tensors; deposition. Self-assembly and “bottom up” nano- various forms of objective time derivatives, such fabrication. Fabrication of and testing of complete as corotational and convected derivatives of ten- nanodevices. A lab fee of $300 is required. sors; viscometric flows of simple fluids; examples of rate and integral type of constitutive equations. MECE E6720x Nano/microscale thermal transport process EEME E8601y Advanced topics in control 3 pts. Lect: 3. Not offered in 2021–2022. theory Nano- and microscale origins of thermal transport 3 pts. Lect: 3. Not offered in 2021–2022. phenomena by molecules, electrons, phonons, Prerequisite(s): EEME E6601 and E4601 or instruc- and photons. Quantum mechanics and statistical tor’s permission. May be taken more than once, physics. Density of states. Kinetic theory of gases. since the content changes from year to year,

ENGINEERING 2021–2022 Undergraduate Minors 204 UNDERGRADUATE MINORS

ndergraduate minors are Associate Dean of Undergraduate or any other course designated APMA, MATH, designed to allow engineering Student Affairs. STAT, IEOR, or COMS that is approved by the and applied science students applied mathematics program adviser. Uto study, to a limited extent, a discipline MINOR IN ANTHROPOLOGY other than their major. Besides MINOR IN APPLIED PHYSICS engineering minors offered by Columbia 1. ANTH UN1002: The interpretation of culture (3) Prospective students should consult the Engineering departments, liberal arts or ANTH UN1008: The rise of civilization (3) first- and second-year requirements for minors are also available. Note: UN1002 serves as a preview to applied physics majors to ensure that A minor requires at least 15 points of sociocultural anthropology, while UN1008 prerequisites for the applied physics credit, and no more than one course can serves as a preview to archaeology. minor are satisfied in the first two years. Coursework counting toward the be taken outside of Columbia or met 2–5. Any four courses in the Anthropology through AP or IB credit. This includes department, in ethnomusicology, or taught applied physics minor may not include courses taken through study abroad. by an Anthropology instructor, regardless of advanced placement credits. In Engineering departments with more department. No distribution requirement. 1. APPH E4901: Problems in applied physics (1) than one major program, a minor in the 2. APPH E3200: Mechanics (3) second program may be permitted, if MINOR IN APPLIED approved by the department. 3. APPH E3100: Intro to quantum mechanics (3) MATHEMATICS No substitutions or changes of any Prospective students should consult 4. APPH E3300: Applied electromagnetism (3) kind from the approved minors are the first- and second-year requirements 5. MSAE E3111: Thermodynamics, kinetic theory, permitted (see lists below). No appeal for applied mathematics majors to and statistical mechanics (3) for changes will be granted. Please note ensure that prerequisites for the applied that the same courses may not be used 6. Two of the following courses mathematics minor are satisfied in the Intro to nuclear science (3) to satisfy the requirements of more than APPH E4010: first two years. APPH E4100: Quantum physics of matter (3) one minor. No courses taken for pass/ Coursework counting toward the APPH E4110: Modern optics (3) fail may be counted for a minor. Minimum applied mathematics minor may not APPH E4112: Laser physics (3) GPA for the minor is 2.0. Departments include advanced placement credits. APPH E4300: Applied electrodynamics (3) outside the Engineering School have no APPH E4301: Intro to plasma physics (3) Any substitutions for the courses listed responsibility for nonengineering minors below require the approval of the offered by Engineering. applied mathematics program adviser. MINOR IN ARCHITECTURE For a student to receive credit for a course taken while studying abroad, 1. APMA E3101: Linear algebra (3) 1. Studio: One of the following courses the department offering the minor must or COMS W3251: Comp. linear algebra (3) ARCH UN1020: Intro to architectural design or MATH UN2010: Linear algebra (3) approve the course in writing, ahead of and visual culture (3) ARCH UN3101: Abstraction (4) the student’s study abroad. 2. APMA E3102: Partial differential equations (3) ARCH UN3103: Perception (4) Students must expect a course load or MATH UN3028: Partial differential equations that is heavier than usual. In addition, (3) 2–4. History/theory courses (see Note below) unforeseen course scheduling changes, 3–5. Three of the following courses: 5. Elective: must be either an approved second problems, and conflicts may occur. The APMA E4300: Intro to numerical methods (3) design studio or an additional history/theory School cannot guarantee a satisfactory APMA E4204: Func of complex variable (3) course APMA E4101: Intro to dynamical systems (3) completion of the minor. Note: A list of the approved history/theory MATH UN2500: Analysis and optimization (3) courses is available at the departmental Students interested in establishing STAT GU4203: Probability theory (3) a new minor should consult with the STAT GR4204: Statistical inference (3) office each semester.

ENGINEERING 2021–2022 MINOR IN ART HISTORY 2. ENME E3105: Mechanics (4) 4. COMS W3203: Discrete mathematics (4) 205 1–7. Seven courses in art history, covering 3. ENME E3113: Mechanics of solids (3) 5. COMS W3261: Comp science theory (3) four of the following areas: (a) ancient 4–6. Electives: Three of the following courses: 6. CSEE W3827: Fund of computer systems (3) Mediterranean, (b) medieval Europe, CIEN E3000: The art of structural design (3) or a 4000-level COMS technical elective ENME E3161: Fluid mechanics (4) (c) Renaissance and baroque, (d) 18th, 7. APMA E2101 (or E3101): Intro to applied ENME E3114: Exp mechanics of materials (4) 19th, and 20th century, and (e) non- mathematics (Applied math I: linear algebra) (3) ENME E3332: A first course in finite elements or MATH UN2010 (or E2020): Linear Western (3) algebra (3) MECE E3414: Adv strength of materials (3) or COMS W3251: Computational linear MINOR IN BIOMEDICAL CIEN E3125: Structural design (3) algebra (4) ENGINEERING CIEN E4241: Geotech eng fundamentals (3) or STAT GU4001( or SIEO W3600): Intro to CIEE E3250: Hydrosystems engineering (3) The Biomedical Engineering program probability and statistics (3) CIEE E4163: Environ eng: wastewater (3) offers a minor that consists of the CIEN E3129: Project mgmt for construction (3) following six courses. Participation in the CIEN E4131: Prin of construction tech (3) MINOR IN DANCE minor is subject to the approval of the The dance minor consists of five major program adviser. MINOR IN COMPUTER SCIENCE 3-point courses. Please note that no Students who pass the Computer Science performance/choreography courses 1. BIOL UN2005: Introduction to biology, I (3) Advanced Placement Exam A with a 4 below count toward the nontech requirement for Engineering students. 2. BIOL UN2006: Introduction to biology, II (3) or 5 will receive 3 points and exemption from COMS W1004. Taking COMS W1007 1–2. History/criticism: Two of the following: 3. BMEN E3010: Biomedical engineering, I (3) is recommended but not required for DNCE BC2565: World dance history (3) 4. BMEN E3020: Biomedical engineering, II (3) those students exempt from COMS DNCE BC2570: Dance in New York City (3) DNCE BC2575: Choreography for the 5. BMEN E4001: Quantitative physiology, I (3) W1004. Participation in the minor is subject American musical (3) to the approval of the major program 6. BMEN E4002: Quantitative physiology, II (3) DNCE BC3000: From the page to the adviser. For further information, please dance stage (3) see the QuickGuide at cs.columbia.edu/ DNCE BC3001: Western theatrical dance MINOR IN CHEMICAL education/undergrad/seasguide. from the Renaissance to the 1960s (3) ENGINEERING Beginning with the class of 2023, the DNCE BC3200: Dance in film (3) Of the six courses required, at least CS core requirements will change as DNCE BC3567: Dance of India (3) three must have the CHEN, CHEE, or noted below. The following are required DNCE BC3570: Latin American and Caribbean dance (3) CHAP designator: courses toward the CS Core for the DNCE BC3576: Dance criticism (3) 1. CHEN E2100: Intro to chemical engineering (3) class of 2023 and beyond: DNCE BC3577: Performing the political (3) DNCE BC3578: Traditions of African- 2. CHEE E3010: Prin of chemical engineering 1. COMS W1004: Intro to computer science and American dance (3) thermodynamics (3) programming in Java (3) or MSAE E3111: Thermodynamics, kinetic or COMS W1007: Honors intro to comp sci (3) 3–4. Performance/choreography: Two of the theory, and statistical mechanics (3) 2. COMS W3134: Data structures in Java (3) following: ​ or MECE E3301: Thermodynamics (3) or COMS W3137: Honors data structures and DNCE BC2563: Dance composition: form or BMEN E4210: Thermodynamics of biological algorithms (4) (3) systems (3) DNCE BC2564: Dance composition: content 3. COMS W3157: Advanced programming (4) (3) 3. CHEN E3110: Transport phenomena, I (3) DNCE BC2567: Music for dance (3) or EAEE E4900: Applied transport and 4. COMS W3203: Discrete mathematics (4) DNCE BC2580: Tap as an American art chemical rate phenomena (3) 5. COMS W3251: Computational linear algebra form (3) or MECE E3100: Intro to mech of fluids (3) (4) DNCE BC3565: Composition: collaboration or ENME E3161: Fluid mechanics (4) and the creative process (3) or BMEN E3220: Fluid biomechanics (4) 6. COMS W3261: Comp science theory (3) DNCE BC3601-3604: Rehearsal and 4. CHEN E4230: Reaction kinetics and 7. CSEE W3827: Fund of computer systems (3) performance in dance (1–3) reactor design (3) or a 4000-level COMS technical elective 5. One elective 5–6. Two of the following courses: The following are required courses Any 3000-level or higher CHEN or cross-listed MINOR IN EARTH AND (CHAP, BMCH, CHEE, CHBM, CHOR, MECH) towards the CS Core for the class of ENVIRONMENTAL ENGINEERING course 2022 and earlier. 1. COMS W1004: Intro to computer science and 1–3. Three of the following courses: programming in Java (3) EAEE E3103: Energy, minerals, and mat syst (3) MINOR IN CIVIL or COMS W1007: Honors intro to comp sci (3) CIEE E3255: Environmental control and ENGINEERING pollution reduction systems (3) Data structures in Java (3) 2. COMS W3134: EAEE E4001: Industrial ecology of earth res (3) 1. CIEN E3121: Structural analysis (3) Honors data structures and or COMS W3137: EAEE E4003: Intro to aquatic chemistry (3) or ENME E3161: Fluid mechanics (4) algorithms (4) EAEE E4004: Physical processing and recovery or MECE E3100: Intro to mech of fluids (3) 3. COMS W3157: Advanced programming (4) of solids (3) EAEE E4006: Field methods for environ eng (3)

