2009–2010 The Fu Foundation School of Engineering and Applied Science Applied and Engineering of School Foundation Fu The 2009–2010

The Fu Foundation School of Engineering and Applied Science Bulletin 2009–2010

The Fu Foundation School of Engineering and Applied Science 500 West 120th Street New York, New York 10027

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Mission of the Engineering School The Fu Foundation School of Engineering and Applied Science, as part of a world-class teaching and research university, strives to provide the best in both undergraduate and graduate education. We are preparing engineering leaders who will solve the problems of the new century, fostering scientific inquiry but never losing sight of its human implications. The School’s programs are designed to produce well-educated engineers who can put their knowledge to work for society. This broad educational thrust takes advantage of the School’s links to a great liberal arts college and to distinguished graduate programs in law, business, and medicine. Recognizing that engineers are problem solvers and inventors, students are encouraged to pursue entrepreneurship, a blending of business and new technology. Through a synergy of teaching and research, we seek to educate a distinguished cadre of leaders in engineering and applied science who will thrive in an atmosphere of recently emerging technologies.

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A MESSAGE FROM THE DEANS

s students of the Columbia Fu through a minor, or your involvement in entre- Foundation School of Engineering preneurship initiatives, research opportunities, A and Applied Science, you are among and community-based service learning. The the select few who have joined our community overarching connector of these two founda- for an education that will enable you to become tions, the crossbeam of the π, is Columbia’s the next leaders in the fields of engineering famed liberal arts Core Curriculum, the and applied science. You, too, will become umbrella that positions engineering and part of the history of this School, which is applied science within the context of the larg- inextricably entwined with Columbia University’s er society, for the betterment of the human and with that of the City of New York. condition and the sustainability of our planet. Sir Isaac Newton said: “If I have seen far- Some of the most exciting work in engi- ther, it is by standing on the shoulders of neering and applied science today takes place giants.” Some of Columbia’s early giants at the intersection of disciplines. Research in include John Stevens, Class of 1768, whose materials science, bioengineering, and nano- technology made early steamboats and loco- technology are but a few examples of where motives possible. His work provided inspira- the biological, physical, and digital worlds tion for William Barclay Parsons, Class of intersect and where you have the opportunity 1882, the chief engineer of New York City’s to have a profound impact on society. first subway system and the first Columbia Engineering is not just crunching numbers engineer to have a global presence, going or solving problems; it is seeing how problems to Shanghai in 1898 to become a primary affect society and how society actually changes surveyor for China’s 1,000-mile-long railway because of the solutions you provide. You route. Later Columbia inventors who fostered have an opportunity here as students to a shrinking globe were Michael Pupin, the become involved in the community, so that, developer of the transatlantic undersea tele- as you move into your professional life, you graph cable, and Edwin Armstrong, who will become a leader who has an impact on revolutionized modern radio communications. the human condition and the sustainability of Just this May, our alumnus-astronaut Michael our planet, whether it is locally, nationally, or Massimino ’84, on an eleven-day mission to globally. service Hubble Space Telescope, became the You are part of a school that offers great first person in space to use Twitter. We are opportunities for learning and advancement excited that you have seized the opportunity within a premier research university that is to join this list of very notable engineers and situated in the laboratory of the City of New applied scientists. York. We look forward to your becoming part Now, our School is meeting the challenge of the Columbia SEAS family as you embark of educating you as a leader of the next wave on making your mark on society at large. of engineers and applied scientists by foster- ing an engineering education paradigm that is symbolized by the Greek letter π. The first Feniosky Peña-Mora foundation, or support column, of the π is the Dean depth of knowledge you gain in your engi- neering or applied science major. The second Morton B. Friedman foundation is the knowledge you acquire Vice Dean

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TABLE OF CONTENTS

About the School and 1 Graduate School Departmental 42 Humanities and Social Sciences 200 University Funding Mathematics 200 HISTORY OF THE SCHOOL 2 Alternative Funding Sources 42 Physics 201 RESOURCES AND FACILITIES 5 Other Financial Aid—Federal, 43 Statistics 203 State, and Private Programs Undergraduate Studies 9 Employment 44 Campus and Student Life 205 Contact Information 44 THE UNDERGRADUATE 10 CAMPUS LIFE 206 PROGRAMS STUDENT SERVICES 212 Policy on Degree Requirements 10 Faculty and Administration 45 The First Year–Sophomore Program 10 Departments and Academic 53 Scholarships, Fellowships, 215 Study Abroad 14 Awards, and Prizes Combined Plan Programs 15 Programs The Junior–Senior Programs 16 KEY TO COURSE LISTINGS 54 University and School 227 Programs in Preparation for 18 APPLIED PHYSICS AND 56 Policies, Procedures, and Other Professions APPLIED MATHEMATICS Regulations Joint Programs 19 Registered Programs 19 BIOMEDICAL ENGINEERING 69 ACADEMIC PROCEDURES 228 AND STANDARDS UNDERGRADUATE ADMISSIONS 21 CHEMICAL ENGINEERING 81 Admission as a First-Year Student 21 ACADEMIC STANDING 232 CIVIL ENGINEERING AND 92 Applicants with Advanced Standing 22 ENGINEERING MECHANICS POLICY ON CONDUCT AND 234 Campus Visits and Interviews 23 DISCIPLINE COMPUTER ENGINEERING 103 UNDERGRADUATE TUITION, 24 PROGRAM OFFICIAL UNIVERSITY 238 FEES, AND PAYMENTS REGULATIONS COMPUTER SCIENCE 108 FINANCIAL AID FOR 26 STUDENT GRIEVANCES, 242 UNDERGRADUATE STUDY EARTH AND ENVIRONMENTAL 120 ACADEMIC CONCERNS, AND Determining Eligibility 26 ENGINEERING COMPLAINTS Financial Aid Awards 27 ELECTRICAL ENGINEERING 134 How to Apply for Financial Aid 28 Directory of University 245 Tax Withholding for Nonresident 29 INDUSTRIAL ENGINEERING 151 Resources Alien Scholarship and AND OPERATIONS RESEARCH COLUMBIA UNIVERSITY 246 Fellowship Recipients RESOURCE LIST MATERIALS SCIENCE AND 167 Graduate Studies 31 ENGINEERING PROGRAM MAPS 252 THE GRADUATE PROGRAMS 32 MECHANICAL ENGINEERING 174 INDEX 254 The Master of Science Degree 32 The Professional Degree 34 Undergraduate Minors 187 Academic Calendar (see inside back Doctoral Degrees: Eng.Sc.D. 34 cover) and Ph.D. Interdisciplinary Courses 195 Special Nondegree Students 35 and Courses in Other COLUMBIA VIDEO NETWORK 36 Divisions of the University INTERDISCIPLINARY 196 GRADUATE ADMISSIONS 37 ENGINEERING COURSES GRADUATE TUITION, FEES, 39 COURSES IN OTHER DIVISIONS 197 AND PAYMENTS OF THE UNIVERSITY FINANCIAL AID FOR GRADUATE 41 Biological Sciences 197 STUDY Business 197 Financing Graduate Education 41 Chemistry 197 Instructions for Financial Aid 41 Earth and Environmental Sciences 198 Applicants 160-0450_Bulletin0910REV.qxd 7/23/09 12:05 PM Page 1

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2 HISTORY OF THE SCHOOL

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

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neers of the far-reaching political impli- THE NEW CENTURY largest patent income from inventions cations of that technology as well. No one could have imagined the explo- created by its faculty. The University is After receiving a master’s degree sive growth of technology and its inter- the only academic institution that holds from the School in 1929, Admiral Hyman disciplinary impact. The Engineering patents in the patent pool for the manu- George Rickover served during the School is in a unique position to take facture of MPEG-2, the technology that Second World War as head of the elec- advantage of the research facilities and enables DVDs and high definition TV. trical section of the Navy’s Bureau of talents housed at Columbia to form Another exciting patent that holds great Ships. A proponent of nuclear sea relationships among and between other promise is a laser-based method that power, Rickover directed the planning schools and departments within the makes possible, among other things, and construction of the world’s first University. The School’s newest depart- the sharper display screens found in nuclear submarine, the 300-foot-long ment, Biomedical Engineering, with high-end smart phones. Sequential lat- Nautilus, launched in 1954. close ties to the Medical School, is but eral solidification (SLS) is based on one example. Interdisciplinary centers breakthrough research in understanding THE TECHNOLOGICAL AGE are the norm, with cross-disciplinary how a substance is rapidly melted and research going on in biomedical imaging, solidified. The result is an optimal crys- Today, The Fu Foundation School of environmental chemistry, materials science, talline material that enables a new gen- Engineering and Applied Science, as medical digital libraries, nanotechnology, eration of smart phones. Within a short it was named in 1997, continues to digital government, new media technolo- time, thanks to the innovations taking provide leadership for scientific and gies, and GK-12 education. The School place in SEAS labs, it may be possible educational advances. Even Joseph and its departments have links to the to put an entire computer on a sheet of Engelberger, Class of 1946, the father Departments of Physics, Chemistry, glass or plastic. of modern robotics, could not have Earth Science, and Mathematics, as anticipated the revolutionary speed with well as the College of Physicians and which cumbersome and expensive “big ENGAGED Surgeons, the Graduate School of science”computers would shrink to the ENTREPRENEURSHIP Journalism, Lamont-Doherty Earth size of a wallet. Entrepreneurship has emerged as an Observatory, Teachers College, and the In 1986 the Engineering School was important central educational theme Graduate School of Architecture, one of the first schools in the country within The Fu Foundation School of Planning and Preservation. The trans- to use videotapes as tools for distance Engineering and Applied Science. SEAS forming gift of The Fu Foundation has learning. Today Columbia Video Network promotes engineering innovation and catapulted the School into the forefront continues to be in the forefront of dis- engaged entrepreneurship through the of collaborative research and teaching tance learning at the graduate level Center for Technology, Innovation, and and has given students the opportunity through its online education programs. Community Engagement (CTICE). The to work with prize-winning academicians, Named as one of Forbes Magazine’s School offers a 15-credit, interdiscipli- including Nobel laureates, from many “Best of the Web,” CVN offers the nary minor in entrepreneurship made up disciplines. opportunity for students anywhere in the of both SEAS and Columbia Business world to enroll in certificate programs or School courses, and now provides a obtain a master’s or professional degree THE NEW RESEARCH four-year entrepreneurship experience from Columbia Engineering and Applied For the past several years, Columbia for all interested SEAS students, regard- Science via the World Wide Web. has been first among the handful of less of major. research universities that earn the

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A FORWARD-LOOKING an engineer can navigate the future, all perspective. It is also these Core cours- TRADITION undergraduates must complete a modi- es that most closely tie today’s student But, for all its change, there is still a con- fied but equally rigorous version of to the alumni of centuries past. Through tinuous educational thread that remains Columbia College’s celebrated Core a shared exposure to the nontechnical the same. The Fu Foundation School Curriculum. It is these selected courses arts, all Columbia engineering stu- of Engineering and Applied Science still in contemporary civilization in the West dents—past, present, and future—gain remains an institution of manageable and other global cultures that best pre- the humanistic tools needed to build size within a great university. Committed pare a student for advanced course lives not solely as technical innovators, to the educational philosophy that a work; a wide range of eventual profes- but as social and political ones as well. broad, rigorous exposure to the liberal sions; and a continuing, life-long pursuit arts provides the surest chart with which of knowledge, understanding, and social

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RESOURCES AND FACILITIES 5

A COLLEGE WITHIN THE Asian in Chinatown; and sports teams ments over the years, Columbia engi- UNIVERSITY from the Jets to the Yankees, New York neers have been responsible for the A unique educational opportunity, is the crossroads of the world. design, analysis, and maintenance of New Columbia University’s Fu Foundation New York is fast becoming a major York’s enormous infrastructure of munici- School of Engineering and Applied player in high-tech research and devel- pal services and communications links, Science (SEAS) offers programs to both opment, where Fortune 500 companies as well as its great buildings, bridges, undergraduate and graduate students traded on Wall Street seek partnerships tunnels, and monuments. who undertake a course of study leading with high-tech start-up ventures in to the bachelor’s, master’s, or doctoral Tribeca. And as more and more compa- THE UNIVERSITY AT LARGE degree in engineering and applied science. nies discover the advantages of locating Columbia University occupies two major Combining the advantages of a small in New York’s greater metropolitan area, campuses, as well as additional special- college with the extensive resources of they join such long-standing facilities as purpose facilities throughout the area. a major research university, students at AT&T Laboratories, Bell Communications Besides the main campus located on the School pursue their academic inter- Research, Exxon Research, IBM Research the Upper West Side in Morningside ests under the guidance of outstanding Laboratories, International Paper, Heights, further uptown in Washington senior faculty members who teach both NYNEX, and many other major compa- Heights is the Health Sciences campus, undergraduate and graduate level courses. nies involved in high-tech R&D. As part which includes Columbia’s medical Encouraged by the faculty to undertake of the research community themselves, school (the College of Physicians and research at all levels, students at the Columbia students have exceptional Surgeons), the Mailman School of Public School receive the kind of personal opportunities for contact with industry Health, the New York State Psychiatric attention that only Columbia’s exception- both on and off campus. Senior repre- Institute, and other health professions ally high faculty-student ratio affords. sentatives of these companies often visit programs. The Health Sciences Division Columbia to lecture as adjunct faculty is an equal partner with NewYork- members or as special speakers, and THE NEW YORK ADVANTAGE Presbyterian Hospital in the Columbia- undergraduate and graduate students Presbyterian Medical Center, the world’s Besides the faculty, the single greatest frequently undertake research or intern- first academic medical center. The facility at a Columbia student’s disposal ships with these and other companies, medical center opened in 1928 when is without doubt the City of New York. oftentimes leading to offers of full-time Columbia’s health-related schools and Within easy reach by walking, bus, sub- employment after graduation. Presbyterian Hospital (which has since way, or taxi, New York’s broad range of In addition to its ties to private indus- merged with New York Hospital to social, cultural, and business communi- try, Columbia also has a historically close become NewYork-Presbyterian Hospital) ties offer an unparalleled opportunity relationship with the public sector of New moved to the Washington Heights loca- for students to expand their horizons or York, stretching back to the eighteenth tion. The Engineering School’s new deepen their understanding of almost century. No other city in the world offers Biomedical Engineering Department any human endeavor imaginable. With as many impressive examples of the built has offices on both the Morningside art from small SoHo galleries to major environment—the world’s most famous and Health Sciences campuses. Uptown museums; music from Harlem collection of skyscrapers, long-span Beyond its schools and programs, jazz clubs to the Metropolitan Opera; bridges, road and railroad tunnels, one of the measure of Columbia’s true breadth theatre from performance art in the East the world’s largest subway and water and depth must take into account its Village to musicals on Broadway; food supply systems. Involved in all aspects of seventy-odd internationally recognized from French on the Upper East Side to the city’s growth and capital improve-

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6 centers and institutions for specialized and equipped to meet the laboratory and CUIT Client Service Center research, which study everything from research needs of both undergraduate 102 Philosophy Hall human rights to molecular recognition, and graduate students, the School is the Monday-Friday: 10:00 a.m.–6:00 p.m. as well as the close affiliations it holds with site of an almost overwhelming array of Teachers and Barnard Colleges, the basic and advanced research installa- Columbia University Information Techno- Juilliard School, the American Museum of tions, from the Columbia Genome Center logy (CUIT) provides Columbia University Natural History, and both the Jewish and and Nanoscale Science and Engineering students, faculty, and staff with central Union Theological Seminaries. Columbia Center to the School’s newest major computing and communications services, also maintains major off-campus facilities center, the Energy Frontier Research including computer accounts, e-mail, tele- such as the Lamont-Doherty Earth Center, which will examine new and phone and cable TV service, and course Observatory in Palisades, N.Y., and the more efficient ways to extract solar energy. management and student information Nevis Laboratories in Irvington, N.Y. Details about specific programs’ labora- applications. CUIT manages the Columbia Involved in many cooperative ventures, tories and equipment can be found in wireless network and the high-speed cam- Columbia also conducts ongoing research the sections describing those programs. pus Ethernet network, which is available to at such facilities as Brookhaven National all students in residence hall rooms. CUIT also manages an array of computer labs, Laboratory in Upton, N.Y., and the NASA SEAS COMPUTING FACILITIES Goddard Institute for Space Studies terminal clusters, ColumbiaNet kiosk sta- The Botwinick Multimedia Learning located just off the Morningside campus. tions, and electronic classrooms, and pro- Laboratory at Columbia University has vides a variety of technical support services changed the way engineers are educated via the CUIT Helpdesk. CUIT services THE MORNINGSIDE HEIGHTS here. include the following: CAMPUS Created with both education and inter- The Fu Foundation School of Engineering action in mind, the lab provides students • Computer account IDs provide access and Applied Science is located on and instructors with fifty state-of-the-art to Columbia’s secure online informa- Columbia’s Morningside campus. One of Apple MacPro workstations, a full set of tion resources, campus computer the handsomest urban institutions in the professional-grade engineering software labs, and printing on CUIT printers. All country, the thirty-two acres of the tools, and a collaborative classroom learn- Columbia students, faculty, and staff Morningside campus comprise over sixty ing environment to help them engage in are assigned an ID account (called buildings of housing; recreation and real-world interactions with community University Network ID or UNI). research facilities; centers for the humani- clients, SEAS faculty, and professional uni.columbia.edu. ties and social and pure sciences; and practitioners. It is home to the School’s • Columbia’s Web site provides access professional schools in architecture, busi- introductory first-year engineering course, to hundreds of online services and ness, the fine arts, journalism, law, and as well as advanced classes in 3-D mod- resources, including extensive aca- other fields. eling and animation, technology and soci- demic, scholarly, and administrative ety, and entrepreneurship. resources, a myriad of library catalogs THE FU FOUNDATION The classroom features a wide-screen and references, the Directory of SCHOOL OF ENGINEERING SMART Board, two high-definition LCD Classes, registration information, cam- AND APPLIED SCIENCE projectors, and a Sony EVI-HD1 PTZ pus publications, and events listings. camera with direct-to-disk recording via The Fu Foundation School of www.columbia.edu HD-SDI using a Kona3 video capture card. Engineering and Applied Science occu- • Technical support is available through pies three laboratory and classroom the CUIT Helpdesk, which provides buildings at the north end of the cam- CENTRAL COMPUTING assistance to the Morningside campus pus, including the Schapiro Center for RESOURCES online, by phone, or in person. (See Engineering and Physical Science Columbia University Information beginning of this section for hours and Research. In September 2010 the Technology (CUIT) contact information.) Interdisciplinary Science and Engineering www.columbia.edu/cuit • Courseworks@Columbia is the Building currently under construction is University course management sys- scheduled to open and will house SEAS Contact the CUIT Helpdesk for tem. It allows instructors to develop laboratories in nanotechnology and Technical Support and maintain course Web sites easily, distribute class materials, link to on- biomedical imaging. Because of the E-mail: [email protected] School’s close proximity to the other line reserves, administer quizzes and By phone: 212-854–1919 Morningside facilities and programs, tests, communicate with students, Monday–Thursday: 8:00 a.m.–11:00 p.m. Columbia engineering students have and promote online discussions. Friday: 8:00 a.m.–7:00 p.m. ready access to the whole of the courseworks.columbia.edu Saturday: 10:00 a.m.–6:00 p.m. University’s resources. • Electronic classrooms provide multi- Sunday: 3:00 p.m.–11:00 p.m. Comprising multiple programs of media capabilities such as computer study, with facilities specifically designed In person (some consultations may and projection systems, DVD and require an appointment): CD-ROM players, VCRs, and audio

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systems. www.columbia.edu/ is a gateway to the print and electronic study abroad, preparation for the job 7 cuit/classrooms collections and services. search or for the graduate/professional • Public computer kiosks are available in The Ambrose Monell Engineering school application process, and plan- various locations around the Library has a collection of more than ning for productive careers. Above all Morningside campus for accessing 216,000 volumes and receives about else, it is a process of discovery and Columbia’s Web site resources and 900 serials. The collection includes civil, learning, which provides a foundation e-mail. www.columbia.edu/ mechanical, electrical, and chemical for achieving goals throughout life. The cuit/facilities/cnet engineering; computer science; metal- Center can work with students on all • Computer labs and clusters provide lurgy; mining (a good retrospective these aspects of their career search. students, faculty, and researchers with collection); operations research; applied The Center maintains a Web site that access to a range of software. Some physics; applied mathematics; and contains information on career search locations have part-time consultants nuclear engineering. Via LibraryWeb, the strategies and tools, upcoming events, to provide lab help. www.columbia. Engineering Library provides access to career fairs, full- and part-time job listings, edu/cuit/facilities/labs full-text electronic journals and a collec- and internships. The Center encourages • Printing facilities are available through- tion of many specialized databases in students and alumni to visit the Center out the Morningside campus and engineering and the sciences, e.g., and to register to use Columbia’s job Barnard College, including CUIT com- Compendex, Inspec, Web of Science, and internship database, LionSHARE, in puter labs, libraries, residence halls, ACM Digital Library, and IEEE Electronic order to maximize the level of resources and other computer clusters and Library. and assistance they can receive. electronic classrooms. Printing is pro- Individual career counseling is also vided by the NINJa printing system CENTER FOR CAREER available to assist all students and alumni on high-speed, high-volume printers. EDUCATION served by the Center. Topics addressed www.columbia.edu/cuit/facilities/ in counseling may include self-assess- Center for Career Education printers ment, career exploration, and career Columbia University • Computer security resources are avail- search tools and strategies. East Campus, Lower Level able online, including links to download The Center recognizes the special Mail Code 5727 antivirus and anti-spyware software. interests of graduate students in the 2960 Broadway The site also provides information on University with programs, workshops, New York, NY 10027 how to protect your system when and one-on-one counseling opportuni- working online. www.columbia.edu/ Delivery: 70–74 Morningside Drive ties that focus on both academic and cuit/security Phone: 212-854-5609 nonacademic careers. On-campus • Electronic Data Service (EDS), run Fax: 212-854-5640 recruiting and LionSHARE are, of jointly by CUIT and the Libraries, pro- E-mail: [email protected] course, available to graduate students. vides computing support for researchers www.careereducation.columbia.edu The Center also maintains a dossier with data-intensive applications, service, managed by Interfolio, for grad- The Columbia University Center for including special accounts, statistical uate students and alumni who hold Career Education helps students and software, and finding and selecting graduate degrees. A dossier consists of alumni develop the key competencies appropriate data. www.columbia.edu/ letters of reference and other credentials necessary to make informed decisions cuit/eds that speak to a candidate’s scholarship, and take the necessary steps to achieve • Telephone and cable TV service is research interests, and teaching experi- their career goals. The Center establishes available to students living in University ence. It is typically used in applying for connections and facilitates interaction residence halls. www.columbia.edu/ teaching positions at either the second- among undergraduate students, gradu- acis/telecom/students ary level or the college level and for ate students, alumni, employers, and graduate/professional school and fellow- organizations to generate opportunities ship applications. Students can register THE COLUMBIA UNIVERSITY that help students pursue their personal online for the service at www.interfolio.com. LIBRARIES and professional career objectives. It is recommended that candidates for The Columbia University Libraries system The Center for Career Education pro- teaching positions open a credentials file is the nation’s sixth largest academic vides career development opportunities in the late summer or early autumn of library system, with 9.7 million volumes, for students beginning with their first the year preceding their availability for 117,264 serials, as well as extensive year at Columbia and offering a series employment. Undergraduate students or collections of electronic resources, man- of coordinated programs, workshops, alumni with undergraduate degrees from uscripts, rare books, and microforms seminars, and individual one-on-one SEAS should contact the Center for and other nonprint formats. The collec- counseling. Career development is a Student Advising for dossier management. tions and services are organized into 25 lifelong process that may include self- The Center manages full-time and libraries, supporting specific academic assessment, competency development, internship opportunities for students or professional disciplines. The Library’s networking, informational interviewing, throughout the year in two capacities. Web site at www.columbia.edu/ cu/lweb internships, summer work experience,

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8 On-campus recruiting is conducted The Center for Career Education also country. Services for international stu- throughout the academic year and fosters entrepreneurship through Columbia dents include preadmission counseling, allows students to submit their resumes Student Enterprises (CSE). The Columbia document and other immigration-related and cover letters online to any of the Student Enterprises program is a unique services, the International Orientation opportunities from employers who have opportunity to learn about and develop program, social and cultural activities, chosen to recruit on campus. These valuable entrepreneurship and enterprise and a program for the spouses of stu- opportunities are listed in LionSHARE. leadership skills through managing and dents. The ISSO also provides credential LionSHARE also hosts full-time, part- working for student-run enterprises. The analysis services to the admissions offices time, and temporary on- and off-campus program consists of student-managed of the University. The ISSO is open year- employment opportunities advertised businesses such as the Columbia round, and international students are year round. While at Columbia, students Bartending Agency and School of urged to make use of its services during are encouraged to take advantage of Mixology, Inside NY (a distinctive tourist their stay at the University and are also internships that offer opportunities to guide to New York), and the Columbia invited to visit the ISSO Web site at gain first-hand knowledge of a career University Tutoring and Translation www.columbia.edu/cu/isso, with com- field. Agency. The participants of the program prehensive information for both prospec- The Center offers international intern- receive training and develop transferable tive and current students. ship opportunities through two programs, business skills applicable to all indus- The staff of the International Students Columbia Experience Overseas (CEO) tries. The program also promotes stu- and Scholars Office is available for per- and Encouraging Dynamic Global dent initiatives in business and increases sonal advisement and for help in learning Entrepreneurs (EDGE). The CEO program services on campus, enhancing the qual- about the campus and New York City. offers Columbia students high-quality ity of student life and creating job oppor- The ISSO is an essential source of infor- internship experiences in a diverse array tunities for Columbia University students. mation regarding immigration and Depart- of industries in London and Hong Kong To gain a complete understanding ment of State regulations that affect through alumni and employer partner- of all Center for Career Education students studying in the United States. ships. EDGE Scotland is a summer pro- programs and resources, please visit The staff can also assist with many other gram in entrepreneurship and enterprise the Center in the lower level of East non-academic matters. The ISSO pro- leadership offered in collaboration with Campus. For additional information and vides information about cultural activities Scottish Enterprise Dunbartonshire and questions, please call 212-854-5609. in the New York area and has reduced- the University of Glasgow, with support rate tickets for plays, concerts, and from the European Union, the Scottish THE INTERNATIONAL other events. Executive, and others. It takes place in STUDENTS AND SCHOLARS Students are required to check in Dunbartonshire, an economically under- OFFICE (ISSO) with the ISSO within a week of their developed area of Scotland. Student International Students and arrival at Columbia. The office’s street consulting teams are challenged to solve Scholars Office address is 524 Riverside Drive in Inter- real-world business problems by analyz- Columbia University national House North, just north of 122nd ing business climate, identifying oppor- Mail Code 5724 Street. The orientation program for new tunities for innovation, and proposing 2960 Broadway international students arriving for the solutions and initiatives to create a more New York, NY 10027 September term takes place during entrepreneurial and economically vibrant orientation week, usually the last week Phone: 212-854-3587 culture. The Center also offers an intern- in August or the first week in September. e-mail [email protected] ship program in California with many For further information, consult the engineering and technology internships The International Students and Scholars International Students and Scholars and two New York–based internship Office (ISSO) offers many services for Office using the contact information programs, the Columbia Arts Experience international students as well as American above. and a civic engagement program called citizens and permanent residents who Columbia Communities in Action. have received their education in another

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Undergraduate Studies 160-0450_Bulletin0910REV.qxd 7/23/09 12:05 PM Page 10

10 THE UNDERGRADUATE PROGRAMS

he undergraduate programs at faculty projects in which students may THE FIRST YEAR— The Fu Foundation School of participate, lists necessary qualifications, SOPHOMORE PROGRAM T Engineering and Applied Science and details whether the student’s partici- Students entering The Fu Foundation (SEAS) not only are academically excit- pation will be voluntary, for academic School of Engineering and Applied ing and technically innovative but also credit, or for monetary compensation. Science are encouraged to consider the lead into a wide range of career paths In addition to in-depth exploration of wide range of possibilities open to them, for the educated citizen of the twenty-first engineering and applied science, SEAS both academically and professionally. To century. Whether you want to become a undergraduates explore the humanities this end, the first and second years of professional engineer, work in industry or and social sciences with Columbia College the four-year undergraduate program government, or plan to pursue a career in students through intellectually challeng- comprise approximately 66 semester the physical and social sciences, medi- ing Core Curriculum courses taught by points of credit that expose students to cine, law, business, or education, SEAS the Faculty of Arts and Sciences. These a cross-fertilization of ideas from different will provide you with an unparalleled courses in art, literature, music, major disciplines within the University. The education. cultures, and economics, among others, sequence of study proceeds from an SEAS firmly believes that students provide students with a broad, intellectu- engagement with engineering and scien- gain the most when engineering is ally disciplined, cultural perspective on tific fundamentals, along with humanities brought up front, early in the four-year the times they live in and the work they do. and social sciences, toward an increas- curriculum. Therefore, first-year students ingly focused training in the third and use the networked, high-performance POLICY ON DEGREE fourth years designed to give students workstations and multimedia software of REQUIREMENTS mastery of certain principles and arts the Botwinick Multimedia Learning central to engineering and applied science. The Committee on Instruction and Laboratory as part of their technical core faculty of The Fu Foundation School of requirements. Here students apply fun- Engineering and Applied Science review Liberal Arts Core for SEAS Students: damental principles degree requirements and curricula mat- 27-Point Nontechnical Requirement of engineering design to modeling ters each year, and the bulletin reflects This requirement provides a broad liberal advanced engineering and applied these faculty recommendations and cur- arts component that enhances the SEAS science problems. Later in the four-year ricular changes in its yearly reprinting. professional curriculum to help students program, students often use the School policy requires students to fulfill all meet the challenges of the twenty-first Laboratory’s symbolic, numeric, and general degree requirements as stated century. Our students are destined to graphical computing power in ever deep- in the bulletin of the first year of their be leaders in their professions and will ening integration with classroom, labora- matriculation into the School. Students require sophisticated communication, tory, and research work of their chosen declare their major during the first planning, and management skills. engineering program. semester of their sophomore year. The SEAS Committee on Instruction While pursuing their own interests, Requirements for the major or minor are established the school’s nontechnical undergraduate students are encouraged in accordance with the bulletin during requirement so that students would to participate in a broad range of ongoing the year in which the student declares learn perspectives and principles of the faculty research projects encompassed the major or minor. humanities and social sciences as part by the Undergraduate Research Involve- of a well-rounded and multiperspective ment Program (URIP). An annual URIP education. Through discussion, debate, publication sent to students describes and writing, students improve their ability

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to engage in ethical, analytic, discursive, Global Core ASIAN AMERICAN STUDIES: All courses and imaginative thinking that will prove (any 2 courses from approved list 6–8 ASTRONOMY: No courses indispensable later in life. 3. One of the following two courses: BIOLOGICAL SCIENCES: No courses • SEAS students must take 16 to 18 HUMA W1121 BUSINESS: No courses points of credit of required courses in Masterpieces of Western art list A and 9 to 11 elective points cho- or CHEMISTRY: No courses HUMA W1123 sen from the approved courses in list CLASSICS: All courses Masterpieces of Western music 3 B. The total combined number of non- COLLOQUIA: All courses technical points (from lists A and B, 4. ECON W1105 below) must add up to at least 27. Principles of economics COMPARATIVE ETHNIC STUDIES: All courses Neither list can be modified by advis- (This course can be satisfied through Advanced Placement; see the Advanced COMPARATIVE LITERATURE AND SOCIETY ing deans or faculty advisers. Placement chart on page 14.) Note: SEAS All courses • Advanced Placement (AP) credit in students may not take BC1003 Introduction COMPUTER SCIENCE: No courses appropriate subject areas can be to economic reasoning as a substitute for applied toward the 9-point elective ECON W1105. 4 CREATIVE WRITING: All courses nontechnical requirement. DANCE All courses except performance classes If electing Global Core, students B. Elective Nontechnical Courses must take two courses from the (9–11 points of credit) DRAMA AND THEATRE ARTS List of Approved Courses (www.college. The following course listing by depart- All courses except workshops, rehearsal, or columbia.edu/bulletin/core/mc.php) for a ment specifies the Columbia College, performance classes, THTR BC2120 Technical letter grade. Barnard, or SEAS courses that either production, THTR BC3135 Set design, and THTR fulfill or do not fulfill the nontechnical BC3134 Lighting design A. Required Nontechnical Courses requirement. EARTH AND ENVIRONMENTAL SCIENCES (16–18 points of credit) (Professional, workshop, lab, project, No courses These courses must be taken at scientific, studio, music instruction, and EAST ASIAN LANGUAGES AND CULTURE Columbia. master’s-level professional courses do All courses Points not satisfy the 27-point nontechnical requirement.) ECOLOGY, EVOLUTION AND ENVIRONMENTAL 1. ENGL C1010 BIOLOGY: No courses except EEEB W4700 University writing 3 AFRICAN-AMERICAN STUDIES: All courses ECONOMICS 2. One of the following two-semester sequences: AMERICAN STUDIES: All courses All courses except: HUMA C1001-C1002Masterpieces of Western W3211 Intermediate microeconomics ANCIENT STUDIES: All courses literature and philosophy (All students register- W3213 Intermediate macroeconomics ing for this course should be prepared to dis- ANTHROPOLOGY: W3412 Introduction to econometrics cuss the first six books of the Iliad on the first All courses in sociocultural anthropology W3025 Financial economics day of class.) All courses in archaeology except field work W4020 Economics of uncertainty and information or No courses in biological/physical anthropology W4211 Advanced microeconomics COCI C1101-C1102 [V1010, V1011, W3204, V3940, G4147-G4148, W4213 Advanced macroeconomics Introduction to contemporary civilization in the W4200, G4700] W4280 Corporate finance West W4412 Advanced econometrics ARCHITECTURE: No courses or W4415 Game theory ART HISTORY AND ARCHEOLOGY: All courses W4911 Seminar in microeconomics

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12 W4913 Seminar in macroeconomics PHYSICS: No courses puter technologies (4 points), in the W4918 Seminar in applied econometrics Botwinick Multimedia Learning POLITICAL SCIENCE: All courses except: BC1003 Introduction to economic reasoning W4209 Game theory Laboratory. In this course, students (equivalent to ECON W1105) W4291 Advanced topics in quantitative research learn the basics of engineering design BC1007 Mathematical methods for economics W4292 Advanced topics in quantitative research along with professional and teamwork BC2411 Statistics for economics W4360 Math methods for political science skills through participation BC3014 Entrepreneurship W4910 Principles of quantitative political BC3018 Econometrics in community service projects for real research BC3033 Intermediate macroeconomic theory clients in local communities. W4911 Analysis of political data BC3035 Intermediate microeconomic theory While students need not officially W4912 Multivariate political analysis BC3038 International money and finance commit to a particular branch of engi- BC2411 Statistics for economics PSYCHOLOGY neering until the third semester, most Only: EDUCATION: All courses programs recommend, and in some W1001 The science of psychology cases may require, that particular cours- ENGLISH AND COMPARATIVE LITERATURE W2235 Thinking and decision making es be taken earlier for maximum efficien- All courses W2240 Human communication cy in program planning. For information W2280 Introduction to developmental FILM STUDIES concerning these requirements, stu- psychology All courses except: W2610 Introduction to personality dents should turn to the individual pro- lab courses, and W2620 Abnormal behavior gram sections in this bulletin. W3850 Senior seminar in screenwriting W2630 Social psychology W4005 The film medium: script analysis W2640 Introduction to social cognition Professional-Level Courses for FRENCH AND ROMANCE PHILOLOGY V2680 Social and personality development First- and Second-Year Students All courses W3615 Children at risk First- and second-year students are W3630 Seminar in social cognition GERMANIC LANGUAGES: All courses required to take at least one professional- RELIGION: All courses level course chosen from the list below. GREEK: All courses SEAS: The faculty strongly encourages students HISTORY: All courses Only: to schedule two of these courses. (The HISTORY AND PHILOSOPHY OF SCIENCE SCNC W3010 Science, technology and society Botwinick Multimedia Learning All courses BMEN E4010 Ethics for biomedical engineers Laboratory course in computer and EEHS E3900 History of telecommunications engineering design technology, ENGI HUMAN RIGHTS: All courses E1102, which is required of every first- SLAVIC LANGUAGES: All courses ITALIAN: All courses year student, is not included in this list.) SOCIOLOGY: JAZZ STUDIES: All courses Each course is designed to acquaint All courses except: SEAS students with rigorous intellectual SOCI V3212 Statistics and methods LATIN: All courses effort in engineering and applied science LATINO STUDIES: All courses SPANISH AND PORTUGUESE: All courses early in their academic careers. If a stu- dent chooses to take the second pro- LINGUISTICS: All courses except CLLN W4202 SPEECH: No courses fessional-level course, such a 1000-level MATHEMATICS: No courses STATISTICS: No courses course may, at the discretion of each MEDIEVAL AND RENAISSANCE STUDIES SUSTAINABLE DEVELOPMENT: No courses department, be used as an upper-level technical elective normally satisfied by All courses URBAN STUDIES: All courses 3000-level or higher courses. MIDDLE EASTERN AND ASIAN LANGUAGE VISUAL ARTS: No more than one course, which The courses stipulate minimal AND CULTURES: All courses must be at the 3000 level or higher prerequisites. Each course serves as an MUSIC WOMEN AND GENDER STUDIES: All courses introduction to the area of study in addi- All courses except performance or instrument tion to teaching the subject matter. Each instruction classes (which do not count toward course is taught by regular department the 128 credits required for graduation) Technical Course Requirements faculty and thus provides a double intro- PHILOSOPHY The prescribed First Year-Sophomore duction to both subject area and faculty. All courses except: Program curriculum requires students to The courses are: F1401 Elementary logic complete a program of technical course APPH E1300y Physics of the human body V3411 Introduction to symbolic logic work introducing them to five major W4137 Non-classical logic The human body analyzed from the basic princi- areas of technical inquiry: engineering, ples of physics: energy balance in the body, G4431 Introduction to set theory mechanics of motion, fluid dynamics of the heart G4424 Modal logic mathematics, physics, chemistry, and and circulation, vibrations in speaking and hear- CSPH G4801 Mathematical logic, I computer science. ing, muscle mechanics, vision, gas exchange and CSPH G4802 Incompleteness results in logic All first-year SEAS undergraduate transport in the lungs, structural properties and Courses in logic students take ENGI E1102: Design limits, and other topics. fundamentals using the advanced com- PHYSICAL EDUCATION: No courses

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APAM E1601y Introduction to computational GRAP E1115x and y Engineering graphics tioning activities, Friday-only classes at 13 mathematics and physics Visualization and simulation in virtual environ- Baker Field, and special courses that Mathematics and physics problems solved by ments; computer graphics methods for presenta- utilize off-campus facilities during week- using computers. Topics include elementary inter- tion of data. 3-D modeling; animation; rendering; ends and vacation periods. The courses polation of functions, solution of nonlinear algebraic image editing; technical drawing. equations, curve-fitting and hypothesis testing, offered by the department for each term wave propagation, fluid motion, gravitational and MECE E1001x Mechanical engineering: are included in the online Directory of celestial mechanics, and chaotic dynamics. micro-machines to jumbo jets Classes, and a description of the sched- The role of mechanical engineering in developing uled activities for each time preference is BMEN E1001x Engineering in medicine many of the fundamental technological advances posted in the Physical Education Office, The present and historical role of engineering in on which today’s society depends. Topics include 336 Dodge Physical Fitness Center, and medicine and health care delivery. Engineering airplanes, automobiles, robots, and modern man- is included on the Department of Physical approaches to understanding organismic and cellular ufacturing methods, as well as the emerging fields Education and Intercollegiate Athletics function in living systems. Engineering in the diagnosis of micro-electro-mechanical machines (MEMS) and treatment of disease. Medical imaging, med- and nanotechnology. The physical concepts that Web site (www.gocolumbialions.com). ical devices: diagnostic and surgical instruments, govern the operation of these technologies will be Students may register for only one sec- drug delivery systems, prostheses, artificial organs. developed from basic principles and then applied tion of physical education each term. in simple design problems. Students will also be CHEN E1040y Molecular engineering and exposed to state-of-the art innovations in each Music Instruction Courses product design case study. Music instruction and performance Examines the ways in which chemical and biologi- courses do not count toward the 128 cal sciences are interpreted through analytical MSAE E1001y Atomic-scale engineering of design and engineering frameworks to generate new materials points of credit required for a B.S. degree. products that enhance human endeavor. Culture An introduction to the nanoscale science and Please note that this includes courses of chemical engineering and the wide variety of engineering of new materials. The control and taken at Teachers College, Columbia chemical engineering practices, through lectures manipulation of atomic structure can create new College, and the School of the Arts. by department faculty and practicing chemical solids with unprecedented properties. Computer engineers, trips to industrial facilities, reverse hard drives, compact disc players, and liquid crys- Visual Arts Courses engineering of chemical products, and a chemical tal displays (LCDs) are explored to understand design competition. the role of new materials in enabling technologies. Students are allowed to take courses in Group problem-solving sessions are used to the Visual Arts Department for general CIEN E1201y Design of buildings, bridges, develop understanding. credit to be applied toward the B.S. and spacecraft degree. However, no more than one Basic principles according to which many struc- Physical Education visual arts course, which must be taken at tures are designed, constructed, and maintained Two terms of physical education (C1001- the 3000 level or higher, may count toward in service. How strength and safety are treated the nontechnical elective requirement. and the role of the computer at this design stage. C1002) are a degree requirement for Performance requirements, such as noise and students in The Fu Foundation School motion limitations. Classic and new materials of of Engineering and Applied Science. No Advanced Placement construction, their important features, and labora- more than 4 points of physical education Prior to entering Columbia, students tory demonstration of properties. Management of courses may be counted toward the may have taken the College Entrance both design and construction projects, and follow- degree. A student who intends to partic- Examination Board’s Advanced Place- up assessment monitoring and control. ipate in an intercollegiate sport should ment Examinations in a number of tech- register for the appropriate section of nical and nontechnical areas. Students EAEE E1100y A better planet by design Sustainable development and management of C1005: Intercollegiate athletics. Inter- may be assigned to an advanced-level Earth resources (water, minerals, energy, and collegiate athletes who attend regularly course in mathematics, chemistry, or land) are now recognized globally as an essential receive 1 point of credit up to the maximum physics. A maximum of 16 points may goal. A “systems analytic” approach to under- of 4. Those who are advised to follow a be applied. standing feedbacks and interactions between restricted or adapted activity program In the required pure science areas, human activity and the environment is introduced. should contact Professor Torrey in the the number of advanced placement Elements of integrated assessment, modeling, Department of Physical Education and academic credits awarded to students forecasting and decision analysis are illustrated by means of case studies of current resource and Intercollegiate Athletics. The physical of engineering and applied science environment concerns. education program offers a variety of varies from the levels awarded for liberal activities in the areas of aquatics, dance, arts programs, notably in mathematics, ELEN E1201x and y Introduction to electrical fitness, martial arts, individual and dual physics, chemistry, and computer sci- engineering, with laboratory in circuit design lifetime sports, team sports, and outdoor ence. The benefit of advanced placement Exploration of selected topics and their applica- education. Most activities are designed is acceleration through certain First tion. Electrical variables, circuit laws, nonlinear for the beginner/intermediate levels. Year–Sophomore Program requirements and linear elements, ideal and real sources, Advanced courses are indicated on the transducers, operational amplifiers in simple cir- and thus the opportunity of taking spe- cuits, external behavior of diodes and transistors, schedule. The majority of the activities cialized courses earlier. first order RC and RL circuits. Digital representa- are offered in ten time preferences. Each year the school reviews the tion of a signal, digital logic gates, flipflops. However, there are early-morning condi- CEEB advanced placement curriculum

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14 Advanced Placement Credit Chart and makes determinations as to appro- In order to receive AP credit, students must be in possession of appropriate transcripts or scores. priate placements, credit, and/or exemption. Please see the Advanced Subject AP Advanced Requirements or Placement Status Placement Credit Chart at left. Score Credit

Art history 5 3* No exemption from HUMA W1121 International Baccalaureate (IB) Biology 4 or 5 3 No exemption Entering students may be granted 6 points of credit for each score of 6 or 7 Chemistry 4 or 5 3 Requires completion of CHEM C2407 with grade of C or better. on IB Higher Level Examinations if 4 or 5 6 Requires completion of CHEM C3045-C3046 taken in disciplines offered as under- with grade of C or better. graduate programs at Columbia. Computer 4 or 5 3* Exemption from COMS W1004 Students should consult their adviser science A or AB for further clarification.

English Language and 5 3* No exemption British Advanced Level composition Examinations Literature and 5 3* No exemption Pending review by the appropriate composition department at Columbia, students with Economics grades of A or B on British Advanced Micro & macro 5 & 4 4* Exemption from ECON W1105 (Test must be in Level examinations are granted 6 points both with a score of 5 in one and at least 4 in the other.) of credit if the examinations were taken in disciplines offered as undergraduate French programs at Columbia College. The Language 4 or 5 3* Literature 4 or 5 3* appropriate transcript should be submit- ted to the Center for Student Advising, German 4 or 5 3* 403 Lerner. language

Government Other National Systems and politics Pending review by the appropriate United States 5 3* Comparative 5 3* department at Columbia, students whose secondary school work was in History other national systems (such as the European 5 3* United States 5 3* French Baccalauréat or the German Abitur) may be granted credit in certain Italian language 4 or 5 3* disciplines for sufficiently high scores. Latin literature 4 or 5 3* The appropriate transcript should be Mathematics submitted to the Center for Student Calculus AB 4 or 5 3** Requires completion of MATH V1102 with a Advising, 403 Lerner. grade of C or better. Calculus BC 4 3** Requires completion of MATH V1102 with a grade of C or better. STUDY ABROAD Calculus BC 5 6 Requires completion of MATH V1201 (or Engineering today is a global profession. V1207) with a grade of C or better. Engineers are increasingly being called Music theory 5 3* Exemption from MUSI V1002. MUSI V2318- upon to work with other engineers from V2319 determined by department. across the world or they may even find Physics themselves living abroad on an overseas C-E&M 4 or 5 3 Requires beginning with and completion of assignment. Learning problem-solving PHYS C2801 with grade of C or better. skills in a foreign context will help engi- C-MECH 4 or 5 3 Requires beginning with and completion of neering students to expand their hori- PHYS C2801 with grade of C or better. Physics B 4 or 5 3* No exemption zons, and their adaptability to cross-cul- tural communication will make them a Spanish valuable addition to a team of engineers. Language 4 or 5 3* Literature 4 or 5 3* Study abroad allows engineering stu- dents to discover the field through the *Up to 3 AP credits may be applied toward minor requirements. perspective of engineers working in a **SEAS students with a 4 or 5 on Calculus AB or a 4 on Calculus BC must begin with different language and culture, enabling Calculus II. If a SEAS student with these scores goes directly into Calculus III, he or she will not be awarded credit and may have to go back and complete Calculus II. Students with them to learn the relationship of culture A-level or IB calculus credit must start with Calculus II.

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to science and develop the range of • have at least a 3.0 GPA Summer study-abroad programs 15 transferable skills that employers are • be making good progress toward allow students to earn credits for language seeking today. Study abroad will help finishing the Core Curriculum instruction and nontechnical electives. students develop intellectually, emotion- • have at least intermediate proficiency Students can participate in Columbia- ally, culturally, and socially. in the local language, if it is not English approved summer programs for transfer SEAS undergraduate students can (Please note: For programs in coun- credit or on Columbia-sponsored pro- study abroad for either a semester or a tries where the language of instruction grams for direct credit. The Columbia- full academic year. Students from every is not English, students must take all sponsored summer programs include engineering major have studied abroad course work in the local language.) the Chinese Language Program in without adding any time to their course Students’ study-abroad plans must be Beijing, the Business Chinese and of study at Columbia. Most do so in the approved by the Office of Global Initiatives Internship Program in Shanghai, the spring semester of their sophomore year by October 15 for spring programs and Italian Cultural Studies Program in or in their junior year. SEAS students March 15 for fall and academic-year Venice, and the Columbia University have the option of studying engineering programs. A review of each student’s Programs in Paris at Reid Hall. at one of SEAS’s partner universities academic and disciplinary records is Noncredited internships abroad—the where course equivalencies have been conducted as part of this process. EDGE and CEO programs—are coordi- worked out: University College London Students on academic or disciplinary nated by the Center for Career Education. (UK); the Ecole Polytechnique (FR)* or probation are not permitted to study Please visit the Center’s Web site for the Ecole Centrale de Paris (FR).* Other abroad during the term of their probation. more information. Other internship partnerships are currently being negoti- Study-abroad students remain options are listed on the Web site of ated—check the Office of Global enrolled at Columbia, and tuition is paid the Office of Global Initiatives. Initiatives’ Web site for the latest updates: to Columbia. Students participating in www.engineering.columbia.edu/ Columbia-approved programs pay hous- Academic Credit global_initiatives. ing costs directly to their host or spon- Students in Columbia-sponsored pro- Students who would like further soring institution. Students receiving grams receive direct Columbia credit, options can choose a peer university. financial aid at Columbia will remain and the courses and grades appear on The Office of Global Initiatives (510 Mudd) eligible for financial aid when they study students’ academic transcripts. These and departmental advisers will review abroad with Columbia’s approval. include Reid Hall, Paris; the Berlin requests, and if approved, will help stu- Students who wish to be considered Consortium for German Studies; the dents work out their course equivalen- for financial aid while studying abroad Kyoto Center for Japanese Studies; and cies so they can graduate on time. should consult the Office of Financial Aid the Tsinghua University program in Beijing. It is essential that students begin and Educational Financing (407 Lerner). Credit from approved programs is planning as early as possible—ideally certified as transfer credit toward the this would be during their first year— Study-Abroad Program Information Columbia degree upon successful com- by meeting with Dr. Régine Lambrech, Choosing the right university abroad is pletion of the program verifiable by aca- director of the Office of Global Initiatives an important step in planning to study demic transcript. Students must earn a and Education in 510 Mudd (rl2488@ abroad. Study-abroad options vary grade of C or better in order for credits columbia.edu). She will help students widely in size, geographical location, to transfer. Course titles and grades for choose their overseas university destina- academic philosophy, language require- approved programs do not appear on tion and will explain all SEAS study ments, living arrangements, and oppor- the Columbia transcript, and the grades abroad formalities. Students then also tunities for research and internships. are not factored into students’ GPAs. gain approval from their departmental Students must establish a set of goals Faculty from the SEAS academic advisers to ensure that their work abroad for the study-abroad experience, taking departments have the responsibility to meets the requirements of their majors. into account their foreign-language skills assess all work completed abroad and Students must also register with the and adaptability to new environments, make decisions about how these courses Office of Global Programs (204 Lewisohn) as well as their research objectives and fit into major requirements. It is impera- for study abroad by November 15 for professional aspirations. tive that students gain course-by-course spring programs and April 15 for fall and Students should visit the Office of approval from their department prior to academic-year programs. Global Initiatives’ Web site to review the departure on a study-abroad program. various lists of program options and The Office of Global Initiatives will pro- Eligibility Requirements consult with OGI staff for specific infor- vide students with the forms necessary In order to participate in a semester- mation or help in choosing an institution to obtain this approval. or year-long study-abroad program, that offers the best courses in their engi- students must: neering major.

*Fluent French and excellent mathematical skills are mandatory for study here.

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16 COMBINED PLAN PROGRAMS a B.S. degree from SEAS within five same as above, with the additional The Fu Foundation School of Engineer- years. Students complete the require- requirement that if the applicant has ing and Applied Science maintains ments for the liberal arts degree along already graduated from the affiliated cooperative program relationships with with a pre-engineering course of study school, he or she must apply to the institutions nationwide, and with other in three years at their college and Combined Plan Program within one year Columbia University undergraduate divi- then complete at Columbia. Combined of graduating. sions. These programs allow students Plan students, who are guaranteed For further information on the 3-2 to complete the equivalent of the First housing, are required to complete all B.A./B.S. program and the 4-2 B.S. Year–Sophomore Program and transfer SEAS requirements within four consecu- program, you are encouraged to e-mail directly to a field of specialization in the tive semesters. Please note that no your questions to: combinedplan@ School, beginning their study at the change of major is allowed after matric- columbia.edu. You may also call 212- School as junior-level students. A list of ulation. 854-2522 or contact Combined Plan participating Combined Plan institutions Guaranteed admission into The Fu Coordinators, Office of Undergraduate is on page 17. Foundation School of Engineering and Admissions, 212 Hamilton Hall, Mail Applied Science’s undergraduate Code 2807, 1130 Amsterdam Avenue, The Combined Plan (3-2) Program Combined Plan Program is offered to New York, NY 10027. within Columbia University applicants who have met the following The 4-2 M.S. program is designed Students who follow this program apply requirements: to allow students to complete an M.S. through their own school at Columbia 1. have been enrolled at an affiliated degree at SEAS in two years after com- College, Barnard College, or the School school for at least the past two pletion of a B.A. degree at one of the of General Studies for admission. Under years; affiliated schools. This program will allow this plan, the pre-engineering student 2. have received an overall GPA of students the opportunity to take under- studies in the appropriate college for 3.0 or higher, including all science, graduate engineering courses if neces- three years, then attends The Fu math, and pre-engineering courses; sary. Please contact the Office of Graduate Foundation School of Engineering and 3. have received three favorable Student Services, The Fu Foundation Applied Science for two years and is recommendations, from the School of Engineering and Applied awarded the Bachelor of Arts degree Combined Plan liaison and both Science, 524 S. W. Mudd, Mail Code and the Bachelor of Science degree in a science and a math instructor 4708, 500 West 120th Street, New engineering upon completion of the fifth at the home institution; York, NY 10027. You may also e-mail year. This five-year program is optional 4. have successfully completed the questions to at Columbia, but the School recom- course load stipulated by the [email protected]. mends it to all students who wish articulation agreement between The following colleges are affiliated greater enrichment in the liberal arts the home institution and Columbia, with SEAS in the Combined Plan; and pure sciences. which includes (a) the science admission requirements and other and math prerequisite courses information may be obtained from The Combined Plan with listed in the Pre-Combined Plan them or by contacting the Office Other Affiliated Colleges Curriculum Guide and (b) the of Undergraduate Admissions. For more major and distribution require- information, go to www.studentaffairs. There are over one hundred liberal arts ments prescribed by the home columbia.edu/admissions/engineering/ colleges, including those at Columbia, in institution. combined. which a student can enroll in a Combined Admission to SEAS at the end of the Plan program leading to two degrees. junior year is guaranteed for those stu- The Combined Plan— Every affiliated school has a liaison dents who have a grade-point average Affiliated Colleges and Universities officer who coordinates the program at Adelphi University, Garden City, NY of 3.0 or better; are recommended by his or her home institution.Inasmuch as Albertson College, Caldwell, ID the liaison officer; and have completed each liberal arts college requires the Albion College, Albion, MI the appropriate steps outlined in 1–4 completion of a specified curriculum to Alfred University, Alfred, NY above. Allegheny College, Meadville, PA qualify for the baccalaureate from that Another available option is the 4-2 Arcadia University, Glenside, PA institution, students interested in this B.S. degree program. This is designed Augustana College, Sioux Falls, SD program should inform the liaison officer to allow students to graduate from their Austin College, Sherman, TX as early as possible, preferably in the first Baldwin-Wallace College, Berea, OH liberal arts college with a B.A. degree year. Bard College, Annandale-on-Hudson, NY and then transfer to SEAS to complete The 3-2 Combined Plan Program Barnard College, New York, NY a B.S. degree in two years. Students B.A./B.S. at The Fu Foundation School Bates College, Lewiston, ME should have followed a related course of Engineering and Applied Science is Beloit College, Beloit, WI of study at their liberal arts college. Bethany College, Bethany, WV designed to provide students with the Requirements for guaranteed admission Birmingham-Southern College, Birmingham, AL opportunity to receive both a B.A. degree to the 4-2 B.S. degree program are the Bowdoin College, Brunswick, ME from an affiliated liberal arts college and Brandeis University, Waltham, MA

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Carleton College, Northfield, MN State University of New York, Fredonia, NY undergraduates in engineering, or by 17 Carroll College, Helena, MT State University of New York, Geneseo, NY their attainments as alumni in the field Centenary College of Louisiana, Shreveport, LA State University of New York, Binghamton, NY of engineering, and to foster a spirit of Centre College, Danville, KY Sweet Briar College, Sweet Briar, VA liberal culture in engineering colleges.” Claremont McKenna College, Claremont, CA University of Puget Sound, Tacoma, WA Clark University, Worcester, MA University of Richmond, Richmond, VA Columbia’s chapter, New York Alpha, Colgate University, Hamilton, NY University of the South, Sewanee, TN is the ninth oldest and was founded in College of Notre Dame, Baltimore, MD University of the Virgin Islands, St. Thomas, VI 1902. Many Columbia buildings have College of the Holy Cross, Worcester, MA Ursinus College, Collegeville, PA been named for some of the more College of William and Mary, Williamsburg, VA Wabash College, Crawfordsville, IN prominent chapter alumni: Charles Colorado College, Colorado Springs, CO Washington and Jefferson College, Washington, PA Fredrick Chandler, Michael Idvorsky Columbia College, New York, NY Washington and Lee University, Lexington, VA Pupin, Augustus Schermerhorn, and, Davidson College, Davidson, NC Wells College, Aurora, NY of course, Harvey Seeley Mudd. Denison University, Granville, OH Wesleyan University, Middletown, CT DePauw University, Greencastle, IN Whitman College, Walla Walla, WA Undergraduate students whose Dillard University, New Orleans, LO Whitworth College, Spokane, WA scholarship places them in the top Doane College, Crete, NE Willamette University, Salem, OR eighth of their class in their next-to-last Drew University, Madison, NJ William Jewell College, Liberty, MO year or in the top fifth of their class in Earlham College, Richmond, IN Williams College, Williamstown, MA their last college year are eligible for Eckerd College, St. Petersburg, FL Wittenberg University, Springfield, OH membership consideration. These Elon College, NC Wofford College, Spartanburg, SC scholastically eligible students are further Fairfield University, Fairfield, CT Yeshiva University, New York, NY Fordham University, Bronx, NY considered on the basis of personal Franklin and Marshall College, Lancaster, PA integrity, breadth of interest both inside Georgetown University, Washington, DC THE JUNIOR–SENIOR and outside engineering, adaptability, Gettysburg College, Gettysburg, PA PROGRAMS and unselfish activity. Grinnell College, Grinnell, IA Students may review degree progress Hamilton College, Clinton, NY via DARS (Degree Audit Reporting Taking Graduate Courses as Hartwick College, Oneonta, NY System) as presented on Student Hastings College, Hastings, NE an Undergraduate Services Online. Required courses not Hendrix College, Conway, AR With the faculty adviser’s approval, Hobart and William Smith Colleges, Geneva, NY completed by this time are detailed as a student may take graduate courses Hofstra University, Hempstead, NY deficiencies and must be completed while still an undergraduate in the Jacksonville University, Jacksonville, FL during summer session or carried as School. Such work may be credited Juniata College, Huntingdon, PA overload courses during the final two toward one of the graduate degrees Knox College, Galeburg, IL years of study. offered by the Faculty of Engineering Lawrence University, Appleton, WI Having chosen their program major, Lewis and Clark College, Portland, OR and Applied Science, subject to the students are assigned to an adviser Loyola University Chicago, Chicago, IL following conditions: (1) the course must MacMurray College, Jacksonville, IL in the department in which the program be accepted as part of an approved Marietta College, Marietta, OH is offered. In addition to the courses graduate program of study; (2) the Miami University, Oxford, OH required by their program, students course must not have been used to fulfill Middlebury College, Middlebury, VT must continue to satisfy certain distribu- a requirement for the B.S. degree and Millsaps College, Jackson, MI tive requirements, choosing elective must be so certified by the Dean; and Morehouse College, Atlanta, GA courses that provide sufficient content in Muhlenberg College, Allentown, PA (3) the amount of graduate credit earned engineering sciences and engineering Nebraska Wesleyan University, Lincoln, NE by an undergraduate cannot exceed Oberlin College, Oberlin, OH design. The order and distribution of the 15 points. Undergraduates may not take Occidental College, Los Angeles, CA prescribed course work may be changed CVN courses. Pacific Lutheran University, Tacoma, WA with the adviser’s approval. Specific Pitzer College, Claremont, CA questions concerning course require- The Bachelor of Science Degree Providence College, Providence, RI ments should be addressed to the Students who complete a four-year Queens College, Flushing, NY appropriate department or division. Randolph-Macon College, Ashland, VA sequence of prescribed study are The Vice Dean’s concurrent approval is Reed College, Portland, OR awarded the Bachelor of Science required for all waivers and substitutions. Rollins College, Winter Park, FL degree. The general requirement for St. John Fisher College, Rochester, NY the Bachelor of Science degree is the St. Lawrence University, Canton, NY Tau Beta Pi completion of a minimum of 128 aca- Sarah Lawrence College, Bronxville, NY The Tau Beta Pi Association, a national School of General Studies, Columbia University, demic credits with a minimum cumula- engineering honor society, was founded New York, NY tive grade-point average (GPA) of 2.0 (C) in 1885 “to mark in a fitting manner Scripps College, Claremont, CA at the time of graduation. The program Seattle Pacific University, Seattle, WA those who have conferred honor upon requirements, specified elsewhere in this Simon’s Rock College of Bard, Great Barrington, MA their Alma Mater by distinguished schol- bulletin, include the First Year–Sophomore Spelman College, Atlanta, GA arship and exemplary character as course requirements, the Junior-Senior

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18 major departmental requirements, and of the fourth year at SEAS; a minimum ble admissions requirements of most technical and nontechnical elective GPA of 3.0 in the College Core and other professional schools. Undergraduate requirements. Students who wish to courses; and the successful completion students should, however, make careful transfer points of credit may count no of any prerequisites for the College inquiry into the kinds of specific prepara- more than 68 transfer points toward the major or concentration. To be admitted tory work that may be required for degree, and must satisfy the University’s to the program, a plan needs to be in admission into highly specialized pro- residence requirements by taking at place for the student to complete the grams such as medicine. least 60 points of credit at Columbia. major or concentration in the fifth year. The bachelor’s degree in engineering Interested students should contact Pre-Med and applied science earned at Columbia their Advising Center for further information. Engineering students seeking admission University prepares students to enter a to dental, medical, optometric, osteo- wide range of professions. Students are, Minors pathic, or veterinary schools directly however, encouraged to consider gradu- Undergraduates in The Fu Foundation after college must complete all entrance ate work, at least to the master’s degree School of Engineering and Applied requirements by the end of the junior level, which is increasingly considered Science may choose to add minors to year, and should plan their program necessary for many professional careers. their programs. This choice should be accordingly. Students should consult The Engineering Accreditation made in the fall of their sophomore year, with their adviser and the Office of Commission (EAC) of the Accreditation when they also decide on a major. Preprofessional Advising to plan an Board for Engineering and Technology In considering a minor, students must appropriate program. Students should (ABET), an organization formed by the understand that all minors are not, and also connect with the Office of major engineering professional societies, cannot, be available to all students. In Preprofessional Advising to learn more accredits university engineering programs addition, the School cannot guarantee about extracurricular and research on a nationwide basis. Completion of an that a selected minor can be completed opportunities related to premed studies. accredited program of study is usually the within the usual residence period need- It is necessary to apply for admission first step toward a professional engineer- ed for a major. Indeed, students choos- to health professions schools a little over ing license. Advanced study in engineering ing minors should expect to encounter one year in advance of the entry date. If at a graduate school sometimes presup- scheduling difficulties. The potential for candidates are interested in going directly poses the completion of an accredited the successful completion of a minor on to health professions school following program of undergraduate study. depends on the student’s major and graduation, they should complete all The following undergraduate programs the minor chosen, as well as the course requirements and the Medical College are accredited by the Engineering Accre- schedules and availability, which may Admissions Test (MCAT) by the summer ditation Commission of the Accreditation change from year to year. The list of following the junior year. It is, however, Board for Engineering and Technology: minors, as well as their requirements, entirely acceptable to delay application chemical engineering, civil engineering, appear in the section “Undergraduate and entrance to these schools several Earth and environmental engineering, Minors,” beginning on page 188. years beyond graduation, if desired. electrical engineering, and mechanical Candidates planning for an applica- engineering. For a complete listing of all PROGRAMS IN PREPARATION tion to medical or dental school will also programs registered with the State of FOR OTHER PROFESSIONS need to be evaluated by the Premedical New York, including ABET programs, Advisory Committee prior to application. The Fu Foundation School of Engineer- see page 20. A Premedical Advisory Committee appli- ing and Applied Science prepares its cation is made available each year in students to enter any number of gradu- The 4-1 Program at Columbia College December. Please consult with the ate programs and professions outside of Students who are admitted as first-year Office of Preprofessional Advising for what is generally thought of as the engi- students to The Fu Foundation School more information regarding this process. neering field. In an increasingly techno- of Engineering and Applied Science, and The Engineering School’s curriculum logical society, where the line between subsequently complete the four-year covers many of the premedical courses humanities and technology is becoming program for the Bachelor of Science required by medical schools. However, increasingly blurred, individuals with a degree, have the opportunity to apply in addition to completing the mathemat- thorough grounding in applied mathe- for admission to either Columbia College ics, chemistry, and physics courses matics and the physical and engineering or Barnard College and, after one addi- required by the First Year–Sophomore sciences find themselves highly sought tional year of study, receive the Bachelor Program, most medical schools ask for after as professionals in practically all of Arts degree. a full year of organic chemistry, a full fields of endeavor. The program will be selective, and year of biology, and a full year of English. Engineering students interested in admission will be based on the following The following courses are required pursuing graduate work in such areas factors: granting of the B.S. at SEAS at by medical schools: as architecture, business, education, the end of the fourth year; fulfillment of journalism, or law will find themselves One year of calculus for some schools the College Core requirements by the end well prepared to meet the generally flexi- One year of physics, with lab

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One year of general chemistry, with lab New York State Initial Certification in JOINT PROGRAMS 19 One year of biology, with lab Adolescence Education Grades 7–12 (BME labs will qualify) for Teachers of Mathematics and the School of Law One year of organic chemistry, with lab Sciences or in Childhood Education Each year The Fu Foundation School One year of English Grades 1–6 of Engineering and Applied Science may Biochemistry or additional biology The Barnard Education Program pro- nominate two highly qualified juniors (required by some schools) vides courses leading to certification to for a joint program with the Columbia For further information, please teach in New York State (with reciprocal University School of Law, enabling stu- consult the Office of Preprofessional agreements with forty-one other states) dents to complete the requirements for Advising at 212-854-8722 or at either the elementary or secondary the degrees of Bachelor of Science and [email protected]. level. Students gain experience and Doctor of Jurisprudence in six years develop skills in urban school classrooms. instead of seven. Students should speak Pre-Law Interested students should apply for to the Office of Pre-Professional Advising in the fall semester to express their inter- Students fulfilling the curriculum of The admission to the program and supply est and prepare to take the LSAT by Fu Foundation School of Engineering an essay and letters of recommendation February of their junior year. The applica- and Applied Science are well prepared no later than the first Monday in October tion process is conducted March through to apply to and enter professional of the junior year. These forms may be April. schools of law, which generally do not downloaded from the Barnard College require any specific pre-law course work. Office of Education Web site or picked School of International and Schools of law encourage undergradu- up in the 336 Milbank Hall office. Course- Public Affairs ate students to complete a curriculum work required includes courses in characterized by rigorous intellectual psychology and education, including The Fu Foundation School of Engineer- training involving relational, syntactical, practicum and student teaching, totaling ing and Applied Science and the School and abstract thinking. A sound liberal 23–26 points of credit depending on of International and Public Affairs at education is best for most pre-law stu- level of certification sought (please see Columbia offer a joint program enabling dents. While selecting courses, keep the Web site for specific courses). a small number of students to complete in mind the need to hone your writing Certification to teach mathematics the requirements for the degrees of skills, your communication skills, and requires 36 points in mathematics. Pure Bachelor of Science and Master of your capacity for logical analysis. science courses required are: 36 points International Affairs in five years instead Courses in history, political science, in the sciences, of which 15 must be in of six. Not only an excellent academic economics, statistics, and anthropology the area of the certification sought: chem- record but also maturity, fluency in an help students understand the structure istry, biology, physics, or Earth science. appropriate foreign language, and perti- of society and the problems of social Application deadline is the first Monday nent experience will determine admis- ordering with which the law is concerned. in October of the student’s junior year. sion to this program. Applications are The study of philosophy, literature, fine Students who plan to study abroad dur- processed in the junior year by the arts, foreign languages, and other cul- ing their junior year should apply during Center for Student Advising. tures imparts familiarity with traditions of the fall semester of their sophomore universal thought and trends that influ- year. Students should decide on their REGISTERED PROGRAMS interest in teacher certification by the ence legal developments nationally and The New York State Department of end of the first year in order to start internationally. The examination of human Education requires that this bulletin course work in the sophomore year. behavior through sociology and psychol- include a listing of registered programs, ogy will aid a prospective law student in Barnard College Education Program both undergraduate and graduate (see understanding the types and effects of 336 Milbank Hall chart on page 20). Enrollment in other behavior to which the law relates. 212-854-7072 than registered or otherwise approved The systematic ordering of abstrac- programs may jeopardize a student’s eli- tions and ideas in logic and the sciences gibility for certain student aid awards. contributes much to a pre-law student’s The letter “X” or the name of a ability to analyze, understand, and degree on the chart indicates that a rationally organize his or her thoughts. program is registered with the New York Finally, it is useful in some fields of law State Department of Education. for a student to have a fundamental knowledge of technology, engineering, computers, and accounting.

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20 Programs Registered with the New York State Department of Education

Program Title HEGIS code B.S. M.S. Professional M.Phil. Eng.Sc.D. Ph.D.

Applied Mathematics 913 X X X X

Applied Physics 919 X X X X X

Biomedical Engineering 905 X X X X X

Chemical Engineering 906 X X Chemical Engineer X X X

Civil Engineering 908 X Civil Engineer

Civil Engineering and Engineering Mechanics 908 X X X X

Combined Plan w/Affiliated College; Dual B.S. (M.S.)/B.A. 999 X X

Computer Engineering 999 X X

Computer Science 701 X X X X X 909 Computer Systems Engineer

Computer Science/Business: Dual M.S./M.B.A. 701 X

Earth and Environmental Engineering 918 X X X X X

Earth and Environmental Engineering/Business: Dual M.S./M.B.A. 913 X

Electrical Engineering 909 X X Electrical Engineer X X X

Electrical Engineering: Dual B.S./M.S. 909 X X

Engineering Mechanics 921 X Mechanics Engineer

Financial Engineering 913 X Financial Engineer*

Financial Engineering/Business: Dual M.S./M.B.A. 913 X

Industrial Engineering 913 X X Industrial Engineer X X X

Industrial Engineering/Business: Dual M.S./M.B.A. 913 X

Materials Science and Engineering 915 X X X X X

Mechanical Engineering 910 X X Mechanical Engineer X X X

Medical Physics 1299 X

Metallurgical Engineering 914 Metallurgical Engineer

Mining Engineering 918 Engineer of Mines

Mining Engineering and Applied Geophysics 918 X

Operations Research 913 X X X X X

Operations Research: Engineering and Management Systems 913 X X*

Operations Research: Financial Engineering 913 X

Solid State Science and Engineering 919 X X X X

*State approval pending.

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UNDERGRADUATE ADMISSIONS 21

Office of Undergraduate Admissions the School seeks students with unique Decision letters are mailed out in Columbia University achievements and talents as well as early April. 212 Hamilton Hall, Mail Code 2807 diverse economic, social, and geographic 1130 Amsterdam Avenue backgrounds. The Early Decision Program New York, NY 10027 Accordingly, the School of Engineer- Candidates for whom Columbia is the ing and Applied Science prescribes first choice may apply under the Early Fax: 212-854-3393 no standardized course of study for Decision Program. In order to qualify for Phone: 212-854-2522 secondary school students applying for this program, all application materials www.studentaffairs.columbia. first-year admission. The School does, must be postmarked by November 1. edu/admissions however, strongly recommend the fol- In mid-December, Early Decision lowing academic preparation: applicants receive notice of their accept- ADMISSION AS A FIRST-YEAR • 4 years of mathematics (preferably ance, denial, or deferral to regular deci- STUDENT through calculus) sion status. Applicants admitted under Each autumn The Fu Foundation School • 1 year of physics the Early Decision program are obligated of Engineering and Applied Science • 1 year of chemistry to accept Columbia’s offer of admission enrolls approximately 300 highly qualified • 4 years of English and must withdraw their applications at other colleges if they are provided with a men and women, chosen from a wide and recommends as well: range of applicants. All become full, financial aid package that enables them • 3 years or more of a foreign language active participants in a rich and diverse to attend Columbia. • 3 or 4 years of history and social studies university setting. Therefore, the Admis- sions Committee is interested in achieve- Required Standardized Testing The Application Process ments not only in mathematics and Please go to www.studentaffairs. science, but also in other fields: English, Students are strongly encouraged to columbia.edu/admissions for our stan- the social sciences, languages, and the apply online. You may also download a dardized testing requirements. You must arts. Considerable value is placed on paper copy of the application. Information register with the appropriate testing personal qualities and attributes like about both the online application and agency well in advance of the date on diversity of interests, special abilities, the downloadable application will be which you wish to be tested. Please maturity, motivation, curiosity, and inde- available by September 1, 2009, at note that scores reported to Columbia’s pendence. Secondary school records www.studentaffairs.columbia.edu/ School of General Studies (2095) will not and recommendations are carefully admissions/applications. If you do not reach our office and will not be consid- evaluated to ascertain the content and have access to the Internet, please call ered for evaluation. Columbia reserves difficulty of the applicant’s preparatory the Office of Undergraduate Admissions the right not to evaluate a candidate studies and the degree to which this at 212-854-2522 to request an application. whose scores are not reported directly preparation correlates with standardized Part 1 of the application should be by the testing agency. Please do not tests. Of importance also is the candi- filled out and submitted as early as utilize the “rush” service in sending your date’s participation in extracurricular or possible along with the $70 application test scores to Columbia. Doing so does community activities. Here the emphasis fee or an official fee waiver request. not speed up the processing of your is placed on the depth and significance All parts of the application must be test scores. We obtain all testing via a of involvement rather than on the num- postmarked no later than the first busi- secure Web site to which we are provided ber of activities. For its final selection, ness day following January 1. (See access by the appropriate testing below for Early Decision deadlines.)

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22 agency. Scores that are sent via the given in May by the College Entrance applied to all undergraduates. HEOP “rush” service are sent to us in paper Examination Board. In addition, required support is available to students wishing form, which we are no longer able to courses may be waived on the basis of to pursue only the Bachelor of Science process. faculty placement conferences, permit- degree or Columbia’s Combined Plan Applicants may submit results of the ting students with special preparation to Program for both the Bachelor of Arts American College Testing (ACT) exami- advance in prescribed sequences. No and Bachelor of Science in five years. nations in lieu of the SAT, but may not credit is given for college courses taken The National Opportunity Program substitute any other examinations for the prior to high school graduation, but (NOP) is a replication of the Higher required SAT Subject Tests. appropriate placements may be made. Education Opportunity Program and The Test of English as a Foreign provides access to a Columbia educa- Language (TOEFL) or International English C. Prescott Davis Scholars Program tion for students outside of New York Language Testing System (IELTS) is Each year, outstanding high school State. Requirements for NOP are the required of all applicants whose principal seniors are nominated for selection as same as those for HEOP, except for the language of instruction has not been C. Prescott Davis Scholars by the New York State residency requirement. English and who have not lived in an Admissions Committee. After a rigorous For further information concerning English-speaking environment for at selection process, the Scholars are cho- the Engineering School’s Opportunity least five years. sen to participate throughout their four Programs, contact: Applicants must be certain when undergraduate years in academic and Opportunity Programs and taking standardized tests to have their co-curricular opportunities, including Undergraduate Services results reported directly to Columbia research with faculty, professional intern- Columbia University University by the testing agency. ships, and meetings with world-renowned New York, NY 10027 Students are required to report all stan- scholars, innovators, and leaders. Phone: 212-854-3514 dardized testing. The following codes www.studentaffairs.columbia.edu/asp/ should be used when completing test Higher Education Opportunity programs registration forms: Program (HEOP) and National Opportunity Program (NOP) SAT Reasoning, SAT Subject Tests, APPLICANTS WITH The Higher Education Opportunity TOEFL: use code 2111 ADVANCED STANDING Program (HEOP) is sponsored by the ACT: use code 2719 (TRANSFER APPLICANTS) New York State Department of Educational Testing Service Education and Columbia University. The Students with strong academic records Rosedale Road program is designed for New York State in pre-engineering programs at two-year Princeton, NJ 08541 residents who have particular educational community colleges are eligible for Phone: 609-921-9000 and economic needs with regard to sophomore or junior standing in The Fu www.ets.org admission requirements. HEOP students Foundation School of Engineering and Applied Science upon transfer to American College Testing Program must be U.S. citizens or permanent resi- Columbia. Community college students Box 313 dents who have lived in New York State who are considering applying to the Iowa City, IW 52243 for one year prior to enrolling in college. School of Engineering and Applied Phone: 319-337-1270 HEOP’s individualized counseling and Science are encouraged to complete a www.act.org tutoring services help students meet the challenges of a major university and pro- course of study similar to the School’s Test of English as a Foreign Language fessional school. New students attend First Year–Sophomore Program. Credit Box 899 an intensive pre-first-year Summer Bridge and placement in the School will be Princeton, NJ 08451 Program on the Columbia campus. determined by the equivalence of the 609-771-7100 Students in the School’s under-graduate courses taken by the student to those www.toefl.org Higher Education Opportunity Program described in this bulletin. can follow a five-year curriculum which The School also accepts applications International English Language Testing spreads the first and second-year for transfer into the sophomore or junior System requirements over three years and allows year from students in four-year programs www.ielts.org for the inclusion of several extra courses at arts and sciences colleges and engi- designed to provide academic support. neering schools. Transfers, who are Advanced Placement Because of the different pace of this guaranteed housing, may enter The School gives recognition to the program, students are considered to be Columbia only in September and may Advanced Placement program. Appro- making minimum satisfactory progress count no more than 68 points of credit priate placement and credit will be given when they complete 24 points of credit toward the Columbia degree. Transfer to students who score according to the in one academic year. HEOP students’ students must also satisfy the University’s School’s criteria (see page 14) in the academic performance is otherwise residence requirements by taking at Advanced Placement examinations evaluated by the same standards least 60 points at Columbia.

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Transfer applicants should provide grams at one of the affiliated Combined and campus tours through the Visitors 23 the scores of College Board Examin- Plan schools listed on page 19 of this Center, located in 213 Low Library. ations as part of their application. bulletin should apply directly to the affili- Group information sessions are con- Applicants must submit results of the ated school’s admissions office. ducted by members of the admissions SAT or the American College Testing Third-year undergraduate students staff and offer the opportunity to learn (ACT) examinations. Results of the SAT already in a Combined Plan program more about Columbia University’s aca- Subject Tests are required only if the should apply to the Columbia University demic and student life as well as admis- tests were taken in high school. School of Engineering and Applied sions and financial aid. Campus tours Students in a non-English–speaking Science Combined Plan Program. The immediately follow the information environment and whose primary lan- deadlines for applying to these programs, session and are led by a current under- guage of instruction has not been each of which is described in the sec- graduate student. Engineering tours, English for at least five years are tion “The Undergraduate Programs’’ of designed to offer prospective students required to take an English proficiency this bulletin, are: an in-depth look into The Fu Foundation examination, TOEFL or IELTS. These • February 15 preferred deadline for the School of Engineering and Applied students must submit the results of at 3-2 Combined Plan Prgram Science, are led by current Columbia least one of the exams and will be • March 14 final deadline for the 3-2 engineering students and are available required to take an English placement Combined Plan Program every Friday at 1:00 p.m., except for test on arrival, before registration. • March 15 for the 4-2 Combined Plan holidays. Please note that the Transfer Applications can only be B.S. Program Engineering School tour is designed to completed online at the Web site of the • February 15 for the 4-2 Combined supplement, but not replace, the Office of Undergraduate Admissions, at Plan M.S. Program Undergraduate Admissions information www.studentaffairs.columbia.edu/ session and general campus tour. For For further information on the 3-2 and admissions/aboutapplying/transfer.php. further information and a detailed schedule 4-2 B.S. programs, visit www.engineering. Applications must be received by March of visit opportunities, please go to www. columbia.edu/admissions/cp. You may 15 for September admission. studentaffairs.columbia.edu/admissions/ also contact the Office of Undergraduate visiting. Admissions by phone, at 212-854-2522, The Combined Plan Programs Columbia does not conduct inter- or by e-mail at combinedplan@columbia. The Combined Plan programs at The Fu views on campus. Interviews are instead edu. For further information on the 4-2 Foundation School of Engineering and conducted around the country and the M.S. program, contact the Office of Applied Science are designed to provide world by the members of the Alumni Graduate Student Services (see the students the opportunity to receive both Representative Committee. The Univ- address on the inside front cover) or a Bachelor of Arts or Bachelor of Science ersity provides the names of candidates phone 212-854-6438. degree from an affiliated liberal arts col- to the Committee, which conducts inter- lege and a Bachelor of Science or Master views from October through February. of Science degree from Columbia. CAMPUS VISITS AND Candidates will be contacted by a Details concerning these programs are INTERVIEWS Committee member during this time if contained in the section “The Under- Prospective students are encouraged to interviews are available. Candidates graduate Programs’’ of this bulletin. visit the Columbia campus throughout should not call or write the Admissions Secondary school students who wish the year. The Office of Undergraduate Office to arrange alumni interviews. to follow one of the Combined Plan pro- Admissions hosts information sessions

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24 UNDERGRADUATE TUITION, FEES, AND PAYMENTS

he 2009–2010 tuition and fees TUITION mium in addition to the Health Service are estimated. Tuition and fees Undergraduate students enrolled in The fee. Visit www.health.columbia.edu for T are prescribed by statute and are Fu Foundation School of Engineering detailed information about medical insur- subject to change at the discretion of and Applied Science pay a flat tuition ance coverage options and directions for the Trustees. charge of $19,648 per term, regardless making confirmation, enrollment, or waiv- University charges such as tuition, of the number of course credits taken. er requests. fees, and residence hall and meal plans are billed in the first Student Account MANDATORY FEES PERSONAL EXPENSES Statement of the term, which is sent out Orientation fee: $400 (one-time charge Students should expect to incur miscel- in July and December of each year for in the first term of registration) laneous personal expenses for such the upcoming term. This account is Student Life fee: $541 per term items as clothing, linen, laundry, dry payable and due in full on or before the Health Service fee: $387 per term cleaning, and so forth. Students should payment due date announced in the International Services charge: $50 per also add to the above expenses the Statement, typically at the end of August term (international students only) cost of two round trips between home or early January before the beginning of Transcript fee: $95 (one-time charge) and the University to cover travel during the billed term. Any student who does the summer and the month-long, midyear not receive the first Student Account break. Statement is expected to pay at regis- OTHER FEES The University advises students to tration. Application and late fees open a local bank account upon arrival If the University does not receive the • Application for undergraduate in New York City. Since it often takes as full amount due for the term on or before admission: $70 long as three weeks for the first deposit the payment due date of the first State- • Application for undergraduate to clear, students should plan to cover ment, a late payment charge of $150 transfer admission: $70 immediate expenses using either a credit will be assessed. An additional charge • Late registration fee card, traveler’s checks, or cash draft of 1 percent per billing cycle may be during late registration: $50 drawn on a local bank. Students are imposed on any amount past due there- after late registration: $100 urged not to arrive in New York without after. sufficient start-up funds. Students with an overdue account Books and course materials: balance may be prohibited from register- Depends upon course ing, changing programs, or obtaining a LABORATORY CHARGES Laboratory fees: See course listings diploma or transcripts. In the case of Students may need to add another persistently delinquent accounts, the Room and board (estimated): $10,200 $100 to $300 for drafting materials or University may utilize the services of an laboratory fees in certain courses. Each attorney and/or collection agent to col- student taking laboratory courses must HEALTH INSURANCE lect any amount past due. If a student’s furnish, at his or her own expense, account is referred for collection, the Columbia University offers the Student the necessary notebooks, blank forms, student may be charged an additional Medical Insurance Plan, which provides and similar supplies. In some laboratory amount equal to the cost of collection, both Basic and Comprehensive levels of courses, a fee is charged to cover including reasonable attorney’s fees and coverage. Full-time students are auto- expendable materials and equipment expenses incurred by the University. matically enrolled in the Basic level of maintenance. Students engaged in the Plan and billed for the insurance pre- special tests, investigations, theses, or

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

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26 FINANCIAL AID FOR UNDERGRADUATE STUDY

Office of Financial Aid and Educational application forms described in the sec- for example, increased income or a Financing tion “How to Apply for Financial Aid.’’ change in the number of family mem- Columbia University The difference between the family con- bers attending college—will result in 407 Alfred Lerner Hall tribution and the total cost of attendance changes in the family contribution. In Mail Code 2802 at Columbia (including tuition, room, addition, the individual elements in the 2920 Broadway board, fees, books, travel, and personal financial aid package may vary from New York, NY 10027 expenses) represents the student’s year to year. demonstrated need. The Office of Financial Aid and Phone: 212-854-3711 The family contribution to the cost of Educational Financing reserves the right Fax: 212-854-5353 attending Columbia consists of two ele- to revise a financial aid award if the stu- E-mail: [email protected] ments: the parent contribution and the dent withdraws from school or if any www.studentaffairs.columbia. student contribution. The parent contri- information reported on financial aid edu/finaid bution is determined through an evalua- applications conflicts with information tion of parent income and assets, family on tax returns or other verification docu- Admission to Columbia is need-blind for size, and the number of family members ments. If a family’s financial circum- all students who are U.S. citizens, U.S. attending college. The student contribu- stances change after submission of the permanent residents, Canadian citizens, tion consists of a percentage of the financial aid application, an appeal may or Mexican citizens. Financial aid is student’s assets and a minimum contri- be made to the Office of Financial Aid awarded only to students who demon- bution from income. Each student is and Educational Financing, in writing, strate need. Columbia is committed to expected to work during the summer for a reconsideration of the financial aid meeting the full demonstrated financial and save a certain amount to contribute package. An appeal may be made at need of all applicants admitted as first- to educational costs. any time during the year if circumstances year students. Financial aid is available The minimum contribution from earn- warrant; otherwise appeals in direct for all four undergraduate years, provid- ings is currently: response to award letters must be ing students continue to demonstrate made in writing within two weeks of financial need. First year $2,400 receipt of aid packages. While transfer admission is need- Sophomore $2,700 blind, financial aid resources for transfer Junior $2,900 students are very limited. Therefore, The Senior $3,000 Satisfactory Academic Progress Students must continue to make satis- Fu Foundation School of Engineering The expected summer earnings factory academic progress toward the and Applied Science is unable to meet amount is separate from the amount degree to remain eligible for financial the full need of transfer applicants, with that students are expected to earn by aid. Satisfactory academic progress is the exception of students who enter the working a part-time job during the aca- reviewed at the end of each term by the Combined Plan Program and those who demic year. Committee on Academic Screening. All transfer from Columbia College. Eligibility for Columbia grant aid is students are considered for financial normally limited to eight terms of under- aid purposes to be making satisfactory DETERMINING ELIGIBILITY graduate study. Students must reapply academic progress as long as they are for financial aid each year and be regis- Columbia determines the amount each allowed to continue enrollment. For tered for a minimum of 12 points during family can contribute to educational details of The Fu Foundation School of any term for which aid is requested. costs through an evaluation of the family’s Engineering and Applied Science’s financial information as reported on the Changes in the family’s circumstances—

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process for evaluating student’s aca- cial aid packages include a combination of Financial Aid and Educational Finan- demic progress, see the section on of grant and “self-help.’’ The self-help cing if any outside awards are received. Conduct and Discipline in this bulletin. portion of a financial aid package con- Students who receive financial aid A student who is required to withdraw sists of a part-time job during the aca- from Columbia grant permission to the because of failure to make satisfactory demic year. Grants from government Office of Financial Aid and Educational academic progress may appeal the sources or directly from Columbia cover Financing to release relevant personal, decision to the Committee on Academic any remaining need beyond that covered academic, and financial information to Screening. Upon returning to the School by the self-help award. persons or organizations outside of Engineering and Applied Science fol- Columbia determines the institutional, Columbia in order to institute or to con- lowing a required withdrawal period, a federal, and New York State financial aid tinue financial assistance that they might student regains eligibility for financial aid. programs for which each student is eligi- be eligible to receive from such sources. ble and awards funds appropriately. In Students can expect that Columbia will FINANCIAL AID AWARDS addition to applying to Columbia for assis- respect their right to privacy and release tance, all financial aid applicants are information only as necessary. Financial aid is awarded in the form of a expected to apply for any other grant/ The following sources of financial aid “package,’’ consisting of a combination scholarship aid for which they may be may be included in a financial aid pack- of the various types of financial aid for eligible. Students must notify the Office age from Columbia. which the student is eligible. Most finan-

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28 A. Grants and Scholarships Columbia maintains an extensive deducted from the loan at the time that Through the Columbia University Grant listing of student employment opportuni- it is disbursed. Repayment begins sixty (CUG) program, need-based grants are ties, both for federal work-study posi- days after the second disbursement of made to full-time matriculated Columbia tions and other student employment the loan. students without expectation of repay- options, which do not receive federal ment. Grants are funded through a vari- funding. These listings are available via HOW TO APPLY FOR ety of University resources, including www.studentaffairs.columbia.edu/finaid/ FINANCIAL AID forms/workstudy.php. annual gifts and endowed accounts. In order to be considered for need-based Federal Work-Study Student Employ- Federal Supplemental Educational institutional financial aid at any time ment. The Work-Study Payroll Office is Opportunity Grants (SEOG) are grants during their four years of undergraduate dedicated to assisting Columbia stu- made under Title IV of the Higher study, students must apply for financial dents with all processes related to hiring Education Act of 1965, as amended, aid at the time they apply for admission. and payment. The Federal Work-Study from funds supplied entirely by the fed- Exceptions may be granted only in the (FWS) program is designed to promote eral government. These funds are case of extenuating circumstances that part-time employment for students who awarded to students who demonstrate result in a significant change in the fami- are in need of earnings to help finance financial need and are made without ly’s financial situation. Continuing stu- their education and to encourage partici- expectation of repayment. The amount dents must reapply for financial aid each pation in community service. The goal of of an individual grant may range from year. Continuing Student financial aid Columbia University’s FWS program is to $200 to $4,000 per year. application forms are made available by provide student assistance that supports The Federal Pell Grant program is the Office of Financial Aid and Educational a wide range of career objectives and authorized by the Education Amend- Financing in mid-March. The student’s departmental needs within the University ments of 1972. Under this program the name and Columbia ID number should and the community. federal government provides grants to be printed on all documents submitted students who qualify on the basis of to the Office of Financial Aid and C. Financing Options financial need. Pell grants range from Educational Financing. Financial aid $976 to $5,350. In addition to Columbia’s commitment to applicants whose application materials The New York State Tuition meeting 100 percent of every student’s are submitted after the published dead- Assistance Program (TAP) provides demonstrated financial need, Columbia lines cannot be guaranteed institutional grants to full-time, matriculated New is committed to assisting families in financial aid. York State residents who meet New meeting their family contributions. The All Columbia application materials can York State’s eligibility standards. Current following financing options are available be accessed through www.studentaffairs. TAP award amounts range from $275 to assist families in making educational columbia.edu/finaid. to $5,000. costs more affordable. Other grants/scholarships may be Monthly Payment Plan: Columbia available to students from a variety of offers an interest-free monthly payment 1. College Scholarship Service (CSS) outside sources. These include, but are plan through which parents may make PROFILE Form not limited to, awards sponsored by five equal monthly payments each term First-time applicants (first-year and secondary schools, civic organizations, rather than paying the term’s bill in full transfer applicants, and continuing stu- parental employers, corporations, and at the beginning of each term. The only dents who are applying for financial aid the National Merit and National Achieve- cost associated with the plan is a nomi- for the first time) must register with CSS ment Scholarship programs. Outside nal enrollment fee. for the PROFILE Form by visiting CSS scholarships are used to reduce the Parent Loans for Undergraduate online at www.collegeboard.com/profile. self-help component of the financial aid Students (PLUS): Through the PLUS Applicants who register online should package. Only after self-help has been program, parents may borrow for a complete the CSS Profile online (requires completely eliminated will the scholar- child’s educational expenses. Loans are a secure browser and credit card). All ships begin to reduce any Columbia made by banks and other commercial students must include the Columbia grant. lenders from their own funds, with University School of Engineer-ing and guarantees by the federal government. Applied Science’s CSS code on their B. Student Employment Under the PLUS program, parents may PROFILE Form. All students who receive financial aid borrow up to the total cost of attendance CSS code for SEAS: 2111 from Columbia are expected to have a less any other financial aid received. The deadlines to submit online are: Parents need not demonstrate need to part-time job to help meet the cost of November 15: First-year early decision education. Most students work on or qualify; however, they must be citizens March 1: First-year regular decision near campus, but there are many inter- or permanent residents of the United April 20: Transfer applicants esting and rewarding jobs throughout States and must pass a standard credit May 5: Continuing students New York City as well. check. A fee of up to 3 percent will be

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2. Free Application for Federal Columbia recommends waiting until First-year and transfer applicants and Student Aid (FAFSA) after federal income tax returns have continuing students should complete the First-year applicants should obtain been completed before completing CSS Noncustodial PROFILE. The dead- a FAFSA online at www.fafsa.ed.gov, the FAFSA form, but no later than the lines for completing this form are: from their high school guidance office, following deadlines: November 15: First-year early decision or by calling 1-800-4FED-AID. March 1: First-year candidates, both early candidates Transfer applicants should obtain and regular decision March 1: First-year regular decision candidates a FAFSA online, from their current col- April 20: Transfer applicants May 5: Continuing students April 20: Transfer applicants lege’s financial aid office, or by calling May 5: Continuing students the number above. Continuing students should apply 3. Noncustodial Profile 4. Business/Farm Information online each year. Columbia believes that the principal If the student or parents own all or part All students must include the responsibility for meeting educational of a business, corporations, or partner- Columbia University School of costs belongs to the family and offers ship, or are farm tenants, a complete Engineering and Applied Science’s financial aid only to supplement the fam- copy of the most recent business tax school code on the FAFSA form. ily’s resources. If the student’s natural parents are divorced or separated, return (including all schedules) must be FAFSA code for SEAS: E00486 Columbia requires each parent to pro- submitted to Columbia. Sole proprietors Students and their parents submit- vide financial information as part of the must submit Schedule C. The deadlines ting the FAFSA online should request student’s application for financial aid. to return these documents to the finan- PIN numbers from the FAFSA Web site, The parent with whom the applicant cial aid office are: so that they may complete the FAFSA lives most of the year should complete November 15: First-year early decision with an online signature. FAFSA appli- the PROFILE Form and the FAFSA. candidates cants without PIN numbers may print The noncustodial parent should submit March 1: First-year regular decision candidates a signature page and mail it in to the an income tax return and the CSS FAFSA Processor. All online FAFSA April 20: Transfer applicants Noncustodial Profile (online form provided May 5: Continuing students applicants should wait for and print out as a link once the CSS PROFILE is sub- the confirmation page, to ensure that mitted). their online submission has been received.

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30 5. Federal income tax returns TAX WITHHOLDING FOR The International Students and Signed copies of parent and student NONRESIDENT ALIEN Scholars Office has prepared a packet federal income tax returns, including SCHOLARSHIP AND of tax information, which is revised W-2 forms and all schedules, are FELLOWSHIP RECIPIENTS annually and is available to students. required for verification of the information United States tax law requires the International Students and Scholars reported on the PROFILE Form and University to withhold tax at the rate of Office FAFSA. The financial aid office strongly 14 percent on scholarship and fellow- Columbia University encourages families of first-year appli- ship grants paid to nonresident aliens 524 Riverside Drive, Mail Code 5724 cants to complete their federal income which exceed the cost of tuition, books, New York, NY 10027 taxes in February. Signed copies of fed- fees, and related classroom expenses. Phone: 212-854-3587 eral tax returns for parents and, if appli- Certain countries have entered into Fax: 212-854-8579 cable, for students should be submitted tax treaties with the United States, The tax law is complex and may vary to the financial aid office as soon as they which may serve to reduce this rate of with regard to individual circumstances. are completed. The preferred deadlines withholding. However, even when such Therefore, as the University is not in a for submission of signed federal tax a treaty applies, the student and the position to offer individual tax advice, returns are: University must report the full amount of students are advised to consult with a such excess to the Internal Revenue March 1: First-year candidates qualified tax professional and/or the Service. If a student claims tax treaty (early and regular decision) consulate of their country of residence. April 20: Transfer applicants benefits, he or she must also report this May 5: Continuing students amount to his or her country of residence.

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Graduate Studies 160-0450_Bulletin0910REV.qxd 7/23/09 12:05 PM Page 32

32 THE GRADUATE PROGRAMS

raduate programs of study in credit of course work completed at 30-point minimum that must be taken The Fu Foundation School of Columbia University. The student must at Columbia for each degree. G Engineering and Applied Science enroll for at least 15 of these points Competence in written and spoken are not formally prescribed, but are while registered as a matriculating English is required of every degree planned to meet the particular needs student in a degree program in the candidate. See pages 37–38 for English and interests of each individual student. Engineering School. (See also the sec- proficiency requirements. Departmental requirements for each tion “Special Nondegree Students” on For graduation, a candidate for degree, which supplement the general page 35 and the chapter “Columbia any degree except a doctoral degree requirements given below, appear in the Video Network.”) Students wishing to must file an Application for Degree or sections on individual graduate programs. change from the Ph.D. degree to the Certificate on the date specified in the Applicants for a graduate program Eng.Sc.D. degree must therefore enroll Academic Calendar. Candidates for a are required to have completed an under- for at least 15 points while registered in doctoral degree must apply for the final graduate degree and to furnish an official the School. For residence requirements examination. If the degree is not earned transcript as part of the admissions for students registered in the Graduate by the next regular time for the issuance application. Ordinarily the candidate for School of Arts and Sciences or those of diplomas subsequent to the date of a graduate degree will have completed wishing to change from the Eng.Sc.D. filing, the application must be renewed. an undergraduate course in the same degree to the Ph.D. degree, see the bul- Degrees are awarded three times a field of engineering in which he or she letin of the Graduate School of Arts and year—in October, February, and May. seeks a graduate degree. However, if Sciences. the student’s interests have changed, Students admitted to graduate study THE MASTER OF SCIENCE it may be necessary to make up such are expected to enter upon and continue DEGREE basic undergraduate courses as are their studies in each succeeding regular The Master of Science degree is offered essential to graduate study in his or term of the academic year. Any such in many fields of engineering and applied her new field of interest. student who fails to register for the fol- science upon the satisfactory comple- In order to complete the requirements lowing term will be assumed to have tion of a minimum of 30 points of credit for any graduate degree, the student withdrawn unless a leave of absence of approved graduate study extending must plan a program with the depart- has been granted by the Office of over at least one academic year. ment of major interest and then have it Graduate Student Services. While a suitable Master of Science approved by the Office of Graduate While many candidates study on a program will necessarily emphasize Student Services; the program may be full-time basis, it is usually possible to some specialization, the program should modified later with the permission of the obtain all or a substantial part of the be well balanced, including basic sub- department and the Assistant Dean. No credit requirement for the master’s, pro- jects of broad importance as well as more than one term of course work or, fessional, or Eng.Sc.D. degrees through theory and applications. The history of in the case of part-time students, no part-time study. modern economic, social, and political more than 15 points of credit of course Under special conditions, and with institutions is important in engineering, work, completed before the program the prior approval of the department and this is recognized in the prescribed is approved, may be counted toward of his or her major interest and of the undergraduate program of the School. the degree. Students registered in the Assistant Dean, a student may be per- If the candidate’s undergraduate educa- School have a minimum requirement for mitted to take a required subject at tion has been largely confined to pure each Columbia degree of 30 points of another school. However, credit for science and technology, a program of such courses will not reduce the

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general studies, totaling from 6 to 8 page 17 of this bulletin) with majors in York, NY 10027; you should also con- points, may be required. Supplementary mathematics, physics, chemistry, or cer- tact the Combined Plan liaison at your statements covering these special tain other physical sciences to receive the school for program information. You requirements are issued by the School’s M.S. degree after two years of study at may, in addition, e-mail questions to separate departments. An applicant who Columbia in the following fields of engi- [email protected]. lacks essential training will be required neering and applied science: biomedical, to strengthen or supplement the under- chemical, civil, computer, Earth and Joint Program with the School of graduate work by taking or repeating environmental, electrical, industrial, and Business in Industrial Engineering certain undergraduate courses before mechanical engineering; applied physics; The Graduate School of Business and proceeding to graduate study. No grad- applied mathematics; engineering the Engineering School offer a joint uate credit (that is, credit toward the mechanics; operations research; materials program leading to the degrees of minimum 30-point requirement for the science; and computer science. Master of Business Administration and Master of Science degree) will be Each applicant must produce evidence the Master of Science in Industrial allowed for such subjects. Accordingly, of an outstanding undergraduate record, Engineering. (See “Industrial Engineer- Master of Science programs may including superior performance in ing and Operations Research.”) include from 35 to 45 points and may physics and mathematics through differ- require three terms for completion. ential equations. The program of study Joint Program with the School of Doctoral research credits cannot be will be individually worked out in consul- Business in Operations Research used toward M.S. degree requirements. tation with a faculty adviser and will be The Graduate School of Business and All degree requirements must be designed to integrate undergraduate the Engineering School offer a joint completed within five years of the begin- work with the field of engineering or program leading to the degrees of ning of graduate study. Under extraordi- applied science the student chooses to Master of Business Administration and nary circumstances, a written request for follow. During the first year, the program the Master of Science in Operations an extension of this time limit may be will consist primarily of basic undergrad- Research. (See “Industrial Engineering submitted to the student’s department uate courses; during the second year, of and Operations Research.”) for approval by the department chairman graduate courses in the selected field. and the Assistant Dean. A minimum The student must complete at least 30 Joint Program with the School of grade-point average of 2.5 is required credits of graduate study to qualify for Business in Earth Resources for the M.S. degree. A student who, at the degree. Engineering the end of any term, has not attained A student whose background may The Graduate School of Business and the grade-point average required for require supplementary preparation in the Engineering School offer a joint pro- the degree may be asked to withdraw. some specific area, or who has been gram leading to the degrees of Master out of school for a considerable period, of Business Administration and the The 4-2 Master of Science Program will have to carry a heavier than normal Master of Science in Earth Resources course load or extend the program The 4-2 Master of Science Program Engineering. (See “Earth and Environ- beyond two years. provides the opportunity for students mental Engineering.”) holding bachelor’s degrees from affiliated Please contact the Office of Graduate Student Services, The Fu Foundation liberal arts colleges (see the listing under Special Studies with the Harriman School of Engineering and Applied the heading ‘‘The Combined Plan— Institute Affiliated Colleges and Universities,’’ on Science, 524 S. W. Mudd, Mail Code 4708, 500 West 120th Street, New A candidate for an advanced degree in

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34 the Engineering School may combine The Fu Foundation School of Engineer- programs are subject to review by the these studies with work in the Harriman ing and Applied Science, and the Doctor Committee on Instruction of the School. Institute. Upon completion of the course of Philosophy, administered by the In no case will more than 15 points of requirements in the Institute and satis- Graduate School of Arts and Sciences. credit be approved for the dissertation faction of the language requirement (in The Eng.Sc.D. and Ph.D. programs and research and studies directly any language indigenous to the former have identical academic requirements connected therewith without special USSR), the student may qualify for the with regard to courses, thesis, and approval by this Committee. Normally, professional certificate of the Harriman examinations, but differ in residence a doctoral candidate specializes in a Institute. The manner in which the requirements and in certain administra- field of interest acceptable to a depart- Institute and departmental requirements tive details. ment of the School. are combined is to be determined by the Doctoral students may submit a peti- Departmental requirements may student in consultation with departmen- tion to the Office of Graduate Student include comprehensive written and oral tal and Institute advisers. Advanced Services to change from the Eng.Sc.D. qualifying examinations. Thereafter, studies and research may, where appro- degree to the Ph.D. degree or from the the student must write a dissertation priate, be supervised by faculty members Ph.D. degree to the Eng.Sc.D. degree. embodying original research under the from both the School and the Institute. The petition must be submitted within sponsorship of a member of his or her the first year of enrollment or by the department and submit it to the depart- THE PROFESSIONAL DEGREE completion of 30 points. Any petitions ment. If the department recommends submitted after this period will not be the dissertation for defense, the student An undergraduate engineering degree is considered. Doctoral degree status applies for final examination, which is prerequisite for admission to the profes- can be changed only once; students, held before an examining committee sional degree program. The program therefore, must determine which doctoral appointed by the Dean. This application leading to the professional degrees in degree program is most appropriate must be made at least three weeks chemical, civil, computer, electrical, for their academic and professional before the date of the final examination. industrial, mechanical, metallurgical and endeavors. A student must have a satisfactory mining engineering, and engineering grade-point average to be admitted to mechanics is planned for engineers who Requirements for the Degrees the doctoral qualifying examination. wish to do advanced work beyond the Consult the department requirements level of the M.S. degree but who do not A student must obtain the master’s for details. desire to emphasize research. degree (M.S.) before enrolling as a can- The candidate for the degree of The professional degree is awarded didate for either the Ph.D. or Eng.Sc.D. Doctor of Engineering Science must for satisfactory completion of a graduate degree. Application for admission as a submit evidence that his or her disserta- program at a higher level of course work doctoral candidate may be made while a tion has been filed in compliance with than is normally completed for the M.S. student is enrolled as a master’s degree requirements set by the Faculty of degree. Students who find it necessary candidate. The minimum requirement in Engineering and Applied Science. to include master’s-level courses in their course work for either doctoral degree The defense of the dissertation con- professional degree program will, in gen- is 60 points of credit beyond the bache- stitutes the final test of the candidate’s eral, take such courses as deficiency lor’s degree. qualifications. It must be demonstrated courses. A candidate is required to Candidates for the Ph.D. degree that the candidate has made a contribu- maintain a grade-point average of at must register full time and complete six tion to knowledge in a chosen area. In least 3.0. A student who, at the end of Residence Units. A master’s degree content the dissertation should, there- any term, has not attained the grade- from an accredited institution may be fore, be a distinctly original contribution point average required for the degree accepted in the form of advanced in the selected field of study. In form may be asked to withdraw. At least 30 standing as the equivalent of one year it must show the mastery of written points of credit of graduate work beyond of residence (30 points of credit or two English which is expected of a university the M.S. degree, or 60 points of gradu- Residence Units) for either doctoral graduate. ate work beyond the B.S. degree, are degree. An application for advanced Ph.D. candidates should obtain a required for the professional degree. standing must be completed during the copy of the bulletin of the Graduate The final 30 points required for the first semester of study. Candidates for School of Arts and Sciences, in which professional degree must be completed the Eng.Sc.D. degree must (in addition are printed the faculty requirements in no more than five years. to the 60-point requirement) accumulate 12 points of credit in the departmental for the Ph.D. degree. These are supple- course E9800: Doctoral research instruc- mented by the requirements of the DOCTORAL DEGREES: tion. A holder of the professional degree department of major interest. ENG.SC.D. AND PH.D. who wishes to continue work toward Two doctoral degrees in engineering are the Eng.Sc.D. degree will be required to Doctoral Research Instruction offered by the University: the Doctor of complete not less than 30 additional In order that the University may recover Engineering Science, administered by points of credit in residence. All doctoral the costs that are not defrayed by the

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University’s income from tuition, charges This requirement does not include the Many graduate courses in The Fu 35 for research required for the Eng.Sc.D. summer session. Foundation School of Engineering and are assessed as given below. Applied Science are offered in the late Ph.D. candidates should consult the Completion of Requirements afternoon and evening in order to make bulletin of the Graduate School of Arts The requirements for the Eng.Sc.D. them available to working individuals and Sciences for the research instruc- degree must be completed in no more who wish to further their knowledge in tion requirements that apply to them. than seven years. The seven-year time the areas of engineering and applied An Eng.Sc.D. candidate is required period begins at the time the student science. Individuals who find it difficult to do the following: becomes a candidate for the Eng.Sc.D. or impossible to attend classes on the 1.At the time the student begins doctoral degree or a candidate for the profes- Columbia campus may be able to research, the student is eligible to sional degree, whichever occurs first, receive instruction from the School register for E9800 (3, 6, 9, or 12 and extends to the date on which the through the Columbia Video Network points of credit). Twelve points must dissertation defense is held. without leaving their work sites. have been accumulated by the time Extension of the time allowed for Individuals interested in this program the student is to receive the degree. completion of the degree may be granted should read the section describing the 2.Registration for E9800 at a time other on recommendation of the student’s CVN, which follows in this bulletin. than that prescribed above is not per- sponsor and the department chairman Special students receive grades and mitted, except by written permission to the Dean when special circumstances must maintain satisfactory attendance of the Dean. warrant. Such extensions are initiated and performance in classes or laborato- 3.Although 12 points of E9800 are by submitting a statement of work in ries and will be subject to the same required for the doctoral degree, no progress and a schedule for completion rules as degree candidates. Should a part of this credit may count toward together with the sponsor’s recommen- special student decide to pursue a the minimum residence requirement dation to the department chairman. degree program, work completed as a of 30 points (or 60 points beyond the special student may be considered for advanced standing, but no more than bachelor’s degree). SPECIAL NONDEGREE 15 points of course work completed 4.If a student is required to take course STUDENTS work beyond the minimum residence as a special student may be counted Qualified persons who are not interested requirements, the 12 points of doctoral toward a graduate degree. in a degree program but who wish only research instruction must still be taken For additional information and regula- to take certain courses may be permitted in addition to the required course work. tions pertaining to special students, see to register as special students, provided 5.A student must register continuously “Graduate Admissions.” facilities are available. through the autumn and spring terms.

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36 COLUMBIA VIDEO NETWORK

Columbia Video Network the classes that best fit the needs of up to 15 credits taken as a CVN nonde- Columbia University new and continuing students around the gree student may be counted toward a 540 S. W. Mudd, Mail Code 4719 world. During the summer semester (and degree when applying through CVN, 500 West 120th Street occasionally the autumn and spring subject to the approval of the student’s New York, NY 10027 terms), CVN makes prerecorded courses departmental adviser. Earning credit as a available. nondegree student does not guarantee www.cvn.columbia.edu SEAS currently offers M.S. degrees in acceptance into a degree program. E-mail: [email protected] the following disciplines through CVN: Only CVN students may transfer up Phone: 212-854-6447 • Applied mathematics to 6 credits from another university • Biomedical engineering toward an M.S. or P.D. degree, subject BACKGROUND • Chemical engineering to the approval of the student’s adviser and the department. Continuing a tradition of nearly 250 years • Civil engineering Columbia undergraduates and Ph.D. of academic excellence and innovation, • Computer science students are prohibited from taking CVN Columbia University’s Fu Foundation • Earth and environmental engineering courses. School of Engineering and Applied Science • Electrical engineering established the Columbia Video Network • Operations research (CVN) in 1986 to meet a growing need • Methods in finance PROGRAM BENEFITS within the engineering community for a • Engineering and management systems The CVN program allows working pro- graduate distance education program. • Materials science and engineering fessionals to enroll in courses and earn Classes and degrees offered through • Mechanical engineering graduate engineering degrees without CVN are fully accredited; the degrees For students who wish to do leaving their communities, their families, are granted by Columbia University. advance work beyond the M.S., but or their jobs. The key component of Classes available through CVN do not wish to emphasize research, CVN is flexibility without compromise to are taught on campus by Columbia Professional Degrees are also available the high-caliber teaching, resources, and University faculty in multimedia class- in the following areas: computer science, standards inherent in The Fu Foundation rooms. Faculty and students meet in electrical engineering, industrial engi- School of Engineering and Applied classrooms equipped with cameras, neering/operations research, and Science. CVN students are a part of the TM electronic writing tablets, and SMART mechanical engineering. Columbia community and may take boards. The recorded lectures are fully classes on campus. To further enhance downloadable for study at home, office, the sense of community, CVN has devel- STUDENT REGISTRATION or on the road. oped a completely automated online CVN students take the same classes, Students who have earned an under- Student Center. It provides a place have the same homework assignments, graduate degree in engineering, mathe- where CVN students and faculty can take the same exams, and earn the matics, or related field can apply to take communicate. Homework and exams same degrees as on-campus students classes for credit or audit without first are submitted and graded there, and in Master of Science (M.S.) or enrolling in a degree program at the course notes and other reference mate- Professional Degree (P.D.) programs. University or taking the GRE or TOEFL rials are available for downloading. exams by registering as nondegree stu- Professors and teaching assistants dents. CVN also offers Certificates of are available via e-mail or phone to COURSE OFFERINGS AND Professional Achievement programs in DEGREE PROGRAMS address academic questions. CVN’s various fields, which may lead to study administrative staff is available to assist CVN makes select SEAS graduate in a related M.S. or P.D. program. with registration procedures, technical courses available to off-campus students Although you need not be admitted queries, and academic advising so in autumn (September–December) and to a degree program to begin taking working professionals can devote their spring (January–May) terms. CVN admin- classes through CVN, you should apply energies to their studies, their families, istrators work closely with faculty repre- as soon as possible if you would like to and their careers. sentatives from each department to select earn a degree from Columbia University;

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GRADUATE ADMISSIONS 37

Office of Graduate Student Services as a special nondegree student may be by Columbia’s American Language The Fu Foundation School of counted toward a degree. Program (ALP). Engineering and Applied Science • Ph.D. and Eng.Sc.D. candidates Columbia University must attain level 10 on the English APPLICATION REQUIREMENTS 524 S. W. Mudd, Mail Code 4708 Certification Test (ECT) offered by 500 West 120th Street Applicants must submit an online appli- Columbia’s American Language New York, NY 10027 cation and required supplemental mate- Program (ALP). rials, as described below. When filing the The ECT is administered in two parts. Phone: 212-854-6438 online application, the candidate should Part I is a multiple-choice exam and Fax: 212-854-5900 obtain one official transcript from each Part II is an essay. Students are required E-mail: [email protected] postsecondary institution attended and to take both parts, and a level 8 must Apply online at: www.engineering. submit them in the original sealed enve- be scored on Part I in order to take columbia.edu lope. Consideration for admission will be based not only on the completion of an Part II. The basic requirement for admission earlier course of study, but also upon The ECT must be taken at Orienta- as a graduate student is a bachelor’s the quality of the record presented and tion (the fee for this administration of the degree received from an institution of upon such evidence as can be obtained exam will be covered by SEAS). A stu- acceptable standing. Ordinarily, the concerning the candidate’s personal fit- dent who misses this administration of applicant will have majored in the field ness to pursue professional work. the ECT must take the exam at his or in which graduate study is intended, Additionally, candidates must provide her own expense at the beginning of the but in certain programs, preparation in three letters of recommendation and the first semester enrolled and submit the a related field of engineering or science results of required standardized exams. official score to the Graduate Student is acceptable. The applicant will be The Graduate Record Examination (gen- Services Office. (CVN students are admitted only if the undergraduate eral) is required for all candidates. GRE exempt from the ECT.) record shows promise of productive scores are valid for five years from the A student who does not pass the and effective graduate work. test date. The Test of English as a ECT at the required level of proficiency Students who hold an appropriate Foreign Language (TOEFL) is required of must retake it at his or her own expense degree in engineering may apply for all candidates who received their bache- until the required level of proficiency is admission to study for the Ph.D. degree. lor’s degree in a country in which English achieved. The ALP may regulate how However, students are required to obtain is not the official and spoken language. often the examination is taken. the master’s degree first. Applications for TOEFL scores are valid for two years It is strongly recommended that admission as a doctoral candidate may from the test date. Applicants can only students enroll in an appropriate ALP be made after completion of 15 points apply to one degree program per admis- course if they have not achieved the of work as a candidate for the master’s sion term. required proficiency after the first exami- degree. nation. For more information on the Students may be admitted in one of administration of the ECT, please contact the following six classifications: candi- ENGLISH PROFICIENCY the Graduate Student Services Office. date for the M.S. degree, candidate for REQUIREMENT Admitted graduate students who are the M.S. degree leading to the Ph.D. APPLICATION FEES degree, candidate for the professional required to submit official TOEFL results A nonrefundable application processing degree, candidate for the Doctor of must attain levels of proficiency as fee of $70 is required of all degree and Engineering Science degree, candidate described below. Students will not be nondegree applicants who apply using a for the Doctor of Philosophy degree (see cleared for graduation unless they satisfy hard-copy or online application. Failure also the bulletin of the Graduate School the following requirements: to submit the application fee can delay of Arts and Sciences), or special student • M.S. and Professional Degree candi- processing of application materials. (not a degree candidate). Note: Not dates must reach level 8 on the more than 15 points of credit completed English Certification Test (ECT) offered

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38

GRADUATE ADMISSION Applicants who wish to be considered option is also appropriate for individuals CALENDAR for scholarships, fellowships, and assist- who missed applications deadlines. Applicants are admitted twice yearly, for antships should file complete applica- Applications for special student status the fall and spring semesters. tions for fall admission. are available at the Office of Graduate Student Services and must be submitted • Fall admission application deadlines: during the first week of the fall or spring December 1, for Ph.D., Eng.Sc.D., ONE-TERM SPECIAL STUDENT semester. and M.S. leading to Ph.D. programs, STATUS If a one-term special student subse- and applicants to the M.S. program Individuals who meet the eligibility quently wishes either to continue taking in financial engineering. February 15, requirements, who are U.S. citizens or classes the following term or to become for professional, M.S. only, and non- U.S. permanent residents, and who wish a degree candidate, a formal application degree applicants. to take courses for enrichment, may must be made through the Office of • Spring admission application secure faculty approval to take up to Graduate Student Services. deadlines: October 1, for all depart- two graduate-level courses for one term ments and degree levels. only as a one-term special student. This

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GRADUATE TUITION, FEES, AND PAYMENTS 39

he 2009–2010 tuition and fees TUITION OTHER FEES are estimated. Tuition and fees Graduate students enrolled in M.S., Application and late fees T are prescribed by statute and are Professional Degree, and Eng.Sc.D. • Application for graduate admission subject to change at the discretion of programs pay $1,310 per credit, except paper copy: $70 the Trustees. when a special fee is fixed. Graduate online: $70 University charges such as tuition, tuition for Ph.D. students is $17,698 per • Late registration fee fees, and residence hall and meal plans Residence Unit. The Residence Unit, during late registration: $50 are billed in the first Student Account full-time registration for one semester after late registration: $100 Statement of the term, which is sent out rather than for individual courses Books and course materials: in July and December of each year for the (whether or not the student is taking Depends upon course upcoming term. This account is payable courses), provides the basis for tuition Laboratory fees: See course listings and due in full on or before the payment charges. Ph.D. students should consult due date announced in the Statement, the bulletin for the Graduate School of HEALTH INSURANCE typically at the end of August or early Arts and Sciences. January before the beginning of the billed Columbia University offers the Student term. Any student who does not receive Medical Insurance Plan, which provides COMPREHENSIVE FEE/ the first Student Account Statement is both Basic and Comprehensive levels of MATRICULATION AND expected to pay at registration. coverage. Full-time students are auto- If the University does not receive the FACILITIES matically enrolled in the Basic level of full amount due for the term on or before Eng.Sc.D. candidates engaged only in the Plan and billed for the insurance pre- the payment due date of the first State- research, and who have completed their mium in addition to the Health Service ment, a late payment charge of $150 will twelve (12) credits of Doctoral Research fee. Visit www.health.columbia.edu for be assessed. An additional charge of 1 Instruction (see “The Graduate Programs’’ detailed information about medical percent per billing cycle may be imposed in this bulletin), are assessed a Compre- insurance coverage options and on any amount past due thereafter. hensive Fee of $1,538 per term by The directions for making confirmation, Students with an overdue account Fu Foundation School of Engineering enrollment, or waiver requests. balance may be prohibited from register- and Applied Science. ing, changing programs, or obtaining Ph.D. candidates engaged only in PERSONAL EXPENSES research are assessed $1,538 per term a diploma or transcripts. In the case of Students should expect to incur miscel- for Matriculation and Facilities by the persistently delinquent accounts, the laneous personal expenses for such Graduate School of Arts and Sciences. University may utilize the services of an items as food, clothing, linen, laundry, attorney and/or collection agent to col- dry cleaning, and so forth. lect any amount past due. If a student’s MANDATORY FEES The University advises students to account is referred for collection, the University facilities fee open a local bank account upon arrival student may be charged an additional • Full-time master’s programs: in New York City. Since it often takes as amount equal to the cost of collection, $303 per term long as three weeks for the first deposit including reasonable attorney’s fees and • All other full-time programs: to clear, students should plan to cover expenses incurred by the University. $288 per term immediate expenses using either a credit Health Service fee: $387 per term card, traveler’s checks, or cash draft International Services charge: $50 per drawn on a local bank. Students are term (international students only) urged not to arrive in New York without Transcript fee: $95 (one-time charge) sufficient start-up funds.

