Bulletin Bulletin -2012 2011

Columbia | Engineering 2 011 - 2 012 500 West 120th Street 120th West 500 10027 York New York, New Academic Calendar 2011–2012 The following Academic Calendar was correct and complete when complied; however, the University reserves the right to revise or amend it, in whole or in part, at any time. Information on the current Academic Calendar may be obtained in the Student Service Center, 205 Kent, 212-854-4330, or visit the Registrar’s website at www.columbia.edu/cu/registrar.

AUTUMN TERM 2011 SPRING TERM 2012

August January 29–Sept. 5 New student orientation program. 10–13 Registration by appointment for all classes. 16 Birthday of Martin Luther King Jr. University holiday. September 17 First day of classes. 2 Registration by appointment for first-year 17–20, 23–27 Change of program by appointment. students. 27 Last day to (1) register for academic credit, 5 Labor Day. University holiday. (2) change course programs, (3) submit 6 First day of classes. written notice of withdrawal from the spring term to the Dean of Student Affairs Undergraduate Admissions Need more information? 6–9, 12–16 Change of program by appointment. 16 Last day to (1) register for academic credit, for full refund of tuition and special fees. You can find the contact information Office of Undergraduate Admissions (2) change course programs, (3) submit No adjustment of fees for individual 212 Hamilton Hall, Mail Code 2807 for the people who know in the written notice of withdrawal from the courses dropped after this date. 1130 Amsterdam Avenue Columbia University Resource List autumn term to the Dean of Student February New York, NY 10027 on pages 242–244 or visit the Columbia Engineering Affairs for full refund of tuition and special fees. No adjustment of fees for individual 1 Last day to confirm, update, or request a Phone: 212-854-2522 website, www.engineering.columbia.edu. courses dropped after this date. waiver from the Student Medical Fax: 212-854-3393 For the most current information, visit our online 30 Last day to confirm, update, or request a Insurance Plan. E-mail: [email protected] waiver from the Student Medical 8 February degrees conferred. bulletin at www.bulletin.engineering.columbia.edu. www.studentaffairs.columbia.edu/admissions Insurance Plan.

Financial Aid March October 5 Midterm date. Office of Financial Aid and Educational Financing 19 October degrees conferred. 12–16 Spring holiday. Office: 618 Lerner Hall 20 Midterm date. 22 Last day to drop Engineering courses Mailing: 100 Hamilton Hall, Mail Code 2802 without academic penalty. Last day 1130 Amsterdam Avenue to change grading option. New York, NY 10027 November Phone: 212-854-3711 1 Last day to apply for February degrees. April Fax: 212-854-5353 7 Academic holiday. 9–13 Registration by appointment for fall 2012. 8 Election Day. University holiday. 30 Last day of classes. Undergraduate Inquiry E-mail: [email protected] 14–18 Registration by appointment for spring Graduate Inquiry E-mail: [email protected] 2012. May www.studentaffairs.columbia.edu/finaid 17 Last day to drop Engineering courses 1–3 Study days. without academic penalty. Last day to 4–11 Final examinations. Graduate Student Services change a grading option. 5 Last day for continuing students to 24–25 Thanksgiving holiday. Graduate Admissions, Financial Aid, and Student Affairs apply for financial aid for the 2012–2013 academic year. 524 S. W. Mudd, Mail Code 4708 13 Baccalaureate Service. 500 West 120th Street December 14 Engineering Class Day. New York, NY 10027 1 Last day to apply for May degrees. 16 2012 University Commencement. Phone: 212-854-6438 12 Last day of classes. Fax: 212-854-5900 13–15 Study days. E-mail: [email protected] 16–23 Final examinations. www.engineering.columbia.edu 24–Jan. 16 Winter holiday. Bulletin 2011 -2012 Mission of the Engineering School Columbia University’s Fu Foundation School of Engineering and Applied Science, as part of a world-class teaching and research university, strives to educate socially responsible engineering and applied science leaders whose work results in the betterment of the human condition, locally, nationally, and globally. We push beyond the boundaries of current research by fostering a community of scientific inquiry in critical areas of knowledge, including “CyberBioPhysicalTM Systems,” where the biological, physical, and digitial worlds integrate and fuse, and where the innovative solutions will be found to solve current grand challenges in health— in mind and body; sustainability—in energy, climate, or water; information—theoretical or applied; and systems, open or closed. Our School seeks to create an entrepreneurial ecosystem to bring the innovations developed in our classrooms and laboratories out into the world to directly improve and enhance society on a global scale.

engineering 2011–2012 a message from the dean

s students of The Fu Foundation two foundations, the crossbeam of the π, is School of Engineering and Applied Columbia’s famed liberal arts Core Curriculum, A Science at Columbia University, you the umbrella that positions engineering and are part of a long line of engineering and applied science within the context of the applied science leaders who have studied at larger society, for the betterment of the human Columbia. Across the centuries, our alumni condition and the sustainability of our planet. have exemplified the excellence, leadership, Some of you will choose to make an impact and impact that defines Columbia Engineering. by bringing together your knowledge and John Stevens (Class of 1768), inventor of the leadership in pandisciplinary research, perhaps steamboat, William Barclay Parsons (Class in an area that I call “CyberBioPhysical™ of 1882), chief engineer of New York’s first Systems”—where the biological, physical, and subway line, Robert C. Merton (Class of 1965), digital worlds intersect and fuse. These areas Nobel laureate in economics, and NASA bring together our knowledge of sensors, Astronauts Gregory Johnson (Class of 1985), materials, nanotechnology, and biological who successfully piloted the space shuttle systems and hold promise as a frontier for the Endeavour on its last mission, and Michael J. development of innovative solutions to the most Massimino (Class of 1984), who twice repaired challenging problems of modern society. the Hubble Space Telescope, are but some You are part of a School that offers great examples. opportunities for learning and advancement You are among the select few who have within a premier research university that is joined our community for an education that situated in the vibrant and cosmopolitan city will enable you to become part of the next of New York. I encourage you to take full generation of socially responsible engineering advantage of all these opportunities. and applied science leaders whose work results in the betterment of the human condition. You, too, will become part of the history of this School, which is inextricably entwined with Columbia University’s and with the city of New York. We foster an engineering education paradigm that is symbolized by the Greek letter π. The first support column of the π is the depth of knowledge you gain in Feniosky Peña-Mora your engineering or applied science major. Dean The second is the knowledge you acquire through a minor, or your involvement in entrepreneurship initiatives, research opportunities, and community-based service- learning. The overarching connector of these

engineering 2011–2012 table of contents­

About the School and 1 Graduate School Departmental 40 Mathematics 201 University Funding Physics 201 History of the School 2 Alternative Funding Sources 40 Statistics 203 Resources and Facilities 5 Other Financial Aid—Federal, 41 State, and Private Programs Campus and Student Life 205 Employment 42 Undergraduate Studies 9 Campus life 206 Contact Information 42 the Undergraduate Programs 10 student services 211 Policy on Degree Requirements 10 Faculty and Administration 43 The First-Year/Sophomore Program 10 Scholarships, Fellowships, 215 Study Abroad 13 Awards, and Prizes Combined Plan Programs 15 Departments and Academic 53 The Junior-Senior Programs 16 Programs University and School 227 Programs in Preparation for 17 key to course listings 54 Other Professions Policies, Procedures, and applied physics and 56 Joint Programs 18 Regulations applied mathematics Registered Programs 18 academic procedures 228 biomedical engineering 69 and standards Undergraduate Admissions 20 Admission as a First-Year Student 20 chemical engineering 80 academic standing 232 Applicants with Advanced Standing 21 policy on conduct and 234 Campus Visits and Interviews 22 civil engineering and 91 engineering mechanics discipline Undergraduate TUITION, 23 essential Policies for the FEES, AND PAYMENTS computer engineering 102 program columbia community 237 FINANCIAL AID FOR 25 student grievances, 238 UNDERGRADUATE STUDY computer science 107 academic concerns, and Determining Eligibility 25 earth and environmental 120 complaints Financial Aid Awards 26 engineering How to Apply for Financial Aid 26 241 Tax Withholding for Nonresident 27 electrical engineering 134 Directory of University Alien Scholarship and Resources industrial engineering 152 Fellowship Recipients Columbia university 242 and operations research resource list

Graduate Studies 29 materials science and 168 maps 245 The graduate programs 30 engineering program The Master of Science Degree 30 index 247 mechanical engineering 176 The Professional Degree 31 Academic Calendar (see inside back Doctoral Degrees: Eng.Sc.D. 32 Undergraduate Minors 189 cover) and Ph.D. Special Nondegree Students 33 Interdisciplinary Courses 195 columbia video network 34 and Courses in Other Divisions of the University graduate admissions 35 Interdisciplinary 196 graduate tuition, fees, 37 engineering courses and payments courses in other divisions 197 financial aid for graduate 39 of the university study Biological Sciences 197 Financing Graduate Education 39 Business 197 Instructions for Financial Aid 39 Chemistry 197 Applicants Earth and Environmental Sciences 198 Humanities and Social Sciences 200 About the School and University 2 history of the school

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

engineering 2011–2012 3

After receiving a master’s degree of distance learning at the graduate level and GK-12 education. The School from the School in 1929, Admiral through its online education programs. and its departments have links to the Hyman George Rickover served during Named as one of Forbes Magazine’s Departments of Physics, Chemistry, the Second World War as head of the “Best of the Web,” CVN offers the Earth Science, and Mathematics, as electrical section of the Navy’s Bureau opportunity for students anywhere in the well as the College of Physicians and of Ships. A proponent of nuclear sea world to enroll in certificate programs or Surgeons, the Graduate School of power, Rickover directed the planning obtain a master’s or professional degree Journalism, Lamont-Doherty Earth and construction of the world’s first from Columbia Engineering via the web. Observatory, Teachers College, nuclear submarine, the 300-foot-long Columbia Business School, and the Nautilus, launched in 1954. Graduate School of Architecture, The New Century Planning and Preservation. The No one could have imagined the transforming gift of The Fu Foundation The Technological Age explosive growth of technology and its has catapulted the School into the Today, The Fu Foundation School of interdisciplinary impact. The Engineering forefront of collaborative research and Engineering and Applied Science, as School is in a unique position to take teaching and has given students the it was named in 1997, continues to advantage of the research facilities opportunity to work with prize-winning provide leadership for scientific and and talents housed at Columbia to academicians, including Nobel laureates, educational advances. Even Joseph form relationships among and between from many disciplines. Engelberger, Class of 1946, the father other schools and departments within of modern robotics, could not have the University. The School’s newest anticipated the revolutionary speed with department, Biomedical Engineering, The New Research which cumbersome and expensive “big with close ties to the Medical School, For the past several years, Columbia science” computers would shrink to the is but one example. Interdisciplinary has been among the handful of research size of a wallet. centers are the norm, with cross- universities that earn the largest patent In 1986 the Engineering School was disciplinary research going on in income from inventions created by one of the first schools in the country biomedical imaging, environmental its faculty. The University is the only to use videotapes as tools for distance chemistry, materials science, medical academic institution that holds patents learning. Today Columbia Video digital libraries, nanotechnology, digital in the patent pool for the manufacture Network continues to be in the forefront government, new media technologies, of MPEG-2, the technology that

engineering 2011–2012 4 enables DVDs and high definition TV. School promotes engineering innovation navigate the future, all undergraduates Another exciting patent that holds great and engaged entrepreneurship through must complete a modified but equally promise is a laser-based method that a range of programs and offers a rigorous version of Columbia College’s makes possible, among other things, 15-credit, interdisciplinary minor in celebrated Core Curriculum. It is these the sharper display screens found in entrepreneurship made up of both selected courses in contemporary high-end smart phones. Sequential Engineering and Business School civilization in the West and other global lateral solidification (SLS) is based on courses. The School also provides a cultures that best prepare a student for breakthrough research in understanding four-year entrepreneurship experience advanced course work; a wide range of how a substance is rapidly melted for all interested Columbia Engineering eventual professions; and a continuing, and solidified. The result is an optimal students, regardless of major. life-long pursuit of knowledge, crystalline material that enables a new understanding, and social perspective. generation of smart phones. Within a It is also these Core courses that most A Forward-Looking short time, thanks to the innovations closely tie today’s student to the alumni Tradition taking place in Columbia Engineering of centuries past. Through a shared But, for all its change, there is still labs, it may be possible to put an entire exposure to the nontechnical areas, all a continuous educational thread computer on a sheet of glass or plastic. Columbia Engineering students—past, that remains the same. Columbia present, and future—gain the humanistic Engineering still remains an institution tools needed to build lives not solely as Engaged Entrepreneurship of manageable size within a great technical innovators, but as social and Entrepreneurship has emerged as an university. Committed to the educational political ones as well. important central educational theme philosophy that a broad, rigorous within The Fu Foundation School of exposure to the liberal arts provides the Engineering and Applied Science. The surest chart with which an engineer can

engineering 2011–2012 Resources and Facilities 5

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

engineering 2011–2012 6 major off-campus facilities such as the innovative solutions to some of modern Central Computing Lamont-Doherty Earth Observatory society’s most challenging problems Resources in Palisades, N.Y., and the Nevis in health, sustainability, information, Columbia University Information Laboratories in Irvington, N.Y. Involved and systems. With the School’s close Technology (CUIT) in many cooperative ventures, Columbia proximity to the Northwest Corner Helpdesk Support Center also conducts ongoing research at Science and Engineering Building and 202 Philosophy Hall such facilities as Brookhaven National the many other Morningside facilities Monday–Friday: 10:00 a.m.–6:00 p.m. Laboratory in Upton, N.Y., and the and programs, Columbia Engineering NASA Goddard Institute for Space students have ready access to the Phone: 212-854-1919 Studies located just off the Morningside whole of the University’s resources. Monday–Thursday: 8:00 a.m.–11:00 p.m. campus. Offering multiple programs of study, Friday: 8:00 a.m.–7:00 p.m. with facilities specifically designed and Saturday: 10:00 a.m.–6:00 p.m. equipped to meet the laboratory and The Morningside Heights Sunday: 3:00 p.m.–11:00 p.m. research needs of both undergraduate Campus and graduate students, the School is E-mail: [email protected] The Fu Foundation School of the site of an almost overwhelming www.columbia.edu/acis/support/ Engineering and Applied Science is array of basic and advanced research located on Columbia’s Morningside installations, from the Columbia Genome CUIT provides Columbia University campus. One of the handsomest Center and Nanoscale Science and students, faculty, and staff with a urban institutions in the country, the Engineering Center to the School’s myriad of central computing and thirty-two acres of the Morningside newest major center, the Energy Frontier communications services, including campus comprise over sixty buildings Research Center, which is examining Columbia’s wireless and high-speed of housing; recreation and research new and more efficient ways to extract campus Ethernet network, available to all facilities; centers for the humanities solar energy. Details about specific students in residence hall rooms. CUIT and social and pure sciences; and programs’ laboratories and equipment also manages an array of computer labs, professional schools in architecture, can be found in the sections describing terminal clusters, ColumbiaNet kiosk business, the fine arts, journalism, law, those programs. stations, electronic classrooms, and and other fields. provides a variety of technical support columbia Engineering services via the CUIT Helpdesk. The Fu Foundation School Computing Facilities CUIT services include the following: of Engineering and Applied • E-mail accounts and CubMail, a The Botwinick Multimedia Learning Science Web-based program for accessing Laboratory at Columbia University The Fu Foundation School of Columbia e-mail. It provides a secure has redefined the way engineers are Engineering and Applied Science and convenient way to send and educated here. occupies four laboratory and receive mail from anywhere, using any Designed with both education and classroom buildings at the north Web browser. interaction in mind, the lab provides end of the campus, including the • Computer account IDs provide students and instructors with 50 state- recently completed Northwest Corner access to Columbia’s secure online of-the-art Apple Mac Pro workstations Science and Engineering Building, information resources, campus connected to central servers and a a new interdisciplinary teaching and computer labs, and printing on CUIT network-based RAID storage array, a research building on the Morningside printers. All Columbia students, faculty, full set of professional-grade engineering campus. It was designed by the and staff are assigned an ID account software tools, and a collaborative world-renowned architect Jose Rafael (called University Network ID or UNI). classroom learning environment to help Moneo to serve as a physical and • Columbia’s website provides them engage in real-world interactions intellectual bridge, linking laboratories access to hundreds of online with community clients, Engineering and maximizing the ready sharing services and resources, including faculty, and professional practitioners. and exchange of ideas, resources, extensive academic, scholarly, and It is home to the School’s introductory and information. With its beehive-like administrative resources, a myriad first-year engineering course, as well as setting, the new building is already of library catalogs and references, advanced classes in 3-D modeling and enhancing existing collaborations the Directory of Classes, registration animation, technology and society, and and stimulating new ones, enabling information, campus publications, and entrepreneurship. researchers across the University to events listings. The classroom features a wide- work together to create new areas of • Technical support is available through screen SMART Board, two high- knowledge, in fields such as “Cyber the CUIT Helpdesk, which provides definition LCD projectors, and a Sony BioPhysical™ Systems,” where the technical assistance to students on EVI-HD1 PTZ camera with direct-to-disk biological, physical, and digital worlds the Morningside campus online, by recording via HD-SDI using a Kona3 fuse. This pandisciplinary frontier is phone, or in person. (See beginning video capture card. the nexus at which engineering and of this section for hours and contact applied scientific advances will provide information.)

engineering 2011–2012 • CourseWorks is the University course over 11 million volumes, over 150,000 necessary steps to achieve their career 7 management system. It allows journals and serials, as well as extensive goals. CCE establishes connections instructors to easily develop and electronic resources, manuscripts, rare and facilitates interaction among maintain course websites, distribute books, microforms, maps, graphic and undergraduate students, graduate class materials, link to online reserves, audio-visual materials. The services and students, alumni, employers, and administer quizzes and tests, collections are organized into 22 libraries organizations to generate opportunities communicate with students, and and various academic technology that help students pursue their personal promote online discussions. centers. The Libraries employ more than and professional career objectives. • Electronic classrooms are equipped 550 professional and support staff. The CCE encourages students and with multimedia capabilities such as website of the Libraries is the gateway alumni to visit the Center and to register computer and projection systems, to its services and resources. for Columbia’s job and internship DVD and CD-ROM players, VCRs, and The Ambrose Monell Engineering database, LionSHARE, to maximize audio systems. Library, located in 422 Mudd, contains the level of resources and assistance • Public computer kiosks are available more than 50,000 print volumes they can receive. CCE’s website (www. in various locations around the pertaining to all areas of engineering careereducation.columbia.edu) contains Morningside campus for accessing as well as applied physics, applied information on career search strategies Columbia’s web resources and e-mail. mathematics, and computer science. and tools, a calendar of events, • Computer labs and clusters provide Engineering course reserve materials special events such as career fairs and students, faculty, and researchers with are circulated from here, and there networking nights, job and internship access to a range of software. Some are 24 public computing workstations resources and access to LionSHARE. locations have consultants to provide and two scanners. The Science & CCE provides career development lab help. Engineering Library, located in 401 opportunities for students beginning • Printing facilities are available Northwest Corner Building, contains a in their first year at Columbia, offering throughout the Morningside campus core collection of 15,000 print volumes a series of coordinated programs, and Barnard College. These high- covering astronomy, biology, chemistry, workshops, seminars, and individual speed, high-volume printers are physics, and psychology. It houses the one-to-one counseling. Career located in CUIT computer labs, Digital Science Center’s 53 high-end development is a lifelong process libraries, residence halls, and other workstations with specialized software that may include self-assessment, computer clusters and electronic such as AutoCad, ChemBioDraw, competency development, networking, classrooms. Matlab, MAYA and Mathematica, eight informational interviewing, internships, • Computer security is extremely scanners, and two reservable group summer work experience, study important at Columbia and CUIT study/presentation practice rooms. abroad, and preparation for the job provides several resources online, Online, CUL provides access to search or for the graduate/professional including links to download antivirus extensive collections of electronic journals, school application process. Above all and anti-spyware software. The site ebooks (including handbooks), standards, else, it is a process of discovery and also provides information on how to patents, and society publications. learning, which provides a foundation protect your system, data, and privacy Databases such as Compendex, INSPEC, for achieving goals throughout life. CCE when working online. Scopus and Web of Science help patrons partners with students on all of these • Electronic Data Service, run jointly to pinpoint relevant engineering and aspects of the career search. by CUIT and the Libraries, provides science research. CCE manages full-time and computing support for researchers internship opportunities for students with data-intensive applications, throughout the year. On-campus Center for Career including statistical software, and recruiting is conducted throughout the Education finding and selecting appropriate data. academic year and allows students to East Campus, Lower Level • Telephone and cable TV service is submit their resumes and cover letters Mailing: 2960 Broadway, MC 5727 available to students living in University online to employers who have chosen to Delivery: 70–74 Morningside Drive residence halls. recruit on campus. These opportunities New York, NY 10027 are listed in LionSHARE. There, students columbia university will also find full-time, part-time, Phone: 212-854-5609 Libraries and temporary on- and off-campus Fax: 212-854-5640 Phone: 212-854-2976 employment opportunities advertised E-mail: [email protected] E-mail: [email protected]. year-round. The annual Engineering careereducation.columbia.edu columbia.edu Consortium Career Fair brings more library.columbia.edu than 100 employers to campus to The Columbia University Center recruit for engineering and technology for Career Education (CCE) helps Columbia University Libraries/Information positions. While at Columbia, students students and alumni develop the key Services (CUL/IS) is one of the top five are encouraged to take advantage competencies necessary to make academic research library systems in of internships, which offer hands-on informed decisions and take the North America. The collections include experience in a career field.

engineering 2011–2012 8 CCE also offers Columbia students for graduate students and alumni. A residents who have received their high-quality domestic and international dossier consists of letters of reference education in another country. Services internship experiences through alumni and other credentials that speak to for international students include pre- and employer partnerships in a a candidate’s scholarship, research admission counseling, document and diverse array of industries, including interests, and teaching experience. It is other immigration-related services, the engineering and technology. Current typically used in applying for teaching International Orientation program, social internship programs include the Science, positions at either the secondary and cultural activities, and a program for Technology, Engineering Program school or the college level and for the spouses of students. The ISSO also (STEP), CU In California, the Virtual graduate/professional school and provides credential analysis services to Internship Program (VIP), and Columbia fellowship applications. Students can the admissions offices of the University. Experience Overseas (CEO), which register online (www.interfolio.com) for The ISSO is open year-round, and offers internships in London, Hong the service. It is recommended that international students are urged to make Kong, Beijing, Shanghai, and Singapore. candidates for teaching positions open use of its services during their stay at the CCE also offers two New York–based a credentials file in the late summer University and are also invited to visit the internship programs, the Columbia Arts or early autumn of the year preceding ISSO website at www.columbia.edu/cu/ Experience and a civic engagement their availability for employment. isso, with comprehensive information for program, Columbia Communities in Undergraduate students or alumni with both prospective and current students. Action. Additionally, CCE partners with undergraduate degrees from Columbia The staff of the International Students Columbia Engineering on specialized Engineering should contact the Center and Scholars Office is available for events such as Engineering Speed for Student Advising for dossier personal advisement and for help in Networking Night, employer information management. learning about the campus and New sessions, and workshops tailored to To gain a complete understanding York City. The ISSO is an essential department and student club needs. of all Center for Career Education source of information regarding CCE fosters leadership through programs and resources, please visit immigration and Department of State Columbia Student Enterprises (CSE). the Center in the lower level of East regulations that affect students studying CSE is a unique opportunity to learn Campus. For additional information and in the United States. The staff can also about and develop valuable skills questions, please call 212-854-5609. assist with many other non-academic through managing and working for matters. The ISSO provides information student-run enterprises including the about cultural activities in the New York the International Columbia Bartending Agency and area and has reduced-rate tickets for Students and Scholars School of Mixology, Inside NY (a plays, concerts, and other events. Office distinctive tourist guide to New York), Students are required to check in International House North and the Columbia University Tutoring with the ISSO within a week of their 524 Riverside Drive, Suite 200 and Translation Agency. The participants arrival at Columbia. The office’s street Mailing: 2960 Broadway, MC 5724 in the program receive training and address is 524 Riverside Drive in New York, NY 10027 develop transferable business skills International House North, just north of applicable to all industries. 122nd Street. The orientation program Phone: 212-854-3587 In addition, CCE recognizes the for new international students arriving Fax: 212-851-1235 special interests of graduate students for the September term takes place E-mail: [email protected] with programs, workshops, and one-to- during orientation week, usually the www.columbia.edu/cu/isso one counseling opportunities that focus last week in August or the first week on both academic and nonacademic in September. For further information, The International Students and Scholars careers. On-campus recruiting and consult the International Students Office (ISSO) offers many services LionSHARE are, of course, available to and Scholars Office using the contact for international students as well as graduate students. CCE also maintains information above. a dossier service, managed by Interfolio, American citizens and permanent

engineering 2011–2012 Undergraduate Studies 10 the Undergraduate Programs

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

engineering 2011–2012 students improve their ability to engage master’s-level professional courses do W4415 Game theory 11 in ethical, analytic, discursive, and not satisfy the 27-point nontechnical W4911 Seminar in microeconomics imaginative thinking that will prove requirement.) W4913 Seminar in macroeconomics indispensable later in life. W4918 Seminar in econometrics AFRICAN-AMERICAN STUDIES: All courses • Engineering students must take 16 to BC1003 Introduction to economic reasoning (equivalent to ECON W1105) 18 points of credit of required courses AMERICAN STUDIES: All courses BC1007 Mathematical methods for economics in list A and 9 to 11 elective points ANCIENT STUDIES: All courses BC2411 Statistics for economics chosen from the approved courses BC3014 Entrepreneurship in list B. The total combined number ANTHROPOLOGY: All courses in sociocultural anthropology BC3018 Econometrics of nontechnical points (from lists A All courses in archaeology except field work BC3033 Intermediate macroeconomic theory and B, below) must add up to at least No courses in biological/physical anthropology BC3035 Intermediate microeconomic theory 27. Neither list can be modified by [V1010, V1011, W3204, V3940, G4147-G4148, BC3038 International money and finance advising deans or faculty advisers. W4200, G4700] EDUCATION: All courses • Advanced Placement (AP) credit in appropriate subject areas can be ARCHITECTURE: No courses ENGINEERING: Only applied toward the 9-point elective ART HISTORY AND ARCHEOLOGY: BMEN E4010 Ethics for biomedical engineers nontechnical requirement. All courses EEHS E3900 History of telecommunications If electing Global Core, students must SCNC W3010 Science, technology and society ASIAN AMERICAN STUDIES: All courses take two courses from the List of ENGLISH AND COMPARATIVE LITERATURE: Approved Courses (www.college. ASTRONOMY: No courses All courses columbia.edu/bulletin/core/mc.php) for a BIOLOGICAL SCIENCES: No courses FILM STUDIES: All courses except lab courses, letter grade. and BUSINESS: No courses W3850 Senior seminar in screenwriting A. Required Nontechnical Courses CHEMISTRY: No courses W4005 The film medium: script analysis (16–18 points of credit) These courses must be taken at CLASSICS: All courses FRENCH AND ROMANCE PHILOLOGY: All courses Columbia. COLLOQUIA: All courses GERMANIC LANGUAGES: All courses 1. ENGL C1010: University writing (3 points) COMPARATIVE ETHNIC STUDIES: All courses GREEK: All courses 2. One of the following two-semester sequences: COMPARATIVE LITERATURE AND SOCIETY: HUMA C1001-C1002: Masterpieces of All courses HISTORY: All courses Western literature and philosophy (All students registering for this course should be prepared COMPUTER SCIENCE: No courses HISTORY AND PHILOSOPHY OF SCIENCE: All courses to discuss books 1–12 of the Iliad on the first CREATIVE WRITING: All courses day of class) or (This is an exception to the workshop rule.) HUMAN RIGHTS: All courses COCI C1101-C1102: Introduction to contempo- rary civilization in the West or Global Core (any DANCE: All courses except performance classes ITALIAN: All courses 2 courses from approved list) (6–8 points) DRAMA AND THEATRE ARTS: All courses JAZZ STUDIES: All courses 3. One of the following two courses: HUMA except workshops, rehearsal, or performance LATIN: All courses W1121: Masterpieces of Western art, or classes, THTR BC2120 Technical production, HUMA W1123: Masterpieces of Western THTR BC3135 Set design, and THTR BC3134 LATINO STUDIES: All courses music (3 points) Lighting design LINGUISTICS: All courses except CLLN W4202 4. ECON W1105: Principles of economics. (This EARTH AND ENVIRONMENTAL SCIENCES: MATHEMATICS: No courses course can be satisfied through Advanced No courses Placement; see the Advanced Placement EAST ASIAN LANGUAGES AND CULTURE: MEDIEVAL AND RENAISSANCE STUDIES: chart on page 14.) Note: Engineering stu- All courses All courses dents may not take BC1003: Introduction to MIDDLE EASTERN AND ASIAN LANGUAGE economic reasoning as a substitute for ECON ECOLOGY, EVOLUTION AND AND CULTURES: All courses W1105. (4 points) ENVIRONMENTAL BIOLOGY: No courses except EEEB W4700 MUSIC: All courses except performance courses, B. Elective Nontechnical Courses ECONOMICS: All courses except instrument instruction courses, and workshops (9–11 points of credit) W3025 Financial economics The following course listing by PHILOSOPHY: All courses except W3211 Intermediate microeconomics F1401 Introduction to logic department specifies the Columbia W3213 Intermediate macroeconomics V3411 Symbolic logic College, Barnard, or Columbia W3412 Introduction to econometrics W4137 Non-classical logics Engineering courses that either fulfill W4020 Economics of uncertainty and information G4431 Introduction to set theory or do not fulfill the nontechnical W4211 Advanced microeconomics G4424 Modal logic requirement. W4213 Advanced macroeconomics CSPH W4801 Mathematical logic, I (Professional, workshop, lab, project, W4251 Industrial organization CSPH G4802 Incompleteness results in logic scientific, studio, music instruction, and W4280 Corporate finance Courses in logic W4412 Advanced econometrics

engineering 2011–2012 12 PHYSICAL EDUCATION: No courses most programs recommend, and in medicine and health care delivery. Engineering some cases may require, that particular approaches to understanding organismic and PHYSICS: No courses courses be taken earlier for maximum cellular function in living systems. Engineering POLITICAL SCIENCE: All courses except efficiency in program planning. in the diagnosis and treatment of disease. W4209 Game theory and political theory For information concerning these Medical imaging, medical devices: diagnostic and surgical instruments, drug delivery systems, W4291 Advanced topics in quantitative research requirements, students should turn to W4292 Advanced topics in quantitative research prostheses, artificial organs. Medical informatics the individual program sections in this W4360 Math methods for political science and organization of the health care system. bulletin. W4910 Principles of quantitative political Current trends in biomedical engineering research research. W4911 Analysis of political data Professional-Level Courses for CHEN E1040y Molecular engineering and W4912 Multivariate political analysis First- and Second-Year Students product design First- and second-year students PSYCHOLOGY: Only Examines the ways in which chemical and W1001 The science of psychology are required to take at least one biological sciences are interpreted through W2235 Thinking and decision making professional-level course chosen from analytical, design, and engineering frameworks W2240 Human communication the list below. The faculty strongly to generate products that enhance human W2280 Introduction to developmental psychology encourages students to schedule two endeavor. Culture of chemical engineering W2610 Introduction to personality of these courses. (ENGI E1102, which and the wide variety of chemical engineering W2620 Abnormal behavior is required of every first-year student, is practices, through lectures by department W2630 Social psychology not included in this list.) faculty and practicing chemical engineers, W2640 Introduction to social cognition Each course is designed to acquaint trips to industrial facilities, reverse-engineering W2680 Social and personality development Engineering students with rigorous of chemical products, and a chemical design competition. W3615 Children at risk intellectual effort in engineering and W3630 Seminar in social cognition applied science early in their academic CIEN E1201y The art of structural design RELIGION: All courses careers. If a student chooses to take Basic scientific and engineering principles used the second professional-level course, for the design of buildings, bridges, and other SLAVIC LANGUAGES: All courses such a 1000-level course may, at the parts of the built infrastructure. Application of SOCIOLOGY: All courses except discretion of each department, be used these principles to the analysis and design SOCI V3212 Statistics and methods as an upper-level technical elective of a number of actual large-scale structures. History of major structural design innovations normally satisfied by 3000-level or higher SPANISH AND PORTUGUESE: All courses and the engineers who introduced them. Critical courses. SPEECH: No courses examination of the unique aesthetic/artistic The courses stipulate minimal perspectives inherent in structural design. STATISTICS: No courses prerequisites. Each course serves as Management, socioeconomic, and ethical issues an introduction to the area of study SUSTAINABLE DEVELOPMENT: No courses involved in the design and construction of in addition to teaching the subject large-scale structures. Recent developments in URBAN STUDIES: All courses matter. Each course is taught by regular sustainable engineering, including green building VISUAL ARTS: No more than one course, which department faculty and thus provides a design and adaptable structural systems. double introduction to both subject area must be at the 3000-level or higher (This is an EAEE E1100y A better planet by design exception to the workshop rule.) and faculty. Development of the infrastructure for providing The courses are: WOMEN AND GENDER STUDIES: All courses safe and reliable resources (energy, water APPH E1300y Physics of the human body and other materials, transportation services) to support human societies while attaining Technical Course Requirements The human body analyzed from the basic principles of physics: energy balance in the environmental objectives. Introduction of a The prescribed First Year–Sophomore body, mechanics of motion, fluid dynamics of typology of problems by context, and common Program curriculum requires students to the heart and circulation, vibrations in speaking frameworks for addressing them through the complete a program of technical course and hearing, muscle mechanics, gas exchange application of appropriate technology and work introducing them to five major and transport in the lungs, vision, structural policy. An interdisciplinary perspective that areas of technical inquiry: engineering, properties and limits, and other topics. focuses on the interaction between human mathematics, physics, chemistry, and and natural systems is provided. Alternatives APAM E1601y Introduction to computational computer science. for resource provision and forecasts of their mathematics and physics All first-year Engineering potential environmental impacts through a Mathematics and physics problems solved by context provided by real-world applications and undergraduate students take ENGI using computers. Topics include elementary problems. E1102: Design fundamentals using the interpolation of functions, solution of nonlinear advanced computer technologies (4 algebraic equations, curve-fitting and hypothesis ELEN E1201x and y Introduction to electrical points). In this course, students learn the testing, wave propagation, fluid motion, engineering basics of engineering design along with gravitational and celestial mechanics, and Exploration of selected topics and their professional and teamwork skills. chaotic dynamics. application. Electrical variables, circuit laws, While students need not officially nonlinear and linear elements, ideal and real BMEN E1001x Engineering in medicine sources, transducers, operational amplifiers in commit to a particular branch of The present and historical role of engineering in simple circuits, external behavior of diodes and engineering until the third semester,