ENGINEERING 2021–2022 206 EAEE E4009: GIS for resource, environment, 5–6. Electives: Two of the following courses: recommended that students take UN3412 and infrastructure management (3) ECON UN2105: American economy (3) in the semester following the statistics EAEE E4150: Air pollution prevention and ECON UN2257: Global economy (3) course. control (3) ECON UN3025: Financial economics (3) • Some courses done as part of the EAEE E4160: Solids and hazardous waste ECON UN3265: Econ of money and economics minor may count toward management (3) banking (3) fulfilling the School’s nontechnical EAEE E4200: Prod of inorganic materials (3) ECON GU4020: Econ of uncertainty and requirements. However, other courses, EAEE E4257: Environ data analysis and info (3) such as UN3412: Intro to econometrics, modeling (3) ECON GU4211: Advanced microeconomics (3) may not be applied toward satisfaction EAEE E4361: Econ of earth res industries (3) ECON GU4213: Advanced macroeconomics (3) of the nontechnical course requirements. EACH E4560: Particle technology (3) ECON GU4228: Urban economics (3) To determine which economic class ECON GU4230: Economics of NYC (3) can count toward the nontech elective 4–6. Three of the following courses: ECON GU4235: Historical foundations of requirement, please consult the nontech CHEE E3010: Prin of chemical engineering modern economics (3) elective section of this bulletin for further thermodynamics (3) ECON GU4251: Industrial organization (3) details. CHEE E3110: Transport phenomena, I (3) ECON GU4260: Market design (3) • Students with AP credit for economics CIEN E3141: Soil mechanics (3) ECON GU4280: Corporate finance (3) and an exemption for UN1105 may use CIEE E3250: Hydrosystems engineering (3) ECON GU4301: Economic growth and the credit toward the minor. ECIA W4100: Mgmt and dev of water systems development (3) • Transfer or study abroad credits may not (3) CIEE E4163: Environ eng: wastewater (3) ECON GU4321: Economic development (3) be applied to fulfill the requirements of EAEE E4190: Photovoltaic systems eng (3) ECON GU4370: Political economy (3) MECE E4211: Energy: sources and conv (3) the economics minor. ECON GU4400: Labor economics (3) CIEN E4250: Waste contain design and prac (3) ECON GU4412: Advanced econometrics (3) CHEE E4252: Intro to surface and colloid MINOR IN ELECTRICAL ECON GU4415: Game theory (3) chem (3) ECON GU4438: Economics of race in the ENGINEERING CIEE E4252: Environmental engineering (3) U.S. (3) CIEE E4257: Groundwater contaminant 1. ELEN E1201: Intro to electrical eng (3.5) ECON GU4465: Public economics (3) transport and remediation (3) (May be replaced by a similar course or roughly ECON GU4480: Gender and applied CHEN E4410: Environmental control equivalent experience) economics (3) technology (3) ECON GU4500: International trade (3) 2. ELEN E3201: Circuit analysis (3.5) ECON GU4505: Int’l monetary theory and 3. CSEE W3827: Fund of computer systems (3) MINOR IN EAST ASIAN STUDIES policy (3) 1–5. Any two of the survey courses on ECON GU4615: Law and economics (3) 4. ELEN E3081 and ELEN E3082: Chinese, Japanese, Korean, or Tibetan ECON GU4625: Economics of the Electrical engineering labs (2) civilization (ASCE UN1359, UN1361, environment (3) 5. ELEN E3801: Signals and systems (3.5) UN1363, UN1365), plus three elective ECON GU4700: Financial crises (3) courses dealing with East Asia. The ECON GU4750: Globalization and its risks (3) 6. ELEN E3106: Solid-state dev and mat (3.5) elective courses may be taken in ECON GU4850: Cognitive mechanisms and or ELEN E3401: Electromagnetics (4) departments outside of East Asian economic behavior (4) Languages and Cultures. The minor does Note: Not available to computer not include a language requirement. engineering majors However, one semester of an East Asian Note: Electives may be taken only after the completion of both UN3211 and language class may be used to fulfill one MINOR IN ENGINEERING of the three electives, as long as at least UN3213, with the exception of UN2257 two semesters of that language have and UN2105, which may be taken after MECHANICS completion of UN1105. Some of the been taken. Placement exams may not 1. ENME E3105: Mechanics (4) be used in place of these courses. elective courses listed above have additional prerequisites. Courses may 2. ENME E3113: Mechanics of solids (3) be taken only after the completion of all 3. ENME E3161: Fluid mechanics (4) MINOR IN ECONOMICS prerequisites. Please see the Columbia or MECE E3100: Intro to mech of fluids (3) 1. ECON UN1105: Principles of economics (4) College bulletin for course descriptions and complete lists of prerequisites. 4–6. Electives: Three of the following: 2. ECON UN3211: Intermediate microeconomics ENME E3106: Dynamics and vibrations (3) (4) 7. Statistics: One of the following three ENME E3114: Exp mechanics of materials (4) 3. ECON UN3213: Intermediate macroeconomics probability and statistics options (course or or MECE E3414: Adv strength of materials (3) (4) sequence): CIEN E3121: Structural analysis (3) a. SIEO W3600 (or STAT GU4001): Intro to ENME E4202: Advanced mechanics (3) 4. ECON UN3412: Introduction to probability and statistics ENME E4113: Advanced mechanics of solids (3) econometrics (4) b. IEOR E3658: Probability and ENME E4114: Mech of fracture and fatigue (3) Note: UN1105 is a prerequisite for UN3211, E4307: Applied statistical models ENME E4214: Theory of plates and shells (3) UN3213, and UN3412. Students must have c. STAT UN4203 (or GR5203): Intro to ENME E4215: Theory of vibrations (3) completed Calculus I before taking UN3213, probability and statistics and STAT MECE E3301: Thermodynamics (3) Calculus III before taking UN3211, and one UN4204 (or GR5204): Statistical inference of the introductory statistics courses (see Notes: list) before taking UN3412. • The statistics course must be finished before taking UN3412, and it is

ENGINEERING 2021–2022 MINOR IN ENGLISH AND 3000/4000- level German or CompLit- excluding MSAE E4301 (Materials science 207 COMPARATIVE LITERATURE German courses taught in German or laboratory). English 1–5. Any five courses in the English Department with no distribution MINOR IN MECHANICAL MINOR IN GREEK OR LATIN requirement. No speech courses, only one ENGINEERING writing course as above and excluding 1–4. A minimum of 13 points in the chosen ENGL CC1010, may be taken; total 15 language at the 1200 level or higher 1–4. Four of the following courses: points. MECE E3100: Intro to mechanics of fluids (3) 5. 3 points in ancient history of the or ENME E3161: Fluid mechanics (4) appropriate civilization or CHEN E3110: Transport phenomena, I (3) MINOR IN ENTREPRENEURSHIP or EAEE E3200: App transport and AND INNOVATION MINOR IN HISPANIC STUDIES chemical rate phenomena (3) Minimum: 15 points ENME E3105: Mechanics (4) 1. SPAN UN3300: Adv language through content ENME E3106: Dynamics and vibrations (3) 1–2. Required courses: (3) MECE E3301: Thermodynamics (3) IEOR E2261: Accounting and finance (3) or CHEE E3010: Principles of chemical and IEOR E4998: Managing technological 2. SPAN UN3330: Intro to the study of Hispanic engineering thermodynamics (3) innovation and entrepreneurship (3) cultures (3) or MSAE E3111: Thermodynamics, kinetic 3–5. Electives: Three of the following courses: 3–4. SPAN UN3349 and UN3350: Hispanic theory, and statistical mechanics (3) BIOT GU4180: Entrepreneurship in biotech (3) cultures, I and II (3, 3) ENME E3113: Mechanics of solids (3) BUSI W3021: Marketing management (3) 5. One additional 3000-level elective course MECE E3408: Comp graphics and design (3) CHEN E4020: Protection of industrial and in the Department of Latin American and MECE E3311: Heat transfer (3) intellectual property (3) Iberian Cultures MECE E3610: Materials and processes in CIEN E4136: Global entrepreneurship in civil manufacturing (3) engineering (3) Note: Please see the director of EEME E3601: Classical control systems (3) COMS W4444: Program and problem solving(3) undergraduate studies in the Department 5–6. Electives: Two additional mechanical COMS W4460: Principles of innovation in of Latin American and Iberian Cultures for engineering courses from either the above biotechnology (3) more information and to declare the minor. list or the following (not all courses in this ECON GU4280: Corporate finance (3) list are given every year): IEOR E4003: Corporate finance for engineers(3) MINOR IN HISTORY MECE E3401: Mechanics of machines (3) IEOR E4510: Project management (3) MECE E3450: Computer-aided design (3) IEOR E4550: Entrepreneurial business 1–5. Minimum 5 courses in the History Any 3-credit 4000-level courses listed in the creation for engineers (3) Department with no distribution or seminar Mechanical Engineering Bulletin can also IEOR E4560: Lean launchpad (3) requirements. Transfer or study-abroad be used to fulfill these additional course (by application only with adviser approval) credits may not be applied. requirements.

MINOR IN FRENCH MINOR IN INDUSTRIAL ENGINEERING MINOR IN MIDDLE EASTERN, 1–2. FREN UN3333: Intro to literary study I (3) SOUTH ASIAN, AND AFRICAN 1. IEOR E3658: Probability for engineers (4) and UN3334: Intro to literary study II (3) STUDIES or STAT GU4001: Intro to probability and 3–5. Three additional courses in French statistics (3) beyond satisfaction of the language 1–5. Five courses, to be chosen with the requirement 2. IEOR E3608: Foundations of optimization (3) approval of the MESAAS Director of 3. IEOR E3402: Production inventory planning Undergraduate Studies; no elementary or MINOR IN FRENCH AND and control (4) intermediate language courses may be counted. FRANCOPHONE STUDIES 4. IEOR E4003: Corporate finance for engineers(3) Required: 15 points beyond second-year French 5–6. Electives: Two IEOR courses of interest MINOR IN MUSIC 1–2. FREN UN3420 and UN3421: Intro to and approved by a faculty adviser1 French and francophone studies, I and II(3, 3) 1. MUSI UN2318-2319: Music theory, I and II (3, 3) Note: In addition to the required courses, 3–5. Three additional courses in French students majoring in operations research 2. MUSI UN1312-1313: Intro ear training (1) beyond satisfaction of the language and its concentrations (EMS or FE) minoring 3. MUSI UN2314: Ear training, I (1) requirement in industrial engineering must take three industrial engineering courses that are not 4. One of the following courses: MINOR IN GERMAN used to satisfy the requirements of their MUSI UN3128: History of Western music, I (3) major. MUSI UN3129: History of Western music, II (3) Required: 15 points beyond second-year German 1 5–6. Any two electives at the 3000 or 4000 1. GERM UN3001 or 3002: Adv German, I or II (3) Electives should be 3000-level or higher. level. See also the Engineering-approved 2. GERM UN3333: Intro to German literature (3) nontechnical electives in music (page 10). MINOR IN MATERIALS SCIENCE 3. One of the period survey courses in Notes: German literature and culture, GERM 1–5. Any five MSAE E3000 or MSAE E4000- • Students must successfully place out of UN3442, UN3443, UN3444, UN3445 level courses, excluding MSAE E3900 MUSI UN1002: Fundamentals of music (Undergraduate research), and excluding (3.0 points). 4–5. Two courses taken from any MSAE E3156, E3157 (Design project), and