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40 LABORATORY CHARGES damage will be notified that a charge is Refund Policy When Dropping Students may need to add another being made against them. The amount Individual Courses $100 to $300 for drafting materials or of the charge will be stated at that time Tuition for courses dropped by the last laboratory fees in certain courses. Each or as soon as it can be determined. day of the Change of Program period student taking laboratory courses must is refunded in full. There is no refund of furnish, at his or her own expense, the TUITION AND FEE REFUNDS tuition for individual courses dropped necessary notebooks, blank forms, and after the last day of the Change of Students who make a complete with- similar supplies. In some laboratory Program period. The Change of drawal from a term are assessed a with- courses, a fee is charged to cover Program period is usually the first two drawal fee of $75. Late fees, application expendable materials and equipment weeks of the fall or spring semesters fees, withdrawal fees, tuition deposits, maintenance; the amount of the fee is (please note that the first week of the special fees, computer fees, special shown with the descriptions in the semester usually begins on a Tuesday). examination fees, and transcript fees course listings. Students engaged in Please note: The prorated schedule are not refundable. special tests, investigations, theses, or above does not pertain to individual The Health Service Fee, Health research work are required to meet the classes dropped (unless your entire Insurance Premium, University facilities costs of expendable materials as may schedule consists of only one class). fees, and student activity fees are not be necessary for this work and in accor- The prorated schedule pertains to with- refundable after the change of program dance with such arrangements as may drawals. Withdrawal is defined as drop- period. be made between the student and the ping one’s entire program. Students who withdraw within the department immediately concerned. For students receiving federal student first 60 percent of the academic period aid, refunds will be made to the federal are subject to a pro rata refund calcula- aid programs in accordance with Depart- DAMAGES tion, which refunds a portion of tuition ment of Education regulations. Refunds All students will be charged for damage based on the percentage of the term will be credited in the following order: to instruments or apparatus caused by remaining after the time of withdrawal. their carelessness. The amount of the This calculation is made from the date Federal Unsubsidized Stafford Loans charge will be the actual cost of repair, the student’s written notice of withdraw- Federal Stafford Loans and, if the damage results in total loss of al is received by the Office of Graduate Federal Perkins Loans the apparatus, adjustment will be made Student Services. Federal PLUS Loans (when disbursed in the charge for age or condition. To through the University) ensure that there may be no question Percentage Refund for Withdrawal Federal Pell Grants as to the liability for damage, students during First Nine Weeks of Term Federal Supplemental Educational Opportunity Grants should note whether the apparatus is in Prorated for calendars of a different Other Title IV funds good condition before use and, in case duration, if the entire program is dropped: of difficulty, request instruction in its Withdrawing students should be 1st week 100% proper operation. Where there is danger aware that they will not be entitled to 2nd week 90% of costly damage, an instructor should any portion of a refund until all Title IV 3rd week 80% be requested to inspect the apparatus. programs are credited and all outstand- 4th week 80% Liability for breakage will be decided by ing charges have been paid. 5th week 70% the instructor in charge of the course. 6th week 60% When the laboratory work is done by 7th week 60% a group, charges for breakage will be 8th week 50% divided among the members of the 9th week 40% group. The students responsible for any 10th week and after 0%

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FINANCIAL AID FOR GRADUATE STUDY 41

FINANCING GRADUATE INSTRUCTIONS FOR Application Process EDUCATION FINANCIAL AID APPLICANTS Before you can complete the Free The academic departments of The Fu Application for Federal Student Aid Foundation School of Engineering and Forms (FAFSA) form, you must obtain a per- Applied Science and the Office of Prospective and continuing graduate sonal identification number (PIN) from Financial Aid and Educational Financing students of The Fu Foundation School the U.S. Department of Education. The seek to ensure that all academically qual- of Engineering and Applied Science PIN serves as your identifier and your ified students have enough financial sup- must do the following to be considered personal electronic signature on the port to enable them to work toward their for all forms of graduate financing (both FAFSA. It will also allow you to access degree. Possible forms of support for departmentally administered and finan- your personal information in various tuition, fees, books, and living expenses cial aid–administered funds): U.S. Department of Education systems. are: institutional grants, fellowships, 1a. Prospective Students—complete Apply for your PIN at www.pin.ed.gov. teaching and research assistantships, an application for admission and sub- Approximately three business days after readerships, preceptorships, on- or off- mit it to The Fu Foundation School of you request your PIN, you will receive an campus employment, and student loans. Engineering and Applied Science’s e-mail with instructions on how to The Office of Financial Aid and Educational Office of Graduate Student Services; retrieve it electronically. If you ask to be Financing works closely with students to 1b. Continuing Students—preregister for notified of your PIN by mail, it will arrive develop reasonable financial plans for classes during the preregistration in seven to ten business days via the completing a degree. period; U.S. Postal Service. Columbia University graduate funds 2. complete a Free Application for Once you have your PIN, you must are administered by two separate Federal Student Aid (FAFSA) form and complete a FAFSA-on-the-Web applica- branches of the University, and the submit it to the U.S. Department of tion at www.fafsa.ed.gov. Columbia application materials required by the Education (only U.S. citizens or per- University prefers that you apply for two branches differ slightly. Institutional manent residents must complete the financial aid online. Information collected grants, fellowships, teaching and FAFSA; if you are a noncitizen, you do on the FAFSA will help Columbia to research assistantships, readerships, not need to submit this form); determine your need for financial aid. and preceptorships are all departmentally 3. complete an Express TAP applica- You must give permission for the appli- administered funds. Questions and tion and submit it to the New York cation data to be sent to Columbia problems regarding these awards should State Higher Education Services University by entering the Fu Foundation be directed to your academic depart- Corporation (only U.S. citizens or School of Engineering and Applied ment. Federal Stafford loans, federal permanent residents who reside in Science Title IV school code (E00120) unsubsidized Stafford loans, federal New York State must complete the on the FAFSA form. Perkins loans, and New York State TAP Express TAP application; if you are Once your FAFSA-on-the-Web grants are administered by the Office of not a New York State resident, you application is complete, your online con- Financial Aid and Educational Financing. do not need to submit this form); firmation page will give you a link to the Questions and problems with regard to 4. file a Columbia University Enrollment TAP-on-the-Web application. New York awards should be directed to your finan- Status Sheet. Complete the form State uses the information provided on cial aid adviser. and submit it to the Office of Financial your TAP application to determine your Aid and Educational Financing. eligibility for a Tuition Assistance Program (TAP) grant. The TAP-on-the-Web online

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42 form will be partially completed with Applied Science offer an extensive array research, and other related activities. some information from your FAFSA. of funding. Funding decisions, based Teaching and research assistantships Review this data, supply any missing solely on merit, and contingent upon require up to twenty hours of work per information, and submit the completed making satisfactory academic progress, week. The appointments generally last form. If you do not finish the online are made by the departments. As a from nine to twelve months. If you are TAP-on-the-Web application, you will be prospective student you must apply for participating in faculty research that fulfills mailed a paper Express TAP Application. admission and complete the financial aid degree requirements, you may apply for As with the TAP-on-the-Web applica- forms as stated on page 41. Continuing a research assistantship. Readers and tion, your Express TAP Application will students must preregister for classes preceptors receive partial tuition exemp- also be partially completed with some of during the preregistration period and tion and a stipend. Assistantships are your FAFSA data. Verify that the partially complete the applicable forms as stated awarded on the basis of academic merit. completed data is correct, complete the on page 41. Outside scholarships for All applicants for admission and continuing remainder of the form, and return it to which you qualify must be reported to students maintaining satisfactory aca- HESC in the envelope provided. your department and the Office of demic standing will be considered for Preregister for classes during the pre- Financial Aid and Educational Financing. these funds. Applicants should contact registration period if you are a continuing The Fu Foundation School of Engineer- the department directly for information. student. All students must complete the ing and Applied Science reserves the Graduate Engineering Financial Aid right to adjust your institutional award if ALTERNATIVE FUNDING Application available from the Office of you hold an outside scholarship, fellow- SOURCES Financial Aid and Educational Financing. ship, or other outside funding. The Graduate Engineering Financial Aid External Awards Application provides the University with Institutional Grants Because it is not possible to offer full information about your planned program, Institutional grants are awarded to grad- grant and fellowship support to all including the number of courses in which uate students on the basis of academic graduate students and because of the you plan to enroll. merit. Recipients must maintain satisfac- prestige inherent in holding an award tory academic standing. All applicants through open competition, applicants Deadlines for admission and continuing students are encouraged to consider major Apply for financial aid at the same time maintaining satisfactory academic stand- national and international fellowship that you apply for admissions. Your ing will be considered for these funds. opportunities. It is important that admissions application must be received prospective graduate students explore by the December 1 deadline to be Fellowships every available source of funding for eligible for The Fu Foundation School Fellowships are financial and intellectual graduate study. of Engineering and Applied Science awards for academic merit that provide In researching outside funding you departmental funding (institutional stipends to be used by fellows to further may look to faculty advisers, career grants, fellowships, teaching and their research. If you are awarded a fel- services offices, deans of students, and research assistantships, readerships, lowship, you are expected to devote offices of financial aid where frequently and preceptorships). Spring admissions time to your own work, and you are not you may find resource materials, books, applicants will not be considered for required to render any service to the and grant applications for a wide variety departmental funding. University or donor. You may publish of funding sources. You must notify both Incoming applicants and continuing research produced by your fellowship your academic department at The Fu students must complete their FAFSA work. As a fellow, you may not engage Foundation School of Engineering and form after January 1 and by May 1. in remunerative employment without Applied Science and the Office of Financial Guidelines for continuing students consent of the Dean. All applicants for Aid and Educational Financing of any are available from departmental advisers admission and continuing students outside awards that you will be receiving. in advance of the established deadline. maintaining satisfactory academic All continuing supported students must standing will be considered for these Funding for International Students preregister for classes during the prereg- funds. Applicants should contact the To secure a visa, international students istration period. department directly for information. See must demonstrate that they have suffi- Complete the Graduate Engineering pages 216–218 for a complete listing cient funding to complete the degree. Financial Aid Application available of fellowships. Many international students obtain sup- from the Office of Financial Aid and port for their educational expenses from Educational Financing by May 1. Assistantships their government, a foundation, or a Teaching and research assistantships, private agency. GRADUATE SCHOOL available in many departments, provide International students who apply DEPARTMENTAL FUNDING tuition exemption and a living stipend. by the December 15 deadline and are The graduate departments of The Fu Duties may include teaching, laboratory admitted to a graduate program in The Foundation School of Engineering and supervision, participation in faculty Fu Foundation School of Engineering

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and Applied Science are automatically To apply for funds, you must com- New York State Tuition Assistance 43 considered for departmental funding plete a Free Application for Federal Program (TAP) (institutional grants, fellowships, teaching Student Aid (FAFSA) form, a Graduate Legal residents of New York State who and research assistantships, readerships, Engineering Financial Aid Application, are enrolled in a full-time degree program and preceptorships) upon completion of and an Express TAP application (if you of at least 12 points a term, or the the required financial aid forms referred are a New York State resident). Loan equivalent, may be eligible for awards to above. Spring admissions applicants borrowers must complete a Columbia under this program. To apply for TAP, will not be considered for departmental University Loan Entrance Interview. The list the Columbia University school code funding. Continuing international students information supplied on the FAFSA form (E00120) on the FAFSA form. When the must preregister for classes during the is used to determine your eligibility for FAFSA has been processed, an Express preregistration period and complete an federal aid. The Enrollment Status Sheet TAP application will be mailed to you. enrollment status form to be considered provides the University with information Review the information, change any for departmental funding. about your planned program, including incorrect items, sign the form, and Most loan programs are restricted to the number of courses in which you plan return it to the address indicated. U.S. citizens and permanent residents. to enroll. The Express TAP application However, international students may acts as your request for New York State Veterans’ Benefits apply for these domestic loan programs Tuition Assistance Program funds. Various Department of Veterans Affairs with a cosigner who is a citizen or per- Columbia University prefers that the programs provide educational benefits manent resident in the United States. FAFSA be filed after January 1, but for sons, daughters, and spouses of Depending on the loan program, you preferably before May 1, for fall enroll- deceased or permanently disabled may need a valid U.S. Social Security ment. Students must give permission for veterans as well as for veterans and in- number. the application data to be sent to service personnel who served on active Students who study at The Fu Columbia University by entering The Fu duty in the U.S. Armed Forces after Foundation School of Engineering and Foundation School of Engineering and January 1, 1955. In these programs Applied Science on temporary visas Applied Science Title IV school code the amount of benefits varies. Under should fully understand the regulations (E00120) on the FAFSA form. most programs the student pays tuition concerning possible employment under It is your responsibility to supply and fees at the time of registration but those visas. Before making plans for accurate and complete information on receives a monthly allowance from employment in the United States, inter- the FAFSA and to notify the Office of Veterans Affairs. national students should consult with Financial Aid and Educational Financing Since interpretation of regulations the International Students and Scholars immediately of any changes in your governing veterans’ benefits is subject Office (ISSO), located at 524 Riverside enrollment plans, housing status, or to change, veterans and their depend- Drive, Suite 200; 212-854-3587. Their financial situation, including information ents should keep in touch with the Web site is www.columbia.edu/cu/isso/ about any institutional or outside schol- Department of Veterans Affairs. For isso.html. arships you will be receiving. additional information and assistance in The Graduate Engineering Financial completing the necessary forms, contact OTHER FINANCIAL AID— Aid Application is available from the Office 1-800-827-1000, or consult their Web FEDERAL, STATE, AND of Financial Aid and Educational Financing site at www.va.gov. PRIVATE PROGRAMS or can be downloaded from their Web site located at www.engineering.columbia. Federal Family Education Loans Eligibility edu/graduate/financing. Federal Subsidized Stafford Student To be considered for nondepartmental Determination of your financial need Loan Program financial aid (federal Stafford loans, fed- is based upon the number of courses eral unsubsidized Stafford loans, federal for which you register. If you enroll in Federal Unsubsidized Stafford Loan Perkins loans, and New York State TAP fewer courses than you initially reported Program on your Columbia University Enrollment grants), you must be a U.S. citizen or Federal Perkins Loan permanent resident admitted as at least Status Sheet, your financial aid may be Federal Graduate PLUS Loan a half-time student to a degree program reduced. in The Fu Foundation School of Engi- University-administered federal and Detailed information regarding the above neering and Applied Science. If you are state awards are not automatically loan programs may be found on the taking courses but are not yet admitted renewed each year. Continuing graduate Student Financial Services Web site: into a degree program, then you do not students must submit a Renewal FAFSA www.columbia.edu/cu/sfs/docs/ qualify for federal or state aid. In addi- each year by the Columbia University Grad_Fin_Aid. tion, to preserve your aid eligibility, you deadline. Renewal depends on the annual must maintain satisfactory academic reevaluation of your need, the availability Columbia Comprehensive progress, as defined in “The Graduate of funds, and satisfactory progress Educational Financing Plan Programs” section. toward the completion of your degree Columbia University has developed the requirements.

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44 Comprehensive Educational Financing a private loan with the assistance of a Off-Campus Employment in Plan to assist students and parents creditworthy U.S. citizen or permanent New York City with their financing needs. The plan is resident. In some cases, as an inter- One of the nation’s largest urban areas, a combination of federal, institutional, national student, you must have a valid the city offers a wide variety of opportu- and private sources of funds that we U.S. Social Security number. Contact nities for part-time work. Many students hope will meet the needs of our diverse the financial aid office for more details gain significant experience in fields related student population, providing options to on this loan program. to their research and study while they part-time, full-time, and international stu- meet a portion of their educational dents. The suggested lenders listed in EMPLOYMENT expenses. this plan were selected as a result of a Students on fellowship support must competitive Request for Proposal (RFP) obtain the permission of the Dean before CONTACT INFORMATION process conducted in 2005. The criteria accepting remunerative employment. for selection included competitive rates For questions about institutional grants, Students who study at The Fu and terms, supportive customer service, fellowships, teaching and research Foundation School of Engineering and and a flexible application and fund dis- assistantships, readerships, and precep- Applied Science on temporary visas bursement process. torships, contact your academic depart- should fully understand the regulations The Columbia Comprehensive ment. concerning possible employment under Educational Financing Plan offers pay- For questions about on- or off-campus those visas. Before making plans for ment plans, loan programs, and tuition nonneed-based employment, contact employment in the United States, inter- insurance options as well as limited loan the Center for Career Education (CCE), national students should consult with options for international students. located at East Campus, Lower Level, the International Students and Scholars Information regarding the Columbia 212-854-5609, www.careereducation. Office (ISSO) located at 524 Riverside Comprehensive Educational Financing columbia.edu. Drive, Suite 200; 212-854-3587. Their Plan may be obtained through the Office For questions about federal work- Web site is www.columbia.edu/cu/isso/ of Financial Aid and Educational Financing. study employment, New York State TAP isso.html. grants, and student loans, contact: Private Loans On-Campus Employment Office of Financial Aid and Educational Several private loan programs are avail- The Center for Career Education main- Financing able to both U.S. citizens and international tains an extensive listing of student Columbia University students attending Columbia University. employment opportunities. The Center 407 Lerner Hall, Mail Code 2802 These loans were created to supplement for Career Education (CCE) is located at New York, New York 10027 federal and institutional aid. These loan East Campus, Lower Level, 212-854-5609, programs require that you (the applicant) Phone: 212-854-3711 www.careereducation.columbia. edu. have a good credit standing and not be Fax: 212-854-8223 in default on any outstanding loans. E-mail: [email protected] International students may be eligible for www.engineering.columbia.edu/ graduate/financing

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46 FACULTY AND ADMINISTRATION

OFFICERS William E. Bailey Bruno A. Boley Associate Professor of Materials Science Professor of Civil Engineering Lee C. Bollinger and of Applied Physics and Applied B.C.E, College of the City of New York, B.A., J.D. Mathematics 1943; M.Ac.E., Polytechnic Institute of President of Columbia University B.S. and B.A., Brown, 1993; M.S., Brooklyn, 1945; Eng.Sc.D., 1946 Stanford, 1995; Ph.D., 1999 Claude M. Steele Allen H. Boozer B.A., M.A., Ph.D. Guillaume Bal Professor of Applied Physics Provost Professor of Applied Mathematics B.A., Virginia, 1966; Ph.D., Cornell, 1970 Diploma, École Polytechnique, 1993; Feniosky Peña-Mora Ph.D., University of Paris, 1997 Mark A. Borden B.S., M.S., Sc.D. Assistant Professor of Chemical Engineering Dean Scott Banta B.S., Arizona (Tucson), 1999; Associate Professor of Chemical Ph.D., California (Davis), 2003 Morton B. Friedman Engineering B.S., M.S., D.Sc. B.S., University of Maryland, Baltimore, Truman R. Brown Vice Dean 1997; M.S., Rutgers, 2000; Ph.D., 2002 Percy K. and Vida L. W. Hudson Professor of Biomedical Engineering and Professor Anna Marie O’Neill Peter Belhumeur of Radiology (Health Sciences) B.B.A. Professor of Computer Science B.S., Massachusetts Institute of Technology, Associate Dean B.S., Brown, 1985; M.S., Harvard, 1991; 1964; Ph.D., 1970 Ph.D., 1993 Jack McGourty Mark A. Cane B.A., M.S., Ph.D. Steven M. Bellovin G. Unger Vetlesen Professor of Earth and Associate Dean for Undergraduate Studies Professor of Computer Science Environmental Sciences and Professor of B.A., Columbia, 1972; M.S., North Applied Physics and Applied Mathematics Andrew Laine Carolina (Chapel Hill), 1977; Ph.D., 1987 B.A., Harvard, 1965; M.A., 1966; Ph.D., B.S., M.S., D.Sc. Massachusetts Institute of Technology, 1975 Secretary Keren Bergman Professor of Electrical Engineering Luca Carloni FACULTY B.S., Bucknell University, 1988; M.S., Associate Professor of Computer Science Massachusetts Institute of Technology, B.S., Bologna (Italy), 1995; M.S., Alfred V. Aho 1991; Ph.D., 1994 California (Berkeley), 1997; Ph.D., 2004 Lawrence Gussman Professor of Computer Science Raimondo Betti Marco Castaldi B.A.Sc., Toronto, 1963; M.A., Princeton, Professor of Civil Engineering Assistant Professor of Earth and Environ- 1965; Ph.D., 1967 B.S., Rome, 1985; M.S., Southern mental Engineering (Henry Krumb School California, 1988; Ph.D., 1991 of Mines) Peter K. Allen B.S., Manhattan College, 1992; Professor of Computer Science Daniel Bienstock M.S., UCLA, 1994; Ph.D., 1997 B.A., Brown, 1971; M.S., Oregon, 1976; Professor of Industrial Engineering and Ph.D., Pennsylvania, 1985 Operations Research and of Applied Rui Castro Physics and Applied Mathematics Assistant Professor of Electrical Dimitris Anastassiou B.S., Brandeis, 1982; Ph.D., Massachusetts Engineering Professor of Electrical Engineering Institute of Technology, 1985 Aerospace Engineer Degree, Instituto Dipl., National Technical University of Superior Tecnico (Portugal), 1998; Athens (Greece), 1974; M.S., California, Simon J. L. Billinge Ph.D., Rice, 2007 1975; Ph.D., 1979 Professor of Materials Science and of Applied Physics and Applied Mathematics Siu-Wai Chan Gerard H. A. Ateshian B.A., Oxford, 1986; Professor of Materials Science (Henry Professor of Mechanical Engineering Ph.D., Pennsylvania,1992 Krumb School of Mines) and of Applied and of Biomedical Engineering Physics and Applied Mathematics B.S., Columbia, 1986; M.S., 1987; Jose Blanchet B.S., Columbia, 1980; Sc.D., Massachusetts M.Phil., 1990; Ph.D., 1991 Assistant Professor of Industrial Institute of Technology, 1985 Engineering and Operations Research Daniel Attinger B.S., Instituto Tecnológico Autónomo de Kartik Chandran Assistant Professor of Mechanical México, 2000; Ph.D., Stanford, 2004 Assistant Professor of Earth and Engineering Environmental Engineering M.S., EPFL Lausanne, 1997; Ph.D., B.S., Indian Institute of Technology ETH Zurich, 2001 (Roorkee), 1995; Ph.D., University of Connecticut, 1999

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Shih-Fu Chang Paul Diament Gavin Gong Professor of Electrical Engineering Professor of Electrical Engineering Assistant Professor of Earth and Environ- B.S., National Taiwan University, 1985; M.S., B.S., Columbia, 1960; M.S., 1961; mental Engineering (Henry Krumb School California (Berkeley), 1991; Ph.D., 1993 Ph.D., 1963 of Mines) B.E., Cooper Union, 1991; M.S., Praveen Chaudhari Paul F. Duby Massachusetts Institute of Technology, Professor of Materials Science (Henry Professor of Mineral Engineering 1994; Ph.D., 2003 Krumb School of Mines) and of Applied Ing. Civil M.E., Brussels, 1956; Eng.Sc.D., Physics and Applied Mathematics Columbia, 1962 Luis Gravano B.S., Indian Institute of Technology, 1961; Associate Professor of Computer Science M.S., Massachusetts Institute of Christopher J. Durning B.S., Lujan (Argentina), 1990; Technology, 1963; Ph.D., 1966 Professor of Chemical Engineering M.S., Stanford, 1994; Ph.D., 1997 B.S., Columbia, 1978; M.A., Princeton, Xi Chen 1979; Ph.D., 1982 Eitan Grinspun Associate Professor of Earth and Assistant Professor of Computer Science Environmental Engineering Stephen A. Edwards B.A., Toronto (Ontario), 1997; M.S., B.E., Xi’an Jiaotong University (P.R. China), Associate Professor of Computer Science California Institute of Technology, 2000; 1994; M.E., Tsinghua University (P.R. China), B.S., California Institute of Technology, Ph.D., 2003 1997; S.M., Harvard, 1998; Ph.D., 2001 1992; M.S., California (Berkeley), 1994; Ph.D., 1997 Jonathan L. Gross Nicola Chiara Professor of Computer Science Assistant Professor of Civil Engineering Dan Ellis B.S., Massachusetts Institute of B.S., Università degli Studi di Palermo Associate Professor of Electrical Technology, 1964; M.A., Dartmouth, (Italy), 1995; M.S., University of Texas, Engineering 1966; Ph.D., 1968 2001; Ph.D., Columbia, 2006 B.A., Cambridge University, 1987; M.S., Massachusetts Institute of Technology, Carl C. Gryte Maria Chudnovsky 1992; Ph.D., 1996 Professor of Chemical Engineering Associate Professor of Industrial B.Sc., Toronto, 1964; M.Sc., 1966; Ph.D., Engineering and Operations Research Steven K. Feiner Polytechnic Institute of Brooklyn, 1970 B.A., Israel Institute of Technology, 1996; Professor of Computer Science M.S.C. Technion, 1999; M.A. Princeton, B.A., Brown, 1973; Ph.D., 1985 X. Edward Guo 2002; Ph.D., 2003 Professor of Biomedical Engineering Morton B. Friedman B.S., Peking University, 1984; M.S., Rama Cont Professor of Civil Engineering and of Harvard-MIT, 1990; Ph.D., 1994 Associate Professor of Industrial Applied Physics and Applied Mathematics Engineering and Operations Research B.S., New York University, 1948; Xuedong He Diplôme, Ecole Polytechnique (France), M.S., 1950; D.Sc., 1953 Assistant Professor of Industrial 1994; D.E.A., Ecole Normale Supérieure Engineering and Operations Research (France), 1995; Doctorat, Université de Guillermo Gallego B.S., Peking University, 2005; Paris XI, 1998 Professor of Industrial Engineering and D.Phil., Oxford, 2009 Operations Research Patricia J. Culligan B.S., California (San Diego), 1980; Tony F. Heinz Professor of Civil Engineering Ph.D., Cornell, 1988 David M. Rickey Professor of Optical B.Sc., University of Leeds, 1982; M.Phil., Communications (Electrical Engineering) Cambridge University, 1985; Ph.D., 1989 Pierre Gentine and Professor of Physics (Arts and Assistant Professor of Applied Sciences) Gautam Dasgupta Mathematics B.S., Stanford, 1978; Ph.D., California Professor of Civil Engineering B.S., SupAero (France), 2002; M.S., (Berkeley), 1982 B.Engr., Calcutta, 1967; M.Engr., 1969; Massachusetts Institute of Technology, Ph.D., California (Berkeley), 1974 2006; M.S., Sorbonne, 2009; Ph.D., Irving P. Herman Massachusetts Institute of Technology, Professor of Applied Physics George Deodatis 2009 B.S., Massachusetts Institute of The Santiago and Robertina Calatrava Technology, 1972; Ph.D., 1977 Family Professor of Civil Engineering Donald Goldfarb B.S., National Technical University of Athens, Alexander and Hermine Avanessians Henry Hess 1982; M.S., Columbia, 1984; Ph.D., 1987 Professor of Industrial Engineering and Associate Professor of Biomedical Operations Research Engineering Emanuel Derman B.Ch.E., Cornell, 1963; M.A., Princeton, B.S., Technical University Clausthal Professor of Industrial Engineering and 1965; Ph.D., 1966 (Germany), 1993; M.Sc., Technical Operations Research University Berlin, 1996; Ph.D. Free B.Sc., University of Cape Town, 1965; University Berlin, 1999 M.A., Columbia, 1968; Ph.D., 1973

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48 Andreas H. Hielscher Jingyue Ju S. G. Steven Kou Associate Professor of Biomedical Engin- Professor of Chemical Engineering Professor of Industrial Engineering and eering and of Radiology (Health Sciences) B.S., Inner Mongolia University, 1985; Operations Research B.S., University of Hannover (Germany), M.S., Chinese Academy of Sciences, M.A., Columbia, 1992; Ph.D., 1995 1987; M.S., 1991; Ph.D., Rice University, 1988; Ph.D., Southern California, 1993 1995 Harish Krishnaswamy Soulaymane Kachani Assistant Professor of Electrical Elizabeth M. C. Hillman Associate Professor of Operations Engineering Assistant Professor of Biomedical Engin- Research B.Tech., Indian Institute of Technology eering and of Radiology (Health Sciences) B.S., Ecole Centrale Paris, 1998; M.S., (Madras), 2001; M.S., Southern California, M.Sci., University College London, 1998; Massachusetts Institute of Technology, 2003; Ph.D., 2009 Ph.D., 2002 1999; Ph.D., 2002 Sanat K. Kumar Julia Hirschberg Gail E. Kaiser Professor of Chemical Engineering Professor of Computer Science Professor of Computer Science B.Tech., Indian Institute of Technology, B.A., Eckert College, 1968; Ph.D., B.S., Massachusetts Institute of 1981; S.M., Massachusetts Institute of Michigan, 1976; MSEE, Pennsylvania, Technology, 1979; M.S., 1980; Technology, 1984; Ph.D., 1987 1982; Ph.D., 1985 Ph.D., Carnegie Mellon, 1985 Ioannis Kymissis James C. Hone Lance C. Kam Assistant Professor of Electrical Associate Professor of Mechanical Assistant Professor of Biomedical Engineering Engineering Engineering M.Eng., Massachusetts Institute of B.S., Yale, 1990; Ph.D., California B.S., Washington University, 1991; Technology, 1999; Ph.D., 2003 (Berkeley), 1998 M.S., University of Hawaii, 1994; Ph.D., Rensselaer, 1999 Jeffrey Kysar Hayden Huang Associate Professor of Mechanical Assistant Professor of Biomedical John R. Kender Engineering Engineering Professor of Computer Science B.S., Kansas State, 1987; M.S., 1992; B.S., Johns Hopkins, 1995; S.M., B.S., Detroit, 1970; M.S., Michigan, 1972; S.M., Harvard, 1993; Ph.D., 1998 Massachusetts Institute of Technology, Ph.D., Carnegie-Mellon, 1980 1997; Ph.D., 2002 Klaus S. Lackner Angelos Keromytis Maurice Ewing and T. Lamar Worzel Clark T. Hung Associate Professor of Computer Science Professor of Geophysics (Earth and Professor of Biomedical Engineering B.S., Crete, Heraclion, 1996; M.S., Environmental Engineering, Henry Krumb Sc.B., Brown, 1990; M.S.E., Pennsylvania, Pennsylvania, 1997; Ph.D., 2001 School of Mines) 1992; Ph.D., 1995 B.S., Heidelberg, 1974; M.S., 1976; David E. Keyes Ph.D., 1978 James S. Im Fu Foundation Professor of Applied Professor of Materials Science (Henry Mathematics Andrew F. Laine Krumb School of Mines) and of Applied B.S.E., Princeton, 1978; Professor of Biomedical Engineering Physics and Applied Mathematics Ph.D., Harvard, 1984 and of Radiology (Health Sciences) B.S., Cornell, 1984; Ph.D., Massachusetts B.S., Cornell, 1977; M.S., Connecticut, Institute of Technology, 1989 Martha Allen Kim 1980; M.S., Washington (St. Louis), 1983; Assistant Professor of Computer Science D.Sc., 1989 Garud Iyengar B.A., Harvard, 2002; M.E., Università della Associate Professor of Industrial Svizzera Italiana (Lugano, Switzerland), 2003; Upmanu Lall Engineering and Operations Research Ph.D., University of Washington, 2008 Alan and Carol Silberstein Professor of B. Tech., Indian Institute of Technology, Earth and Environmental Engineering 1993; M.S., Stanford, 1995; Ph.D., 1998 Peter Kinget (Henry Krumb School of Mines) and Civil Associate Professor of Electrical Engineering Christopher R. Jacobs Engineering B.Tech., Indian Institute of Technology Associate Professor of Biomedical Ph.D., Katholieke Universiteit Leuven (Kampur), 1976; M.S., University of Texas, Engineering (Belgium), 1996 1980; Ph.D., 1981 B.S., Washington University, 1988; M.S., Stanford, 1989; Ph.D., 1994 Jeffrey T. Koberstein Aurel A. Lazar Percy K. and Vida L. W. Hudson Professor of Electrical Engineering Tony Jebara Professor of Chemical Engineering B.S., Bucharest Polytechnical Institute, Associate Professor of Computer Science B.S., University of Wisconsin, 1974; 1971; M.S., Darmstadt Institute of B.S., McGill, 1996; M.S., Massachusetts Ph.D., University of Massachusetts, 1979 Technology, 1976; Ph.D., Princeton, 1980 Institute of Technology, 1998; Ph.D., 2002 Elisa E. Konofagou Edward F. Leonard Predrag Relja Jelenkovic Associate Professor of Biomedical Professor of Chemical Engineering Professor of Electrical Engineering Engineering B.S., Massachusetts Institute of Dipl.Ing., Belgrade University, 1991; B.S., Université de Paris VI (France), Technology, 1953; M.S., Pennsylvania, M.S., Columbia, 1993; M.Phil., 1995; 1992; M.S., University of London, 1993; 1955; Ph.D., 1960 Ph.D., 1996 Ph.D., University of Houston, 1999

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Jung-Chi Liao Kathleen R. McKeown Steven M. Nowick 49 Assistant Professor of Mechanical Henry and Gertrude Rothschild Professor Professor of Computer Science Engineering of Computer Science B.A., Yale, 1976; M.A., Columbia, 1979; B.S., National Taiwan University, 1993; B.A., Brown, 1976; M.S., Pennsylvania, Ph.D. Stanford, 1993 M.S., Massachusetts Institute of 1979; Ph.D., 1982 Technology, 1997; Ph.D., 2001 Ismail C. Noyan V. Faye McNeill Professor of Materials Science (Henry Qiao Lin Assistant Professor of Chemical Engineering Krumb School of Mines) and of Applied Associate Professor of Mechanical B.S., California Institute of Technology, Physics and Applied Mathematics Engineering 1999; M.S., Massachusetts Institute of B.S., Middle East Technical University B.S., Tsinghua University (Beijing), 1985; Technology; Ph.D., 2005 (Turkey), 1978; Ph.D., Northwestern, 1984 M.S., 1988; Ph.D., California Institute of Technology, 1993 Christian Meyer Mariana Olvera-Cravioto Professor of Civil Engineering Assistant Professor of Industrial Hoe I. Ling Vordiplom, Technical University of Berlin, Engineering and Operations Research Professor of Civil Engineering 1965; M.S., California (Berkeley), 1966; B.S., Instituto Technológico Autónomo B.S., Kyoto University, 1988; M.S., Ph.D., 1970 de México, 2000; M.S. Stanford, 2004; University of Tokyo, 1990; Ph.D., 1993 Ph.D., 2006 Vishal Misra Richard W. Longman Associate Professor of Computer Science Richard M. Osgood Jr. Professor of Mechanical Engineering B.S., Indian Institute of Technology, 1992; Higgins Professor of Electrical Engineering and Civil Engineering M.S., Massachusetts (Amherst), 1996; and Professor of Applied Physics B.S., California (Riverside), 1965; M.S., Ph.D., 2000 B.S., U.S. Military Academy, 1965; M.S., California (San Diego), 1967; M.A., 1969; Ohio State, 1968; Ph.D., Massachusetts Ph.D., 1969 Vijay Modi Institute of Technology, 1973 Professor of Mechanical Engineering Helen H. Lu B.Tech., Indian Institute of Technology Ben O’Shaughnessy Associate Professor of Biomedical (Bombay), 1978; Ph.D., Cornell, 1984 Professor of Chemical Engineering Engineering B.Sc., Bristol (England), 1977; B.S., Pennsylvania, 1992; M.S., 1997; Barclay Morrison III Ph.D., Cambridge (England), 1984 Ph.D., 1998 Associate Professor of Biomedical Engineering B.S.E., Johns Hopkins University, 1992; Ah-Hyung Alissa Park Tal Malkin M.S.E., Pennsylvania, 1994; Ph.D., 1999 Lenfest Earth Institute; Assistant Assistant Professor of Computer Science Professor of Climate Change, Earth and B.S., Bar-Ilan University (Israel), 1993; Van C. Mow Environmental Engineering M.S., Weizmann Institute of Science Stanley Dicker Professor of Biomedical B.S., University of British Columbia, 1998; (Israel), 1995; Ph.D., Massachusetts Engineering and Professor of Orthopedic M.S., 2000; Ph.D., Ohio State, 2005 Institute of Technology, 2000 Engineering (Orthopedic Surgery, Health Sciences) Thomas S. Pedersen Jeremy J. Mao B.A.E., Rensselaer Polytechnic Institute, Associate Professor of Applied Physics Associate Professor of Orthodontics 1962; Ph.D., 1966 M.Sc., Technical University of Denmark, (Health Sciences) and Associate 1995; Ph.D., Massachusetts Institute of Professor of Biomedical Engineering Arvind Narayanaswamy Technology, 2000 Ph.D., University of Alberta (Canada), Assistant Professor of Mechanical 1992; M.S.D., 1996; D.D.S., University Engineering Itsik Pe’er of Illinois–Chicago, 2002 B.Tech., Indian Institute of Technology, Assistant Professor of Computer Science 1997; Ph.D., Massachusetts Institute of B.S., Tel Aviv University, 1990; M.S., 1995; Chris A. Marianetti Technology, 2007 Ph.D., 2002 Assistant Professor of Materials Science and of Applied Physics and Applied Gerald A. Navratil Aron Pinczuk Mathematics Thomas Alva Edison Professor of Professor of Applied Physics and of B.S., Ohio State, 1997; M.S., 1998; Ph.D., Applied Physics Physics (Arts and Sciences) Massachusetts Institute of Technology, 2004 B.S., California Institute of Technology, Licenciado, Buenos Aires (Argentina), 1973; M.S., Wisconsin, 1974; Ph.D., 1976 1962; Ph.D., Pennsylvania, 1969 Michael E. Mauel Professor of Applied Physics Shree Kumar Nayar Lorenzo M. Polvani B.S., Massachusetts Institute of Technology, T. C. Chang Professor of Computer Science Professor of Applied Mathematics and of 1978; M.S., 1979; Sc.D., 1983 B.S., Birla Institute of Technology (India), Earth and Environmental Sciences (Arts 1984; M.S., North Carolina State, 1986; and Sciences) Nicholas F. Maxemchuk Ph.D., Carnegie-Mellon, 1990 B.Sc., McGill, 1981; M.Sc., 1982; Ph.D., Professor of Electrical Engineering Massachusetts Institute of Technology, B.S., The City College of New York, 1968; Jason Nieh 1988 M.S., Pennsylvania, 1970; Ph.D., 1975 Associate Professor of Computer Science B.S., Massachusetts Institute of Technology, 1989; M.S., Stanford, 1990; Ph.D., 1999

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50 Kenneth A. Ross Kenneth L. Shepard Horst Stormer Professor of Computer Science Professor of Electrical Engineering Professor of Physics (Arts and Sciences) B.Sc., Melbourne, 1986; Ph.D., Stanford, 1991 B.S.E., Princeton, 1987; M.S.E.E., and of Applied Physics Stanford, 1988; Ph.D., 1992 B.S., Goethe-Universität–Frankfurt Dan Rubenstein (Germany), 1970; Diploma, 1974; Associate Professor of Computer Science Samuel K. Sia Ph.D., Stuttgart (Germany), 1977 B.S., Massachusetts Institute of Assistant Professor of Biomedical Technology, 1992; M.A., California (Los Engineering John E. Taylor Angeles), 1994; Ph.D., Massachusetts B.Sc., University of Alberta (Edmonton, Assistant Professor of Civil Engineering (Amherst), 2000 Canada), 1997; Ph.D., Harvard, 2002 B.S., Tulane, 1991; M.S., 1996; M.S., Swiss Federal Institute of Technology, Paul Sajda Karl Sigman 1997; Ph.D., Stanford, 2006 Associate Professor of Biomedical Professor of Industrial Engineering and Engineering Operations Research Elon Terrell B.S., Massachusetts Institute of B.A., California (Santa Cruz), 1980; M.A., Assistant Professor of Mechanical Technology, 1989; M.S., Pennsylvania, California (Berkeley), 1983; M.S., 1984; Engineering 1992; Ph.D., 1994 Ph.D., 1986 B.S., University of Texas (Austin), 2002; M.S., 2004; Ph.D., Carnegie Mellon, 2007 Peter Schlosser Nabil Simaan Vinton Professor of Earth and Assistant Professor of Mechanical Rene B. Testa Environmental Engineering (Henry Krumb Engineering Professor of Civil Engineering School of Mines) and Professor of Earth B.S., M.S., Ph.D., Technion (Israel B.E., McGill, 1959; M.S., Columbia, 1960; and Environmental Sciences (Arts and Institute of Technology), 2002 Eng.Sc.D., 1963 Sciences) B.S./M.S., Heidelberg, 1981; Ph.D., 1985 Andrew Smyth Joseph F. Traub Associate Professor of Civil Engineering Edwin Howard Armstrong Professor of Christopher H. Scholz B.A./B.Sc., Brown, 1992; M.S., Rice, Computer Science Professor of Earth and Environmental 1994; Ph.D., Southern California B.S., College of the City of New York, Sciences (Arts and Sciences) and of (Los Angeles), 1998 1954; M.S., Columbia, 1955; Ph.D., 1959 Applied Physics and Applied Mathematics B.S., Nevada, 1964; Ph.D., Massachusetts Adam H. Sobel Yannis P. Tsividis Institute of Technology, 1967 Associate Professor of Applied Physics Batchelor Memorial Professor of and Applied Mathematics and of Environ- Electrical Engineering Henning G. Schulzrinne mental Sciences (Arts and Sciences) B.E., Minnesota, 1972; M.S., California Julian Clarence Levi Professor of B.A., Wesleyan, 1989; Ph.D., Mass- (Berkeley), 1973; Ph.D., 1976 Mathematical Methods and Computer achusetts Institute of Technology, 1998 Science and Professor of Computer Latha Venkataraman Science and of Electrical Engineering Ponisseril Somasundaran Assistant Professor of Applied Physics B.S., Technical University of Darmstadt LaVon Duddleson Krumb Professor of B.S., Massachusetts Institute of Technology, (Germany), 1984; M.S., Cincinnati, 1987; Mineral Engineering 1993; M.S., Harvard, 1997; Ph.D., 1999 Ph.D., Massachusetts (Amherst), 1992 B.Sc., Kerala (India), 1958; B.E., Indian Institute of Science, 1961; M.S., California Gordana Vunjak-Novakovic Amiya K. Sen (Berkeley), 1962; Ph.D., 1964 Professor of Biomedical Engineering Professor of Electrical Engineering and B.S., University of Belgrade, 1972; of Applied Physics Marc W. Spiegelman S.M., 1975; Ph.D., 1980 Dipl., Indian Institute of Science, 1952; Professor of Earth and Environmental M.S., Massachusetts Institute of Sciences (Arts and Sciences) and of Haim Waisman Technology, 1958; Ph.D., Columbia, 1963 Applied Physics and Applied Mathematics Assistant Professor of Civil Engineering B.A., Harvard, 1985; Ph.D., Cambridge B.S., Technion (Israel Institute of Rocco A. Servedio (England), 1989 Technology), 1999; M.S., 2002; Ph.D., Associate Professor of Computer Science Rensselaer Polytechnic Institute, 2005 A.B., Harvard, 1993; M.S., 1997; Clifford Stein Ph.D., 2001 Professor of Industrial Engineering and Wen I. Wang Operations Research Thayer Lindsley Professor of Electrical Lakshminarasimhan Sethumadhavan B.S.E., Princeton, 1987; M.S., Mass- Engineering and Professor of Applied Assistant Professor of Computer Science achusetts Institute of Technology, 1989; Physics B.S.E., University of Madras, 2000; M.S., Ph.D., 1992 B.S., National Taiwan, 1975; M.E.E., University of Texas, 2005; Ph.D., 2007 Cornell, 1979; Ph.D., 1981 Salvatore J. Stolfo Jay Sethuraman Professor of Computer Science Xiaodong Wang Associate Professor of Industrial B.S., Brooklyn, 1974; M.S., New York Associate Professor of Electrical Engineering and Operations Research University, 1976; Ph.D., 1979 Engineering B.E., Birla Institute of Technology and B.S., Shanaha Jiaotong University, 1992; Science (India), 1991; M.S., Indian M.S., Purdue, 1995; Ph.D., Princeton, 1998 Institute of Science, 1994; Ph.D., Mass- achusetts Institute of Technology, 1999

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Michael I. Weinstein Tuncel M. Yegulalp Huk Yuk Cheh 51 Professor of Applied Mathematics Professor of Mining Samuel Ruben–Peter G. Viele Professor B.S., Union College, 1977; M.S., Courant M.S., Technical University (Istanbul), 1961; Emeritus of Electrochemistry Institute–NYU, 1979; Ph.D., 1982 Eng.Sc.D., Columbia, 1968 Rene Chevray Alan C. West Yechiam Yemini Professor Emeritus of Mechanical Samuel Ruben–Peter G. Viele Professor Professor of Computer Science Engineering of Electrochemistry and Chemical B.Sc., Hebrew (Jerusalem), 1972; M.Sc., Engineering 1974; Ph.D., California (Los Angeles), 1978 C. K. Chu B.S., Case Western Reserve, 1985; Professor Emeritus of Electrical Ph.D., California (Berkeley), 1989 Huiming Yin Engineering Assistant Professor of Civil Engineering Ward Whitt B.S., Hohai University, 1995; M.S., Peking Edward G. Coffman Jr. Wai T. Chang Professor of Industrial University, 1998; Ph.D., Iowa, 2004 Fu Foundation Professor Emeritus of Engineering and Operations Research Applied Mathematics A.B., Dartmouth, 1964; Ph.D., Cornell, 1969 Charles A. Zukowski Professor of Electrical Engineering Cyrus Derman Chris H. Wiggins B.S., Massachusetts Institute of Techno- Professor Emeritus of Operations Associate Professor of Applied logy, 1982; M.S., 1982; Ph.D., 1985 Research Mathematics B.A., Columbia, 1993; Ph.D., Princeton, Gil Zussman Frank L. DiMaggio 1998 Assistant Professor of Electrical Robert A. W. and Christine S. Carleton Engineering Professor Emeritus of Civil Engineering Chee Wei Wong B.S., Technion (Israel Institute of Associate Professor of Mechanical Technology), 1995; M.Sc., 1999; Atle Gjelsvik Engineering Ph.D., 2004 Professor Emeritus of Civil Engineering B.S., California (Berkeley), 1999; M.S., Massachusetts Institute of Technology, Fletcher H. Griffis 2001; Ph.D., 2003 FACULTY MEMBERS-AT-LARGE Professor Emeritus of Civil Engineering Martin Chalfie Henryk Wozniakowski Chairman, Department of Biological Robert A. Gross Professor of Computer Science Sciences Percy K. and Vida L.W. Hudson Professor M.S., Warsaw, 1969; Ph.D., 1972 Emeritus of Applied Physics and Steven A. Goldstein Dean Emeritus Cheng-Shie Wuu Chairman, Department of Earth and Professor of Clinical Radiation Oncology Environmental Sciences Cyril M. Harris (in Public Health, Environmental Health Charles Batchelor Professor Emeritus of Sciences, and Applied Physics) R. Glenn Hubbard Electrical Engineering and Professor B.S., National Tsinghua University Dean of the Graduate School of Business Emeritus of Architecture (Taiwan), 1979; M.S., 1982; Ph.D., Kansas, 1985 Igor Kricherer Herbert H. Kellogg Chairman, Department of Mathematics Stanley-Thompson Professor Emeritus Junfeng Yang of Chemical Metallurgy Assistant Professor of Computer Science Andrew J. Millis B.S., Tsinghua University (Beijing), 2000; Chairman, Department of Physics John T. F. Kuo M.S., Stanford, 2002; Ph.D., 2007 Maurice Ewing and J. Lamar Worzel Henry C. Pinkham Professor Emeritus of Geophysics Mihalis Yannakakis Dean, Graduate School of Arts and Percy K. and Vida L. W. Hudson Sciences W. Michael Lai Professor of Computer Science Professor Emeritus of Mechanical Dipl., National Technical University of Michele M. Moody-Adams Engineering Athens (Greece), 1975; M.S., Ph.D., Dean, Columbia College Princeton, 1979 Leon Lidofsky Colin Nuckolls Professor Emeritus of Applied Physics David D. W. Yao Chairman, Department of Chemistry and Nuclear Engineering Professor of Industrial Engineering and Operations Research Eugene S. Machlin M.A.Sc., Toronto, 1981; Ph.D., 1983 EMERITI AND Henry Marion Howe Professor Emeritus RETIRED OFFICERS of Metallurgy Y. Lawrence Yao (NOT IN RESIDENCE) Professor of Mechanical Engineering Thomas C. Marshall B.E., Shanghai Jiao Tong University, Theodore R. Bashkow Professor Emeritus of Applied Physics 1982; M.S., Wisconsin (Madison), 1984; Professor Emeritus of Computer Science Ph.D., 1988 Henry E. Meadows Jr. Daniel N. Beshers Professor Emeritus of Electrical Professor Emeritus of Metallurgy Engineering

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52 Gertrude F. Neumark Omar Wing Lindsay N. Montanari Howe Professor Emerita of Materials Professor Emeritus of Electrical Alumni Relations Coordinator Science and Engineering and Professor Engineering Emerita of Applied Physics and Applied Jocelyn Morales Mathematics Edward S. Yang Admissions Officer, Graduate Student Professor Emeritus of Electrical Engineering Services Arthur S. Nowick Henry Marion Howe Professor Emeritus Anna Marie O’Neill of Metallurgy ADMINISTRATIVE OFFICERS Associate Dean Jeff Ballinger Glenn K. Rightmire Director, Web Communications Fredrik C. Palm Associate in Mechanical Engineering Assistant Dean for Faculty Development Audrey Bauer and Diversity Enders Robinson Manager, Human Resources and Facilities Maurice Ewing and J. Lamar Worzel Services Feniosky Peña-Mora Professor Emeritus of Applied Geophysics Dean Ryan T. Carmichael Mischa Schwartz Parents Fund Program Officer Elaine Ragland Charles Batchelor Professor Emeritus of Executive Assistant to the Dean Electrical Engineering Paul Cassidy Associate Director, Finance and Rebecca Rodriguez Jordan L. Spencer Administration Associate Director, Entrepreneurship Professor Emeritus of Chemical Engineering Grace Chung Evelyn Roman-Lazen Executive Director, Columbia Video Director, K-12 Programs Thomas E. Stern Network Dicker Professor Emeritus of Electrical Kevin G. Shollenberger Engineering Timothy Cross Dean of Student Affairs and Associate Director, Strategic Initiatives Vice President for Undergraduate Robert D. Stoll Student Life Professor Emeritus of Civil Engineering Régine Lambrech Director Global Initiatives and Education Tiffany M. Simon Malvin Carl Teich Assistant Dean for Graduate Student Professor Emeritus of Engineering Bruce Lincoln Services Science Entrepreneur in Residence Jonathan R. Stark Nickolas J. Themelis Morton B. Friedman Student Affairs Officer, Graduate Student Stanley-Thompson Professor Emeritus Vice Dean Services of Chemical Metallurgy (Earth and Environmental Engineering, Henry Krumb Timothy G. Greene Dana Vlcek School of Mines) Stewardship Officer Director, Corporate and Community Relations Stephen H. Unger Margaret Kelly Professor Emeritus of Computer Science Associate Director, Communications Alex Yepes and of Electrical Engineering Associate Director, SBDC Jack McGourty Rimas Vaicaitis Associate Dean for Undergraduate Renwick Professor Emeritus of Studies Civil Engineering Anne Mongillo Howard W. Vreeland Associate Director, Academic Affairs and Professor Emeritus of Graphics Special Programs

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54 KEY TO COURSE LISTINGS

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

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HOW COURSES ARE DIRECTORY OF CLASSES IEOR Industrial Engineering and NUMBERED Operations Research Room assignments and course changes The course number that follows each for all courses are available online at INAF International Affairs designator consists of a capital letter www.columbia.edu/cu/bulletin/uwb. INTA Earth and Environmental Engineering/ followed by four digits. The capital letter The School reserves the right to with- Civil Engineering/ indicates the University division or affiliate draw or modify the courses of instruction International and Public Affairs offering the course: or to change the instructors at any time. MATH Mathematics B Business MEBM Mechanical Engineering/ C Columbia College Biomedical Engineering E Engineering and Applied Science MECE Mechanical Engineering G Graduate School of Arts and Sciences MSAE Materials Science and Engineering/ Solid-State Science and Engineering P Mailman School of Public Health MSIE Management Science/Industrial S Summer Session Engineering and Operations Research U International and Public Affairs MUSI Music V Interschool course with Barnard PHED Physical Education W Interfaculty course PHIL Philosophy Z American Language Program PHYS Physics POLS Political Science The first digit indicates the level of the course, as follows: PSLG Physiology and Cellular Biophysics 0 Course that cannot be credited toward any PSYC Psychology degree RELI Religion 1 Undergraduate course SCNC Science 2 Undergraduate course, intermediate SIEO Statistics/Industrial Engineering 3 Undergraduate course, advanced and Operations Research 4 Graduate course that is open to qualified SOCI Sociology undergraduates SPAN Spanish 6 Graduate course STAT Statistics 8 Graduate course, advanced VIAR Visual Arts 9 Graduate research course or seminar

An x following the course number means that the course meets in the fall semester; y indicates the spring semester.

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56 APPLIED PHYSICS AND APPLIED MATHEMATICS 200 S. W. Mudd, MC 4701, 212-854-4457 Applied Physics and Applied Mathematics: www.apam.columbia.edu Materials Science and Engineering: www.seas.columbia.edu/matsci

CHAIR Malvin A. Ruderman Arthur Ramirez RESEARCH SCIENTISTS POSTDOCTORAL RESEARCH Irving P. Herman Physics Lawrence N. Rothenberg Mark Adams SCIENTISTS 208 S. W. Mudd Christopher H. Scholz Steven A. Sabbagh Jacek Chowdhary Manus Biggs Earth and Environmental Shalom J. Wind Jerry I. Dadap Brian Grierson DEPARTMENTAL Sciences Yimei Zhu Darren Garnier Jeremy Hanson ADMINISTRATOR Amiya K. Sen Igor Geogdzhayev Sarah Kang Dina Amin Electrical Engineering ADJUNCT ASSOCIATE Mark Holzer Oksana Katsuro-Hopkins Marc W. Spiegelman PROFESSORS Holger Reimerdes Ian Langmore PROFESSORS Horst Stormer Brian Cairns George Tselioudis Jeremy Marzuola Guillaume Bal Wen I. Wang Edmond Chow Yuanchong Zhang Denis Potapenko Daniel Bienstock Electrical Engineering Hamish Ramsay Industrial Engineering and Michael I. Weinstein ADJUNCT ASSISTANT ASSOCIATE RESEARCH Shuguang Wang Operations Research Cheng Shie Wuu PROFESSORS SCIENTISTS Jonathon Wright Simon J. L. Billinge Radiation Oncology David Maurer Mikhail Alexandrov Jingbo Wu Allen H. Boozer Ron Schmitt Yonghua Chen Mark A. Cane ASSOCIATE PROFESSORS Ui-Jin Chung ASSOCIATE Earth and Environmental William E. Bailey ADJUNCT LECTURER Chris Farrow John C. Arbo Sciences Thomas S. Pedersen Oksana Katsuro-Hopkins Scott Gianelli Siu-Wai Chan Adam H. Sobel Limin Huang SPECIAL LECTURERS Praveen Chaudhari Chris H. Wiggins SENIOR RESEARCH Pavol Juhas Daniel N. Beshers Morton B. Friedman SCIENTISTS Alexander Limanov C. K. Chu Civil Engineering and ASSISTANT PROFESSORS Joze Bevk Li Liu Engineering Mechanics Pierre Gentine James Bialek Chenguang Lu SPECIAL RESEARCH Irving P. Herman Chris A. Marianetti Rainer Bleck David Maurer SCIENTIST James S. Im Latha Venkataraman Leonard Druyan Catherine Naud Thomas C. Marshall David E. Keyes Qiancheng Ma Jan Perlwitz Philip Kim ADJUNCT PROFESSORS Steven A. Sabbagh Anastasia Romanou Michael E. Mauel Vittorio M. Canuto Shalom J. Wind Ruoxian Ying Gerald A. Navratil Barbara E. Carlson Gertrude F. Neumark C. Julian Chen ADJUNCT SENIOR ADJUNCT ASSOCIATE Ismail C. Noyan Anthony Del Genio RESEARCH SCIENTISTS RESEARCH SCIENTISTS Richard M. Osgood Jr. Supratik Guha David Lang Manolis Antonoyiannakis Electrical Engineering Timothy M. Hall C. Julian Chen Conal Murray Aron Pinczuk Ron L. Miller Matthew Putman Lorenzo M. Polvani Stephen L. Ostrow

he Department of Applied Physics materials science and engineering are physics: trapped particle instabilities and and Applied Mathematics includes described on pages 169. stochastic particle motion; (3) confine- T undergraduate and graduate ment of toroidal nonneutral plasmas; studies in the fields of applied physics, Current Research Activities in (4) plasma source operation and heating applied mathematics, and materials Applied Physics and Applied techniques; and (5) the development of science and engineering. The graduate Mathematics new plasma measurement techniques. program in applied physics includes Plasma physics and fusion energy. The results from our fusion science plasma physics and controlled fusion; In experimental plasma physics, research experiments are used as a basis for col- solid-state physics; optical and laser is being conducted on (1) equilibrium, laboration with large national and inter- physics; medical physics; atmospheric, stability, and transport in fusion plasmas: national experiments. For example, our oceanic, and earth physics; and applied high-beta tokamaks, spherical tokamaks, recent demonstration of active feedback mathematics. The graduate programs in and levitated dipoles; (2) magnetospheric control of high temperature plasma

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instability is guiding research on NSTX at port in molecular nanostructures; and ocean, climate modeling, cloud physics, the Princeton Plasma Physics Laboratory, the DOE Energy Frontier Research radiation transfer, remote sensing, geo- on the DIII-D tokamak at General Atomics, Center, which focuses on conversion physical/geological fluid dynamics, geo- and for the design of the next generation of sunlight into electricity in nanometer- chemistry. The department engages in burning plasma experiment, ITER. In sized thin films. ongoing research and instruction with theoretical plasma physics, research is the NASA Goddard Institute for Space conducted in the fluid theory of plasma Applied mathematics. Current research Studies and the Lamont-Doherty Earth equilibrium and stability, active control of encompasses analytical and numerical Observatory. Five faculty members share MHD instabilities, the kinetic theory of analysis of deterministic and stochastic appointments with the Department of transport, and the development of tech- partial differential equations, large-scale Earth and Environmental Sciences. niques based on the theory of general scientific computation, fluid dynamics, In addition to the department faculty coordinates and dynamical systems. dynamical systems and chaos, as well and graduate students, many others The work is applied to magnetic fusion, as applications to various fields of physics participate in these projects, including non-neutral and space plasmas. and biology. The applications to physics full-time research faculty, faculty and include condensed-matter physics, plasma students from other departments, and Optical and laser physics. Active areas physics, nonlinear optics, medical imag- visiting scientists. of research include inelastic light scatter- ing, and the earth sciences, notably ing in nanomaterials, optical diagnostics atmospheric, oceanic, and climate Laboratory Facilities in Applied of film processing, new laser systems, science, and solid earth geophysics Physics and Applied Mathematics nonlinear optics, ultrafast optoelectron- (see below). The applications to biology The Plasma Physics Laboratory, founded ics, photonic switching, optical physics include cellular biophysics, machine in 1961, is one of the leading university of surfaces, laser-induced crystallization, learning, and functional genomics, laboratories for the study of plasma and photon integrated circuits. including collaborations with Columbia’s physics in the United States. There are Center for Computational Biology and four experimental facilities. The Solid-state physics. Research in solid- Bioinformatics (C2B2), the Center for Columbia High-Beta Tokamak (HBT-EP) state physics covers nanoscience and Computational Learning Systems supports the national program to devel- nanoparticles, electronic transport and (CCLS), the NIH-funded Center for op controlled fusion energy. It utilizes inelastic light scattering in low-dimen- Multiscale Analysis of Genetic and high voltage, pulsed power systems, sional correlated electron systems, frac- Cellular Networks (MAGNet), and the and laser and magnetic diagnostics to tional quantum Hall effect, heterostruc- NIH-funded NanoMedicine Center for study the properties of high-beta plas- ture physics and applications, molecular Mechanical Biology. Extensive collabora- mas and the use of feedback stabiliza- beam epitaxy, grain boundaries and tions exist with national climate research tion to increase the achievable beta. A interfaces, nucleation in thin films, centers (the Geophysical Fluid Dynamics collaborative program with the Princeton molecular electronics, nanostructure Laboratory and the National Center for Plasma Physics Laboratory and the DIII- analysis, and electronic structure calcu- Atmospheric Research) and with nation- D tokamak group at General Atomics is lation. Research opportunities also exist al laboratories of the U.S. Department of studying the properties of high-beta within the interdisciplinary NSF Materials Energy, custodians of the nation’s most plasmas in order to maximize fusion Research Science and Engineering powerful supercomputers. Center, which focuses on complex films power production in these large, neutral composed of nanocrystals; the NSF Atmospheric, oceanic, and earth beam-heated tokamaks and spherical Nanoscale Science and Engineering physics. Current research focuses on tori. The plasma physics group and MIT Center, which focuses on electron trans- the dynamics of the atmosphere and the have jointly constructed the Levitated

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58 Dipole Experiment (LDX), a large plasma the National Center for Atmospheric cialization through technical electives. confinement experiment incorporating a Research; the San Diego Supercomputing The applied physics curriculum offers levitated superconducting ring. The Center; the National Energy Research students the skills, experience, and Columbia Non-neutral Torus (CNT) is an Supercomputer Center in Berkeley, preparation necessary for several career experiment devoted to the first study of California; the National Leadership Class options, including opportunities to minor non-neutral plasmas confined on mag- Facility at Oak Ridge, Tennessee; the IBM in economics and to take business-related netic surfaces. The Columbia Linear SUR cluster at Brookhaven National Lab- courses. In recent years, applied physics Machine (CLM) is a continuously operat- oratory in Upton, New York; and others. graduates have entered graduate pro- ing, linear mirror device for the study of Facilities, and research opportunities, grams in many areas of applied physics collisionless plasma instabilities, plasma, also exist within the interdepartmental or physics, enrolled in medical school, transport, and feedback stabilization. Materials Research Science and Engi- or been employed in various technical or Columbia’s Collisionless Terrella neering Center, which focuses on com- financial areas immediately after receiv- Experiment investigates plasma trans- plex films composed of nanoparticles. ing the B.S. degree. port in magneto-spheric geometry and Opportunities for undergraduate the generation of strong plasma flow Current Research Activities and research exist in the many research pro- from nonlinear electrostatic potentials. Laboratory Facilities in Materials grams in applied physics. These include Experimental research in solid-state Science and Engineering fusion and space plasma physics, optical physics and laser physics is conducted See page 168. and laser physics, and condensed matter within the department and also in asso- physics. Undergrad-uate students can ciation with the Columbia Center for receive course credit for research or an UNDERGRADUATE PROGRAMS Integrated Science and Engineering and independent project with a faculty mem- the School of Mines. Facilities include The Department of Applied Physics and ber. Opportunities also exist for under- laser processing and spectroscopic Applied Mathematics offers three under- graduate students in the applied physics apparatus, ultrahigh vacuum chambers graduate programs: applied physics, program to participate in this research for surface analysis, picosecond and applied mathematics, and materials through part-time employment during femtosecond lasers, a molecular beam science and engineering. The materials the academic year and full-time employ- epitaxy machine, and a clean room that science and engineering program is ment during the summer, either at includes photo-lithography and thin film described on pages 168–169. Columbia or as part of the NSF REU fabrication systems. Within this field, The applied physics and applied math- program nationwide. Practical research the Laser Diagnostics and Solid-State ematics programs provide an excellent experience is a valuable supplement to Physics Laboratory conducts studies in preparation for graduate study or for the formal course of instruction. Applied laser spectroscopy of semiconductor careers in which mathematical and techni- physics students participate in an infor- thin films and superlattices, and laser cal sophistication are important. Using the mal undergraduate seminar to study diagnostics of thin film processing. The large number of electives in these pro- current and practical problems in Laser Lab focuses on the study of mate- grams, students can tailor their programs applied physics, and obtain hands-on rials under high pressure, laser surface to fit their personal and career interests. By experience in at least two advanced chemical processing, and new semicon- focusing their technical electives, students laboratory courses. ductor structures. Research is also con- can obtain a strong base of knowledge in Majors are introduced to two areas ducted in the shared characterization a specialized area. In addition to formal of application of applied physics (AP) by laboratories and clean room operated by minors, some areas of specialization that a course in each of two areas. Approved the NSF Materials Research Science are available are described on pages areas and courses are: 59–60. All technical electives are normally and Engineering Center and the NSF DYNAMICAL SYSTEMS at the 3000 level or above. Nanoscale Science and Engineering APMA E4101 or PHYS G4003 Center. OPTICAL OR LASER PHYSICS: The department maintains an exten- UNDERGRADUATE PROGRAM APPH E4110 or E4112 sive network of workstations and desktop IN APPLIED PHYSICS NUCLEAR SCIENCE: APPH E4010 PLASMA PHYSICS: APPH E4301 computers. The department has recently The applied physics program stresses PHYSICS OF FLUIDS: APPH E4200 acquired a SiCortex supercomputer with the basic physics that underlies most CONDENSED MATTER PHYSICS: PHYS G4018 1,458 cores, which is used for a wide developments in engineering and the BIOPHYSICAL MODELING: APMA E4400 range of departmental computational mathematical tools that are important to In addition to these courses, courses activities. The research of the Plasma Lab both physicists and engineers. Since the listed in the Specialty Areas in Applied is supported by a dedicated data acquisi- advances in most branches of technology Physics can be used to satisfy this tion/data analysis system, and the lead to rapid changes in state-of-the-art requirement with preapproval of the applied math group has access to a techniques, the applied physics program applied physics adviser. Beowulf cluster. Through the Internet, provides the student with a broad base All students must take 30 points of researchers in the department are cur- of fundamental science and mathematics electives in the third and fourth years, rently using supercomputing facilities at while retaining the opportunity for spe-

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of which 17 points must be technical UNDERGRADUATE DOUBLE PHYS G4018y: Solid-state physics 59 courses approved by the adviser. MAJOR IN APPLIED PHYSICS APMA E4101y: Introduction to dynamical The 17 points include 2 points of an AND APPLIED MATHEMATICS systems advanced laboratory in addition to APPH Students satisfy all requirements for • Earth and Atmospheric Sciences E4018. Technical electives must be at both majors, except for the seminar The Earth sciences provide a wide the 3000 level or above unless prior requirements. They are required to take range of problems of interest to physi- approval is obtained from the depart- both senior seminars, APMA E4903 and cists and mathematicians ranging ment. A number of approved technical APPH E4903 (taking one in the junior from the dynamics of the Earth’s electives are listed in the section on spe- year and one in the senior year, due to climate to earthquake physics to cialty areas following. The remaining timing conflicts), but not the junior semi- dynamics of Earth’s deep interior. The points of electives are intended primarily nars, APMA E4901 and APPH E4901. Lamont-Doherty Earth Observatory, as an opportunity to complete the four- A single course may be used to fulfill a which is part of Columbia University, year, 27-point nontechnical requirement, requirement in both majors. Students provides enormous resources for but any type of course work can satisfy must maintain a GPA at or above 3.75, students interested in this area. them. and must graduate with at least 143 points, 15 above the regular 128-point A. ATMOSPHERE, OCEANS AND CLIMATE UNDERGRADUATE PROGRAM requirement. These extra 15 points APPH E4200x: Physics of fluids IN APPLIED MATHEMATICS should be technical electives appropriate APPH E4210y: Geophysical fluid dynamics for one or both majors. The applied mathematics program is EESC W4008y: Introduction to atmospheric To apply, a student first obtains the science flexible and intensive. A student must approval of both the general undergrad- ESC W4925x: Introduction to physical take the required courses listed below, uate AP adviser and the general under- oceanography or prove equivalent standing, and then EES W4930y: Earth’s oceans and atmos- graduate AM adviser, and then the may elect the other courses from math- phere approval of the Dean. ematics, computer science, physics, Earth and environmental sciences, B. SOLID EARTH GEOPHYSICS biophysics, economics, business and SPECIALTY AREAS IN APPLIED APPH E4200x: Physics of fluids finance, or other application fields. Each PHYSICS AND APPLIED EESC W4941y: Principles of geophysics student tailors his or her own program in MATHEMATICS EESC W4001x: Advanced general geology EESC W4113x: Introduction to mineralogy close collaboration with an adviser. He Both applied physics and applied math- EESC W4701y: Introduction to igneous or she must also register for the applied ematics students can focus their techni- petrology mathematics seminar during both the cal electives and develop a strong base EESC W4950x: Mathematical methods in junior and senior years. During the junior of knowledge in a specialty area. There the Earth sciences year, the student attends the seminar is no requirement to focus electives, so (See also courses listed under lectures for 0 points; during the senior students may take as many or as few of Scientific Computation and Computer year, he or she attends the seminar the recommended courses in a specialty Science, page 60) lectures as well as tutorial problem area as is appropriate to their schedules sessions for 3 or 4 points. and interests. Some specialties are given • Basic Physics and Astrophysics While it is common for students below, but this is not an exclusive list Fundamental physics and astrophysics in the program to go on to graduate and others can be worked out in coordi- can be emphasized. Not only is astro- school, many graduating seniors will nation with the student’s adviser. The physics providing a deeper under- find employment directly in industry, courses that are often taken, or in some standing of the universe, but it is also government, education, or other fields. cases need to be taken, in the junior testing the fundamental principles of Of the 27 points of elective content year are denoted with a “J.” physics. in the third and fourth years, at least 15 PHYS W3002y: From quarks to the cosmos: points of technical courses approved by Technical Electives applications of modern physics the adviser must be taken. The remaining • Applications of Physics ASTR C3601x: General relativity, black holes, points of electives are intended primarily Courses that will give a student a and cosmology (J) as an opportunity to complete the four- broad background in applications of ASTR C3602y: Physical cosmology and extra- galactic astronomy (J) year, 27-point nontechnical requirement, physics are: but any type of course work can satisfy APMA E4101x: Introduction to dynamical them. MSAE E3103x: Elements of materials science (J) systems ELEN E3000x: Introduction to circuits, systems, ASTR G4001y: Astrophysics, I Transfers into the applied mathematics and electronics (J) program from other majors require a GPA APPH E4010x: Introduction to nuclear science • Business and Finance of 3.0 or above, and the approval of the APPH E4110x: Modern optics The knowledge of physics and mathe- applied mathematics program chair. APPH E4112y: Laser physics matics that is gained in the applied APPH E4200x: Physics of fluids APPH E4301y: Introduction to plasma physics physics and applied mathematics

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60 programs is a strong base for a career MATH W4386x-W4387y: Geometrical concepts • Scientific Computation and in business or finance. in physics Computer Science MATH W4032x: Fourier analysis Advanced computation has become a A. ECONOMICS MATH W4062y: Mathematical analysis, II core tool in science, engineering, and ECON W3211x,y: Intermediate microeco- mathematics and provides challenges • Quantitative Biology nomics (J) for both physicists and mathemati- Traditionally biology was considered a ECON W3213x,y: Intermediate macroeco- cians. Courses that build on both descriptive science in contrast to the nomics (J) practical and theoretical aspects of quantitative sciences that are based on computing and computation include: B. INDUSTRIAL ENGINEERING AND mathematics, such as physics. This OPERATIONS RESEARCH view no longer coincides with reality. APMA E4300y: Introduction to numerical methods IEOR E4003x: Industrial economics Researchers from biology as well as APMA E4301x: Numerical methods for partial IEOR E4201x: The engineering of from the physical sciences, applied differential equations management, I mathematics, and computer science AMCS E4302: Parallel scientific computing IEOR E4202y: The engineering of are rapidly building a quantitative base MATH V3020x: Number theory and cryptogra- management, II of biological knowledge. Students can phy (J) COMS W3137x,y: Data structures and algo- C. FINANCE acquire a strong base of knowledge in quantitative biology, both biophysics rithms (or COMS W3139y: SIEO W4150x,y: Probability and statistics (J) and computational biology, while com- Honors data structures and IEOR E4106y: Introduction to operations algorithms) (J) pleting the applied physics or applied research: stochastic models COMS W3157x,y: Advanced programming (J) (J) mathematics programs. COMS W3203x,y: Discrete mathematics: intro- IEOR E4700x: Introduction to financial PROFESSIONAL-LEVEL COURSE: duction to combinatorics engineering APPH E1300y: Physics of the human body and graph theory (J) MATH W4071x: Mathematics of finance COMS W4203y: Graph theory ECIE W4280: Corporate finance RECOMMENDED: COMS W4701x,y: Artificial intelligence BIOL C2005x-C2006y: Introduction to molecu- COMS W4771y: Machine learning • Mathematics Applicable to Physics lar and cellular biology, Applied physics students can special- I & II • Solid-State Physics APMA E4400y: Introduction to biophysical ize in the mathematics that is applica- Much of modern technology is based on modeling ble to physics. This specialization is solid-state physics, the study of solids particularly useful for students interest- OTHER TECHNICAL ELECTIVES (A COURSE and liquids. Courses that will build a ed in theoretical physics. IN A LEAST TWO AREAS RECOMMENDED): strong base for a career in this area are: APMA E4101x: Introduction to dynamical A. BIOLOGICAL MATERIALS MSAE E3103x: Elements of material science (J) systems ELEN E3106x: Solid-state devices and CHEN E4650x: Biopolymers APMA E4001y: Principles of applied mathe- materials (J) BIOL W4070x: The biology and physics matics MSAE E4206x: Electronic and magnetic of single molecules APMA E4301x: Numerical methods for partial properties of solids differential equations B. BIOMECHANICS PHYS G4018y: Solid-state physics APMA E4302x: Parallel scientific computing MSAE E4207y: Lattice vibrations and crystal MATH V3386x: Differential geometry BMEN E3320y: Fluid biomechanics (J) defects MATH W4386x-W4387y: Geometrical con- BMEN E4300y: Solid biomechanics (J) PHYS W3083y: Electronics laboratory (J) cepts in physics C. GENOMICS AND BIOINFORMATICS UNDERGRADUATE PROGRAM • Fundamental Mathematics in ECBM E3060x: Introduction to genomic IN MATERIALS SCIENCE AND Applied Mathematics information science and technology (J) ENGINEERING This specialization is intended for stu- BIOL W3037y: Whole genome bioinformatics (J) See page 168. dents who desire a more solid founda- CBMF W4761y: Computational genomics tion in the mathematical methods and underlying theory. For example, this D. NEUROBIOLOGY GRADUATE PROGRAMS specialization could be followed by BIOL W3004x: Cellular and molecular Financial aid is available for students students with an interest in graduate neurobiology (J) pursuing a doctorate. Fellowships, work in applied mathematics. BIOL W3005y: Systems neurobiology (J) scholarships, teaching assistantships, ELEN G4011x: Computational neuroscience APMA E4101x: Introduction to dynamical and graduate research assistantships are awarded on a competitive basis. The systems The second term of biology will be con- Aptitude Test of the Graduate Record APMA E4150x: Applied functional analysis sidered a technical elective if a student Examination is required of candidates SIEO W4150x,y: Introduction to probability has credits from at least two other of the for admission to the department and for and statistics (J) recommended courses in quantitative MATH V3386x: Differential geometry financial aid; the Advanced Tests are biology at the 3000 level or above. recommended.

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M.S. Program in Applied Physics IEOR E4004: Introduction to operations research: This is a two-semester nondegree program. 61 The program of study leading to the deterministic models Students are admitted to the department IEOR E4007: Optimization: models and methods degree of Master of Science, while as certificate-track students. IEOR E4106: Introduction to operations research: emphasizing continued work in basic stochastic models physics, permits many options in several SIE0 W4150: Introduction to probability and Ph.D. and Eng.Sc.D. Programs applied physics specialties. The program statistics After completing the M.S. program in may be considered simply as additional IEOR E4403: Advanced engineering and corpo- applied physics, doctoral students spe- education in areas beyond the bachelor’s rate economics cialize in one applied physics field. Some level, or as preparatory to doctoral stud- IEOR E4407: Game theoretic models of operations programs have specific course require- SIE0 W4606: Elementary stochastic processes, ies in the applied physics fields of plasma ments for the doctorate; elective courses IEOR E4700: Introduction to financial engineering physics, laser physics, solid-state physics, are determined in consultation with the and applied mathematics. Specific Other elective courses include: program adviser. Successful completion course requirements for the master’s MECE E4100: Mechanics of fluids of an approved 30-point program of degree are determined in consultation MSAE E4215: Mechanical behavior of structural study is required in addition to success- with the program adviser. materials ful completion of a written qualifying EEME E6601: Introduction to control theory examination taken after two semesters M.S. Program in Applied Physics / of graduate study. An oral examination, Concentration in Applied Mathematics M.S. Program in Medical Physics taken within one year after the written This 30-point program leads to a This CAMPEP-approved 36-point pro- qualifying examination, and a thesis pro- professional M.S. degree. Students gram in medical physics leads to the posal examination, taken within two years must complete five core courses and M.S. degree. It is administered by faculty after the written qualifying examination, five electives. The core courses provide from the School of Engineering and are required of all doctoral candidates. a student with a foundation in the funda- Applied Science in collaboration with mentals of applied mathematics and faculty from the College of Physicians M.S., Eng.Sc.D., and Ph.D. contribute 15 points of graduate credit and Surgeons and the Mailman School Programs in Materials Science and toward the degree. Students must com- of Public Health. It provides preparation Engineering plete five of the following seven courses: toward certification by the American See page 169. Board of Radiology. The program con- APMA E4001: Principles of applied mathematics APMA E4101: Introduction to dynamical systems sists of a core curriculum of medical Applied Mathematics physics courses, anatomy, lab, seminar, APMA E4150: Applied functional analysis This academic program, for students APMA E4200: Partial differential equations and two practicums. Specific course registered in the Department of Applied APMA E4204: Functions of a complex variable requirements are APPH E4010, Physics and Applied Mathematics, APMA E4300: Introduction to numerical methods E4710/11, E4500, E4550, E4600, and emphasizes applied mathematics APMA E4301: Numerical methods for partial APBM E4650, and, in the Mailman differential equations research in nonlinear dynamics, fluid School of Public Health, EHSC P6330, APMA E6301: Analytic methods for partial differ- mechanics, and scientific computation P9319, P9330, and P9335. Some ential equations with a current emphasis on geophysical, opportunities for specialization exist. APMA E6302: Numerical analysis for partial biophysical, and plasma physics appli- differential equations A passing grade on a comprehensive cations. examination is required for graduation. A student must select five elective Applied mathematics deals with the This examination, on subjects covered courses from those listed below (or any use of mathematical concepts and tech- in the curriculum, is taken at the end of of those not used to satisfy the core niques in various fields of science and the program of study. requirements from the list above) for a engineering. Historically, mathematics total of 15 points of graduate credit. was first applied with great success Certificate of Professional Additional courses not listed below can in astronomy and mechanics. Then it Achievement in Medical Physics be applied toward the elective require- developed into a main tool of physics, This graduate program of instruction ments, subject to the approval of the other physical sciences, and engineer- leads to the Certificate of Professional faculty adviser. Computer science elec- ing. It is now important in the biological, Achievement and requires satisfactory tive courses include: geological, and social sciences. With the completion of at least four of the follow- CS0R W4231: Analysis of algorithms coming of age of the computer, applied ing courses: C0MS W4236: Introduction to computational mathematics has transcended its tradi- complexity APPH E4500: Health physics tional style and now assumes an even C0MS W4241: Numerical algorithms and APPH E4600: Dosimetry greater importance and a new vitality. EHSC P6330: Radiation science complexity Compared with the pure mathemati- C0MS W4252: Computational learning theory EHSC P9319: Clinical nuclear medicine physics cian, the applied mathematician is more EHSC P9330: Diagnostic radiological physics Industrial engineering/operations EHSC P9335: Radiation therapy physics interested in problems coming from research elective courses include: APBM E4650: Anatomy for physicists and other fields. Compared with the engineer IEOR E4003: Industrial economics engineers and the physical scientist, he or she is

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62 APPLIED PHYSICS PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) MATH V1202 (3) MATHEMATICS1 and ODE (3)2

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

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

ENGLISH C1010 (3) COMPOSITION Z1003 (0) C1010 (3) (three tracks, choose one) Z0006 (0) Z1003 (0) C1010 (3)

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

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

COMPUTER A computer language of the student’s choice at the 1000 level or higher SCIENCE

PHYSICAL C1001 (1) C1002 (1) EDUCATION

GATEWAY LAB E1102 (4) either semester

1With the permission of the faculty adviser, students with advanced standing may start the calculus sequence at a higher level. 2Applied physics majors should satisfy their ODE requirement with the Mathematics Department (ordinarily MATH E1210). Students who take APMA E2101 prior to declaring their major in applied physics may use this course to satisfy their ODE requirement.

more concerned with the formulation of careers in plasma research, controlled centrate are laser modification of surfaces, problems and the nature of solutions. fusion, and space research. This includes the free-electron laser, optical diagnos- Compared with the computer scientist, basic training in relevant areas of applied tics of film processing, inelastic light he or she is more concerned with the physics, with emphasis on plasma scattering in nano-materials, nonlinear accuracy of approximations and the physics and related areas leading to optics, ultrafast optoelectronics photonic interpretation of results. Needless to say, extensive experimental and theoretical switching, optical physics of surfaces, even in this age of specialization, the research in the Columbia University and photon integrated circuits. Specific work of mathematicians, scientists, and Plasma Physics Laboratory. Specific course requirements for the optical and engineers frequently overlaps. Applied course requirements for the plasma laser physics doctoral program are set mathematics, by its very nature, has physics doctoral program are APPH with the academic adviser. occupied a central position in this inter- E4018, E4200, E4300, E6101, E6102, play and has remained a field of fascina- and E9142 or E9143, or equivalents Solid-State Physics tion and excitement for active minds. taken at another university. This academic program encompasses the study of the electrical, optical, mag- Materials Science and Engineering Optical and Laser Physics netic, thermal, high-pressure, and ultra- Program This academic program involves a basic fast dynamical properties of solids, with See page 169. training in relevant areas of applied physics an aim to understanding them in terms with emphasis in quantum mechanics, of the atomic and electronic structure. Plasma Physics quantum electronics, and related areas The program emphasizes the formation, This academic program is designed to of specialization. Some active areas of processing, and properties of thin films, emphasize preparation for professional research in which the student may con- low-dimensional structures—such as

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63 APPLIED PHYSICS: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

PHYS W3003 (3) APPH E3100 (3) APPH E4300 (3) Course in second Mechanics Intro. to quantum mechanics Applied electrodynamics AP area (3)

MSAE E3111 (3) APPH E3300 (3) APPH E4100 (3) APPH E4018 (2) Thermodynamics Applied electromagentism Quantum physics Laboratory REQUIRED COURSES APMA E3101 (3) APMA E3102 (3) Course in first Linear algebra Partial differential equations AP area (3)

APPH E4901 (1) APPH E4903 (2) 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

1They must include at least 2 points of laboratory courses. If PHYS W3081 is taken as part of the first two years of the program, these technical electives need not include laboratory courses. Technical electives must be at the 3000 level or above unless prior approval is obtained.

one- and two-dimensional electron balance in the body, the mechanics of motion, APMA E3101 or the equivalent. Basic concepts gases, nanocrystals, and surfaces of fluid dynamics of the heart and circulation, vibra- and assumptions of quantum mechanics, Schro- electronic and optoelectronic interest. tions in speaking and hearing, muscle mechanics, dinger’s equation, solutions for one-dimensional gas exchange and transport in the lungs, vision, problems including square wells, barriers and the Facilities include a microelectronics labo- structural properties and limits, electrical proper- harmonic oscillator, introduction to the hydrogen ratory, high-pressure diamond anvil cells, ties and the development and sensing of magnetic atom, atomic physics and x-rays, electron spin. a molecular beam epitaxy machine, fields, and the basics of equilibrium and regulatory ultrahigh vacuum systems, lasers, equip- control. In each case, a simple model of the body APAM E3105x Programming methods for ment for the study of optical properties, organ, property, or function will be derived and scientists and engineers and the instruments in the shared facili- then applied. The course is approved as a SEAS Lect: 2.5. Lab: 1. 3 pts. Not given in 2009–2010. ties of the Materials Research Science technical elective. Introduction to modern techniques of computer and Engineering Center and the Nano- programming for the numerical solutions to famil- APAM E1601y Introduction to computational iarity with basic and advanced concepts of modern scale Science and Engineering Center. mathematics and physics numerical programming and acquire practical There are also significant resources for Lect: 3. 3 pts. Instructor to be announced. experience solving representative problems in electrical and optical experimentation at Introduction to computational methods in applied math and physics. low temperatures and high magnetic mathematics and physics. Students develop solu- fields. Specific course requirements for tions in a small number of subject areas to acquire APPH E3300y Applied electromagnetism the solid-state physics doctoral program experience in the practical use of computers to solve Lect: 3. 3 pts. Professor Venkataraman. are set with the academic adviser, in mathematics and physics problems. Topics change Corequisite: APMA E3102. Vector analysis, electro- from year to year. Examples include elementary consultation with the Committee on static fields, Laplace’s equation, multipole expansions, interpolation of functions, solution of nonlinear electric fields in matter: dielectrics, magnetostatic Materials Science and Engineering/ algebraic equations, curve-fitting and hypothesis fields, magnetic materials, and superconductors. Solid-State Science and Engineering. testing, wave propagation, fluid motion, gravitational Applications of electromagnetism to devices and and celestial mechanics, and chaotic dynamics. research areas in applied physics. The basic requirement for this course is one year COURSES IN APPLIED PHYSICS of college-level calculus and physics; programming APPH E3900x and y Undergraduate research APPH E1300y Physics of the human body experience is not required. in applied physics Lect. 3. 3 pts. Professor Herman. 0 to 4 pts. Members of the faculty. Prerequisites: PHYS C1201 or C1401, and APPH E3100y Introduction to quantum This course may be repeated for credit, but no Calculus I; corequisites: PHYS C1202 or C1402, mechanics more than 6 points of this course may be counted and Calculus II. This introductory course analyzes Lect: 3. 3 pts. Professor Pedersen. toward the satisfaction of the B.S. degree require- the human body from the basic principles of Prerequisites: PHYS C1403 or the equivalent, ments. Candidates for the B.S. degree may con- physics. Topics to be covered include the energy and differential and integral calculus. Corequisite: duct an investigation in applied physics or carry

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64 APPLIED MATHEMATICS PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) MATH V1202(3) MATHEMATICS1 and ODE (3)2

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

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

ENGLISH C1010 (3) COMPOSITION Z1003 (0) C1010 (3) (three tracks, choose one) Z0006 (0) Z1003 (0) C1010 (3)

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

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

COMPUTER A computer language of the student’s choice at the 1000 level or higher SCIENCE PHYSICAL EDUCATION C1001 (1) C1002 (1)

GATEWAY LAB E1102 (4) either semester

1With the permission of the faculty adviser, students with advanced standing may start the calculus sequence at a higher level. 2Applied mathematics majors should satisfy their ODE requirement with the Mathematics Department (ordinarily MATH E1210). Students who take APMA E2101 prior to declaring their major in applied physics may use this course to satisfy their ODE requirement.

out a special project under the supervision of the spectroscopy physics, and superconductivity. monic oscillator, angular momentum identical staff. Credit for the course is contingent upon the particles, quantum statistics, perturbation theory submission of an acceptable thesis or final report. APPH E4090x Nanotechnology and applications to the quantum physics of Lect: 3. 3 pts. Offered in alternate years. atoms, molecules, and solids. APPH E4010x Introduction to nuclear science Professor Herman. Lect: 3. 3 pts. Professor Ostrow. Prerequisites: APPH E3100 and MSAE E3103 or APPH E4110x Modern optics Prerequisites: MATH V1202 and E1210 and PHYS their equivalents with the instructor’s permission. Lect: 3. 3 pts. Offered in alternate years. C1403 or their equivalents. This introductory course The science and engineering of creating materi- Not given in 2009–2010. is for individuals with an interest in medical physics als, functional structures, and devices on the Prerequisite: APPH E3300 or the equivalent. Ray and other branches of radiation science. Topics nanometer scale. Carbon nanotubes, nanocrys- optics, matrix formulation, wave effects, interfer- covered include basic concepts, nuclear models, tals, quantum dots, size-dependent properties, ence, Gaussian beams, Fourier optics, diffraction, semi-empirical mass formula, interaction of radia- self-assembly, nanostructured materials. Devices image formation, electromagnetic theory of light, tion with matter, nuclear detectors, nuclear struc- and applications, nanofabrication. Molecular polarization and crystal optics, coherence, guided ture and instability, radioactive decay processes engineering, bionanotechnology. Imaging and wave and fiber optics, optical elements, photons, and radiation, particle accelerators, and fission manipulating at the atomic scale. Nanotechnology selected topics in nonlinear optics. and fusion processes and technologies. in society and industry. APPH E4112y Laser physics APPH E4018y Applied physics laboratory APPH E4100x Quantum physics of matter Lect: 3. 3 pts. Not given in 2009–2010. Lab: 4. 2 pts. Professor Mauel. Lect: 3. 3 pts. Professor Venkataraman. Recommended but not required: APPH E3100 Prerequisite: ELEN E3401 or the equivalent. Prerequisite: APPH E3100. Corequisite: APMA and E3300 or their equivalents. Optical res- Typical experiments are in the areas of plasma E3102 or the equivalent. Basic theory of quantum onators, interaction of radiation and atomic sys- physics, microwaves, laser applications, optical mechanics, well and barrier problems, the har- tems, theory of laser oscillation, specific laser

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65 APPLIED MATHEMATICS: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

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

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

1MATH V2010 may be substituted for APMA E3101; APMA E4200 or MATH V3028 may be substituted for APMA E3102; MATH V3007 may be substituted for APMA E4204. 2One course from Group A and one course from Group B required for graduation. Group A: SIEO W3658: Probability; SIEO W4105: Probability; SIEO W3600: Introduction to probability and statistics; SIEO W4150: Introduction to probability and statistics; MATH W4155: Probability theory. Group B: STAT W3105: Introduction to statistics; STAT W3107: Statistical inference; STAT W4107: Statistical inference; STAT W4109: Probability and statistical inference; SIEO W 4606: Elementary stochastic processes; IEOR E3106: Introduction to stochastic models; IEOR E4106: Introduction to operations research: stochastic models; IEOR E4703: Monte Carlo simulation; COMS W4771: Machine learning. 3With an adviser’s permission, an approved technical elective may be substituted. 4Any course in science or engineering at the 3000 level or above qualifies as a technical elective.

systems, rate processes, modulation, detection, tor’s permission. The physics of solar energy, and Rossby waves, geostrophic adjustment and harmonic generation, and applications. including solar radiation, the analemma, atmos- quasigeostrophy, baroclinic and barotropic insta- pheric effects, thermodynamics of solar energy, bilities, Sverdrup balance, boundary currents, CHAP E4120x Statistical mechanics physics of solar cells, energy storage and trans- Ekman layers. Lect: 3. 3 pts. Professor O’Shaughnessy. mission, and physics and economics in the solar Prerequisite: CHEN E3210 or equivalent thermo- era. APPH E4300x Applied electrodynamics dynamics course, or the instructor’s permission. Lect: 3. 3 pts. Professor Boozer. Fundamental principles and underlying assump- APPH E4200x Physics of fluids Prerequisites: PHYS W3003 and APPH E3300 tions of statistical mechanics. Boltzmann’s entropy Lect: 3. 3 pts. Professor Mauel. or their equivalents. Overview of properties and hypothesis and its restatement in terms of Prerequisites: APMA E3102 or the equivalent, interactions of static electric and magnetic fields. Helmholtz and Gibbs free energies and for PHYS C1401 or C1601 or the equivalent. An Study of phenomena of time-dependent electric open systems. Correlation times and lengths. introduction to the physical behavior of fluids for and magnetic fields, including induction, waves, Exploration of phase space and observation science and engineering students. Derivation of and radiation as well as special relativity. timescale. Correlation functions. Fermi-Dirac and basic equations of fluid dynamics: conservation Applications are emphasized. Bose-Einstein statistics. Fluctuation-response of mass, momentum, and energy. Dimensional theory. Applications to ideal gases, interfaces, analysis. Vorticity. Laminar boundary layers. APPH E4301y Introduction to plasma physics liquid crystals, microemulsions and other complex Potential flow. Effects of compressibility, stratifica- Lect: 3. 3 pts. Professor Maurer. fluids, polymers, Coulomb gas, interactions tion, and rotation. Waves on a free surface; shal- Prerequisite: APPH E4300. Definition of a plasma. between charged polymers and charged inter- low water equations. Turbulence. Plasmas in laboratories and nature, plasma pro- faces, ordering transitions. duction. Motion of charged particles in electric APPH E4210y Geophysical fluid dynamics and magnetic fields, adiabatic invariants. APPH E4130y Physics of solar energy Lect: 3. 3 pts. Professor Polvani. Heuristic treatment of collisions, diffusion, trans- Lect: 3. 3 pts. Professor Chen. Prerequisites: APMA E3101 and E3102 or the port, and resistivity. Plasma as a conducting fluid. Prerequisites: General physics (PHYS C1403 or equivalents and APPH E4200 or the equivalent, Electrostatic and magnetostatic equilibria of plas- C1602), general chemistry (one term, such as or permission of the instructor. Fundamental con- mas. Waves in cold plasmas. Demonstration of CHEM C1403), and mathematics, including ordi- cepts in the dynamics of rotating, stratified flows. laboratory plasma behavior, measurement of nary differential equations and complex numbers Geostrophic and hydrostatic balances, potential plasma properties. Illustrative problems in fusion, (such as MATH V1202 or E1210), or the instruc- vorticity, f and beta plane approximations, gravity space, and nonneutral or beam plasmas.

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66 APPH E4500y Health physics physics majors and minors in the junior year. thin films, superlattices, and particles. Surface Lect: 3. 3 pts. E. A. Christman. Discussion of specific and self-contained prob- magnetism and spectroscopies. High-speed mag- Prerequisite: APPH E4010. This course presents lems in areas such as applied electrodynamics, netization dynamics. Spin electronics. the fundamental principles of health physics: the physics of solids, and plasma physics. Topics physics of dose deposition, radiation dosimetry, change yearly. APPH E6101x Plasma physics, I elementary shielding and radiation protection Lect: 3. 3 points. Professor Katsuro-Hopkins. devices, description and proper use (calibration APPH E4903x Seminar: problems in Prerequisite: APPH E4300. Debye screening. and maintenance) of health physics instrumenta- applied physics Motion of charged particles in space- and time- tion, and the regulatory and administrative Lect: 1. Tutorial: 1. 2 pts. Professors Herman and varying electromagnetic fields. Two-fluid descrip- requirements of health physics programs. Venkataraman. tion of plasmas. Linear electrostatic and electro- Required for, and can be taken only by, all applied magnetic waves in unmagnetized and magnetized APPH E4550y Medical physics seminar physics majors in the senior year. Discussion of plasmas. The magnetohydrodynamic (MHD) Lect: 1. 0 pts. J. C. Arbo. specific and self-contained problems in areas model, including MHD equilibrium, stability, and Required for all graduate students in the medical such as applied electrodynamics, physics of MHD waves in simple geometries. Fluid theory physics program. Practicing professionals and solids, and plasma physics. Formal presentation of transport. faculty in the field present overviews of selected of a term paper required. Topics change yearly. topics in medical physics. APPH E6102y Plasma physics, II APPH E4990x and y Special topics in Lect: 3. 3 pts. Professor Boozer. APPH E4600x Fundamentals of radiological applied physics Prerequisite: APPH E6101x. Magnetic coordi- physics and radiation dosimetry Lect: 3. 1–3 pts. Instructors to be announced. nates. Equilibrium, stability, and transport of Lect: 3. 3 pts. J. A. Meli. Prerequisite: Permission of the instructor. Topics toroidal plasmas. Ballooning and tearing instabili- Co- or prerequisite: APPH E4010. Basic radiation and instructors change from year to year. For ties. Kinetic theory, including Vlasov equation, physics: radioactive decay, radiation producing advanced undergraduate students and graduate Fokker-Planck equation, Landau damping, kinetic devices, characteristics of the different types of students in engineering, physical sciences, and transport theory. Drift instabilities. radiation (photons, charged and uncharged parti- other fields. cles) and mechanisms of their interactions with APPH E6110x Laser interactions with matter materials. Essentials of the determination, by APAM E4999x and y and S4999 Curricular Lect: 3. 3 pts. Offered in alternate years. measurement and calculation, of absorbed doses practical training Not given in 2009–2010. from ionizing radiation sources used in medical 1 pt. Members of the faculty. Prerequisites: APPH E4112 or the equivalent, and physics (clinical) situations and for health physics Prerequisites: Internship and adviser’s approval quantum mechanics. Principles and applications purposes. (must be obtained in advance). Only for master’s of laser-matter coupling, non-linear optics, three- students in the Department of Applied Physics and four-wave mixing, harmonic generation, laser APBM E4650y Anatomy for physicists and Applied Mathematics who may need relevant processing of surfaces, laser probing of materials, and engineers work experience as part of their program of study. spontaneous and stimulated light scattering, satu- Lect. 3. 3 pts. Members of the faculty. Final report required. This course may not be ration spectroscopy, multiphoton excitation, laser Prerequisite: BMEN E4002 or the instructor’s taken for pass/fail or audited. isotope separation, transient optical effects. permission. A systemic approach to the study of the human body from a medical imaging point of APPH E6081x Solid state physics, I APAM E6650x and y, and S6650 view: skeletal, respiratory, cardiovascular, diges- Lect: 3. 3 pts. Professor Pinczuk. Research project tive, and urinary systems, breast and women’s Prerequisite: APPH E3100 or the equivalent. 1 to 6 pts. Members of the faculty. issues, head and neck, and central nervous sys- Knowledge of statistical physics on the level of This course may be repeated for credit. A special tem. Lectures are reinforced by examples from MSAE E3111 or PHYS G4023 is strongly recom- investigation of a problem in nuclear engineering, clinical two- and three-dimensional and functional mended. Crystal structure, reciprocal lattices, medical physics, applied mathematics, applied imaging (CT, MRI, PET, SPECT, U/S, etc.). classification of solids, lattice dynamics, anhar- physics, and/or plasma physics consisting of monic effects in crystals, classical electron models independent work on the part of the student and APPH E4710x-E4711y Radiation instrumenta- of metals, electron band structure, and low- embodied in a formal report. tion and measurement laboratory, I and II dimensional electron systems. Lect: 1. Lab: 4. 3 pts. J. C. Arbo. APPH E9142x-E9143y Co- or prerequisite: APPH E4010. Lab fee: $50 APPH E6082y Solid state physics, II Applied physics seminar each term. E4710: theory and use of α, β, γ, and Lect: 3. 3 pts. Professor Kim. Sem: 3. 3 pts. Instructor to be announced. X ray detectors and associated electronics for Prerequisite: APPH E6081 or the instructor’s per- These courses may be repeated for credit. counting, energy spectroscopy, and dosimetry; mission. Semiclassical and quantum mechanical Selected topics in applied physics. radiation safety; counting statistics and error electron dynamics and conduction, dielectric propagation; mechanisms of radiation emission properties of insulators, semiconductors, defects, APAM E9301x and y, and S9301 and interaction. E4711: additional detector types; magnetism, superconductivity, low-dimensional Doctoral research applications and systems including coincidence, structures, and soft matter. 0 to 15 pts. Members of the faculty. low-level, and liquid scintillation counting; neutron Prerequisite: The qualifying examination for the activation; TLD disometry; diagnostic x-ray and APPH E6091y Magnetism and magnetic doctorate. Required of doctoral candidates. fluoro Q/C; planar gamma camera imaging; image materials analysis. Lect: 3. 3 points. Offered in alternate years. APAM E9800x and y, and S9800 Not given in 2009–2010. Doctoral research instruction APPH E4901x Seminar: problems in Prerequisite: MSAE E4206, APPH E6081, or the 3, 6, 9, or 12 pts. Members of the faculty. applied physics equivalent. Types of magnetism. Band theory of A candidate for the Eng.Sc.D. degree must register Lect: 1. 1 pt. Professors Herman and Venkataraman. ferromagnetism. Magnetic metals, insulators, and for 12 points of doctoral research instruction. Required for, and can be taken only by, all applied semiconductors. Magnetic nanostructures: ultra- Registration for APAM E9800 may not be used

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to satisfy the minimum residence requirement a special project under the supervision of the boundary value problems. Solutions in orthogonal 67 for the degree. staff. Credit for the course is contingent upon the curvilinear coordinate systems. Applications of submission of an acceptable thesis or final report. Fourier integrals, Fourier and Laplace transforms. APAM E9900x and y, and S9900 Problems from the fields of vibrations, heat con- Doctoral dissertation APMA E4001y Principles of applied mathematics duction, electricity, fluid dynamics, and wave prop- 0 pts. Members of the faculty. Lect: 3. 3 pts. Professor Schmitt. agation are considered. A candidate for the doctorate may be required to Prerequisites: Introductory linear algebra required. register for this course every term after the Ordinary differential equations recommended. APMA E4204x Functions of a complex variable course work has been completed, and until the Review of finite-dimensional vector spaces and Lect: 3. 3 pts. Professor Polvani. dissertation has been accepted. elementary matrix theory. Linear transformations, Prerequisite: MATH V1202 or the equivalent. change of basis, eigenspaces. Matrix representa- Complex numbers, functions of a complex vari- tion of linear operators and diagonalization. able, differentiation and integration in the complex COURSES IN APPLIED Applications to difference equations, Markov plane. Analytic functions, Cauchy integral theorem MATHEMATICS processes, ordinary differential equations, and sta- and formula, Taylor and Laurent series, poles and bility of nonlinear dynamical systems. Inner product residues, branch points, evaluation of contour APMA E2101y Introduction to applied spaces, projection operators, orthogonal bases, integrals. Conformal mapping. Schwarz-Christoffel mathematics Gram-Schmidt orthogonalization. Least squares transformation. Applications to physical problems. Lect: 3. 3 pts. Professor Spiegelman. method, pseudo-inverses, singular value decompo- Prerequisite: Calculus III. A unified, single-semes- sition. Adjoint operators, Hermitian and unitary APMA E4300y Introduction to numerical methods ter introduction to differential equations and linear operators, Fredholm Alternative Theorem. Fourier Lect: 3. 3 pts. Professor Chow. algebra with emphases on (1) elementary analyti- series and eigenfunction expansions. Introduction Prerequisites: MATH V1201, MATH E1210, and cal and numerical technique and (2) discovering to the theory of distributions and the Fourier APMA E3101, or their equivalents. Some pro- the analogs on the continuous and discrete sides Integral Transform. Green’s functions. Application gramming experience and Matlab will be extreme- of the mathematics of linear operators: superposi- to partial differential equations. ly useful. Introduction to fundamental algorithms tion, diagonalization, fundamental solutions. and analysis of numerical methods commonly Concepts are illustrated with applications using APMA E4101x Introduction to dynamical used by scientists, mathematicians, and engi- the language of engineering, the natural sciences, systems neers. Ths course is designed to give a funda- and the social sciences. Students execute scripts Lect: 3. 3 pts. Professor Weinstein. mental understanding of the building blocks of in Mathematica and MATLAB (or the like) to illus- Prerequisites: APMA E2101 (or MATH V1210) and scientific computing that will be used in more trate and visualize course concepts (programming APMA E3101 or their equivalents, or the instruc- advanced courses in scientific computing and not required). tor’s permission. An introductiion to the analytic numerical methods for PDEs. Topics include and geometric theory of dynamical systems; basic numerical solutions of algebraic systems, linear APMA E3101x Linear algebra existence, uniqueness, and parameter dependence least-squares, eigenvalue problems, solution of Lect: 3. 3 pts. Professor Gentine. of solutions to ordinary differential equations; con- nonlinear systems, optimization, interpolation, Matrix algebra, elementary matrices, inverses, stant coefficient and parametrically forced systems; numerical integration and differentiation, initial rank, determinants. Computational aspects of fundamental solutions; resonance; limit points, value problems, and boundary value problems for solving systems of linear equations: existence- limit cycles, and classification of flows in the plane systems of ODEs. All programming exercises will uniqueness of solutions, Gaussian elimination, (Poincare-Bendixson Theory); conservative and be in Matlab. scaling, ill-conditioned systems, iterative tech- dissipative systems; linear and nonlinear stability niques. Vector spaces, bases, dimension. analysis of equilibria and periodic solutions; stable APMA E4301x Numerical methods for partial Eigenvalue problems, diagonalization, inner and unstable manifolds; bifurctions, e.g. Andronov- differential equations products, unitary matrices. Hopf; sensitive dependence and chaotic dynamics; Lect: 3. 3 pts. Professor Spiegelman. selected applications. Prerequisites: APMA E4300 and E3102 or E4200, APMA E3102y Partial differential equations or their equivalents. Numerical solution of partial Lect: 3. 3 pts. Professor Langmore. APMA E4150x Applied functional analysis differential equtions (PDE) arising in various physi- Prerequisite: MATH E1210 or the equivalent. Lect: 3. 3 pts. Professor Bal. cal fields of application. Finite difference, finite Introduction to partial differential equations; integral Prerequisites: Advanced calculus and a course in element, and spectral methods. Elementary finite theorems of vector calculus. Partial differential basic analysis, or the instructor’s permission. volume methods for conservation laws. Time equations of engineering in rectangular, cylindri- Introduction to modern tools in functional analysis stepping, method of lines, and simultaneous cal, and spherical coordinates. Separation of the that are used in the analysis of deterministic and space-time discretization. Direct and iterative variables. Characteristic-value problems. Bessel stochastic partial differential equations and in the methods for boundary-value problems. Applied functions, Legendre polynomials, other orthogonal analysis of numerical methods: metric and numerical analysis of PDE, including sources of functions; their use in boundary value problems. normed spaces, Banach space of continuous numerical error and notions of convergence and Illustrative examples from the fields of electro- functions, measurable spaces, the contraction stability, to an extent necessary for successful magnetic theory, vibrations, heat flow, and fluid mapping theorem, Banach and Hilbert spaces, numerical modeling of physical phenomena. mechanics. bounded linear operators on Hilbert spaces and Applications will include the Poisson equation, heat their spectral decomposition, and (time permit- equation, wave equation, and nonlinear equations APMA E3900x and y Undergraduate research ting) distributions and Fourier transforms. of fluid, solid, and gas dynamics. Homework in applied mathematics assignments will involve substantial programming. 0 to 4 pts. Members of the faculty. APMA E4200x Partial differential equations This course may be repeated for credit, but no Lect: 3. 3 pts. Professor Sobel. AMCS E4302x Parallel scientific computing more than 6 points may be counted toward the Prerequisite: A course in ordinary differential equa- Lect: 3. 3 pts. Offered in alternate years. satisfaction of the B.S. degree requirements. tions. Techniques of solution of partial differential Professor Chow. Candidates for the B.S. degree may conduct an equations. Separation of the variables. Orthogon- Prerequisites: APMA E3101, E3102, and E4300, investigation in applied mathematics or carry out ality and characteristic functions, nonhomogeneous or their equivalents. Corequisites: APMA E4301

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68 and programming ability in C/C++ or FORTRAN/F90. year. For advanced undergraduate students instructors from the Applied Mathematics An introduction to the concepts, the hardware and and graduate students in engineering, physical Committee and the staff change from year to software environments, and selected algorithms sciences, biological sciences, and other fields. year. For students in engineering, physical and applications of parallel scientific computing, sciences, biological sciences, and other fields. with an emphasis on tightly coupled computations APMA E6209x Approximation theory that are capable of scaling to thousands of Lect: 3. 3 pts. Offered in alternate years. APMA E8308y Asymptotic methods in processors. Includes high-level descriptions of Not given in 2009–2010. applied mathematics motivating applications and low-level details of Prerequisite: MATH W4061 or some knowledge Lect: 3. 3 pts. Offered in alternate years. implementation, in order to expose the algorithmic of modern analysis. Theory and application of Professor Marzuola. kernels and the shifting balances of computation approximate methods of analysis from the view- Prerequisite: APMA E4204 or the equivalent. and communication between them. Students run point of functional analysis. Approximate numeri- Asymptotic treatment of ordinary and partial demonstration codes provided on a Linux cluster. cal and analytical treatment of linear and nonlin- differential equations in problems arising in Modest programming assignments using MPI and ear algebraic, differential, and integral equations. applied mathematics. Asymptotic series. PETSc culminate in an independent project lead- Topics include function spaces, operators in Asymptotic evaluation of integrals. Expansion ing to an in-class report. normed and metric spaces, fixed point theorems of solutions of ordinary differential equations: con- and their applications. nection problem and turning points. Stoke’s phe- APMA E4400y Introduction to biophysical nomenon. Differential equations with a parameter: modeling APMA E6301y Analytic methods for partial ‘‘boundary layer’’ phenomenon. Application to Lect: 3. 3 pts. Professor Wiggins. differential equations partial differential equations: problems from fluid Prerequisites: PHYS W1401 or the equivalent and Lect: 3. 3 pts. Professor Bal. dynamics, wave propagation theory, electromag- APMA E2101 or MATH E1210 or the equivalent. Prerequisite: Advanced calculus, basic concepts netic theory. Introduction to physical and mathematical models in analysis, APMA E3101 and E4200 or their of cellular and molecular biology. Physics at the equivalents, or permission of the instructor. APMA E9101x-E9102y and S9101-S9102 cellular scale (viscosity, heat, diffusion, statistical Introduction to analytic theory of PDEs of funda- Research mechanics). RNA transcription and regulation of mental and applied science; wave (hyperbolic), 1 to 4 pts. Members of the faculty. genetic expression. Genetic and biochemical net- Laplace and Poisson equations (elliptic), heat Prerequisite: The permission of the supervising works. Bioinformatics as applied to reverse engi- (parabolic) and Schroedinger (dispersive) equa- faculty member. This course may be repeated. neering of naturally occurring networks and to tions; fundamental solutions, Green’s functions, Advanced study in a special area. forward engineering of synthetic biological net- weak/distribution solutions, maximum principle, works. Mathematical and physical aspects of energy estimates, variational methods, method APMA E9810x or y Mathematical earth functional genomics. of characteristics; elementary functional analysis sciences seminar and applications to PDEs; introduction to nonlin- Lect. 1. 0 pts. Professor Polvani. APMA E4901x Seminar: problems in ear PDEs, shocks; selected applications. Current research in problems at the interface applied mathematics between applied mathematics and earth and Lect: 1. 0 pt. Professor Wiggins. APMA E6302x Numerical analysis of partial environmental sciences. This course is required for, and can be taken only differential equations by, all applied mathematics majors in the junior Lect: 3. 3 pts. Offered in alternate years. APMA E9815x or y Geophysical fluid year. Prerequisites or corequisites: APMA E4200 Not given in 2009–2010. dynamics seminar and E4204, or their equivalents. Introductory semi- Prerequisite: APMA E3102 or E4200. Numerical Lect. 3. 1 to 3 pts. Instructors to be announced. nars on problems and techniques in applied math- analysis of initial and boundary value problems Problems in the dynamics of geophysical fluid ematics. Typical topics are nonlinear dynamics, for partial differential equations. Convergence flows. May be repeated for up to 10 points of scientific computation, economics, operations and stability of the finite difference method, the credit. research, etc. spectral method, the finite element method, and applications to elliptic, parabolic, and hyperbolic APMA E4903x Seminar: problems in equations. COURSES IN MATERIALS applied mathematics SCIENCE AND ENGINEERING Lect: 1. Tutorial: 2. 3 or 4 pts. Professor Wiggins. APMA E6304y Integral transforms See page 171. This course is required for, and can be taken only Lect: 3. 3 pts. Not given in 2009–2010. by, all applied mathematics majors in the senior Prerequisites: APMA E4204 and MATH E1210, or year. Prerequisites or corequisites: APMA E4200 their equivalents. Laplace, Fourier, Hankel, and and E4204, or their equivalents. For 4 pts. credit, Mellin transforms. Selection of suitable transform term paper required. Examples of problem areas for a given partial differential equation boundary are nonlinear dynamics, asymptotics, approxima- value problem. Operational properties of transforms. tion theory, numerical methods, etc. Inversion theorems. Approximate evaluation of Approximately three problem areas are studied inversion integrals for small and large values of per term. parameter. Application to the solution of integral equations. APMA E4990x and y Special topics in applied mathematics APMA E6901x and y Special topics in Lect: 3. 1–3 pts. Instructors to be announced. applied mathematics Prerequisites: Advanced calculus and junior year Lect: 3. 3 pts. x: Professor Langmore; applied mathematics, or their equivalents. This y: Not given in 2009–2010. course may be repeated for credit. Topics and Prerequisites: Advanced calculus and junior year instructors from the Applied Mathematics applied mathematics, or their equivalents. This Committee and the staff change from year to course may be repeated for credit. Topics and

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BIOMEDICAL ENGINEERING 69 351 Engineering Terrace, MC 8904, 212-854-4460; [email protected] www.bme.columbia.edu

CHAIR LABORATORY MANAGER Van C. Mow JOINT FACULTY AFFILIATES Van C. Mow Keith Yeager Stanley Dicker Professor Dimitris Anastassiou Peter K. Allen Michael P. Sheetz Professor of Electrical Professor of Computer VICE CHAIR COMPUTER SYSTEMS Gordana Vunjak-Novakovic Engineering Science Andrew F. Laine ADMINISTRATOR Aniruddha Das Ernest W. April Robert J. Foster ASSOCIATE PROFESSORS Assistant Professor of Associate Professor of DEPARTMENTAL Henry Hess Psychiatry Anatomy and Cell Biology ADMINISTRATOR CHAIR OF UNDERGRADUATE Andreas H. Hielscher Shunichi Homma Robert DeLaPaz Shila Maghji STUDIES Christopher R. Jacobs Margaret Milliken Hatch Professor of Radiology Barclay Morrison III Elisa E. Konofagou Professor of Medicine Kung Ming Jan BUSINESS MANAGER Helen H. Lu Elizabeth S. Olson Associate Professor of Kidest Shenkoru CHAIR OF GRADUATE Jeremy J. Mao Assistant Professor of Clinical Medicine STUDIES Barclay Morrison III Otolaryngology/Head and Jung-Chi Liao ADMINISTRATIVE COORDI- Gordana Vunjak-Novakovic Paul Sajda Neck Surgery Assistant Professor of NATOR FOR STUDENT R. Theodore Smith Mechanical Engineering AFFAIRS OMBUDS ASSISTANT PROFESSORS Associate Professor of Zheng Feng Lu Jarmaine Lomax Lance Kam Elizabeth Hillman Ophthalmology Associate Professor of Hayden Huang Clinical Radiology ADMINISTRATIVE ASSISTANT PROFESSORS Lance C. Kam ADJUNCT PROFESSORS Richard N. Pierson FOR FISCAL AFFAIRS Gerard H. A. Ateshian Samuel K. Sia Ernest Feleppa Professor of Clinical Michelle Cintron Truman R. Brown Shiro Matsuoka Medicine Percy Kay and Vida L. W. John Pile-Spellman ADMINISTRATIVE ASSISTANT Hudson Professor ADJUNCT ASSOCIATE Professor of Radiology and FOR DEPARTMENTAL X. Edward Guo PROFESSOR Neurosurgery AFFAIRS Clark T. Hung Nicolas W. Chbat Henry M. Spotnitz Paulette Louisaint Andrew F. Laine George G. Humphreys II Edward F. Leonard Professor of Surgery

iomedical engineering is an biomedical systems and devices. engineering, and biomedical imaging. evolving discipline in engineering Modern engineering encompasses Programs in biomedical engineering are B that draws on collaboration sophisticated approaches to measure- taught by its own faculty, members of among engineers, physicians, and sci- ment, data acquisition and analysis, other SEAS departments, and faculty from entists to provide interdisciplinary insight simulation, and systems identification. other University divisions who have strong into medical and biological problems. These approaches are useful in the study interests and involvement in biomedical The field has developed its own knowl- of individual cells, organs, entire organ- engineering. Several of the faculty hold joint edge base and principles that are the isms, and populations of organisms. The appointments in Biomedical Engineering foundation for the academic programs increasing value of mathematical models and other University departments. designed by the Department of in the analysis of living systems is an Courses offered by the Department Biomedical Engineering at Columbia. important sign of the success of con- of Biomedical Engineering are comple- The programs in biomedical engi- temporary activity. The programs offered mented by courses offered by other neering at Columbia (B.S., M.S., Ph.D., in the Department of Biomedical departments in The Fu Foundation Eng.Sc.D., and M.D./Ph.D.) prepare stu- Engineering seek to emphasize the con- School of Engineering and Applied dents to apply engineering and applied fluence of basic engineering science and Science, and by many departments in science to problems in biology, medi- applied engineering with the physical the Faculty of Medicine, the School of cine, and the understanding of living sys- and biological sciences, particularly in Dentistry and Oral Surgery, and the tems and their behavior, and to develop the areas of biomechanics, cell and tissue Mailman School of Public Health, as well

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70 as the science departments within the porates equipment normally reserved for The undergraduate curriculum is Graduate School of Arts and Sciences. advanced research and provides excep- designed to provide broad knowledge The availability of these courses in a uni- tional access to current practices in bio- of the physical and engineering sciences versity that contains a large medical medical engineering and related sciences. and their application to the solution of center and enjoys a basic commitment Adjacent to the new laboratories is a biological and medical problems. to interdisciplinary research is important lounge that serves as a meeting point for Students are strongly encouraged to to the quality and strength of the program. biomedical engineering undergraduate take courses in the order specified in the Educational programs at all levels are and graduate students. course tables on pages 74–77; implica- based on engineering and biological fun- Research facilities of the Biomedical tions of deviations should be discussed damentals. From this basis, the program Engineering faculty include the Liu Ping with a departmental adviser before reg- branches into concentrations along three Laboratory for Functional Tissue Research istration. The first two years provide a tracks: biomechanics, cell and tissue (Professor Mow), the Hatch MRI Research strong grounding in the physical and engineering, and biomedical imaging. Center (Professor Brown), the Heffner chemical sciences, engineering funda- The intrinsic breadth included within Biomedical Imaging Laboratory (Professor mentals, and mathematics. This back- these tracks, plus a substantial elective Laine), the Laboratory for Intelligent ground is used to provide a unique content, prepare bachelor’s and mas- Imaging and Neural Computing (Professor physical approach to the study of bio- ter’s students to commence professional Sajda), the Biophotonics and Optical logical systems. The last two years of activity in any area of biomedical engi- Radiology Laboratory (Professor Hielscher), the undergraduate program provide neering or to go on to graduate school the Bone Bioengineering Laboratory substantial exposure to modern biology for further studies in related fields. The (Professor Guo), the Cell and Tissue and include courses in engineering and program also provides excellent prepa- Engineering Laboratory (Professor Hung), engineering science that extend the ration for the health sciences and the the Biomaterial and Interface Tissue work of the first two years. The program study of medicine. Graduates of the Engineering Laboratory (Professor Lu), also offers three tracks to guide students doctoral program are prepared for the Neurotrauma and Repair Laboratory in the choice of technical courses, while research activities at the highest level. (Professor Morrison), the Laboratory sharing a common core curriculum. The Areas of particular interest to Columbia for Stem Cells and Tissue Engineering tracks are different from one another, faculty include orthopaedic and muscu- (Professor Vunjak-Novakovic), the Ultra- and there is great breadth within each. loskeletal biomechanics (Professors sound and Elasticity Imaging Laboratory These qualities allow the faculty to pre- Ateshian, Guo, Hess, Huang, Jacobs, (Professor Konofagou), the Microscale pare students for activity in all contem- and Mow), cardiovascular biomechanics Biocomplexity Laboratory (Professor porary areas of biomedical engineering. (Professor Homma), cellular and tissue Kam), the Molecular and Microscale Graduates of the program are equipped engineering and artificial organs Bioengineering Laboratory (Professor for employment in the large industrial (Professors Hung, Kam, Leonard, Sia), the Laboratory for Functional sector devoted to health care, which H. H. Lu, Morrison, Sia, and Vunjak- Optical Imaging (Professor Hillman), includes pharmaceuticals, medical Novakovic), auditory biophysics the Cell and Molecular Biomechanics devices, artificial organs, prosthetics (Professor Olson), and biomedical Laboratory (Professor Jacobs), and the and sensory aids, diagnostics, medical imaging (Professors Brown, Hielscher, Biomechanics and Mechanotransduction instrumentation, and medical imaging. Hillman, DeLaPaz, Konofagou, Laine, Z. Laboratory (Professor Huang). These Graduates also accept employment F. Lu, Pile-Spellman, Sajda, and Smith). laboratories are supplemented with core in oversight organizations (FDA, NIH, facilities, including a tissue culture facility, OSHA, and others), medical centers, Facilities a histology facility, a confocal micro- and research institutes. They are pre- The Department of Biomedical Engineer- scope, an atomic force microscope, a 2- pared for graduate study in biomedical ing has been supported by University photon microscope, an epifluorescence engineering and several related areas of funding, awards from the Whitaker microscope, a freezer room, biomechan- engineering and the health sciences. Foundation, and research funding from ics facilities, a machine shop, and a speci- Students in all three tracks of the pro- the NIH, NSF, and numerous research men prep room. gram can meet entrance requirements foundations. The extensive new facilities for graduate training in the various allied health professions. No more than three that have recently been added both at the UNDERGRADUATE PROGRAM additional courses are required in any of Medical Center and Morningside campus The objectives of the undergraduate the tracks to satisfy entrance require- include new teaching and research program in biomedical engineering are ments for most U.S. medical schools. laboratories that provide students with as follows: unusual access to contemporary research All biomedical engineering students equipment specially selected for its 1.professional employment in areas are expected to register for nontechnical relevance to biomedical engineering. An such as the medical device industry, electives, both those specifically required undergraduate wet laboratory devoted engineering consulting, biomechanics, by the School of Engineering and to biomechanics and cell and tissue biomedical imaging, and biotechnology; Applied Science and those needed to engineering has been added, together 2.graduate studies in biomedical engi- meet the 27-point total of nontechnical with a biomedical imaging and data pro- neering or related fields; electives required for graduation. cessing laboratory. Each laboratory incor- 3.attendance at medical or dental school.

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First and Second Years I and II sequence (BMEN E4001-E4002) ules leading to a bachelor’s degree in 71 As outlined in this bulletin, in the first which is taught by biomedical engineer- biomedical engineering. two years all engineering students are ing faculty and emphasizes quantitative It is strongly advised that students expected to complete a sequence of applications of engineering principles in take required courses during the specific courses in mathematics, physics, chem- understanding biological systems and term that they are designated in the istry, computer science, engineering, phenomena from molecular to organ course tables, as conflicts may arise if English composition, and physical edu- system levels. In the fields of biomedical courses are taken out of sequence. cation, as well as nontechnical electives engineering, experimental techniques Students are required to take up to 9 including the humanities. For most of and principles are fundamental skills that points (6 points in the imaging track) of these sequences, the students may good biomedical engineers must master. “technical electives,” allowing for explo- choose from two or more tracks. If there Beginning in junior year, all students take ration of related technical topics. A tech- is a question regarding the acceptability the three-semester sequence Biomedical nical elective is defined as a 3000-level of a course as a nontechnical elective, engineering laboratory, I-III (BMEN E3810, or above course in SEAS or courses please consult the approved listing of BMEN E3820, BMEN E3830). In this taught by the Departments of Biology, courses beginning on page 11 or con- three-semester series, students learn Chemistry, and Biochemistry. tact your advising dean for clarification. through hands-on experience the princi- Please see the charts in this section ples and methods of biomedical engi- Technical Elective Requirements for a specific description of course neering experimentation, measurement Students are required to take at least requirements. techniques, quantitative theories of bio- 48 points of engineering content course- In addition, a professional-level engi- medical engineering, data analysis, and work toward their degree. The 48-point neering course is required. Students independent design of biomedical engi- requirement is a criterion established by may select from a variety of offerings neering experiments, the scope of which the Accreditation Board for Engineering within SEAS. For students interested in cover a broad range of topics from all and Technology (ABET). Taking into con- biomedical engineering, we recommend three tracks—biomechanics, cell and sideration the number of engineering taking BMEN E1001: Engineering in tissue engineering, and biomedical imag- content points conferred by the required medicine or APPH E1300y: Physics of ing. In the senior year, students take the courses of the BME curriculum, a portion the human body in fulfillment of this required course Ethics for biomedical of technical electives must be clearly requirement. Note that E1201: engineers (BMEN E4010), a SEAS non- engineering in nature (Engineering Introduction to electrical engineering is technical elective that covers a wide Content Technical Electives), specifically required and cannot be double counted range of ethical issues expected to con- as defined below: front biomedical engineering graduates to satisfy the professional-level course 1.Technical elective courses with as they enter biotechnology industry, requirement. For the computer science sufficient engineering content that research, or medical careers. Also in requirement, students must take COMS can count toward the 48 units of the senior year, students are required to W1005. engineering courses required for take a two-semester capstone design All students must take APMA E2101: ABET accreditation: course, Biomedical engineering design Introduction to applied mathematics in a. all 3000-level or higher courses (BMEN E3910 and BMEN E3920), in addition to ELEN E1201: Introduction to in the Department of Biomedical which students work within a team to electrical engineering and ENME E3105: Engineering, except: BMEN E4010, tackle an open-ended design project in Mechanics in their second year. For the E4103, E4104, E4105, E4106, biomedical engineering. The underlying classes of 2010 and later, students must E4107 and E4108 (Note that only philosophy of these core requirements is also take STAT W1211: Introduction to 3 points of BMEN E3998 may be to provide our biomedical engineering statistics. counted toward technical elective students with a broad knowledge and degree requirements.) understanding of topics in the field of Third and Fourth Years b. all 3000-level or higher courses biomedical engineering. Parallel to these The biomedical engineering programs in the Department of Mechanical studies in core courses, students take at Columbia at all levels are based on Engineering, except: MECE E4007: track-specific required courses to obtain engineering and biological fundamentals. Creative engineering and entrepre- an in-depth understanding of their cho- This is emphasized in our core require- neurship sen concentration. The curriculum of all ments across all tracks. In the junior c. all 3000-level or higher courses three academic tracks—biomechanics, year, all students begin their biomedical in the Department of Chemical cell and tissue engineering, and biomed- engineering study with the two-semester Engineering, except: CHEN E4020: ical imaging—prepares students who Introduction to molecular and cellular Safeguarding intellectual and busi- wish to pursue careers in medicine by biology, I and II (BIOL C2005-C2006 ), ness property satisfying most requirements in the pre- which gives students a comprehensive d. all 3000-level or higher courses medical programs with no more than overview of modern biology from molec- in the Department of Electrical three additional courses. Some of these ular to organ system levels. Parallel to Engineering, except: EEHS E3900: additional courses may also be counted these biology studies, all students take History of telecommunications: as nonengineering technical electives. the two-semester Quantitative physiology, from the telegraph to the Internet Please see the course tables for sched-

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72 e. all 3000-level or higher courses ate program leading to the Master of of Biomedical Engineering also admits in the Civil Engineering and Science degree (M.S.), the Doctor of students into the 4-2 program, which pro- Engineering Mechanics program, Philosophy degree (Ph.D.), the Doctor of vides the opportunity for students holding except: CIEN E4128, E4129, Engineering Science degree (Eng.Sc.D.), a bachelor’s degree from certain physi- E4130, E4131, E4132, E4133, and the M.D./Ph.D. degree program. cal sciences to receive the M.S. degree E4134, E4135, and E4136 Applicants who have a Master of after two years of study at Columbia. f. all 3000-level or higher courses Science degree or equivalent may apply in the Earth and Environmental directly to the doctoral degree program. CURRICULUM AND EXAM Engineering program All applicants are expected to have REQUIREMENTS earned the bachelor’s degree in engi- 2.Courses from the following depart- neering or in a cognate scientific pro- ments are not allowed to count Master’s Degree gram. The Graduate Record Exam-ina- toward the required 48 units of In consultation with an appointed faculty tion (General Test only) is required of all engineering courses: adviser, M.S. students should select a applicants. Students whose bachelor’s a. Department of Applied Physics program of 30 points of credit of graduate degree was not earned in a country and Applied Mathematics courses (4000 level or above) appropri- where English is the dominant spoken b. Department of Computer Science ate to their career goals. This program language are required to take the TOEFL c. Department of Industrial must include the course in computational test. M.S. degree candidates must Engineering and Operations modeling of physiological systems (BMEN reach level 8 on the English Placement Research E6003); two semesters of BMEN E9700: Test (EPT) offered by Columbia’s d. Program of Materials Science and Biomedical engineering seminar; at least American Language Program (ALP). Engineering four other biomedical engineering courses; Doctoral degree candidates must attain and at least one graduate-level mathe- The cell and tissue engineering track level 10 on the English Placement Test matics course. Students with deficiency requires 4.5 of the required 9 points of (EPT). The ALP examination must be in physiology course work are required technical electives to be from engineer- taken at orientation upon arrival. It is to take the BMEN E4001-E4002 sequence ing courses; in the biomechanics track, strongly recommended the students before taking BMEN E6003. Candidates 2.5 points of technical electives must be enroll in an appropriate ALP course if must achieve a minimum grade-point from engineering courses; in the imaging they have not achieved the required average of 2.5. For students interested track, the requirements satisfy the 48 proficiency after the first examination. in obtaining research experience, up to points of engineering content. Once 48 In addition, the individual tracks require 6 credits of research (BMEN E9100) points of engineering-content technical applicants to have taken the following may be applied toward the M.S. degree. electives are satisfied, students may foundation courses: choose any course above the 3000 level • Biomechanics: One year of biology Doctoral Degree in SEAS as well as biology, chemistry, and/or physiology, solid mechanics, Students admitted to the doctoral and biochemistry as technical electives. statics and dynamics, fluid mechanics, degree program should select courses The accompanying charts describe ordinary differential equations. to prepare for the doctoral qualifying the eight-semester degree program • Cell and Tissue Engineering: examination and register for research schedule of courses leading to the One year of biology and/or physiology, rotations during the first two semesters bachelor’s degree in biomedical engi- one year of organic chemistry or of graduate study. To facilitate future neering. biochemistry with laboratory, fluid collaboration with clinicians and biomed- mechanics, rate processes, ordinary ical scientists, students are encouraged GRADUATE PROGRAM differential equations. to consider courses at the Health The graduate curriculum in biomedical • Biomedical Imaging: One year of Sciences campus or in the Department engineering employs the same three biology and/or physiology and/or of Biological Sciences. tracks that compose the undergraduate biochemistry. Linear algebra, ordinary Doctoral students must complete a curriculum: biomechanics, cell and tis- differential equations, Fourier analysis, program of 30 points of credits beyond sue engineering, and biomedical imag- digital signal processing. the M.S. degree. The course in compu- ing. Initial graduate study in biomedical Applicants lacking some of these tational modeling of physiological sys- engineering is designed to expand the courses may be considered for admission tems (BMEN E6003) is required for the student’s undergraduate preparation with stipulated deficiencies that must be doctoral program. At least two graduate in the direction of the track chosen. satisfied in addition to the requirements mathematics courses must be taken, In addition, sufficient knowledge is of the degree program. The Fu Foundation which may include the mathematics acquired in other areas to facilitate School of Engineering and Applied course required for the M.S. degree. broad appreciation of problems and Science does not admit students hold- Students must register for BMEN effective collaboration with specialists ing the bachelor’s degree directly to E9700: Biomedical engineering seminar from other scientific, medical, and engi- doctoral studies; admission is offered and for research rotations during the neering disciplines. The Department of either to the M.S. program or to the M.S. first two semesters of graduate study. Biomedical Engineering offers a gradu- program/doctoral track. The Department Remaining courses should be selected

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in consultation with the student’s faculty regulations of The Fu Foundation School teins. The role of enzymes and gene regulatory 73 adviser to prepare for the doctoral quali- of Engineering and Applied Science, each elements in natural biological functions as well fying examination and to develop expertise student is expected to submit a thesis and as in biotechnology and genetic engineering. in a clearly identified area of biomedical defend it before a committee of five faculty, Recombination and other macromolecular processes viewed as mathematical operations engineering. Up to 12 credits of research two of whom hold primary appointments with simulation and visualization using simple (BMEN E9500) may be applied toward in another department. Every doctoral computer programming. This course shares doctoral degree course requirements. candidate is required to have had accept- lectures with ECBM E4060, but the work require- All graduate students admitted to the ed at least one first-author full-length ments differ somewhat. doctoral degree program must satisfy the paper for publication in a peer-reviewed equivalent of three semesters’ experience journal prior to recommendation for award BMEN E3150y The cell as a machine in teaching (one semester for M.D./Ph.D. of the degree. Lect: 3. 3 pts. Not given in 2009–2010. students). This may include supervising Prerequisite: MATH V1101 or V1105. Corequistite: and assisting undergraduate students in One semester of cell biology or biochemistry, and COURSES IN BIOMEDICAL laboratory experiments, grading, and one semester of general physics or equivalent. Cells ENGINEERING as complex micron-sized machines, basic physical preparing lecture materials to support the See also the sections for Applied Physics, aspects of cell components (diffusion, mechanics, teaching mission of the department. The Chemical Engineering, Computer Science, electrostatics, hydrophobicity), energy transduction Department of Biomedical Engineering is and Computer Engineering in this bul- (motors, transporters, chaperones, synthesis com- the only engineering department that offers plexes), basic cell functions. Biophysical principles, letin, and the Columbia College and Ph.D. training to M.D./Ph.D. students. feedback controls for robust cell function, adaptation Graduate School of Arts and Sciences These candidates are expected to com- to environmental perturbations. bulletins for courses in the biological sci- plete their Ph.D. program within 3.5 years, ences: biomedical informatics, cell biology, with otherwise the same requirements. BMEN E3320y Fluid biomechanics microbiology, and physiology. Lect: 3. 3 pts. Professor Huang. Prerequisites: MATH E1210. The principles of Doctoral Qualifying Examination BMEN E1001x Engineering in medicine continuum mechanics as applied to biological Doctoral candidates are required to pass Lect: 3. 3 pts. Professor Hung and guest lecturers. fluid flows and transport. Course covers continuum a qualifying examination. This examination The present and historical role of engineering in formulations of basic conservation laws, Navier- is given once a year, in January. It should medicine and health care delivery. Engineering Stokes equations, mechanics of arterial and venous be taken after the student has completed approaches to understanding organismic and blood flow, blood rheology and non-Newtonian 30 points of graduate study. The qualifying cellular function in living systems. Engineering in properties, flow and transport in the microcircula- the diagnosis and treatment of disease. Medical examination consists of oral and written tion, oxygen diffusion, capillary filtration. imaging, medical devices: diagnostic and surgical examinations. The oral examination con- instruments, drug delivery systems, prostheses, BMCH E3500y Biological transport and rate sists of the analysis of assigned scientific artificial organs. Medical informatics and organi- processes papers, and the written examination zation of the health care system. Current trends Lect: 3. 3 pts. Professor Leonard. covers three areas: applied mathematics, in biomedical engineering research. Prerequisites: CHEM C3443, MATH E1210. quantitative biology and physiology, and Corequisite: BIOL C2005. Convective and diffusive track-specific material. Students must BMEN E2300x or y Biomechanics track movement and reaction of molecules in biological declare a track (biomedical imaging, 0 pts. systems. Kinetics of homogeneous and heteroge- biomechanics, or cell and tissue engi- Rising juniors are required to register for this neous reactions in biological environments. neering) at the time of registration for course in the spring of their sophomore year if Mechanisms and models of transport across they choose the biomechanics track. the qualifying examination. A minimum membranes. Convective diffusion with and with- out chemical reaction. Diffusion in restricted cumulative grade-point average of 3.2 is BMEN E2400x or y Biomedical imaging track spaces. Irreversible thermodynamic approaches required to register for this examination. 0 pts. to transport and reaction in biological systems. Rising juniors are required to register for this Doctoral Committee and Thesis course in the spring of their sophomore year if BMEN E3810y Biomedical engineering Students who pass the qualifying exami- they choose the biomedical imaging track. laboratory, I nation choose a faculty member to serve Lab: 4. 3 pts. Instructor to be announced. as their research adviser. Each student is BMEN E2500x or y Cell and tissue engineering Statistical analysis of experimental measure- ments: normal distribution, test of significance, expected to submit a research proposal track 0 pts. linear regression, correlation, error analysis and and present it to a thesis committee that Rising juniors are required to register for this propagation. MATLAB programming, EKG signal consists of three to five faculty members. course in the spring of their sophomore year if acquisition and processing, microscopy, cell The committee considers the scope of the they choose the cell and tissue engineering track. counting and scaffold encapsulation, mechanical proposed research, its suitability for doc- testing of linear and nonlinear biomaterials. toral research and the appropriateness of ECBM E3060x Introduction to genomic infor- the research plan. The committee may mation science and technology BMEN E3820x Biomedical engineering approve the proposal without reservation Lect: 3. 3 pts. Professor Anastassiou. laboratory, II or may recommend modifications. In gen- Introduction to the information system paradigm Lab: 4. 3 pts. Instructor to be announced. eral, the student is expected to submit of molecular biology. Representation, organiza- Statistical analysis of experimental measurements: tion, structure, function, and manipulation of the analysis of variance, power analysis. Circuit imple- his/her research proposal after five semes- biomolecular sequences of nucleic acids and pro- mentation of nerve conduction, alginate bead forma- ters of doctoral studies. In accord with

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74 BIOMEDICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS CLASSES OF 2009–2011

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

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

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

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

ENGLISH C1010 (3) COMPOSITION Z1003 (0) C1010 (3) (three tracks, choose one) Z0006 (0) Z1003 (0) C1010 (3)

COMPUTER SCIENCE COMS W1005 (3) Matlab (in semester I or III)

PHYSICAL EDUCATION C1001 (1) C1002 (1)

GATEWAY LAB E1102 (4) either semester

HUMA C1001, C0CI C1101, HUMA C1002, C0CI C1102, or Global Core (3–4) or Global Core (3–4) NONTECHNICAL REQUIREMENTS HUMA W1121 (3) ECON W1105 (4) and or W1123 (3) W1155 recitation (0)

ELEN E1201 APMA E2101 Professional-level course Intro. to EE (3.5) Intro. to applied math (3) TECHNICAL REQUIREMENTS (except ELEN E1201) (either semester) ENME E3105 Mechanics (4)

tion, mechanical testing and optical strain analysis, optimization, biocompatibility, impact on patient health oretical, computational, or engineering design galvanotaxis, image segmentation and analysis of and comfort, health care costs, regulatory issues, and work. May be repeated, but no more than 3 points cells, computer aided design, library resources. medical ethics. Selection and execution of a project may be counted toward degree requirements involving the design of an actual engineering device as engineering technical electives. Requires BMEN E3830y Biomedical engineering or system. Introduction to entrepreneurship, biomed- approval of instructor prior to registration. laboratory, III ical start-ups, and venture capital. Semester I: statisti- Lab: 4. 3 pts. Instructor to be announced. cal analysis of detection/classification systems, devel- BMEN E4000x or y Special topics Experimental design. Cell adhesion, membrane opment of design prototype, need, approach, benefits Lect: 3. 3 pts. Professor Jacobs. transport, osmosis, ultrasound, design of cell and competition analysis. Semester II: spiral develop Additional current topics in biomedical engineering encapsulation and drug delivery system, respira- process and testing, iteration and refinement of the taught by regular or visiting faculty. The same subject tory impedance. Selected clinical demonstrations: initial design/prototype and business plan development. matter is not usually considered in different years. body compositions, magnetic resonance imaging, A laboratory fee of $100 is collected each semester. echocardiography, blood pressure. BMEN E4001x Quantitative physiology, I: BMEN E3998x or y, or s Projects in biomedical cells and molecules BMEN E3910x-E3920y Biomedical engineering engineering Lect: 3. 3 pts. Professor Jacobs. design, I and II Hours to be arranged. 1 to 3 pts. Professors Prerequisites or corequisites: CHEM C3443 or Lect: 1. Lab: 3. 4 pts. Professors Hillman and Anastassiou, Ateshian, Brown, Das, Guo, Hess, the equivalent and BIOL C2005. Physiological Vunjak-Novakovic. Hielscher, Hillman, Homma, Huang, Hung, Jacobs, systems at the cellular and molecular level are A two-semester design sequence to be taken in the Kam, Konofagou, Laine, Leonard, H. H. Lu, Mao, examined in a highly quantitative context. Topics senior year. Elements of the design process, with Morrison, Mow, Sajda, Sheetz, Sia, and Vunjak- include chemical kinetics, molecular binding and specific applications to biomedical engineering: con- Novakovic. enzymatic processes, molecular motors, biologi- cept formulation, systems synthesis, design analysis, Independent projects involving experimental, the- cal membranes, and muscles.