engineering 2011–2012 transistors, first order RC and RL circuits. Digital schedule. The majority of the activities physics, chemistry, and computer 13 representation of a signal, digital logic gates, flip- are offered in ten time preferences. science. The benefit of advanced flops. A lab is an integral part of the course. However, there are early-morning placement is acceleration through GRAP E1115x and y Engineering graphics conditioning activities, Friday-only certain First Year–Sophomore Program Visualization and simulation in virtual classes at Baker Field, and special requirements and thus the opportunity environments; computer graphics methods for courses that utilize off-campus facilities of taking specialized courses earlier. presentation of data. 3D modeling; animation; during weekends and vacation periods. Each year the school reviews the rendering; image editing; technical drawing. The courses offered by the department CEEB advanced placement curriculum MECE E1001x Mechanical engineering: for each term are included in the online and makes determinations as to micro-machines to jumbo jets Department of Intercollegiate Athletics appropriate placements, credit, and/or The role of mechanical engineering in developing and Physical Education Directory exemption. Please see the Advanced many of the fundamental technological advances of Classes, and a description of the Placement Credit Chart. on which today’s society depends. Topics scheduled activities for each time include airplanes, automobiles, robots, and preference is posted in the Physical International Baccalaureate (IB) modern manufacturing methods, as well as the Education Office, 336 Dodge Physical Entering students may be granted 6 emerging fields of micro-electro-mechanical Fitness Center, and is included on the points of credit for each score of 6 or 7 machines (MEMS) and nanotechnology. The www.gocolumbialions.com website. on IB Higher Level Examinations if taken physical concepts that govern the operation of Students may register for only one in disciplines offered as undergraduate these technologies will be developed from basic section of physical education each term. principles and then applied in simple design programs at Columbia. Students should problems. Students will also be exposed to state- consult their adviser for further clarification. Music Instruction Courses of-the art innovations in each case study. Music instruction and performance British Advanced Level Examinations MSAE E1001y Atomic-scale engineering of courses do not count toward the 128 Pending review by the appropriate new materials points of credit required for a B.S. department at Columbia, students with An introduction to the nanoscale science and degree. Please note that this includes engineering of new materials. The control and grades of A or B on British Advanced courses taken at Teachers College, manipulation of atomic structure can create Level examinations are granted 6 points Columbia College, and the School of new solids with unprecedented properties. of credit if the examinations were taken the Arts. Computer hard drives, compact disc players, and in disciplines offered as undergraduate liquid crystal displays (LCDs) are explored to programs at Columbia College. The understand the role of new materials in enabling Visual Arts Courses appropriate transcript should be technologies. Group problem-solving sessions Students are allowed to take courses submitted to the Center for Student are used to develop understanding. in the Visual Arts Department for Advising, 403 Lerner. general credit to be applied toward the B.S. degree. However, no more than Physical Education Other National Systems one visual arts course, which must be Two terms of physical education Pending review by the appropriate taken at the 3000 level or higher, may (C1001-C1002) are a degree department at Columbia, students count toward the nontechnical elective requirement for Columbia Engineering whose secondary school work was in requirement. This 3000 course is an students. No more than 4 points other national systems may be granted exception to the rule that no workshop of physical education courses may credit in certain disciplines for sufficiently classes can fulfill the non-tech elective be counted toward the degree. A high scores. The appropriate transcript requirement. student who intends to participate in should be submitted to the Center for an intercollegiate sport should register Student Advising, 403 Lerner. for the appropriate section of C1005: Advanced Placement Intercollegiate athletics. Intercollegiate Prior to entering Columbia, students athletes who attend regularly receive 1 may have taken the College Entrance Study Abroad point of credit up to the maximum of Examination Board’s Advanced Placement Engineering today is a global profession. 4. Those who are advised to follow a Examinations in a number of technical Engineers are increasingly being called restricted or adapted activity program and nontechnical areas. Students may upon to work with other engineers from should contact Professor Torrey in the be assigned to an advanced-level across the world or they may even find Department of Intercollegiate Athletics course in mathematics, chemistry, or themselves living abroad on an overseas and Physical Education. The physical physics. A maximum of 16 points may assignment. Learning problem-solving education program offers a variety be applied. skills in a foreign context will help of activities in the areas of aquatics, In the required pure science areas, engineering students to expand their fitness, martial arts, individual and dual the number of advanced placement horizons, and their adaptability to cross- lifetime sports, team sports, and outdoor academic credits awarded to students cultural communication will make them a education. Most activities are designed of engineering and applied science valuable addition to a team of engineers. for the beginner/intermediate levels. varies from the levels awarded for liberal Study abroad allows engineering Advanced courses are indicated on the arts programs, notably in mathematics, students to discover the field through

engineering 2011–2012 14 Advanced Placement Credit Chart the perspective of engineers working In order to receive AP credit, students must be in possession of appropriate transcripts or scores. in a different language and culture, enabling them to learn the relationship of Subject AP Advanced Requirements or culture to science and develop the range Score Placement Status Credit of transferable skills that employers Art history 5 3* No exemption from HUMA W1121 are seeking today. Study abroad will Biology 4 or 5 3 No exemption help students develop intellectually, Chemistry 4 or 5 3 Requires completion of CHEM C1604 emotionally, culturally, and socially. with grade of C or better Columbia Engineering undergraduate 4 or 5 6 Requires completion of CHEM C3045-C3046 students can study abroad for either with grade of C or better a semester (fall, spring or summer) or, Computer exceptionally, for a full academic year. science A or AB 4 or 5 3* Exemption from COMS W1004 Students from every engineering major English have studied abroad without adding Language and any time to their course of study at composition 5 3* No exemption Columbia. Most do so in the spring Literature and semester of their sophomore year or in composition 5 3* No exemption their junior year. Economics Micro & macro 5 & 4 4* Exemption from ECON W1105 (Test must be in both with a score of 5 in one Engineering students have two study and at least 4 in the other) abroad options: 1. the option of studying engineering French Language 4 or 5 3* at one of Columbia Engineering’s Literature 4 or 5 3* partner universities: University College London (UK); the École German language 4 or 5 3* Polytechnique (FR) or the École Centrale de Paris (FR)—courses Government and politics at these two institutions are United States 5 3* predominantly taught in French. Comparative 5 3* Other partnerships are currently History being negotiated—check the Office European 5 3* of Global Programs website for the United States 5 3* latest updates. Italian language 4 or 5 3* 2. Students who would like further study abroad options can choose a Latin literature 4 or 5 3* peer university for direct enrollment Mathematics or a program of study with a Calculus AB 4 or 5 3** requires completion of MATH V1102 third-party provider. The Office of with a grade of C or better Calculus BC 4 3** requires completion of MATH V1102 Global Programs can help students with a grade of C or better identify the appropriate choice for Calculus BC 5 6 Requires completion of MATH V1201 (or their country of interest and their V1207) with a grade of C or better major. The Assistant Dean for Music theory 5 3* Exemption from MUSI V1002 Undergraduate Student Affairs and MUSI V2318-V2319 determined by department Global Programs and departmental Physics advisers will review requests, and C-E&M 4 or 5 3 Requires beginning with and completion of if approved, will help students PHYS C2801 with grade of C or better work out their course equivalencies C-MECH 4 or 5 3 Requires beginning with and completion of so they can graduate on time. PHYS C2801 with grade of C or better Physics B 4 or 5 3* No exemption Students can choose to take non- technical electives overseas, or with Spanish departmental permission, they may Language 4 or 5 3* Literature 4 or 5 3* choose technical electives or courses in their major. *Up to 3 AP credits may be applied toward minor requirements. **SEAS students with a 4 or 5 on Calculus AB or a 4 on Calculus BC must begin with It is essential that students begin 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 planning as early as possible—ideally A-level or IB calculus credit must start with Calculus II. this would be during their first year. Students are encouraged to meet with the Office of Global Programs to review

engineering 2011–2012 possible overseas destinations and widely in size, geographical location, Academic Credit 15 to decide on an appropriate abroad academic philosophy, language Students in Columbia-sponsored experience. The Assistant Dean will requirements, living arrangements, programs receive direct Columbia credit, explain all Columbia Engineering study and opportunities for research and and the courses and grades appear on abroad formalities and requirements. internships. Students must establish students’ academic transcripts. These Students then must gain approval from a set of goals for the study-abroad include Reid Hall, Paris; the Berlin their departmental advisers to ensure experience, taking into account their Consortium for German Studies; the that their work abroad meets the foreign-language skills and adaptability Kyoto Center for Japanese Studies; the requirements of their majors. Students to new environments, as well as their Columbia University Summer Arabic must register with the Office of Global research objectives and professional Language Program in Amman, Jordan Programs, 606 Kent Hall, for study aspirations. and the Tsinghua University program in abroad by November 15 for spring Students must visit the Office of Beijing. programs and March 15 for summer, Global Programs’ website to review the Credit from approved programs that fall, and academic-year programs. various lists of program options and are not Columbia sponsored is certified then consult with the Assistant Dean for as transfer credit toward the Columbia Eligibility Requirements specific information or help in choosing degree upon successful completion In order to participate in a semester- an institution that offers the best courses of the program verifiable by academic or yearlong study-abroad program, in their engineering major. Early planning transcript. Students must earn a grade students must: is crucial so that study abroad plans of C or better in order for credits to • Have at least a 3.0 GPA can be integrated into the student’s transfer. Course titles and grades for • Be making good progress toward curriculum plan. approved programs do not appear on finishing the first and second year Summer study-abroad programs the Columbia transcript, and the grades requirements allow students to earn credits for are not factored into students’ GPAs. • Have at least intermediate proficiency language instruction and nontechnical Faculty from the Columbia in the local language, if it is not electives. Students can either participate Engineering academic departments English. (Please note: For programs in Columbia-approved summer have the responsibility to assess all in countries where the language of programs for transfer credit or on work completed abroad and make instruction is not English, students Columbia-sponsored programs for decisions about how these courses fit must take all course work in the local direct credit. The Columbia-sponsored into major requirements. It is imperative language.) summer programs include the Chinese that students gain course-by-course Students’ study-abroad plans must Language Program in Beijing, the approval from their department prior to be approved by the Assistant Dean Business Chinese and Internship departure on a study-abroad program. by October 15 for spring programs Program in Shanghai, the Italian The Assistant Dean for Undergraduate and March 15 for summer, fall and Cultural Studies Program in Venice, the Student Affairs and Global Programs academic-year programs. A review Columbia University Summer Arabic will provide students with the forms of each student’s academic and Language Program in Amman, Jordan necessary to obtain this approval. disciplinary records is conducted as and the Columbia University Programs in Paris at Reid Hall. part of this process. Students on Combined Plan Programs academic or disciplinary probation are Non-credit-bearing internships, Office of Undergraduate Admissions not permitted to study abroad during the including the CEO program in London, 212 Hamilton Hall, MC 2807 term of their probation. Hong Kong, Singapore, Shanghai, 1130 Amsterdam Avenue Study-abroad students remain Beijing, and Amman are coordinated by New York, NY 10027 enrolled at Columbia, and tuition is paid the Center for Career Education. Please to Columbia. Students participating visit the Center’s website for more Phone: 212-854-2522 in Columbia-approved programs pay information. Fax: 212-854-1209 housing costs directly to their host In addition, the Summer Ecosystems E-mail: [email protected] or sponsoring institution. Students Experience for Undergraduate Education www.studentaffairs.columbia.edu/ receiving financial aid at Columbia will through the Center for Environmental admissions/engineering/combined remain eligible for financial aid when they Research and Conservation (CERC) study abroad with Columbia’s approval. provides opportunities for engineering Columbia Engineering maintains Students who wish to be considered students in Brazil, Puerto Rico, the cooperative program relationships with for financial aid while studying abroad Dominican Republic, and Jordan. institutions nationwide and with other should consult the Office of Financial Aid Other internship options may be Columbia University undergraduate and Educational Financing (618 Lerner). possible through Columbia Engineering international partner institutions. divisions. These programs allow students to complete the equivalent of the First Program Information Year–Sophomore Program and transfer Choosing the right university abroad is directly to a field of specialization in the an important step in planning to study School, beginning their study at the abroad. Study-abroad options vary School as junior-level students.

engineering 2011–2012 16 The Combined Plan (3-2) Program degree and then transfer to Columbia Columbia’s chapter, New York Alpha, within Columbia University Engineering to complete a B.S. degree is the ninth oldest and was founded in Students who follow this program apply in two years. Students should have 1902. Many Columbia buildings have through their own school at Columbia followed a related course of study been named for some of the more College, Barnard College, or the School at their liberal arts college. Students prominent chapter alumni: Charles of General Studies for admission. graduating from an affiliated school must Fredrick Chandler, Michael Idvorsky Under this plan, the pre-engineering apply to the Combined Plan Program Pupin, Augustus Schermerhorn, and, of student studies in the appropriate within one year of graduating. course, Harvey Seeley Mudd. college for three years, then attends The 4-2 M.S. program is designed to Undergraduate students whose Columbia Engineering for two years allow students to complete a Columbia scholarship places them in the top and is awarded the Bachelor of Arts Engineering M.S. degree in two years eighth of their class in their next-to-last degree and the Bachelor of Science after completion of a B.A. degree at one year or in the top fifth of their class in degree in engineering upon completion of the affiliated schools. This program their last college year are eligible for of the fifth year. This five-year program will allow students the opportunity to membership consideration. These scho- is optional at Columbia, but the School take undergraduate engineering courses lastically eligible students are further recommends it to all students who wish if necessary. Further information may be considered on the basis of personal greater enrichment in the liberal arts and found on page 31. integrity, breadth of interest both inside pure sciences. and outside engineering, adaptability, and unselfish activity. The Junior-Senior The Combined Plan with Other Programs Taking Graduate Courses as an Affiliated Colleges Students may review degree progress Undergraduate There are more than one hundred via DARS (Degree Audit Reporting liberal arts colleges, including those at System) as presented on Student With the faculty adviser’s approval, a Columbia, in which a student can enroll Services Online. Required courses not student may take graduate courses in a Combined Plan program leading completed by this time are detailed as while still an undergraduate in the to two degrees. Every affiliated school deficiencies and must be completed School. Such work may be credited has a liaison officer who coordinates the during summer session or carried as toward one of the graduate degrees program at his or her home institution. overload courses during the final two offered by the Engineering Faculty, Each liberal arts college requires the years of study. subject to the following conditions: (1) completion of a specified curriculum Having chosen their program major, the course must be accepted as part to qualify for the baccalaureate from students are assigned to an adviser in of an approved graduate program of that institution, students interested in the department in which the program study; (2) the course must not have this program should inform the liaison is offered. In addition to the courses been used to fulfill a requirement officer as early as possible, preferably required by their program, students for the B.S. degree and must be so in the first year. Visit the Office of must continue to satisfy certain distribu- certified by the Dean; and (3) the Undergraduate Admissions website for tive requirements, choosing elective amount of graduate credit earned by a complete list of affiliated schools and courses that provide sufficient content an undergraduate cannot exceed 15 curriculum requirements. in engineering sciences and engineer- points. Undergraduates may not take The 3-2 Combined Plan Program ing design. The order and distribution CVN courses. B.A./B.S. is designed to provide students of the prescribed course work may be with the opportunity to receive both a changed with the adviser’s approval. The Bachelor of Science Degree B.A. degree from an affiliated liberal arts Specific questions concerning course Students who complete a four-year college and a B.S. degree from Columbia requirements should be addressed to sequence of prescribed study are Engineering in five years. Students the appropriate department or division. awarded the Bachelor of Science complete the requirements for the liberal The Vice Dean’s concurrent approval is degree. The general requirement for arts degree along with a pre-engineering required for all waivers and substitutions. the Bachelor of Science degree is course of study in three years at their the completion of a minimum of 128 college and then complete two years Tau Beta Pi academic credits with a minimum at Columbia. Combined Plan students The Tau Beta Pi Association, a national cumulative grade-point average (GPA) are required to complete all Columbia engineering honor society, was founded of 2.0 (C) at the time of graduation. Engineering requirements within four in 1885 “to mark in a fitting manner The program requirements, specified consecutive semesters. Please note those who have conferred honor upon elsewhere in this bulletin, include that no change of major is allowed after their Alma Mater by distinguished the First Year–Sophomore course admission. scholarship and exemplary character requirements, the Junior-Senior major Another available option is the 4-2 as undergraduates in engineering, or by departmental requirements, and B.S. degree program. This is designed their attainments as alumni in the field technical and nontechnical elective to allow students to graduate from of engineering, and to foster a spirit of requirements. Students who wish to their liberal arts college with a B.A. liberal culture in engineering colleges.” transfer points of credit may count no

engineering 2011–2012 more than 68 transfer points toward year at the School; a minimum GPA flexible admissions requirements 17 the degree, and must satisfy the of 3.0 in the College Core and other of most professional schools. University’s residence requirements courses; and the successful completion Undergraduate students should, by taking at least 60 points of credit of any prerequisites for the College however, make careful inquiry into the at Columbia. Courses may not be major or concentration. To be admitted kinds of specific preparatory work that repeated for credit. to the program, a plan needs to be in may be required for admission into The bachelor’s degree in place for the student to complete the highly specialized programs such as engineering and applied science major or concentration by the end of medicine. earned at Columbia University their fifth year. prepares students to enter a wide Interested students should contact their Pre-Med range of professions. Students are, advising dean for further information. Engineering students seeking admission however, encouraged to consider to dental, medical, optometric, graduate work, at least to the master’s Minors osteopathic, or veterinary schools degree level, which is increasingly Columbia Engineering undergraduates directly after college must complete all considered necessary for many may choose to add minors to their entrance requirements by the end of professional careers. programs. This choice should be made the junior year, and should plan their The Engineering Accreditation in the fall of their sophomore year, program accordingly. Students should Commission (EAC) of the Accreditation when they also decide on a major. consult with their adviser and the Board for Engineering and Technology In considering a minor, students Office of Preprofessional Advising to (ABET), an organization formed by must understand that all minors are plan an appropriate program. Students the major engineering professional not, and cannot, be available to all should also connect with the Office of societies, accredits university students. In addition, the School Preprofessional Advising to learn more engineering programs on a nationwide cannot guarantee that a selected about extracurricular and research basis. Completion of an accredited minor can be completed within the opportunities related to premed studies. program of study is usually the first usual residence period needed for It is necessary to apply for step toward a professional engineering a major. Indeed, students choosing admission to health professions license. Advanced study in engineering minors should expect to encounter schools a little over one year at a graduate school sometimes scheduling difficulties. The potential in advance of the entry date. If presupposes the completion of an for the successful completion of a candidates are interested in going accredited program of undergraduate minor depends on the student’s major directly on to health professions study. and the minor chosen, as well as the school following graduation, they The following undergraduate course schedules and availability, should complete all requirements programs are accredited by the which may change from year to and the Medical College Admissions Engineering Accreditation Commission year. The list of minors, as well as Test (MCAT) by the summer following of the Accreditation Board for their requirements, appear on pages the junior year. It is, however, entirely Engineering and Technology: biomedical 190–195. acceptable to delay application and engineering, chemical engineering, civil entrance to these schools several engineering, Earth and environmental years beyond graduation. Programs in Preparation engineering, electrical engineering, and Candidates planning for an for Other Professions mechanical engineering. application to medical or dental school Columbia Engineering prepares its will also need to be evaluated by the students to enter any number of The 4-1 Program at Columbia Premedical Advisory Committee prior graduate programs and professions College to application. A Premedical Advisory outside of what is generally thought Students who are admitted as first-year Committee application is made of as the engineering field. In an students to Columbia Engineering, and available each year in December. increasingly technological society, subsequently complete the four-year Please consult with the Office of where the line between humanities and program for the Bachelor of Science Preprofessional Advising for more technology is becoming increasingly degree, have the opportunity to apply information regarding this process. blurred, individuals with a thorough for admission to either Columbia Engineering’s curriculum covers grounding in applied mathematics and College or Barnard College and, after many of the premedical courses the physical and engineering sciences one additional year of study, receive the required by medical schools. find themselves highly sought after as Bachelor of Arts degree. However, in addition to completing the professionals in practically all fields of The program will be selective, and mathematics, chemistry, and physics endeavor. admission will be based on the following courses required by the First Year– Engineering students interested in factors: granting of the B.S. at Columbia Sophomore Program, most medical pursuing graduate work in such areas Engineering at the end of the fourth schools ask for a full year of organic as architecture, business, education, year; fulfillment of the College Core chemistry, a full year of biology, and a journalism, or law will find themselves requirements by the end of the fourth full year of English. well prepared to meet the generally

engineering 2011–2012 18 The following courses are required New York State Initial Certification instead of seven. Juniors should speak by medical schools: in Adolescence Education Grades to the Office of Preprofessional Advising • One year of calculus for some 7–12 for Teachers of Mathematics in the fall semester to express their schools and the Sciences or in Childhood interest and prepare to take the LSAT • One year of physics, with lab Education Grades 1–6 by February of their junior year. The • One year of general chemistry, with lab Barnard College Education Program application process is conducted March • One year of biology, with lab (BME 335-336 Milbank Hall through April. labs will qualify) 3009 Broadway • One year of organic chemistry, with lab New York, NY 10027 School of International and Public • One year of English Affairs • Biochemistry or additional biology Phone: 212-854-7072 Columbia Engineering and the School (required by some schools) education.barnard.edu of International and Public Affairs For further information, please offer a joint program enabling a small consult the Office of Preprofessional The Barnard Education Program number of students to complete Advising at 212-854-8722 or provides courses leading to certification the requirements for the degrees of preprofessional@columbia. to teach in New York State (with Bachelor of Science and Master of reciprocal agreements with 41 other International Affairs in five years instead Pre-Law states) at either the elementary of six. Not only an excellent academic Students fulfilling Engineering’s or secondary level. Students gain record but also maturity, fluency in curriculum are well prepared to apply experience and develop skills in urban an appropriate foreign language, and to and enter professional schools of school classrooms. Interested students pertinent experience will determine law, which generally do not require any should apply for admission to the admission to this program. For more specific prelaw course work. Schools of program and supply an essay and letters information, please contact your law encourage undergraduate students of recommendation no later than the first advising dean. to complete a curriculum characterized Monday in October of the junior year. by rigorous intellectual training involving Course work required includes courses Registered Programs relational, syntactical, and abstract in psychology and education, including The New York State Department of thinking. A sound education is best for practicum and student teaching, totaling Education requires that this bulletin most prelaw students. While selecting 23–26 points of credit depending on include a listing of registered programs, courses, keep in mind the need to hone level of certification sought. both undergraduate and graduate (see your writing skills, your communication Certification to teach mathematics chart on page 19). Enrollment in other skills, and your capacity for logical requires 36 points in mathematics. Pure than registered or otherwise approved analysis. science courses required are: 36 points programs may jeopardize a student’s Courses in history, political science, in the sciences, of which 15 must be eligibility for certain student aid awards. economics, statistics, and anthropology in the area of the certification sought: The letter “X” or the name of a help students understand the structure chemistry, biology, physics, or Earth degree on the chart indicates that a of society and the problems of science. program is registered with the New York social ordering with which the law is Application deadline is the first State Department of Education. concerned. The study of philosophy, Monday in October of the student’s literature, fine arts, foreign languages, junior year. Students who plan to study and other cultures imparts familiarity abroad during their junior year should with traditions of universal thought and apply during the fall semester of their trends that influence legal developments sophomore year. Students should nationally and internationally. The decide on their interest in teacher examination of human behavior certification by the end of the first year through sociology and psychology in order to start course work in the will aid a prospective law student in sophomore year. understanding the types and effects of behavior to which the law relates. Joint Programs The systematic ordering of abstractions and ideas in logic and the sciences contributes much to a School of Law prelaw student’s ability to analyze, Each year Columbia Engineering may understand, and rationally organize nominate two highly qualified juniors his or her thoughts. Finally, it is useful for a joint program with the Columbia in some fields of law for a student University School of Law, enabling to have a fundamental knowledge of students to complete the requirements technology, engineering, computers, for the degrees of Bachelor of Science and accounting. and Doctor of Jurisprudence in six years

engineering 2011–2012 Programs Registered with the New York State Department of Education 19

Program Title HEGIS code b.S. M.S. professional M.Phil. eng.Sc.D. ph.D.

Applied Mathematics 913 X X X x x

Applied Physics 919 X X X X x x x

Biomedical Engineering 905 X X 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 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 x x 909 Computer Systems Engineer

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

Computer Science/Journalism: Dual M.S. 701 x

Earth and Environmental Engineering 918 X X 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 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 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 x x *State approval pending

engineering 2011–2012 20 Undergraduate Admissions

Office of Undergraduate Admissions talents as well as diverse economic, The Early Decision Program 212 Hamilton Hall, MC 2807 social, and geographic backgrounds. Candidates for whom Columbia is the 1130 Amsterdam Avenue Accordingly, Columbia Engineering first choice may apply under the Early New York, NY 10027 prescribes no standardized course of Decision Program. In order to qualify for study for secondary school students this program, all application materials Phone: 212-854-2522 applying for first-year admission. must be postmarked by November 1. Fax: 212-854-3393 The School does, however, strongly In mid-December, Early Decision E-mail: [email protected] recommend the following academic applicants receive notice of their accep- www.studentaffairs.columbia.edu/ preparation: tance, denial, or deferral to regular deci- admissions • Four years of mathematics sion status. Applicants admitted under (preferably through calculus) the Early Decision program are obligated Admission as a First-Year • One year of physics to accept Columbia’s offer of admission Student • One year of chemistry and must withdraw their applications at Each autumn The Fu Foundation • Four years of English other colleges if they are provided with a School of Engineering and Applied and recommends as well: financial aid package that enables them Science enrolls approximately 300 highly • Three years or more of a foreign to attend Columbia. qualified men and women, chosen language from a wide range of applicants. All • Three or four years of history and Required Standardized Testing become full, active participants in a social studies Please go to the Office of rich and diverse university setting. Undergraduate Admissions website for Therefore, the Admissions Committee The Application Process our standardized testing requirements. is interested in achievements not only Students are strongly encouraged to You must register with the appropriate in mathematics and science, but also in apply online. Columbia utilizes The testing agency well in advance of the other fields: English, the social sciences, Common Application and requires date on which you wish to be tested. languages, and the arts. Considerable a supplement. Both are available as Please note that scores reported to value is placed on personal qualities of August 1, 2011, on the Office of Columbia’s School of General Studies and attributes like diversity of interests, Undergraduate Admissions website. If (2095) will not reach our office and special abilities, maturity, motivation, you do not have access to the Internet, will not be considered for evaluation. curiosity, and independence. Secondary please call the Office of Undergraduate Columbia reserves the right not to school records and recommendations Admissions at 212-854-2522 to request evaluate a candidate whose scores are carefully evaluated to ascertain the an application. are not reported directly by the testing content and difficulty of the applicant’s The Common Application and agency. Please do not utilize the “rush” preparatory studies and the degree supplement should be filled out and service in sending your test scores to to which this preparation correlates submitted as early as possible along Columbia. Doing so does not speed up with standardized tests. Of importance with the $80 application fee or an official the processing of your test scores. We also is the candidate’s participation in fee waiver request. obtain all testing via a secure website extracurricular or community activities. All parts of the application must be to which we are provided access by the Here the emphasis is placed on the postmarked no later than January 1. appropriate testing agency. Scores that depth and significance of involvement (See below for Early Decision deadlines.) are sent via the “rush” service are sent rather than on the number of activities. Decision letters are mailed out in to us in paper form, which we are no For its final selection, the School seeks early April. longer able to process. students with unique achievements and

engineering 2011–2012 Applicants may submit results of preparation to advance in prescribed regard to admission requirements. 21 the American College Testing (ACT) sequences. No credit is given for college HEOP students must be U.S. citizens examinations in lieu of the SAT, but may courses taken prior to high school or permanent residents who have lived not substitute any other examinations for graduation, but appropriate placements in New York State for one year prior to the required SAT Subject Tests. may be made. enrolling in college. The Test of English as a Foreign HEOP’s individualized counseling Language (TOEFL) or International Egleston Scholars and tutoring services help students English Language Testing System The Egleston Scholars Program meet the challenges of a major (IELTS) is required of all applicants is named after Professor Thomas university and professional school. whose principal language of instruction Egleston, who founded the Columbia New students attend an intensive pre- has not been English and who have not School of Mines in 1864. Known in his first-year Summer Bridge Program lived in an English-speaking environment time as one of the foremost experts on on the Columbia campus. Students for at least five years. mining and metallurgy, Egleston served in the School’s undergraduate Higher Applicants must be certain when as president of the American Institute Education Opportunity Program can taking standardized tests to have their of Mining Engineers and twice received follow a five-year curriculum which results reported directly to Columbia France’s highest decoration, the Légion spreads the first and second-year University by the testing agency. d’honneur. The Thomas Egleston requirements over three years and Students are required to report all Medal for Distinguished Engineering allows for the inclusion of several extra standardized testing. The following Achievement was established in 1939 courses designed to provide academic codes should be used when completing in his honor and is the School’s most support. test registration forms: prestigious alumni award, recognizing Because of the different pace of this SAT Reasoning, SAT Subject Tests, graduates of Columbia Engineering who program, students are considered to be TOEFL: use code 2116 have made exceptional contributions to making minimum satisfactory progress ACT: use code 2719 the world of engineering and applied sci- when they complete 24 points of credit ence. In this spirit, the Egleston Scholars in one academic year. HEOP students’ Educational Testing Service Program recognizes undergraduate academic performance is otherwise Rosedale Road students of Columbia Engineering who evaluated by the same standards Princeton, NJ 08541 embody the mission of the School at applied to all undergraduates. HEOP Phone: 609-921-9000 large: “to educate socially-responsible support is available to students wishing www.ets.org engineering and applied science leaders to pursue only the Bachelor of Science whose work results in the betterment of degree or Columbia’s Combined Plan American College Testing Program the human condition, locally, nationally, Program for both the Bachelor of Arts Box 313 and globally.” and Bachelor of Science in five years. Iowa City, IW 52243 The National Opportunity Program Phone: 319-337-1270 C. Prescott Davis Scholars Program (NOP) is a replication of the Higher www.act.org Education Opportunity Program Each year, outstanding high school and provides access to a Columbia seniors are nominated for selection Test of English as a Foreign Language education for students outside of New as C. Prescott Davis Scholars by the Box 899 York State. Requirements for NOP are Admissions Committee. After a rigorous Princeton, NJ 08451 the same as those for HEOP, except selection process, the Scholars are 609-771-7100 for the New York State residency chosen to participate throughout their www.toefl.org requirement. four undergraduate years in academic For further information concerning and cocurricular opportunities, including International English Language Testing the Engineering School’s Opportunity research with faculty, professional System Programs, contact: internships, and meetings with world- www.ielts.org renowned scholars, innovators, and Academic Success Programs leaders. Advanced Placement Columbia University The School gives recognition to New York, NY 10027 Higher Education Opportunity the Advanced Placement program. Phone: 212-854-3514 Program (HEOP) and National Appropriate placement and credit will be www.studentaffairs.columbia.edu/asp/ Opportunity Program (NOP) given to students who score according programs to the School’s criteria (see page 14) in The Higher Education Opportunity the Advanced Placement examinations Program (HEOP) is sponsored by applicants with given in May by the College Entrance the New York State Department of advanced standing Examination Board. In addition, required Education and Columbia University. (Transfer Applicants) courses may be waived on the basis The program is designed for New York Columbia Engineering accepts of faculty placement conferences, State residents who have particular applications for transfer into the permitting students with special educational and economic needs with

engineering 2011–2012 22 sophomore or junior year from students SAT Subject Tests are required only Campus Visits and in four-year programs at arts and if the tests were taken in high school. Interviews sciences colleges and engineering Students in a non-English-speaking Prospective students are encouraged schools. The School also accepts environment and whose primary to visit the Columbia campus applications from students with language of instruction has not been throughout the year. The Office of strong academic records in pre- English for at least five years are Undergraduate Admissions hosts engineering programs at two-year required to take an English proficiency information sessions and campus tours community colleges. All students who examination, TOEFL or IELTS. These through the Visitors Center, located in are considering applying to Columbia students must submit the results of at 213 Low Library. Group information Engineering are encouraged to complete least one of the exams and may be sessions are conducted by members a course of study similar to the School’s required to take an English placement of the admissions staff and offer First Year–Sophomore Program. test on arrival, before registration. the opportunity to learn more about Transfers, who are guaranteed housing, Transfer Applications can only be Columbia University’s academic and may enter Columbia only in September completed online at the website of the student life as well as admissions and and may count no more than 68 points Office of Undergraduate Admissions. financial aid. Campus tours immediately of credit toward the Columbia degree. www.studentaffairs.columbia.edu/ follow the information session and Transfer students must also satisfy the admissions/applications/transfer.php are led by a current undergraduate University’s residence requirements by Applications must be received by March student. Engineering tours, designed to taking at least 60 points at Columbia. 15 for September admission. offer prospective students an in-depth Credit for transfer students to look into The Fu Foundation School of Columbia Engineering is determined by The Combined Plan Programs Engineering and Applied Science, are the equivalence of the courses taken The Combined Plan programs at The Fu led by current Columbia engineering at a previous institution with courses Foundation School of Engineering and students and are available every Friday at Columbia. A minimum final course Applied Science are designed to provide at 1:00 p.m., except for holidays. Please grade of B must be achieved in order students the opportunity to receive note that the Engineering School tour for transfer credit to be awarded. At both a Bachelor of Arts or Bachelor is designed to supplement, but not the time of admission, transfer students of Science degree from an affiliated replace, the Undergraduate Admissions are provided with a tentative credit liberal arts college and a Bachelor of information session and general campus evaluation, which is an evaluation based Science or Master of Science degree tour. For further information and a on the student’s transcript. Prior to from Columbia. Details concerning these detailed schedule of visit opportunities, enrolling, transfer students are required programs are contained in the The please see Visiting Columbia on the to submit course descriptions and/or Undergraduate Programs section of this Undergraduate Admissions website syllabi for all courses for which they wish bulletin. (www.studentaffairs.columbia.edu/ to receive credit. The classes for the first Secondary school students who wish admissions). year-sophomore program are evaluated to follow one of the Combined Plan pro- Columbia does not conduct and a determination is made by the grams at one of the affiliated Combined interviews on campus. Interviews are Center for Student Advising as to the Plan schools should apply directly to the instead conducted around the country degree to which the materials covered affiliated school’s admissions office. and the world by the members of the overlap with the similar course at Third-year undergraduate students Alumni Representative Committee. Columbia. If the overlap is deemed to be already in a Combined Plan program The University provides the names of sufficient, the student will receive both should apply to the Columbia University candidates to the Committee, which credit and exemption for that class. It is School of Engineering and Applied conducts interviews from October possible however for students to receive Science Combined Plan Program. through February. Candidates will be credit for a class taken elsewhere, The deadlines for applying to these contacted by a Committee member but not an exemption. For classes to programs, each of which is described in during this time if interviews are fulfill the nontechnical, technical, and the Undergraduate Programs section of available. Candidates should not call or major course requirements, students this bulletin, are: write the Admissions Office to arrange are required to submit petitions to the alumni interviews. Center for Student Advising. These • February 15 preferred deadline for petitions are reviewed by the appropriate the 3-2 Combined Plan Program faculty committee and a determination is • March 15: final deadline for the 3-2 made as to whether or not the student Combined Plan Program should receive credit and/or exemption. • March 15 for the 4-2 Combined Transfer applicants should Plan B.S. Program provide the scores of College Board • February 15 for the 4-2 Combined Examinations as part of their application. Plan M.S. Program Applicants must submit results of the For further information on the 3-2 and SAT or the American College Testing 4-2 B.S. and 4-2 M.S. programs, refer (ACT) examinations. Results of the to pages 15–16.