ENGINEERING 2021–2022 208 • Steps 4 and 5 must be completed to fulfill I. PERCEPTION AND COGNITION EAEE E2100: Better planet by design (3) the nontechnical elective requirement for Courses numbered in the 2200s, 3200s, or CIEE E3250: Hydrosystems engineering (3) 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 of ECIA W4100: Mgmt and dev of water systems (3) Courses numbered in the 2400s, 3400s, nontechnical electives. APPH E4130: Physics of solar energy (3) or 4400s EAEE E4190: Photovoltaic systems eng and III. SOCIAL, PERSONALITY, AND ABNORMAL sustainability (3) MINOR IN OPERATIONS Courses numbered in the 2600s, 3600s, MECE E4211: Energy sources and conversion (3) RESEARCH or 4600s MECE E4312: Solar thermal engineering (3) 1. I EOR E3658: Probability for engineers (4) EAEE E4257: Environmental data analysis (3) or STAT GU4001: Intro to probability and MINOR IN RELIGION MECE E4314: Dynamics of green buildings (3) 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 applications (3) 5. One of the following courses: 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 (3) 1. SOCI UN1000: The social world (3) analysis (4) PLAN A4304: Intro to housing (3) 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 and control (3) is strongly recommended. Sociology; total 6 points planning (3) Economics of the Note: In addition to the required courses, ECON GU4625: students majoring in industrial engineering MINOR IN STATISTICS environment (3) 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 4. STAT UN2104: App categorical data not available, requesting approval 1–5. Any five courses in the Philosophy analysis (3) for a similar course from the groups Department with no distribution "Economics" or "Law, Policy and Human 5. STAT UN3105: Appl. statistical methods (3) requirement; total 15 points. See also Rights," respectively from the Columbia the list of exceptions under Elective 6. STAT UN3106: Applied data mining (3) College Sustainable Development course Nontechnical Courses. list 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 in POLS UN1501: Intro to comparative politics (3) Statistics, substitute for courses. Students POLS UN1601: International politics (3) may count up to two courses toward 3–5. Any three courses in the Political both the Statistics minor and another Science Department with no distribution Engineering major. requirement; total 9 points MINOR IN SUSTAINABLE ENGINEERING MINOR IN PSYCHOLOGY Total of six courses from the following Minimum: 15 points 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 2021–2022 Interdisciplinary Courses and Professional Development and Leadership Program 210 INTERDISCIPLINARY ENGINEERING COURSES

f the following courses, some across the MS programs. Focuses on the School's tion and professional development of doctoral may be requirements for vision of Engineering for Humanity in five areas: students. This course provides the academic degree programs, and others Sustainability, Health, Security, Connectedness, framework for fieldwork experience required for and Creativity. the student’s program of study. Fieldwork docu- Omay be taken as electives. See your mentation and faculty adviser approval is required departmental program of study or consult ENGI E4201s Global engineering fieldwork prior to registration. A final written report must with an adviser for more information. 1 pt. Lect: 1. be submitted. This course will count toward the Prerequisite(s): Students must be enrolled in degree program and cannot be taken for pass/ ENGI E1102x and y The art of engineering the Global Engineering Track (GET) specializa- fail credit or audited. With approval from the 4 pts. Lect: 4. Professor Vallancourt. tion. Instructor's written approval. Final reports department chair or the doctoral program direc- Core requirement for all entering SEAS students. A required. May not be audited. International stu- tor, doctoral students can register for this course bridge between the science-oriented, high school dents must consult with the International Students at most twice. In rare situations, exceptions may way of thinking and the engineering point of view. and Scholars Office. be granted by the Dean's Office to register for the Fundamental concepts of math and science are course more than twice (e.g., doctoral students reviewed and reframed in an engineering context, ENGI E4300x Design justice: human-centered funded by industrial grants who wish to perform with numerous examples of each concept drawn design and social justice 3 pts. Professors Chilton, Patton, and West. doctoral fieldwork for their corporate sponsor). from all disciplines of engineering represented at The doctoral student must be registered for this Columbia. Nontechnical issues of importance in Prerequisite(s): IEME E4200 or COMS W4170 or instructor's permission. Introduction to Human- course during the same term as the fieldwork professional engineering practice such as ethics, experience. engineering project management, and societal Centered Design and Innovation. Unpack the role impact are addressed. Lab fee: $350. of design in the market economy for an individual consumer, for a designer/developer, and for an For information on courses in other ENGI W4100y Research to revenue enterprise or other organization. Consider how divisions of the University, please consult 3 pts. Lect: 3. Professors Sia and Toubia. designing in good faith for most can lead to the bulletins of Columbia College An interschool course with Columbia Business injustice for some. Examine how to use the PROP and the Graduate School of Arts and School that trains engineering and business stu- framework of the Columbia School of Social dents to identify and pursue innovation opportuni- Work—power, race, oppression, and privilege can Sciences. ties that rely on intellectual property coming out be executed through the design process. Equip of academic research. Idea generation, market students with tools to engage in the design pro- research, product development, and financing. cess and to facilitate the engagement of others. Teams develop and present business model Explore strategies for guiding design and innova- for a technological invention. This course has tion toward more just solutions. limited enrollment by application and is open to advanced undergraduate students and graduate ENGI E4990x and y Advanced master's students. Consult with department for questions research on fulfillment of technical elective requirement. 1–6 pts. Advanced master's research for students within ENGI E4200x Global Engineering departments that offer master's research special- 3 pts. Lect 3. ization. Students may enroll for 1–6 credits per Prerequisite(s): Students must be enrolled in the semester, for a maximum of 12 credits required for Global Engineering Track (GET) specialization. the master's program. Note: open to students in Introduces students to contemporary cases in master's research only. engineering that impact the world globally and locally. Taught by Columbia Engineering faculty ENGI E8000x, y, and s Doctoral fieldwork members, approaching cases in an interdisci- 1 pts. Professor Kachani plinary manner, brings students together from Fieldwork is integral to the academic prepara-

ENGINEERING 2021–2022 PROFESSIONAL DEVELOPMENT AND LEADERSHIP 211

he Professional Development PROFESSIONAL DEVELOPMENT Doctoral Courses and Leadership (PDL) program AND LEADERSHIP STAFF ENGI E6001x and y Professional development educates students to maximize Gabriella Lilienthal, Program Manager and leadership for first year doctoral performanceT and achieve their full Jenny Mak, Executive Director students potential to become engineering Elizabeth Strauss, Director 0 pts. The PDL Instructional Team. leaders. Core sessions focus on [email protected] For first year doctoral students, emphasizing the development of skills and perspectives pdl.engineering.columbia.edu skills needed for success in orienting them to Columbia and doctoral studies, including teach- needed to compete and succeed in a ing and presentation skills (i.e., Microteaching, fast-changing technical climate. Topics PROFESSIONAL DEVELOPMENT how to grade, hold office hours, conduct recita- include professional portfolio (resume, AND LEADERSHIP CORE tions, etc.); cultivating relationships with mentors, cover letter, business writing, social faculty, and colleagues; inclusivity; managing FACULTY media presence), communication skills, your budget; wellness; research and academic Chuck Garcia: Communication leadership, ethics, life management integrity and ethics. Helio Fred Garcia: Ethics and Integrity (stress, sleep, and time management) Sophia Hyoseon Lee: English Communication E6002x and y Professional development and and more. Elective sessions include Jenny Mak: Resume leadership for second year doctoral students 0 pts. The PDL Instructional Team. effective presentations, emotional Elizabeth Strauss: Business Writing intelligence, data visualization, and For second year doctoral students, emphasizing the skills needed for continued success in the interview preparation. PROFESSIONAL DEVELOPMENT doctoral program, including presentation and M.S. students must complete the communication skills; academic writing skills; professional development and leadership AND LEADERSHIP COURSES academic conference preparation; resiliency and course, ENGI E4000, as a graduation M.S. Course project management skills. requirement. Doctoral students will be ENGI E4000x and y Professional development E6003x and y Professional development and enrolled in ENGI E6001–6004 and and leadership for engineers and applied leadership for third year doctoral students should consult their program for specific scientists 0 pts. The PDL Instructional Team. PDL requirements. Undergraduate 0 pts. The PDL Instructional Team. For third year doctoral students to facilitate students are encouraged to participate The PDL course aims to enhance and expand career exploration including teaching, presenta- in the professional development and Columbia Engineering graduate students' inter- tion and communication skills; public speaking and facilitation; CV and resume writing; and leadership program. personal, professional, and leadership skills, through five core sessions, covering (1) in-person Getting Things Done. communication skills; (2) resume; (3) business E6004x and y Professional development and writing; (4) social media and the job search; and leadership for fourth year doctoral students (5) academic and professional ethics and integrity. 0 pts. The PDL Instructional Team. ENGI E4000 also requires 5 elective sessions to For fourth year doctoral students supporting job further students' development based on their search and degree completion, including search- personal interests. Students must select at least ing for job opportunities (Academia, Industry); one life management elective and one interview interview preparation; creating an academic elective. This course is offered at the Pass/D/Fail portfolio; conducting a job talk; negotiation and grading option. mediation skills.