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75 BIOMEDICAL ENGINEERING: THIRD AND FOURTH YEARS CLASSES OF 2009–2011

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

BIOL C2005 (4) BIOL C2006 (4) BMEN E3910 (4) BMEN 3920 (4) Introductory biol. I Introductory biol. II BME design I BME design II REQUIRED BMEN E4001 (3) BMEN E4002 (3) BMEN E3820 (3) BMEN E3830 (3) COURSES: ALL TRACKS Quantitative physiol. I Quantitative physiol. II BME laboratory II BME laboratory III

STAT W1211 (3) BMEN E3810 (3) BMEN E4010 (2)4 Intro. to statistics BME laboratory I Ethics for BMEs

NONTECH ELECTIVES 0–3 points 3 points 0–3 points 3 points

BMEN E2500 (0) BMCH E3500 (3) BMEN E4501 (3) BMEN E4502 (3) Biol. transport. proc. Tissue eng. I Tissue eng. II BMEN E4210 (4) or CELL & TISSUE ENG.1 Thermo. biolog. sys. BMEN E3320 (3) Technical elective (6) Fluid biomech. MSAE E3103 (3) Elements of mat. sci. Technical elective (3)

BMEN E2300 (0) BMEN E3320 (3) ENME E3113 (3) BMEN 4300 (3) Fluid biomech. Mech. of solids Solid biomech. MECE E3100 (3) BIOMECH.2 Mech. of fluids Technical elective (3) MECE E3301 (3) Thermodynamics

Technical elective (6)

BMEN E2400 (0) BMEN E4420 (3) ELEN E4810 (3) BMEN E4410 (3) TRACK-SPECIFIC COURSES Biosig. proc. & Dig. sig. processing Ultrasound imaging ELEN E3801 (3.5) modeling or Signals & systems BMEN E4894 (3) BMEN E4898 (3) BIOMED. Technical elective (3) Biomed. imaging Biophotonics IMAGING3

BMEN E4430 (3) Principles of MRI

Technical elective (3)

TOTAL POINTS 16–17 19 19 15

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

BMEN E4002y Quantitative physiology, II: progresses to considerations of the major physio- wide range of ethical issues expected to confront organ systems logical systems of the human body (nervous, graduates as they enter the biotechnology indus- Lect: 3. 3 pts. Professor Morrison. circulatory, respiratory, renal). try, research, or medical careers. Topics vary and Prerequisites or corequisites: CHEM C3443; incorporate guest speakers from Physicians and BIOL C2005, C2006. Students are introduced to BMEN E4010y Ethics for biomedical engineers Surgeons, Columbia Law School, Columbia a quantitative, engineering approach to cellular Lect: 2. 2 pts. Professor Loike. College, and local industry. biology and mammalian physiology. Beginning Prerequisite: Senior status in biomedical engi- with biological issues related to the cell, the course neering or the instructor’s permission. Covers a

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76 BIOMEDICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS CLASS OF 2012 AND LATER

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

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

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

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

ENGLISH C1010 (3) COMPOSITION Z1003 (0) C1010 (3) (three tracks, choose one) Z0006 (0) Z1003 (0) C1010 (3)

COMPUTER SCIENCE COMS W1005 (3) Matlab (in semester I or III)

PHYSICAL EDUCATION C1001 (1) C1002 (1)

GATEWAY LAB E1102 (4) either semester

HUMA C1001, C0CI C1101, HUMA C1002, C0CI C1102, or Global Core (3–4) or Global Core (3–4) NONTECHNICAL HUMA W1121 (3) REQUIREMENTS or W1123 (3) ECON W1105 (4) and W1155 recitation (0)

ELEN E1201 APMA E2101 Intro. to EE (3.5) Intro. to applied math (3) Professional-level course TECHNICAL (except ELEN E1201) ENME E3105 REQUIREMENTS (either semester) Mechanics (4)

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

BMEB W4011x Computational neuroscience: Lect: 3. 3 pts. Professor Anastassiou. medical engineering graduate student interested Circuits in the brain Introduction to the information system paradigm of in acquiring in-depth knowledge of anatomy rele- Lect: 3. 3 pts. Professors Lazar and Yuste. molecular biology. Representation, organization, vant to his/her doctoral research. Lectures and Prerequisite: ELEN E3801 or BIOL W3004. structure, function, and manipulation of the biomol- tutorial sessions may be taken with or without the Biophysics of computation, the Hodgkin-Huxley ecular sequence of nucleic acids and proteins. The associated laboratory (BMEN E4104). neuron, modeling and analysis of ion channels, role of enzymes and gene regulatory elements in basic dendritic integration. Integrate-and-fire and natural biological functions as well as in biotech- BMEN E4104x Anatomy laboratory: thorax other spiking neuron models, stimulus representa- nology and genetic engineering. Recombination and abdomen tion and the neural code, time encoding and stim- and other macromolecular processes viewed as Lab: 2. 2 pts. Professor April. ulus recovery, information representation with mathematical operations with simulation and visu- Prerequisite: graduate standing in biomedical time encoding machines, fast algorithms for stim- alization using simple computer programming. This engineering. Corequisite: BMEN E4103. ulus recovery, elements of spike processing and course shares lectures with ECBM E3060, but the neural computation. Modeling synapses and work requirements differ somewhat. BMEN E4105x Anatomy of the extremities synaptic transmission, synaptic plasticity and Lect: 2. 2 pts. Professor April. learning algorithms. Projects in Matlab. BMEN E4103x Anatomy of the thorax and abdomen Prerequisite: Graduate standing in biomedical Lect: 2. 2 pts. Professor April. engineering. This course is designed for the bio- ECBM E4060x Introduction to genomic Prerequisite: Graduate standing in biomedical medical engineering graduate student interested information science and technology engineering. This course is designed for the bio- in acquiring in-depth knowledge of anatomy rele-

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77 BIOMEDICAL ENGINEERING: THIRD AND FOURTH YEARS CLASS OF 2012 AND LATER

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

BIOL C2005 (4) BIOL C2006 (4) BMEN E3910 (4) BMEN 3920 (4) Introductory biol. I Introductory biol. II BME design I BME design II REQUIRED BMEN E3810 (3) BMEN E3820 (3) BMEN E3830 (3) BMEN E4010 (2)4 COURSES: ALL TRACKS BME laboratory I BME laboratory II BME laboratory III Ethics for BMEs

BMEN E4001 (3) BMEN E4002 (3) Quantitative physiol. I Quantitative physiol. II

NONTECH ELECTIVES 0–3 points 3 points 0–3 points 3 points

BMEN E2500 (0) BMCH E3500 (3) BMEN E4501 (3) BMEN E4502 (3) Biol. transport. proc. Tissue eng. I Tissue eng. II BMEN E4210 (4) or CELL & TISSUE ENG.1 Thermo. biolog. sys. BMEN E3320 (3) Technical elective (6) Fluid biomech. MSAE E3103 (3) Elements of mat. sci. Technical elective (3)

BMEN E2300 (0) BMEN E3320 (3) ENME E3113 (3) BMEN 4300 (3) Fluid biomech. Mech. of solids Solid biomech. MECE E3100 (3) BIOMECH.2 Mech. of fluids MECE E3301 (3) Technical elective (3) Thermodynamics

Technical elective (6)

BMEN E2400 (0) BMEN E4420 (3) ELEN E4810 (3) BMEN E4410 (3) TRACK-SPECIFIC COURSES Biosig. proc. & Dig. sig. processing Ultrasound imaging ELEN E3801 (3.5) modeling or Signals & systems BMEN E4894 (3) BMEN E4898 (3) BIOMED. Biomed. imaging Biophotonics IMAGING3

BMEN E4430 (3) Technical elective (3) Principles of MRI

Technical elective (3)

TOTAL POINTS 16–17 16 19 15

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

vant to his/her doctoral research. Lectures and BMEN E4107x Anatomy of the head and neck BMEN E4108x Anatomy laboratory: head and neck tutorial sessions may be taken with or without the Lect: 2. 2 pts. Professor April. Lab: 2. 2 pts. Professor April. associated laboratory (BMEN E4106). Prerequisite: Graduate standing in biomedical Prerequisite: Graduate standing in biomedical engineering. This course is designed for the bio- engineering. Corequisite: BMEN E4107. BMEN E4106x Anatomy laboratory: extremities medical engineering graduate student interested Lab: 2. 2 pts. Professor April. in acquiring in-depth knowledge of anatomy rele- BMEN E4210x Thermodynamics of biological Prerequisite: Graduate standing in biomedical vant to his/her doctoral research. Lectures and systems engineering. Corequisite: BMEN E4105. tutorial sessions may be taken with or without the Lect: 4. 4 pts. Professor Sia. associated laboratory (BMEN E4108).

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78 Prerequisites: CHEM C1404 and MATH V1202. lyzed. The mechanobiology of contractile cells mission or senior standing. Dynamic system mod- Corequisite: BIOL C2005 or the equivalent. including fibroblasts and myocytes; cell and eling and simulation of cardiovascular, respiratory, Introduction to the thermodynamics of biological molecular biology of mechanosensing by cells and thermoregulatory systems. Open and closed systems, with a focus on connecting microscopic such as stem cells, chondrocytes, osteoblasts, physiological loops. Internal and external con- molecular properties to macroscopic states. Both and osteocytes. trollers: baroreflex, chemoreflex, and ventilator. classical and statistical thermodynamics will be Fundamentals of time and frequency domain applied to biological systems; phase equilibria, BMEN E4400x Wavelet applications in analyses and stability. Emulation of normal and chemical reactions, and colligative properties. biomedical image and signal processing pathophysiological conditions. Clinical relevance Topics in modern biology, macromolecular behavior Lect: 3. 3 pts. Not given in 2009–2010. and decision support. Matlab and SIMULINK in solutions and interfaces, protein-ligand binding, Prerequisite: The instructor’s permission. An programming environments will be utilized. and the hydrophobic effect. introduction to methods of wavelet analysis and processing techniques for the quantification of BMEN E4450y Dental and craniofacial tissue BMEN E4300y Solid biomechanics biomedical images and signals. Topics include engineering Lect: 3. 3 pts. Professor Mow. frames and overcomplete representations, multi- Lect: 3. 3 pts. Not given in 2009–2010. Prerequisites: MECE E3105 and ENME E3113. resolution algorithms for denoising and image Prerequisites: MSAE E3103, BMEN E4210, and This course introduces applications of continuum restoration, multiscale texture segmentation and BMEN E4501 or equivalent. Principles of dental and mechanics to the understanding of various biolog- classification methods for computer-aided diagnosis. craniofacial bioengineering, periodontal tissue engi- ical tissue properties. The structure, function, and neering; beyond guided tissue regeneration, cranio- mechanical properties of various tissues in biolog- BMEN E4410y Principles of ultrasound in facial regeneration by stem cells and engineered ical systems, such as blood vessels, muscle, skin, medicine scaffolds, biomaterials. Engineering approaches in brain tissue, bone, tendon, cartilage, ligaments, Lect: 3. 3 pts. Professor Konofagou. tissue regeneration, bone biology and development; etc., will be examined. The focus will be on the Prerequisite: Calculus, Fourier analysis. Physics instructive cues for tissue engineers. establishment of basic governing mechanical prin- of diagnostic ultrasound and principles of ultra- ciples and constitutive relations for each tissue. sound imaging instrumentation. Propagation of BMEN E4501x Tissue engineering, I: Experimental determination of various tissue plane waves in lossless media; ultrasound propa- biomaterials and scaffold design properties will be introduced and demonstrated. gation through biological tissues; single-element Lect: 3. 3 pts. Professor H. H. Lu. The important medical and clinical implications of and array transducer design; pulse-echo and Prerequisites: BIOL C2005-C2006, BMEN tissue mechanical behavior will be emphasized. Doppler ultrasound instrumentation, performance E4001-E4002. An introduction to the strategies evaluation of ultrasound imaging systems using and fundamental bioengineering design criteria in BMEN E4301x Structure, mechanics, and tissue-mimicking phantoms, ultrasound tissue the development of biomaterials and tissue engi- adaptation of bone characterization; ultrasound nonlinearity and bub- neered grafts. Material structural-functional rela- Lect: 3. 3 pts. Instructor to be announced. ble activity; harmonic imaging; acoustic output of tionships, biocompatibility in terms of material and Introduction to structure, physiology, and biome- ultrasound systems; biological effects of ultrasound. host responses. Through discussions, readings, chanics of bone. Structure, function, and physiology and a group design project, students acquire an of skeletal bones; linear elastic properties of cortical BMEN E4420y Biomedical signal processing understanding of cell-material interactions and and trabecular bone; anisotropy and constitutive and signal modeling identify the parameters critical in the design and models of bone tissue; failure and damage mechan- Lect: 3. 3 pts. Professor Sajda. selection of biomaterials for biomedical applications. ics of bone; bone adaptation and fracture healing; Prerequisites: APMA E3101 and ELEN E3202, experimental determination of bone properties; and or the instructor’s permission. Fundamental con- BMEN E4502y Tissue engineering, II: morphological analysis of bone microstructure. cepts of signal processing in linear systems and biological tissue substitutes stochastic processes. Estimation, detection, and Lect: 3. 3 pts. Professor Hung. BMEN E4305y Cardiac mechanics filtering methods applied to biomedical signals. Prerequisites: BIOL C2005-C2006 and BMEN Lect: 3. 3 pts. Not given in 2009–2010. Harmonic analysis, auto-regressive model, E4001-E4002. An introduction to the strategies Prerequisites: BMEN E3310 and E3320 or equiv- Wiener and matched filters, linear discriminants, and fundamental bioengineering design criteria alents. Cardiac anatomy, passive myocardial con- and independent components. Methods are behind the development of cell-based tissue sub- stitutive properties, electrical activation, ventricular developed to answer concrete questions on spe- stitutes. Topics include biocompatibility, biological pump function, ventricular-vascular coupling, cific data sets in modalities such as ECG, EEG, grafts, gene therapy-transfer, and bioreactors. invasive and noninvasive measures of regional MEG, Ultrasound. Lectures accompanied by data and global function, models for predicting ventric- analysis assignments using MATLAB. BMEN E4540y Bioelectrochemistry ular ‘wall stress. Alterations in muscle properties Lect: 3. 3 pts. Professor Pilla. and ventricular function resulting from myocardial BMEN E4430x Principles of magnetic Prerequisite: Elementary physical and organic infarction, heart failure, and left ventricular assist. resonance imaging chemistry. Application of electrochemical kinetics Lect: 3. 3 pts. Professor Brown. to interfacial processes occurring in biomedical BMEN E4340y Introduction to cell mechanics Prerequisite: APMA E1201, PHYS C1403, or the systems. Basics of electrochemistry, electrochemical Lect: 3. 3 pts. Professor Jacobs. instructor’s permission. Fundamental principles instrumentation, and relevant cell and electro- Prerequisite: BMEN E3320. Introduction to how of Magnetic Resonance Imaging (MRI), including physiology reviewed. Applications to interpretation cells function as mechanical structures and how the underlying spin physics and mathematics of of excitable and nonexcitable membrane phenom- mechanical factors influence cellular behavior. image formation with an emphasis on the applica- ena, with emphasis on heterogeneous mechanistic Topics include basics of cell biology, continuum tion of MRI to neuroimaging, both anatomical and steps. Examples of therapeutic devices created mechanics, and statistical mechanics. Concepts functional. The course will examine both theory as a result of bioelectrochemical studies. applied to the mechanical behavior of cells, and experimental design techniques. cytoskeletal polymers, polymer networks, and BMEN E4550y Micro- and nano-structures in membranes. Experimental approaches in cell BMEN E4440y Physiological control systems cellular engineering mechanics are surveyed and compared and Lect: 3. 3 pts. Professor Chbat. Lect: 3. 3 pts. Professor Kam. mechanics of cellular motility and adhesion ana- Prerequisites: APMA E2101 and instructor’s per- Prerequisites: BIOL W2005 and BIOL W2006 or

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the equivalent. Design, fabrication, and applica- nary systems; breast and women’s issues; head inner ear, and the mechanical processing of sound 79 tion of micro- and nano-structured systems for and neck; and central nervous system. Lectures within the inner ear. cell engineering. Recognition and response of are reinforced by examples from clinical two- and cells to spatial aspects of their extracellular envi- three-dimensional and functional imaging (CT, CBMF W4761y Computational genomics ronment. Focus on neural, cardiac, co-culture, MRI, PET, SPECT, U/S, etc.). Lect: 3. 3 pts. Professor Leslie. and stem cell systems. Molecular complexes at Prerequisites: Working knowledge of at least one the nanoscale. BIOL G4700y Seminar in stem cell biology programming language, and some background Lect: 3. 3 pts. Professors Bulinsk, Kalderon, Hung, in probability and statistics. Computational tech- BMEN E4560y Dynamics of biological Vunjak-Novakovic. niques for analyzing and understanding genomic membranes Alternating weeks of high-level research seminars data, including DNA, RNA, protein, and gene Lect: 3. 3 pts. Not given in 2009–2010. with guest speakers and class discussions will expression data. Basic concepts in molecular Prerequisite: Undergraduate cell biology or BMEN cover selected topics at the forefront of stem cell biology relevant to these analyses. Emphasis on E4001. The structure and dynamics of biological biology research in a course designed for Ph.D. techniques from artificial intelligence and machine (cellular) membranes are discussed, with an and advanced master’s students. Grading based learning. String-matching algorithms, dynamic emphasis on biophysical properties. Topics will on class participation, written assignments every programming, hidden Markov models, expecta- include membrane composition, fluidity, lipid other week, and a term paper with an original tion-maximization, neural networks, clustering asymmetry, lipid-protein interactions, membrane synthesis of ideas or a research proposal. algorithms, support vector machines. Students turnover, membrane fusion, transport, lipid phase with life sciences backgrounds who satisfy the behavior. In the second half of the semester, stu- BMME E4702x Advanced musculoskeletal prerequisites are encouraged to enroll. dents will lead discussions of recent journal articles. biomechanics Lect: 2.5. Lab: 0.5. 3 pts. Not given in 2009–2010. BMEN E4810y Artificial organs BMEN E4570x Science and engineering of Advanced analysis and modeling of the musculo- Lect: 3. 3 pts. Professor Leonard. body fluids skeletal system. Topics include advanced concepts Analysis and design of replacements for the Lect: 3. 3 pts. Professor Matsuoka. of 3-D segmental kinematics, musculoskeletal heart, kidneys, and lungs. Specification and real- Prerequisites: General chemistry, organic chem- dynamics, experimental measurements of joint ization of structures for artificial organ systems. istry, and basic calculus. Body fluids as a dilute kinematics and anatomy, modeling of muscles solution of polyelectrolyte molecules in water. and locomotion, multibody joint modeling, intro- BMEN E4894x Biomedical imaging Study of physical behavior as affected by the duction to musculoskeletal surgicalsimulations. Lect: 3. 3 pts. Professor Hielscher. presence of ions in surrounding environments. This course covers image formation, methods of The physics of covalent, ionic, and hydrogen BMEN E4737x Computer control of medical analysis, and representation of digital images. bonds are reviewed, in relation to the structure/ instrumentation Measures of qualitative performance in the context properties of the body fluid. Selected physiological Lect: 2. Lab: 1. 3 pts. Not given in 2009–2010. of clinical imaging. Algorithms fundamental to the processes are examined in physical-chemical Prerequisite: Basic knowledge of the C program- construction of medical images via methods of terms for polymers. ming language. Acquisition and presentation of computed tomography, magnetic resonance, data for medical interpretation. Operating princi- and ultrasound. Algorithms and methods for the BMEN E4590x BioMems: cellular and molecu- ples of medical devices: technology of medical enhancement and quantification of specific features lar applications sensors, algorithms for signal analysis, computer of clinical importance in each of these modalities. Lect: 3. 3 pts. Not given in 2009–2010. interfacing and programming, interface design. Prerequisites: CHEM C3443 or CHEN C3545 or the Laboratory assignments cover basic measure- BMEN E4898y Biophotonics equivalent and MATH V1201. Corequisites: BIOL ment technology, interfacing techniques, use of Lect: 3. 3 pts. Professor Hielscher. W2005 or the equivalent. Topics include biomicro- Labview software instrument interrogation and Prerequisite: BMEN E4894, PHYS C1403, or the electromechanical, microfluidic, and lab-on-a-chip control, automated ECG analysis, ultrasonic instructor’s permission. This course provides a systems in biomedical engineering, with a focus on measurements, image processing applied to broad-based introduction into the field of biopho- cellular and molecular applications. Microfabrication x-ray images and CAT scans. tonics. Fundamental concepts of optical, thermal, techniques, biocompatibility, miniaturization of ana- and chemical aspects of the light-tissue interac- lytical and diagnostic devices, high-throughput cellu- BMEN E4738y Transduction and acquisition tions are presented. The application of these con- lar studies, microfabrication for tissue engineering, of biomedical data cepts for medical therapy and diagnostics is dis- and in vivo devices. Lect: 2. Lab: 1. 3 pts. Not given in 2009–2010. cussed. The course includes theoretical modeling Data transduction and acquisition systems used of light-tissue interactions as well as optical med- BMEN E4601y Cellular electricity in biomedicine. Assembly of bio-transducers and ical instrument design and methods of clinical Lect: 2 Lab: 3. 3 pts. Not given in 2009–2010. the analog/digital circuitry for acquiring electrocar- data interpretation. Bioelectricity of the cell membrane. Basis of cell diogram, electromyogram, and blood pressure resting voltage, voltage changes that lead to the signals. Each small group will develop and con- BMEN E6003x: Computational modeling of action potential and electrical oscillations used struct a working data acquisition board, which will physiological systems in sensing systems. Laboratory includes building be interfaced with a signal generator to elucidate Lect: 3. 3pts. Professor Morrison. electronic circuits to measure capacitance of arti- the dynamics of timing constraints during retrieval Prerequisites: BMEN E4001-E4002 and APMA ficial membranes and ion pumping in frog skin. of bio-data. E4200 or the equivalent. Advanced modeling and quantitative analysis of selected molecular, cellu- APBM E4650x Anatomy for physicists and BMEN E4750y Sound and hearing lar, or organ systems. Four systems are analyzed, engineers Lect: 3. 3 pts. Professor Olson. with emphasis on biologic systems. Systems may Lect: 3. 3 pts. Instructor to be announced. Prerequisites: General physics sequence and two include muscle contraction, respiratory physiology, Prerequisite: Engineering or physics background. semesters of calculus. Introductory acoustics, nerve transmission, pharmacokinetics, circulatory A systemic approach to the study of the human basics of waves and discrete mechanical systems. control, auditory signal processing, cell signaling, body from a medical imaging point of view: skele- The mechanics of hearing—how sound is transmit- molecular transport, excitable membranes, and/or tal, respiratory, cardiovascular, digestive, and uri- ted through the external and middle ear to the statistical data analysis.

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80 EEBM E6020y Methods of computational MEBM E6310x–E6311y Mixture theories for Homma, Huang, Hung, Jacobs, Kam, Konofagou, neuroscience biological tissues, I and II Laine, Leonard, H. H. Lu, Mao, Morrison, Mow, Lecture: 3. 4.5 pts. Instructor to be announced. Lect: 3. 3 pts. Professor Arteshian. Sajda, Sheetz, Sia, and Vunjak-Novakovic. Prerequisite: BMEB W4011 or the instructor’s per- Prerequisites: MECE E6422 and APMA E4200 Candidates for the M.S. degree and candidates for mission. Formal methods in computational neuro- or the equivalent. Development of governing equa- the M.S. degree leading to the doctoral degree science, including methods of signal processing, tions for mixtures with solid matrix, interstitial fluid, may conduct an investigation of some problem in communications theory, information theory, sys- and ion constituents. Formulation of constitutive biomedical engineering. No more than 6 points in tems and control, system identification and models for biological tissues. Linear and nonlinear this course may be counted for graduate credit, machine learning. Molecular models of transduc- models of fibrillar and viscoelastic porous matrices. and this credit is contingent upon the submission tion pathways. Robust adaptation and integral Solutions to special problems, such as confined of an acceptable term report. feedback. Stimulus representation and groups. and unconfined compression, permeation, indenta- Stochastic and dynamical systems models of tion and contact, and swelling experiments. BMEN E9500x or y, or s Doctoral research spike generation. Neural diversity and ensemble 1 to 6 pts. Professors Anastassiou, Ateshian, encoding. Time encoding machines and neural BMEN E6400x Analysis and quantification of Brown, Das, Guo, Hess, Hielscher, Hillman, codes. Stimulus recovery with time decoding medical images Homma, Huang, Hung, Jacobs, Kam, Konofagou, machines. MIMO models of neural computation. Lect: 3. 3 pts. Professor Laine. Laine, Leonard, H. H. Lu, Mao, Morrison, Mow, Synaptic plasticity and learning algorithms. Major Novel methods of mathematical analysis applied Sajda, Sheetz, Sia, and Vunjak-Novakovic. project(s) in Matlab. to problems in medical imaging. Design require- All doctoral candidates (Ph.D., Eng.Sc.D., and ments for screening protocols, treatment therapies, M.D./Ph.D.) are required to make an original BMEE E6030y Neural modeling and and surgical planning. Sensitivity and specificity in investigation of a problem in biomedical engineer- neuroengineering screening mammography and chest radiographs, ing, the results of which are presented in the Lect: 3. 3 pts. Professor Sajda. computer- aided diagnosis systems, surgical plan- dissertation. No more than 12 points of credit in Prerequisites: APMA E3101, ELEN 3202, and ning in orthopaedics, analysis of cardiac perform- this course may be granted toward the degree. ELEN-BMEN E4011, or the equivalent, or the ance, functional magnetic resonance imaging, Doctoral candidates admitted as M.S. candidates instructor’s permission. Engineering perspective positron emission tomography, and echocardiog- leading to the doctoral degree should not register on the study of multiple levels of brain organiza- raphy data. for this course. tion, from single neurons to cortical modules and systems. Mathematical models of spiking neu- BMEN E6420y Advanced microscopy: BMEN E9700x or y Biomedical engineering rons, neural dynamics, neural coding, and biologi- fundamentals and applications seminar cally based computational learning. Architectures Lect: 3. 3 pts. Professor Hilliman. Sem: 1. 0 pt. Professor Sia. and learning principles underlying both artificial Prerequisites: PHYS C1401, C1402, C1403 or All matriculated graduate students are required to and biological neural networks. Computational C1601, C1602, C2601 or C2801, C2802, or the attend the seminar as long as they are in residence. models of cortical processing, with an emphasis equivalent (general physics sequence). Funda- No degree credit is granted. The seminar is a on the visual system. Applications of principles in mentals of techniques including confocal, two principal medium of communication among those neuroengineering; neural prostheses, neuromor- photon, atomic force, and electron microscopy. with biomedical engineering interests within the phic systems, and biomimetics. Course will Application of methods to modern biomedical University. Guest speakers from other institutions, include a computer simulation laboratory. imaging targets. Analysis and interpretation of Columbia faculty, and students within the microscopy data. Department who are advanced in their studies EEBM E6090x or y, E6099x Topics in computa- frequently offer sessions. tional neuroscience and neuroengineering BMEN E6500x Tissue and molecular engineer- Lect: 2. 3 pts. Not given in 2009–2010. ing laboratory BMEN E9800x or y, or s Doctoral research Prerequisite: The instructor’s permission. Lect: 4. 4 pts. Professor Huang. instruction Selected advanced topics in computational neuro- Prerequisites: BIOL C2005 and C2006, or the 3, 6, 9, or 12 pts. Professors Anastassiou, Ateshian, science and neuroengineering. Content varies instructor’s permission. Hands-on experiments in Brown, Das, Guo, Hess, Hielscher, Hillman, from year to year, and different topics rotate molecular and cellular techniques, including fabri- Homma, Huang, Hung, Jacobs, Kam, Konofagou, through the course numbers 6090-6099. cation of living engineered tissues. Covers sterile Laine, Leonard, H. H. Lu, Mao, Morrison, Mow, technique, culture of mammalian cells, microscopy, Sajda, Sheetz, Sia, and Vunjak-Novakovic. BMEN E6301y Modeling of biological tissues basic subcloning and gel electrophoresis, creation Only candidates for the Eng.Sc.D. degree in with finite elements of cell-seeded scaffolds, and the effects of biomedical engineering must register for 12 points Lect: 3. 3 pts. Not given in 2009–2010. mechanical loading on the metabolism of living of doctoral research instruction. Registration may Prerequisite: MECE E6422 or ENME E6315, or cells or tissues. Theory, background, and practi- not be used to satisfy the minimum residence the equivalent. Structure-function relations and cal demonstration for each technique will be requirement for the degree. Not for Ph.D. candi- linear/ nonlinear constitutive models of biological presented. Lab required. dates. tissues: anisotropic elasticity, viscoelasticity, porous media theories, mechano-electrochemical EEBM E9070x or y Seminar in computational BMEN E9900x or y, or s Doctoral dissertation models, infinitesimal and large deformations. neuroscience and neuroengineering 0 pts. Professors Anastassiou, Ateshian, Brown, Emphasis on the application and implementation Lect: 3. 3 pts. Not given in 2009–2010. Das, Guo, Hess, Hielscher, Hillman, Homma, of constitutive models for biological tissues into Prerequisite: Open to doctoral candidates and Huang, Hung, Jacobs, Kam, Konofagou, Laine, existing finite-element software packages. Model qualified M.S. candidates with the instructor’s per- Leonard, H. H. Lu, Mao, Morrison, Mow, Sajda, generation from biomedical images by extraction mission. Study of recent developments in compu- Sheetz, Sia, and Vunjak-Novakovic. of tissue geometry, inhomogeneity, and anisotropy. tational neuroscience and neuroengineering. A candidate for the doctorate in biomedical Element-by-element finite element solver for engineering is required to register for this course large-scale image-based models of trabecular BMEN E9100x or y, or s Master’s research in every term after the student’s course work has bone. Implementation of tissue remodeling simu- 1 to 6 pts. Professors Anastassiou, Ateshian, been completed and until the dissertation has lations in finite element models. Brown, Das, Guo, Hess, Hielscher, Hillman, been accepted.

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CHEMICAL ENGINEERING 81 801 S. W. Mudd, MC 4721, 212-854-4453 www.cheme.columbia.edu

CHAIR PROFESSORS ASSOCIATE PROFESSORS ADJUNCT ASSOCIATE Alan C. West Christopher J. Durning Scott A. Banta PROFESSORS George W. Flynn Aghavni Bedrossian-Omer DEPARTMENTAL Chemistry ASSISTANT PROFESSORS Michael I. Hill ADMINISTRATOR Carl C. Gryte Mark A. Borden Lynn H. Lander Teresa Colaizzo Jingyue Ju V. Faye McNeill Jeffrey T. Koberstein ADJUNCT ASSISTANT Sanat Kumar LECTURER PROFESSORS Edward F. Leonard Jordan Spencer Louis Mattas Ben O’Shaughnessy Jack McGourty Nicholas J. Turro ADJUNCT PROFESSORS Chemistry Robert I. Pearlman Alan C. West David Zudkevitch

hemical engineering is a highly implants and prosthetics and numerous cell activation; the engineering and interdisciplinary field concerned others. Increasingly, chemical engineers biochemistry of sequencing the human C with materials and processes are involved in new technologies genome; the chemistry and physics of at the heart of a broad range of tech- employing highly novel materials whose surface-polymer interactions; the bio- nologies. Practicing chemical engineers unusual response at the molecular level physics of cellular processes in living are the experts in charge of the devel- endows them with unique properties. organisms; the physics of thin polymer opment and production of diverse prod- Examples include environmental tech- films; the chemistry of smart polymer ucts in traditional chemical industries as nologies, emerging biotechnologies of materials with environment-sensitive well as many emerging new technolo- major medical importance employing surfaces; biosensors with tissue engi- gies. The chemical engineer guides the DNA- or protein-based chemical sen- neering applications; the physics and passage of the product from the labora- sors, controlled-release drugs, new agri- chemistry of DNA-DNA hybridization tory to the marketplace, from ideas cultural products, and many others. and melting; the chemistry and physics and prototypes to functioning articles Driven by this diversity of applica- of DNA microarrays with applications and processes, from theory to reality. tions, chemical engineering is perhaps in gene expression and drug discovery; This requires a remarkable depth and the broadest of all engineering disci- the physics and chemistry of nanoparticle- breadth of understanding of physical plines: chemistry, physics, mathematics, polymer composites with novel electronic and chemical aspects of materials and biology, and computing are all deeply and photonic properties. Many experi- their production. involved. The research of the faculty mental techniques are employed, from The expertise of chemical engineers of Columbia’s Chemical Engineering neutron scattering to fluorescence is essential to production, marketing, Department is correspondingly broad. microscopy, and the theoretical work and application in such areas as phar- Some of the areas under active investi- involves both analytical mathematical maceuticals, high-performance materials gation are the fundamental physics, physics and numerical computational in the aerospace and automotive indus- chemistry, and engineering of polymers analysis. tries, biotechnologies, semiconductors and other soft materials; the electro- Students enrolling in the Ph.D. pro- in the electronics industry, paints and chemistry of fuel cells and other interfacial gram will have the opportunity to con- plastics, petroleum refining, synthetic engineering phenomena; the bioengi- duct research in these and other areas. fibers, artificial organs, biocompatible neering of artificial organs and immune Students with degrees in chemical engi-

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82 neering and other engineering disciplines, of microporous polymer membrane for- diffusion of particles in thin polymer films; in chemistry, in physics, in biochemistry, mation with the aim of improving ultrafil- interactions of charged polymer minigels and in other related disciplines are all tration membrane technology; synthesis with interfaces. natural participants in the Ph.D. program and structural characterization of bio- Bioinductive and Biomimetic and are encouraged to apply. The active polymer surfaces in order to realize Materials. The thrust of this research is Department of Chemical Engineering at new in-vivo devices; contact angle, x-ray to develop new strategies for the molec- Columbia is committed to a leadership photoelectron spectroscopy, and reflec- ular design of polymeric and soft materi- role in research and education in frontier tivity analysis, and lattice model simula- als for biological and biomedical applica- areas of research and technology where tion, of responsive polymer surfaces tions. Ongoing research pertains to the progress derives from the conjunction of based on unique polymeric ‘‘surfactants’’ development of bioactive hydrogel coat- many different traditional research disci- in order to develop ‘‘smart’’ surface-active ings for applications in glucose sensors. plines. Increasingly, new technologies and materials; preparation and IR/fluorescence The objective of the coatings is to con- fundamental research questions demand characterization of DNA-decorated sur- trol the tissue-sensor interactions by this type of interdisciplinary approach. faces for ‘‘recognition’’ of DNA in solution incorporating cell-signaling motifs into The undergraduate program provides in order to further medical diagnostic the hydrogel in such a manner that the a chemical engineering degree that is technologies; preparation and characteri- hydrogel induces the formation of new a passport to many careers in directly zation via TEM, AFM, and reflectivity of vascular tissue within the surface coat- related industries as diverse as bio- nano-particle– block copolymer compos- ing. In this fashion, the biosensor can chemical engineering, environmental ites with the aim of very high density continue to operate in vivo, even if management, and pharmaceuticals. The magnetic storage media; self-consistent there is an immune response leading to degree is also used by many students field theory of nano-particle–block copoly- fibrous encapsulation. Complementary as a springboard from which to launch mer composites; computer simulation research programs are aimed at devel- careers in medicine, law, management, and theory of unique ‘‘living’’ polymeriza- oping methods for patterning biological banking and finance, politics, and so on. tion processes important to synthetic surfaces in order to prepare new bio- For those interested in the fundamen- polymer production and biological sys- compatible surfaces as well as to fabri- tals, a career of research and teaching tems; theory and simulation of irreversible cate antigen/antibody and protein arrays is a natural continuation of their under- polymer adsorption. for diagnostic applications. graduate studies. Whichever path the Genomics Engineering. Research student may choose after graduation, Interfacial Engineering and and development of novel bioanalytical the program offers a deep understand- Electrochemistry. Research efforts reagents, systems, and processes using ing of the physical and chemical nature within the department are focused on chemical science, engineering principles, of things and provides an insight into an mass transfer and reaction mechanisms and experimental biological approaches exploding variety of new technologies in electrochemical systems, and the to study problems in genomics are that are rapidly reshaping the society effects that such variables have on actively pursued in the Department of we live in. process design and materials properties. Chemical Engineering in collaboration Applications of the research program with the Columbia Genome Center: Current Research Activities include fuel cells, electrodeposition, and high-throughput DNA sequencing; novel corrosion. Both electrochemical and Science and Engineering of Polymers gene chip development and fundamental microscopy methods are used exten- and Soft Materials. Theoretical and understanding of the processes involved; sively for characterization. A significant experimental studies of novel or impor- applying the cutting-edge genomic tech- numerical simulation component of the tant macromolecules and their applica- nologies to study fundamental biology research programs also exists. tions, especially surface-active species: and for disease gene discovery. ultrasonic sensor, scanning probe micro- scopy and reflectivity studies of adsorp- Biophysics and Soft Matter Physics. Facilities for Teaching and Research tion and self-assembly of highly branched Theoretical and experimental biophysics The Department of Chemical Engineer- ‘‘dendrimers’’ at the solid-liquid interface, of biological soft matter: actin filament ing is continually striving to provide with the aim of creating novel surface growth kinetics and its role in living cell access to state-of-the-art research coatings; fluorescence tracer studies of motility; DNA hybridization, melting and instrumentation and computational facili- molecular level mobility in ultrathin poly- unzipping; DNA microarrays in biotech- ties for its undergraduate and graduate mer films with the aim of improving reso- nology; model gene circuits; DNA mobility students, postdoctoral associates, and lution in lithography; reflectivity studies in 2D microfluidics. Physics of synthetic faculty. Departmental equipment is and computer simulation of flexible poly- soft matter: nano-particles in mesostruc- considered to be in most cases shared, mer adsorption and the response of tured polymer phases and phase transi- which means that equipment access is adsorbed polymer layers to imposed tions; universal scaling laws in reacting usually open to all qualified individuals flows with the aim of improving polymer polymer systems and polymerization phe- with a need to use particular instrumen- processing operations; optical micro- nomena; polymer-interface adsorption tation. scopy studies and numerical simulation phenomena; polymer interfacial reactions;

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The most extensive collection of fluorescence (TIRF) instrument with an tometer (Jobin Yvon, Inc. Fluorolog-3), 83 instrumentation in the department is automated, temperature-controlled flow Waters HPLC, and a sequencing gel associated with the polymer and soft cell has been built for dedicated investi- electrophoresis apparatus (Life Tech- matter research faculty. Faculty banded gations of surface processes involving nologies Model S2), as well as the facili- together to create a unique shared-facili- fluorescently tagged biological and ties required for state-of-the-art synthetic ties laboratory, completed at the end of synthetic molecules. The instrument chemistry. The division of DNA sequenc- 2001. The shared facilities include a fully can operate at different excitation wave- ing and chemical biology at the Columbia equipped polymer synthesis lab with lengths (typically HeNe laser, 633 nm, Genome Center consists of 6,000 sq. ft. four fumes hoods, a 10’x16’ soft wall using Cy5 labeled nucleic acids). of laboratory space and equipment nec- clean room, metal evaporator system, Fluorescence is collected by a highly essary for carrying out the state-of-the- a Milligen 9050 peptide synthesizer, and sensitive photomultiplier tube and art DNA analysis. The laboratory has polymer thin film preparation and sub- logged to a personal computer. Because one Amersham Pharmacia Biotech strate cleaning stations. Also installed fluorescence is only excited in the MegaBace1000 sequencer, three ABI are new, computer-controlled thermal evanescent wave region near an inter- 377 sequencers with complete 96 land analysis, rheometric, and light-scattering face, signals from surface-bound fluo- upgrades, a Qiagen 9600 Biorobot, a setups. Specialized instrumentation for rescent species can be determined with Hydra 96 microdispenser robot, and surface analysis includes an optical/laser minimal background interference from standard molecular biology equipment. system dedicated to characterization of fluorophores in bulk solution. NSF-Columbia MRSEC Shared polymer surface dynamics by Fluor- Chemistry Department. Access to Facilities. Through their participation in escence Recovery after Photobleaching NMR and mass spectrometry facilities is an NSF-MRSEC grant, faculty also have and a PHI 5500 X-ray photoelectron possible through interactions with faculty access to shared facilities located in the spectrophotometer with monochromator members who also hold appointments Schapiro Center for Engineer-ing and that is capable of angle-dependent in the Chemistry Department. The NMR Physical Science Research at Columbia depth profiling and XPS imaging. The facility consists of a 500 MHz, a 400 University. The shared facilities include a system can also perform SIMS and ion MHz, and two 300 MHz instruments that Scintag X2 X-ray diffractometer aligned scattering experiments. A digital image are operated by students and postdocs for low-angle reflectivity work, and a analysis system for the characterization after training. The mass spectrometry Beaglehole Instruments Picometer mod- of sessile and pendant drop shapes is facility is run by students for routine ulated ellipsometer. As needed, these also available for the purpose of polymer samples and by a professional mass capabilities are available for characteri- surface and interfacial tension measure- spectrometrist for more difficult samples. zation of the surface coverage and com- ments as well as contact angle analysis. The Chemistry Department also provides position of modified surfaces and thin An X-ray reflectometer that can perform access to the services of a glass blower organic films. Access to atomic force X-ray standing wave–induced fluores- and machine shop and to photochemical microscopy, scanning and transmission cence measurements is also housed in and spectroscopic facilities. These facili- electron microscopy, and scanning tun- the new shared equipment laboratory, ties consist of (1) two nanosecond laser neling microscopy is possible through along with instrumentation for character- flash photolysis instruments equipped collaborations within the NSF-MRSEC izing the friction and wear properties of with UV-VIS, infrared, EPR, and NMR program and with colleagues in the polymeric surfaces. The laboratory also detection; (2) three EPR spectrometers; Chemistry and Materials Science houses an infrared spectrometer (Nicolet (3) two fluorescence spectrometers; (4) a Departments. The NSF-Columbia Magna 560, MCT detector) with a variable single photon counter for analysis of the MRSEC facility is located within five angle grazing incidence, temperature- lifetimes and polarization of fluorescence minutes’ walking distance from the controlled attenuated-total-reflectance, and phosphorescence; and (5) a high- Chemical Engineering Department. transmission, and liquid cell accessories. performance liquid chromatographic These facilities are suitable for mid-IR, instrument for analysis of polymer molec- spectroscopic investigations of bulk UNDERGRADUATE PROGRAM ular weight and dispersity. materials as well as thin films. The labo- ratory also has a UV-Vis spectrometer Columbia Genome Center. Because of Chemical Engineering (a Cary 50), an SLM Aminco 8000 spec- its affiliation with the Columbia Genome The undergraduate program in chemical trofluorimeter, and a high-purity water Center (CGC), the Department of engineering at Columbia, recently revised, system (Millipore Biocel) used for prepa- Chemical Engineering also has access has five formal educational objectives: ration of biological buffers and solutions. to over 3,000 sq. ft. of space equipped A. Prepare students for careers in indus- Facilities are available for cell tissue cul- with a high-throughput DNA sequencer tries that require technical expertise in ture and for experiments involving bio- (Amersham Pharmacia Biotech Mega- chemical engineering. compatibilization of materials or cellular Bace1000), a nucleic acid synthesizer engineering. In addition, gel electro- (PE Biosystems 8909 Expedite Nucleic B. Prepare students to assume leader- phoresis apparatus is available for the Acid/Peptide Synthesis System), an UV/ ship positions in industries that molecular weight characterization of VIS spectrophotometer (Perkin-Elmer require technical expertise in chemical nucleic acids. A total-internal-reflection- Lambda 40), a fluorescence spectropho- engineering.

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84 C. Enable students to pursue graduate- The first and sophomore years of • One technical elective must be within level studies in chemical engineering study introduce general principles of chemical engineering (i.e. with the and related technical or scientific fields science and engineering and include a designator BMCH, CHEN, CHEE, or (e.g., biomedical or environmental broad range of subjects in the humanities CHAP). engineering, materials science). and social sciences. Although the program • The technical electives must include 6 for all engineering students in these first points of “advanced natural science” D. Provide a strong foundation for stu- two years is to some extent similar, course work, including chemistry, dents to pursue alternative career there are important differences. The physics, biology, and certain engineer- paths, especially careers in business, Professional Engineering Elective, usually ing courses. Qualifying engineering management, finance, law, medicine, taken in Semester II, is designed to courses are determined by Chemical or education. provide an overview of an engineering Engineering Department advisers. E. Establish in students a commitment discipline. Those wishing to learn about The junior-senior technical electives to life-long learning and service within chemical engineering are encouraged provide the opportunity to explore their chosen profession and society. to take CHEN E1040: Molecular engineer- new interesting areas beyond the core ing and product design, taught by the The expertise of chemical engineers is requirements of the degree. Often, Chemical Engineering Department. essential to production, marketing, and students satisfy the technical electives Students who major in chemical engineer- application in such areas as pharmaceuti- by taking courses from another SEAS ing are not currently required to take cals, high performance materials as in the department in order to obtain a minor computer science or programming, and automotive and aerospace industries, from that department. Alternately, you should in their sophomore year take semiconductors in the electronics indus- may wish to take courses in several new CHEN E3100: Material and energy bal- try, paints and plastics, consumer prod- areas, or perhaps to explore familiar ances (see table on page 86). ucts such as food and cosmetics, petrole- subjects in greater depth, or you may In the junior-senior sequence one um refining, industrial chemicals, synthetic wish to gain experience in actual labora- specializes in the chemical engineering fibers, and just about every bioengineering tory research. Three points of CHEN major. The table on page 87 spells out and bio-technology area from artificial E3900: Undergraduate research project the core course requirements, which are organs to biosensors. Increasingly, chemi- may be counted toward the technical split between courses emphasizing engi- cal engineers are involved in exciting new elective content. neering science and those emphasizing technologies employing highly novel The program details discussed practical and/or professional aspects of materials, whose unusual response at the above, and the accompanying tables, the discipline. Throughout, skills required molecular level endows them with unique apply to undergraduates who are enrolled of practicing engineers are developed properties. Examples include controlled at Columbia as freshmen and declare (e.g. writing and presentation skills, release drugs, materials with designed the chemical engineering major in the competency with computers). interaction with in vivo environments, sophomore year. However, the chemical The table on page 87 shows that a “nanomaterials” for electronic and optical engineering program is designed to be significant fraction of the junior-senior applications, agricultural products, and a readily accessible to participants in any program is reserved for electives, both host of others. This requires a depth and of Columbia’s Combined Plans and to technical and nontechnical. Nontechnical breadth of understanding of physical and transfer students. In such cases, the electives are courses that are not quanti- chemical aspects of materials and their guidance of one of the departmental tative, such as those taught in the human- production that is without parallel. advisers in planning your program is ities and social sciences. These provide The chemical engineering degree also required (contact information for the an opportunity to pursue interests in areas serves as a passport to exciting careers departmental UG advisers is listed on other than engineering. A crucial part of in directly related industries as diverse as the department’s Web site). the junior-senior program is the 12-point biochemical engineering, environmental Columbia’s program in chemical technical elective requirement. Technical management, and pharmaceuticals. engineering leading to the B.S. degree electives are science and/or technology Because the deep and broad-ranging is fully accredited by the Engineering based and feature quantitative analysis. nature of the degree has earned it a high Accreditation Commission of the Generally, technical electives must be reputation across society, the chemical Accreditation Board for Engineering 3000 level or above but there are a few engineering degree is also a natural and Technology (ABET). exceptions: PHYS C1403, PHYS C2601, platform from which to launch careers BIOL C2005, BIOL C2006, and BIOL in medicine, law, management, banking Requirements for a Minor in W2501. The technical electives are sub- and finance, politics, and so on. Many Chemical Engineering ject to the following constraints: students choose it for this purpose, to See page 189. have a firm and respected basis for a • One technical elective must be within SEAS but taken outside of chemical range of possible future careers. For those Requirements for a Minor in engineering (that is, a course with a interested in the fundamentals, a career Biomedical Engineering of research and teaching is a natural designator other than BMCH, CHEN, Students majoring in chemical engineer- continuation of undergraduate studies. CHEE, or CHAP). ing who wish to include in their records

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a minor in biomedical engineering may related fields such as physics, chemistry, understanding of cellular function and 85 do so by taking BMEN E4001 or E4002; biochemistry, and others are encour- therefore human pathologies. At Columbia BIOL C2005; BMEN E4501 and E4502; aged to apply to this highly interdiscipli- Chemical Engineering, we focus on sev- and any one of several chemical engi- nary program. eral unique aspects of soft matter, such neering courses approved by the BME as their special surface and interfacial Department. See also page 189. Areas of Concentration properties. This concentration is similar After satisfying the core requirement of in thrust to that of the ‘‘Biophysics and GRADUATE PROGRAM Chemical process analysis (CHEN Soft Matter’’ concentration, except here there is greater emphasis on synthetic The graduate program in chemical engi- E4010), Transport phenomena, III (CHEN rather than biological soft matter, with neering, with its large proportion of elec- E4110), and Statistical mechanics particular emphasis on interfacial proper- tive courses and independent research, (CHAP E4120), chemical engineering ties and materials with important related offers experience in any of the fields of graduate students are free to choose applications. Synthetic polymers are departmental activity mentioned in previ- their remaining required courses as they by far the most important material in ous sections. For both chemical engi- desire, subject to their research adviser’s this class. neers and those with undergraduate approval. However, a number of areas of educations in other related fields such graduate concentration are suggested CHEE E4252: Introduction to surface and colloid as physics, chemistry, and biochemistry, below, with associated recommended chemistry CHEN E4620: Introduction to polymers the Ph.D. program provides the oppor- courses. Each concentration provides CHEN E4640: Polymer surfaces and interfaces tunity to become expert in research students with the opportunity to gain in-depth knowledge about a particular CHEN E6620y: Physical chemistry of macro- fields central to modern technology and molecules research field of central importance to science. CHEN E6910: Theoretical methods in polymer the department. Graduate students out- physics M.S. Degree side the department are very welcome CHEN E6920: Physics of soft matter to participate in these course concentra- The requirements are (1) the core courses: tions, many of which are highly interdis- Biophysics and Soft Matter Physics. Chemical process analysis (CHEN ciplinary. The department strongly Soft matter denotes polymers, gels, E4010), Transport phenomena, III (CHEN encourages interdepartmental dialogue self-assembled surfactant structures, E4110), and Statistical mechanics at all levels. colloidal suspensions, and many other (CHAP E4120); and (2) 21 points of complex fluids. These are strongly fluc- 4000- or 6000-level courses, approved Science and Engineering of Polymers tuating, floppy, fluidlike materials that by the graduate coordinator or research and Soft Materials. Soft materials can nonetheless exhibit diverse phases adviser, of which up to 6 may be include diverse organic media with with remarkable long-range order. In the Master’s research (CHEN 9400). supramolecular structure having scales last few decades, statistical physics has Students with undergraduate prepara- in the range 1–100 nm. Their small-scale achieved a sound understanding of the tion in physics, chemistry, biochemistry, structure imparts unique, useful macro- scaling and universality characterizing pharmacy, and related fields may take scopic properties. Examples include large length scale properties of much advantage of a special two-year pro- polymers, liquid crystals, colloids, and synthetic soft condensed matter. More gram leading directly to the master’s emulsions. Their ‘‘softness’’ refers to recently, ideas and techniques from soft degree in chemical engineering. This the fact that they typically flow or distort condensed matter physics have been program enables such students to avoid easily in response to moderate shear applied to biological soft matter such having to take all undergraduate courses and other external forces. They exhibit as DNA, RNA, proteins, cell membrane in the bachelor’s degree program. a great many unique and useful macro- surfactant assemblies, actin and tubulin scopic properties stemming from the structures, and many others. The aim is Doctoral Degrees variety of fascinating microscopic struc- to shed light on (1) fundamental cellular The Ph.D. and D.E.S. degrees have tures, from the simple orientational order processes such as gene expression essentially the same requirements. of a nematic liquid crystal to the full peri- or the function of cellular motors and All students in a doctoral program must odic ‘‘crystalline’’ order of block copoly- (2) physical mechanisms central to the (1) earn satisfactory grades in the three mer mesophases. Soft materials provide exploding field of biotechnology involving core courses (CHEN E4010, CHEN ideal testing grounds for such funda- systems such as DNA microarrays and E4110, CHAP E4120); (2) pass a qualify- mental concepts as the interplay between methods such as genetic engineering. ing exam; (3) defend a proposal of order and dynamics or topological The practitioners in this highly interdisci- research within twelve months of pass- defects. They are of primary importance plinary field include physicists, chemical ing the qualifying exam; (4) defend their to the paint, food, petroleum, and engineers, biologists, biochemists, and thesis; and (5) satisfy course require- other industries as well as a variety of chemists. ments beyond the three core courses. advanced materials and devices. In The ‘‘Biophysics and Soft Matter’’ For detailed requirements, please con- addition, most biological materials are concentration is closely related to the sult the departmental office or graduate soft, so that understanding of soft mate- ‘‘Science and Engineering of Polymers coordinator. Students with degrees in rials is very relevant to improving our and Soft Materials’’ concentration, but

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86 CHEMICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

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

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

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

ENGLISH C1010 (3) COMPOSITION Z1003 (0) C1010 (3) (three tracks, choose one) Z0006 (0) Z1003 (0) C1010 (3)

One core humanities Three core humanities NONTECH elective (3–4 points)2 electives (11 points)2

TECH Professional engineering REQUIRED ELECTIVES elective (3)1

CHEM. ENG. CHEN E3100 (4)3 REQUIREMENT Material & energy balances

COMPUTER SCIENCE

PHYSICAL EDUCATION C1001 (1) C1002 (1)

GATEWAY LAB E1102 (4) either semester

TOTAL POINTS4 16.5 16.5 17.5 17

1Students are encouraged to take CHEN 1040: Molecular engineering and product design. 2Four core humanities electives should be taken as follows: In Semester III, HUMA C1001, C1101 (4), or any initial course in one of the Global Core sequences offered by the College (3–4); in Semester IV, HUMA C1002, C1102 (4), or the second course in the Global Core sequence elected in Semester III (3–4); also in Semester IV, ECON W1105 (4) with W1105 recitation (0) and either HUMA C1121 or C1123 (3). 3Should be taken in Semester III, but may be moved upon adviser’s approval to Semester V if CHEM C3543: Organic chemistry lab is taken in Semester III. 4Taking the first track in each row and E1102 in Semester II.

here greater emphasis is placed on bio- and fascinating biological issues are. Genomic Engineering. Genomic engi- logical materials and cellular biophysics. CHAP E4120: Statistical mechanics neering may be defined as the develop- Both theory and experiment are catered CHEN E6920: Physics of soft matter ment and application of novel technologies to. Students will be introduced to statis- BIOC G6300: Biochemistry/molecular biology— for identifying and evaluating the signifi- tical mechanics and its application to soft eukaryotes, I cance of both selected and all nucleotide matter research and to cellular biophysics. BIOC G6301: Biochemistry/molecular biology— sequences in the genomes of organisms. In parallel, the student will learn about eukaryotes, II An interdisciplinary course concentration CHEN E4750: The genome and the cell genomics and cellular biology to develop in genomic engineering is available to CMBS G4350: Cellular molecular biophysics an understanding of what the central graduate students, and to selected

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87 CHEMICAL ENGINEERING: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

CHEN E3110 (4) CHEN E3120 (4) CHEN E4500 (4) CHEN E4510 (4) Transp. phenomena I Transp. phenomena II Process & product design I Process & product design II CHEE E3010 (4) CHEN E3210 (4) CHEN E4140 (3) REQUIRED Principles of chem. Chem. eng. Chem. & biochem. CHEN E4320 (4) COURSES eng. thermodynamics thermodynamics separations Molecular phenomenon in chem. eng. CHEN E4230 (3) CHEN E4300 (2) Reaction kinetics & Chem. eng. control reactor design

1 REQUIRED LABS CHEN C3543 (3) CHEN 3810 (3) Org. chem. lab Chem. eng. lab

NONTECH 3 points 3 points 3 points

TECH2 3 points 3 points 3 points 3 points REQUIRED ELECTIVES

TOTAL POINTS (normal track) 17 17 15 14

1May be taken in Semester III with adviser’s permission if CHEN E3100: Material and energy balances is taken in Semester V. 2The total of 12 points of required technical electives must include one chemical engineering course, one engineering course outside of chemical engineering, and 6 points of “advanced natural science” courses (i.e., chemistry, physics, biology, materials science, and certain chemical engineering courses—contact a departmental adviser for details).

undergraduate students. The National information interacts with the develop- E4700) provides students with a solid Science Foundation is sponsoring the mental state and environment of cells basis for understanding both the princi- development of this concentration, which in order to determine their behavior. ples that underlie genomic technologies is believed to be the first of its kind. Prof. E. F. Leonard directs the program and how these principles are applied. Courses in the concentration equip stu- and teaches CHEN E4750. The other The Genomics sequencing laboratory dents in engineering and computer sci- instructors are Profs. D. Anastassiou (CHEN E4760) provides hands-on expe- ence to help solve technical problems (ECBM E4060), Jingyue Ju (CHEN rience in high-throughput DNA sequenc- encountered in the discovery, assembly, E4700, CHEN E4730), and C. Leslie ing, as conducted in a bioscience organization, and application of genomic (CBMF W4761). The departments of research laboratory. The genome and information. The courses impart an Chemical, Biomedical, and Electrical the cell (CHEN E4750) conveys a broad understanding of the fundamental goals Engineering and of Computer Science but precise, organized, and quantitative and problems of genomic science and credit these courses toward require- overview of the cell and its genome: gene-related intracellular processes; ments for their doctorates. Students how the genome, in partnership with elucidate the physical, chemical, and may take individual courses so long as extragenomic stimuli, influences the instrumental principles available to they satisfy prerequisite requirements or behavior of the cell and how mecha- extract sequence information from the have the instructor’s permission. All lec- nisms within the cell enable genomic genome; and teach the concepts used ture courses in the program are available regulation. Computational genomics to organize, manipulate, and interrogate through the Columbia Video Network, (CBMF W4761) introduces students the genomic database. which offers a certificate for those to basic and advanced computational The concentration consists of five students completing a prescribed set techniques for analyzing genomic data. courses that address the principal areas of the courses. Interested parties can obtain further of genomic technology: sequencing and The course Introduction to genomic information, including a list of cognate other means of acquiring genomic infor- information science and technology courses that are available and recom- mation; bioinformatics as a means of (ECBM E4060) provides the essential mended, from Professor Leonard assembling and providing structured concepts of the information system par- ([email protected]). access to genomic information; and adigm of molecular biology and genetics. methods of elucidating how genomic Principles of genomic technology (CHEN

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88 Interfacial Engineering and tices, through lectures by department faculty and BMCH E3500y Transport in biological systems Electrochemistry. Electrochemical practicing chemical engineers, trips to industrial Lect: 3. 3 pts. Professor Leonard. processes are key to many alternative facilities, reverse engineering of chemical prod- Prerequisites: CHEM C3443 and MATH E1210. ucts, and a chemical design competition. Corequisite: BIOL C2005. Convective and diffu- energy systems (batteries and fuel cells), sive movement and reaction of molecules in to electrical and magnetic-device manu- CHEE E3010x Principles of chemical biological systems. Kinetics of homogeneous facturing (interconnects and magnetic- engineering thermodynamics and heterogeneous reactions in biological envi- storage media), and to advanced mate- Lect: 4. 4 pts. Professor Castaldi. ronments. Mechanisms arid models of transport rials processing. Electrochemical Prerequisite: CHEM C1403. Introduction to across membranes. Convective diffusion with and processes are also involved in corrosion thermodynamics. Fundamentals are emphasized: without chemical reaction. Diffusion in restricted and in some waste-treatment systems. the laws of thermodynamics are derived and their spaces. Irreversible thermodynamic approaches to transport and reaction in biological systems. Key employers of engineers and scien- meaning explained and elucidated by applications to engineering problems. Pure systems are treated, tists with knowledge of electrochemical/ followed by an introduction to mixtures and phase CHEN E3810y Chemical engineering laboratory interfacial engineering include compa- equilibrium. Lab: 3. 3 pts. Professors Borden and Spencer. nies from the computer, automotive, and Prerequisite: Completion of core chemical engi- chemical industries. Knowledge of basic CHEN E3100x Material and energy balances neering curricula through the fall semester of sen- electrochemical principles, environmental Lect: 4. 4 pts. Professor McNeill. ior year (includes CHEN E3110, E3120, E4230, sciences, and/or materials science can Prerequisites: First-year chemistry and physics E3100, E3010, E3210, E4140, E4500), or the be useful to a career in this area. or equivalents. This course serves as an introduc- instructor’s permission. The course emphasizes tion to concepts used in the analysis of chemical active, experiment-based resolution of open- CHEN E4201: Engineering applications of engineering problems. Rigorous analysis of mate- ended problems involving use, design, and opti- electrochemistry rial and energy balances on open and closed sys- mization of equipment, products, or materials. CHEN E4252: Introduction to surface and tems is emphasized. An introduction to important Under faculty guidance students formulate, carry colloid science processes in the chemical and biochemical indus- out, validate, and refine experimental procedures, CHEN E6050: Advanced electrochemistry tries is provided. and present results in oral and written form. The CHEN E3900: Undergraduate research project course develops analytical, communications, and Bioinductive and Biomimetic CHEN E3110x Transport phenomena, I cooperative problem-solving skills in the context of problems that span from traditional, large-scale Materials. This is a rapidly emerging Lect: 4. 4 pts. Instructor to be announced. separations and processing operations to molecu- area of research, and the department’s Prerequisites: Classical mechanics, vector calcu- lus, ordinary differential equations. Focuses on lar-level design of materials or products. Sample course concentration is under develop- the momentum and energy transport in pure (one- projects include scale up of apparatus, process ment. At present, students interested in component) Newtonian fluids, i.e. elementary fluid control, chemical separations, heterogeneous catal- this area are recommended to attend mechanics, elementary conduction-dominated ysis and mathematical model development. Safety Polymer surfaces and interfaces (CHEN heat transfer, and forced convection heat transfer awareness is integrated throughout the course. E4640); and Physical chemistry of in fluids. This is an introductory-level course. It macromolecules (CHEN E6620). Other includes a review of the mathematical methods CHEN E3900x and y Undergraduate research project courses in the ‘‘Science and Engineering needed (vector calculus and ordinary differential equations). Applications to problems important 0 to 6 pts. The staff. of Polymers and Soft Materials’’ concen- in modern chemical engineering are used to illus- Candidates for the B.S. degree may conduct an tration are also relevant. When complete, trate concepts. investigation of some problem in chemical engi- the concentration will include courses neering or applied chemistry or carry out a special directly addressing biomaterials and CHEN E3120y Transport phenomena, II project under the supervision of the staff. Credit immunological response. Lect: 4. 4 pts. Professor Durning. for the course is contingent upon the submission Prerequisite: CHEN E3110, of which this course of an acceptable thesis or final report. No more is a continuation. Focuses on the mass transport than 6 points in this course may be counted toward COURSES IN CHEMICAL in isothermal mixtures of Newtonian fluids, i.e., the satisfaction of the B.S. degree requirements. ENGINEERING elementary diffusion-dominated mass transfer, See also Center for Biomedical and forced convection mass transfer in fluid mix- CHEN E4010x Mathematical methods in Engineering. Note: Check the depart- tures. Includes instruction in new mathematical chemical engineering methods needed (introductory partial differential Lect: 3. 3 pts. Professor Leonard. ment Web site for the most current equations). Applications to problems important Open to undergraduates only with the instructor’s course offerings/descriptions. in modern chemical engineering are used to permission. Application of selected mathematical illustrate concepts. methods to solution of chemical engineering CHEN E1040y Molecular engineering and problems. product design CHEN E3210y Chemical engineering thermo- Lect: 3. 3 pts. Professor West. dynamics CHEN E4020x Protection of industrial and An introductory course intended to expose stu- Lect: 3. 4 pts. Professor Koberstein. intellectual property dents to chemical engineering. Examines the Prerequisites: CHEN E3010 and E3100. This Lect: 3. 3 pts. Professor Pearlman. ways in which chemical and biological sciences course deals with fundamental and applied To expose engineers, scientists, and technology are interpreted through analytical, design, and thermodynamic principles that form the basis of managers to areas of the law they are most engineering frameworks to generate products that chemical engineering practice. Topics include likely to be in contact with during their careers. enhance human endeavor. Students are intro- phase equilibria, methods to treat ideal and non- Principles are illustrated with various case studies, duced to the culture of chemical engineering and ideal mixtures, and estimation of properties using together with active student participation. the wide variety of chemical engineering prac- computer-based methods.

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CHEN E4030y Biocolloid engineering design self-learning exercises, and computer process CHEN E4410x Environmental control technology 89 Lect: 3. 3 pts. Professor Borden. simulation. Lect: 3. 3 pts. Professor Zudkevitch. Prerequisite: CHEE E4252 or the instructor’s per- Prerequisite: CHEN E3010 or the equivalent. mission. Introduction to biocolloid engineering CHEN E4201x Engineering applications of Causes of pollution and effect on life. Legal and design for applications in molecular imaging electrochemistry aspects, OSHA and EPA rules. Pollution at home and targeted drug and gene delivery. Emphasis Lect: 3. 3pts. Professor West. and at work; radon, fumes, and dust; ventilation, on self-assembling structures including microbub- Prerequisites: Physical chemistry and a course dust collection, carbon adsorption. Fuel and acid bles, micelles, vesicles, emulsions, and polymer in transport phenomena. Engineering analysis gases, smog and dispersion. Treatment of complexes. Treatment of biocompatibility and of electrochemical systems, including electrode ground, saline, and waste water. Primary and interactions with cells, biological fluids, and physi- kinetics, transport phenomena, mathematical secondary (biological) treatment. Tertiary water ological systems. modeling, and thermodynamics. Common experi- treatment with membranes, ion exchange, car- mental methods are discussed. Examples from bon, and sieves. Solid and hazardous waste. CHEE E4050y Principles of industrial electro- common applications in energy conversion and Visit New York City waste water treatment plant. chemistry metallization are presented. Lect: 3. 3 pts. Professor Duby. CHEN E4500x Process and product design, I Prerequisite: CHEN E3010. A presentation of CHEN E4230y Reaction kinetics and Lect: 3. 4 pts. Professor Kumar. the basic principle underlying electrochemical reactor design Prerequisites: CHEN E4140 and E3100. An intro- processes. Thermodynamics, electrode kinetics, Lect: 3. 3 pts. Professor Leonard. duction to the process engineering function. The and ionic mass transport. Examples of industrial Prerequisite: CHEN E3010. Reaction kinetics, design of chemical process, process equipment, and environmental applications illustrated by applications to the design of batch and continu- and plants and the economic and ecological means of laboratory experiments: electroplating, ous reactors. Multiple reactions, non-isothermal evaluation of the chemical engineering project. refining, and winning in aqueous solutions and reactors. Analysis, modeling of reactor behavior. Use of statistics to define product quality is illus- in molten salts; electrolytic treatment of wastes; Required recitation. trated with case studies. primary, secondary, and fuel cells. CHEE E4252x Introduction to surface and CHEN E4510y Process and product design, II CHEN E4110x Transport phenomena, III colloid chemistry Lect: 4. 4 pts. Professors Kumar and Hill. Lect: 3. 3 pts. Professor Durning. Lect: 3. 3 pts. Professor Somasundaran. Prerequisite: CHEN E4500. Students carry out a Prerequisite: CHEN E3120. Tensor analysis; Prerequisite: Elementary physical chemistry. semester-long process or product design course kinematics of continua; balance laws for one- Thermodynamics of surfaces, properties of sur- with significant industrial involvement. The project component media; constituitive laws for free energy factant solutions and surface films, electrostatic culminates with a formal written design report and and stress in one-component media; exact and and electrokinetic phenomena at interfaces, a public presentation. asymptotic solutions to dynamic problems in fluids adsorption; interfacial mass transfer and modern and solids; balance laws for mixtures; constitutive experimental techniques. CHEE E4530y Corrosion of metals laws for free energy, stress and diffusion fluxes Lect: 3. 3 pts. Professor Duby. in mixtures; solutions to dynamic problems in CHEN E4300x Chemical engineering control Prerequisite: CHEN E3010. The theory of electro- mixtures. Lab: 2. 2 pts. Professor Borden. chemical corrosion, corrosion tendency, rates, Prerequisites: Ordinary differential equations and passivity. Application to various environments. CHAP E4120x Statistical mechanics (including Laplace transforms), CHEN E3100, and Cathodic protection and coatings. Corrosion testing. Lect: 3. 3 pts. Professor O’Shaughnessy. CHEN E4230. An introduction to process control Prerequisite: CHEN E3010 or equivalent thermo- applied to chemical engineering through lecture CHEN E4600x Atmospheric aerosols dynamics course, or the instructor’s permission. and laboratory. Concepts include the dynamic Lect: 3. 3 pts. Professor McNeill. Fundamental principles and underlying assump- behavior of chemical engineering systems, feed- Prerequisite: CHEN E3120 or the instructor’s per- tions of statistical mechanics. Boltzmann’s back control, controller tuning, and process stability. mission. Atmospheric aerosols and their effects entropy hypothesis and its restatement in terms on atmospheric composition and climate. Major of Helmholtz and Gibbs free energies and for CHEN E4320x Molecular phenomena in topics are aerosol sources and properties, field open systems. Correlation times and lengths. chemical engineering and laboratory techniques for characterization, Exploration of phase space and observation Lect: 3. 4 pts. Professor O’Shaughnessy. gas-aerosol interactions, secondary organic timescale. Correlation functions. Fermi-Dirac and This new course located strategically at the end aerosols, and aerosol direct and indirect effects Bose-Einstein statistics. Fluctuation-response of the curriculum is intended to provide students on climate. theory. Applications to ideal gases, interfaces, with a molecular basis for the engineering concepts liquid crystals, microemulsions and other complex covered in the curriculum. It is meant to both CHEN E4620y Introduction to polymers and fluids, polymers, Coulomb gas, interactions validate the basic science and math foundations soft materials between charged polymers and charged inter- developed earlier and to stimulate the student Lect: 3. 3 pts. Professor Durning. faces, ordering transitions. toward applying modern molecular concepts of Prerequisites: An elementary course in physical chemical engineering that will define their future. chemistry or thermodynamics. Organic chemistry, CHEN E4140x Chemical and biochemical statistics, calculus and mechanics are helpful, but separations CHEN E4330y Advanced chemical kinetics not essential. An introduction to the chemistry and Lect: 3. 3 pts. Professor Banta. Lect: 3. 3 pts. Professor McNeill. physics of soft materials systems (polymers, col- Prerequisites: CHEN E3100, E3120, and E3210, Prerequisite: CHEN E4230y or the instructor’s loids, organized surfactant systems, and others), or the instructor’s permission. Design and analy- permission. Complex reactive systems. Catalysis. emphasizing the connection between microscopic sis of unit operations employed in chemical and Heterogeneous systems, with an emphasis on structure and macroscopic physical properties. biochemical separations. Emphasis is placed on coupled chemical kinetics and transport phenom- To develop an understanding of each system, learning the fundamental aspects of distillation, ena. Reactions at interfaces (surfaces, aerosols, illustrative experimental studies are discussed gas adsorption, and crystallization through a com- bubbles). Reactions in solution. along with basic theoretical treatments. High bination of lectures, open-ended problem solving, molecular weight organic polymers are discussed

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90 first (basic notions, synthesis, properties of single CHEN E4700x Principles of genomic CHEN E4760y Genomics sequencing laboratory polymer molecules, polymer solution and blend technologies Lect: 1. Lab: 2. 3 pts. Professor Ju. thermodynamics, rubber and gels). Colloidal Lect: 3. 3 pts. Professor Ju. Prerequisites: Undergraduate-level biology, organic systems are treated next (dominant forces in Prerequisites: BIOL C2005 and 2006, CHEM chemistry, and the instructor’s permission. The colloidal systems, flocculation, preparation and C3045 and C3046, or equivalents. Chemical chemical, biological, and engineering principles manipulation of colloidal systems) followed by a and physical aspects of genome structure and involved in the genomics sequencing process will discussion of self-organizing surfactant systems organization, genetic information flow from DNA be illustrated throughout the course for engineering (architecture of surfactants, micelles and surfac- to RNA to protein. Nucleic acid hybridization and students to develop the hands-on skills in conducting tant membranes, phase behavior). sequence complexity of DNA and RNA. Genome genomics research. mapping and sequencing methods. The engineer- CHEN E4640x or y Polymer surfaces and ing of DNA polymerase for DNA sequencing and CHEN E4800x Protein engineering interfaces polymerase chain reaction, Fluorescent DNA Lect: 3. 3 pts. Professor Banta. Lect: 3. 3 pts. Instructor to be announced. sequencing and high-throughput DNA sequencer Prerequisite: CHEN E4230 (may be taken Prerequisites: CHEN E4620 or the instructor’s development. Construction of gene chip and concurrently) or the instructor’s permission. permission. A fundamental treatment of the ther- micro array for gene expression analysis. Tech- Fundamental tools and techniques currently used modynamics and properties relating to polymer nology and biochemical approach for functional to engineer protein molecules. Methods used to surfaces and interfaces. Topics include the char- genomics analysis. Gene discovery and genetics analyze the impact of these alterations on differ- acterization of interfaces, theoretical modeling of database search method. The application of ent protein functions, with specific emphasis on interfacial thermodynamics and structure, and genetic database for new therapeutics discovery. enzymatic catalysis. Case studies reinforce con- practical means for surface modification. cepts covered and demonstrate the wide impact CHEN E4740x: Biological transport and rate of protein engineering research. Application of CHEN E4645x or y Inorganic polymers, hybrid phenomena, II basic concepts in the chemical engineering cur- materials and gels Lect: 3. 3 pts. Professor Leonard. riculum (reaction kinetics, mathematical modeling, Lect: 3. 3 pts. Professor Koberstein. Prerequisites: Any two of the following: CHEN thermodynamics) to specific approaches utilized Prerequisite: Organic chemistry. The focus of the E3110; BIOL C2005; CHEN E3210 or BMCH in protein engineering. first part of the course is on the preparation, char- E3500. Analysis of transport and rate phenomena acterization, and applications of inorganic poly- in biological systems and in the design of bio- CHEN E6050y Advanced electrochemistry mers, with a heavy emphasis on those based on mimetic transport-reaction systems for technologi- Lect: 3. 3 pts. Not given in 2009–2010. main-group elements. Main topics are characteri- cal and therapeutic applications. Modeling of Prerequisite: The instructor’s permission. An zation methods, polysiloxanes, polysilanes, homogeneous and heterogeneous biochemical advanced overview of the fundamentals of elec- polyphosphazenes, ferrocene-based polymers, reactions. The bases of biological transport: roles trochemistry, with examples taken from modern other phosphorous-containing polymers, boron- of convection, ordinary diffusion, forced diffusion. applications. An emphasis is placed on mass containing polymers, preceramic inorganic poly- Systems where reaction and transport interact transfer and scaling phenomena. Principles are mers, and inorganic-organic hybrid composites. strongly. Applications to natural and artificial tis- reinforced through the development of mathematical The focus of the second part of the course is on sue beds, tumor modeling, controlled release, models of electrochemical systems. Course proj- gels, both physical and chemical. Topics will natural and artificial organ function. ects will require computer simulations. The course include gel chemistry, including epoxies, is intended for advanced graduate students, polyurethanes, polyesters, vinyl esters, and CHEN E4750y The genome and the cell conducting research involving electrochemical hydrogels, as well as theoretical methods used Lect: 3. 3 pts. Not given in 2009–2010. technologies. to characterize the gel point and gel properties. Prerequisite: BIOL C2005 and MATH E1210, or equivalents. The utility of genomic information lies CHEE E6220y Equilibria and kinetics in CHEN E4660y Biochemical engineering in its capacity to predict the behavior of living cells hydrometallurgical systems Lect: 3. 3 pts. Not given in 2009–2010. in physiological, developmental, and pathological Lect: 3. 3 pts. Professor Duby. Prerequisite: BMEN E4001 or the equivalent. situations. The effect of variations in genome struc- Prerequisite: CHEE E4050 or EAEE E4003. Engineering of biochemical and microbiological ture between individuals within a species, including Detailed examination of chemical equilibria reaction systems. Kinetics, reactor analysis, and those deemed healthy or diseased, and among in hydrometallurgical systems. Kinetics and design of batch and continuous fermentation and species, can be inferred statistically by compar- mechanisms of homogeneous and heterogeneous enzyme processes. Recovery and separations in isons of sequences with behaviors, and mechanisti- reaction in aqueous solutions. biochemical engineering systems. cally, by studying the action of molecules whose structure is encoded within the genome. This CHEE E6252y Applied surface and colloid CHEN 4680x Soft materials laboratory course examines known mechanisms that elucidate chemistry Lect/lab: 3. 3 pts. Professors Durning and the combined effect of environmental stimulation Lect: 2. Lab: 3. 3 pts. Professor Somasundaran. Koberstein. and genetic makeup on the behavior of cells in Prerequisite: CHEN E4252. Applications of sur- Prerequisites: Two years of undergraduate homeostasis, disease states, and during develop- face chemistry principles to wetting, flocculation, science courses and the instructors’ permission. ment, and includes assessments of the probable flotation, separation techniques, catalysis, mass Covers modern characterization methods for soft effect of these behaviors on the whole organism. transfer, emulsions, foams, aerosols, membranes, materials (polymers, complex fluids, biomaterials). Quantitative models of gene translation and intra- biological surfactant systems, microbial surfaces, Techniques include diffential scanning calorimetry, cellular signal transduction will be used to illustrate enhanced oil recovery, and pollution problems. dynamic light scattering, gel permeation chroma- switching of intracellular processes, transient and Appropriate individual experiments and projects. tography, rheology, and spectroscopic methods. permanent gene activation, and cell commitment, Team taught by several faculty and open to development, and death. graduate and advanced undergraduate students (limit 15).

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CHEN E6620y Physical chemistry of papers and textbook materials providing tions. No more than 15 points of credit toward the 91 macromolecules overviews to various biological areas including degree may be granted when the dissertation is Lect: 3. 3 pts. Professors Durning and Koberstein. evolution, immune system, development and cell accepted by the department. Modern studies of static and dynamic behavior in specialization, the cytoskeleton and cell motility, macromolecular systems. Topics include single- DNA transcription in gene circuits, protein net- CHEN E9600x and y Advanced research chain behavior adsorption, solution thermodynam- works, recombinant DNA technology, aging, and problems ics, the glass transition, diffusion, and viscoelastic gene therapy. 2 to 10 pts. The staff. behavior. The molecular understanding of experi- Prerequisites: Recommendation of the professor mentally observed phenomena is stressed. CHEN E9000x and y Chemical engineering concerned and approval of the master’s research colloquium department. For postdoctoral students and other CHEN E6920y Physics of soft matter Col: 1. 0 pts. The staff. qualified special students who wish to pursue Lect: 2. 3 pts. Not given in 2008–2009. All graduate students are required to attend the research under the guidance of members of the Prerequisite: The instructor’s permission. Physics department colloquium as long as they are in department. Not open to undergraduates or to of polymers, biopolymers (especially DNA), residence. No degree credit is granted. candidates for the degrees of Ch.E., M.S., Ph.D., membranes, gels, and other types of soft matter. or Eng.Sc.D. Statistical mechanics, scaling theory, self-consis- CHEN E9400x and y Master’s research tent field theory; experimental surveys. Dilute, 1 to 6 pts. The staff. CHEN E9800x and y, and s Doctoral research semidilute, and concentrated polymer solutions. Prescribed for M.S. and Ch.E. candidates; elec- instruction Mesophases and self-assembly in soft matter. tive for others with the approval of the depart- 3, 6, 9, or 12 pts. The staff. Polymers at interfaces, polymer-membrane ment. Degree candidates are required to conduct A candidate for the Eng.Sc.D. degree in chemical interactions. Fluctuating double helix models of an investigation of some problem in chemical engineering must register for 12 points of doctoral DNA, DNA melting, pattern recognition in DNA. engineering or applied chemistry and to submit research instruction. Registration in CHEN E9800 Polyelectrolytes, charged biopolymers, DNA a thesis describing the results of their work. No may not be used to satisfy the minimum residence charge-induced condensation. more than 6 points in this course may be counted requirement for the degree. for graduate credit, and this credit is contingent CHEN E8100y Topics in biology upon the submission of an acceptable thesis. CHEN E9900x and y, and s Doctoral Lect: 3. 3 pts. Professor O’Shaughnessy. The concentration in pharmaceutical engineering dissertation This research seminar introduces topics at the requires a 2-point thesis internship. 0 pts. The staff. forefront of biological research in a format and Open only to certified doctoral candidates. A can- language accessible to quantitative scientists and CHEN E9500x and y, and s Doctoral research didate for the doctorate in chemical engineering engineers lacking biological training. Conceptual 1 to 15 pts. The staff. may be required to register for this course in and technical frameworks from both biological Prerequisite: The qualifying examinations for the every term after the student’s course work has and physical science disciplines are utilized. The doctorate. Open only to certified candidates for been completed, and until the dissertation has objective is to reveal to graduate students where the Ph.D. and Eng.Sc.D. degrees. Doctoral candi- been accepted. potential lies to apply techniques from their own dates in chemical engineering are required to disciplines to address pertinent biological ques- make an original investigation of a problem in tions in their research. Classes entail reading, chemical engineering or applied chemistry, the criticism, and group discussion of research results of which are presented in their disserta-

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92 CIVIL ENGINEERING AND ENGINEERING MECHANICS 610 S.W. Mudd, MC 4709, 854-3143; [email protected] www.civil.columbia.edu

CHAIR PROFESSORS ASSOCIATE PROFESSORS ADJUNCT STAFF Robert Ratay Upmanu Lall Raimondo Betti Andrew Smyth William Becker Robert A. Rubin Bruno A. Boley Logan Brant Vincent Tirolo DEPARTMENTAL Patricia J. Culligan ASSISTANT PROFESSORS Aine M. Brazil Richard L. Tomasetti ADMINISTRATOR Gautam Dasgupta Nicola Chiara Julius Chang Pawel Woelke Elaine MacDonald George Deodatis John E. Taylor Eli B. Gottlieb Bojidar Yanev Morton B. Friedman Haim Waisman Bettina Gurpide Theodore P. Zoli Upmanu Lall Huiming Yin William M. Hart Earth and Environmental Wilfred Laufs STAFF ASSOCIATE Engineering LECTURER Samuel A. Leifer Adrian Brügger Hoe I. Ling Jose I. Sanchez Aly M. Mohammad Richard W. Longman Nasri Munfah INFORMATION Mechanical Engineering Robert D. Mutch TECHNOLOGY MANAGER Christian Meyer Mysore Nagaraja Jon A. Van Feniosky Peña-Mora Reza Nikain Rene B. Testa Gary F. Panariello Tom Papachristos Thomas Panayotidi Daniel Peterson

he Department of Civil Engineer- MISSION tutive equations for geologic materials, ing and Engineering Mechanics The Department aims to provide students failure of materials and components, T focuses on two broad areas of with a technical foundation anchored in properties of fiber-reinforced cement instruction and research. The first, the theory together with the breadth needed composites, damage mechanics. classical field of civil engineering, deals to follow diverse career paths, whether • Multihazard risk assessment and miti- with the planning, design, construction, in the profession via advanced study or gation: integrated risk studies of the and maintenance of the built environ- apprenticeship, or as a base for other civil infrastructure form a multihazard ment. This includes buildings, founda- pursuits. perspective including earthquake, tions, bridges, transportation facilities, wind, flooding, fire, blast, and terror- nuclear and conventional power plants, Current Research Activities ism. The engineering, social, financial, hydraulic structures, and other facilities Current research activities in the and decision-making perspectives of essential to society. The second is the Department of Civil Engineering and the problem are examined in an inte- science of mechanics and its applica- Engineering Mechanics are centered in grated manner. tions to various engineering disciplines. the areas outlined below. A number of • Probabilistic mechanics: random Frequently referred to as applied these activities impact directly on prob- processes and fields to model uncertain mechanics, it includes the study of the lems of societal importance, such as loads and material/soil properties, non- mechanical and other properties of mate- rehabilitation of the infrastructure, miti- linear random vibrations, reliability and rials, stress analysis of stationary and gation of natural or man-made disas- safety of structural systems, computa- movable structures, the dynamics and ters, and environmental concerns. tional stochastic mechanics, stochastic vibrations of complex structures, aero- finite element and boundary element Solid mechanics: mechanical proper- and hydrodynamics, and the mechanics techniques, Monte Carlo simulation ties of new and exotic materials, consti- of biological systems. techniques, random micromechanics.

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93

• Structural control and health monitor- fiber-reinforced cement composites, department are in the S. W. Mudd ing: topics of research in this highly utilization of industrial by-products Building and the Engineering Terrace. cross-disciplinary field include the and waste materials, beneficiation of development of “smart” systems for dredged material. Computing the mitigation and reduction of struc- Earthquake engineering: response of The department manages a substantial tural vibrations, assessment of the structures to seismic loading, seismic computing facility of its own in addition health of structural systems based on risk analysis, active and passive control to being networked to all the systems their vibration response signatures, of structures subject to earthquake operated by the University. The depart- and the modeling of nonlinear sys- excitation, seismic analysis of long-span ment facility enables its users to perform tems based on measured dynamic cable-supported bridges. symbolic and numeric computation, behavior. three-dimensional graphics, and expert Flight structures: aeroelasticity, aeroa- Fluid mechanics: solid-laden turbulent systems development. Connections to coustics, active vibration and noise con- flows, porous surface turbulence, flow wide-area networks allow the facility’s trol, smart structures, noise transmission through porous media, numerical simu- users to communicate with centers into aircraft, and vibro-acoustics of lation of flow and transport processes, throughout the world. All faculty and stu- space structures. flow and transport in fractured rock. dent offices and department laboratories Construction engineering and man- are hardwired to the computing facility, Environmental engineering/water agement: contracting strategies; alter- which is also accessible remotely to resources: modeling of flow and pollu- native project delivery systems, such as users. Numerous personal computers tant transport in surface and subsurface design-build, design-build-operate, and and graphics terminals exist throughout waters, unsaturated zone hydrology, design-build-finance-operate; minimizing the department, and a PC lab is avail- geoenvironmental containment systems, project delays and disputes; advanced able to students in the department in analysis of watershed flows including technologies to enhance productivity addition to the larger school-wide facility. reservoir simulation. and efficiency; strategic decisions in Structures: dynamics, stability, and global engineering and construction Laboratories design of structures, structural failure markets. The Robert A. W. Carleton Strength of and damage detection, fluid and soil Materials Laboratory is a very large facil- Infrastructure delivery and manage- structure interaction, ocean structures ity equipped for research into all types ment: decision support systems for subjected to wind-induced waves, of engineering materials and structural infrastructure asset management; inelastic dynamic response of reinforced elements. The Heffner Laboratory for assessing and managing infrastructure concrete structures, earthquake-resist- Hydrologic Research is a newly estab- assets and systems; capital budgeting ant design of structures. lished facility for both undergraduate processes and decisions; innovative instruction and research in all aspects of Geotechnical engineering: soil behav- financing methods; procurement strate- fluid mechanics and its applications. The ior, constitutive modeling, reinforced soil gies and processes; data management Eugene Mindlin Laboratory for Structural structures, geotechnical earthquake practices and systems; indicators of Deterioration Research is a teaching and engineering, liquefaction and numerical infrastructure performance and service. research facility dedicated to all facets analysis of geotechnical systems. of the assessment of structures and the Structural materials: cement-based FACILITIES processes of deterioration of structural materials, micro- and macro-models of The offices and laboratories of the performance. The concrete laboratory is

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94 CIVIL ENGINEERING PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

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

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

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

MECHANICS ENME-MECE E3105 (4) either semester

CIEN E3004 (3) CIVIL ENGINEERING CIEN E1201 (3) or equivalent Urban infra. systems

ENGLISH C1010 (3) COMPOSITION Z1003 (0) C1010 (3) (three tracks, choose one) Z0006 (0) Z1003 (0) C1010 (3)

HUMA C1001, C0CI C1101, HUMA C1002, C0CI C1102, REQUIRED or Global Core (3–4) or Global Core (3–4) NONTECHNICAL ELECTIVES HUMA W1121 or ECON W1105 (4) and W1123 (3) W1155 recitation (0)

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

PHYSICAL C1001 (1) C1002 (1) EDUCATION

GATEWAY LAB E1102 (4) either semester

1EAEE is recommended for students concentrating in environmental engineering and water resources.

equipped to perform a wide spectrum of Center for Infrastructure Studies intended to prepare students with firm experimental research in cement-based The Center was established in the technical bases while nurturing decision- materials. The Donald M. Burmister Soil department to provide a professional making and leadership potential. Mechanics Laboratory is used in both environment for faculty and students The civil engineering program is undergraduate and graduate instruction from a variety of disciplines to join with designed to enable the student, upon for static and dynamic testing of soils and industry and government to develop and completion of the B.S. degree program, foundations. The geotechnical centrifuge apply the technological tools and knowl- to enter the profession—for example, in located in the Carleton Laboratory is edge bases needed to deal with the industry, on a construction project, in a used for geotechnical and geoenviron- massive problems of the city, state, and consulting engineering office, through a mental research. regional infrastructure. The Center is government agency—or to begin gradu- active in major infrastructure projects ate study, or both. The program is fully The Institute of Flight Structures through a consortium of universities and accredited by the Engineering Accredita- The Institute of Flight Structures was agencies. tion Commission (EAC) of the Accredita- established within the department tion Board for Engineering and Technology (ABET) and provides a broad traditional through a grant by the Daniel and Florence UNDERGRADUATE PROGRAMS Guggenheim Foundation. It provides a civil engineering background that focuses The Department of Civil Engineering and base for graduate training in aerospace on basic theory and design. Technical Engineering Mechanics offers under- and aeronautical related applications of electives can be selected to obtain a graduate programs in civil engineering structural analysis and design. strong technical base in a particular field and engineering mechanics. Both are

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95 CIVIL ENGINEERING: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

ENME E3113 (3) CIEN E3125 (3) CIEN E4111 (3) Mech. of solids Structural design Uncertainty & risk in infrastructure systems ENME E3161 (4) CIEN E3126 (1) CORE REQUIRED Fluid mech. Computer-aided CIEN E3129 (3) COURSES struct. design Proj. mgmt. for construction

CIEN E3141 (4) Soil mech.

ENME E3106 (3) ENME E3114 (4) CIEN E4332 (3) CIEN E3128 (4) Dynamics & vibrations Exper. mech. of materials Finite element anal. Design projects GEOTECH ENG. (GE) CIEN E3121 (3) CIEN E3127 (3) OR Struct. anal. Struct. design projects (SE) STRUCT. ENG. (SE) or CIEN E4241 (3) Geotech. eng. fund. (GE)

TECH 3 points 3 points 12 points ELECTIVES

ENME E3114 (4) CIEN E4133 (3) CIEN E4131 (3) Exper. mech. of materials Capital facility planning Princ. of constr. tech. & financing CIVIL ENG. & CIEN E3121 (3) CIEN E3128 (4) CONSTR. Struct. anal. CIEN E3127 (3) or Design projects MNGMT. or CIEN E4241 (3) CIEE E3250 (3) Hydrosystems eng.

TECH CONCENTRATIONS ELECTIVES 6 points 3 points 9 points

CIEE E3255 (3) CIEN E4163 (3) CIEN E4250 (3) Environ. control / pollution Environ. eng. Waste containm. wastewater design & practice CIEE E3250 (3) or WATER RES./ Hydrosystems eng. CIEE E4260 (4) CIEN E4257 (3) ENVIRON. Urban ecology studio contam. transport ENG. CIEN E3303 (1) in subsurface sys. Independent studies EAEE E4006 (3) Field methods for environ. eng.

TECH 6 points 3 points 9 points ELECTIVES

NONTECH ELECTIVES 3 points 3 points

15 16 TOTAL POINTS 16 17 (water res./environ. eng. 16) (water res./environ. eng. 15)

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96 ENGINEERING MECHANICS PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

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

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

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

MECHANICS ENME-MECE E3105 (4) any semester

ENGLISH C1010 (3) COMPOSITION Z1003 (0) C1010 (3) (three tracks, choose one) Z0006 (0) Z1003 (0) C1010 (3)

HUMA C1001, C0CI C1101, HUMA C1002, C0CI C1102 REQUIRED or Global Core (3–4) or Global Core (3–4) NONTECHNICAL ELECTIVES HUMA W1121 or ECON W1105 (4) and W1123 (3) W1155 recitation (0)

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

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

PHYSICAL C1001 (1) C1002 (1) EDUCATION

GATEWAY LAB E1102 (4) either semester

of civil engineering or other engineering sciences that underlie all technological 4.To provide a basis for effective writing disciplines. development so our graduates will be and communication as well as a back- The engineering mechanics program well equipped to adapt to changing ground to foster awareness of societal provides a strong analytical background technology in the profession. issues. in mechanics for students planning to 2.To provide the broad and fundamental continue on to graduate school and to technical base needed by graduates Engineering Mechanics pursue research. Admission to the engi- who will enter the profession through The prerequisites for this program are neering mechanics program requires a the increasingly common path of a the courses listed in the First Year– grade point average of B or better and specialized M.S., but also provide suit- Sophomore Program, or their equiva- maintenance of performance while in the able preparation to those who choose lents, with the provision that ENME program. to enter the professional workforce E3105: Mechanics be taken in the soph- with a B.S. to develop specialized omore year and that the student have Program Objectives expertise by way of apprenticeship. obtained a grade of B or better. In developing and continually updating 3.To provide the breadth and choices in our program to achieve the stated our programs that can accommodate Civil Engineering mission of the Department, we seek and foster not only students with The prerequisites for this program are to achieve the following objectives: differing technical objectives, but also the courses listed in the First Year– those who will use their technical back- 1.To provide a firm foundation in the Sophomore Program or their equiva- ground to follow other career paths. basic math, science, and engineering lents. The civil engineering program

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97 ENGINEERING MECHANICS: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

ENME E3113 (3) ENME E3114 (4) CIEN E4332 (3) ENME E4202 (3) Mech. of solids Experimental mech. Finite element Advanced mech.

ENME E3161 (4) CIEN E3121 (3) ENME E4113 (3) Fluid mechanics Structural analysis Advanced solids REQUIRED COURSES APMA E3101 (3) APMA E3102 (3) ENME E4215 (3) Applied math. I Applied math. II Theory of vibrations

ENME E3106 (3) Dynamics & vibrations

TECH 3 points 6 points 6 points 9 points

NONTECH 3 points 3 points ELECTIVES

TOTAL POINTS 16 16 18 15

offers three areas of concentration: Engineering Science (Eng.Sc.D.) and and financing, strategic management, civil engineering and construction Doctor of Philosophy (Ph.D.). These managing engineering and construc- management, geotechnical engineering programs are flexible and may involve tion processes, construction industry or structural engineering, and water concentrations in structures, construc- law, construction techniques, manag- resources/environmental engineering. tion engineering, reliability and random ing civil infrastructure systems, civil An optional minor can be selected in processes, soil mechanics, fluid engineering and construction entre- architecture, education, economics, mechanics, hydrogeology, continuum preneurship and any of the engineering departments mechanics, finite element methods, • Environmental engineering and in the School. In the junior and senior computational mechanics, experimental water resources: transport of water- years, 18 credits of technical electives mechanics, vibrations and dynamics, borne substances, hydrology, sedi- are allocated. earthquake engineering, or any combi- ment transport, hydrogeology, and The department offers a first-year nation thereof, such as fluid-structure geoenvironmental design of contain- design course, CIEN E1201: The art of interaction. The Graduate Record ment systems structural design, which all students are Examination (GRE) is required for required to take in the spring semester admission to the department. Engineering Mechanics of the first year or later. An equivalent Programs in engineering mechanics offer course could be substituted for E1201. Civil Engineering comprehensive training in the principles By selecting technical electives, students of applied mathematics and continuum Minor in Architecture may focus on one of several areas of mechanics and in the application of Civil engineering program students may concentration or prepare for future these principles to the solution of engi- want to consider a minor in architecture endeavors such as architecture. Some neering problems. The emphasis is on (see page 189). typical concentrations are: basic principles, enabling students to • Structural engineering: applications choose from among a wide range of GRADUATE PROGRAMS to steel and concrete buildings, technical areas. Students may work on problems in such disciplines as systems The Department of Civil Engineering and bridges, and other structures analysis, acoustics, and stress analysis, Engineering Mechanics offers graduate • Geotechnical engineering: soil and in fields as diverse as transporta- programs leading to the degree of Master mechanics, engineering geology, tion, environmental, structural, nuclear, of Science (M.S.), the professional and foundation engineering and aerospace engineering. Program degrees Civil Engineer and Mechanics • Construction engineering and areas include: Engineer and the degrees of Doctor of management: capital facility planning

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98 • Continuum mechanics: solid and unique aesthetic/artistic perspectives inherent in engineering, water resourses/environmental engi- fluid mechanics, theories of elastic structural design. Consideration of management, neering, structural engineering, and construction and inelastic behavior, and damage socioeconomic, and ethical issues involved in the engineering and management. design and construction of large-scale structures. mechanics Introduction to some recent developments in sus- CIEN E3129x Project management for • Vibrations: nonlinear and random vib- tainable engineering, including green building construction rations; dynamics of continuous media, design and adaptable structural systems. Lect: 3. 3 pts. Professor Taylor. of structures and rigid bodies, and of Prerequisite: Senior standing in civil engineering combined systems, such as fluid- CIEN E3004y Urban infrastructure systems or permission of the instructor. Introduction to structure interaction; active, passive, Lect: 3. 3 pts. Professor Chiara. project management for design and construction and hybrid control systems for struc- Introduction to (a) the infrastructure systems that processes. Elements of planning, estimating, tures under seismic loading; dynamic support urban socioeconomic activities and (b) scheduling, bidding, and contractual relationships. fundamental system design and analysis methods. Computer scheduling and cost control. Critical soil-structure interaction effects on the Coverage of water resources, vertical, transporta- path method. Design and construction activities. seismic response of structures tion, communications and energy infrastructure. Field supervision. • Random processes and reliability: Emphasis upon the purposes that these systems problems in design against failure serve, the factors that influence their performance, CIEN E3141y Soil mechanics under earthquake, wind, and wave the basic mechanics that govern their design and Lect: 3. Lab: 3. 4 pts. Professor Ling. loadings; noise, and turbulent flows; operation, and the impacts that they have region- Prerequisite: ENME E3113. Index properties analysis of structures with random ally and globally. Student teams complete a and classification; compaction; permeability and semester-long design/analysis project with equal properties seepage; effective stress and stress distribution; emphasis given to water resources/environmental consolidation; shear strength of soil; consolidation; • Fluid mechanics: turbulent flows, engineering, geotechnical engineering, and con- slope stability.. two-phase flows, fluid-structure inter- struction engineering and management topics. action, fluid-soil interaction, flow in CIEE E3250y Hydrosystems engineering porous media, computational methods CIEN E3121y Structural analysis Lect: 3. 3 pts. Professor Gong. for flow and transport processes, and Lect: 3. 3 pts. Professor Deodatis. Prerequisite(s): CHEN E3110 or ENME E3161 flow and transport in fractured rock Methods of structural analysis. Trusses, arches, or equivalent, SIEO W3600 or equivalent, or the under mechanical loading cables, frames; influence lines; deflections, force instructor's permission. A quantitative introduction method, displacement method, computer applica- • Computational mechanics: finite ele- to hydrologic and hydraulic systems, with a focus tions. on integrated modeling and analysis of the water ment and boundary element tech- cycle and associated mass transport for water niques, symbolic computation, and CIEN E3125y Structural design resources and environmental engineering. bioengineering applications Lect: 3. 3 pts. Professor Betti. Coverage of unit hydrologic processes such as Prerequisite: ENME E3113. Design criteria for precipitation, evaporation, infiltration, runoff gen- A flight structures program is varied structural applications, including buildings eration, open channel and pipe flow, subsurface designed to meet the needs of industry and bridges; design of elements using steel, flow and well hydraulics in the context of example in the fields of high-speed and space concrete, masonry, wood, and other materials. watersheds and specific integrative problems flight. The emphasis is on mechanics, such as risk-based design for flood control, provi- mathematics, fluid dynamics, flight CIEN E3126y Computer-aided structural design sion of water, and assessment of environmental structures, and control. The program is Lect: 1. Lab: 1. 1 pt. Professor Betti. impact or potential for non-point source pollution. a part of the Guggenheim Institute of Corequisite: CIEN E3125y. Introduction to soft- Spatial hydrologic analysis using GIS andwater- shed models. Note: This course is to be joint listed Flight Struct-ures in the department. ware for structural analysis and design with lab. Applications to the design of structural elements with CIEN, and replaces the previous CIEN 3250. Specific information regarding degree and connections. Lab required. requirements is available in the depart- CIEE E3255y Environmental control and pollu- ment office. CIEN E3127x Structural design projects tion reduction systems Lect: 3. 3 pts. Professor Meyer. Lect: 3. 3 pts. Professor Castaldi. Prerequisites: CIEN E3125 and E3126 or the Prerequisite: ENME E3161 or MECE E3100. COURSES IN CIVIL instructor’s permission. Design projects with Review of engineered systems for prevention and ENGINEERING (CIEN) various structural systems and materials. control of pollution. Fundamentals of material and See also Engineering Mechanics energy balances and reaction kinetics. Analysis of (ENME), at the end of this section. CIEN E3128y Design projects engineered systems to address environmental Lect: 4. 4 pts. Professor Meyer. problems, including solid and hazardous waste, CIEN E1201y The art of structural design Prerequisite: CIEN E3125 and CIEN E3126. and air, water, soil, and noise pollution. Life cycle Lect: 3. 3 pts. Professor Deodatis. Capstone design project in civil engineering. This assessments and emerging technologies. Introduction to the basic scientific and engineering project integrates structural, geotechnical, and principles used for the design of buildings, bridges, environmental/water resources design problems CIEN E3260y Engineering for developing and other parts of the built infrastructure. Application with construction management tasks and sustain- communities of these principles to the analysis and design of a ability, legal, and other social issues. The project Lect. 3. 3 pts. Professor Culligan. number of actual large-scale structures. Experimental is completed in teams, and communication skills Introduction to engineering problems faced by verification of these principles through laboratory are stressed. Outside lecturers will address developing communities and exploration of design experiments. Coverage of the history of major important current issues in engineering practice. solutions in the context of a real project with a structural design innovations and of the engineers Every student in the course will be exposed with community client. Emphasis is on the design of who introduced them. Critical examination of the equal emphasis to issues related to geotechnical sustainable solutions that take account of social,

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economical, and governance issues and that can CIEN E4111x Uncertainty and risk in emphasis upon civil infrastructure systems. Project 99 be implemented now or in the near future. This infrastructure systems feasibility and evaluation. Design of project delivery course is open to all undergraduate engineering Lect: 3. 3 pts. Professor Smyth. systems to encourage best value, innovation, and students. Multidisciplinary teamwork and Prerequisites: Working knowledge of calculus. private sector participation. Fundamentals of engi- approaches are stressed. Outside lecturers Introduction to basic probability; hazard function; neering economy and project finance. Elements of address issues specific to developing communities reliability function; stochastic models of natural life-cycle cost estimation and decision analysis. and the particular project under consideration. and technological hazards; extreme value distri- Environmental, institutional, social, and political butions; Monte Carlo simulation techniques; fun- factors. Case studies from transportation, water CIEN E3303x and y Independent studies in damentals of integrated risk assessment and risk supply, and wastewater treatment. civil engineering for juniors management; topics in risk-based insurance; 1–3 pts. By conference. The faculty. case studies involving civil infrastructure systems, CIEN E4134y Construction industry law A project on civil engineering subjects approved environmental systems, mechanical and aerospace Lect. 3. 3 pts. Professors Rubin and Quintas. by the chairman of the department. Lab fee: $200. systems, construction management. Prerequisite: Graduate standing or the instructor’s permission. Practical focus upon legal concepts CIEN E3304x and y Independent studies in CIEN E4129x and y Managing engineering and applicable to the construction industry. Provides civil engineering for seniors construction processes sufficient understanding to manage legal aspects, 1–3 pts. By conference. The faculty. Lect: 3. 3 pts. Professor Nagaraja. instead of being managed by them. Topics A project on civil engineering subjects approved Prerequisite: Senior standing in civil engineering include contractual relationships, contract per- by the chairman of the department. Lab fee: $200. or the instructor’s permission. Introduction to the formance, contract flexibility and change orders, principles, methods, and tools necessary to man- liability and negligence, dispute avoidance/resolu- CIEN E4010y Transportation engineering age design and construction processes. Elements tion, surety bonds, insurance, and site safety. Lect: 3. 3 pts. Professor Peterson. of planning, estimating, scheduling, bidding, and Comprehensive multidisciplinary course in engineer- contractual relationships. Valuation of project CIEN E4135y Strategic management in global ing and planning design principles applied to under- cash flows. Critical path method. Survey of con- design and construction standing major transportation systems, from people struction procedures. Cost control and effective- Lect. 3. 3 pts. Professor Taylor. to planes. Fundamentals of pedestrian, road, rail, ness. Field supervision. Core concepts of strategic planning, manage- aviation and marine planning, designing, financing, ment, and analysis within the global design and legislating, and analyzing. Engineering principles of CIEN E4130x Design of construction systems construction industry. Global industry analysis, human control, vehicles, feedback control and signal Lect: 3. 3 pts. Professor Tirolo. strategic planning models, industry trends, and systems, lane systems, energy, goods movement, net- Prerequisite: CIEN E 3125 or the equivalent, or project network dynamics. Strategies for informa- works, and parking. Novel system design presentation. the instructor’s permission. Introduction to the tion technology, emerging markets, and globaliza- design of systems that support construction activi- tion. Case studies to demonstrate key concepts CIEN E4021x Elastic and plastic analysis ties and operations. Determination of design loads in real-world environments. of structures during construction. Design of excavation support Lect: 3. 3 pts. Professor Meyer. systems, earth retaining systems, temporary sup- CIEN 4136y Global entrepreneurship in civil Prerequisite: CIEN E3121 or the equivalent. ports and underpinning, concrete formwork and engineering Overview of classical indeterminate structural shoring systems. Cranes and erection systems. Lect: 3. 3 pts. Not given in 2009–2010. analysis methods (force and displacement meth- Tunneling systems. Instrumentation and monitor- Capstone practicum where teams develop busi- ods), approximate methods of analysis, plastic ing. Students prepare and present term projects. ness plans for a new enterprise serving the global analysis methods, collapse analysis, shakedown architecture, engineering, and construction industry. theorem, structural optimization. CIEN E4131x and y Principles of construction The innovation process; identification of attractive techniques entrepreneurial opportunities and global market CIEN E4022y Bridge design and management Lect: 3. 3 pts. Professors Hart and Papachristos. segments; development of an entry strategy; Lect: 3. 3 pts. Professor Yanev. Prerequisite: CIEN E4129 or the equivalent. product/service development planning; acquisition Prerequisite: CIEN E3125 or the equivalent. Current methods of construction, cost-effective of financing; protecting intellectual property; group Bridge design history, methods of analysis, loads: designs, maintenance, safe work environment. dynamics and organizational design; plans for static, live, dynamic. Design: allowable stress, Design functions, constructability, site and envi- recruiting and retaining personnel; personnel ultimate strength, load resistance factor, supply/ ronmental issues. compensation/incentives. Invited industry speakers. demand. Steel and concrete superstructures: suspension, cable-stayed, prestressed, arches. CIEN E4132y Prevention and resolution CIEN E4163x Environmental engineering: Management of the assets, life-cycle cost, of construction disputes wastewater expected useful life, inspection, maintenance, Lect: 3. 3 pts. Professor Nikain. Lect: 3. 3 pts. Professor Becker. repair, reconstruction. Bridge inventories, condi- Prerequisite: CIEN E4129 or the equivalent. Prerequisites: Introductory chemistry (with labora- tion assessments, data acquisition and analysis, Contractual relationships in the engineering and tory) and fluid mechanics. Fundamentals of water forecasts. Selected case histories and field visits. construction industry and the actions that result pollution and wastewater characteristics. Chemistry, in disputes. Emphasis on procedures required to microbiology, and reaction kinetics. Design of pri- CIEN E4100y Earthquake and wind engineering prevent disputes and resolve them quickly and mary, secondary, and advanced treatment sys- Lect: 3. 3 pts. Professor Smyth. cost-effectively. Case studies requiring oral and tems. Small community and residential systems. Prerequisite: ENME E3106 or the equivalent. written presentations. Basic concepts of seismology. Earthquake CIEN E4210x Forensic structural engineering characteristics, magnitude, response spectrum, CIEN E4133x Capital facility planning and Lect: 3. 3 pts. Professor Ratay. dynamic response of structures to ground motion. financing Prerequisite: CIEN E3125 or the equivalent. Base isolation and earthquake-resistant design. Lect: 3. 3 pts. Professor Chang. Review of significant failures, civil/structural engi- Wind loads and aeroelastic instabilities. Extreme Prerequisite: CIEN E4129 or the equivalent. Planning neering design and construction practices, ethical winds. Wind effects on structures and gust factors. and financing of capital facilities with a strong standards and the legal positions as necessary

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100 background to forensic engineering. Discussion CIEN E4234y Design of large-scale building CIEN 4245x Tunnel design and construction of standard-of-care. Study of the process of engi- structures Lect: 3. 3 pts. Professor Munfah. neering evaluation of structural defects and fail- Lect: 3. 3 pts. Professors Tomasetti, Brazil, This course covers the engineering design and ures in construction and in service. Examination Panariello, and Gottlieb. construction of different types of tunnel, including of the roles, activities, conduct, and ethics of the Prerequisites: CIEN E3121 and CIEN E3127. cut and cover tunnel, rock tunnel, soft ground forensic consultant and expert witness. Students Modern challenges in the design of large-scale tunnel, immersed tube tunnel, and jacked tunnel. are assigned projects of actual cases of nonper- building structures will be studied. Tall buildings, The design for the liner, excavation, and instru- formance or failure of steel, concrete, masonry, large convention centers, and major sports mentation are also covered. A field trip will be geotechnical and temporary structures, in order to stadiums present major opportunities for creative arranged to visit the tunneling site. perform, discuss, and report their own investiga- solutions and leadership on the part of engineers. tions under the guidance of the instructor. This course is designed to expose the students CIEN E4246y Earth retaining structures to this environment by having them undertake the Lect: 3. 3 pts. Professor Leifer. CIEN E4212x Structural assessment and failure complete design of a large structure from initial Prerequisite: CIEN E3141. Retaining structures, Lect: 3. 3 pts. Not given in 2009–2010. design concepts on through all the major design bulkheads, cellular cofferdams, and braced exca- Prerequisites: ENME E3113 and CIEN E3121. decisions. The students work as members of a vations. Construction dewatering and underpinning. Laboratory and field test methods in assessment design team to overcome the challenges inherent Instrumentation to monitor actual performances. of structures for rehabilitation and to determine in major projects. Topics include overview of major Ground improvement techniques, including earth causes of failure; ASTM and other applicable projects, project criteria, and interface with archi- reinforcement, geotextiles, and grouting. To alter- standards; case histories of failures and rehabili- tecture, design of foundations and structural sys- nate with CIEN E4243. tation in wood, steel, masonry, and concrete tems, design challenges in the post 9/11 environ- structures. ment and roles, responsibilities, and legal issues. CIEE E4252x Environmental engineering Lect: 3. 3 pts. Professor Gong. CIEN E4213x Elastic and inelastic buckling CIEN E4241x Geotechnical engineering Prerequisites: CHEM C1403, or the equivalent; of structures fundamentals ENME E3161 or the equivalent. Engineering Lect: 3. 3 pts. Professor Laufs. Lect: 3. 3 pts. Professor Mohammad. aspects of problems involving human interaction Stability of framed structures in the elastic and Prerequisite: CIEN E3141 or the instructor’s with the natural environment. Review of funda- inelastic ranges. Lateral buckling of beams. permission. Bearing capacity and settlement of mental principles that underlie the discipline of Torsional buckling of compression members. shallow and deep foundations; earth pressure environmental engineering, i.e., constituent trans- Buckling of plates of plate-stiffener combinations. theories; retaining walls and reinforced soil retain- port and transformation processes in environmen- Linear stability analysis of cylindrical shells and ing walls; sheet pile walls; braced excavation; tal media such as water, air, and ecosystems. discussion of its limitations. Discussion of the slope stability. Engineering applications for addressing environ- semi-empirical nature of the elastoplastic relations mental problems such as water quality and treat- used in the case of plates and shells. CIEN E4242x Geotechnical earthquake ment, air pollutant emissions, and hazardous engineering waste remediation. Presented in the context of CIEN E4226y Advanced design of steel Lect: 3. 3 pts. Professor LIng. current issues facing practicing engineers and structures Prerequisite: CIEN E3141 or the equivalent. government agencies, including legal and regula- Lect: 3. 3 pts. Professor Woelke. Seismicity, earthquake intensity, propagation of tory framework, environmental impact assess- Prerequisite: CIEN E3125 or the equivalent. seismic waves, design of earthquake motion, ments, and natural resource management. Review of loads and structural design approach- seismic site response analysis, in situ and labora- es. Material considerations in structural steel tory evaluation of dynamic soil properties, seismic CIEN E4253x Finite elements in geotechnical design. Behavior and design of rolled steel, welded, performance of underground structures, seismic engineering cold-formed light-gauge, and composite concrete/ performance of port and harbor facilities, evaluation Lect: 3. 3 pts. Professor Ling. steel members. Design of multi-story buildings and mitigation of soil liquefaction and its conse- Prerequisites: CIEN E3141 and CIEN E4332. and space structures. quences. Seismic earth pressures, slope stability, State-of-the-art computer solutions in geotechni- safety of dams and embankments, seismic code cal engineering; 3-D consolidation, seepage CIEN E4232y Advanced design of concrete provisions and practice. To alternate with E4244. flows, and soil-structure interaction; element and structures mesh instabilities. To be offered in alternate years Lect: 3. 3 pts. Professor Panayotidi. CIEN E4243x Foundation engineering with CIEN E4254. Prerequisite: CIEN E3125 or the equivalent. Lect: 3. 3 pts. Professor Brant. Design of concrete slabs, deep beams, walls, Prerequisite: CIEN E3141 or the equivalent. CIEN E4257y Contaminant transport in and other plane structures; introduction to design Conventional types of foundations and foundation subsurface systems of prestressed concrete structures. problems: subsurface exploration and testing. Lect: 3. 3 pts. Professor Mutch. Performance of shallow and deep foundations Prerequisite: CIEE E3250 or the equivalent. CIEN E4233x Design of large-scale bridges and evaluation by field measurements. Case his- Single and multiple phase transport in porous Lect: 3. 3 pts. Professor Zoli. tories to illustrate typical design and construction media; contaminant transport in variably saturated Prerequisites: CIEN E3121 or the equivalent and problems. To alternate with CIEN E4246. heterogeneous geologic media; physically based CIEN E3127 or the equivalent. Design of large- numerical models of such processes. scale and complex bridges, with emphasis on CIEN E4244y Geosynthetics and waste cable-supported structures. Static and dynamic containment CIEE E4260x Urban ecology studio loads, component design of towers, superstruc- Lect: 3. 3 pts. Professor Brant. Lect: 3. Lab: 3. 4 pts. Professor Culligan. tures, and cables; conceptual design of major Prerequisite: CIEN E4241 or the equivalent. Prerequisite: Senior standing or the instructor’s bridge types, including arches, cable-stayed Properties of geosynthetics. Geosynthetic design permission. Joint studio run with the Graduate bridges, and suspension bridges. for soil reinforcement. Geosynthetic applications School of Architecture, Planning and Preservation in solid waste containment system. To alternate (GSAPP) that explores solutions to problems of with CIEN E4242. urban density. Engineering and GSAPP students

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will engage in a joint project that addresses habit- CIEN E6248x Experimental soil mechanics CIEN E9900x and y, and s Doctoral dissertation 101 ability and sustainability issues in an urban envi- Lect: 2.5. 3 pts. Not given in 2009–2010. The staff. ronment and also provides community service. Prerequisite: CIEN E3141. Advanced soil testing, A candidate for the doctorate may be required Emphasis will be on the integration of science, including triaxial and plane strain compression to register for this course every term after the engineering, and design within a social context. tests; small-strain measurement. Model testing; student’s course work has been completed and Interdisciplinary approaches and communication application (of test results) to design. until the dissertation has been accepted. will be stressed. The studio can be used as a replacement for the capstone design project in CIEN E9101x and y, and s Civil engineering CEEM water resources/environmental engineer- research COURSES IN ENGINEERING ing concentration, or the undergraduate design 1 to 4 pts. By conference. The faculty. MECHANICS project in Earth and Environmental Engineering. Advanced study in a specialized field under the See also Civil Engineering. supervision of a member of the department staff. CIEN E6131x Quantitative infrastructure risk Before registering, the student must submit an ENME-MECE E3105x or y Mechanics management outline of the proposed work for approval of the Lect: 4. 4 pts. Professors Betti and Hone. Lect: 3. 3 pts. Professor Chiara. supervisor and the department chair. Prerequisites: PHYS C1402 and MATH V1101- Prerequisite: IEOR E4003 or CIEN E4133, or the V1102 and V1201. Elements of statics; dynamics equivalent. Core concepts of risk analysis, risk CIEN E9120x and y, and s Independent of a particle and systems of particles; dynamics mitigation, and quantitative risk management studies in flight sciences of rigid bodies. applied to civil infrastructure systems. State of 3 pts. By conference. Professor Vaicaitis. art of simulation applied to infrastructure risk Prerequisite: The instructor’s permission. This ENME E3106x Dynamics and vibrations management during construction and operation. course is geared toward students interested in Lect: 2. 3 pts. Professor Smyth. Public Private Partnership (PPP) risk manage- flight sciences and flight structures. Topics related Prerequisite: MATH E1210. Corequisite: ENME ment: identification, quantification, mitigation of to aerodynamics, propulsion, noise, structural E3105. Kinematics of rigid bodies; momentum risks in transportation and energy PPP systems. dynamics, aeroelasticity, and structures may be and energy methods; vibrations of discrete and Risk management during construction using the selected for supervised study. A term paper will continuous systems; eigen-value problems; natu- envelop method. be required. ral frequencies and modes. Basics of computer simulation of dynamic problems using MATLAB CIEN 6132y Advanced systems and technolo- CIEN E9130x and y, and s Independent or Mathematica. gies for global project collaboration studies in construction Lect: 3. 3 pts. Professor Taylor. 3 pts. By conference. Professor Wilson. ENME E3113x Mechanics of solids Prerequisite: CIEN E4129 or the equivalent. Prerequisite: Department chair’s and instructor’s Lect: 3. 3 pts. Professor Yin. Systems and technologies that support collabora- permission. Independent study of engineering and Stress, stress resultants, equilibrium. tive work in global projects. Information technolo- construction industry problems. Topics related to Deformation. Material behavior in two dimensions. gies for design, visualization, project management, capital planning and financing, project manage- Thermal stresses. Problems in flexure and and collaboration in globally distributed networks of ment, contracting strategies and risk allocation, torsion, pressure vessels. Buckling. design, fabrication, and construction organizations, dispute mitigation and resolution, and infrastruc- including Web-based, parametric computer-aided ture assessment and management may be select- ENME E3114y Experimental mechanics of modeling, project organizational simulation, and ed for supervised study. A term paper is required. materials other emerging applications. Global team project Lect: 2. Lab: 3. 4 pts. Professor Yin. with students at collaborating universities abroad. CIEN E9165x and y, and s Independent Prerequisite: ENME E3113. Material behavior and studies in environmental engineering constitutive relations. Mechanical properties of CIEN E6133y Advanced construction and 4 pts. By conference. The faculty. metals and cement composites. Cement hydra- infrastructure risk management using reel Prerequisite: CIEN E4252 or the equivalent. tion. Modern construction materials. Experimental options Emphasizes a one-on-one study approach to investigation of material properties and behavior Lect: 3. 3 pts. Professor Chiara. specific environmental engineering problems. of structural elements, including fracture, fatigue, Prerequisite: CIEN E6131. Advanced concepts of Students develop papers or work on design prob- bending, torsion, and buckling. risk analysis and management applied to civil engi- lems pertaining to the treatment of solid and liquid neering systems. Identifying and valuing flexibility waste, contaminant migration, and monitoring and ENME E3161x Fluid mechanics in construction and operation. Tools to perform risk sampling programs for remediation design. Lect: 3. Lab: 3. 4 pts. Professor Waisman. analysis in flexible civil infrastructure systems. Prerequisites: ENME E3105 and ordinary differ- Valuation methods for real options. Risk flexibility CIEN E9201x and y, and s Civil engineering ential equations. Fluid statics. Fundamental prin- analysis: integrating real options analysis with reports ciples and concepts of flow analysis. Differential quantitative risk analysis. Applications to case 1 to 4 pts. By conference. The faculty. and finite control volume approach to flow analy- studies on construction management, life-cycle A project on some civil engineering subject sis. Dimensional analysis. Application of flow cost analysis for infrastructure assets, public- approved by the chairman. analysis: flow in pipes, external flow, flow in open private partnerships projects, real estate develop- channels. ments, and renewable energy infrastructure projects. CIEN E9800x and y, and s Doctoral research instruction ENME E4113x Advanced mechanics of solids CIEN E6246y Advanced soil mechanics 3, 6, 9, or 12 pts. The staff. Lect: 3. 3 pts. Professor Yin. Lect: 2.5. 3 pts. Not given in 2009–2010. A candidate for the Eng.Sc.D. degree in civil Stress and deformation formulation in two- and Prerequisite: CIEN E3141. Stress-dilatancy of “engineering must register for 12 points of doctoral three-dimensional solids; viscoelastic and plastic sand; failure criteria; critical state soil mechanics; research instruction. Registration in CIEN E9800 material in one and two dimensions. limit analysis; finite element method and case may not be used to satisfy the minimum residence histories of consolidation analysis. requirement for the degree.