engineering 2011–2012 Undergraduate Tuition, Fees, and Payments 23

he 2011–2012 tuition and fees Tuition insurance premium in addition to the are estimated. Tuition and fees Undergraduate students enrolled in The Health Service fee. Visit the Health T are prescribed by statute and are Fu Foundation School of Engineering Services website (www.health.columbia. subject to change at the discretion of and Applied Science pay a flat tuition edu) for detailed information about the Trustees. charge of $21,544 per term, regardless medical insurance coverage options University charges such as tuition, of the number of course credits taken. and directions for making confirmation, fees, and residence hall and meal plans enrollment, or waiver requests. are billed in the first Student Account Mandatory Fees Statement of the term, which is sent Personal Expenses out in July and December of each year Orientation fee: $416 (one-time charge Students should expect to incur for the upcoming term. This account in the first term of registration) miscellaneous personal expenses for is payable and due in full on or before Student Life fee: $651 per term such items as clothing, linen, laundry, the payment due date announced in Health Service fee: $450 per term dry cleaning, and so forth. Students the Statement, typically at the end International Services charge: $50 per should also add to the above expenses of August or early January before term (international students only) the cost of two round trips between the beginning of the billed term. Any Transcript fee: $95 (one-time charge) home and the University to cover travel student who does not receive the first during the summer and the month-long, Student Account Statement is expected Other Fees midyear break. to pay at registration. Application and late fees The University advises students to If the University does not receive • Application for undergraduate open a local bank account upon arrival the full amount due for the term on or admission: $80 in New York City. Since it often takes as before the payment due date of the • Application for undergraduate transfer long as three weeks for the first deposit first Statement, a late payment charge admission: $80 to clear, students should plan to cover of $150 will be assessed. An additional • Late registration fee during late immediate expenses using either a charge of 1 percent per billing cycle may registration: $50; credit card, traveler’s checks, or cash be imposed on any amount past due after late registration: $100 draft drawn on a local bank. Students thereafter. are urged not to arrive in New York Students with an overdue account Books and course materials: Depends without sufficient start-up funds. balance may be prohibited from upon course registering, changing programs, or obtaining a diploma or transcripts. Laboratory fees: See course listings Laboratory Charges In the case of persistently delinquent Students may need to add another Room and board (estimated): $11,000 accounts, the University may utilize the $100 to $300 for drafting materials or services of an attorney and/or collection laboratory fees in certain courses. Each agent to collect any amount past due. Health Insurance student taking laboratory courses must If a student’s account is referred for Columbia University offers the Student furnish, at his or her own expense, the collection, the student may be charged Medical Insurance Plan, which provides necessary notebooks, blank forms, and an additional amount equal to the cost both Basic and Comprehensive levels similar supplies. In some laboratory of collection, including reasonable of coverage. Full-time students are courses, a fee is charged to cover attorney’s fees and expenses incurred automatically enrolled in the Basic expendable materials and equipment by the University. level of the Plan and billed for the maintenance. Students engaged in

engineering 2011–2012 24 special tests, investigations, theses, Tuition and Fee Refunds For students receiving federal student or research work are required to meet Students who make a complete aid, refunds will be made to the federal the costs of expendable materials as withdrawal from a term are assessed aid programs in accordance with may be necessary for this work and in a withdrawal fee of $75. Late fees, Department of Education regulations. accordance with such arrangements as application fees, withdrawal fees, tuition Refunds will be credited in the following may be made between the student and deposits, special fees, computer fees, order: the department immediately concerned. special examination fees, and transcript Federal Unsubsidized Stafford Loans fees are not refundable. Federal Stafford Loans Federal Perkins Loans Damages The Health Service Fee, Health Insurance Premium, University facilities Federal PLUS Loans (when disbursed All students will be charged for damage fees, and student activity fees are not through the University) to instruments or apparatus caused by refundable after the change of program Federal Pell Grants their carelessness. The amount of the period. Federal Supplemental Educational charge will be the actual cost of repair, Students who withdraw within the Opportunity Grants and, if the damage results in total loss of first 60 percent of the academic period Other Title IV funds the apparatus, adjustment will be made are subject to a refund calculation, in the charge for age or condition. To which refunds a portion of tuition based Withdrawing students should be ensure that there may be no question on the percentage of the term remaining aware that they will not be entitled as to the liability for damage, students after the time of withdrawal. This to any portion of a refund until all should note whether the apparatus is in calculation is made from the date the Title IV programs are credited and all good condition before use and, in case student’s written notice of withdrawal is outstanding charges have been paid. of difficulty, request instruction in its received by the Dean’s Office. proper operation. Where there is danger of costly damage, an instructor should be requested to inspect the apparatus. Percentage Refund for Withdrawal Liability for breakage will be decided by during First Nine Weeks of Term the instructor in charge of the course. Prorated for calendars of a different When the laboratory work is done duration: by a group, charges for breakage will 1st week 100% be divided among the members of the 2nd week 90% group. The students responsible for any 3rd week 80% damage will be notified that a charge is 4th week 80% being made against them. 5th week 70% The amount of the charge will be 6th week 60% stated at that time or as soon as it can 7th week 60% be determined. 8th week 50% 9th week 40% 10th week and after 0%

engineering 2011–2012 financial aid for undergraduate study 25

Office of Financial Aid and of attendance at Columbia (including may vary from year to year. Educational Financing tuition, room, board, fees, books, travel, The Office of Financial Aid and 618 Lerner Hall and personal expenses) represents the Educational Financing reserves the right 2920 Broadway, MC 2802 student’s demonstrated need. to revise a financial aid award if the New York, NY 10027 The family contribution to the cost student withdraws from school or if any of attending Columbia consists of two information reported on financial aid Phone: 212-854-3711 elements: the parent contribution and applications conflicts with information Fax: 212-854-5353 the student contribution. The parent on tax returns or other verification E-mail: [email protected] contribution is determined through an documents. If a family’s financial www.studentaffairs.columbia.edu/finaid evaluation of parent income and assets, circumstances change after submission family size, and the number of family of the financial aid application, an Admission to Columbia is need-blind for members attending college. The student appeal may be made to the Office of all students who are U.S. citizens, U.S. contribution consists of a percentage Financial Aid and Educational Financing, permanent residents, or granted U.S. of the student’s assets and a minimum in writing, for a reconsideration of the refugee visas. Financial aid is awarded contribution from income. Each student financial aid package. An appeal may only to students who demonstrate need. is expected to work during the summer be made at any time during the year Columbia is committed to meeting and save a certain amount to contribute if circumstances warrant; otherwise the full demonstrated financial need to educational costs. appeals in direct response to award of all applicants admitted as first-year The minimum contribution from letters must be made in writing within students. Financial aid is available for earnings is currently: two weeks of receipt of aid packages. all four undergraduate years, providing First Year $2,400 students continue to demonstrate Sophomore $2,810 Satisfactory Academic Progress financial need. Junior $3,020 Students must continue to make While transfer admission is need- Senior $3,150 satisfactory academic progress toward blind, financial aid resources for transfer The expected summer earnings the degree to remain eligible for financial students are very limited. Therefore, The amount is separate from the amount aid. Satisfactory academic progress is Fu Foundation School of Engineering that students are expected to earn reviewed at the end of each term by and Applied Science is unable to meet by working a part-time job during the the Committee on Academic Screening. the full need of transfer applicants, with academic year. All students are considered for financial the exception of students who transfer Eligibility for Columbia grant aid aid purposes to be making satisfactory from Columbia College. is normally limited to eight terms of academic progress as long as they are undergraduate study. Students must allowed to continue enrollment. For reapply for financial aid each year and Determining Eligibility details of The Fu Foundation School be registered for a minimum of 12 Columbia determines the amount each of Engineering and Applied Science’s points during any term for which aid family can contribute to educational process for evaluating student’s is requested. Changes in the family’s costs through an evaluation of the academic progress, see the section on circumstances—for example, increased family’s financial information as reported Conduct and Discipline in this bulletin. income or a change in the number of on the application forms described in A student who is required to withdraw family members attending college— the section How to Apply for Financial because of failure to make satisfactory will result in changes in the family Aid. The difference between the academic progress may appeal the contribution. In addition, the individual family contribution and the total cost decision to the Committee on Academic elements in the financial aid package

engineering 2011–2012 26 Screening. Upon returning to the School made under Title IV of the Higher hiring and payment. The Federal Work- of Engineering and Applied Science Education Act of 1965, as amended, Study (FWS) program is designed to following a required withdrawal period, a from funds supplied entirely by the promote part-time employment for student regains eligibility for financial aid. federal government. These funds are students who are in need of earnings awarded to students who demonstrate to help finance their education and to financial need and are made without encourage participation in community Financial Aid Awards expectation of repayment. The amount service. The goal of Columbia Financial aid is awarded in the form of a of an individual grant may range from University’s FWS program is to provide “package,” consisting of a combination $200 to $4,000 per year. student assistance that supports a of the various types of financial aid The Federal Pell Grant program wide range of career objectives and for which the student is eligible. Most is authorized by the Education departmental needs within the University financial aid packages include a Amendments of 1972. Under this and the community. combination of grant and “self-help.” program the federal government The self-help portion of a financial aid provides grants to students who C. Financing Options package consists of a part-time job qualify on the basis of financial need. during the academic year. Grants from In addition to Columbia’s commitment to Pell grants may range from $1,176 to government sources or directly from meeting 100 percent of every student’s $5,550. Columbia cover any remaining need demonstrated financial need, Columbia The New York State Tuition beyond that covered by the self-help is committed to assisting families in Assistance Program (TAP) provides award. meeting their family contributions. The grants to full-time, matriculated New Columbia determines the institutional, following financing options are available York State residents who meet New federal, and New York State financial to assist families in making educational York State’s eligibility standards. Current aid programs for which each student is costs more affordable. TAP award amounts range from $425 eligible and awards funds appropriately. Monthly Payment Plan: Columbia to $4,925. In addition to applying to Columbia for offers an interest-free monthly payment Other grants/scholarships may be assistance, all financial aid applicants plan through which parents may make available to students from a variety of are expected to apply for any other five equal monthly payments each term outside sources. These include, but are grant/ scholarship aid for which they rather than paying the term’s bill in not limited to, awards sponsored by may be eligible. Students must notify the full at the beginning of each term. The secondary schools, civic organizations, Office of Financial Aid and Educational only cost associated with the plan is a parental employers, corporations, and Financing if any outside awards are nominal enrollment fee. the National Merit and National Achieve- received. Parent Loans for Undergraduate ment Scholarship programs. Outside Students who receive financial aid Students (PLUS): Through the PLUS scholarships are used to reduce the from Columbia grant permission to the program, parents may borrow for a self-help component of the financial Office of Financial Aid and Educational child’s educational expenses. Under the aid package. Only after self-help has Financing to release relevant personal, PLUS program, parents may borrow been completely eliminated will the academic, and financial information up to the total cost of attendance scholarships begin to reduce any to persons or organizations outside less any other financial aid received. Columbia grant. Columbia in order to institute or to Parents need not demonstrate need to continue financial assistance that they qualify; however, they must be citizens B. Student Employment might be eligible to receive from such or permanent residents of the United sources. Students can expect that All students who receive financial aid States and must pass a standard credit Columbia will respect their right to from Columbia are expected to have check. A fee of up to 4 percent will be privacy and release information only as a part-time job to help meet the cost deducted from the loan at the time that necessary. of education. Most students work it is disbursed. Repayment begins 60 The following sources of financial on or near campus, but there are days after the second disbursement of aid may be included in a financial aid many interesting and rewarding jobs the loan. package from Columbia. throughout New York City as well. Columbia maintains an extensive How to Apply for listing of student employment opportuni- A. Grants and Scholarships Financial Aid ties, both for federal work-study posi- Through the Columbia University Grant In order to be considered for need- tions and other student employment (CUG) program, need-based grants are based institutional financial aid at options, which do not receive federal made to full-time matriculated Columbia any time during their four years of funding. These listings are available students without expectation of undergraduate study, students must online. (studentaffairs.columbia.edu/ repayment. Grants are funded through a apply for financial aid at the time finaid/forms/workstudy.php) variety of University resources, including they apply for admission. Exceptions Federal Work-Study Student annual gifts and endowed accounts. may be granted only in the case Employment. The Work-Study Payroll Federal Supplemental Educational of extenuating circumstances that Office is dedicated to assisting Columbia Opportunity Grants (SEOG) are grants result in a significant change in the students with all processes related to

engineering 2011–2012 family’s financial situation. Continuing that they may complete the FAFSA with November 15: First-year early decision 27 students must reapply for financial aid an online signature. FAFSA applicants candidates each year. The student’s name and without PIN numbers may print a sig- March 1: First-year regular decision candidates and combined plan Columbia ID number should be printed nature page and mail it in to the FAFSA April 20: Transfer applicants on all documents submitted to the Processor. All online FAFSA applicants May 5: Continuing students Office of Financial Aid and Educational should wait for and print out the confir- Financing. Financial aid applicants mation page, to ensure that their online 5. Federal Income Tax Returns whose application materials are submission has been received. Signed copies of parent and student submitted after the published deadlines Columbia recommends waiting until federal income tax returns, including cannot be guaranteed institutional after federal income tax returns have W-2 forms and all schedules, financial aid. been completed before completing are required for verification of the All Columbia application materials the FAFSA form, but no later than the information reported on the PROFILE can be accessed through www. following deadlines: Form and FAFSA. The financial aid studentaffairs.columbia.edu/finaid. March 1: First-year candidates (early and office strongly encourages families of regular decision) and combined plan first-year applicants to complete their 1. College Scholarship Service (CSS) April 20: Transfer applicants federal income taxes in February. Signed PROFILE Form May 5: Continuing students copies of federal tax returns for parents First-time applicants (first-year and and, if applicable, for students should 3. Noncustodial Profile transfer applicants, and continuing be submitted to the financial aid office Columbia believes that the principal students who are applying for financial as soon as they are completed. The responsibility for meeting educational aid for the first time) must register with preferred deadlines for submission of costs belongs to the family and offers CSS for the PROFILE Form by visiting signed federal tax returns are: CSS online at www.collegeboard.com/ financial aid only to supplement the profile. Applicants who register online family’s resources. If the student’s March 1: First-year candidates (early and regular decision) and combined should complete the CSS Profile online natural parents are divorced or plan (requires a secure browser and credit separated, Columbia requires each April 20: Transfer applicants card). All students must include the parent to provide financial information May 5: Continuing students Columbia University School of Engineer- as part of the student’s application for ing and Applied Science’s CSS code on financial aid. The parent with whom Tax Withholding for their PROFILE Form. the applicant lives most of the year Nonresident Alien CSS code for Columbia: 2116 should complete the PROFILE Form and the FAFSA. The noncustodial parent Scholarship and The deadlines to submit online are: should submit an income tax return and Fellowship Recipients the CSS Noncustodial Profile (online United States tax law requires the November 15: First-year early decision University to withhold tax at the rate March 1: First-year regular decision form provided as a link once the CSS April 20: Transfer applicants PROFILE is submitted). of 14 percent on scholarship and May 5: Continuing students First-year and transfer applicants and fellowship grants paid to nonresident continuing students should complete aliens which exceed the cost of tuition, 2. Free Application for Federal the CSS Noncustodial PROFILE. The books, fees, and related classroom Student Aid (FAFSA) deadlines for completing this form are: expenses. Certain countries have entered into First-year applicants should obtain a November 15: First-year early decision tax treaties with the United States, FAFSA online at www.fafsa.ed.gov/, candidates which may serve to reduce this rate of from their high school guidance office, March 1: First-year regular decision withholding. However, even when such or by calling 1-800-4FED-AID. candidates and combined plan April 20: Transfer applicants a treaty applies, the student and the Transfer applicants should obtain May 5: Continuing students University must report the full amount a FAFSA online, from their current of such excess to the Internal Revenue college’s financial aid office, or by calling 4. Business/Farm Information Service. the number above. If a student claims tax treaty benefits, he Continuing students should apply If the student or parents own all or or she must also report this amount to online each year. part of a business, corporations, or his or her country of residence. All students must include the partnership, or are farm tenants, a The International Students and Columbia University School of complete copy of the most recent Scholars Office has prepared a packet Engineering and Applied Science’s business tax return (including all of tax information, which is revised school code on the FAFSA form. schedules) must be submitted to annually and is available to students. FAFSA code for Columbia: 002707 Columbia. Sole proprietors must submit Students and their parents submitting Schedule C. The deadlines to return the FAFSA online should request PIN these documents to the financial aid numbers from the FAFSA website, so office are:

engineering 2011–2012 28

International Students and Phone: 212-854-3587 The tax law is complex and may vary Scholars Office Fax: 212-851-1235 with regard to individual circumstances. International House North E-mail: [email protected] Therefore, as the University is not in a 524 Riverside Drive, Suite 200 www.columbia.edu/cu/isso position to offer individual tax advice, Mailing: 2960 Broadway, MC 5724 students are advised to consult with New York, NY 10027 a qualified tax professional and/or the consulate of their country of residence.

engineering 2011–2012 Graduate Studies 30 the graduate programs

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

engineering 2011–2012 statements covering these special Each applicant must produce evi- program leading to the degrees of 31 requirements are issued by the School’s dence of an outstanding undergraduate Master of Business Administration and separate departments. An applicant record, including superior performance the Master of Science in Operations who lacks essential training will be in physics and mathematics through Research. (See Industrial Engineering required to strengthen or supplement differential equations. The program of and Operations Research.) the undergraduate work by taking or study will be individually worked out in repeating certain undergraduate courses consultation with a faculty adviser and Joint Program with the School before proceeding to graduate study. will be designed to integrate undergrad- of Business in Earth Resources No graduate credit (that is, credit toward uate work with the field of engineering or Engineering the minimum 30-point requirement for applied science the student chooses to The Graduate School of Business the Master of Science degree) will be follow. During the first year, the program and the Engineering School offer a allowed for such subjects. Accordingly, will consist primarily of basic undergrad- joint program leading to the degrees Master of Science programs may uate courses; during the second year, of of Master of Business Administration include from 35 to 45 points and may graduate courses in the selected field. and the Master of Science in Earth require three terms for completion. The student must complete at least 30 Resources Engineering. (See Earth and Doctoral research credits cannot be credits of graduate study to qualify for Environmental Engineering.) used toward M.S. degree requirements. the degree. All degree requirements must be A student whose background may Special Studies with the Harriman completed within five years of the require supplementary preparation in Institute beginning of graduate study. Under some specific area, or who has been A candidate for an advanced degree in extraordinary circumstances, a written out of school for a considerable period, the Engineering School may combine request for an extension of this time will have to carry a heavier than normal these studies with work in the Harriman limit may be submitted to the student’s course load or extend the program Institute. Upon completion of the department for approval by the beyond two years. course requirements in the Institute and department chairman and the Assistant Please contact the Office of satisfaction of the language requirement Dean. A minimum grade-point average Graduate Student Services, The Fu (in any language indigenous to the of 2.5 is required for the M.S. degree. Foundation School of Engineering and former USSR), the student may qualify A student who, at the end of any term, Applied Science, 524 S. W. Mudd, Mail for the professional certificate of the has not attained the grade-point average Code 4708, 500 West 120th Street, Harriman Institute. The manner in required for the degree may be asked to New York, NY 10027; you should also which the Institute and departmental withdraw. contact the Combined Plan liaison at requirements are combined is to After the first semester of enrollment, your school for program information. be determined by the student in an M.S. student may submit an You may, in addition, e-mail questions consultation with departmental and application to apply and transfer to to [email protected]. Institute advisers. Advanced studies another academic program. If the and research may, where appropriate, student is not successful with the Dual Degree Program with the be supervised by faculty members from application process, then he or she must School of Journalism in Computer both the School and the Institute. make sure requirements for the original Science academic program are completed. The Graduate School of Journalism and the Engineering School offer a dual The Professional Degree The 4-2 Master of Science Program degree program leading to the degrees An undergraduate engineering degree The 4-2 Master of Science Program of Master in Science in Journalism and is prerequisite for admission to the provides the opportunity for students the Master of Science in Computer professional degree program. The holding bachelor’s degrees from affili- Science. (See Computer Science.) program leading to the professional ated liberal arts colleges (see the list- degrees in chemical, civil, computer, ing under the heading The Combined Joint Program with the School of electrical, industrial, mechanical, Plan—Affiliated Colleges and Universities Business in Industrial Engineering metallurgical and mining engineering, and engineering mechanics is planned with majors in mathematics, physics, The Graduate School of Business for engineers who wish to do advanced chemistry, or certain other physical and the Engineering School offer a work beyond the level of the M.S. sciences to receive the M.S. degree joint program leading to the degrees degree but who do not desire to after two years of study at Columbia in of Master of Business Administration emphasize research. the following fields of engineering and and the Master of Science in Industrial The professional degree is awarded applied science: biomedical, chemical, Engineering. (See Industrial Engineering for satisfactory completion of a civil, computer, Earth and environmental, and Operations Research.) electrical, industrial, and mechanical graduate program at a higher level of engineering; applied physics; applied course work than is normally completed Joint Program with the School of mathematics; engineering mechanics; for the M.S. degree. Students who Business in Operations Research operations research; materials science; find it necessary to include master’s- The Graduate School of Business and and computer science. level courses in their professional the Engineering School offer a joint

engineering 2011–2012 32 degree program will, in general, take Candidates for the Ph.D. degree demonstrated that the candidate has such courses as deficiency courses. must register full time and complete six made a contribution to knowledge in a A candidate is required to maintain a Residence Units. A master’s degree chosen area. In content the dissertation grade-point average of at least 3.0. from an accredited institution may should, therefore, be a distinctly original A student who, at the end of any be accepted in the form of advanced contribution in the selected field of term, has not attained the grade-point standing as the equivalent of one year study. In form it must show the mastery average required for the degree may be of residence (30 points of credit or two of written English which is expected of a asked to withdraw. At least 30 points Residence Units) for either doctoral university graduate. of credit of graduate work beyond the degree. An application for advanced Ph.D. candidates should obtain a M.S. degree, or 60 points of graduate standing must be completed during copy of the bulletin of the Graduate work beyond the B.S. degree, are the first semester of study. Candidates School of Arts and Sciences, in which required for the professional degree. for the Eng.Sc.D. degree must (in are printed the faculty requirements The final 30 points required for the addition to the 60-point requirement) for the Ph.D. degree. These are professional degree must be completed accumulate 12 points of credit in the supplemented by the requirements of in no more than five years. departmental course E9800: Doctoral the department of major interest research instruction. A holder of the professional degree who wishes to Doctoral Degrees: Doctoral Research Instruction continue work toward the Eng.Sc.D. Eng.Sc.D. and Ph.D. In order that the University may recover degree will be required to complete not the costs that are not defrayed by the Two doctoral degrees in engineering less than 30 additional points of credit University’s income from tuition, charges are offered by the University: the Doctor in residence. All doctoral programs are for research required for the Eng.Sc.D. of Engineering Science, administered subject to review by the Committee are assessed as given below. by The Fu Foundation School of on Instruction of the School. In no Ph.D. candidates should consult Engineering and Applied Science, and case will more than 15 points of credit the bulletin of the Graduate School the Doctor of Philosophy, administered be approved for the dissertation and of Arts and Sciences for the research by the Graduate School of Arts and research and studies directly connected instruction requirements that apply to Sciences. The Eng.Sc.D. and Ph.D. therewith without special approval by them. programs have identical academic this Committee. Normally, a doctoral An Eng.Sc.D. candidate is required requirements with regard to courses, candidate specializes in a field of interest to do the following: thesis, and examinations, but differ in acceptable to a department of the residence requirements and in certain School. 1. At the time the student begins administrative details. Departmental requirements may doctoral research, the student is Doctoral students may submit include comprehensive written and oral eligible to register for E9800 (3, 6, 9, a petition to the Office of Graduate qualifying examinations. Thereafter, or 12 points of credit). Twelve points Student Services to change from the the student must write a dissertation must have been accumulated by the Eng.Sc.D. degree to the Ph.D. degree or embodying original research under time the student is to receive the from the Ph.D. degree to the Eng.Sc.D. the sponsorship of a member of his degree. degree. The petition must be submitted or her department and submit it to 2. Registration for E9800 at a time within the first year of enrollment or the department. If the department other than that prescribed above by the completion of 30 points. Any recommends the dissertation for is not permitted, except by written petitions submitted after this period will defense, the student applies for final permission of the Dean. not be considered. Doctoral degree examination, which is held before an 3. Although 12 points of E9800 are status can be changed only once; examining committee appointed by the required for the doctoral degree, no students, therefore, must determine Dean. This application must be made part of this credit may count toward which doctoral degree program is most at least three weeks before the date of the minimum residence requirement appropriate for their academic and the final examination. A student must of 30 points (or 60 points beyond the professional endeavors. have a satisfactory grade-point average bachelor’s degree). to be admitted to the doctoral qualifying 4. If a student is required to take course Requirements for the Degrees examination. Consult the department work beyond the minimum residence A student must obtain the master’s requirements for details. requirements, the 12 points of degree (M.S.) before enrolling as a The candidate for the degree doctoral research instruction must still candidate for either the Ph.D. or Eng. of Doctor of Engineering Science be taken in addition to the required Sc.D. degree. Application for admission must submit evidence that his or her course work. as a doctoral candidate may be made dissertation has been filed in compliance 5. A student must register continuously while a student is enrolled as a master’s with requirements set by the Faculty of through the autumn and spring terms. degree candidate. The minimum Engineering and Applied Science. This requirement does not include the requirement in course work for either The defense of the dissertation summer session. doctoral degree is 60 points of credit constitutes the final test of the beyond the bachelor’s degree. candidate’s qualifications. It must be

engineering 2011–2012 33

Completion of Requirements Special Nondegree Network (CVN), which follows in this The requirements for the Eng.Sc.D. Students bulletin. degree must be completed in no more Qualified persons who are not interested Special students receive grades than seven years. The seven-year time in a degree program but who wish and must maintain satisfactory period begins at the time the student only to take certain courses may be attendance and performance in classes becomes a candidate for the Eng. permitted to register as special students, or laboratories and will be subject to Sc.D. degree or a candidate for the provided facilities are available. the same rules as degree candidates. professional degree, whichever occurs Many graduate courses in The Fu Should a special student decide first, and extends to the date on which Foundation School of Engineering and to pursue a degree program, work the dissertation defense is held. Applied Science are offered in the completed as a special student may be Extension of the time allowed for late afternoon and evening in order considered for advanced standing, but completion of the degree may be to make them available to working no more than 15 points of course work granted on recommendation of the individuals who wish to further their completed as a special student may be student’s sponsor and the department knowledge in the areas of engineering counted toward a graduate degree. chairman to the Dean when special and applied science. Individuals who For additional information and regula- circumstances warrant. Such extensions find it difficult or impossible to attend tions pertaining to special students, see are initiated by submitting a statement classes on the Columbia campus may Graduate Admissions. of work in progress and a schedule for be able to receive instruction from the completion together with the sponsor’s School through the Columbia Video recommendation to the department Network without leaving their work sites. chairman. Individuals interested in this program should read the section describing the distance learning Columbia Video

engineering 2011–2012 34 columbia video network

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

engineering 2011–2012 graduate admissions 35

Office of Graduate Student Services Application Requirements Language Program (ALP). 524 S. W. Mudd, MC 4708 Applicants must submit an online • M.Phil., Ph.D., and Eng.Sc.D. 500 West 120th Street application and required supplemental candidates must attain level 10 on New York, NY 10027 materials, as described below. When the English Proficiency Essay Exam filing the online application, the offered by Columbia’s American Phone: 212-854-6438 candidate should obtain one official Language Program (ALP). Fax: 212-854-5900 transcript from each post-secondary E-mail: [email protected] institution attended and submit The English Proficiency Essay Exam www.engineering.columbia.edu them in the original sealed envelope. must be taken at Orientation (the fee Consideration for admission will be for this administration of the exam will The basic requirement for admission based not only on the completion of an be covered by SEAS). A student who as a graduate student is a bachelor’s earlier course of study, but also upon misses this administration of the Essay degree received from an institution of the quality of the record presented and Exam must take the exam at his or her acceptable standing. Ordinarily, the upon such evidence as can be obtained own expense at the beginning of the first applicant will have majored in the field concerning the candidate’s personal semester enrolled and submit the official in which graduate study is intended, fitness to pursue professional work. score to the Graduate Student Services but in certain programs, preparation in Additionally, candidates must provide Office. (CVN students are exempt from a related field of engineering or science three letters of recommendation and the the English Proficiency requirement.) is acceptable. The applicant will be results of required standardized exams. A student who does not pass the admitted only if the undergraduate The Graduate Record Examination Essay Exam at the required level of record shows promise of productive and (general) is required for all candidates. proficiency may be required to enroll in effective graduate work. GRE scores are valid for five years from an appropriate ALP course. For more Students who hold an appropriate the test date. The Test of English as a information on the administration of degree in engineering may apply Foreign Language (TOEFL) or International the Essay Exam, please contact the for admission to study for the Ph.D. English Language Testing System (IELTS) Graduate Student Services Office. degree. However, students are is required of all candidates who received The Graduate Student Services Office required to obtain the master’s degree their bachelor’s degree in a country reserves the right to modify the English first. Applications for admission as a in which English is not the official and Proficiency requirement at any given time. doctoral candidate may be made after spoken language. TOEFL and IELTS completion of 15 points of work as a scores are valid for two years from the test Application Fees candidate for the master’s degree. date. Applicants can only apply to one The following nonrefundable application Students may be admitted in one degree program per admission term. fees are required: of the following six classifications: • Eng.Sc.D., M.S. leading to Ph.D., and candidate for the M.S. degree, English Proficiency Ph.D. applicants: $80 candidate for the M.S. degree leading Requirement • M.S. only, professional degree, and to the Ph.D. degree, candidate for the nondegree applicants: $95 professional degree, candidate for the Admitted graduate students who Doctor of Engineering Science degree, are required to submit official TOEFL candidate for the Doctor of Philosophy or IELTS results must attain levels Graduate Admission degree (see also the bulletin of the of proficiency as described below. Calendar Students will not be cleared for Graduate School of Arts and Sciences), Applicants are admitted twice yearly, for graduation unless they satisfy the or special student (not a degree the fall and spring semesters. following requirements: candidate). Note: Not more than 15 • Fall admission application deadlines: points of credit completed as a special December 1 for Ph.D., Eng.Sc.D., • M.S. and Professional Degree nondegree student may be counted and M.S. leading to Ph.D. programs, candidates must reach level 8 on toward a degree. and applicants to the M.S. program the English Proficiency Essay Exam in financial engineering; February offered by Columbia’s American

engineering 2011–2012 36 15 for professional, M.S. only, and process for graduate study. Contact be submitted during the first week of the nondegree applicants. your academic department or the Office fall or spring semester. • Spring admission application of Graduate Student Services for further If a one-term special student deadlines: October 1 for all details. subsequently wishes either to continue departments and degree levels. taking classes the following term or to become a degree candidate, a formal One-Term Special Student Applicants who wish to be considered application must be made through the Status for scholarships, fellowships, and Office of Graduate Student Services. assistantships should file complete Individuals who meet the eligibility applications for fall admission. requirements, who are U.S. citizens or U.S. permanent residents, and who Transfer Applicants Master degree students are not eligible EXPRESS APPLICATION wish to take courses for enrichment, for transfer credits. Columbia Engineering seniors already may secure faculty approval to take Students possessing a conferred enrolled in a B.S. program with a up to two graduate-level courses for M.S. degree may be awarded 2 minimum GPA of 3.5 are eligible to one term only as a one-term special residence units toward their Ph.D., as submit an express application. student. This option is also appropriate for individuals who missed applications well as 30 points of advanced standing This online application, which waives deadlines. Applications for special toward their Ph.D. or Eng.Sc.D. with the submission of GRE scores, letters of student status are available at the Office departmental approval. recommendation, and official transcripts, of Graduate Student Services and must streamlines and simplifies the application

engineering 2011–2012 Graduate tuition, fees, and payments 37

he 2011–2012 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 $1,472 per credit, except - Eng.Sc.D., M.S. leading to Ph.D., the Trustees. when a special fee is fixed. Graduate and Ph.D. applicants: $80 University charges such as tuition, tuition for Ph.D. students is $18,778 per - M.S. only, professional degree, and fees, and residence hall and meal plans Residence Unit. The Residence Unit, nondegree applicants: $95 are billed in the first Student Account full-time registration for one semester • Late registration fee: Statement of the term, which is sent out rather than for individual courses - during late registration: $50 in July and December of each year for the (whether or not the student is taking - after late registration: $100 upcoming term. This account is payable courses), provides the basis for tuition and due in full on or before the payment charges. Ph.D. students should consult Books and course materials: due date announced in the Statement, the bulletin for the Graduate School of Depends upon course typically at the end of August or early Arts and Sciences. Laboratory fees: See course listings January before the beginning of the billed term. Any student who does not receive Comprehensive Fee/ the first Student Account Statement is Health Insurance Matriculation and expected to pay at registration. Columbia University offers the Student Facilities If the University does not receive Medical Insurance Plan, which provides the full amount due for the term on or Eng.Sc.D. candidates engaged only both Basic and Comprehensive levels before the payment due date of the in research, and who have completed of coverage. Full-time students are first Statement, a late payment charge their twelve (12) credits of Doctoral automatically enrolled in the Basic of $150 will be assessed. An additional Research Instruction (see “The Graduate level of the Plan and billed for the charge of 1 percent per billing cycle may Programs” in this bulletin), are assessed insurance premium in addition to the be imposed on any amount past due a Comprehensive Fee of $1,615 per Health Service fee. Visit www.health. thereafter. term by The Fu Foundation School of columbia.edu (www.health.columbia. Students with an overdue account Engineering and Applied Science. edu) for detailed information about balance may be prohibited from Ph.D. candidates engaged only in medical insurance coverage options registering, changing programs, or research are assessed $1,615 per term and directions for making confirmation, obtaining a diploma or transcripts. for Matriculation and Facilities by the enrollment, or waiver requests. In the case of persistently delinquent Graduate School of Arts and Sciences. accounts, the University may utilize the Personal Expenses services of an attorney and/or collection Mandatory Fees Students should expect to incur agent to collect any amount past due. University facilities fee miscellaneous personal expenses for If a student’s account is referred for • Full-time master’s programs: such items as food, clothing, linen, collection, the student may be charged $393 per term laundry, dry cleaning, and so forth. an additional amount equal to the cost • All other full-time programs: The University advises students to of collection, including reasonable $361 per term open a local bank account upon arrival attorney’s fees and expenses incurred Health Service fee: $450 per term in New York City. Since it often takes as by the University. International Services charge: $50 per long as three weeks for the first deposit term (international students only) to clear, students should plan to cover Transcript fee: $95 (one-time charge) immediate expenses using either a

engineering 2011–2012 38 credit card, traveler’s checks, or cash group. The students responsible for any Refund Policy When Dropping draft drawn on a local bank. Students damage will be notified that a charge is Individual Courses are urged not to arrive in New York being made against them. The amount Tuition for courses dropped by the last without sufficient start-up funds. of the charge will be stated at that time day of the Change-of-Program period or as soon as it can be determined. is refunded in full. There is no refund of Laboratory Charges tuition for individual courses dropped after the last day of the Change-of- Students may need to add another Tuition and Fee Refunds Program period. The Change-of- $100 to $300 for drafting materials or Students who make a complete Program period is usually the first two laboratory fees in certain courses. Each withdrawal from a term are assessed weeks of the fall or spring semesters student taking laboratory courses must a withdrawal fee of $75. Late fees, (please note that the first week of the furnish, at his or her own expense, the application fees, withdrawal fees, tuition semester usually begins on a Tuesday). necessary notebooks, blank forms, and deposits, special fees, computer fees, Please note: The prorated schedule similar supplies. In some laboratory special examination fees, and transcript above does not pertain to individual courses, a fee is charged to cover fees are not refundable. classes dropped (unless your entire expendable materials and equipment The Health Service Fee, Health schedule consists of only one class). maintenance; the amount of the fee Insurance Premium, University facilities The prorated schedule pertains to is shown with the descriptions in the fees, and student activity fees are not withdrawals. Withdrawal is defined as course listings. Students engaged in refundable after the change of program dropping one’s entire program. special tests, investigations, theses, period. For students receiving federal or research work are required to meet Students who withdraw within student aid, refunds will be made to the the costs of expendable materials as the first 60 percent of the academic federal aid programs in accordance with may be necessary for this work and in period are subject to a pro rata refund Department of Education regulations. accordance with such arrangements as calculation, which refunds a portion Refunds will be credited in the following may be made between the student and of tuition based on the percentage of order: the department immediately concerned. the term remaining after the time of Federal Unsubsidized Stafford Loans withdrawal. This calculation is made Federal Stafford Loans from the date the student’s written Damages Federal Perkins Loans notice of withdrawal is received by the All students will be charged for damage Federal PLUS Loans (when disbursed Office of Graduate Student Services. to instruments or apparatus caused by through the University) their carelessness. The amount of the Federal Pell Grants Percentage Refund for Withdrawal charge will be the actual cost of repair, Federal Supplemental Educational during First Nine Weeks of Term and, if the damage results in total loss of Opportunity Grants the apparatus, adjustment will be made Prorated for calendars of a different Other Title IV funds in the charge for age or condition. To duration, if the entire program is ensure that there may be no question dropped: Withdrawing students should be as to the liability for damage, students aware that they will not be entitled should note whether the apparatus is in 1st week 100% to any portion of a refund until all good condition before use and, in case 2nd week 90% Title IV programs are credited and all of difficulty, request instruction in its 3rd week 80% outstanding charges have been paid. proper operation. Where there is danger 4th week 80% of costly damage, an instructor should 5th week 70% be requested to inspect the apparatus. 6th week 60% Liability for breakage will be decided by 7th week 60% the instructor in charge of the course. 8th week 50% When the laboratory work is done by 9th week 40% a group, charges for breakage will be 10th week and after 0% divided among the members of the

engineering 2011–2012 financial aid for graduate study 39

Financing Graduate Instructions for Application Process Education Financial Aid Applicants Before you can complete the Free The academic departments of Columbia Application for Federal Student Aid Engineering and the Office of Financial Forms (FAFSA) form, you must obtain a Aid and Educational Financing seek to Columbia Engineering prospective and personal identification number (PIN) from ensure that all academically qualified continuing graduate students must the U.S. Department of Education. The students have enough financial support do the following to be considered for PIN serves as your identifier and your to enable them to work toward their all forms of graduate financing (both personal electronic signature on the degree. Possible forms of support for departmentally administered and FAFSA. It will also allow you to access tuition, fees, books, and living expenses financial aid–administered funds): your personal information in various are: institutional grants, fellowships, 1a. Prospective Students—complete an U.S. Department of Education systems. teaching and research assistantships, application for admission and submit Apply for your PIN at www.pin.ed.gov. readerships, preceptorships, on- or it to The Fu Foundation School of Approximately three business days after off-campus employment, and student Engineering and Applied Science’s you request your PIN, you will receive loans. The Office of Financial Aid and Office of Graduate Student Services; an e-mail with instructions on how to Educational Financing works closely with 1b. Continuing Students—preregister retrieve it electronically. If you ask to be students to develop reasonable financial for classes during the preregistration notified of your PIN by mail, it will arrive plans for completing a degree. period; in seven to ten business days via the Columbia University graduate 2. Complete a Free Application for U.S. Postal Service. funds are administered by two Federal Student Aid (FAFSA) form Once you have your PIN, you separate branches of the University, and submit it to the U.S. Department must complete a FAFSA-on-the-Web and the application materials required of Education (only U.S. citizens, application at www.fafsa.ed.gov. by the two branches differ slightly. permanent residents and federally Columbia University prefers that you Institutional grants, fellowships, eligible noncitizens must complete the apply for financial aid online. Information teaching and research assistantships, FAFSA; International students do not collected on the FAFSA will help readerships, and preceptorships are need to complete a FAFSA.); Columbia to determine your need for all departmentally administered funds. 3. Complete an Express TAP application financial aid. You must give permission Questions and problems regarding and submit it to the New York for the application data to be sent to these awards should be directed to your State Higher Education Services Columbia University by entering the Fu academic department. Federal Student Corporation (only U.S. citizens or Foundation School of Engineering and Loans (Subsidized, Unsubsidized, permanent residents who reside in Applied Science Title IV school code Graduate PLUS and Perkins), private New York State must complete the 002707 on the FAFSA form. student 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 Financial Aid and Educational Financing. do not need to submit this form); confirmation page will give you a link to Questions and problems with regard 4. Students who want to borrow the TAP-on-the-Web application. New to awards should be directed to your student loans must also complete York State uses the information provided financial aid adviser. the Graduate Engineering Student on your TAP application to determine Loan Request Form and submit it your eligibility for a Tuition Assistance to the Office of Financial Aid and Program (TAP) grant. The TAP-on- Educational Financing. the-Web online form will be partially completed with some information from