ENGINEERING 2021–2022 212 GRADUATE CAREER ENGLISH COMMUNICATION PLACEMENT COURSES Ryan Day, Manager M.S. Courses Jenny Mak, Executive Director Elizabeth Strauss, Director ENGI E5000x, y, and s Workplace careers.engineering.columbia.edu communication in English E5001x, y, and s Professional presentation While enrolled in a graduate program at E5002x, y, and s Professional communication Columbia Engineering you will also be coached in English E5003x, y, and s Academic writing by your dedicated Career Placement Officer. E5009x, y, and s English communication We look forward to working with you on your independent studies professional development and job search 0 pts. Lect: 1.7. Professor Lee. throughout your time at Columbia. English communication proficiency is important for academic achievement and career success. In Gerald Contiangco small group settings, interactions with instructor Industrial Engineering and Operations Research and fellow students to improve communication (BA) and writing skills. Individual tutoring sessions offered. Note: open only to Columbia Engineering master's students. Grading is Pass/D/Fail. Ivy Elkins Computer Science Ph.D. Courses

David Fitzgerald ENGI E7000x, y, and s English communication Industrial Engineering and Operations Research E7001x, y, and s Professional presentation E7002x, y, and s Advanced academic writing (OR) E7009x, y, and s English communication independent studies Kristen Henlin 0 pts. Lect: 1.7. Professor Lee. Applied Physics, Applied Mathematics, Medical English communication proficiency is important Physics, Material Science and Engineering; for academic achievement and career success. In Biomedical Engineering small group settings, interactions with instructor and fellow students to improve communication John Hyde and writing skills. Individual tutoring sessions Data Science offered. Note: open only to Columbia Engineering Ph.D. and M.S. to Ph.D.-track students. Grading is Mercedes Kriesel Pass/D/Fail. Industrial Engineering and Operations research (FE)

Jennifer Lee Electrical Engineering, Computer Engineering

Mindi Levinson Industrial Engineering and Operations Research (MSE & IE)

Emily McCormack Civil Engineering and Engineering Mechanics; Mechanical Engineering

Raina Ranaghan Chemical Engineering; Earth and Environmental Engineering

ENGINEERING 2021–2022 University and School Policies, Procedures, and Regulations 214 ACADEMIC PROCEDURES AND STANDARDS

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

ENGINEERING 2021–2022 undergraduate registration is defined than 15 credits per term or 9 credits for these dates, undergraduate students 215 as at least 12 semester credits per term. the last term. must petition the Committee on However, in order to complete the A graduate student who has Academic Standing; graduate students degree, students must be averaging matriculated in an M.S. program or is must petition the Office of Graduate 16 points per term. Students may not a nondegree student is considered Student Affairs. For courses dropped register for point loads greater than 21 to be making normal progress if he after these dates, no adjustment of points per term without approval from or she has earned a cumulative GPA fees will be made. Failure to attend a the Committee on Academic Standing. of 2.5 or minimum GPA required by class will be indicated by a permanent To be eligible to receive the Bachelor the academic department, whichever unofficial withdrawal (UW) on the of Science degree, a student must is higher. Candidates in the Doctor of transcript. complete the courses prescribed in Engineering Science (Eng.Sc.D.) program a faculty-approved major/program (or are expected to achieve a 3.0 GPA or Transfer Credits faculty-authorized substitutions) and minimum GPA required by the academic Undergraduate students may obtain achieve a minimum cumulative grade- department, whichever is higher. academic credit toward the B.S. point average (GPA) of 2.0. Although Graduate students (on-campus and degree by completing coursework at the minimum number of academic online students) who do not meet the other accredited four-year institutions. credits is 128 for the B.S. degree, some minimum cumulative GPA of the school Normally, this credit is earned during programs of the School require a greater and the department will be placed the summer. To count as credit toward number of credits in order to complete on academic probation. During the the degree, a course taken elsewhere all the requirements. Undergraduate probation period students must meet must have an equivalent at Columbia engineering degrees are awarded only with their department to discuss and University and the student must achieve to students who have completed at least develop an academic plan to improve a grade of at least B. An exception 60 points of coursework at Columbia. their overall GPA. If the student does to this policy is made for students No credit is earned for duplicate courses not meet the academic benchmarks enrolled in an approved study abroad or for courses that are taken pass/ required by their department after the program. Students in an approved fail and the final grade is a P, with the term in which they have been placed on study abroad program will receive exception of two nontechnical electives probation, then they may be asked to transfer credit if they earn a grade of C at the 3000 level or above and physical leave the School permanently. Degree or higher. To transfer credit, a student education courses, as noted below. requirements for master’s degrees must obtain prior approval from his or Undergraduates in the programs must be completed within five years; her CSA adviser and the department accredited by the Engineering those for the doctoral degrees must before taking such courses. A course Accreditation Commission of ABET be completed within seven years. A description and syllabus should be (Biomedical Engineering, Chemical minimum cumulative GPA of 2.5 (in all furnished as a part of the approval Engineering, Civil Engineering, Earth courses taken as a degree candidate) is process. Courses taken before the and Environmental Engineering, required for the M.S. degree; a minimum receipt of the high school diploma may Electrical Engineering, and Mechanical GPA of 3.0 or minimum GPA required by not be credited toward the B.S. degree. Engineering) satisfy ABET requirements the academic department, whichever A maximum of 6 credits may be applied by taking the courses in prescribed is higher, is required for the Doctor of toward the degree for college courses programs, which have been designed Engineering Science (Eng.Sc.D.) and taken following the receipt of a high by the departments so as to meet the the Doctor of Philosophy degrees. school diploma and initial enrollment at ABET criteria. The minimum residence requirement Columbia University. for each Columbia graduate degree is Master's degree students are not Attendance 30 points of coursework completed at eligible for transfer credits. Students are expected to attend Columbia. Students possessing a conferred their classes and laboratory periods. M.S. degree upon entry into a Ph.D. Instructors may consider attendance Changes in Registration program may be awarded 2 residence in assessing a student’s performance An undergraduate student who wishes units toward their Ph.D., as well as and may require a certain level of to drop or add courses or to make 30 points of advanced standing attendance for passing a course. other changes in his or her program toward their Ph.D. or Eng.Sc.D. with of study after the change of program departmental approval. Graduate period must obtain the approval of Graduate students are required his or her CSA adviser. A student who Examinations to complete the School’s degree wishes to drop or add a course in his or Midterm examinations: Instructors requirements as outlined on page 22 her major must also obtain department generally schedule these in late October (The Graduate Programs). Full-time approval. The deadline for making and mid-March. graduate registration is defined as at program changes in each term is shown Final examinations: These are given least 12 credits per term. M.S. students in the Academic Calendar. Note: the at the end of each term. The Master may not register for point loads greater drop-date for Columbia Core courses is University Examination Schedule is the second week of the semester. After

ENGINEERING 2021–2022 216 available online and is confirmed by B–=2.67). Grades of P, INC, UW, and MU exceed one year. After a year, the IN will November 1 for the fall term and April will not be included in the computation of be automatically changed into an F or 1 for the spring term. This schedule is the grade-point average. the contingency grade. sent to all academic departments and R (registration credit; no qualitative YC (year course): a mark given at is available for viewing on the Columbia grade earned): not accepted for degree the end of the first term of a course website. Students should consult with credit in any program. R credit is not in which the full year of work must be their instructors for any changes to the available to undergraduate students completed before a qualitative grade is exam schedule. Examinations will not for academic classes. In some divisions assigned. The grade given at the end be rescheduled to accommodate of the University, the instructor may of the second term is the grade for the travel plans. stipulate conditions for the grade and entire course. Note: If a student has three final report a failure if those conditions CP (credit pending): given only in examinations scheduled during one are not satisfied. The R notation will graduate research courses in which calendar day, as certified by the be given only to those students who student research projects regularly Registrar, an arrangement may be made indicate, upon registration and to the extend beyond the end of the term. with one of the student’s instructors instructor, their intention to take the Upon completion, a final qualitative to take that examination at another, course for R, or who, with the approval grade is then assigned and credit mutually convenient time during the of the instructor, file written notice of allowed. The mark of CP implies final examination period. This refers change of intention with the registrar satisfactory progress. to a calendar day, not a 24-hour time not later than the last day for change of MU (make-up examination): given period. Undergraduate students unable program. Students wishing to change to a student who has failed the final to make suitable arrangements on their to R credit after this date are required examination in a course but who has own should contact their CSA adviser. to submit written approval from the been granted the privilege of taking Graduate students should contact the Office of Graduate Student Affairs and a second examination in an effort to Office of Graduate Student Affairs. the course instructor to the registrar. improve his or her final grade. The The request to change to R credit must privilege is granted only when there Transcripts and Certifications be made by the last day to change a is a wide discrepancy between the For information on the Federal Family course grading option. A course that quality of the student’s work during the Education Rights and Privacy Act has been taken for R credit may not be term and his or her performance on (FERPA) of 1974, please visit repeated later for examination credit the final examination, and when, in the facets.columbia.edu—Essential Policies and cannot be uncovered under any instructor’s judgment, the reasons justify for the Columbia Community. Information circumstances. The mark of R does not a make-up examination. A student may on obtaining University transcripts and count toward degree requirements for be granted the mark of MU in only two certifications will be found as a subhead graduate students. The mark of R is courses in one term, or, alternatively, under Essential Resources. automatically given in Doctoral Research in three or more courses in one term if Instruction courses. their total point value is not more than Report of Grades UW (unofficial withdrawal): given to 7 credits. The student must remove students who discontinue attendance MU by taking a special examination Grades can be viewed by using the in a course but are still officially administered as soon as the instructor Student Services Online feature located registered for it, or who fail to take a can schedule it. on the Student Services home page at final examination without an authorized P/F (pass/fail): Undergraduates may columbia.edu/students. If you need an excuse. select to take only one course that is official printed report, you must request IN (incomplete): granted only in offered for a letter grade pass/fail each a transcript (please see Transcripts and the case of incapacitating illness as semester. In general, courses taken Certifications above). certified by the Health Services at pass/fail do not count toward degree All graduate students must have a Columbia, serious family emergency, or requirements including the 128-point current mailing address on file with the circumstances of comparable gravity. requirement. There are two exceptions Registrar’s Office. Undergraduate students request an IN to this rule. Physical Education classes by filling out the Incomplete Request do count toward the 128 degree Transcript Notations Form with their CSA adviser prior to the requirement, even though students do The grading system is as follows: A, final exam for the course in the semester not receive letter grades for the class. excellent; B, good; C, satisfactory; D, of enrollment. Students requesting an Additionally, undergraduate students poor but passing; F, failure (a final IN must gain permission from both the may take up to two courses of the grade not subject to re-examination). Committee on Academic Standing (CAS) 9-11 nontechnical elective credit on Occasionally, P (Pass) is the only passing and the instructor. Graduate students a P/F basis. These courses must be option available. The grade-point should contact their instructor. If granted at the 3000-level or higher and must average is computed on the basis of the an IN, students must complete the be courses that can be taken P/F by following index: A=4, B=3, C=2, D=1, F=0. required work within a period of time students attending Columbia College Designations of + or – (used only with A, stipulated by the instructor but not to (e.g., instruction classes in foreign B, C) are equivalent to 0.33 (i.e., B+=3.33;