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102 ENME E4114y Mechanics of fracture and ENME E6220x Random processes in mechanics COURSES IN GRAPHICS fatigue Lect: 2.5. 3 pts. Professor Deodatis. Lect: 3. 3 pts. Professor Testa. Prerequisite: ENME E4215 or the equivalent. GRAP E1115x or y Engineering graphics Prerequisite: Undergraduate mechanics of solids Random variables, stationary and ergodic random Lect: 1. Lab: 3. 3 pts. Mr. Sanchez. course. Elastic stresses at a crack; energy and processes, correlation functions, and power Open to all students. Visualization and simulation stress intensity criteria for crack growth; effect of spectra. Input-output relations of linear systems: in virtual environments; computer graphics methods plastic zone at the crack; fracture testing applica- analysis of response of discrete and continuous for presentation of data. 3-D modeling; animation; tions. Fatigue characterization by stress-life and structures to random loadings. Crossing rates, rendering; image editing; technical drawing. Lab strain-life; damage index; crack propagation; fail peak distributions, and response analysis of fee: $300. safe and safe life analysis. nonlinear structures to random loading. Simulation of stationary random processes. GRAP E2005y Computer-aided engineering ENME E4202y Advanced mechanics graphics Lect: 3. 3 pts. Professor Dasgupta. ENME E6315x Theory of elasticity Lect: 1.5. Lab: 2.5. 3 pts. Not given in 2009–2010. Prerequisite: ENME E3105 or the equivalent. Lect: 2.5. 3 pts. Instructor to be announced. Prerequisite: MATH V1105. Basic concepts needed Differentiation of vector functions. Review of kine- Foundations of continuum mechanics. General to prepare and understand engineering drawings matics. Generalized coordinates and constraint theorems of elasticity. Application to stress analy- and computer-aided representations: preparation equations. Generalized forces. Lagrange’s equa- sis and wave propagation. of sketches and drawings, preparation and tions. Impulsive forces. Collisions. Hamiltonian. transmission of graphic information. Lectures Hamilton’s principle. ENME E6333y Finite element analysis, II and demonstrations, hands-on computer-aided Lect: 2.5. 3 pts. Professor Waisman. graphics laboratory work. Term project. ENME E4214y Theory of plates and shells Prerequisite: CIEN E4332 or the instructor’s Lect: 3. 3 pts. Professor Dasgupta. permission. Galerkin finite element formulation. GRAP E3115y Advanced computer modeling Prerequisite: ENME 3113. Static flexural response Convergence requirements. Element and mesh and animation of thin, elastic, rectangular, and circular plates. instabilities. Stress calculation. Finite elements Lect: 1. Lab: 3. 3 pts. Mr. Sanchez. Exact (series) and approximate (Ritz) solutions. in heat flow and dynamics. Nonlinear problems. Prerequisite: GRAP E1115 or the instructor’s per- Circular cylindrical shells. Axisymmetric and Introduction to boundary element method. mission. Explores applications of 3-D modeling, non-axisymmetric membrane theory. Shells of animation, and rendering techniques in the arts, arbitrary shape. ENME E8320y Viscoelasticity and plasticity architecture, engineering, entertainment, and sci- Lect: 3. 4 pts. Professor Chen. ence. Visualization through conceptual modeling ENME E4215x Theory of vibrations Prerequisite: ENME E6315 or the equivalent, or and animation techniques for product design and Lect: 3. 3 pts. Professor Betti. the instructor’s permission. Constitutive equations realistic presentations. Lab fee: $300. Frequencies and modes of discrete and continu- of viscoelastic and plastic bodies. Formulation ous elastic systems. Forced vibrations–steady- and methods of solution of the boundary value, GRAP E4005y Computer graphics in engineering state and transient motion. Effect of damping. problems of viscoelasticity and plasticity. Lect: 3. 3 pts. Professor Dasgupta. Exact and approximate methods. Applications. Prerequisites: Any programming language and ENME E8323y Nonlinear vibrations linear algebra. Numerical and symbolic (algebraic) ENME E4332x Finite element analysis, I Lect: 2.5. 3 pts. Instructor to be announced. problem solving with Mathematica. Formulation Lect: 3. 3 pts. Professor Waisman. Prerequisite: ENME E4215 or the equivalent. for graphics application in civil, mechanical, and Prerequisites: Mechanics of solids, structural Free and forced motion of simple oscillators with bioengineering. Example of two- and three-dimen- analysis, elementary computer programming, lin- nonlinear damping and stiffness. Exact, perturba- sional curve and surface objects in C++ and ear algebra. Matrix methods of structural analysis: tion, iteration, and graphical methods of solution. Mathematica; special projects of interest to elec- displacement method and flexibility methods. Stability of motion. Chaotic vibrations. trical and computer science. Principle of stationary potential energy. Rayleigh- Ritz approximation. Finite element approximation. Displacement-based elements for structural mechanics. Isoparametric formulation.

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COMPUTER ENGINEERING PROGRAM 103 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, 212-854-3105 / 450 Computer Science www.compeng.columbia.edu

posted at www.compeng.columbia.edu/ pages/ugrad. IN CHARGE Martha A. Kim Simha Sethumadhavan Steven M. Nowick Assistant Professor of Assistant Professor of Students will be prepared to work on 508 Computer Science Computer Science Computer Science all aspects of the design of digital hard- Vishal Misra Kenneth L. Shepard ware, as well as on the associated soft- COMPUTER ENGINEERING Associate Professor of Professor of Electrical COMMITTEE Computer Science Engineering ware that is now often an integral part of Luca Carloni Steven M. Nowick Stephen H. Unger computer architecture. They will also be Associate Professor of Professor of Computer Professor Emeritus of well equipped to work in the growing Computer Science Science Computer Science (and Stephen A. Edwards Daniel Rubenstein Electrical Engineering) field of telecommunications. Students Associate Professor of Associate Professor of Charles A. Zukowski will have the prerequisites to delve more Computer Science Computer Science Professor of Electrical Engineering deeply into either hardware or software areas, and enter graduate programs in computer science, electrical engineering, or computer engineering. For example, he computer engineering program providing hands-on experience in they could take more advanced courses is run jointly by the Computer designing and using a computer net- in VLSI, communications theory, comput- T Science and Electrical Engineer- work (CSEE 4140). er architecture, electronic circuit theory, ing departments. It offers both B.S. and Students in the programs have two software engineering, or digital design. M.S. degrees. “home” departments. The Electrical Minors in electrical engineering and The program covers some of engi- Engineering Department maintains stu- computer science are not open to com- neering’s most active, exciting, and criti- dent records and coordinates advising puter engineering majors, due to exces- cal areas, which lie at the interface appointments. sive overlap. between CS and EE. The focus of the major is on computer systems involving UNDERGRADUATE PROGRAM Technical Electives both digital hardware and software. This undergraduate program incorpo- The Computer Engineering Program Some of the key topics covered are rates most of the core curricula in both includes 15 points of technical electives. computer design (i.e., computer archi- electrical engineering and computer Any 3000-level or higher courses listed tecture); embedded systems (i.e., the science so that students will be well in the Computer Science or Electrical design of dedicated hardware/software prepared to work in the area of computer Engineering sections of this bulletin can for cell phones, automobiles, robots, engineering, which substantially overlaps be used for this requirement with the games, and aerospace); digital and VLSI both fields. Both hardware and software following exceptions: ELEN E3000, circuit design; computer networks; design aspects of computer science are included, EEHS 3900/4900, EEJR E4901, COMS automation (i.e. CAD); and parallel and and, in electrical engineering, students W3101, COMS W4400, COMS W4405, distributed systems (including architec- receive a solid grounding in circuit theory courses used for other computer engi- tures, programming, and compilers). and in electronic circuits. The program neering requirements (including COMS The undergraduate major includes includes several electrical engineering W3203 and either CSEE W4840, EECS one substantial senior design course, laboratory courses as well as the Computer E4340, or CSEE W4140), and courses either designing an entire microproces- Science Department’s advanced program- that have significant overlap with other sor (EECS 4340), or an embedded sys- ming course. Detailed lists of require- required or elective courses (e.g., tem (CSEE 4840) (including both soft- ments can be found in the charts on COMS W3137 and COMS W3139). ware and hardware components), or the following pages, and on a checklist Up to one course may be chosen from

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104 COMPUTER ENGINEERING PROGRAM: FIRST AND SECOND YEARS EARLY-STARTING STUDENTS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

MATHEMATICS MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) MATH V1202 (3) and APMA E2101 (3)3

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

PHYSICS C1601 (3.5) C1602 (3.5) Lab C1493 (3) or (three tracks, choose one) chem. lab C1500 (3)

C2801 (4.5) C2802 (4.5) Lab W3081 (2) or chem. lab C1500 (3)

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

Lab C1500 (3) either semester or physics lab C1493 (3)

ELEN E1201 (3.5) ELEN E3801 (3.5) COMS W3137 (3) or Intro. to elec. eng. (either semester) Signals & systems W3139 (4) CORE REQUIRED Data structures COURSES CSEE W3827 (3) Fund. of computer sys.

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

ENGLISH C1010 (3) COMPOSITION Z1003 (0) C1010 (3) (three tracks, choose one) Z0006 (0) Z1003 (0) C1010 (3)

HUMA C1001, C0CI C1101, HUMA C1002, C0CI C1102, REQUIRED or Global Core (3–4) or Global Core (3–4) NONTECHNICAL 1 ELECTIVES HUMA W1121 or ECON W1105 (4) and W1123 (3)1 W1155 recitation (0)

COMPUTER COMS W1004 (3)2 COMS W1007 (3) or W3203 (3) SCIENCE W1009 Discrete math.

PHYSICAL C1001 (1) C1002 (1) EDUCATION

GATEWAY LAB E1102 (4) either semester

1Some of these courses can be postponed to the junior or senior year to make room for taking the required core computer engineering courses. 2Only required if needed to prepare for COMS W1007/W1009. 3APMA E2101 may be replaced by MATH E1210 and either APMA E3101 or MATH V2010.

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105 COMPUTER ENGINEERING: THIRD AND FOURTH YEARS EARLY-STARTING STUDENTS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

IEOR E3658 (3) ELEN E3331 (3) COMS W4118 (3) COMS W4115 (3) Probability Electronic circuits Operating systems Programming lang.

CORE REQUIRED COMS W3157 (3) COMS W3261 (3) COURSES Advanced programming Computer sci. theory

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

ELEN E3081 (1) ELEN E3083 (1) EECS E4340 (3) Circuit analysis lab Electronic circuits lab Computer hardware design or CSEE W4840 (3) REQUIRED LABS Embedded sys. design or CSEE W4140 (4) Networking lab

TECH 15 points required; see details on pages 103–105

NONTECH Complete 27-point requirement; see page 11 or www.seas.columbia.edu for details ELECTIVES (administered by the advising dean)

TOTAL POINTS1 16.5 17 15 15

For a discussion about programming languages used in the program, please see www.compeng.columbia.edu. Check the late-starting student chart for footnotes about various courses. 1“Total points” assumes that 20 points of nontechnical electives and other courses are included.

outside the departments with adviser ing” charts that follow, present examples Record Examination (GRE), General Test approval. Courses at the 3000 level or only; actual schedules may be customized only, is required of all applicants. higher in other areas of engineering, in consultation with academic advisers. Students must take at least 30 points math, and science can be considered of courses at Columbia University at for approval, as long as they do not sig- GRADUATE PROGRAM or above the 4000 level. These must nificantly overlap with other required or include at least 15 points from the The Computer Engineering Program elective courses. Economics courses courses listed below that are deemed offers a course of study leading to the cannot be used as technical electives. core to computer engineering. At least degree of Master of Science (M.S.). 6 points must be included from each The basic courses in the M.S. program Starting Early department. CSEE and EECS courses come from the Electrical Engineering can count toward either department Students are strongly encouraged to and Computer Science Departments. minimum. Other courses may be chosen begin taking core computer engineering Students completing the program are with the prior approval of a faculty adviser courses as sophomores. They start with prepared to work (or study further) in in the Computer Engineering Program. ELEN E1201: Introduction to electrical such fields as digital computer design, engineering in the second semester of digital communications, and the design CORE COMPUTER ENGINEERING COURSES their first year and may continue with of embedded computer sytems. COMS W4115: Programming language and trans- other core courses one semester after Applicants are generally expected to lators COMS W4118: Operating systems, I that. For sample “early-starting” pro- have a bachelor’s degree in computer CSEE W4119: Computer networks grams, see the charts on the following engineering, computer science, or two pages. It must be emphasized that CSEE W4140: Networking lab electrical engineering with at least a 3.2 CSEE W4180: Network security these charts, as well as the “late-start- GPA in technical courses. The Graduate CSEE W4823: Advanced logic design

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106 COMPUTER ENGINEERING PROGRAM: FIRST AND SECOND YEARS LATE-STARTING STUDENTS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

MATHEMATICS MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) MATH V1202 (3) and APMA E2101 (3)3

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

PHYSICS C1601 (3.5) C1602 (3.5) Lab C1493 (3) or (three tracks, choose one) chem. lab C1500 (3)

C2801 (4.5) C2802 (4.5) Lab W3081 (2) or chem. lab C1500 (3)

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

Lab C1500 (3) either semester or physics lab C1493 (3)

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

ENGLISH C1010 (3) COMPOSITION Z1003 (0) C1010 (3) (three tracks, choose one) Z0006 (0) Z1003 (0) C1010 (3)

HUMA C1001, COCI C1101, HUMA C1002, C0CI C1102, REQUIRED or Global Core (3–4) or Global Core (3–4) NONTECHNICAL ELECTIVES HUMA W1121 or ECON W1105 (4) and W1123 (3) W1155 recitation (0)

COMPUTER COMS W1004 (3)1 COMS W1007 (3) or W3203 (3)2 SCIENCE W1009 Discrete math.

PHYSICAL C1001 (1) C1002 (1) EDUCATION

GATEWAY LAB E1102 (4) either semester

1Only required if needed to prepare for COMS W1007/W1009. 2Transfer 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, prerequi- site constraints make it difficult to complete the remaining computer engineering program by the end of the senior year. 3APMA E2101 may be replaced by MATH E1210 and either APMA E3101 or MATH V2010.

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107 COMPUTER ENGINEERING: THIRD AND FOURTH YEARS LATE-STARTING STUDENTS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

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

COMS W3137 (3) or ELEN E3331 (3) W3139 (4) Electronic circuits CSEE W4119 (3) or CSEE W4823 (3) CORE REQUIRED Data structures Computer networks Advanced logic design COURSES COMS W3261 (3)3 ELEN E3201 (3.5) Models of comp. Circuit analysis CSEE W3827 (3) ELEN E3801 (3.5) Fund. of computer systems Signals & systems

ELEN E3081 (1)2 ELEN E3083 (1)2 EECS E4340 (3) Circuit analysis lab Electronic circuits lab Computer hardware design REQUIRED LABS or CSEE W4840 (3) ELEN E3084 (1)2 ELEN E3082 (1)2 Embedded sys. design Signals & systems lab Digital systems lab or CSEE W4140 Networking lab

TECH 15 points required; see details on pages 103–1054

NONTECH Complete 27-point requirement; see page 11 or www.seas.columbia.edu for details

ELECTIVES (administered by the advising dean)

TOTAL POINTS5 15 17 15 18

For a discussion about programming languages used in the program, please see www.compeng.columbia.edu. 1SIEO W3600, SIEO W4105, STAT W4105, and SIEO W4150 can be used instead of IEOR E3658, but W3600 and W4150 may not provide enough probability background for elective courses such as ELEN E3701. Students completing an economics minor who want such a background can take IEOR E3658 and augment it with STAT W1211. 2If 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. 3COMS W3261 can be taken one semester later than pictured. 4The total points of technical electives is reduced to 12 if APMA E2101 has been replaced by MATH E1210 and either APMA E3101 or MATH V2010. 5Assuming technical electives taken Semesters VII and VIII, and 9 points of nontechnical electives taken Semesters VI, VII, and VIII.

CSEE W4824: Computer architecture EECS E4340: Computer hardware design The overall program must include at CSEE W4825: Digital systems design* ELEN E4702: Communication theory least 15 points of 6000-level ELEN, CSEE W4840: Embedded systems design ELEN E4810: Digital signal processing EECS, CSEE, or COMS courses (exclu- COMS E6118: Operating systems, II* ELEN E4830: Digital image processing sive of seminars). No more than 9 points CSEE E6180: Modeling and performance ELEN E4896: Music signal processing* COMS E6181: Advanced internet services ELEN E6321: Advanced digital electronic circuits of research may be taken for credit. No CSEE E6824: Parallel computer architecture ELEN E6488: Optical interconnects and intercon- more than 3 points of a nontechnical CSEE W6831: Sequential logic circuits* nection networks elective (at or above the 4000 level) may CSEE W6832: Topics in logic design theory* ELEN E6761: Computer communication be included. A minimum GPA of at least CSEE E6847: Distributed embedded systems networks, I 2.7 must be maintained, and all degree CSEE W6861: Computer-aided design of digital ELEN E6762: Computer communication requirements must be completed within systems networks, II* five years of the beginning of the first ELEN E4321: Digital VLSI circuits ELEN E6850: Visual information systems course credited toward the degree. ELEN E4332: VLSI design lab* ELEN E6860: Advanced digital signal processing

*Occasionally offered.

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108 COMPUTER SCIENCE 450 Computer Science, MC 0401, 212-939-7000 www.cs.columbia.edu

CHAIR PROFESSORS ASSOCIATE PROFESSORS ASSOCIATED FACULTY ASSOCIATE RESEARCH Shree Kumar Nayar Alfred V. Aho Luca Carloni Theodore R. Bashkow SCIENTISTS 450 Computer Science Peter K. Allen Stephen A. Edwards (professor emeritus) Marta Arias* 212-939-7004 Peter Belhumeur Luis Gravano Edward G. Coffman Jr. Jiang Chen* Steven M. Bellovin Tony Jebara Dana Pe’er Wei Chu* VICE CHAIR Steven K. Feiner Angelos D. Keromytis Clifford Stein Mona Diab* Vishal Misra Jonathan L. Gross Vishal Misra Steven H. Unger Nizar Habash* 512 Computer Science Julia Hirschberg Jason Nieh (professor emeritus) Claire Monteleoni* 212-939-7061 Gail E. Kaiser Daniel S. Rubenstein Vladimir Vapnik* Anargyros Papageorgiou John R. Kender Rocco Servedio Cynthia Rudin* ASSOCIATE CHAIR Kathleen R. McKeown SENIOR RESEARCH Ansaf Salleb-Audissi* FOR UNDERGRADUATE Shree Kumar Nayar ASSISTANT PROFESSORS SCIENTISTS EDUCATION Steven M. Nowick Eitan Grinspun David L. Waltz* Adam Cannon Kenneth A. Ross Martha Allen Kim Arthur G. Wershulz 459 Computer Science Henning G. Schulzrinne Tal Malkin Moti Yung 212-939-7016 Salvatore J. Stolfo Itsik Pe’er Joseph F. Traub Simha Sethumadhavan RESEARCH SCIENTISTS DEPARTMENTAL Henryk Wozniakowski Junfeng Yang Rebecca Passonneau ADMINISTRATOR Mihalis Yannakakis Owen Rambow* Patricia Hervey Yechiam Yemini LECTURER IN DISCIPLINE Adam Cannon

*Columbia Center for Computational Learning Systems

he function and influence of the and design to programming and marketing. computer-aided digital design, computer computer is pervasive in con- The computer science curriculum vision, databases and digital libraries, T temporary society. Today’s com- at Columbia places equal emphasis on data mining and knowledge discovery, puters process the daily transactions theoretical computer science and math- distributed systems, mobile and wear- of international banks, the data from ematics and on experimental computer able computing, natural-language pro- communications satellites, the images technology. A broad range of upper-level cessing, networking, operating systems, in video games, and even the fuel and courses is available in such areas as programming systems, robotics, user ignition systems of automobiles. artificial intelligence, computational com- interfaces, and real-time multimedia. Computer software is as common- plexity and the analysis of algorithms, The computer facilities include a place in education and recreation as it combinatorial methods, computer archi- shared infrastructure of Sun and Linux is in science and business. There is vir- tecture, computer-aided digital design, multiprocessor file servers, NetApp file tually no field or profession that does computer communications, databases, servers, a student interactive teaching not rely upon computer science for the mathematical models for computation, and research lab of high-end multimedia problem-solving skills and the produc- optimization, and software systems. workstations, a Microsoft programming tion expertise required in the efficient laboratory with 15 Windows XP work- processing of information. Computer Laboratory Facilities stations, a Unix/Linux laboratory with scientists, therefore, function in a wide The department has well-equipped lab 63 Linux workstations, a large vonware variety of roles, ranging from pure theory areas for research in computer graphics, system for teaching, a large cluster of

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109

Linux servers for computational work, UNDERGRADUATE PROGRAM to arrange for participation by consulting and a cluster of Sun servers. The Computer science majors at Columbia individual faculty members. research infrastructure includes hun- study an integrated curriculum, partially Most graduates of the computer dreds of workstations and PCs running in areas with an immediate relationship science program at Columbia step Solaris, Windows XP, Linux, and Mac to the computer, such as programming directly into career positions in computer OSX; 7 terabytes of disk space are languages, operating systems, and science with industry or government, backed up by a 48TB Sun Thumper and computer architecture, and partially in or continue their education in graduate a Sun StorEdge LT02 with 100-tape theoretical computer science and math- degree programs. Many choose to library unit. ematics. Thus, students obtain the combine computer science with a sec- Research labs contain Puma 500 background to pursue their interests ond career interest by taking additional and IBM robotic arms; a UTAH-MIT both in applications and in theoretical programs in business administration, dexterous hand; an Adept-1 robot; three developments. medicine, or other professional studies. mobile research robots; a real-time Practical experience is an essential For further information on the under- defocus range sensor; PC interactive 3- component of the computer science graduate computer science program, D graphics workstations with 3-D posi- program. Undergraduate students are please see the home page at www.cs. tion and orientation trackers; prototype often involved in advanced faculty columbia.edu/education/undergrad and wearable computers, wall-sized stereo research projects using state-of-the-art the Quick Guide at www.cs.columbia. projection systems; see-through head- computing facilities. Qualified majors edu/education/undergrad/seasguide. mounted displays; a networking testbed sometimes serve as consultants at the with three Cisco 7500 backbone routers, Computer Center, which operates sev- Technical Electives traffic generators, Ethernet switches, eral labs with microcomputers and ter- All technical electives except those Sun Ray thin clients, and a 17-node minals available at convenient locations noted in each track must be approved (34CPU) IBM Netfinity cluster. The on the campus. by the adviser. In every case, the techni- department uses a 3COM SIP IP phone Upper-level students in computer cal elective course must be at the 3000 system. The protocol was developed in science may assist faculty members level or higher. All technical electives the department. with research projects, particularly in the should be taken in computer science. The servers are connected on a development of software. Ongoing facul- With the adviser’s approval, however, gigabit network; all have remote con- ty projects include algorithmic analysis, courses in other departments may be soles and remote power for easy main- computational complexity, software tool taken as technical electives; in every tenance after hours. The rest of the design, distributed computation, model- such case, the subject of the course department’s computers are connected ing and performance evaluation, com- must have a strong and obvious con- via a switched 100 Mb/s Ethernet net- puter networks, computer architecture, nection with computer science. COMS work, which has direct connectivity to CAD for digital systems, computer W4400: Computers and society and the campus OC-3 Internet and Internet2 graphics, programming environments, ELEN E4901: Telecommunication net- gateways. The campus has 802.11a/b expert systems, natural language works and applications are not accept- wireless LAN coverage. processing, computer vision, robotics, able as technical electives and are the The research facility is supported by multicomputer design, user interfaces, only advanced computer science cours- a full-time staff of professional system VLSI applications, artificial intelligence, es that cannot be taken as electives. administrators and programmers, aided combinatorial modeling, virtual environ- Students are encouraged to select by a number of part-time student system ments, and microprocessor applica- one of the following five preapproved administrators. tions. Students are strongly encouraged groupings of electives called “tracks.”

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110 COMPUTER SCIENCE PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

MATHEMATICS MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) COMS W3210 (3)

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

one-semester lecture (3–4) CHEMISTRY C1403 or C1404 or (choose one course) C3045 or C1604 either semester

ENGLISH C1010 (3) COMPOSITION Z1003 (0) C1010 (3) (three tracks, choose one) Z0006 (0) Z1003 (0) C1010 (3)

HUMA C1001, COCI C1101, HUMA C1002, ECON W1105 (4) or Global Core (3–4) COCI C1102, or REQUIRED and Global Core (3–4) NONTECHNICAL ELECTIVES W1105 recitation (0) either semester HUMA C1121 or C1123 (3) either semester

REQUIRED Professional-level course (3) (see page 12) either semester TECH ELECTIVES

COMS W1009 (3) or COMS W3137 (4) or COMS W1004 (3) COMS W1007 (3) COMS W3139 (4) COMPUTER Intro. to computer science Object-oriented programming Data structures SCIENCE either semester and and COMS W3203 (3) COMS W3157 (4) Discrete math Adv. programming

PHYSICAL C1001 (1) C1002 (1) EDUCATION

GATEWAY LAB E1102 (4) either semester

An advanced version of each track is Exam, either A or AB, with a 4 or 5 will REQUIRED: 3 courses available by invitation for qualified students receive 3 points of credit and exemption CSOR W4231: Analysis of algorithms who wish an extra opportunity for from COMS W1004. COMS W4236: Introduction to computational advanced learning. Note: A maximum of one course complexity COMS W4241: Numerical algorithms and com- The following courses are required passed with a grade of D may be count- plexity as a preparation for all tracks: COMS ed toward the major or minor. W1004, W1007 (or W1009), W3137 (or W3139), W3157, W3203, W3210, Track 1: Foundations of CS Track W3251, W3261, CSEE W3827, and The foundations track is suitable for SIEO W4150 (SIEO W3600 is an students who plan to concentrate on accepted substitute for W4150). theoretical computer science in graduate Collectively these courses are called school or in mathematical topics such the CS Core Curriculum. as communications security or scientific Students who pass the Computer computation in their career plans. Science Advanced Placement (AP) Register for track course COMS E0001.

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111 COMPUTER SCIENCE: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

COMS W3251 (3) SIEO W4150 (3) Computational lin. algebra or SIEO W3600 (4) REQUIRED COMS W3261 (3) Prob. & stat. COURSES Computer sci. theory

CSEE W3827 (3) Fund. of computer sys.

NONTECH 3 points 6 points 3 points

TECH 3 points 6 points 12 points 9 points ELECTIVES

TOTAL POINTS 15 15–16 15 9

The primary programming languages for the undergraduate major are C and Java, and students are expected to learn both at an early stage. The language for COMS W1004/W1007/W1009/W3137/W3139 is Java. COMS W1004 is waived for students who have had AP computer science in high school.

BREADTH: 2 courses Any COMS W48xx course Any COMS W40xx course with adviser approval Any COMS 3000- or 4000-level courses except COMS W4444: Programming and problem solving COMS W4165: Pixel processing those countable toward the CS core or founda- COMS W3902: Undergraduate thesis COMS W4252: Computational learning theory tions of CS track COMS W3998: Undergraduate projects in Any COMS W47xx course if not used as a computer science required course ELECTIVES: any 5 courses from the or COMS W4901: Projects in computer science COMS W4995: Special topics I (with adviser following list COMS W4995-W4996: Special topics in computer approval; may be repeated) COMS W4203: Graph theory science COMS W4996: Special topics II (with adviser COMS W4205: Combinatorial theory COMS E6901: Projects in computer science approval; may be repeated) COMS W4252: Computational learning theory Any COMS E61xx or E68xx course (with adviser Any COMS W67xx course COMS W4261: Introduction to cryptography approval) COMS E6998: Topics in computer science, I COMS W4281: Quantum computing Note: No more than 6 units of project/thesis courses (with adviser approval) COMS W4444: Programming and problem solving (COMS W3902, COMS W3998, COMS W4901, COMS E6999: Topics in computer science, II COMS W4771: Machine learning COMS E6901) can count toward the major. (with adviser approval) COMS W4772: Advanced machine learning COMS W4995: Math foundations of machine Track 3: Artificial Intelligence Track Up to 2 courses from the following list learning The artificial intelligence track is for stu- COMS W3902: Undergraduate thesis (with adviser approval; may be repeated) COMS E6232: Analysis of algorithms, II dents interested in machine learning, COMS E6261: Advanced crytography COMS W3998: Undergraduate projects in robots, and systems capable of exhibit- COMS E6717: Information theory computer science (with adviser COMS E6998: Approximation algorithms ing “human-like” intelligence. A total approval; may be repeated) of ten required, breadth, and elective COMS W4901: Projects in computer science Track 2: Systems Track courses are to be chosen from the (with adviser approval; may be The systems track is for students inter- following schedule. Register for track repeated) ested in the implementation of software course COMS E0003. COMS E6901: Projects in computer science (with adviser approval; may be repeated) and/or hardware systems. Register for REQUIRED: 1 course Up to 1 course from the following list track course COMS E0002. COMS W4701: Artificial intelligence COMS W4111: Introduction to databases REQUIRED: 3 courses Plus any 2 courses from: COMS W4160: Computer graphics COMS W4115: Programming languages and COMS W4705: Natural language processing COMS W4170: User interface design translators COMS W4731: Computer vision COMS W4999: Computing and the humanities COMS W4118: Operating systems COMS W4733: Computational aspects of robotics Note: No more than 6 units of project/thesis CSEE W4119: Networking COMS W4771: Machine learning courses (COMS W3902, COMS W3998, COMS W4901, COMS E6901) can count toward the major. BREADTH: 2 courses BREADTH: 2 courses Any COMS 3000- or 4000-level course except Any 3-point COMS 3000- or 4000-level courses Track 4: Applications Track those countable for the CS core or systems track except those countable toward the CS core or The applications track is for students elective courses for the artificial intelligence track ELECTIVES: any 5 courses from the interested in the implementation of inter- following list ELECTIVES: Up to 5 courses from the active multimedia applications for the Any COMS W41xx course following list

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112 Internet and wireless networks. Register or COMS W4901: Projects in computer science grams are flexible, and each student is for track course COMS E0004. COMS W4995-W4496: Special topics in computer urged to design his or her own program science, I and II (with under the guidance of a faculty adviser. REQUIRED: 3 courses adviser approval) The student’s program should focus on a COMS W4115: Programming languages and COMS E6901: Projects in computer science translators Any COMS E691x course (with adviser approval) particular field of computer science. COMS W4170: User interface design Note: No more than 6 units of project/thesis Among the fields of graduate study in COMS W4701: Artificial intelligence courses (COMS W3902, COMS W3998, COMS computer science are analysis of algo- W4901 COMS E6901) can count toward the major. BREADTH: 2 courses rithms, artificial intelligence, expert sys- tems, natural language understanding, Any COMS 3000- or 4000-level courses except Track 6: Advanced those countable toward the CS core or applica- computer vision, multicomputer design, The advanced track of the B.S. in tions tracks VLSI applications, combinatorial model- Computer Science provides extra ing, combinatorial optimization, computa- ELECTIVES: 5 courses from the following list opportunity for advanced learning. tional complexity, computer architecture Any COMS W41xx course It comprises accelerated versions of and design, computer communications Any COMS W47xx course the other five tracks. Entry is only by COMS W3902: Undergraduate thesis networks, computer graphics, database collective faculty invitation, extended to COMS W3998: Undergraduate projects in machines and systems, microprocessors, computer science students who have already completed parallel computation, programming envi- or COMS W4901: Projects in computer science the core courses and the required ronments, programming languages, COMS W4995-W4996: Special topics in computer courses for one of those tracks. robotics, user interfaces, software design, science, I and II (with REQUIRED TRACK COURSES computational biology, computer security, adviser approval) and machine learning. COMS E6901: Projects in computer science or A student designates one of the five other track other COMS E69xx course (with areas and completes the set of required track Graduate students are encouraged adviser approval) courses for that track, prior to entry into the actively to pursue research. Faculty mem- Any COMS E69xx course (with adviser approval) Advanced Track. There are two or three courses, bers of the Department of Computer depending on the designated area. Note: No more than 6 units of project/thesis courses Science are engaged in experimental and (COMS W3902, COMS W3998, COMS W4901, BREADTH REQUIREMENT theoretical research in most of the fields in COMS E6901) can count toward the major. Two breadth courses of the designated track. which courses are offered. The degree of Track 5: Vision and Graphics Track ELECTIVES doctor of philosophy requires a dissertation Objective: The vision and graphics track At least two 4000-level lecture courses from the based on the candidate’s original research, exposes students to interesting new menu for the designated track, plus two 6000- which is supervised by a faculty member. fields and focuses on visual information level courses in the designated track area. The professional degree program also provides the student with the with topics in vision, graphics, human- THESIS opportunity to specialize beyond the computer interaction, robotics, model- There is a required 6-point senior thesis. ing, and learning. Students learn about level of the Master of Science program. INVITATION fundamental ways in which visual infor- The program leading to the degree of Only the top 20% of computer science majors in mation is captured, manipulated, and Computer Systems Engineer is particu- course performance in computer science courses larly suited to those who wish to advance experienced. Register for track course will be considered for invitation during the junior their professional development after a COMS E0005. year. (A student in the advanced track who does not maintain this status may be required to return period of industrial employment. REQUIRED: 2 courses to his or her previously selected track area.) COMS W4731: Computer vision COMS W4160: Computer graphics COURSES IN COMPUTER GRADUATE PROGRAMS SCIENCE BREADTH: 2 courses COMS W1001x and y Introduction to informa- Any COMS 3000- or 4000-level courses except The Department of Computer Science those countable toward the CS core or vision and offers graduate programs leading to the tion science graphics track degree of Master of Science, the profes- Lect: 3. 3 pts. Professor Cannon. Basic introduction to concepts and skills in infor- sional degree of Computer Systems ELECTIVES: 6 courses from the following list mation sciences: human-computer interfaces, Engineer and the degree of Doctor of COMS W4162: Advanced computer graphics representing information digitally, organizing and COMS W4165: Pixel processing Philosophy. Both the Aptitude Test and searching information on the World Wide Web, COMS W4167: Computer animation Advanced Tests of the Graduate Record principles of algorithmic problem solving, intro- COMS W4170: User interface design Examination (GRE) are required for duction to database concepts, introduction to COMS W4172: 3D user interface design admission to the department’s graduate programming in Python. COMS W4701: Artificial intelligence programs. Applicants for September COMS W4733: Computational aspects of robotics admission should take the GREs by COMS W1003x or y Introduction to computer COMS W4735: Visual interfaces to computers science and programming in C October of the preceding year. Applicants COMS W4771: Machine learning Lect: 3. 3 pts. Instructor to be announced. COMS W4995: Video game technology and design for January admission should take these A general introduction to computer science con- COMS W3902: Undergraduate thesis exams by April of the preceding year. cepts, algorithmic problem-solving capabilities, COMS W3998: Undergraduate projects in The course requirements in all pro- and programming skills in C. Columbia University computer science

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students may receive credit for only one of the COMS W3101x and y Programming languages garbage collection. Storage management. Design 113 following three courses: W1003, W1004, or W1005. Lect: 1. 1 pt. Instructors to be announced. and analysis of algorithms. Taught in C/C++. Prerequisite: Fluency in at least one programming Note: Due to significant overlap, students may COMS W1004x and y Introduction to computer language. Introduction to a programming language. receive credit for only one of the following four science and programming in Java Each section is devoted to a specific language. courses: COMS W3133, W3134, W3137, or W3139. Lect: 3. 3 pts. Professor Cannon. Intended only for those who are already fluent in A general introduction to computer science for at least one programming language. Sections COMS W3157x and y Advanced programming science and engineering students interested in may meet for one hour per week for the whole Lect: 4. 4 pts. Professor Schulzrinne. majoring in computer science or engineering. Covers term, for three hours per week for the first third of Prerequisite: COMS W1007 or W1009. Practical, fundamental concepts of computer science, algo- the term, or for two hours per week for the first hands-on introduction to programming techniques rithmic problem-solving capabilities, and introduc- six weeks. May be repeated for credit if different and tools for professional software construction, tory Java programming skills. Assumes no prior languages are involved. including learning how to write code to given speci- programming background. Columbia University fications as well as document the results. Provides students may receive credit for only one of the COMS W3133x or y Data structures in C introductory overview of C and C++ in a UNIX following three courses: W1003, W1004, or W1005. Lect: 3. 3 pts. Instructor to be announced. environment, for students with Java background. Prerequisite: COMS W1003 or knowledge of C. Also introduces scripting languages (perl) and COMS W1005x and y Introduction to computer Not intended for computer science majors. Data- basic Web programming. UNIX programming science and programming in MATLAB types and structures: arrays, stacks, singly and utilities are also covered. Lab required. Lect: 3. 3 pts. Paul Blaer. doubly linked lists, queues, trees, sets, and graphs. A general introduction to computer science con- Programming techniques for processing such COMS W3203x and y Discrete mathematics: cepts, algorithmic problem-solving capabilities, and structures: sorting and searching, hashing, garbage introduction to combinatorics and graph theory programming skills in MATLAB. Assumes no prior collection. Storage management. Rudiments of Lect: 3. 3 pts. x: Professor Gross; y: Professor programming background. Columbia University the analysis of algorithms. Taught in C. Note: Due Grunschlag. students may receive credit for only one of the to significant overlap, students may receive credit Prerequisite: Any introductory course in computer following three courses: W1003, W1004, or W1005. for only one of the following four courses: COMS programming. Logic and formal proofs, sequences W3133, W3134, W3137, or W3139. and summation, mathematical induction, binomial COMS W1007x and y Object-oriented program- coefficients, elements of finite probability, recur- ming and design in Java COMS W3134x and y Data structures in Java rence relations, equivalence relations and partial Lect: 3. 3 pts. Professor Kender. Lect: 3. 3 pts. Professor Hershkop. orderings, and topics in graph theory (including Prerequisites: COMS W1004 or AP Computer Science Prerequisite: COMS W1004 or knowledge of isomorphism, traversability, planarity, and colorings). with a grade of 4 or 5. The second course for majors Java. Not intended for computer science majors. in computer science. A rigorous treatment of object- Data types and structures: arrays, stacks, singly COMS W3210y Scientific computation oriented concepts using Java as an example lan- and doubly linked lists, queues, trees, sets, and Lect: 3. 3 pts. Professor Traub. guage. Development of sound programming and graphs. Programming techniques for processing Prerequisites: Two terms of calculus. Introduction design skills, problem solving and modeling of such structures: sorting and searching, hashing, to computation on digital computers. Design and real-world problems from science, engineering, garbage collection. Storage management. Rudiments analysis of numerical algorithms. Numerical solu- and economics using the object- oriented paradigm. of the analysis of algorithms. Taught in Java. tion of equations, integration, recurrences, chaos, Note: Due to significant overlap, students may differential equations. Introduction to Monte Carlo COMS W1009x Honors introduction to receive credit for only one of the following four methods. Properties of floating point arithmetic. computer science courses: COMS W3133, W3134, W3137, or W3139. Applications to weather prediction, computational Lect: 3. 3 pts. Instructor to be announced. finance, computational science, and computational Prerequisite: COMS W1004 or AP computer science COMS W3137x and y Data structures and engineering. with a grade of 4 or 5. An honors-level introduc- algorithms tion to computer science, intended primarily for Lect: 3. 4 pts. x: Professor Allen; y: Instructor COMS W3251x Computational linear algebra students considering a major in computer science. to be announced. Lect: 3. 3 pts. Professor Papageorgiou. Computer science as a science of abstraction. Prerequisite: COMS W1007. Corequisite: COMS Prerequisite: Two terms of calculus. Computational Creating models for reasoning about and solving W3203. Data types and structures: Arrays, stacks linear algebra, solution of linear systems, sparse problems. The basic elements of computers and singly and doubly linked lists, queues, trees, sets, linear systems, least squares, eigenvalue prob- computer programs. Implementing abstractions and graphs. Programming techniques for pro- lems, and numerical solution of other multivariate using data structures and algorithms. Taught in Java. cessing such structures: sorting and searching, problems as time permits. hashing, garbage collection. Storage manage- ECBM E3060x Introduction to genomic ment. Design and analysis of algorithms. Taught COMS W3261x and y Computer science theory information science and technology in Java. Note: Due to significant overlap, Lect: 3. 3 pts. Professor Pasik. Lect: 3. 3 pts. Professor Anastassiou. students may receive credit for only one of the Prerequisites: COMS W3137 and W3203. Introduction to the information system paradigm of following four courses: COMS W3133, W3134, Regular languages: deterministic and nondeter- molecular biology. Representation, organization, W3137, or W3139. ministic, finite automata, regular expressions. structure, function and manipulation of the biomolecu- Contest-free languages: context-free grammars, lar sequences of nucleic acids and proteins. The role COMS W3139y Honors data structures push-down automata. Turing machines, the Chomsky of enzymes and gene regulatory elements in natural and algorithms hierarchy, and the Church-Turing thesis. Introduction biological functions as well as in biotechnology and Lect: 4. 4 pts. Instructor to be announced. to complexity theory and NP completeness. genetic engineering. Recombination and other Prerequisite: COMS W3157. Corequisite: COMS macromolecular processes viewed as mathematical W3203. An honors introduction to data types CSEE W3827x and y Fundamentals of computer operations with simulation and visualization using and structures: arrays, stacks, singly and doubly systems simple computer programming. This course shares linked lists, queues, trees, sets, and graphs. Lect: 3. 3 pts. Instructor to be announced. lectures with ECBM E4060, but the work require- Programming techniques for processing such Prerequisite: An introductory programming course. ments differ somewhat. structures: sorting and searching, hashing, Fundamentals of computer organization and digi-

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114 tal logic. Boolean algebra, Karnaugh maps, basic 1.5 hours per week for the whole term or 3 hours synchronization and interprocess communication, gates and components, flipflops and latches, per week for a half term. May be repeated for memory management, virtual memory, interrupt counters and state machines, basics of combina- credit if different technologies are involved. handling, processor scheduling, device manage- tional and sequential digital design. Assembly ment, I/O, and file systems. Case study of the language, instruction sets, ALUs, single-cycle COMS W4111x and y Introduction to databases UNIX operating system. A programming project and multicycle processor design, introduction to Lect: 3. 3 pts. Professor Gravano. is required. pipelined processors, caches, and virtual memory. Prerequisites: COMS W3137 or W3134, fluency in Java; or the instructor’s permission. The funda- CSEE W4119x and y Computer networks COMS W3902x and y Undergraduate thesis mentals of database design and application Lect: 3. 3 pts. x: Professor Misra; y: Professor 1 to 6 pts. development using databases: entity-relationship Yemini. Prerequisite: Agreement by a faculty member to modeling, logical design of relational databases, Corequisite: SIEO W3600 or W3658 or equivalent. serve as thesis adviser. An independent theoretical relational data definition and manipulation lan- Introduction to computer networks and the technical or experimental investigation by an undergraduate guages, SQL, XML, query processing, physical foundations of the Internet, including applications, major of an appropriate problem in computer science database tuning, transaction processing, security. protocols, local area networks, algorithms for rout- carried out under the supervision of a faculty mem- Programming projects are required. ing and congestion control, security, elementary ber. A formal written report is mandatory and an oral performance evaluation. Several programming presentation may also be required. May be taken COMS W4112y Database system implementation assignments and a lab project may be required. over more than one term, in which case the grade Lect: 2.5. 3 pts. Professors Gravano or Ross is deferred until all 6 points have been completed. Prerequisites: COMS W4111; fluency in Java or CSEE W4140x or y Networking laboratory Consult the department for section assignment. C++. COMS W3827 is recommended. The princi- Lect: 3. 4 pts. Professor Stavrou. ples and practice of building large-scale database Pre/corequisites: CSEE W4119 or equivalent COMS W3995x or y Special topics in computer management systems. Storage methods and coursework; students need one of the pre/coreq- science indexing, query processing and optimization, uisites or the instructor’s permission. In this Lect: 3. 3 pts. Instructor to be announced. materialized views, transaction processing and hands-on networking lab course, students will Prerequisite: The instructor’s permission. Consult recovery, object-relational databases, parallel learn how to put “principles into practice.” The the department for section assignment. Special and distributed databases, performance consider- course will cover the technologies and protocols topics arranged as the need and availability arise. ations. Programming projects are required. of the Internet using equipment currently available Topics are usually offered on a one-time basis. to large Internet service providers such as CISCO Since the content of this course changes each COMS W4115x and y Programming languages routers and end systems. A set of laboratory time it is offered, it may be repeated for credit. and translators experiments will provide hands-on experience Lect: 3. 3 pts. x: Professor Edwards; y: Professor Aho. with engineering wide-area networks and will COMS W3998x and y Undergraduate projects Prerequisites: COMS W3137 or the equivalent, familiarize students with the Internet Protocol (IP), in computer science W3261, and CSEE W3827, or the instructor’s per- Address Resolution Protocol (ARP), Internet 1 to 3 pts. Instructor to be announced. mission. Modern compiler implementation and Control Message Protocol (ICMP), User Datagrtam Prerequisite: Approval by a faculty member programming language design. Language styles Protocol (UDP) and Transmission Control who agrees to supervise the work. Consult the including imperative, object-oriented, declarative, Protocol (TCP), the Domain Name System (DNS), department for section assignment. Independent functional, and scripting languages. Language routing protocols (RIP, OSPF, BGP), network project involving laboratory work, computer pro- design issues including syntax, control structures, management protocols (SNMP), and application- gramming, analytical investigation, or engineering data types, procedures and parameters, binding, level protocols (FTP, TELNET, SMTP). design. May be repeated for credit, but not for a scope, run-time organization, and exception total of more than 3 points of degree credit. handling. Implementation of language translation COMS W4156x or y Advanced software tools including compilers and interpreters. engineering ECBM E4060x Introduction to genomic Language translation concepts including lexical, Lect: 3. 3 pts. Professor Kaiser. information science and technology syntactic, and semantic analysis; code genera- Prerequisites: Any one or more of COMS W4111, Lect: 3. 3 pts. Professor Anastassiou. tion; and an introduction to code optimization. W4115, W4118, or W4444. Assumes substantial Introduction to the information system paradigm Teams implement a language and its compiler. prior software development experience in one or of molecular biology. Representation, organiza- more of C++, Java, or C#, as well as basic famil- tion, structure, function, and manipulation of the COMS W4117x or y Compilers and interpreters iarity with using SQL. Focuses primarily on com- biomolecular sequences of nucleic acids and Lect. 3. 3 pts. Instructor to be announced. ponent model frameworks (EJB, .NET/COM+, proteins. The role of enzymes and gene regulatory Prerequisite: COMS W4115 or the instructor’s Web Services) and quality assurance (code elements in natural biological functions as well permission. Continuation of COMS W4115, with inspection, unit and integration testing, stress as in biotechnology and genetic engineering. broader and deeper investigation into the design testing). Introduction to UML. Surveys other soft- Recombination and other macromolecular processes and implementation of contemporary language ware life-cycle topics as time permits. Centers viewed as mathematical operations with simulation translators, be they compilers or interpreters. on an intense semester-long multi-iteration team and visualization using simple computer program- Topics include: parsing, semantic analysis, code project building an N-tier application. ming. This course shares lectures with ECBM generation and optimization, run-time environ- E3060, but the work requirements differ somewhat. ments, and compiler-compilers. A programming COMS W4160y Computer graphics project is required. Lect: 3. 3 pts. Professor Ramamoorthi. COMS W4101x or y Topics in computer Prerequisites: COMS 3137 or 3139; 4156 is science technology COMS W4118x Operating systems, I recommended. Strong programming background 1.5 pts. Instructor to be announced. Lect: 3. 3 pts. Professor Keromytis. and some mathematical familiarity including linear Prerequisites: Fluency in at least one program- Prerequisites: CSEE W3827 and knowledge of C algebra is required. Introduction to computer ming language and familiarity with computer sys- and programming tools as covered in COMS graphics. Topics include 3D viewing and projec- tems. Introduction to current topics in computer W3157 or W3101, or the instructor’s permission. tions, geometric modeling using spline curves, science technology. Each section will be devoted Design and implementation of operating systems. graphics systems such as OpenGL, lighting and to a specific technology. Sections may meet for Topics include process management, process shading, and global illumination. Significant imple-

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mentation is required: the final project involves ware support. 3D interaction devices and dis- Prerequisite: COMS W3261. Develops a quantita- 115 writing an interactive 3D video game in OpenGL. plays. Virtual and augmented reality. Tangible tive theory of the computational difficulty of prob- user interfaces. Review of relevant 3D math. lems in terms of the resources (eg. time, space) COMS W4162x or y Advanced computer graphics needed to solve them. Classification of problems Lect: 3. 3pts. Professor Ramamoorthi. COMS W4180x or y Network security into complexity classes, reductions, and com- Prerequisites: COMS 4160 or the equivalent, or Lect: 3. 3 pts. Professor Bellovin. pleteness. Power and limitations of different the instructor’s permission. A second course in Prerequisite: COMS W3137 or W3139, and modes of computation such as nondeterminism, computer graphics covering more advanced topics W4119, or the instructor’s permission. randomization, interaction, and parallelism. including image and signal processing, geometric Introduction to network security concepts and modeling with meshes, advanced image synthe- mechanisms; measures employed in countering COMS W4241y Numerical algorithms and sis including ray tracing and global illumination, such threats. Concepts and tools available in complexity and other topics as time permits. Emphasis will be order to assume an appropriate security posture. Lect: 3. 3 pts. Professor Traub. placed both on implementation of systems and Foundations of network security and an in-depth Prerequisite: Knowledge of a programming lan- important mathematical and geometric concepts review of commonly used security mechanisms guage. Some knowledge of scientific computation such as Fourier analysis, mesh algorithms and and techniques; security threats and network- is desirable. Modern theory and practice of com- subdivision, and Monte Carlo sampling for render- based attacks, applications of cryptography, putation on digitial computers. Introduction to ing. Note: Course will be taught every two years. authentication, access control, intrusion detection concepts of computational complexity. Design and and response, security protocols (IPsec, SSL, analysis of numerical algorithms. Applications to COMS W4165x Computational techniques in Kerberos), denial of service attacks and defens- computational finance, computational science, and pixel processing es, viruses and worms, software vulnerabilities, computational engineering. Lect: 3. 3 pts. Instructor to be announced. Web security, wireless security, and privacy. Prerequisites: COMS W3137, W3251 (recom- COMS W4252x or y Introduction to computa- mended), and a good working knowledge of UNIX COMS W4187x or y Security architecture and tional learning theory and C. Intended for graduate students and advanced engineering Lect: 3. 3 pts. Professor Servedio. undergraduates. An intensive introduction to Lect: 3. 3 pts. Professor Bellovin. Prerequisite: COMS W4231 (or W4236), or image processing—digital filtering theory, image Prerequisites: COMS W4118; W4180 and/or COMS W3203 and the instructor’s permission, enhancement, image reconstruction, antialiasing, W4119 recommended. Secure programming. or W3261 and the instructor’s permission. warping, and the state of the art in special effects. Cryptograhic engineering and key handling. Possibilities and limitations of performing learning Topics form the basis of high-quality rendering in Access controls. Tradeoffs in security design. by computational agents. Topics include computa- computer graphics and of low-level processing for Design for security. tional models of learning, polynomial time learn- computer vision, remote sensing, and medical ability, learning from examples, and learning from imaging. Emphasizes computational techniques COMS W4203y Graph theory queries to oracles. Computational and statistical for implementing useful image-processing functions. Lect: 3. 3 pts. Professor Gross. limitations of learning. Applications to Boolean Prerequisite: COMS W3203. General introduction functions, geometric functions, automata. COMS W4167x or y Computer animation to graph theory. Isomorphism testing, algebraic Lect: 3. 3pts. Professor Grinspun. specification, symmetries, spanning trees, tra- COMS W4261x or y Introduction to cryptography Prerequisites: COMS W3137 or W3139, and W4156 versability, planarity, drawings on higher-order Lect: 2.5. 3 pts. Professor Malkin. is recommended. Previous familiarity with C is rec- surfaces, colorings, extremal graphs, random Prerequisites: Comfort with basic discrete math ommended. Intensive introduction to computer ani- graphs, graphical measurement, directed graphs, and probability. Recommended: COMS W3261 or mation, including fundamental theory and algorithms Burnside-Polya counting, voltage graph theory. W4231. An introduction to modern cryptography, for computer animation, keyframing, kinematic rig- focusing on the complexity-theoretic foundations ging, simulation, dynamics, free-form animation, COMS W4205x Combinatorial theory of secure computation and communication in behavioral/procedural animation, particle systems, Lect: 3. 3 pts. Professor Gross. adversarial environments; a rigorous approach, postproduction; small groups implement a significant Prerequisites: COMS W3203 and a course in based on precise definitions and provably secure animation project; advanced topics as time permits. calculus. Sequences and recursions, calculus of protocols. Topics include private and public key finite differences and sums, elementary number encryption schemes, digital signatures, authenti- COMS W4170x User interface design theory, permutation group structures, binomial cation, pseudorandom generators and functions, Lect: 3. 3 pts. Professor Feiner. coefficients, Stilling numbers, harmonic numbers, one-way functions, trapdoor functions, number Prerequisite: COMS W3137. Introduction to the theory generating functions. theory and computational hardness, identification and practice of computer user interface design, and zero knowledge protocols. emphasizing the software design of graphical CSOR W4231x Analysis of algorithms, I user interfaces. Topics include basic interaction Lect: 3. 3 pts. Professor Yannakakis. COMS W4281x or y Introduction to quantum devices and techniques, human factors, interaction Prerequisites: COMS W3137 or W3139, and computing styles, dialogue design, and software infrastructure. W3203. Introduction to the design and analysis Lect. 3. 3 pts. Prof. Wozniakowski. Design and programming projects are required. of efficient algorithms. Topics include models of Prerequisites: Knowledge of linear algebra. Prior computation, efficient sorting and searching, algo- knowledge of quantum mechanics is not required COMS W4172y 3D user interfaces and rithms for algebraic problems, graph algorithms, although helpful. Introduction to quantum comput- augmented reality dynamic programming, probabilistic methods, ing. Shor’s factoring algorithm, Grover’s database Lect: 3. 3 pts. Professor Feiner. approximation algorithms, and NP-completeness. search algorithm, the quantum summation algorithm. Prerequisite: COMS W4160 or COMS W4170, or Note: This course is the same as CSOR W4231 Relationship between classical and quantum the instructor’s permission. Design, development, (CS and IEOR departments). computing. Potential power of quantum computers. and evaluation of 3D user interfaces. Interaction techniques and metaphors, from desktop to COMS W4236y Introduction to computational EECS W4340x Computer hardware design immersive. Selection and manipulation. Travel complexity Lect: 3. 3 pts. Instructor to be announced. and navigation. Symbolic, menu, gestural, and Lect: 3. 3 pts. Professor Yannakakis and Prerequisites: ELEN E3331 and CSEE W3827. multimodal interaction. Dialogue design. 3D soft- Professor Servedio. Practical aspects of computer hardware design

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116 through the implementation, simulation, and pro- or the instructor’s permission. Computational COMS W4735x or y Visual interfaces to computers totyping of a PDP-8 processor. High-level and approaches to natural language generation and Lect: 3. 3 pts. Instructor to be announced. assembly languages, I/O, interrupts, datapath and understanding. Recommended preparation: some Prerequisite: COMS W3137. Visual input as data control design, pipelining, busses, memory archi- previous or concurrent exposure to AI or machine and for control of computer systems. Survey and tecture. Programmable logic and hardware proto- learning. Topics include information extraction, analysis of architecture, algorithms, and underly- typing with FPGAs. Fundamentals of VHDL for summarization, machine translation, dialogue sys- ing assumptions of commercial and research sys- register-transfer level design. Testing and valida- tems, and emotional speech. Particular attention tems that recognize and interpret human ges- tion of hardware. Hands-on use of industry CAD is given to robust techniques that can handle tures, analyze imagery such as fingerprint or iris tools for simulation and synthesis. Lab required. understanding and generation for the large amounts patterns, generate natural language descriptions of text on the Web or in other large corpora. of medical or map imagery. Explores foundations COMS W4444x Programming and problem solving Programming exercises in several of these areas. in human psychophysics, cognitive science, and Lect: 3. 3 pts. Professor Ross. artificial intelligence. Prerequisites: COMS W3137 and W3824. Hands- COMS W4706x Spoken language processing on introduction to solving open-ended computational Lect: 3. 3pts. Professor Hirschberg. COMS W4737x or y Biometrics problems. Emphasis on creativity, cooperation, Prerequisites: COMS W3133, W3134, or W3137, Lect: 3. 3 pts. Professor Belhumeur. and collaboration. Projects spanning a variety of or the instructor’s permission. Computational Prerequisite: A background at the sophomore areas within computer science, typically requiring approaches to speech generation and under- level in computer science, engineering, or like the development of computer programs. General- standing. Topics include speech recognition and discipline. In this course we will explore the latest ization of solutions to broader problems, and understanding, speech analysis for computational advances in biometrics as well as the machine specialization of complex problems to make them linguistics research, and speech synthesis. learning techniques behind them. Students will manageable. Team-oriented projects, with student Speech applications including dialogue systems, learn how these technologies work and how they presentations and in-class participation required. data mining, summarization, and translation. are sometimes defeated. Grading will be based Exercises involve data analysis and building a on homework assignments and a final project. COMS W4560x Introduction to computer appli- small text-to-speech system. There will be no midterm or final exam. This cations in health care and biomedicine course shares lectures with COMS E6737. Lect: 3. 3 pts. Professor Chiang. COMS W4725x or y Knowledge representation Students taking COMS E6737 are required to Prerequisites: Experience with computers and a and reasoning complete additional homework problems and passing familiarity with medicine and biology. Lect: 3. 3 pts. Instructor to be announced. undertake a more rigorous final project. Students Undergraduates in their senior or junior years may Prerequisite: COMS 4701. General aspects of will only be allowed to earn credit for COMS take this course only if they have adequate back- knowledge representation (KR). The two funda- W4737 or COMS E6737 and not both. ground in mathematics and receive permission mental paradigms (semantic networks and frames) from the instructor An overview of the field of bio- and illustrative systems. Topics include hybrid sys- CBMF W4761x or y Computational genomics medical informatics, combining perspectives from tems, time, action/plans, defaults, abduction, and Lect: 3. 3 pts. Instructor to be announced. medicine, computer science, and social science. case-based reasoning. Throughout the course Prerequisites: Either (1) ECBM E4060 or (2) Use of computers and information in health care particular attention will be paid to design tradeoffs COMS W1003, W1004, or W1007 and SIEO and the biomedical sciences, covering specific between language expressiveness and reasoning W4150, or SIEO W3600. Computational tech- applications and general methods, current issues, complexity, and issues relating to the use of KR niques for analyzing and understanding genomic capabilities and limitations of biomedical informat- systems in larger applications. data, including DNA, RNA, protein and gene ics. Biomedical informatics studies the organiza- expression data. Basic concepts in molecular tion of medical information, the effective manage- COMS W4731x or y Computer vision biology relevant to these analyses. Emphasis on ment of information using computer technology, Lect: 3. 3 pts. Professor Nayar. techniques from artificial intelligence and machine and the impact of such technology on medical Prerequisites: The fundamentals of calculus, linear learning. String-matching algorithms, dynamic research, education, and patient care. The field algebra, and C programming. Students without any programming, hidden Markov models, expecta- explores techniques for assessing current infor- of these prerequisites are advised to contact the tion-maximization, neural networks, clustering mation practices, determining the information instructor prior to taking the course. Introductory algorithms, support vector machines. Students needs of health care providers and patients, course in computer vision. Topics include image with life sciences backgrounds who satisfy the developing interventions using computer technology, formation and optics, image sensing, binary images, prerequisites are encouraged to enroll. and evaluating the impact of those interventions. image processing and filtering, edge extraction and boundary detection, region growing and segmen- COMS W4771y Machine learning COMS W4701x or y Artificial intelligence tation, pattern classification methods, brightness Lect: 3. 3 pts. Professor Jebara. Lect: 3. 3 pts. x: Professor McKeown; and reflectance, shape from shading and photo- Prerequisites: Any introductory course in linear y: Professor Stolfo. metric stereo, texture, binocular stereo, optical flow algebra and any introductory course in statistics Prerequisite: COMS W3137. Provides a broad and motion, 2-D and 3-D object representation, are both required. Highly recommended: COMS understanding of the basic techniques for building object recognition, vision systems and applications. W4701 or knowledge of artificial intelligence. intelligent computer systems. Topics include state- Topics from generative and discriminative machine space problem representations, problem reduction COMS W4733x or y Computational aspects learning including least squares methods, support and and-or graphs, game playing and heuristic of robotics vector machines, kernel methods, neural networks, search, predicate calculus, and resolution theorem Lect: 3. 3 pts. Professor Allen. Gaussian distributions, linear classification, linear proving, AI systems and languages for knowledge Prerequisite: COMS W3137. Introduction to robot- regression, maximum likelihood, exponential representation, machine learning, and concept ics from a computer science perspective. Topics family distributions, Bayesian networks, Bayesian formation and other topics such as natural language include coordinate frames and kinematics, com- inference, mixture models, the EM algorithm, processing may be included as time permits. puter architectures for robotics, integration and graphical models, and hidden Markov models. use of sensors, world modeling systems, design Algorithms implemented in Matlab. COMS W4705x Natural language processing and use of robotic programming languages, and Lect: 3. 3 pts. Professor Hirschberg. applications of artificial intelligence for planning, COMS W4772x Advanced machine learning Prerequisite: COMS W3133, W3134, or W3137, assembly, and manipulation. Lect: 3. 3 pts. Professor Jebara.

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Prerequisites: COMS W4771 or the instructor’s COMS W4901x and y Projects in computer tion, query processing, semantics, or transaction 117 permission; knowledge of linear algebra and intro- science management. A substantial project is typically ductory probability or statistics is required. An 1 to 3 pts. Instructor to be announced. required. May be repeated for credit with instruc- exploration of advanced machine learning tools Prerequisite: Approval by a faculty member who tor’s permission. for perception and behavior learning. How can agrees to supervise the work. A second-level inde- machines perceive, learn from, and classify human pendent project involving laboratory work, computer COMS E6117x or y Topics in programming activity computationally? Topics include appearance- programming, analytical investigation, or engineer- languages and translators based models, principal and independent compo- ing design. May be repeated for credit, but not for Lect: 2. 3 pts. Professor Aho. nents analysis, dimensionality reduction, kernel a total of more than 3 points of degree credit. Prerequisite: COMS W4115 or the instructor’s methods, manifold learning, latent models, regres- Consult the department for section assignment. permission. Concentration on the design and sion, classification, Bayesian methods, maximum implementation of programming languages and entropy methods, real-time tracking, extended COMS W4910x Curricular practical training tools focused on advanced applications in new Kalman filters, time series prediction, hidden 1 pt. Instructor to be announced. areas in software verification, distributed systems, Markov models, factorial HMMs, input-output Prerequisite: Obtained internship and the faculty programming in the large, and Web computing. HMMs, Markov random fields, variational methods, adviser’s permission. Only for M.S. students in A substantial project is typically required. May be dynamic Bayesian networks, and Gaussian/ the Department of Computer Science who need repeated for credit. Dirichlet processes. Links to cognitive science. relevant work experience as part of their program of study. Final report required. This course may COMS E6118y Operating systems, II CSEE W4823x or y Advanced logic design not be taken for pass/fail credit or audited. Lect: 2: 3 pts. Professor Nieh. Lect: 3. 3 pts. Professor Nowick. Prerequisite: COMS W4118. Corequisite: COMS Prerequisite: CSEE W3827 or a half-semester COMS W4995x or y Special topics in W4119. Continuation of COMS W4118, with introduction to digital logic, or the equivalent. An computer science, I emphasis on distributed operating systems. Topics introduction to modern digital system design. Lect: 3. 3 pts. x: Professor Belhumeur; include interfaces to network protocols, distrib- Advanced topics in digital logic: controller synthesis y: instructor to be announced. uted run-time binding, advanced virtual memory (Mealy and Moore machines); adders and multipli- Prerequisite: The instructor’s permission. Special issues, advanced means of interprocess commu- ers; structured logic blocks (PLDs, PALs, ROMs); topics arranged as the need and availability arises. nication, file system design, design for extensibility, iterative circuits. Modern design methodology: Topics are usually offered on a one-time basis. security in a distributed environment. Investigation register transfer level modelling (RTL); algorithmic Since the content of this course changes each is deeper and more hands-on than in COMS state machines (ASMs); introduction to hardware time it is offered, it may be repeated for credit. W4118. A programming project is required. description languages (VHDL or Verilog); system- Consult the department for section assignment. level modeling and simulation; design examples. COMS E6123x or y Programming environ- COMS W4996x or y Special topics in ments and software tools (PEST) CSEE W4824x or y Computer architecture computer science, II Lect: 2. 3 pts. Professor Kaiser. Lect: 3. 3 pts. Professor Carloni. Lect: 3. 3 pts. Instructor to be announced. Prerequisite: At least one COMS W41xx or COMS Prerequisite: CSEE W3827 or the equivalent. Prerequisite: The instructor’s permission. A con- E61xx course and/or COMS W4444, or the Focuses on advanced topics in modern computer tinuation of COMS W4995 when the special topic instructor’s permission. Strongly recommended: architecture, illustrated by recent case studies. extends over two terms. COMS W4156. Software methodologies and Fundamentals of quantitative analysis. Pipelined, technologies concerned with development and out-of-order, and speculative execution. Superscalar, COMS W4999y Computing and the humanities operation of today’s software systems. Reliability, VLIW, and vector processors. Embedded proces- Lect: 3. 3 pts. Instructor to be announced. security, systems management, and societal sors. Memory hierarchy design. Multiprocessors Text databases. Language applications, such as issues. Emerging software architectures such as and thread-level parallelism. Synchronization and machine translation, information and retrieval, enterprise and grid computing. Term paper and cache coherence protocols. Interconnection networks. computational stylistics (determining authorship). programming project. Seminar focus changes Digital library applications, including issues in text frequently to remain timely. CSEE W4825y Digital systems design acquisition, text markup, networking display, and Lect: 3. 3 pts. Instructor to be announced. user interfaces. Educational applications. Legal COMS E6125y Web-enhanced information Prerequisite: CSEE W3827. Dynamic logic, reasoning, history applications involving inferenc- management (WHIM) field programmable gate arrays, logic design lan- ing and databases. Lect: 2. 3 pts. Professor Kaiser. guages, multipliers. Special techniques for multi- Prerequisite: At least one COMS W41xx or COMS level NAND and NOR gate circuits. Clocking COMS E6111y Advanced database systems E61xx course and/or COMS W4444, or the instruc- schemes for one- and two-phrase systems. Fault Lect: 2. 3 pts. Professor Gravano. tor’s permission. Strongly recommended: COMS checking: scan method, built-in test. Survey of Prerequisite: COMS W4111 and knowledge of W4111. History of hypertext, markup languages, logic simulation methods. Other topics to be Java or the instructor’s permission. Continuation groupware, and the Web. Evolving Web proto- added as appropriate. of COMS W4111, the course covers latest trends cols, formats and computation paradigms such as in both database research and industry: informa- HTTP, XML, and Web Services. Novel application CSEE W4840y Embedded systems tion retrieval, Web search, data mining, data domains enabled by the Web and societal issues. Lect: 3. 3 pts. Professor Edwards. warehousing, OLAP, decision support, multimedia Term paper and programming project. Seminar Prerequisite: CSEE W4823. Embedded system databases, and XML and databases. focus changes frequently to remain timely. design and implementation combining hardware Programming projects required. and software, I/O, interfacing, and peripherals. COMS E6160x or y Topics in computer graphics Weekly laboratory sessions and term project on COMS E6113y Topics in database systems Lect: 2. 3 pts. Professors Ramamoorthi and design of a microprocessor-based embedded Lect: 2. 3 pts. Instructor to be announced. Belhumeur. system including at least one custom peripheral. Prerequisite: COMS W4111. Concentration on Prerequisite: COMS W4160 or the instructor’s Knowledge of C programming and digital logic some database paradigm, such as deductive, permission. An advanced graduate course, involv- required. Lab required. heterogeneous, or object-oriented, and/or some ing study of an advanced research topic in com- database issue, such as data modeling, distribu- puter graphics. Content varies between offerings,

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118 and the course may be repeated for credit. Recent will cover the following topics: legal and social able security. Contents varies between offerings. offerings have included appearance models in framework for privacy; data mining and databas- May be repeated for credit. graphics and high-quality real-time rendering. es; anonymous commerce and internet usage; traffic analysis; policy and national security con- COMS E6291x or y Theoretical topics in COMS E6174y Interaction design: a perceptual siderations. Classes are seminars, with students computer science approach presenting papers and discussing them. Seminar Lect: 3. 3 pts. Instructor to be announced. Lect: 3. 3 pts. Professor Paley. focus changes frequently to remain timely. Prerequisite: The instructor’s permission. Prerequisite: CS W4170 or the instructor’s per- Concentration on some theoretical aspect of com- mission. Design methology for special-purpose COMS E6185x or y Intrusion and anomaly puter science. Content varies from year to year. user interfaces. Emphasis on how psychology detection systems May be repeated for credit. and perception inform good design. Interviewing Lect: 2. 2 pts. Professor Stolfo and task modeling, participatory design, and low- Prerequisite and corequisite: COMS W4180. COMS E6732x or y Computational imaging fidelity prototyping. Applications of brain research, Network security. The state of threats against Lect: 3. 3 pts. Professor Nayar. graphic design, and art to develop custom user computers, and networked systems. An overview Prerequisite: COMS W4731 or the instructor’s interfaces components, screen layouts, and inter- of computer security solutions and why they fail, permission. Computational imaging uses a combi- action techniques for application-specific systems. including vulnerability assessment, firewalls, nation of novel imaging optics and a computational vpn’s. Provides a detailed treatment for network module to produce new forms of visual information. COMS E6176x or y User interfaces for mobile and host-based intrusion detection and intrusion Survey of the state of the art in computational and wearable computing prevention systems and the classes of attacks imaging. Review of recent papers on omni direc- Lect: 2. 3 pts. Professor Feiner. each covers. Considerable depth is provided on tional and panoramic imaging, catadioptric imag- Prerequisite: COMS W 4170 or the instructor’s anomaly detection systems to detect new, zero- ing, high dynamic range imaging, mosaicing and permission. Introduction to research on user inter- day attacks. Covers issues and problems in superresolution. Classes are seminars with the faces for mobile and wearable computing through e-mail (spam and viruses) and insider attacks instructor, guest speakers, and students present- lectures, invited talks, student-led discussions of (masquerading and impersonation). Science ing papers and discussing them. important papers, and programming projects. Designing requirement: partial fulfillment. and authoring for mobility and wearability. Ubiquitous/ COMS E6733x or y 3-D photography pervasive computing. Collaboration with other COMS E6204x or y Topics in graph theory Lect: 2. 3pts. Professor Allen. users. Display, interaction, and communication Lect: 2. 3 pts. Professor Gross. Prerequisite: Experience with at least one of the technologies. Sensors for tracking position, orien- Prerequisite: COMS W4203 or the instructor’s permis- following topics: computer graphics, computer tation, motion, environmental context, and personal sion. Content varies from year to year. This course vision, pixel processing, robotics, or computer- context. Applications and social consequences. may be repeated for credit. Concentration on some aided design, or the instructor’s permission. aspect of graph theory, such as topological graph Programming proficiency in C, C++, or Java. 3-D CSEE E6180x or y Modeling and performance theory, algebraic graph theory, enumerative graph photography—the process of automatically creat- Lect: 2. 3 pts. x: instructor to be announced; theory, graphical optimization problems, or matroids. ing 3-D, texture-mapped models of objects in y: Professor Misra. detail. Applications include robotics, medicine, Prerequisites: COMS W4118 and SIEO W4150. COMS E6206x or y Topics in combinatorial theory graphics, virtual reality, entertainment, and digital Introduction to queueing analysis and simulation Lect: 2. 3 pts. Professor Gross. movies, etc. Topics include 3-D data acquisition techniques. Evaluation of time-sharing and multi- Prerequisite: COMS W4203 or W4205, or the devices, 3-D modeling systems, and algorithms processor systems. Topics include priority queueing, instructor’s permission. Concentration on some to acquire, create, augment, manipulate, render, buffer storage, disk access, interference and bus con- aspect of combinatorial theory. Content varies from animate, and physically build such models. The tention problems, and modeling of program behaviors. year to year. This course may be repeated for credit. course is divided into three parts. The first third is devoted to lectures introducing the concept of 3-D COMS E6181x or y Advanced Internet services COMS E6232x or y Analysis of algorithms, II photography and advanced modeling. The second Lect: 2. 3 pts. Professor Schulzrinne. Lect: 2. 3 pts. Instructor to be announced. part will be student presentations of related papers In-depth survey of protocols and algorithms need- Prerequisite: COMS W4231. Continuation of in the field. The third part will be a series of group ed to transport multimedia information across the COMS W4231. projects centered around using 3-D photography Internet, including audio and video encoding, mul- to model objects (buildings, rooms, people, etc.). ticast, quality-of-service, voice-over-IP, streaming COMS E6253y Advanced topics in computa- media, and peer-to-peer multimedia systems. tional learning theory CSEE E6734y Computational photography Includes a semester-long programming project. Lect: 3. 3 pts. Professor Servedio. Lect: 3. 3 pts. Professor Belhumeur. Prerequisites: COMS W4231 or equivalent; Prerequisite: COMS W4160, W4731, or a working COMS E6183x Advanced topics in network COMS W4252 or W4236 helpful but not required. knowledge of photography are recommended. security In-depth study of inherent abilities and limitations Students should have knowledge in any of three Lect: 3. 3 pts. Professor Keromytis. of computationally efficient learning algorithms. core areas: computer vision, computer graphics, or Prerequisites: COMS W4180, W4119, and W4261 Algorithms for learning rich Boolean function photography. Computational techniques are used recommended. Review the fundamental aspects classes in online, Probably Approximately Correct, to produce a new level of images and visual repre- of security, including authentication, authorization, and exact learning models. Connections with sentations. Topics include HDR imaging, feature access control, confidentiality, privacy, integrity, computational complexity theory emphasized. matching using RANSAC, image mosaics, image- and availability. Review security techniques and Substantial course project or term paper required. based rendering, motion magnification, camera tools, and their applications in various problem lens arrays, programmable lighting, face detection, areas. Study the state of the art in research. COMS E6261x or y Advanced cryptography single- and multiview geometry, and more. A programming project is required. Lect: 3. 3 pts. Professor Malkin. Prerequisite: COMS W4261. A study of advanced COMS E6735y Visual databases COMS E6184y Seminar on anonymity and privacy cryptographic research topics, such as secure Lect: 3. 3 pts. Professor Kender. Lect: 3. 3 pts. Professor Bellovin. computation, zero knowledge, privacy, anonymity, Prerequisites: COMS W3133, W3134, or W3137 Prerequisite: COMS W4261 or W4180 or CSEE cryptographic protocols. Concentration on theo- required; COMS W4731 or COMS W4735 helpful W4119 or the instructor’s permission. This course retical foundations, rigorous approach, and prov- but not required. Contact instructor if uncertain.

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The analysis and retrieval of large collections of information loss, linear circuits, structure theory. needed. Oral and written reports are required. 119 image and video data, with emphasis on visual Reliability and testability of digital systems. May be taken over more than one semester, semantics, human psychology, and user inter- in which case the grade will be deferred until all faces. Low-level processing: features and similari- CSEE E6847y Distributed embedded systems 12 points have been completed. No more than ty measures; shot detection; key frame selection; Lect: 2. 3 pts. Professor Carloni. 12 points of COMS E6901 may be taken. Consult machine learning methods for classification. Prerequisite: Any course numbered in the the department for section assignment. Middle-level processing: organizational rules for COMS4110s, CSEE4800s, or ELEN4300s, or the videos, including unedited (home, educational), instructor’s permission. An interdisciplinary gradu- COMS E6902x and y Thesis semiedited (sports, talk shows), edited (news, ate-level seminar on the design of distributed 1 to 9 pts. Instructor to be announced. drama); human memory limits; progressive refine- embedded systems. Emphasis is put on system Available to MS and CSE candidates. An inde- ment; visualization techniques; incorporation of robustness in the presence of highly variable pendent investigation of an appropriate problem audio and text. High-level processing: extraction communication delays and heterogeneous com- in computer science carried out under the super- of thematic structures; ontologies, semantic fil- ponent behaviors. The course has a two-fold vision of a faculty member. A formal written report ters, and learning; personalization of summaries structure: the study of the enabling technologies is essential and an oral presentation may also and interfaces; detection of pacing and emotions. (VLSI circuits, communication protocols, embed- be required. May be taken over more than one Examples and demonstrations from commercial ded processors, RTOSs), models of computation, semester, in which case the grade will be deferred and research systems throughout. Substantial and design methods is coupled with the analysis until all 9 points have been completed. No more course project or term paper required. of modern domain-specific applications, including than 9 points of COMS E6902 may be taken. on-chip micro-networks, multiprocessor systems, Consult the department for section assignment. COMS E6737x or y Biometrics fault-tolerant architectures, and robust deploy- Lect: 3. 3 pts. Professor Belhumeur. ment of embedded software. Common research COMS E6998x and y Topics in computer Prerequisites: A background at the sophomore challenges include design complexity, reliability, science, I level in computer science, engineering, or like scalability, safety, and security. The course 3 pts. Instructor to be announced. discipline. In this course we will explore the latest requires substantial reading, class participation, Prerequisite: The instructor’s permission. Selected advances in biometrics as well as the machine and a research project. topics in computer science. Content varies from learning techniques behind them. Students will year to year. May be repeated for credit. learn how these technologies work and how they CSEE E6861y Computer-aided design of digital are sometimes defeated. Grading will be based systems COMS E6999x and y Topics in computer on homework assignments and a final project. Lect: 2. 3 pts. Professor Nowick. science, II There will be no midterm or final exam. This Prerequisites: (1) One semester of advanced digi- 3 pts. Instructor to be announced. course shares lectures with COMS W4737. tal logic (CSEE W4823 or the equivalent, or the Prerequisite: COMS E6998. Continuation of Students taking COMS E6737 are required to instructor’s permission); (2) a basic course in data COMS E6998. complete additional homework problems and structures and algorithms (COMS W3133, W3134, undertake a more rigorous final project. Students W3137, W3139, or W3157, or the equivalent) and COMS E9800x and y Directed research in will only be allowed to earn credit for COMS familiarity with programming. Introduction to mod- computer science W4737 or COMS E6737 and not both. ern digital CAD synthesis and optimization tech- 1 to 15 pts. Instructor to be announced. niques. Topics include modern digital system Prerequisite: Submission of an outline of the pro- CSEE E6824y Parallel computer architecture design (high-level synthesis, register-transfer level posed research for approval by the faculty member Lect: 3. 3 pts. Professor Sethumadhavan. modeling, algorithmic state machines, optimal who will supervise. The department must approve Prerequisite: CSEE W8424. Parallel computer scheduling algorithms, resource allocation and the number of points. May be repeated for credit. principles, machine organization, and design of binding, retiming), controller synthesis and opti- This course is only for Eng.Sc.D. candidates. parallel systems, including parallelism detection mization, exact and heuristic two-level logic mini- methods, synchronization, data coherence, and mization, advanced multilevel logic optimization, COMS E9910x and y Graduate research, I interconnection networks. Performance analysis optimal technology mapping to library cells (for 1 to 6 pts. Instructor to be announced. and special-purpose parallel machines. delay, power, and area minimization), advanced Prerequisite: Submission of an outline of the pro- data structures (binary delusion diagrams), SAT posed research for approval by the faculty mem- CSEE E6831y Sequential logic circuits solvers and their applications, stati timing analysis, ber who will supervise. The department must Lect: 3. 3 pts. Professor Unger. and introduction to testability. Includes hands-on approve the number of credits. May be repeated Prerequisite: CSEE W3827 or any introduction to small design projects using and creating CAD for credit.This course is only for MS candidates logic circuits. Generation and manipulation of flow tools. General Education Requirement: Quantitave holding GRA or TA appointments. Note: It is not table descriptions to asynchronous sequential and Deductive Reasoning (QUA). required that a student take Graduate research, I functions. Coding of flow tables to satisfy various prior to taking Graduate research, II. Consult the design criteria. Delays, races, hazards, metastabili- COMS E6900x and y Tutorial in computer science department for section assignment. ty. Analysis of latches to determine key parame- 1 to 3 pts. Instructor to be announced. ters. Bounds of input rates. Clocking schemes for Prerequisite: Permission of the instructor. A reading COMS E9911x and y Graduate research, II synchronous systems. Synthesis of self-timed sys- course in an advanced topic for a small number 1 to 15 pts. Instructor to be announced. tems using 4-phase or 2-phase handshakes. of students, under faculty supervision. Prerequisites: Submission of an outline of the proposed research for approval by the faculty CSEE E6832x or y Topics in logic design theory COMS E6901x and y Projects in computer member who will supervise. The department must Lect: 3. 3 pts. Professors Theobald and Ivancic. science approve the number of points. May be repeated Prerequisite: CSEE W3827 or any introduction to 1 to 12 pts. Instructor to be announced. for credit. This course is only for MS/PhD track logic circuits. A list of topics for each offering of Prerequisite: Permission of the instructor. Software students. Note: It is not required that a student the course is available in the department office or hardware projects in computer science. Before take Graduate research, I prior to taking Graduate one month before registration. May be taken registering, the student must submit a written research, II. Consult the department for section more than once if topics are different. Iterative proposal to the instructor for review. The proposal assignment. logic circuits applied to pattern recognition. should give a brief outline of the project, estimated Finite state machines; alternative representations, schedule of completion, and computer resources

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120 EARTH AND ENVIRONMENTAL ENGINEERING Henry Krumb School of Mines 918 S. W. Mudd, MC 4711, 212-854-2905 www.eee.columbia.edu

OUR MISSION Earth and Environmental Engineering at the Henry Krumb School of Mines fosters excellence in education and research for the development and application of science and technology to maximize the quality of life for all, through the sustainable use and responsible management of Earth’s resources.

CHAIR PROFESSORS ASSISTANT PROFESSORS ADJUNCT PROFESSORS ASSOCIATE RESEARCH Klaus Lackner Paul F. Duby Marco Castaldi William Becker SCIENTISTS Klaus Lackner Kartik Chandran Raymond S. Farinato Irina Chernyshova VICE CHAIR Upmanu Lall Gavin Gong Robert Farrauto S. Murthy Khandrika Tuncel M. Yegulalp Ismail C. Noyan Ah-Hyung (Alissa) Park Yuri Gorokhovich Hyung Chul Kim Peter Schlosser D. R. Nagaraj DEPARTMENTAL Ponisseril Somasundaran LECTURER DOHERTY RESEARCH ADMINISTRATOR Nickolas J. Themelis Chris Gazze ADJUNCT ASSISTANT SCIENTIST Peter Rennée Nicholas J. Turro PROFESSORS Wade McGillis Tuncel M. Yegulalp Scott Kaufman ADMINISTRATIVE ASSISTANT Sri Rangarajan SENIOR RESEARCH Gary S. Hill ASSOCIATE PROFESSOR Greg Yetman SCIENTIST Xi Chen Vasilis Fthenakis

EARTH RESOURCES AND department in the U.S. It became the • The Earth Engineering Center. The THE ENVIRONMENT foundation for Columbia’s School of Engi- current research areas include energy, The Earth and Environmental Engineering neering and Applied Sciences and has materials, and water resources. program fosters education and research been a pioneer in many areas of mining in the development and application of and metallurgy, including the first mining EARTH AND ENVIRONMENTAL technology for the sustainable develop- (Peele) and mineral processing (Taggart) ENGINEERING (EEE) ment, use, and integrated management handbooks, flotation, chemical thermo- Starting in 1996, the educational pro- of Earth’s resources. Resources are dynamics and kinetics, surface and col- grams of Columbia University in mining identified as minerals, energy, water, air, loid chemistry, and materials science. and mineral engineering were trans- and land, as well as the physical, chemi- Nearly one hundred years after its formed into the present program in cal, and biological components of the formation, the School of Mines was Earth and Environmental Engineering environment. There is close collaboration renamed Henry Krumb School of Mines (EEE). This program is concerned with with other engineering disciplines, the (HKSM) in honor of the generous the environmentally sound extraction Lamont-Doherty Earth Observatory, the Columbia benefactor of the same name. and processing of primary materials International Research Institute for Climate The Henry Krumb School of Mines (minerals, fuels, water), the management Prediction, the Center for Environmental (SEAS) supports three components: and development of land and water Research and Conservation, and other • The Department of Earth and resources, and the recycling or disposal Columbia Earth Institute units. Environmental Engineering (EEE), of used materials. EEE offers the one of the nine departments of SEAS. Bachelor of Science (B.S.) in Earth and THE HENRY KRUMB SCHOOL • Columbia’s interdepartmental program Environmental Engineering, the Master OF MINES AT COLUMBIA in Materials Science and Engineering of Science (M.S.) in Earth Resources UNIVERSITY (MSE). This program, administered by Engineering, the professional degrees the Department of Applied Physics The School of Mines of Columbia of Engineer of Mines and Metallurgical and Applied Mathematics, is described University was established in 1864 and Engineer, and the doctorate degrees in another section of this bulletin. was the first mining and metallurgy (Ph.D., Eng.Sc.D.) in EEE.

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The EEE program welcomes ing changing climate, demographic, ses of energy systems. LCA provides a Combined Plan students. An EEE minor and usage dynamics framework for quantifying the potential is offered to all Columbia engineering • target analyses toward public and environmental impacts of material and students who want to enrich their aca- private investment in future water energy inputs and outputs of a process demic record by concentrating some of resource development, local and or product from “cradle to grave.” The their technical electives on Earth/envi- regional ecosystem services provided mission of the Center is to guide technol- ronment subjects. There is close collab- by water and the essential life-support ogy and energy policy decisions with data- oration between EEE and the Depart- water needs of societies based, well-balanced, and transparent ments of Civil Engineering and Earth • identify and test appropriate technolo- descriptions of the environmental profiles and Environmental Sciences, including gies for the storage, treatment, and of energy systems. For more information: several joint appointments. conveyance of water to improve www.seas.columbia.edu/clca EEE and the Earth Engineering reliable, cost-efficient access Center for Sustainable Use of Center are the contributions of The Fu • identify and compare locally appropri- Resources (SUR). The Center for Foundation School of Engineering and ate policy instruments that facilitate the Sustainable Use of Resources builds Applied Science to The Earth Institute of implementation of selected incentives on the strengths of past research at Columbia University, a major education for higher-value, higher-efficiency water Columbia and North Carolina State on and research initiative of the University. use, while promoting equity of use and recycling, composting, waste-to-energy, The Department of Earth and life support functions and landfill engineering. Also, the Center Environmental Engineering combines • test and demonstrate the applicability will clearly define the impacts of all solid the longstanding and proud tradition of of the policy and technology develop- waste technologies and practices with Columbia’s School of Mines with for- ments in real-world settings, working regard to greenhouse gas emissions and ward-thinking courses and programs, with local institutions and private-sector will, on a case-by-case basis, establish innovative research, and a deep con- developers or users in an open and and validate protocols that account for cern for the environment. public process greenhouse gas emissions and savings • develop and disseminate the knowl- that may be easily replicated and readily edge base that results from our activi- RESEARCH CENTERS accepted. SUR will also identify technolo- ties to support global water resource ASSOCIATED WITH EARTH gies that can replace some virgin feed- development and decision making, AND ENVIRONMENTAL stock with appropriate local waste including the development of a forum, ENGINEERING streams. Through its publications, meet- the Global Roundtable on Water ings, and Web page, SUR will dissemi- Columbia Water Center. The Columbia (GROW), to facilitate international policy nate information on the best waste man- Water Center, in collaboration with other and technical action to improve our agement technologies and methods that, Earth Institute units and external part- collective water future. on a life-cycle basis, will result in reducing ners, is leading intellectual inquiry into an For more information: www.water.columbia. the impacts of waste management on assessment, prediction, and solution of edu global climate change. An equally impor- the potentially global crisis of freshwater Center for Life Cycle Analysis (LCA). tant objective of the Center is to provide scarcity. Goals are to: The Center for Life Cycle Analysis of graduate-level training, at the participat- • develop multiscale predictive capabili- Columbia University was formed in the ing universities, in the ways and means ties (e.g., new data sets and modeling spring of 2006 with the objective of con- of sustainable resource utilization to engi- tools) for local, regional, and global ducting comprehensive life cycle analy- neers and scientists from the U.S. and water resource assessment, recogniz-

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122 around the world, in particular from the systems, there are several gas chromato- manage the impacts of seasonal climate developing world, where the need for graphic systems equipped with electron fluctuations, in order to improve human modern management of wastes is most capture detectors that are used for welfare and the environment, especially acute. The Earth Engineering Center, in measurements of SF6 in continental in developing countries. This mission is collaboration with the Department of waters and CFCs and SF6 in the atmos- to be conducted through strategic and Earth and Environmental Engineering, has phere. GC/MS capability is being added applied research, education and capaci- already been engaged in this role, and to the spectrum of analytical capabilities. ty building, and provision of forecast and some of our alumni are working in various For more information: www.ldeo.columbia. information products, with an emphasis parts of the waste management industry. edu/~noblegas on practical and verifiable utility and There have been more than twenty the- partnerships. For more information: Industry/University Cooperative ses written on various aspects of waste iri.columbia.edu Research Center for Advanced management, including in-depth studies Studies in Novel Surfactants (IUCS). Langmuir Center for Colloids and of implementing advanced processes IUCS was established in 1998 by the Interfaces (LCCI). This Center brings and methodologies in Chile, China, Henry Krumb School of Mines, together experts from mineral engineering, Greece, and India. For more information: Department of Chemical Engineering, applied chemistry, chemical engineering, www.surcenter.org and Department of Chemistry at biological sciences, and chemistry to Earth Engineering Center. The mission Columbia University. The Center encom- probe complex interactions of colloids of the Earth Engineering Center is to passes detailed structure-property and interfaces with surfactants and develop and promote engineering metho- assessment of several classes of sur- macromolecules. LCCI activities involve dologies that provide essential material to face-active molecules, including significant interaction with industrial humanity in ways that maintain the overall oligomeric, polymeric, and bio-mole- sponsors and adopt an interdisciplinary balance between the constantly increas- cules. The aim of IUCS is to develop approach toward state-of-the-art research ing demand for materials, the finite and characterize novel surfactants for on interfacial phenomena. Major areas of resources of the Earth, and the need for industrial applications such as coatings, research at LCCI are thin films, surfac- clean water, soil, and air. The Center is dispersions, deposition, gas hydrate tant and polymer adsorption, environ- dedicated to the advancement of indus- control, personal care products, soil mental problems, enhanced oil recovery, trial ecology, i.e., the reconfiguring of decontamination, waste treatment, cor- computer tomography, corrosion and industrial activities and products with full rosion prevention, flotation, and con- catalysis mechanisms, membrane tech- knowledge of the environmental conse- trolled chemical reactions. The proposed nology, novel separations of minerals, quences. Research is being conducted research thus focuses on the design and biocolloids, microbial surfaces, and on a variety of geoenvironmental issues development of specialty surfactants, interfacial spectroscopy. with the intent to quantify, assess, and characterization of their solution and Lenfest Center for Sustainable ultimately manage adverse human effects interfacial behavior, and identification of Energy. The mission of the Lenfest on the environment. Research areas include suitable industrial applications for these Center for Sustainable Energy is to management of water and energy resources, materials. develop technologies and institutions to hydrology and hydrogeology, numerical The goals of IUCS are to perform ensure a sufficient supply of environ- modeling of estuarine flow and transport industrially relevant research to address mentally sustainable energy for all processes, and integrated waste the technological needs in commercial humanity. To meet this goal, the Center management. For more information: surfactant and polymer systems; devel- supports research programs in energy www.columbia.edu/cu/earth op new and more efficient surface-active science, engineering, and policy across reagents for specific applications in the Environmental Tracer Group. The Columbia University to develop technical industry and methodologies for optimiz- Environmental Tracer Group uses natural and policy solutions that will satisfy the ing their performance; promote the use and anthropogenic (frequently transient) world’s future energy needs without of environmentally benign surfactants in tracers, as well as deliberately released threatening to destabilize the Earth’s a wide array of technological processes; tracers, to investigate the physics and natural systems. and build a resource center to perform chemistry of transport in environmental The mission of the Lenfest Center is and provide state-of-the-art facilities for systems. The tracers include natural or shaped by two global challenges. First, characterization of surface-active anthropogenically produced isotopes the Center seeks to reduce the emission reagents. For more information: (e.g., tritium or radioactive hydrogen, of carbon dioxide into the atmosphere www.columbia.edu/cu/iucrc helium and oxygen isotopes, or radiocar- and to forestall a disruption of global cli- bon), as well as noble gases and chemi- International Research Institute for mate systems that would impose nega- cal compounds (e.g., CFCs and SF6). Climate Prediction (IRI). The IRI is the tive consequences for human welfare. The ETG analytical facilities include four world’s leading institute for the develop- Second, the Center seeks to create mass spectrometric systems that can be ment and application of seasonal to energy options that will meet the legiti- used in the analysis of tritium and noble interannual climate forecasts. The mis- mate energy demands of a larger and gases in water, sediments, and rocks. sion of the IRI is to enhance society’s increasingly wealthy world population. In In addition to the mass spectrometric capability to understand, anticipate, and order to meet these two challenges, the

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Center seeks to develop new sources, SCHOLARSHIPS, FELLOWSHIPS, 2.Graduates will be able to pursue 123 technologies, and infrastructures. AND INTERNSHIPS careers in industry, government agen- The Lenfest Center focuses primarily The department arranges for undergrad- cies, and other organizations con- on the technological and institutional uate Earth engineering summer intern- cerned with the environment and the development of the three energy resources ships after the sophomore and junior provision of primary and secondary sufficient to support the world’s project- years. Undergraduates can also partici- materials and energy, as well as con- ed population in 2100 without increased pate in graduate research projects under tinue their education as graduate stu- carbon emissions: solar, nuclear, and the work-study program. Graduate dents in related disciplines. fossil fuels combined with carbon cap- research and teaching assistantships, 3.Graduates will possess the basic skills ture and storage. Although each of as well as fellowships funded by the needed for the practice of Earth and these options can, in theory, be devel- Department, are available to qualified environmental engineering, including oped on a scale to satisfy global graduate students. GRE scores are measurement and control of material demand, they each face a combination required of all applicants for graduate flows through the environment; of technological and institutional obsta- studies. assessment of environmental impact cles that demand research and develop- of past, present, and future industrial ment before they can be deployed. activities; and analysis and design of UNDERGRADUATE PROGRAM The Center’s main activities are processes for remediation, recycling, based within the range of natural sci- The Bachelor of Science (B.S.) degree and disposal of used materials. ence and engineering disciplines. At the in Earth and environmental engineering 4.Graduates will practice their profes- same time, it integrates technological prepares students for careers in the sion with excellent written and com- research with analysis of the institutional, public and private sector concerned munication skills and with professional economic, and political context within with primary materials (minerals, fuels, ethics and responsibilities. which energy technologies are commer- water) and the environment. Graduates cialized and deployed. For more infor- are also prepared to continue with fur- The Curriculum ther studies in Earth/environmental sci- mation: www.energy.columbia.edu The first two years of the EEE program ences and engineering, business, public are similar to those of other engineering Waste to Energy Research and policy, international studies, law, and programs. Students are provided with a Technology Council (WTERT). The medicine. The EEE program is accredited strong foundation in basic sciences and Waste to Energy Research and as an environmental engineering program mathematics, as well as the liberal arts Technology Council brings together by the Accreditation Board for Engi- core. Specific to the EEE program is an engineers, scientists, and managers neering and Technology (ABET). from industry, universities, and govern- early and sustained introduction to Earth science and environmental engineering, ment with the objective of advancing the What Is Earth and Environmental and options for a number of science goals of sustainable waste management Engineering? courses to meet the specific interests globally. The mission of WTERT is to It is now recognized by the U.S. and identify the best available technologies of each student. The junior and senior other nations that continuing economic years of the program consist of a group for the treatment of various waste mate- development must be accompanied by rials, conduct additional academic of required courses in engineering sci- intelligent use of Earth’s resources and ence and a broad selection of technical research as required, and disseminate that engineers can contribute much to this information by means of its publica- electives organized into three distinct the global efforts for sustainable devel- concentrations, representing major areas tions, the WTERT Web, and annual opment. The technologies that have meetings. In particular, WTERT strives to of focus within the department. been developed for identifying, extract- Several Columbia departments, increase the global recovery of energy ing, and processing primary materials and materials from used solids and to such as Civil Engineering, Mechanical are also being applied to the twenty- Engineering, and Earth and Environmental advance the economic and environmen- first-century problems of resource recovery tal performance of waste-to-energy Sciences (Lamont-Doherty Earth Obser- from used materials, pollution preven- vatory), as well as the Mailman School (WTE) technologies in the U.S. and tion, and environmental remediation. worldwide. The guiding principle is that of Public Health, contribute courses to The EEE undergraduate program the EEE program. EEE students are responsible management of wastes encompasses these technologies. must be based on science and the best strongly encouraged to work as summer interns in industry or agencies on proj- available technology and not what Undergraduate Program Objectives seems to be inexpensive now but can ects related to Earth and environmental 1.Graduates equipped with the neces- be very costly in the near future. For engineering. The department helps stu- sary tools (mathematics, chemistry, more information: www.seas.columbia. dents get summer internships. physics, Earth sciences, and engineer- edu/earth/wtert ing science) will understand and Technical Elective Concentrations implement the underlying principles Students majoring in Earth and environ- used in the engineering of processes mental engineering select one of the and systems.

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124 following three preapproved technical EESC W4404: Regional dynamics, climate and ronmental management/development elective concentrations. Note that the climate impacts careers. The focus of the program is the eight-course sequence for each preap- environmentally sound mining and pro- Sustainable Energy and Materials proved concentration includes two sci- cessing of primary materials (minerals, Concentration ence courses during sophomore year energy, and water) and the recycling or Preapproved course sequence: (fall semester) and six technical elective CHEM C3443: Organic chemistry (SEM III) proper disposal of used materials. The courses during junior and senior years. EESC V2200: Solid earth system (SEM III) program also includes technologies for Any deviations from a preapproved MECE E3311: Heat transfer (SEM VI) assessment and remediation of past concentration must be approved by an EAEE E4001: Industrial ecology of Earth damage to the environment. Students undergraduate faculty adviser. Alterna- resources (SEM VII) can choose a pace that allows them tives for junior/senior electives within EAEE E4900: Applied transport and chemical to complete the MS-ERE requirements rate phenomena (SEM VII) each concentration are listed, and others while being employed. MECE E4302: Advanced thermodynamics (SEM VIII) may be considered among 3000- to EESC W3015: The Earth’s carbon cycle (SEM VIII) MS-ERE graduates are specially 4000-level courses of any SEAS depart- MECE E4211: Energy: sources and conversion qualified to work for engineering, finan- ment, as well as courses listed in the (SEM VIII) cial, and operating companies engaged section “Courses in Other Divisions” in in mineral processing ventures, the Alternatives for junior/senior electives: this bulletin. However, at least four of the CHEN E3110: Transport phenomena I environmental industry, environmental six junior/senior electives must consist of CHEN E3120: Transport phenomena II groups in all industries, and for city, engineering topics. Alternatives for soph- EAEE E3101: Earth resource production systems state, and federal agencies responsible omore-year science courses are shown MSAE E3103: Elements of materials science for the environment and energy/resourse in the EEE program table. CHEM C3071: Introduction to organic chemistry conservation. At the present time, the A student may also choose to develop CHEM G4230: Statistical thermodynamics U.S. environmental industry comprises EAEE E4550: Catalysis for emissions control an individual concentration conforming to nearly 30,000 big and small businesses EESC W4008: Introduction to atmospheric science his/her specific interests, provided that it EAEE E4560: Particle technology with total revenues of over $150 billion. satisfies ABET engineering accreditation Sustainable development and environ- criteria. Therefore, this must be developed Environmental Health Engineering mental quality has become a top priority in close consultation with and approved Concentration of government and industry in the by a faculty adviser. Preapproved course sequence: United States and many other nations. CHEM C3443: Organic chemistry (SEM III) This M.S. program is offered in EESC V2100: Climate system (SEM III) Water Resources and Climate Risks collaboration with the Departments EAEE E4006: Field methods for environmental Concentration of Civil Engineering and Earth and Preapproved course sequence: engineering (SEM VI) Environmental Sciences. Many of the PHYS C1403: Introduction to classical and quantum EAEE E4009: GIS for resource, environmental waves (SEM III) and infrastructure management teaching faculty are affiliated with EESC V2100: Climate system (SEM III) (SEM VII) Columbia’s Earth Engineering Center. EAEE E4006: Field methods for environmental EHSC P6300: Environmental health sciences For students with a B.S. in engineer- engineering (SEM VI) (SEM VII) ing, at least 30 points (ten courses) are EAEE E4257: Environmental data analysis and EAEE E4009: GIS for resource, environmental, required. For students with a nonengi- modeling (SEM VIII) and infrastructure management neering B.S. or a B.A., preferably with a (SEM VII) EAEE E4150: Air pollution prevention and control science major, up to 48 points (total of EAEE E4350: Planning and management of urban (SEM VIII) hydrologic systems (SEM VII) EHSC P6309: Biochemistry basic to environmen- sixteen courses) may be required for EAEE E4257: Environmental data analysis and tal health (SEM VIII) makeup courses. All students are required modeling (SEM VIII) Alternatives for junior/senior electives: to carry out a research project and write ECIA W4100: Management and development of EAEE E4001: Industrial ecology of Earth a thesis worth 3–6 points. A number water systems (SEM VIII) resources of areas of study are available for the CIEE E4257: Contaminant transport in subsurface EAEE E4900: Applied transport and chemical MS-ERE, and students may choose systems (SEM VIII) rate phenomena courses that match their interest and Alternatives for junior/senior electives: EAEE E4950: Environmental biochemical career plans. The areas of study include: processes EAEE E4001: Industrial ecology of Earth • alternative energy and carbon man- CIEE E4257: Contaminant transport in resources agement CIEE E4260: Urban ecology studio subsurface systems • climate risk assessment and manage- CIEE E4163: Environmental engineering: wastewater ment GRADUATE PROGRAMS CIEN E4250: Waste containment design and • environmental health engineering practice • integrated waste management M.S. in Earth Resources Engineering CIEN E4255: Flow in porous media • natural and mineral resource develop- (MS-ERE) APPH E4200: Physics of fluids ment and management EESC W4008: Introduction to atmospheric science The MS-ERE program is designed for • novel technologies: surficial and col- EESC W4401: Quantitative models of climate- engineers and scientists who plan to loidal chemistry and nanotechnology sensitive natural and human systems pursue, or are already engaged in, envi-

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• urban environments and spatial analysis one of the central tasks for modern lifetime and then must be replaced by 125 Additionally, there are four optional con- engineering. The purpose of the sustain- converting more greenfields to landfills. centrations in the program, in each of able energy concentration is to expose This method is not sustainable because which there are a number of required students to modern energy technologies it wastes land and valuable resources. specific core courses and electives. and infrastructures and to the associated Also, it is a major source of greenhouse In each case, students are required to environmental, health, and resource gases and of various contaminants of air carry out a research project and write a limitations. Emphasis will be on energy and water. In addition to MSW, the U.S. thesis (3–6 points). The concentrations generation and use technologies that alone generates billions of tons of indus- are described briefly below; details and aim to overcome the limits to growth trial and extraction wastes. Also, the by- the lists of specific courses for each that are experienced today. Energy and product of water purification is a sludge track are available from the department. economic well-being are tightly coupled. or cake that must be disposed in some Fossil fuel resources are still plentiful, way. The IWM concentration prepares Water Resources and Climate Risks but access to energy is limited by envi- engineers to deal with the major problem Climate-induced risk is a significant ronmental and economic constraints. of waste generation by exposing them to component of decision making for the A future world population of 10 billion environmentally better means for dealing planning, design, and operation of water people trying to approach the standard with wastes: waste reduction, recycling, resource systems, and related sectors of living of the developed nations cannot composting, and waste-to-energy via such as energy, health, agriculture, eco- rely on today’s energy technologies and combustion, anaerobic digestion, or logical resources, and natural hazards infrastructures without severe environ- gasification. Students are exposed not control. Climatic uncertainties can be mental impacts. Concerns over climate only to the technical aspects of integrat- broadly classified into two areas: (1) change and changes in ocean chemistry ed waste management but also to the those related to anthropogenic climate require reductions in carbon dioxide associated economic, policy, and urban change; (2) those related to seasonal- emissions, but most alternatives to con- planning issues. to century-scale natural variations. The ventional fossil fuels, including nuclear Since the initiation of the Earth and climate change issues impact the design energy, are too expensive to fill the gap. environmental engineering program in of physical, social, and financial infra- Yet access to clean, cheap energy is 1996, there have been several graduate structure systems to support the sectors critical for providing minimal resources: research projects and theses that exem- listed above. The climate variability and water, food, housing, and transportation. plify the engineering problems that will predictablilty issues impact systems Concentration-specific classes will be encompassed in this concentration: operation, and hence design. The goal sketch out the availability of resources, • design of an automated materials of the M.S. concentration in water their geographic distribution, the eco- recovery facility resources and climate risks is to provide nomic and environmental cost of resource • analysis of the bioreactor landfill (1) a capacity for understanding and extraction, and avenues for increasing • generation of methane by anaerobic quantifying the projections for climate energy utilization efficiency, such as co- digestion of organic materials change and variability in the context of generation, district heating, and distrib- • design of corrosion inhibitors decisions for water resources and related uted generation of energy. Classes will • flocculation modeling sectors of impact; and (2) skills for inte- discuss technologies for efficiency improve- • analysis of formation of dioxins in grated risk assessment and mangement ment in the generation and consumption high-temperature processes for operations and design, as well as for sector; energy recovery from solid wastes; • combination of waste-to-energy and regional policy analysis and manage- alternatives to fossil fuels, including solar anaerobic digestion ment. Specific areas of interest include: and wind energy, and nuclear fission • application of GIS in siting new WTE • numerical and statistical modeling of and fusion; and technologies for facilities global and regional climate systems addressing the environmental concerns • corrosion phenomena in WTE and attendant uncertainties over the use of fossil fuels and nuclear combustion chambers • methods for forecasting seasonal to energy. Classses on climate change, air • mathematical modeling of transport interannual climate variations and their quality, and health impacts focus on the phenomena in a combustion chamber sectoral impacts consequences of energy use. Policy and • effect of oxygen enrichment on • models for design and operation of its interactions with environmental sci- combustion of paper and other water resource systems, considering ences and energy engineering will be types of solid wastes climate and other uncertainties another aspect of the concentration. • feasibility study and design of • integrated risk assessment and man- Additional specialization may consider WTE facilities agement across water resources and region specific energy development. related sectors Environmental Health Engineering Integrated Waste Management (IWM) The purpose of this concentration is Sustainable Energy Humanity generates nearly 2 billion tons to train professionals who can address Building and shaping the energy infra- of municipal solid wastes (MSW) annually. both the public health and engineering structure of the twenty-first century is Traditionally, these wastes have been aspects of environmental problems. discarded in landfills that have a finite

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126 EARTH AND ENVIRONMENTAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) APMA E2101 (3) MATHEMATICS or Honors Math I (4) Honors Math II (4) MATH E1210 (3) ODE

C1401 (3) C1402 (3)

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

CHEMISTRY or C1604 (3.5) C2507 (3)

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

C1010 (3) HUMA C1001, C0CI C1101, HUMA C1002, C0CI C1102, or or Global Core (3–4) or Global Core (3–4) REQUIRED Z1003 (4) C1010 (3) NONTECHNICAL or ECON W1105 (4) and ELECTIVES ALP0006 (0) Z1003 (4) or C1010 (3) W1155 recitation (0)

HUMA C1121 or C1123 (3)

EAEE E1100 (3) A EESC W4001 (4) better planet by design or REQUIRED or other departmental EESC V2100 (4.5) PROFESSIONAL professional-level course or AND TECHNICAL EESC V2200 (4.5) ELECTIVES EEAE E2002 (3) Alternative energy sources

COMPUTER Computer language: COMS W1003 (3) or W1004 (3) any semester SCIENCE PHYSICAL C1001 (1) C1002 (1) EDUCATION

GATEWAY LAB E1102 (4) either semester

The identification and evaluation of envi- professionals, public health practitioners Joint Degree Programs ronmental problems frequently revolve and engineers, who usually have very The Graduate School of Business and around the risks to human health, little understanding of the role of the the School of Engineering and Applied whereas the development of remediation other profession in this process. The Science offer a joint program leading to or prevention strategies frequently goal is to train those specialists collabo- the M.B.A. degree from the Graduate involves engineering approaches. ratively, through the Departments of School of Business and the M.S. degree Currently, these two critical steps in Earth and Environmental Engineering in Earth resources engineering from addressing environmental problems and Environmental Health Sciences. the School of Engineering and Applied are handled by two separate groups of Science. The purpose of this program

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127 EARTH AND ENVIRONMENTAL ENGINEERING PROGRAM: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

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

CIEE E4252 (3) CIEE E3250 (3) EAEE E4003 (3) EAEE E4160 (3) Environmental engineering Hydrosystems engineering Aquatic chemistry Solid and hazardous waste management

ENME E3161 (4) SIEO W3600 (4) EAEE E3801 (2) Fluid mechanics Introduction to Earth and environmental or probability and statistics engineering lab, II MECE E3100 (3) Introduction to mechanics REQUIRED of fluids COURSES

CHEE E3010 (4) EAEE E3800 (2) Principles of chemical Earth and environmental engineering thermodynamics engineering lab, I or MSAE E3111 (3) EAEE E3901 (3) Thermodynamics, Environmental microbiology kinetic theory, and statistical mechanics or MECE E3301 (3) Thermodynamics

TECHNICAL 3 points 6 points 9 points ELECTIVES NONTECHNICAL 3 points 3 points 3 points ELECTIVES

TOTAL POINTS 15–17 18 16 17

is to train students who wish to pursue all other intellectual and performance recycling of used materials; manage- Earth resource management careers. requirements for these degrees are the ment of industrial residues and used Students are expected to register same. All applicants should use the products; materials-related application full time for three terms in the Graduate School of Engineering forms. The scope of industrial ecology. School of Business and for two terms in includes the design and use of sensors • management of water resources: the School of Engineering and Applied for measurement at molecular scale; the understanding, prediction, and man- Science. It is possible, however, to study understanding of surface, colloid, aque- agement of the processes that govern in the School of Engineering and Applied ous, and high-temperature phenomena; the quantity and quality of water Science part time. Interested persons the integrated management of multiple resources, including the role of climate; should contact Professor Tuncel resources and the mitigation of natural development/operation of water Yegulalp at 212-854-2984 or by e-mail and environmental hazards, at regional resource facilities; management of to [email protected]. to global scales. The management of water-related hazards. the interaction between human activities, • energy resources and carbon Doctoral Programs Earth resources, and ecosystems is of management: mitigation of environ- EEE offers two doctoral degrees: primary interest. mental impacts of energy production; (1) the Eng.Sc.D. degree, administered The engineering objectives of EEE energy recovery from waste materials; by The Fu Foundation School of research and education include: advancement of energy efficient systems; Engineering and Applied Science; and • provision and disposal of materials: new energy sources; development of (2) the Ph.D. degree, administered by environmentally sustainable extraction carbon sequestration strategies. the Graduate School of Arts and and processing of primary materials; • sensing and remediation: under- Sciences. Qualifying examinations and manufacturing of derivative products; standing of transport processes at

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128 different scales and in different media; Development of the infrastructure for providing power generation and a discussion of its impact containment systems; modeling flow safe and reliable resources (energy, water, and on the global biogeochemical cycles. and transport in surface and subsur- other materials, transportation services) to sup- port human societies while attaining environmental face systems; soil/water decontamina- MSAE E3111x Thermodynamics, kinetic theory, objectives. Introduction of a typology of problems and statistical mechanics tion and bioremediation. by context and common frameworks for address- Lect: 3. 3 pts. Professor Duby. ing them through the application of appropriate An introduction to the basic thermodynamics of The Professional Degrees technology and policy. An interdisciplinary per- systems, including concepts of equilibrium, entropy, The department offers the professional spective that focuses on the interaction between thermodynamic functions, and phase changes. degrees of Engineer of Mines (E.M.) and human and natural systems is provided. Alternatives Basic kinetic theory and statistical mechanics, for resource provision and forecasts of their Metallurgical Engineer (Met.E.). In order including diffusion processes, concept of phase potential environmental impacts through a context space, classical and quantum statistics, and to gain admission to both degree pro- provided by real world applications and problems. applications thereof. grams, students must have an under- graduate degree in engineering and EAEE E2002x Alternative energy resources EAEE E3112y Introduction to rock mechanics complete at least 30 credits of graduate Lect: 3. 3 pts. Professors Walker and Lackner. Lect: 3. 3 pts. Not given in 2009–2010. work beyond the M.S. degree, or 60 Unconventional, alternative energy resources. Prerequisites: EAEE E3101 and ENME E3111, or credits of graduate work beyond the Technological options and their role in the world their equivalents. Rock as an engineering material, B.S. degree. These programs are energy markets. Comparison of conventional and geometry and strength of rock joints, geotechnical unconventional, renewable and nonrenewable planned for engineers who wish to do classification of rock masses, strength and failure energy resources and analysis of the conse- of rock, field investigations prior to excavation in advanced work beyond the level of the quences of various technological choices and rock, rock reinforcement, analysis and support of M.S. degree but who do not desire to constraints. Economic considerations, energy rock slopes and tunnels, and case histories. emphasize research. availability, and the environmental consequences The professional degrees are awarded of large-scale, widespread use of each particular MSAE E3141y Processing of metals and semi- for satisfactory completion of a graduate technology. Introduction to carbon dioxide capture conductors program at a higher level of course work and carbon dioxide disposal as a means of sus- Lect: 3. 3 pts. Professor Duby. taining the fossil fuel option. than is normally completed for the M.S. Prerequisites: MSAE E3103 or equivalent. Synthesis and production of metals and semicon- degree. Students who find it necessary EAEE E3101y Earth resource production systems ductors with engineered microstructures for to include master’s-level courses in their Lect: 3. 3 pts. Professor Yegulalp. desired properties. Includes high-temperature, professional degree program will, in Technologies and equipment common to a wide aqueous, and electrochemical processing; ther- general, take such courses as deficiency range of surface and subsurface engineering mal and mechanical processing of metals and courses. A candidate is required to activities: mine reclamation, hazardous waste alloys; casting and solidification; diffusion, maintain a grade-point average of at remediation, discovering and operating surface microstructural evolution, and phase transforma- least 3.0. A student who, at the end of and underground mines, detection and removal of tions; modification and processing of surfaces hidden underground objects, waste disposal, and interfaces; deposition and removal of thin any term, has not attained the grade- dredging and harbor rehabilitation, and tunneling films. Processing of Si and other materials for point average required for the degree for transportation or water distribution systems. elemental and compound semiconductor-based may be asked to withdraw. The final These methods and equipment are examined as electronic, magnetic, and optical devices. 30 credits required for the professional they apply across the spectrum from mining to degree must be completed in no more environmental engineering projects. The aim is to EAEE E3185y Summer fieldwork for Earth and than five years. provide a broad background for earth and envi- environmental engineers Specific requirements for both pro- ronmental engineers in careers involving minerals 0.5 pts. Instructor to be announced. and industrial, large-scale environmental projects. fessional degrees include a set of core Undergraduates in Earth and environmental engineering may spend up to 3 weeks in the field courses and a number of electives EAEE E3103x Energy, minerals and materials under staff direction. The course consists of mine, appropriate for the specific area of systems landfill, plant, and major excavation site visits and concentration. All course work must Lect: 3.3 pts. Professors Lackner and Yegulalp. brief instruction of surveying methods. A final report lead to the successful completion of a Prerequisite: MSAE E3111 or MECE E3301 and is required. project in mining engineering. A list of ENME E3161 or MECE E3100 or the equivalent. core courses and electives is available Overview of energy resources, resource manage- EAEE E3221x Environmental geophysics at the department office. ment from extraction and processing to recycling Lect. 3. 3 pts. Instructor to be announced. and final disposal of wastes. Resource availability Introduction to applied and environmental geo- and resource processing in the context of the physics methods. Overview of principles of geo- COURSES IN EARTH global natural and anthropogenic material cycles; physics, geophysical methods and techniques AND ENVIRONMENTAL thermodynamic and chemical conditions including (seismic, ground penetrating radar, resistivity, ENGINEERING nonequilibrium effects that shape the resource frequency em, and magnetics), and theory and base; extractive technologies and their impact on practical aspects of data processing and inver- See also courses in applied chemistry the environment and the biogeochemical cycles; sion. Examination of geophysical case studies in the section in this chapter titled chemical extraction from mineral ores, and metal- for engineering and environmental purposes. ‘‘Chemical Engineering.” lurgical processes for extraction of metals. In analogy to metallurgical processing, power gener- CIEE E3250x Hydrosystems engineering EAEE E1100y A better planet by design ation and the refining of fuels are treated as Lect: 3. 3 pts. Professor Gong. Lec.: 3. 3 pts. Professors Lall and Park. extraction and refining processes. Large scale of Prerequisite: CHEN E3110 or ENME E3161 or the

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equivalent, SIEO W3600 or the equivalent, or the acceptable thesis or final report. This course EAEE E4004x Physical processing and 129 instructor’s permission. A quantitative introduction cannot substitute for the undergraduate design recovery of solids to hydrologic and hydraulic systems, with a focus project (E3999x-E3999y). Lect: 3. 3 pts. Not given in 2009–2010. on integrated modeling and analysis of the water Generalized treatment of processes for solids cycle and associated mass transport for water EAEE E3901y Environmental microbiology separation. Applications to materials processing resources and environmental engineering. Lect: 3. 3 pts. Professor Chandran. and handling; mining; solid waste, recycling, and Coverage of unit hydrologic processes such as Prerequisite: CHEM C1404 or the equivalent. resource recovery; construction materials and precipitation, evaporation, infiltration, runoff gen- Fundamentals of microbiology, genetics and debris; scrap materials, yard and park wastes. eration, open channel and pipe flow, subsurface molecular biology, principles of microbial nutrition, Economic considerations and context. Relevant flow and well hydraulics in the context of example energetics and kinetics, application of novel and materials properties and bulk materials analyses. watersheds, and specific integrative problems such state-of-the-art techniques in monitoring the struc- Process system flow-sheets and analysis. as risk-based design for flood control, provision of ture and function of microbial communities in the Solid/solid, solid/liquid, and solid/gas separation water, and assessment of environmental impact environment, engineered processes for biochemi- process. Liberation, concentration, and auxiliary or potential for non-point source pollution. Spatial cal waste treatment and bioremediation, microor- processes. Design of separation machines: types hydrologic analysis using GIS and watershed models. ganisms and public health, global microbial ele- and intensities of force involved; scaling-up fac- mental cycles. tors. Laboratory demonstrations and a field trip CIEE E3255y Environmental control and will be included. pollution reduction systems EAEE E3998x-E3999y Undergraduate design Lect: 3. 3 pts. Professor Castaldi. project EAEE E4005x Near-surface engineering Prerequisites: ENME E3161 or MECE E3100. Lect: 1. Lab: 2. 2 pts (each semester). The staff. geophysics Review of engineered systens for prevention and Prerequisite: Senior standing. Students must Lect: 3. 3 pts. Not given in 2009–2010. control of pollution. Fundamentals of material and enroll for both E3998x and E3999y during their Geophysical methods as applicable to engineer- energy balances and reaction kinetics. Analysis senior year. Selection of an actual problem in ing problems. Principles of geophysics and nonin- of engineered systems to address environmental Earth and environmental engineering, and design vasive imaging techniques (inversion technology) problems, including solid and hazardous waste, of an engineering solution including technical, and benefits and pitfalls of geophysics vs. direct and air, water, soil, and noise pollution. Life cycle economic, environmental, ethical, health and imaging methods. Discussion of theory of each assessments and emerging technologies. safety, and social issues. Use of software for method. Discussion of data acquisition, process- design, visualization, economic analysis, and ing and interpretation for each method. Treatment EAEE E3800y Earth and environmental engi- report preparation. Students may work in teams. of several case studies. Class-wide planning and neering laboratory, I Presentation of results in a formal report and execution of small-scale geophysical survey. Lect: 1. Lab: 3. 2 pts. Professors Duby, public presentation. Chandran, and Castaldi. EAEE E4006y Field methods for environmental Prerequisite: CHEE E3010. Corequisite: EAEE EAEE E4000x or y GIS lab access engineering E3255. Experiments on fundamental aspects of Students must sign up for this class in order to Lect: 1.5. Lab: 2. 3 pts. Professor McGillis. Earth and environmental engineering with empha- gain access to EEE GIS lab. A laboratory fee of Principles and methods for designing, building, sis on the applications of chemistry, biology, and $50 is collected. and testing systems to sense the environment. thermodynamics to environmental processes: Monitoring the atmosphere, water bodies and energy generation, analysis and purification of EAEE E4001x Industrial ecology of Earth boundary interfaces between the two. Sensor water, environmental biology, and biochemical resources systems for monitoring heat and mass flows, treatment of wastes. Students will learn the labo- Lect: 3. 3 pts. Instructor to be announced. chemicals, and biota. Measurements of velocity, ratory procedures and use analytical equipment Industrial ecology examines how to reconfigure temperature, flux and concentration in the field. firsthand, hence demonstrating experimentally the industrial activities so as to minimize the adverse The class will involve planning and execution of theoretical concepts learned in class. environmental and material resource effects on a study to sense a local environmental system. the planet. Engineering applications of methodol- EAEE E3801x Earth and environmental engi- ogy of industrial ecology in the analysis of current EAEE E4007y Environmental geophysics neering laboratory, II processes and products and the selection or field studies Lect: 1. Lab: 3. 2 pts. Professors Duby, design of environmentally superior alternatives. Lect: 3. 3 pts. Instructor to be announced. Chandran, and Castaldi. Home assignments of illustrative quantitative Application of geophysical methods to noninva- Prerequisite: EAEE E3800. Corequisite: EAEE problems. sive assessment of the near surface. First part E4003. A continuation of EAEE E3800, with consists of series of two-hour lectures of physics emphasis on the principles underlying water EAEE E4003x Introduction to aquatic and math involved in instrumental methods and analysis for inorganic, organic, and bacterial con- chemistry data acquisition and processing. In the field (nine taminants. Lect: 3. 3 pts. Professor Duby. field days) students plan surveys; collect and Prerequisite: CHEN E3010 or the equivalent. analyze geophysical data in teams; learn how EAEE E3900x and y, and s Undergraduate Principles of physical chemistry applied to equilib- to integrate geophysical data with invasive data, research in Earth and environmental engineering ria and kinetics of aqueous solutions in contact hydrological, geological, engineering, and con- Directed study. 0–3 pts. The staff. with minerals and anthropogenic residues. The taminant transport models; and develop a com- This course may be repeated for credit, but no scientific background for addressing problems of prehensive and justifiable model of the subsurface. more than 3 points of this course may be counted aqueous pollution, water treatment, and sustain- Geophysical methods include GPR (Ground toward the satisfaction of the B.S. degree require- able production of materials with minimum envi- Penetrating Radar), conductivity, and magnetic ments. Candidates for the B.S. degree may con- ronmental impact. Hydrolysis, oxidation-reduction, and seismic methods. Field applications include duct an investigation in Earth and environmental complex formation, dissolution and precipitation, infrastructure/environmental assessment, archeo- engineering, or carry out a special project under predominance diagrams; examples of natural water logical studies, and high resolution geology. the supervision of EAEE faculty. Credit for the systems, processes for water treatment and for course is contingent on the submission of an the production of inorganic materials from minerals.

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130 EAEE E4009x Geographic information EAEE E4150y Air pollution prevention and control bulk solids in tunnels, mines, and large excava- systems (GIS) for resource, environmental, Lect: 3. 3 pts. Professor Fthenakis. tions. Design of hoisting, cable transport, rail and and infrastructure management Adverse effects of air pollution, sources and trackless haulage systems, conveyor belts, selec- Lect: 3. 3 pts. Professor Gorokhovich. transport media, monitoring and modeling of air tion of loaders, excavators, off-highway trucks, Prerequisite: The instructor’s permission. Basic quality, collection and treatment techniques, pollu- and draglines for large excavations. concepts of geomatics, spatial data representa- tion prevention through waste minimalization and tion and organization, and analytical tools that clean technologies, laws, regulations, standards, CHEE E4252x Introduction to surface and comprise GIS are introduced and applied to a and guidelines. colloid chemistry variety of problems including watershed protec- Lect: 3. 3 pts. Professor Somasundaran. tion, environmental risk assessment, material EAEE E4160y Solid and hazardous waste Prerequisite: Elementary physical chemistry. Thermo- mass balance, flooding, asset management, and management dynamics of surfaces, properties of surfactant solu- emergency response to natural or man-made Lect: 3. 3 pts. Professor Somasundaran. tions and surface films, electrostatic and electrokinetic hazards. Technical content includes geography Generation, composition, collection, transport, phenomena at interfaces, adsorption; interfacial and map projections, spatial statistics, database storage, and disposal of solid and hazardous mass transfer and modern experimental techniques. design and use, interpolation and visualization of waste. Impact on the environment and public spatial surfaces and volumes from irregularly health. Government regulations. Recycling and CIEE E4252y Environmental engineering spaced data, and decision analysis in an applied resource recovery. Lect: 3. 3 pts. Professor Gong. setting. Taught in a laboratory setting using ArcGIS. Prerequisites: CHEM C1403, or the equivalent; Access to New York City and other standard data- CIEE E4163x Environmental engineering: ENME E3161 or the equivalent. Engineering bases. Term projects emphasize information syn- wastewater aspects of problems involving human interaction thesis toward the solution of a specific problem. Lect: 3. 3 pts. Professor Becker. with the natural environment. Review of funda- Prerequisites: Introductory chemistry (with lab) mental principles that underlie the discipline of EAEE E4011y Industrial ecology for and fluid mechanics. Fundamentals of water pol- environmental engineering, i.e., constituent trans- manufacturing lution and wastewater characteristics. Chemistry, port and transformation processes in environmen- Lect: 3. 3 pts. Not given in 2009–2010. microbiology, and reaction kinetics. Design of tal media such as water, air, and ecosystems. Prerequisite: EAEE E4001 or the instructor’s primary, secondary, and advanced treatment sys- Engineering applications for addressing environ- permission. Application of industrial ecology to tems. Small community and residential systems. mental problems such as water quality and treat- Design for Environment (DFE) of processes and ment, air polution emissions, and hazardous products using environmental indices of resource EAEE E4190x Photovoltaic systems engineer- waste remediation. Presented in the context of consumption and pollution loads. Introduction of ing and sustainability current issues facing the practicing engineers and methodology for Life Cycle Assessment (LCA) of Lect: 3. 3pts. Professor Fthenakis. government agencies, including legal and regula- manufactured products. Analysis of several DFE Prerequisite: Senior Standing or the instructor’s tory framework, environmental impact assessments, and LCA case studies. Term project required on permission. A systems approach for intermittent and natural resource management. use of DFE/LCA on a specific product/process: renewable energy involving the study of (a) product design complete with materials and resources, generation, demand, storage, trans- CIEE E4257y Groundwater contaminant process selection, energy consumption, and mission, economics, and politics. Study of current transport and remediation waste loadings; (b) LCA of an existing industrial and emerging photovoltaic technologies, with Lect: 3.3 pts. Professor Mutch. or consumer product using a commercially estab- focus on basic sustainability metrics (e.g., cost, Prerequisite: CIEE E3250 or the equivalent. lished method. resource availability, and life-cycle environmental Single- and multiple-phase transport in porous impacts). The status and potential of first- and media; contaminant transport in variably saturated CHEE E4050x Industrial and environmental second-generation photovoltaic technologies heterogeneous geologic media; physically based electrochemistry (e.g., crystalline and amorphous Si, CdTe, CIGS) numerical models of such processes. Lect: 3. 3 pts. Professor Duby. and emerging third-generation ones. Storage Prerequisite: CHEN E3010. A presentation of options to overcome the intermittency constraint. EAEE E4257y (section 001) Environmental the basic principle underlying electrochemical Large scales of renewable energy technologies data analysis and modeling processes. Thermodynamics, electrode kinetics, and plug-in hybrid electric cars. Lect: 3. 3 pts. Professors Yegulalp, Lall, and and ionic mass transport. Examples of industrial Gorokhovich. and environmental applications illustrated by EAEE E4200y Production of inorganic materials Prerequisite: SIEO W3600 or SIEO W4250, or the means of laboratory experiments: electroplating, Lect: 3. 3 pts. Professor Duby. equivalent. Statistical methods for the analysis of refining, and winning in aqueous solutions and Prerequisite: CHEN E3010 or the equivalent. the space and time structure in environmental in molten salts; electrolytic treatment of wastes; Production and recycling of inorganic materials in data. Application to problems of climate variation primary, secondary, and fuel cells. aqueous and high-temperature systems. Industrial and change; hydrology; air, water, and soil pollu- and environmental applications of hydrometallurgy, tion dynamics; disease propagation; ecological ECIA W4100y Management and development pyrometallurgy, and electrometallurgy. Reactor change; and resource assessment. Applications of water systems systems for, e.g., leaching, precipitation, and are developed using the ArcView Geographical Lect: 3. 3 pts. Professor Lall and Dr. Arumugam. solvent extraction, bath and flash smelting reac- Information System (GIS), integrated with currently Decision analytic framework for operating, man- tors, rotary kilns, and fluid bed reactors. Thermo- available statistical packages. Team projects that aging, and planning water systems, considering dynamic and kinetic factors and material/energy lead to publication-quality analyses of data in changing climate, values, and needs. Public and balances involved in the design and performance various environmental fields of interest. An inter- private sector models explored through U.S.-inter- of such reactors in typical applications. disciplinary perspective is emphasized in this national case studies on topics ranging from inte- applications-oriented class. grated watershed management to the analysis EAEE E4241x Solids handling and transport of specific projects for flood mitigation, water systems EAEE E4350x Planning and management of and wastewater treatment, or distribution system Lect: 3. 3 pts. Not given in 2009–2010. urban hydrologic systems evaluation and improvement. Analysis and design of transportation systems for Lect: 3. 3 pts. Professor Rangarajan.