engineering 2011–2012 40 your FAFSA. Review this data, supply making satisfactory academic progress, week. The appointments generally last any missing information, and submit are made by the departments. As a from nine to twelve months. If you are the completed form. If you do not finish prospective student you must apply for participating in faculty research that the online TAP-on-the-Web application, admission and complete the financial fulfills degree requirements, you may you will be mailed a paper Express aid forms as stated on page 39. apply for a research assistantship. TAP Application. As with the TAP-on- Continuing students must preregister for Readers and preceptors receive partial the-Web application, your Express classes during the preregistration period tuition exemption and a stipend. TAP Application will also be partially and complete the applicable forms Assistantships are awarded on the completed with some of your FAFSA as stated in the Application Process basis of academic merit. All applicants data. Verify that the partially completed section. Outside scholarships for which for admission and continuing students data is correct, complete the remainder you qualify must be reported to your maintaining satisfactory academic of the form, and return it to HESC in the department and the Office of Financial standing will be considered for these envelope provided. Aid and Educational Financing. The funds. Applicants should contact the Preregister for classes during the School reserves the right to adjust your department directly for information. preregistration period if you are a institutional award if you hold an outside continuing student. Students who want scholarship, fellowship, or other outside Alternative Funding to borrow student loans must complete funding. Sources and submit the Graduate Engineering Student Loan Request Form available Institutional Grants External Awards online at www.studentaffairs.columbia. Institutional grants are awarded to Because it is not possible to offer full edu/finaid/downloads. The Graduate graduate students on the basis of grant and fellowship support to all Engineering Student Loan Request Form academic merit. Recipients must graduate students and because of the provides the University with information maintain satisfactory academic prestige inherent in holding an award about your planned program, including standing. All applicants for admission through open competition, applicants the number of courses in which you plan and continuing students maintaining are encouraged to consider major to enroll and the amount and type of satisfactory academic standing will be national and international fellowship loans for which you are applying. considered for these funds. opportunities. It is important that prospective graduate students explore Deadlines Fellowships every available source of funding for Apply for financial aid at the same time Fellowships are financial and intellectual graduate study. that you apply for admissions. Your awards for academic merit that provide In researching outside funding you admissions application must be received stipends to be used by fellows to further may look to faculty advisers, career by the December 1 deadline to be their research. If you are awarded a services offices, deans of students, and eligible for The Fu Foundation School fellowship, you are expected to devote offices of financial aid where frequently of Engineering and Applied Science time to your own work, and you are not you may find resource materials, books, departmental funding (institutional required to render any service to the and grant applications for a wide grants, fellowships, teaching and University or donor. You may publish variety of funding sources. You must research assistantships, readerships, research produced by your fellowship notify both your Columbia Engineering and preceptorships). Spring admissions work. As a fellow, you may not engage academic department and the Office of applicants will not be considered for in remunerative employment without Financial Aid and Educational Financing departmental funding. consent of the Dean. All applicants of any outside awards that you will be Incoming applicants and continuing for admission and continuing students receiving. students must complete their FAFSA maintaining satisfactory academic form after January 1 and by May 1. standing will be considered for these Funding for International Students Guidelines for continuing students funds. Applicants should contact the To secure a visa, international students are available from departmental advisers department directly for information. See must demonstrate that they have in advance of the established deadline. the complete listing of fellowships on sufficient funding to complete the All continuing supported students pages 221–222. must preregister for classes during the degree. Many international students preregistration period. obtain support for their educational Assistantships expenses from their government, a Teaching and research assistantships, foundation, or a private agency. Graduate School available in many departments, provide International students who apply Departmental Funding tuition exemption and a living stipend. to doctoral programs of study by the Duties may include teaching, laboratory December 1 deadline and are admitted The graduate departments of Columbia supervision, participation in faculty to a Columbia Engineering doctoral Engineering offer an extensive array research, and other related activities. program are automatically considered of funding. Funding decisions, based Teaching and research assistantships for departmental funding (institutional solely on merit, and contingent upon require up to twenty hours of work per grants, fellowships, teaching and

engineering 2011–2012 research assistantships, readerships, Request Form, and an Express TAP New York State Tuition Assistance 41 and preceptorships) upon completion of application (if you are a New York Program (TAP) the required financial aid forms referred State resident). Federal Student Loan Legal residents of New York State who to above. Spring admissions applicants borrowers must also complete a are enrolled in a full-time degree pro- will not be considered for departmental Columbia University Loan Entrance gram of at least 12 points a term, or the funding. Continuing international Interview and a Master Promissory equivalent, may be eligible for awards students must preregister for classes Note. The information supplied on the under this program. To apply for TAP, during the preregistration period and FAFSA form is used to determine your list the Columbia University school code complete an enrollment status form to eligibility for federal aid. The Express 002707 on the FAFSA form. When be considered for departmental funding. TAP application acts as your request the FAFSA has been processed, an Most private student loan programs for New York State Tuition Assistance Express TAP application will be mailed are restricted to U.S. citizens and Program funds. to you. Review the information, change permanent residents. However, Columbia University prefers that any incorrect items, sign the form, and international students may be eligible to the FAFSA be filed after January return it to the address indicated. apply for these domestic loan programs 1, but preferably before May 1, for with a credit worthy cosigner who is fall enrollment. Students must give Veterans’ Benefits a citizen or permanent resident in the permission for the application data Various Department of Veterans Affairs United States. Depending on the loan to be sent to Columbia University by programs provide educational benefits program, you may need a valid U.S. entering The Fu Foundation School of for sons, daughters, and spouses of Social Security number. Engineering and Applied Science Title deceased or permanently disabled Students who study at Columbia IV school code 002707 on the FAFSA veterans as well as for veterans and Engineering on temporary visas form. in-service personnel who served on should fully understand the regulations It is your responsibility to supply active duty in the U.S. Armed Forces concerning possible employment under accurate and complete information after January 1, 1955. In these those visas. Before making plans for on the FAFSA and to notify the Office programs the amount of benefits varies. employment in the United States, of Financial Aid and Educational Under most programs the student international students should consult Financing immediately of any changes pays tuition and fees at the time of with the International Students and in your enrollment plans, housing registration but receives a monthly Scholars Office (ISSO), located at 524 status, or financial situation, including allowance from Veterans Affairs. Riverside Drive, Suite 200; 212-854- information about any institutional Since interpretation of regulations 3587. Their website is www.columbia. or outside scholarships you will be governing veterans’ benefits is edu/cu/isso/. receiving. subject to change, veterans and their The Graduate Engineering Student dependents should keep in touch with Loan Request Form is available online Other Financial Aid— the Department of Veterans Affairs. For at www.studentaffairs.columbia.edu/ Federal, State, and Private additional information and assistance in finaid/downloads. Programs completing the necessary forms, contact Determination of your eligibility for 1-800-827-1000, or consult their financial aid is, in part, based upon Eligibility website (www.va.gov). the number of courses for which you To be considered for nondepartmental Detailed information regarding register. If you enroll in fewer courses financial aid (federal Stafford loans, the veteran population at Columbia than you initially reported on your federal unsubsidized Stafford loans, and policies including the Veteran’s Graduate Engineering Student Loan federal Perkins loans, and New York Readmission Provision may be found Request Form, your financial aid may State TAP grants), you must be a on the Veterans Affairs website be reduced. U.S. citizen or permanent resident (veteranaffairs.columbia.edu). University-administered federal and admitted as at least a half-time student state awards are not automatically to a degree program in Columbia Direct Loans renewed each year. Continuing Engineering. If you are taking courses graduate students must submit a Federal Subsidized Student Loan but are not yet admitted into a degree Renewal FAFSA each year by the program, then you do not qualify Program Columbia University deadline. Renewal for federal or state aid. In addition, Federal Unsubsidized Loan Program depends on the annual reevaluation to preserve your aid eligibility, you of your need, the availability of funds, Federal Perkins Loan must maintain satisfactory academic and satisfactory progress toward the progress, as defined in “The Graduate Federal Graduate PLUS Loan completion of your degree Programs” section. Detailed information regarding the To apply for funds, you must above loan programs may be found on complete a Free Application for the Student Financial Services web- Federal Student Aid (FAFSA) form, a site (www.columbia.edu/cu/sfs/docs/ Graduate Engineering Student Loan Grad_Fin_Aid).

engineering 2011–2012 42 Columbia Comprehensive Employment Contact Information Educational Financing Plan Students on fellowship support must For questions about institutional grants, Columbia University has developed the obtain the permission of the Dean before fellowships, teaching and research Comprehensive Educational Financing accepting remunerative employment. assistantships, readerships, and Plan to assist students and parents Students who study at The Fu preceptorships, contact your academic with their financing needs. The plan is Foundation School of Engineering and department. a combination of federal, institutional, Applied Science on temporary visas For questions about on- or off- and private sources of funds that should fully understand the regulations campus non-need-based employment, we hope will meet the needs of our concerning possible employment under contact the Center for Career Education, diverse student population, providing those visas. Before making plans for located at East Campus, Lower Level, options to part-time, full-time, and employment in the United States, 212-854-5609, www.careereducation. international students. international students should consult columbia.edu. with the International Students and For questions about federal work- Private Loans Scholars Office (ISSO) located at 524 study employment, New York State TAP Several private loan programs are Riverside Drive, Suite 200; 212-854- grants, and student loans, contact: available to both U.S. citizens and 3587. Their website is www.columbia. international students attending edu/cu/isso/ isso.html. Office of Financial Aid and Columbia University. These loans were Educational Financing created to supplement federal and On-Campus Employment 618 Lerner Hall institutional aid. These loan programs The Center for Career Education Mailing: 100 Hamilton Hall require that you (the applicant) have maintains an extensive listing of student 1130 Amsterdam Avenue, MC 2802 a good credit standing and not be employment opportunities. The Center for New York, NY 10027 in default on any outstanding loans. Career Education (CCE) is located at East International students may be eligible Campus, Lower Level, 212-854-5609, Phone: 212-854-3711 for a private loan with the assistance www.careereducation.columbia.edu. Fax: 212-854-8223 of a creditworthy U.S. citizen or E-mail: [email protected] permanent resident. In some cases, Off-Campus Employment in New www.studentaffairs.columbia.edu/finaid as an inter-national student, you must York City have a valid U.S. Social Security One of the nation’s largest urban number. Contact the financial aid areas, the city offers a wide variety of office for more details on this loan opportunities for part-time work. Many program. students gain significant experience in fields related to their research and study while they meet a portion of their educational expenses.

engineering 2011–2012 Faculty and Administration 44 Faculty and administration

Officers Katayun Barmak Mark A. Cane Lee C. Bollinger, J.D. Philips Electronics Professor of Applied G. Unger Vetlesen Professor of Earth and President of the University Physics and Applied Mathematics Environmental Sciences and Professor of B.A., Cambridge (England), 1983; Applied Physics and Applied Mathematics John H. Coatsworth, Ph.D. M.A., 1987; S.M., MIT, 1985; Ph.D., 1989 B.A., Harvard, 1965; M.A., 1966; Interim Provost of the University Ph.D., MIT, 1975 Peter Belhumeur Feniosky Peña-Mora, Sc.D. Professor of Computer Science Adam Cannon Dean B.S., Brown, 1985; Lecturer in Machine Learning M.S., Harvard, 1991; Ph.D., 1993 B.S., California (Los Angeles), 1991; Andrew Laine, D.Sc. M.S., 1997; Ph.D., Johns Hopkins, 2000 Secretary Steven M. Bellovin Professor of Computer Science Luca Carloni Faculty B.A., Columbia, 1972; M.S., North Associate Professor of Computer Science Alfred V. Aho Carolina (Chapel Hill), 1977; Ph.D., 1987 B.S., Bologna (Italy), 1995; M.S., Lawrence Gussman Professor of California (Berkeley), 1997; Ph.D., 2004 Computer Science Keren Bergman B.A.Sc., Toronto (Canada), 1963; Professor of Electrical Engineering Marco J. Castaldi M.A., Princeton, 1965; Ph.D., 1967 B.S., Bucknell University, 1988; Associate Professor of Earth and M.S., MIT, 1991; Ph.D., 1994 Environmental Engineering (Henry Peter K. Allen Krumb School of Mines) Professor of Computer Science Raimondo Betti B.S., Manhattan College, 1992; M.S., B.A., Brown, 1971; M.S., Oregon, 1976; Professor of Civil Engineering California (Los Angeles), 1994; Ph.D., 1997 Ph.D., Pennsylvania, 1985 B.S., Rome (Italy), 1985; M.S., Southern California, 1988; Ph.D., 1991 Augustin Chaintreau Dimitris Anastassiou Assistant Professor of Computer Science The Charles Batchelor Professor of Daniel Bienstock Magistère, Ecole Normale Supérieure Electrical Engineering Professor of Industrial Engineering and (France), 2001; D.E.A., Université Dipl., National Technical University of Operations Research and of Applied Pierre et Marie Curie (France), 2002; Athens (Greece), 1974; M.S., California Physics and Applied Mathematics Ph.D., INRIA-Ecole Normale Supérieure (Berkeley), 1975; Ph.D., 1979 B.S., Brandeis, 1982; Ph.D., MIT, 1985 (France), 2006

Gerard H. A. Ateshian Simon J. L. Billinge Siu-Wai Chan Professor of Mechanical Engineering Professor of Materials Science and of Professor of Materials Science (Henry and of Biomedical Engineering Applied Physics and Applied Mathematics Krumb School of Mines) and of Applied B.S., Columbia, 1986; M.S., 1987; B.A., Oxford (England), 1986; Physics and Applied Mathematics M.Phil., 1990; Ph.D., 1991 Ph.D., Pennsylvania, 1992 B.S., Columbia, 1980; Sc.D., MIT, 1985

William E. Bailey Jose Blanchet Kartik Chandran Associate Professor of Materials Science Assistant Professor of Industrial Associate Professor of Earth and and of Applied Physics and Applied Engineering and Operations Research Environmental Engineering Mathematics B.S., Instituto Tecnológico Autónomo de B.S., Indian Institute of Technology B.S. and B.A., Brown, 1993; México (Mexico), 2000; Ph.D., Stanford, (India), 1995; Ph.D., University of M.S., Stanford, 1995; Ph.D., 1999 2004 Connecticut, 1999

Guillaume Bal Bruno A. Boley Shih-Fu Chang Professor of Applied Mathematics Professor of Civil Engineering Professor of Electrical Engineering and Diplôme, École Polytechnique (France), B.C.E., College of the City of New York, of Computer Science 1993; Ph.D., University Paris VI, 1997 1943; M.Ac.E., Polytechnic Institute of B.S., National Taiwan University Brooklyn, 1945; Eng.Sc.D., 1946 (Taiwan), 1985; M.S., California Scott A. Banta (Berkeley), 1991; Ph.D., 1993 Associate Professor of Chemical Engineering Allen H. Boozer B.S., University of Maryland, Baltimore, Professor of Applied Physics Xi Chen 1997; M.S., Rutgers, 2000; Ph.D., 2002 B.A., Virginia, 1966; Ph.D., Cornell, 1970 Assistant Professor of Computer Science B.S., Tsinghua University (P.R. China), 2003; Ph.D., 2007

engineering 2011–2012 45

Xi Chen Paul Diament Morton B. Friedman Associate Professor of Earth and Professor of Electrical Engineering Professor of Civil Engineering and of Evironmental Engineering B.S., Columbia, 1960; M.S., 1961; Applied Physics and Applied Mathematics B.E., Xi’an Jiaotong University (P.R. China), Ph.D., 1963 B.S., New York University, 1948; 1994; M.E., Tsinghua University (P.R. China), M.S., 1950; D.Sc., 1953 1997; S.M., Harvard, 1998; Ph.D., 2001 Paul F. Duby Professor of Mineral Engineering Guillermo Gallego Maria Chudnovsky Ing. Civil M.E., Brussels (Belgium), 1956; Professor of Industrial Engineering and Associate Professor of Industrial Eng.Sc.D., Columbia, 1962 Operations Research Engineering and Operations Research B.S., California (San Diego), 1980; B.A., Technion (Israel), 1996; M.Sc., 1999; Vincent Duchêne Ph.D., Cornell, 1988 M.A., Princeton, 2002; Ph.D., 2003 Assistant Professor of Applied Physics and Applied Mathematics Roxana Geambasu Michael Collins B.S., Ecole Normale Supérieure (France), Assistant Professor of Computer Vikram S. Pandit Professor of 2008; M.S., Université Bordeaux 1 Science Computer Science (France), 2008; Ph.D., Université Pierre B.S., Polytechnic University of Bucharest B.A., Cambridge (England), 1992; et Marie Curie (France), 2011 (Romania), 2005; M.S., Washington M.Phil., 1993; Ph.D., Pennsylvania, 1999 (Seattle), 2007; Ph.D., 2011 Christopher J. Durning Rama Cont Professor of Chemical Engineering Pierre Gentine Associate Professor of Industrial B.S., Columbia, 1978; Assistant Professor of Earth and Engineering and Operations Research M.A., Princeton, 1979; Ph.D., 1982 Environmental Engineering Diplôme, École Polytechnique (France), B.Sc., SupAéro (France), 2002; M.S., 1994; D.E.A., Ecole Normale Supérieure Stephen A. Edwards MIT, 2006; M.S., Sorbonne (France), (France), 1995; Doctorat, Université de Associate Professor of Computer Science 2009; Ph.D., MIT, 2009 Paris XI (France), 1998 B.S., Caltech, 1992; M.S., California (Berkeley), 1994; Ph.D., 1997 Donald Goldfarb Patricia J. Culligan Alexander and Hermine Avanessians Professor of Civil Engineering Dan Ellis Professor of Industrial Engineering and B.Sc., University of Leeds (England), Associate Professor of Electrical Operations Research 1982; M.Phil., Cambridge (England), Engineering B.Ch.E., Cornell, 1963; 1985; Ph.D., 1989 B.A., Cambridge (England), 1987; M.A., Princeton, 1965; Ph.D., 1966 M.S., MIT, 1992; Ph.D., 1996 Gautam Dasgupta Vineet Goyal Professor of Civil Engineering Dirk Englund Assistant Professor of Industrial B.Engr., Calcutta (India), 1967; M.Engr., Assistant Professor of Electrical Engineering and Operations Research 1969; Ph.D., California (Berkeley), 1974 Engineering and of Applied Physics B.Tech., Indian Institute of Technology B.S., Caltech, 2002; M.S., Ph.D., (India), 2003; M.S., Carnegie Mellon, George Deodatis Stanford, 2008 2005; Ph.D., 2008 The Santiago and Robertina Calatrava Family Professor of Civil Engineering Steven K. Feiner Luis Gravano B.S., National Technical University of Professor of Computer Science Associate Professor of Computer Science Athens (Greece), 1982; M.S., Columbia, B.A., Brown, 1973; Ph.D., 1985 B.S., Lujan (Argentina), 1990; 1984; Ph.D., 1987 M.S., Stanford, 1994; Ph.D., 1997 Jacob Fish Emanuel Derman Robert A. W. and Christine S. Carleton Eitan Grinspun Professor of Professional Practice of Professor of Civil Engineering Associate Professor of Computer Science Industrial Engineering and Operations B.S., Technion (Israel), 1982; M.S., B.A., Toronto (Canada), 1997; Research 1985; Ph.D., Northwestern, 1989 M.S., Caltech, 2000; Ph.D., 2003 B.Sc., University of Cape Town (South Africa), 1965; M.A., Columbia, 1968; George W. Flynn Jonathan L. Gross Ph.D., 1973 Higgins Professor of Chemistry and Professor of Computer Science Professor of Chemical Engineering B.S., MIT, 1964; M.A., Dartmouth, 1966; B.S., Yale, 1960; Ph.D., 1968 M.A., Harvard, 1962; Ph.D., 1965; Postdoctoral Fellow, MIT, 1964–1966

engineering 2011–2012 46 X. Edward Guo Julia Hirschberg Soulaymane Kachani Professor of Biomedical Engineering Professor of Computer Science Associate Professor of Professional B.S., Peking University (China), 1984; B.A., Eckert College, 1968; Ph.D., Practice of Operations Research M.S., Harvard-MIT, 1990; Ph.D., 1994 Michigan, 1976; MSEE, Pennsylvania, B.S., Ecole Centrale Paris (France), 1982; Ph.D., 1985 1998; M.S., MIT, 1999; Ph.D., 2002 Martin Haugh Lecturer in Discipline, Industrial James C. Hone Gail E. Kaiser Engineering and Operations Research Associate Professor of Mechanical Professor of Computer Science B.S., University College, Cork (Ireland), Engineering B.S., MIT, 1979; M.S., 1980; 1993; M.S., 1993; M.S., Oxford, 1994; B.S., Yale, 1990; Ph.D., California Ph.D., Carnegie Mellon, 1985 Ph.D., MIT, 2001 (Berkeley), 1998 Lance C. Kam Xuedong He Hayden Huang Associate Professor of Biomedical Assistant Professor of Industrial Assistant Professor of Biomedical Engineering Engineering and Operations Research Engineering B.S., Washington (St. Louis), 1991; M.S., B.S., Peking University (China), 2005; B.S., Johns Hopkins, 1995; S.M., MIT, University of Hawaii, 1994; Ph.D., RPI, 1999 D.Phil., Oxford (England), 2009 1997; Ph.D., 2002 John Kender Tony F. Heinz Clark T. Hung Professor of Computer Science David M. Rickey Professor of Optical Professor of Biomedical Engineering B.S., Detroit, 1970; M.S., Michigan, Communications (Electrical Engineering) and Sc.B., Brown, 1990; M.S.E., 1972; Ph.D., Carnegie Mellon, 1980 Professor of Physics (Arts and Sciences) Pennsylvania, 1992; Ph.D., 1995 B.S., Stanford, 1978; Ph.D., California Angelos D. Keromytis (Berkeley), 1982 James S. Im Associate Professor of Computer Science Professor of Materials Science (Henry B.S., Crete, Heraclion (Greece), 1996; Irving P. Herman Krumb School of Mines) and of Applied M.S., Pennsylvania, 1997; Ph.D., 2001 Professor of Applied Physics Physics and Applied Mathematics B.S., MIT, 1972; Ph.D., 1977 B.S., Cornell, 1984; Ph.D., MIT, 1989 Martha A. Kim Assistant Professor of Computer Science Henry Hess Garud Iyengar B.A., Harvard, 2002; M.E., Università della Associate Professor of Biomedical Professor of Industrial Engineering and Svizzera Italiana (Lugano, Switzerland), Engineering Operations Research 2003; Ph.D., Washington (Seattle), 2008 B.S., Technical University Clausthal B. Tech., Indian Institute of Technology (Germany), 1993; M.Sc., Technical (India), 1993; M.S., Stanford, 1995; Philip Kim University Berlin (Germany), 1996; Ph.D., Ph.D., 1998 Professor of Applied Physics and of Free University Berlin (Germany), 1999 Physics (Arts and Sciences) Christopher R. Jacobs B.S., Seoul National (South Korea), Andreas H. Hielscher Associate Professor of Biomedical 1990; S.M., 1992; M.S., Harvard, 1996; Professor of Biomedical Engineering Engineering Ph.D., 1999 and of Radiology (Health Sciences) and B.S., Washington (St. Louis), 1988; of Electrical Engineering M.S., Stanford, 1989; Ph.D., 1994 Peter Kinget B.S., University of Hannover (Germany), Associate Professor of Electrical 1987; M.S., 1991; Ph.D., Rice, 1995 Tony Jebara Engineering Associate Professor of Computer Science Ph.D., Katholieke Universiteit Leuven B.S., McGill (Canada), 1996; M.S., MIT, Michael I. Hill (Belgium), 1996 1998; Ph.D., 2002 Associate, Chemical Engineering B.S., Columbia, 1983; M.S., 1989 Jeffrey T. Koberstein Pedrag R. Jelenkovic Percy K. and Vida L. W. Hudson Professor of Electrical Engineering Elizabeth M. C. Hillman Professor of Chemical Engineering Dipl.Ing., Belgrade University (Serbia), Assistant Professor of Biomedical B.S., University of Wisconsin, 1974; 1991; M.S., Columbia, 1993; M. Phil., Engineering and of Radiology Ph.D., University of Massachusetts, 1979 1995; Ph.D., 1996 (Health Sciences) M.Sci., University College London Elisa E. Konofagou Jingyue Ju (England), 1998; Ph.D., 2002 Associate Professor of Biomedical Samuel Ruben–Peter G. Viele Professor Engineering and of Radiology (Health of Engineering Sciences) B.S., Inner Mongolia University, 1985; B.S., Université de Paris VI (France), M.S., Chinese Academy of Sciences 1992; M.S., University of London (China), 1988; Ph.D., Southern (England), 1993; Ph.D., University of California, 1993 Houston, 1999

engineering 2011–2012 S. G. Steven Kou Aurel A. Lazar Michael E. Mauel 47 Professor of Industrial Engineering and Professor of Electrical Engineering Professor of Applied Physics Operations Research B.S., Bucharest Polytechnical Institute B.S., MIT, 1978; M.S., 1979; Sc.D., 1983 M.A., Columbia, 1992; Ph.D., 1995 (Romania), 1971; M.S., Darmstadt Institute of Technology (Germany), 1976; Ph.D., Nicholas Maxemchuk Harish Krishnaswamy Princeton, 1980 Professor of Electrical Engineering Assistant Professor of Electrical B.S., The City College of New York, Engineering Edward F. Leonard 1968; M.S., Pennsylvania, 1970; B.Tech., Indian Institute of Technology Professor of Chemical Engineering Ph.D., 1975 (India), 2001; M.S., Southern California, B.S., MIT, 1953; M.S., Pennsylvania, 2003; Ph.D., 2009 1955; Ph.D., 1960 Kathleen McKeown Henry and Gertrude Rothschild Sanat K. Kumar Jung-Chi Liao Professor of Computer Science Professor of Chemical Engineering Assistant Professor of Mechanical B.A., Brown, 1976; M.S., Pennsylvania, B.Tech., Indian Institute of Technology Engineering 1979; Ph.D., 1982 (India), 1981; S.M., MIT, 1984; Ph.D., B.S., National Taiwan University (Taiwan), V. Faye McNeill 1987 1993; M.S., MIT, 1997; Ph.D., 2001 Assistant Professor of Chemical Engineering Aaron Kyle Qiao Lin B.S., Caltech, 1999; M.S., MIT; Ph.D., 2005 Lecturer in Biomedical Engineering Associate Professor of Mechanical B.S., Kettering University, 2002; Engineering Christian Meyer Ph.D., Perdue, 2007 B.S., Tsinghua University (P.R. China), Professor of Civil Engineering 1985; M.S., 1988; Ph.D., Caltech, 1993 Vordiplom, Technical University of Ioannis Kymissis Berlin (Germany), 1965; M.S., California Associate Professor of Electrical Hoe I. Ling (Berkeley), 1966; Ph.D., 1970 Engineering Professor of Civil Engineering M.Eng., MIT, 1999; Ph.D., 2003 B.S., Kyoto University (Japan), 1988; M.S., Vishal Misra University of Tokyo (Japan), 1990; Ph.D., 1993 Associate Professor of Computer Science Jeffrey W. Kysar B.S., Indian Institute of Technology Professor of Mechanical Engineering Tim Leung (India), 1992; M.S., Massachusetts B.S., Kansas State, 1987; M.S., 1992; Assistant Professor of Industrial (Amherst), 1996; Ph.D., 2000 S.M., Harvard, 1993; Ph.D., 1998 Engineering and Operations Research B.S., Cornell, 2003; Ph.D., Princeton, 2008 Vijay Modi Klaus S. Lackner Professor of Mechanical Engineering Maurice Ewing and T. Lamar Worzel Richard W. Longman B.Tech., Indian Institute of Technology Professor of Geophysics (Earth and Professor of Mechanical Engineering (India), 1978; Ph.D., Cornell, 1984 Environmental Engineering, Henry and of Civil Engineering Krumb School of Mines) B.S., California (Riverside), 1965; Barclay Morrison III B.S., Heidelberg (Germany), 1974; M.S., M.S., California (San Diego), 1967; Associate Professor of Biomedical 1976; Ph.D., 1978 M.A., 1969; Ph.D., 1969 Engineering B.S.E., Johns Hopkins, 1992; M.S.E., Andrew F. Laine Helen H. Lu Pennsylvania, 1994; Ph.D., 1999 Professor of Biomedical Engineering and Associate Professor of Biomedical of Radiology (Health Sciences) Engineering Van C. Mow B.S., Cornell, 1977; M.S., Connecticut, B.S., Pennsylvania, 1992; M.S., 1997; Stanley Dicker Professor of Biomedical 1980; M.S., Washington (St. Louis), Ph.D., 1998 Engineering and Professor of Orthopedic 1983; D.Sc., 1989 Engineering (Orthopedic Surgery, Health Tal Malkin Sciences) Upmanu Lall Associate Professor of Computer Science B.A.E., RPI, 1962; Ph.D., 1966 Alan and Carol Silberstein Professor of B.S., Bar-Ilan University (Israel), 1993; Earth and Environmental Engineering M.S., Weizmann Institute of Civil Kristin Myers (Henry Krumb School of Mines) and of Engineering and Engineering Mechanics Assistant Professor of Mechanical Civil Engineering (Israel), 1995; Ph.D., MIT, 2000 Engineering B.Tech., Indian Institute of Technology B.S., University of Michigan, 2002; (India), 1976; M.S., University of Texas, Chris A. Marianetti M.S., MIT, 2005; Ph.D., 2008 1980; Ph.D., 1981 Assistant Professor of Materials Science and of Applied Physics and Applied Mathematics B.S., Ohio State, 1997; M.S., 1998; Ph.D., MIT, 2004

engineering 2011–2012 48 Arvind Narayanaswamy Ah-Hyung Alissa Park José I. Sánchez Assistant Professor of Mechanical Lenfest Junior Professor in Lecturer in Civil Engineering and Engineering Applied Climate Science Engineering Mechanics B.Tech., Indian Institute of Technology B.S., University of British Columbia B.A., Pontifica Universidad Católica (India), 1997; Ph.D., MIT, 2007 (Canada), 1998; M.S., 2000; Ph.D., Ohio Madre y Maestre (Dominican Republic), State, 2005 1991; M.A., Pratt, 1994; M.S., Gerald A. Navratil Columbia, 1996 Thomas Alva Edison Professor Dana Pe’er of Applied Physics Assistant Professor Biological Sciences Peter Schlosser B.S., Caltech, 1973; M.S., Wisconsin, and of Computer Science Vinton Professor of Earth and 1974; Ph.D., 1976 B.S., Hebrew (Israel), 1995; Environmental Engineering (Henry M.S., 1999; Ph.D., 2003 Krumb School of Mines) and Professor Shree K. Nayar of Earth and Environmental Sciences T. C. Chang Professor of Computer Science Itsik Pe’er (Arts and Sciences) B.S., Birla Institute of Technology (India), Associate Professor of Computer Science B.S./M.S., Heidelberg (Germany), 1981; 1984; M.S., North Carolina State, 1986; B.S., Tel Aviv University (Israel), 1990; Ph.D., 1985 Ph.D., Carnegie Mellon, 1990 M.S., 1995; Ph.D., 2002 Henning G. Schulzrinne Jason Nieh Feniosky Peña-Mora Julian Clarence Levi Professor of Associate Professor of Computer Science Morris A. and Alma Schapiro Professor Mathematical Methods and Computer B.S., MIT, 1989; M.S., Stanford, 1990; and Professor of Civil Engineering and Science and Professor of Computer Ph.D., 1999 Engineering Mechanics and of Computer Science and of Electrical Engineering Science and of Earth and Environmental B.S., Technical University of Darmstadt Steven M. Nowick Engineering (Germany), 1984; M.S., Cincinnati, 1987; Professor of Computer Science B.S., Universidad Nacional Pedro Ph.D., Massachusetts (Amherst), 1992 B.A., Yale, 1976; M.A., Columbia, 1979; Henríquez Ureña (Dominican Republic), Ph.D., Stanford, 1993 1987; S.M., MIT, 1991; Sc.D., 1994 Amiya K. Sen Professor of Electrical Engineering and Ismail Cevdet Noyan Aron Pinczuk of Applied Physics Professor of Materials Science (Henry Professor of Applied Physics and of Dipl., Indian Institute of Science (India), 1952; Krumb School of Mines) and of Applied Physics (Arts and Sciences) M.S., MIT, 1958; Ph.D., Columbia, 1963 Physics and Applied Mathematics Licenciado, Buenos Aires (Argentina), B.S., Middle East Technical University 1962; Ph.D., Pennsylvania, 1969 Mingoo Seok (Turkey), 1978; Ph.D., Northwestern, 1984 Assistant Professor of Electrical Lorenzo M. Polvani Engineering Mariana Olvera-Cravioto Professor of Applied Mathematics and B.S., Seoul National (South Korea), 2005; Assistant Professor of Industrial of Earth and Environmental Sciences M.S., Michigan, 2010; Ph.D., 2010 Engineering and Operations Research (Arts and Sciences) B.S., Instituto Technológico Autónomo B.Sc., McGill (Canada), 1981; M.Sc., Rocco A. Servedio de México (Mexico), 2000; M.S., 1982; Ph.D., MIT, 1988 Associate Professor of Computer Science Stanford, 2004; Ph.D., 2006 A.B., Harvard, 1993; M.S., 1997; Kenneth A. Ross Ph.D., 2001 Richard M. Osgood Jr. Professor of Computer Science Higgins Professor of Electrical B.Sc., Melbourne (Australia), 1986; Lakshminarasimhan Sethumadhavan Engineering and Professor of Applied Ph.D., Stanford, 1991 Assistant Professor of Computer Science Physics B.S.E., University of Madras (India), B.S., U.S. Military Academy, 1965; Dan Rubenstein 2000; M.S., University of Texas, 2005; M.S., Ohio State, 1968; Ph.D., MIT, 1973 Associate Professor of Computer Science Ph.D., 2007 B.S., MIT, 1992; M.A., California (Los Ben O’Shaughnessy Angeles), 1994; Ph.D., Massachusetts Jay Sethuraman Professor of Chemical Engineering (Amherst), 2000 Associate Professor of Industrial B.Sc., Bristol (England), 1977; Ph.D., Engineering and Operations Research Cambridge (England), 1984 Paul Sajda B.E., Birla Institute of Technology and Associate Professor of Biomedical Science (India), 1991; M.S., Indian Engineering and of Radiology (Health Institute of Science (India), 1994; Sciences) Ph.D., MIT, 1999 B.S., MIT, 1989; M.S., Pennsylvania, 1992; Ph.D., 1994