ENGINEERING 2021–2022 language and core curriculum classes a student's Legal Name. However, to the next business day.) Doctoral 217 are not eligible to be taken pass/fail). whenever reasonably possible, a students must deposit their dissertations These courses may not count toward student's "Preferred Name" will be used. two days before the above conferral the minor, and cannot be uncovered Please see registrar.columbia.edu/ dates in order to graduate. under any circumstances. Please note content/name-and-address-changes for Students who fail to earn the degree that physical education classes are the further details. by the conferral date for which they only courses taught solely on a P/F basis Students may change their name of applied must file another application for that may apply toward the 128 credits record by submitting a name change a later conferral date. for the degree. The P/F option does affidavit to the Student Service Center. not count toward degree requirements Affidavits are available from this office or Diplomas for graduate students and cannot be online at registrar.columbia.edu. There is no charge for the preparation uncovered under any circumstances. and conferral of an original diploma. W (official withdrawal): a mark given GRADUATION If your diploma is lost or damaged, to students who are granted a leave Columbia University awards degrees there will be a charge of $100 for of absence after the drop deadline for three times during the year: in February, a replacement diploma. Note that the semester. The grade of W, meaning May, and October. There is one replacement diplomas carry the “official withdrawal,” will be recorded as commencement ceremony in May. signatures of current University officials. the official grade for the course in lieu Applications for replacement diplomas of a letter grade. The grade of W will are available on our website: registrar. Application or Renewal of Application zero out the credits for the class so the columbia.edu/registrar-forms/application- for the Degree student’s GPA will not be affected. replacement-diploma. Any questions In general, students can download an regarding graduation or diploma application for the degree from the Name Changes processing should be addressed to Registrar's website and file it according Columbia University recognizes that [email protected]. to the instructions on the form, or some students prefer to identify pick up and file it from their schools themselves by a First Name and/or or departments, but there are several Middle Name, other than their Legal exceptions. Candidates for Master of Name. For this reason, beginning in the Science degrees may pick up and file Spring 2016 semester, the University has their application for the degree with enabled students to use a "Preferred the Diploma Division, 210 Kent Hall, or Name" where possible in the course of through the registrar’s website: registrar. University business and education. columbia.edu/registrar-forms/application- Under Columbia's Preferred Name degree-or-certificate. Candidates for policy, any student may choose to doctoral and Master of Philosophy identify a Preferred First and/or Middle degrees should inquire at their Name in addition to the Legal Name. departments but must also follow the Students may request this service via a instructions of the Dissertation Office, link on SSOL. The student's Preferred 107 Low Library. Name may be used in many University General deadlines for applying for contexts, including SSOL, class rosters, graduation are November 1 for February, CourseWorks, and Canvas, and on ID December 1 for May, and August 1 for Cards. For some other records, the October. (When a deadline falls on a University is legally required to use weekend or holiday, the deadline moves

ENGINEERING 2021–2022 218218 ACADEMIC STANDING

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

ENGINEERING 2021–2022 student’s departmental adviser when from their faculty adviser and/or academic regarding the readmission procedures 219219 the student has declared a major. All department prior to and returning from an from medical leave. proposed courses will be reviewed approved voluntary medical leave. A return from a voluntary medical by the appropriate faculty who teach A voluntary medical leave for an leave request must be made before the equivalent classes at Columbia undergraduate student is for a minimum the start of the fall or spring semester. University. All courses that are being of one year and cannot be longer than Graduate students may apply for taken to fulfill a major requirement or as two years. A voluntary medical leave for a readmission following a one-term a technical elective must be approved graduate student is for a minimum of one voluntary medical leave of absence. by the student’s departmental adviser. semester, up to two years. If the student As part of the readmission process, Courses being taken to count as a does not return within the two-year time graduate students need to submit a nontech elective or to count as general frame, he or she will be permanently personal statement and supporting credit would only require the approval withdrawn from the School. Students may medical documentation. Graduate of the Undergraduate Committee only return in the fall or spring term, not students should contact the Office on Academic Standing. The existing in summer sessions. of Graduate Student Affairs for procedures for the approval of outside When a voluntary medical leave of more information. The deadlines for credit will be followed in these cases. absence is granted during the course petitioning a readmission are June 1 Students must receive a grade of B or of the semester, the semester will be for the fall semester and November 1 better for the credit to be transferred. deleted if the leave begins prior to the for the spring semester. The deadlines The Office of Graduate Student drop deadline. If after the drop deadline, for petitioning a return from a voluntary Affairs monitors the academic progress the course grades will normally be W medical leave for graduate students of graduate students in consultation (official withdrawal) in all courses. In after one semester are June 1 for the fall with the departments. Students will certain circumstances, a student may semester and November 1 for the spring be placed on Academic Probation qualify for an incomplete, which would semester. Students are not eligible to if their cumulative GPA is below 2.5 have to be completed by the first week return from a medical leave during the or minimum GPA required by the of the semester in which the student summer. academic department, whichever is returns to Columbia. If the Incomplete is During the course of the leave, higher. Students who are on Academic not completed by that time, a W will be students are not permitted to take any Probation and do not return to good inserted as the final grade. courses for the purpose of transferring standing after one semester may be In exceptional cases, an credit and are not permitted to be on dismissed from the program. undergraduate student may apply campus. For more information about for readmission following a one-term the voluntary medical leave of absence voluntary medical leave of absence. policy, consult your CSA adviser; VOLUNTARY MEDICAL LEAVE OF In addition to providing a personal graduate students should consult the ABSENCE statement and supporting medical Office of Graduate Student Affairs. A voluntary medical leave of absence documentation for the voluntary for an undergraduate student is granted medical leave readmission committee VOLUNTARY PERSONAL LEAVE by the James H. and Christine Turk to review, the student will also need OF ABSENCE Berick Center for Student Advising to to provide a well-developed academic an undergraduate student whose health plan that has been approved by the A voluntary personal leave of absence prevents him or her from successfully departmental adviser and the Berick (VPLOA) may be granted by the pursuing full-time study. Undergraduates Center for Student Advising as part Committee on Academic Standing to who take a voluntary medical leave of the readmission process. This plan undergraduate students who request of absence are guaranteed housing must demonstrate that his or her return a temporary withdrawal from Columbia upon their return if they were already to Columbia Engineering following a Engineering for a nonmedical reason. guaranteed housing. one-semester leave of absence will Students considering a voluntary A voluntary medical leave of absence allow the student to properly follow the personal leave must discuss this option for a graduate student is granted by the sequence of courses as required for the in advance with their CSA adviser. Office of Graduate Student Affairs, so major and to meet all other graduation Voluntary leaves are granted for a please consult with this office for more requirements. Students must apply for period of one academic year only information. readmission from a medical leave by for undergraduate students; VPLOAs Documentation from a physician or November 1 for the fall semester and will ordinarily not be granted for one counselor must be provided before such June 1 for the spring semester. The final semester, or for more than one year. a leave is granted. In order to apply decision regarding whether or not a Students must be in good academic for readmission following a voluntary student will be allowed to be readmitted standing at the time of the leave and medical leave, a student must submit after a medical leave will be made must be able to complete their major proof of recovery from a physician or by the Medical Leave Readmission and degree in eight semesters. counselor. Graduate students may also Committee. Students should consult the A voluntary personal leave of be required to meet with a medical medical leave policy statement available absence for a graduate student is provider at Columbia. Doctoral students on the website of the Berick Center for granted by the Office of Graduate must have a faculty adviser and funding Student Advising for more information Student Affairs. A graduate student must

ENGINEERING 2021–2022 220 be registered for at least one semester on the website of the Berick Center for as they can demonstrate that they and have a minimum cumulative 2.5 Student Advising for more information can remain in sequence with their GPA to request a voluntary personal regarding the readmission procedures coursework and have the prior approval leave. Additionally, doctoral students from a voluntary personal leave of of the departmental adviser. must have a faculty adviser and absence. The deadlines for petitioning Students who decide not to return funding from their faculty adviser and/ a return from a voluntary personal must notify the James H. and Christine or academic department prior to and leave for graduate students after one Turk Berick Center for Student Advising returning from an approved voluntary semester are June 1 for the fall semester of their decision. The date of separation personal leave of absence. The and November 1 for the spring. for the leave of absence will be the date deadline to request a VPLOA for a given Students may not take courses of separation for withdrawal. Leaves term is the last day to drop classes for transferable credit while on leave. may not extend beyond four semesters. during that term. VPLOA requests made Finally, students who choose to take Students who do not notify the Berick after the drop deadline will be denied. voluntary personal leaves are not Center for Student Advising of their A graduate student may request to guaranteed housing upon return to the intentions by the end of the two-year return from a voluntary personal leave of University. International students should period will be permanently withdrawn. absence for the fall, spring, or summer contact the International Students and semester. A request to return must be Scholars Office to ensure that a leave LEAVE FOR MILITARY DUTY made before the semester starts. Please will not jeopardize their ability to return Please refer to Military Leave of contact the Office of Graduate Student to Columbia Engineering. Absence Policy in Essential Policies for Affairs for more information. the Columbia Community When a voluntary personal leave of UNDERGRADUATE EMERGENCY (facets.columbia.edu) for recent absence is granted during the course FAMILY LEAVE OF ABSENCE updates regarding leave for military of the semester, the semester will be duty. deleted if the leave begins prior to the Students who must leave the University drop deadline. If after the drop deadline, for urgent family reasons that neces- sitate a semester-long absence (e.g., the course grades will normally be a INVOLUNTARY LEAVE family death or serious illness in the W (official withdrawal) in all courses. In OF ABSENCE POLICY family) may request an emergency fam- certain circumstances, a student may Please refer to Involuntary Leave of ily leave of absence. Documentation qualify for an incomplete, which would Absence Policy in Essential Policies of the serious nature of the emer- have to be completed by the first week for the Columbia Community gency must be provided. Students must of the semester in which the student facets.columbia.edu). returns to Columbia. If the Incomplete is request an emergency family leave of not completed by that time, a W will be absence from their advising dean in inserted as the final grade. the James H. and Christine Turk Berick READMISSION In exceptional cases, an Center for Student Advising. Students seeking readmission must undergraduate may apply for When an emergency family leave of submit evidence that they have readmission following a one-term absence is granted during the course achieved the purposes for which they voluntary personal leave of absence. of the semester, the semester will be left. Consequently, specific readmission The student will need to provide deleted if the leave begins prior to the procedures are determined by the to the Committee on Academic drop deadline. If after the drop deadline, reasons for the withdrawal. Further Standing a well-developed academic the course grades will normally be W information for undergraduate students plan that has been approved by the (official withdrawal) in all courses. In is available in the Berick Center for departmental adviser and the Berick certain circumstances, a student may Student Advising. Graduate students Center for Student Advising as part of qualify for an incomplete, which would should see the Office of Graduate the admission process. This plan must have to be completed by the first week Student Affairs. demonstrate that his or her return to of the semester in which the student Students applying for readmission Columbia Engineering following a one- returns to Columbia. If the Incomplete is should complete all parts of the semester personal leave of absence will not completed by that time, a W will be appropriate readmission procedures by allow the student to properly follow the inserted. June 1 for the autumn term or November sequence of courses as required for the To return, students must notify the 1 for the spring term. major and to meet all other graduation Berick Center for Student Advising as requirements by their eighth semester. soon as possible, ideally by November The Committee on Academic Standing 1 for the spring semester and June 1 will review the student’s academic for the fall semester. Students must plan and request for readmission. The request readmission in writing and deadlines for petitioning for readmission submit a statement describing their are June 1 for the fall semester and readiness to return. Once readmission November 1 for the spring semester. is granted, housing will be guaranteed. Undergraduates should consult the SEAS students may request permission medical leave policy statement available to return after one semester as long