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Prerequisite: ENME E3161 or the equivalent. Intro- particulate systems, particle technology is often for solving nonlinear problems, and simulating 131 duction to runoff and drainage systems in an urban treated as art rather than science. In this course, incremental excavation and loading on the sur- setting, including hydrologic and hydraulic analyses, the fundamental principles governing the key face and underground. flow and water quality monitoring, common regu- aspects of particle science and technology will be latory issues, and mathematical modeling. Appli- introduced, along with various industrial examples. EAEE E6150y Industrial catalysis cations to problems of climate variation, land use Lect: 3. 3pts. Professor Farrauto. changes, infrastructure operation and receiving EAEE E4900x Applied transport and chemical Prerequisite: EAEE E4550 or the equivalent, or water quality, developed using statistical packages, rate phenomena the instructor’s permission. Fundamental princi- public-domain models, and Geographical Information Lect: 3. 3 pts. Professor Lackner. ples of kinetics, characterization and preparation Systems (GIS). Team projects that can lead to Introduction to fluid dynamics, heat and mass of catalysts for production of petroleum products publication of quality analyses in relevant fields of transfer, and some applications in heterogeneous for conventional transportation fuels, specialty interest. Emphasis on the unique technical, regu- reaction systems. Effect of velocity, temperature, chemicals, polymers, food products, hydrogen latory, fiscal, policy, and other interdisciplinary and concentration gradients and material proper- and fuel cells, and the application of catalysis in issues that pose a challenge to effective planning ties on fluid flow, heat and mass transfer, and rate biomass conversion to fuel. Update of the ever- and management of urban hydrologic systems. of chemical reactions; differential and overall bal- changing demands and challenges in environ- ance; engineering concepts and semi-empirical mental applications, focusing on advanced catalytic EAEE E4361y Economics of Earth resource correlations; application to chemical and materials applications as described in modern literature and industries processing and environmental problems. patents. All students are required to prepare and Lect: 3. 3 pts. Professor Yegulalp. present a literature review project to improve their Prerequisite: EAEE E3101 or the instructor’s EAEE E4901y Environmental microbiology presentation skills related to the application of permission. Definition of terms. Survey of Earth Lect: 3. 3 pts. Professor Chandran. catalysis. resource industries: resources, reserves, produc- Basic microbiological principles; microbial metab- tion, global trade, consumption of mineral com- olism; identification and interactions of microbial EAEE E6151y Applied geophysics modities and fuels. Economics of recycling and populations responsible for the biotransformation Lect: 3. 3 pts. Not given in 2009–2010. substitution. Methods of project evaluation: esti- of pollutants; mathematical modeling of microbially Potential field data, prospecting, wave equations. mation of operating costs and capital require- mediated processes; biotechnology and engineering Huygens’ principle, Green’s functions, Kirchoff ments, project feasibility, risk assessment, and applications using microbial systems for pollution equation, WKB approximation, ray tracing. Wave environmental compliance. Cost estimation for control. propagation, parameters. Computer applications. reclamation/remediation projects. Financing of Wavelet processing, filters and seismic data. reclamation costs at abandoned minesites and EAEE E4950x Environmental biochemical Stratified Earth model, seismic processing and waste-disposal postclosure liability. processes profiling. Radon transform and Fourier migration. Lect: 3. 3 pts. Professor Chandran. Multidimensional geological interpretation. CHEE E4530y Corrosion of metals Prerequisites: EAEE E4901 or CIEE E4252 or Lect: 3. 3 pts. Professor Duby. EAEE E4003 or the instructor’s approval. EAEE E6200y Theory and applications of Prerequisite: CHEN E3010 or the equivalent. Qualitative and quantitative considerations in extreme value statistics in engineering and The theory of electrochemical corrosion, corrosion engineered environmental biochemical processes. Earth sciences tendency, rates, and passivity. Application to Characterization of multiple microbial reactions in Lect: 3. 3 pts. Professor Yegulalp. various environments. Cathodic protection and a community and techniques for determining Prerequisite: STAT G4107 or equivalent back- coatings. Corrosion testing. associated kinetic and stoichiometric parameters. ground in probability and statistical inference, or Engineering design of several bioreactor configu- the instructor’s permission. Introduction of funda- EAEE E4550x Catalysis for emissions control rations employed for biochemical waste treatment. mental concepts in extreme value statistics. The Lect: 3. 3 pts. Professors Castaldi and Farrauto. Mathematical modeling of engineered biological exact and asymptotic theory of extremes. Develop- Prerequisites: ENME E3161 and MSAE E3111 or reactors using state-of-the-art simulation packages. ment of statistical methodology for estimating the the equivalent. Fundamentals of heterogeneous parameters of asymptotic extremal distributions catalysis, including modern catalytic preparation EAEE E4980 Urban environmental technology from experimental data. Examples of applications techniques. Analysis and design of catalytic emis- and policy of extreme value statistics to regional and global sions control systems. Introduction to current Lect: 3. 3 pts. Not given in 2009–2010. earthquake forecasting, laboratory testing of rocks industrial catalytic solutions for controlling Progress of urban pollution engineering via con- and metals, fatigue failure, floods, droughts, gaseous emissions. Introduction to future catalyti- taminant abatement technology, government policy, extreme wind velocities, and rainfalls. cally enabled control technologies. and public action in urban polution. Pollutant impact on modern urban environmental quality, EAEE E6208y Combustion chemistry and EACE E4560x Particle technology (section 1) natural resources, and government, municipal, processes Lect: 3. 3 pts. Professor Park. and social planning and management programs. Lect: 3. 3 pts. Professor Castaldi. Prerequisites: ENME E3161 and MSAE E3111 or Strong emphasis on current and twentieth-century Prerequisite: EAEE E4900 or the equivalent, or the equivalent. Introduction to engineering waste management in New York City. the instructor’s permission. The fundamentals of processes involving particulates and powders. combustion phenomena and the intrinsic chem- The fundamentals of particle characterization, EAEE E6132y Numerical methods in istry of combustion processes. The theory of the multiphase flow behavior, particle formation, pro- geomechanics essential combustion processes such as ignition, cessing and utilization of particles in various engi- Lect: 3. 3 pts. Not given in 2009–2010. sustained reaction, stability, and flame quenching. neering applications with examples in energy and Prerequisite: EAEE E3112 and CIEN E4241, Processes that govern reactant consumption and environment related technologies. Engineering of or the instructor’s permission. A detailed survey product formation, in particular by-products that functionalized particles and design of multiphase of numerical methods used in geomechanics, are formed that result in pollutant emissions and reactors and processing units with emphasis on emphasizing the Finite Element Method (FEM). the impacts and implications that combustion has fluidization technology. Particle technology is an Review of the behavior of geological materials. locally and globally on the environment. Detailed interdisciplinary field. Due to the complexity of Water and heat flow problems. FEM techniques examination of the entire range of combustion

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132 systems from diffusion flame processes to current EAEE E6240x or y Physical hydrology thermodynamics and rate phenomena to the design developing technologies including millisecond cat- Lect: 3. 3 pts. Professor Gong. and control of electrochemical engineering processes. alytic combustion processes, noncarbon fueled Prerequisite: Engineering hydrology or the equiv- combustion, fuel cells and plasma combustion. alent. Spatial/temporal dynamics of the hydrologic EAEE E8233x and y Research topics in cycle and its interactions with landforms and veg- particle processing EAEE E6210x Quantitative environmental risk etation. Hydroclimatology at regional to planetary Points: 0 to 1. Professor Somasundaran. analysis scales, focusing on mechanisms of organization Emergent findings in the interactions of particles Lect: 3. 3 pts. Professor Yegulalp. and variation of water fluxes as a function of with reagents and solutions, especially inorgan- Prerequisite: EAEE E3101, SIEO W4150, or the season, location, reservoir (ocean, atmosphere, ics, surfactants, and polymers in solution, and equivalent. Comprises the tools necessary for land), and time scale. Land-atmosphere interac- their role in grinding, flotation, agglomeration, technical professionals to produce meaningful risk tion and the role of vegetation and soil moisture. filtration, enhanced oil recovery, and other analyses. Review of relevant probability and sta- Topography as an organizing principle for land- mineral processing operations. tistics; incorporation of probability in facility failure water fluxes. Geomorphology and the evolution analysis. Availability, assessment, and incorporation of river networks. Sedimentation, erosion, and hill EAEE E8273x-E8274y Mining engineering of risk-related data. Contaminant transport to slope hydrology. Dynamics of water movement reports exposed individuals; uptake, morbidity, and mortality. over land, in rivers, and in the subsurface, with 0 to 4 pts. Professor Yegulalp. Computational tools necessary to risk modeling. an emphasis on modeling interfaces. Integrated May be substituted for formal thesis, EAEE E9271, Use and applicability of resulting measurements models and the scale problem. Emphasis on upon recommendation of the student’s adviser. of risk, and their use in public policy and regulation. data-based spatial/temporal modeling and explo- ration of outstanding theoretical challenges. EAEE E9271x and y, and s Earth and environ- EAEE E6212x Carbon sequestration mental engineering thesis Lect. 3. 3 pts. Professor Lackner. CHEE E6252y Applied surface and colloid 0 to 6 pts. The staff. Prerequisite: EAEE E4900 or the equivalent, or chemistry Research work culminating in a creditable disser- the instructor’s permission. New technologies for Lect: 2. Lab: 3. 3 pts. Professors Somasundaran tation on a problem of a fundamental nature capturing carbon dioxide and disposing of it away and Farinato. selected in conference between student and from the atmosphere. Detailed discussion of the Prerequisite: CHEE E4252. Applications of sur- adviser. Wide latitude is permitted in choice of extent of the human modifications to the natural face chemistry principles to wetting, flocculation, a subject, but independent work of distinctly carbon cycle, the motivation and scope of future flotation, separation techniques, catalysis, mass graduate character is required in its handling. carbon management strategies, and the role of transfer, emulsions, foams, aerosols, membranes, carbon sequestration. Introduction of several car- biological surfactant systems, microbial surfaces, EAEE E9273x-E9274y Earth and environmental bon sequestration technologies that allow for the enhanced oil recovery, and pollution problems. engineering reports capture and permanent disposal of carbon diox- Appropriate individual experiments and projects. 0 to 4 pts. The staff. ide. Engineering issues in their implementation, Lab required. May be substituted for the formal thesis, EAEE economic impacts, and the environmental issues E9271, upon recommendation of the department. raised by the various methods. EAEE E6255x-E6256y Methods and applica- tions of analytical decision making in mineral EAEE E9281x-E9282y Earth and environmental EAEE E6220x Remedial and corrective action industries engineering seminar, I and II Lect: 3. 3 pts. Not given in 2009–2010. Lect: 3. 3 pts. Not given in 2009–2010. Lect: 1.5. 0 or 1 pt. Instructor to be announced. Prerequisite: EAEE E4160 or the equivalent. Prerequisite: The instructor’s permission. Verbal presentation and discussion of current Integrates the engineering aspects of cleanup Advanced study of decision-making problems with findings and related literature, preferably related of hazardous materials in the environment. Site critical survey and applications of quantitative to thesis research project. Lectures will be given assessment/investigation. Site closure, contain- decision-making techniques in mineral industries. by Columbia scientists and representatives from ment, and control techniques and technologies. Systematic development of methods of the formu- state and city agencies on the chosen topic. Techniques used to treat hazardous materials lation, analysis, and resolution of these problems. Students will have to write several papers and in the environment, in situ and removal for treat- assignments on a variety of problems and solu- ment, focusing on those aspects that are unique EAEE E8229x Selected topics in processing tions appropriate to the topic. to the application of those technologies in an minerals and waste uncontrolled natural environment. Management, Lect: 2. Lab: 3. 3 pts. Professors Somasundaran EAEE E9302x and y Mining engineering safety, and training issues. and Nagaraj. research Prerequisite or corequisite: CHEE E4252 or the 0 to 4 pts. Professor Yegulalp. CHEE E6220y Equilibria and kinetics in instructor’s permission. Critical discussion of cur- Graduate research directed toward solution of hydrometallurgical systems rent research topics and publications in the area technicoscientific problems in mining. Lect: 3. 3 pts. Professor Duby. of flotation, flocculation, and other mineral pro- Prerequisite: CHEE E4050 or EAEE E4003. cessing techniques, particularly mechanisms of EAEE E9305x and y, and s Earth and environ- Detailed examination of chemical equilibria in adsorption, interactions of particles in solution, mental engineering research hydrometallurgical systems. Kinetics and mecha- thinning of liquid films, and optimization techniques. 0 to 12 pts. The staff. nisms of homogeneous and heterogeneous reac- Graduate research directed toward solution of a prob- tions in aqueous solutions. EAEE E8231y Selected topics in hydro- and lem in mineral processing or chemical metallurgy. electrometallurgy EAEE E6228y Theory of flotation Lect: 3. 3 pts. Professor Duby. EAEE E9800x and y, and s Doctoral research Lect: 3. 3 pts. Not given in 2009–2010. Prerequisite: EAEE E4003 and CHEE E4050, or the instruction Prerequisite: CHEE E4252 or the instructor’s per- instructor’s permission. Review of current research 3, 6, 9, or 12 pts. The staff. mission. A detailed study of the physicochemical and literature in the field of hydrometallurgy, elec- A candidate for the Eng.Sc.D. degree in mineral principles of the flotation process. trometallurgy, and corrosion. Topics will be selected engineering must register for 12 points of doctoral by the instructor to illustrate the application of research instruction. Registration in EAEE E9800

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may not be used to satisfy the minimum residence MSAE E4215y Mechanical behavior of materials Lect: 1. 1 pt. Members of the faculty. 133 requirement for the degree. Lect: 3. 3 pts. Professor Noyan. MSAE E9301x and y, and s Doctoral research MSAE E4250x Ceramics and composites 0 to 15 pts. Members of the faculty. EAEE E9900x and y, and s Doctoral dissertation Lect: 3. 3 pts. Offered in alternate years. 0 pts. The staff. MSAE E9309x and y, and s Proposal of Professor Guha. A candidate for the doctorate may be required to research for the doctorate register for this course every term after the stu- MSAE E4301x and y Materials science laboratory 0 to 3 pts. Members of the faculty. dent’s course work has been completed, and until 1 to 3 pts. Instructor to be announced. MSAE E9800x and y, and s Doctoral research the dissertation has been accepted. MSAE E4990x and y Special topics in materials instruction science and engineering 3, 6, 9, or 12 pts. Members of the faculty. Lect: 3. 3 pts. Instructors to be announced. COURSES IN MATERIALS MSAE E9900x and y, and s Doctoral dissertation SCIENCE AND ENGINEERING MSAE E6020y Electronic ceramics 0 pts. Members of the faculty. (HENRY KRUMB SCHOOL OF Lect: 3. 3 pts. Offered in alternate years. MINES) Not given in 2009–2010. For complete course descriptions, see MSAE E6081x Solid state physics, I the section ‘‘Materials Science and Lect: 3. 3 pts. Professor Pinczuk. Engineering Program.’’ MSAE E6082y Solid state physics, II MSAE E1001y Atomic-scale engineering of Lect: 3. 3 pts. Professor Kim. new materials MSAE E6091y Magnetism and magnetic materials Lect: 3. 3 pts. Professor Noyan. Lect: 3. 3 pts. Offered in alternate years. MSAE E3103x Elements of materials science Not given in 2009–2010. Lect: 3. 3 pts. Professor Noyan. MSAE E6120x Grain boundaries and interfaces MSAE E3104y Laboratory in materials science Lect: 2. 3 pts. Offered in alternate years. Lect: 1. Lab. 4. 3 pts. Instructor to be announced. Not given in 2009–2010. MSAE E3111x Thermodynamics, kinetic theory, MSAE E6220x Crystal physics and statistical mechanics Lect: 3. 3 pts. Offered in alternate years. Lect: 3. 3 pts. Professor Billinge. Not given in 2009–2010. MSAE E3141y Processing of metals and MSAE E6221x Introduction to dislocation theory semiconductors Lect: 3. 3 pts. Offered in alternate years. Lect: 3. 3 pts. Professor Duby. Not given in 2008–2009. MSAE E3142y Processing of ceramics and MSAE E6225y Techniques in x-ray and polymers neutron diffraction Lect: 3. 3 pts. Instructor to be announced. Lect: 3. 3 pts. Offered in alternate years. Not given in 2009–2010. MSAE E3156x-E3157y Design project 3 pts. Members of the faculty. MSAE E6229x Energy and particle beam processing of materials MSAE E3900x and y Undergraduate research Lect: 3. 3 pts. Not given in 2009–2010. in materials science 0 to 4 pts. Members of the faculty. MSAE E6230x Kinetics of phase transformations Lect: 3. 3 pts. Offered in alternate years. MSAE E4090x Nanotechnology Not given in 2009–2010. Lect: 3. 3 pts. Offered in alternate years. Professor Herman. MSAE E6251y Thin films and layers Lect: 2. 3 pts. Professor Chan. MSAE E4101x Structural analysis of materials Lect: 3. 3 pts. Professor Chan. MSAE E6273x and y, and s Materials science reports MSAE E4132y Fundamentals of polymers and 0 to 6 pts. Members of the faculty. ceramics Lect: 3. 3 pts. Not given in 2009–2010. MSAE E8235x and y Selected topics in materials science MSAE E4202y Thermodynamics and reactions Lect: 3. 3 pts. Instructors to be announced. in solids Lect: 3. 3 pts. Professor Im. MSAE E8236y Anelastic relaxations in crystals Lect: 3. 3 pts. Offered in alternate years. MSAE E4206x Electronic and magnetic Not given in 2009–2010. properties of solids Lect: 3. 3 pts. Professor Marianetti. MSAE E9000x and y Materials science and engineering colloquium MSAE E4207y Lattice vibrations and crystal 0 pts. Members of the faculty. defects Lect: 3. 3 pts. Professor Chan. MSAE E9259x-E9260y Research topics in mate- rials science and metallurgical engineering

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134 ELECTRICAL ENGINEERING 1300 S. W. Mudd, MC 4712, 212-854-3105 www.ee.columbia.edu

CHAIR PROFESSORS ASSOCIATE PROFESSORS ADJUNCT PROFESSORS Robert Soni Shih-Fu Chang Dimitris Anastassiou Dan Ellis Yuliy Baryshnikov Lexing Xie 1305 S. W. Mudd Keren Bergman Predrag R. Jelenkovic Inder Gopal Shih-Fu Chang Peter Kinget Irving Kalet SENIOR RESEARCH Paul Diament Xiaodong Wang Ta-Hsin Li SCIENTIST Tony F. Heinz Truong-Thao Nguyen Robert Laibowitz Aurel A. Lazar ASSISTANT PROFESSORS Yurii Vlasor Nicholas Maxemchuk Rui Castro Shalom Wind ASSOCIATE RESEARCH Steven Nowick Harish Krishnaswamy James Yardley SCIENTIST Computer Science Ioannis (John) Kymissis Vladimir Sokolov VICE CHAIR Richard M. Osgood Jr. Gil Zussman ADJUNCT ASSOCIATE Charles Zukowski Henning G. Schulzrinne PROFESSORS POSTDOCTORAL 1026 Schapiro Computer Science SENIOR LECTURER Yves Baeyens RESEARCH Amiya K. Sen David Vallancourt Andrew Campbell SCIENTISTS/FELLOWS Kenneth L. Shepard Charles Clyde Peck Yee Him Cheung Yannis P. Tsividis Kudva Prabhakar Cory Dean Stephen H. Unger Harish Viswanathan Nadia Pervez Computer Science Siddharth Ramakrishnan Wen I. Wang ADJUNCT ASSISTANT Charles A. Zukowski PROFESSORS Shahram Ebadollahi DEPARTMENTAL James Kozloski ADMINISTRATOR Dmitry Krylov Kevin Corridan Vincent Leung 1303 S. W. Mudd Ching-Yung Lin

ontemporary electrical engineer- microwave and optical frequencies. is dedicated to the continued develop- ing is a broad discipline that The need for increasingly faster and ment of further innovations through its C encompasses a wide range of more sophisticated methods of handling program of academic instruction and activities. A common theme is the use of information poses a major challenge to research. Our undergraduate academic electrical and electromagnetic signals for the electrical engineer. New materials, program in electrical engineering is the generation, transmission, processing, devices, systems, and network concepts designed to prepare the student for a storage, conversion, and control of infor- are needed to build the advanced com- career in industry or business by provid- mation and energy. An equally important munications and information handling ing her or him with a thorough founda- aspect is the human interface and the systems of the future. Previous innova- tion of the fundamental concepts and role of individuals as the sources and tions in electrical engineering have had a analytical tools of contemporary electri- recipients of information. The rates at dramatic impact on the way in which we cal engineering. A wide range of elective which information is transmitted today work and live: the transistor, integrated courses permits the student to empha- range from megabits per second to circuits, computers, radio and television, size specific disciplines such as tele- gigabits per second and in some cases, satellite transmission systems, lasers, communications, microelectronics, as high as terabits per second. The fiber optic transmission systems, and digital systems, or photonics. range of frequencies over which these medical electronics. Undergraduates have an opportunity to processes are studied extends from The faculty of the Electrical Engineer- learn firsthand about current research direct current (i.e., zero frequency), to ing Department at Columbia University activities by participating in a program

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of undergraduate research projects with of electrical engineering and applied nuclear fusion are under investigation. 135 the faculty. physics. It includes the study of semi- A master’s level program in electrical conductor physics and devices, optical Laboratory Facilities engineering permits the graduate student electronics, and quantum optics. The Current research activities are fully sup- to further specialize her/his knowledge emphasis is on laser processing and ported by more than a dozen well- and skills within a wide range of disci- diagnostics for submicron electronics, equipped research laboratories run by plines. For those who are interested in fabrication of compound semiconductor the Department. Specifically, laboratory pursuing a career in teaching or research, optoelectronic devices by molecular research is conducted in the following our Ph.D. program offers the opportunity beam epitaxy, physics of superlattices laboratories: Multimedia Networking to conduct research under faculty super- and quantum wells, and interface Laboratory, Lightwave Communications vision at the leading edge of technology devices such as Schottky barriers, MOS Laboratory, Systems Laboratory, Image and applied science. Research seminars transistors, heterojunctions, and bipolar and Advanced Television Laboratory, are offered in a wide range of areas, transistors. Another area of activity is Laser Processing Laboratory, Molecular including telecommunications, very large the physics and chemistry of microelec- Beam Epitaxy Laboratory, Surface scale integrated circuits, photonics, and tronics packaging. Analysis Laboratory, Microelectronics microelectronics. Research in photonics includes Fabrication Laboratory, Device The Electrical Engineering Department, development of semi conductor light Measurement Laboratory, Ultrafast along with the Computer Science Depart- sources such as LEDs and injection Optoelectronics Laboratory, Columbia ment, also offers B.S. and M.S. programs lasers, fabrication and analysis of quan- Integrated Systems Laboratory (CISL), in computer engineering. Details on those tum confined structures, photo conduc- Lightwave Communications Laboratory, programs can be found in the Computer tors, pin diodes, avalanche photodiodes, Photonics Laboratory, Plasma Physics Engineering section in this bulletin. optical interconnects, and quantum Laboratory (in conjunction with the optics. A major effort is the picosecond Department of Applied Physics). Research Activities optoelectronics program, focusing on Laboratory instruction is provided in The research interests of the faculty the development of new devices and the Introduction to Electrical Engineering encompass a number of rapidly growing their applications to high-speed opto- Laboratory, Marcellus-Hartley Electronics areas, vital to the development of future electronic measurement systems, pho- Laboratory, Microprocessor Laboratory, technology, that will affect almost every tonic switching, and optical logic. In Microwave Laboratory, Optical Electronics aspect of society: communications and addition, research is being performed Laboratory, Solid-State Laboratory, VLSI information processing; solid-state devices; in detection techniques for optical com- Design Laboratory, and Student Projects ultrafast optics and photonics; micro- munications and radar. Members of Laboratory, all on the twelfth floor of the electronic circuits, integrated systems the photonics group play a leading role S. W. Mudd Building. and computer-aided design; systems in a multi-university consortium: The National Center for Integrated Photonics biology; and electromagnetics and plas- UNDERGRADUATE PROGRAM mas. Details on all of these areas can be Technology. The undergraduate program in elec- found at www.ee.columbia.edu/research. Integrated systems research involves trical engineering at Columbia University Communications research focuses the analysis and design of analog, digital, has five formal educational objectives: on wireless communication, multimedia and mixed-signal microelectronic circuits networking, real-time Internet, lightwave and systems. These include novel signal A. Produce graduates with a strong (fiber optic) communication networks, processors and related systems, data foundation in the basic sciences and optical signal processing and switching, converters, radio frequency circuits, low mathematics that will enable them to service architectures, network manage- noise and low power circuits, and fully identify and solve electrical engineer- ment and control, the processing of integrated analog filters that share the ing problems. image and video information, and media same chip with digital logic. VLSI archi- B. Provide our students with a solid engineering. Current studies include tectures for parallel computation, packet foundation in electrical engineering wireless and mobile computing environ- switching, and signal processing are that prepares them for life-long ments, broadband kernels, object-ori- also under investigation. Computer-aided careers and professional growth in ented network management, real-time design research involves the develop- fields of their choice. monitoring and control, lightwave net- ment of techniques for the analysis and C. Provide our students with the basic work architectures, lightweight protocol design of large-scale integrated circuits skills to communicate effectively and design, resource allocation and network- and systems. to develop the ability to function as ing games, real-time Internet services, Electromagnetics research ranges members of multi-disciplinary teams. future all-digital HDTV systems, coding from the classical domains of microwave D. Provide our students with a broad- and modulation. generation and transmission and wave based education so that they can Solid-state device research is con- propagation in various media to modern appreciate diversity of opinion, better ducted in the Columbia Microelectronics applications involving lasers, optical understand ethical issues, and develop Sciences Laboratories. This is an inter- fibers, plasmas, and solid-state devices. a perspective of our profession. disciplinary facility, involving aspects Problems relevant to controlled thermo- E. Provide our students with a relevant

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136 engineering design experience that is laboratory sequence and the design tronics; (c) signals and systems; and (d) integrated across the four year experiences introduced throughout earlier communications and networking. The curriculum. Through these experi- courses is a senior design course (cap- depth requirement provides an opportu- ences, our students will develop an stone design course), which includes nity to pursue particular interests and understanding of the relationship a significant design project that ties exposure to the process of exploring a between theory and practice. together the core program, encourages discipline in depth—an essential process The B.S. program in electrical engi- creativity, explores practical aspects of that can be applied later to other disci- neering at Columbia University seeks to engineering practice, and provides addi- plines, if desired. provide a broad and solid foundation in tional experience with communication The breadth component must con- the current theory and practice of elec- skills in an engineering context. Finally, sist of at least 6 additional points of trical engineering, including familiarity several technical electives are required, engineering courses that are outside of with basic tools of math and science, chosen to provide both breadth and the chosen depth area. These courses an ability to communicate ideas, and depth in a specific area of interest. More can be from other departments within a humanities background sufficient to detailed program objectives and outcomes the school. The breadth requirement understand the social implications of are posted at www.ee.columbia.edu/ precludes overspecialization. Breadth is engineering practice. Graduates should academics/undergrad. particularly important today, as innova- be qualified to enter the profession of The program in electrical engineering tion requires more and more of an inter- engineering, to continue toward a career leading to the B.S. degree is accredited disciplinary approach, and exposure to in engineering research, or to enter other by the Engineering Accreditation other fields is known to help one’s cre- fields in which engineering knowledge is Commission of the Accreditation Board ativity in one’s own main field. Breadth essential. Required nontechnical courses for Engineering and Technology (ABET). also reduces the chance of obsoles- cover civilization and culture, philosophy, There is a strong interaction between cence as technology changes. economics, and a number of additional the Department of Electrical Engineering Any remaining technical elective electives. English communication skills and the Departments of Computer Science, courses, beyond the minimum 12 points are an important aspect of these courses. Applied Physics and Applied Mathematics, of depth and breadth, do not have to be Required science courses cover basic Industrial Engineering and Operations engineering courses (except for students chemistry and physics, whereas math Research, Physics, and Chemistry. without ELEN E1201 or approved trans- requirements cover calculus, differential fer credit for ELEN E1201) but must be equations, probability, and linear algebra. EE Core Curriculum technical. Generally, math and science Basic computer knowledge is also All electrical engineering (EE) students courses that do not overlap with cours- included, with an introductory course on must take a set of core courses, which es used to fill other requirements are using engineering workstations and two collectively provide the student with fun- allowed. rigorous introductory computer science damental skills, expose him/her to the courses. Core electrical engineering breadth of EE, and serve as a spring- Starting Early courses cover the main components of board for more advanced work, or for The EE curriculum is designed to allow modern electrical engineering and illus- work in areas not covered in the core. students to start their study of EE in trate basic engineering principles. Topics These courses are shown on the charts their first year. This motivates students include a sequence of two courses on on the following pages, along with all early and allows them to spread non- circuit theory and electronic circuits, one program requirements. A full curriculum technical requirements more evenly. course on semiconductor devices, one checklist is also posted at www.ee. It also makes evident the need for on electromagnetics, one on signals and columbia.edu/academics/undergrad. advanced math and physics concepts, systems, one on digital systems, and and motivates the study of such concepts. one on communications or networking. Technical Electives Finally, it allows more time for students Engineering practice is developed further The 18-point technical elective require- to take classes in a chosen depth area, through a sequence of laboratory courses, ment for the electrical engineering pro- or gives them more time to explore starting with a first-year course to intro- gram consists of three components: before choosing a depth area. Students duce hands-on experience early and to depth, breadth, and other. A general can start with ELEN E1201: Introduction motivate theoretical work. Simple creative outline is provided here, and more to electrical engineering in the second design experiences start immediately in specific course restrictions can be found semester of their first year, and can this first-year course. Following this is a at www.ee.columbia.edu/academics/ continue with other core courses one sequence of lab courses that parallel the undergrad. For any course not clearly semester after that, as shown in the core lecture courses. Opportunities for listed there, adviser approval is necessary. “early-starting students” chart. It is exploring design can be found both The depth component must consist emphasized that both the early- and within these lab courses and in the par- of at least 6 points of electrical engineer- late-starting sample programs shown in allel lecture courses, often coupled with ing courses in one of four defined areas: the charts are examples only; schedules experimentation and computer simula- (a) photonics, solid-state devices, and may vary depending on student prepa- tion, respectively. The culmination of the electromagnetics; (b) circuits and elec- ration and interests.

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Transfer Students Students in the 3-2 Combined Plan courses listed by the Electrical Engineer- 137 Transfer students coming to Columbia undergraduate program are not eligible ing Department) or courses designated as juniors with sufficient general back- for admission to this program. COMS, of which at least 10 points must ground can complete all requirements be EE courses. Courses to be credited for the B.S. degree in electrical engi- toward the M.S. degree can be taken GRADUATE PROGRAMS neering. Such students fall into one of only upon prior approval of a faculty The Department of Electrical Engineering two categories: adviser in the Department of Electrical offers graduate programs leading to the Engineering. This applies to the summer Plan 1: Students coming to Columbia degree of Master of Science (M.S.), the session as well as the autumn and without having taken the equivalent graduate professional degree of Electrical spring terms. Certain 4000-level courses of ELEN E1201 must take this course Engineer (E.E.), and the degrees of will not be credited toward the M.S. in their junior year. This requires post- Doctor of Engineering Science (Eng.Sc.D.) degree, and no more than 6 points of poning the core courses in circuits and Doctor of Philosophy (Ph.D.). The research may be taken for credit. Up to and electronics until the senior year, Graduate Record Examination (General 3 points of credit for approved graduate and thus does not allow taking elec- Test only) is required of all applicants courses outside of engineering and tives in that area; thus, such students except special students. An undergradu- science may be allowed. The general cannot choose circuits and electronics ate grade point average equivalent to B school requirements listed earlier in this as a depth area. or better from an institution comparable bulletin, such as minimum GPA, must Plan 2: This plan is for students who to Columbia is expected. also be satisfied. All degree require- have taken a course equivalent to Applicants who, for good reasons, ments must be completed within five ELEN E1201 at their school of origin, are unable to submit GRE test results by years of the beginning of the first course including a laboratory component. See the deadline date but whose undergrad- credited toward the degree. More details the bulletin for a description of this course. uate record is clearly superior may file and a checklist for adviser approvals Many pre-engineering programs and an application without the GRE scores. can be found at www.ee.columbia.edu/ physics departments at four-year col- An explanatory note should be added academics/masters. leges offer such courses. Such students to ensure that the application will be can start taking circuits at Columbia processed even while incomplete. If the Professional Degree immediately, and thus can choose cir- candidate’s admissibility is clear, the The professional degree in electrical cuits and electronics as a depth area. decision may be made without the GRE engineering is intended to provide spe- It is stressed that ELEN E1201 or scores; otherwise, it may be deferred cialization beyond the level of the M.S. its equivalent is a key part of the EE until the scores are received. degree, in a focused area of electrical curriculum. The preparation provided There are no prescribed course engineering selected to meet the profes- by this course is essential for a number requirements in any of the regular sional objectives of the candidate. of other core courses. graduate degree programs. Students, in A minimum of 30 points of credit is Sample programs for both Plan 1 consultation with their faculty advisers, required. The prospective E.E. candidate and Plan 2 transfer students can be design their own programs, focusing on follows a program of study formulated in found at www.ee.columbia.edu/ particular fields of electrical engineering. consultation with, and approved by, a academics/undergrad. Among the fields of graduate study are faculty adviser. At least three courses will microelectronics, communications and be in a specific, focused area of electri- B.S./M.S. Program signal processing, integrated circuit and cal engineering, and at least two-thirds system analysis and synthesis, photon- The B.S./M.S. degree program is open of the entire program will be in electrical ics, electromagnetic theory and applica- to a select group of undergraduate stu- engineering or computer science. No tions, plasma physics, and quantum dents. This double degree program thesis is required, but the program may electronics. makes possible the earning of both the optionally include a seminar or project or Graduate course charts for several Bachelor of Science and Master of research for which a report is produced; focus areas can be found at www.ee. Science degrees simultaneously. Up to 6 up to 6 points of such projects may be columbia.edu/academics/masters. points may be credited to both degrees, credited toward the degree. The level of and some graduate classes taken in the the courses will generally be higher than senior year may count toward the M.S. Master of Science Degree is typical of a master’s degree program, degree. Both degrees may be conferred Candidates for the M.S. degree in elec- although courses at the 4000 level at the same time. Interested students trical engineering must complete 30 may be included to prepare for more can find further information at points of credit beyond the bachelor’s advanced work. A candidate is required www.ee.columbia.edu/academics/ degree. A minimum of 15 points of credit to maintain a grade-point average of at undergrad and candiscuss options must be at the 6000 level or higher. No least 3.0. All degree requirements must directly with their faculty adviser. credit will be allowed for undergraduate be completed within five years of the Students must be admitted prior to the courses (3000 or lower). At least 15 beginning of the first course credited start of their seventh semester at SEAS. points must be taken in EE courses (i.e., toward the degree.

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138 Doctoral Degree Concentration in Multimedia 3.Either ELEN E6761: Computer com- The requirements for the Ph.D. and Networking munication networks, I or CSEE Eng.Sc.D. degrees are identical. Both Advisers: Prof. Henning Schulzrinne, W4119: Computer networks. require a dissertation based on the can- Prof. Predrag Jelenkovic 4.At least two approved advanced courses such as: ELEN E4896: Music didate’s original research, conducted 1. Satisfy M.S. degree requirements. signal processing; ELEN E6820: under the supervision of a faculty mem- 2.Both ELEN E6711: Stochastic signals Speech and audio processing and ber. The work may be theoretical or and noise and ELEN E6761: recognition; ELEN E6850: Visual infor- experimental or both. Students who Computer communication networks, I. mation systems; ELEN E6860: wish to become candidates for the doc- 3.Either COMS W4118: Operating systems Advanced digital signal processing; toral degree in electrical engineering or COMS W4111: Database systems. ELEN E688x: Topics in signal process- have the option of applying for admis- 4.COMS E6181: Advanced Internet ing; ELEN E6762: Computer commu- sion to the Eng.Sc.D. program or the services. Ph.D. program. Students who elect the nication networks, II; ELEN E6717: With an adviser’s approval, any of the Eng.Sc.D. degree register in the School Information theory; COMS E6181: courses above can be replaced by the of Engineering and Applied Science; Advanced internet services; ELEN following closely related subjects: CSEE those who elect the Ph.D. degree regis- E6950: Wireless and mobile network- E4140: Networking laboratory; CSEE ter in the Graduate School of Arts and ing, I; or ELEN E6001-E6002: W4119: Computer networks; COMS Sciences. Doctoral candidates must Advanced projects in electrical engi- W4180: Network security; ELEN E6762: obtain a minimum of 60 points of formal neering with an appropriate project. Computer communication networks, II; course credit beyond the bachelor’s A cross-disciplinary project in areas ELEN E6850: Visual information sys- degree. A master’s degree from an related to new media technology is tems; ELEN E6950: Wireless and mobile accredited institution may be accepted especially encouraged. networking, I; ELEN E6951: Wireless as equivalent to 30 points. A minimum and mobile networking, II. Concentration in Lightwave of 30 points beyond the master’s degree (Photonics) Engineering must be earned while in residence in Concentration in Telecommunications Advisers: Prof. Keren Bergman, Prof. the doctoral program. More detailed Engineering Paul Diament, Prof. Richard Osgood, information regarding the requirements Advisers: Prof. Henning Schulzrinne, Prof. Amiya Sen, Prof. Tony Heinz for the doctoral degree may be Prof. Pedrag Jelenkovic, Prof. Ed obtained in the department office and at Coffman, Prof. Nicholas Maxemchuk, 1.Satisfy the M.S. degree requirements. www.ee.columbia.edu/academics/phd. Prof. Gil Zussman 2.Take both ELEN E4411: Fundamentals of photonics and ELEN E6403: Optional M.S. Concentrations 1.Satisfy the M.S. degree requirements. Classical electromagnetic theory (or 2.One basic hardware or software Students in the electrical engineering an equivalent, such as APPH E4300: course such as: ELEN E4321: Digital M.S. program often choose to use some Applied electrodynamics or PHYS VLSI circuits; ELEN E4411: Funda- of their electives to focus on a particular G6092: Electromagnetic theory). mentals of photonics; COMS W4118: field. Students may pick one of a num- 3.One more device/circuits/photonics Operating systems, I; COMS W4111: ber of optional, formal concentration course such as: ELEN E4401: Wave Database systems. templates or design their own M.S. transmission and fiber optics; ELEN 3.One basic systems course such as: program in consultation with an adviser. E6412: Lightwave devices; ELEN ELEN E4702: Communication theory; These concentrations are not degree E6413: Lightwave systems; ELEN ELEN E4703: Wireless communications; requirements. They represent sugges- E4405: Classical nonlinear optics; CSEE W4119: Computer networks; tions from the faculty as to how one ELEN E6414: Photonic integrated cir- ELEN E6761: Computer communica- might fill one’s programs so as to focus cuits; ELEN E4314: Communication tion networks, I. on a particular area of interest. Students circuits; ELEN E4501: Electromagnetic 4.At least two approved courses from may wish to follow these suggestions, devices and energy conversion. a focus area such as Signal/Image but they need not. The degree require- 4.At least two approved courses in Processing and Telecommunications/ ments are quite flexible and are listed in photonics or a related area. Multimedia Networks. the Master of Science Degree section, Concentration in Wireless and above. All students, whether following Concentration in Media Engineering Mobile Communications a formal concentration template or not, Advisers: Prof. Shi-Fu Chang, Prof. Dan Adviser: Prof. Gil Zussman are expected to include breadth in their Ellis, Prof. Xiaodong Wang program. Not all of the elective courses 1.Satisfy M.S. degree requirements. listed here are offered every year. For the 1.Satisfy the basic M.S. degree require- 2.One basic circuits course such as: latest information on available courses, ments. ELEN E4312: Analog electric circuits; visit the Electrical Engineering home 2.Both ELEN E4810: Digital signal ELEN E4314: Communication circuits; page at www.ee.columbia.edu. processing and ELEN E4830: Digital ELEN E6314: Advanced communica- image processing. tion circuits; ELEN E6312: Advanced analog ICs.

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3.Two communications or networking Sensors, actuators, and electro- numbers; elementary computer logic; digital 139 courses such as: CSEE W4119: mechanical systems; ELEN E6151: speech and image coding; basics of compact Computer networks; ELEN E4702: Surface physics and analysis of elec- disks, telephones, modems, faxes, UPC bar codes, and the World Wide Web. Projects include Digital communications; ELEN E4703: tronic materials; ELEN E6331: Principles implementing simple digital logic systems and Wireless communications; ELEN of semiconductor physics, I; ELEN Web pages. Intended primarily for students E6711: Stochastic signals and noise; E6332: Principles of semiconductor outside the School of Engineering and Applied ELEN E4810: Digital signal process- physics, II; ELEN E6333: Semiconductor Science. The only prerequisite is a working ing; ELEN E6950: Wireless and mobile device physics; ELEN E6945: knowledge of elementary algebra. networking, I; ELEN E6951: Wireless Nanoscale fabrication and devices. ELEN E1201y Introduction to electrical and mobile networking, II; ELEN E6761: 4.At least two approved courses in engineering Computer communication networks, I; devices or a related area. Lect: 3. Lab: 1. 3.5 pts. Professor Vallancourt. ELEN E6712: Communication theory; Prerequisite: MATH V1101. Basic concepts of Concentration in Systems Biology ELEN E6713: Topics in communica- electrical engineering. Exploration of selected tions; ELEN E6717: Information theory. Advisers: Prof. Dimitris Anastassiou, topics and their application. Electrical variables, 4.At least two approved courses in wire- Prof. Pedrag Jelenkovic, Prof. Aurel circuit laws, nonlinear and linear elements, ideal less communications or a related area. Lazar, Prof. Kenneth Shepard, Prof. and real sources, transducers, operational ampli- Xiaodong Wang, Prof. Charles Zukowski fiers in simple circuits, external behavior of diodes Concentration in Microelectronic and transistors, first order RC and RL circuits. 1.Satisfy M.S. degree requirements. Digital representation of a signal, digital logic Circuits 2.Take both ECBM E4060: Introduction gates, flipflops. A lab is an integral part of the Advisers: Prof. Yannis Tsividis, Prof. to genomic information science and course. Required of electrical engineering and Charles Zukowski, Prof. Kenneth technology and BMEB W4011: computer engineering majors. Shepard, Prof. Peter Kinget Computational neuroscience, I: ELEN E3043x Solid state, microwave, and 1.Satisfy M.S. degree requirements. circuits in the brain fiber optics laboratory 2.One digital course: ELEN E4321: 3.Take at least one course from CBMF Lect: 1. Lab: 6. 3 pts. Professor W. Wang. Digital VLSI circuits or ELEN E6321: W4761: Computational genomics; Prerequisites: ELEN E3106, and E3401. Optical Advanced digital electronic circuits. CHBC W4510: Molecular systems electronics and communications. Microwave 3.One analog course such as: ELEN biology, I; CHBC W4511: Molecular circuits. Physical electronics. E4312: Analog electronic circuits; systems biology, II; BIST P8139: ELEN E4215: Analog filter synthesis Theoretical genetic modeling ECBM E3060x Introduction to genomic and design; ELEN E6312: Advanced (Biostatistics); ELEN E6010: Systems information science and technology Lect: 3. 3 pts. Professor Anastassiou. analog integrated circuits; ELEN biology; EEBM E6020: Methods in Introduction to the information system paradigm of E6316: Analog circuits and systems in computational neuroscience; BMEE molecular biology. Representation, organization, VLSI; ELEN E4314: Communication E6030: Neural modeling and neuro- structure, function, and manipulation of the biomol- circuits; ELEN E6314: Advanced com- engineering; APMA E4400: ecular sequences of nucleic acids and proteins. munication circuits. Introduction to biophysical modeling; The role of enzymes and gene regulatory elements 4. One additional course such as: ELEN CHEN E4700: Principles of genomic in natural biological functions as well as in biotech- E4332: VLSI design laboratory; ELEN technologies; ELEN E4312: Analog nology and genetic engineering. Recombination and other macromolecular processes viewed as E6211: Circuit theory; ELEN E6261: electronic circuits. mathematical operations with simulation and visu- Computational methods of circuit 4.Take at least one course from ELEN alization using simple computer programming. This analysis; ELEN E6304: Topics in E608x: Topics in systems biology; course shares lectures with ECBM E4060, but the electronic circuits; ELEN E6318: ELEN E6717: Information theory; work requirements differ somewhat. Microwave circuit design.. ELEN E6201: Linear systems theory; 5.At least two additional approved EEME E6601: Introduction to control ELEN E3081x Circuit analysis laboratory courses in circuits or a related area. theory; ELEN E6711: Stochastic models Lab: 3. 1 pt. Professor Zukowski. in information systems; ELEN E6860: Prerequisite: ELEN E1201 or the equivalent. Corequisite: ELEN E3201. Companion lab course Concentration in Microelectronic Advanced digital signal processing; for ELEN E3201. Experiments cover such topics Devices EEBM E6090: Topics in computational Advisers: Prof. Wen Wang, Prof. Richard as: use of measurement instruments; HSPICE neuroscience and neuroengineering; simulation; basic network theorems; linearization Osgood, Prof. Ioannis (John) Kymissis ELEN E6261: Computational methods of nonlinear circuits using negative feedback; 1.Satisfy M.S. degree requirements. of circuit analysis. opamp circuits; integrators; second-order RLC 2.One basic course such as: ELEN circuits. The lab generally meets on alternate weeks. E4301: Introduction to semiconductor COURSES IN ELECTRICAL ELEN E3082y Digital systems laboratory devices or ELEN E4411: ENGINEERING Lab: 3. 1 pt. Instructor to be announced. Fundamentals of photonics. Corequisite: CSEE W3827. Recommended prepara- 3.One advanced course such as: ELEN ELEN E1101x or y The digital information age tion: ELEN E1201 or the equivalent. Companion lab E4193: Modern display science and Lect: 3. 3 pts. Professor Vallancourt. course for CSEE W3827. Experiments cover such technology; ELEN E4944: Principles of An introduction to information transmission and topics as logic gates; flip-flops; shift registers; coun- storage, including technological issues. Binary device microfabrication; ELEN E4503: ters; combinational logic circuits; sequential logic

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140 ELECTRICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS EARLY-STARTING STUDENTS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) MATH V1202 (3) MATHEMATICS and APMA E2101 (3)3

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

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

ELEN E1201 (3.5) Introduction to electrical ELEN E3201 (3.5) ELEN E3331 (3) CORE REQUIRED engineering (either semester) Circuit analysis Electronic circuts COURSES ELEN E3801 (3.5) CSEE E3827 (3) Signals & 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 & systems lab Digital systems lab

ENGLISH C1010 (3) COMPOSITION Z1003 (0) C1010 (3) (three tracks, choose one) Z0006 (0) Z1003 (0) C1010 (3)

REQUIRED HUMA C1001, C0CI C1101, or Major Cultures (3–4); HUMA W1121 or W1123 (3); HUMA C1002, C0CI C1102, or NONTECHNICAL Global Core (3–4); ECON W1105 (4) and W1155 recitation (0); some of these courses can be postponed ELECTIVES to the junior or senior year, to make room for taking the above electrical engineering courses.

COMPUTER 1 SCIENCE COMS W1007 (3) any semester

PHYSICAL C1001 (1) C1002 (1) EDUCATION

GATEWAY LAB E1102 (4) either semester

1COMS W1007 may be replaced by COMS W1003, W1004, or W1009, but impact on later options should be considered (see www.ee.columbia.edu/academics/undergrad). 2If possible, these labs should be taken along with their corresponding lecture courses. 3APMA E2101 may be replaced by MATH E1210 and either APMA E3101 or MATH V2010.

circuits; programmable logic devices. The lab gener- ELEN E3084x Signals and systems laboratory ory of solids. Carrier concentration and transport ally meets on alternate weeks. Lab: 3. 1 pt. Instructor to be announced. in semiconductors. P-n junction and junction tran- Corequisite: ELEN E3801. Companion lab course sistors. Semiconductor surface and MOS transis- ELEN E3083y Electronic circuits laboratory for ELEN E3801. Experiments cover topics such tors. Optical effects and optoelectronic devices. Lab: 3. 1 pt. Professor Vallancourt. as: introduction and use of MATLAB for numerical Prerequisite: ELEN E3081. Corequisite: ELEN and symbolic calculations; linearity and time ELEN E3201x Circuit analysis E3331. Companion lab course for ELEN E3331. invariance; continous-time convolution; Fourier- Lect: 3. Recit: 1. 3.5 pts. Professor Zukowski. Experiments cover such topics as macromodeling series expansion and signal reconstruction; impulse Prerequisite: ELEN E1201 or the equivalent. of nonidealities of opamps using HSPICE; Schmitt response and transfer function; forced response. Corequisite: MATH V1201. A course on analysis triggers and astable multivibrators using opamps The lab generally meets on alternate weeks. of linear and nonlinear circuits and their applica- and diodes; logic inverters and amplifiers using tions. Formulation of circuit equations. Network bipolar junction transistors; logic inverters and ring ELEN E3106x Solid-state devices and materials theorems. Transient response of first- and second- oscillators using MOSFETs; filter design using Lect: 3. Recit. 1. 3.5 pts. Professor Bergman. order circuits. Sinusoidal steady-state analysis. opamps. The lab generally meets on alternate weeks. Prerequisite: MATH V1201 or the equivalent. Frequency response of linear circuits. Poles and Corequisite: PHYS C1403 or PHYS C2601 or zeros. Bode plots. Two port networks. equivalent. Crystal structure and energy band the-

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141 ELECTRICAL ENGINEERING: THIRD AND FOURTH YEARS EARLY-STARTING STUDENTS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

1 PHYSICS C1403 (3) Lab C1494 (3) (tracks continued) C2601 (3.5) Lab C2699 (3) Lab W3081 (2)

ELEN E3106 (3.5) ELEN E3401 (4) Solid-state devices & Electromagnetics materials EE CORE ELEN E3701 (3)2 REQUIRED Intro. to COURSES communication systems or CSEE W4119 (3)2 Computer networks

ELEN E3043 (3) One capstone design Solid state, microwave, course3 (ELEN E3390, & fiber optics lab ELEN E4332, EECS EE REQUIRED LABS E4340, or CSEE W4840) ELEN E3399 (1) EE practice

IEOR E3658 or STAT 41054; and COMS W3137 (or W3133, W3134, or W3139) OTHER REQUIRED (Some of these courses are not offered both semesters. Students with an adequate background COURSES 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 www.ee.columbia.edu/academics/undergrad)

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

NONTECH Complete 27-point requirement; see page 11 or www.seas.columbia.edu for details (administered by the advising dean)

TOTAL POINTS6 16.5 17 16 18

1Chemistry lab (CHEM 1500) may be substituted for physics lab, although this is not generally recommended. 2These courses can be taken in the sophomore year if the prerequisites/corequisites are satisfied. 3The 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. 4SIEO W3600 and W4150 cannot generally be used to replace IEOR E3658 or STAT W4105. 5The total points of technical electives is reduced to 15 if APMA E2101 has been replaced by MATH E1210 and either APMA E3101 or MATH V2010. 6“Total points” assumes that 20 points of nontechnical electives and other courses are included.

ELEN E3331y Electronic circuits ELEN E3390y Electronic circuit design ations, such as manufacturability, impact on the Lect: 3. 3 pts. Professor Vallancourt. laboratory environment, and economics. The project is chosen Prerequisite: ELEN E3201. Operational amplifier Lab: 6. 3 pts. Professor Vallancourt. by the instructor and may change from year to year. circuits. Diodes and diode circuits. MOS and bipo- Prerequisites: ELEN E3082, E3083, E3331, E3401, lar junction transistors. Biasing techniques. Small- and E3801. Advanced circuit design laboratory. ELEN E3399x Electrical engineering practice signal models. Single-stage transistor amplifiers. Students work in teams to specify, design, imple- 1 pt. Analysis and design of CMOS logic gates. A/D ment, and test an engineering prototype. The work Design project planning, written and oral technical and D/A converters. involves technical as well as nontechnical consider- communication, practical aspects of engineering

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142 ELECTRICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS LATE-STARTING STUDENTS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

MATH V1101(3) MATH V1102 (3) MATH V1201 (3) MATH V1202 (3) MATHEMATICS and APMA E2101 (3)3

C1401 (3) C1402 (3) C1403 (3) Lab C1494 (3)4 PHYSICS C1601 (3.5) C1602 (3.5) C2601 (3.5) Lab C2699 (3) (three tracks, choose one) C2801 (4.5) C2802 (4.5) Lab W3081 (2)

one-semester lecture (3–4) CHEMISTRY C1403 or C1404 or C3045 or C1604 ELECTRICAL ELEN E1201 (3.5) either semester1 ENGINEERING

ENGLISH C1010 (3) COMPOSITION Z1003 (0) C1010 (3) (three tracks, choose one) Z0006 (0) Z1003 (0) C1010 (3)

HUMA C1001, C0CI C1101, HUMA C1002, C0CI C1102, REQUIRED or Global Core (3–4) or Global Core (3–4) NONTECHNICAL HUMA W1121 or ECON W1105 (4) and ELECTIVES W1123 (3) W1155 recitation (0)

COMPUTER COMS W1007 (3) either semester2 SCIENCE

PHYSICAL C1001 (1) C1002 (1) EDUCATION

GATEWAY LAB E1102 (4) either semester

1Transfer 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. 2COMS W1007 may be replaced by COMS W1003, W1004, or W1009, but impact on later options should be considered (see www.ee.columbia.edu/academics/undergrad). 3APMA E2101 may be replaced by MATH E1210 and either APMA E3101 or MATH V2010. 4Chemistry lab (CHEM C1500) may be substituted for physics lab, although this is not generally recommended.

as a profession, such as career development and ELEN E3701y Introduction to communication CSEE W3827x and y Fundamentals of societal and environmental impact. systems computer systems Lect: 3. 3 pts. Instructor to be announced. Lect: 3. 3 pts. Instructor to be announced. ELEN E3401y Electromagnetics Prerequisite: ELEN E3801. Corequisite: IEOR Prerequisite: An introductory programming course. Lect: 3. 4 pts. Professor Diament. E3658. A basic course in communication theory, Fundamentals of computer organization and digi- Prerequisites: MATH V1201; PHYS C1402 or PHYS stressing modern digital communication systems. tal logic. Boolean algebra, Karnaugh maps, basic C1602, or equivalents. Basic field concepts. Nyquist sampling, PAM and PCM/DPCM systems, gates and components, flipflops and latches, Interaction of time-varying electromagnetic fields. time division multiplexing, high frequency digital counters and state machines, basics of combina- Field calculation of lumped circuit parameters. (ASK, OOK, FSK, PSK) systems, and AM and FM tional and sequential digital design. Assembly Transition from electrostatic to quasistatic and electro- systems are among the topics covered. Also includ- language, instruction sets, ALUs, single-cycle and magnetic regimes. Transmission lines. Energy trans- ed is an introduction to noise processes, detecting multi-cycle processor design, introduction to fer, dissipation, and storage. Waveguides. Radiation. signals in the presence of noise, Shannon’s theorem pipelined processors, caches, and virtual memory. on channel capacity, and elements of coding theory. EEME E3601x Classical control systems ELEN E3998x and y Projects in electrical Lect. 3. 3 pts. Professor Longman. ELEN E3801x Signals and systems engineering Prerequisite: MATH E1210. Analysis and design Lect: 3. 3.5 pts. Professor X. Wang. 0 to 3 pts. of feedback control systems. Transfer functions; Corequisite: Math V1201. Modeling, description, May be repeated for credit, but no more than block diagrams; proportional, rate, and integral and classification of signals and systems. Continuous- 3 total points may be used for degree credit. controllers; hardware; implementation. Routh sta- time systems. Time domain analysis, convolution. Prerequisite: approval by a faculty member who bility criterion, root locus, Bode and Nyquist plots, Frequency domain analysis, transfer functions. agrees to supervise the work. Independent project compensation techniques. Fourier series. Fourier and Laplace transforms. involving laboratory work, computer programming, Discrete-time systems and the Z transform. analytical investigation, or engineering design.

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143 ELECTRICAL ENGINEERING: THIRD AND FOURTH YEARS1 LATE-STARTING STUDENTS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

ELEN E3106 (3.5) CSEE W3827(3) Solid-state devices & Fund. of computer sys. materials ELEN E3331 (3) ELEN E3201 (3.5) Electronic circuits Circuit analysis EE CORE ELEN E3401 (4) REQUIRED ELEN E3801 (3.5) Electromagnetics COURSES Signals & systems ELEN E3701 (3) Intro. to communication systems or CSEE W4119 (3) Computer networks

ELEN E3081 (1)2 ELEN E3083 (1)2 ELEN E3043 (3) One capstone design Circuit analysis lab Electronic circuits lab Solid state, microwave, course3 ( ELEN E3390, & fiber optics lab ELEN E4332, EE REQUIRED LABS ELEN E3084 (1)2 ELEN E3082 (1)2 EECS E4340, Signals & systems lab Digital systems lab ELEN E3399 (1) or CSEE W4840) EE practice

OTHER REQUIRED IEOR E3658 or STAT W41054; and COMS W3137 (or W3133, W3134, or W3139) 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 www.ee.columbia.edu/academics/undergrad)

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

NONTECH Complete 27-point requirement; see page 11 or www.seas.columbia.edu for details (administered by the advising dean)

6 TOTAL POINTS 15.5 18 16 18

1This 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. 2If possible, these labs should be taken along with their corresponding lecture courses. 3The 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. 4SIEO W3600 and W4150 cannot generally be used to replace IEOR E3658 or STAT W4105. 5The total points of technical electives is reduced to 15 if APMA E2101 has been replaced by MATH E1210 and either APMA E3101 or MATH V2010. 6“Total points” assumes that 9 points of nontechnical electives are included.

BMEB W4011x Computational neuroscience: neuron, modeling and analysis of ion channels, encoding machines, fast algorithms for stimulus Circuits in the brain basic dendritic integration. Integrate-and-fire and recovery, elements of spike processing and neural Lect: 3. 3 pts. Professors Lazar and Yuste. other spiking neuron models, stimulus representa- computation. Modeling synapses and synaptic Prerequisite: ELEN E3801 or BIOL W3004. tion and the neural code, time encoding and stimu- transmission, synaptic plasticity and learning algo- Biophysics of computation, the Hodgkin-Huxley lus recovery, information representation with time rithms. Projects in Matlab.

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144 ECBM E4060x Introduction to genomic ELEN E4301y Introduction to semiconductor incidence and total internal reflection. Transmission information science and technology devices lines and conducting waveguides. Planar and Lect: 3. 3 pts. Professor Anastassiou. Lect: 3. 3 pts. Professor Laibowitz. circular dielectric waveguides; integrated optics Introduction to the information system paradigm Prerequisite: ELEN E3106 or the equivalent. and optical fibers. Hybrid and LP modes. Graded- of molecular biology. Representation, organization, Semiconductor physics. Carrier injection and index fibers. Mode coupling; wave launching. structure, function, and manipulation of the bio- recombination. P-n junction and diodes: Schottky molecular sequences of nucleic acids and proteins. barrier and heterojunctions, solar cells and light- ELEN E4411x Fundamentals of photonics The role of enzymes and gene regulatory elements emitting diodes. Junction and MOS field-effect Lect: 3. 3 pts. Instructor to be announced. in natural biological functions as well as in biotech- transistors, bipolar transistors. Tunneling and Prerequisite: ELEN E3401 or the equivalent. nology and genetic engineering. Recombination charge-transfer devices. Planar resonators. Photons and photon streams. and other macromolecular processes viewed as Photons and atoms: energy levels and band mathematical operations with simulation and visu- ELEN E4312x Analog electronic circuits structure; interactions of photons with matter; alization using simple computer programming. Lect: 3. 3 pts. Professor Tsividis. absorption, stimulated and spontaneous emis- This course shares lectures with ECBM E3060, Prerequisites: ELEN E3331 and E3801. sion; thermal light, luminescence light. Laser but the work requirements differ somewhat. Differential and multistage amplifiers; small-signal amplifiers: gain, saturation, and phase shift; rate analysis; biasing techniques; frequency response; equations; pumping. Lasers: theory of oscillation; CSEE W4119x and y Computer networks negative feedback; stability criteria; frequency laser output characteristics. Photons in semicon- Lect: 3. 3 pts. Professors Misra and Rubenstein compensation techniques. Analog layout tech- ductors: generation, recombination, and injection; Corequisite: IEOR E3658 or SIEO W3600, or the niques. An extensive design project is an integral heterostructures; absorption and gain coefficients. equivalent. Introduction to computer networks and part of the course. Semiconductor photon sources: LEDs; semicon- the technical foundations of the Internet, including ductor optical amplifiers; homojunction and het- applications, protocols, local area networks, algo- ELEN E4314y Communication circuits erojunction laser diodes. Semiconductor photon rithms for routing and congestion control, security, Lect: 3. 3 pts. Professor Tsividis. detectors: p-n, p-i-n, and heterostructure photo elementary performance evaluation. Several Prerequisite: ELEN E4312. Principles of electronic diodes; avalanche photodiodes. written and programming assignments required. circuits used in the generation, transmission, and reception of signal waveforms, as used in analog ELEN E4488x Optical systems CSEE W4140x or y Networking laboratory and digital communication systems. Nonlinearity Lect: 3. 3 pts. Professor Bergman. Lect: 3. 4 pts. and distortion; power amplifiers; tuned amplifiers; Prerequisite: ELEN E3401 or the equivalent. Prerequisite: CSEE W4119 or the equivalent. In oscillators; multipliers and mixers; modulators and Introduction to optical systems based on physical this course, students will learn how to put “princi- demodulators; phase-locked loops. An extensive design and engineering principles. Fundamental ples into practice,” in a hands-on networking lab design project is an integral part of the course. geometrical and wave optics with specific emphasis course. The technologies and protocols of the on developing analytical and numerical tools used Internet will be covered, using equipment currently ELEN E4321x Digital VLSI circuits in optical engineering design. Focus on applications available to large Internet service providers such Lect: 3. 3 pts. Professor Shepard. that employ optical systems and networks, includ- as CISCO routers and end systems. A set of labo- Recommended preparation: ELEN E3331, CSEE ing examples in holographic imaging, tomography, ratory experiments will provide hands-on experi- W3827, and ELEN E3106. Design and analysis Fourier imaging, confocal microscopy, optical signal ence with engineering wide-area networks and of high-speed logic and memory. Digital CMOS processing, fiber optic communication systems, will familiarize students with the Internet Protocol and BiCMOS device modeling. Integrated circuit optical interconnects,and networks. (IP), Address Resolution Protocol (ARP), Internet fabrication and layout. Interconnect and parasitic Control Message Protocol (ICMP), User Datagram elements. Static and dynamic techniques. Worst- ELEN E4501x Electromagnetic devices and Protocol (UDP), Transmission Control Protocol case design. Heat removal and I/O. Yield and energy conversion (TCP), the Domain Name System (DNS), routing circuit reliability. Logic gates, pass logic, latches, Lect: 3. 3 pts. Instructor to be announced. protocols (RIP, OSPF, BGP), network manage- PLAs, ROMs, RAMs, receivers, drivers, repeaters, Prerequisite: ELEN E3401. Linear and nonlinear ment protocols (SNMP), and application-level sense amplifiers. magnetic circuits. Electric and magnetic energy stor- protocols (FTP, TELNET, SMTP). age, loss, and transfer. Circuit behavior of energy EECS E4340y Computer hardware design storage and transfer devices. Field theory of moving ELEN E4193x Modern display science and Lec: 2. Lab: 3. 3 pts. Instructor to be announced. bodies. Dynamical equations of an electromechani- technology Prerequisites: ELEN E3331 and CSEE W3827. cal system. Electromechanical and thermo-electric Lect: 3. 3 pts. Professor Kymissis. Practical aspects of computer hardware design sensors and actuators. Rotating electric energy con- Prerequisites: Linear algebra, differential equations, through the implementation, simulation, and verters. Superconductivity and applications. and basic semiconductor physics. Introduction to prototyping of a PDP-8 processor. High-level and modern display systems in an engineering context. assembly languages, I/O, interrupts, datapath and ELEN E4503x Sensors, actuators, and electro- The basis for visual perception, image representation, control design, pipelining, busses, memory archi- mechanical systems color space, metrics of illumination. Physics of lumi- tecture. Programmable logic and hardware proto- Lect: 3. 3 pts. Instructor to be announced. nescence, propagation and minipulation of light in typing with FPGAs. Fundamentals of VHDL for Prerequisites: ELEN E3201 and E3401, or the anisotropic media, emissive displays, and spatial light register-transfer level design. Testing and valida- equivalents. Electromagnetic energy storage, modulators. Fundamentals of display addressing, the tion of hardware. Hands-on use of industry CAD loss, and transfer. Dynamics of electromechanical Alt-Pleshko theorem, multiple line addressing. Large tools for simulation and synthesis. Lab required. systems. Linearization of nonlinear coupled area electronics, fabrication, and device integration of dynamical equations and equivalent circuits. commercially important display types. A series of ELEN E4401x Wave transmission and fiber optics Electromechanical actuators: acoustic, IC short laboratories will reinforce material from the lec- Lect: 3. 3 pts. Professor Diament. processed micromachines. Electromechanical tures. Enrollment may be limited. Prerequisite: ELEN E3401 or the equivalent. Waves sensors: acoustic, pressure, and acceleration. and Maxwell’s equations. Field energetics, disper- Thermal sensors: polysilicon thermopiles and sion, complex power. Waves in dielectrics and in bipolar transistor temperature sensors. Electro- conductors. Reflection and refraction. Oblique optic sensors: visible light, infrared, and x-ray.

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EEME E4601y Digital control systems CSEE W4824x or y Computer architecture ELEN E6001x-E6002y Advanced projects 145 Lect: 3. 3 pts. Professor Longman. Lect: 3. 3 pts. Professor Carloni. in electrical engineering Prerequisite: ELEN E3801 or EEME E3601, or Prerequisite: CSEE W3287 or the equivalent. 1 to 4 pts. the equivalent. Real-time control using digital Focuses on advanced topics in modern computer May be repeated for up to 6 points of credit. computers. Solving scalar and state-space differ- architecture, illustrated by recent case studies. Graduate-level projects in various areas of electri- ence equations. Discrete equivalents of continu- Fundamentals of quantitative analysis. Pipelined, cal engineering and computer science. In consul- ous systems fed by holds. Z-transfer functions. out-of-order, and speculative execution. tation with an instructor, each student designs his Creating closed-loop difference equation models Superscalar, VLIW, and vector processors. or her project depending on the student’s previous by Z-transform and state variable approaches. Embedded processors. Memory hierarchy design. training and experience. Students should consult The Nyquist frequency and sample rate selection. Multiprocessors and thread-level parallelism. with a professor in their area for detailed arrange- Classical- and modern-based digital control laws. Syncronization and cache coherence protocols. ments no later than the last day of registration. Digital system identification. Interconnection networks. ELEN E6010y Systems biology: Design princi- ELEN E4702x or y Digital communications ELEN E4830y Digital image processing ples for biological circuits Lect: 3. 3 pts. Instructor to be announced. Lect: 3. 3 pts. Professor Chang. Lect: 3. 4.5 pts. Instructor to be announced. Prerequisite: ELEN E3701 or the equivalent. Digital Introduction to the mathematical tools and algo- Prerequisite: ECBM E4060 or the instructor’s per- communications for both point-to-point and switched rithmic implementation for representation and pro- mission. Beyond bioinformatics, cells as systems. applications is further developed. Optimum cessing of digital still and moving pictures. Topics Metabolic networks, transcription regulatory net- receiver structures and transmitter signal shaping include image representation, thresholding, works, signaling networks. Deterministic and sto- for both binary and M-ary signal transmission. halftoning, linear and nonlinear filtering, edge chastic kinetics. Mathematical representation of An introduction to block codes and convolutional detection, image transforms, enhancement, reconstructed networks. Network motifs. Signal codes, with application to space communications. restoration, segmentation, motion analysis, and transduction and neuronal networks. Robustness. coding for data compression. Bacterial chemotaxis and patterning in fruit fly ELEN E4703y Wireless communications development. Kinetic proofreading. Optimal gene Lect: 3. 3 pts. Professor Diament. CSEE W4840 y Embedded systems circuit design. Rules for gene regulation. Random Prerequisite: ELEN E3701 or the equivalent. Wireless Lect: 3. 3 pts. Professor Edwards. networks and multiple time scales. Biological communication systems. System design fundamen- Prerequisite: CSEE W4823 or the equivalent. information processing. Numerical and simulation tals. Trunking theory. Mobile radio propagation. Embedded system design and implementation techniques. Major project(s) in Matlab. Reflection of radio waves. Fading and multipath. combining hardware and software. I/O, interfacing, Modulation techniques; signal space; probability of and peripherals. Weekly laboratory sessions and EEBM E6020y Methods of computational neu- error, spread spectrum. Diversity. Multiple access. term project on design of a microprocessor-based roscience embedded system including at least one custom Lect: 3. 4.5 pts. Professor Lazar. ELEN E4810x Digital signal processing peripheral. Knowledge of C programming and dig- Prerequisite: BMEB W4011 or the instructor’s per- Lect: 3. 3 pts. Professor Ellis. ital logic required. Lab required. mission. Formal methods in computational neuro- Prerequisite: ELEN E3801. Digital filtering in time science, including methods of signal processing, and frequency domain, including properties of dis- ELEN E4896y Music signal processing communications theory, information theory, systems crete-time signals and systems, sampling theory, Lect: 3. 3 pts. Professor Eleftheriadis. and control, system identification and machine transform analysis, system structures, IIR and Prerequisite: A course on discrete-time signal pro- learning. Molecular models of transduction path- FIR filter design techniques, the Discrete Fourier cessing (at the level of ELEN E3801 or, preferably, ways. Robust adaptation and integral feedback. Transform, Fast Fourier Transforms. E4810). An introductory course on the applications Stimulus representation and groups. Stochastic and of signal processing to music, suitable to seniors dynamical systems models of spike generation. ELEN E4815y Random signals and noise and first-year graduate students in electrical engi- Neural diversity and ensemble encoding. Time Lect: 3. 3 pts. Instructor to be announced. neering, computer science, or music. Emphasis is encoding machines and neural codes. Stimulus Prerequisite: IEOR E3658 or the equivalent. placed on the signal processing operations in recovery with time decoding machines. MIMO mod- Characterization of stochastic processes as mod- both recording and live environments. Topics cov- els of neural computation. Synaptic plasticity and els of signals and noise; stationarity, ergodicity, ered include audio and room acoustics; micro- learning algorithms. Major project(s) in Matlab. correlation functions, and power spectra. Gaussian phones and loudspeakers; A/D conversion, dither- processes as models of noise in linear and non- ing, and digital audio formats; analog and digital BMEE E6030y Neural modeling and neuroengi- linear systems; linear and nonlinear transforma- audio mixers; audio effects algorithms; sequencers, neering tions of random processes; orthogonal series rep- samplers, and Digital Audio Workstations (DAW); Lect: 3. 3 pts. Instructor to be announced. resentations. Applications to circuits and devices, mastering for CD and DVD production; and sound Prerequisites: APMA E3101, ELEN E3801, and to communication, control, filtering, and prediction. synthesis algorithms. Throughout the course case BMEB W4011, or the equivalent, or the instruc- studies of real systems will be examined in detail. tor’s permission. Engineering perspective on the CSEE W4823x or y Advanced logic design The course includes a site visit to a state-of-the- study of multiple levels of brain organization, from Lect: 3. 3 pts. Professor Nowick. art professional recording facility. single neurons to cortical modules and systems. Prerequisite: CSEE W3827 or the equivalent. Mathematical models of spiking neurons, neural An introduction to modern digital system design. ELEN E4998x and y Intermediate projects dynamics, neural coding, and biologically based Advanced topics in digital logic: controller synthesis in electrical engineering computational learning. Architectures and learning (Mealy and Moore machines); adders and multipli- 0 to 3 pts. principles underlying both artificial and biological ers; structured logic blocks (PLDs, PALs, ROMs); Prerequisite: The instructor’s permission. May be neural networks. Computational models of cortical iterative circuits. Modern design methodology: reg- repeated for credit, but no more than 3 total processing, with an emphasis on the visual sys- ister transfer level modeling (RTL); algorithmic state points may be used for degree credit. Substantial tem. Applications of principles in neuroengineer- machines (ASMs); introduction to hardware independent project involving laboratory work, ing; neural prostheses, neuromorphic systems description languages (VHDL or Verilog); system- computer programming, analytical investigation, and biomimetics. Course will include a computer level modeling and simulation; design examples. or engineering design. simulation laboratory.

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146 ELEN E6080-6089x or y Topics in systems biology Prerequisites: ELEN E3331 and E3401, or the ples; electro-optics of liquid crystals and photo- Lect: 2. 3 pts. Instructor to be announced. equivalents. Introduction to microwave engineer- refractive materials. Nonlinear optics: second-order Prerequisite: The instructor’s permission. Selected ing and microwave circuit design. Review of nonlinear optics; third-order nonlinear optics; pulse advanced topics in systems biology. Content transmission lines. Smith chart, S-parameters, propagation and solitons. Acousto-optics: interaction varies from year to year, and different topics microwave impedance matching, transformation of light and sound; acousto-optic devices. Photonic rotate through the course numbers 6080-6089. and power combining networks, active and pas- switching and computing: photonic switches; all- sive microwave devices, S-parameter–based optical switches; bistable optical devices. Intro- EEBM E6090-6099x or y Topics in computa- design of RF and microwave amplilfiers. A duction to fiber-optic communications: components tional neuroscience and neuroengineering microwave circuit design project (using micro- of the fiberoptic link; modulation, multiplexing and Lect: 2. 3 pts. Instructor to be announced. wave CAD) is an integral part of the course. coupling; system performance; receiver sensitivity; Prerequisite: The instructor’s permission. coherent optical communications. Selected advanced topics in computational neuro- ELEN E6321y Advanced digital electronic science and neuroengineering. Content varies circuits ELEN E6413y Lightwave systems from year to ear, and different topics rotate Lect: 3. 4.5 pts. Professor Shepard. Lect: 2. 3 pts. Instructor to be announced. through the course numbers 6090-6099. Prerequisite: ELEN E4321. Advanced topics in Prerequisite: ELEN E4411. Recommended prepa- the design of digital integrated circuits. Clocked ration: ELEN E6412. Fiber optics. Guiding, dis- CSEE E6180x or y Modeling and performance and nonclocked combinational logic styles. Timing persion, attenuation, and nonlinear properties of evaluation circuits: latches and flip-flops, phase-locked loops, fibers. Optical modulation schemes. Photonic Lect: 2. 3 pts. Instructor to be announced. delay-locked loops. SRAM and DRAM memory components, optical amplifiers. Semiconductor Prerequisites: COMS W4118 and SIEO W4150 circuits. Modeling and analysis of on-chip inter- laser transmitters. Receiver design. Fiber optic or permission of the instructor. Introduction to connect. Power distribution and power-supply noise. telecommunication links. Nonregenerative trans- queueing analysis and simulation techniques. Clocking, timing, and synchronization issues. mission using erbium-doped fiber amplifier Evaluation of time-sharing and multiprocessor Circuits for chip-to-chip electrical communication. chains. Coherent detection. Local area networks. systems. Topics include priority queueing, buffer Advanced technology issues that affect circuit Advanced topics in light wave networks. storage, disk access, interference and bus con- design. The class may include a team circuit- tention problems, and modeling of program behaviors. design project. ELEN E6488y Optical interconnects and inter- connection networks ELEN E6201x Linear system theory ELEN E6331y Principles of semiconductor Lect: 2. 3 pts. Professor Bergman Lect: 3. 3 pts. Instructor to be announced. physics, I Prerequisite: ELEN E4411 or E4488, or an equiv- Prerequisites: ELEN E3801 and APMA E3101, or Lect: 2. 3 pts.Prerequisite: ELEN E4301. alent photonics course. Introduction to optical the equivalents. Abstract objects, the concepts of Designed for students interested in research in interconnects and interconnection networks for state. Definition and properties of linear systems. semiconductor materials and devices. Topics digital systems. Fundamental optical intercon- Characterization of linear continuous time and dis- include energy bands: nearly free electron and nects technologies, optical interconnection net- crete-time, fixed, and time-varying systems. State- tight-binding approximations, the k.p. method, work design, characterization, and performance space description; fundamental matrix, calculation quantitative calculation of band structures and evaluation. Enabling photonic technologies, by computer and matrix methods. Modes in linear their applications to quantum structure transistors, including free-space structures, hybrid and mono- systems. Adjoint systems. Controllability and photodetectors, and lasers; semiconductor statis- lithic integration platforms for photonic on-chip, observability. Canonical forms and decompositions. tics, Boltzmann transport equation, scattering chip-to-chip, backplane, and node-to-node inter- State estimators. Lyapunov’s method and stability. processes, quantum effect in transport phenome- connects, as well as photonic networks on-chip. na, properties of heterostructures. Quantum ELEN E6312y Advanced analog integrated circuits mechanical treatment throughout. EEME E6601x Introduction to control theory Lect: 3. 4.5 pts. Professor Kinget. Lect: 3. 3 pts. Professor Longman. Prerequisite: ELEN E4312. Integrated circuit device ELEN E6332y Principles of semiconductor Prerequisite: MATH E1210. A graduate-level intro- characteristics and models; temperature- and physics, II duction to classical and modern feedback control supply-independent biasing; IC operational ampli- Lect: 2. 3 pts. Instructor to be announced. that does not presume an undergraduate back- fier analysis and design; feedback amplifiers, stability Prerequisite: ELEN E6331. Optical properties ground in control. Scalar and matrix differential and frequency compensation techniques; noise in including absorption and emission of radiation, equation models, and solutions in terms of state circuits; low-noise design. Computer-aided analysis electron-phonon interactions, radiative and transition matrices. Transfer functions and trans- techniques are extensively used. An extensive phonon-mediated processes, excitons, plasmons, fer function matrices, block diagram manipula- design project is an integral part of the course. polaritons, carrier recombination and generation, tions, closed-loop response. Proportional, rate, and related optical devices, tunneling phenomena, and integral controllers, and compensators. Design ELEN E6314x Advanced communication circuits superconductivity. Quantum mechanical treatment by root locus and frequency response. Controllability, Lect: 3. 4.5 pts. Instructor to be announced. throughout, heavy use of perturbation theory. observability. Luenberger observers, pole place- Prerequisites: ELEN E4314 and E6312. Overview ment, and linear-quadratic cost controllers. of communication systems, modulation and ELEN E6333y Semiconductor device physics detection schemes. Receiver and transmitter Lect: 2. 3 points. Instructor to be announced. EEME E6602y Modern control theory architectures. Noise, sensitivity, and dynamic Prerequisite: ELEN E4301 or the equivalent. Lect: 3. 3 pts. Instructor to be announced. range. Nonlinearity and distortion. Low-noise Physics and properties of semiconductors. Prerequisite: EEME E6601 or EEME E4601 or amplifiers, mixers, and oscillators. Phase-locked Transport and recombination of excess carriers. ELEN E6201, or the instructor’s permission. loops and frequency synthesizers. Power ampli- Schottky, P-N, MOS, and heterojunction diodes. Singular value decomposition. ARX model and fiers. Typical applications include wireless trans- Field effect and bipolar junction transistors. state-space model system identification. Recursive ceivers and optical links. Computer-aided analysis Dielectric and optical properties. Optical devices least squares filters and Kalman filters. LQR, H∞, techniques are extensively used. An extensive including semiconductor lamps, lasers, and detectors. linear robust control, predictive control. Learning design project is an integral part of the course. control, repetitive control, adaptive control. Liapunov ELEN E6412y Lightwave devices and Popov stability. Nonlinear adaptive control, ELEN E6318x or y Microwave circuit design Lect: 2. 3 pts. Instructor to be announced. nonlinear robust control, sliding mode control. Lect: 3. 3 pts. Instructor to be announced. Prerequisite: ELEN E4411. Electro-optics: princi-

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ELEN E6711x Stochastic models in informa- in integrated networks. Content varies from year Prerequisite: ELEN E4810. This course is 147 tion systems to year, and different topics rotate through the designed as an extension to ELEN E4810, with Lect: 3. 4.5 pts. Instructor to be announced. course numbers 6770 to 6779. emphasis on emerging techniques in the area of Prerequisite: IEOR E3658. Foundations: probabil- digital signal processing. Topics include multirate ity review, Poisson processes, discrete-time ELEN E6820y Speech and audio processing signal processing, multidimensional signal pro- Markov models, continuous-time Markov models, and recognition cessing, short-time Fourier transform, signal stationarity, and ergodicity. The course presents a Lect: 3. 4.5 pts. Professor Ellis. expansion in discrete and continuous time, filter sample-path (time domain) treatment of stochastic Prerequisite: ELEN E4810 or the instructor’s per- banks, multiresolution analysis, wavelets, and models arising in information systems, including mission. Fundamentals of digital processing of their applications to image compression and at least one of the following areas: communica- speech and audio signals. Acoustic and perceptu- understanding. Other topics may be included to tions networks (queueing systems), biological al basis of audio. Short-time Fourier analysis and reflect developments in the field. networks (hidden Markov models), Bayesian filterbank models. Speech and audio coding, restoration of images (Gibbs fields), and electric compression, and reconstruction. Acoustic feature CSEE E6861y Computer-aided design of digi- networks (random walks). extraction and classification. Recognition tech- tal systems niques for speech and other sounds, including Lect: 2. 3 pts. Professor Nowick. ELEN E6712x Communication theory hidden Markov models. Prerequisites: (1) One semester of advanced digi- Lect: 3. 3 pts. Instructor to be announced. tal logic (CSEE W4823 or the equivalent, or the Prerequisite: ELEN E4815 or the equivalent, or CSEE E6824y Parallel computer architecture instructor’s permission); (2) a basic course in data the instructor’s permission. Representation of Lect: 3. 3 pts. Professor Sethumadhavan. structures and algorithms (COMS W3133, band-limited signals and systems. Coherent Prerequisite: CSEE W8424. Parallel computer W3134, W3137, W3139, or W3157, or the equiva- and incoherent communications over Gaussian principles, machine organization, and design of lent) and familiarity with programming. channels. Basic digital modulation schemes. parallel systems, including parallelism detection Introduction to modern digital CAD synthesis and Intersymbol inference channels. Fading multipath methods, synchronization, data coherence, and optimization techniques. Topics include modern channels. Carrier and clock synchronization. interconnection networks. Performance analysis digital system design (high-level synthesis, regis- and special-purpose parallel machines. ter-transfer level modeling, algorithmic state ELEN E6717x Information theory machines, optimal scheduling algorithms, Lect: 2. 3 pts. Instructor to be announced. CSEE E6847y Distributed embedded systems resource allocation and binding, retiming), con- Prerequisite: IEOR E3658 or a course in stochas- Lect: 2. 3 pts. Professor Carloni. troller synthesis and optimization, exact and tic processes. Corequisite: ELEN E4815. Mutual Prerequisite: Any course numbered in the heuristic two-level logic minimization, advanced information and entropy. The source coding theo- COMS4110s, CSEE4800s, or ELEN4300s, or the multilevel logic optimization, optimal technology rem. The capacity of discrete memoryless chan- instructor’s permission. An interdisciplinary gradu- mapping to library cells (for delay, power, and nels and the noisy channel coding theorem. The ate-level seminar on the design of distributed area minimization), advanced data structures rate distortion function. Discrete memoryless embedded systems. Emphasis is put on system (binary delusion diagrams), SAT solvers and their sources and single-letter distortion measures. robustness in the presence of highly variable applications, stati timing analysis, and introduc- Bhattacharya bounds, convolutional codes, and communication delays and heterogeneous com- tion to testability. Includes hands-on small design the Viterbi algorithm. ponent behaviors. The course has a two-fold projects using and creating CAD tools. General structure: the study of the enabling technologies Education Requirement: Quantitave and ELEN E6718y Algebraic coding theory (VLSI circuits, communication protocols, embed- Deductive Reasoning (QUA). Lect: 2. 3 pts. Instructor to be announced. ded processors, RTOSs), models of computation, Prerequisite: IEOR E3658. Elementary concepts and design methods is coupled with the analysis ELEN E6880–6889x or y Topics in signal of error control codes. Linear block codes. of modern domain-specific applications, including processing Elements of algebra: Galois fields. Cyclic codes: on-chip micro-networks, multiprocessor systems, Lect: 2. 3 pts. Instructor to be announced. BCH, Reed Solomon, Goppa codes. Coder, decoder fault-tolerant architectures, and robust deploy- Prerequisite: ELEN E4810. Advanced topics in implementation. Decoding algorithms based on ment of embedded software. Common research signal processing, such as multidimensional sig- spectral techniques. Convolutional codes. challenges include design complexity, reliability, nal processing, image feature extraction, scalability, safety, and security. The course image/video editing and indexing, advanced digi- ELEN E6761x Computer communications requires substantial reading, class participation, tal filter design, multirate signal processing, adap- networks, I and a research project. tive signal processing, and waveform coding of Lect: 3. 3 pts. Professor Maxemchuk. signals. Topics vary from year to year, and differ- Prerequisites: IEOR E3658 and CSEE W4119, ELEN E6850x Visual information systems ent topics rotate through the course numbers or the equivalent, or the instructor’s permission. Lect: 2. 3 pts. Professor Chang. 6880-6889. Focus on architecture protocols and performance Prerequisite: ELEN E4830 or the instructor’s per- evaluation of geographically distributed and local mission. Introduction to critical image technologies ELEN E6900–6909x or y Topics in electrical area data networks. Emphasis on layered proto- in advanced visual information systems, such as and computer engineering cols. Data link layer. Network layer: flow and con- content-based image databases, video servers, Lect: 2. 3 pts. Instructor to be announced. gestion control routing. Transport layer. Typical and desktop video editors. Intended for graduate Prerequisite: the instructor’s permission. Selected Local and Metropolitan Area Network standards: students. Topics include visual data representation topics in electrical and computer engineering. Ethernet, DQDB, FDDI. Introduction to internetting. and compression, content-based visual indexing Content varies from year to year, and different Review of relevant aspects of queueing theory to and retrieval, storage system design (data place- topics rotate through the course numbers 6900- provide the necessary analytical background. ment, scheduling, and admission control), com- 6909. pressed video editing, and synchronization issues ELEN E6770-6779x or y Topics in telecommu- of stored video/audio signals. Programming proj- ELEN E6945x or y Device nanofabrication nication networks ects and final presentations are required. Lect: 3. 3 pts. Professor Wind. Lect: 2. 3 pts. Instructor to be announced. Prerequisites: ELEN E3106 and E3401, or the Further study of areas such as communication ELEN E6860y Advanced digital signal equivalents. Recommended: ELEN E4944. This protocols and architectures, flow and congestion processing course provides an understanding of the methods control in data networks, performance evaluation Lect: 2. 3pts. Instructor to be announced. used for structuring matter on the nanometer

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148 length: thin-film technology; lithographic pattern- A candidate for the Eng.Sc.D. degree in electrical quantum interference device (SQUID). Design ing and technologies including photon, electron, engineering must register for 12 points of doctoral and operation of superconducting DC magnet, ion and atom, scanning probe, soft lithography, research instruction. Registration in ELEN E9800 RF receiver, Josephson junction, and integrated and nanoimprinting; pattern transfer; self-assem- may not be used to satisfy the minimum residence SQUID. Principles of biomedical sensoring sys- bly; process integration; and applications. requirement for the degree. tems, including Magnetic Resonance Imaging (MRI), SQUID magnetometer, and NMR spec- ELEN E6950x Wireless and mobile networking, I ELEN E9900x and y, and s Doctoral dissertation troscopy. Medical image formation and processing. Lect: 2. Lab: 1. 4.5 pts. Instructor to be announced. 0 pts. Instructor to be announced. Corequisite: ELEN E6761 or the instructor’s A candidate for the doctorate may be required ELEN E4332y VLSI design laboratory permission. Overview of mobile and wireless to register for this course every term after the Lab: 3. 3 pts. networking. Fundamental concepts in mobile student’s course work has been completed, and Prerequisite: ELEN E4321 or E6316 or EECS wireless systems: propagation and fading, cellular until the dissertation has been accepted. E4340. Design of a large-scale deep submicron systems, channel assignment, power control, CMOS integrated circuit. The class may divide up handoff. Examples of second-generation circuits- Courses in Electrical Engineering into teams to work on different aspects of a single switched systems and standards. Quantitative mixed-signal circuit. The chip(s) is fabricated for Offered Occasionally homework assignments may require use of a testing the following term. Lectures cover use of mathematical software package. computer-aided design tools, design issues spe- ELEN E3000x Introduction to circuits, cific to the project(s), and chip integration issues. ELEN E6951y Wireless and mobile networking, II systems, and electronics Lect: 2. Lab: 1. 3 pts. Instructor to be announced. Lect: 3. Recit: 1. 3.5 pts. ELEN E4405x Classical nonlinear optics Prerequisite: CSEE W4119, ELEN E6761, or the Introductory course in electrical circuits, systems, Lect: 3. 3 pts. instructor’s permission. Third-generation packet electronics, and digital information processing for Prerequisite: ELEN E4401. Waves in anisotropic switched systems, wireless LANs, mobile comput- non-electrical engineers. media. Maxwell’s equations and constitutive rela- ing and communications. Study of some current tions. Fresnel equations. Optical waves in anisotropic research topics. Quantitative homework assign- EEHS E3900y History of telecommunications: crystals. Birefringence. Waves in nonlinear media. ments may require use of a mathematical soft- from the telegraph to the Internet Plasma model. Electro-optic, Pockels, and Kerr ware package. A project based on readings from Lect. 3. 3 pts. effects. Second harmonic generation and phase the literature will be required. Lab required. Historical development of telecommunications matching. Parametric amplification. Backward- from the telegraphy of the mid-1800s to the wave oscillator. Acousto-optic beam deflection ELEN E6999 Curricular practical training Internet at present. Included are the technologies and light modulation. 1 to 3 pts. of telphony, radio, and computer communications. May be repeated for up to 3 points of total credit. The coverage includes both the technologies ELEN E4420x Topics in electromagnetics Prerequisites: Obtained internship and approval themselves and the historical events that shaped, Lect: 3. 3 pts. from a faculty adviser. Only for electrical engi- and in turn were shaped by, the technologies. The Prerequisite: Knowledge of undergraduate elec- neering and computer engineering graduate stu- historical development, both the general context tromagnetic theory. Selected topics in the theory dents who include relevant off-campus work and the particular events concerning communica- and practice of electromagnetics, varying from experience as part of their approved program of tions, is presented chronologically. The social year to year. Topic for current term will be avail- study. Final report required. May not be taken for needs that elicited new technologies and the able in the department office one month before pass/fail credit or audited. consequences of their adoption are examined. registration. This course may be taken more than Throughout the course, relevant scientific and once when topics are different. Possible topics: engineering principles are explained as needed. EEME E8601x Advanced topics in control theory microwave theory and design (generalized wave- These include, among others, the concept and Lect: 3. 3 pts. Professor Longman. guides, excitation and coupling of waveguides, effective use of spectrum, multiplexing to improve See EEME E6601x (page 186). junctions, microwave networks, periodic struc- capacity, digital coding, and networking principles. tures, optical fibers); antennas (filamentary anten- There are no prerequisites, and no prior scientific ELEN E9001x and y, and s; E9002x and y, nas, arrays, aperture radiation, system properties, or engineering knowledge is required. SEAS stu- and s Research pattern synthesis); electrodynamics (special rela- dents may not count this course as a technical 0 to 6 pts. Instructor to be announced. Points of tivity, radiation by charged particles, relativistic elective. The course shares lectures with EEHS credit to be approved by the department. beams, free electron lasers). E4900, but the work requirements differ somewhat. Prerequisite: Submission of an outline of the pro- posed research for approval by the faculty member ELEN E4720y Networking laboratory ELEN E4215y Analog filter synthesis and design who is to supervise the work of the student. The Lab: 3. 3 pts. Lect: 3. 3 pts. research facilities of the department are available Prerequisites: Knowledge of computer program- Prerequisite: ELEN E3201 and E3801, or the to qualified students interested in advanced study. ming plus CSEE W4119 or the equivalent. Covers equivalent. Approximation techniques for magni- practical experience in network programming and tude, phase, and delay specifications, transfer ELEN E9011x and y, and s; E9012x and y, systems. Weekly laboratory sessions on network function realization, sensitivity, passive LC filters, and s Doctoral research programming and systems leading to a term proj- active RC filters, MOSFET-C filters, Gm-C filters, 0 to 6 pts. Instructor to be announced. Points of ect on design, implementation, debugging, and switched-capacitor filters, automatic tuning tech- credit to be approved by the department. integration of network protocols on IP routers. niques for integrated filters. Filter noise. A design Open only to doctoral students who have passed Emphasis on practical experience with (1) net- project is an integral part of the course. the qualifying examinations. Prerequisite: submis- working equipment, including Intel IXP network sion of an outline of the proposed research for processor-based routers, PC-based routers, and ELEN E4302x or y Magnetic sensors and the approval of the faculty member who is to commercial routers; and (2) the ns-2 simulator. instruments for medical imaging supervise the work of the student. Laboratory topics include socket programming, Lect: 2. 5, Lab: 0.5. 3 pts. setting up a commercial router/PC-routers and Prerequisite: ELEN E3106, ELEN E3401, or the ELEN E9800x and y, and s Doctoral research wireless networks, setting routing tables, pro- instructor’s permission. Physics of nuclear mag- instruction gramming network processors, deploying network netic resonance (NMR) and superconducting 3, 6, 9, or 12 pts. Instructor to be announced. algorithms, and debugging UDP and TCP protocols.

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ELEN E4741x Introduction to biological and compound technologies, electronic properties faces in very large-scale integrated circuits. 149 sensory systems of GaAs, growth techniques (bulk and epitaxial), Precision sampling; A/D and D/A converter archi- Lect: 3. 3 pts. surface and etching properties, implantation, tectures; switched capacitor circuits; system con- Corequisite: IEOR E3658. Introduction to vision MESFETS, transferred electron devices, Impatt siderations. and hearing using engineering principles. Nature diodes, HEMTS, HBTs. of sound and light; minimum detectable energy ELEN E6403y Classical electromagnetic theory for human observers; excitation of the visual and ELEN E6151y Surface physics and analysis Lect: 3. 4.5 pts. hearing systems; rods, cones, and hair-cell recep- of electronic materials Prerequisite: One term of undergraduate electro- tors; the experiment of Hecht, Shlaer, and Pirenne; Lect: 2. 3 pts. magnetic theory. A mathematical physics Poisson counting statistics; stimulus-based mod- Prerequisite: The instructor’s permission. Basic approach to electromagnetic phenomena. eling; detection and false-alarm probabilities; de physical principles of methods of surface analy- Poisson, Laplace equations; Green’s functions. Vries-Rose square-root law; Weber’s law; relation sis, surfaces of electronic materials including Theorems of electrostatics. Multipole expansions. of sensory and communication systems. structure and optical properties (auger electron Energy relations and stress tensor. Maxwell’s spectroscopy, x-ray photoemission, ultraviolet equations in stationary and moving media. The CSEE W4825y Digital systems design photoelectron spectroscopy, electron energy loss wave equation, energy and momentum theorems, Lect: 3. 3 pts. spectroscopy, inverse photoemission, photo stim- potentials, choice of gauge. Prerequisite: CSEE W3827. Dynamic logic, field ulated desorption, and low energy electron dif- programmable gate arrays, logic design languages, fraction), physical principles of each approach. ELEN E6414y Photonic integrated circuits multipliers. Special techniques for multilevel NAND Lect: 3. 3 pts. and NOR gate circuits. Clocking schemes for one- ELEN E6211x or y Circuit theory Photonic integrated circuits are important subsys- and two-phrase systems. Fault checking: scan Lect: 3. 3 pts. tem components for telecommunications, optically method, built-in test. Survey of logic simulation Prerequisites: ELEN E3331 and E3801. An controlled radar, optical signal processing, and methods. Other topics to be added as appropriate. axiomatic development of circuit theory. Circuit photonic local area networks. This course will theorems, circuit topology, general methods of introduce the student to the devices and the design EEHS E4900y History of telecommunications: circuit analysis. Normal form characterizations. of these circuits. Principle and modeling of dielec- from the telegraph to the Internet Scattering characterization and sensitivity func- tic waveguides (including silica on silicon- and InP- Lect: 3. 3 pts. tion. Basic network synthesis methods: immit- based materials), waveguide devices (simple and Historical development of telecommunications tance and transfer function realization, multiport star couplers), and surface diffractive elements. from the telegraphy of the mid-1800s to the realization, approximation techniques. Numerical techniques for modelling circuits will be Internet at present. Included are the technologies discussed, including beam propagation and finite of telephony, radio, and computer communications. ELEN E6261y Computational methods of difference codes. Design of other devices will be The coverage includes both the technologies circuit analysis discussed: optical isolators, demultiplexers. themselves and the historical events that shaped, Lect: 3. 3 pts. and in turn were shaped by, the technologies. The Prerequisites: ELEN E3331 and APMA E3101. EEME E6610x Optimal control theory historical development, both the general context Computational algorithms for DC, transient, and Lect: 3. 3 pts. and the particular events concerning communica- frequency analysis of linear and nonlinear circuits. Prerequisite: ELEN E6201 or EEME E6601. tions, is presented chronologically. The social Formulation of equations: state equations, hybrid Objectives of optimal control. Continuous and needs that elicited new technologies and the equations, sparse tableaux. Solution techniques: discrete control problems. Calculus of variations: consequences of their adoption are examined. iterative methods to solve nonlinear algebraic Mayer and Bolza; Pontryagin’s maximum principle. Throughout the course, relevant scientific and equations; piecewise linear methods; sparse Bang-bang and singular controls. Existence of engineering principles are explained as needed. matrix techniques; numerical integration of stiff, optimal control. Hamilton-Jacobi theory and These include, among others, the concept and nonlinear differential equations, companion net- dynamic programming. Numerical methods. effective use of spectrum, multiplexing to improve work models; waveform relaxation. Optimal feedback control regulatory problems. capacity, digital coding, and networking principles. Linear-quadratic-Gaussian estimation. Applications. There are no prerequisites, and no prior scientific ELEN E6302x or y MOS transistors or engineering knowledge is required. SEAS stu- Lect: 2. 3 pts. EEME E6612x or y Control of nonlinear dents may not include this as a technical elective. Prerequisite: ELEN E3106 or the equivalent. dynamic systems This course shares lectures with EEHS E3900, Operation and modelling of MOS transistors. Lect: 3. 3 pts. but the work requirements differ somewhat. MOS two- and three-terminal structures. The Prerequisites: EEME E6601 or ELEN E6201 and MOS transistor as a four-terminal device; general an undergraduate controls course. Fundamental ELEN E4944x Principles of device charge-sheet modelling; strong, moderate, and properties of nonlinear systems; qualitative analy- microfabrication weak inversion models; short-and-narrow-channel sis of nonlinear systems; nonlinear controllability Lect: 3. 3 pts. effects; ion-implanted devices; scaling considera- and observability; nonlinear stability; zero dynam- Science and technology of conventional and tions in VLSI; charge modelling; large-signal tran- ics and inverse systems; feedback stabilization advanced microfabrication techniques for elec- sient and small-signal modeling for quasistatic and linearization; sliding control theory; nonlinear tronics, integrated and discrete components. and nonquasistatic operation. observers; describing functions. Topics include diffusion; ion implantation, thin-film growth including oxides and metals, molecular ELEN E6304x or y Topics in electronic circuits ELEN E6713y Topics in communications beam and liquid-phase epitaxy; optical and Lect: 3. 3 pts. Lect: 3. 3 pts. advanced lithography; and plasma and wet etching. Prerequisite: The instructor’s permission. State- Prerequisite: ELEN E6712 or E4702 or E4703, of-the-art techniques in integrated circuits. Topics or the equivalent, or the instructor’s permission. ELEN E6140x Gallium arsenide materials may change from year to year. Advanced topics in communications, such as turbo processing codes, LDPC codes, multiuser communications, Lect: 3. 3 pts. ELEN E6316x or y Analog systems in VLSI network coding, cross-layer optimization, cognitive Prerequisite: ELEN E4301 or the instructor’s per- Lect: 3. 3 pts. radio. Content may vary from year to year to reflect mission. Materials and device aspects of GaAs Prerequisite: ELEN E6312. Analog-digital inter the latest development in the field.

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150 ELEN E6731y Satellite communication systems CSEE E6832x Topics in logic design theory ELEN E9301y Seminar in electronic devices Lect: 2. 3 pts. Lect: 3. 3 pts. Sem: 2. 3 pts. Prerequisite: ELEN E4702. Introduction to Prerequisite: CSEE W3827 or any introduction to Open to doctoral candidates, and to qualified satellite communication, with emphasis on char- logic circuits. A list of topics for each offering of M.S. candidates with the instructor’s permission. acterization and systems engineering of the t the course is available in the department office Theoretical and experimental studies of semicon- ransmission channel. Power budgets, antennas, one month before registration. May be taken ductor physics, devices, and technology. transponders, multiple access, and frequency more than once if topics are different. Iterative reuse techniques. Noise, intermodulation, interfer- logic circuits applied to pattern recognition. Finite ELEN E9303x or y Seminar in electronic ence, and propagation effects. Modulation methods, state machines; alternative representations, infor- circuits earth terminals, and standards. Digital transmis- mation loss, linear circuits, structure theory. Sem: 2. 3 pts. sion and advanced systems. Reliability and testability of digital systems. Open to doctoral candidates, and to qualified M.S. candidates with the instructor’s permission. ELEN E6762y Computer communications ELEN E6920x or y Topics in VLSI systems design Study of recent developments in electronic circuits. networks, II Lect: 2. 3 pts. Lect: 2. 3 pts. Prerequisite: ELEN E4321. Design automation: lay- ELEN E9402x and y Seminar in quantum Prerequisite: ELEN E6761. Broadband ISDN— out, placement, and routing. Circuit simulation algo- electronics Services and protocols; ATM. Traffic characteriza- rithms and optimization of performance and area. Sem: 2. 3 pts. tion and modeling: Markov-modulated Poisson Multiprocessor computing systems. Verification of Open to doctoral candidates, and to qualified and Fluid Flow processes; application to voice, testing. Topics may change from year to year. M.S. candidates with the instructor’s permission. video, and images. Traffic management in ATM Recent experimental and theoretical develop- networks: admission and access control, flow ELEN E8701y Point processes in information ments in various areas of quantum electronics control. ATM switch architectures; input/output and dynamical systems research. Examples of topics that may be treated queueing. Quality of service (QoS) concepts. Lect: 3. 3 pts. include novel nonlinear optics, lasers, transient Prerequisite: ELEN E6711 or the equivalent. phenomena, and detectors. ELEN E6763y Digital circuit switched networks Recommended preparation: a course in measure Lect: 2. 3 pts. theory or advanced probability theory. Probability ELEN E9403x Seminar in photonics Prerequisite: ELEN E6761 or the instructor’s per- and point processes. Random intensity rate, mar- Sem: 2. 3 pts. mission. Current topics in digital circuit switching: tingales, and the integral representation of point Prerequisite: ELEN E4411. Open to doctoral can- introduction to circuit switching, comparison with process martingales. Recursive estimation, the didates, and to qualified M.S. candidates with the packet switching, elements of telephone traffic engi- theory of innovations, state estimate for queues. instructor’s permission. Recent experimental and neering, space and time switching, call processing Markovian queueing networks. Hypothesis testing, theoretical developments in various areas of pho- in digital circuit-switched systems, overload control the separation between filtering and detection. tonics research. Examples of topics that may be mechanisms, nonhierarchical routing, common Mutual information and capacity for the Poisson- treated include squeezed-light generation, quan- channel signaling, introduction to integrated servic- type channel. Stochastic control, dynamic pro- tum optics, photon detection, nonlinear optical es digital networks. Examples of current systems gramming for intensity control. effects, and ultrafast optics. are introduced throughout. Emphasis on modeling and quantitative performance analysis. Queueing ELEN E9060x or y Seminar in systems biology ELEN E9404x or y Seminar in light wave models introduced where possible. Lect: 2. 3 pts. communications Open to doctoral candidates, and to qualified M.S. Sem: 2. 3 pts. ELEN W6781y Topics in modeling and analy- candidates with the instructor’s permission. Study of Open to doctoral candidates, and to qualified sis of random phenomena recent developments in the field of systems biology. M.S. candidates with the instructor’s approval. Lect: 3. 3 pts. Recent theoretical and experimental develop- Prerequisite: ELEN E6711. Recommended prepa- EEBM E9070x or y Seminar in computational ments in light wave communications research. ration: a course on real analysis and advanced neuroscience and neuroengineering Examples of topics that may be treated include probability theory. Current methodology in Lect: 2. 3 pts. information capacity of light wave channels, research in stochastic processes applied to com- Open to doctoral candidates and qualified M.S. photonic switching, novel light wave network munication, control, and signal processing. Topics candidates with the instructor’s permission. Study of architectures, and optical neural networks. vary from year to year to reflect student interest recent developments in computational neuroscience and current developments in the field. and neuroengineering. ELEN E9701x Seminar in information and communication theories CSEE E6831y Sequential logic circuits ELEN E9101y Seminar in physical electronics Sem: 2. 3 pts. Lect: 3. 3 pts. Sem: 2. 3 pts. Open to doctoral candidates, and to qualified Prerequisite: CSEE W3827 or any introduction to Prerequisite: Quantum electronics and ELEN M.S. candidates with the instructor’s permission. logic circuits. Generation and manipulation of flow E4944, or the instructor’s permission. Advanced top- Recent developments in telecommunication net- table descriptions to asynchronous sequential ics in classical and quantum phenomena that are works, information and communication theories, functions. Coding of flow tables to satisfy various based on ion and electron beams, gas discharges, and related topics. design criteria. Delays, races, hazards, metasta- and related excitation sources. Application to new bility. Analysis of latches to determine key param- laser sources and microelectronic fabrication. ELEN E9801x or y Seminar in signal processing eters. Bounds of input rates. Clocking schemes Lect: 2. 3 pts. for synchronous systems. Synthesis of self-timed ELEN E9201x or y Seminar in circuit theory Open to doctoral candidates, and to qualified systems using 4-phase or 2-phase handshakes. Sem: 2. 3 pts. M.S. candidates with the instructor’s approval. Open to doctoral candidates, and to qualified Recent developments in theory and applications M.S. candidates with the instructor’s permission. of signal processing, machine learning, content Study of recent developments in linear, nonlinear, analysis, and related topics. and distributed circuit theory and analysis tech- niques important to the design of very large-scale integrated circuits.

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INDUSTRIAL ENGINEERING AND OPERATIONS RESEARCH 151 313 S. W. Mudd, MC 4704, 212-854-2941 www.ieor.columbia.edu

CHAIR DIRECTOR: M.S. PROGRAMS Emanuel Derman ASSOCIATE PROFESSORS ADJUNCT FACULTY Clifford Stein IN ENGINEERING Awi Federgruen Maria Chudnovsky Khasha Dehnad 326 S. W. Mudd MANAGEMENT SYSTEMS, Business School Rama Cont David DeRosa INDUSTRIAL ENGINEERING, Guillermo Gallego Garud Iyengar Alexander Eydeland DIRECTOR: ADMINISTRATION, AND OPERATIONS Paul Glasserman Soulaymane Kachani Leon S. Gold ACADEMIC AND RESEARCH Business School Jay Sethuraman Ali Hirsa PROFESSIONAL Soulaymane Kachani Donald Goldfarb Iraj Kani DEVELOPMENT Iannis Karatzas ASSISTANT PROFESSORS Alexander Kuznetsov Jenny S. Mak DIRECTOR: MASTER OF Mathematics Jose Blanchet William J. Latzko 324 S. W. Mudd SCIENCE IN FINANCIAL Peter J. Kolesar Mariana Olvera-Cravioto Michael D. Lipkin ENGINEERING Business School Xuedong He Hanan Luss STUDENT AFFAIRS Emanuel Derman S. G. Steven Kou Allan Malz MANAGER Karl Sigman LECTURER IN DISCIPLINE Leon M. Metzger Adina Berrios Brooks DIRECTOR: DOCTORAL Clifford Stein Martin Haugh Peter V. Norden PROGRAMS M. Suresh Sundaresan Lucius J. Riccio DIRECTOR: Daniel Bienstock Business School David Robbins UNDERGRADUATE Garrett van Ryzin Alexander Stanton PROGRAMS PROFESSORS Business School Leon Tatevossian Garud Iyengar Daniel Bienstock Ward Whitt Leo Tilman Mark Broadie Vlihalis Yannakakis Andrew Webster Business School Computer Science Sheldon Weinig Edward M. Coffman Jr. David D. Yao Larry Wright Electrical Engineering

ndustrial engineering is the branch of such systems to attain specified goals. prediction of the consequences of alter- the engineering profession that is Industrial engineering includes activities nate modes of operating the system. I concerned with the design, analysis, such as production planning and control; The analysis may involve mathematical and control of production and service quality control; inventory, equipment, optimization techniques, probabilistic systems. Originally, an industrial engi- warehouse, and materials management; and statistical methods, experiments, neer worked in a manufacturing plant plant layout; and workstation design. and computer simulations. and was involved only with the operat- Operations research is concerned Engineering management systems ing efficiency of workers and machines. with quantitative decision problems, is a multidisciplinary field in industrial Today, industrial engineers are more generally involving the allocation and engineering, operations research, con- broadly concerned with productivity and control of limited resources. Such prob- temporary technology, business, eco- all of the technical problems of produc- lems arise, for example, in the opera- nomics, and management. It provides tion management and control. They may tions of industrial firms, financial institu- a foundation for decision making and be found in every kind of organization: tions, health care organizations, trans- managing risks in complex systems. manufacturing, distribution, transporta- portation systems, and government. Financial engineering is a multidisci- tion, mercantile, and service. Their The operations research analyst devel- plinary field integrating financial theory responsibilities range from the design ops and uses mathematical and statisti- with economics, methods of engineer- of unit operations to that of controlling cal models to help solve these decision ing, tools of mathematics, and practice complete production and service sys- problems. Like engineers, they are prob- of programming. The field provides tems. Their jobs involve the integration lem formulators and solvers. Their work training in the application of engineering of the physical, financial, economic, requires the formation of a mathematical methodologies and quantitative methods computer, and human components of model of a system and the analysis and to finance.

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152 Current Research Activities University is an interdisciplinary group of 3. to familiarize students with the histori- In industrial engineering, research is researchers from a variety of depart- cal development of industrial engi- conducted in the area of logistics, rout- ments on the Columbia campus. Its per- neering tools and techniques and ing, scheduling, production and supply manent members are Professors Daniel with the contemporary state of the chain management, inventory control, Bienstock, Don Goldfarb, Garud Iyengar, art, and to instill the need for lifelong revenue management, and quality control. Jay Sethuraman, and Cliff Stein, from learning within their profession; and In operations research, new develop- the Indstrial Engineering and Operations 4. to instill in our students an under- ments are being explored in mathematical Research Department, and Professor standing of ethical issues and profes- programming, combinatorial optimization, David Bayer, from the Department of sional and managerial responsibilities. stochastic modeling, computational and Mathematics at Barnard College. mathematical finance, queueing theory, Researchers at CORC specialize in the B.S. in Operations Research reliability, simulation, and both determin- design and implementation of state-of- The operations research program is one istic and stochastic network flows. the-art algorithms for the solution of of several applied science programs In engineering and management sys- large-scale optimization problems aris- offered at the School. At the undergrad- tems, research is conducted in the ing from a wide variety of industrial and uate level, it offers basic courses in areas of logistics, supply chain optimiza- commercial applications. probability, statistics, applied mathemat- tion, and revenue and risk management. ics, simulation, and optimization as well In financial engineering, research is UNDERGRADUATE PROGRAMS as more professionally oriented opera- being carried out in portfolio manage- tions research courses. The curriculum ment; option pricing, including exotic B.S. in Industrial Engineering is well suited for students with an apti- and real options; computational finance, The undergraduate program is designed tude for mathematics applications. such as Monte Carlo simulation and to develop the technical skills and intel- It prepares graduates for professional numerical methods; as well as data lectual discipline needed by our gradu- employment as operations research mining and risk management. ates to become leaders in industrial analysts, e.g., with management con- Projects are sponsored and supported engineering and related professions. The sultant and financial service organiza- by leading private firms and government program is distinctive in its emphasis on tions, as well as for graduate studies in agencies. In addition, our students and quantitative, economic, computer-aided operations research or business. It is faculty are involved in the work of two approaches to production and service flexible enough to be adapted to the research and educational centers: the management problems. It is focused on needs of future medical and law students. Center for Applied Probability (CAP), the providing an experimental and mathe- Center for Financial Engineering (CFE), matical problem-formulating and problem- B.S. in Operations Research: and the Computational and Optimization solving framework for industrial engi- Engineering Management Systems Research Center (CORC). These centers neering work. The curriculum provides a This operations research option is are supported principally by grants from broad foundation in the current ideas, designed to provide students with an the National Science Foundation. models, and methods of industrial engi- understanding of contemporary technol- The Center for Applied Probability neering. It also includes a substantial ogy and management. It is for students (CAP) is a cooperative center involving component in the humanities and social who are interested in a technical-man- the School of Engineering and Applied sciences to help students understand agement background rather than one in Science, several departments in the the societal implications of their work. a traditional engineering field. It consists Graduate School of Arts and Sciences, The industrial engineering program of required courses in industrial engi- and the Graduate School of Business. objectives are: neering and operations research, eco- Its interests are in four applied areas: 1. to provide students with the requisite nomics, business, and computer sci- mathematical and computational finance, analytical and computational skills to ence, intended to provide a foundation stochastic networks, logistics and distri- assess practical situations and aca- for dealing with engineering and man- bution, and population dynamics. demic problems, formulate models of agement systems problems. Elective The Center for Financial Engineering the problems represented or embed- courses are generally intended to pro- (CFE) at Columbia University encourages ded therein, design potential solutions, vide a substantive core in at least one interdisciplinary research on financial and evaluate their impact; technology area and at least one man- engineering and mathematical modeling 2. to prepare students for the workplace agement area. in finance and promoting collaboration by fostering their ability to participate Due to the flexibility of this option, it between Columbia faculty and financial in teams, understand and practice can incorporate the varied educational institutions, through the organization of interpersonal and organizational needs of preprofessional students inter- research seminars, workshops, and the behaviors, and communicate their ested in law, medicine, business, and dissemination of research done by solutions and recommendations finance. In addition, most students are members of the Center. effectively through written, oral, and encouraged to add a minor in economics Computational Optimization electronic presentations; or computer science to their standard Research Center (CORC) at Columbia course schedules.

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B.S. in Operations Research: advanced track will receive recognition level). At least one of the electives must have 153 Financial Engineering on their academic record. W3211 or W3213 as a prerequisite. The operations research concentration OPERATIONS RESEARCH Minors in financial engineering is designed to SIEO W3600 or SIEO W4150: Introduction to provide students with an understanding A number of minors are available for probability and statistics of the application of engineering students wishing to add them to their IEOR E3106 or IEOR E4106: Introduction to methodologies and quantitative methods programs. These minors are described operations research: stochastic models to finance. Financial engineering is a starting on page 186 of this bulletin. IEOR E3608: Introduction to mathematical pro- multidisciplinary field integrating financial IEOR program students may want gramming (or IEOR E4004: Introduction to opera- tions research: deterministic models) theory with economics, methods of to consider minors in economics or one elective with the IEOR designation engineering, tools of mathematics, and computer science. In addition, opera- practice of programming. Students tions research and engineering and Note: It is important to take SIEO W3600, IEOR graduating with this concentration are management systems majors may elect E3608, and IEOR E3106 as early as feasible; they are prerequisites for most other courses in prepared to enter careers in securities, to minor in industrial engineering, and the program. banking, financial management, and industrial engineering majors may elect consulting industries, and fill quantitative to minor in operations research. MATHEMATICS roles in corporate treasury and finance The department does not offer a V1101, V1102, and V1201 (Calculus I, II, and III), departments of general manufacturing minor in engineering management V2010 (Linear algebra) and service firms. systems or financial engineering. COMPUTER SCIENCE Students who are interested in COMS W1004 or W1007: Introduction to computer pursuing the rigorous concentration in Major in Economics— programming financial engineering must demonstrate Operations Research or proficiency in calculus, computer pro- Students in Columbia College and the another approved computer science course that involves substantial work in programming. gramming, linear algebra, ordinary School of General Studies may register differential equations, probability, and for a major in economics and operations statistics. Applications to the concentra- research. This degree provides a student GRADUATE PROGRAMS tion will be accepted during the fall with a foundation in economic theory The Department of Industrial Engineering semester of the sophomore year, and comparable to that provided by the gen- and Operations Research offers courses students will be notified of the depart- eral economics major while at the same and M.S. programs in (1) engineering mental decision by the end of that time introducing the student to the field management systems, (2) financial engi- spring semester. The department is seek- of operations research. The program is neering, (3) industrial engineering, and (4) ing students who demonstrate strength recommended for students with strong operations research. Graduate programs and consistency in all the above-mentioned quantitative skills who are contemplating leading to a Ph.D. or Eng.Sc.D. in indus- areas. Application to this concentration graduate studies in economics, opera- trial engineering or operations research, is available online: www.ieor.columbia. tions research, or business. as well as one leading to the professional edu/pages/undergraduate/financial_eng/ For more information on the major degree of Industrial Engineer, are also bsfe_app.html. in economics and operations research, available. In addition, the department and students should contact the departmen- the Graduate School of Business offer Undergraduate Advanced Track tal advisers: In Economics, Professor combined M.S./M.B.A. degree programs The undergraduate advanced track is Susan Elmes, 1018 International Affairs in industrial engineering, in financial engi- designed for advanced undergraduate Building, 212-854-3680, and in IEOR, neering, and in operations research. students with the desire to pursue fur- Professor Donald Goldfarb, 313 S. W. All degree program applicants are ther higher education after graduation. Mudd, 212-854-8011. required to take the Aptitude Tests of Students with a minimum cumulative the Graduate Record Examination. Required courses GPA of 3.4 and faculty approval have M.S./M.B.A. candidates are also required This program requires a total of 50.5 the opportunity to participate. Students to take the Graduate Management points: 23 points in economics, 11 are invited to apply to the track upon Admissions Test. points in mathematics, 13.5 points in the completion of their sophomore year. A minimum grade point average of industrial engineering and operations Advanced track students are required to 3.0 (B) in an undergraduate engineering research, and 3 points in computer take higher-level IEOR courses, including program is required for admission to the science. the following: M.S. and professional degree programs. IEOR E4004 instead of IEOR E3608 ECONOMICS Students are expected, on entry, to have IEOR E4106 instead of IEOR E3106 ECON W1105: Principles of economics completed courses in ordinary differential IEOR E4403 instead of IEOR E4003 ECON W3211: Intermediate microeconomics equations, in linear algebra, and in a pro- and MATH V2500 ECON W3213: Intermediate macroeconomics gramming language such as C or Java. ECON W3412: Introduction to econometrics Students successfully completing one seminar the requirements of the undergraduate two electives (one must be above the 2000

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154 M.S. in Engineering Management Systems M.S. in Engineering Management Systems (30 points)1 The Master of Science program in engi- neering management systems (EMS) pro- Required Core Courses Management Electives Engineering/Technical Electives (9 points) (minimum 6 points)2 (minimum 6 points)2 vides students with a 30-point (33 points if no background in probability and statis- The department recommends Choose from: Choose from: tics) that emphasizes both technology and that students complete these management perspectives in solving core courses during their first ECIE W4280 Corporate finance IEOR E4000 Production man- agement problems, making decisions, and manag- term of study: FINC B6302 Capital markets & ing risks in complex systems. Students IEOR E4004 Intro to operations investments IEOR E4210 Supply chain management pursuing this degree program are provid- research: deterministic models FINC B8301 Advanced corpo- ed with a rigorous exposure to determin- IEOR E4106 Intro to operations rate finance IEOR E4220 Demand and istic optimization and stochastic model- supply analytics research: stochastic models IEME E4310 The manufacturing ing, a basic coverage of applications in IEOR E4111 Operations enterprise IEOR E4403 Advanced engi- the areas of operations engineering and neering & corporate economics management, and an in-depth coverage consulting IEOR E4201 Engineering of of applications. (SIEO W4150 Intro to probability management IEOR E4404 Simulation Graduates from this program are and statistics must be taken if IEOR E4202 Engineering of IEOR E4405 Production sched- expected to assume positions as busi- students have not taken the management II uling equivalent previously) ness analysts in logistics, supply chain, IEOR E4505 Operations IEOR E4407 Game theoretic revenue management, and consulting research in public policy models of operations firms, and as financial analysts in risk- management departments of investment IEOR E4510 Project manage- IEOR E4418 Logistics and ment transportation management banks, hedge funds, and credit-card and insurance firms. IEOR E4550 Entrepreneurial IEOR E4601 Dynamic pricing The department requires that business creation for engineers and revenue optimization MSEMS students achieve grades of B– IEOR E4705 Studies in opera- or higher in each of the fundamental tions research core courses (IEOR E4004 and IEOR IEOR E4998 Managing techno- E4106). Poor performance in these logical innovation & entrepre- courses is indicative of inadequate neurship preparation and is very likely to lead to serious problems in completing the pro- 1 gram. In addition, students must main- All courses listed are 3 points each unless otherwise specified. 2The remaining electives can be selected from IEOR, the School of International and Public Affaors, the tain a cumulative GPA equivalent to a B– Business School, and the Departments of Economics, Mathematics, and Statistics. At least 18 points out of during every term enrolled. Students fail- 30 (or 33, if taking SIEO W4150) must be taken in IEOR. ing to meet these criteria may be asked to withdraw from the program. basis only. Students start with an eight- intended to enable students with week part I summer session (July 6 to engineering undergraduate degrees to M.S. in Financial Engineering August 28, 2009), and continue through enhance their training in special fields, The department offers a full-time M.S. the 2009–2010 academic year. Students including production planning, inventory in financial engineering. This program is may complete the program in May control, scheduling, and industrial eco- intended to provide a unique technical 2010, August 2010, or December 2010. nomics. background for students interested in The Department requires that stu- MSIE degree candidates are required pursuing career opportunities in financial dents achieve grades of B– or higher in to satisfy a core program of graduate analysis and risk management. In addi- each of the three fundamental core courses: tion to the basic requirements for gradu- courses offered in the first summer. Poor SIEO W4150: Introduction to probability and ate study, students are expected, on performance in these courses is indica- statistics entry, to have attained a high level of tive of inadequate preparation and is IEOR E4000: Production management mathematical and computer program- very likely to lead to serious problems in IEOR E4004: Intro to perations research: deterministic models ming skills, particularly in probability, completing the program. As a result, IEOR E4106: Intro to operations research: students failing to meet this criterion will statistics, linear algebra, and the use of stochastic models a programming language such as C or be asked to withdraw from the program. All students must take at least 18 JAVA. Work experience is desirable but points of graduate work in the IEOR not required. For the Class of M.S. in Industrial Engineering Department (denoted by courses with 2009–2010, the MSFE program requires The Master of Science program in the IEOR designation) and at least 30 the completion of 36 points on a full-time industrial engineering (30 points) is points of graduate studies at Columbia.

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In addition to courses within the 155 Engineering School, students can also M.S. in Financial Engineering—May 2010 Completion (36 points)1 take electives from various schools with- in the University, such as the Business Summer Semester Fall Semester Spring Semester 2 2 2 School, the School of International and (7.5 points) (15 points) (13.5 points) Public Affairs, the Graduate School of Required core courses: Required core courses: Choose four from the courses Arts and Sciences, and the Law School. below, plus one other course in IEOR E4701 Stochastic models IEOR E4007 Optimization for 3 MSIE students may choose concen- consultation with faculty adviser: for financial engineering financial engineering trations in the following areas: IEOR E4500 Applications pro- Production and operations management IEOR E4702 Statistical infer- IEOR E4703 Monte Carlo simu- gramming for financial engineering (www.ieor.columbia.edu/pages/graduate/ ence for financial engineering lation (1.5) IEOR E4602 Quantitative risk ms_industrial_eng/pom.html) IEOR E4707 Continuous time management Regulated industries IEOR E4706 Foundations of finance (www.ieor.columbia.edu/pages/graduate/ financial engineering IEOR E4630 Asset allocation IEOR E4709 Data analysis for ms_industrial_eng/ri.html) financial engineering IEOR E4708 Seminar on impor- The MSIE program can be taken on tant papers in financial engi- Elective a part-time basis or completed in one neering year of full-time study. Students planning IEOR E4710 Term structure to complete this program in one year are modeling expected, on entry, to have completed IEOR E4718 Intro to implied courses in ordinary differential equations, volatility smile in linear algebra, and in a programming language such as C or Java. IEOR E4731 Credit risk and The department requires that MSIE credit derivatives students achieve grades of B– or higher DRAN B8835 Security pricing in each of the fundamental core courses models (IEOR E4004 and IEOR E4106). Poor 1Students may conclude the program in May, August, or December 2010. Please visit the departmental performance in these courses is indica- Web site (www.ieor.columbia.edu/pages/graduate/ms_financial_eng/index.html) for more information. tive of inadequate preparation and is 2All courses listed are for 3 credits, unless stated otherwise. very likely to lead to serious problems in 3Other courses include experimental finance, foreign exchange and related derivative instruments, hedge completing the program. In addition, fund management, structured products, etc. Specific offerings may vary each term. students must maintain a cumulative GPA equivalent to a B– during every term enrolled. Students failing to meet in the University, such as the Business Joint M.S. and M.B.A. these criteria may be asked to withdraw School, the School of International and The joint M.S. and M.B.A. degree pro- from the program. Public Affairs, the Graduate School of gram offered by The Fu Foundation Arts and Sciences, and the Law School. School of Engineering and Applied The MSOR program can be taken on Science and the Graduate School of M.S. in Operations Research a part-time basis or completed in one Business trains students interested in The Master of Science program in oper- year of full-time study. Students planning combining business and engineering ations research (30 points) is designed to complete this program in one year are careers. This option is available for stu- to enable students to concentrate their expected, on entry, to have completed dents in the financial engineering, indus- studies in methodological areas such as courses in ordinary differential equations, trial engineering, and operations mathematical programming, stochastic in linear algebra, and in a programming research programs. models, and simulation. The department language such as C or Java. Admission for the combined program offers a variety of domain-specific cours- The Department requires that MSOR requires filling out separate applications es in areas that include logistics, supply students achieve grades of B– or higher from both schools, meeting the require- chain management, revenue manage- in each of the fundamental core courses ments of both schools; admission ment, risk management, and financial (IEOR E4004 and IEOR E4106). Poor requirements are the same as those for engineering. performance in these courses is indica- the regular M.S. programs and for the All students must take at least 18 tive of inadequate preparation and is M.B.A. Students in the program will points of graduate work in the IEOR very likely to lead to serious problems have advisers assigned from both schools. Department (denoted by courses with in completing the program. In addition, For more information, please visit the IEOR designation) and at least 30 students must maintain a cumulative the department or see the departmental points of graduate studies at Columbia. GPA equivalent to a B– during every Web site at www.ieor.columbia.edu. In addition to courses within the term enrolled. Students failing to meet Engineering School, students can also these criteria may be asked to withdraw take electives from various schools with- from the program.