engineering 2011–2012 Tiffany Shaw Clifford Stein Latha Venkataraman 49 Assistant Professor of Applied Physics and Professor of Industrial Engineering and Associate Professor of Applied Physics Applied Mathematics and of Earth and Operations Research B.S., MIT, 1993; M.S., Harvard, 1997; Environmental Sciences (Arts and Sciences) B.S.E., Princeton, 1987; Ph.D., 1999 B.Sc., University of British Columbia M.S., MIT, 1989; Ph.D., 1992 (Canada), 2004; M.Sc., Toronto Gordana Vunjak-Novakovic (Canada), 2005; Ph.D., 2009 Fred Stolfi Professor of Biomedical Engineering Senior Lecturer in Mechanical B.S., University of Belgrade (Serbia), Michael P. Sheetz Engineering 1972; S.M., 1975; Ph.D., 1980 William R. Kenan Jr. Professor of Cell B.S., Fordham University, 1972; Biology and Professor of Biomedical M.S., RPI, 1976; Ph.D., 2001 Haim Waisman Engineering Assistant Professor of Civil Engineering B.A., Albion, 1968; Ph.D., Caltech, 1972 Salvatore J. Stolfo B.S., Technion (Israel), 1999; M.S., Professor of Computer Science 2002; Ph.D., RPI, 2005 Kenneth L. Shepard B.S., Brooklyn, 1974; M.S., New York Professor of Electrical Engineering University, 1976; Ph.D., 1979 Wen I. Wang and of Biomedical Engineering Thayer Lindsley Professor of Electrical B.S.E., Princeton, 1987; Elon Terrell Engineering and Professor of Applied M.S.E.E., Stanford, 1988; Ph.D., 1992 Assistant Professor of Mechanical Physics Engineering B.S., National Taiwan (Taiwan), 1975; Samuel K. Sia B.S., University of Texas (Austin), 2002; M.E.E., Cornell, 1979; Ph.D., 1981 Associate Professor of Biomedical M.S., 2004; Ph.D., Carnegie Mellon, 2007 Engineering Xiadong Wang B.Sc., University of Alberta (Canada), Rene B. Testa Professor of Electrical Engineering 1997; Ph.D., Harvard, 2002 Professor of Civil Engineering B.S., Shanaha Jiaotong University, B.E., McGill (Canada), 1959; M.S., 1992; M.S., Purdue, 1995; Karl Sigman Columbia, 1960; Eng.Sc.D., 1963 Ph.D., Princeton, 1998 Professor of Industrial Engineering and Operations Research Joseph F. Traub Anthony Webster B.A., California (Santa Cruz), 1980; Edwin Howard Armstrong Professor of Lecturer in the Discipline of Finance in M.A., California (Berkeley), 1983; Computer Science the Department of Industrial Engineering M.S., 1984; Ph.D., 1986 B.S., College of the City of New York, and Operations Research 1954; M.S., Columbia, 1955; Ph.D., 1959 B.S., Rutgers, 1980; M.S., Columbia, Andrew W. Smyth 1983; M.B.A., 1999 Professor of Civil Engineering Van-Anh Truong B.A./B.Sc., Brown, 1992; M.S., Rice, Assistant Professor of Industrial Michael I. Weinstein 1994; Ph.D., Southern California, 1998 Engineering and Operations Research Professor of Applied Mathematics B.S., University of Waterloo (Canada); B.S., Union College, 1977; Adam H. Sobel Ph.D., Cornell, 2007 M.S., Courant Institute-NYU, 1979; Professor of Applied Physics and Applied Ph.D., 1982 Mathematics and of Environmental Yannis P. Tsividis Sciences (Arts and Sciences) Batchelor Memorial Professor of Alan C. West B.A., Wesleyan, 1989; Ph.D., MIT, 1998 Electrical Engineering Samuel Ruben-Peter G. Viele Professor B.E., Minnesota, 1972; M.S., California of Electrochemistry and Chemical (Berkeley), 1973; Ph.D., 1976 Ponisseril Somasundaran Engineering LaVon Duddleson Krumb Professor of B.S., Case Western Reserve, 1985; Nicholas J. Turro Mineral Engineering Ph.D., California (Berkeley), 1989 William P. Schweitzer Professor of B.Sc., Kerala (India), 1958; B.E., Indian Chemistry; Professor of Chemical Institute of Science (India), 1961; M.S., Ward Whitt Engineering and of Environmental California (Berkeley), 1962; Ph.D., 1964 Wai T. Chang Professor of Industrial Engineering and Materials Science Engineering and Operations Research B.A., Wesleyan, 1960; Ph.D., California Marc W. Spiegelman A.B., Dartmouth, 1964; Institute of Technology, 1963; NSF Professor of Earth and Environmental Ph.D., Cornell, 1969 Postdoctoral Fellow, Harvard, 1963–1964 Sciences (Arts and Sciences) and of Applied Physics and Applied Chris H. Wiggins David Vallancourt Mathematics Associate Professor of Applied Mathematics Senior Lecturer in Circuit and Systems in B.A. Harvard, 1985; Ph.D., Cambridge B.A., Columbia, 1993; the Department of Electrical Engineering (England), 1989 Ph.D., Princeton, 1998 B.S., Columbia, 1981; M.S., 1984; Ph.D., 1987

engineering 2011–2012 50 Chee Wei Wong Huiming Yin C. K. Chu Associate Professor of Mechanical Assistant Professor of Civil Engineering Fu Foundation Professor Emeritus of Engineering B.S., Hohai University (China), 1995; M.S., Applied Mathematics B.S., California (Berkeley), 1999; Peking University (China), 1998; Ph.D., M.S., MIT, 2001; Ph.D., 2003 Iowa, 2004 Edward G. Coffman Jr. Professor Emeritus of Electrical Henryk Wozniakowski Charles Zukowski Engineering Professor of Computer Science Professor of Electrical Engineering M.S., Warsaw (Poland), 1969; Ph.D., 1972 B.S., MIT, 1982; M.S., 1982; Cyrus Derman Ph.D., 1985 Professor Emeritus of Operations John Wright Research Assistant Professor of Electrical Engineering Gil Zussman B.S., Illinois (Urbana-Champaign), 2004; Assistant Professor of Electrical Frank L. DiMaggio M.S., 2007; Ph.D., 2009 Engineering Robert A. W. and Christine S. Carleton B.S., Technion (Israel), 1995; M.Sc., Professor Emeritus of Civil Engineering Cheng Shie Wuu 1999; Ph.D., 2004 Professor of Clinical Radiation Oncology Atle Gjelsvik (in Public Health, Environmental Health Faculty Members-at-Large Professor Emeritus of Civil Engineering Sciences, and Applied Physics) Carlos J. Alonso B.S., National Tsing Hua University Dean, Graduate School of Arts and Fletcher H. Griffis (Taiwan), 1979; M.S., 1982; Ph.D., Sciences Professor Emeritus of Civil Engineering Kansas, 1985 Stuart Firestein Robert A. Gross Junfeng Yang Chairman, Department of Biological Percy K. and Vida L.W. Hudson Assistant Professor of Computer Science Sciences Professor Emeritus of Applied Physics B.S., Tsinghua University (P.R. China), and Dean Emeritus 2000; M.S., Stanford, 2002; Ph.D., 2007 Steven L. Goldstein Chairman, Department of Earth and Herbert H. Kellogg Mihalis Yannakakis Environmental Sciences Stanley-Thompson Professor Emeritus Percy K. and Vida L. W. Hudson of Chemical Metallurgy Professor of Computer Science R. Glenn Hubbard Dipl., National Technical University of Dean of the Graduate School of John T. F. Kuo Athens (Greece), 1975; M.S., Ph.D., Business Maurice Ewing and J. Lamar Worzel Princeton, 1979 Professor Emeritus of Geophysics Igor Krichever David D. W. Yao Chairman, Department of Mathematics W. Michael Lai Professor of Industrial Engineering and Professor Emeritus of Operations Research Michele Moody-Adams Mechanical Engineering M.A.Sc., Toronto (Canada), 1981; Ph.D., Dean, Columbia College 1983 Leon Lidofsky Colin Nuckolls Professor Emeritus of Applied Physics Y. Lawrence Yao Chairman, Department of Chemistry and Nuclear Engineering Professor of Mechanical Engineering B.E., Shanghai Jiao Tong University William Zajc Eugene S. Machlin (P.R. China), 1982; M.S., Wisconsin Chairman, Department of Physics Henry Marion Howe Professor Emeritus (Madison), 1984; Ph.D., 1988 of Metallurgy Emeriti and Retired Tuncel M. Yegulalp Thomas C. Marshall Officers (Not in Residence) Professor of Mining Professor Emeritus of Applied Physics M.S., Technical University (Turkey), Daniel N. Beshers 1961; Eng.Sc.D., Columbia, 1968 Professor Emeritus of Metallurgy Henry E. Meadows Jr. Professor Emeritus of Electrical Yechiam Yemini Huk Yuk Cheh Engineering Professor of Computer Science Samuel Ruben-Peter G. Viele Professor B.Sc., Hebrew (Israel), 1972; M.Sc., Emeritus of Electrochemistry Glenn K. Rightmire 1974; Ph.D., California (Los Angeles), Associate in Mechanical Engineering 1978 Rene Chevray Professor Emeritus of Mechanical Engineering

engineering 2011–2012 Enders Robinson Jeff Ballinger Jessie Jones 51 Maurice Ewing and J. Lamar Worzel Associate Director, Administrative Assistant Professor Emeritus of Applied Geophysics Web Communications Margaret Kelly Mischa Schwartz Leslie Barna Executive Director of Communications Charles Batchelor Professor Emeritus of Executive Assistant to the Electrical Engineering Senior Vice Dean Scott Kelly Alumni Programs Coordinator Jordan L. Spencer Audrey Bauer Professor Emeritus of Chemical Associate Director, Human Resources Jane Lowry Engineering and Facilities Services Parents Program Officer

Thomas E. Stern Anna Beardslee Peggy Maher Dicker Professor Emeritus of Electrical Advancement Communications Officer Associate Dean of Advancement Engineering Leora Brovman Cliff Massey Robert D. Stoll Assistant Dean of Undergraduate Alumni Relations Coordinator Professor Emeritus of Civil Engineering Student Affairs and Global Programs Christopher McGarry Horst Stormer Ryan Carmichael Development Officer Il Rabi Professor of Physics (Arts and Associate Director, Advancement Sciences) and Professor of Applied Jack McGourty Physics Paul Cassidy Senior Associate Dean of Corporate, Associate Director, Finance and Government, and Global Engagement Malvin Carl Teich Administration Professor Emeritus of Engineering Kathleen McKeown Science Jenifer Chin Vice Dean of Research Manager, Grants and Contracts Nickolas J. Themelis Lindsay N. Montanari Stanley-Thompson Professor Emeritus N. Travoya Collins Senior Assistant Director, of Chemical Metallurgy (Earth and Assistant Director, Engineering Fund Alumni Relations Environmental Engineering, Henry Krumb School of Mines) Grace Chung Jocelyn Morales Executive Director, Assistant Director, Stephen H. Unger Columbia Video Network Graduate Student Services Professor Emeritus of Computer Science and of Electrical Engineering Patricia Culligan Johanne Morgan Vice Dean of Academic Affairs Financial Analyst Rimas Vaicaitis Renwick Professor Emeritus of Civil Promiti Dutta Marie-Pierre Murry Engineering Assistant Dean of Innovation,Corporate Executive Assistant to the Dean Engagement, and Entrepreneurship Howard W. Vreeland Anna Marie O’Neill Professor Emeritus of Graphics Holly Evarts Associate Dean of Finance Director of Strategic Communications and Administration Omar Wing and Media Relations Professor Emeritus of Electrical Fredrik C. Palm Engineering Melanie Farmer Associate Dean of Faculty, Academic, Senior Writer/Editor and Diversity Affairs Edward S. Yang Professor Emeritus of Electrical Jeanelle Folkes Lourdes Pineiro Engineering Student Services Officer, Development Assistant Graduate Student Services Jack Reilly Administrative officers Morton B. Friedman Executive Assistant and STAFF Senior Vice Dean Feniosky Peña-Mora Rebecca Rodriguez Dean Zachary Howell Associate Director, Associate Director, Engineering Fund Engaged Entrepreneurship Program

engineering 2011–2012 52 Geetha Sampathkumar Jonathan R. Stark Administrative Coordinator Assistant Dean of Graduate Student and Postdoctoral Affairs Starling Sawyer Director of Alumni Relations Elizabeth Strauss Assistant Director, Engineering Fund Ivy Schultz Program Manager, CTICE Jessie Tong Institutional Research Coordinator Kimberly Sheeran Financial Analyst Yannis P. Tsividis Undergraduate Curriculum Kevin Shollenberger Adviser to the Dean Dean of Student Affairs, Columbia College/ Columbia Engineering, and Associate Vice Olga Tymejczyk President for Undergraduate Student Life, Admissions Coordinator, Arts and Sciences Graduate Student Services

Tiffany M. Simon Dana Vlcek Associate Dean of Multimedia Content Coordinator Graduate Student Services Alex Yepes David Simpson Associate Director, CTICE Administrative Assistant

engineering 2011–2012 Departments and Academic Programs 54 KEY to course listings

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

engineering 2011–2012 55

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

engineering 2011–2012 56 applied physics and applied mathematics 200 S. W. Mudd, MC 4701 Phone: 212-854-4457 Applied Physics and Applied Mathematics: www.apam.columbia.edu/ Materials Science and Engineering: www.seas.columbia.edu/matsci

Chair Christopher H. Timothy M. Hall Research Jingbo Wu Irving P. Herman Scholz, Earth and David E. Keyes Scientists Ruoxian Ying 208 S. W. Mudd Environmental Jerome Meli Mark Adams Sciences Ron L. Miller Jacek Chowdhary Adjunct Associate Departmental Amiya K. Sen, Electrical Stephen L. Ostrow Jerry I. Dadap Research Scientists Administrator Engineering Thomas S. Pedersen Darren Garnier Manolis Antonoyiannakis Dina Amin Adam Sobel Lawrence N. Rothenberg Igor Geogdzhayev Conal Murray Marc W. Spiegelman Stephen A. Sabbagh George Tselioudis Matthew Putman Professors Wen I. Wang, Electrical Shalom J. Wind Yuanchong Zhang Guillaume Bal Engineering Yimei Zhu Postdoctoral Katayun Barmak Michael I. Weinstein Adjunct Research Research Scientists Daniel Bienstock, Cheng Shie Wuu, Adjunct Associate Scientist Cedric Bellis Industrial Engineering Radiation Oncology Professors Mark Holzer Manus Biggs and Operations Brian Cairns Sarah Kang Research Associate David Maurer VISITING Associate Kirk Knobelspiesse Simon J. L. Billinge Professors Research Scientist Youjin Lee Allen H. Boozer William E. Bailey Adjunct Assistant Olivier Pinaud Uttam Manna Mark A. Cane, Earth Latha Venkataraman Professors Matteo Palma and Environmental Chris H. Wiggins Seung Yub Lee Associate Research Hyowon Park Sciences Matthew Putman Scientists Young Seouk Park Siu-Wai Chan Assistant Mikhail Alexandrov Harald Rieder Morton B. Friedman, Professors Senior Research Michael Bauer Shuguang Wang Civil Engineering Vincent Duchêne Scientists John Berkery and Engineering Dirk Englund, Electrical Joze Bevk Yonghua Chen Associate Mechanics Engineering James Bialek Chris Farrow John C. Arbo Irving P. Herman Chris A. Marianetti Rainer Bleck Scott Gianell James S. Im Tiffany Shaw, Earth Leonard Druyan Jeremy Hanson Special Lecturers Philip Kim, Physics and Environmental Qiancheng Ma Pavol Juhas Daniel N. Beshers Michael E. Mauel Sciences John Marshall Seung Yub Lee C. K. Chu Gerald A. Navratil Steven A. Sabbagh Alexander Limanov Ismail C. Noyan Adjunct Shalom J. Wind Li Liu Special Research Richard M. Osgood Jr., Professors Chenguang Lu Scientist Electrical Engineering Vittorio M. Canuto Adjunct Senior Catherine Naud Thomas C. Marshall Aron Pinczuk Barbara E. Carlson Research Jan Perlwitz Lorenzo M. Polvani C. Julien Chen ScientistS Denis Potapenko Malvin A. Ruderman, Edward Christman C. Julien Chen Anastasia Romanou Physics Anthony Del Genio David E. Keyes Francesca Turco Supratik Guha

he Department of Applied Physics Current Research Activities in from our fusion science experiments and Applied Mathematics Applied Physics and Applied are used as a basis for collaboration Tincludes undergraduate and Mathematics with large national and international graduate studies in the fields of Plasma physics and fusion energy. experiments. For example, our recent applied physics, applied mathematics, In experimental plasma physics, demonstration of active feedback and materials science and engineering. research is being conducted on (1) control of high temperature plasma The graduate program in applied equilibrium, stability, and transport instability is guiding research on NSTX physics includes plasma physics and in fusion plasmas: high-beta at the Princeton Plasma Physics controlled fusion; solid-state physics; tokamaks, spherical tokamaks, and Laboratory, on the DIII-D tokamak at optical and laser physics; medical levitated dipoles; (2) magnetospheric General Atomics, and for the design physics; atmospheric, oceanic, physics: trapped particle instabilities of the next generation burning plasma and earth physics; and applied and stochastic particle motion; (3) experiment, ITER. In theoretical plasma mathematics. The graduate programs confinement of toroidal nonneutral physics, research is conducted in in materials science and engineering plasmas; (4) plasma source operation the fluid theory of plasma equilibrium are described on pages 170–172. and heating techniques; and (5) and stability, active control of MHD the development of new plasma instabilities, the kinetic theory of measurement techniques. The results transport, and the development of

engineering 2011–2012 techniques based on the theory of Biology and Bioinformatics (C2B2), tori. The plasma physics group and MIT 57 general coordinates and dynamical the Center for Computational Learning have jointly constructed the Levitated systems. The work is applied to Systems (CCLS), the NIH-funded Dipole Experiment (LDX), a large plasma magnetic fusion, non-neutral and space Center for Multiscale Analysis of Genetic confinement experiment incorporating plasmas. and Cellular Networks (MAGNet), a levitated superconducting ring. The and the NIH-funded Nanomedicine Columbia Nonneutral Torus (CNT) Optical and laser physics. Active areas Center for Mechanobiology. Extensive is an experiment devoted to the first of research include inelastic light scatter- collaborations exist with national climate study of non-neutral plasmas confined ing in nanomaterials, optical diagnostics research centers (the Geophysical Fluid on magnetic surfaces. The Columbia of film processing, new laser systems, Dynamics Laboratory and the National Linear Machine (CLM) is a continuously nonlinear optics, ultrafast optoelectron- Center for Atmospheric Research) and operating, linear mirror device for the ics, photonic switching, optical physics with national laboratories of the U.S. study of collisionless plasma instabilities, of surfaces, laser-induced crystallization, Department of Energy, custodians of the plasma, transport, and feedback and photon integrated circuits. nation’s most powerful supercomputers. stabilization. Columbia’s Collisionless Terrella Experiment investigates plasma Solid-state physics. Research in Atmospheric, oceanic, and earth transport in magneto-spheric geometry solid-state physics covers nanoscience physics. Current research focuses on and the generation of strong plasma and nanoparticles, electronic transport the dynamics of the atmosphere and the flow from nonlinear electrostatic and inelastic light scattering in low- ocean, climate modeling, cloud physics, potentials. dimensional correlated electron radiation transfer, remote sensing, Experimental research in solid-state systems, fractional quantum Hall geophysical/geological fluid dynamics, physics and laser physics is conducted effect, heterostructure physics and geochemistry. The department engages within the department and also in applications, molecular beam epitaxy, in ongoing research and instruction with association with the Columbia Center for grain boundaries and interfaces, the NASA Goddard Institute for Space Integrated Science and Engineering and nucleation in thin films, molecular Studies and the Lamont-Doherty Earth the School of Mines. Facilities include electronics, nanostructure analysis, Observatory. Five faculty members share laser processing and spectroscopic and electronic structure calculations. appointments with the Department of apparatus, ultrahigh vacuum chambers Research opportunities also exist within Earth and Environmental Sciences. for surface analysis, picosecond and the interdisciplinary NSF Materials In addition to the faculty and femtosecond lasers, a molecular beam Research Science and Engineering graduate students, many others epitaxy machine, and a clean room that Center, which focuses on complex films participate in these projects, including includes photo-lithography and thin film composed of nanocrystals; the NSF full-time research faculty, faculty and fabrication systems. Within this field, Nanoscale Science and Engineering students from other departments, and the Laser Diagnostics and Solid-State Center, which focuses on electron visiting scientists. Physics Laboratory conducts studies transport in molecular nanostructures; in laser spectroscopy of nanomaterials and semiconductor thin films, and laser and the DOE Energy Frontier Research Laboratory Facilities in Applied diagnostics of thin film processing. Center, which focuses on conversion Physics and Applied Mathematics of sunlight into electricity in nanometer- The Laser Lab focuses on the study The Plasma Physics Laboratory, sized thin films. of materials under high pressure, laser founded in 1961, is one of the leading surface chemical processing, and new university laboratories for the study of Applied mathematics. Current research semiconductor structures. Research plasma physics in the United States. encompasses analytical and numerical is also conducted in the shared There are four experimental facilities. analysis of deterministic and stochastic characterization laboratories and clean The Columbia High-Beta Tokamak partial differential equations, large-scale room operated by the NSF Nanoscale (HBT-EP) supports the national program scientific computation, fluid dynamics, Science and Engineering Center. to develop controlled fusion energy. dynamical systems and chaos, as The department maintains an It utilizes high voltage, pulsed power well as applications to various fields of extensive network of workstations and systems, and laser and magnetic physics and biology. The applications desktop computers. The department diagnostics to study the properties to physics include condensed-matter has recently acquired a SiCortex of high-beta plasmas and the use physics, plasma physics, nonlinear supercomputer with 1,458 cores, which of feedback stabilization to increase optics, medical imaging, and the earth is used for a wide range of departmental the achievable beta. A collaborative sciences, notably atmospheric, oceanic, computational activities. The research program with the Princeton Plasma of the Plasma Lab is supported by and climate science, and solid earth Physics Laboratory and the DIII-D a dedicated data acquisition/data geophysics (see below). The applications tokamak group at General Atomics is analysis system, and the applied math to biology include cellular biophysics, studying the properties of high-beta group has access to a Beowulf cluster. machine learning, and functional plasmas in order to maximize fusion Through the Internet, researchers in genomics, including collaborations with power production in these large, neutral the department are currently using Columbia’s Center for Computational beam-heated tokamaks and spherical supercomputing facilities at the National

engineering 2011–2012 58 Applied Physics program: first and second Years

Semester i Semester iI Semester iII Semester iV

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

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

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

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

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

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

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

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

Center for Atmospheric Research; Undergraduate Programs In addition to formal minors, some areas the San Diego Supercomputing The Department of Applied Physics of specialization that are available are Center; the National Energy Research and Applied Mathematics offers three described on pages 60–62. All technical Supercomputer Center in Berkeley, undergraduate programs: applied phys- electives are normally at the 3000 level California; the National Leadership Class ics, applied mathematics, and materials or above. Facility at Oak Ridge, Tennessee; the science and engineering. The materials IBM SUR cluster at Brookhaven National science and engineering program is Undergraduate Programs Laboratory in Upton, New York; and described on pages 169–170. in Applied Physics others. The applied physics and applied The applied physics program stresses Facilities, and research opportunities, mathematics programs provide an the basic physics that underlies most also exist within the interdepartmental excellent preparation for graduate study developments in engineering and the Materials Research Science and or for careers in which mathematical and mathematical tools that are important Engineering Center, which focuses on technical sophistication are important. to both physicists and engineers. Since complex films composed of nanoparticles. Using the large number of electives in the advances in most branches of these programs, students can tailor their technology lead to rapid changes in Current Research Activities and programs to fit their personal and career state-of-the-art techniques, the applied Laboratory Facilities in Materials interests. By focusing their technical physics program provides the student Science and Engineering electives, students can obtain a strong with a broad base of fundamental base of knowledge in a specialized area. See page 169. science and mathematics while retaining

engineering 2011–2012 59 Applied Physics: Third and Fourth Years

Semester V Semester VI Semester VII Semester VIII

PHYS W3003 (3) APPH E4300 (3) APPH E3100 (3) Mechanics Applied electrodynamics Intro. to quantum mechanics MSAE E3111 (3) APPH E4100 (3) Course in second Thermodynamics Quantum physics AP area (3) Required APPH E3300 (3) Courses Applied electromagnetism APMA E3101 (3) Course in first APPH E4018 (2) Linear algebra AP area (3) Laboratory APMA E3102 (3) Partial differential APPH E4901 (1) APPH E4903 (2) equations Seminar Seminar

Tech1 3 points 3 points 2 points 9 points

NonTech 3 points 3 points 3 points 3 points or Tech E lectives

total points 16 15 16 17

1 They must include at least 2 points of laboratory courses. If PHYS W3081 is taken as part of the first two years of the program, these technical electives need not include laboratory courses. Technical electives must be at the 3000 level or above unless prior approval is obtained. the opportunity for specialization through program nationwide. Practical research All students must take 30 points of technical electives. experience is a valuable supplement electives in the third and fourth years, The applied physics curriculum to the formal course of instruction. of which 17 points must be technical offers students the skills, experience, Applied physics students participate in courses approved by the adviser. The 17 and preparation necessary for several an informal undergraduate seminar to points include 2 points of an advanced career options, including opportunities study current and practical problems in laboratory in addition to APPH E4018. to minor in economics and to take applied physics, and obtain hands-on Technical electives must be at the 3000 business-related courses. In recent experience in at least two advanced level or above unless prior approval years, applied physics graduates have laboratory courses. is obtained from the department. A entered graduate programs in many Majors are introduced to two areas number of approved technical electives areas of applied physics or physics, of application of applied physics (AP) by are listed in the section on specialty enrolled in medical school, or been a course in each of two areas. Approved areas following. The remaining points employed in various technical or financial areas and courses are: of electives are intended primarily as an areas immediately after receiving the opportunity to complete the four-year, B.S. degree. DYNAMICAL SYSTEMS: 27-point nontechnical requirement, but Opportunities for undergraduate APMA E4101 or PHYS G4003 any type of course work can satisfy them. research exist in the many research OPTICAL OR LASER PHYSICS: programs in applied physics. These APPH E4110 or E4112 Undergraduate Programs include fusion and space plasma NUCLEAR SCIENCE: APPH E4010 in Applied Mathematics physics, optical and laser physics, PLASMA PHYSICS: APPH E4301 The applied mathematics program is and condensed matter physics. flexible and intensive. A student must Undergraduate students can receive PHYSICS OF FLUIDS: APPH E4200 take the required courses listed below, or course credit for research or an CONDENSED MATTER PHYSICS: PHYS G4018 prove equivalent standing, and then may independent project with a faculty BIOPHYSICAL modeling: APMA E4400 elect the other courses from mathematics, member. Opportunities also exist for computer science, physics, Earth and undergraduate students in the applied environmental sciences, biophysics, physics program to participate in this In addition to these courses, courses economics, business and finance, or other research through part-time employment listed in the Specialty Areas in Applied application fields. Each student tailors his during the academic year and full-time Physics can be used to satisfy this or her own program in close collaboration employment during the summer, either requirement with preapproval of the with an adviser. He or she must also at Columbia or as part of the NSF REU applied physics adviser. register for the applied mathematics

engineering 2011–2012 60 Applied mathematics program: first and second Years

Semester i Semester iI Semester iII Semester iV

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

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

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

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

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

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

MATLAB course COMS W1005, Introduction to Computer Science and Programming in MATLAB, is required computer for all Applied Mathematics majors and should be taken during freshman year. (It may be substituted with a C++ science or Python course with the permission of the Applied Math Program adviser.)

physical C1001 (1) C1002 (1) education

gateway lab E1102 (4) either semester

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

seminar during both the junior and senior type of course work can satisfy them. seminars, APMA E4901 and APPH years. During the junior year, the student Transfers into the applied E4901. A single course may be used attends the seminar lectures for 0 points; mathematics program from other majors to fulfill a requirement in both majors. during the senior year, he or she attends require a GPA of 3.0 or above, and the Students must maintain a GPA at or the seminar lectures as well as tutorial approval of the applied mathematics above 3.75, and must graduate with at problem sessions for 3 or 4 points. program chair. least 143 points, 15 above the regular While it is common for students 128-point requirement. These extra 15 in the program to go on to graduate points should be technical electives undergraduate Double school, many graduating seniors will appropriate for one or both majors. Major in applied physics find employment directly in industry, To apply, a student first obtains and applied mathematics government, education, or other fields. the approval of both the general Students satisfy all requirements for Of the 27 points of elective content undergraduate AP adviser and the both majors, except for the seminar in the third and fourth years, at least 15 general undergraduate AM adviser, and requirements. They are required to take points of technical courses approved by then the approval of the Dean. both senior seminars, APMA E4903 and the adviser must be taken. The remaining APPH E4903 (taking one in the junior points of electives are intended primarily as year and one in the senior year, due Specialty Areas in APAM an opportunity to complete the four-year, to timing conflicts), but not the junior Both applied physics and applied math- 27-point nontechnical requirement, but any

engineering 2011–2012 61 Applied mathematics: Third and Fourth Years

Semester V Semester VI Semester VII Semester VIII

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

Tech4 3 points 3 points 3 points 6 points

NonTech 3 points 3 points 3 points 3 points E lectives

total points 15 15 16 15

1 MATH V2010 may be substituted for APMA E3101; APMA E4200 or MATH V3028 may be substituted for APMA E3102; MATH V3007 may be substituted for APMA E4204. 2 One course from Group A and one course from Group B required for graduation. Group A: IEOR E3658: Probability; SIEO W4105: Probability; SIEO W3600: Introduction to probability and statistics; SIEO W4150: Introduction to probability and statistics; STAT W3105: Introduction to probability; MATH W4155: Probability theory. Group B: STAT W3107: Statistical inference; STAT W4107: Statistical inference; STAT W4109: Probability and statistical inference; SIEO W 4606: Elementary stochastic processes; IEOR E3106: Introduction to stochastic models; IEOR E4106: Introduction to operations research: stochastic models; IEOR E4703: Monte Carlo simulation; COMS W4771: Machine learning. 3 With an adviser’s permission, an approved technical elective may be substituted. 4 Any course in science or engineering at the 3000 level or above qualifies as a technical elective. ematics students can focus their techni- APMA E4101y: Intro to dynamical systems Solid Earth Geophysics cal electives and develop a strong base APPH E4110x: Modern optics EESC W4001x: Advanced general geology of knowledge in a specialty area. There APPH E4112y: Laser physics EESC W4113x: Intro to mineralogy APPH E4200x: Physics of fluids APPH E4200x: Physics of fluids is no requirement to focus electives, so APPH E4301y: Intro to plasma physics EESC W4701y: Intro to igneous petrology students may take as many or as few of EESC W4941y: Principles of geophysics the recommended courses in a specialty • Earth and Atmospheric Sciences EESC W4950x: Mathematical methods in the area as is appropriate to their schedules Earth sciences The Earth sciences provide a wide and interests. Some specialties are range of problems of interest to given below, but this is not an exclusive (See also courses listed under physicists and mathematicians ranging list and others can be worked out in Scientific Computation and Computer from the dynamics of the Earth’s coordination with the student’s adviser. Science on this page.) climate to earthquake physics to The courses that are often taken, or in dynamics of Earth’s deep interior. The some cases need to be taken, in the • Basic Physics and Astrophysics Lamont-Doherty Earth Observatory, junior year are denoted with a “J.” Fundamental physics and astrophysics which is part of Columbia University, can be emphasized. Not only is provides enormous resources for Technical Electives astrophysics providing a deeper students interested in this area. understanding of the universe, but it is • Applications of Physics also testing the fundamental principles Courses that will give a student a Atmosphere, Oceans, and Climate of physics. broad background in applications of EESC W4008y: Intro to atmospheric science

APPH E4200x: Physics of fluids physics: PHYS W3002y: From quarks to the cosmos: APPH E4210y: Geophysical fluid dynamics applications of modern physics EESC W4925x: Prin of physical oceanography ELEN E3000x: Circuits, systems, and ASTR C3601x: General relativity, black holes, EESC W4930y: Earth’s oceans and electronics (J) and cosmology (J) atmosphere MSAE E3103x: Elements of materials science (J) ASTR C3602y: Physical cosmology (J) APPH E4010x: Intro to nuclear science ASTR G4001y: Astrophysics, I PHYS G4018y: Solid-state physics APMA E4101x: Intro to dynamical systems

engineering 2011–2012 62 • Business and Finance quantitative sciences that are based Honors data structures and The knowledge of physics and on mathematics, such as physics. This algorithms) (J) mathematics that is gained in view no longer coincides with reality. COMS W3157x,y: Advanced programming (J)

the applied physics and applied Researchers from biology as well as COMS W3203x,y: Discrete mathematics: intro mathematics programs is a strong from the physical sciences, applied to combinatorics and graph base for a career in business or mathematics, and computer science theory (J) finance. are rapidly building a quantitative base COMS W4203y: Graph theory of biological knowledge. Students can APMA E4300y: Intro to numerical methods Economics acquire a strong base of knowledge in APMA E4301: Numerical methods for partial ECON W3211x,y: Intermed microeconomics (J) quantitative biology, both biophysics differential equations AMCS E4302: Parallel scientific computing ECON W3213x,y: Intermed macroeconomics(J) and computational biology, while COMS W4701x,y: Artificial intelligence I ndustrial Engineering completing the applied physics or COMS W4771y: Machine learning and Operations Research applied mathematics programs. IEOR E4003x: Industrial economics • Solid-State Physics IEOR E4201x: The eng of management, I Professional-level Course: Much of modern technology is based IEOR E4202y: The eng of management, II APPH E1300y: Physics of the human body on solid-state physics, the study of sol- Finance Recommended: ids and liquids. Courses that will build a MATH W4071x: Mathematics of finance BIOL C2005x-C2006y: Intro biology, I and II strong base for a career in this area are: IEOR E4106y: Intro to operations research: APMA E4400y: Intro to biophysical modeling stochastic models (J) PHYS W3083y: Electronics laboratory (J) SIEO W4150x,y: Probability and statistics (J) Other Technical Electives (a course MSAE E3103x: Elements of material science (J) ECIE W4280: Corporate finance in at least two areas recommended): ELEN E3106x: Solid-state devices and IEOR E4700x: Intro to financial engineering materials (J) Biological Materials PHYS G4018y: Solid-state physics • Mathematics Applicable to Physics BIOL W4070x: The biology and physics of MSAE E4206x: Electronic and magnetic single molecules properties of solids Applied physics students can specialize CHEN E4650x: Biopolymers MSAE E4207y: Lattice vibrations and crystal in the mathematics that is applicable defects to physics. This specialization is Biomechanics particularly useful for students BMEN E3320y: Fluid biomechanics (J) Undergraduate Program interested in theoretical physics. BMEN E4300y: Solid biomechanics (J) in Materials Science and MATH V3386x: Differential geometry Genomics and Bioinformatics Engineering APMA E4001y: Principles of applied mathematics BIOL W3037y: Whole genome bioinformatics (J) See page 169. APMA E4101x: Intro to dynamical systems ECBM E3060x: Intro to genomic information APMA E4301x: Numerical methods for partial science and technology (J) differential equations CBMF W4761y: Computational genomics Graduate Programs APMA E4302x: Parallel scientific computing Financial aid is available for students PHYS G4019y: Mathematical methods of physics Neurobiology pursuing a doctorate. Fellowships, BIOL W3004x: Neurobiology, I (J) scholarships, teaching assistantships, • Fundamental Mathematics in Applied BIOL W3005y: Neurobiology, II (J) and graduate research assistantships Mathematics ELEN G4011x: Computational neuroscience are awarded on a competitive basis. The This specialization is intended for Aptitude Test of the Graduate Record students who desire a more solid The second term of biology will be Examination is required of candidates foundation in the mathematical considered a technical elective if a for admission to the department and for methods and underlying theory. For student has credits from at least two financial aid; the Advanced Tests are example, this specialization could other of the recommended courses in recommended. be followed by students with an quantitative biology at the 3000 level or above. interest in graduate work in applied M.S. Program in Applied Physics mathematics. The program of study leading to the • Scientific Computation and degree of Master of Science, while Computer Science MATH V3386x: Differential geometry emphasizing continued work in basic APMA E4101x: Intro to dynamical systems Advanced computation has become a physics, permits many options in APMA W4150x: Applied functional analysis core tool in science, engineering, and several applied physics specialties. The MATH W4032x: Fourier analysis mathematics and provides challenges program may be considered simply as MATH W4062y: Modern analysis, II for both physicists and mathemati- SIEO W4150x,y: Intro to probability and additional education in areas beyond cians. Courses that build on both statistics (J) the bachelor’s level, or as preparatory practical and theoretical aspects of PHYS W4386x-W4387y: Geometrical concepts to doctoral studies in the applied computing and computation include: in physics physics fields of plasma physics,