ENGINEERING 2021–2022 ACADEMIC INTEGRITY AND DISCIPLINE 221

ACADEMIC INTEGRITY circumstances should immediately Graduate Student Affairs, if feeling Academic integrity defines a university contact their instructor and adviser for overwhelmed, burdened or pressured. and is essential to the mission of advice. • Attend Academic Integrity workshops education. At Columbia, you are For undergraduate students, another offered throughout the academic year. expected to participate in an academic resource is the Academic section of the • If you suspect that an academic community that honors intellectual work Live Well | Learn Well site (wellbeing. integrity violation may have occurred, and respects its origins. The abilities columbia.edu/resources) for Academic know that you can talk to your to synthesize information and produce resources and support. instructor, Advising Dean, Director of original work are key components in the The easiest way to avoid the Academic Integrity, Office of Graduate learning process. As such, a violation temptation to cheat in the first place is to Student Affairs, or the Student of academic integrity is one of the most prepare yourself as best you can. Here Conduct and Community Standards serious offenses that one can commit are some basic suggestions to help you Office to report any allegations of at Columbia. If found responsible, along the way: academic misconduct. violations range from conditional disciplinary probation to expulsion from • Discuss with each of your faculty their Students found responsible for an the University. Compromising academic expectations for maintaining academic academic integrity violation may be integrity not only jeopardizes a student's integrity. disqualified from receiving Latin Honors academic, professional, and social • Understand that you have a student or other distinctions. development; it violates the standards of responsibility to uphold academic our community. As a Columbia student, integrity based on the expectations Plagiarism and you are responsible for making informed outlined in each of your course syllabi. Acknowledgment of Sources choices with regard to academic • Understand instructors' criteria for Columbia has always believed that integrity both inside and outside the academic integrity and their policies writing effectively is one of the most classroom. on citation and group collaboration. important goals a college student can Students rarely set out with the • Clarify any questions or concerns achieve. Students will be asked to do intent of engaging in violations about assignments with instructors as a great deal of written work while at of academic integrity. But classes early as possible. Columbia: term papers, seminar and are challenging at Columbia, and • Develop a timeline for drafts and laboratory reports, and analytic essays students may find themselves final edits of assignments and begin of different lengths. These papers play pressed for time, unprepared for preparation in advance. a major role in course performance, an assignment or exam, or feeling • Avoid plagiarism: acknowledge but more important, they play a major that the risk of earning a poor grade people’s opinions and theories by role in intellectual development. outweighs the need to be thorough. carefully citing their words and always Columbia's academic integrity policy Such circumstances lead some indicating sources. in the Standards & Discipline defines students to behave in a manner that • Assume that collaboration in the plagiarism as "the use of words, compromises the integrity of the completion of assignments is phrases, or ideas belonging to the academic community, disrespects prohibited unless specified by the student, without properly citing or their instructors and classmates, and instructor. acknowledging the source, is prohibited. deprives them of an opportunity to • Utilize the campus resources, This may include, but is not limited to learn. In short, they cheat. Students such as the Berick Center for copying computer programs for the who find themselves in such Student Advising, Counseling and purposes of completing assignments Psychological Services (CPS), and

ENGINEERING 2021–2022 222 for submission." Plagiarism, the use of meaning you will need to make outside the time constraints imposed, words, phrases, or ideas belonging informed choices inside and outside the unauthorized use of prescription to another, without properly citing or the classroom. Columbia offers a medication to enhance academic acknowledging the source, is prohibited. wealth of resources to help students performance, and /or submitting an This may include, but is not limited to, make sound decisions regarding altered examination or assignment to copying computer programs for the academics, extracurricular activities, an instructor for regrading. purposes of completing assignments for and personal issues. Undergraduate • Collaboration, Unauthorized: submission. students should consult an advising collaborating on academic work One of the most prevalent forms dean or meet with the Director of without the instructor's permission is of plagiarism involves students using Academic Integrity in Suite 601 of prohibited. This includes, but is not information from the Internet without Lerner Hall. Graduate students should limited to, unauthorized collaboration proper citation. While the Internet consult or meet their assistant dean in on tests, quizzes, assignments, labs, can provide a wealth of information, the Office of Graduate Student Affairs and projects. sources obtained from the web must in Suite 530 in Mudd. • Dishonesty: falsification, forgery, or be properly cited just like any other misrepresentation of information source. If you are uncertain how to Academic Integrity Policies and to any University official in order to properly cite a source of information Expectations gain an unfair academic advantage that is not your own, whether from the Violations of policy may be intentional in coursework or lab work, on any Internet or elsewhere, it is critical that or unintentional and may include application, petition, or documents you do not hand in your work until dishonesty in academic assignments submitted to this University is you have learned the proper way to or in dealing with University officials, prohibited. This includes, but is not use in-text references, footnotes, and including faculty and staff members. limited to, falsifying information on a bibliographies. Faculty members are Moreover, dishonesty during the Dean’s resume, fabrication of credentials or available to help as questions arise Discipline hearing process may result in academic records, misrepresenting about proper citations, references, and more serious consequences. one's own research, providing the appropriateness of group work Types of academic integrity false or misleading information in on assignments. For undergraduates violations: order to be excused from classes only, students can also check with the or assignments, and/or intentionally Undergraduate Writing Program or • Academic Dishonesty, Facilitation of: underperforming on a placement meet with the Director of Academic assisting another student in a violation exam. Integrity to review citation styles at of academic integrity is prohibited. • Ethics, Honor Codes, and [email protected]. Another This may include but is not limited to Professional Standards, Violation of: option is to connect with Research selling and/or providing notes, exams, any violation of published institutional Librarians for citation management and papers. policies related to ethics, honor workshops. Information on these • Assistance, Unauthorized Giving: codes, or professional standards workshops is posted online on the unauthorized assistance to another of a student's respective school is Columbia Libraries website. Ignorance student or receiving unauthorized aid prohibited. of proper citation methods does not from another person on tests, quizzes, • Failing to Safeguard Work: failure to exonerate one from responsibility. assignments, or examinations without take precautions to safeguard one's the instructor's express permission is own work is prohibited. Personal Responsibility, Finding prohibited. • Giving or Taking Academic Materials, Support, and More Information • Bribery: offering or giving any favor Unauthorized: unauthorized A student’s education at Columbia or thing of value for the purpose of circulation or sharing of past or University is comprised of two improperly influencing a grade or present course material(s) without complementary components: a other evaluation of a student in an the instructor's express permission is mastery over intellectual material academic program is prohibited. prohibited. This includes, but is not within a discipline and the overall • Cheating: wrongfully using or limited to, assignments, exams, lab development of moral character attempting to use unauthorized reports, notebooks, and papers. and personal ethics. Participating materials, information, study aids, • Obtaining Advanced Knowledge: in forms of academic dishonesty or the ideas or work of another in unauthorized advanced access to violates the standards of our order to gain an unfair advantage is exams or other assignments without community at Columbia and severely prohibited. Cheating includes, but an instructor's express permission is inhibits a student’s chance to grow is not limited to, using or consulting prohibited. academically, professionally, and unauthorized materials or using • Plagiarism: the use of words, phrases, socially. As such, Columbia’s approach unauthorized equipment or devices or ideas belonging to another without to academic integrity is informed by on tests, quizzes, assignments, properly citing or acknowledging its explicit belief that students must or examinations, working on any the source is prohibited. This may take full responsibility for their actions, examination, text, quiz, or assignment include, but is not limited to, copying

ENGINEERING 2021–2022 computer programs for the purposes guardians of undergraduate students without a student's consent. For exam- 223 of completing assignments for may also be notified. ple, the release of student disciplinary submission. records is permitted without prior stu- • Sabotage: inappropriately and Dean’s Discipline Process for dent consent to University officials with deliberately harming someone else's Undergraduate and Graduate a legitimate educational interest such academic performance is prohibited. Students as a student's academic adviser and to • Self-Plagiarism: using any material It is expected that all students act in an Columbia Athletics if the student is an portion of an assignment to fulfill honest way and respect the rights of athlete. The University will also release the requirements of more than one others at all times. Dean's Discipline is information when a student gives written course without the instructor's express the process utilized to investigate and permission for information to be shared. permission is prohibited. respond to allegations of behavioral To obtain a FERPA waiver, please visit: • Test Conditions: violations of or academic misconduct. The Dean's columbia.edu/cu/studentconduct/ compromising a testing environment Discipline process is not meant to be documents/FerpaRelease.pdf. To read or violating specified testing an adversarial or legal process, but more about the exceptions that apply to conditions, to intentionally or instead aims to educate students about the disclosure of student records infor- unintentionally create access to an the impact their behavior may have on mation, please visit: essentialpolicies. unfair advantage for oneself or others their own lives as well as on the greater columbia.edu/policy-access-student- is prohibited. community. recordferpa. The process is initiated when an Students found responsible for reportable violations of conduct, DISCIPLINARY PROCEDURES allegation is reported that a student including academic integrity violations, Many policy violations that occur in may have violated University policies. may face reports of such offenses the Residence Halls or within fraternity Students may be subject to Dean's on future recommendations for law, and sorority housing are handled by Discipline for any activity that occurs medical, or graduate school. Students Residential Life. Some serious offenses on or off campus that impinges on the found responsible for any violations are referred directly to Student Conduct rights of other students and community of conduct may be disqualified from and Community Standards. Violations members. This also includes violations receiving Latin Honors or other awards. in University Apartment Housing are of local, state, or federal laws. They may also be disqualified from handled by building managers and Student Conduct and Community participating in internships or other housing officials. Some incidents are Standards is responsible for leadership roles. The parents or referred directly to the School’s housing administering the Dean's Discipline guardians of undergraduate students liaison in the Office of Graduate Student disciplinary process for all disciplinary may also be notified. Affairs. affairs concerning students that are not In matters involving rallies, picketing, reserved to some other body. and other mass demonstrations, the Students are expected to familiarize Rules of University Conduct outlines themselves with the Standards procedures. and Discipline handbook and the Student Conduct and Community comprehensive list of policies and Standards is responsible for all expectations available on the Students disciplinary affairs concerning Conduct and Community Standards undergraduate students that are not website (studentconduct.columbia.edu). reserved to some other body. The For more information about the Office of Graduate Student Affairs is discipline process for undergraduate responsible for all disciplinary affairs students, please review the Academic concerning graduate students that are Integrity website. For more information not reserved to some other body. about the discipline process for Students found responsible for graduate students, please contact the reportable violations of conduct, Office of Graduate Student Affairs. including academic integrity violations, may face reports of such offenses Confidentiality on future recommendations for law, Privacy and Reporting: Disciplinary pro- medical, or graduate school. Students ceedings conducted by the University found responsible for any violations are subject to Education of conduct may be disqualified from Rights and Privacy Act ("FERPA," also receiving Latin Honors or other awards. called "The Buckley Amendment"). They may also be disqualified from There are several important exceptions participating in internships or other to FERPA that will allow the University leadership roles. The parents or to release information to third parties