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156 Doctoral Studies The requirements for the Ph.D. in indus- M.S. in Operations Research (30 points) trial engineering and operations research are identical. Both require the student Required Core Courses SIEO W4150 Intro to Probability and Statistics (3) (9 points) to pass two qualifying examinations— IEOR E4004 Intro to OR: Deterministic Models (3) respectively covering stochastic and IEOR E4106 Intro to OR: Stochastic Models (3) deterministic models—as well as submit IEOR E4004 Simulation (3) and defend a dissertation based on the candidate’s original research, conducted Electives The department suggests a number of elective courses depending on areas under the supervision of a faculty member. (18 points) of focus.The areas of focus include optimization, applied probability, and financial and managerial applications of operations research. The dissertation work may be theoretical or computational or both. Doctoral stu- Optimization IEOR E4000 Production and operations management dents are also required to select a con- The department recom- IEOR E4210 Supply chain management centration for their studies and complete mends taking at least IEOR E4405 Production scheduling a certain amount of course work in one three of the following of the following fields: applied probability, elective courses: IEOR E4418 Logistics and transportation management mathematical programming, financial IEOR E4600 Applied integer programming engineering, or supply chain manage- IEOR E4630 Asset allocation ment and logistics. Doctoral candidates must obtain a minimum of 60 points of Applied Probability IEOR E4000 Production and operations management The department recom- formal course credit beyond the bache- IEOR E4210 Supply chain management mends taking at least lor’s degree. A master’s degree from an three of the following IEOR E4220 Demand and supply analytics accredited institution may be accepted elective courses: IEOR E4407 Game theoretic models of operation as equivalent to 30 points. A minimum IEOR E4601 Dynamic pricing and revenue management of 30 points beyond the master’s degree IEOR E4602 Quantitative risk management must be earned while in residence in the IEOR E4700 Intro to financial engineering doctoral program. Detailed information regarding the requirements for the Students interested in Corporate Finance Derivatives Pricing Management doctoral degree may be obtained in financial and managerial Courses Courses Courses the department office or online at applications of opera- www.ieor.columbia.edu. tions research should IEOR E4403 Advanced IEOR E4700 Intro to At least one of: consider taking: engineering & corporate financial engineering IEOR E4510 economics And at least one of: Project management COURSES IN INDUSTRIAL And at least one of: IEOR E4602 IEOR E4550 ENGINEERING AND FINC B6302 Capital Quantitative risk Entrepreneurial OPERATIONS RESEARCH markets & investments management business creation for For up-to-date course offerings, please FINC B8301 Advanced IEOR E4630 engineers visit www.ieor.columbia.edu. corporate finance Asset allocation IEOR E4998 Managing ECIE W4280 Corporate IEOR E4620 technological innovation IEOR E3106x Introduction to operations finance Pricing models IEOR E4505 research: stochastic models OR in public policy Lect: 3. 3 pts. Professor Sigman. IEOR E4705 For undergraduate students only. Prerequisite: SIEO Studies in OR W3600. Some of the main stochastic models used in engineering and operations research applications: discrete-time Markov chains, Poisson processes, birth and death processes and other continuous Markov integrated production-inventory systems. IEOR E3608x Introduction to mathematical chains, renewal reward processes. Applications: Production scheduling. Term project. programming queueing, reliability, inventory, and finance. Lect: 3. Rec: 1. 4 pts. Professor Chudnovsky. SIEO W3600y Introduction to probability and Prerequisite: Linear algebra (MATH V2010 or IEOR E3402y Production-inventory planning statistics APMA E3101) and data structures. Introduction to and control Lect: 3. Rec: 1. 4 pts. Professor Sigman. mathematical programming models and computa- Lect: 3. Rec: 1. 4 pts. The faculty. Prerequisite: Calculus. Fundamentals of probability tional techniques. Linear programming and the Prerequisites or corequisites: SIEO W3600 and and statistics used in engineering and applied science. simplex method, dynamic programming, produc- IEOR E3608. Inventory management and produc- Probability: random variables, useful distributions, tion planning applications. tion planning. Continuous and periodic review expectations, law of large numbers, central limit models: optimal policies and heuristic solutions, theorem. Statistics: point and confidence interval IEOR E3658x Probability deterministic and probabilistic demands. Material estimation, hypothesis tests, linear regression. Lect: 3. 3 pts. The faculty. requirements planning. Aggregate planning of Prerequisite: A working knowledge of calculus. production, inventory, and work force. Multi-echelon Fundamentals of probability theory. Distributions

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of one or more random variables. Moments. tion methods. Applications from financial engi- IEOR E4208y Seminar in human factors design 157 Generating functions. Law of large numbers and neering will be discussed. Lect: 3. 3 pts. Professor Gold. central limit theorem. Prerequisite: IEOR E4207 or the instructor’s per- IEOR E4106x and y Introduction to operations mission. An in-depth exploration of the application IEOR E3900x, y, and s Undergraduate research research: stochastic models potential of human factor principles for the design or project Lect: 3. 3 pts. Professors Yao and White. of products and processes. Applications to indus- 1 to 3 pts. The faculty. For graduate and undergraduate advanced track trial products, tools, layouts, workplaces, and Prerequisite: Approval by a faculty member who students only. Prerequisite: SIEO W3600 or computer displays. Consideration to environmen- agrees to supervise the work. Independent work W4150. Some of the main stochastic models tal factors, training and documentation. Term proj- involving experiments, computer programming, used in engineering and operations research ect. Registration reservation through the IEOR analytical investigation, or engineering design. applications: discrete-time Markov chains, Department. Poisson processes, birth and death processes IEOR E4000x Production management and other continuous Markov chains, renewal IEOR E4210y Supply chain management Lect: 3. 3 pts. The faculty. reward processes. Applications: queueing, relia- Lect: 3. 3 pts. The faculty. Prerequisites or corequisites: SIEO W4105 and bility, inventory, and finance. Prerequisite: IEOR E3402, E4000, or the instruc- IEOR E4004. An introduction to production man- tor’s permission. Major issues in supply chain man- agement for students not having an industrial SIEO W4150x Introduction to probability and agement, including definition of a supply chain; engineering bachelor’s degree. Topics include statistics role of inventory; supply contracts; bullwhip effect deterministic inventory models, aggregate produc- Lect: 3. 3 pts. Professor Gallego. and information sharing; vendor-managed invento- tion planning, material requirements planning, Prerequisite: A working knowledge of calculus. ries and other distribution strategies; third-party forecasting, stochastic inventory models, and sup- Fundamentals of probability theory and statistical logistics providers; managing product variety; infor- ply chain management. Emphasis is on modeling inference used in engineering and applied sci- mation technology and supply chain management; and its implications for managerial decisions. ence. Probabilistic models, random variables, international issues. Emphasis on quantitative useful distributions, expectations, law of large models and analysis. IEOR E4001y Design and management of numbers, central limit theorem. Statistical infer- production and service systems ence: point and confidence interval estimation, CSOR W4231x Analysis of algorithms, I Lect: 3. 3 pts. Professor Riccio. hypothesis tests, linear regression. Lect: 3. 3 pts. Professor Stein. Prerequisite: IEOR E4000 or E3402. Design and Prerequisites: COMS W3137 and W3203. management problems in production and service IEOR E4201x The engineering of management, I Introduction to the design and anlysis of efficient systems: process design and capacity manage- Lect: 3. 3 pts. Professor Norden. algorithms. Topics covered include models of ment, inventory system design and management, Analytical models of the processes of managing computation, efficient sorting and searching, algo- aggregate planning, staff scheduling, and quality and engineering. Application of recent develop- rithms for algebraic problems, graph algorithms, control system design. ments in industrial engineering, operations dynamic programming, probabilistic methods, research, and computing to management problems approximation algorithms, and NP-completeness. IEOR E4003x Industrial economics in establishing policies and objectives, patterns of Lect: 3. 3 pts. Professor Kachani. organization, decision processes, and communi- IEOR E4307x Industrial forecasting Prerequisites or corequisites: SIEO W3600 (or cation and control systems. Lect: 3. 3 pts. Professor Dehnad. W4150) and IEOR E3608 (or E4004). Introduction Prerequisite: SIEO W3600. Analytical techniques to the economic evaluation of industrial projects. IEOR E4202y The engineering of management, II and forecasting methodologies with application to Economic equivalence and criteria. Deterministic Lect: 3. 3 pts. Professor Norden. industrial problems. Evaluation and comparison approaches to economic analysis. Multiple proj- Prerequisite: IEOR E4201 or the instructor’s of techniques as they pertain to industrial applica- ects and constraints. Analysis and choice under permission. Application of quantitative techniques tions. Term project. risk and uncertainty. to problems of organization and management. Integration of optimization, simulation, gaming, IEOR E4308x Industrial budgeting and finan- IEOR E4004x and y Introduction to operations knowledge bases, expert systems, sensitivity cial control research: deterministic models analyses, and measurement into management Lect: 3. 3 pts. Professor Riccio. Lect: 3. 3 pts. Professors Goldfarb and Chudnovsky. information, decision support, and project man- Prerequisite: ECON W2261. Management control Prerequisite: Linear algebra (MATH V2010 or agement and tracking systems. Practical cases via the budgeting and financial processes. Topics APMA E3101). For students who have not studied and term project. include the preparation, evaluation, and imple- linear programming. Some of the main methods mentation of operating and capital budgets and used in IEOR applications involving deterministic IEOR E4207x Human factors: performance review of their performance. Examples from con- models: linear programming, the simplex method, Lect: 3. 3 pts. Professor Gold. temporary practice. nonlinear, integer and dynamic programming. Open only to IEOR students. Sensory and cogni- tive (brain) processing considerations in the IEME E4310x The manufacturing enterprise IEOR E4007x Optimization models and methods design, development, and operations of systems, Lect: 3. 3 pts. Professor Weinig. for financial engineering products, and tools. User or operator limits and The strategies and technologies of global manu- Lect: 3. 3 pts. s: Professor Iyengar. potential in sensing, perceiving decision making, facturing and service enterprises. Connections Prerequisite: Linear algebra (MATH V2010 or movement coordination, memory, and motivation. between the needs of a global enterprise, the APMA E3101). Linear, quadratic, nonlinear, Registration reservation through the IEOR technology and methodology needed for manu- dynamic, and stochastic programming. Some Department. Note: Registration is limited, and facturing and product development, and strategic discrete optimization techniques will also be intro- a reservation is required through the IEOR planning as currently practiced in industry. duced. The theory underlying the various opti- Department office. mization methods is covered. The emphasis is on modeling and the choice of appropriate optimiza-

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158 INDUSTRIAL ENGINEERING: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

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

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

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

ENGLISH C1010 (3) COMPOSITION Z1003 (0) C1010 (3) (three tracks, choose one) Z0006 (0) Z1003 (0) C1010 (3)

HUMA C1001, C0CI C1101, HUMA C1002, C0CI C1102, REQUIRED or Global Core (3–4) or Global Core (3–4) NONTECHNICAL ECON W1105 (4) and W1155 recitation (0) ELECTIVES either semester HUMA W1121 or W1123 (3) either semester

FIRST- AND SECOND- YEAR DEPT. Professional-level course (3) (see pages 12–13) ENGI E2261 (3) SIEO W3600 (4) REQUIREMENTS

COMS W1004 (Java) (3) or 2 COMPUTER COMS W1007 (Java) (3) SCIENCE and COMS W3134 (3) or COMS W3137 (4)2

PHYSICAL EDUCATION C1001 (1) C1002 (1)

GATEWAY LAB E1102 (4) either semester

1The linear algebra requirement may be filled by either MATH V2010 or APMA E3101.

IEOR E4403x Advanced engineering and telecommunications, computer, and production sys- Prerequisites: IEOR E3608 or E4004. Facility location corporate economics tems. Off-campus M.S. students may register for the problems in application areas such as telecommunica- Lect: 3. 3 pts. Professor Kachani. 3-point lecture only. Undergraduate students must tions networks, product distribution systems and emer- Prerequisites: SIEO W3600 (or W4150) and IEOR register for 4 points. Note: Students who have taken gency services. Emphasis on applications, algorithmic E3608 (or E4004). Key measures and analytical IEOR E4703 may not register for this course. approaches, routing, and network design problems. tools to assess the financial performance of a firm and perform the economic evaluation of industrial IEOR E4405y Production scheduling IEOR E4407x Game theoretic models of operations projects. Deterministic mathematical programming Lect: 3. 3 pts. Professor Stein. Lect: 3. 3 pts. Professor Sethuraman. models for capital budgeting. Concepts in utility Prerequisites: SIEO W3600 or W4150 and IEOR Prerequisites: IEOR E4004 (or E3608), E4106 (or theory, game theory, and real options analysis. E3608 or E4004, and a working knowledge of E3106), and familiarity with differential equations and computer programming. Job shop scheduling: a programming language; or the instructor’s permis- IEOR E4404x and y Simulation parallel machines, machines in series; arbitrary sion. A mathematically rigorous study of game theory Lect: 3. Rec. 1. 4 pts. x: Professor Blanchet; job shops. Algorithms, complexity, and worst-case and auctions, and their application to operations man- y: The faculty. analysis. Effects of randomness: machine break- agement. Topics include introductory game theory, Prerequisites: SIEO W3600 or W4150 and knowl- downs, random processing time. Term project. private value auction, revenue equivalence, mecha- edge of Java, C, C++, or FORTRAN. Generation of nism design, optimal auction, multiple-unit auctions, random numbers from given distributions; variance IEOR E4406x Facilities location, routing, and combinatorial auctions, incentives, and supply chain reduction; statistical output analysis; introduction to network design coordination with contracts. No previous knowledge simulation languages; application to financial, Lect: 3. 3 pts. Professor Luss. of game theory is required.

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159 INDUSTRIAL ENGINEERING: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

MATH E1210 (3) IEOR E3402 (4) IEOR E4201 (3) IEOR E4202 (3) Ordinary diff. equations Production planning Eng. of management, I Eng. of management, II

IEOR E3608 (4) IEOR E4404 (4) IEOR E4003 (3) IEOR E4405 (3) Mathematical prog. Simulation Industrial econ. Prod. scheduling REQUIRED 1 COURSES IEOR E3106 (3) IEOR E4207 (3) IEOR E4412 (3) Stochastic models Human factors Quality control & management COMS W4111 (3) Database sys.

TECHNICAL Choose one (3 pts.): Please consult the list on the departmental Web site: www.ieor.columbia.edu ELECTIVES

NONTECH Complete 27-point requirement. See page 11 or www.engineering.columbia.edu for details ELECTIVES

1Taking required courses later than the prescribed semester is not permitted.

IEOR E4412y Quality control and management studies, analyzes successes and failures in third- effective interaction with other individuals and Lect: 3. 3 pts. Professor Latzko. party logistics, postal, truck and rail pickup and organizations. Prerequisite: SIEO W3600 or W4150. Statistical delivery systems. Investigates large-scale inte- methods for quality control and improvement: grated logistics and transportation systems and IEOR E4600y Applied integer programming graphical methods, introduction to experimental studies the underlying principles governing trans- Lect: 3. 3 pts. Professor Bienstock. design and reliability engineering, and the rela- portation planning, investment and operations. Prerequisites: IEOR E3608 and E4004, linear tionships between quality and productivity. Contem- algebra (MATH V2010 or APMA E3101), and a porary methods for product and process design, IEOR E4500y Applications programming for FE working knowledge of computer programming. production, and delivery of products and services. Lect: 2.5. 3 pts. Professor Bienstock. Applications of mathematical programming tech- Prerequisites: Programming in Java, C, or C++ niques, especially integer programming, with IEOR E4416y Capacity planning: models, and the instructor’s approval. In this course we will emphasis on software implementation. Typical algorithms and applications take a hands-on approach to developing computer applications: capacity expansion, network design, Lect: 3. 3 pts. Professor Luss. applications for OR and FE. Beginning with basic and scheduling. Prerequisite: IEOR E3608 or E4004. Capacity programs, we will work our way to full-blown sys- planning problems are of significant importance in tems with graphical interfaces that exercise impor- IEOR E4601y Dynamic pricing and revenue capital-intensive service and manufacturing indus- tant uses of operations research and financial management tries, including telecommunications networks, power engineering. Examples: simulation of stock price Lect: 2.5. 3 pts. Professor Gallego. generation and transport, transportation networks, evolution, tracking and evaluation of a stock portfolio, Prerequisite: SIEO W4150 and IEOR E4004. and heavy process industries. We will explore a simulation of a transportation system, optimization Focus on capacity allocation, dynamic pricing and large variety of capacity planning models with of an inventory system. In the course of developing revenue management. Perishable and/or limited emphasis on timing, sizing, location, and capacity these applications, we will review topics of interest product and pricing implications. Applications to type decisions. The course will emphasize model- to OR/FE in a holistic fashion. various industries, including service, airlines, ing approaches, key issues, and algorithms. hotel, resource rentals, etc. IEOR E4550x Entrepreneurial business IEOR E4418y Logistics and transportation creation for engineers IEOR E4602y Quantitative risk management management Lect: 3. 3 pts. Professor Robbins. Lect: 2.5. 3 pts. Professor Blanchet. Lect: 3. 3 pts. Professor Kachani. Prerequisites: ECON W1105 and ECON W2261. Prerequisite: SIEO W4150 and IEOR E4106. Risk Prerequisite: IEOR E3608 or E4004, or the Introduces the basic concepts and methodologies management models and tools; measure risk instructor’s permission. Introduces quantitative that are used by the nonengineering part of the using statistical and stochastic methods, hedging, techniques and state-of-the-art practice of opera- world in creating, funding, investing in, relating to, and diversification. Examples include insurance tions research relevant to the design and both the and operating entrepreneurial ventures. The first risk, financial risk, and operational risk. Topics tactical and strategic management of logistical half of the course focuses on the underpinning covered include VaR, estimating rare events, and transportation systems. Discusses a wide principles and skills required in recognizing, ana- extreme value analysis, time series estimation of variety of passenger and freight systems, includ- lyzing, evaluating, and nurturing a business idea. extremal events, axioms of risk measures, hedg- ing air, urban and highway traffic, rail, and mar- The second half focuses on basic legal knowl- ing using financial options, credit risk modeling, itime systems. Explores the practice of revenue edge necessary in creating a business entity, and various insurance risk models. management and dynamic pricing. Through case defending your business assets, and promoting

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160 OPERATIONS RESEARCH: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

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

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

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

ENGLISH C1010 (3) COMPOSITION Z1003 (0) C1010 (3) (three tracks, choose one) Z0006 (0) Z1003 (0) C1010 (3)

HUMA C1001, C0CI C1101, HUMA C1002, C0CI C1102, REQUIRED or Global Core (3–4) or Global Core (3–4) NONTECHNICAL ECON W1105 (4) and W1155 recitation (0) either semester ELECTIVES HUMA W1121 or W1123 (3) either semester

FIRST- AND SECOND- YEAR DEPT. Professional-level course (3) (see pages 12–13) ENGI E2261 (3) SIEO W3600 (4) REQUIREMENTS

COMS W1004 (Java) (3) or COMS W1007 (Java) (3)2 COMPUTER and SCIENCE COMS W3134 (3) or COMS W3137 (4)2

PHYSICAL C1001 (1) C1002 (1) EDUCATION

GATEWAY LAB E1102 (4) either semester

1The linear algebra requirement may be filled by either MATH V2010 or APMA E3101.

IEOR E4620x Pricing models for financial IEOR E4630 Asset allocation Markowitz model, market equilibrium, and the engineering Lect: 2.5. 3 pts. Professor Iyengar. capital asset pricing model. General models for Lect: 2.5. 3 pts. Professor Tatevossian. Introduction to modern asset allocation tech- asset price fluctuations in discrete and continuous Prerequisite: IEOR E4700. Models for pricing and niques. The following topics are covered: bond time. Elementary introduction to Brownian motion hedging equity, fixed-income, credit-derivative portfolio selection, mean-variance portfolio selec- and geometric Brownian motion. Option theory; securities, standard tools for hedging and risk tion, active portfolio selection, robust portfolio Black-Scholes equation and call option formula. management, models and theoretical foundations selection, beyond mean-variance: VaR, CVaR Computational methods such as Monte Carlo for pricing equity options (standard European, and approximation, and implementation details: simulation. American equity options, Asian options), standard parameter estimation, Bayesian approaches, Black-Scholes model (with multi-asset extension), transaction and trading costs. IEOR E4701s Stochastic models for financial asset allocation, portfolio optimization, invest- engineering ments over long-time horizons, and pricing of IEOR E4700x and y Introduction to financial Lect: 3. 3 pts. Professor Cont. fixed-income derivatives (Ho-Lee, Black-Derman- engineering Prerequisite: SIEO W4105 or the equivalent. Toy, Heath-Jarrow-Morton interest-rate model). Lect: 3. 3 pts. Professors Yao and Gallego. Review of elements of probability theory, Poisson Note: Students may not take both IEOR E4630 Prerequisite: IEOR E3106 or IEOR E4106, or the processes, exponential distribution, renewal theory. and DRAN B8835. equivalent. Introduction to investment and finan- Wald’s equation. Introduction to discrete-time cial instruments via portfolio theory and derivative Markov chains and applications to queueing theory, securities, using basic operations research/engi- inventory models, branching processes. neering methodology. Portfolio theory, arbitrage;

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161 OPERATIONS RESEARCH: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

MATH E1210 (3) IEOR E3402 (4) IEOR E4307 (3) IEOR E4405 (3) Ordinary diff. equations Production planning Forecasting Prod. scheduling

IEOR E3608 (4) IEOR E4404 (4) IEOR E4003 (3) Mathematical prog. Simulation Industrial econ. REQUIRED COURSES1 IEOR E3106 (3) IEOR E4600 (3) IEOR E4407 (3) Stochastic models Applied integer prog. Game theoretic models of operations IEOR E4409 (3) Industrial info. sys.

TECHNICAL Choose four electives (12 pts. total): ELECTIVES Please consult the list on the departmental Web site: www.ieor.columbia.edu

NONTECH Complete 27-point requirement. See page 11 or www.engineering.columbia.edu for details ELECTIVES

1Taking required courses later than the prescribed semester is not permitted.

IEOR E4702s Statistical inference for financial Prerequisites: SIEO W4150 and linear algebra regression and test of CAPM, nonlinear regression engineering (MATH V2010 or APMA E3101). Corequisites: and fitting of term structures. Lect: 1.5. 1.5 pts. Professor Kou. IEOR E4701 and E4702 or their equivalents. The course covers basic tools of statistical infer- Bond mathematics. Introduction to forwards, futures, IEOR E4710y Term structure models ence relevant to financial engineering. The statis- and other derivative securities. Discrete-time Lect: 2. 3 pts. The faculty. tical topics covered include point estimation, max- models of equity markets and the term structure. Prerequisites: IEOR E4706, E4707, and proficiency imum likelihood estimators, confidence intervals, Pricing and dynamic hedging of derivative securi- in programming. Interest rate models and numerical the delta method, hypothesis testing, and good- ties. Option pricing and Black-Scholes, introduc- techniques for pricing and hedging interest rate ness of fit tests. The financial examples include tion to real options and portfolio optimization. contracts and fixed income securities. selection bias in finance, estimation of drift and volatility in the geometric Brownian motion model, IEOR E4707x Financial engineering: continuous- IEOR E4718y Introduction to the implied the leptokurtic feature, and difficulties in estimat- time asset pricing volatility smile ing the tail distributions of asset returns. Lect: 3. 3 pts. Professor Cont. Lect: 3. 3 pts. Professor Derman. Prerequisite: IEOR E4701. Corequisite: IEOR Prerequisite: IEOR E4706 or some knowledge of IEOR E4703x Monte Carlo simulation E4706. Modeling, analysis, and computation of derivatives valuation models. During the past fifteen Lect: 3. 3 pts. Professor Blanchet. derivative securities. Applications of stochastic years the behavior of market options prices have Prerequisite: IEOR E4701 or the equivalent. calculus and stochastic differential equations. shown systematic deviations from the classic Multivariate random number generation, boot- Numerical techniques: finite-difference, binomial Black-Scholes model. The course will examine the strapping, Monte Carlo simulation, efficiency method, and Monte Carlo. empirical behavior of implied volatilities, in particu- improvement techniques. Simulation output analysis, lar the volatility smile that now characterizes most Markov-chain Monte Carlo. Applications to financial IEOR E4708y Seminar on classical and new markets, and then discuss the mathematics and engineering. Introduction to financial engineering papers in financial engineering intuition behind new models that can account for simulation software and exposure to modeling with Lect: 3. 3 pts. Professor Derman. the smile, and then examine their consequences real financial data. Note: Students who have taken Prerequisites: IEOR E4701 and E4706. for hedging and valuation. IEOR E4404 may not register for this course. Corequisite: IEOR E4703. Selected topics of special interest to financial engineering M.S. IEOR E4720-E4729s and y Topics in quantita- IEOR E4705x Studies in operations research students. If topics are different, then this course tive finance Lect: 3. 3 pts. Professor Riccio. can be taken more than once for credit. Lect: 2–2.5. 1.5–3 pts. The faculty. Prerequisites: IEOR E3608 (or E4004) and E4106 Selected topics of interest in the area of quantita- (or E3106). Analysis and critique of current opera- IEOR E4709y Data analysis for financial tive finance. Offerings vary each year; possible tions research studies. Blood bank inventory, fire engineering topics include asset management, energy deriva- departments, police departments, and housing Lect: 3. 3 pts. The faculty. tives, experimental finance, foreign exchange and operations research studies are considered. Prerequisite: IEOR E4701. Corequisite: IEOR related derivative instruments, inflation deriva- E4706. Empirical analysis of asset prices: heavy tives, hedge fund management, modeling equity IEOR E4706s Foundations in financial tails, test of the predictability of stock returns. derivatives in Java, mortgage-backed securities, engineering Financial time series: ARMA, stochastic volatility, numerical solutions of partial differential equa- Lect: 3. 3 pts. Professors Kou and Tilman. and GARCH models. Regression models: linear tions, quantitative portfolio management, risk

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162 OPERATIONS RESEARCH: ENGINEERING MANAGEMENT SYSTEMS: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

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

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

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

ENGLISH C1010 (3) COMPOSITION Z1003 (0) C1010 (3) (three tracks, choose one) Z0006 (0) Z1003 (0) C1010 (3)

HUMA C1001, C0CI C1101, HUMA C1002, C0CI C1102, REQUIRED or Global Core (3–4) or Global Core (3–4) NONTECHNICAL ECON W1105 (4) and W1155 recitation (0) ELECTIVES either semester HUMA W1121 or W1123 (3) either semester

FIRST- AND SECOND- YEAR DEPT. Professional-level course (3) (see pages 12–13) ENGI E2261 (3) SIEO W3600 (4) REQUIREMENTS

COMS W1004 (Java) (3) or COMS W1007 (Java) (3)2 COMPUTER and SCIENCE COMS W3134 (3) or COMS W3137 (4)2

PHYSICAL C1001 (1) C1002 (1) EDUCATION

GATEWAY LAB E1102 (4) either semester

1The linear algebra requirement may be filled by either MATH V2010 or APMA E3101.

management, trading and technology in financial underlying stochastic price processes. Students IEOR E4731y Credit derivatives markets. will gain exposure to applications of partial differ- Lect: 2.5. 3 pts. The faculty. ential equations to security pricing in different Prerequisites: IEOR E4701 and E4707. IEOR E4724x Topics in quantitative finance: financial markets (i.e., equity derivatives, fixed Introduction to quantitative modeling of credit risk, hedge fund management income securities, and credit derivative markets). with a focus on the pricing of credit derivatives. Lect: ?. 1.5–3 pts. Professor Metzger. Focus on the pricing of single-name credit deriva- The course covers the critical managerial aspects IEOR E4726y Topics in quantitative finance: tives (credit default swaps) and collateralized debt and characteristics of hedge funds and the hedge experimental finance obligations (CDOs). Detail topics include: default fund industry, including legal regulations, strategies, Lect: ?. 3 pts. Professors Stanton and Lipkin. and credit risk, arbitrage pricing, default times, risk management, performance evaluation, etc. The course introduces concepts to propose trading single-name credit derivatives, structured models schema, organize tests via options/stock databas- for single-name credit risk, multi-name default IEOR E4725y or s Topics in quantitative es, and carry out tests efficiently and accurately. barrier models and multi-name reduced form models. finance: numerical solutions of partial It exposes students to the striking differences differential equations between static, thermodynamic/SDE model solu- IEOR E4900x, y, and s Master’s research or Lect: ?. 1.5–3 pts. Professor Kani. tions and real (time-of-flight) pricing. They will project The course covers derivations and solutions of become familiar with computational techniques for 1 to 3 pts. The faculty. partial differential equations under a variety of modeling and testing proposals for trading strategies. Prerequisite: Approval by a faculty member who

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163 OPERATIONS RESEARCH: ENGINEERING MANAGEMENT SYSTEMS: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

IEOR E3608 (4) IEOR E3402 (4) IEOR E4003 (3) IEOR E4001 (3) Mathematical prog. Production planning Industrial econ. Des. & mgmt. of prod. & service sys. MATH E1210 (3) ECON W3213 (3) IEOR E4404 (4) Ordinary diff. equations Macroeconomics Simulation IEOR E4550 REQUIRED 1 Entrepren. bus. creation COURSES IEOR E3106 (3) COMS W4111 (3) for engrs. Stochastic models Database systems or IEOR E4998 ECON W3211 (3) Managing technol. innov. Microeconomics & entrepreneurship

TECH Technical and technology electives (12 pts. total)2

Management electives (9 pts. total): MANAGEMENT Please consult lists posted on IEOR Web site: www.ieor.columbia.edu ELECTIVES NONTECH Complete 27-point requirement; see page 11 or www.engineering.columbia.edu for details

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

agrees to supervise the work. Independent work Makespan, flow time, sum of weighted tardiness- SIEO W6502y Stochastic processes and involving experiments, computer programming, es. Applications of dynamic programming and applications, II analytical investigation, or engineering design. branch and bound. Lect: 2.5. 3 pts. Not given in 2009–2010. Prerequisites: STAT G6104 and SIEO W6501. IEOR E4998x and y Managing technological IEOR E6403y Routing Recommended corequisite: STAT G6105. With innovation and entrepreneurship Lect: 2. 2 or 3 pts. The faculty. the instructor’s permission, the second term may Lect: 3. 3 pts. Professor McGourty. Prerequisite: IEOR E4004, SIEO W4150, or the be taken without the first. Introduction to martin- This course will focus on the management and instructor’s permission. Vehicle routing in distribu- gales in continuous time. Brownian motion: consequences of technology-based innovation. tion systems. Routing problems in VLSI. Effects construction, basic properties, sample paths. The course explores how new industries are cre- of randomness. Students registering for 3 points Stochastic integration, Ito’s rule, applications. ated, how existing industries can be transformed are required to do a term project. Introduction to stochastic differential equations by new technologies, the linkages between tech- and diffusion processes. Applications to financial nological development and the creation of wealth MSIE W6408y Inventory theory economics: option pricing, consumption/ invest- and the management challenges of pursuing Lect: 2. 3 pts. The faculty. ment problems. strategic innovation. Prerequisite: SIEO W4150 and dynamic program- ming. Construction and analysis of mathematical IEOR E6601y Advanced topics in linear IEOR E4999x, y, and s Curricular practical models used in the design and analysis of inven- programming training tory systems. Deterministic and stochastic Lect: 2. 3 pts. The faculty. 1 to 2 pts. Professor Derman. demands and lead times. Optimality of (s, S) Prerequisite: IEOR E6613 or the equivalent. Prerequisite: Instructor’s written approval. Only policies. Multiproduct and multi-echelon systems. Numerical linear algebra for simplex and interior for IEOR graduate students who need relevant Computational methods. point methods: product-form LU, Cholesky and sym- work experience as part of their program of study. metric indefinite factorizations, sparsity considera- Final reports required. This course may not be SIEO W6501x Stochastic processes and tions. Steepest-edge pivot rules, column generation, taken for pass/fail credit or audited. applications, I and decomposition approaches. Analysis of interior Lect: 2.5. 3 pts. The faculty. point methods including path-following, potential IEOR E6400y Scheduling: deterministic models Prerequisite: SIEO W4105 or the equivalent. reduction, and predictor- corrector methods. Lect: 2. 3 pts. Professor Stein. Advanced treatment of discrete and continuous-time Prerequisite: IEOR E4004. Classification of Markov chains; elements of renewal theory; martin- IEOR E6602y Nonlinear programming deterministic scheduling models. Single machine, gales; Brownian motion, stochastic integrals, Ito’s rule. Lect: 2. 3 pts. Professor Goldfarb. parallel machines, flow shops, and job shops. Prerequisite: IEOR E6613 or the equivalent. Convex sets and functions, convex duality and

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164 OPERATIONS RESEARCH: FINANCIAL ENGINEERING: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

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

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

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

ENGLISH C1010 (3) COMPOSITION Z1003 (0) C1010 (3) (three tracks, choose one) Z0006 (0) Z1003 (0) C1010 (3)

HUMA C1001, C0CI C1101, HUMA C1002, C0CI C1102, REQUIRED or Global Core (3–4) or Global Core (3–4) NONTECHNICAL ECON W1105 (4) and W1155 recitation (0) ELECTIVES either semester HUMA W1121 or W1123 (3) either semester

FIRST- AND SECOND- ENGI E2261 (4) YEAR DEPT. Professional-level course (3) (see pages 12–13) and SIEO W3658 (3) or SIEO W4105 (3) REQUIREMENTS and STAT W3659 (3) or STAT W4107 (3)

COMPUTER COMS W1004 (Java) (3) or COMS W1007 (Java) (3) SCIENCE and COMS W3134 (3) or COMS W3137 (3)2

PHYSICAL C1001 (1) C1002 (1) EDUCATION

GATEWAY LAB E1102 (4) either semester

1The linear algebra requirement may be filled by either MATH V2010 or APMA E3101. 2Computer programming should be taken consecutively with data structures.

optimality conditions. Computational methods: IEOR E6606y Advanced topics in network flows of the set of feasible solutions of an IP problem, steepest descent, Newton and quasi-Newton Lect: 3. 3 pts. The faculty. integral polyhedra, totally unimodular matrices, methods for unconstrained problems, active set, Prerequisite: Knowledge of elementary graph totally dual integral systems, Lovasz’s lattice penalty set, interior point, augmented Lagrangian algorithms and computational complexity, equiva- reduction method, and Lenstra’s IP algorithm. and sequential quadratic programming methods lent to IEOR E6605, or COMS W4203 and W4231. Algorithmical topics to center on branch and for constrained problems. Introduction to nondif- Analysis of algorithms and their complexity for a bound algorithms and the ‘‘facet’’ approach to ferentiable optimization and bundle methods. variety of network routing problems. Topics: overall cutting-plane algorithms. minimum cuts, minimum cost network flows, flows IEOR E6603x Combinatorial optimization with losses and gains, parametric flows, dynamic IEOR E6609y Dynamic programming Lect: 2.5. 3 pts. Not given in 2009–2010. flows, multicommodity flows and applications. Lect: 3. 3 pts. Instructor to be announced. Prerequisites: IEOR E6613 and E6614. Algorithms Prerequisite: IEOR E4701 or E4106 or the equiv- for matching problems. Introduction to matroids; IEOR E6608x Integer programming alent. General discrete time deterministic, dynamic polyhedral combinatorics. Complexity theory and NP Lect: 2. 3 pts. The faculty. programming, discrete time-parameter finite branch- completeness. Perfect graphs and the ellipsoid method. Prerequisite: IEOR E6613 or the equivalent. ing, Markov decision chains, team decisions, cer- Theoretical and algorithmical aspects of integer tainty equivalence, continuous time-parameter programming (IP). Theoretical topics: structure Markov branching decision processes. Applications

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165 OPERATIONS RESEARCH: FINANCIAL ENGINEERING: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

IEOR E3608 (4) IEOR E3402 (4) IEOR E4307 (3) IEOR E4500 (3) Mathematical prog. Production planning Forecasting Applications prog. for FE

IEOR E3106 (3) IEOR E4404 (4) IEOR E4407 (3) IEOR E4630 (3) Stochastic models Simulation Game theoretic models Asset allocation of operations REQUIRED IEOR E4003 (3) IEOR E4700 (3) ECON E3412 (3) COURSES Industrial econ. Intro. to FE IEOR E4620 (3) Intro. to econometrics Pricing models for FE ECON W3213 (3) COMS W4111 (3) Macroeconomics Database systems

ECON W3211 (3) Microeconomics

FE TECH Please consult the list on the departmental Web site: www.ieor.columbia.edu

NONTECH Complete 27-point requirement; see page 11 or www.engineering.columbia.edu for details ELECTIVES

include capital budgeting, portfolio selection, inven- Applications from portfolio optimization, truss IEOR E6703x Advanced financial engineering tory control, systems reliability, and maximization design, inventory theory, revenue management, Lect: 2. 3 pts. Professor Kou. of expected utility with constant risk posture. dynamic programming, etc. Prerequisites: IEOR E4106 or E4701, and SIEO W4150. Review of basic mathematics, including IEOR E6610x Approximation algorithms IEOR E6613x Optimization, I renewal theory and stochastic calculus. Lect: 2. 3 pts. Not given in 2009–2010. Lect: 3. 4.5 pts. Professor Goldfarb. Martingale approach to Black-Scholes formula. Prerequisites: Basic knowledge of linear program- Prerequisite: Linear algebra. Theory and geome- Optimal stopping and American options. Pricing ming and analysis of algorithms or combinatorial try of linear programming. The simplex method. of continuous and discerete exotic options. Term optimization. The design and analysis of efficient Duality theory, sensitivity analysis, column gener- structure models and pricing of bond options. algorithms for providing near-optimal solutions to ation and decomposition. Interior point methods. Jump diffusion models. Applications, including NP-hard problems. Classic algorithms and recent Introduction to nonlinear optimization: convexity, pricing of real and electricity options and hedging techniques for approximation algorithms. optimality conditions, steepest descent and of real options. Newton's method, active set and barrier methods. IEOR E6611x Semidefinite and second-order IEOR E6704y Queueing theory and applications cone programming IEOR E6614y Optimization, II Lect: 2. 3 pts. Professor Sigman. Lect: 2. 3 pts. Professor Iyengar. Lect: 3. 4.5 pts. Professor Stein. Prerequisite: IEOR E4106 or E4701. Introduction Duality theory for semidefinite programming Prerequisite: Linear algebra. An introduction to to congestion and related stochastic models. (SDP) and second-order cone programming combinatorial optimization, network flows and Topics include birth and death models, measures (SOCP). Jordan algebras and symmetrical cones. discrete algorithms. Shortest path problems, max- of performance, Little’s Law, conservation law, Formulating engineering problems such as robust imum flow problems. Matching problems, bipartite PASTA, work in system, service disciplines and linear programming, truss design, filter design, and cardinality nonbipartite. Introduction to priorities, regenerative processes, stability and and antenna design as SDPs and SOCPs. SDP discrete algorithms and complexity theory: stationary distributions, approximations and and SOCP approximations for combinatorial opti- NP-completeness and approximation algorithms. bounds. Examples from telecommunications, mization problems. production, inventory, and computer science. IEOR E6702x Reliability theory IEOR E6612 Robust optimization Lect: 2. 3 pts. Not given in 2008–2009. IEOR E6706y Queueing networks Lect: 2. 3 pts. Professor Iyengar. Prerequisites: IEOR E4701 or E4106, and SIEO Lect: 2. 3 pts. Professor Yao. Prerequisites: Linear algebra (APMA E3101 or W4150. An overview of the techniques available Prerequisite: IEOR E4106 or E4701. An the equivalent) and optimization (IEOR E6613 or to formulate the reliability structure of a problem, introduction to the analysis of queuing networks. the equivalent). Robust convex optimization prob- to model the various element probabilities, to esti- Applications to computer and communication sys- lems, reformulating robust problems as nominal mate parameters of element probability distribu- tems. The course covers reversibility, local balance, problems, computational techniques. Adjustably tions based on data, and to unite these steps to open and closed network models, computational robust optimization. Chance constrained prob- obtain the reliability function of a system. procedures, and other related topics. lems and robust chance constrained problems.

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166 IEOR E6707y Advanced topics in queueing IEOR E6712y Stochastic models, II IEOR E9800x and y, and s Doctoral research theory Lect: 3. 4.5 pts. Professor Yao. instruction Lect: 2. 3 pts. Professor Whitt. Prerequisite: IEOR E6711 or the equivalent. 3, 6, 9, or 12 pts. The faculty. Prerequisite: IEOR E6704 or the instructor’s per- Continuation of IEOR E6711, covering further A candidate for the Eng.Sc.D. degree in industrial mission. Queueing models with general arrival topics in stochastic modeling in the context of engineering or operations research must register and service processes, Loyne’s construction, queueing, reliability, manufacturing, insurance for 12 points of doctoral research instruction. Harris recurrence, coupling, stability, steady-state risk, financial engineering, and other engineering Registration in IEOR E9800 may not be used to moments and tail asymptotics, heavy-traffic and applications. Topics from among generalized satisfy the minimum residence requirement for light-traffic approximations. Recent literature and semi-Markov processes; processes with a the Ph.D. degree. open problems are discussed. nondiscrete state space; point processes; stochastic comparisons; martingales; introduction IEOR E9901x and y Operations research IEOR E6708x Discrete event stochastic systems to stochastic calculus. seminar Lect: 2. 3 pts. Not given in 2009–2010. Sem: 2. 1 to 3 pts. The faculty. Prerequisites: IEOR E4004, E4404, and E4106. IEOR E6801x Monte Carlo methods Open to doctoral candidates, and qualified M.S. Modeling, analysis, control, and optimization of Lect: 2. 3 pts. Professor Blanchet. candidates with the instructor’s permission. This discrete event stochastic systems. Generalized Prerequisites: IEOR E4106 or E4701, and SIEO course may be repeated for credit. Selected top- semi-Markov process models; sample path analy- 4150, plus a working knowledge of programming. ics of interest. Topics may vary from year to year. sis; stochastic optimization optimal control. No prior knowledge of simulation is required. Applications to manufacturing and communication Random variate generation, discrete event simula- IEOR E9940x or y Industrial engineering problems. tion, Monte Carlo simulation, simulation output seminar analysis, variance reduction, improving simulation Sem: 2. 1 to 3 pts. The faculty. IEOR E6710y Markovian decision processes efficiency, simulation-based derivative-estimation/ Open to doctoral candidates and qualified M.S. Lect: 2. 3 pts. Instructor to be announced. sensitivity-analysis, and quasi–Monte Carlo tech- candidates with the instructor’s permission. The Prerequisite: IEOR E4106 or E4701. Dynamic niques. Application of these techniques to financial course may be repeated for credit. Selected top- systems observed periodically and partially con- engineering and performance analysis/ optimiza- ics of interest. Topics may vary from year to year. trolled by decisions made at each time of obser- tion of computer networking, telecommunications, vation. Methods of determining optimal decision and production systems. policies. Applications to inventory, inspection, maintenance, and replacement theories. IEOR E8100 Advanced topics in IEOR Lect: 1–3. 1 to 3 pts. Instructor to be announced. IEOR E6711x Stochastic models, I Prerequisite: Faculty adviser’s permission. Lect: 3. 4.5 pts. Professor Whitt. Selected topics of current research interest. Prerequisite: SIEO W4105 or the equivalent. May be taken more than once for credit. Advanced treatment of stochastic modeling in the context of queueing, reliability, manufacturing, IEOR E9101x and y, and s Research insurance risk, financial engineering and other 1 to 6 pts. The faculty. engineering applications. Review of elements of Before registering, the student must submit an probability theory; exponential distribution; renewal outline of the proposed work for approval by the theory; Wald’s equation; Poisson processes. supervisor and the chair of the Department. Introduction to both discrete and continuous-time Advanced study in a specialized field under the Markov chains; introduction to Brownian motion. supervision of a member of the department staff. This course may be repeated for credit.

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MATERIALS SCIENCE AND ENGINEERING PROGRAM 167 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 www.apam.columbia.edu www.seas.columbia.edu/matsci

IN CHARGE OF MATERIALS COMMITTEE ON MATERIALS Praveen Chaudhari Gertrude F. Neumark Ponisseril Somasundaran SCIENCE AND ENGINEERING SCIENCE AND ENGINEERING/ Professor of Materials Science Howe Professor of Materials Professor of Mineral Engineering James S. Im SOLID-STATE SCIENCE AND Paul F. Duby Science and Engineering and Yasutomo Uemura 1106 S. W. Mudd ENGINEERING Professor of Mineral Engineering Professor of Applied Physics and Professor of Physics William E. Bailey Christopher J. Durning Applied Mathematics Wen I. Wang IN CHARGE OF SOLID-STATE Associate Professor of Materials Professor of Chemical Ismail C. Noyan Professor of Electrical SCIENCE AND ENGINEERING Science Engineering Professor of Materials Science Engineering Siu-Wai Chan Simon J. Billinge Irving P. Herman Richard M. Osgood Jr. Chee Wei Wong 1136 S. W. Mudd Professor of Materials Science Professor of Applied Physics Professor of Electrical Associate Professor of Irving P. Herman Louis E. Brus James S. Im Engineering Mechanical Engineering 208 S. W. Mudd Professor of Chemistry Professor of Materials Science Aron Pinczuk Siu-Wai Chan Chris A. Marianetti Professor of Applied Physics and Professor of Materials Science Assistant Professor of Materials Physics Science

aterials science and engineer- Henry Krumb School of Mines (HKSM) niques to reveal details of structure, ing (MSE) focuses on under- with advisory input from the Depart- ranging from the atomic to the macro- M standing, designing, and ments of Chemistry and Physics. scopic scale—details essential to under- producing technology-enabling materials Students interested in materials sci- standing properties such as mechanical by analyzing the relationships among the ence and engineering enroll in the mate- strength, electrical conductivity, and synthesis and processing of materials, rials science and engineering program in technical magnetism. These studies also their properties, and their detailed struc- the Department of Applied Physics and give insight into problems of the deterio- ture. This includes a wide range of Applied Mathematics. Those interested ration of materials in service, enabling materials such as metals, polymers, in the solid-state science and engineering designers to prolong the useful life of ceramics, and semiconductors. Solid- specialty enroll in the doctoral program their products. Materials science and state science and engineering focuses within Applied Physics and Applied engineering also focus on new ways to on understanding and modifying the Mathematics or Electrical Engineering. synthesize and process materials, from properties of solids from the viewpoint The faculty in the interdepartmental bulk samples to ultrathin films to epitaxial of the fundamental physics of the atom- committee constitute but a small fraction heterostructures to nanocrystals. This ic and electronic structure. of those participating in this program, involves techniques such as UHV sputter- Undergraduate and graduate pro- who include Professors Bailey, Billinge, ing; molecular beam epitaxy; plasma grams in materials science and engi- Chan, Herman, Im, Marianetti, Neumark, etching; laser ablation, chemistry, and neering are coordinated through the Noyan, Pinczuk, and Stormer from recrystallization; and other nonequilibri- Materials Science and Engineering Applied Physics and Applied Mathematics; um processes. The widespread use of Program in the Department of Applied Brus, Durning, Flynn, Koberstein, new materials and the new uses of Physics and Applied Mathematics. This O’Shaughnessy, and Turro from Chemical existing materials in electronics, com- program promotes the interdepartmental Engineering; Duby, Somasundaran, munications, and computers have inten- nature of the discipline and involves and Themelis from EAEE; and Heinz, sified the demand for a systematic the Departments of Applied Physics Osgood, and Wang from Electrical approach to the problem of relating and Applied Mathematics, Chemical Engineering. properties to structure and necessitates Engineering and Applied Chemistry, Materials science and engineering a multidisciplinary approach. Electrical Engineering, and Earth and uses optical, electron, and scanning Solid-state science and engineering Environmental Engineering (EAEE) in the probe microscopy and diffraction tech- uses techniques such as transport

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168 measurements, X-ray photoelectron neering and materials science and engi- industrial and government laboratories. spectroscopy, inelastic light scattering, neering. The research facilities in solid- The materials science and engineer- luminescence, and nonlinear optics to state science and engineering are listed in ing undergraduate curriculum requires understand electrical, optical, and mag- the sections for each host department. sixteen courses in the third and fourth netic properties on a quantum mechani- Facilities, and research opportunities, also years, of which four are restricted elec- cal level. Such methods are used to exist within the interdepartmental Materials tives. This program allows students to investigate exciting new types of struc- Research Science and Engineering Center, specialize in a subdiscipline of MSAE if tures, such as two-dimensional electron which focuses on complex films com- they so choose. Students must take gases in semiconductor heterostructures, posed of nanoparticles. twelve required courses and four elec- superconductors, and semiconductor tives. At least two electives must be in surfaces and nanocrystals. UNDERGRADUATE PROGRAM the Type A category, and at most two IN MATERIALS SCIENCE may be in the Type B category. The Type Current Research Activities AND ENGINEERING B electives are listed under different materials subdisciplines for guidance. Current research activities in the materials This program provides the basis for Still, some courses listed under different science and engineering program at developing, improving, and understanding categories may appeal to students inter- Columbia focus on thin films and elec- materials and processes for electronic, ested in a given area. For example, tronic materials that enable significant structural, and other applications. It CHEE E4252: Introduction to surface advances in information technologies. draws from physics, chemistry, and and colloidal chemistry should also be Specific topics under investigation include other disciplines to provide a coherent considered by students interested in bio- interfaces, stresses, and grain boundaries background for immediate application in materials and environmental materials. in thin films; lattice defects and electrical engineering or for subsequent advanced properties of semiconductors; laser pro- study. The emphasis is on fundamentals Type A electives are: cessing and ultrarapid solidification of relating atomic- to microscopic-scale CHEE E4530: Corrosion of metals thin films; nucleation in condensed sys- phenomena to materials properties MSAE E4207: Lattice vibrations and crystal defects tems; optical and electric properties of and processing, including design and MSAE E4250: Ceramics and composites wide-band semiconductors; synthesis of control of industrially important materials ELEN E4944: Principles of device microfabrication nanocrystals, carbon nanotubes, and processes. Core courses and electives nanotechnology-related materials; depo- combine rigor with flexibility and provide Type B electives are: sition, in-situ characterization, electronic opportunities for focusing on such areas BIOMATERIALS testing, and ultrafast spectroscopy of as electronic materials, polymers, ceramics, BMEN E4300: Solid biomechanics magnetoelectronic ultrathin films and biomaterials, structural materials, and BMEN E4301: Structure, mechanics, and heterostructures. In addition, there is metals and mineral processing. There adaptation of bone BMEN E4501: Tissue engineering, I: biological research in surface and colloid chemistry are also opportunities for combining tissue substitutes involving both inorganic and organic materials science and engineering with materials such as surfactants, polymers, interests in areas such as medicine, ELECTRONIC MATERIALS and latexes, with emphasis on materials/ business, law, or government. APPH E3100: Introduction to quantum mechanics environment interactions. The unifying theme of understanding APPH E3300: Applied electromagnetism The research activities in solid-state and interrelating materials synthesis, APPH E4100: Quantum physics of matter science and engineering are described processing, structure, and properties APPH E4110: Modern optics ELEN E4301: Introduction to semiconductor later in this section. forms the basis of our MSAE program devices and is evident in the undergraduate cur- ELEN E4411: Fundamentals of photonics Laboratory Facilities riculum and in faculty research activities. Facilities and research opportunities These activities include work on poly- ENVIRONMENTAL MATERIALS also exist within the interdepartmental crystalline silicon for flat panel displays; EAEE E4001: Industrial ecology of Earth resources Materials Research Science and high-temperature superconductors for EAEE E4160: Solid and hazardous waste Engineering Center (MRSEC), Nanoscale power transmission and sensors; semi- management Science and Engineering Center (NSEC), conductors for laser and solar cell appli- MECHANICAL PROPERTIES OF MATERIALS and Energy Frontier Research Center cations; magnetic heterostructures for ENME E3114: Experimental mechanics of solids (EFRC), which focus on complex films information storage and novel computa- ENME E4113: Advanced mechanics of solids formed from nanoparticles, molecular tion architectures; electronic ceramics for ENME E4114: Mechanics of fracture and fatigue electronics, and solar energy conversion, batteries, gas sensors, and fuel cells; MECE E4608: Manufacturing processes respectively. Modern clean room facilities electrodeposition and corrosion of met- SOFT MATERIALS AND SURFACES with optical and e-beam lithography, thin als; and the analysis and design of high- CHEE C3443: Organic chemistry (note that film deposition, and surface analytical temperature reactors. Through involve- C3444 is not allowed) probes (STM, SPM, XPS) are available. ment with our research groups, students CHEE E4252: Introduction to surface and More specialized equipment exists in indi- gain valuable hands-on experience and colloid chemistry vidual research groups in solid state engi- are often engaged in joint projects with APMA E4400: Introduction to biophysical modeling

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OTHER nation, candidates must submit a written Thin film synthesis and processing in 169 MSAE E3900: Undergraduate research in proposal and defend it orally before a this program include evaporation, sput- materials science Proposal Defense Committee consisting tering, electrodeposition, and plasma Alternative courses can be taken as of three members of the faculty, including and laser processing. For analyzing electives with the approval of the under- the adviser. Doctoral candidates must materials structures and properties, graduate adviser. Of the 24 points of submit a thesis to be defended before a faculty and students employ electron elective content in the third and fourth Dissertation Defense Committee con- microscopy, scanning probe microscopy, years, at least 12 points of restricted sisting of five faculty members, including cathodoluminescence and electron electives approved by the adviser must two professors from outside the doctoral beam–induced current imaging, photolu- be taken. Of the remaining 12 points of program. Requirements for the Eng.Sc.D. minescence, dielectric and anelastic electives allotted, a sufficient number (administered by the School of Engi- relaxation techniques, ultrasonic meth- must actually be taken so that no fewer neering and Applied Science) and the ods, magnetotransport measurements, than 64 points of courses are credited Ph.D. (administered by the Graduate and X-ray diffraction techniques. Faculty to the third and fourth years. Those School of Arts and Sciences) are listed members have research collaborations remaining points of electives are intended elsewhere in this bulletin. with Lucent, Exxon, Philips Electronics, primarily as an opportunity to complete IBM, and other New York area research the four-year, 27-point nontechnical Areas of Research and manufacturing centers, as well as requirement, but any type of course Materials science and engineering is major international research centers. work can satisfy them. concerned with synthesis, processing, Scientists and engineers from these structure, and properties of metals, institutions also serve as adjunct faculty members at Columbia. The National GRADUATE PROGRAMS IN ceramics, polymers, and other materials, Synchrotron Light Source at Brookhaven MATERIALS SCIENCE AND with emphasis on understanding and National Laboratory is used for high- ENGINEERING exploiting relationships among structure, properties, and applications require- resolution X-ray diffraction and absorp- Master of Science Degree ments. Our graduate research programs tion measurements. Entering students typically have Candidates for the Master of Science encompass projects in areas as diverse undergraduate degrees in materials degree follow a program of study formu- as polycrystalline silicon, electronic science, metallurgy, physics, chemistry, lated in consultation with, and approved ceramics grain boundaries and inter- or other science and engineering disci- by, a faculty adviser. A minimum of 30 faces, microstructure and stresses in plines. First-year graduate courses points of credit must be taken in graduate microelectronics thin films, oxide thin provide a common base of knowledge courses within a specific area of study films for novel sensors and fuel cells, and technical skills for more advanced of primary interest to the candidate. All wide-band-gap semiconductors, optical courses and for research. In addition to degree requirements must be completed diagnostics of thin-film processing, course work, students usually begin an within five years. A candidate is required ceramic nanocomposites, electro-depo- association with a research group, indi- to maintain at least a 2.5 grade point sition and corrosion processes, magnetic vidual laboratory work, and participation average. Applicants for admission are thin films for giant and colossal magne- in graduate seminars during their first year. required to take the Graduate Record toresistance, chemical synthesis of Examinations. A research report (6 points nanoscale materials, nanocrystals, car- of credit, MSAE E6273) is required. bon nanotubes, nanostructure analysis GRADUATE SPECIALTY IN Special reports (3 points of credit) are using X-ray and neutron diffraction tech- SOLID-STATE SCIENCE AND acceptable for Columbia Video Network niques, and electronic structure calcula- ENGINEERING (CVN) students. tion of materials using density functional Solid-state science and engineering is and dynamical mean-field theories. an interdepartmental graduate specialty Doctoral Program Application targets for polycrystalline sili- that provides coverage of an important con are thin film transistors for active At the end of the first year of graduate area of modern technology that no single matrix displays and silicon-on-insulator study, doctoral candidates are required department can provide. It encompasses structures for ULSI devices. Wide-band- to take a comprehensive written qualify- the study of the full range of properties gap II–VI semiconductors are investigat- ing examination, which is designed to of solid materials, with special emphasis ed for laser applications. Novel applica- test the ability of the candidate to apply on electrical, magnetic, optical, and tions are being developed for oxide thin course work in problem solving and cre- thermal properties. The science of solids films, including uncooled IR focal plane ative thinking. The standard is first-year is concerned with understanding these arrays and integrated fuel cells for graduate level. There are two four-hour properties in terms of the atomic and portable equipment. Long-range appli- examinations over a two-day period. electronic structure of the materials in cations of high-temperature supercon- Candidates in the program must take question. Insulators (dielectrics), semi- ductors include efficient power transmis- an oral examination within one year of conductors, ceramics, and metallic sion and highly sensitive magnetic field taking the qualifying examination. Within materials are all studied from this view- sensors. two years of taking the qualifying exami- point. Quantum and statistical mechan-

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170 MATERIALS SCIENCE AND ENGINEERING PROGRAM: FIRST AND SECOND YEARS

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

MATHEMATICS1 MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) MATH V1202 (3) and ODE (3)

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

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

ENGLISH C1010 (3) COMPOSITION Z1003 (0) C1010 (3) (three tracks, choose one) Z0006 (0) Z1003 (0) C1010 (3)

HUMA C1001, C0CI C1101, HUMA C1002, C0CI C1102, REQUIRED or Global Core (3–4) or Global Core (3–4) NONTECHNICAL ELECTIVES HUMA W1121 (3) ECON W1105 (4) and or W1123 (3) W1155 recitation (0)

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

COMPUTER A computer language of the student’s choice at the 1000 level or higher SCIENCE

PHYSICAL C1001 (1) C1002 (1) EDUCATION

GATEWAY LAB E1102 (4) either semester

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

ics are key background subjects. The (Professor Herman, Applied Physics and and Applied Mathematics); structural engineering aspects deal with the design Applied Mathematics); chemical physics analysis and high Tc superconductors of materials to achieve desired proper- of surfaces and photoemission (Professor (Professor Chan, Henry Krumb School ties and the assembling of materials into Osgood, Electrical Engineering/Applied of Mines/Applied Physics and Applied systems to produce devices of interest Physics and Applied Mathematics); Mathematics); X-ray microdiffraction and to modern technology, e.g., for computers molecular beam epitaxy leading to semi- stresses (Professor Noyan, Henry Krumb and for energy production and utilization. conductor devices (Professor Wang, School of Mines/ Applied Physics and Electrical Engineering/Applied Physics Applied Mathematics); magnetic proper- Areas of Research and Applied Mathematics); lumines- ties of thin films (Professor Bailey, Henry The graduate specialty in solid-state sci- cence in heavily doped wide-band-gap Krumb School of Mines/Applied Physics ence and engineering includes research semiconductors (Professor Neumark, and Applied Mathematics); the structure programs in the Fractional Quantum Hall Henry Krumb School of Mines/Applied of nanomaterials (Professor Billinge, Henry Effect and electronic transport (Professor Physics and Applied Mathematics); and Krumb School of Mines/Applied Physics Stormer, Physics/ Applied Physics and inelastic light scattering in low-dimen- and Applied Mathematics); electronic Applied Mathematics); nonlinear optics sional electron gases within semicon- structure calculations of materials (Professor of surfaces (Professor Heinz, Electrical ductors (Professor Pinczuk, Applied Marianetti, Henry Krumb School of Mines/ Engineering/ Physics); semiconductor Physics and Applied Mathematics/ Applied Physics and Applied Mathematics); nanocrystals (Professor Brus, Chemistry/ Physics); large-area electronics and thin- and optical nanostructures (Professor Chemical Engineering); optics of semi- film transistors (Professor Im, Henry Wong, Henry Krumb School of conductors, including at high pressure Krumb School of Mines/Applied Physics Mines/Mechanical Engineering).

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171 MATERIALS SCIENCE AND ENGINEERING: THIRD AND FOURTH YEARS

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

MSAE E3103 (3) MSAE E3104 (3) MSAE E3156 (3) MSAE E3157 (3) Elements of mat. sci. Laboratory in mat. sci. Design project Design project

MSAE E 3111 (3) MSAE E3141 (3) MSAE E4101 (3) MSAE E4202 (3) REQUIRED Thermodynamics, Processing of metals Structural analysis Thermodynamics and COURSES kinetic theory, and and semiconductors of materials reactions in solids statistical mechanics MSAE E3142 (3)3 MSAE E4206 (3) MSAE E4215 (3) ENME E3113 (3)1 Processing of ceramics Electronic and magnetic Mechanical behavior Mechanics of solids and polymers properties of solids of materials

ELECTIVES 6 points2 6 points2 6 points2 6 points2

TOTAL POINTS 15 15 15 15

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

Program of Study ELEN E6403: Classical electromagnetic theory Atomic and crystal structures, structural defects, The applicant for the graduate specialty or alloying and phase diagrams. The influence of microstructure on the strength and physical must be admitted to one of the partici- PHYS G6092: Electromagnetic theory, I properties of metals and alloys, semiconductors, pating programs: applied physics and MSAE E4206: Electronic and magnetic properties ceramics, glasses, and polymers. applied mathematics, or electrical engi- of solids neering. A strong undergraduate back- MSAE E4207: Lattice vibrations and crystal MSAE E3104y Laboratory in materials science ground in physics or chemistry and in defects Lect: 1. Lab: 4. 3 pts. Professor Marianetti. MSAE E6220: Crystal physics mathematics is important. Corequisite: MSAE E3103. Metallographic specimen MSAE E6240: Impurities and defects in semicon- preparation, optical microscopy, quantitative metallog- The doctoral student must meet the ductor materials raphy, hardness and tensile testing, plastic deforma- formal requirements for the Eng.Sc.D. or MSAE E6241: Theory of solids tion, annealing, phase diagrams, brittle fracture of Ph.D. degree set by the department in PHYS G6018: Physics of the solid state glass, temperature and strain rate dependent defor- which he or she is registered. However, PHYS G6037: Quantum mechanics mation of polymers. Written and oral reports. the bulk of the program for the specialty MSAE E3111x Thermodynamics, kinetic theory, will be arranged in consultation with a COURSES IN MATERIALS and statistical mechanics member of the interdepartmental SCIENCE AND ENGINEERING Lect: 3. 3 pts. Professor Billinge. Committee on Materials Science and For related courses, see also Applied An introduction to the basic thermodynamics of Engineering/ Solid-State Science and Physics and Applied Mathematics, systems, including concepts of equilibrium, Engineering. At the end of the first year entropy, thermodynamic functions, and phase Chemical Engineering and Applied of graduate study, doctoral candidates changes. Basic kinetic theory and statistical Chemistry, Earth and Environmental are required to take a comprehensive mechanics, including diffusion processes, concept Engineering, and Electrical Engineering. of phase space, classical and quantum statistics, written examination concentrating on and applications thereof. solid-state science and engineering. MSAE E1001y Atomic-scale engineering of The following are regarded as core new materials MSAE E3141y Processing of metals and semi- courses of the specialty: Lect: 3. 3 pts. Professor Noyan. conductors An introduction to the nanoscale science and Lect: 3. 3 pts. Professor Duby. APPH E4100: Quantum physics of matter engineering of new materials. The control and Prerequisite: MSAE E3103 or the equivalent. Synthesis APPH E4112: Laser physics manipulation of atomic structure can create new and production of metals and semi-conductors with APPH-MSAE E6081-E6082: Solid state physics, solids with unprecedented properties. Computer engineered microstructures for desired properties. I and II hard drives, compact disc players, and liquid Includes high-temperature, aqueous, and electro- CHEM G4230: Statistical thermodynamics crystal displays (LCDs) are explored to under- chemical processing; thermal and mechanical pro- or stand the role of new materials in enabling tech- cessing of metals and alloys; casting and solidifica- CHAP E4120: Statistical mechanics nologies. Group problem-solving sessions are tion; diffusion, microstructural evolution, and phase ELEN E4301: Introduction to semiconductor used to develop understanding. transformations; modification and processing of devices surfaces and interfaces; deposition and removal of MSAE E3103x Elements of materials science ELEN E4944: Principles of device microfabrication thin films. Processing of Si and other materials for Lect: 3. 3 pts. Professor Noyan. ELEN E6331-E6332: Principles of semiconductor elemental and compound semiconductor-based Prerequisites: CHEM C1404 and PHYS C1011. physics electronic, magnetic, and optical devices.

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172 MSAE E3142y Processing of ceramics and Prerequisite: MSAE E3103 or the instructor’s per- ceramics, and electronic materials devices. Materials polymers mission. The science and engineering of polymer, reliability and fracture prevention emphasized. Lect: 3. 3 pts. Instructor to be announced. ceramic, and composite inorganic materials. Prerequisite: MSAE E3103 or the equivalent. Fundamental aspects of structure, processing, MSAE E4250x Ceramics and composites Established and novel methods involved in the and properties. Polymers: classification, synthe- Lect: 3. 3 pts. Offered in alternate years. processing of polymers and ceramics. The funda- sis, elastomers, thermoplastics, thermosets. Professor Guha. mental aspects of the structure and properties of Ceramics: crystal structure, morphology, classifi- Prerequisites or corequisites: MSAE E3142 and polymers and ceramic materials; strategy in the cation, oxides, nitrides, carbides, silicates. MSAE E3104, or the instructor’s permission. preparatory, synthesis, and processing methods Electrical, mechanical, thermal, and optical prop- The science and engineering of ceramic and for obtaining them. Topics include polymer syn- erties. Common and advanced technological composite inorganic materials, including oxides, thesis, elastomers, thermoplastics, thermoset applications, electrical/optical devices, catalytic nitrides, carbides, silicates, and complex materi- materials, design and molding processes. Ceramics: and environmental applications. als. Structure, composition, and classification. inorganic glasses and composites, materials Preparation: synthesis and processing of ceram- production and principle inorganic chemistry. MSAE E4202y Thermodynamics and reactions ics; modern techniques; crystal growth and reac- in solids tion kinetics. The properties of ceramics and MSAE E3156x-E3157y Design project Lect: 3. 3 pts. Professor Im. composites: structure-property relations; electri- 3 pts. Members of the faculty. Prerequisite: The instructor’s permission. Free cal, mechanical, thermal, and optical properties. Prerequisite: Senior standing. May be repeated energy of phases, the relationship between phase Common and advanced technological applica- with the permission of the undergraduate adviser. diagrams and metastability. Thermodynamics of tions of ceramics and composites: industrial E3156: A design problem in materials science or surfaces and interfaces, effect of particle size on utilization, electrical/optical devices, catalytic metallurgical engineering selected jointly by the phase equilibria, Gibbs adsorption of solute at and environmental applications. student and a professor in the department. The interfaces, grain boundaries, surface energy. project requires research by the student, directed Nucle-ation and growth, spinodal decomposition MSAE E4301x and y Materials science reading, and regular conferences with the profes- of phases. Diffusion in metals, intermetallic com- laboratory sor in charge. E3157: Completion of the research, pounds and ionic crystals. Diffusion along interfaces. 1 to 3 pts. Instructor to be announced. directed reading, and conferences, culminating in Prerequisite: The instructor’s permission. a written report and an oral presentation to the MSAE E4206x Electronic and magnetic Materials science laboratory work so conducted department. properties of solids as to fulfill particular needs of special students. Lect: 3. 3 pts. Professor Marianetti. MSAE E3900x and y Undergraduate research Prerequisites: PHYS C1401, C1402, and C1403, MSAE E4990x and y Special topics in in materials science or the equivalent. A survey course on the elec- materials science and engineering 0 to 4 pts. Members of the faculty. tronic and magnetic properties of materials, ori- Lect: 3. 3 pts. Instructors to be announced. This course may be repeated for credit, but no ented toward materials for solid-state devices. Prerequisite: The instructor’s permission. This more than 6 points may be counted toward the Dielectric and magnetic properties, ferroelectrics course may be repeated for credit. Topics and satisfaction of the B.S. degree requirements. and ferromagnets. Conductivity and superconduc- instructors change from year to year. For Candidates for the B.S. degree may conduct an tivity. Electronic band theory of solids: classifica- advanced undergraduate students and graduate investigation in materials science or carry out a tion of metals, insulators, and semiconductors. students in engineering, physical sciences, and special project under the supervision of the staff. Materials in devices: examples from semiconduc- other fields. Credit for the course is contingent upon the sub- tor lasers, cellular telephones, integrated circuits, MSAE E4999x and y and S4999 Curricular mission of an acceptable thesis or final report. and magnetic storage devices. Topics from practical training physics are introduced as necessary. MSAE E4090x Nanotechnology 1 pt. Members of the faculty. Lect. 3. 3 pts. Offered in alternate years. MSAE E4207y Lattice vibrations and crystal Prerequisites: Internship and adviser’s approval Professor Herman. defects (must be obtained in advance}. Only for master’s Prerequisites: APPH E3100 and MSAE E3103 or Lect: 3. 3 pts. Professor Chan. students in the Department of Applied Physics and their equivalents with instructor’s permission. The An introductory course in topics of solid state Applied Mathematics who may need relevant work science and engineering of creating materials, physics other than electronics and magnetic prop- experience as part of their program of study. Final functional structures and devices on the nanometer erties. Elastic waves in solids. Phonons and lat- report required. This course may not be taken for scale. Carbon nanotubes, nanocrystals, quantum tice vibrations. Brillouin zones. Thermal properties pass/fail or audited. dots, size-dependent properties, self-assembly, of solids. Defects, such as point defects in metals, MSAE E6020y Electronic ceramics nanostructured materials. Devices and applications, ionic crystals, semiconductors, and ceramics. Lect: 3. 3 pts. Offered in alternate years. nanofabrication. Molecular engineering, bionano- Not given in 2009–2010. technology. Imaging and manipulating at the atomic MSAE E4215y Mechanical behavior of Structure and bonding of ceramics and glasses. scale. Nanotechnology in society and industry. materials Lect: 3. 3 pts. Professor Noyan. Point defects and diffusion. Electronic and ionic MSAE E4101x Structural analysis of materials Prerequisite: MSAE E3103. Recommended conduction. Dielectric, ferroelectric, magnetic, Lect: 3. 3 pts. Professor Chan. preparation: A course in mechanics of materials. and optical ceramics. Prerequisite or corequisite: MSAE E3103 or the Review of states of stress and strain and their MSAE E6081x Solid state physics, I instructor’s permission. Geometry of crystals, basic relations in elastic, plastic, and viscous materials. Lect: 3. 3 pts. Professor Pinczuk. diffraction theory. X-ray diffraction. Techniques and Dislocation and elastic-plastic concepts introduced Prerequisite: APPH E3100 or the equivalent. theory of electron microscopy. Analysis of crystal to explain work hardening, various materials- Knowledge of statistical physics on the level of structures and orientations. Microstructure charac- strengthening mechanisms, ductility, and tough- MSAE E3111 or PHYS G4023 is strongly recom- terization and analysis of crystalline defects. ness. Macroscopic and microstructural aspects of mended. Crystal structure; reciprocal lattices; brittle and ductile fracture mechanics, creep and classification of solids; lattice dynamics; anharmonic MSAE E4132y Fundamentals of polymers fatigue phenomena. Case studies used through- effects in crystals; stress and strain; classical and ceramics out, including flow and fracture of structural alloys, electron models of metals; and periodic, nearly Lect: 3. 3 pts. Not given in 2009–2010. polymers, hybrid materials, composite materials,

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periodic, and more advanced analysis of electron construction, radiation sources, analytical repre- MSAE E9000x and y Materials science and 173 band structure. sentation of diffraction peaks, diffraction line engineering colloquium broadening, Fourier analysis of peak shape, texture 0 pts. Members of the faculty. MSAE E6082y Solid state physics, II analysis, diffraction analysis of stress and strain, Speakers from industry are invited to speak on Lect: 3. 3 pts. Professor Kim. diffraction analysis of order-disorder thermal dif- the recent impact of materials science and engi- Prerequisite: MSAE E6081x or the instructor’s fuse scattering, small angle scattering, instrumen- neering innovations. permission. Semiclassical and quantum mechani- tation in diffraction experiments, error analysis. cal electron dynamics and conduction; dielectric MSAE E9259x-E9260y Research topics in mate- properties of insulators; semiconductors; defects; MSAE E6229x Energy and particle beam rials science and metallurgical engineering magnetism; superconductivity; low-dimensional processing of materials Lect: 1. 1 pt. Members of the faculty. structures; and soft matter. Lect: 3. 3 pts. Not given in 2009–2010. Discussion of a group of technical papers related Prerequisite: MSAE E4202 or the instructor’s to a topic of current research interest. MSAE E6091y Magnetism and magnetic materials permission. Laser-, electron-, and ion-beam Lect: 3. 3 pts. Offered in alternate years. modification of materials to achieve unique micro- MSAE E9301x and y, and s Doctoral research Not given in 2009–2010. structures and metastable phases for electronic 0 to 15 pts. Members of the faculty. Prerequisite: MSAE E4206, APPH E6081, or the and structural applications. Fundamentals of Prerequisite: The qualifying examination for the equivalent. Types of magnetism. Band theory of energy deposition and heat flow during laser- and doctorate. Required of doctoral candidates. ferromagnetism. Magnetic metals, insulators, and electron-beam irradiation. Atomic displacement MSAE E9309x and y, and s Proposal of semiconductors. Magnetic nanostructures: ultra- processes in ion-irradiated materials. Beam- research for the doctorate thin films, superlattices, and particles. Surface induced microstructural evolution, crystallization, 0 to 3 pts Members of the faculty magnetism and spectroscopies. High-speed surface alloying, rapid solidification, and A written report prepared by the prospective doc- magnetization dynamics. Spin electronics. metastable phase formation. Review of current toral candidate defining the proposed research for industrial applications. MSAE E6120x Grain boundaries and interfaces the dissertation, and oral defense of the proposal Lect: 2. 3 pts. Offered in alternate years. MSAE E6230y Kinetics of phase transformations at the time of the qualifying examinations. Not given in 2009–2010. Lect: 3. 3 pts. Offered in alternate years. MSAE E9800x and y, and s Doctoral research Prerequisite: The instructor’s permission. Not given in 2009–2010. instruction Suggested background: basic knowledge of mate- Prerequisite: MSAE E4202 or the instructor’s per- 3, 6, 9, or 12 pts. Members of the faculty. rials science, dislocations, and point defects. The mission. Principles of nonequilibrium thermodynam- A candidate for the Eng.Sc.D. degree must regis- course gives an overview of the classic approaches ics; stochastic equations; nucleation, growth, and ter for 12 points of doctoral research instruction. in studying grain boundaries. Topics include coarsening reactions in solids; spinodal decompo- Registration in MSAE E9800 may not be used to boundary geometry and structure, boundary inter- sition; eutectic and eutectoid transformations. actions with crystal defects, boundaries as short- satisfy the minimum residence requirement for circuit diffusion paths, applications of boundary MSAE E6251y Thin films and layers the degree. concepts to interfaces, and roles of grain bound- Lect: 3. 3 pts. Professor Chan. MSAE E9900x and y, and s Doctoral dissertation aries in material properties and in kinetic phe- Vacuum basics, deposition methods, nucleation 0 pts. Members of the faculty. nomena in polycrystalline materials. and growth, conditions for epitaxy, relation between A candidate for the doctorate may be required to microstructure and deposition conditions, stress, register for this course every term after the MSAE E6220x Crystal physics adhesion, interconnects, and electromigration. Lect: 3. 3 pts. Offered in alternate years. course work has been completed, and until the Not given in 2009–2010. MSAE E6273x and y, and s Materials science dissertation has been accepted. Prerequisite: MSAE E4206 or the instructor’s per- reports mission. The course develops the idea of a tensor 0 to 6 pts. Members of the faculty. Courses in other programs relevant to and applies it to stress and, together with consid- Formal written reports and conferences with the materials science and engineering: erations of crystal symmetry, to the study of the appropriate member of the faculty on a subject of CHEE E4050: Principles of industrial electro- physical constants of crystals, such as diamag- special interest to the student but not covered in chemistry netic and paramagnetic susceptibility, dielectric the other course offerings. CHEN E4201: Engineering applications of constants, thermal expansivity, piezoelectric con- stants, and others. The physical properties are MSAE E8235x and y Selected topics in electrochemistry also studied against the background material of materials science CHEE E4252: Introduction to surface and MSAE E4206. Lect: 3. 3 pts. Instructors to be announced. colloid chemistry This course may be repeated for credit. Selected CHEE E4530: Corrosion of metals MSAE E6221x Introduction to dislocation theory topics in materials science. Topics and instructors CHEN E4620: Introduction to polymer science Lect: 3. 3 pts. Offered in alternate years. change from year to year. For students in engi- CHEN E4630: Polymer laboratory Not given in 2009–2010. neering, physical sciences, biological sciences, CIEN E4212: Structural assessment Prerequisite: MSAE E4215 or a course in theory and related fields. CIEN E4332: Finite element analysis, I of elasticity, or the instructor’s permission. Point CHEN E3110: Transport phenomena, I: and line imperfections. Theory of dislocations. MSAE E8236y Anelastic relaxations in crystals theory and methodology of rate Relation between imperfections and structure- Lect: 3. 3 pts. Offered in alternate years. phenomena Not given in 2009–2010. sensitive properties. EAEE E4011: Industrial ecology of manufacturing Prerequisite: The instructor’s permission. Formal EAEE E4160: Solid and hazardous waste MSAE E6225y Techniques in x-ray and theory of anelastic relaxation phenomena. management neutron diffraction Detailed study of the mechanisms of anelasticity EAEE E4900: Applied transport and chemical Lect: 3. 3 pts. Offered in alternate years. and internal friction in crystals, including the role rate phenomena Not given in 2009–2010. of point defects, dislocations, grain boundaries, EAEE E6228: Theory of flotation Prerequisite: MSAE E4101. Crystal symmetry, electron-phonon interactions, and ferromagnetic ENME E3113: Mechanics of solids diffraction, reciprocal space and Ewald sphere domain effects. ENME E6315: Theory of elasticity

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174 MECHANICAL ENGINEERING 220 S. W. Mudd, MC 4703, 212-854-2965 www.columbia.edu/cu/mechanical

CHAIR PROFESSORS ASSISTANT PROFESSORS ADJUNCT FACULTY MANAGER OF Y. Lawrence Yao Gerard H. A. Ateshian Daniel Attinger Pejman Akbari INSTRUCTIONAL 248 S. W. Mudd Richard W. Longman Jung-Chi Liao Ines Basalo LABORATORIES Vijay Modi Arvind Narayanaswamy Homayoon Beiqi Robert G. Stark DEPARTMENTAL Y. Lawrence Yao Nabil Simaan Reza Jazar ADMINISTRATOR Elon Terrell W. Michael Lai Sandra Morris ASSOCIATE PROFESSORS Michael McGough 220 S. W. Mudd James Hone LECTURER Mohammad H. N. Naraghi Jeffery W. Kysar Fred Stolfi Elias Panides Qiao Lin Vijay Srinivasan Chee Wei Wong Graham Walker

echanical engineering is a cal engineering is perhaps the broadest transfer, control, instrumentation, diverse subject that derives its and most diverse of engineering disci- design, and manufacturing to realize/ M breadth from the need to plines. Hence mechanical engineers play understand mechanical systems. design and manufacture everything from a central role in such industries as auto- Specialized mechanical engineering small individual parts/devices (e.g., motive (from the car chassis to its every subjects include biomechanics, cartilage micro-scale sensors, inkjet printer noz- subsystem—engine, transmission, sen- tissue engineering, energy conversion, zles) to large systems (e.g., spacecraft sors); aerospace (airplanes, aircraft laser-assisted materials processing, and machine tools). The role of a engines, control systems for airplanes combustion, MEMS, microfluidic mechanical engineer is to take a prod- and spacecraft); biotechnology (implants, devices, fracture mechanics, nanome- uct from an idea to the marketplace. In prosthetic devices, fluidic systems for chanics, mechanisms, micro-power order to accomplish this, a broad range pharmaceutical industries); computers generation, tribology (friction and wear), of skills are needed. The particular and electronics (disk drives, printers, and vibrations. The American Society of skills in which the mechanical engineer cooling systems, semiconductor tools); Mechanical Engineers (ASME) currently acquires deeper knowledge are the microelectromechanical systems, or lists thirty-six technical divisions, from ability to understand the forces and the MEMS (sensors, actuators, micro power advanced energy systems and aero- thermal environment that a product, its generation); energy conversion (gas tur- space engineering to solid waste engi- parts, or its subsystems will encounter; bines, wind turbines, solar energy, fuel neering and textile engineering. design them for functionality, aesthetics, cells); environmental control (HVAC, The breadth of the mechanical engi- and the ability to withstand the forces air-conditioning, refrigeration, compres- neering discipline allows students a variety and the thermal environment they will be sors); automation (robots, data/image of career options beyond some of the subjected to; determine the best way to acquisition, recognition, and control); industries listed above. Regardless of manufacture them and ensure they will manufacturing (machining, machine the particular future path they envision operate without failure. Perhaps the one tools, prototyping, microfabrication). for themselves after they graduate, their skill that is the mechanical engineer’s To put it simply, mechanical engi- education would have provided them exclusive domain is the ability to analyze neering deals with anything that moves, with the creative thinking that allows and design objects and systems with including the human body, a very com- them to design an exciting product or motion. plex machine. Mechanical engineers system, the analytical tools to achieve Since these skills are required for vir- learn about materials, solid and fluid their design goals, the ability to meet tually everything that is made, mechani- mechanics, thermodynamics, heat several sometimes conflicting con-

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straints, and the teamwork needed to hardening. In addition, the role that the matic relationship, optimization, and design, market, and produce a system. constitutive relations play in the fracture design of linkages and spatial mecha- These skills also prove to be valuable in and failure of materials is emphasized. nisms, and the development of novel other endeavors and can launch a career (Kysar) robotic mechanical architectures. These in medicine, law, consulting, manage- In the area of molecular mechanics in new robotic architectures include parallel ment, banking, finance, and so on. biology, mechanical effects on stem cell robots, hybrid robots, snakelike robots, For those interested in applied scien- differentiation is studied to understand and flexible and flexure-based robots. tific and mathematical aspects of the the underlying molecular mechanisms. The theoretical aspects of this research discipline, graduate study in mechanical The molecular motion in living cells is include applications of line geometry engineering can lead to a career of monitored to examine how the dynam- tools and screw theory for analysis and research and teaching. ics of molecules determine the specifici- synthesis of robotic devices, applications ty of stem cell differentiation. Mechanics of actuation redundancy and kinematic Current Research Activities of molecular motors is studied to corre- redundancy for stiffness control, and Current research activities in the late their functions with cell differentia- applications of algebraic geometry meth- Department of Mechanical Engineering tion. (Liao) ods for robot synthesis. The applied aspects of this research include task- are in the areas of controls and robotics, Control, Design, and Manufacturing. based design and construction of new energy and micropower generation, fluid Control research emphasizes iterative devices/robots for robotic medical assis- mechanics, heat/mass transfer, mechan- learning control (ILC) and repetitive con- tance in the surgical arena. (Simaan) ics of materials, manufacturing, material trol (RC). ILC creates controllers that In the area of advanced manufactur- processing, MEMS, nanotechnology, learn from previous experience perform- ing processes and systems, current and orthopedic biomechanics. ing a specific command, such as robots research concentrates on laser materials on an assembly line, aiming for high- Biomechanics and Mechanics of processing. Investigations are being car- precision mechanical motions. RC Materials. Some of the current research ried out in laser micromachining; laser learns to cancel repetitive disturbances, in biomechanics is concerned with the forming of sheet metal; microscale laser such as precision motion through gearing, application of continuum theories of shock-peening, material processing machining, satellite precision pointing, mixtures to problems of electromechani- using improved laser-beam quality. Both particle accelerators, etc. Time optimal cal behavior of soft biological tissues, numerical and experimental work is con- control of robots is being studied for contact mechanics, lubrication of ducted using state-of-the-art equipment, increased productivity on assembly diarthrodial joints, and cartilage tissue instruments, and computing facilities. lines through dynamic motion planning. engineering. (Ateshian) Close ties with industry have been Research is also being conducted on In the area of the mechanics of established for collaborative efforts. (Yao) materials, research is performed to bet- improved system identification, making ter understand material constitutive mathematical models from input-output Energy, Fluid Mechanics, and behavior at the micro- and mesolength data. The results can be the starting Heat/Mass Transfer. In the area of scales. This work is experimental, theo- point for designing controllers, but they energy, one effort addresses the design retical, and computational in nature. The are also studied as a means of assess- of flow/mass transport systems for the ultimate goal is to formulate constitutive ing damage in civil engineering struc- extraction of carbon dioxide from air. relationships that are based on physical tures from earthquake data. (Longman) Another effort addresses the develop- concepts rather than phenomenology, Robotics and mechanism synthesis ment of distributed sensors for use in as in the case of plasticity power-law research focuses on the analysis of kine- micrositing and performance evaluation

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176 of energy and environmental systems. friendly lubricants are also being identified group with facilities in optical (including The design and testing of components and characterized. (Terrell) ultrafast) characterization, device and systems for micropower generation nanofabrication, and full numerical inten- MEMS and Nanotechnology. In these is part of the thermofluids effort as well sive simulations is available. Current areas, research activities focus on power as part of the MEMS effort. (Modi) efforts include silicon nanophotonics, generation systems, nanostructures for In the area of fluid mechanics, study quantum dot interactions, negative photonics, fuel cells and photovoltaics, of low-Reynolds-number chaotic flows refraction, dramatically enhanced nonlin- and microfabricated adaptive cooling is being conducted both experimentally earities, and integrated optics. This effort skin and sensors for flow, shear, and and numerically, and the interactions seeks to advance our understanding of wind speed. Basic research in fluid with molecular diffusion and inertia are nanoscale optical physics, enabled now dynamics and heat/mass transfer phe- presently being investigated. Other areas by our ability to manufacture, design, nomena at small scales also support of investigation include the fluid mechan- and engineer precise subwavelength these activities. (Attinger, Hone, Lin, ics of inkjet printing, drop on demand, nanostructures, with derived applica- Modi, Narayanaswamy, Wong) the suppression of satellite droplets, tions in high-sensitivity sensors, high- We study the dynamics of microcan- shock wave propagation, and remedia- bandwidth data communications, and tilevers and atomic force microscope tion in high-frequency printing systems. biomolecular sciences. Major ongoing cantilevers to use them as microscale (Attinger, Modi) collaborations across national laborato- thermal sensors based on the reso- In the area of microscale transport ries, industrial research centers, and nance frequency shifts of vibration phenomena, current research is focused multiuniversities support this research. modes of the cantilever. Bi-material on understanding the transport through (Wong) microcantilever-based sensors are used interfaces, as well as the dynamics of In the area of microscale power gen- to determine the thermophysical proper- interfaces. For instance, an oscillating eration, efforts are dedicated to build a ties of thin films. (Narayanaswamy) microbubble creates a microflow pattern micromotor using acoustic energy ampli- Research in the area of nanotechnol- able to attract biological cells. High- fied by a microbubble. (Attinger) ogy focuses on nanomaterials such as speed visualization is used together with Research in the area of microtribolo- nanotubes and nanowires and their innovative laser measurement techniques gy—the study of friction, lubrication, and applications, especially in nanoelectro- to measure the fluid flow and temperature wear at the microscale—analyzes the mechanical systems (NEMS). A labora- field with a very high resolution. (Attinger). surface contact and adhesive forces tory is available for the synthesis of In the area of nanoscale thermal between translating and rotating sur- carbon nanotubes and semiconductor transport, our research efforts center on faces in MEMS devices. Additionally, the nanowires using chemical vapor deposi- the enhancement of thermal radiation tribological behavior between sliding tion (CVD) techniques and to build transport across interfaces separated by micro- and nano-textured surfaces is devices using electron-beam lithography a nanoscale gap. The scaling behavior of also of interest, due to the prospects of and various etching techniques. This nanoscale radiation transport is meas- enhanced lubrication and reduced fric- effort will seek to optimize the fabrica- ured using a novel heat transfer measure- tion. (Terrell) tion, readout, and sensitivity of these ment technique based on the deflection Research in BioMEMS aims to devices for numerous applications, such of a bi-material atomic force microscope design and create MEMS and as sensitive detection of mass, charge, cantilever. Numerical simulations are also micro/nanofluidic systems to control and magnetic resonance. (Hone, Wong, performed to confirm these measure- the motion and measure the dynamic Modi) ments. The measurements are also used behavior of biomolecules in solution. In the area of nanoscale imaging in to infer extremely small variations of van Current efforts involve modeling and biology, a super-resolution microscopy der Waals forces with temperature. This understanding the physics of micro/ (nanoscopy) system is built to break the enhancement of radiative transfer will ulti- nanofluidic devices and systems, diffraction limit of light. The super-resolu- mately be used to improve the power exploiting polymer structures to enable tion microscopy system is to be used to density of thermophotovoltaic energy micro/nanofluidic manipulation, and inte- observe molecular dynamics in living conversion devices. (Narayanaswamy) grating MEMS sensors with microfluidics cells. A high-speed scanning system is Research in the area of tribology—the for measuring physical properties of designed and implemented to track study of friction, lubrication, and wear— biomolecules. (Lin) molecular dynamics in a video rate. focuses on studying the wear damage Control of sample motion in nanometer Biological Engineering and Biotech- and energy loss that is experienced in resolution is achieved by integrating sin- nology. Active areas of research in the power generation components such as gle photon detection and nano-position- musculoskeletal biomechanics laboratory piston rings, fuel injection systems, ing systems. (Liao) include theoretical and experimental geartrains, and bearings. Next-generation Research in the area of optical nan- analysis of articular cartilage mechanics; lubricants, additives, surface coatings, otechnology focuses on devices smaller theoretical and experimental analysis and surface finishes are being studied in than the wavelength of light, for exam- of cartilage lubrication, cartilage tissue order to determine their effects on friction ple, in photonic crystal nanomaterials engineering, and bioreactor design; and wear. Additionally, environmentally and NEMS devices. A strong research growth and remodeling of biological tis-

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sues; cell mechanics; and mixture theory ized instruments for label-free character- mated image acquisition and processing 177 for biological tissues with experiments ization of thermodynamic and other for sample preparation and analysis and computational analysis (Ateshian). physical properties of biomolecules; and (Simaan, Yao). The Hone group is involved in a num- subcutaneously implantable MEMS affin- A technology that couples the power ber of projects that employ the tools of ity biosensors for continuous monitoring of multidimensional microscopy (three micro- and nano-fabrication toward the of glucose and other metabolites (Lin). spatial dimensions, time, and multiple study of biological systems. With collab- The advanced robotics and mecha- wavelengths) with that of DNA array orators in biology and applied physics, nism application lab (ARMA) is focused technology is investigated in an NIH-funded the group has developed techniques to on surgical intervention using novel project. Specifically, a system is devel- fabricate metal patterns on the molecular robotic architectures. Examples of these oped in which individual cells selected scale (below 10 nanometers) and attach architectures include flexible snakelike on the basis of optically detectable biomolecules to create biofunctionalized robots, parallel robots, and cooperative multiple features at critical time points in nanoarrays. The group is currently using robotic systems. The current research dynamic processes can be rapidly and these arrays to study molecular recogni- activity is focused on providing safer robotically micromanipulated into reac- tion, cell spreading, and protein crystal- and deeper interaction with the anatomy tion chambers to permit amplified DNA lization. Professor Hone is a co-PI of the using minimally invasive approaches, synthesis and subsequent array analy- NIH-funded Nanotechnology Center for surgery through natural orifices, surgical sis. Customized image processing and Mechanics in Regenerative Medicine, task planning based on dexterity and pattern recognition techniques are which seeks to understand and modify performance measures, and manipula- developed, including Fisher’s linear dis- at the nanoscale force- and geometry- tion of flexible organs. The ongoing criminant preprocessing with neural net, sensing pathways in health and disease. funded research projects include NIH- a support vector machine with improved The Hone group fabricates many of the funded grants on designing next-gener- training, multiclass cell detection with tools used by the center to measure and ation robotic slaves for incisionless sur- error correcting output coding, and ker- apply force on a cellular level. (Hone) gical intervention (surgery through natu- nel principal component analysis (Yao). In the area of molecular bioengineer- ral opening); minimally invasive surgery ing, proteins are engineered to under- for the throat and upper airways; image- Facilities for Teaching and Research stand their mechanical effects on stem guided insertable robotic platforms for The undergraduate laboratories, occu- cell differentiation. Molecular motors are less invasive surgery (surgery that is pying an area of approximately 6,000 designed and engineered computation- carried out using a single incision in the square feet of floor space, are the site of ally and experimentally to identify key abdomen); and robotic assistance for experiments ranging in complexity from structural elements of motor functions. cochlear implant surgery (NSF funded, basic instrumentation and fundamental Fluorescent labels are added to the mol- Simaan). exercises to advanced experiments in ecules of interest to follow their dynam- Mass radiological triage is critical such diverse areas as automatic con- ics in living cells and to correlate their after a large-scale radiological event trols, heat transfer, fluid mechanics, stress mechanical characteristics with the because of the need to identify those analysis, vibrations, microcomputer- process of stem cell differentiation. (Liao) individuals who will benefit from medical based data acquisition, and control of Microelectromechanical systems intervention as soon as possible. The mechanical systems. (MEMS) are being exploited to enable goal of the ongoing NIH-funded research Equipment includes microcomputers and facilitate the characterization and project is to design a prototype of a fully and microprocessors, analog-to-digital manipulation of biomolecules. MEMS automated, ultra high throughput bio- and digital-to-analog converters, lasers technology allows biomolecules to be dosimetry. This prototype is supposed and optics for holography and interfer- studied in well-controlled micro/nanoen- to accommodate multiple assay prepa- ometry, a laser-Doppler velocimetry sys- vironments of miniaturized, integrated ration protocols that allow the determi- tem, a Schlieren system, dynamic strain devices, and may enable novel biomed- nation of the levels of radiation exposure indicators, a servohydraulic material ical investigations not attainable by that a patient received. The input to testing machine, a photoelastic testing conventional techniques. The research this fully autonomous system is a large machine, an internal combustion engine, interests center on the development of number of capillaries filled with blood of a dynamometer, subsonic and supersonic MEMS devices and systems for label- patients collected using finger sticks. wind tunnels, a cryogenic apparatus, free manipulation and interrogation of These capillaries are processed by the computer numerically controlled vertical biomolecules. Current research efforts system to distill the micronucleus assay machine centers (VMC), a coordinate primarily involve microfluidic devices that in lymphocytes, with all the assays being measurement machine (CMM), and a exploit specific and reversible, stimulus- carried out in situ in multi-well plates. rapid prototyping system. A CNC wire dependent binding between biomole- The research effort on this project electrical discharge machine (EDM) is cules and receptor molecules to enable involves the automation system design also available for the use of specialized selective purification, concentration, and and integration including hierarchical projects for students with prior arrange- label-free detection of nucleic acid, protein, control algorithms, design and control of ment. The undergraduate laboratory also and small molecule analytes; miniatur- custom built robotic devices, and auto- houses experimental setups for the

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178 MECHANICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS STANDARD TRACK

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

MATHEMATICS MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) MATH V1202 (3) and APMA E2101 (3)

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

one semester lecture (3–4) CHEMISTRY C1403 or C1404 or Lab C1500 (3)1 C3045 or C1604

ENGLISH C1010 (3) COMPOSITION Z1003 (0) C1010 (3) (three tracks, choose one) Z0006 (0) Z1003 (0) C1010 (3)

HUMA C1001, C0CI C1101, HUMA C1002, C0CI C1102, REQUIRED or Global Core (3–4) or Global Core (3–4) NONTECHNICAL COURSES HUMA W1121 or ECON W1105 (4) and W1123 (3) W1155 recitation (0)

REQUIRED (3) Student’s choice, see list of ENME-MECE E3105 (4) either semester TECHNICAL first- and second-year technical electives COURSES (professional-level courses; see pages 12–13)2

COMPUTER Computer language: W1003 (3) or W1004 (3) any semester SCIENCE

PHYSICAL C1001 (1) C1002 (1) EDUCATION

GATEWAY LAB E1102 (4) either semester

1May substitute Physics Lab C1493 (3), C1494 (3), or W3081 (2). 2ELEN E1201 (see semester VI) satisfies this requirement. However, MECE E1001 is strongly encouraged. 3May substitute BIOL W2001 or higher.

understanding and performance evalua- for the construction and testing of analog data acquisition board. The data acquisi- tion of a complete small steam power and digital electronic circuits aid the stu- tion system serves as an oscilloscope, generation system, a heat exchanger, dents in learning the basic components additional function generator, and spec- and a compressor. Part of the under- of the microcomputer architecture. The trum analyzer for the student team. The graduate laboratory is a staffed machine laboratory is divided into work centers for computer also contains a complete shop with machining tools such as stan- two-person student laboratory teams. microcomputer software development dard vertical milling machines, engine Each work center is equipped with sev- system, including editor, assembler, sim- and bench lathes, programmable sur- eral power supplies (for low-power elec- ulator, debugger, and C compiler. The face grinder, bandsaw, drill press, tool tronics and higher power control), a laboratory is also equipped with a grinders, and a power hacksaw. The function generator, a multimeter, a proto- portable oscilloscope, an EPROM eraser shop also has a tig welder. board for building circuits, a microcom- (to erase microcomputer programs from A mechatronics laboratory affords puter circuit board (which includes the the erasable chips), a logic probe, and the opportunity for hands-on experience microcomputer and peripheral compo- an analog filter bank that the student with microcomputer-embedded control nents), a microcomputer programmer, teams share, as well as a stock of ana- of electromechanical systems. Facilities and a personal computer that contains a log and digital electronic components.

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179 MECHANICAL ENGINEERING: THIRD AND FOURTH YEARS STANDARD TRACK

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

MECE E3018 (3) MECE E3028 (3) MECE E3038 (3) MECE E3410 (4) Lab I Lab II Lab III Engineering design

MECE E3100 (3) MECE E3408 (3) MECE E3409 (3) Fluids I Graphics & design CAD

REQUIRED MECE E 3301 (3) MECE E3311 (3) MECE E3601 (3) COURSES Thermodynamics Heat transfer Classical control sys.

ENME E3105 (4)1 MECE E4608 (3) Mechanics Manufacturing proc.

ENME E3113 (3) ELEN E1201 (3.5) Mechanics of solids Intro. elec. eng.

TECHNICAL ELECTIVES 6 points 6 points

NONTECH 3 points 6 points ELECTIVES

TOTAL POINTS2 15 15.5 15 16

1Strongly recommended to be taken in Semester III or IV. 2Students must complete 128 points to graduate.

The department maintains a modern (www.columbia.edu/cu/lweb). nationally and throughout the world. computer-aided design laboratory E-mail and computing services are Highly qualified students are permit- equipped with fifteen Silicon Graphics maintained by Columbia University ted to pursue an honors course consist- workstations and software tools for Information Technology (CUIT) ing of independent study under the design, CAD, FEM, and CFD. (www.columbia.edu/cuit). guidance of a member of the faculty. The research facilities are located Upon graduation the student may within individual or group research labo- UNDERGRADUATE PROGRAM wish to enter employment in industry or ratories in the department, and these The objectives of the undergraduate government, or continue with graduate facilities are being continually upgraded. program in mechanical engineering are study. Alternatively, training in mechanical To view the current research capabilities as follows: engineering may be viewed as a basis please visit the various laboratories The Mechanical Engineering Depart- for a career in business, patent law, within the research section of the depart- ment at Columbia University is dedicated medicine, or management. Thus, the ment Web site (www.me.columbia.edu/ to graduating mechanical engineers who: department’s undergraduate program pages/research/index.html). The students provides a sound foundation for a variety and staff of the department can, by prior 1.practice mechanical engineering in a of professional endeavors. arrangement, use much of the equip- broad range of industries; The program in mechanical engineer- ment in these research facilities. Through 2.pursue advanced education, research ing leading to the B.S. degree is accred- their participation in the NSF-MRSEC and development, and other creative ited by the Engineering Accreditation center, the faculty also have access and innovative efforts in science, engi- Commission of the Accreditation Board to shared instrumentation and the neering, and technology, as well as for Engineering and Technology (ABET). clean room located in the Shapiro other professional careers; Of the 21 points of elective content Center for Engineering and Physical 3.conduct themselves in a responsible, in the third and fourth years, at least 12 Science Research. Columbia University’s professional, and ethical manner; points of technical courses, including at extensive library system has superb 4.participate as leaders in their fields of least 6 points from the Department of scientific and technical collections expertise and in activities that support service and economic development Mechanical Engineering, must be taken.

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180 MECHANICAL ENGINEERING PROGRAM: FIRST AND SECOND YEARS EARLY DECISION TRACK

SEMESTER I SEMESTER II SEMESTER III SEMESTER IV

MATHEMATICS MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) MATH V1202 (3) and APMA E2101 (3)

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

one semester lecture (3–4) Lab C1500 (3)2 CHEMISTRY C1403 or C1404 or C3045 or C1604

ENGLISH C1010 (3) COMPOSITION Z1003 (0) C1010 (3) (three tracks, choose one) Z0006 (0) Z1003 (0) C1010 (3)

REQUIRED HUMA C1001, C0CI C1101, HUMA C1002, C0CI C1102, NONTECHNICAL or Global Core (3–4) or Global Core (3–4) COURSES

(3) Student’s choice, ENME E3105 (4) ENME E3113 (3) ELEN E1201 (3.5) REQUIRED see list of first- and second- Mechanics Mechanics of solids Intro. elec. eng. TECHNICAL year technical electives COURSES (professional-level courses; MECE E3408 (3) see page 12)1 Graphics & design

COMPUTER Computer language: W1003 (3) or W1004 (3) any semester SCIENCE PHYSICAL EDUCATION C1001 (1) C1002 (1)

GATEWAY LAB E1102 (4) either semester

1ELEN E1201 (see semester IV) satisfies this requirement. However, MECE E1001 is strongly encouraged. 2May substitute Physics Lab C1493 (3), C1494 (3), or W3081 (2). 3May substitute BIOL W2001 or higher.

Those remaining points of electives are shows a demonstrated commitment to ment strongly encourages all seniors intended primarily as an opportunity to professionalism and an established to take this exam and offers a review complete the four-year, 27-point non- record of abilities that will help a job can- course covering material relevant to technical requirement. Consistent with didate stand out in the field. Ideally, the the exam, including a practice exam to professional accreditation standards, FE exam should be taken in the senior simulate the testing experience. The FE courses in engineering science and year while the technical material learned exam is given in the fall and spring of courses in design must have a com- while pursuing the undergraduate degree each year. The review course is offered bined credit of 48 points. Students is still fresh in the student’s mind. In addi- in the spring semester, concluding should see their advisers for details. tion to the FE exam, achieving P.E. licen- before the spring exam. sure requires some years of experience Fundamentals of Engineering (FE) and a second examination, which tests GRADUATE PROGRAMS Exam knowledge gained in engineering practice. The FE exam is a state licensing exam For more information, please see Master of Science Degree Program and the first step toward becoming a www.columbia.edu/cu/mechanical/ The program leading to the Master of Professional Engineer (P.E.). P.E. licensure misc-pages/FE_Exam.html. Science degree in mechanical engineer- is important for engineers to obtain—it The Mechanical Engineering Depart- ing requires completion of a minimum

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181 MECHANICAL ENGINEERING: THIRD AND FOURTH YEARS EARLY DECISION TRACK

SEMESTER V SEMESTER VI SEMESTER VII SEMESTER VIII

MECE E3018 (3) MECE E3028 (3) MECE E3038 (3) MECE E3410 (4) Lab I Lab II Lab III Engineering design

REQUIRED MECE E3100 (3) MECE E3311 (3) MECE E3409 (3) COURSES Fluids I Heat transfer CAD

MECE E 3301 (3) MECE E4608 (3) MECE E3601 (3) Thermodynamics Manufacturing proc. Classical control sys.

REQUIRED HUMA W1121 or ECON W1105 (4) and NONTECHNICAL COURSES W1123 (3) W1155 recitation (0)

TECHNICAL 3 points 3 points 6 points ELECTIVES

NONTECH ELECTIVES 3 points 3 points 6 points

TOTAL POINTS1 15 16 15 16

1Students must complete a minimum of 128 points to graduate.

of 30 points of approved course work power generation. Nevertheless, the fol- special track advisory committee. The consisting of no fewer than ten courses. lowing guidelines must be adhered to: name of the special track will be listed A thesis based on either experimental, 1.The sequence of courses selected on a student’s transcript. The currently computational, or analytical research is must not be haphazard, but rather available special tracks are listed below. optional and may be counted in lieu of show a clearly discernible specialty. M.S. in Mechanical Engineering with up to 6 points of course work. In general, 2.All courses must be at the graduate Concentration in Energy Systems attainment of the degree requires one level, i.e., numbered 4000 or higher, Advisers: Profs. Daniel Attinger and Vijay academic year of full-time study, although with some 6000-level courses included. Modi it may also be undertaken on a part-time 3.Every program must contain at least basis over a correspondingly longer period. one course in mathematics (APMA or The concentration in energy systems A minimum grade point average of 2.5 MATH designators) or their equivalent, provides the M.S. candidate with a global is required for graduation. covering material beyond what the understanding of current energy chal- The M.S. degree in mechanical engi- student has taken previously. It should lenges. Advanced thermofluidic knowl- neering requires a student to take a appear early in the sequence in order edge is provided to design and optimize sequence of courses that shows a to serve as a basis for the technical energy systems, with a strong emphasis “clearly discernible specialty or concen- course work. on renewable energies. Courses related tration.” In consultation with his/her 4.Out-of-department study is encour- to energy and environmental policy, two adviser an M.S. student can develop a aged, but at least five courses should strong areas of Columbia as a global concentration specifically tailored to be in mechanical engineering. university, can be integrated into the his/her interests and objectives, and we course sequence. This concentration is Rather than apply for the standard refer to this as the standard track. a suitable preparation for careers in track, students can apply for a special Alternatively, M.S. students can pick energy production and energy consulta- track in either energy systems or in from a set of predefined concentrations, tion. micro/nanoscale engineering. The or special tracks. Requirements: While satisfying the requirements for a special track are Typical choices of concentration in general mechanical engineering require- identical to those of the standard track, the standard track include such subjects ments, take at least five courses from: with one exception: a special track stu- as mechanics of solids and fluids, ther- MECE E4211: Energy: sources and conversion dent must take at least 15 of his/her modynamics, heat transfer, manufactur- MECE E4302: Advanced thermodynamics points from a list determined by a spe- ing engineering, robotics, kinematics, MECE E4312: Solar thermal engineering cial track adviser in consultation with a dynamics and vibrations, controls, and MECE E4314: Energy dynamics of green buildings

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182 MECE E6100: Advanced mechanics of fluids an analytical nature with those empha- submits a research proposal and pres- MECE E6104: Case studies in computational fluid sizing the applied aspects of one or ents it to a faculty committee. The com- dynamics more fields in mechanical engineering. mittee considers whether the proposed MECE E6313: Advanced heat transfer For the professional degree, the student problem is suitable for doctoral research, APPH E4130: Physics of solar energy EAEE E6126: Carbon sequestration must have a grade point average of 3.0 whether the plan of attack is well formu- EAEE E6208: Combustion chemistry or processes or better. lated and appropriate to the problem, INTA W4200: Alternative energy resources When a student becomes a prospec- and whether the student is adequately ARCH A4684: Sustainable design tive candidate for either the Doctor of prepared. It may approve the plan with- SIPA U4727: Environmental politics and policy Engineering Science (Eng.Sc.D.) or Doctor out reservation, or it may recommend management of Philosophy (Ph.D.) degree, a faculty modifications or additions. This is the SIPA U6060: International energy systems and adviser is assigned whose task is to last formal requirement until the disserta- business structures help choose a program of courses, pro- tion is submitted for approval. M.S. in Mechanical Engineering with vide general advice on academic matters, All doctoral students are required to Concentration in Micro/Nanoscale and monitor academic performance. successfully complete four semesters Engineering The doctoral candidate is expected of the mechanical engineering seminar Advisers: Profs. James Hone and to attain a level of mastery in some area MECE E9500. Jeff Kysar of mechanical engineering, and must therefore choose a field and concentrate The concentration in micro/nanoscale COURSES IN MECHANICAL in it by taking the most advanced courses engineering provides the M.S. candidate ENGINEERING offered. This choice of specialty is nor- with an understanding of engineering mally made by the time the student has MECE E1001x Mechanical engineering: challenges and opportunities in micro- completed 30 points of credit beyond micromachines to jumbo jets and nanoscale systems. The curriculum the bachelor’s degree, at which time a Lect: 3 3 pts. Professor Ateshian. addresses fundamental issues of complete course program is prepared This introductory course explores the role of mechanics, fluid mechanics, optics, heat mechanical engineering in developing many of and submitted to the departmental doc- transfer, and manufacturing at small-size the fundamental technological advances on toral committee for approval. The student scales. Application areas include MEMS, which today’s society depends. Students will be must maintain a grade point average of bio-MEMS, microfluidics, thermal exposed to several mature and emerging tech- 3.2 or better in graduate courses. nologies through a series of case studies. Topics systems, and carbon nanostructures. The department requires the include airplanes, automobiles, robots, and Requirements: While satisfying the prospective candidate to pass a qualify- modern manufacturing methods, as well as the general mechanical engineering require- ing examination. Given once a year, in emerging fields of micro-electro-mechanical ments, take at least five courses from: machines (MEMS) and nanotechnology. The January, it is usually taken after the stu- MECE E4212: Microelectromechanical systems physical concepts that govern the operation of dent has completed 30 points beyond MECE E4213: BioMEMS these technologies will be developed from basic MECE E6105: Transport phenomena in the the bachelor’s degree. However, it may principles and then applied in simple design prob- presence of interfaces not be delayed past the next examina- lems. Students will also be exposed to state-of- MECE E6700: Carbon nanotubes tion given after completion of 45 points. the art innovations in each case study. MECE E6710: Nanofabrication laboratory The examination comprises a written MECE E6720: Nano/microscale thermal transport test, given in two parts over two days, MECE E3018x Mechanical engineering processes in which questions may be selected laboratory, I MECE E8990: Small scale mechanical behavior Lect: 1. Lab: 5. 3 pts. Professor Kysar. from a broad set in all areas of mechanical ELEN E4503: Sensors, actuators, and electro- Introduction to engineering instrumentation and engineering and applied mathematics, mechanical systems measurement of pressure, fluid flow, temperature, ELEN E6945: Device nanofabrication devised to test the candidate’s ability to stress, viscosity, etc., based upon digital data BMEN E4590: BioMEMS: cellular and molecular think creatively. There is also an oral acquisition and processing. Experimental exami- applications examination based on some research nation of basic mechanics, such as beams and MSAE E4090: Nanotechnology project the student has undertaken. simple structures. Probability theory: distribution, A candidate who fails the examination tests of significance, correlation, ANOVA, linear regression, and design of experiments. A lab fee Doctoral/Professional Degree may be permitted to repeat it once in of $50 is collected. Programs the following year. Students who wish to continue their After passing the qualifying examina- MECE E3028y Mechanical engineering studies beyond the master’s degree tion, the student chooses a faculty laboratory, II level but are unwilling to embark upon a member in the pertinent area of special- Lect: 1. Lab: 5. 3 pts. Professor Wong. program of research of the kind required ization who then serves as the research Experiments in engineering and physical phenom- for a doctoral degree may continue in adviser. This adviser helps select a ena: aerofoil lift and drag in wind tunnels, laser doppler anemometry in immersed fluidic chan- a program leading to the professional research problem and supervises the nels, supersonic flow and shock waves, Rankine degree of Mechanical Engineer (MECE). research, writing, and defense of the thermodynamical cycle for power generation, and The course of study consists of a mini- dissertation. Once a specific problem structural truss mechanics and analysis. A lab fee mum of 30 points of work beyond the has been identified and a tentative plan of $50 is collected. master’s degree, combining courses of for the research prepared, the student

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MECE E3038y Mechanical engineering analysis of general loading states and deforma- Kysar, Liao, Lin, Longman, Modi, Narayanaswamy, 183 laboratory, III tion of machine components using singularity Simaan, Stolfi, Terrell, Wong, and Yao. Hours to Lect: 1. Lab: 5. 3 pts. Professor Stolfi. functions and energy methods. Theoretical intro- be arranged by faculty supervising the work. Mechatronic control of mechanical and electro- duction to static failure theories, fracture mechan- Prerequisites: Approval by faculty member who mechanical systems. Control of various thermody- ics, and fatigue failure theories. Introduction to agrees to supervise the work. Normally not to be namic cycles, including an internal combustion engine conceptual design and design optimization prob- taken in a student’s final semester. Independent (Otto cycle). Reverse engineering of an electro- lems. Design of machine components such as project involving theoretical, computational, mechanical product. A lab fee of $50 is collected. springs, shafts, fasteners, lead screws, rivets, experimental or engineering design work. May welds. Modeling, analysis, and testing of machine be repeated, but no more than 3 points may be MECE E3100x Introduction to mechanics assemblies for prescribed design problems. counted toward degree requirements. Projects of fluids Problems will be drawn from statics, kinematics, requiring machine-shop use must be approved Lect: 3. 3 pts. Professor Attinger. dynamics, solid modeling, stress analysis, and by the laboratory supervisor. Prerequisite: ENME E3105. Basic continuum design optimization. concepts. Liquids and gases in static equilibrium. MECE E4058x and y Mechatronics and Continuity equation. Two-dimensional kinematics. MECE E3410y Engineering design embedded microcomputer control Equation of motion. Bernoulli’s equation and Lect: 4. 4 pts. Professor Stolfi. Lect: 3. 3 pts. Professor Stolfi. applications. Equations of energy and angular Prerequisite: Senior standing. Elements of the Prerequisite: ELEN E1201. Recommended: momentum. Dimensional analysis. Two-dimen- design process: concept formulation, systems ELEN E3000. Enrollment limited to 12 students. sional laminar flow. Pipe flow, laminar, and turbu- synthesis, design analysis optimization. Selection Mechatronics is the application of electronics and lent. Elements of compressible flow. and execution of a project involving the design of microcomputers to control mechanical systems. an actual engineering device or system. A labora- Systems explored include on/off systems, sole- ENME-MECE E3105x and y Mechanics tory fee of $125 is collected. noids, stepper motors, dc motors, thermal sys- Lect: 4. 4 pts. Professor Hone. tems, magnetic levitation. Use of analog and digi- Prerequisites: PHYS C1401, and MATH V1101- MECE E3411y Fundamentals of engineering tal electronics and various sensors for control. V1102 and V1201. Elements of statics, dynamics Lect: 3. 1 pt. Professor Stolfi. Programming microcomputers in Assembly and C. of a particle, systems of particles, and rigid bodies. Prerequisite: Senior standing. Review of core Lab required; a lab fee of $75 is collected. courses in mechanical engineering, including MECE E3301x Thermodynamics mechanics, strength of materials, fluid mechanics, MECE E4100y Mechanics of fluids Lect: 3. 3 pts. Professor Basalo. thermodynamics, heat transfer, materials and Lect: 3. 3 pts. Instructor to be announced. Classical thermodynamics. Basic properties and processing, control, and mechanical design and Prerequisite: MECE E3100 or the equivalent. concepts, thermodynamic properties of pure sub- analysis. Review of additional topics, including Fluid dynamics and analyses for mechanical engi- stances, equation of state, work, heat, the first engineering economics and ethics in engineering. neering and aerospace applications: boundary and second laws for flow and nonflow processes, The course culminates with a comprehensive layers and lubrication, stability and turbulence, energy equations, entropy, and irreversibility. examination, similar to the Fundamentals of and compressible flow. Turbomachinery Introduction to power and refrigeration cycles. Engineering examination. as well as additional selected topics.