MATH V3020x: Number theory and cryptography (J) laser physics, solid-state physics, and • Quantitative Biology COMS W3137x,y: Data structures and algo- applied mathematics. Specific course Traditionally biology was considered a rithms (or COMS W3139y: requirements for the master’s degree descriptive science in contrast to the

engineering 2011–2012 are determined in consultation with the MSAE E4215: Mechanical behavior of structural courses are determined in consultation 63 program adviser. materials with the program adviser. Successful EEME E6601: Intro to control theory completion of an approved 30-point M.S. Program in Applied Physics/ program of study is required in addition Concentration in Applied M.S. Program in Materials Science to successful completion of a written Mathematics and Engineering qualifying examination taken after two This 30-point program leads to a profes- See page 170. semesters of graduate study. An oral sional M.S. degree. Students must com- examination, taken within one year after plete five core courses and five electives. M.S. Program in Medical Physics the written qualifying examination, and a thesis proposal examination, taken within The core courses provide a student This CAMPEP-approved 36-point two years after the written qualifying with a foundation in the fundamentals program in medical physics leads to examination, are required of all doctoral of applied mathematics and contribute the M.S. degree. It is administered candidates. 15 points of graduate credit toward the by faculty from the School of degree. Students must complete five of Engineering and Applied Science in the following seven courses: collaboration with faculty from the Applied Mathematics College of Physicians and Surgeons This academic program, for students APMA E4001: Principles of applied mathematics and the Mailman School of Public registered in the Department of Applied APMA E4101: Intro to dynamical systems Health. It provides preparation toward Physics and Applied Mathematics, APMA E4150: Applied functional analysis certification by the American Board emphasizes applied mathematics APMA E4200: Partial differential equations of Radiology. The program consists research in nonlinear dynamics, fluid APMA E4204: Functions of a complex variable mechanics, and scientific computation, APMA E4300: Intro to numerical methods of a core curriculum of medical and with a current emphasis on geophysical, APMA E4301: Numerical methods for partial nuclear physics courses, anatomy, lab, biophysical, and plasma physics differential equations seminar, a tutorial, and two practicums. APMA E6301: Analytic methods for partial Specific course requirements are APPH applications. differential equations E4010, E4710/11, E4500, E4501, Applied mathematics deals with APMA E6302: Numerical analysis for partial E4550, E4600, and APBM E4650, the use of mathematical concepts differential equations and, in the Mailman School of Public and techniques in various fields of Health, EHSC P6330, P9319, P9330, science and engineering. Historically, A student must select five elective and P9335. Some opportunities for mathematics was first applied with great courses from those listed below (or any specialization exist. A passing grade on success in astronomy and mechanics. of those not used to satisfy the core a comprehensive examination is required Then it developed into a main tool of requirements from the list above) for for graduation. This examination, on physics, other physical sciences, and a total of 15 points of graduate credit. subjects covered in the curriculum, is engineering. It is now important in Additional courses not listed below taken after two terms of study. the biological, geological, and social can be applied toward the elective sciences. With the coming of age of requirements, subject to the approval of the computer, applied mathematics has Certificate of Professional the faculty adviser. Computer science transcended its traditional style and now Achievement in Medical Physics elective courses include: assumes an even greater importance This graduate program of instruction and a new vitality. leads to the Certificate of Professional CSOR W4231: Analysis of algorithms, I Compared with the pure Achievement and requires satisfactory COMS W4236: Intro to computational complexity mathematician, the applied mathematician COMS W4241: Numerical algorithms and completion of at least four of the is more interested in problems coming complexity following courses: COMS W4252: Computational learning theory from other fields. Compared with the engineer and the physical scientist, APPH E4500: Health physics he or she is more concerned with the Industrial engineering/operations APPH E4600: Dosimetry research elective courses include: APBM E4650: Anatomy for physicists and engineers formulation of problems and the nature of EHSC P6330: Radiation science solutions. Compared with the computer IEOR E4003: Industrial economics EHSC P9319: Clinical nuclear medicine physics scientist, he or she is more concerned IEOR E4004: Intro to operations research: EHSC P9330: Diagnostic radiology physics with the accuracy of approximations and deterministic models EHSC P9335: Radiation therapy physics the interpretation of results. Needless to IEOR E4007: Optimization: models and methods say, even in this age of specialization, the IEOR E4106: Intro to operations research: This is a two-semester nondegree work of mathematicians, scientists, and stochastic models program. Students are admitted to the engineers frequently overlaps. Applied SIE0 W4150: Intro to probability and statistics department as certificate-track students. mathematics, by its very nature, has IEOR E4403: Advanced engineering and corporate occupied a central position in this interplay economics IEOR E4407: Game theoretic models of operations Ph.D. and Eng.Sc.D. Programs and has remained a field of fascination STAT W4606: Elementary stochastic processes After completing the M.S. program and excitement for active minds. IEOR E4700: Intro to financial engineering in applied physics, doctoral students specialize in one applied physics field. Materials Science Other elective courses include: Some programs have specific course and Engineering Program MECE E4100: Mechanics of fluids requirements for the doctorate; elective See page 171.

engineering 2011–2012 64 Plasma Physics at low temperatures and high magnetic programming and acquire practical experience This academic program is designed to fields. Specific course requirements for solving representative problems in math and physics. emphasize preparation for professional the solid-state physics doctoral program APPH E3300y Applied electromagnetism careers in plasma research, controlled are set with the academic adviser, in 3 pts. Lect: 3. Professor Venkataraman. fusion, and space research. This consultation with the Committee on Corequisite: APMA E3102. Vector analysis, includes basic training in relevant areas Materials Science and Engineering/Solid- electrostatic fields, Laplace’s equation, multipole of applied physics, with emphasis State Science and Engineering. expansions, electric fields in matter: dielectrics, magnetostatic fields, magnetic materials, and on plasma physics and related areas superconductors. Applications of electromagnetism leading to extensive experimental and Courses in Applied Physics to devices and research areas in applied physics. theoretical research in the Columbia University Plasma Physics Laboratory. APPH E1300y Physics of the human body APPH E3900x and y Undergraduate research Specific course requirements for the 3 pts. Lect: 3. Professor Herman. in applied physics 0–4 pts. Members of the faculty. plasma physics doctoral program are Prerequisites: PHYS C1201 or C1401, and Calculus I; corequisites: PHYS C1202 or This course may be repeated for credit, but APPH E4018, E4200, E4300, E6101, no more than 6 points of this course may be E6102, and E9142 or E9143, or C1402, and Calculus II. This introductory course analyzes the human body from the basic counted toward the satisfaction of the B.S. equivalents taken at another university. principles of physics. Topics to be covered degree requirements. Candidates for the B.S. include the energy balance in the body, the degree may conduct an investigation in applied Optical and Laser Physics mechanics of motion, fluid dynamics of the physics or carry out a special project under the This academic program involves heart and circulation, vibrations in speaking supervision of the staff. Credit for the course is contingent upon the submission of an acceptable a basic training in relevant areas and hearing, muscle mechanics, gas exchange thesis or final report. of applied physics with emphasis and transport in the lungs, vision, structural properties and limits, electrical properties and the in quantum mechanics, quantum APPH E4010x Introduction to nuclear science development and sensing of magnetic fields, and electronics, and related areas of 3 pts. Professor Ostrow. the basics of equilibrium and regulatory control. Prerequisites: MATH V1202 and E1210 and PHYS specialization. Some active areas of In each case, a simple model of the body organ, C1403 or their equivalents. This introductory research in which the student may property, or function will be derived and then course is for individuals with an interest in medical concentrate are laser modification of applied. The course is approved as a Columbia physics and other branches of radiation science. surfaces, optical diagnostics of film Engineering technical elective. Topics covered include basic concepts, nuclear processing, inelastic light scattering in APAM E1601y Introduction to computational models, semiempirical mass formula, interaction nanomaterials, nonlinear optics, ultrafast mathematics and physics of radiation with matter, nuclear detectors, nuclear structure and instability, radioactive decay process optoelectronics photonic switching, 3 pts. Lect: 3. Professor Mauel. and radiation, particle accelerators, and fission and optical physics of surfaces, and photon Introduction to computational methods in applied mathematics and physics. Students develop fusion processes and technologies. integrated circuits. Specific course solutions in a small number of subject areas APPH E4018y Applied physics laboratory requirements for the optical and laser to acquire experience in the practical use of 2 pts. Lab: 4. Professor Navratil. physics doctoral program are set with computers to solve mathematics and physics Prerequisite: ELEN E3401 or equivalent. the academic adviser. problems. Topics change from year to year. Typical experiments are in the areas of plasma Examples include elementary interpolation physics, microwaves, laser applications, optical of functions, solution of nonlinear algebraic Solid-State Physics spectroscopy physics, and superconductivity. equations, curve-fitting and hypothesis testing, This academic program encompasses wave propagation, fluid motion, gravitational and APPH E4090x Nanotechnology the study of the electrical, optical, celestial mechanics, and chaotic dynamics. The 3 pts. Lect: 3. Offered in alternate years. magnetic, thermal, high-pressure, and basic requirement for this course is one year of Instructor to be announced. ultrafast dynamical properties of solids, college-level calculus and physics; programming Prerequisites: APPH E3100 and MSAE E3103 or their equivalents with instructor’s permission. with an aim to understanding them experience is not required. The science and engineering of creating in terms of the atomic and electronic APPH E3100y Introduction to quantum materials, functional structures and devices on the structure. The program emphasizes the mechanics nanometer scale. Carbon nanotubes, nanocrystals, formation, processing, and properties of 3 pts. Lect: 3. Instructor to be announced. quantum dots, size dependent properties, self- thin films, low-dimensional structures— Prerequisites: PHYS C1403 or equivalent, and assembly, nanostructured materials. Devices such as one- and two-dimensional differential and integral calculus. Corequisites: and applications, nanofabrication. Molecular APMA E3101 or equivalent. Basic concepts and electron gases, nanocrystals, surfaces engineering, bionanotechnology. Imaging and assumptions of quantum mechanics, Schrodinger’s of electronic and optoelectronic interest, manipulating at the atomic scale. Nanotechnology equation, solutions for one-dimensional problems, in society and industry. and molecules. Facilities include a including square wells, barriers, and the harmonic microelectronics laboratory, high- oscillator, introduction to the hydrogen atom, APPH E4100x Quantum physics of matter pressure diamond anvil cells, a molecular atomic physics and X-rays, electron spin. 3 pts. Lect: 3. Professor Venkataranam. beam epitaxy machine, ultrahigh vacuum Prerequisite: APPH E3100. Corequisite: APMA APAM E3105x Programming methods for E3102 or equivalent. Basic theory of quantum systems, lasers, equipment for the study scientists and engineers mechanics, well and barrier problems, the of optical properties, and the instruments 3 pts. Lect: 2.5. Lab: 1. Not offered in 2011–2012. harmonic oscillator, angular momentum identical in the shared facilities of the Nano-scale Introduction to modern techniques of computer particles, quantum statistics, perturbation theory Science and Engineering Center and the programming for the numerical solutions to problems and applications to the quantum physics of Energy Frontier Research Center (EFRC). in physics, mathematics, and engineering using atoms, molecules, and solids. Fortran 90. Students develop familiarity with basic There are also significant resources for and advanced concepts of modern numerical electrical and optical experimentation

engineering 2011–2012 APPH E4110x Modern optics and Rossby waves, geostrophic adjustment characteristics of the different types of radiation 65 3 pts. Lect: 3. Not offered in 2011–2012. and quasigeostrophy, baroclinic and barotropic (photons, charged and uncharged particles) Prerequisite: APPH E3300. Ray optics, instabilities, Sverdrup balance, boundary and mechanisms of their interactions with matrix formulation, wave effects, interference, currents, Ekman layers. materials. Essentials of the determination, by Gaussian beams, Fourier optics, diffraction, measurement and calculation, of absorbed APPH E4300x Applied electrodynamics image formation, electromagnetic theory of light, doses from ionizing radiation sources used in 3 pts. Lect: 3. Professor Navratil. polarization and crystal optics, coherence, guided medical physics (clinical) situations and for Prerequisite: APPH E3300. Overview of wave and fiber optics, optical elements, photons, health physics purposes. properties and interactions of static electric and selected topics in nonlinear optics. magnetic fields. Study of phenomena of time APBM E4650x Anatomy for physicists and APPH E4112y Laser physics dependent electric and magnetic fields including engineers 3 pts. Lect: 3. Not offered in 2011–2012. induction, waves, and radiation as well as special 3 pts. Lect: 3. Members of the faculty. Prerequisites: Recommended but not required: relativity. Applications are emphasized. Prerequisite: Engineering or physics background. APPH E3100 and E3300 or their equivalents. A systemic approach to the study of the human APPH E4301y Introduction to plasma physics Optical resonators, interaction of radiation and body from a medical imaging point of view: 3 pts. Lect: 3. Instructor to be announced. atomic systems, theory of laser oscillation, specific skeletal, respiratory, cardiovascular, digestive, Prerequisite: PHYS W3008 or APPH E3300. laser systems, rate processes, modulation, Definition of a plasma. Plasmas in laboratories and urinary systems, breast and women’s issues, detection, harmonic generation, and applications. and nature, plasma production. Motion of head and neck, and central nervous system. CHAP E4120x Statistical mechanics charged particles in electric and magnetic Lectures are reinforced by examples from clinical 3 pts. Lect: 3. Professor O’Shaughnessy. fields, adiabatic invariants. Heuristic treatment two- and three-dimensional and functional Prerequisite: CHEN E3210 or equivalent of collisions, diffusion, transport, and resistivity. imaging (CT, MRI, PET, SPECT, U/S, etc.). thermodynamics course, or instructor’s Plasma as a conducting fluid. Electrostatic and APPH E4710x-E4711y Radiation instrumentation permission. Fundamental principles and magnetostatic equilibria of plasmas. Waves and measurement laboratory, I and II underlying assumptions of statistical mechanics. in cold plasmas. Demonstration of laboratory 3 pts. Lect: 1. Lab: 4. Professor Arbo. Boltzmann’s entropy hypothesis and its plasma behavior, measurement of plasma Prerequisite: APPH E4010 or Corequisite: APPH restatement in terms of Helmholtz and Gibbs properties. Illustrative problems in fusion, space, E4010. Laboratory fee: $50 each term. E4710: free energies and for open systems. Correlation and nonneutral or beam plasmas. theory and use of alpha, beta, gamma, and times and lengths. Exploration of phase space APPH E4500y Health physics x-ray detectors and associated electronics for and observation timescale. Correlation functions. 3 pts. Lect: 3. Professor Christman. counting, energy spectroscopy, and dosimetry; Fermi-Dirac and Bose-Einstein statistics. Prerequisite: APPH E4600 or Corequisite: APPH radiation safety; counting statistics and error Fluctuation-response theory. Applications to ideal E4600. This course presents the fundamental propagation; mechanisms of radiation emission gases, interfaces, liquid crystals, microemulsions principles of health physics: the physics of dose and interaction. E4711, prerequisite APPH and other complex fluids, polymers, Coulomb deposition, radiation dosimetry, elementary E4710: additional detector types; applications gas, interactions between charged polymers and shielding and radiation protection devices, and systems including coincidence, low-level, and charged interfaces, ordering transitions. description and proper use (calibration and liquid scintillation counting; neutron activation; APPH E4130x Physics of solar energy maintenance) of health physics instrumentation, TLD dosimetry; gamma camera imaging. 3 pts. Lect: 3. Professor Chen. and the regulatory and administrative APPH E4901x Seminar: problems in applied Prerequisites: General physics (PHYS C1403 requirements of health physics programs. physics or C1602) and mathematics, including ordinary APPH E4501y Medical health physics tutorial 1 pt. Lect: 1. Professor Herman. differential equations and complex numbers 0 pts. This course is required for, and can be taken (such as MATH V1202 or E1210) or permission only by, all applied physics majors and minors of instructor. The physics of solar energy Prerequisite: Permission of the course coordinator. Required for, and limited to, M.S. in the junior year. Discussion of specific and including solar radiation, the analemma, self-contained problems in areas such as applied atmospheric efforts, thermodynamics of solar degree candidates in the Medical Physics Program. Course addresses procedures for electrodynamics, physics of solids, and plasma energy, physics of solar cells, energy storage physics. Topics change yearly. and transmission, and physics and economics personnel and area monitoring, radiation and in the solar era. contamination surveys, instrument calibration, APPH E4903x Seminar: problems in applied radioactive waste disposal, radiation safety physics APPH E4200x Physics of fluids compliance, licensure requirements, and other 2 pts. Lect: 1. Tutorial:1. Professor Herman. 3 pts. Lect: 3. Professor Mauel. matters contributing to professional competence This course is required for, and can be taken Prerequisites: APMA E3102 or equivalent; PHYS in the field of medical health physics. Course only by, all applied physics majors in the C1401 or C1601 or equivalent. An introduction includes lectures, seminars, tours, and hand-on senior year. Discussion of specific and self- to the physical behavior of fluids for science experience. This two-week tutorial is offered contained problems in areas such as applied and engineering students. Derivation of basic immediately following spring semester final electrodynamics, physics of solids, and plasma equations of fluid dynamics: conservation of examinations and is taken for Pass/Fail only. physics. Formal presentation of a term paper mass, momentum, and energy. Dimensional required. Topics change yearly. analysis. Vorticity. Laminar boundary layers. APPH E4550y Medical physics seminar Potential flow. Effects of compressibility, 0 pts. Lect: 1. APPH E4990x and y Special topics in applied stratification, and rotation. Waves on a free Required for all graduate students in the Medical physics surface; shallow water equations. Turbulence. Physics Program. Practicing professionals and 1–3 pts. Not offered in 2011–2012. faculty in the field present selected topics in Prerequisite: Permission of the instructor. This APPH E4210y Geophysical fluid dynamics medical physics. course may be repeated for credit. Topics 3 pts. Lect: 3. Professor Polvani. and instructors change from year to year. For APPH E4600x Fundamentals of radiological Prerequisites: APMA E3101, E3102 (or advanced undergraduate students and graduate physics and radiation dosimetry equivalents) and APPH E4200 (or equivalent), or students in engineering, physical sciences, and 3 pts. Lect: 3. Professor Meli. permission from instructor. Fundamental concepts other fields. in the dynamics of rotating, stratified flows. Prerequisite: APPH E4010 or Corequisite: Geostrophic and hydrostatic balances, potential APPH E4010. Basic radiation physics: vorticity, f and beta plane approximations, gravity radioactive decay, radiation producing devices,

engineering 2011–2012 66 APAM E4999x and y–S4999 Curricular Equilibrium, stability, and transport of torodial language of engineering, the natural sciences, practical training plasmas. Ballooning and tearing instabilities. and the social sciences. Students execute 1 pt. Members of the faculty. Kinetic theory, including Vlasov equation, scripts in Mathematica and MATLAB (or the Prerequisite: Obtained internship and approval Fokker-Planck equation, Landau damping, kinetic like) to illustrate and visualize course concepts from adviser. Only for master’s students in the transport theory. Drift instabilities. (programming not required). Department of Applied Physics and Applied APMA E3101x Linear algebra Mathematics who may need relevant work APPH E6110x Laser interactions with matter 3 pts. Lect: 3. Professor Duchêne. experience as part of their program of study. 3 pts. Lect: 3. Not offered in 2011–2012. Matrix algebra, elementary matrices, inverses, Final report required. This course may not be Prerequisites: APPH E4112 or equivalent, and rank, determinants. Computational aspects of taken for pass/fail or audited. quantum mechanics. Principles and applications of laser-matter coupling, nonlinear optics, three- solving systems of linear equations: existence- APPH E6081x Solid state physics, I and four-wave mixing, harmonic generation, uniqueness of solutions, Gaussian elimination, 3 pts. Lect: 3. Professor Pinczuk. laser processing of surfaces, laser probing of scaling, ill-conditioned systems, iterative Prerequisites: APPH E3100 or the equivalent. materials, spontaneous and stimulated light techniques. Vector spaces, bases, dimension. Knowledge of statistical physics on the level scattering, saturation spectroscopy, multiphoton Eigenvalue problems, diagonalization, inner of MSAE E3111 or PHYS G4023 strongly excitation, laser isotope separation, transient products, unitary matrices. recommended. Crystal structure, reciprocal optical effects. APMA E3102y Partial differential equations lattices, classification of solids, lattice dynamics, 3 pts. Lect: 3. Professor Sobel. anharmonic effects in crystals, classical electron APAM E6650x and y–S6650 Research project Prerequisite: MATH E1210 or equivalent. models of metals, electron band structure, and 1–6 pts. Members of the faculty. Introduction to partial differential equations; low-dimensional electron structures. This course may be repeated for credit. A special integral theorems of vector calculus. Partial investigation of a problem in nuclear engineering, APPH E6082y Solid state physics, II differential equations of engineering in medical physics, applied mathematics, applied 3 pts. Lect: 3. Professor Kim. rectangular, cylindrical, and spherical physics, and/or plasma physics consisting of Prerequisite: APPH E6081 or the instructor’s coordinates. Separation of the variables. independent work on the part of the student and permission. Semiclassical and quantum Characteristic-value problems. Bessel functions, embodied in a formal report. mechanical electron dynamics and Legendre polynomials, other orthogonal conduction, dielectric properties of insulators, APPH E9142x-E9143y Applied physics seminar functions; their use in boundary value problems. semiconductors, defects, magnetism, 3 pts. Sem: 3. Not offered in 2011–2012. Illustrative examples from the fields of superconductivity, low-dimensional structures, These courses may be repeated for credit. electromagnetic theory, vibrations, heat flow, and and soft matter. Selected topics in applied physics. fluid mechanics. APPH E6085x Computing the electronic APAM E9301x and y–S9301 Doctoral research APAM E3105x Programming methods for structure of complex materials 0–15 pts. Members of the faculty. scientists and engineers 3 pts. Lect: 3. Offered in alternate years. Prerequisite: Qualifying examination for the 3 pts. Lect: 2.5. Lab: 1. Not offered in 2011–2012. Prerequisite: APPH E3100 or equivalent. Basics doctorate. Required of doctoral candidates. Introduction to modern techniques of computer of density functional theory (DFT) and its programming for the numerical solutions to application to complex materials. Computation APAM E9800x and y–S9800 Doctoral familiarity with basic and advanced concepts of electronics and mechanical properties of research instruction of modern numerical programming and acquire materials. Group theory, numerical methods, 3, 6, 9, or 12 pts. Members of the faculty. practical experience solving representative basis sets, computing, and running open source A candidate for the Eng.Sc.D. degree must problems in math and physics. DFT codes. Problem sets and a small project. register for 12 points of doctoral research instruction. Registration for APAM E9800 may APMA E3900x and y Undergraduate research APPH E6091y Magnetism and magnetic not be used to satisfy the minimum residence in applied mathematics materials requirement for the degree. 0–4 pts. Members of the faculty. 3 pts. Lect. 3. Offered in alternate years. This course may be repeated for credit, but APAM E9900x and y–S9900 Doctoral Professor Bailey. no more than 6 points of this course may be dissertation Prerequisites: MSAE E4206, APPH E6081, or counted toward the satisfaction of the B.S. 0 pts. Members of the faculty. equivalent. Types of magnetism. Band theory degree requirements. Candidates for the B.S. A candidate for the doctorate may be required of ferromagnetism. Magnetic metals, insulators, degree may conduct an investigation in applied to register for this course every term after the and semiconductors. Magnetic nanostructures: mathematics or carry out a special project coursework has been completed, and until the ultrathin films, superlattices, and particles. under the supervision of the staff. Credit for the dissertation has been accepted. Surface magnetism and spectroscopies. High course is contingent upon the submission of an speed magnetization dynamics. Spin electronics. acceptable thesis or final report. APPH E6101x Plasma physics, I Courses in Applied APMA E4001y Principles of applied 3 pts. Lect: 3. Instructor to be announced. Mathematics mathematics Prerequisite: APPH E4300. Debye screening. 3 pts. Lect: 3. Professor Duchêne. APMA E2101y Inroduction to applied Motion of charged particles in space- and Prerequisites: Introductory Linear Algebra mathematics time-varying electromagnetic fields. Two-fluid required. Ordinary Differential Equations 3 pts. Lect: 3. Professor Spiegelman. description of plasmas. Linear electrostatic and recommended. Review of finite-dimensional Prerequisite: Calculus III. A unified, single- electromagnetic waves in unmagnetized and vector spaces and elementary matrix theory. semester introduction to differential equations magnetized plasmas. The magnetohydrodynamic Linear transformations, change of basis, and linear algebra with emphases on (MHD) model, including MHD equilibrium, eigenspaces. Matrix representation of linear (1) elementary analytical and numerical stability, and MHD waves in simple geometries. operators and diagonalization. Applications technique and (2) discovering the analogs to difference equations, Markov processes, Fluid theory of transport. on the continuous and discrete sides of the ordinary differential equations, and stability of APPH E6102y Plasma physics, II mathematics of linear operators: superposition, nonlinear dynamical systems. Inner product 3 pts. Lect: 3. Professor Boozer. diagonalization, fundamental solutions. Concepts spaces, projection operators, orthogonal Prerequisite: APPH E6101. Magnetic coordinates. are illustrated with applications using the bases, Gram-Schmidt orthogonalization. Least

engineering 2011–2012 squares method, pseudo-inverses, singular APMA E4300y Introduction to numerical Prerequisites: PHYS W1401 or equivalent, and 67 value decomposition. Adjoint operators, methods APMA E2101 or MATH E1210 or equivalent. Hermitian and unitary operators, Fredholm 3 pts. Lect: 3. Instructor to be announced. Introduction to physical and mathematical Alternative Theorem. Fourier series and Prerequisites: MATH V1201, MATH E1210, models of cellular and molecular biology. Physics eigenfunction expansions. Introduction to the and APMA E3101 or their equivalents. Some at the cellular scale (viscosity, heat, diffusion, theory of distributions and the Fourier Integral programming experience and MATLAB will be statistical mechanics). RNA transcription and Transform. Green’s functions. Application to extremely useful. Introduction to fundamental regulation of genetic expression. Genetic and Partial Differential Equations. algorithms and analysis of numerical methods biochemical networks. Bioinformatics as applied commonly used by scientists, mathematicians to reverse-engineering of naturally-occurring APMA E4101y Introduction to dynamical and engineers. This course is designed to give networks and to forward-engineering of synthetic systems a fundamental understanding of the building biological networks. Mathematical and physical 3 pts. Lect: 3. Professor Wiggins. blocks of scientific computing that will be used in aspects of functional genomics. Prerequisites: APMA E2101 (or MATH V1210) more advanced courses in scientific computing APMA E4901x Seminar: problems in applied and APMA E3101 or their equivalents, or and numerical methods for PDEs. Topics include mathematics permission of instructor. An introduction to the numerical solutions of algebraic systems, linear 0 pts. Lect: 1. Professor Wiggins. analytic and geometric theory of dynamical least-squares, eigenvalue problems, solution of This course is required for, and can be taken systems; basic existence, uniqueness and non-linear systems, optimization, interpolation, only by, all applied mathematics majors in parameter dependence of solutions to ordinary numerical integration and differentiation, initial the junior year. Prerequisites or corequisites: differential equations; constant coefficient and value problems and boundary value problems for APMA E4200 and E4204 or their equivalents. parametrically forced systems; Fundamental systems of ODEs. All programming exercises will Introductory seminars on problems and solutions; resonance; limit points, limit cycles be in MATLAB. and classification of flows in the plane (Poincare- techniques in applied mathematics. Typical Bendixson Theorem); conservative and APMA E4301x Numerical methods for partial topics are nonlinear dynamics, scientific dissipative systems; linear and nonlinear stability differential equations computation, economics, operations research, analysis of equilibria and periodic solutions; 3 pts. Lect: 3. Professor Spiegelman. etc. Prerequisites: APMA E4300 and E3102 or stable and unstable manifolds; bifurcations, APMA E4903x Seminar: problems in applied E4200 or equivalents. Numerical solution of e.g., Andronov-Hopf; sensitive dependence and mathematics partial differential equations (PDE) arising chaotic dynamics; selected applications. 3–4 pts. Lect: 1. Tutorial: 2. Professor Wiggins. in various physical fields of application. This course is required for all applied APMA E4150x Applied functional analysis Finite difference, finite element, and spectral mathematics majors in the senior year. 3 pts. Lect: 3. Professor Bal. methods. Elementary finite volume methods Prerequisites or corequisites: APMA E4200 and Prerequisites: Advanced calculus and course for conservation laws. Time stepping, E4204 or their equivalents. For 4 pts. credit, term in basic analysis, or instructor’s approval. method of lines, and simultaneous space- paper required. Examples of problem areas are Introduction to modern tools in functional time discretization. Direct and iterative nonlinear dynamics, asymptotics, approximation analysis that are used in the analysis of methods for boundary-value problems. theory, numerical methods, etc. Approximately deterministic and stochastic partial differential Applied numerical analysis of PDE, including three problem areas are studied per term. equations and in the analysis of numerical sources of numerical error and notions of methods: metric and normed spaces, Banach convergence and stability, to an extent APMA E4990x and y Special topics in applied space of continuous functions, measurable necessary for successful numerical modeling mathematics spaces, the contraction mapping theorem, of physical phenomena. Applications will 1–3 pts. Lect: 3. Instructor to be announced. Banach and Hilbert spaces bounded linear include the Poisson equation, heat equation, Prerequisites: Advanced calculus and junior operators on Hilbert spaces and their wave equation, and nonlinear equations of year applied mathematics, or their equivalents. spectral decomposition, and time permitting fluid, solid, and gas dynamics. Homework This course may be repeated for credit. Topics distributions and Fourier transforms. assignments will involve substantial and instructors from the Applied Mathematics programming. Committee and the staff change from year to APMA E4200x Partial differential equations year. For advanced undergraduate students 3 pts. Lect: 3. Professor Bal. AMCS E4302x Parallel scientific computing and graduate students in engineering, physical Prerequisite: Course in ordinary differential 3 pts. Lect: 3. Instructor to be announced. sciences, biological sciences, and other fields. equations. Techniques of solution of partial Prerequisites: APMA E3101, E3102, and differential equations. Separation of the variables. E4300, or their equivalents. Corequisites: APMA APMA E6209x Approximation theory Orthogonality and characteristic functions, E4301, and programming ability in C/C++ or 3 pts. Lect: 2. Not offered in 2011–2012. nonhomogeneous boundary value problems. FORTRAN/F90. An introduction to the concepts, Prerequisite: MATH W4061 or some knowledge Solutions in orthogonal curvilinear coordinate the hardware and software environments, and of modern analysis. Theory and application systems. Applications of Fourier integrals, Fourier selected algorithms and applications of parallel of approximate methods of analysis from the and Laplace transforms. Problems from the fields scientific computing, with an emphasis on tightly viewpoint of functional analysis. Approximate of vibrations, heat conduction, electricity, fluid coupled computations that are capable of scaling numerical and analytical treatment of linear and dynamics, and wave propagation are considered. to thousands of processors. Includes high-level nonlinear algebraic, differential, and integral descriptions of motivating applications and equations. Topics include function spaces, APMA E4204x Functions of a complex low-level details of implementation, in order to operators in normed and metric spaces, fixed variable expose the algorithmic kernels and the shifting point theorems and their applications. 3 pts. Lect. 3. Instructor to be announced. balances of computation and communication Prerequisite: MATH V1202 or equivalent. between them. Students run demonstration APMA E6301y Analytic methods for partial Complex numbers, functions of a complex codes provided on a Linux cluster. Modest differential equations variable, differentiation and integration in the programming assignments using MPI and PETSc 3 pts. Lect: 2. Professor Weinstein. complex plane. Analytic functions, Cauchy culminate in an independent project leading to an Prerequisites: Advanced calculus, basic integral theorem and formula, Taylor and Laurent in-class report. concepts in analysis, APMA E3101, and series, poles and residues, branch points, E4200 or their equivalents, or permission of evaluation of contour integrals. Conformal APMA E4400y Introduction to biophysical the instructor. Introduction to analytic theory of mapping. Schwarz-Christoffel transformation. modeling PDEs of fundamental and applied science; wave Applications to physical problems. 3 pts. Lect: 3. Not offered in 2011–2012. (hyperbolic), Laplace and Poisson equations

engineering 2011–2012 68 (elliptic), heat (parabolic) and Schroedinger APMA E6901x and y–E6901y Special topics in APMA E9101x-E9102y Research (dispersive) equations; fundamental solutions, applied mathematics 1–4 pts. Members of the faculty. Green’s functions, weak/distribution solutions, 3 pts. Lect: 3. Instructor to be announced. Prerequisite: Permission of the supervising maximum principle, energy estimates, variational Prerequisites: Advanced calculus and junior faculty member. This course may be repeated. methods, method of characteristics; elementary year applied mathematics, or their equivalents. Advanced study in a special area. functional analysis and applications to PDEs; This course may be repeated for credit. Topics APMA E9810x or y Mathematical earth introduction to nonlinear PDEs, shocks; selected and instructors from the Applied Mathematics science seminar applications. Committee and the staff change from year to 0 pts. Lect: 1. Professor Polvani. year. For students in engineering, physical APMA E6302x Numerical analysis of partial Prerequisite: Instructor’s permission. Current sciences, biological sciences, and other fields. differential equations research in problems at the interface 3 pts. Lect: 2. Not offered in 2011–2012. APMA E8308y Asymptotic methods in applied between applied mathematics and earth and Prerequisite: APMA E3102 or E4200. Numerical mathematics environmental sciences. analysis of initial and boundary value problems 3 pts. Lect: 2. Not offered in 2011–2012. APMA E9815x or y Geophysical fluid for partial differential equations. Convergence Prerequisite: APMA E4204 or equivalent. dynamics seminar and stability of the finite difference method, the Asymptotic treatment of ordinary and partial 1–3 pts. May be repeated for up to 10 points of spectral method, the finite element method and differential equations in problems arising credit. Not offered in 2011–2012. applications to elliptic, parabolic, and hyperbolic in applied mathematics. Asymptotic series. Prerequisite: Instructor’s permission. Problems in equations. Asymptotic evaluation of integrals. Expansion the dynamics of geophysical fluid flows. of solutions of ordinary differential equations: APMA E6304y Integral transforms connection problem and turning points. Stoke’s 3 pts. Lect: 2. Not offered in 2011–2012. phenomenon. Differential equations with a Prerequisites: APMA E4204 and MATH E1210, Courses in Materials parameter: “boundary layer” phenomenon. or their equivalents. Laplace, Fourier, Hankel, Application to partial differential equations: science and engineering and Mellin transforms. Selection of suitable problems from fluid dynamics, wave propagation See page 172. transform for a given partial differential equation theory, electromagnetic theory. boundary value problem. Operational properties of transforms. Inversion theorems. Approximate evaluation of inversion integrals for small and large values of parameter. Application to the solution of integral equations.

engineering 2011–2012 biomedical engineering 69 351 Engineering Terrace, MC 8904 Phone: 212-854-4460 E-mail: [email protected] www.bme.columbia.edu

Interim Chair Computer Systems Associate Joint Faculty Adjunct Associate Andreas H. Hielscher Administrator Professors Dimitris Anastassiou, Professor Robert J. Foster Henry Hess Professor of Electrical Nicolas W. Chbat Departmental Christopher R. Jacobs Engineering Aniruddha Das, Affiliates Administrator Chair of Elisa E. Konofagou Assistant Professor of Shila Maghji Undergraduate Helen H. Lu Psychiatry Peter K. Allen, Professor Studies Jeremy J. Mao Shunichi Homma, of Computer Science Business Manager X. Edward Guo Barclay Morrison III Professor of Medicine Robert DeLaPaz, Kidest Shenkoru Paul Sajda Elizabeth S. Olson, Professor of Radiology Chair of Graduate Assistant Professor of Kung Ming Jan, Administrative Studies Assistant Otolaryngology/Head Associate Professor of Coordinator for Helen H. Lu Professors and Neck Surgery Clinical Medicine Student Affairs Elizabeth Hillman Lawrence Schwartz, Jung-Chi Liao, Jarmaine Lomax Ombuds Hayden Huang Professor of Radiology Assistant Professor Lance Kam Lance C. Kam Michael P. Sheetz, of Mechanical Administrative Samuel K. Sia Professor of Cell Engineering Assistant for Professors Biology Zheng Feng Lu, Fiscal Affairs Gerard H. A. Ateshian Lecturer in R. Theodore Smith, Associate Professor of Michelle Cintron X. Edward Guo Discipline Associate Professor of Clinical Radiology Andreas H. Hielscher Aaron Matthew Kyle Ophthalmology John Pile-Spellman, Administrative Clark T. Hung Professor of Radiology Assistant for Andrew F. Laine Departmental Adjunct and Neurosurgery Edward F. Leonard Professors Henry M. Spotnitz, Affairs Van C. Mow, Paulette Louissaint Ernest Feleppa Professor of Surgery Stanley Dicker Shiro Matsuoka Professor Laboratory Gordana Vunjak- Manager Novakovic Keith Yeager