ENGINEERING 2021–2022

Directory of University Resources 226 COLUMBIA UNIVERSITY RESOURCE LIST

UNDERGRADUATE ADMISSIONS Student Engagement Undergraduate Writing Program 515 Lerner, MC 2601 310 Philosophy, MC 4995 Undergraduate Admissions 212-854-3612 212-854-3886 212 Hamilton, MC 2807 cc-seas.columbia.edu/engagement [email protected] 212-854-2522 college.columbia.edu/core/uwp [email protected] undergrad.admissions.columbia.edu COLUMBIA COLLEGE GRADUATE STUDENT AFFAIRS 208 Hamilton, MC 2805 UNDERGRADUATE ADVISING 212-854-2441 Graduate Student Affairs college.columbia.edu/ 530 S. W. Mudd, MC 4708 James H. and Christine Turk Berick 212-854-6438 Center for Student Advising gradengineering.columbia.edu/ 403 Lerner Hall, MC 1201 CORE CURRICULUM PROGRAM 212-854-6378 Center for the Core Curriculum Graduate Admissions [email protected] 202 Hamilton, MC 2811 1220 S. W. Mudd, MC 4708 cc-seas.columbia.edu/csa 212-854-2453 212-854-4688 college.columbia.edu/core [email protected] UNDERGRADUATE STUDENT LIFE gradengineering.columbia.edu/ admissions 505–515 Lerner, MC 2601 Art Humanities 212-854-3612 826 Schermerhorn, MC 5517 cc-seas.columbia.edu/studentlife 212-854-4505 COLUMBIA VIDEO NETWORK arthum.college.columbia.edu/ 540 S. W. Mudd, MC 4719 Multicultural Affairs 505 Lerner, MC 2607 212-854-6447 Music Humanities [email protected] 212-854-0720 621 Dodge, MC 1813 cvn.columbia.edu cc-seas.columbia.edu/OMA 212-854-3825 college.columbia.edu/core/classes/mh Intercultural Resource Center (IRC) CAREER SUPPORT 552 West 114th Street, MC 5755 Contemporary Civilization Center for Career Education 212-854-0720 514 Fayerweather, MC 2811 East Campus, Lower Level, MC 5727 cc-seas.columbia.edu/ 212-854-5682 212-854-5609 multicultural/aboutus/irc.php college.columbia.edu/core/conciv [email protected] careereducation.columbia.edu Residential Life Literature Humanities 515 Lerner, MC 4205 202 Hamilton, 212-854-2453 Graduate Career Placement Center 212-854-3612 Mail Code 2811 646-832-5941 cc-seas.columbia.edu/reslife college.columbia.edu/lithum [email protected] career.engineering.columbia.edu.

ENGINEERING 2021–2022 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 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

EQUAL OPPORTUNITY AND Insurance and Immunization Dodge Physical Fitness Center AFFIRMATIVE ACTION Compliance 212-854-3439 103 Low Library, MC 4333 John Jay, 3rd Floor, MC 3601 Insurance Office: 212-854-3286 212-854-5511 INTERNATIONAL STUDENTS AND eoaa.columbia.edu [email protected] SCHOLARS (ISSO) Immunization Compliance Office: Office: 524 Riverside Drive, Ground 212-854-7210 Student Services for Gender-Based Floor [email protected] and Sexual Misconduct Mailing: 2960 Broadway, MC 5724 Wien Hall, Suite 108C 212-854-3587 212-854-1717 Student Health Insurance Plan [email protected] Administrators studentconduct.columbia.edu/gbm isso.columbia.edu Aetna Student Health 1-800-859-8471 FINANCIAL AID (UNDERGRADUATE) www.aetnastudenthealth.com/ LIBRARIES columbia Undergraduate Financial Aid and Information Educational Financing Alice! Health Promotion 535 W. 114th Street Office: 618 Lerner John Jay, 3rd Floor, MC 3601 212-854-7309 Mailing: 100 Hamilton, MC 2802 212-854-5453 library.columbia.edu 212-854-3711 [email protected] [email protected] Counseling and Psychological Services Science & Engineering Library cc-seas.financialaid.columbia.edu Lerner, 8th floor, MC 2606 401 Northwest Corner 24/7 Support: 212-854-7878 212-851-2950

FINANCIAL AID (GRADUATE) Disability Services MATH/SCIENCE DEPARTMENTS 108A Wien Hall, MC 3711 Federal Loans Voice/TTY: 212-854-2388 Financial Aid and Educational Financing Biological Sciences [email protected] 615 Lerner, MC 2802 600 Fairchild, MC 2402 212-854-4581 212-854-3711 Medical Services sfs.columbia.edu/financial-aid/graduate , 4th Floor Chemistry 212-854-6655 (Gay Health Advocacy 344 Havemeyer, MC 3178 Institutional Financial Aid Project) 212-854-2202 (Grants, Fellowships, Assistantships) 24/7 Support: 212-854-7426 Office of Graduate Student Affairs 530 S. W. Mudd, MC 4708 Sexual Violence Response Earth and Environmental Sciences 212-854-6438 Lerner, 7th floor 106 Geoscience, Lamont-Doherty 24/7 Support: 212-854-HELP (4357) Earth Observatory, 845-365-8550 [email protected]

ENGINEERING 2021–2022 228 Mathematics PUBLIC SAFETY STUDENT SERVICE CENTER 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 Statistics 212-854-0411 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 2021–2022 229

ENGINEERING 2021–2022 230 COLUMBIA UNIVERSITY THE MORNINGSIDE CAMPUS & ENVIRONS

ENGINEERING 2021–2022 THE MORNINGSIDE HEIGHTS AREA OF NEW YORK CITY 231

ENGINEERING 2021–2022 232 INDEX

A applications Business, Graduate School of for degrees, 217 joint programs with, 23, 168 academic advising. See James H. and Christine Turk Berick Center for graduate, 28–29 Butler Library, 227 Student Advising undergraduate, 17 academic calendar, inside back cover applied chemistry. See Chemical C academic community, conduct Engineering, Department of expected in, 221 applied mathematics calendar academic dishonesty, 222 courses in, 60–62 academic, inside back cover academic honors, 218 minor in, 204 for graduate admissions, 29 academic integrity, 221–223 applied physics career support academic monitoring, 218–219 courses in, 57–60 Center for Career Education academic procedures and standards, minor in, 204 (CCE), 34, 226 214–217 Applied Physics and Applied Graduate Career Placement academic progress, satisfactory, 20, Mathematics, Department of, 48–61 Center (GCP), 226 214–217 current research activities, 48–49 Carleton Commons, 6 academic standing, 218–220 graduate programs, 54–57 Center for Applied Probability (CAP), ABET, 15, 64, 66, 79, 93, 124, 126, 142, laboratory facilities, 49–50 158 193 specialty areas, 53–54 Center for Career Education (CCE), 34, addresses of Columbia University undergraduate programs, 50–54 226 departments and resources, 226– architecture, minor in, 93, 204 Center for Financial Engineering, 158 228 art history, minor in, 205 Center for Life Cycle Analysis (CLCA), administrative officers, lists of, 36, assistantships, 32–33 125 42–44 athletic programs, 11, 13 Chaplain, University, Office of the, 227 admissions attendance, 215 chemical engineering graduate, 28–29, 226. See also courses in, 82–87 minor in, 81, 205 Graduate Student Affairs B undergraduate, 17, 226 Chemical Engineering, Department of, advanced placement, 12–13 Bachelor of Science degree (B.S.), 15–16 78–87 advanced standing, of transfer Barnard Education Program, 17 facilities and laboratories, 79 students, 29 Biological Sciences, Department of, 227 graduate programs, 81 advising centers. See James H. and biomedical engineering undergraduate program, 79–81 Christine Turk Berick Center for courses in, 71–77 Chemistry, Department of, 227 Student Advising minor in, 205 civil engineering Alice! Columbia University’s Health Biomedical Engineering, Department courses in, 95–101 Promotion program, 227 of, 63–77 minor in, 205 American Language Program (ALP), 29 graduate programs, 69–71 Civil Engineering and Engineering anthropology, minor in, 204 undergraduate program, 64–68 Mechanics, Department of, Botwinick Multimedia Learning 88–101 Laboratory, 5 current research activities, 88–88