MECE E3311y Heat transfer EEME E3601x Classical control systems MECE E4211y Energy: sources and conversion Lect: 3. 3 pts. Professor Narayanaswamy. Lect: 3. 3 pts. Professor Longman. Lect: 3. 3 pts. Professor Modi. Steady and unsteady heat conduction. Radiative Prerequisite: MATH E1210. Analysis and design Prerequisite: MECE E3301. Energy sources such heat transfer. Internal and external forced and of feedback control systems. Transfer functions; as oil, gas, coal, gas hydrates, hydrogen, solar, free convective heat transfer. Change of phase. block diagrams; proportional, rate, and integral and wind. Energy conversion systems for electri- Heat exchangers. controllers; hardware, implementation. Routh cal power generation, automobiles, propulsion, stability criterion, root locus, Bode and Nyquist and refrigeration. Engines, steam and gas tur- MECE E3401x Mechanics of machines plots, compensation techniques. bines, wind turbines; devices such as fuel cells, Lect: 3. 3 pts. Professor Lin. thermoelectric converters, and photovoltaic cells. Prerequisites: ENME E3105 and MECE E3408. MECE E3900x-E3901y Honors tutorial in Specialized topics may include carbon-dioxide Introduction to mechanisms and machines, ana- mechanical engineering sequestration, cogeneration, hybrid vehicles, and lytical and graphical synthesis of mechanism, 3 pts. Professors Ateshian, Attinger, Hone, Kysar, energy storage devices. displacement analysis, velocity analysis, acceler- Liao, Lin, Longman, Modi, Narayanaswamy, ation analysis of linkages, dynamics of mecha- Simaan, Stolfi, Terrell, Wong, and Yao. Hours MECE E4212x Microelectromechanical systems nism, cam design, gear and gear trains, and individually arranged. Lect: 1.5. Lab: 3. 3 pts. Professor Wong. computer-aided mechanism design. Individual study; may be selected after the first Enrollment limited to 16 students. MEMS markets term of the junior year by students maintaining a and applications; scaling laws; silicon as a mechani- MECE E3408y Computer graphics and design 3.2 grade-point average. Normally not to be taken cal material; sensors and actuators; micromechanical Lect: 3. 3 pts. Instructor to be announced. in a student’s final semester. Course format may analysis and design; substrate (bulk) and surface Introduction to drafting, engineering graphics, vary from individual tutorial to laboratory work to micromachining; computer-aided design; packag- computer graphics, solid modeling, and mechani- seminar instruction under faculty supervision. ing; testing and characterization; microfluidics. cal engineering design. Interactive computer Written application must be made prior to registra- graphics and numerical methods applied to the tion outlining proposed study program. Projects MECE E4213y Biomicroelectromechanical solution of mechanical engineering design prob- requiring machine-shop use must be approved by systems (BioMEMS): design, fabrication, lems. A laboratory fee of $175 is collected. the laboratory supervisor. and analysis Lect: 3. 3 pts. Professor Lin. MECE E3409x Machine design MECE E3998 x and y Projects in mechanical Prerequisites: MECE E3100 and MECE E3311, Lect: 3. 3 pts. Professor Simaan. engineering or a course in transport phenomena, or the Prerequistie: MECE E3408. Computer-aided 1 to 3 pts. Professors Ateshian, Attinger, Hone, instructor’s permission. Silicon and polymer

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184 micro/nanofabrication techniques; hydrodynamic and passive solar design. Global energy implica- MECE E4502x Computational geometry for microfluidic control; electrokinetic microfluidic tions. Green buildings. Building-integrated photo- CAD/CAM control; microfluidic separation and detection; voltaics. Roof-mounted gardens and greenhouses. Lect: 3. 3 pts. Professor Srinivasan. sample preparation; micro bioreactors and tem- Financial assessment tools and case studies. Prerequisite: FORTRAN or PASCAL. Analysis of perature control; implantable MEMS including geometric problems and the design of efficient sensors, actuators, and drug delivery devices. MECE E4400x and y Computer laboratory methodologies to obtain solutions to these prob- access lems. Algorithms to be studied include geometric MECE E4302y Advanced thermodynamics 0 pts. Professor Ateshian. searching, convex hulls, triangulations, Voronoi Lect: 3. 3 pts. Instructor to be announced. Sign up for this class to obtain a computer diagrams, intersections, hidden surfaces. Emphasis Prerequisite: MECE E3301. Advanced classical account and access to the Department of will be on practical aspects of these algorithms, thermodynamics. Availability, irreversibility, gener- Mechanical Engineering Computer Laboratory. and on applications of the solutions in computer- alized behavior, equations of state for nonideal Open to mechanical engineering graduate stu- aided product design and manufacturing. gases, mixtures and solutions, phase and chemi- dents only. A laboratory fee of $50 is collected. cal behavior, combustion. Thermodynamic proper- EEME E4601y Digital control systems ties of ideal gases. Applications to automotive MECE E4404x Lubrication theory and design Lect: 3. 3 pts. Professor Longman. and aircraft engines, refrigeration and air condi- Lect: 3. 3 pts. Professor Terrell. Prerequisite: MECE E3601 or ELEN E3202. tioning, and biological systems. Prerequisite: MECE E3100. Fluid friction. The Real-time control using digital computers. Solving hydrodynamic and hydrostatic theories of lubrica- scalar and state-space difference equations. MECE E4304x Turbomachinery tion. Plane surfaces and thrust bearing design. Discrete equivalents of continuous systems fed Lect: 3. 3 pts. Professor Akbari. Journal bearings; load-carrying capacity and by holds. Z-transer functions. Creating closed- This course will introduce you to the basics of temperature rise. Principles of bearing design for loop difference equation models by Z-transform theory, design, selection, and applications of tur- efficient lubrication. Oil flow in bearings. Bearings and state variable approaches. The Nyquist fre- bomachinery. Turbomachines are widely used in with semi-fluid lubrication. Fluid and nonfluid quency and sample rate selection. Classical- and many engineering applications, such as energy lubricants. Bearing materials. modern-based digital control laws. Digital system conversion, power plants, air-conditioning, pump- identification. ing, refrigeration, and vehicle engines, as there MECE E4430y Automotive dynamics are pumps, blowers, compressors, gas turbines, Lect: 3. 3 pts. Professor Jazar. MECE E4602y Introduction to robotics jet engines, wind turbines, etc. Applications are Prerequisites: ENME 3105 or the equivalent; Lect: 3. 3 pts. Professor Jazar. drawn from energy conversion technologies, recommended: ENME 3106 or the equivalent. Overview of robot applications and capabilities. HVAC, and propulsion. The course will provide Automobile dynamic behavior is divided into three Linear algebra, kinematics, statics, and dynamics you with a basic understanding of the different subjects: vehicle subsystems, ride, and handling. of robot manipulators. Survey of sensor technology: kinds of turbomachines. Vehicle subsystems include tire, steering, mecha- force, proximity, vision, compliant manipulators. nisms, suspensions, gearbox, engine, clutch, etc. Motion planning and artificial intelligence; manipu- IEME E4310x The manufacturing enterprise Regarding ride, vibrations and ride comfort are lator programming requirements and languages. Lect. 3. 3pts. Professor Weinig. analyzed, and suspension optimization of a The strategies and technologies of global manu- quarter car model is treated. Regarding handling, MECE E4604x Product design for manufac- facturing and service enterprises. Connections vehicle dynamic behavior on the road is analyzed, turability between the needs of a global enterprise, the with emphasis on numerical simulations using Lect: 3. 3 pts. Professor Walker. technology and methodology needed for manu- planar as well as roll models. Prerequisites: Manufacturing process, computer facturing and product development, and strategic graphics, engineering design, mechanical design. planning as currently practiced in industry. MECE E4431 Space vehicle dynamics and General review of product development process; control market analysis and product system design; prin- MECE E4312y Solar thermal engineering Lect: 3. 3 pts. Not given in 2009–2010. ciples of design for manufacturing; strategy for Lect: 3. 3 pts. Professor Attinger. Prerequisite: ENME-MECE E3105; ENME E4202 material selection and manufacturing process Prerequisite: MECE E3311. Fundamentals of recommended. Space vehicle dynamics and con- choice; component design for machining; casting; solar energy transport: radiation heat transfer, trol, rocket equations, satellite orbits, initial trajec- molding; sheet metal working and inspection; convection, conduction, and phase change tory designs from earth to other planets, satellite general assembly processes; product design for processes. Heat exchangers and solar collectors: attitude dynamics, gravity gradient stabilization of manual assembly; design for robotic and auto- basic methods of thermal design, flow arrange- satellites, spin-stabilized satellites, dual-spin matic assembly; case studies of product design ments, effects of variable conditions, rating satellites, satellite attitude control, modeling, and improvement. procedures. Solar energy concentration. Piping dynamics, and control of large flexible spacecraft. systems: series and parallel arrangements, fluid MECE E4608y Manufacturing processes movers. Thermal response and management of MECE E4501y Geometrical modeling Lect: 3. 3 pts. Professor Yao. photovoltaic energy conversion. Solar energy Lect: 3. 3 pts. Professor Srinivasan. Prerequisite: ENME E3113 or the equivalent. storage. Solar cooling, solar thermal power, and Prerequisite: COMS W1005. Relationship Processes and materials of manufacture: metal cogeneration. Applications to the design of solar between 3-D geometry and CAD/CAM; represen- cutting, forming, stamping, forging, welding, thermal engineering systems. tations of solids; geometry as the basis of analy- powder metallurgy; classification and fabricating sis, design, and manufacturing; constructive solid characteristics of metals and composites; MECE E4314y Energy dynamics of green geometry and the CSG tree; octree representation plastics, adhesives. buildings and applications; surface representations and Lect: 3. 3 pts. Professors Naraghi and McGough. intersections; boundary representation and MECE E4609y Computer-aided manufacturing Prerequisites: MECE E3301 and MECE E3311. boundary evaluation; applied computational Lect: 3. 3 pts. Professor Walker. Introduction to analysis and design of heating, geometry; analysis of geometrical algorithms Prerequisites: An introductory course on manufac- ventilating, and air-conditioning systems. Heating and associated data structures; applications of turing processes, and knowledge of computer and cooling loads. Humidity control. Solar gain geometrical modeling in vision and robotics. aided design and mechanical design or the

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instructor’s permission. Computer-aided design, reports required. This course may not be taken quantities. Transport processes in a turbulent 185 free-form surface modeling, tooling and fixturing, for pass/fail credit or audited. International stu- medium. Turbulent shear flows: deterministic computer numeric control, raid prototyping, dents must also consult with the International and random structures. Experimental techniques, process engineering, fixed and programmable Students and Scholars Office. prediction methods, and simulation. automation, industrial robotics. MECE E6100x Advanced mechanics of fluids MEBM E6310x–E6311y Mixture theories for MECE E4610x Advanced manufacturing Lect: 3. 3 pts. Professor Panides. biological tissues, I and II processes Prerequisites: MATH E1210 and MECE E3100. Lect: 3. 3 pts. Professor Ateshian. Lect: 3. 3 pts. Professor Yao. Eulerian and Lagrangian descriptions of motion. Prerequisites: MECE E6422 and APMA E4200, Prerequisites: Introductory courses on manufac- Stress and strain rate tensors, vorticity, integral or the equivalent. Development of governing turing processes and heat transfer, knowledge of and differential equations of mass, momentum, equations for mixtures with solid matrix, interstitial engineering materials, or the instructor’s permis- and energy conservation. Potential flow. fluid, and ion constituents. Formulation of consti- sion. Principles of nontraditional manufacturing, tutive models for biological tissues. Linear and nontraditional transport and media. Emphasis on MECE E6102y Computational heat transfer nonlinear models or fibrillar and viscoelastic laser assisted materials processing, laser material and fluid flow porous matrices. Solutions to special problems, interactions with applications to laser material Lect: 3. 3 pts. Not given in 2009–2010. such as confined and unconfined compression, removal, forming, and surface modification. Prerequisites: MECE E3100 and E3311; FOR- permeation, indentation and contact, and swelling Introduction to electrochemical machining, electri- TRAN. Mathematical description of pertinent experiments. cal discharge machining, and abrasive water jet physical phenomena. Basics of finite-difference machining. methods of discretization, explicit and implicit MECE E6313x Advanced heat transfer schemes, grid sizes, stability, and convergence. Lect: 3. 3 pts. Professor Naraghi. MEBM E4702x Advanced musculoskeletal Solution of algebraic equations, relaxation. Heat Prerequisite: MECE E3311. Corequisite: MECE biomechanics conduction. Incompressible fluid flow, stream E6100. Application of analytical techniques to the Lect: 3. 3 pts. Not given in 2009–2010. function-vorticity formulation. Forced and natural solution of multi-dimensional steady and transient Advanced analysis and modeling of the muscu- convection. Use of primitive variables, turbulence problems in heat conduction and convection. loskeletal system. Topics include advanced modeling, and coordinate transformations. Lumped, integral, and differential formulations. concepts of 3-D segmental kinematics, muscu- Topics include use of sources and sinks, loskeletal dynamics, experimental measurements MECE E6104y Case studies in computational laminar/turbulent forced convection, and natural of joints kinematics and anatomy, modeling of fluid dynamics convection in internal and external geometries. muscles and locomotion, multibody joint modeling, Lect: 3. 3 pts. Professor Panides. introduction to musculoskeletal surgical simulations. Prerequisites: APMA E4200 and MECE E6100. MECE E6400y Advanced machine dynamics Corequisites: APMA E4300 and MECE E4400. Lect: 3. 3 pts. Not given in 2009–2010. MEBM 4703y Molecular mechanics in biology Hands-on case studies in computational fluid Prerequisite: MECE E3401. Review of classical Lect: 3. 3 pts. Professor Liao. dynamics, including steady and transient flows, dynamics, including Lagrange’s equations. Prerequisite: ENME E3105, APMA E2101, or the heat and mass transfer, turbulence, compressible Analysis of dynamic response of high-speed instructor’s permission. Mechanical understanding flow, and multiphase flow. Identifying assumptions, machine elements and systems, including mass- of biological structures including proteins, DNA computational domain selection, model creation spring systems, cam-follower systems, and gear- and RNA in cells and tissues. Force response of and setup, boundary conditions, choice of conver- ing; shock isolation; introduction to gyrodynamics. proteins and DNA, mechanics of membranes, bio- gence criteria, visualization and interpretation of physics of molecular motors, mechanics of pro- computed results. Taught in the Mechanical MECE E6422x-E6423x or y Introduction to the tein-protein interactions. Introduction to modeling Engineering Computer Laboratory with computa- theory of elasticity, I and II and simulation techniques, and modern biophysi- tional fluid dynamics software. Lect: 3. 3 pts. Professor Lai. cal techniques such as single molecule FRET, Corequisite: APMA E4200. Analysis of stress optical traps, AFM, and super-resolution imaging, MECE E6105y Transport phenomena in the and strain. Formulation of the problem of elastic for understanding molecular mechanics and presence of interfaces equilibrium. Torsion and flexure of prismatic bars. dynamics. Lect: 3. 3 pts. Not given in 2009–2010. Problems in stress concentration, rotating disks, Prerequisites: MECE E3301 and MECE E3311; shrink fits, and curved beams; pressure vessels, MECE E4990x or y Special topics in mechani- MECE E4100 or the equivalent, or the instructor’s contact and impact of elastic bodies, thermal cal engineering permission; CHEE E4252 or the equivalent, or the stresses, propagation of elastic waves. Lect: 3. 3 pts. Instructor to be announced. instructor’s permission. Surface energy and capil- Prerequisite: The instructor’s permission. Topics lary phenomena. Wetting and spreading of liquids, MECE E6424x Vibrations in machines, I and instructors change from year to year. For wetting line pinning and hysteresis, dynamics of Lec: 3. 3 pts. Professor Stolfi. advanced undergraduate students and graduate wetting. Surfactants. Bubbles: nucleation, stability, Prerequisite: MECE E3401. Review of vibration students in engineering, physical sciences, and dynamics, microstreaming. Jets and drops: analysis of systems and mechanisms with one other fields. generation, dynamics, stability, and impact with degree of freedom. Natural frequencies. Forced surfaces. Measurement of transport phenomena vibrations. Effects of dry and viscous friction. MECE E4999x and y (sect. 001) Curricular involving interfaces. Interfacial transport phenomena Energy methods of Rayleigh and Ritz. Suppression practical training involving thermal, chemical, or electrical gradients. and elimination of vibration. Vibration isolation. 1 pt. Professor Yao. Applications in microfluidic systems. Measuring instruments. Critical speeds in machin- Prerequisite: Instructor’s written approval. Only ery. Synchronous whirl. Half-frequency whirl. for ME graduate students who need relevant MECE E6200y Turbulence Influence of bearing characteristics on critical intern or fieldwork experience as part of their Lect: 3. 3 pts. Not given in 2009–2010. speeds. Effect of gyroscopic moments. Systems program of study as determined by the instructor. Prerequisite: MECE E6100. Introductory concepts with multiple degrees of freedom. Dynamic vibra- Written application must be made prior to regis- and statistical description. Kinematics of random tion absorbers. Self-tuning absorbers of pendulum tration outlining proposed study program. Final velocity fields, dynamics of vorticity, and scalar and roller types. Lagrangian equations of motion

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186 as applied to vibrating systems. General equa- EEME E6620x or y Applied signal recognition MECE E8100y Advanced topics in fluid tions for transverse critical speeds of shafts. and classification mechanics Surging of helical springs. Lect: 3. 3 pts. Not given in 2009–2010. Lect: 2. 3 pts. Not given in 2009–2010. Prerequisite: MATH E1210, APMA E3101, knowledge Prerequisite: MECE E6100. This course may be EEME E6601x Introduction to control theory of a programming language, or the instructor’s taken more than once, since its content has mini- Lect: 3. 3 pts. Professor Longman. permission. Applied recognition and classification mal overlap between consecutive years. Selected Prerequisite: MATH E1210. A graduate-level intro- of signals using a selection of tools borrowed topics from viscous flow, turbulence, compressible duction to classical and modern feedback control from different disciplines. Applications include flow, rarefied gas dynamics, computational methods, that does not presume an undergraduate back- human biometrics, imaging, geophysics, machin- and dynamical systems theory, non-Newtonian ground in control. Scalar and matrix differential ery, electronics, networking, languages, communi- fluids, etc. equation models and solutions in terms of state cations, and finance. Practical algorithms are transition matrices. Transfer functions and trans- covered in signal generation; modeling; feature EEME E8601y Advanced topics in control theory fer function matrices, block diagram manipula- extraction; metrics for comparison and classifica- Lect: 3. 3 pts. Not given in 2009–2010. tions, closed loop response. Proportional, rate, tion; parameter estimation; supervised, unsuper- Prerequisites: EEME E6601 and E4601, or the and integral controllers, and compensators. vised, and hierarchical clustering and learning; instructor’s permission. This course may be taken Design by root locus and frequency response. optimization; scaling and alignment; signals as more than once, since the content changes from year Controllability and observability. Luenberger codes emitted from natural sources; information; to year, electing different topics from control theory observers, pole placement, and linear-quadratic and extremely large-scale search techniques. such as learning and repetitive control, adaptive con- cost controllers. trol, system identification, Kalman filtering, etc. MECE E6700y Carbon nanotube science and EEME E6602y Modern control theory technology MECE E8990x and y Special topics in mechani- Lect: 3. 3 pts. Not given in 2009–2010. Lect: 3. 3 pts. Not given in 2009–2010. cal engineering Prerequisite: EEME E6601 or EEME 4601 or Prerequisite: Knowledge of introductory solid Lect: 3. 3 pts. Instructor to be announced. ELEN E6201, or the instructor’s permission. state physics (e.g. PHYS G4018, APPH E6081, Prerequisites: Instructor’s permission. This course Singular value decomposition. ARX model or MSAE E3103) or the instructor’s permission. may be taken for credit more than once. The instruc- and state space model system identification. Basic science of solid state systems. Crystal tor from the Mechanical Engineering Department and Recursive least squares filters and Kalman filters. structure, electronic and phonon bandstructures the topics covered in the course will vary from year to LQR, H∞, linear robust control, predictive control. of nanotubes. Synthesis of nanotubes and other year. This course is intended for students with gradu- Learning control, repetitive control, adaptive nanomaterials. Experimental determination of ate standing in mechanical engineering and other control. Liapunov and Popov stability. Nonlinear nanotube structures and techniques for nanoscale engineering and applied sciences. adaptive control, nonlinear robust control, sliding imaging. Theory and measurement of mechanical, mode control. thermal, and electronic properties of nanotubes MECE E9000x and E9001y, and s Graduate and nanomaterials. Nanofabrication and nano- research and study EEME E6610y Optimal control theory electronic devices. Applications of nanotubes. 1 to 3 pts. Professors Ateshian, Attinger, Hone, Lect: 3. 3 pts. Not given in 2009–2010. Kysar, Liao, Lin, Longman, Modi, Narayanaswamy, Prerequisite: EEME E6601 or EEME E4601 or MEEE E6710x or y Nanofabrication laboratory Simaan, Stolfi, Terrell, Wong, and Yao. the instructor’s permission. Covers topics in cal- Lecture: 1. Lab: 5. 3 pts. Professor Hone. Theoretical or experimental study or research in culus of variations, Pontryagin maximum principle, Prerequisite: ELEN E6945 or the instructor’s per- graduate areas in mechanical engineering and quadratic cost optimal control, predictive control, mission. Laboratory in techniques for fabrication engineering science. dynamic programming for optimal control, Kalman at the nanometer scale. Electron-beam lithogra- filtering, numerical methods for solution. Some phy. Plasma etching and 3D nanofabrication. Thin MECE E9500x or y Graduate seminar applications discussed include minimum energy film deposition. Self-assembly and ‘bottom-up’ 0 pts. Instructor to be announced. subway operation (our solution saved 11 percent nanofabrication. Fabrication of and testing of Pass/fail only. All doctoral students are required in tests on the Flushing Line, and the method was complete nanodevices. A lab fee of $300 is to successfully complete four semesters of the adopted by the Transit Authority, saving many required. mechanical engineering seminar MECE 9500. millions of dollars per year), minimum time robot optimal control allowing one to run assembly lines MECE E6720x Nano/microscale thermal trans- MECE E9800x and y, and s Doctoral research faster for increased productivity. port processes instruction Lect: 3. 3 pts. Professor Liao. 3, 6, 9, or 12 pts. Professors Ateshian, Attinger, Hone, MECE E6614y Advanced topics in robotics Nano and microscale origins of thermal transport Kysar, Liao, Lin, Longman, Modi, Narayanaswamy, and mechanism synthesis phenomena by molecules, electrons, phonons, Simaan, Stolfi, Terrell, Wong, and Yao. Lect. 3. 3 pts. Professor Simaan. and photons. Quantum mechanics and statistical A candidate for the Eng.Sc.D. degree in mechani- Prerequisite: APMA E2101, APMA E3101, MECE physics. Density of states. Kinetic theory of cal engineering must register for 12 points of doc- E4602 (or COMS W4733). Recommended: gases. Boltzmann transport equation (BTE), clas- toral research instruction. Registration in MECE MECE E3401 or the instructor’s permission. sical and quantum size effects. Landauer formal- E9800 may not be used to satisfy the minimum Kinematic modeling methods for serial, parallel, ism for transport via nanostructures. Macroscopic residence requirement for the degree. redundant, wire-actuated robots and multifingered constitutive equations from BTE. Application to hands with discussion of open research prob- electronics cooling, thermoelectric and ther- MECE E9900x and y Doctoral dissertation lems. Introduction to screw theory and line geom- mophotovoltaic devices, and energy conversion. 0 pts. Professors Ateshian, Attinger, Hone, Kysar, etry tools for kinematics. Applications of homo- Liao, Lin, Longman, Modi, Narayanaswamy, topy continuation methods and symbolic-numeri- MECE E8020x-E8021y Master’s thesis Simaan, Stolfi, Terrell, Wong, and Yao. cal methods for direct kinematics of parallel 1 to 3 pts. Professors Ateshian, Attinger, Hone, A candidate for the doctorate may be required robots and synthesis of mechanisms. Course Kysar, Liao, Lin, Longman, Modi, Narayanaswamy, to register for this course every term after his/her uses textbook materials as well as a collection of Simaan, Stolfi, Terrell, Wong, and Yao. course work has been completed and until the recent research papers. Interpretive research in graduate areas in dissertation has been accepted. mechanical engineering and engineering science.

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188 UNDERGRADUATE MINORS

ndergraduate minors are designed MINOR IN AMERICAN STUDIES SIEO W4105: Probability 3.0 points to allow engineering and applied Minimum: 18 points. STAT W4107: science students to study, to a Statistical inference 3.0 points U 1. AMST W101: Introduction to American limited extent, a discipline other than studies 3.0 points or any other course designated APMA, their major. Besides engineering minors MATH, STAT, IEOR, or COMS that is 2–6. Five additional courses in American offered by SEAS departments, new lib- approved by the applied mathematics Studies with no distribution or seminar eral arts minors are available. requirements. Students are encouraged to program adviser. A minor requires at least 15 points of take seminars. credit, and no more than one course MINOR IN APPLIED PHYSICS can be taken outside of Columbia or met through AP or IB credit. This MINOR IN APPLIED Prospective students should consult the includes courses taken through study MATHEMATICS first- and second-year requirements for abroad. In SEAS departments with more Prospective students should consult the applied physics majors to ensure that than one major program, a minor in the first- and second-year requirements for prerequisites for the applied physics second program may be permitted, if applied mathematics majors to ensure minor are satisfied in the first two years. approved by the department. that prerequisites for the applied mathe- Course work counting toward the No substitutions or changes of any matics minor are satisfied in the first two applied physics minor may not include kind from the approved minors are per- years. advanced placement credits. mitted (see lists below). No appeal for Course work counting toward the 1. APPH E4901: Seminar: problems changes will be granted. Please note applied mathematics minor may not in applied physics 1.0 points that the same courses may not be used include advanced placement credits. 2. PHYS W3003: Mechanics 3.0 points to satisfy the requirements of more than Any substitutions for the courses listed one minor. No courses taken for pass/fail below require the approval of the 3. APPH E3100: Introduction to may be counted for a minor. Minimum applied mathematics program adviser. quantum mechanics 3.0 points GPA for the minor is 2.0. Departments 1. APMA E3101: 4. APPH E3300: outside SEAS have no responsibility for Linear algebra 3.0 points Applied electromagnetism 3.0 points nonengineering minors offered by SEAS. or 5. MSAE E3111: Thermodynamics, For a student to receive credit for a MATH V2010: Linear algebra 3.0 points kinetic theory, and statistical course taken while studying abroad, the 2. APMA E3102: mechanics 3.0 points department offering the minor must Partial differential equations 3.0 points 6. Two of the following courses: approve the course in writing, ahead of or APPH E4010: the student’s study abroad. MATH V3028: Introduction to nuclear science 3.0 points Students must expect a course load Partial differential equations 3.0 points APPH E4100: that is heavier than usual. In addition, 3–5. Any three of the following courses: Quantum physics of matter 3.0 points unforeseen course scheduling changes, APMA E4300: APPH E4110: Modern optics 3.0 points problems, and conflicts may occur. The Introduction to numerical methods 3.0 points APPH E4112: School cannot guarantee a satisfactory APMA E4204: Functions of Laser physics 3.0 points completion of the minor. a complex variable 3.0 points APPH E4300: APMA E4101: Introduction to: Applied electrodynamics 3.0 points dynamical systems 3.0 points APPH E4301: MATH V2500: Introduction to plasma physics 3.0 points Analysis and optimization 3.0 points

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MINOR IN ARCHITECTURE Core BME Requirements MECE E3100: Introduction to 1. Studio course (choose one from the 1. BIOL C2005: Introductory biology, I 4.0 points mechanics of fluids 3.0 points MECE E3301: following): 2. BMEN E4001: Thermodynamics 3.0 points ARCH V1020: Introduction to Quantitative physiology, I 3.0 points or architectural design and or MSAE E3111: visual culture 3.0 points BMEN E4002: Thermodynamics, kinetic theory, ARCH V3101: Quantitative physiology, II 3.0 points and statistical mechanics 3.0 points Arch representation: abstraction 4.0 points ARCH V3103: I. CELL AND TISSUE ENGINEERING TRACK III. BIOMEDICAL IMAGING TRACK Arch representation: perception 4.0 points 3. CHEN E3010: Chemical engineering 3. BMEN E4894: thermodynamics 4.0 points Biomedical imaging 3.0 points 2–4. History/theory courses (see Note below) or 4–5. Two from the following courses: 5. Elective course (must be either an BMEN E4210: Thermodynamics BMEN E4430: Principles of approved second design studio or an addi- of biological systems 4.0 points magnetic resonance imaging 3.0 points tional history/theory course) 4. BMEN E4501: BMEN E4400: Note: A list of the approved history/theory Tissue engineering, I 3.0 points Wavelet applications in biomedical image and signal processing 3.0 points courses is available at the departmental 5. BMEN E4502: BMEN E4898: office each semester. Tissue engineering, II 3.0 points Phototonics 3.0 points 6. One from the following courses: BMEN E4410: Ultrasound in MINOR IN ART HISTORY BMEN E3320: diagnostic imaging 3.0 points Fluid biomechanics 3.0 points BMEN E4420: Biomedical signal processing 1–7. Seven courses in art history, covering BMEN E4570: Science and engineering and signal modeling 3.0 points four of the following areas: (a) ancient of body fluids 3.0 points 6. One from the following courses: Mediterranean, (b) medieval Europe, (c) ECBM E3060: Introduction to ELEN E3801: Renaissance and baroque, (d) 18th, 19th, genomic information 3.0 points Signals and systems 3.0 points and 20th century, and (e) non-Western. CHEN E3110: ELEN E4810: Transport phenomena, I 4.0 points Digital signal processing 3.0 points CHEN E4700: Principles of MINOR IN BIOMEDICAL ELEN E4830: genomic technologies 3.0 points Digital image processing 3.0 points ENGINEERING MSAE E3103: The Biomedical Engineering program Elements of materials science 3.0 points offers a minor in one of three tracks: (I) II. BIOMECHANICS TRACK MINOR IN CHEMICAL cellular engineering, (II) biomechanics, 3. BMEN E4300: ENGINEERING and (III) biomedical imaging. Students Solid biomechanics 3.0 points Of the six courses required, at least who wish to get a minor in biomedical three must have the CHEN, CHEE, engineering should take the core BME 4. BMEN E3320: Fluid biomechanics 3.0 points or CHAP designator: requirements, as well as select courses from one of the three tracks, described 5–6. Two from the following course groups: 1. CHEN E3100: Material and energy balances 4.0 points below. Participation in the minor is ENME E3113: subject to the approval of the major Mechanics of solids 3.0 points 2. CHEN E3010: Principles of chemical ENME E3161: program adviser. engineering thermodynamics 4.0 points Fluid mechanics 4.0 points or or

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190 MSAE E3111: Thermodynamics, Fluid mechanics 4.0 points 5. COMS W3203: kinetic theory, and statistical ENME E3114: Experimental Discrete mathematics 3.0 points mechanics 3.0 points mechanics of materials 4.0 points 6. COMS W3261: or MECE E3414: Advanced strength Computer science theory 3.0 points MECE E3301: of materials 3.0 points Thermodynamics 3.0 points ENME E4332: 7. CSEE W3827: Fundamentals of Finite element analysis, I 3.0 points computer systems 3.0 points 3. CHEN E3110: CIEN E3125: or Transport phenomena, I 4.0 points Structural design 3.0 points a 4000-level COMS technical elective or one of the following: CIEN E4241: Geotechnical EAEE E4900: Applied transport and engineering fundamentals 3.0 points chemical rate phenomena 3.0 points CIEE E3250: MINOR IN DANCE MECE E3100: Introduction to Hydrosystems engineering 3.0 points The SEAS dance minor consists of five mechanics of fluids 3.0 points CIEE E4163: Environmental 3-point courses. Please note that no ENME E3161: engineering: wastewater 3.0 points Fluid mechanics 4.0 points performance/choreography courses CIEN E3129: Project management below count toward the nontech 4. CHEN E4230: for construction 3.0 points requirement for SEAS students. Reaction kinetics and reactor design 3.0 points CIEN E4131: Principles of construction techniques 3.0 points 1–2. Two from the following history/criticism 5–6. Two courses from the following: courses: Any 3000-level or higher BMCH, CHEN, Note: At least three of the courses must DNCE BC 2565: World dance history CHAP, or CHEE course be courses that are not required in the DNCE BC 2566: Western theatrical dance APMA E3101: student’s major. from the Renaissance to Applied mathematics, I 3.0 points the 1960’s APMA E3102: DNCE BC2570: Dance in New York City MINOR IN COMPUTER Applied mathematics, II 3.0 points DNCE BC 3000: From the page to the BMEN E3320: SCIENCE dance stage Fluid biomechanics 3.0 points Students who pass the Computer DNCE BC 3570: Latin American and BMEN E4001: Science Advanced Placement Exam, Caribbean dance: Quantitative physiology, I 3.0 points either A or AB, with a 4 or 5 will receive identities in motion BMEN E4002: 3 points and exemption from COMS DNCE BC 3574: Seminar on contemporary Quantitative physiology, II 3.0 points W1004. An additional elective is to be choreographers and their ELEN E3201: works recommended but not required. Parti- Circuit analysis 3.5 points DNCE BC 3576: Dance criticism cipation in the minor is subject to the ELEN E3301: DNCE BC 3577: Performing the political Electronic circuits 3.0 points approval of the major program adviser. DNCE BC 3578: Traditions of African- SIEO W3600: Introduction to For further information, please see the American dance probability and statistics 4.0 points QuickGuide at www.cs.columbia. 3–4. Two from the following performance/ IEOR W4105: Probability 3.0 points edu/education/undergrad/seasguide. IEOR W4106: choreography courses: Stochastic models 3.0 points 1. COMS W1004: Introduction to computer DNCE BC 2555: Ensemble repertory: MSAE E3103: Elements of science and programming in Java 3.0 points modern DNCE BC 3571: Solo repertory materials science 3.0 points 2. COMS W1007: Object-oriented DNCE BC 2563: Dance composition: form MSAE E3142: Processing of programming and design 3.0 points DNCE BC 2564: Dance composition: content ceramics and polymers 3.0 points or DNCE BC 3565: Group forms: advanced COMS W1009: Introduction to dance composition computer science (honors) 3.0 points MINOR IN DNCE BC 2567: Music for dance CIVIL ENGINEERING 3. COMS W3133: DNCE BC 2557: Evolution of classic 1. CIEN E3121: Structural analysis 3.0 points Data structures in C 3.0 points Spanish dance or or DNCE BC 2580: Tap as an American art form ENME E3161: Fluid mechanics 4.0 points COMS W3134: DNCE BC 3590: Rehearsal and performance Data structures in Java 3.0 points in dance or or 5. One elective. MECE E3100: Introduction to mechanics of COMS W3137: Data structures fluids 3.0 points and algorithms 4.0 points or MINOR IN EARTH AND 2. ENME E3105: Mechanics 4.0 points COMS W3139: Data structures ENVIRONMENTAL 3. ENME E3113: and algorithms (honors) 4.0 points ENGINEERING Mechanics of solids 3.0 points 4. COMS W3157: 1–3. Three courses from the following: 4–6. Electives (any three) Advanced programming 4.0 points EAEE E3101: Earth resource CIEN E1201: Design of buildings, production systems 3.0 points bridges, and spacecraft 3.0 points EAEE E3103: Energy, minerals and ENME E3161: materials systems 3.0 points

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EAEE E3255: Environmental control and pollu- MINOR IN EAST ASIAN ECON W4457: Industrial organization of art, 191 tion reduction systems 3.0 points STUDIES entertainment and communi- EAEE E4003: Introduction to cations 1–5. Any two of the survey courses on Chinese, aquatic chemistry 3.0 points ECON W4465: Public economics Japanese, Korean, or Tibetan civilization EAEE E4004: Physical processing ECON W4480: Gender and applied (ASCE V2359, V2361, V2363, V2365), plus and recovery of solids 3.0 points economics three elective courses dealing with East EAEE E4006: Field methods for ECON W4490: Economics of the Internet Asia. The elective courses may be taken environmental engineering 3.0 points ECON W4500: International trade in departments outside of East Asian EAEE E4001: Industrial ecology ECON W4505: International monetary theory Languages and Cultures. The minor does of earth resources 3.0 points and policy not include a language requirement. EAEE E4160: Solids and ECON W4615: Law and economics However, one semester of an East Asian hazardous waste management 3.0 points ECON W4625: Economics of the environment language class may be used to fulfill one EAEE E4257: Environmental data ECON W4750: Globalization and its risks of the three electives, as long as at least analysis and modeling 3.0 points two semesters of that language have been EAEE E4361: Economics of Note: Electives may be taken only after taken. Placement exams may not be used Earth resource industries 3.0 points the completion of both ECON W3211 in place of these courses. EAEE E4150: Air pollution and W3213, with the exception of ECON prevention and control 3.0 points W2257, which may be taken after com- EAEE E4200: Production of MINOR IN ECONOMICS pletion of ECON W1105. Some of the inorganic materials 3.0 points 1. ECON W1105: Principles of economics elective courses listed above have addi- EAEE E4009: GIS for resource, tional prerequisites. Courses may be 2. ECON W3211: Intermediate microeconomics environment and infrastructure taken only after the completion of all management 3.0 points 3. ECON W3213: Intermediate macroeconomics prerequisites. Please see the Columbia EAEE E4560: Particle technology 3.0 points 4. ECON W3412: Introduction to econometrics College bulletin for course descriptions 4–6. Three courses from the following and complete lists of prerequisites. (other environmentally related courses Note: W1105 is a prerequisite for 7. One from the following statistics courses may also be approved): W3211, W3213, and W3412. Students (or sequence of courses): ECIA W4100: Management and must have completed Calculus I before STAT W1211: Introduction to statistics development of water systems 3.0 points taking W3213, Calculus III before taking SIEO W3600: Introduction to probability and CIEN E3141: W3211, and one of the introductory statistics Soil mechanics 3.0 points statistics courses (see list) before taking IEOR W3658: Probability CIEE E3250: W3412. and Hydrosystems engineering 3.0 points STAT W3659 or W4107: Statistical inference MECE E4211: Energy: sources 5–6. Two electives from the following: SIEO W4150: Introduction to probability and and conversion 3.0 points ECON W2257: Global economy statistics CIEN E4250: Waste containment ECON W4280: Corporate finance design and practice 3.0 points ECON V3025: Financial economics Notes: CIEE E4252: ECON V3265: Economics of money and • The statistics course must be finished Environmental engineering 3.0 points banking before taking ECON W3412, and it CIEE E4260: ECON W4020: Economics of uncertainty is recommended that students take Urban ecology studios 3.0 points and information ECON W3412 in the semester follow- CHEE E4252: Intro to surface and ECON W4080: Globalization, incomes and ing the statistics course. colloid chemistry 3.0 points inequality • Generally speaking, course work done CIEE E4257: Groundwater ECON W4211: Advanced microeconomics contaminant transport and ECON W4213: Advanced macroeconomics as part of the economics minor counts remediation 3.0 points ECON W4228: Urban economics toward fulfilling the School’s nontechni- CIEE E4163: Environmental ECON G4235: Historical foundations of cal requirements. However, ECON engineering: wastewater 3.0 points modern economics W3412: Introduction to econometrics, CHEN E4410: Environmental ECON W4251: Industrial organization which may be used as a course in the control technology 3.0 points ECON G4301: Economic growth and devel- minor program, may not be applied CHEN E3010: opment toward satisfaction of the nontechnical Principles of chemical engineering ECON W4321: Economic development course requirements; refer to the non- thermodynamics 3.0 points ECON W4329: Economics of sustainable technical section on pages 11–12 of this CHEN E3110: development bulletin for further details. Transport phenomena, I 4.0 points ECON W4345: World economic problems SIEO W3600: Introduction to ECON W4370: Political economy • Students with AP credit for economics probability and statistics 4.0 points ECON W4400: Labor economics and an exemption for ECON W1105 ECON W4412: Advanced econometrics may use the credit toward the minor. ECON W4415: Game theory • Transfer or study abroad credits may ECON W4438: Economics of race in the not be applied to fulfill the require- United States ments of the economics minor.

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192 MINOR IN ELECTRICAL MINOR IN ENGLISH AND MINOR IN GREEK OR LATIN ENGINEERING COMPARATIVE LITERATURE 1–4. A minimum of 13 points in the chosen 1. ELEN E1201: Introduction to electrical engi- 1–5. Any five courses in the English language at the 1200-level or higher. neering 3.5 points Department with no distribution require- 5. 3 points in ancient history of the appropri- (May be replaced by a similar course or ment. No speech courses, only one writ- ate civilization. roughly equivalent experience) ing course as above and excluding ENGL C1010, may be taken; total 15 points. 2. ELEN E3201: Circuit analysis 3.5 points MINOR IN HISPANIC STUDIES 3. CSEE W3827: Fundamentals of MINOR IN FRENCH 1. SPAN W3300: Advanced language computer systems 3.0 points through content 3.0 points 1–2. FREN W3333: 4. ELEN E3081 and ELEN E3082: Major literary works to 1800 3.0 points 2. SPAN W3330: Introduction to Electrical engineering labs 2.0 points and the study of Hispanic cultures 3.0 points FREN W3334: Major literary works 5. ELEN E3801: 3. SPAN W3349: Hispanic cultures, I: since 1800 3.0 points Signals and systems 3.5 points Islamic Spain through the colonial 6. ELEN E3106: Solid-state devices 3–5. Three additional courses in French period 3.0 points beyond satisfaction of the language and materials 3.5 points 4. SPAN W3350: Hispanic cultures, II: requirement, including one course or Enlightenment to the present 3.0 points ELEN E3401: Electromagnetics 4.0 points in French cultural studies. 5. One additional 3000- or 4000-level elective Note: Not available to computer engi- course in the Department of Spanish and neering majors. MINOR IN FRENCH AND Portuguese FRANCOPHONE STUDIES Note: Please see the director of under- Required: 15 points beyond second- MINOR IN ENGINEERING graduate studies in the Department of year French. MECHANICS Spanish and Portuguese for more infor- 1. ENME E3105: Mechanics 4.0 points 1–2. FREN W3420: Introduction to French mation. and francophone studies, I 3.0 points 2. ENME E3113: and Mechanics of solids 3.0 points FREN W3421: Introduction to French MINOR IN HISTORY 3. ENME E3161: and francophone studies, II 3.0 points 1–5. Minimum 15 points in the History Department with no distribution or Fluid mechanics 4.0 points 3–5. Three additional courses in French seminar requirements. Transfer or or beyond satisfaction of the language study-abroad credits may not be applied. MECE E3100: requirement, including one course Mechanics of fluids 3.0 points in French cultural studies and one in 4–6. Electives (any two): francophone literature. MINOR IN INDUSTRIAL ENME E3106: ENGINEERING Dynamics and vibrations 3.0 points MINOR IN GERMAN 1. SIEO W3600: Introduction to ENME E3114: Experimental probability and statistics 4.0 points mechanics of materials 4.0 points Required: 15 points beyond second- or year German. 2. IEOR E3608: Introduction to mathematical programming 4.0 points MECE E3414: Advanced strength 1. GERM V3001 or V3002: of materials 3.0 points Advanced German, I or II 3.0 points 3. IEOR E3402: Production-inventory CIEN E3121: planning and control 3.0 points Structural analysis 3.0 points 2. GERM W3333: Introduction to ENME E4202: German literature 3.0 points 4. IEOR E4003: Advanced mechanics 3.0 points Industrial economics 3.0 points 3–4. Any two of the period survey courses ENME E4113: Advanced mechanics in German literature and culture, GERM 5–6. Electives: Two IEOR courses of interest of solids 3.0 points W3442, W3443, W3444, W3445; at least and approved by a faculty adviser. ENME E4114: Mechanics of one of these must focus on pre–20th- fracture and fatigue 3.0 points century culture. Note: In addition to the required cours- ENME E4214: es, students majoring in operations Theory of plates and shells 3.0 points 5. One course taken from any 3000/4000 level research or engineering and manage- ENME E4215: German or CompLit-German courses ment systems minoring in industrial Theory of vibrations 3.0 points taught in German or English. engineering must take three industrial MECE E3301: Thermodynamics 3.0 points engineering courses that are not used to satisfy the requirements of their major. Note: At least three of the courses must be courses that are not required in the student’s major.

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MINOR IN MATERIALS MECE E3100: Introduction to MINOR IN MIDDLE EAST 193 SCIENCE AND ENGINEERING mechanics of fluids 3.0 points AND ASIAN LANGUAGES or one of the following: 1. MSAE E3103: AND CULTURES ENME E3161: Elements of materials science 3.0 points 1–5. Five courses, to be chosen with the approval Fluid mechanics 4.0 points of the MEALAC Director of Undergraduate 2–3. Two from the following courses: CHEN E3110: Studies; no elementary or intermediate MSAE E3111: Transport phenomena, I 4.0 points language courses may be taken. Thermodynamics, kinetic theory, and EAEE E4900: Applied transport and statistical mechanics 3.0 points chemical rate phenomena 3.0 points MSAE E3141: Processing of metals and ENME E3105: Mechanics 4.0 points MINOR IN MUSIC semiconductors 3.0 points MECE E3301: 1. MUSI V2318-V2319: Diatonic harmony MSAE E3142: Processing of Thermodynamics 3.0 points and counterpoint 6.0 points ceramics and polymers 3.0 points or one from the following: MSAE E4090: Nanotechnology 3.0 points CHEN E3010: Principles of chemical 2. MUSI V1312-V1313: MSAE E4101: Structural analysis engineering thermodynamics 4.0 points Introductory ear training 1.0 points of materials 3.0 points MSAE E3111: 3. MUSI V2314: Ear training, I 1.0 points MSAE E4206: Electronic and Thermodynamics, kinetic theory, magnetic properties of solids 3.0 points and statistical mechanics 3.0 points) 4. One course from the following: MSAE E4215: Mechanical behavior ENME E3113: MUSI V3128: History of Western of materials 3.0 points Mechanics of solids 3.0 points music I: Middle Ages to baroque 3.0 points MSAE E4250: MECE E3408: Computer graphics MUSI V3129: History of Western Ceramics and composites 3.0 points and design 3.0 points music II: classical to 20th century 3.0 points MECE E3311: Heat transfer 3.0 points 4–6. Three from the following courses 5–6. Any two electives at the 3000 or 4000 MECE E4608: (other materials-related courses may be level. See also the SEAS-approved non- Manufacturing processes 3.0 points acceptable): technical electives in music (page 15). MECE E3409: APPH E4100: Computer-aided design 3.0 points Quantum physics of matter 3.0 points Notes: EEME E3601: CHEE E4050: • Students must successfully place out Classical control systems 3.0 points Industrial and environmental of MUSI V1002: Fundamentals of electrochemistry 3.0 points 5–6. Electives: Two additional mechanical Western music (3.0 points). CHEE E4252: Introduction to surface engineering courses from either the • Requirement 4 and 5 must be com- and colloid chemistry 3.0 points above list or the following (not all cours- pleted to fulfill the nontechnical elective CHEE E4530: es in this list are given every year): requirement for graduation. Corrosion of metals 3.0 points MECE E3401: • Students are strongly encouraged to CHEE E4620: Introduction to Mechanics of machines 3.0 points take HUMA W1123: Masterpieces of polymer science 3.0 points MECE E4058: CHEN E4630: Mechatronics and embedded Western music (3.0 points) from the Polymer laboratory 3.0 points microcomputer control 3.0 points list of nontechnical electives. CHEM C3443-C3444: MECE E4100: Organic chemistry 3.5 points Mechanics of fluids 3.0 points MINOR IN ELEN E4411: MECE E4211: Energy: sources OPERATIONS RESEARCH Fundamentals of photonics 3.0 points and conversion 3.0 points ELEN E4301: Introduction to MECE E4212: 1. IEOR E3106: Stochastic models 3.0 points semiconductor devices 3.0 points Microelectromechanical systems 3.0 points 2. SIEO W3600: Introduction to ELEN E4944: Principles of device MECE E4302: probability and statistics 4.0 points microfabrication 3.0 points Advanced thermodynamics 3.0 points ENME E4113: MECE E4404: Lubrication theory 3. IEOR E3608: Introduction to Advanced mechanics of solids 3.0 points and design 3.0 points mathematical programming 4.0 points ENME E4114: Mechanics of MECE E4501: 4. IEOR E4404: Simulation 3.0 points fracture and fatigue 3.0 points Geometrical modeling 3.0 points MECE E4608: MECE E4502: Computational 5–6. Electives: Two IEOR courses of interest Manufacturing processes 3.0 points geometry for CAD/CAM 3.0 points and approved by a faculty adviser. IEOR MECE E4701: EEME E4601: E3402: Production-inventory planning Introductory biomechanics 3.0 points Digital control systems 3.0 points and control (3.0 points) is strongly MECE E4602: recommended. Introduction to robotics 3.0 points MINOR IN MECHANICAL Note: In addition to the required courses, MECE E4604: Product design for ENGINEERING manufacturability 3.0 points students majoring in industrial engineer- 1–4. Any four courses from the following MECE E4609: ing or engineering management systems (equivalent substitution courses require Computer-aided manufacturing 3.0 points must take three operations research the approval of the mechanical engineer- MECE E4610: Advanced courses that are not used to satisfy the ing program adviser): manufacturing processes 3.0 points requirements of their major.

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194 MINOR IN PHILOSOPHY MINOR IN RELIGION MINOR IN TECHNOLOGICAL 1–5. Any five courses in the Philosophy 1–5. Five courses (total 15 points), one of ENTREPRENEURSHIP Department with no distribution require- which must be at the 2000 level. Minimum: 15 points ment; total 15 points. See also the list 1–3. Required courses: of exceptions on page 17. MINOR IN SOCIOLOGY ENGI E2261: Introduction to Note: Please be aware that some philos- accounting and finance 3.0 points 1. SOCI W1000: The social world 3.0 points BUSI W3021: Marketing and ophy courses may not count as nontech- marketing management 3.0 points nical electives. Please refer to the listing 2. SOCI W2200: Evaluation of evidence 3.0 points IEOR E4998: Managing technological on page xx. innovation and entrepreneurship 3.0 points 3. SOCI W3000: Social theory 3.0 points 4–5. Electives (either two courses from list A MINOR IN POLITICAL SCIENCE 4–5. Any two 2000-, 3000-, or 4000-level or one course from list A and one from 1–2. Two from the following courses: courses offered by the Department of list B): W1201: Introduction to American Sociology; total 6 points. A. Engineering electives (at least one) government and politics 3.0 points Note: The year’s array of elective courses CHEN E4020: Protection of industrial and business property 3.0 points W1501: Comparative politics: can be found online in the Columbia an introduction 3.0 points CIEN E4136: Entrepreneurship in civil College or General Studies bulletin. W1601: Introduction to engineering and construction 3.0 points international politics 3.0 points COMS W4444: Programming and MINOR IN STATISTICS problem solving 3.0 points 3–5. Any three courses in the Political BMEN E3998: Projects in 1. STAT W1211: Science Department with no distribution biomedical engineering 3.0 points Introduction to statistics 3.0 points requirement; total 9 points. IEOR E4550: Entrepreneurial business 2. STAT W2110: creation for engineers 3.0 points MINOR IN PSYCHOLOGY Introduction to applied statistics 3.0 points ISME E4310: The manufacturing enterprise 3.0 points Five courses required, including PSYC 3. STAT W3105: Probability 3.0 points Either SCNC W3010: Science, technology, W1001 and courses in at least two of 4. STAT W3107: Statistical inference 3.0 points and society or URBS V3310: Science and the three groups listed below (for exam- technology in urban environments ple, you could select two courses from 5. STAT W4315: Linear regression 3.0 points (but not both) 3.0 points Group I and two from Group III along 6. One Statistics Department 4000-level B: Other electives (no more than one) with the required W1001); total 15 course, excluding STAT W4105, W4107, ECON W4280: points (minimum). W4150, and W4109. Corporate finance 3.0 points 1. PSYC W1001: The science of psychology Notes: IEOR W4308: Industrial budgeting and finance control 3.0 points 2–5. Any four courses from, at a minimum, • Students may substitute STAT two of the three groups below: W1111 or W4150 for W1211. • Well-prepared students may substi- I. PERCEPTION AND COGNITION tute additional 4000-level statistics Courses numbered in the 2200s, 3200s, or 4200s. Also PSYC W1420, W1480, or courses (to be taken after STAT W1490. W4315) for W1211 and/or W2110. • Students whose schedules do not II. PSYCHOBIOLOGY AND NEUROSCIENCE permit taking STAT W3105 or W3107 PSYC W1010: may substitute W4105 for W3105, Mind, brain, and behavior 3.0 points W4107 for W3107, or W4109 for Courses numbered in the 2400s, 3400s, or 4400s. Also PSYC W1440. both W3105 and W3107. Students may also substitute equivalent courses III. SOCIAL, PERSONALITY, AND ABNOR- from the IEOR Department with MAL: Courses numbered in the 2600s, approval of the Statistics Department 3600s, or 4600s. Also PSYC W1450 or director of undergraduate studies. W1455.

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196 TITLEINTERDISCIPLINARY ENGINEERING COURSES

f the following courses, some of contemporary technological innovations, stu- ee rights, confidential relationships, unfair compe- may be requirements for degree dents learn how science and technology fit into tition, trademarks, and the like. Principles of law programs, and others may be the bigger picture; i.e. how technologies techni- are illustrated by case studies. O cally develop from concept to diffusion into society, taken as electives. See your depart- how they work, and how they are bi-directionally IEOR E4998x and y Managing technological mental program of study or consult with related to social forces, cultural values, economic innovation and entrepreneurship an adviser for more information. trends, environmental factors, and political influ- Lect: 3. 3 pts. Professor McGourty. ences. An essential part of the course work is This course will focus on the management and ENGI E1102x and y Design fundamentals participation in a community-based learning proj- consequences of technology-based innovation. using advanced computer technologies ect, working with local nonprofit organizations. The course explores how new industries are cre- Lect: 4. 4 pts. Professor McGourty. ated, how existing industries can be transformed Core requirement for all entering SEAS students. EEHS E3900y History of telecommunications: by new technologies, the linkages between tech- Students learn the basics of engineering design from the telegraph to the Internet nological development and the creation of wealth from problem definition to detailed conceptual Lect: 3. 3 pts. Professors Schwartz and Nebeker. and the management challenges of pursuing design. Computer technologies such as advanced Historical development of telecommuncations strategic innovation. three-dimensional graphical and computational from the telegraphy of the mid-1800s to the applications are applied in the service of authentic Internet at present. Included are the technologies URBS V3310x Science and technology in community-based design projects, using the of telephony, radio, and computer communica- urban environments state-of-the-art design facility, the Botwinick tions. The coverage includes both the technolo- Lect: 3. 3 pts. Professors Cross and McGourty. Multimedia Learning Laboratory. Aligned with the gies themselves and the historical events that Prerequisite: Students must have declared their technical components of the design, students shaped, and in turn were shaped by, the tech- concentration/major. The course examines the develop collaboration, communication, problem nologies. The historical development, both the role of science and technology in urban settings, solving, and project management skills, as well as general context and the particular events con- using examples from modern cities. It explores a life-long orientation of social responsibility and cerning communications, is presented chronologi- how technology shapes towns and cities, and community service. Lab fee: $300. cally. The social needs that elicited new technolo- how urban environments—including politics, gies and the consequences of their adoption are economics, culture, and the natural environ- ENGI E2261x Introduction to accounting and examined. Throughout the course, relevant scien- ment—have influenced the development, accept- finance tific and engineering principles are explained as ance, and application of technology. An essential Lect: 3. 3 pts. Professor Webster. needed. These include, among others, the con- part of the course work is participation in a com- Prerequisite: ECON W1105. The concepts and cept and effective use of spectrum, multiplexing munity-based learning project, working with local methods underlying the financial statements of to improve capacity, digital coding, and network- nonprofit organizations. business corporations. Attention to problems of ing principles. There are no prerequisites, and asset valuation, income determination, cash no prior scientific or engineering knowledge is flows, and cost and profit behavior in response to required. SEAS students may not count this changes in the level of business activity. Analysis course as a technical elective. of selected corporate financial statements, capital structure, and leverage. Strategies and analytical ENGI/CHEN E4020x Safeguarding intellectual methods for the evaluation of capital projects. and business property Lect: 3. 3 pts. Professor Pearlman. SCNC W3010x and y Science, technology Designed for both University engineering students and society and engineers in industry to provide a broad Lect: 3. 3 pts. Professor McGourty. background in those aspects of the law that are Prerequisite: Students must have declared their most frequently encountered in a professional concentration/major. By investigating the scientific engineering career. Topics include patents, pro- and technical evolution and subsequent diffusion tection of know-how, contracts, employer-employ-

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his listing of courses has been BIOC C3501 Biochemistry: structure and reasonable breakage. In addition, stu- selected with specific engineering metabolism program requirements in mind. Lect: 3. Recit: 1. 4 pts. B. Stockwell and L. Tong. dents may be charged for lab handouts T Prerequisites: One year of college-level biology For information on these courses and and excessive breakage, for cleaning of and one year of organic chemistry, or the instruc- additional courses offered by these tor’s permission. Biochemistry, organic chemistry, equipment returned dirty, and for check- departments, please consult the bulletins and structural biology. Structure and function of ing out late. of Columbia College, the School of both proteins and small molecules in biological Continuing Education, the School of systems. The first half of the course covers pro- CHEM C1403x-C1404y General chemistry General Studies, and the Graduate tein structure and enzyme kinetics. The second Lect: 3.5 pts. L. Brus, R. Friesner, R. Gonzalez, G. Parkin, and J. Valentini. School of Arts and Sciences. half of the course will focus on the organic chem- istry involved in metabolic pathways. Only students with scheduling conflicts need report to the Chemistry Department (340 BIOLOGICAL SCIENCES Havemeyer) during registration. Preparation BUSINESS equivalent to one year of high school chemistry is BIOL C2005x Introductory biology, I: biochem- assumed and concurrent registration in MATH istry, genetics, and molecular biology BUSI W3021x and y Introduction to V1101. Students lacking such preparation should Lect: 3. Recit: 2. 4 pts. L. Chasin and marketing management plan independent study of chemistry over the D. Mowshowitz. 3 pts. Instructor to be announced. summer or take CHEM F0001 before taking Prerequisite: One year of college chemistry, or a No previous background in marketing is required C1403. Topics include stoichiometry, states of strong high school chemistry background. for the course. Introduction to the basic concepts matter, chemical equilibria, acids and bases, Recommended introductory biology course for of marketing. Students develop an understanding chemical thermodynamics, nuclear properties, biology and related majors and for premedical of, and the decision-making capabilities for, for- electronic structures of atoms, periodic properties, students. Fundamental principles of biochemistry, mulating marketing strategies for the complex chemical bonding, molecular geometry, introduc- molecular biology, and genetics. situations that characterize real-life marketing tion to organic and biological chemistry, solid- problems. state and materials science, polymer science and BIOL C2006y Introductory biology, II: cell biol- macromolecular structures, chemical kinetics, coordination chemistry, and electrochemistry. ogy, development, and physiology CHEMISTRY Lect: 3. Recit: 2. 4 pts. D. Mowshowitz. Although C1403 and C1404 are separate cours- es, students are expected to take the two terms Prerequisite: ENVB W2001 or BIOL C2005 or the Courses of Instruction instructor’s permission. The recommended sec- sequentially. The order of presentation of the top- ond term of biology for biology and related majors Pre-engineering students should refer to ics may differ from the order presented here and and for premedical students. Cellular biology and the First Year–Sophomore Program to from year to year. Recitation section required. development; physiology of cells and organisms. determine the chemistry requirements for admission to particular Junior-Senior CHEM C1500x or y General chemistry laboratory BIOL W2501x or y Contemporary biology Programs. Special attention should be Lab: 3 pts. S. Hansen and J. Ulichny. Prerequisite or corequisite: CHEM C1403. Fee laboratory given to the requirements for admission $140. An introduction to basic techniques of mod- Lab: 4. 3 pts. C. Hazen. to chemical engineering, biomedical Each section limited to twenty-four students. Early ern experimental chemistry, including quantitative engineering, materials science and met- registration is advised. Students must come to the procedures and chemical analysis. first day of class to secure their place. Strongly allurgical engineering, and other related recommended prerequisite or required corequi- fields. CHEM C1604x Second semester general site: BIOL C2005 or F2401. Laboratory fee: $150. chemistry (intensive) Emphasis on experimental techniques and data Laboratory Fee Lect: 3.5 pts. G. Flynn analysis in a variety of biological disciplines. Prerequisite: A grade of B or better in CHEM The laboratory fee covers the cost of C1403 or F1403 or acceptable performance on nonreturnable items, chemicals, and the department placement exam. Corequisite:

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198 MATH V1102. Topics include gases (kinetic theory statistical mechanics of chemical systems and the CHEM C3546y Advanced organic chemistry of gases); binary collision model for chemical connection of statistical mechanics to thermody- (laboratory) reactions; chemical kinetics; acid-base equilibria; namics. Recitation section required. Lab: 3 pts. A. Ghurbanyan. thermochemistry (thermodynamics I); spontaneous Prerequisite: CHEM C3543 or C3545. processes (thermodynamics II); chemical bonding CHEM C3085x-C3086y Physical and analytical Corequisite: C3444. Laboratory fee: $125. in polyatomic molecules. Recitation section required. chemistry laboratory A project laboratory with emphasis on complex Lab: 4 pts. L. Avila. synthesis and advanced techniques, including CHEM C2507y Intensive general chemistry Prerequisite or corequisite: CHEM C3079-C3080. qualitative organic analysis and instrumentation. laboratory C3085 is prerequisite to C3086. Fee: $125 per Lab: 3 pts. L. Avila. term. Techniques of experimental physical chem- Prerequisite: CHEM C1604 or C3045 and the istry and instrumental analysis, including infrared EARTH AND ENVIRONMENTAL instructor’s permission. Fee: $140. An introduc- and ultraviolet spectrophotometry, magnetic reso- SCIENCES tion to basic techniques and practices of modern nance, electroanalytical methods, calorimetry, Undergraduates in the four-year course experimental chemistry, including qualitative pro- reaction kinetics, hydrodynamic methods, and of study in the School of Engineering cedures and chemical analysis. This course applications of digital computers to the analysis and Applied Science may take courses differs from CHEM C1500 in its emphasis on of experimental data. numbered to 4999 but may enter courses instrumentation and methods. of higher numbers only if CHEM C3098x and y Supervised independent CHEM C3045x-C3046y Intensive organic research (1) the course is expressly included in chemistry for first-year students (lecture) Lab: 4 pts. J. Valentini. the prescribed curriculum or Lect: 3.5 pts. R. Breslow and J. Leighton. Prerequisite: Tthe permission of the professor in (2) special permission is obtained from Prerequisite: A grade of 5 on the Chemistry charge for entrance, and the permission of the the Department of Earth and Advanced Placement Examination and an accept- departmental representative for aggregate points Environmental Sciences. able grade on the department placement exam. in excess of 12 or less than 4. Laboratory fee: Not open to students who have taken other courses $105 per term. This course may be repeated for EESC V1011x Earth, origin, evolution, in college-level chemistry. Premedical students credit (see major and concentration require- processes, future may take CHEM C3045, C3046, and C3545 to ments). Individual research under the supervision Lect: 3. Lab: 3.4 pts. Professors Mutter and Nettles. meet the minimum requirements for admission to of a member of the staff. Research areas include Students who wish to take only the lectures medical school. This course covers the same organic, physical, inorganic, analytical, and bio- should register for EESC V1411. What is the material as CHEM C3443-C3444 but is intended logical chemistry. nature of our planet and how did it form? From for students who have learned the principles of geochemical and geophysical perspectives we general chemistry in high school. The level of CHEM C3443x-C3444y Organic chemistry explore Earth’s internal structure, its dynamical instruction will be appropriate for those who have (lecture) character expressed in plate tectonics, and ask not had a college course in general chemistry. Lect: 3.5 pts. D. Sames and S. Snyder. if its future behavior can be known. Students enrolled in CHEM C3045-C3046 are Prerequisites: CHEM C1404 (or C1604) and expected to enroll concurrently in CHEM C2507, C1500 or their equivalents. The principles of EESC V1030x Oceanography the intensive general chemistry laboratory course. organic chemistry. The structure and reactivity of 3 pts. Professor Hoenisch. Recitation section required. organic molecules are examined from the stand- Explore the geology of the sea floor, understand point of modern theories of chemistry. Topics what drives ocean currents and how ocean CHEM C3071y Introduction to inorganic include stereochemistry, reactions of organic mol- ecosystems operate. Case studies and discus- chemistry ecules, mechanisms of organic reactions, synthe- sions centered on ocean-related issues facing Lect: 3 pts. Not given in 2009–2010. ses and degradations of organic molecules, and society. Prerequisite: CHEM C3444 (or F3444) or C3046. spectroscopic techniques of structure determina- Principles governing the structure and reactivity of tion. Recitation section required. EESC V1201y Environmental risks and inorganic compounds surveyed from experimental disasters and theoretical viewpoints. Topics include inor- CHEM C3543x and y Organic chemistry 3 pts. Professor Ekstrom. ganic solids, aqueous and nonaqueous solutions, (laboratory) Prerequisites: High-school science and mathe- the chemistry of selected main group elements, Lab: 3 pts. A. Ghurbanyan. matics. An introduction to risks and hazards in the transition metal chemistry, metal clusters, metal Prerequisite: CHEM C1500. Corequisite: CHEM environment. Different types of hazards are ana- carbonyls, and organometallic chemistry. C3443. Students planning to take a full year of lab- lyzed and compared: natural disasters, such as oratory should enroll in CHEM C3543 and C3546. tornados, earthquakes, and meteorite impacts; CHEM C3079x-C3080y Physical chemistry, Laboratory fee: $125. Techniques of experimental acute and chronic health effects caused by expo- I and II organic chemistry, with emphasis on understanding sure to radiation and toxic substances such as Lect: 4 pts. A. Cacciuto and D. Reichman. fundamental principles underlying the experiments radon, asbestos, and arsenic; long-term societal Prerequisites: CHEM C1403-C1404 or C3045- and methodology of solving laboratory problems effects due to environmental change, such as C3046; PHYS C1401-C1402, or the equivalent; involving organic molecules. sea level rise and global warming. Emphasizes MATH V1101-V1102 or V1207-V1208. the basic physical principles controlling the haz- Recommended parallel: CHEM C3085-C3086. CHEM C3545x Organic chemistry (laboratory) ardous phenomena and develops simple quantita- Elementary but comprehensive treatment of the Lab: 3 pts. A. Ghurbanyan. tive methods for making scientifically reasoned fundamental laws governing the behavior of indi- Prerequisites: CHEM C3045, C3046, and C2407. assessments of the threats (to health and wealth) vidual atoms and molecules and collections of Laboratory fee: $125. The course covers the same posed by various events, processes, and expo- them. C3079: The thermodynamics of chemical material as CHEM C3543, but is intended for those sures. Discusses methods of risk mitigation systems at equilibrium and the chemical kinetics students who have taken CHEM C3045-C3046. and sociological, psychological, and economic of nonequilibrium systems. C3080: The quantum aspects of risk control and management. mechanics of atoms and molecules, the quantum

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EESC W3018y Weapons of mass destruction EESC W4085x Geodynamics sphere; chemistry of precipitation, weathering 199 3 pts. Professor Richards. 3 pts. Offered in alternate years. Professor Buck. reactions, rivers, lakes, estuaries, and ground- Prerequisite: one semester of a lab science or Prerequisites: Calculus, differential equations, intro- waters; stable isotopes and radioactive tracers permission of the instructor. A review of the history ductory physics. Physical processes that control of transport processes in continental waters. and environmental consequences of nuclear, plate tectonics and the evolution of planetary interi- chemical, and biological weapons of mass ors and surfaces; analytical descriptions of these EESC W4924y Introduction to atmospheric destruction (WMD); of how these weapons work, processes; weekly physical model demonstrations. chemistry what they cost, how they have spread, how they 3 pts. Offered in alternate years. Professor Shindell. might be used, how they are currently controlled EESC W4113x Introduction to mineralogy A survey of trace gas photochemistry important by international treaties and domestic legislation, 3. Lab: 3. 4 pts. Offered in alternate years. in the Earth’s atmosphere. Major topics are com- and what issues of policy and technology arise in Professor Walker. position, including biogenic and anthropogenic current debates on WMD. What aspects of the Prerequisites: Introductory geology or the equiva- inputs, and chemical processes, including reaction manufacture of WMD are easily addressed, and lent and elementary college physics and chem- kinetics and photochemistry. Specific applications what aspects are technically challenging? It may istry, or the instructor’s permission. Elementary to tropospheric air quality, including smog, be expected that current events/headlines will be crystallography and crystal structures, optical acid rain, and stratospheric ozone, including discussed in class. properties of minerals, mineral associations and the Antarctic ozone hole, are covered, with an phase equilibria, economic minerals. Laboratory: emphasis on the response to anthropogenic EESC W4001x Advanced general geology identification of minerals in hand specimens, pollutants and climate change. 3 pts. Lab: 3. 4 pts. Professors Scholz and Anders. chemical and physical tests, and use of the Prerequisite: One semester of college-level calcu- petrographic microscope. EESC W4925x Principles of physical lus, physics, and chemistry. Fee: $35. A concen- oceanography trated introduction to the solid Earth, its interior, EESC W4230y Crustal deformation 3 pts. Professor Gordon. and near-surface geology. Intended for students 3 pts. Professors Anders and Scholz. Recommended preparation: A solid background in with good backgrounds in the physical sciences Prerequisites: Introductory geology and one year mathematics, physics, and chemistry. Physical but none in geology. Laboratory and field trips. of calculus. Recommended preparation: higher properties of seawater, water masses and their dis- levels of mathematics. Introduction to the tribution, sea-air interaction influence on the ocean EESC W4008x Introduction to atmospheric deformation processes in the Earth’s crust. structure, basic ocean circulation pattern, relation science Fundamental theories of stress and strain; rock of diffusion and advection with respect to distribu- Lect: 3. 3 pts. Professor Del Genio. behavior in both brittle and ductile fields; earth- tion of ocean properties, and introduction to ocean Prerequisite: Advanced calculus and general quake processes; ductile deformation; large-scale dynamics. physics, or the instructor’s permission. Basic crustal contractional and extensional events. physical processes controlling atmospheric EESC W4926y. Principles of chemical structure: thermodynamics; radiation physics EESC W4300x The Earth’s deep interior oceanography and radiative transfer; principles of atmospheric 3 pts. Professor Ekstrom. 3 pts. Offered in alternate years. dynamics; cloud processes; applications to Prerequisites: Calculus, differential equations, Professors Anderson and Hoenisch. Earth’s atmospheric general circulation, climatic one year of college physics, and EESC W4950 or Recommended preparation: A solid background variations, and the atmospheres of the other planets. its equivalent. An introduction to properties of the in mathematics, physics, and chemistry. Given in Earth’s mantle, fluid outer core, and solid inner alternate years. Factors controlling the concentra- EESC W4009x. Chemical geology core. Current knowledge of these features is tion and distribution of dissolved chemical species 4 pts. Offered in alternate years. Professor Walker. explored, using observations of seismology, heat within the sea. Application of tracer and natural Prerequisite: Physical chemistry or the instructor’s per- flow, gravity, and geomagnetism, plus information radioisotope methods to large-scale mixing of the mission. Thermodynamics as applied to earth systems. on the Earth’s bulk composition. ocean, the geological record preserved in marine sediments, the role of ocean processes in the EESC W4050x Global assessment and EESC W4701x or y. Introduction to igneous global carbon cycle, and biogeochemical processes monitoring using remote sensing petrology influencing the distribution and fate of elements in 3 pts. Offered in alternate years. Professor Small. 4 pts. Offered in alternate years. Professor the ocean. Prerequisite: permission of the instructors. Kelemen. Recommended preparation: some college-level Prerequisites: EESC V1011-V1012 or the equiva- EESC W4930y Earth’s oceans and atmosphere physics or math. Enrollment limited to 24 stu- lent. Recommended preparation: EESC W4113 3 pts. Professor Gordon. dents. General introduction to fundamentals of and knowledge of chemistry. Fee: $15. Students Recommended preparation: A good background remote sensing and image processing. Example not enrolled in terrestrial geology may elect to in the physical sciences. Physical properties of applications in the Earth and environmental write a substantial term paper in lieu of the labo- water and air. Overview of the stratification and sciences are explored through the analysis of ratory course. Compositional characteristics of circulation of Earth’s oceans and atmosphere and remote sensing imagery in a state-of-the-art igneous and metamorphic rocks and how they their governing processes; ocean-atmosphere visualization laboratory. Lab required. can be used as tools to investigate earth processes. interaction; resultant climate system; natural and Development of igneous and metamorphic rocks anthropogenic forced climate change. EESC W4076y Geologic mapping in a plate-tectonic framework. 3 pts. Professors Walker and Anders. EESC W4941x or y Principles of geophysics Field work on weekends in April and for two EESC W4885y The chemistry of continental 3 pts. Offered in alternate years. Instructor to be weeks in mid-May, immediately following the end waters announced. of examinations. Estimated expenses: $250. The 3 pts. Offered in alternate years. Instructors to Prerequisite: Calculus through MATH V1202 principles and practice of deciphering geologic be announced. and physics through PHYS C1007. The structure history by observing rocks in the field, making Recommended preparation: A solid background and properties of the Earth as inferred from geological maps, constructing geological cross- in basic chemistry. Introduction to geochemical geophysical investigations: gravity, isostasy, sections, and writing short reports. cycles involving the atmosphere, land, and bio- earthquakes, seismic exploration, geomagnetism,

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200 marine geophysics, satellite observations, tides. allocation of resources, and the circumstances a limited number of monuments and artists rang- Recommended for nongeophysics majors or under which it does so efficiently. Why such an ing from early Athens to the present, the course those with little previous geophysics background. economy has fluctuations and how they may be focuses on the formal structure of works of archi- controlled. tecture, sculpture, painting, and other media, EESC W4947y Plate tectonics as well as the historical contexts in which these 3 pts. Professor Abers. ENGL C1010x or y University writing works were made and understood. Prerequisites: Physical geology. Prepares students 3 pts. The staff. for research and oral exams. Evolution of the Teaches general techniques and strategies for HUMA W1123x or y Masterpieces of Western interiors and surfaces of Earth, Venus, Mars and academic reading and writing. Students read and music the moons of Jupiter. Planetary accretion, tidal discuss a range of published essays, complete 3 pts. heating, convection, magma oceans, formation of regular reading and writing exercises, write several Popularly known as “Music Hum,” this course continents, mantle plumes, sea-floor spreading, longer essays, and undertake a collaborative aims to instill in students a basic comprehension kinematics of triple junctions, surface repaving, research and writing project designed by the of the many forms of the Western musical imagi- subduction, sedimentation, catastrophic impacts class. Students placed in C1010 whose names nation. The course involves students actively in and floods, and the building of mountain chains. fall in the first part of the alphabet must take the the process of critical listening, both in the class- course in the fall. Students whose names fall in room and in concerts. Although not a history of EESC W4949x Introduction to seismology the second part of the alphabet take the course in Western music, the course is taught in chronolog- 3 pts. Offered in alternate years. Professors the spring. The alphabet will be split somewhere ical format and includes masterpieces by Josquin Ekstrom and Menke. between K and O. The exact place for the split des Prez, Monteverdi, Bach, Handel, Mozart, Prerequisites: Elementary college physics and will be posted before fall registration. Haydn, Beethoven, Verdi, Wagner, Schoenberg, mathematics (including calculus). Basic methods Stravinsky, Louis Armstrong, and Duke Ellington, of seismogram analysis. Classification of seismic Global Core among others. waves and elementary theory of body waves and The Global Core requirement consists of courses normal modes. Elementary aspects of seismic that examine areas not the primary focus of prospecting, earthquake source theory, instru- Literature Humanities and Contemporary MATHEMATICS mentation, discrimination between explosions and Civilization and that, like other Core courses, are earthquakes, inversion of seismic data to infer broadly introductory, interdisciplinary, and tempo- Courses for First-Year Students Earth structure, earthquake engineering, earth- rally or spatially expansive. Courses in the Global Depending on the program, completion quake insurance and hazards mitigation, estima- Core are organized around a set of primary texts of Calculus III or IV satisfies the basic tion of seismic risk, and earthquake prediction. or artifacts, which may range from texts of literate mathematics requirement. Normally stu- traditions to media (e.g. film), ritual performances dents who have taken an AP Calculus or oral sources, produced in the regions of the course begin with either Calculus II or HUMANITIES AND world in question. Global Core courses fall into SOCIAL SCIENCES two categories: those that focus on a specific cul- Calculus III. Refer to the AP guidelines For listings of additional courses of inter- ture or civilization, tracing its appearance and/or on page 14 for placement information. est to engineering students, consult existence across a significant span of time and The sequence ends with MATH E1210: sometimes across more than one present-day the bulletins of Columbia College; the Ordinary differential equations. country or region; and those that address several School of General Studies; the Graduate Students who wish to transfer from world settings or cultures comparatively (and may one calculus course to another are School of Architecture, Planning, and include Europe and the West), in terms of a com- allowed to do so beyond the date speci- Preservation; the Graduate School of mon theme, a set of analytic questions, or inter- Business; and the Graduate School of actions between different world regions. Students fied on the Academic Calendar. They are Arts and Sciences. must complete two courses from the Global Core considered to be adjusting their level, List of Approved Courses for a letter grade. not changing their program. They must, COCI C1101-C1102 Introduction to contempo- however, obtain the approval of the new rary civilization in the West HUMA C1001x-C1002y Masterpieces of instructor and the Center for Student 4 pts. Western literature and philosophy Advising before reporting to the 4 pts. Taught by members of the Departments of Registrar. Anthropology, Architecture, Classics, English and Taught by members of the Departments of Classics, English and Comparative Literature, French, Comparative Literature, French, German, History, MATH V1101 Calculus I Italian, Journalism, Middle East and Asian German, Italian, Middle East and Asian Languages Lect: 3 pts. Languages and Cultures, Philosophy, Political and Cultures, Philosophy, Religion, Slavic Functions, limits, derivatives, introduction to Science, Religion, Slavic Languages, Sociology, Languages, and Spanish; and members of the integrals. and Spanish; members of the Society of Fellows Society of Fellows in the Humanities. Major works in the Humanities; and Senior Scholars. Major by over twenty authors, ranging in time, theme, MATH V1102 Calculus II works by over twenty authors, ranging from Plato and genre from Homer to Virginia Woolf. Students Lect. 3 pts. to modern writers. Students are expected to write are expected to write at least two papers, to Prerequisite: Calculus I or the equivalent. at least three papers, to complete two examina- complete two examinations each semester, and Methods of integration, applications of integrals, tions each semester, and to participate actively in to participate actively in class discussions. series, including Taylor’s series. class discussions. HUMA W1121x or y Masterpieces of Western art MATH V1201 Calculus III ECON W1105x or y Principles of economics 3 pts. Lect. 3 pts. 4 pts. Recitation section required (W1155). Popularly known as “Art Hum,” this course Prerequisite: Calculus II or the equivalent. Vector How a market economy determines the relative teaches students how to look at, think about, and algebra, complex numbers and exponential, prices of goods, factors of production, and the engage in critical discussion of the visual arts. Not a historical survey, but an analytical study of vector differential calculus.

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MATH V1202 Calculus IV MATH W4032x Fourier analysis currents, magnetic fields, alternating currents, 201 Lect: 3 pts. Lect: 3 pts. M. Lipyanskiy. electromagnetic waves, polarization, geometrical Prerequisite: Calculus II and III. Multiple integrals, Prerequisite: MATH V1201 and linear algebra, optics, interference and diffraction. line and surface integrals, calculus of vector or MATH V1202. Fourier series and integrals, dis- fields, Fourier series. crete analogues, inversion and Poisson summa- PHYS C1403x Introduction to classical and tion, formulae, convolution, Heisenberg uncertainty quantum waves MATH V1207x-V1208y Honors math A-B principle. Emphasis on the application of Fourier Lect: 3 pts. Professor Brooijmans. Lect. and recit. 4 pts. M. Thaddeus. analysis to a wide range of disciplines. Prerequisite: PHYS C1402. Corequisite: MATH Prerequisite: Score of 5 on the Advanced V1201 or the equivalent. Classical waves and the Placement BC calculus exam. The second term of MATH W4041x-W4642y Introduction to wave equation, Fourier series and integrals, nor- this course may not be taken without the first. modern algebra mal modes, wave-particle duality, the uncertainty Multivariable calculus and linear algebra from a Lect: 3 pts. P. Gallagher. principle, basic principles of quantum mechanics, rigorous point of view. The second term of this course may not be taken energy levels, reflection and transmission coeffi- without the first. Prerequisite: MATH V1202 and cients, applications to atomic physics. MATH E1210x or y Ordinary differential V2010 or the equivalent. Groups, homomor- equations phisms, rings, ideals, fields, polynominals, and PHYS C1493x Introduction to experimental Lect: 3 pts. T. Perutz. field extensions. Galois theory. physics Prerequisite: MATH V1201 or the equivalent. Lab and lecture: 3 pts. Lect: Tues., 3:10–4:00 p.m. Special differential equations of order one. MATH W4061x-W4062y Introduction to Lab: 3 hours weekly to be arranged. Instructor to Linear differential equations with constant and modern analysis be announced. variable coefficients. Systems of such equations. Lect: 3 pts. D. De Silva. Prerequisites: PHYS C1401 and C1402. Transform and series solution techniques. The second term of this course may not be taken Laboratory work associated with the two prerequi- Emphasis on applications. without the first. Prerequisite: MATH V1202 or site lecture courses. Experiments in mechanics, the equivalent. Real numbers, metric spaces, thermodynamics, electricity, magnetism, optics, MATH V2010 x and y Linear algebra elements of general topology. Continuous and and wave motion. (Students cannot receive credit Lect: 3 pts. differentiable functions. Implicit functions. for both PHYS C1493 and C1494.) Prerequisite: MATH VI201 or the equivalent. Integration, change of variables. Function spaces. Vector spaces, linear transformations, matrices, Further topics chosen by the instructor. PHYS C1494y Introduction to experimental quadratic and hermitian forms, reduction to physics canonical forms. MATH W4065x Honors complex variables Lab and lecture: 3 pts. Lect: Tues., 3:10–4:00 p.m. Lect: 3 pts. K. Tignor. Lab: 3 hours weekly to be arranged. Instructor to MATH V2500y Analysis and optimization Prerequisite: MATH V1207, V1208, or W4061. be announced. Lect: 3 pts. H. Pinkham. A theoretical introduction to analytic functions. Prerequisites: PHYS C1401, C1402, and C1403. Prerequisites: MATH V1102 and V1201 or the Holomorphic functions, harmonic functions, power Laboratory work associated with the three prereq- equivalent, and MATH V2010. Mathematical series, Cauchy-Riemann equations, Cauchy’s uisite lecture courses. Experiments in mechanics, methods for economics. Quadratic forms, integral formula, poles, Laurent series, residue thermodynamics, electricity, magnetism, optics, Hessian, implicit functions. Convex sets, convex theorem. Other topics as time permits: elliptic wave motion, atomic and nuclear physics. functions. Optimization, constrained optimization, functions, the gamma and zeta functions, the (Students cannot receive credit for both PHYS Kuhn-Tucker conditions. Elements of the calculus Riemann mapping theorem, Riemann surfaces, C1493 and C1494.) of variations and optimal control. Nevanlinna theory. PHYS C1601x Physics, I: mechanics and MATH V3007y Complex variables relativity PHYSICS Lect: 3 pts. Chiu-chu Liu. Lect: 3.5 pts. Rec: 1 hour weekly to be arranged. Prerequisite: MATH V1202. An elementary course The general four-term pre-engineering Professor Christ. in functions of a complex variable. Fundamental physics sequence consists of PHYS Corequisite: MATH V1102 or the equivalent. properties of the complex numbers, differentiability, C1401, C1402, C1403, and C1494 Fundamental laws of mechanics, kinematics and Cauchy-Riemann equations, Cauchy integral (laboratory); or PHYS C1601, C1602, dynamics, work and energy, rotational dynamics, oscillations, gravitation, fluids, introduction to spe- theorem, Taylor and Laurent series, poles, and C2601, and C2699 (laboratory). essential singularities. Residue theorem and cial relativity and relativistic kinematics. The course conformal mapping. is preparatory for advanced work in physics and PHYS C1401x Introduction to mechanics and related fields. thermodynamics MATH V3027x Ordinary differential equations Lect: 3 pts. Professors Dodd and Hughes. PHYS C1602y Physics, II: thermodynamics, Lect: 3 pts. P. Daskalopoulos. Corequisite: MATH V1101 or the equivalent. electricity, and magnetism Prerequisite: MATH V1201 or the equivalent. Fundamental laws of mechanics, kinematics and Lect: 3.5 pts. Professor Weinberg. Equations of order one, linear equations, series dynamics, work and energy, rotational dynamics, Prerequisite: PHYS C1601. Corequisite: MATH solutions at regular and singular points, boundary oscillations, gravitation, fluids, temperature and V1201 or the equivalent. Temperature and heat, value problems. Selected applications. heat, gas laws, the first and second laws of ther- gas laws, the first and second laws of thermody- modynamics. MATH V3028y Partial differential equations namics, kinetic theory of gases, electric fields, direct currents, magnetic fields, alternating Lect: 3 pts. P. Daskalopoulos. PHYS C1402y Introduction to electricity, currents, electromagnetic waves. The course Prerequisite: MATH V3027 or the equivalent. magnetism, and optics is preparatory for advanced work in physics and Introduction to partial differential equations. Lect: 3 pts. Professors Dodd and Hughes. related fields. First-order equations. Linear second-order equa- Prerequisite: PHYS C1401. Corequisite: MATH tions, separation of variables, solution by series V1102 or the equivalent. Electric fields, direct expansions. Boundary value problems.

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202 PHYS C2601x Physics, III: classical and to Lagrange’s formulation of mechanics, coupled PHYS G4019x Mathematical methods of quantum waves oscillators, and normal modes. physics Lect: 3.5 pts. Rec: 1 hour weekly to be arranged. Lect: 3 pts. Professor Halpin-Healy. Professor Kim. PHYS W3007y Electricity and magnetism Prerequisite: Differential and integral calculus. Prerequisite: PHYS C1602 or C1402. Corequisite: Lect: 3 pts. Professor Nicolis. Highlights of complex analysis, differential equa- MATH V1202 or the equivalent. Classical waves Prerequisite: General physics; differential and tions, integral equations, Green’s functions, and the wave equation, geometrical optics, inter- integral calculus. Electrostatics and magnetostat- special functions, Fourier and other transforms, ference and diffraction, Fourier series and inte- ics, Laplace’s equation and boundary-value prob- approximation methods, group theory and repre- grals, normal modes, wave-particle duality, the lems, multipole expansions, dielectric and mag- sentations, differential geometry and manifolds. uncertainty principle, basic principles of quantum netic materials, Faraday’s law, AC circuits, Emphasis is placed on applications to physical mechanics, energy levels, reflection and transmis- Maxwell’s equations, Lorentz covariance, and spe- problems. sion coefficients, the harmonic oscillator. The cial relativity. course is preparatory for advanced work in PHYS G4021x-G4022y Quantum mechanics, physics and related fields. PHYS W3008x Electromagnetic waves I and II and optics Lect: 3 pts. Professor Mueller. PHYS C2699y Experiments in classical and Lect: 3 pts. Professor Marka. Prerequisite: PHYS C2601 or C2802, or the modern physics Prerequisite: PHYS W3007. Maxwell’s equations equivalent. The formulation of quantum mechan- Lab and lecture: 3 pts. Lect: Tues., 3:10–4:00 p.m. and electromagnetic potentials, the wave equa- ics in terms of state vectors and linear operators, Lab: 3 hours weekly to be arranged. Instructor to tion, propagation of plane waves, reflection and three-dimensional spherically symmetric poten- be announced. refraction, geometrical optics, transmission lines, tials, the theory of angular momentum and spin, Prerequisites: PHYS C1601 (or C1401), C1602 wave guides, resonant cavities, radiation, interfer- time-independent and time-dependent perturba- (or C1402), and C2601. Laboratory work associ- ence of waves, and diffraction. tion theory, scattering theory, identical particles. ated with the three prerequisite lecture courses. Selected phenomena from atomic physics, Experiments in mechanics, thermodynamics, PHYS W3081x or y Intermediate laboratory work nuclear physics, and elementary particle physics electricity, magnetism, optics, wave motion, Lab: 2 pts. Professors May and Aprile. are described and then interpreted using quantum atomic and nuclear physics. Primarily for junior and senior physics majors. mechanical models. Other majors require the instructor’s permission. PHYS C2801x-C2802y Accelerated physics, May be repeated for credit by performing different PHYS G4023x Thermal and statistical physics I and II experiments. The laboratory has 13 individual Lect: 3 pts. Professor Heinz. Lect: 4.5 pts. Rec: 1 hour weekly to be arranged. experiments available, of which two are required Prerequisite: PHYS G4021 or the equivalent. Professor Cole. per 2 points. Each experiment is chosen by the Thermodynamics, kinetic theory, and methods Prerequisite: Advanced placement in physics and student in consultation with the instructor. Each of statistical mechanics; energy and entropy; mathematics, or the equivalent, and the instruc- section meets one afternoon per week, with regis- Boltzmann, Fermi, and Bose distributions; ideal tor’s permission. (A special placement meeting is tration in each section limited by the laboratory and real gases; blackbody radiation; chemical held during Orientation.) This accelerated two- capacity. Experiments (classical and modern) equilibrium; phase transitions; ferromagnetism. semester sequence covers the subject matter of cover topics in electricity, magnetism, optics, PHYS C1601, C1602, and C2601 and is intended atomic physics, and nuclear physics. PHYS G4040x General relativity for students who have an exceptionally strong Lect: 3 pts. Not given in 2009–2010. background in both physics and mathematics. PHYS W3083y Electronics laboratory Prerequisites: PHYS G4003 and W3007. Tensor The course is preparatory for advanced work in Lab: 3 pts. Professor Parsons. algebra, tensor analysis, introduction to Riemann physics and related fields. There is no accompa- Registration is limited to the capacity of the labo- geometry. Motion of particles, fluid, and fields nying laboratory; however, students are encour- ratory. Corequisite or prerequisite: PHYS W3003 in curved spacetime. Einstein equation. aged to take the intermediate laboratory, PHYS or W3007. A sequence of experiments in solid- Schwarzschild solution; test-particle orbits W3081, in the following year. state electronics, with introductory lectures. and light bending. Introduction to black holes, gravitational waves, and cosmological models. PHYS W3002y From quarks to the cosmos: PHYS G4003y Advanced mechanics applications of modern physics Lect: 3 pts. Professor Pontón. STATISTICS Lect: 3.5 pts. Professor Marka. Prerequisite: Differential and integral calculus, Engineering students interested in a sur- Prerequisites: PHYS C2601 or C2802. This differential equations, and PHYS W3003 or the course reinforces basic ideas of modern physics equivalent. Lagrange’s formulation of mechanics, vey of the mathematical theory of proba- through applications to nuclear physics, high- calculus of variations and the Action Principle, bility and statistics should consider the energy physics, astrophysics, and cosmology. Hamilton’s formulation of mechanics, rigid body pair STAT W3105: Probability theory and The ongoing Columbia research programs in motion, Euler angles, continuum mechanics, W3107: Statistical inference. Students these fields are used as practical examples. introduction to chaotic dynamics. seeking a quicker overview that focuses The course is preparatory for advanced work more on probability theory should con- in physics and related fields. PHYS G4018y Solid-state physics sider SIEO W4150. STAT W4105 and Lect: 3 pts. Professor Uemura. W4107 are the equivalent of W3105 and PHYS W3003x Mechanics Prerequisites: PHYS G4021 and G4023, or the Lect: 3 pts. Professor Blaer. equivalent. Introduction to solid-state physics: W3107, respectively; but graduate stu- Prerequisite: General physics; differential and crystal structures, properties of periodic lattices, dents may not register for W3105 and integral calculus. Newtonian mechanics, oscilla- electrons in metals, band structure, transport W3107. STAT W4109 (6 pts) covers the tions and resonance, conservative forces and properties, semiconductors, magnetism, and same material as W3105 and W3107 in potential energy, central forces, noninertial frames superconductivity. a single semester. STAT W4315: Linear of reference, rigid body motion, an introduction regression models takes W3105 and

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W3107 as prerequisites; like other Prerequisites: MATH V1101 and V1102 or the STAT W4201x and y Advanced data analysis advanced offerings in statistics, it covers equivalent. A quick calculus-based tour of the 3 pts. D. Alemayehu and instructor to be both theory and practical aspects of fundamentals of probability theory and statistical announced. inference. Probabilistic models, random variables, Prerequisite: A one-term introductory statistics modeling and data analysis. Advanced useful distributions, expectations, laws of large course. This is a course on getting the most out offerings in probability theory, stochastic numbers, central limit theorem. Statistical infer- of data. The emphasis will be on hands-on experi- processes, and mathematical finance ence: point and confidence interval estimation, ence, involving case studies with real data and generally take STAT W3105 as a prereq- hypothesis tests, linear regression. Students using common statistical packages. The course uisite; advanced offerings in statistical seeking a more thorough introduction to probability covers, at a very high level, exploratory data theory and methods generally take STAT and statistics should consider STAT W3105 and analysis, model formulation, goodness-of-fit testing, W4107 and, in several cases, W4315 as W3107. and other standard and nonstandard statistical procedures, including linear regression, analysis prerequisites; an exception is STAT STAT W3105x Introduction to probability of variance, nonlinear regression, generalized W4220: Data mining, which has a 3 pts. Instructor to be announced. linear models, survival analysis, time series Prerequisites: MATH V1101 and V1102 or the course in computer programming as analysis, and modern regression methods. equivalent. A calculus-based introduction to prob- prerequisite and STAT W3107 as coreq- Students will be expected to propose a data set ability theory.Topics covered include random vari- uisite. STAT 4201 is a high-level survey of their choice for use as case study material. ables, conditional probability, expectation, inde- of applied statistical methods. pendence, Bayes’ rule, important distributions, STAT W4240x Data mining Please note that STAT W3000 has joint distributions, moment-generating functions, 3 pts. D. Madigan. been renumbered as W3105 and STAT central limit theorem, laws of large numbers, and Prerequisite: COMS W1003, W1004, W1005, W3659 has been renumbered as Markov’s inequality. W1007, or the equivalent. Corequisite: STAT W3107. For a description of the follow- STAT W3107y Introduction to statistical inference W3107. Data mining is a dynamic and fast-grow- ing course offered jointly by the 3 pts. Instructor to be announced. ing field at the interface of statistics and computer Departments of Statistics and Industrial Prerequisite: STAT W3105 or W4105, or the science. The emergence of massive datasets Engineering and Operations Research, equivalent. Calculus-based introduction to the containing millions or even billions of observa- see ‘‘Industrial Engineering and theory of statistics. Useful distributions, law of tions provides the primary impetus for the field. Operations Research’’: large numbers and central limit theorem, point Such datasets arise, for instance, in large-scale estimation, hypothesis testing, confidence inter- retailing, telecommunications, astronomy, compu- SIEO W4150x and y Introduction to probability vals maximum likelihood, likelihood ratio tests, tational and statistical challenges.This course will and statistics nonparametric procedures, theory of least provide an overview of current research in data 3 pts. I. Hueter and L. Wright. squares, and analysis of variance. mining and will be suitable for graduate students

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204 from many disciplines. Specific topics covered STAT W4335x Sample surveys STAT W4606x and y Elementary stochastic include databases and data warehousing, 3 pts. Instructor to be announced. processes exploratory data analysis and visualization, Introductory course on the design and analysis of 3 pts. M. Brown and instructor to be announced. descriptive modeling, predictive modeling, pattern sample surveys. How sample surveys are con- Prerequisite: STAT W4105 or the equivalent. and rule discovery, text mining, Bayesian data ducted, why the designs are used, how to ana- Review of elements of probability theory. Poisson mining, and causal inference. lyze survey results, and how to derive from first processes. Exponential distribution. Renewal principles the standard results and their general- theory. Wald’s equation. Introduction to discrete STAT W4290 y Statistical methods in finance izations. Discussions include detail surveys from time Markov chains and applications to queueing 3 pts. Instructor to be announced. areas including public health, social work, opinion theory, inventory models, branching processes. Prerequisites: STAT W4105 and W4107. This is polling, and other topics of interest. a master-level course introducing statistical STAT W4635y. Stochastic processes for methodologies in quantitative finance. Financial STAT W4413x Nonparametric statistics finance applications and statistical methodologies are 3 pts. Instructor to be announced. 3 pts. Instructor to be announced. intertwined in all lectures, with several research Prerequisite: STAT W4107. Statistical inference Prerequisites: STAT W3105 or the equivalent. topics being introduced through problems in a without parametric model assumption. Hypothesis This course covers theory of stochastic processes term project. Lecture notes by the instructor will testing using ranks, permutations, and order applied to finance. It covers concepts of martin- be distributed. The course will cover linear statistics. Semi-parametric analysis of censored gales, Markov chain models, Brownian motion. regression with applications to single and multi- survival data. Analysis of discrete outcomes. Stochastic integration, Ito’s formula as a theoreti- factor pricing models, multivariate analysis and Contingency tables. Applications. cal foundation of processes used in financial their applications in Markowitz’s portfolio manage- modeling. It also introduces basic discrete and ment, estimation and modeling of volatilities, cal- STAT W4437x and y Time series analysis continuous time models of asset price evolutions culation of value-at-risk, nonparametric methods 3 pts. Instructor to be announced. in the context of the following problems in with applications to option pricing and interest Prerequisite: STAT W4315 or the equivalent. Least- finance: portfolio optimization, option pricing, spot rate markets. squares smoothing and prediction, linear systems, rate interest modeling. Fourier analysis and spectral estimation. Impulse STAT W4315x and y Linear regression models response and transfer function. Fourier series, the STAT W4840x Theory of interest 3 pts. Instructor to be announced. fast Fourier transform algorithm, autocorrelation 3 pts. N. Rajah. Prerequisites: STAT W3107 or the equivalent, function, and spectral density. Univariate Box- No prerequisite. Introduction to the mathematical MATH V2110 or the equivalent. Corequisites: Jenkins modeling and forecasting. Emphasis on theory of interest as well as the elements of eco- MATH V1101, V1102, and V2110. Simple and practical applications in examples from the physical nomic and financial theory of interest. Topics multiple regression, including testing, estimation sciences, social sciences, and business. Computing include rates of interest and discount; simple, and confidence procedures, modeling, regression is an integral part of the course. compound, real, nominal, effective, dollar (time)- diagnostics and plots, polynomial regression, weighted; present, current, future value; discount fixed effects ANOVA and ANCOVA models, non- STAT W4543y Survival analysis function; annuities; stocks and other financial linear regression, multiple comparisons, co-linearity 3 pts. Instructor to be announced. instruments; definitions of key terms of modern and confounding, model selection. Emphasis on Prerequisite: STAT W4315 or the equivalent. financial analysis; yield curves; spot (forward) geometric approach to the theory and the use of Survival distributions, types of censored data, rates; duration; immunization; and short sales. a statistical package to analyze data. estimation for various survival models, nonpara- The course will cover determining equivalent metric estimation of survival distributions, measures of interest, discounting, accumulating, STAT W4325x Generalized linear models the proportional hazard and accelerated lifetime determining yield rates, and amortization. 3 pts. Instructor to be announced. models for covariate data, regression analysis Statistical methods for rates and proportions, with lifetime data. Extensive use of the computer ordered and nominal categorical responses, to analyze data. Applications in clinical trials and contingency tables, odds-ratios, exact inference, acturial science. logistic regression, Poisson regression, general- ized linear models.

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he Fu Foundation School of grams, it is also small enough to promote • provides information on preprofessional Engineering and Applied Science the close interaction among students, studies, study abroad, and major dec- T attracts and admits an excep- faculty, and administration that has created laration and completion, as well as tionally interesting, diverse, and multicul- a strong sense of community on campus. various leadership, career, graduate tural group of students, and it takes With its mission of providing a wide school, and research opportunities; steps to provide a campus environment range of services designed to enhance refers to additional campus resources that promotes the continued expansion the student experience from the time • designs and facilitates programming of each student’s ideas and perspec- of admission through graduation, the to meet the unique developmental tives. Starting with the residence halls, in Division of Student Affairs is the hub of needs of each class and to enhance which nearly all first-year undergraduate undergraduate student life. Admissions, community among students, faculty, students live, the University assigns Financial Aid and Educational Financing, and administrators rooms to both Engineering and Center for Student Advising, Residential • interprets and disseminates informa- Columbia College undergraduate stu- Programs, Office of Multicultural Affairs, tion regarding University polices, pro- dents, ensuring that all students will Parent and Family Programs, Office of cedures, resources, and programs live either with or near a student attend- Judicial Affairs and Community • educates and empowers students to ing the other program. Standards, Events and Communica- take responsibility in making informed Once students have moved into their tions, Student and Alumni Programs, decisions new campus home they will find them- Student Development and Activities, and Each student is assigned to an advis- selves part of a residential system that Office of Student Group Advising are ing dean who advises in his or her aca- offers undergraduates a network of integral components of the Division. The demic area of interest. When a student social and academic support. Designed integrated effort of these units assures declares a major, a faculty member is to make students aware of the vast that individual students receive support appointed to guide him or her for the number of social and academic oppor- in both their academic and cocurricular next two years. Advising deans regularly tunities available to them at the pursuits. The Division of Student Affairs is refer students to their academic depart- University, these networks provide an responsible for assisting students in all ments to receive coordinated expert advice umbrella of comprehensive advising to matters beyond actual course instruction in their engineering course selections. help students articulate and realize their and helping to create a special spirit and goals while at Columbia. More informa- sense of community for students. Preprofessional Advising tion about the residence halls can be The Office of Preprofessional Advising found in the chapter ‘‘Housing and CENTER FOR STUDENT works closely with the Center for Student Residence Life’’ in this bulletin. ADVISING Advising and with the Center for Career The Center for Student Advising reflects Education to provide information for DIVISION OF STUDENT AFFAIRS the mission of the University in striving students who plan a career in law or the Undergraduate life is not confined to the to support and challenge the intellectual health professions. The Office advises classroom. A blend of academic, educa- and personal growth of its students and and assists students throughout their tional, social, and cocurricular activities by creating a developmental, diverse, and four years, but works most closely with contributes to the Columbia experience. open learning environment. Individually students during their application year While The Fu Foundation School of Engi- and collaboratively, each center: and with alumni who apply for admission neering and Applied Science is large • provides individual and group academic after graduation. Information sheets, forms, enough to support a wide variety of pro- advisement, exploration, and counseling and helpful resources are available in

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the Office of Preprofessional Advising. Student Council and its associated class and political dialogue at Columbia Students will work with their advising councils are the elected representative University’s Morningside Campus. The deans as primary preprofessional advis- body of undergraduates with The Fu InterSchool Governing Board recognizes ers; these advisers will be instrumental Foundation School of Engineering and student organizations whose membership in writing committee evaluations for Applied Science. Its members represent spans across the various undergraduate some professional schools. student interests on committees and and graduate schools. projects addressing a wide range of For more information on the Inter- COMMUNITY DEVELOPMENT issues facing the Columbia community Greek Council (IGC), see Residential and help shape the quality of life for Programs, below. For more information The Community Development team Columbia students. on Club Sports, see Intercollegiate works to foster a vibrant and welcoming Working in conjunction with the Athletics Program (page 210), and for undergraduate community through orga- Student Council, the Activities Board at more information on Community Impact nizational advising, leadership develop- Columbia (ABC), Student Governing see Office of the University Chaplain ment, advocacy, diversity education, Board (SGB), Inter-Greek Council (IGC), (page 209). All the governing groups civic engagement, and community pro- Community Impact (CI), Club Sports, provide networking, leadership, and gramming. The team includes the Office and Interschool Governing Board (IGB) professional development opportunities of Student Development and Activities, oversee the management and funding of for students. the Office of Multicultural Affairs, the over 300 student organizations. Columbia University graduate stu- Office of Student Group Advising, and The ABC provides governance for over dents can participate in and enjoy hun- the Office of Residential Programs. 160 recognized student organizations, dreds of diverse, University-affiliated Knowing that students’ learning contin- including cultural organizations, perform- social, religious, cultural, academic, ues beyond the classroom, Columbia ance-based and theatrical groups, media athletic, political, literary, professional, University strongly encourages students and publications groups, competition and public service, and other organizations. to become involved in programs and special interests groups and preprofes- At SEAS, graduate students are encour- activities to enhance their educational sional organizations and societies. The aged to become active members of the experience and personal growth. A wide preprofessional organizations and societies Engineering Graduate Student Council array of student organizations addresses are of special interest to engineering stu- (EGSC). The EGSC is a recognized both student interests and professional dents. These societies reflect the range of group that consists of representatives concerns, including the arts, politics, academic disciplines and interests to be from each of the nine academic depart- identity, culture, and religion. Joining found among students and include the ments at SEAS. The objectives of the such groups offers an exciting and Asian-American Society of Engineers, EGSC are to foster interaction among dynamic opportunity to develop leader- National Society of Black Engineers, graduate engineering students, to serve ship skills that will serve students well the Society of Women Engineers, the as a voice for graduate engineering stu- throughout their lives. American Institute of Aeronautics and dents, and to sponsor social and educa- Astronautics, and the Biomedical tional events of interest to the graduate Student Organizations Engineering Society, just to name a few. engineering community. Programs and activities at Columbia The SGB provides governance for are shaped primarily by students who approximately 100 recognized student Office of Student Development assume leadership and volunteer organizations that are faith-based, spiri- and Activities positions in hundreds of organizations tual, political, activist, and humanitarian The Office of Student Development and across the campus. The Engineering and that encourage open interreligious Activities (SDA) provides programs and

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208 services designed to support a wide make friends and settle into life at self-discovery takes place along with a range of co-curricular activities that help Columbia before classes begin. greater awareness and appreciation of build a sense of community, support Undergraduate students may e-mail cultural history within and between com- responsible student governance and [email protected] or call 212-854- munities on campus. We endeavor to student group involvement, and further 5808 for additional information on NSOP. empower students, faculty, and staff students’ leadership development and Orientation for graduate students is with the tools to be able to successfully personal growth. scheduled during the week prior to the navigate their environments and thus be Student Development and Activities beginning of each semester. For more able to positively change and impact the staff members advise student organiza- information on orientation for graduate community at large. tions recognized through the Activities students, contact the Office of Graduate Programs and services provided by Board of Columbia (ABC), as well as Student Services. Multicultural Affairs include the Columbia the student governments of The Fu Mentoring Initiative, a program connect- Foundation School of Engineering and Office of Student Group Advising ing incoming students with returning Applied Science and Columbia College. The Office of Student Group Advising students, and returning students with SDA serves as resources for event (OSGA) is committed to supporting the alumni; Respecting Ourselves and planning, organizational leadership, programming of our faith-based, spiritu- Others Through Education (ROOTED), and budgeting. The Office of Student al, political, activist, and humanitarian a peer diversity faciliation program; Development and Activities offers lead- student organizations. In reaching to Dessert and Discussion, the signature ership training workshops and helps fulfill this commitment, OSGA provides lecture series; and the Intercultural networking among student leaders and programming in leadership skills, pro- House (ICH), a unique residential experi- administrative offices. In addition, the gram development, and organizational ence that is supportive of Multicultural SDA administers the Urban New York management to all undergraduate stu- Affairs’ social justice goals. Program, the New Student Orientation dent organizations recognized by the Program, the Columbia Urban Student Governing Board (SGB) and Residential Programs Experience Program, and the Columbia organizations recognized by the The Residential Programs staff, super- Outdoor Orientation Program. Interschool Governing Board (IGB). vised by the Assistant Dean of Community OSGA assists students in their develop- Development and Residential Programs, Orientation ment as individuals, community mem- includes 8 professional staff, 13 gradu- All new students are required to partici- bers, and leaders. ate students, and 130 undergraduates pate in an orientation program that is Issues of social responsibility and who contribute to the growth, well- designed to acquaint them with the civic engagement are central to the mis- being, and personal and intellectual University and its traditions, the adminis- sion of OSGA and the student organiza- development of students. The staff tration and faculty of The Fu Foundation tions that OSGA supports. OSGA strives strives to enhance the quality of residen- School of Engineering and Applied to encourage open dialogue at Columbia tial life by cultivating an atmosphere con- Science, upperclass students, and New University’s Morningside Campus and ducive to educational pursuits and the York City. The New Student Orientation seeks to find connections among stu- development of community within the Program (NSOP) for new undergraduate dent groups. The Office of Student student body. These contributions form students begins the week prior to the Group Advising works to enhance the an integral part of a Columbia education start of the fall semester. NSOP is undergraduate educational experience by stimulating mutual understanding and intended to assist all new students with by fostering a dynamic and enriching by fostering an atmosphere based on the transition to college life. University community, supporting the appreciation of the differences and Orientation is busy, exciting, and a lot responsible student governance and similarities characterizing such a diverse of fun, but it is also a week in which co-curricular activities, and offering pro- cultural community. important academic decisions are made. grams and opportunities focused on The undergraduate student staff, Scheduled into the program are informa- civic and community engagement. resident advisers (RAs), and community tion sessions and opportunities to meet Through advising, the office encourages advisers (CAs) serve as role models for with academic advisers. Through large critical thinking and the free exchange of their residents. They facilitate discussions group programs and small group activi- ideas by all of the student organizations about community standards, provide ties, student will be introduced to faculty it supports. community building programs, and serve members, deans, resident advisers, and as a resource for the residents. Their other students. NSOP includes walking Office of Multicultural Affairs RAs/CAs serve as the front line of a lay- tours of New York City, social events, The Office of Multicultural Affairs is ered on-call system and are trained to and information sessions on University devoted to promoting a just society and respond to the variety of issues that services and co-curricular opportunities. exploring issues of interculturalism and emerge in community life. As backup, During NSOP, new students have the diversity within and beyond the Columbia they have graduate assistants (GAs), campus to themselves. This provides University community. By promoting associate directors (ADs), and a dean-on- students with a unique opportunity to forums that address diversity issues, duty.

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The Faculty in Residence Program community. To achieve this goal, the General Studies, and the graduate 209 allows students, alumni, and faculty to Office of Judicial Affairs partners with schools are invited along with faculty meet formally and informally throughout various offices on campus to create pro- and senior administrators to discuss the year. Faculty members in residence in grams designed to educate students ideas and opinions about Columbia’s three residence halls invite students to regarding the potential impact of their past, present, and future. dine in their apartments; organize special actions on both their individual lives and In addition to student programming, programs around issues of interest; pro- the community at large. In addition, the community service is also a main func- vide opportunities for academic growth Office of Judicial Affairs and Community tion of the Center. As a center for all and challenges within the residence halls; Standards works with student groups to undergraduate, graduate, and profes- and help students establish links with facilitate the development of skills and sional schools at Columbia, the Earl Hall major cultural, political, and professional processes students can use to hold Center offers any student a number of institutions in New York City. In addition, each other accountable when they great opportunities. Columbia University’s the faculty member in residence partners encounter inappropriate behavior. The largest community service program, with the SEAS alumni office to provide Office of Judicial Affairs and Community Community Impact, which is located in opportunities for students to network and Standards also holds students account- the Earl Hall Center, involves more than gain exposure to a variety of careers. able for inappropriate behavior through 900 student and neighborhood volunteers Begun in fall 2006, the Gateway the Dean’s Discipline process when nec- in twenty-six programs, including GED, Residential Initiative allows SEAS first- essary. Earth Coalition, Peace Games, a soup years, sophomores, juniors, and seniors kitchen, and student help for the aging. to live together clustered in the Living OFFICE OF THE UNIVERSITY Besides Earl Hall, the Center includes Learning Center (LLC) housed in Hartley CHAPLAIN St. Paul’s Chapel. One of Columbia’s and Wallach Halls. This initiative seeks to oldest and most beautiful buildings, the The Office of the University Chaplain is bridge the academic and co-curricular Chapel not only hosts weddings and located in the Earl Hall Center and experience for SEAS students. various religious services, but also fea- includes the United Campus Ministries, Mentorship between students, connec- tures many speakers and performances. the Common Meal Program, and “Music tion among the class years, and alumni The Postcrypt Coffeehouse at St. Paul’s at St. Paul’s.” The mission of the Center interaction are the foundations for the suc- Chapel is a favorite spot for artists to is to build community within the cess of the program. play music, read poetry, or exhibit artwork. University and with its neighbors while The administrative offices for the providing students with an opportunity Fraternities and Sororities Center are open during regular business to explore the relationship between faith hours, but the buildings have more Fraternities and sororites have brown- and learning. The Center is as diverse as extensive hours—as late as 11:00 p.m. stones near the campus and some of the university it serves. United Campus on weekends. For more information, the organizations without brownstones Ministries, which includes denominations please call the Earl Hall Center at 212- have a suite within the residence halls. of Christian, Jewish, Islamic, and 854-1474 or 212-854-6242. There is a full-time Assistant Director for Eastern practices, provides students Greek Life and Leadership Development. with individual counseling, religious and The InterGreek Council (IGC) is the nonreligious group support, referrals, LERNER HALL self-governing student organization that and personal assistance. Columbia’s new student center, Lerner provides guidelines and support to the The University Chaplain is the direc- Hall, officially opened in the fall of 1999. three Greek councils: The Interfraternity tor of the Earl Hall Center. As University Located on the southwest corner of Council (IFC), Panhellenic Council, and Chaplain, Jewelnel Davis supports the campus, this 225,000-square-foot student Multicutural Greek Council (MGC). coherence and unity that connects the center was designed by Bernard Tschumi, There are thirty-three recognized Greek University. She focuses on a nexus of the former Dean of Columbia’s Graduate organizations whose membership totals issues including religion, spirituality, race, School of Architecture, Planning and over one thousand undergraduates. ethnicity, sexual identity, gender, social Preservation. Architectural features of Fraternity and sorority members share justice, and community service. Lerner Hall, such as the glass facade in service, scholastic, philanthropic, cul- One point of focus for Chaplain Davis and ramps, allow the campus to clearly tural, and leadership experiences. This is accessibility to students. Students view the activities within the building, active and vibrant community adds to often e-mail her, make appointments and offer those within Lerner scenic the diversity of the residential experience. with her individually or in groups, or views of the campus. speak with the chaplain associates or Undergraduate students are likely to OFFICE OF JUDICIAL AFFAIRS program coordinators—student liaisons visit Lerner to check the mail from the AND COMMUNITY STANDARDS who work directly with Chaplain Davis 7,000 student mailboxes located along The Office of Judicial Affairs and on student programming initiatives. the ramps. Students may check their Community Standards was created to The Common Meal Program is a weekly e-mail in Lerner’s computer center or by assist students in the maintenance of a gathering to which student leaders plugging in their laptop computers at safe, honest, and responsible campus from Columbia College, Barnard, SEAS, one of Lerner’s Ethernet-outfitted lounges.

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Students will also visit Lerner to interact Psychological Services, and Columbia’s Foundation School of Engineering and with one another in various ways. They Alice! The Health Education Program. Applied Science has always been an active may strategize and plan events with participant in these programs. While their student organizations in one of the OFFICE OF GRADUATE Columbia’s intercollegiate athletic program student club offices, or in the meeting STUDENT SERVICES is governed by Ivy League regulations, rooms designated for student club Columbia is also a member of the The Office of Graduate Student Services usage. Students may also meet friends Eastern College Athletic Conference and at The Fu Foundation School of Engi- in one of Lerner’s two dining locations, the National Collegiate Athletic Association. neering and Applied Science is integral for an event in the auditorium, in various Columbia sponsors men’s varsity teams to the School’s teaching, research, and lounges, or in one of the building’s in baseball, basketball, cross-country, service mission, and works to enhance multipurpose spaces that are ideal for fencing, football, golf, rowing (heavy- the educational opportunities available to exercise classes. weight and lightweight), soccer, swim- students. This Office provides leadership In addition to providing spaces for ming and diving, tennis, track and field for the integration of educational programs student interaction, Lerner is home to (indoor and outdoor), and wrestling. and services that enhance recruitment, the Columbia University Bookstore. Lerner Women in all undergraduate divisions retention, and quality of campus life for also features retail services, including a of Columbia and in Barnard College graduate students at SEAS. It strives to travel agency, a copy center, and an compete together as members of demonstrate sensitivity and concern in electronic banking center. Included in University-wide athletic teams. The addressing the needs of the School’s the building are orchestra/band rehearsal arrangement, called a consortium under population. The Office is dedicated to and art exhibition spaces, and various NCAA rules, is one of only three in the providing service to prospective, new, administrative offices (Student Affairs, nation and the only one on a Division I and continuing students pursuing a Student Services, Residential Programs, level. Currently, there are women’s varsity graduate education in engineering or Judicial Affairs, Multicultural Affairs, teams in archery, basketball, cross- applied science. Center for Student Advising, Financial country, fencing, field hockey, golf, Aid, and Educational Financing). lacrosse, rowing, soccer, softball, swim- These offices also include Student INTERCOLLEGIATE ATHLETICS ming and diving, tennis, track and field Development and Activities, the Double PROGRAM (indoor and outdoor), and volleyball. Discovery Center, Columbia TV, WKCR, Columbia has a long tradition of success Columbia’s commitment to success Disability Services, Counseling and in intercollegiate athletics, and The Fu in intercollegiate sporting competition

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has been matched by the determination Eligibility for Intercollegiate Athletics who share a common athletic interest 211 of alumni and administrators to upgrade Any student in the Engineering School to organize and collectively pursue this the University’s sports facilities. The who is pursuing the undergraduate pro- activity. Clubs are organized on recre- Baker Field Athletics Complex, a few gram or an approved combined pro- ational, instructional, and competitive miles up the Hudson River on the northern gram toward a first degree is eligible for levels, and their activities range from tip of Manhattan, has been completely intercollegiate athletics. To be eligible for informal play to regular practice or rebuilt and expanded. The complex fea- athletic activities, the student must: instruction and intercollegiate and tour- tures a precast concrete football stadium nament competition. A list of the intra- • be a candidate for a bachelor’s degree capable of seating 17,000 spectators; mural activities and sports clubs as well • be registered for at least 12 points of an Olympic-quality synthetic track; a as all information regarding the program credit 3,500-seat soccer stadium; softball and can be obtained in the Intramural Office, • make appropriate progress toward the baseball fields; and an Astroturf field 331 Dodge Fitness Center or on the Web degree as defined by the NCAA, the hockey field. At Columbia’s Dick Savitt site, www.gocolumbialions.com. Ivy League, and Columbia University. Tennis Center at the Baker Athletics These criteria are monitored by the Complex there are six hard tennis Director of Compliance and certified CAMPUS SAFETY AND courts, all of which are covered by a by the Office of the Registrar. SECURITY state-of-the-art air dome for winter use. • have attended the University for not At Columbia University, the safety and The 1929 Boathouse includes a three- more than eight terms well-being of our students, faculty, and bay shell house, complete with an • not have completed the requirements staff is a priority. Columbia’s campuses upper level that includes an erg and for the bachelor’s degree and their environs are safe and have a weight room. very low crime rate for an urban university. Columbia’s Dodge Physical Fitness Questions about athletic eligibility should The University is required by federal Center draws thousands of students be referred to the appropriate academic law to publish an annual security report each day for recreation, physical educa- adviser or the Director of Compliance in containing information with respect to tion classes, intramural play, club com- the Department of Intercollegiate campus security policies and statistics petition, and varsity sport contests and Athletics and Physical Education. on the incidence of certain crimes practices. The Center houses most on and around our campuses. This indoor sports and is available to all reg- Recreational Programs information is available at the Web site istered students. Major athletic facilities In addition to the activity courses for the United States Department of on campus include two full-size gymna- (see page 13), the Physical Education Education (ope.ed.gov/Security/search. siums for basketball, volleyball, and bad- Department offers a comprehensive asp); by requesting a copy of the report minton; eight squash and handball Intramural and Club Sports Program. from: Campus Crime Report, courts; the eight-lane Uris pool with Through intramurals, the student has the Department of Public Safety, Columbia three diving boards; a fully equipped opportunity to participate in both individ- University, 111 Low Library, Mail Code three-level exercise and weight room ual and team sports. Individual activities 4301, 535 West 116th Street, New facility; two aerobic dance/martial arts function through tournaments, while the York, NY 10027 (Attn: Mr. Rocco Osso); rooms; a fencing room; a wrestling room; team activities feature both league and or at the Web site for Public Safety an indoor running track; and two fully play-off competition. Club sports are (www.columbia.edu/cu/publicsafety). equipped saunas. designed to allow groups of individuals

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212 STUDENT SERVICES

UNIVERSITY HOUSING dence hall rooms are either single or International House, a privately owned double. Single and double rooms are student residence near the campus, has Undergraduate Housing available in all halls except Carman, accommodations for about five hundred The residence halls are an important which has only doubles, and Hogan, graduate students, both international focus for campus life outside the class- which is all singles. and American, who attend various area room, with the University housing over The residence halls are also home to colleges and universities. It provides a 95 percent of the undergraduate popu- a variety of Special Interest Communities. supportive and cross-cultural environ- lation in residence halls on or near the These communities provide an opportu- ment with many activities and resources, campus. A trained Residential Programs nity for students with a common interest and it is conveniently located two blocks staff lives with the students in the halls. to live together and develop programs from the Engineering building. For more They work to create an atmosphere in their area of interest. The themes information, write or call: International conducive to educational pursuits and may vary from year to year. The current House, 500 Riverside Drive, New York, the development of community among communities are Symposium House, NY 10027; 212-316-8400; or check the diverse student body. Throughout GreenBorough, Metta House, Pan their Web site at www.ihouse-nyc.org. the year the Residential Programs staff African House, Casa Latina, Community There are also a number of off-campus presents programs in the residence halls Health House, 114 Rue de Fleurus, housing opportunities. The University and off campus that are both social and Students for a Substance Free Space, operates Off-Campus Housing Assis- educational. and Q-House, among others. First-year tance (OCHA), which lists rooms and Columbia guarantees housing for all students are not eligible to live in Special apartments in rental properties not undergraduate students (except trans- Interest Communities but are welcome owned or operated by the University. fers) who have filed their intent to reside to attend events. Only students with a valid ID or admis- on campus by the stated deadline and Upper-class Columbia students also sion acceptance letter are permitted to who have continuously registered as full- have the option of living in certain Barnard use the facility. OCHA is open through- time students. Each spring, continuing College halls. Rooms in Barnard and out the winter and summer vacation students participate in a room-selection Columbia halls are chosen by a room periods except academic holidays. process to select their accommodations selection process, which takes place Students should call 212-854-2773 for for the next academic year. Students each spring. office hours. OCHA also operates a Web who take an unauthorized leave of absence For more information, please visit page at www.columbia.edu/ cu/ire/ocha. are placed on the nonguaranteed wait the housing Web site at There is also a list of alternative housing list upon their return and are on the wait www.columbia.edu/cu/housing. opportunities maintained by the Office of list for each subsequent year. Graduate Student Services in 524 S. W. A variety of residence hall accommo- Graduate Housing Mudd. Students are sent the Alternative dations are available to Columbia students. Graduate students have a number of Housing flyer in their orientation packets. Carman, John Jay, Wien, Furnald, McBain, housing opportunities in the Morning- UAH applications are sent along with Schapiro, and Broadway Residence Hall side Heights neighborhood. The three acceptance packets from the Office of are traditional corridor-style residence main sources are University Apartment Graduate Student Services. They are halls, and all but Wien, John Jay, and Housing (UAH), International House, also available in the Office of Graduate Carman have kitchens on each floor. and off-campus listings. UAH operates Student Services and the UAH Office. East Campus, 47 Claremont, Hartley- Columbia-owned apartments and dor- Additional information is also available Wallach Living Learning Center, Hogan, mitory-style suites in the Morningside on the Columbia Students Page: River, Ruggles, 600 West 113th Street, area within walking distance of the cam- www.columbia.edu/cu/students. Watt, and Woodbridge offer suite-style pus. For further information, see UAH’s Graduate housing through UAH is living, and all have kitchens. All resi- Web site at www.columbia.edu/cu/ire. processed for the fall and spring terms

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only. Summer sublets are also available The dining plans are transacted through Columbia Card and can be used for through individual referrals. The UAH Columbia’s ID Card, called the Columbia meals in John Jay Dining Hall for brunch Office maintains an active listing for Card, which serves as a convenient way and dinner. those interested. to enjoy dining all over campus without Due to the growing demand for hous- carrying cash. Kosher Dining Plan ing, graduate housing is no longer guar- All students who participate in a dining anteed, but every effort is made to Meals plan, including first year, upperclass, accommodate interested students. It is The meals portion of the dining plan General Studies, or graduate students critical that housing applications be enables students to help themselves to are eligible for the Columbia Kosher submitted as soon as possible and that unlimited servings of food served buffet- Dining Plan. Signing up for this dining instructions in the acceptance packet be style in John Jay Dining Hall. Brunch and plan allows access to a restricted kosher followed. Housing applications received dinner are served Monday through Sunday. area within John Jay Dining Hall as well after the set date are not guaranteed as Express Meals to go. CU kosher housing. The order of priority for selection Dining Dollars meals can also, for an additional charge, is: graduate fellowship recipients, Zone 1 In addition to meals, Dining Dollars com- be exchanged for a kosher meal at students (those who live further than 250 prise the other portion of the first-year Barnard’s Hewitt Hall (kosher to kosher miles from campus), and then Zone 2 dining plan. Each Dining Dollar is equal only). To sign up, the student selects a students (those who live between 50 and to one dollar and operates as a declining plan from either the First Year Dining 250 miles from campus). All continuing balance account, much like a debit card. Plan or the Upperclass Dining Plan students and applications from Zone 3 Columbia Dining Services maintains options, according to the student’s sta- areas (within 50 miles) are automatically twelve dining facilities conveniently located tus, then elects to enroll in the Kosher placed on a waiting list. on campus. Each of the locations Dining Plan. The addition of the Kosher UAH-approved students can begin accepts Dining Dollars, an alternative to Dining Plan adds 10 percent to the cost viewing apartments and moving in cash payment that is accessed by the of the selected plan. Visit the H&D during the last week of August for the Customer Service Center in 118 Hartley Columbia Card (student ID card). fall term, and early January for the Hall (enrollment allowed at any point With Dining Dollars, students will spring term. Students will be properly throughout the term) to sign up. notified of Graduate Orientation and enjoy the ease and flexibility of cashless transactions as well as the savings of Registra-tion, which are generally held Locations/Menus/Hours the week before the first day of class. If sales tax on all food purchases. Dining Locations, menus, and hours of all a student needs to move in earlier, prop- Dollars will roll over from year to year campus dining facilities can be found er documentation from the department until graduation. at www.columbia.edu/cu/dining. in support of the request is necessary. Upperclass and Graduate Students Many upperclass and graduate students HEALTH SERVICES AND DINING SERVICES who dine on campus open a Dining INSURANCE Dollars account; however, some choose First-Year Students to enroll in an upperclass/graduate Health Services at Columbia provides All first-year students in residence are student dining plan. integrated and accessible services and required to enroll in one of four dining Dining Services offers four plans— programs that support the well-being of plans, ranging from 210 meals and 150 150 meals per term, 100 meals per the campus community and the personal Columbia Dining Dollars per term to 115 term, 75 meals per term, or 50 meals per and academic development of students. meals and 500 Dining Dollars per term. term. All plans are accessed by the We offer a variety of programs and serv-

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214 ices specifically designed to meet stu- workshops, and consultation with a Health Service Program covers on- dents’ health needs. We are comprised learning specialist. Students seeking campus services, including routine and of more than 100 individuals: medical reasonable accommodations or support urgent medical appointments, short- providers, nutritionists, disability special- services from ODS are required to regis- term mental health counseling, disability ists, health educators, therapists, psy- ter with the office and provide disability services, educational programs, and chiatrists, peer counselors, student per- documentation before receiving services. sexual violence services. The Health sonnel, support staff, and administrative Registration and documentation guide- Service Program also provides supple- professionals. Our programs are lines are available online. Alfred Lerner mental coverage for emergency health arranged in five departments. Hall, 7th floor. care, outpatient chemical dependency treatment, and outpatient mental health Primary Care Medical Services Sexual Violence Prevention and care. The Health Service Program is (PCMS) provides comprehensive care Response Program (SVPRP) provides mandatory for all full-time students, and for routine, urgent, and chronic medical comprehensive and integrated educa- the fee will automatically appear on stu- needs of students. We also provide sex- tion, support, and advocacy about sexu- dents’ E-bill. Students pay no additional ual health, reproductive, and gynecologi- al and relationship violence. Through charge for accessing on-campus services. cal services, travel medicine, LGBTQ innovative programming and community health care, confidential HIV testing, collaboration, SVPRP empowers stu- Columbia Student Medical Insurance immunizations, and specialist referrals. dents to heal from sexual violence, make Plan covers off-campus medical services. Through our Open Communicator func- informed decisions, and take action to The plan has two levels: Comprehensive tion, students can make appointments end sexual and relationship violence. and Basic. All full-time students are online and view their primary care provider Alfred Lerner Hall, Room 301. automatically enrolled in and billed for information (bios and photos are available the Basic insurance plan, but may All Health Services programs adhere to online). When Primary Care is closed, a upgrade to the Comprehensive plan strict standards of confidentiality in com- clinician-on-call can provide telephone online. Students may submit a request pliance with state and federal laws. advice about urgent medical conditions. to waive the insurance requirement John Jay Hall, 3rd and 4th floors. online by providing proof of comparable Contact Health Services at insurance coverage (alternate plans Counseling and Psychological Columbia must meet Columbia’s criteria for com- Services (CPS) offers short-term indi- www.health.columbia.edu parable coverage, available online). The vidual and couples counseling for stu- 212-854-2284 Columbia Plan includes local, national, dents and their partners, student life and worldwide health coverage, and support groups, medication consultation, On-Campus Emergency Resources discounts on dental and vision care. training, and emergency consultation. CAVA (Ambulance): 212-854-5555 Students are encouraged to make Part-time students are encouraged Rape Crisis/Anti-Violence Support appointments and to select a CPS to enroll in the Columbia Plan. Enrolling Center: 212-854-HELP, 212-854-WALK clinician (bios and photos are available in the Columbia Plan will automatically Public Safety: 212-854-5555 online). When CPS is closed, a clinician- enroll students in the Health Service on-call can provide telephone advice Program, as the two plans are meant to about urgent mental health concerns. Off-Campus Emergency Resources work together to provide comprehensive Alfred Lerner Hall, 8th floor. St. Luke’s-Roosevelt Hospital medical care. Emergency Room 212-523-3335 Alice! Health Promotion Program seeks Psychiatric Emergency 212-523-3347 Immunization Requirements All stu- to help students achieve their personal dents must fulfill two New York State and academic goals by disseminating public health immunization requirements Your Health at Columbia useful, current health information in a before registering for classes. straightforward and accessible manner, Columbia students have access to com- Students must document immunity to connecting students to appropriate prehensive health care through a net- measles, mumps, and rubella (MMR) resources, cultivating healthy attitudes work of on- and off-campus services. and make an informed decision about and behaviors that encourage students On-campus medical and counseling receiving the meningitis vaccine. The to make informed decisions about their appointments are covered through the Columbia MMR documentation form is health, and fostering a culture that val- Health Service Program. Off-campus available online—complete the form, ues and supports a healthy community. medical services, such as emergency then mail, fax, or bring it to the Alice! provides workshops and programs room visits or prescriptions, are covered Immunization Office. Students record for students, and runs Go Ask Alice!, a through a student’s insurance plan. their meningitis decision online. health question-and answer Web site. Columbia requires all full-time and resi- Directions for completing each require- Wien Hall, 1st floor. dential students to enroll in both the ment are available at our Web site. Health Service Program and an accept- Office of Disability Services (ODS) able insurance plan. To meet the insur- Insurance and Immunization coordinates reasonable accommoda- ance requirement, students may enroll in Questions tions and support services for eligible the Columbia Student Medical Insurance students, including assistive technology, Plan or provide proof of comparable www.health.columbia.edu networking groups, academic skills insurance coverage. E-mail: [email protected]

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216 SCHOLARSHIPS, FELLOWSHIPS, AWARDS, AND PRIZES

FELLOWSHIPS Robert A.W. and Christine S. Carleton GEM Fellowship Fellowships in Civil Engineering The GEM fellowship provides African- H. Dean Baker Fellowship (1982) Fellowships awarded to graduate students Americans, Hispanic Americans, and Awarded to support deserving graduate in the Department of Civil Engineering Native Americans access to graduate students in mechanical engineering. and Engineering Mechanics. education. The fellowship includes tuition, fees, a stipend, and a paid sum- mer internship. Applicants for this fellow- Boris A. Bakhmeteff Research Chiang Chen Fellowship (2004) ship must be engineering or applied sci- Fellowship in Fluid Mechanics Chiang Chen Industrial Charity Foundation. ence majors. Provides a stipend for the academic Awarded to students in mechanical year, with tuition exemption to be engineering. arranged by the recipient’s department, Governor’s Committee on to a candidate for a doctoral degree in Professor Bergen Davis Fellowship Scholarship Achievement any department at Columbia University Gift of Dr. Samuel Ruben. To be awarded One year awards based on financial whose research is in fluid mechanics. to a student in chemical engineering and need. Renewal is based on academic applied chemistry upon the recommen- progress, financial need, and availability of funds. The student applies directly to Quincy Ward Boese Fellowships dation of the senior professor in chemical the GCSA; the awards are matched by Predoctoral fellowships awarded annually engineering active in electrochemistry the School and are not in supplement to to students studying under the Faculty research. initial School awards. of Engineering and Applied Science. George W. Ellis Fellowships Carl Gryte Fellowship (2007) Roy S. Bonsib Memorial Fellowship Awarded annually for graduate study in Gift from friends of Professor Carl (1957) any division of the University. Open to Campbell Gryte. Awarded to needy Awarded to worthy students for advanced graduate students who are residents of and deserving graduate students. study or research in engineering. the state of Vermont or who have been graduated from a Vermont college or university. Daniel and Florence Guggenheim Arthur Brant Fellowship (1997) Fellowships Gift of Arthur Brant. Awarded to gradu- Two fellowships for the study of engi- ate students of the Henry Krumb School Michael Frydman Endowed neering mechanics in the Institute of of Mines in the field of applied geophysics. Fellowship (2000) To support a fellowship to a deserving Flight Structures. master’s student in the financial engi- Samuel Willard Bridgham-William neering program of the Department of M. D. Hassialis Memorial Fellowship Petit Trowbridge Fellowship Industrial Engineering and Operations (2002) A combined fellowship awarded annually Research. Gift of former students of the late Krumb for research. Professor Emeritus Hassialis. Awarded Robert F. Gartland Fellowship to graduate students of the Henry Krumb William Campbell Fellowships for Awarded annually for graduate study in School of Mines in the field of Earth Encouraging Scientific Research the Department of Industrial Engineer-ing resources economics and management. Four or five fellowships awarded annually and Operations Research. Preference is for research in the general field of metals. given to students who are native-born Higgins Fellowships U.S. citizens and who intend to pursue Fellowships awarded annually to first-year a career in business or finance. graduate students.

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Leta Stetter Hollingworth Fellowship Otto Kress Fellowship (1990) Nichoplas Fellowship Awarded annually to women who are Bequest of Mrs. Florence T. Kress in Designated for male students of Greek graduates of the University of Nebraska, memory of her husband, Otto Kress. extraction or born in Greece and gradu- with preference given to those who were Awarded to postgraduate students. ated from any Greek college or university. born in Nebraska or received their earlier Recipients will be eligible to receive education there. Holders are eligible to Henry Krumb Fellowships benefits for not more than two years. apply for reappointment for one year. A Annual fellowships in mining engineering, gift of Harry L. Hollingworth in memory metallurgy, and ore dressing. Anthony Pesco Fellowship (2006) of his wife. Gift of Dr. Anthony Pesco (1982, 1983, John F. T. Kuo Fellowship (1992) 1987) to support graduate students in Edward J. Ignall Research Fellowship Established by Dr. I. J. Won and other the Chemical Engineering Department Awarded annually to encourage and students of Professor Emeritus Kuo for who wish to pursue careers in academia. help support the research activities of a the support of graduate students in graduate student in the Department of applied geophysics. Piyasombatkul Fellowship (2007) Industrial Engineering and Operations Gift from Mr. and Mrs. Chatchai Research who is selected by the depart- Charles and Sarah Lapple Fellowship Piyasombatkul. Preference for students ment chair. Gift of family, friends, and (2004) from Southeast Asia or Presidential former students in memory of Professor Bequest of Charles (1936, 1937) and Fellow candidates. Edward J. Ignall. Sarah Lapple. Awarded to support deserving students in the Department Presidential Distinguished George M. Jaffin Fellowship of Chemical Engineering. Fellowships Awarded for graduate study and research These fellowships are awarded annually leading to the Ph.D. degree in orthope- Kuo and Grace Li Memorial to selected incoming Ph.D., Eng.Sc.D., dic biomechanics by the Department of Fellowship (1993) and master’s/Ph.D. students. Fellow- Bioengineering of the Hospital for Joint Gift from the Li Foundation Inc. Awarded ships include tuition plus an annual Diseases, Orthopedic Institute, and the to deserving graduate students interested stipend of $24,000 for up to four years, Department of Mechanical Engineering. in mining, mineral resources, metallurgy, including three months of summer It carries tuition exemption and a twelve- and materials science. research. All applications for admission month stipend of up to $10,000. are considered for these new fellowships. Ralph H. McKee Fellowship (1979) Herbert H. Kellogg Fellowship (1988) Bequest of Ralph H. Mckee. Income to Queneau Fellowship Fund Funded by former students and friends be used for fellowships and/or scholar Donated by Bernard R. Queneau. of Professor Emeritus H. H. Kellogg and ships in the fields of mathematics or Awarded to a deserving graduate the generous contribution of Professor chemical engineering. student in the Department of Earth Kellogg. Awarded to graduate students and Environmental Engineering. of the Henry Krumb School of Mines in the field of mineral engineering and Benjamin Miller Memorial Fellowship David M. Rickey Endowed Fellowship chemical metallurgy. Awarded to a graduate student in the Department of Industrial Engineering and (2000) Operations Research. Preference will be Gift of David M. Rickey (1979). Awarded given to students concerned with work in to students studying electrical engineer- government-industry regulatory policy, pro- ing under the holder of the David M. curement procedures and trade regulations. Rickey Professorship.