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

engineering 2011–2012 70 breadth included within these tracks, Ping Laboratory for Functional Tissue Students are strongly encouraged to plus a substantial elective content, Research (Professor Mow), the Heffner take courses in the order specified in prepare bachelor’s and master’s Biomedical Imaging Laboratory the course tables on pages 74–75; students to commence professional (Professor Laine), the Laboratory implications of deviations should be activity in any area of biomedical for Intelligent Imaging and Neural discussed with a departmental adviser engineering or to go on to graduate Computing (Professor Sajda), the before registration. The first two school for further studies in related Biophotonics and Optical Radiology years provide a strong grounding in fields. The program also provides Laboratory (Professor Hielscher), the physical and chemical sciences, excellent preparation for the health the Bone Bioengineering Laboratory engineering fundamentals, and sciences and the study of medicine. (Professor Guo), the Cell and Tissue mathematics. This background is used Graduates of the doctoral program are Engineering Laboratory (Professor to provide a unique physical approach prepared for research activities at the Hung), the Biomaterial and Interface to the study of biological systems. The highest level. Tissue Engineering Laboratory last two years of the undergraduate Areas of particular interest to (Professor Lu), the Neurotrauma program provide substantial exposure to Columbia faculty include orthopaedic and Repair Laboratory (Professor modern biology and include courses in and musculoskeletal biomechanics Morrison), the Laboratory for Stem engineering and engineering science that (Professors Ateshian, Guo, Hess, Huang, Cells and Tissue Engineering (Professor extend the work of the first two years. Jacobs, and Mow), cardiovascular Vunjak-Novakovic), the Ultra- sound The program also offers three tracks to biomechanics (Professor Homma), cellular and Elasticity Imaging Laboratory guide students in the choice of technical and tissue engineering and artificial organs (Professor Konofagou), the Microscale courses, while sharing a common core (Professors Hung, Kam, Leonard, H. H. Biocomplexity Laboratory (Professor curriculum. The tracks are different from Lu, Morrison, Sia, and Vunjak-Novakovic), Kam), the Molecular and Microscale one another, and there is great breadth auditory biophysics (Professor Olson), Bioengineering Laboratory (Professor within each. These qualities allow the and biosignals and biomedical imaging Sia), the Laboratory for Functional faculty to prepare students for activity (Professors Hielscher, Hillman, DeLaPaz, Optical Imaging (Professor Hillman), in all contemporary areas of biomedical Konofagou, Laine, Z. F. Lu, Pile-Spellman, the Cell and Molecular Biomechanics engineering. Graduates of the program Sajda, and Smith). Laboratory (Professor Jacobs), and the are equipped for employment in the large Biomechanics and Mechanotransduction industrial sector devoted to health care, Facilities Laboratory (Professor Huang), the which includes pharmaceuticals, medical The Department of Biomedical Nanobiotechnology and Synthetic devices, artificial organs, prosthetics Engineering has been supported by Biology Laboratory (Professor Hess). and sensory aids, diagnostics, medical University funding, awards from the These laboratories are supplemented instrumentation, and medical imaging. Whitaker Foundation, and research with core facilities, including a tissue Graduates also accept employment funding from the NIH, NSF, and culture facility, a histology facility, a in oversight organizations (FDA, NIH, numerous research foundations. The confocal microscope, an atomic force OSHA, and others), medical centers, and extensive new facilities that have microscope, a 2-photon microscope, an research institutes. They are prepared recently been added both at the Medical epifluorescence microscope, a freezer for graduate study in biomedical Center and Morningside campus include room, biomechanics facilities, a machine engineering and several related areas new teaching and research laboratories shop, and a specimen prep room. of engineering and the health sciences. that provide students with unusual Students in all three tracks of the program can meet entrance requirements access to contemporary research Undergraduate Program equipment specially selected for its for graduate training in the various The objectives of the undergraduate relevance to biomedical engineering. An allied health professions. No more than program in biomedical engineering are undergraduate wet laboratory devoted three additional courses are required as follows: to biomechanics and cell and tissue in any of the tracks to satisfy entrance engineering has been added, together requirements for most U.S. medical 1. Professional employment in areas with a biosignals and biomedical schools. such as the medical device industry, imaging and data processing laboratory. All biomedical engineering students engineering consulting, biomechanics, Each laboratory incorporates equipment are expected to register for nontechnical biomedical imaging, and biotechnology; normally reserved for advanced research electives, both those specifically required 2. Graduate studies in biomedical and provides exceptional access by the School of Engineering and engineering or related fields; to current practices in biomedical Applied Science and those needed to 3. Attendance at medical or dental school. engineering and related sciences. meet the 27-point total of nontechnical Adjacent to the new laboratories is a electives required for graduation. The undergraduate curriculum is lounge that serves as a meeting point for designed to provide broad knowledge biomedical engineering undergraduate First and Second Years of the physical and engineering sciences and graduate students. and their application to the solution As outlined in this bulletin, in the first Research facilities of the Biomedical of biological and medical problems. two years all engineering students are Engineering faculty include the Liu expected to complete a sequence

engineering 2011–2012 of courses in mathematics, physics, and phenomena from molecular to term that they are designated in the 71 chemistry, computer science, organ system levels. In the fields of course tables, as conflicts may arise if engineering, English composition, biomedical engineering, experimental courses are taken out of sequence. and physical education, as well as techniques and principles are Students are required to take up to nontechnical electives including fundamental skills that good biomedical 9 points (6 points in the imaging track) the humanities. For most of these engineers must master. Beginning of “technical electives,” allowing for sequences, the students may choose in junior year, all students take the exploration of related technical topics. from two or more tracks. If there is a three-semester sequence Biomedical A technical elective is defined as a question regarding the acceptability of a engineering laboratory, I–III­­ (BMEN 3000-level or above course in SEAS or course as a nontechnical elective, please E3810, E3820, E3830). In this three- courses taught by the Departments of consult the approved listing of courses semester series, students learn through Biology, Chemistry, and Biochemistry. beginning on page 10 or contact your hands-on experience the principles and advising dean for clarification. methods of biomedical engineering Technical Elective Requirements Please see the charts in this experimentation, measurement Students are required to take at least section for a specific description of techniques, quantitative theories of 48 points of engineering content biomedical engineering, data analysis, course requirements. coursework toward their degree. The and independent design of biomedical In addition, a professional-level 48-point requirement is a criterion engineering experiments, the scope of engineering course is required. Students established by the Accreditation Board which cover a broad range of topics may select from a variety of offerings for Engineering and Technology (ABET). from all three tracks—biomechanics, cell within SEAS. For students interested in Taking into consideration the number and tissue engineering, and biosignals biomedical engineering, we recommend of engineering content points conferred and biomedical imaging. In the senior taking BMEN E1001: Engineering in by the required courses of the BME year, students take the required course medicine or APPH E1300y: Physics curriculum, a portion of technical Ethics for biomedical engineers (BMEN of the human body in fulfillment of electives must be clearly engineering in E4010), an Engineering nontechnical this requirement. Note that E1201: nature (Engineering Content Technical elective that covers a wide range of Electives), specifically as defined below: Introduction to electrical engineering is ethical issues expected to confront required and cannot be double counted biomedical engineering graduates as 1. Technical elective courses with to satisfy the professional-level course they enter biotechnology industry, sufficient engineering content that requirement. For the computer science research, or medical careers. Also in can count toward the 48 units of requirement, students must take COMS the senior year, students are required engineering courses required for W1005. to take a two-semester capstone ABET accreditation: All students must take APMA E2101: design course, Biomedical engineering a. All 3000-level or higher courses Introduction to applied mathematics in design (BMEN E3910 and E3920), in in the Department of Biomedical ELEN E1201: Introduction addition to which students work within a team to Engineering, except BMEN E4010, to electrical engineering, ENME tackle an open-ended design project in E4103, E4104, E4105, E4106, E3105: Mechanics and STAT W1211: biomedical engineering. The underlying E4107 and E4108. (Note that only Introduction to statistics in their second philosophy of these core requirements 3 points of BMEN E3998 may be year. is to provide our biomedical engineering counted toward technical elective students with a broad knowledge and degree requirements.) Third and Fourth Years understanding of topics in the field b. All 3000-level or higher courses The biomedical engineering programs of biomedical engineering. Parallel to in the Department of Mechanical at Columbia at all levels are based on these studies in core courses, students Engineering, except MECE engineering and biological fundamentals. take track-specific required courses E4007: Creative engineering and This is emphasized in our core to obtain an in-depth understanding entrepreneurship requirements across all tracks. In the of their chosen concentration. The c. All 3000-level or higher courses junior year, all students begin their curriculum of all three academic in the Department of Chemical biomedical engineering study with the tracks—biomechanics, cell and tissue Engineering, except CHEN E4020: two-semester Introduction to molecular engineering, and biosignals and Safeguarding intellectual and and cellular biology, I and II (BIOL biomedical imaging—prepares students business property C2005-C2006), which gives students who wish to pursue careers in medicine d. All 3000-level or higher courses a comprehensive overview of modern by satisfying most requirements in the in the Department of Electrical biology from molecular to organ system pre-medical programs with no more Engineering, except EEHS E3900: levels. Parallel to these biology studies, than three additional courses. Some of History of telecommunications: all students take the two-semester these additional courses may also be from the telegraph to the Internet Quantitative physiology, I and II counted as nonengineering technical e. All 3000-level or higher courses sequence (BMEN E4001-E4002) which electives. Please see the course tables in the Civil Engineering and is taught by biomedical engineering for schedules leading to a bachelor’s Engineering Mechanics program, faculty and emphasizes quantitative degree in biomedical engineering. except CIEN E4128, E4129, applications of engineering principles It is strongly advised that students E4130, E4131, E4132, E4133, in understanding biological systems take required courses during the specific

engineering 2011–2012 72 E4134, E4135, and E4136 Master of Science degree or equivalent Curriculum and Exam f. All 3000-level or higher courses may apply directly to the doctoral degree Requirements in the Earth and Environmental program. All applicants are expected Engineering program to have earned the bachelor’s degree Master’s Degree 2. Courses from the following in engineering or in a cognate scientific In consultation with an appointed faculty departments are not allowed to program. The Graduate Record Exam- adviser, M.S. students should select count toward the required 48 units of ination (General Test only) is required of a program of 30 points of credit of engineering courses: all applicants. Students whose bachelor’s graduate courses (4000 level or above) a. Department of Applied Physics and degree was not earned in a country appropriate to their career goals. This Applied Mathematics where English is the dominant spoken program must include the course in b. Department of Computer Science language are required to take the TOEFL computational modeling of physiological c. Department of Industrial test. M.S. degree candidates must reach systems (BMEN E6003); two semesters Engineering and Operations level 8 on the English Placement Test of BMEN E9700: Biomedical engineering Research (EPT) offered by Columbia’s American seminar; at least four other biomedical d. Program of Materials Science and Language Program (ALP). Doctoral engineering courses; and at least one Engineering degree candidates must attain level 10 graduate-level mathematics course. on the English Placement Test (EPT). Students with deficiency in physiology The cell and tissue engineering The ALP examination must be taken course work are required to take the track requires 4.5 of the required 9 at orientation upon arrival. It is strongly BMEN E4001-E4002 sequence before points of technical electives to be recommended the students enroll in taking BMEN E6003. Candidates must from engineering courses; in the an appropriate ALP course if they have achieve a minimum grade-point average biomechanics track, 2.5 points of not achieved the required proficiency of 2.5. A thesis based on experimental, technical electives must be from after the first examination. In addition, computational, or analytical research engineering courses; in the imaging the individual tracks require applicants is optional and may be counted in lieu track, the requirements satisfy the 48 to have taken the following foundation of 6 points of course work. Students points of engineering content. Once 48 courses: wishing to pursue the Master’s Thesis points of engineering-content technical • Biomechanics: One year of biology option should register for BMEN E9100 electives are satisfied, students may and/or physiology, solid mechanics, Master’s Research and consult with choose any course above the 3000 statics and dynamics, fluid mechanics, their BME faculty adviser. level in Columbia Engineering as well as ordinary differential equations. biology, chemistry, and biochemistry as • Cell and Tissue Engineering: One Doctoral Degree technical electives. year of biology and/or physiology, Students admitted to the doctoral The accompanying charts describe one year of organic chemistry or degree program should select courses the eight-semester degree program biochemistry with laboratory, fluid to prepare for the doctoral qualifying schedule of courses leading to the mechanics, rate processes, ordinary examination and register for research bachelor’s degree in biomedical differential equations. rotations during the first two semesters engineering. • Biosignals and Biomedical Imaging: of graduate study. To facilitate future One year of biology and/or physiology collaboration with clinicians and and/or biochemistry. Linear algebra, Graduate Programs biomedical scientists, students are ordinary differential equations, Fourier The graduate curriculum in biomedical encouraged to consider courses at analysis, digital signal processing. the Health Sciences campus or in the engineering employs the same three Applicants lacking some of these tracks that compose the undergraduate Department of Biological Sciences. courses may be considered for Doctoral students must complete curriculum: biomechanics, cell and admission with stipulated deficiencies tissue engineering, and biosignals and a program of 30 points of credits that must be satisfied in addition to the beyond the M.S. degree. The course in biomedical imaging. Initial graduate study requirements of the degree program. in biomedical engineering is designed computational modeling of physiological Columbia Engineering does not admit systems (BMEN E6003) is required to expand the student’s undergraduate students holding the bachelor’s degree preparation in the direction of the track for the doctoral program. At least directly to doctoral studies; admission two graduate mathematics courses chosen. In addition, sufficient knowledge is offered either to the M.S. program or is acquired in other areas to facilitate must be taken, which may include the to the M.S. program/doctoral track. The mathematics course required for the broad appreciation of problems and Department of Biomedical Engineering effective collaboration with specialists M.S. degree. Students must register for also admits students into the 4-2 BMEN E9700: Biomedical engineering from other scientific, medical, and program, which provides the opportunity engineering disciplines. The Department seminar and for research rotations during for students holding a bachelor’s degree the first two semesters of graduate study. of Biomedical Engineering offers a from certain physical sciences to receive graduate program leading to the Master Remaining courses should be selected the M.S. degree after two years of study in consultation with the student’s faculty of Science degree (M.S.), the Doctor at Columbia. of Philosophy degree (Ph.D.), and the adviser to prepare for the doctoral Doctor of Engineering Science degree qualifying examination and to develop (Eng.Sc.D.). Applicants who have a expertise in a clearly identified area of

engineering 2011–2012 biomedical engineering. Up to 12 points doctoral studies. In accord with paradigm of molecular biology. Representation, 73 of research (BMEN E9500) may be regulations of The Fu Foundation organization, structure, function and manipulation applied toward doctoral degree course School of Engineering and Applied of the biomolecular sequences of nucleic requirements. Science, each student is expected to acids and proteins. The role of enzymes and gene regulatory elements in natural biological All graduate students admitted submit a thesis and defend it before a functions as well as in biotechnology and to the doctoral degree program committee of five faculty, two of whom genetic engineering. Recombination and must satisfy the equivalent of three hold primary appointments in another other macromolecular processes viewed semesters’ experience in teaching (one department. Every doctoral candidate is as mathematical operations with simulation semester for M.D./Ph.D. students). required to have had accepted at least and visualization using simple computer This may include supervising and one first-author full-length paper for programming. This course shares lectures with assisting undergraduate students in publication in a peer-reviewed journal ECBM E4060, but the work requirements differ laboratory experiments, grading, and prior to recommendation for award of somewhat. preparing lecture materials to support the degree. BMEN E3150y The cell as a machine the teaching mission of the department. 3 pts. Lect: 3. Not offered in 2011–2012. The Department of Biomedical Courses in Biomedical Prerequisite: MATH V1101 or equivalent. Engineering is the only engineering Engineering Corequisites: One semester of BIOL C2005 or BIOC C3501, and one semester of PHYS department that offers Ph.D. training to See also the sections for Applied M.D./Ph.D. students. These candidates C1401 or equivalent Cells as complex micron- Physics, Chemical Engineering, sized machines, basic physical aspects of cell are expected to complete their Computer Science, and Computer components (diffusion, mechanics, electrostatics, Ph.D. program within 3.5 years, with Engineering in this bulletin, and the hydrophobicity), energy transduction (motors, otherwise the same requirements. Columbia College and Graduate transporters, chaperones, synthesis complexes), School of Arts and Sciences bulletins basic cell functions. Biophysical principles, Doctoral Qualifying Examination for courses in the biological sciences: feedback controls for robust cell function, Doctoral candidates are required to pass biomedical informatics, cell biology, adaptation to environmental perturbations. a qualifying examination. This examination microbiology, and physiology. BMEN E3320y Fluid biomechanics is given once a year, in January. It 3 pts. Lect: 3. Professor Huang. should be taken after the student has Prerequisite: APMA E2101. The principles of BMEN E1001x Engineering in medicine continuum mechanics as applied to biological fluid completed 30 points of graduate study. 3 pts. Lect: 3. Professor Konofagou. flows and transport. Course covers continuum The qualifying examination consists of The present and historical role of engineering in formulations of basic conservation laws, Navier- oral and written examinations. The oral medicine and health care delivery. Engineering Stokes equations, mechanics of arterial and examination consists of the analysis of approaches to understanding organismic and venous blood flow, blood rheology and non- assigned scientific papers, and the written cellular function in living systems. Engineering Newtonian properties, flow and transport in the in the diagnosis and treatment of disease. examination covers three areas: applied microcirculation, oxygen diffusion, capillary filtration. mathematics, quantitative biology and Medical imaging, medical devices: diagnostic physiology, and track-specific material. and surgical instruments, drug delivery systems, BMCH E3500y Biological transport and prostheses, artificial organs. Medical informatics Students must declare a track (biosignals rate processes and organization of the health care system. 3 pts. Lect: 3. Professor Vunjak-Novakovic. and biomedical imaging, biomechanics, or Current trends in biomedical engineering Prerequisites: CHEM C3443, APMA E2101. cell and tissue engineering) at the time of research. Corequisites: BIOL C2005. Convective and registration for the qualifying examination. diffusive movement and reaction of molecules BMEN E2300x or y Biomechanics track A minimum cumulative grade-point in biological systems. Kinetics of homogeneous 0 pts. Professor Laine. average of 3.2 is required to register for and heterogeneous reactions in biological Rising juniors are required to register for this this examination. environments. Mechanisms and models of course in the spring of their sophomore year if transport across membranes. Convective they choose the biomechanics track. Doctoral Committee and Thesis diffusion with and without chemical reaction. BMEN E2400x or y Biosignals and biomedical Diffusion in restricted spaces. Irreversible Students who pass the qualifying imaging track thermodynamic approaches to transport and examination choose a faculty member 0 pts. Professor Laine. reaction in biological systems. to serve as their research adviser. Rising juniors are required to register for this BMEN E3810x Biomedical engineering Each student is expected to submit a course in the spring of their sophomore year if laboratory, I research proposal and present it to a they choose the biosignals and biomedical imaging 3 pts. Lab: 4. Professor Kyle. track. thesis committee that consists of three Statistical analysis of experimental to five faculty members. The committee BMEN E2500x or y Cellular and tissue measurements: normal distribution, test of considers the scope of the proposed engineering track significance, linear regression, correlation, research, its suitability for doctoral 0 pts. Professor Laine. error analysis and propagation. MATLAB research and the appropriateness Rising juniors are required to register for this programming, EKG signal acquisition and of the research plan. The committee course in the spring of their sophomore year if processing, microscopy, cell counting and may approve the proposal without they choose the cell and tissue engineering track. scaffold encapsulation, mechanical testing of linear and nonlinear biomaterials. reservation or may recommend ECBM E3060x Introduction to genomic modifications. In general, the student information science and technology is expected to submit his/her research 3 pts. Lect: 3. Professor Varadan. proposal after five semesters of Introduction to the information system

engineering 2011–2012 74 biomedical engineering 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)

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

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

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

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

physical C1001 (1) C1002 (1) education

gateway lab E1102 (4) either semester

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

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

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

BMEN E3820y Biomedical engineering resonance imaging, echocardiography, blood regression), development of design prototype, laboratory, II pressure. need, approach, benefits and competition analy- 3 pts. Lab: 4. Professor Kyle. sis. Semester II: spiral develop process and test- BMEN E3910x-E3920y Biomedical engineering Statistical analysis of experimental ing, iteration and refinement of the initial design/ design, I and II measurements: analysis of variance, power prototype, and business plan development. 4 pts. Lect: 1. Lab: 3. Professors Hillman and Kyle. analysis. Circuit implementation of nerve A two-semester design sequence to be taken in BMEN E3998x or y Projects in biomedical conduction, alginate bead formation, mechanical the senior year. Elements of the design process, testing and optical strain analysis, galvanotaxis, engineering with specific applications to biomedical engineer- image segmentation and analysis of cells, 1–3 pts. Hours to be arranged. Members of the ing: concept formulation, systems synthesis, computer aided design, library resources. faculty. design analysis, optimization, biocompatibility, Independent projects involving experimental, BMEN E3830x Biomedical engineering impact on patient health and comfort, health care theoretical, computational, or engineering design laboratory, III costs, regulatory issues, and medical ethics. work. May be repeated, but no more than 3 points 3 pts. Lab: 4. Professor Kyle. Selection and execution of a project involving the of this or any other projects or research course Experimental design. Cell adhesion, membrane design of an actual engineering device or system. may be counted toward the technical elective transport, osmosis, ultrasound, design of Introduction to entrepreneurship, biomedical degree requirements as engineering technical cell encapsulation and drug delivery system, start-ups, and venture capital. Semester I: statisti- electives. respiratory impedance. Selected clinical cal analysis of detection/classification systems demonstrations: body compositions, magnetic (receiver operation characteristic analysis, logistic

engineering 2011–2012 75 biomedical engineering Program: Third and Fourth Years

Semester V Semester VI Semester VII Semester VIII

BIOL C2005 (4) BIOL C2006 (4) BMEN E3910 (4) Introductory biol. I Introductory biol. II BME design, I BMEN 3920 (4) BME design, II Required BMEN E3810 (3) BMEN E3820 (3) BMEN E3830 (3) Courses: BME laboratory, I BME laboratory, II BME laboratory, III all tracks BMEN E4010 (2)4 Ethics for BMEs BMEN E4001 (3) BMEN E4002 (3) Quantitative physiol., I Quantitative physiol., II

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

BMEN E2500 (0) BMCH E3500 (3) BMEN E4501 (3) BMEN E4502 (3) BMEN E4210 (4) Biol. transport. proc. cell and Tissue eng., I Tissue eng., II tissue Thermo. biolog. sys. or engineering1 BMEN E3320 (3) Technical elective (6) Technical elective (3) MSAE E3103 (3) Fluid biomech. Elements of mat. sci.

ENME E3113 (3) Mech. of solids BMEN E2300 (0) BMEN 4300 (3) BMEN E3320 (3) Solid biomech. biomechanics2 MECE E3301 (3) MECE E3100 (3) Fluid biomech. Thermodynamics Mech. of fluids Technical elective (3) Technical elective (6)

ELEN E4810 (3) Dig. sig. processing

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

total points 16–17 16 19 15

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

BMEN E4000x Special topics: Analysis and BMEN E4001x Quantitative physiology, I: introduced to a quantitative, engineering approach quantification of medical images cells and molecules to cellular biology and mammalian physiology. 3 pts. Lect: 3. Professor Laine. 3 pts. Lect: 3. Professor Kam. Beginning with biological issues related to the cell, Novel methods of mathematical analysis Prerequisites: CHEM C3443 or equivalent; BIOL the course progresses to considerations of the applied to problems in medical imaging. Design C2005. Physiological systems at the cellular and major physiological systems of the human body requirements for screening protocols, treatment molecular level are examined in a highly quantitative (nervous, circulatory, respiratory, renal). therapies, and surgical planning. Sensitivity and context. Topics include chemical kinetics, molecular BMEN E4010y Ethics for biomedical engineers specificity in screening mammography and chest binding and enzymatic processes, molecular motors, 2 pts. Lect: 2. Professor Loike. radiographs, computer aided diagnosis systems, biological membranes, and muscles. Prerequisite: senior status in biomedical surgical planning in orthopaedics, quantitative BMEN E4002y Quantitative physiology, II: engineering or the instructor’s permission. analysis of cardiac performance, functional organ systems Covers a wide range of ethical issues expected magnetic resonance imaging, positron emission 3 pts. Lect: 3. Professor Morrison. to confront graduates as they enter the tomography, and echocardiography data. Prerequisites or corequisites: CHEM C3443 or biotechnology industry, research, or medical equivalent; BIOL C2005-C2006. Students are careers. Topics vary and incorporate guest

engineering 2011–2012 76 speakers from Physicians and Surgeons, BMEN E4106x Anatomy laboratory: BMEN E4305y Cardiac mechanics Columbia Law School, Columbia College, and extremities 3 pts. Lect: 3. Not offered in 2011–2012. local industry. 2 pts. Lab: 2. Professor April. Prerequisites: BMEN E3310 and BMEN E3320 Prerequisites: Graduate standing in Biomedical or equivalents. Cardiac anatomy, passive BMEB W4020x Computational neuroscience: Engineering. Corequisites: BMEN E4105. myocardial constitutive properties, electrical circuits in the brain activation, ventricular pump function, ventricular- 3 pts. Lect: 3. Professor Lazar. BMEN E4107x Anatomy of the head and neck vascular coupling, invasive and noninvasive Prerequisite: ELEN E3801 or BIOL W3004. 2 pts. Lect: 2. Professor April. measures of regional and global function, models The biophysics of computation: modeling Prerequisite: Graduate standing in Biomedical for predicting ventricular wall stress. Alterations biological neurons, the Hodgkin-Huxley neuron, Engineering. This course is designed for the in muscle properties and ventricular function modeling channel conductances and synapses Biomedical Engineering graduate student resulting from myocardial infarction, heart failure, as memristive systems, bursting neurons and interested in acquiring in-depth knowledge of and left ventricular assist. central pattern generators, I/O equivalence anatomy relevant to his/her doctoral research. and spiking neuron models. Information Lectures and tutorial sessions may be taken BMEN E4340x Biomechanics of cells representation and neural encoding: stimulus with or without the associated laboratory 3 pts. Lect: 3. Professor Jacobs. representation with time encoding machines, (BMEN E4108). Prerequisites: BMEN E3320 and BMEN the geometry of time encoding, encoding with E4300 or equivalents. Survey of experiments neural circuits with feedback, population time BMEN E4108x Anatomy laboratory: head and theoretical analyses of the mechanical encoding machines. Dendritic computation: and neck behavior of individual living nonmuscle cells. elements of spike processing and neural 2 pts. Lab: 2. Professor April. Emphasis on quantitative analytic description computation, synaptic plasticity and learning Prerequisites: Graduate standing in Biomedical using continuum mechanics and molecular algorithms, unsupervised learning and spike Engineering. Corequisites: BMEN E4107. level theory from the standpoint of statistical time-dependent plasticity, basic dendritic BMEN E4210x Thermodynamics of biological mechanics and mechanical models. Mechanics integration. Projects in MATLAB. systems of erythrocytes, leukocytes, endothelial cells, and fibroblasts; models of aggregation, adhesion, ECBM E4060x Introduction to genomic 4 pts. Lect: 4. Professor Sia. locomotion, amoeba motility, cell division and information Prerequisites: CHEM C1404 and MATH morphogenesis; molecular level models of actin, 3 pts. Lect: 3. Professor Varadan. V1202. Corequisite: BIOL C2005 or equivalent. myosin, microtubules, and intermediate filaments Prerequisites: None. Introduction to the Introduction to the thermodynamics of biological and relation to mechanical properties of cells and information system paradigm of molecular systems, with a focus on connection microscopic cytoskeleton. Alternative models of cytoskeletal biology. Representation, organization, structure, molecular properties to macroscopic states. Both mechanics, foam theory, tensegrity. Analysis of function and manipulation of the biomolecular classical and statistical thermodynamics are experimental techniques including micropipette sequence of nucleic acids and proteins. The applied to biological systems; phase equilibria, studies, optical and magnetic cytometry, and role of enzymes and gene regulatory elements chemical reactions, and colligative properties. nanoindentation. in natural biological functions as well as Topics in modern biology, macromolecular in biotechnology and genetic engineering. behavior in solutions and interfaces, protein- BMEE E4400y Wavelet applications in Recombination and other macromolecular ligand binding, and the hydrophobic effect. biomedical image and signal processing processes viewed as mathematical operations BMEN E4300y Solid biomechanics 3 pts. Lect: 3. Not offered in 2011–2012. with simulation and visualization using simple 3 pts. Lect: 3. Professor Jacobs. Prerequisites: AMAP 3101 or equivalent. An computer programming. Prerequisites: ENME-MECE E3105 and ENME introduction to methods of wavelet analysis and processing techniques for the quantification of BMEN E4103x Anatomy of the thorax and E3113. This course introduces applications biomedical images and signals. Topics include: abdomen of continuum mechanics to the understanding frames and overcomplete representations, multi- 2 pts. Lect: 2. Professor April. of various biological tissues properties. The resolution algorithms for denoising and image res- Prerequisite: graduate standing in Biomedical structure, function, and mechanical properties toration, multiscale texture segmentation and clas- Engineering. This course is designed for the of various tissues in biological systems, such sification methods for computer aided diagnosis. Biomedical Engineering graduate student as blood vessels, muscle, skin, brain tissue, interested in acquiring in-depth knowledge of bone, tendon, cartilage, ligaments, etc., are BMEN E4410y Ultrasound in diagnostic anatomy relevant to his/her doctoral research. examined. The focus is on the establishment imaging Lectures and tutorial sessions may be taken of basic governing mechanical principles 3 pts. Lect: 3. Professor Konofagou. with or without the associated laboratory (BMEN and constitutive relations for each tissue. Prerequisites: MATH V1105 or equivalent, E4104). Experimental determination of various tissue Fourier analysis. Physics of diagnostic properties is introduced and demonstrated. The ultrasound and principles of ultrasound imaging BMEN E4104x Anatomy laboratory: thorax important medical and clinical implications tissue instrumentation. Propagation of plane waves and abdomen mechanical behavior are emphasized. in lossless medium; ultrasound propagation 2 pts. Lect: 2. Professor April. through biological tissues; single-element Prerequisites: Graduate standing in Biomedical BMEN E4301x Structure, mechanics, and and array transducer design; pulse-echo and Engineering. Corequisites: BMEN E4103. adaptation of bone 3 pts. Lect: 3. Professor Guo. Doppler ultrasound instrumentation, performance BMEN E4105x Anatomy of the extremities Introduction to structure, physiology, and evaluation of ultrasound imaging systems using 2 pts. Lect: 2. Professor April. biomechanics of bone. Structure, function, tissue-mimicking phantoms, ultrasound tissue Prerequisite: Graduate standing in Biomedical and physiology of skeletal bones; linear characterization; ultrasound nonlinearity and Engineering. This course is designed for the elastic properties of cortical and trabecular bubble activity; harmonic imaging; acoustic Biomedical Engineering graduate student bone; anisotropy and constitutive models of output of ultrasound systems; biological effects interested in acquiring in-depth knowledge of bone tissue; failure and damage mechanics of ultrasound. anatomy relevant to his/her doctoral research. of bone; bone adaptation and fracture Lectures and tutorial sessions may be taken healing; experimental determination of bone with or without the associated laboratory (BMEN properties; and morphological analysis of bone E4106). microstructure.

engineering 2011–2012 BMEN E4420y Biomedical signal processing regeneration by stem cells and engineered semester, students will lead discussions of 77 and signal modeling scaffolds, biomaterials: Engineering approaches recent journal articles. 3 pts. Lect: 3. Professor Sajda. in tissue regeneration, bone biology and BMEN E4570x Science and engineering of Prerequisites: APMA E3101 and ELEN E3202 development: instructive cues for tissue engineers. or instructor’s permission Fundamental concepts body fluids BMEN E4501x Tissue engineering, I: of signal processing in linear systems and 3 pts. Lect: 3. Professor Matsuoka. biomaterials and scaffold design stochastic processes. Estimation, detection, and Prerequisites: General chemistry, organic 3 pts. Lect: 3. Professor Hess. filtering methods applied to biomedical signals. chemistry, and basic calculus. Body fluids as Prerequisites: BIOL C2005-C2006; BMEN Harmonic analysis, auto-regressive model, a dilute solution of polyelectrolyte molecules E4001-E4002. An introduction to the strategies Wiener and Matched filters, linear discriminants, in water. Study of physical behavior as and fundamental bioengineering design criteria and independent components. Methods are affected by the presence of ions in surrounding in the development of biomaterials and tissue developed to answer concrete questions on environments. The physics of covalent, ionic, engineered grafts. Material structural-functional specific data sets in modalities such as ECG, and hydrogen bonds are reviewed, in relation relationships, biocompatibility in terms of material EEG, MEG, ultrasound. Lectures accompanied to the structure/properties of the body fluid. and host responses. Through discussions, by data analysis assignments using MATLAB. Selected physiological processes are examined readings, and a group design project, students in physical-chemical terms for polymers. BMEN E4430x Principles of magnetic acquire an understanding of cell-material BMEN E4590y BioMems: cellular and resonance imaging interactions and identify the parameters critical 3 pts. Lect: 3. Instructor to be announced. in the design and selection of biomaterials for molecular applications Prerequisites: APAM E3101, MATH E1210, biomedical applications. 3 pts. Lect: 3. Professor Sia. PHYS C1403 or instructors’ permission. Prerequisites: Chemistry CHEM C3443 or BMEN E4502y Tissue engineering, II: Fundamental principles of Magnetic Resonance CHEN C3545 or equivalent and MATH V1201. biological tissue substitutes Imaging (MRI), including the underlying spin Corequisite: BIOL W2005 or equivalent. 3 pts. Lect: 3. Professor Hung. physics and mathematics of image formation Topics include biomicroelectromechanical, Prerequisites: BIOL C2005-C2006, BMEN with an emphasis on the application of MRI to microfluidic, and lab-on-a-chip systems in E4001-E4002. An introduction to the strategies neuroimaging, both anatomical and functional. biomedical engineering, with a focus on cellular and fundamental bioengineering design criteria The course examines both theory and and molecular applications. Microfabrication behind the development of cell-based tissue experimental design techniques. techniques, biocompatibility, miniaturization substitutes. Topics include biocompatibility, of analytical and diagnostic devices, high- MEBM E4439x Modeling and identification of biological grafts, gene therapy-transfer, and throughput cellular studies, microfabrication for dynamic systems bioreactors. tissue engineering, and in vivo devices. 3 pts. Lect: 3. Professor Chbat. BMEN E4540y Bioelectrochemistry BMEN E4601y Cellular electricity Prerequisites: APMA E2101, ELEN E3801 or 3 pts. Lect: 3. Not offered in 2011–2012. 3 pts. Lect: 2. Lab: 1. Not offered in 2011–2012. co-requisite EEME E3601, or permission of Prerequisites: CHEM C3079 and C3443 or Bioelectricity of the cell membrane. Basis of cell instructor. Generalized dynamic system modeling equivalent. Application of electrochemical resting voltage, voltage changes that lead to the and simulation. Fluid, thermal, mechanical, kinetics to interfacial processes occurring in action potential and electrical oscillations used diffusive, electrical, and hybrid systems are biomedical systems. Basics of electrochemistry, in sensing systems. Laboratory includes building considered. Nonlinear and high order systems. electrochemical instrumentation, and relevant electronic circuits to measure capacitance of System identification problem and Linear cell and electrophysiology reviewed. Applications artificial membranes and ion pumping in frog Least Squares method. State-space and noise to interpretation of excitable and nonexcitable skin. Lab required. representation. Kalman Filter. Parameter membrane phenomena, with emphasis on estimation via prediction-error and subspace APBM E4650x Anatomy for physicists and heterogeneous mechanistic steps. Examples approaches. Iterative and bootstrap methods. of therapeutic devices created as a result of engineers Fit criteria. Wide applicability: medical, energy, bioelectrochemical studies. 3 pts. Lect: 3. Instructor to be announced. others. Matlab and Simulink environments. Prerequisites: Engineering or physics BMEN E4550x Micro- and nanostructures in background. A systemic approach to the study BMEN E4440y Physiological control systems cellular engineering 3 pts. Lect: 3. Professor Chbat. of the human body from a medical imaging point 3 pts. Lect: 3. Not offered in 2011–2012. Prerequisites: APMA E2101 and with instructor’s of view: skeletal, respiratory, cardiovascular, Prerequisites: BIOL W2005 and W2006 or approval or senior standing Dynamic system digestive, and urinary systems, breast and equivalent. Design, fabrication, and application modeling and simulation of cardiovascular, women’s issues, head and neck, and central of micro-/nanostructured systems for cell respiratory, and thermoregulatory systems. Open nervous system. Lectures are reinforced engineering. Recognition and response of and closed physiological loops. Internal and by examples from clinical two- and three- cells to spatial aspects of their extracellular external controllers: baroreflex, chemoreflex, and dimensional and functional imaging (CT, MRI, environment. Focus on neural, cardiac, ventilator. Fundamentals of time and frequency PET, SPECT, U/S, etc.). coculture, and stem cell systems. Molecular domain analyses and stability. Emulation of BMME E4702x Advanced musculoskeletal complexes at the nanoscale. normal and pathophysiological conditions. biomechanics Clinical relevance and decision support. MATLAB BMEN E4560y Dynamics of biological 3 pts. Lect: 2.5. Lab: 0.5. Not offered in and SIMULINK programming environments are membranes 2011–2012. utilized. 3 pts. Lect: 3. Not offered in 2011–2012. Advanced analysis and modeling of the BMEN E4450y Dental and craniofacial tissue Prerequisites: BIOL C2005, BMEN E4001 or musculoskeletal system. Topics include equivalent. The structure and dynamics of advanced concepts of 3D segmental kinematics, engineering biological (cellular) membranes are discussed, 3 pts. Lect: 3. Not offered in 2011–2012. musculoskeletal dynamics, experimental with an emphasis on biophysical properties. Prerequisites: MSAE E3103, BMEN E4210, E4501, measurements of joint kinematics and anatomy, Topics include membrane composition, fluidity, or equivalent. Principles of dental and craniofacial modeling of muscles and locomotion, multibody lipid asymmetry, lipid-protein interactions, bioengineering, periodontal tissue engineering: joint modeling, introduction to musculoskeletal membrane turnover, membrane fusion, transport, beyond guided tissue regeneration, craniofacial surgical simulations. lipid phase behavior. In the second half of the