ENGINEERING 20212022

201663_213-236.indd 232 8/4/21 11:40 PM facilities and laboratories, 89–92 Counseling and Psychological Services graduate programs, 127–129 233 graduate programs, 93–95 (CPS), 221, 227 research centers, 125–126 undergraduate programs, 89–92 courses scholarships, fellowships, and classes pro­fessions other than engineering, internships, 126 attendance at, 215 16–17 undergraduate program, 126 registration and enrollment in, 214 interdisciplinary engineering, 210 See also Henry Krumb School of colleges and universities in Combined key to listings, 46–47 Mines Plan program, 14 in Engineering School departments. Earth and Environmental Sciences, Columbia College, 226 See individual departments Department of (Columbia College), Columbia Dining, 227 credit, points of, required for degree 227 Columbia Genome Center (CGC), 78 graduate, 22–25, 215 Earth Engineering Center, 123 Columbia Health, 227 undergraduate, 8–13, 214–215 East Asian studies, Columbia Housing, 227 minor in, 206 Columbia University economics D Columbia Engineering—Yesterday minor in, 206 and Today, 2–6 damages, payment for, 19, 31 electrical engineering email addresses, list of, 226–228 dance, minor in, 205 courses in, 146–156 maps of campus, 230–231 Data-Driven Analysis, specialization minor in, 206 policy, procedures, and regulations, in, 144 Electrical Engineering, Department of, 214–223 Dean’s discipline, 223 136–156 Columbia University’s Health Dean’s List, 218 B.S./M.S. program, 143 Promotion Program (Alice!), 227 Degree Audit Reporting System specialization options in the M.S. Columbia Video Network (CVN), 26–27, (DARS), 14 program, 143–146 226 degrees graduate programs, 143–146 application to, 26 application for, 217 laboratory facilities, 137 Columbia Water Center, 123 doctoral, requirements, 24–25, 215 research activities, 136–137 Combined Plan programs, 14 See also individual degrees undergraduate program, 137–143 commencement ceremony, 217 diplomas, 217 email Committee on Academic Standing, Disability Services, University Office addresses of Columbia University 215–216, 218 of, 227 resources and staff, 226–228 Committee on Instruction, 9, 24, 218 discipline, academic, 221–223 emeriti and retired officers, list of, Computational and Optimization Dean’s, 223 41–42 Research Center (CORC), 158 procedures for administering, employment, student, 34 Computer Engineering Program, 102–106 221–223 Engineering Accreditation Commission graduate program, 104–106 dishonesty, academic, 221–222 (EAC), 15 undergraduate program, 102–104 distance education. See Columbia engineering courses, interdisciplinary, computer science Video Network 210–212 courses in, 113–122 Doctor of Engineering Science (Eng. Engineering Library, 227 minor in, 205 Sc.D.), 24–25 engineering mechanics Computer Science, Department of, Doctor of Philosophy (Ph.D.), 24 courses in, 99–101 107–122 Dodge Physical Fitness Center, 227 graduate program in, 94–95 dual degree program, with School dual degree minor in, 206 of Journalism, 23, 113 with the School of Journalism, in undergraduate program in, 92–93 laboratory facilities, 106 computer science, 23, 112 See also Civil Engineering and graduate programs, 112–113 See also joint programs Engineering Mechanics, undergraduate program, 107–112 Department of Computing Support Center, 227 Engineering, School of E conduct courses. See individual departments expected in the academic Earl Hall Center, 227 department and course codes, community, 221–222 Earth and environmental engineering 46–47 unacceptable, subject to discipline, courses in, 129–135 departments and programs, 48–202 221–223 minor in, 205–206 faculty and administration, 36–44 Core Curriculum of Columbia Earth and Environmental Engineering, engineering students program offices, 226 Department of, 123–135 interdisciplinary courses for, 210–212

ENGINEERING 2021–2022 234 See also students G Institute of Flight Structures, 90 English and comparative literature, institutional grants, 32 German, minor in, 207 minor in, 207 Insurance, Student Medical Plan, 18, grade-point average (GPA), 13, 15, 215, enrollment, 214 30, 227 217, 218–219 entrepreneurship and innovation, minor integrated circuits and systems, grades, report of, 216 in, 207 specialization in, 144 grading system, explained, 216–217 Equal Opportunity and Affirmative integrity, academic, 221–223 graduate courses, taking as an Action, Office of, 227 Intercultural Resource Center (IRC), 226 undergraduate, 15 examinations, midterm and final, interdisciplinary engineering courses, graduate programs, 22–25 215–216 210–212 admission to, 28–29 International and Public Affairs, School applying to, 28–29 of, joint programs with, 17 F requirements, 22–25 International English Language Testing See also individual programs faculty System (IELTS), 28 Graduate Career Placement (GCP), 226 lists of, 36–42 International Students and Scholars Graduate Record Examination (GRE), 28 members-at-large, list of, 41 Office (ISSO), 227 Graduate Student Affairs, Office of, 25, Family Educational Rights and Privacy internships, 126 Act (FERPA), 216, 223 28, 226 federal financial aid, 20, 33, 227 graduate students fees degree requirements for, 215 J discipline process for, 221–223 graduate, 30–31 James H. and Christine Turk Berick financial aid for, 32–34, 227 refunds of, 19, 31 Center for Student Advising, 8, 219, tuition and fees, 30–31 undergraduate, 18–19 226 graduation, 217 See also payments joint programs graphics, courses in, 101 fellowships, 32 with Data Science Institute, 23 Greek or Latin, minor in, 207 financial aid with the Graduate School of eligibility for, 20 Business, in industrial engineering, employment and, 34 H 23, 167 federal, 33 with the School of International and health insurance, 18, 30–31 to graduate students, 32–34, 227 Public Affairs, 17 health service. See Columbia Health how to apply for, 20 with School of Journalism, 23–24 Henry Krumb School of Mines (HKSM), private programs, 33–34 See also dual degree 123 to undergraduate students, 20, 227 Junior-Senior programs, 14–16 financial engineering See also Earth and Environmental graduate program in, 164 Engineering, Department of First Year–Sophomore Program course Hispanic studies, minor in, 207 L history, minor in, 207 requirements laboratory charges, 18–19, 31 honors, academic, 218, 221 nontechnical, 9–11 Langmuir Center for Colloids and professional-level, 11 Interfaces (LCCI), 126 technical, 11 I Latin, Greek or, minor in, 207 4-1 Combined Plan B.S. program, 17 leave(s) of absence industrial engineering 4-2 Combined Plan M.S. program, 23 family, 220 courses in, 168–176 Free Application for Federal Student involuntary, 220 minor in, 207 Aid (FAFSA), 32–33 medical, 219 Industrial Engineering and Operations French military, 220 Research, Department of, 157–176 and francophone studies, minor in, voluntary, personal, 219–220 current research activities, 158 207 Lenfest Center for Sustainable Energy, graduate programs, 164–168 minor in, 207 126 joint programs, 23, 168 Fu Foundation School of Engineering Library, Science & Engineering, 227 minors, 206–208 and Applied Science, The. See Libraries, Columbia University, 227 undergraduate programs, 158–164 Engineering, School of lightwave (photonics) engineering, Industry/University Cooperative Fundamentals of Engineering (FE) specialization in, 145 Research Center for Particulate and exam, 23, 193–194 loans, student, 33 Surfactant Systems (CPaSS), 125

ENGINEERING 2021–2022 M maps of, 230–231 Professional Development and 235 Multicultural Affairs, 226 Leadership Program, 11, 23, 29, 54, Makerspace, 5–6 music 68, 78, 92, 102, 110, 127, 143, 164, 181, management science and engineering, instruction courses, 10 195, 211 graduate program in, 166–167 minor in, 207–208 professions other than engineering, maps of Columbia Morningside Heights Engineering programs in campus, 230–231 preparation for, 16–17 marks. See grading system N psychological services, counseling Master of Science degree (M.S.), names, student, change of, 217 and, 227 22–24 nanomaterials, 178–179 psychology, minor in, 208 materials chemistry/soft materials, 181 networking, specialization in, 144 Public Safety, Office of, 228 materials for green energy, 179 New York City, 4 materials for health and biotechnology, New York State 179–181 R initial certification in adolescence materials for next generation education, 17 readmission, 220 electronics, 179 Nondegree students, 25, 29 refunds of tuition and fees, 19, 31 materials science nontechnical requirements, 9–13 registrar, 228 courses in, 183–185 See also Student Service Center minor in, 207 registration, 214 Materials Science and Engineering O changes in, 215 program (MSE), 55, 61, 123, 177–185 officers of Columbia Engineering religion, minor in, 208 current research activities, 177–178 list of, 36, 42–44 report of grades, 216 graduate programs, 181–183 retired, list of, 41–42 Residence Units, and the Ph.D., 24 graduate specialty in solid-state Ombuds Office, 228 resources, Columbia University, list of, science and engineering, 182–183 operations research 226–228 interdepartmental committee and, 177 graduate program in, 168 Rules of University Conduct, 221–223 laboratory facilities, 178 minor in, 208 undergraduate program, 178–181 undergraduate programs in, 158–164 Mathematics, Department of, 228 S See also Industrial Engineering and mechanical engineering Operations Research, Department of sanctions, for academic dishonesty, 218 courses in, 196–202 optical and laser physics, graduate School of Engineering. See minor in, 207 program in, 56 Engineering School Mechanical Engineering, Department Science & Engineering Library, 227 of, 186–202 Sexual Violence Response, 227 current research activities, 186–189 P Social Security number, registration facilities for teaching and research, payments and, 214 189–191 timely and overdue, 18, 30 sociology, minor in, 208 graduate programs, 194–196 See also fees solid-state physics, graduate program undergraduate program, 191–194 Pearson Test of English (PTE), 28 in, 56–57 medical care and insurance, 18, 30, 227 personal expenses of students, 18, 31 solid-state science and engineering Medical College Admissions Test philosophy, minor in, 208 areas of research, 183 (MCAT), 16 physical education, 11, 13 graduate specialty in, 182–183 medical leave of absence, 219 Physical Education, Intercollegiate sports, 11, 13 medical physics, graduate program Athletics and, Department of, 227 Statistics, Department of, 228 in, 55 Physics, Department of, 228 statistics, minor in, 208 medical services and Columbia Health plagiarism, 221–222 Student Advising, Center for, 226 program, 227 plasma physics, graduate program in, Student Conduct and Community microelectronic devices, specialization 56 Standards, 228 in, 145 Plasma Physics Laboratory, 49 Student Engagement, 226 Middle Eastern, South Asian, and political science, minor in, 208 Student Financial Planning, Office of, African Studies, minor in, 207 prelaw program, 17 32–34, 227 military leave of absence, 220 premed program, 16 Student Financial Services. See minors, academic, 16, 204–208 preprofessional advising, 8–9, 16–17 Student Service Center Morningside Heights campus, 5

ENGINEERING 2021–2022 236 student loans, 33 Test of English as a Foreign Language V Student Medical Insurance Plan, 18, (TOEFL), 28–29 Veteran Affairs, Department of, 33 30–31, 227 3-2 Combined Plan B.A./B.S. program, veterans, educational benefits for, student records, rights pertaining to, 14 33–34 223 transcripts, 216 visual arts courses, 10–11 Student Research Program, 8 transfer credits, 215 Student Service Center, 228 transfer students, 29 students tuition W contributions of, to educational graduate, 30–31 Waste to Energy Research and costs, 18–19, 30–31 refunds of, 18, 31 Technology Council (WTERT), 125 employment and earnings of, 33–34 undergraduate, 18–19 water resources and climate risks, international, 33 specialization in, 127 name changes of, 217 U wireless and mobile communications, nondegree, status, 25, 29 specialization in, 144 personal expenses of, 18, 31 Undergraduate Financial Aid and transfer, 29 Educational Financing, 227 See also engineering students; Undergraduate Global Engagement, graduate students; undergraduates Center of, 13–14, 227 study abroad, 13–14 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 sustainable waste management, financial aid for, 20 127–128 minor programs for, 16, 204–208 systems biology and neuroengineering, programs in Engineering School for, specialization in, 145 8–17 tuition and fees of, 18–19 See also students T University Chaplain, Office of the, 227 Tau Beta Pi, 14 teacher certification, obtaining, 17 telephone numbers of Columbia University departments and resources, 226–228

ENGINEERING 2021–2022