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218 Lydia C. Roberts Graduate ENDOWED SCHOLARSHIPS Edwin D. Becker Scholarship Fund Fellowships AND GRANTS (1993) Awarded annually. Open to persons born Gift of Edwin D. Becker (1956). in Iowa who have been graduated from Cvi Abel Memorial Scholarship (2003) Preference is given to students from the an Iowa college or university. In addition Gift of Jack Abel. Rocky Mountain states. to the stipend, the fellow is reimbursed the cost of traveling once from Iowa to Aigrain Family Scholarship (2008) John E. Bertram Memorial New York City and back. Special provi- Gift of Jacques and Nicolleta Aigrain, Scholarship (1990) sions: holders may not concentrate their parents, Class of 2008. Gift of Mrs. Lucy Bertram and friends studies in law, medicine, dentistry, veteri- in honor of John E. Bertram. Awarded nary medicine, or theology, and each Walter H. Aldridge (1936) to students in electrical engineering or holder must, when accepting the award, Gift of Walter H. Aldridge. computer science. state that it is his or her purpose to return to Iowa for at least two years after com- Alvey-Ferguson Company Jerry and Evelyn Bishop Scholarship pleting studies at Columbia; holders are Scholarship (1948) (1984) eligible for reappointment. Gift of the Alvey-Ferguson Company. Gift of Jerry (1942) and Evelyn Bishop for students in the Combined Plan Program. Leo Rubinstein Endowed Fellowship Erwin H. Amick Memorial Scholarship Preference is given to students in the (2005) (1970) program who attended Columbia College. Bequest of Leo Rubinstein (1963) and Gift of various donors for students in chemi- gift of Frederick Rubinstein. Awarded to cal engineering and applied chemistry. Paul H. Blaustein Scholarship (1994) deserving students studying applied Gift of Barbara Blaustein, Stacey mathematics or industrial design. Nathaniel Arbiter Scholarship (1985) Blaustein Divack and Joshua Divack. Gift of various donors in honor of Frank E. Stinchfield Fellowship in Professor Nathaniel Arbiter for graduate Philip P. Bonanno Scholarship (1999) Orthopedic Biomechanics and undergraduate students in the Donated by Philip P. Bonanno (1955), Awarded for graduate study and Henry Krumb School of Mines in the Fidelity Investments Charitable Gift Fund. research in the Department of Mechanical following specializations in order of Awarded to a deserving undergraduate. Engineering through the Orthopedic preference: mineral beneficiation, mines, Research Laboratory of the Department and physical metallurgy. of Orthopedic Surgery, College of Cornelius A. Boyle Scholarship (1962) Physicians and Surgeons, it carries Bequest of Cornelius A. Boyle. tuition exemption and a twelve-month Attardo Scholarship (1999) stipend of up to $15,000. For needy and deserving students in the Lauren Breakiron Fund (1999) Fu Foundation School of Engineering For a student continuing in The Fu and Applied Science. Gift of Michael J. Nickolas and Liliana Themelis Foundation School of Engineering and Attardo (1963). Fellowship in Earth and Applied Science. Preference given to Environmental Engineering (2000) United States citizens. Gift of Lauren P. Gift of Nickolas and Liliana Themelis. Jee Yin and Choi Heung Au Breakiron (1956). Scholarship Fund (2002) Gift of Michael M. Au (1990) to support Theodore and Jennifer Tsung Edwin W. and Mary Elizabeth Bright undergraduate scholarships at The Fu Fellowship Scholarship in Mechanical Foundation School of Engineering and Gift of Theodore T. Tsung (1982). Engineering (1985) Applied Science, with a preference to be Awarded for graduate study in the Gift of Edwin W. (1942) and Mary given to needy and deserving students Department of Electrical Engineering. Elizabeth Bright. Awarded to a deserving who have graduated from Stuyvesant mechanical engineering student who is a High School in New York City. native-born U.S. citizen. Christian R. Viros Fellowship All French citizens and French nationals Frank and Harriet Ayer Scholarship are eligible to apply. This fellowship is Lewis G. Burnell Memorial (1977) made possible by the generosity of Mr. Scholarship (2001) Bequest of Frank A. Ayer. Graduates of Viros, a 1975 graduate of SEAS. The Gift of Roger W. Burnell in memory of his Deerfield Academy are given first preference. fellowship will include tuition and an father, Lewis G. Burnell. Income to award annual stipend of $10,000. an annual scholarship to a needy and Cesare Barbieri Scholarship (1953) deserving undergraduate student in The Gift of Cesare Barbieri Fund. Fu Foundation School of Engineering and Erwin S. and Rose F. Wolfson Applied Science. Memorial Engineering Fellowship (1979) William S. Barstow Scholarship (1935) Gift of Erwin S. and Rose F. Wolfson. Gift of William S. Barstow.

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Burns and Roe, Arthur J. Fiehn Class of 1951 Endowed Scholarship James and Donna Down Scholarship 219 Scholarship (1989) (2001) (1997) Gifts from various donors in memory of Gift of members of the Class of 1951 in Gift of James (1973) and Donna Down Arthur J. Fiehn (1946). commemoration of the fiftieth anniver- to be awarded annually to a deserving sary of their graduation. Awarded to a minority undergraduate who has Byron Fellowship (1980) deserving undergraduate. demonstrated academic achievement. Bequest of Verna and Oscar Byron (1914). Class of 1952 Endowed Scholarship Stancliffe Bazen Downes Scholarship Samuel J. Clarke Scholarship (1960) (2002) (1945) Bequest of Agnes Robertson Clarke. Established by Alexander Feiner to be Bequest of Bezena Treat Downes awarded to a deserving undergraduate. Merriman in honor of her brother, for a student in civil engineering. Class of 1885 (1910) Gift of the Class of 1885 School of Hugo Cohn Scholarship (1984) Mines in commemoration of the twenty- Awarded annually with preference given Brooke Lynn Elzweig Scholarship fifth anniversary of their graduation. to electrical engineering students. Gift of (2002) Hugo Cohn (1909). Gift of Gary Elzweig (1977). Income to support an annual scholarship for a Class of 1889 (1939) deserving undergraduate student with Gift of the Class of 1889 College and Herbert J. Cooper Scholarship (1999) high financial need. Engineering. Gift of Mrs. Deborah Cooper and the Estate of Herbert J. Cooper (1946). Awarded to a deserving undergraduate. Jack B. Freeman Scholarship (1994) Class of 1900 (1940) Supports an undergraduate at SEAS Gift of the Class of 1900 College and who also plays varsity baseball. Gift of Engineering. Milton L. Cornell Scholarship (1958) Gift of various donors in memory of Jack B. Freeman (1955). Milton L. Cornell. Class of 1902 (1952) Pier-Luigi Focardi Scholarship (1964) Gift of the Class of 1902 College and Bequest of Clara G. Focardi. Engineering. Paul and Lillian Costallat Scholarship (1972) Gift of Paul and Lillian Costallat. Ford/EEOC Scholarship Class of 1906 (1940) Designated for minorities and women. Gift of the Class of 1906 in honor of Preference is given to Ford employees, Frank D. Fackenthal (1906). Frederick Van Dyke Cruser Scholarship (1980) their spouses, or children. Bequest of Maude Adelaide Cruser. Class of 1907 (1937) For students in chemical engineering Z. Y. Fu Scholarship (1993) Gift of the Class of 1907. Preference is with financial need. Gift of The Fu Foundation for undergrad- given to sons and descendants of class uate scholarship support for the School members. Cytryn Family Endowed Scholarship of Engineering and Applied Science. (2002) Class of 1909 (1959) Gift of the Cytryn Family Fund to provide General Motors Scholarship Gift of the Class of 1909 in honor of financial aid to deserving undergraduates. Designated for minorities and women. John J. Ryan. Preference is given to General Motors Frank W. Demuth Scholarship (1965) employees, their spouses, or children. Class of 1913 (1963) Bequest of Frank W. Demuth (1914). Gift of the Class of 1913 in commemo- Ben and Ethelyn Geschwind ration of the fiftieth anniversary of their Endowed Scholarship (2004) graduation. Freda Imber Dicker Endowed Scholarship Fund (2000) Gift of Benjamin and Ethelyn (1984) Gift of Dr. Stanley Dicker (1961) in honor Geschwind. Awarded to a deserving Class of 1914 (1937) of the hundredth anniversary of his undergraduate in the School of Gift of the Class of 1914 College and mother’s birth (March 5, 1900). Engineering. Engineering for a pre-engineering or prearchitecture student. Jack Dicker Endowed Scholarship Alger C. Gildersleeve Scholarship (2003) (1955) Class of 1950 Endowed Scholarship Gift of Dr. Stanley Dicker (1961) in honor Bequest of Josephine M. Gildersleeve, (2000) of his father, to support a deserving in honor of Alger G. Gildersleeve (1889). Gift of members of the Class of 1950 in junior or senior in the Department of commemoration of the fiftieth anniver- Biomedical Engineering. sary of their graduation. Awarded to a deserving undergraduate.

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220 Frederick A. Goetze Scholarship A. A. Halden Scholarship (1962) Jonathan Lewis Isaacs Memorial (1960) Established by bequests from Dorothy Scholarship (2001) Gift of William A. Baum, in honor of the C. Halden and Barbara Schwartz in This scholarship was endowed in 2001 former Dean of the School of memory of Alfred A. Halden. by Gary F. Jonas ’66 and Jonathan L. Engineering. Isaacs ’66 as the Future Entrepreneurs The Hamann Scholarship (1970) Scholarship to acknowledge the thirty- Sarah E. Grant Memorial Scholarship Bequest of Adolf M. Hamann (1910). fifth anniversary of their graduation from (1997) Columbia School of Engineering and Applied Science. On April 30, 2003, Gift of Geoffrey T. (1982) and Annette M. Alfred M. and Cornelia H. Haring Mr. Isaacs died at the young age of fifty- Grant in memory of their daughter, Scholarship (1965) seven, and the scholarship was then Sarah, to be awarded annually to a Gift of the Aeroflex Foundation for an renamed in his memory by Gary F. deserving undergraduate who has annual scholarship in the School of Jonas, with the support of Jon’s wife, demonstrated academic achievement. Mines. Charlotte Isaacs.

Adam R. Greenbaum Memorial H. Field Haviland Scholarship Fund Sheldon E. Isakoff Endowed Scholarship Fund (1988) Scholarship Fund (2000) Established in memory of Adam R. Scholarships to be awarded equally Gift of Sheldon E. (1945) and Anita Greenbaum by his parents, relatives, between The Fu Foundation School of Isakoff. Awarded to a deserving chemi- and friends following his death in Engineering and Applied Science and cal engineering undergraduate. February 2001, when he was a sopho- Columbia College. Bequest of Henry F. more. The scholarship is given to a Haviland (1902). SEAS sophomore who was named to Alfred L. Jaros Memorial Scholarship the Dean’s List as a first-year, as Adam (1967) Harold T. Helmer Scholarship (1965) was, with a preference to students from Gift of various donors, in memory of Bequest of Harold T. Helmer. New Jersey and New York. Alfred L. Jaros (1911).

David Bendel Hertz Luther E. Gregory Scholarship (1963) Cavalier Hargrave Jouet Scholarship College/Engineering Interschool Bequest of Luther E. Gregory (1893). (1941) Scholarship (1989) Bequest of Belinda Hearn Jouet, Gift of David B. Hertz (1939). Awarded in in memory of C. H. Jouet (1882). Robert Gross Fund (1999) alternate years to the College and to the Gifts of friends of Robert Gross. Engineering School to a student electing For an applied physics student. to receive a B.A. from Columbia College Alfred E. Kadell Scholarship (1995) and a B.S. from The Fu Foundation Bequest of the Estate of Alfred E. Kadell Wallace K. Grubman-Graham School of Engineering and Applied Science. (1921). Scholarship (1998) Gift of Wallace Grubman (1950) and Edward Gurnee Hewitt Scholarship Wayne Kao Scholarship (1988) the Grubman Graham Foundation to (1980) Awarded annually to undergraduate support an undergraduate student in Bequest of Mary Louise Cromwell. students. Gift of Mabel C. Kao in chemical engineering. memory of Wayne Kao (1949). Prentice Hiam Memorial Scholarship Lawrence A. Gussman Scholarship (2007) Stanley A. and Minna Kroll (1987) Gift of Atul Khanna (1983). Preference Scholarship for Engineering and Gift of Lawrence Gussman (1938). given to international students. Computer Science (1987) Awarded annually to students studying Gift of Stanley A. Kroll (1928). For under- computer science. James T. Horn Scholarship (1938) graduates who are studying electrical Gift of Sarah L. and Mary T. Horn, in engineering or computer science. Haight Family Scholarship (2004) memory of their brother, James T. Horn Gift of Deborah E. Haight (2000). (1884). Henry Krumb Scholarship (1945) Awarded to a talented and deserving Gift of Henry Krumb for annual scholar- undergraduate. Richard and Janet Hunter ships in mining engineering, metallurgy, Scholarship (2000) and ore dressing. Ralph W. Haines Scholarship (2002) Gift of Richard (1967) and Janet Hunter. Gift of Ralph W. Haines (1969) for needy Scholarship awarded to 3-2 program Jacob Kurtz Memorial Scholarship and deserving students in The Fu participants entering the School of (1982) Foundation School of Engineering and Engineering and Applied Science, with Gift of Kulite Semiconductor Products, Applied Science. prefereces given to graduates from Inc., and Kulite Tungsten, for undergrad- Whitman College. uates, preferably studying in the fields of metallurgy or solid-state physics. In memory of Jacob Kurtz (1917).

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Ronald A. Kurtz Scholarship Fund Bruce and Doris Lister Frank C. Mock and Family 221 (1990) Endowed Scholarship (2000) Scholarship (1987) Gift of Kulite Tungsten. Gift of Bruce A. Lister (1943, 1947) to Bequest of Frank C. Mock (1913). support a needy and deserving under- For students in electrical engineering Lahey Scholarship (1932) graduate student in The Fu Foundation with financial need. Bequest of Richard Lahey. School of Engineering and Applied Science. New Hope Foundation Scholarship Charles and Sarah Lapple (2006) Scholarship (2004) Anna Kazanjian and Guy Longobardo Gift of Lee and Margaret Lau. Awarded Bequest from the Estate of Charles E. Scholarship (2007) to a deserving undergraduate with Lapple and Sarah V. Lapple to be used Gift of Anna Kazanjian (1949, 1952) and preference to students from Ontario, to provide scholarships to deserving Guy (1949, 1950, 1962) Longobardo. Canada, or mainland China. undergraduate students in The Fu Preference given to students studying Foundation School of Engineering and mechanical engineering. A. Peers Montgomery Memorial Applied Science. The students receiving Scholarship (1990) the scholarship shall be designated Donald D. MacLaren Scholarship Gift of the family of A. Peers Lapple Scholars. (1995) Montgomery (1926). For an undergraduate student who is Frank H. Lee Memorial Scholarship studying biochemical engineering. John J. Morch Scholarship (1963) for Combined Plan Students (1986) Established by Donald D. MacLaren Bequest of John J. Morch. Awarded annually to a student in the (1945). Combined Plan Program in honor of Seeley W. Mudd Scholarship (1958) Professor Frank H. Lee. Manelski Family Scholarship (2004) Gift of the Seeley W. Mudd Foundation. Gift of Darren E. Manelski (1991) to Several awarded annually for mainte- Leung Endowed Scholarship (2006) support needy and deserving students nance, not for tuition. Recipient must be Gift of Lawrence Leung. Awarded annu- of The Fu Foundation School of a U.S. citizen, and his or her grandfather ally to a deserving undergraduate. Engineering and Applied Science. must have been born a U.S. citizen. Special application required. James F. Levens Scholarship (1973) Ernest Marquardt Scholarship (1968) Bequest of Ola Levens Poole for Bequest of Ernest Marquardt (1912). Mary Y. Nee Endowed Scholarship students in chemical engineering and (2008) applied chemistry. Louis F. Massa Scholarship (1952) Gift of Mary Yuet-So Nee (1984). Bequest of Louis F. Massa (1890). George J. Lewin Scholarship (1965) Frederick Noel Nye Scholarship Gift of George J. Lewin (1917) and Ralph Edward Mayer Scholarship (1971) friends. Preference given to hearing- (1924) Bequest of Frederick Noel Nye (1927). impaired students. Contributed by friends in memory of Professor Ralph Edward Mayer. Parker Family Endowed Scholarship Alvin and Richard H. Lewis (2001) Scholarship Henry Michel Scholarship (2005) Gift of Peter D. Parker (1972, 1974). Gift of Alvin and Helen S. Lewis in mem- Gift of Mrs. Mary-Elizabeth Michel Income to award an annual scholarship ory of their son, Richard Lewis (1963). in memory of Henry Michel (1949). to a needy and deserving undergraduate Scholarship awarded to deserving student in The Fu Foundation School of James M. and Elizabeth S. Li undergraduate students with preference Engineering and Applied Science. Endowed Scholarship (2006) given to civil engineering majors. Gift of James (1968, 1970, 1976) Robert I. Pearlman Scholarship (1989) and Elizabeth Li. Awarded to students Stuart Miller Endowed Scholarship Gift of Robert I. Pearlman (1955). majoring in industrial engineering and in Engineering (2003) Awarded annually to students in the operations. Gift of Stuart Miller, to be used to School of Engineering and Applied provide support for an undergraduate Science. Preference is given to students Robert D. Lilley Memorial Scholarship engineering student. from single-parent households. and Fellowship (1988) For students who are in their final year John K. Mladinov Scholarship (1994) Robert Peele Scholarship (1925) of the 3-2 Combined Plan Program and Gift of Barbara P. Mladinov in honor of Gift of E. E. Olcott (1874). who have a commitment to community her husband, John K. Mladinov (1943). service. Awarded to a deserving undergraduate with a minor in liberal arts.

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222 Brainerd F. Phillipson Scholarship Harry B. Ryker (1947) Jared K. Shaper Scholarship (1936) Bequest of Miss Helen L. Ryker in memory For deserving and qualified candidates Gift of an anonymous donor in memory of her brother, Harry Benson Ryker (1900). for degrees in engineering. of Brainerd F. Phillipson. Thomas J. Sands Endowed Edith Shih Interschool Scholarship Andre Planiol Scholarship (1967) Scholarship Fund (2001) Fund (2008) Bequest of Andre Planiol for a student Gift of Thomas J. Sands to support a Gift of Edith Shih, Esq. (Teachers College from France. scholarship for a needy and deserving 1977–1978). undergraduate student at The Fu Roy Howard Pollack Scholarship Foundation School of Engineering and Silent Hoist and Crane Company (1998) Applied Science. (1950) Bequest of Roy Howard Pollack to be Gift of the Silent Hoist and Crane Company. used for scholarships for junior or senior Peter K. Scaturro Scholarship Fund students in The Fu Foundation School of (1997) David W. Smyth Scholarship (1957) Engineering and Applied Science. Gift of Peter K. Scaturro (1982, 1985) Bequest of Mrs. Millicent W. Smyth, to be used to support scholarships to in memory of her husband, David W. Polychrome-Gregory Halpern students in SEAS or Columbia College, Smyth (1902). Scholarship with preference given to scholar-athletes from Archbishop Molloy H.S. in For graduate and undergraduate stu- Gene F. Straube Fund (2007) Briarwood, Queens, NY. dents in chemical engineering and Gift of Gene F. Straube (SEAS 1950, CC applied chemistry. 1949). The fund shall provide scholar- Norman A. Schefer Scholarship (1999) ships to undergraduate students who Professor William H. Reinmuth Gift of Norman A. Schefer (1950) and Fay graduated from a high school or prep Scholarship (1988) J. Lindner Foundation. Awarded annually school in northern California, and who Gift of Curtis Instruments, Inc., awarded to a deserving and talented student at are pursing studies in electrical engi- in alternate years to Columbia College the School of Engineering. neering, computer engineering, or com- and the Engineering School. Preference puter science. will be given to college students studying Samuel Y. Sheng Scholarship (2007) chemistry and to engineering students Gift of Samuel Y. Sheng (1951). Awarded Steve Tai and Kin-Ching Wu studying electrochemistry. Established in to students who demonstrate academic Endowed Scholarship Fund (2001) honor of Professor William H. Reinmuth. excellence. Gift of Steve Tai (1980) for an annual scholarship to a needy and deserving Kevin T. Roach Endowed Scholarship Mark Schlowsky-Fischer Scholarship undergraduate student at The Fu (2003) (2005) Foundation School of Engineering and Gift of Kevin T. Roach (1977). Income to Gift of George Schlowsky (1965) in Applied Science. provide tuition assistance to undergradu- memory of Mark Schlowsky-Fischer ate students in engineering at Columbia (1997). Scholarship awarded to deserving Tai Family Scholarship (2003) University. undergraduate students with preference Gift of Timothy Tai to be used to support given to computer science majors. Asian students demonstrating financial The Frederick Roeser Fund for need and outstanding academic potential, Student Aid (1934) Ralph J. Schwarz Scholarship (1993) with preference given to Hong Kong, An annual loan to help pay educational Gift of the Class of 1943 and other donors Taiwanese, mainland Chinese, and Chinese- expenses, which is awarded to students in memory of Ralph J. Schwarz (1943). To American applicants for admission. A T. chosen by the Committee on Scholar- be awarded to academically outstanding Tai Family Scholar will be named in a ships. The amount is individually deter- students who require financial aid. first-year class, and with suitable academic mined and is to be repaid only if and achievement and continuing need, when the student can do so without David C. and Gilbert M. Serber would retain that honor until graduation. personal sacrifice. Repayments go into Memorial Scholarship (1950) the Frederick Roeser Research Fund for Gift of the Serber family, for a student Grace C. Townsend Scholarship (1941) research in physics and chemistry. in civil engineering, in honor of David Bequest of Miss Grace C. Townsend. Serber (1896). Edgar Lewisohn Rossin Scholarship Theodosios and Ekaterine Typaldos (1949) Varsha H. Shah Scholarship (2003) Endowed Scholarship Fund (2000) Bequest of Edgar L. Rossin, to provide Gift of Hemant and Varsha Shah to Gift of Andreas (1969) and Renee a scholarship for students in mining support undergraduate female minority Typaldos and the Community engineering. students. Foundation of New Jersey. Awarded to deserving undergraduates. Preference is given to Greek-American students.

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Upton Fellowship Max Yablick Memorial Scholarship (1986) Con Edison Minority and Female 223 For the children of employees of D. C. Bequest of Max Yablick (1914). Awarded Scholarship Program Heath and Company of Lexington, annually with preference given to gradu- To aid deserving and promising minority Massachusetts. ates of Hebrew day schools and to or female students from within the Con students in the Combined Plan Program Edison service territory who will be pur- Kenneth Valentine Memorial with Yeshiva University. suing a career in engineering, by provid- Scholarship (1986) ing a renewable scholarship of at least Bequest of Julia H. Valentine, in memory Theresa Ann Yeager Memorial $1,500 and a job internship. Financial of Kenneth Valentine (1914). Awarded Scholarship (1983) need must be demonstrated. annually with preference given to students Gift of the family of Theresa Ann Yeager in chemical engineering. (1981) to support a woman who is Consolidated Natural Gas Company enrolled in The Fu Foundation School of Fellowship Frank Vanderpoel Scholarship (1936) Engineering and Applied Science. For graduate students in chemical engi- Bequest of Frank Vanderpoel. neering and applied chemistry.

RESIDENCE HALL William E. Verplanck Scholarship DuPont Fellowship SCHOLARSHIPS (1957) In chemical engineering. Gift of Mrs. T. Bache Bleecker and Class of 1887 Mines Residence Edward F. Verplanck (1912) in memory of Scholarship Everard A. Elledge Memorial their father, William E. Verplanck (1876). Awarded annually to a third-year degree Scholarship (1985) candidate, with preference given to Gift of Carol G. Elledge, in memory of Arnold Von Schrenk Scholarship descendants of members of the Class Everard A. Elledge (1942). (1943) of 1887 Mines. Bequest of Mrs. Helen von Schrenk in Ioannou Scholarship (1999) memory of her husband, Arnold von Class of 1896 Arts and Mines Donated by Constantine and Cecilia Schrenk. Scholarship Ioannou, Constantine D & B, Ltd. Awarded annually to a degree candidate Awarded to a deserving undergraduate, George Wascheck Scholarship in Columbia College, the Engineering preference given to a Greek-American Bequest of George Wascheck (1926). School, or the Graduate School of student. Architecture and Planning, with prefer- J. Watumull Scholarship (1989) ence given to descendants of members Moses and Hannah Malkin For students in the Graduate School of the Class of 1896 Arts and Mines. Scholarship Fund Gift (2004) of Arts and Sciences and in the Gift of Moses and Hannah Malkin for an Engineering School who are of East Class Of 1916 College and undergraduate engineering scholarship. Indian ancestry. Engineering Fund Gift of the Class of 1916 College and Monsanto Chemical Company Wells and Greene Scholarship Engineering. Scholarship Bequest of Josephine Wells Greene. Open to students in Barnard College, Columbia College, and the Engineering ANNUAL GIFT FELLOWSHIPS School who are pursuing a program of Herbert A. Wheeler Scholarship AND SCHOLARSHIPS study in chemical engineering or directed (1923) Each year the University receives gifts of toward it. Gift of Herbert A. Wheeler. money, some of which are renewals, for fellowships and scholarships. The fellow- Louis Morin Scholars and Fellows Frederick C. Winter Scholarship ships and scholarships made available in (2000) (1966) recent years as a result of such gifts are: Gift of the Louis Morin Charitable Trust. Gift of various donors in memory of Designated for Jewish undergraduates, Frederick C. Winter (1943). Asian Columbia Alumni Association Ph.D.s, and postdocs. Scholarship (1999) William F. Wurster Scholarship (1974) General financial aid for Asian students. The National Action Council for Awarded to a student of chemical engi- Minorities in Engineering Inc. neering and applied chemistry. Gifts of Columbia-Whitman Memorial Incentive Grants Program William F. Wurster (1913). Scholarship Renewable grants ranging from $250 Awarded from time to time to a Whitman to $2,500 for minority students in good Robert H. and Margaret H. Wyld College preengineering junior for study in academic standing who continue to Scholarship the Columbia Engineering School toward have financial need. These awards Gift of Robert H. (1904) and Margaret H. the B.S. degree. Maximum value: full supplement the funds a student raises Wyld. tuition and fees for the academic year. through work, family, schools, founda- The holder may apply for renewal. tions, and government grant programs.

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224 New York Chapter of the American Edwin Howard Armstrong Edward A. Darling Prize in Society for Metals Scholarship Memorial Awards Mechanical Engineering In metallurgy. Awarded by the Faculty of Electrical Established in 1903 by a gift from the Engineering to one outstanding graduat- late Edward A. Darling, formerly superin- Procter and Gamble Fellowship ing senior and one outstanding candi- tendent of Buildings and Grounds; a In chemical engineering and applied date for the M.S. degree, to honor the certificate and $100 cash prize awarded chemistry. late Edwin Howard Armstrong, professor annually to the most faithful and deserv- of electrical engineering and noted ing student of the graduating class in inventor of wideband FM broadcasting, mechanical engineering. Benjamin A. Tarver Jr. Memorial Fund the regenerative circuit, and other basic (2002) circuits of communications and electronics. Gifts of Benjamin A. Tarver Sr. and vari- Adam J. Derman Memorial Prize ous donors in memory of Benjamin A. Established in 1989 by family and Tarver Jr. (2004), who passed away on Theodore R. Bashkow Award friends in memory of Adam J. Derman, April 8, 2002. A cash award presented to a computer a member of SEAS class of 1989 and a science senior who has excelled in graduate student in the Department of independent projects. This is awarded Industrial Engineering and Operations The Weinig Scholars Program at the in honor of Professor Theodore R. Research. A certificate and cash prize School of Engineering and Applied Bashkow, whose contributions as a awarded annually by the Department of Science (1995) researcher, teacher, and consultant have Industrial Engineering and Operations For engineering students who are of significantly advanced the art of computer Research to a member of the graduating high academic achievement. science. class who has demonstrated exceptional ability to make computer-oriented Westmoreland Davis Fellowship Charles F. Bonilla Medal contributions to the fields of industrial For male graduate students from Virginia. The Bonilla Medal is an award for out- engineering and operations research. standing academic merit. It is presented MEDALS AND PRIZES annually to that student in the graduat- The William L. Everitt Student Awards ing class in the Department of Chemical Of Excellence American Society of Civil Engineers Engineering who best exemplifies the Given to two students who rank in the Associate Member Forum Award qualities of Professor Charles F. Bonilla. top 10 percent of their class, have an Awarded annually to that member of the active interest in telecommunications, graduating class in civil engineering who The Tullio J. Borri ’51 Award in and are active in a professional organi- has been most active in promoting the Civil Engineering zation. aims of the Society. A certificate and cash prize presented annually by the Department of Civil Zvi Galil Award for Improvement in American Society of Civil Engineers Engineering and Engineering Mechanics Engineering Student Life Robert Ridgeway Award to a senior for outstanding promise of Given annually to the student group that Awarded to the senior showing the most scholarly and professional achievement most improves engineering student life promise for a professional career in civil in civil engineering. This award has been during the academic year. Established engineering. made possible by gifts from the stock- in honor of Zvi Galil, dean of the School holder/employees and the board of from 1995 to 2007. American Society of Mechanical directors of the Damon G. Douglas Engineers Company, a New Jersey-based general Jewell M. Garrelts Award In recognition of outstanding efforts contractor, in appreciation of Mr. Borri’s Awarded to an outstanding graduating and accomplishments on behalf of many years of dedicated service and senior who will pursue graduate study in the American Society of Mechanical visionary leadership as chairman and the department that was so long and Engineers Student Section at Columbia president. successfully shepherded by Professor University. Jewell M. Garrelts. This award is made Computer Engineering possible by gifts from alumni and friends The Applied Mathematics Undergraduate Prize of Professor Garrelts and from the Faculty Award Awarded each year by vote of the Garrelts family in honor of an outstanding Awarded to an outstanding senior in the computer engineering faculty to an engineer, educator, and administrator. applied mathematics program. outstanding senior in the computer engineering program. Stephen D. Guarino Memorial Award The Applied Physics Faculty Award in Industrial Engineering and Awarded to an outstanding graduating The Computer Science Department Operations Research (2003) senior in the applied physics program. Award of Excellence A certificate and cash prize established A $200 cash prize to the student who by a gift from Roger Guarino (1951) in has demonstrated outstanding ability in memory of his son. To be awarded to the field of computer science. one outstanding senior in the Industrial

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Engineering and Operations Research Illig Medal Henry L. Michel Award in 225 Department who, in the opinion of the Established in 1898 by a bequest from Civil Engineering faculty and Board of Managers of the William C. Illig, E.M., 1882, and awarded Established by the Columbia Engineering Columbia Engineering School Alumni by the faculty to a member of the gradu- School Alumni Association in memory of Association, has been active in under- ating class for commendable proficiency Henry M. Michel (1949), who built Parsons graduate activities and has displayed in his or her regular studies. Brinkerhoff and MacDonald into one of leadership, school spirit, and scholarship the world’s leading engineering companies. achievement. Eliahu I. Jury Award A certificate and cash prize is presented Established 1991 for outstanding annually by the Department of Civil Wlliam A. Hadley Award in Mehanical achievement by a graduate student in Engineering and Engineering Mechanics Engineering the areas of systems communication or to a student or group of students in the Established in 1973 by Lucy Hadley in signal processing. Civil Engineering Depart-ment who memory of her husband. The award is demonstrate outstanding promise of leadership and professional achievement made annually in the form of a certificate Charles Kandel Award in civil and construction engineering. and cash to that student in the graduating Medal and cash prize presented annually The award is in support of a project with class in mechanical engineering who has by the Columbia Engineering School emphasis on the construction industry best exemplified the ideals of character, Alumni Association to that member in which the students participate. scholarship, and service of Professor of the graduating class who has best William A. Hadley. promoted the interests of the School through participation in extracurricular Paul Michelman Award for Exemplary Thomas “Pop” Harrington Medal activities and student-alumni affairs. Service to the Computer Science Presented annually to the student who Department This award is given to a Ph.D. student in best exemplifies the qualities of charac- The Andrew P. Kosoresow Memorial computer science who has performed ter that Professor Harrington exhibited Award for Excellence in Teaching exemplary service to the department, during his forty years of teaching. The and Service devoting time and effort beyond the call medal is made possible by Dr. Myron A. Awarded each year by the Department to further the department’s goals. It is Coler. of Computer Science to up to three given in memory of Dr. Paul Michelman computer science students for out- ’93, who devoted himself to improving Yuen-huo Hung and Chao-chin Huang standing contributions to teaching in our department through service while Award in Biomedical Engineering the department and exemplary service excelling as a researcher. This award has been endowed to honor to the department and its mission. the grandfathers of Professor Clark T. Mindlin Scholar in Civil Engineering Hung in the Department of Biomedical Dongju Lee Memorial Award and Engineering Mechanics Engineering. His paternal grandfather, Established in 2005 by family and friends This award will be made each year to Yuen-huo Hung, was a surgeon in Taipei in memory of Dongju Lee (DJ), graduate a graduate student in the Department of who was renowned for his practice of student in the Department of Civil Civil Engineering and Engineering medicine and for his compassion toward Engineering and Engineering Mechanics, Mechanics in recognition of outstanding patients. Professor Hung’s maternal 1999–2003. A certificate and cash prize promise of a creative career in research grandfather, Chao-chin Huang, was a awarded annually by the department to and/or practice. This award is made famous politician in Taiwan who dedicat- a doctoral student specializing in geo- possible by gifts of friends, colleagues, ed his life to the citizens of his country, technical/geoenvironmental engineering and former students of Professor serving as mayor of Taipei, speaker of and of outstanding promise for a career Raymond D. Mindlin, and, above all, by the Taiwan Provincial Assembly, and in research and academia. consul general to the United States. This the Mindlin family. It is intended to honor award is given to a graduating doctoral the Mindlin brothers, Raymond, Eugene, Sebastian B. Littauer Award student in the Department of Biomedical and Rowland, who excelled in their Established in 1979 in honor of Professor Engineering who embodies the collective respective scientific fields of engineering Littauer, a certificate and cash prize pre- attributes of these distinguished individ- research, engineering practice, and sented annually by the Department of uals. This student will have demonstrat- medical practice. Industrial Engineering and Operations ed great potential for making significant Research to a senior for outstanding contributions to the fields of biomedical Millman Award promise of scholarly and professional engineering and public health, and for A certificate and prize, in honor of Jacob achievement in operations research. serving as an ambassador of biomedical Millman, awarded to two of the most engineering. outstanding teaching assistants for the Mechanical Engineering academic year. Certificate of Merit In recognition of excellence in under- graduate studies.

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226 Russell Mills Award Francis B. F. Rhodes Prize Richard Skalak Memorial Prize Presented to a computer science major Established in 1926 by Eben Erskine The Richard Skalak Memorial Prize was for excellence in computer science in Olcott of the Engineering Class of 1874, founded in recognition of the pioneering memory of Russell C. Mills, a Ph.D. can- in memory of his classmate, Francis Bell contributions of Richard Skalak to the didate in computer science who exem- Forsyth Rhodes, School of Mines, 1874, development of the biomedical engi- plified academic excellence by his and awarded from time to time to the neering program at Columbia University. boundless energy and intellectual curiosity. member of the graduating class in mate- Dr. Skalak was an inspirational teacher rials science and metallurgical engineering and scholar who taught students and The Moles’ Student Award in who has shown the greatest proficiency colleagues to appreciate the value of Civil Engineering in his or her course of study. broad interactions between engineering Awarded to the student in engineering and medicine, particularly in the fields of whose academic achievement and School of Engineering and Applied cardiovascular mechanics, tissue engi- enthusiastic application show outstand- Science Scholar/Athlete Award neering, and orthopedics. The Richard ing promise of personal development Presented from time to time by the Skalak Memorial Prize is awarded annu- leading to a career in construction engi- Office of the Dean to that graduating ally to a senior biomedical engineering neering and management. student who has distinguished himself or student who exemplifies the qualities of herself as a varsity athlete and scholar. outstanding engineering scholarship and breadth of scientific curiosity that form The James F. Parker Memorial Award the basis for lifelong learning and discovery. (Mechanical Engineering Design School of Engineering Award) Student Activities Award James F. Parker served and represented This award is presented to an under- George Vincent Wendell Columbia engineering students as their graduate degree candidate in The Fu Memorial Medal dean from 1975 to 1984. He also distin- Foundation School of Engineering and Established in 1924 by the friends in the guished himself in the pursuit and analysis Applied Science who by virtue of his or alumni and faculty of the late Professor of two-dimensional art. In recognition of her willingness, energy, and leadership George Vincent Wendell to honor and his special combination of talents and has significantly contributed to the perpetuate his memory; a certificate and their integration, the School of Engineering co-curricular life of the School. medal awarded annually by choice of and Applied Science salutes the gradu- the class and the faculty to that member of the graduating class who best exem- ating student who has distinguished Robert Simon Memorial Prize plifies his ideals of character, scholarship, her- or himself as a designer. A person The Robert Simon Memorial Prize was and service. of creative and innovative inclination established in 2001 to honor Robert receives the James Parker Medal, as Simon, a Columbia alumnus who spent evidenced by outstanding performance a lifetime making valuable contributions Undergraduate Citation in in courses integrating engineering analy- to computational and mathematical sci- Civil Engineering sis and design. ences, and is awarded annually by the Department of Applied Physics and Robert Peele Prize Applied Mathematics to the doctoral A prize of $500 awarded from time to student who has completed the most time to that member of the graduating outstanding dissertation. Should no dis- class in mining engineering who has sertation qualify in a given year, the prize shown the greatest proficiency in his or may be awarded to either the most out- her course of studies. standing student who has completed a Master of Science degree in the depart- Claire S. and Robert E. Reiss Prize ment or to the most outstanding gradu- Gift of Robert Reiss, InterVentional ating senior in the department. Technologies Inc. Awarded to a graduat- ing senior in biomedical engineering judged by faculty most likely to con- tribute substantially to the field.

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228 ACADEMIC PROCEDURES AND STANDARDS

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

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averaging 16 points per term. Students Graduate Changes in Registration may not register for point loads greater A graduate student who has matriculated A student who wishes to drop or add than 21 points per term without approval in an M.S. program or is a special stu- courses or to make other changes in his from the Committee on Academic dent is considered to be making normal or her program of study after the add/drop Standing. progress if at the completion of 9 credits, period must obtain the signature of his To be eligible to receive the Bachelor he or she has earned a cumulative GPA or her adviser. A student who wishes to of Science degree, a student must of 2.5. Candidates in the Doctor of drop or add a course in his or her major complete the courses prescribed in a Engineering Science (Eng.Sc.D.) and must obtain department approval. The faculty-approved major/program (or professional programs are expected to deadline for making program changes in faculty-authorized substitutions) and achieve a 3.0 grade point average at the each term is shown in the Academic achieve a minimum cumulative grade- completion of 9 points of course work. Calendar. After this date, undergraduate point average (GPA) of 2.0. While the Thereafter, graduate students are students must petition their Committee minimum number of academic credits is considered to be making minimum satis- on Academic Standing; graduate 128 for the B.S. degree, some programs factory progress if they successfully students must petition the Office of of the School require a greater number complete at least 75 percent of all courses Graduate Student Services. For courses of credits in order to complete all the they have registered for as candidates dropped after these dates, no adjust- requirements. Undergraduate engineer- for the degree with grades of C- or ment of fees will be made. Failure to ing degrees are awarded only to stu- better. Students placed on academic attend a class without officially dropping dents who have completed at least 60 probation because of their grades are the class will result in a grade indicating points of course work at Columbia. nonetheless considered to be making permanent unofficial withdrawal (UW). Undergraduates in the programs minimum satisfactory progress for their accredited by the Engineering Accredita- first term on probation (see chapter Transfer Credits tion Commission of the ABET (chemical ‘‘Academic Standing,’’ following). Undergraduate students may obtain engineering, civil engineering, Earth and Degree requirements for master’s and academic credit toward the B.S. degree environmental engineering, electrical professional degrees must be completed by completing course work at other engineering, and mechanical engineer- within five years; those for the doctoral accredited institutions. Normally, this ing) satisfy ABET requirements by taking degrees must be completed within credit is earned during the summer. To the courses in prescribed programs, seven years. A minimum cumulative count as credit toward the degree, a which have been designed by the grade-point average of 2.5 (in all courses course taken elsewhere must have an departments so as to meet the ABET taken as a degree candidate) is required equivalent at Columbia and the student criteria. for the M.S. degree; a minimum GPA must achieve a grade of at least C. The of 3.0 is required for the professional institution must be an accredited four- Attendance degree and the Doctor of Engineering year college. To transfer credit, a student Students are expected to attend Science (Eng.Sc.D.) degree. The mini- must obtain prior approval from his or their classes and laboratory periods. mum residence requirement for each her adviser and the department before Instructors may consider attendance in Columbia degree is 30 points of course taking such courses. A course descrip- assessing a student’s performance and work completed at Columbia. tion and syllabus should be furnished as may require a certain level of attendance a part of the approval process. Courses for passing a course. taken before the receipt of the high school diploma may not be credited

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230 toward the B.S. degree. A maximum of Student Service Center, 205 Kent. The Clearinghouse, 13454 Sunrise Valley 6 credits may be credited toward the guidelines are available on ColumbiaWeb. Drive, Suite 300, Herndon, VA 20171. degree for college courses taken follow- Questions about the interpretation of the ing the receipt of a high school diploma guidelines should be referred to the Report of Grades and initial enrollment. University’s General Counsel, 412 Low Students are notified by e-mail when Graduate students are not eligible for Library. grades are submitted. Grades can then transfer credits. You may obtain an official transcript be viewed the following day by using the of your academic record at Columbia Student Services Online feature located Examinations University by writing to: on the Student Services home page at Midterm examinations: Instructors Student Service Center www.columbia.edu/students. If you generally schedule these in late October Columbia University need an official printed report, you must and mid-March. Mail Code 9202 request a transcript (please see Final examinations: These are given 1150 Amsterdam Avenue Transcripts and Certifications above). at the end of each term. The Master New York, NY 10027 All graduate students must have a University Examination Schedule is Attention: Transcripts current mailing address on file with the available online and is confirmed by Please include the following informa- Registrar’s Office. November 1 for the fall term and April 1 tion with your request: current and former for the spring term. This schedule is sent names; personal identification number Transcript Notations to all academic departments and is (PID) if known; schools attended and The grading system is as follows: available for viewing on the Columbia dates of attendance; degrees awarded A, excellent; B, good; C, satisfactory; Web site. Students should consult with and dates awarded; number of tran- D, poor but passing; F, failure (a final their instructors for any changes to the scripts desired and complete address grade not subject to re-examination). exam schedule. Examinations will not be for each; your current address and Occasionally, P (Pass) is the only pass- rescheduled to accommodate travel plans. telephone number; your signature ing option available. The grade-point Note: If a student has three final authorizing the release of your transcript. average is computed on the basis of the examinations scheduled during one cal- You may also order transcripts in person following index: A=4, B=3, C=2, D=1, endar day, as certified by the Registrar, at 205 Kent Hall on the Morningside F=0. Designations of + or – (used only an arrangement may be made with one campus (9:00 a.m.–5:00 p.m., Monday– with A, B, C) are equivalent to 0.33 (i.e., of the student’s instructors to take that Friday). Currently enrolled students may B+ =3.33; B– = 2.67). Grades of P, INC, examination at another, mutually con- order transcripts for themselves and for UW, and MU will not be included in the venient time during the final examination colleges and universities via the Student computation of the grade-point average. period. This refers to a calendar day, Services Web page at www.columbia. The mark of R (registration credit; no not a twenty-four-hour time period. edu/cu/students. There is no charge for qualitative grade earned): not accepted Undergraduate students unable to make issuing transcripts; however, all students for degree credit in any program. R suitable arrangements on their own pay a one-time transcript fee of $75 credit is not available to undergraduate should contact their adviser. Graduate upon their first registration at the students. In some divisions of the students should contact the Office of University. The normal processing time University, the instructor may stipulate Graduate Student Services. for transcripts is two to three business conditions for the grade and report a days. If you mail in your request for a failure if those conditions are not satis- Transcripts and Certifications transcript, you should allow several fied. The R notation will be given only to The University abides by the provisions additional days for delivery to and from those students who indicate, upon reg- of the Federal Family Educational Rights the University. istration and to the instructor, their inten- and Privacy Act (FERPA) of 1974. This Currently enrolled students may order tion to take the course for R, or who, act ensures a wide range of rights, certifications of their enrollment and with the approval of the instructor, file including but not limited to information degrees in person or on the Student written notice of change of intention with about student records that the University Services Web page as described above. the Registrar not later than the last day maintains, who maintains them, who Certifications are provided while you wait for change of program. Students wish- has access to them, and for what pur- if you come to 205 Kent to request them. ing to change to R credit after this date poses access is granted. The act also There is no charge for certifications. are required to submit the Dean’s written permits the University to release “direc- The Student Service Center no approval to the Registrar. A course tory information” without a student’s longer handles requests by noncurrent which has been taken for R credit may consent. In addition, the act guarantees students, by alumni, or by third parties. not be repeated later for examination students access to their records and Their requests should be made either credit. The mark of R is automatically restricts the access of others. by calling the National Student Clearing- given in Doctoral Research Instruction Students who wish to restrict access house: 703-742-4200; by e-mail: courses. to their directory information may do so degreeverify@studentclearinghouse. org; The mark of UW: given to students on the Morningside campus at the or by regular mail: National Student who discontinue attendance in a course

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but are still officially registered for it, or tered as soon as the instructor can should inquire at their departments but 231 who fail to take a final examination with- schedule it. must also follow the instructions of the out an authorized excuse. The mark of P/F (pass/fail): this grad- Dissertation Office, 107 Low Library. The mark of INC (incomplete): granted ing option is designed to allow students General deadlines for applying for only in the case of incapacitating illness to extend their academic inquiry into graduation are November 1 for February, as certified by the Health Services at new areas of study. No course taken December 1 for May, and August 1 for Columbia, serious family emergency, or for pass/fail may be used to satisfy a October. (When a deadline falls on a circumstances of comparable gravity. student’s program and degree require- weekend or holiday, the deadline moves Undergraduate students request on INC ments. The P/F option does not count to the next business day.) Doctoral stu- by filling out the Incomplete Request toward degree requirements for graduate dents must deposit their dissertations Form with their advising dean. The students. two days before the above conferral deadline is the last day of class in the dates in order to graduate. semester of enrollment. Students Credit for Internships Students who fail to earn the degree requesting an INC must gain permission Students who participate in noncom- by the conferral date for which they from both the Committee on Academic pensated off-campus internships may applied must file another application for Standing (CAS) and the instructor. have the internships noted on their a later conferral date. Graduate students should contact their transcripts. Approval for this notation instructor. If granted an INC, students may be obtained from your adviser. Diplomas must complete the required work within Formal notification from the employer There is no charge for the preparation a period of time stipulated by the is required. Graduate students may and conferral of an original diploma. If instructor but not to exceed one year. petition the office of Graduate Student your diploma is lost or damaged, there After a year, the INC will be automatically Services for this notation. will be a charge of $100 for a replace- changed into an F or contingency grade. ment diploma. Note that replacement The mark of YC (year course): a mark Name Changes diplomas carry the signatures of current given at the end of the first term of a Students may change their name of University officials. Applications for course in which the full year of work record only while currently enrolled in replacement diplomas may be requested must be completed before a qualitative the University. There is no charge for by calling the Student Service Center, grade is assigned. The grade given at this service, but students must submit Graduation, Degree Audit, and Diploma the end of the second term is the grade a name change affidavit to the Student Division, 212-854-4400. for the entire course. Service Center. Affidavits are available The mark of CP (credit pending): from this office. When you graduate or given only in graduate research courses cease to enroll in the University, your in which student research projects regu- name of record is considered final and larly extend beyond the end of the term. may not be changed unless you enroll Upon completion, a final qualitative again at the University. grade is then assigned and credit allowed. The mark of CP implies satis- factory progress. GRADUATION The mark of MU (make-up examina- Columbia University awards degrees tion): given to a student who has failed three times during the year: in February, the final examination in a course but May, and October. There is one com- who has been granted the privilege of mencement ceremony in May. Only stu- taking a second examination in an effort dents who have completed their require- to improve his or her final grade. The ments for the degree may participate in privilege is granted only when there is graduation ceremonies. a wide discrepancy between the quality of the student’s work during the term Application or Renewal of and his or her performance on the final Application for the Degree examination, and when, in the instruc- In general, students pick up and file an tor’s judgment, the reasons justify a application for a degree at their schools make-up examination. A student may be or departments, but there are several granted the mark of MU in only two exceptions. Candidates for master of courses in one term, or, alternatively, in science and professional degrees must three or more courses in one term if pick up and file their application for the their total point value is not more than 7 degree with the Student Service Center, credits. The student must remove MU 205 Kent Hall. Candidates for doctoral by taking a special examination adminis- and master of philosophy degrees

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ACADEMIC HONORS Indicators of academic well-being are housing upon their return. A medical grades that average above 2.0 each leave of absence for a graduate student Dean’s List term, in a coordinated program of study, is granted by the Office of Graduate To be eligible for Dean’s List honors, an with no incomplete grades. Student Services. Documentation from a undergraduate student must achieve a Possible academic sanctions include: physician or counselor must be provided grade-point average of 3.5 or better and • Warning: C– or below in any core sci- before such a leave is granted. In order complete at least 15 graded credits with ence course; low points toward to apply for readmission following a no incompletes or grades lower than C. degree completion medical leave, a student must submit • Academic Probation: Students will be proof of recovery from a physician or Honors Awarded with the Degree placed on academic probation if they counselor. A medical leave is for a mini- At the end of the academic year, a – fall below a 2.0 GPA in a given mum of one year and cannot be longer select portion of the candidates for the semester than two years. If the student does not Bachelor of Science degree who have – have not completed 12 points suc- return within the two-year time frame, achieved the highest academic cumula- cessfully in a given semester they will be permanently withdrawn from tive grade-point average are accorded – are a first-year student and have the School. During the course of the Latin honors. Latin honors are awarded not completed chemistry, physics, leave, students are not permitted to take in three categories (cum laude, magna University Writing, Gateway Lab, any courses for the purpose of transfer- cum laude, and summa cum laude) to and calculus during the first year. ring credit and are not permitted to be no more than 25 percent of the graduat- – receive a D, F, UW, or unauthorized on the campus. For the complete policy, ing class, with no more than 5 percent Incomplete in any first-year/sopho- consult your advising dean. summa cum laude, 10 percent magna more required courses cum laude, and 10 percent cum laude. – receive a D, F, UW or unauthorized VOLUNTARY LEAVE OF Honors are awarded on the overall Incomplete in any course required ABSENCE record of graduating seniors who have for the major A voluntary leave of absence may be completed a minimum of six semesters – receive straight C’s in the core sci- granted by the Committee on Academic at Columbia. Students may not apply for ence courses (chemistry, calculus, Standing to undergraduate students honors. physics) who request a temporary withdrawal • Continued Probation: Students who from The Fu Foundation School of are already on probation and fail to ACADEMIC MONITORING Engineering and Applied Science for a meet the minimum requirements as nonmedical reason. Students consider- The Fu Foundation School of Engineer- stated in their sanction letter ing a voluntary leave must discuss this ing and Applied Science Committee on • Strict Probation: Students who are option in advance with their advising Academic Standing determines aca- already on probation and are far below dean. Voluntary leaves are granted for a demic policies and regulations for the minimum expectations; this action is period of one calendar year only; VLOAs School except in certain instances when typically made when there are signs of will not be granted for one semester, or decisions are made by the faculty as a severe academic difficulty for more than one year. Students must whole. The Committee on Academic • Dismissal: Students who have a history be in good academic standing at the Standing is expected to uphold the poli- of not meeting minimum requirements time of the leave, and must be able to cies and regulations of the Committee will be dismissed from The Fu complete their major and degree in eight on Instruction and determine when cir- Foundation School of Engineering semesters. Students may not take cumstances warrant exceptions to them. and Applied Science. The Office of Graduate Student courses for transferable credit while on Services will monitor the academic leave. Finally, students who choose to progress of graduate students in consul- MEDICAL LEAVE OF ABSENCE take voluntary leaves are not guaranteed tation with the departments. A medical leave of absence for an housing upon return to the University. Academic performance is reviewed undergraduate student is granted by the International students should contact the by advisers at the end of each semester. Committee on Academic Standing to a International Students and Scholars The Committee on Academic Standing, student whose health prevents him or Office to ensure that a leave will not in consultation with the departments, her from successfully pursuing full-time jeopardize their ability to return to SEAS. meets to review undergraduate grades study. Undergraduates who take a med- and progress toward the degree. ical leave of absence are guaranteed

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LEAVE FOR MILITARY DUTY nated or reduced to an acceptable level REQUIRED MEDICAL LEAVE Any student who is a member of the through reasonable and realistic accom- FOR STUDENTS WITH National Guard or other reserve compo- modations and/or on-campus supports. EATING DISORDERS nent of the armed forces of the United This policy will not be used in lieu of With eating disorders, a medical leave is States or of the state-organized militia disciplinary actions to address violations sometimes necessary to protect the and is called or ordered to active duty of Columbia University rules, regulations, safety of a student. Usually this is will be granted a military leave of or policies. A student who has engaged because the student’s illness is advanced absence for the period of active duty in behavior that may violate rules, regu- enough to require hospitalization or and for one year thereafter. Upon return lations, or policies of the University com- intensive day treatment beyond the from military leave of absence, the stu- munity may be subject to the Dean’s scope of University medical and psycho- dent will be restored to the educational Discipline Process of his/her particular logical resources. A medical leave is also status attained prior to being called or school. A student may be required to sometimes deemed necessary when an ordered to such duty without loss of participate in the disciplinary process for individual student’s eating disorder has academic credits earned, scholarships his/her school coincident with placing negatively impacted the integrity of the or grants awarded, or tuition or other the student while on an involuntary leave University’s learning environment. fees paid prior to the commencement of of absence. A student who is placed on Before an involuntary medical leave active duty. The University will credit any an involuntary leave of absence while on is considered, efforts will be made to tuition or fees paid for the period of the academic and/or disciplinary status will encourage the student to take a volun- military leave of absence to the next return on that same status. tary medical leave, thus preserving, to enrollment period or will refund the Before an involuntary leave is consid- the extent possible, confidentiality and tuition and fees paid to the student, at ered, efforts may be made to encourage privacy. The policy will be invoked only the student’s option. Students returning the student to take a voluntary medical in extraordinary circumstances, when a from military duty are guaranteed hous- leave of absence. These procedures are student is unable or unwilling to request ing. described in the Medical Leave of a voluntary medical leave of absence. Students in need of a military leave of Absence Policy on page 232. A read- For the complete policy and guide- absence should contact the Dean of mission process may still be required of lines, consult your advising dean in the Students for their school. a student electing a voluntary medical Center for Student Advising. leave to determine his/her readiness to return to school. A student will not be INVOLUNTARY LEAVE OF READMISSION deemed ready to return to school if ABSENCE POLICY returning may increase the risk of self- Students seeking readmission to The Fu The Dean of Students or his/her harm and/or harm to others. Foundation School of Engineering and designee may place a student on an International students are advised Applied Science must submit evidence involuntary leave of absence for reasons that an involuntary leave of absence will that they have achieved the purposes of personal or community safety. This likely affect their student visa status and for which they left. Consequently, specif- process will be undertaken only in should consult with the International ic readmission procedures are deter- extraordinary circumstances when there Students and Scholars Office (ISSO). mined by the reasons for the withdrawal. is compelling information to suggest that When safety is an immediate con- Further information for undergraduate the student is engaging in or is at cern, the Dean of Students or his/her students is available in the Center for heightened risk of engaging in behavior designee may remove a student from Student Advising. Graduate students that could lead to serious injury to others, the campus pending final decision on an should see the Office of Graduate including as a result of physical or psy- involuntary leave. If this action is Student Services. chological illness. In addition, the invol- deemed necessary, the student will be Students applying for readmission untary leave process may be initiated if, given notice of the removal. An opportu- should complete all parts of the appro- based on an individualized assessment nity to be heard by the Dean of Students priate readmission procedures by June from Counseling and Psychological and, if desired, appeal the final decision 1 for the autumn term or October 1 for Services or other University personnel, it will be provided at a later time. the spring term. is determined that there is a significant For the complete policy and guide- risk that the student will harm him/her- lines, consult your advising dean in the self, and that the risk cannot be elimi- Center for Student Advising.

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LIFE IN THE ACADEMIC University Conduct. Copies of the full or she has been victimized should speak COMMUNITY text are available at the Office of the with an adviser in the Center for Student The Fu Foundation School of Engineer- University Senate, 406 Low Memorial Advising, a member of the Residential ing and Applied Science within Columbia Library. Programs staff, or a member of the University is a community. Admitted stu- Office of Judicial Affairs and Community Standards; graduate students should dents, faculty, and administrators come DISCIPLINE together and work through committees speak with an officer in the Office of The continuance of each student upon and other representative bodies to pur- Graduate Student Services. the rolls of the University, the receipt of sue and to promote learning, scholarly While every subtlety of proper behav- academic credits, graduation, and the inquiry, and free discourse. As in any ior cannot be detailed here, examples conferring of the degree are strictly community, principles of civility and rea- of other actions that would subject a subject to the disciplinary powers of soned interaction must be maintained. student to discipline are: the University. Thus, methods for addressing social as Although ultimate authority on matters • dishonesty in academic assignments well as academic behaviors exist. of student discipline is vested in the or in dealings with University officials, Trustees of the University, the Dean of including members of the faculty RULES OF UNIVERSITY the School and his staff are given • knowingly or recklessly endangering CONDUCT responsibility for establishing certain the health or safety of others • intentionally or recklessly destroying, The Rules of University Conduct (Chapter standards of behavior for SEAS students damaging, or stealing property XLIV of the Statutes of the University) pro- beyond the regulations included in the • possession, distribution, or use of vide special disciplinary rules applicable Statutes of the University and for defin- illegal drugs to demonstrations, rallies, picketing, and ing procedures by which discipline will • possession of weapons the circulation of petitions. These rules be administered. • refusal to show identification at the are designed to protect the rights of free We expect that in and out of the request of a University official; failure expression through peaceful demonstra- classroom, on and off campus, each to respond to the legitimate request tion while at the same time ensuring the student in the School will act in an hon- of a University official exercising his proper functioning of the University and est way and will respect the rights of or her duty the protection of the rights of those who others. Freedom of expression is an • threatening, harrassing, or abusing may be affected by such demonstrations. essential part of University life, but it others The Rules of University Conduct are does not include intimidation, threats of • violating local, state, or federal laws University-wide and supersede all other violence, or the inducement of others to • violating the ‘‘Rules of University rules of any school or division. Minor engage in violence or in conduct which Conduct’’ (copies of which are avail- violations of the Rules of Conduct are harasses others. We state emphatically able in 406 Low Library and other referred to the normal disciplinary proce- that conduct which threatens or harasses locations mentioned above) dures of each school or division (‘‘Dean’s others because of their race, sex, reli- • violating the rules of the residence Discipline’’). A student who is charged gion, disability, sexual orientation, or for halls as outlined in the “Guide to with a serious violation of the Rules has any other reason is unacceptable and Living”; this also applies to all fraternity the option of choosing Dean’s Discipline will be dealt with very severely. If each and sorority housing or a more formal hearing procedure of us at Columbia can live up to these • violating the University’s Alcohol Policy provided in the Rules. standards, we can be confident that all • violating the University’s Sexual All University faculty members, stu- in our community will benefit fully from Assault Policy (see page 239) dents, and staff members are responsi- the diversity to be found here. Any • violating the rules governing Columbia ble for compliance with the Rules of undergraduate student who believes he

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University Information Technology concerning undergraduate students that hearing, at least two members of the (CUIT) policies and procedures are not reserved to some other body. staff of the Dean of Student Affairs pres- • selling or otherwise commercializing The Office of Graduate Student Services ent the accused student with the infor- notes (whether taken in class by a is responsible for all disciplinary affairs mation that supports the allegation that student or distributed to the class concerning graduate students that are he/she has violated SEAS or University by an instructor), syllabi, exams, or not reserved to some other body. policy(ies). The student is then asked to content on a University or individual respond and will be given an opportunity faculty member Web site that is not Dean’s Discipline Process for to present information on his or her accessible to anyone outside of the Undergraduate Students behalf. University community The purpose of the Dean’s Discipline At the conclusion of the hearing, the • representing any commercial interest process is twofold. First, it is used to hearing administrators will make a deter- on campus or operating any business determine the accused student’s mination, based on all of the information on campus without authorization from responsibility for the alleged violation(s) available to them, regarding whether the the Associate Dean of Career Services of SEAS or University policy(ies). In addi- accused student is responsible for the tion, it is an opportunity for the student violation(s). The standard of proof that the hearing administers will use to make DISCIPLINARY PROCEDURES to engage in a meaningful conversation this determination is the preponderance Many policy violations that occur in the regarding his or her role as a member of the Columbia community. The Dean’s of the evidence standard. This standard Residence Halls rules are handled by the allows for a finding of responsibility if the Associate Directors of Residential Discipline process is not an adversarial process, nor is it a legalistic one, and information provided shows that it is Programs. Some serious offenses are more likely than not that a violation of referred directly to the Office of Judicial therefore the technical rules of evidence applicable to civil and criminal court Columbia policy(ies) occurred. If the stu- Affairs and Community Standards. dent is found responsible, the degree of Violations in University Apartment Housing cases do not apply. After a complaint is received a stu- seriousness of the offense and the stu- are handled by building managers and dent’s previous disciplinary record, if any, housing officials. Some incidents are dent may be removed from housing and/or placed on interim suspension by will determine the severity of the sanc- referred directly to the School’s housing tion that will be issued. The student will liaison in the Office of Graduate Student the Student Affairs staff if it is deter- mined that the student’s behavior makes be notified of the outcome of the hear- Services. ing in writing. Most violations of rules concerning his or her presence on campus a danger to the normal operations of the institu- A student found responsible after a fraternities or sororities as organizations hearing has the right to request an are handled by the Assistant Director of tion, or to the safety of himself or herself or others or to the property of the appeal of the decision and the resulting Greek Life and Leadership. Some seri- sanctions. There are three grounds upon ous offenses are referred directly to the University or others. When a complaint is received, the which an appeal of the decision may be Office of Judicial Affairs and Community made. A student found responsible for Standards. Office of Judicial Affairs and Community Standards determines whether Dean’s the violation of Columbia policy(ies) may In matters involving rallies, picketing, request a review of the decision if (1) the and other mass demonstrations, the Discipline is an appropriate response or if the complaint should be referred else- student has new information, unavailable Rules of University Conduct outlines at the time the hearing; (2) the student procedures. where. If Dean’s Discipline is to occur, a student is informed in writing of the has concerns with the process that may The Office of Judicial Affairs (located change or affect the outcome of the within the Division of Student Affairs) is complaint made against him/her and of the next step in the process. At the decision; or (3) the student feels that responsible for all disciplinary affairs the sanction issued is too severe. The

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236 request for review must be made in ACADEMIC DISHONESTY assignment or exam, or feeling that the writing to the individual indicated in the Academic dishonesty includes but is not risk of earning a poor grade outweighs decision letter and must be received limited to intentional or unintentional dis- the need to be thorough. Such circum- within ten calendar days (or as indicated honesty in academic assignments or in stances lead some students to behave in the hearing outcome letter) after the dealing with University officials, including in a manner that compromises the student receives notice of the hearing faculty and staff members. integrity of the academic community, outcome. For more information about Here are the most common types of disrespects their instructors and class- the discipline process for undergraduate academic dishonesty: mates, and deprives them of an oppor- students, please visit the Office of Judicial tunity to learn. In short, they cheat. If • plagiarism (the use of words, phrases, Affairs and Community Standards Web you ever find yourself in such circum- or ideas belonging to another, without site at www.studentaffairs.columbia.edu/ stances, you should immediately contact properly citing or acknowledging the judicial affairs. your instructor and your adviser for source) advice. Just keep in mind how hard you • cheating on examinations have worked to get to this point in your Discipline Process for Graduate • unauthorized collaboration on an academic career, and don’t jeopardize Students assignment your Columbia education with a moment When sufficient evidence exists, a stu- • receiving unauthorized assistance on of unwise decision making. dent is charged with a particular offense an assignment The easiest way to avoid the tempta- and a hearing is scheduled. Present at a • copying computer programs tion to cheat in the first place is to hearing for graduate students are the • forgery prepare yourself as best you can. Here charged student and at least two mem- • submitting work for one course that are some basic suggestions to help you bers of the Office of Graduate Student has already been used for another along the way: Services staff. At the hearing, the stu- course dent is presented with the evidence that • unauthorized distribution of assign- • Understand what your instructors supports the accusation against him or ments and exams deem as academic dishonesty and her and is asked to respond to it. The • lying to a professor or University officer their policy on citation and group student may then offer his or her own • obtaining advance knowledge of collaboration. evidence and suggest other students exams or other assignments without • Clarify any questions or concerns with whom the deans or their designee permission about assignments with instructors as might speak. On the basis of the early as possible. A student alleged to have engaged in strength of the evidence and the stu- • Develop a timeline for drafts and final academic dishonesty will be subject to dent’s response, the deans or their edits of assignments and begin prepa- the Dean’s Discipline process (see page designee reach a determination and ration in advance. 233). notify the student of their decision after • Avoid plagiarism: acknowledge peo- Students found responsible for aca- the hearing. The student can be exoner- ple’s opinions and theories by carefully demic dishonesty may face reports of ated, found guilty of the accusations, or citing their words and always indicat- such offenses on future recommenda- found not guilty due to insufficient evi- ing sources. tions for law, medical, or graduate dence; if he or she is found to have • Utilize the campus’s resources, school. The parents or guardians of committed an infraction, the penalty can such as the advising centers and students found responsible may also range from a warning to disciplinary pro- Counseling and Psychological be notified. bation to suspension or dismissal. The Services, if you are feeling over- student may also be barred from certain whelmed, burdened, or pressured. University facilities or activities. An ACADEMIC INTEGRITY • Assume that collaboration in the com- accused student has the right to appeal Academic integrity defines a university pletion of assignments is prohibited a decision that results from a disciplinary and is essential to the mission of educa- unless specified by the instructor. hearing. The appeal must be made in tion. At Columbia students are expected writing within the time period specified in to participate in an academic community Plagiarism and Acknowledgment the letter regarding the decision, and to that honors intellectual work and of Sources the person specified in the letter. respects its origins. In particular, the Columbia has always believed that abilities to synthesize information and learning to write effectively is one of the Confidentiality produce original work are key compo- most important goals a college student In general, under University policy and nents in the learning process. As such, can achieve. Students will be asked to federal law, information about Dean’s academic dishonesty is one of the most do a great deal of written work while at Disciplinary proceedings against a stu- serious offenses a student can commit Columbia: term papers, seminar and dent is confidential and may not be dis- at Columbia and can be punishable by laboratory reports, and analytic essays closed to others. A limited exception to dismissal. of different lengths. These papers play a this principle is that the outcome of Students rarely set out with the intent major role in course performance, but Dean’s Disciplinary proceedings alleging of engaging in academic dishonesty. more important, they play a major role in a crime of violence may be disclosed But classes are challenging at Columbia, intellectual development. Plagiarism, the both to the accuser and the accused. and students will often find themselves use of words, phrases, or ideas belong- pressed for time, unprepared for an ing to another, without properly citing or

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acknowledging the source, is consid- and bibliographies. Faculty members are Participating in forms of academic dis- 237 ered one of the most serious violations available to help as questions arise about honesty violates the standards of our of academic integrity and is a growing proper citations, references, and the community at Columbia and severely problem on university campuses. appropriateness of group work on inhibits a student’s chance to grow aca- One of the most prevalent forms of assignments. You can also check with demically, professionally, and socially. As plagiarism involves students using infor- the Undergraduate Writing Program. such, Columbia’s approach to academic mation from the Internet without proper Ignorance of proper citation methods integrity is informed by its explicit belief citation. While the Internet can provide a does not exonerate one from responsibility. that students must take full responsibility wealth of information, sources obtained for their actions, meaning you will need from the Web must be properly cited Personal Responsibility, Finding to make informed choices inside and just like any other source. If you are Support and More Information outside the classroom. Columbia offers uncertain how to properly cite a source A student’s education at Columbia a wealth of resources to help students of information that is not your own, University is comprised of two comple- make sound decisions regarding aca- whether from the Internet or elsewhere, mentary components: a mastery over demics, extracurricular activities, and it is critical that you do not hand in your intellectual material within a discipline personal issues. If you don’t know work until you have learned the proper and the overall development of moral where to go, see your advising dean. way to use in-text references, footnotes, character and personal ethics.

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RESERVATION OF gious holidays as much as possible. If a OFFICE OF EQUAL UNIVERSITY RIGHTS suitable arrangement cannot be worked OPPORTUNITY AND This bulletin is intended for the guidance out between the student and the AFFIRMATIVE ACTION of persons applying for or considering instructor involved, they should consult The University’s Office of Equal Opportunity application for admission to Columbia the appropriate dean or director. If an and Affirmative Action (EOAA) has over- University and for the guidance of additional appeal is needed, it may be all responsibility for the University’s equal Columbia students and faculty. The bul- taken to the Provost. opportunity and nondiscrimination poli- letin sets forth in general the manner in cies and has been designated to coordi- which the University intends to proceed ACADEMIC DISCIPLINE nate compliance activities under these with respect to the matters set forth policies and applicable federal, state, See “Discipline,” page 234. herein, but the University reserves the and local laws. Students, faculty, and right to depart without notice from the staff may contact the EOAA Office to terms of this bulletin. The bulletin is THE FEDERAL FAMILY inquire about their rights under the not intended to be, and should not be EDUCATIONAL RIGHTS University’s policies, request mediation regarded as, a contract between the AND PRIVACY ACT (FERPA) or counseling, or seek information about University and any student or other person. See “Transcripts and Certifications,” filing a complaint. Complaints by stu- page 230. dents against students are governed by ATTENDANCE the Equal Educational Opportunity and Student Nondiscrimination Policies and Students are held accountable for COLUMBIA UNIVERSITY Procedures on Discrimination and absences incurred owing to late enrollment. OMBUDS OFFICE Harassment, which are available online The Ombuds Office is a neutral and at www.columbia.edu/cu/vpaa eoaa/ confidential resource for informal conflict RELIGIOUS HOLIDAYS docs/student_discrim.html. Complaints resolution, serving the entire Columbia It is the policy of the University to by students against employees are University community—students, faculty, respect its members’ religious beliefs. governed by the Equal Employment and employees. In compliance with New York State law, Opportunity and Nondiscrimination For further information, contact Ombuds each student who is absent from school Policies and Procedures on Discrimination, Officer Marsha Wagner or Associate because of his or her religious beliefs will Discriminatory Harassment and Sexual Ombuds Officer Bathabile K. S. be given an equivalent opportunity to Harassment, which are available online Mthombeni at 660 Schermerhorn register for classes or make up any at www.columbia.edu/cu/vpaa/eoaa/ Extension; telephone: 212-854-1234; examination, study, or work require- docs/nondispol.html. All students and e-mail: [email protected]; Web ments that he or she may have missed applicants for admission are protected site: www.columbia.edu/cu/ombuds. because of such absence due to reli- from coercion, intimidation, interference, On Wednesdays the Ombuds Officer is gious beliefs, and alternative means will or retaliation for filing a complaint or at the Columbia Medical Center office, be sought for satisfying the academic assisting in an investigation under any of 101 Bard Hall, 50 Haven Avenue; requirements involved. the applicable policies and laws. For fur- telephone: 212-304-7026 Officers of administration and of ther information, contact Susan Rieger, instruction responsible for scheduling of Associate Provost, Office of Equal academic activities or essential services Opportunity and Affirmative Action, are expected to avoid conflict with reli- Columbia University, 103 Low Library,

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MC 4333, 535 West 116th Street, New Definitions Romantic Relationship Advisory York, NY 10027; 212-854-5511. For purposes of these policies and pro- Statement cedures, discrimination, discriminatory Consensual, romantic relationships Equal Educational Opportunity and harassment, and sexual harassment are between faculty and other employees and Student Nondiscrimination Policies defined as follows: students are generally not considered Columbia University is committed to Discrimination is defined as sexual harassment and are not prohibited providing a learning environment free (1) treating members of a protected by University policy. These relationships, from unlawful discrimination and harass- class less favorably because of their however, are susceptible to being char- ment and to fostering a nurturing and membership in that class; or (2) having acterized as nonconsensual, and even vibrant community founded upon the a policy or practice that has a dispropor- coercive, if there is an inherent power fundamental dignity and worth of all of tionately adverse impact on protected differential between the parties, and can its members. Consistent with this com- class members. lead to complaints of sexual harassment. mitment and with applicable laws, it is Discriminatory harassment is The full text of the Romantic Relationship the policy of the University not to toler- defined as substantially interfering with Advisory Statement may be found online ate unlawful discrimination or harass- an individual’s educational experience by at www.columbia.edu/cu/vpaa/eoaa/ ment in any form and to provide stu- subjecting him or her to severe or docs/romance.html. dents who feel that they are victims of threatening conduct or to repeated discrimination or harassment with mech- humiliating or abusive conduct, based DISABILITY ACCOMMODATION anisms for seeking redress. Columbia on his or her membership in a protected Students seeking an accommodation for University does not discriminate against class. This includes sexual harassment, a disability should contact the Office of any person in the administration of its which is described below in further Disability Services at 212-854-2388. educational policies, admissions poli- detail. cies, scholarship and loan programs, Unwelcome sexual advances, and athletic and other University-admin- requests for sexual favors, and other UNIVERSITY PROCEDURES istered programs or permit the harass- verbal or physical conduct of a sexual REGARDING ISSUES OF ment of any student or applicant on the nature constitute sexual harassment DISCRIMINATION AND basis of race, color, sex, gender (includ- when: (1) submission to such conduct is DISCRIMINATORY ing gender identity and expression), made either explicitly or implicitly a term HARASSMENT pregnancy, religion, creed, marital sta- or condition of an individual’s education; Any person who believes that he or she tus, partnership status, age, sexual ori- or (2) submission to or rejection of such has been the subject of discrimination or entation, national origin, disability, mili- conduct by an individual is used as the discriminatory harassment may initially tary status, or any other legally protect- basis for academic decisions affecting choose to deal with the alleged offender ed status. Nothing in this policy shall that individual; or (3) such conduct has directly. The University also offers several abridge academic freedom or the the purpose or effect of unreasonably options for those seeking the interven- University’s educational mission. interfering with an individual’s academic tion of the offices and individuals who Prohibitions against discrimination and performance or creating an intimidating, are authorized to respond to their com- harassment do not extend to statements hostile, demeaning, or offensive aca- plaints. These include informal counsel- or written materials that are germane to demic or living environment. ing, mediation, and formal processes for the classroom subject matter. having their complaints reviewed.

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Confidential Guidance and Office or the Mediation Clinic may be Procedure for Complaint against a Counseling found on the Web at www.columbia.edu/ Member of the Faculty or Staff The University has crafted a “safe haven” cu/vpaa/eoaa/docs/mediation.pdf. Office of Equal Opportunity and for those individuals who want to Affirmative Action approach a knowledgeable person for Formal Complaint Procedures Student complaints of discrimination or discriminatory harassment against a confidential advice or to solicit feedback Procedure for Complaint against University employee should be filed with regarding their interpretation of events. Another Student the Office of Equal Opportunity and Individuals who wish to take advantage Dean’s Discipline Affirmative Action. These complaints will of this option may contact either the Student complaints of discrimination be processed under the Equal Employment University Ombuds Officer (see or discriminatory harassment against Opportunity and Nondiscrimination www.columbia.edu/cu/ombuds), or a another student should be filed with Policies and Procedures on Discrimina- member of the University Panel on the Dean of the school in which the tion, Discriminatory Harassment and Discrimination and Sexual Harassment accused student is enrolled. Complaints Sexual Harassment. (see www.columbia.edu/cu/ombuds). against students are investigated under These officers are not authorized to the appropriate Dean’s Discipline proce- Grievances Procedures conduct formal investigations. dure of the accused student’s school. Students should consult SEAS policies Students found to have engaged in dis- on Student Grievances, Academic Mediation crimination or discriminatory harassment Concerns and Complaints (see page Students may choose to resolve their will be subject to discipline up to and 242) for the appropriate procedure to complaints through mediation by the including expulsion. complain about a faculty member’s Office of Equal Opportunity and conduct in an instructional setting. Procedure for Complaint against a Affirmative Action, the University The policy may be found online at: Student Organization Ombuds Office, or the Mediation Clinic www.engineering.columbia.edu/ Students who wish to file a complaint of at Columbia Law School. Mediation is about_seas/grievances.php. an informal, voluntary, and confidential discrimination or discriminatory harass- process whereby parties can participate ment against a student organization in a search for a fair and workable solu- should do so in consultation with the tion. Guidelines for mediation by the EOAA Dean of Students of their own school.

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SEXUAL ASSAULT POLICY Policy 3.mediation through an accredited 241 On February 25, 2000, the University The University’s Policy on Sexual Assault mediator affiliated with the University, Senate adopted a Sexual Misconduct requires that standards of sexual conduct such as the Ombuds Officer. Policy and Disciplinary Procedure that be observed on campus, that violations Complaints may also be filed with the can be used as an alternative to Dean’s of these standards are subject to disci- New York City Police Department. Discipline; the policy and procedure pline, and that resources and structures Choosing to pursue a disciplinary have been renamed the Sexual Assault be sufficient to meet the physical and action can be a difficult and confusing Policy and the Disciplinary Procedure for emotional needs of individuals who have decision. The Manager of the Sexual Assault respectively. The policy experienced sexual assault. Columbia Disciplinary Procedure for Sexual Assault prohibits sexual assault by any student University’s policy defines sexual assault is available to assist you in understand- and is University wide, applying to all as nonconsensual, intentional physical ing your options for complaint resolution, students in all schools of the University, contact of a sexual nature, such as as are trained peer advocates from the including Teacher’s College and Barnard unwelcome physical contact with a Rape Crisis/Anti-Violence Support Center. College. The Disciplinary Procedure for person’s genitals, buttocks, or breasts. Helen Arnold, Manager Sexual Assault is an option that applies Sexual assault occurs when the act is Disciplinary Procedure for Sexual Assault to all students with the exception of committed either by (a) physical force, [email protected] students within the Law School, Jewish violence, threat or intimidation; (b) ignor- 701A Lerner, Mail Code 2617 Theological Seminary, and/or Union ing the objections of another person; 2920 Broadway Theological Seminary. Complaints of (c) causing another’s intoxication or New York, NY 10027 sexual assault for these schools are impairment through the use of drugs 212-854-1717 addressed through Dean’s Discipline. or alcohol; or (d) taking advantage of fax: 212-854-2728 If the student being accused attends another person’s incapacitation, state www.columbia.edu/cu/dpsa CC/SEAS, the Disciplinary Procedure of intimidation, helplessness, or other for Sexual Assault will be the exclusive inability to consent. Complaints about nonstudent mechanism for filing a complaint. members of the University community Copies of the policy and procedure Complaint Resolution Options should be directed to the Office of Equal Opportunity and Affirmative Action at are available from the Administrative Three University-based options are Columbia, the Dean of Studies Office at Coordinator of the Disciplinary Procedure available for resolution of complaints of Barnard, or the Office of the Associate for Sexual Assault, 701A Lerner, Mail sexual assault against a student: Code 2617, 2920 Broadway, New York, Dean at Teachers College. 1.Dean’s Discipline within the school of NY 10027; telephone: 212-854-1717; fax: the charged student; 212-854-2728; www.columbia.edu/cu/ 2.the University’s Disciplinary Procedure dpsa. The policy and procedure can for Sexual Assault ; or also be found in the Office of the Dean of Students of every school.

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he following procedures are part B). They also should not be used when in this manner, they may ask for help of a process to ensure that stu- students believe that they have been the from a departmental faculty mediator, T dent concerns about experiences victim of sexual harassment or discrimi- who will assist students with com- in the classroom or with faculty are nation (see item C) or that faculty have plaints about faculty members, other addressed in an informed and appropri- engaged in scholarly or scientific mis- academic personnel, or administrators. ate manner. conduct (see item D). The name of the faculty mediator Due to the size and diverse nature We welcome students’ thoughts on is posted in the department office of our scholarly community, each school ways to clarify or enhance these proce- and on the departmental Web page. maintains its own processes for dures. If you are an Engineering student, Students may also ask the depart- addressing issues raised by students, please e-mail Vice Dean Morton ment chair or administrator to direct including their concerns about experi- Friedman at [email protected]. them to the faculty mediator. The fac- ences in the classroom or with faculty ulty mediator tries to resolve any issue at their school. Experience has shown A. COMPLAINTS ABOUT by informal meetings with the student that most student concerns are best FACULTY AND STAFF and others, including faculty as seems resolved in a collaborative way at the ACADEMIC MISCONDUCT appropriate. Students who are dissat- school level. The Fu Foundation School isfied with the outcome may request In fulfilling their instructional responsibili- of Engineering and Applied Sciences a meeting with the department chair. ties, faculty are expected to treat their (SEAS) offers several informal paths for The chair will review the mediator’s students with civility and respect. They students to use, as described in this recommendation and seek informally “should make every effort to be accurate statement. to resolve the student’s complaint. and should show respect for the rights If a student’s concerns are not satis- 2.Students may bring their concerns to of others to hold opinions differing from fied through this process, or if the stu- the University’s Ombuds Officer, who their own. They should confine their dent believes that a direct complaint to serves as an informal, confidential classes to the subject matter covered the Dean is more appropriate, formal resource for assisting members of the by the course and not use them to grievance procedures are available University with conflict resolution. The advocate any cause” (2000 Faculty through the Vice Dean of the School. Ombuds Officer provides information, Handbook). A fuller description of faculty These procedures should be used for counseling, and referrals to appropri- rights and obligations may be found in complaints about SEAS faculty. For those ate University offices and will also the Faculty Handbook, which is online at faculty who are not members of SEAS, mediate conflicts if both parties agree. www.columbia.edu/cu/vpaa/fhb/ the student should consult the proce- The Ombuds Officer does not have main.html. Students who feel that mem- dures of the school in which they serve. the authority to adjudicate disputes bers of the Engineering faculty have For academic complaints relating to and does not participate in any formal not met those obligations may take the SEAS faculty, these procedures, like University grievance proceedings. following steps (the procedure below those of other schools, provide for a Further information on the Ombuds also applies to complaints against final appeal to the University Provost. Office may be found at www. columbia. instructional and administrative staff): The procedures under item A do not edu/cu/ombuds/. take the place of the grievance proce- 1.Students are encouraged to seek a 3.Students may seek a grievance hear- dures already established to address resolution to their complaints about ing if informal mediation fails. The disputes over grades, academic dishon- faculty misconduct by talking directly grievance procedures students should esty, or issues of behavioral concerns as with the faculty member. If they feel follow will depend upon the school they relate to student conduct (see item uncomfortable handling the situation within which the faculty member is

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appointed and the nature of the is warranted. If so, the Vice Dean will normally issues his or her decision within alleged misconduct. convene an ad hoc committee consist- 30 working days of receiving the com- If the faculty member holds an appoint- ing of the Assistant Dean for Graduate mittee’s report. ment in SEAS, the student may use the Student Services (graduate students) or The Dean may discipline faculty procedures described below to address the Associate Dean of Student Affairs members who are found to have com- the issues listed below. If the faculty (undergraduate students), who acts mitted professional misconduct. Any member belongs to another school, stu- as chair; a faculty member chosen by sanctions will be imposed in a manner dents must use the procedure of that the Vice Dean; and a student chosen that is consistent with the University’s school. They may, however, ask for help by one of the student councils (an policies and procedures on faculty disci- from the departmental faculty mediator, undergraduate or a graduate student pline. In particular, if the Dean believes chair, and the School’s deans in identify- to correspond to the status of the that the offense is sufficiently serious ing and understanding the appropriate student grieving). to merit dismissal, he or she can initiate procedures. The faculty member is given the the procedures in Section 75 of the Conduct that is subject to formal student’s letter of complaint and invited University Statutes for terminating grievance procedure includes: to submit a written response. The tenured appointments, and nontenured Committee reviews both statements and appointments before the end of their • failure to show appropriate respect is given access to any other written doc- stated term, for cause. in an instructional setting for the rights uments relevant to the complaint. It will Either the student or the faculty of others to hold opinions differing normally interview both the grievant and member may appeal the decision of the from their own; the faculty member and may, at its dis- Dean to the Provost. Findings of fact, • misuse of faculty authority in an cretion, ask others to provide testimony. remedies given the student, and penal- instructional setting to pressure The merits of the grievance are evaluated ties imposed on the faculty member are students to support a political or within the context of University and SEAS all subject to appeal. A written appeal social cause; and school policy. must be submitted to the Provost within • conduct in the classroom or another The investigative committee serves 15 working days of the date of the letter instructional setting that adversely in an advisory capacity to the Dean of informing them of the Dean’s decision. affects the learning environment. the School. It is expected to complete Normally, the Provost will take no its investigation in a timely manner and longer than 30 working days to evaluate Formal grievance procedure submit a written report to the Dean, who an appeal. The Provost usually confines at SEAS may accept or modify its findings and his or her review to the written record If the informal mediation mentioned any recommendations it may have made but reserves the right to collect informa- above failed, the student should com- to remedy the student’s complaint. The tion in any manner that will help to make pose and submit to the Vice Dean of the Dean will inform both the student and his or her decision on the appeal. School a written statement documenting the faculty member of his decision in The Provost will inform both the stu- the grievance and should also include a writing. dent and the faculty member of his or description of the remedy sought. This The committee ordinarily convenes her decision in writing. If the Provost should be done no later than 30 working within 10 working days of receiving the decides that the faculty member should days after the end of the semester in complaint from the Vice Dean and ordi- be dismissed for cause, the case is which the grievance occurred. narily completes its investigation and subject to further review according to The Vice Dean will review the com- sends the Dean its report within 30 the procedures in Section 75 of the plaint to determine if a grievance hearing working days of convening. The Dean University Statutes, as noted above.

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244 Otherwise the decision of the Provost is If the students do not feel comfort- and Affirmative Action. The procedures final and not subject to further appeal. able speaking with the class instructor for handling such complaints are All aspects of an investigation of a about the matter, they should then bring described in the statement Discrimina- student grievance are confidential. The the issue to the attention of their class tion and Sexual Harassment Policy and proceedings of the grievance committee dean (undergraduate students) or Procedure, which is on the Web at are not open to the public. Only the stu- department chair (graduate students). www.columbia.edu/cu/vpaa/eoaa/docs/ dent grievant and the faculty member If the students are unable thus to discrim_sexharass.html. accused of misconduct receive copies resolve the matter to their satisfaction of the decisions of the Dean and the and believe that a procedural issue is D. SCIENTIFIC OR Provost. Everyone who is involved with involved, they should bring the matter to SCHOLARLY MISCONDUCT the investigation of a grievance is the attention of the Vice Dean. The Vice Complaints against the School’s faculty expected to respect the confidentiality Dean will work with the student and the that allege scientific or scholarly mis- of the process. faculty to determine whether there has conduct are evaluated using other been a procedural breach and if so, take procedures. These are contained in the immediate steps to remedy the matter. If B. DISPUTES OVER GRADES Columbia University Institutional Policy the Vice Dean, together with appropriate OR OTHER ACADEMIC on Misconduct in Research, available faculty other than the instructor, decides EVALUATIONS at www.columbia.edu/research/policy_ that there is no need for further action, The awarding of grades and all other misconduct.pdf. the student will be informed and the academic evaluations rests entirely with decision will be final. the faculty. If students have a concern relating to a particular grade or other assessment of their academic work, C. DISCRIMINATION AND the student first should speak with the SEXUAL HARASSMENT instructor of the class to understand If the alleged misconduct involves how the grade or other evaluation was discrimination and sexual harassment, a derived and to address the student’s student should file a complaint with the specific concern. Associate Provost for Equal Opportunity

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ADMISSIONS (GRADUATE) CENTER FOR STUDENT ADVISING Chad Gifford, Advising Dean See Graduate Student Services Monique Rinere, Dean of Advising [email protected]

Lavinia Lorch, Senior Assistant Dean Dawn Hemphill, Advising Dean ADMISSIONS (UNDERGRADUATE) [email protected] [email protected] 212 Hamilton, 212-854-2522 Andrew Plaa, Senior Assistant Dean Elizabeth McArdle, Advising Dean Mail Code 2807 [email protected] [email protected] Jessica Marinaccio, Dean of Sunday Coward, Assistant Dean Jay Orenduff, Advising Dean Undergraduate Admissions [email protected] [email protected] [email protected] Ellen Richmond, Assistant Dean Danielle Wong-Asuncion, Advising Dean Peter Johnson, Director of Admissions [email protected] [email protected] [email protected] Nathaniel Wood, Jr., Assistant Dean Monica Avitsur, Program Coordinator Alice Huang, Senior Associate Director [email protected] [email protected] [email protected] Dahlia Adu-Peasah, Advising Dean Marcela Calidonio, Program Coordinator Joanna May, Director of Outreach and [email protected] [email protected] Admissions Operations [email protected] Brianna Avery, Advising Dean Kathleen Finn, Advising Counselor [email protected] [email protected] Meaghan McCarthy, Director of Visitor Relations and On-Campus Programming Leora Brovman, Advising Dean Rebecca Hossain, Advising Counselor [email protected] [email protected] [email protected] Angie Carillo, Advising Dean Jennifer Prudencio, Advising Counselor ADVISING CENTERS [email protected] [email protected] See Center for Student Advising Jason Collado, Advising Dean Lindsay Sage, Advising Counselor [email protected] [email protected]

ALICE!, COLUMBIA UNIVERSITY’S Manoushka Constant, Advising Dean Megan Rigney, Director HEALTH EDUCATION PROGRAM [email protected] [email protected] See Health Services at Columbia Alex España, Advising Dean Cynthia Cogdill, Assistant Director [email protected] [email protected] CENTER FOR CAREER EDUCATION Rob Ferraiuolo, Advising Dean Nikki Cunningham, Assistant Director East Campus, Lower Level [email protected] [email protected] 212-854-5609 Mail Code 5727 Aileen Forbes, Advising Dean Timekah Clare, Administrative Assistant www.careereducation.columbia.edu [email protected] [email protected] [email protected] Joshua Gaynor, Advising Dean Joyce Osei, Administrative Assistant [email protected] [email protected]

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Donna Peters, Administrative Assistant Literature Humanities Melinda Aquino, Interim Associate Dean [email protected] 202 Hamilton, 212-854-2453 of Student Affairs/Multicultural Affairs Mail Code 2811 [email protected] Margaret Temple, Administrative Assistant Professor Gareth Williams, Chair Marta Esquilin, Associate Director [email protected] [email protected] All inquiries concerning Lit Hum Tamara White, Administrative Assistant should be directed to the Center for Kimberly Roberts, Assistant Director [email protected] Core Curriculum (listed above). [email protected]

Lea Robinson, Assistant Director University Writing COLUMBIA COLLEGE AND SCHOOL [email protected] Writing Center OF ENGINEERING AND APPLIED Undergraduate Writing Program Erin Reed, Administrative Assistant SCIENCE CORE CURRICULUM 310 Philosophy, Mail Code 4995 [email protected] PROGRAM OFFICES 212-854-3886 Center for the Core Curriculum Office of Residential Programs 202 Hamilton, 212-854-2453 Nicole Wallack, Interim Director 515 Lerner, 212-854-6805 Mail Code 2811 [email protected] (for general inquiries) Mail Code 4205 [email protected] (for Writing Roosevelt Montas, Associate Dean Center) Cristen Scully Kromm, Assistant Dean of the Core Curriculum of Community Development and [email protected] Residential Programs COLUMBIA VIDEO NETWORK [email protected] Art Humanities 540 S. W. Mudd, 212-854-8210 826 Schermerhorn, 212-854-4505 Mail Code 4719 Hikaru Kozuma, Director of Residential Mail Code 5517 Programs Grace Chung, Executive Director [email protected] Chair to be announced [email protected] Darleny Cepin, Associate Director of Music Humanities Residential Programs—West Campus COMMUNITY DEVELOPMENT 621 Dodge, 212-854-3825 [email protected] Christina Boubaris, Executive Assistant Mail Code 1813 [email protected] Adam Fertmann, Associate Director of Chair to be announced Residential Programs—The Block Office of Multicultural Affairs [email protected] Contemporary Civilization 401 Lerner, 212-854-0720 Scott Helfrich, Associate Director of 202 Hamilton, 212-854-2453 Mail Code 2607 Residential Programs—Living Learning Mail Code 2811 Intercultural Resource Center Center (LLC) Professor Michael Stanislawski, Chair 552 West 114th Street, 212-854-7461 [email protected] MC 5755 Deb Pawlikowski, Associate Director of Residential Programs—South Field [email protected]

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248 Kristin Sylvester, Associate Director of Jason Anthony, Associate Director, Alessandra Garber, Development Officer Residential Programs—East Campus Office of Student Group Advising [email protected] [email protected] [email protected] Margaret R. Kelly, Associate Director Victoria Lopez-Herrara, Assistant Walter Rodriguez, Associate Director, [email protected] Director of Greek Life and Leadership Office of Student Group Advising Timothy G. Greene, Stewardship Officer Development [email protected] [email protected] [email protected] Lindsay N. Montanari, Alumni Relations Chris Becker, Administrative Assistant COMPUTING SUPPORT CENTER Coordinator [email protected] Walk-in Support Center [email protected] 102 Philosophy, Mail Code 4926 Stacy Swift, Administrative Coordinator 212-854-1919 Scott T. Kelly, Alumni Relations [email protected] [email protected] Coordinator [email protected] Office of Student Development and Mailing Address Activities 401 Watson, Mail Code 6001 515 Lerner, 212-854-3611 DINING SERVICES Mail Code 2601 See Housing and Dining COUNSELING AND Robert Taylor, Executive Director, PSYCHOLOGICAL SERVICES Student Development and Activities See Health Services at Columbia DISABILITY SERVICES [email protected] See Health Services at Columbia

Cynthia Jennings, Director of New DEAN OF COLUMBIA COLLEGE Student Orientation and Class Year 208 Hamilton, 212-854-2441 EARL HALL/ST. PAUL’S CHAPEL Programming Mail Code 2805 212-854-6242, Mail Code 2008 [email protected] Michele M. Moody-Adams, Dean of Jewelnel Davis, University Chaplain Tailisha Gonzalez, Manager of Student the College 212-854-1493 Development and Activities Leadership [email protected] Kathryn Yatrakis, Dean of Academic Affairs in Programs [email protected] [email protected] DIVISION OF STUDENT AFFAIRS Benjamin Young, Director of Broadcasting DEAN’S OFFICE: COLUMBIA DEAN OF THE FU FOUNDATION and Operations (WKCR-FM) COLLEGE AND THE FU FOUNDATION SCHOOL OF ENGINEERING AND [email protected] SCHOOL OF ENGINEERING AND APPLIED SCIENCE APPLIED SCIENCE Davis Milch, Manager of Media, Performing 510 S. W. Mudd, 212-854-2993 600 Lerner Arts, and Publications Production Mail Code 4714 212-854-2446, 212-854-2961 [email protected] Feniosky Peña-Mora, Dean Mail Code 2607 Peter Cerneka, Assistant Director, Morton B. Friedman, Vice Dean Kevin G. Shollenberger, Dean of Student Student Development and Activities [email protected] Affairs and Associate Vice President, [email protected] Arts and Sciences Anna Marie O’Neill, Associate Dean Leo Padraza, Assistant Director, Student [email protected] [email protected] Development and Activities Programs Susan Tucker, Assistant Manager to and Special Events Jack McGourty, Associate Dean the Dean [email protected] [email protected] [email protected] Leah Dimond, Administrative Assistant Kathryn Wittner, Associate Dean of [email protected] DEVELOPMENT AND ALUMNI Student Affairs/Student and Alumni RELATIONS AT THE FU FOUNDATION Programs Office of Student Group Advising SCHOOL OF ENGINEERING AND [email protected] 505 Lerner, 212-854-4196 APPLIED SCIENCE Mail Code 2609 510 S. W. Mudd, 212-854-4472 Eleanor J. B. Daugherty, Associate Dean Mail Code 4718 of Student Affairs/Administration and Todd Smith, Associate Dean of Student Planning Affairs/Office of Student Group Advising Ryan Carmichael, Parents Fund [email protected] [email protected] Program Officer [email protected]

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ENGINEERING AND APPLIED Electrical Engineering FINANCIAL AID (GRADUATE) 249 SCIENCE DEPARTMENTS AND 1312 S. W. Mudd, 212-854-3105 Mail Federal Financial Aid PROGRAMS Code 4712 (Loans, Work Study) Applied Physics and Applied Professor Shi-Fu Chang, Chair Financial Aid and Educational Financing Mathematics [email protected] 615 Lerner, 212-854-3711 200 S. W. Mudd, 212-854-4457 Mail Code 2802 Mail Code 4701 Industrial Engineering and Jacqueline Perez, Senior Assistant Operations Research Professor Irving P. Herman, Chair Director of Financial Aid 331 S. W. Mudd, 212-854-2941 [email protected] [email protected] Mail Code 4704 Professor Ismail C. Noyan, Vice Chair Marjorie Ortiz, Assistant Director of [email protected] Professor Clifford Stein, Chair Financial Aid Program in Applied Mathematics [email protected] [email protected] Program in Applied Physics Program in Materials Science and Mechanical Engineering Institutional Financial Aid Engineering 220 S. W. Mudd, 212-854-2966 (Grants, Fellowships, Assistantships) Program in Medical Physics Mail Code 4703 Graduate Student Services Professor Y. Lawrence Yao, Chair 524 S. W. Mudd, 212-854-6438 Biomedical Engineering [email protected] Mail Code 4708 351 Engineering Terrace 212-854-4460, Mail Code 8904 Tiffany M. Simon, Assistant Dean EQUAL OPPORTUNITY AND [email protected] Professor Van C. Mow, Chair AFFIRMATIVE ACTION OFFICE [email protected] 103 Low Library, 212-854-5511 GRADUATE STUDENT SERVICES Professor Andrew F. Laine, Vice Chair Mail Code 4333 524 S. W. Mudd, 212-854-6438 [email protected] Susan Rieger, Associate Provost Mail Code 4708 [email protected] Chemical Engineering Tiffany M. Simon, Assistant Dean 801 S. W. Mudd, 212-854-4453 [email protected] Mail Code 4721 FINANCIAL AID AND EDUCATIONAL Jocelyn Morales, Admissions Officer FINANCING (UNDERGRADUATE) Professor Alan C. West, Chair [email protected] 407 Lerner, 212-854-3711 [email protected] Mail Code 2802 Jonathan Stark, Student Affairs Officer [email protected] Civil Engineering and Engineering Pamela Mason, Senior Associate Mechanics Director of Financial Aid and Admissions 610 S. W. Mudd, 212-854-3143 [email protected] HEALTH SERVICES AT COLUMBIA Mail Code 4709 Jacqueline Perez, Senior Assistant Primary Care Medical Services Professor Upmanu Lall, Chair Director of Financial Aid John Jay, 3rd and 4th floors [email protected] [email protected] 212-854-2284 Mail Code 3601 José Carlos Rivera, Senior Assistant Computer Science www.health.columbia.edu Director of Financial Aid 450 Computer Science, 212-939-7000 [email protected] Appointments: 212-854-2284 Mail Code 0401 Evangelia Nonis, Assistant Director of Clinician on Call (for after-hours Professor Shree Nayar, Chair Financial Aid medical and psychological consultation [email protected] [email protected] (Sept. 1–May 31): 212-854-9797

Earth and Environmental Engineering Marjorie Ortiz, Assistant Director of Enrollment/Immunization Office (Henry Krumb School of Mines) Financial Aid Wien Hall, 212-854-7210 918 S. W. Mudd, 212-854-2905 [email protected] Mail Code 3712 Mail Code 4711 Emergency Medical Services (CAVA) Professor Klaus Lackner, Chair 212-854-5555 or 99 from a campus phone [email protected]

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250 Gay Health Advocacy Project (GHAP), other forms of violence, and assistance MATH/SCIENCE DEPARTMENTS including HIV Testing to the friends and loved ones of survivors. Biological Sciences 212-854-7970 600 Fairchild, 212-854-4581 Student Medical Insurance Plan HOUSING AND DINING Mail Code 2402 Administrators: Chickering Benefit Customer Service Center Deborah Mowshowitz, Director of Planning Insurance Agency, Inc. 118 Hartley, 212-854-2775 Undergraduate Programs 1-800-859-8471 Mail Code 3003 [email protected] www.aetnastudenthealth.com www.columbia.edu/cu/biology Office of Dining Services Travel Medicine Clinic (CU on the Road): 102 Wallach, 212-854-2782 212-854-2284 Chemistry Mail Code 3001 344 Havemeyer, 212-854-2202 [email protected] Alice!, Columbia University’s Mail Code 3174 Health Promotion Program Office of Housing Services James J. Valentini, Director of Wien Hall, 212-854-5453 125 Wallach, 212-854-2946 Undergraduate Studies Mail Code 3711 Mail Code 3003 [email protected] www.alice.columbia.edu [email protected] Presents a wide range of health educa- Earth and Environmental Sciences tion and skill-building programs, includ- 106 Geoscience, Lamont-Doherty INTERCULTURAL RESOURCE ing Go Ask Alice!, a health question- Earth Observatory, 845-365-8550 CENTER (IRC) and-answer Internet service. See Community Development Nicholas Christie-Blick, Co-director of Undergraduate Studies Counseling and Psychological [email protected] Services INTERNATIONAL STUDENTS AND 845-365-8821 Lerner, 8th floor, 212-854-2878 SCHOLARS OFFICE Mail Code 2606 524 Riverside Drive, Suite 200 Walter C. Pitman, Co-director of 212-854-3587 Undergraduate Studies Individual, couple, and group counseling Mailing Address: 2960 Broadway, [email protected] for emotional stress, emergency consul- Mail Code 5724 845-365-8397 tation, and referral, as well as skill-build- ing workshops and outreach programs. Richard B. Tudisco, Associate Provost Mathematics www.health.columbia.edu/docs/ and Director 410 Mathematics, 212-854-2432 about_us/cps.html [email protected] Mail Code 4426 Immigration and Documentation Services Office of Disability Services International Student Orientation Patrick Gallagher, Director of 700 Lerner, Voice: 212-854-2388 International Student Workshops Undergraduate Studies TDD: 212-854-2378 [email protected] Mail Code 2605 JUDICIAL AFFAIRS AND Physics Coordinates services, programs, and COMMUNITY STANDARDS 704 Pupin, Mail Code 5255 policies to support and arrange appro- 607 Lerner, 212-854-1389 212-854-3348 priate accommodations for students Mail Code 4205 with disabilities. Allan S. Blaer, Director of LIBRARIES Undergraduate Studies Rape Crisis/Anti-Violence Support [email protected] Butler Library Information Center (RC/AVSC) 234 Butler, 212-854-2271 112 Hewitt (Barnard Quad) Statistics Mail Code 1121 Business Line: 212-854-4366 1255 Amsterdam Avenue 24-hour Peer Advocates: Room 1005, 212-851-2132 Engineering Library (Monell) 212-854-WALK (9255) Mail Code 4690 422 S. W. Mudd, Mail Code 4707 Peer Counselors (7 days a week): Circulation: 212-854-2976 Ji Meng Loh, Director of 212-854-HELP (4357) Reference: 212-854-3206 Undergraduate Studies Provides services and support to Fax: 212-854-3323 [email protected] survivors of sexual assault, relationship violence, childhood sexual abuse, and

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OFFICE OF STUDENT GROUP REGISTRAR 251 ADVISING 210 Kent See Community Development Mail Code 9202

John Carter, Deputy Registrar OMBUDS OFFICE 212-854-1458 600 Schermerhorn Ext., 212-854-1234 [email protected] Mail Code 5558 Jennifer Caplan, Associate Registrar 212-854-5596 PHYSICAL EDUCATION AND [email protected] INTERCOLLEGIATE ATHLETICS Brady Sloan, Associate Registrar Dodge Physical Fitness Center 212-854-8112 212-854-2548 [email protected] Mail Code 1931 Lenore Hubner, Assistant Registrar Ken Torrey, Chair, Physical Education 212-854-3240 212-854-4001 [email protected] [email protected] Melbourne Francis, Assistant Registrar Jacqueline Blackett, Associate Athletics 212-854-7528 Director for Student Athlete Support [email protected] Services 212-854-2544 [email protected] RESIDENTIAL PROGRAMS Academic and personal advising for See Community Development varsity athletes. STUDENT DEVELOPMENT PUBLIC SAFETY OFFICE AND ACTIVITIES 111 Low Library See Community Development 212-854-2797 (24 hours a day) Mail Code 4301 STUDENT SERVICE CENTER [email protected] 205 Kent, 212-854-4400 James F. McShane, Associate Vice Mail Code 9206 President for Public Safety Cashiering: 212-854-1518 [email protected] For quick answers to your questions, CAMPUS EMERGENCIES: From visit: askus.columbia.edu. on-campus Rolm phones dial 99 for fire, security, ambulance, or any crime problem; off-campus: 212-854-5555

Escort Service: 212-854-SAFE

RAPE CRISIS/ANTI-VIOLENCE SUPPORT CENTER (RC/AVSC) See Health Services at Columbia

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252 COLUMBIA UNIVERSITY THE MORNINGSIDE CAMPUS & ENVIRONS

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THE MORNINGSIDE HEIGHTS AREA OF NEW YORK CITY 253

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254 INDEX

A alumni relations, development and, 248 athletic programs, 13, 210–211 Alumni Representative Committee, 23 attendance, 229, 238 Academic Advising. See Center for Student Advising Ambrose Monell Engineering Library, 7 American College Testing (ACT) academic calendar, inside back cover B academic community, conduct examinations, 22 expected in, 234 American Language Program (ALP), 37 Bachelor of Science degree (B.S.), 17–18 academic concerns, grievances, and American studies, minor in, 188 Baker Field Athletics Complex, 211 complaints, student, 242–244 annual gift fellowships and Barnard Education Program, 19 academic discipline, 234–236 scholarships, list of, 223–224 bioinductive and biomimetic materials, academic dishonesty, 236 applications program in, 88 academic honors, 232 for degrees, 231 Biological Sciences, Department of, 250 academic integrity, 236–237 graduate, 37 courses for engineering students, 197 academic monitoring, 232 prerequisite tests, 21–22 biomedical engineering academic procedures and standards, process for, 21 courses in, 73–80 228–231 undergraduate, 21–22 minor in, 189 academic progress, satisfactory, applied chemistry. See Chemical Biomedical Engineering, Department 26–27, 228–231 Engineering, Department of of, 69–80, 249 academic standing, 232–233 applied mathematics graduate program, 72–73 Accreditation Board for Engineering courses in, 67–68 undergraduate program, 70–72 and Technology (ABET), 18, 84, minor in, 188 biophysics and soft matter physics, 136, 179 applied physics program in, 85–86 Activities Board at Columbia (ABC), courses in, 63–67 Bookstore, Columbia University, 210 207, 208 minor in, 188 Botwinick Multimedia Learning addresses of Columbia University Applied Physics and Applied Laboratory, 6, 12 departments and resources, Mathematics, Department of, Business, Graduate School of 246–251 56–68, 249 courses for engineering students, administrative officers, lists of, current research activities, 56–57 197 46, 51–52 graduate programs, 60–63 joint programs with, 33, 126–127, admissions laboratory facilities, 57–58 155 graduate, 37–38, 246 specialty areas, 59–60 Business/farm information, 29 undergraduate, 21–23, 246 undergraduate programs, 58–60 architecture, minor in, 189 advanced placement, 13–14, 22 C advanced standing, of transfer art history, minor in, 189 students, 22–23 assault, sexual, policy on, 241 C. Prescott Davis Scholars, 22 advising centers. See Center for assistantships, 42 cable TV service, 7 Student Advising Associate Provost for Equal calendar Alice! Columbia University’s Health Opportunity and Affirmative Action, academic, inside back cover Promotion Program, 214, 250 238–239, 249 for graduate admissions, 38

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campus life, 206–211 facilities and laboratories, 93–94 reservation of rights, 238 campus safety and security, 211 graduate programs, 97–98 resources, phone numbers, and career counseling, 7–8 undergraduate programs, 94–97 e-mail addresses, list of, 246–251 Center for Applied Probability (CAP), 152 classes visits and tours, 23 Center for Career Education (CCE), attendance at, 229 Web site, 6 7–8, 44, 296 registration and enrollment in, Columbia University Bookstore, 210 Center For Financial Engineering, 152 228, 229 Columbia University Enrollment Status Center for Infrastructure Studies, 94 classrooms, electronic, 6–7 Sheet, 41 Center for Life Cycle Analysis (LCA), 121 Club Sports, 207 Columbia University Grant (CUG) Center for Student Advising, College Scholarship Service (CSS) program, 28 206–207, 246–247 PROFILE Form, 28 Columbia University Information Center for Sustainable Use of colleges and universities, in Combined Technology (CUIT), 6–7 Resources (SUR), 121–122 Plan program, 16–17 Columbia University Libraries, 7 Certificate of Professional Achievement Columbia Arts Experience, 8 Columbia University’s Health Promotion program, 36 Columbia Bartending Agency and Program (Alice!), 214, 250 certification of enrollment, 230 School of Mixology, 8 Columbia University Tutoring and Chapel, St. Paul’s, 209, 248 Columbia Card (ID card), 213 Translation Agency, 8 Chaplain, University, Office of the, 209 Columbia College and engineering Columbia Video Network (CVN), chemical engineering students, 206–211 36, 247 courses in, 88–91 Columbia Comprehensive Educational application to, 36 minor in, 189–190 Financing Plan, 44 Columbia Water Center, 121 Chemical Engineering, Department of, Columbia Dining Dollars, 213 Combined Plan programs, 16–17, 23 81–91, 249 Columbia Experience Overseas (CEO), 8 commencement ceremony, 231 current research activities, 82 Columbia Genome Center (CGC), 83 Committee on Academic Standing, facilities and laboratories, 82–83 Columbia Microelectronic Sciences 228, 232 graduate program, 85–88 Laboratories, 135 Committee on Instruction, 232 undergraduate program, 83–85 Columbia Panel on Discrimination and Common Meal Program, 209 Chemistry, Department of, 250 Sexual Harassment, 240 Community Impact, 209 courses for engineering students, Columbia Student Enterprises (CSE), 8 community service, 209 197–198 Columbia University complaint procedures, formal, 240 facilities and laboratories, 83 campuses, schools, affiliations, and complaints, academic concerns, and civil engineering research facilities, 5–8 grievances, student, 242–244 courses in, 98–102 history of, 2–4 Computational and Optimization minor in, 190 maps of campus, 252, 253 Research Center (CORC), 152 Civil Engineering and Engineering New York City roots of, 5 computer accounts, obtaining, 6 Mechanics, Department of, policy, procedures, and regulations, Computer Engineering Program, 103–107 92–102, 249 228–244 graduate program, 105–107 current research activities, 92–93 Provost, 243–244 undergraduate program, 103–104

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256 computer kiosks, public, 7 Dining Dollars, 213 East Asian studies, minor in, 191 computer labs and clusters, 7 dining facilities, locations, 213 economics computer science Dining Services, 213, 250 minor in, 191 courses in, 112–119 diplomas, 231 and operations research, major in, minor in, 190 Disability Services, University Office of, 163 Computer Science, Department of, 214, 239, 250 electrical engineering 108–119, 249 discipline, academic, 234–237 courses in, 139–150 laboratory facilities, 108–109 Dean’s, 235–236 minor in, 192 graduate programs, 112 procedures for administering, Electrical Engineering, Department of, undergraduate program, 109–112 235–236 134–150, 249 computer security resources, 7 discrimination B.S./M.S. program, 137 computing facilities, University, 6–7 and sexual harassment policy and concentration options in the M.S. Computing Support Center, 248 procedure, 238–239 program, 138–139 conduct dishonesty, academic, 237 graduate programs, 137–139 expected in the academic disputes over grades or other academic laboratory facilities, 135 community, 234 evaluations, 244 research activities, 135 unacceptable, subject to discipline, distance education. See Columbia undergraduate program, 135–137 234–236 Video Network electronic classrooms, 6–7 Core Curriculum of Columbia Division of Student Affairs, 206, 235, Electronic Data Service (EDS), 7 University, 4 248 e-mail program offices, 247 Doctor of Engineering Science addresses of Columbia University Counseling and Psychological Services (Eng.Sc.D.), 34–35 resources and staff, 246–251 (CPS), 214, 250 Doctor of Philosophy (Ph.D.), 34–35 as service of CUIT, 6–7 courses Dodge Physical Fitness Center, 211 emergency resources, 214 for professions other than emeriti and retired officers, list of, 51–52 engineering, 18–19 employment, student, 28, 44 E interdisciplinary engineering, 196 Encouraging Dynamic Global key to listings, 54–55 Earl Hall Center, 209, 248 Entrepreneurs (EDGE), 8 in other divisions of the University, Early Decision program, 21 endowed scholarships and grants, of interest to engineering students, Earth and environmental engineering list of, 218–223 197–202 courses in, 126–133 Engineer of Mines (professional in SEAS departments. See individual minor in, 190–191 degree), 128 departments Earth and Environmental Engineering, Engineering Accreditation Commission Courseworks @ Columbia, 6 Department of (DEEE), 120–133, 249 (EAC), 18 credit, points of, required for degree graduate programs, 124–128 engineering courses, interdisciplinary, graduate, 32–35, 229 joint degree programs, 126–127 196 undergraduate, 10–15, 17–19, research centers, 121–123 Engineering, School of. See Fu 228–229 scholarshihps, fellowships, and Foundation School of Engineering internships, 123 and Applied Science undergraduate program, 123–124 Engineering Graduate Student Council D See also Henry Krumb School of (EGSC), 207 damages, payment for, 25, 40 Mines engineering management systems dance, minor in, 190 Earth and Environmental Engineering graduate program in, 154 Dean’s discipline, 235–236 (EEE) program, 120–121 undergraduate program in, 152 Dean’s List, 232 Earth and Environmental Sciences, engineering mechanics Degree Audit Reporting System Department of (Columbia College), courses in, 101–102 (DARS), 17 250 graduate program in, 97–98 degrees courses for engineering students, minor in, 192 application for, 231 198–200 undergraduate program in, 96 doctoral, requirements, 34–35, Earth Engineering Center (EEC), See also Civil Engineering 229, 231 122 and Engineering Mechanics, See also individual degrees Earth resources engineering program, Department of development and alumni relations, 248 124–126 engineering societies, 207

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engineering students fellowships, 42 G 257 and campus life, 206–211 lists of, 216–218, 233–234 Gateway Residential Initiative, 209 courses for, offered by other financial aid genomic engineering, program in, 86–87 University divisions, 197–204 award packages, 27–28 German, minor in, 192 interdisciplinary courses for, 196 eligibility for, 26–27 grade-point average (GPA), 230 See also students employment and, 28, 44 grades, report of, 230 Engineering Student Council, 207 federal, 29–30, 43 grading system, explained, 230–231 English and comparative literature, to graduate students, 41–44, 249 graduate courses, taking as an minor in, 192 how to apply for, 28–30 undergraduate, 17 English proficiency requirement, 37 private programs, 44 Graduate Record Examination (GRE), enrollment, 228 state, 43 37 certification of, 230 tax withholding from, for nonresident Graduate Student Services, Office of, environmental health engineering, aliens, 30 234, 236, 249 concentration in, 124, 125–126 to undergraduate students, 26–30, graduate programs, 32–35 Environmental Tracer Group, 122 249 admission to, 37–38 Equal Opportunity and Affirmative Financial Aid and Educational applying to, 37–38 Action, Office of, 238–239, 240 Financing, Office of, 26, 41, 44, 249 planning and approval, 32 examinations, midterm and final, 230 financial engineering prerequisites for admission to, 32 graduate program in, 154 See also individual programs joint programs in, 155 F graduate students undergraduate program in, 152 degree requirements for, 229, 231 faculty First Year–Sophomore Program course discipline process for, 236 and staff academic misconduct, requirements financial aid for, 41–44, 249 complaints about, 242–244 nontechnical, 10–12 housing, 212–213 lists of, 46–52 professional-level, 12–13 special students as, 35, 38 members-at-large, list of, 51 technical, 12 tuition and fees, 39–40 romantic relationships with 4-2 Combined Plan B.S. program, graduation, 231 students, 239 16, 23 grants and scholarships, 28 Faculty in Residence, 209 4-2 Combined Plan M.S. program, endowed, list of, 218–223 family contributions to educational 16, 23, 33 graphics, courses in, 102 costs, 26 fraternities and sororities, 209 Greek or Latin, minor in, 192 Family Educational Rights and Privacy Free Application for Federal Student grievance procedures, 240, 243–244 Act (FERPA), 230, 238 Aid (FAFSA), 29, 41–42, 43 grievances, academic concerns, and Federal Family Education Loan French complaints, student, 242–244 Program, 43 and francophone studies, minor in, federal financial aid, 27–28, 43–44 192 Federal Graduate PLUS Loan, 43 minor in, 192 H federal income tax returns, 30 Fu Foundation School of Engineering harassing or threatening behavior, 239 Federal Pell Grants, 28 and Applied Science, The (SEAS) harrassment Federal Perkins Loan, 43 courses. See individual departments discriminatory, 239 Federal Stafford Loan Dean of, 234, 248 sexual, 239 Subsidized, 43 department and course codes, 54–55 Harriman Institute, Special Studies Unsubsidized, 43 departments and programs, 56–186 with, 33–34 Federal Supplemental Educational development and alumni relations health insurance, 24, 39. See also Opportunity Grants (SEOG), 28 at, 248 Student Medical Insurance Plan Federal Work-Study Program (FWS), faculty and administration, 48–52 Health Service Program, 214 28 history of, 2–4 Health Services at Columbia, fees resources and facilities, 5–8 213–214, 249–250 graduate, 39–40 Vice Dean of, 243–244 Henry Krumb School of Mines (HKSM), refunds of, 25, 40 See also Columbia University 120. See also Earth and Environ- undergraduate, 24–25 Fundamentals of Engineering (FE) mental Engineering, Department of See also payments exam, 180 Higher Education Opportunity Program (HEOP), 22

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258 Hispanic studies, minor in, 192 internet access, 6 M history, minor in, 192 Interschool Governing Board, 207, 208 Manager of the Disciplinary Procedure holidays, religious, 238 internships, 231 for Sexual Assault, 241 honors, academic, 232 interviews, of undergraduate maps of Columbia Morningside Housing and Dining, 250 applicants, 23 Heights campus, 252, 253 housing, University and off-campus, Intramural and Club Sports Program, marks. See grading system 212–213. See also residence halls 211 Master of Science degree (M.S.), Humanities and Social Sciences, 32–34 Department of, courses for J materials science and engineering engineering students, 200 courses in, 133, 171–173 John Jay Dining Hall, 213 minor in, 193 joint programs I Materials Science and Engineering with the Graduate School of program (MSE), 120, 167–173 immunization requirements, 214 Business, in Earth resources current research activities, 168 income tax returns, 30 engineering, 33, 126–127 graduate programs, 169–171 industrial engineering with the Graduate School of graduate specialty in solid-state courses in, 156–166 Business, in financial engineering, science and engineering, 169–171 graduate programs in, 154–155 155 interdepartmental committee and, 167 joint programs, 33, 155 with the Graduate School of laboratory facilities, 168 minor in, 192 Business, in industrial engineering, undergraduate program, 168–169 undergraduate programs in, 152 33, 155 Mathematics, Department of, 250 Industrial Engineering and Operations with the Graduate School of courses for engineering students, Research, Department of, Business, in operations research, 200–201 151–166, 249 33, 155 meal plans. See dining plans current research activities, 152 with the School of International and Mechanical Engineer (professional graduate programs, 153–156 Public Affairs, 19 degree), 182 undergraduate programs, 152–153 with the School of Law, 19 mechanical engineering Inside New York, 8 Judicial Affairs and Community courses in, 182–186 Institute of Flight Structures, 94 Standards, Office of, 209, 234, minor in, 193 institutional grants, 42 235–236, 250 Mechanical Engineering, Department Insurance, Medical, Plan, Student, 214 Junior–Senior programs, 17–19 of, 174–186, 249 integrated waste management, current research activities, 175–177 concentration in, 125 L facilities for teaching and research, integrity, academic, 236–237 177–179 Intercollegiate Athletics laboratory charges, 24–25, 40 graduate programs, 180–182 eligibility for, 211 Langmuir Center for Colloids and undergraduate program, 179–180 programs in, 210–211 Interfaces (LCCI), 122 medals and prizes, list of, 224–226 Intercollegiate Athletics and Physical Latin, Greek or, minor in, 192 media engineering, concentration in, Education, Department of, 210–211 Law, School of, joint programs with, 19 138 Intercultural Resource Center, 247 leave(s) of absence medical care and insurance, 213–214 interdisciplinary engineering courses, involuntary, 233 Medical College Admissions Test 196 medical, 228, 232, 233 (MCAT), 18 interfacial engineering and electro- military, 233 medical leave of absence, chemistry, program in, 88 voluntary, 228, 232 228, 232, 233 Inter-Greek Council, 207 Lenfest Center for Sustainable Energy, medical physics, graduate program in, International and Public Affairs, 122 61 School of, joint programs with, 19 Lerner Hall, 209–210 Metallurgical Engineer (professional International English Language Testing libraries, 7, 250 degree), 125 System, 22 LibraryWeb, 7 microelectronic circuits, concentration International Research Center for lightwave (photonics) engineering, in, 139 Climate Prediction (IRI), 122 concentration in, 138 microelectronic devices, concentration International Students and Scholars LionSHARE, 7–8 in, 139 Office (ISSO), 8, 228, 250 loans, student, 43

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Middle East and Asian languages and joint programs with the Graduate psychological, counseling and, 259 cultures, minor in, 193 School of Business, 33, 155 services, 214 military leave of absence, 233 minor in, 193 psychology, minor in, 194 minors, academic, 18, 188–194 undergraduate programs in, Public Safety, Office of, 211, 251 misconduct 152–153 academic, complaints about faculty See also Industrial Engineering and R and staff, 242–244 Operations Research, Department of scientific or scholarly, 244 optical and laser physics, graduate Rape Crisis/Anti-Violence Support sexual. See assault, sexual program in, 62 Center, 250 monthly payment plan, 28 orientation, 208 readmission, 233 Morningside Heights campus, 6 recreational programs, 211 maps of, 252, 253 refunds of tuition and fees, 25, 40 P Multicultural Affairs, 208, 247 registered programs (with New York multimedia networking, concentration Panel on Discrimination and Sexual State Department of Education), in, 138 Harassment, 240 19–20 music Parent Loans for Undergraduate registrar, 251 instruction courses, 13 Students (PLUS), 28 See also Student Service Center minor in, 193 parents registration, 228 contributions to educational costs, 26 changes in, 229 noncustodial, financial statement of, regulations, University, official, N 29 228, 238–241 names, student, change of, 231 payments religion, minor in, 194 National Opportunity Program (NOP), financing options, 28 religious holidays, 238 22 timely and overdue, 24, 39 report of grades, 230 New Student Orientation Program See also fees residence hall scholarships, list of, 223 (NSOP), 208 Pell Grants, 28 residence halls, 208–209, 212–213 New York City, 5 Perkins Loans, 43 violation of rules of, 234 New York State personal expenses of students, 24, 39 Residence Units, and the Ph.D., 34 initial certification in adolescence philosophy, minor in, 194 Residential Programs, 208–209, 247 education, 19 physical education, 13 resources, Columbia University, list of, Tuition Assistance Program (TAP), and intercollegiate athletics, 210–211 246–251 28, 43 Physical Education, Intercollegiate and, Respecting Ourselves and Others Noncustodial Parent’s Statement Form, Department of, 211, 251 Through Education (ROOTED), 208 29 Physics, Department of, 250 Romantic Relationship Advisory nondiscriminatory policies, equal courses for engineering students, Statement, 239 educational opportunity and 201–202 romantic relationships, faculty/staff and student, 239 plagiarism, 236–237 student, 239 nontechnical requirements, 10–12 plasma physics, graduate program in, 62 Rules of University Conduct, 234 NSF-Columbia MRSEC shared Plasma Physics Laboratory, 57–58 facilities, 83 political science, minor in, 194 S polymers and soft materials, science and engineering of, program in, 85 safety and security, campus, 211 O Postcrypt Coffeehouse, 209 St. Paul’s Chapel, 209, 248 Off-Campus Housing Assistance pre-law program, 19 sanctions, for academic dishonesty, (OCHA), 212 pre-med program, 18 236 officers of SEAS preprofessional advising, 18–19, 206–207 SAT tests, 22 list of, 46, 52 preprofessional societies, 207 scholarships retired, list of, 51–52 Primary Care Medical Services, 214, 249 annual gift fellowships and, list of, Ombuds Office, 238, 240, 242, 251 printing facilities, 7 223–224 Ombuds Officer, 240, 247 prizes, medals and, list of, 224–226 and grants, 28 operations research professional degree programs, 34 and grants, endowed, list of, courses in, 156–166 professions other than engineering, 218–223 graduate program in, 153–156 SEAS programs in preparation for, residence hall, list of, 223 18–19

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260 School of Engineering (SEAS). See Fu student loans, 43–44 transfer students, 22–23 Foundation School of Engineering Student Medical Insurance Plan, 214 tuition and Applied Science student organizations, 207 graduate, 39–40 science and engineering of polymers student records, rights pertaining to, refunds of, 25, 40 and soft materials, program in, 85 230 undergraduate, 24–25 SEAS. See Fu Foundation School of Student Service Center, 230, 251 Tuition Assistance Program (TAP), Engineering and Applied Science student services, 212–214 New York State, 28, 43 secondary school preparation, recom- students tutoring, 8 mended for first-year students, 21 and campus life, 206–211 security resources, computer, 6 contributions of, to educational U Senior Advisement Center. See Junior costs, 26 Senior Academic Advising Center employment and earnings of, 28, 44 Undergraduate Research Involvement Sexual Assault, Manager of the international, 8, 42–43 Program (URIP), 10 Disciplinary Procedure for, 241 name changes of, 231 undergraduates sexual assault policy and procedures, new, orientation for, 208 applications and admissions of, 21–23 241 personal expenses of, 24, 39 degree requirements for, 228–229 Sexual Violence Prevention and romantic relationships with faculty financial aid for, 26–30 Response Program, 214 or staff, 239 housing for, 212 Social Security number, registration special, status, 38 minor programs for, 186–192 and, 228 transfer, 22–23 programs in SEAS for, 10–20 sociology, minor in, 194 See also engineering students; tuition and fees of, 24–25 solid-state physics, graduate program graduate students; undergraduates See also students in, 62–63 study abroad, 14–15 United Campus Ministries, 209 solid-state science and engineering summer courses at other institutions, University Apartment Housing (UAH), areas of research, 170 229–230 212–213 graduate specialty in, 169–171 summer earnings, 26 University Chaplain, Office of the, 209 sororities, fraternities and, 209 sustainable energy University Panel on Discrimination and Special Interest Communities, 212 and materials, concentration in, 124 Sexual Harassment, 240 special student status, 35, 38 concentration in, 125 University regulations, official, sports, 13, 210–211. See also systems biology, concentration in, 139 228, 238–241 physical education staff, romantic relationships with T V students, 239 Stafford Loans, 43 Tau Beta Pi, 17 Veteran Affairs, Department of, 43 Statistics, Department of, 250 tax withholding, on tuition aid to veterans, educational benefits for, 43 courses for engineering students, nonresident alien students, 30 Vice Dean, 243–244 202–204 teacher certification, obtaining, 19 visual arts courses, 13 statistics, minor in, 194 technological entrepreneurship, Student Advising, Center for, minor in, 194 W 206–207, 246 telecommunications engineering, Student Affairs, Division of, 206, 235, concentration in, 138 248 telephone and cable TV services, 7 Waste to Energy Research and Student and Alumni Mentoring telephone Helpdesk, 6 Technology Council (WERT), 123 Programs, 206 telephone numbers of Columbia water resources and climate risks, Student Development and Activities University departments and concentration in, 124, 125 (SDA), 207–208, 248 resources, 246–251 wireless and mobile communications, Student Financial Services. See Test of English as a Foreign Language concentration in, 138–139 Student Service Center (TOEFL), 22, 37 wireless network, 6–7 Student Governing Board (SGB), 207 tests, preadmission, 21–22 women’s athletics, 210 student grievances, academic 3-2 Combined Plan B.A./B.S. Work-Study Payroll Office, 28 concerns, and complaints, 242–244 program, 16–17, 23 Student Group Advising, Office of, transcripts, 230–231 208, 248 transfer credits, 229–230

SEAS 2009–2010 2009–2010 The Fu Foundation School of Engineering and Applied Science Applied and Engineering of School Foundation Fu The 2009–2010

The Fu Foundation School of Engineering and Applied Science Bulletin 2009–2010

The Fu Foundation School of Engineering and Applied Science 500 West 120th Street New York, New York 10027

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