engineering 2011–2012 78 BMEN E4737x Computer control of medical images. Measures of qualitative performance Neural diversity and ensemble encoding. Time instrumentation in the context of clinical imaging. Algorithms encoding machines and neural codes. Stimulus 3 pts. Lect: 2. Lab: 1. Not offered in 2011–2012. fundamental to the construction of medical recovery with time decoding machines. MIMO Prerequisite: Basic knowledge of the C images via methods of computed tomography, models of neural computation. Synaptic plasticity programming language. Acquisition and magnetic resonance, and ultrasound. Algorithms and learning algorithms. Major project(s) in presentation of data for medical interpretation. and methods for the enhancement and MATLAB. Operating principles of medical devices: quantification of specific features of clinical BMEE E6030y Neural modeling and technology of medical sensors, algorithms importance in each of these modalities. for signal analysis, computer interfacing and neuroengineering BMEN E4898y Biophotonics programming, interface design. Laboratory 3 pts. Lect: 3. Professor Sajda. 3 pts. Lect: 3. Professor Hielscher. assignments cover basic measurement Prerequisites: APMA E3101, ELEN E3801, and Prerequisites: BMEN E4894 Biomedical technology, interfacing techniques, use of BMEB W4011, or equivalent, or instructor’s imaging, PHYS C1403 Classical and quantum Labview software instrument interrogation and permission. Engineering perspective on the study waves, or instructor’s permission. This course control, automated ECG analysis, ultrasonic of multiple levels of brain organization, from provides a broad-based introduction into the measurements, image processing applied to single neurons to cortical modules and systems. field of Biophotonics. Fundamental concepts of x-ray images and CAT scans. Mathematical models of spiking neurons, neural optical, thermal, and chemical aspects of the dynamics, neural coding, and biologically-based BMEN E4738y Transduction and acquisition light-tissue interactions will be presented. The computational learning. Architectures and learning of biomedical data application of these concepts for medical therapy principles underlying both artificial and biological 3 pts. Lect: 2. Lab: 1. Not offered in 2011–2012. and diagnostics will be discussed. The course neural networks. Computational models of cortical Data transduction and acquisition systems used includes theoretical modeling of light-tissue processing, with an emphasis on the visual system. in biomedicine. Assembly of bio-transducers interactions as well as optical medical instrument Applications of principles in neuroengineering; and the analog/digital circuitry for acquiring design and methods of clinical data interpretation. neural prostheses, neuromorphic systems electrocardiogram, electromyogram, and blood and biomimetics. Course includes a computer BMEN E6001x Advanced scaffold design and pressure signals. Each small group will develop simulation laboratory. Lab required. engineering complex tissues and construct a working data acquisition board, 3 pts. Lect: 2.5. Lab: 0.5. Professor H. Lu. EEBM E6090-6099x or y Topics in which will be interfaced with a signal generator Prerequisites: BMEN E4501 or equivalent. to elucidate the dynamics of timing constraints computational neuroscience and Corequisites: BMEN E4001 or E4002. Advanced during retrieval of bio-data. Lab Required. neuroengineering biomaterial selection and biomimetic scaffold 3 pts. Lect: 2. Not offered in 2011–2012. BMEN E4750y Sound and hearing design for tissue engineering and regenerative Prerequisite: Instructor’s permission. Selected 3 pts. Lect: 3. Professor Olson. medicine. Formulation of bio-inspired design advanced topics in computational neuroscience Prerequisites: PHYS C1401 and MATH V1105- criteria, scaffold characterization and testing, and neuroengineering. Content varies from year MATH V1106. Introductory acoustics, basics of and applications on forming complex tissues or to year, and different topics rotate through the waves and discrete mechanical systems. The organogenesis. Laboratory component includes course numbers 6090-6099. mechanics of hearing—how sound is transmitted basic scaffold fabrication, characterization and through the external and middle ear to the inner in vitro evaluation of biocompatibility. Group BMEN E6301y Modeling of biological tissues ear, and the mechanical processing of sound projects target the design of scaffolds for select with finite elements within the inner ear. tissue engineering applications. 3 pts. Lect: 3. Not offered in 2011–2012. Prerequisite: MECE E6422, or ENME E6315, CBMF W4761y Computational genomics BMEN E6003x Computational modeling of or equivalent. Structure-function relations and 3 pts. Lect: 3. Professor Leslie. physiological systems linear/nonlinear constitutive models of biological Prerequisites: Working knowledge of at least one 3 pts. Lect: 3. Professor Morrison. tissues: anisotropic elasticity, viscoelasticity, programming language, and some background Prerequisites: BMEN E4001 and E4002 or porous media theories, mechano-electrochemical in probability and statistics. Computational equivalent, and APMA E4200 or equivalent. models, infinitesimal and large deformations. techniques for analyzing and understanding Advanced computational modeling and Emphasis on the application and implementation genomic data, including DNA, RNA, protein quantitative analysis of selected physiological of constitutive models for biological tissues and gene expression data. Basic concepts in systems from molecules to organs. Selected into existing finite element software packages. molecular biology relevant to these analyses. systems are analyzed in depth with an emphasis Model generation from biomedical images by Emphasis on techniques from artificial on modeling methods and quantitative analysis. extraction of tissue geometry, inhomogeneity and intelligence and machine learning. String- Topics may include cell signaling, molecular anisotropy. Element-by-element finite element matching algorithms, dynamic programming, transport, excitable membranes, respiratory solver for large-scale image based models hidden Markov models, expectation - physiology, nerve transmission, circulatory of trabecular bone. Implementation of tissue maximization, neural networks, clustering control, auditory signal processing, muscle remodeling simulations in finite element models. algorithms, support vector machines. Students physiology, data collection and analysis. with life sciences backgrounds who satisfy the MEBM E6310x-E6311y Mixture theories for EEBM E6020y Methods of computational prerequisites are encouraged to enroll. biological tissues, I and II neuroscience 3 pts. Lect: 3. Not offered in 2011–2012. BMCH E4810y Artificial organs 4.5 pts. Lect: 3. Instructor to be announced. Prerequisites: MECE E6422 and APMA E4200, 3 pts. Lect: 3. Professor Leonard. Prerequisites: BMEB W4011. Formal methods in or equivalent Development of governing Analysis and design of replacements for the computational neuroscience including methods equations for mixtures with solid matrix, heart, kidneys, and lungs. Specification and of signal processing, communications theory, interstitial fluid, and ion constituents. Formulation realization of structures for artificial organ information theory, systems and control, system of constitutive models for biological tissues. systems. identification and machine learning. Molecular Linear and nonlinear models of fibrillar and models of transduction pathways. Robust BMEN E4894x Biomedical imaging viscoelastic porous matrices. Solutions to special adaptation and integral feedback. Stimulus 3 pts. Lect: 3. Professor Hielscher. problems, such as confined and unconfined representation and groups. Stochastic and This course covers image formation, methods compression, permeation, indentation and dynamical systems models of spike generation. of analysis, and representation of digital contact, and swelling experiments.

engineering 2011–2012 BMEN E6400x Analysis and quantification of background, and practical demonstration for each are presented in the dissertation. No more 79 medical images technique will be presented. Lab required. than 12 points of credit in this course may be 3 pts. Lect: 3. Professor Laine. granted toward the degree. BMEN E8001y Current topics in Novel methods of mathematical analysis nanobiotechnology and synthetic biology BMEN E9700x or y Biomedical engineering applied to problems in medical imaging. Design 3 pts. Lect: 3. Professor Hess. seminar requirements for screening protocols, treatment Targeted toward graduate students; 0 pts. Sem: 1. Professor Kam. therapies, and surgical planning. Sensitivity and undergraduate student may participate with All matriculated graduate students are required specificity in screening mammography and chest permission of the instructor. Review and to attend the seminar as long as they are radiographs, computer aided diagnosis systems, critical discussion of recent literature in in residence. No degree credit is granted. surgical planning in orthopaedics, quantitative nanobiotechnology and synthetic biology. The seminar is the principal medium of analysis of cardiac performance, functional Experimental and theoretical techniques, critical communication among those with biomedical magnetic resonance imaging, positron emission advances. Quality judgments of scientific impact engineering interests within the University. tomography, and echocardiography data. and technical accuracy. Styles of written and Guest speakers from other institutions, Columbia BMEN E6420y Advanced microscopy: graphical communication, the peer review faculty, and students within the Department fundamentals and applications process. who are advanced in their studies frequently 3 pts. Lect: 3. Not offered in 2011–2012. offer sessions. Fri., 11:00 a.m.–12:15 p.m., 614 EEBM E9070x or y Seminar in computational Prerequisites: Physics C1401, C1402, C1403 Schermerhorn Hall neuroscience and neuroengineering or C1601, C1602, C2601 or C2801, C2802, 3 pts. Lect: 3. BMEN E9800x or y Doctoral research or equivalent (general Physics sequence). Prerequisites: Open to doctoral candidates, instruction Fundamentals of techniques including and qualified M.S. candidates with the 3–12 pts. Members of the faculty. confocal, two-photon, atomic force and electron instructor’s permission. Study of recent A candidate for the Eng.Sc.D. degree in microscopy. Application of methods to modern developments in computational neuroscience and biomedical engineering must register for biomedical imaging targets. Analysis and neuroengineering. 12 points of doctoral research instruction. interpretation of microscopy data. Enrollment Registration may not be used to satisfy the beyond the cap must be completed using an add/ BMEN E9100x or y Master’s research minimum residence requirement for the degree. drop form in consultation with class instructor. 1–6 pts. Members of the faculty. Candidates for the M.S. degree may conduct BMEN E9900x or y Doctoral dissertation BMEN E6500x Tissue and molecular an investigation of some problem in biomedical 0 pts. Members of the faculty. engineering laboratory engineering culminating in a thesis describing A candidate for the doctorate in biomedical 4 pts. Lect: 4. Professor Huang. the results of their work. No more than 6 points engineering or applied biology may be required Prerequisites: Biology BIOL C2005 and BIOL in this course may be counted for graduate to register for this course in every term after the C2006 or permission of instructor. Hands-on credit, and this credit is contingent upon the student’s course work has been completed and experiments in molecular and cellular techniques, submission of an acceptable thesis. until the dissertation has been accepted. including fabrication of living engineered tissues. Covers sterile technique, culture of mammalian BMEN E9500x or y Doctoral research cells, microscopy, basic subcloning and gel 1–6 pts. Members of the faculty. electrophoresis, creation of cell-seeded scaffolds, Doctoral candidates are required to make and the effects of mechanical loading on the an original investigation of a problem in metabolism of living cells or tissues. Theory, biomedical engineering, the results of which

engineering 2011–2012 80 Chemical Engineering 801 S. W. Mudd, MC 4721 Phone: 212-854-4453 www.cheme.columbia.edu

Chair Professors Associate Professor Adjunct Professors Sanat K. Kumar Christopher J. Durning Scott A. Banta Stanley Leshaw George W. Flynn, Chemistry Robert I. Pearlman Departmental Jingyue Ju Assistant Professor Administrator Jeffrey T. Koberstein V. Faye McNeill Adjunct Teresa Colaizzo Sanat K. Kumar Associate Professors Edward F. Leonard Aghavni Bedrossian-Omer Ben O’Shaughnessy Michael I. Hill Nicholas J. Turro, Chemistry Alan C. West

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

engineering 2011–2012 chemical nature of things and provides chemical science, engineering principles, Interfacial Engineering and 81 an insight into an exploding variety and experimental biological approaches Electrochemistry. Research efforts of new technologies that are rapidly to study problems in genomics are within the department are focused on reshaping the society we live in. actively pursued in the Department of mass transfer and reaction mechanisms Chemical Engineering in collaboration in electrochemical systems, and the Current Research Activities with the Columbia Genome Center: effects that such variables have on Science and Engineering of Polymers high-throughput DNA sequencing; novel process design and materials properties. and Soft Materials. Theoretical gene chip development and fundamental Applications of the research program and experimental studies of novel or understanding of the processes involved; include fuel cells, electrodeposition, important macromolecules and their applying the cutting-edge genomic and corrosion. Both electrochemical applications, especially surface-active technologies to study fundamental and microscopy methods are used species: ultrasonic sensor, scanning biology and for disease gene discovery. extensively for characterization. probe microscopy and reflectivity studies A significant numerical simulation of adsorption and self-assembly of highly Biophysics and Soft Matter Physics. component of the research programs branched “dendrimers” at the solid- Theoretical and experimental biophysics also exists. liquid interface, with the aim of creating of biological soft matter: actin filament novel surface coatings; fluorescence growth kinetics and its role in living Facilities for Teaching and tracer studies of molecular level mobility cell motility; DNA hybridization, melting Research in ultrathin polymer films with the aim and unzipping; DNA microarrays in The Department of Chemical Engineering of improving resolution in lithography; biotechnology; model gene circuits; DNA is continually striving to provide access to reflectivity studies and computer mobility in 2D microfluidics. Physics of state-of-the-art research instrumentation simulation of flexible polymer adsorption synthetic soft matter: nanoparticles in and computational facilities for its and the response of adsorbed polymer mesostructured polymer phases and undergraduate and graduate students, layers to imposed flows with the aim phase transitions; universal scaling postdoctoral associates, and faculty. of improving polymer processing laws in reacting polymer systems and Departmental equipment is considered to operations; optical microscopy studies polymerization phenomena; polymer- be in most cases shared, which means and numerical simulation of microporous interface adsorption phenomena; that equipment access is usually open to polymer membrane formation with polymer interfacial reactions; diffusion all qualified individuals with a need to use the aim of improving ultrafiltration of particles in thin polymer films; particular instrumentation. membrane technology; synthesis and interactions of charged polymer minigels The most extensive collection of structural characterization of bio-active with interfaces. instrumentation in the department polymer surfaces in order to realize is associated with the polymer and new in-vivo devices; contact angle, Bioinductive and Biomimetic soft matter research faculty. Faculty x-ray photoelectron spectroscopy, and Materials. The thrust of this research banded together to create a unique reflectivity analysis, and lattice model is to develop new strategies for the shared-facilities laboratory, completed simulation, of responsive polymer molecular design of polymeric and soft at the end of 2001. The shared facilities surfaces based on unique polymeric materials for biological and biomedical include a fully equipped polymer “surfactants” in order to develop “smart” applications. Ongoing research pertains synthesis lab with four fumes hoods, surface-active materials; preparation and to the development of bioactive hydrogel a 10'x16' soft wall clean room, metal IR/fluorescence characterization of DNA- coatings for applications in glucose evaporator system, a Milligen 9050 decorated surfaces for “recognition” sensors. The objective of the coatings is peptide synthesizer, and polymer thin of DNA in solution in order to further to control the tissue-sensor interactions film preparation and substrate cleaning medical diagnostic technologies; by incorporating cell-signaling motifs stations. Also installed are new, preparation and characterization into the hydrogel in such a manner that computer-controlled thermal analysis, via TEM, AFM, and reflectivity of the hydrogel induces the formation of rheometric, and light-scattering setups. nanoparticle-block copolymer new vascular tissue within the surface Specialized instrumentation for surface composites with the aim of very high coating. In this fashion, the biosensor analysis includes an optical/laser density magnetic storage media; self- can continue to operate in vivo, even if system dedicated to characterization consistent field theory of nanoparticle- there is an immune response leading to of polymer surface dynamics by Fluor- block copolymer composites; computer fibrous encapsulation. Complementary escence Recovery after Photobleaching simulation and theory of unique “living” research programs are aimed at and a PHI 5500 X-ray photoelectron polymerization processes important developing methods for patterning spectrophotometer with monochromator to synthetic polymer production and biological surfaces in order to prepare that is capable of angle-dependent biological systems; theory and simulation new biocompatible surfaces as well as depth profiling and XPS imaging. of irreversible polymer adsorption. to fabricate antigen/antibody and protein The system can also perform SIMS arrays for diagnostic applications. and ion scattering experiments. A Genomics Engineering. Research digital image analysis system for the and development of novel bioanalytical characterization of sessile and pendant reagents, systems, and processes using

engineering 2011–2012 82 drop shapes is also available for after training. The mass spectrometry 1. Prepare students for careers in the purpose of polymer surface and facility is run by students for routine industries that require technical interfacial tension measurements as samples and by a professional mass expertise in chemical engineering. well as contact angle analysis. An X-ray spectrometrist for more difficult reflectometer that can perform X-ray samples. The Chemistry Department 2. Prepare students to assume standing wave–induced fluorescence also provides access to the services of leadership positions in industries measurements is also housed in the a glass blower and machine shop and that require technical expertise in new shared equipment laboratory, along to photochemical and spectroscopic chemical engineering. with instrumentation for characterizing facilities. These facilities consist of (1) 3. Enable students to pursue the friction and wear properties of two nanosecond laser flash photolysis graduate-level studies in chemical polymeric surfaces. The laboratory instruments equipped with UV-VIS, engineering and related technical or also houses an infrared spectrometer infrared, EPR, and NMR detection; scientific fields (e.g., biomedical or (Nicolet Magna 560, MCT detector) (2) three EPR spectrometers; (3) two environmental engineering, materials with a variable angle grazing incidence, fluorescence spectrometers; (4) a single science). temperature-controlled attenuated- photon counter for analysis of the total-reflectance, transmission, and lifetimes and polarization of fluorescence 4. Provide a strong foundation for liquid cell accessories. These facilities and phosphorescence; and (5) a high- students to pursue alternative career are suitable for mid-IR, spectroscopic performance liquid chromatographic paths, especially careers in business, investigations of bulk materials as well instrument for analysis of polymer management, finance, law, medicine, as thin films. The laboratory also has molecular weight and dispersity. or education. a UV-Vis spectrometer (a Cary 50), an SLM Aminco 8000 spectrofluorimeter, Columbia Genome Center. Because of 5. Establish in students a commitment and a high-purity water system its affiliation with the Columbia Genome to life-long learning and service (Millipore Biocel) used for preparation Center (CGC), the Department of within their chosen profession and of biological buffers and solutions. Chemical Engineering also has access society. Facilities are available for cell tissue to more than 3,000 sq. ft. of space The expertise of chemical engineers culture and for experiments involving equipped with a high-throughput DNA is essential to production, marketing, biocompatibilization of materials or sequencer (Amersham Pharmacia and application in such areas as cellular engineering. In addition, gel Biotech Mega-Bace1000), a nucleic pharmaceuticals, high performance electrophoresis apparatus is available for acid synthesizer (PE Biosystems 8909 materials as in the automotive and the molecular weight characterization of Expedite Nucleic Acid/Peptide Synthesis aerospace industries, semiconductors nucleic acids. A total-internal-reflection- System), an UV/VIS spectrophotometer in the electronics industry, paints and fluorescence (TIRF) instrument with (Perkin-Elmer Lambda 40), a plastics, consumer products such as an automated, temperature-controlled fluorescence spectrophotometer (Jobin food and cosmetics, petroleum refining, flow cell has been built for dedicated Yvon, Inc. Fluorolog-3), Waters HPLC, industrial chemicals, synthetic fibers, investigations of surface processes and a sequencing gel electrophoresis and just about every bioengineering and involving fluorescently tagged biological apparatus (Life Technologies Model biotechnology area from artificial organs and synthetic molecules. The instrument S2), as well as the facilities required to biosensors. Increasingly, chemical can operate at different excitation for state-of-the-art synthetic chemistry. engineers are involved in exciting new wavelengths (typically HeNe laser, The division of DNA sequencing and technologies employing highly novel 633 nm, using Cy5 labeled nucleic chemical biology at the Columbia materials, whose unusual response at acids). Fluorescence is collected by Genome Center consists of 6,000 sq. the molecular level endows them with a highly sensitive photomultiplier tube ft. of laboratory space and equipment unique properties. Examples include and logged to a personal computer. necessary for carrying out the state-of- controlled release drugs, materials Because fluorescence is only excited the-art DNA analysis. The laboratory with designed interaction with in vivo in the evanescent wave region near an has one Amersham Pharmacia Biotech environments, “nanomaterials” for interface, signals from surface-bound MegaBace1000 sequencer, three ABI electronic and optical applications, fluorescent species can be determined 377 sequencers with complete 96 land agricultural products, and a host of with minimal background interference upgrades, a Qiagen 9600 Biorobot, a others. This requires a depth and from fluorophores in bulk solution. Hydra 96 microdispenser robot, and breadth of understanding of physical standard molecular biology equipment. and chemical aspects of materials and Chemistry Department. Access to their production that is without parallel. NMR and mass spectrometry facilities is Undergraduate Program The chemical engineering degree possible through interactions with faculty also serves as a passport to exciting members who also hold appointments careers in directly related industries as in the Chemistry Department. The NMR Chemical Engineering diverse as biochemical engineering, facility consists of a 500 MHz, a 400 The undergraduate program in chemical environmental management, and MHz, and two 300 MHz instruments that engineering at Columbia has five formal pharmaceuticals. Because the deep are operated by students and postdocs educational objectives:

engineering 2011–2012 and broad-ranging nature of the degree interests in areas other than engineering. Columbia’s Combined Plans and to 83 has earned it a high reputation across A crucial part of the junior-senior transfer students. In such cases, the society, the chemical engineering program is the 15-point (5 courses) guidance of one of the departmental degree is also a natural platform from technical elective requirement. Technical advisers in planning your program is which to launch careers in medicine, electives are science and/or technology required (contact information for the law, management, banking and finance, based and feature quantitative analysis. departmental UG advisers is listed on politics, and so on. Many students Generally, technical electives must be the department’s website: www.cheme. choose it for this purpose, to have a 3000 level or above but there are a columbia.edu). firm and respected basis for a range few exceptions: PHYS C1403, PHYS Columbia’s program in chemical of possible future careers. For those C2601, BIOL C2005, BIOL C2006, and engineering leading to the B.S. degree interested in the fundamentals, a career BIOL W2501. The technical electives are is fully accredited by the Engineering of research and teaching is a natural subject to the following constraints: Accreditation Commission of the continuation of undergraduate studies. Accreditation Board for Engineering and The first and sophomore years • One technical elective must be within Technology (ABET). of study introduce general principles SEAS but taken outside of chemical of science and engineering and engineering (that is, a course with a Requirements for a Minor in designator other than BMCH, CHEN, include a broad range of subjects in Chemical Engineering CHEE, or CHAP). the humanities and social sciences. See page 191. Although the program for all engineering • Two technical electives must be within students in these first two years is to chemical engineering (i.e., with the Requirements for a Minor in some extent similar, there are a few designator BMCH, CHEN, CHEE, or Biomedical Engineering important differences for chemical CHAP). Students majoring in chemical engineering majors. The Professional engineering who wish to include in Engineering Elective, usually taken in • The technical electives must include their records a minor in biomedical Semester II, is designed to provide an 9 points (3 courses) of “advanced engineering may do so by taking BMEN overview of an engineering discipline. natural science” course work, which E4001 or E4002; BIOL C2005; BMEN Those wishing to learn about chemical can include chemistry, physics, E4501 and E4502; and any one of engineering are encouraged to take biology, and certain engineering several chemical engineering courses CHEN E1040: Molecular engineering courses. Qualifying engineering approved by the BME Department. See and product design, taught by the courses are determined by Chemical also, Minor in Biomedical Engineering, Chemical Engineering Department. Engineering Department advisers. page 190. Students who major in chemical engineering are not required to take The junior-senior technical electives computer science or programming, provide the opportunity to explore Graduate Programs since they receive instructional use of new interesting areas beyond the core The graduate program in chemical computational methods in their junior requirements of the degree. Often, engineering, with its large proportion year. They should take CHEN E3100: students satisfy the technical electives of elective courses and independent Material and energy balances in their by taking courses from another SEAS research, offers experience in any sophomore year (see table on page 88). department in order to obtain a minor of the fields of departmental activity In the junior-senior sequence one from that department. Alternately, you mentioned in previous sections. For specializes in the chemical engineering may wish to take courses in several both chemical engineers and those major. The table on page 89 spells new areas, or perhaps to explore with undergraduate educations in out the core course requirements, familiar subjects in greater depth, or you other related fields such as physics, which are split between courses may wish to gain experience in actual chemistry, and biochemistry, the Ph.D. emphasizing engineering science and laboratory research. Up to 6 points of program provides the opportunity to those emphasizing practical and/or CHEN E3900: Undergraduate research become expert in research fields central professional aspects of the discipline. project may be counted toward the to modern technology and science. Throughout, skills required of practicing technical elective content. (Note that engineers are developed (e.g., writing if more than 3 points of research is M.S. Degree pursued, an undergraduate thesis is and presentation skills, competency with The requirements are (1) the core required.) computers). courses: Chemical process analysis The program details discussed The table also shows that a (CHEN E4010), Transport phenomena, above apply to undergraduates who significant fraction of the junior-senior III (CHEN E4110), and Statistical are enrolled at Columbia as freshmen program is reserved for electives, both mechanics (CHAP E4120); and (2) 21 and declare the chemical engineering technical and nontechnical. Nontechnical points of 4000- or 6000-level courses, major in the sophomore year. electives are courses that are not approved by the graduate coordinator However, the chemical engineering quantitative, such as those taught in or research adviser, of which up to program is designed to be readily the humanities and social sciences. 6 may be Master’s research (CHEN These provide an opportunity to pursue accessible to participants in any of

engineering 2011–2012 84 chemical engineering: first and second Years

Semester i Semester iI Semester iII Semester iV

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

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

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

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

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

Professional engineering

required required tech E lectives elective (3)1

CHEN E3100 (4)3 chem. eng. Material and energy requirement balances

computer science

physical C1001 (1) C1002 (1) education

gateway lab E1102 (4) either semester

total points4 16.5 16.5 17.5 17

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

9400). Students with undergraduate undergraduate courses in the bachelor’s core courses (CHEN E4010, E4110, preparation in physics, chemistry, degree program. CHAP E4120); (2) pass a qualifying biochemistry, pharmacy, and related exam; (3) defend a proposal of research fields may take advantage of a special Doctoral Degrees within twelve months of passing the two-year program leading directly The Ph.D. and D.E.S. degrees have qualifying exam; (4) defend their thesis; to the master’s degree in chemical essentially the same requirements. All and (5) satisfy course requirements engineering. This program enables such students in a doctoral program must beyond the three core courses. For students to avoid having to take all (1) earn satisfactory grades in the three detailed requirements, please consult

engineering 2011–2012 85 chemical engineering: Third and Fourth Years

Semester V Semester VI Semester VII Semester VIII

CHEN E3120 (3) Transp. phenomena, II CHEN E3110 (3) Transp. phenomena, I CHEN E3210 (3) CHEN E4500 (4) Chem. eng. Process and product CHEE E3010 (3) thermodynamics design, I CHEN E4510 (4) Required Principles of chem. Process and product Courses eng. thermodynamics CHEN E4230 (3) CHEE E4140 (3) design, II Reaction kinetics and Eng. separations CHEN E3020 (2) reactor design processes Analysis of chem. eng. problems, I CHEN E3220 (2) Analysis of chem. eng. problems, II

CHEN C3543 (3)1 CHEN E4300 (2) CHEN 3810 (3) Required labs Org. chem. lab Chem. eng. control Chem. eng. lab

nontech 3 points 3 points 3 points

tech2 3 points 3 points 3 points 6 points required E lectives

total points (normal track) 17 17 15 13

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

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

engineering 2011–2012 86 with particular emphasis on interfacial understanding of what the central and requirements for their doctorates. properties and materials with important fascinating biological issues are. Students may take individual courses related applications. Synthetic polymers CHAP E4120: Statistical mechanics so long as they satisfy prerequisite are by far the most important material in CHEN E6920: Physics of soft matter requirements or have the instructor’s this class. BIOC G6300: Biochemistry/molecular biology— permission. All lecture courses in the eukaryotes, I program are available through the BIOC G6301: Biochemistry/molecular biology— CHEE E4252: Introduction to surface and colloid eukaryotes, II Columbia Video Network, which offers a chemistry CHEN E4750: The genome and the cell certificate for those students completing CHEN E4620: Introduction to polymers and soft CMBS G4350: Cellular molecular biophysics a prescribed set of the courses. materials The course Introduction to genomic CHEN E4640: Polymer surfaces and interfaces Genomic Engineering. Genomic CHEN E6620y: Physical chemistry of macro- information science and technology molecules engineering may be defined as the (ECBM E4060) provides the essential CHEN E6910: Theoretical methods in polymer development and application of concepts of the information system physics novel technologies for identifying and paradigm of molecular biology and CHEN E6920: Physics of soft matter evaluating the significance of both genetics. Principles of genomic selected and all nucleotide sequences technology (CHEN E4700) provides Biophysics and Soft Matter Physics. in the genomes of organisms. An students with a solid basis for Soft matter denotes polymers, gels, interdisciplinary course concentration understanding both the principles that self-assembled surfactant structures, in genomic engineering is available to underlie genomic technologies and colloidal suspensions, and many other graduate students, and to selected how these principles are applied. The complex fluids. These are strongly undergraduate students. The National Genomics sequencing laboratory (CHEN fluctuating, floppy, fluid-like materials that Science Foundation is sponsoring the E4760) provides hands-on experience can nonetheless exhibit diverse phases development of this concentration, in high-throughput DNA sequencing, with remarkable long-range order. In the which is believed to be the first of its as conducted in a bioscience research last few decades, statistical physics has kind. Courses in the concentration equip laboratory. The genome and the cell achieved a sound understanding of the students in engineering and computer (CHEN E4750) conveys a broad but scaling and universality characterizing science to help solve technical problems precise, organized, and quantitative large length scale properties of much encountered in the discovery, assembly, overview of the cell and its genome: synthetic soft condensed matter. More organization, and application of genomic how the genome, in partnership with recently, ideas and techniques from soft information. The courses impart an extragenomic stimuli, influences the condensed matter physics have been understanding of the fundamental goals behavior of the cell and how mechanisms applied to biological soft matter such and problems of genomic science and within the cell enable genomic regulation. as DNA, RNA, proteins, cell membrane gene-related intracellular processes; Computational genomics (CBMF W4761) surfactant assemblies, actin and tubulin elucidate the physical, chemical, and introduces students to basic and structures, and many others. The aim is instrumental principles available to advanced computational techniques for to shed light on (1) fundamental cellular extract sequence information from the analyzing genomic data. processes such as gene expression genome; and teach the concepts used Interested parties can obtain or the function of cellular motors and to organize, manipulate, and interrogate further information, including a list of (2) physical mechanisms central to the genomic database. cognate courses that are available the exploding field of biotechnology The concentration consists of five and recommended, from Professor involving systems such as DNA courses that address the principal areas Leonard ([email protected]). microarrays and methods such as of genomic technology: sequencing genetic engineering. The practitioners in and other means of acquiring genomic Interfacial Engineering and this highly interdisciplinary field include information; bioinformatics as a means Electrochemistry. Electrochemical physicists, chemical engineers, biologists, of assembling and providing structured processes are key to many alternative biochemists, and chemists. access to genomic information; energy systems (batteries and fuel The “Biophysics and Soft Matter” and methods of elucidating how cells), to electrical and magnetic- concentration is closely related to the genomic information interacts with the device manufacturing (interconnects “Science and Engineering of Polymers developmental state and environment and magnetic- storage media), and and Soft Materials” concentration, of cells in order to determine their to advanced materials processing. but here greater emphasis is placed behavior. Professor E. F. Leonard Electrochemical processes are also on biological materials and cellular directs the program and teaches CHEN involved in corrosion and in some biophysics. Both theory and experiment E4750. The other instructors are Profs. waste-treatment systems. Key are catered to. Students will be D. Anastassiou (ECBM E4060), Jingyue employers of engineers and scientists introduced to statistical mechanics and Ju (CHEN E4700, E4730), and C. Leslie with knowledge of electrochemical/ its application to soft matter research (CBMF W4761). The departments of interfacial engineering include and to cellular biophysics. In parallel, Chemical, Biomedical, and Electrical companies from the computer, the student will learn about genomics Engineering and of Computer automotive, and chemical industries. and cellular biology to develop an Science credit these courses toward Knowledge of basic electrochemical

engineering 2011–2012 principles, environmental sciences, and/ CHEN E3020x Analysis of chemical CHEN E3210y Chemical engineering 87 or materials science can be useful to a engineering problems, I thermodynamics career in this area. 2 pts. Lect: 1. Lab: 1. Professor Ortiz. 3 pts. Lect: 3. Professor Kumar. Prerequisites: vector calculus, ordinary Prerequisites: CHEE E3010 and CHEN E3100. differential equations. Corequisites: CHEN Corequisite: CHEN E3220. This course deals CHEN E4201: Engineering applications of E3010, E3110. Computational solutions with fundamental and applied thermodynamic electrochemistry of chemical engineering problems in principles that form the basis of chemical CHEN E4252: Introduction to surface and colloid thermodynamics, transport phenomena, and engineering practice. Topics include phase science reaction design. equilibria, methods to treat ideal and nonideal CHEN E6050: Advanced electrochemistry mixtures, and estimation of properties using CHEN E3900: Undergraduate research project CHEN E3100x Material and energy balances computer-based methods. 4 pts. Lect: 4. Professor McNeill. Bioinductive and Biomimetic Prerequisites: First-year Chemistry and Physics CHEN E3220y Analysis of chemical Materials. This is a rapidly emerging or equivalents. This course serves as an engineering problems, II area of research, and the department’s introduction to concepts used in the analysis 2 pts. Lect: 1. Lab: 1. Professor Ortiz. of chemical engineering problems. Rigorous Prerequisite: CHEN E3020. Corequisites: course concentration is under analysis of material and energy balances on CHEN E3210, E3120. Computational development. At present, students open and closed systems is emphasized. An solutions of chemical engineering problems in interested in this area are recommended introduction to important processes in the thermodynamics, transport phenomena, and to attend Polymer surfaces and chemical and biochemical industries is provided. reaction design. interfaces (CHEN E4640); and Physical CHEN E3110x Transport phenomena, I BMCH E3500y Transport in biological chemistry of macromolecules (CHEN 3 pts. Lect: 3. Professor Hill. systems E6620). Other courses in the “Science Prerequisites: mechanics, vector calculus, ordinary 3 pts. Lect: 3. Not offered in 2011–2012. and Engineering of Polymers and differential equations. Corequisite: CHEN E3020. Prerequisites: CHEM C3443 and MATH E1210. Soft Materials” concentration are Analysis of momentum and energy transport Corequisites: BIOL C2005. Convective and also relevant. When complete, the processes at molecular, continuum, and system diffusive movement and reaction of molecules concentration will include courses scales for systems of simple fluids (gases and low- in biological systems. Kinetics of homogeneous molecular-weight liquids). Molecular-level origins of directly addressing biomaterials and and heterogeneous reactions in biological fluid viscosity, continuum fluid mechanics analysis environments. Mechanisms arid models of immunological response. of laminar flows, and the resulting dimensionless transport across membranes. Convective correlations of kinematic and mechanical diffusion with and without chemical reaction. Courses in Chemical characteristics of a system needed for engineering Diffusion in restricted spaces. Irreversible design (e.g., friction factor vs. Reynolds number thermodynamic approaches to transport and Engineering correlations). Molecular origins of fluid conductivity, reaction in biological systems. See also section for Biomedical continuum heat transfer analysis, and the resulting Engineering. Note: Check the correlations of a system’s thermal characteristics CHEN E3810y Chemical engineering laboratory department website for the most current useful in engineering design (e.g., Nusselt number 3 pts. Lab: 3. Professor Banta. course offerings and descriptions. correlations). Examples are reviewed of analyses typical in chemical engineering technologies. Prerequisites: Completion of core chemical CHEN E1040y Molecular engineering and Essential mathematical methods are reviewed or engineering curricula through the fall semester product design introduced in context. of senior year (includes: CHEN E3110, E3120, 3 pts. Lect: 3. Not offered in 2011–2012. E4230, E3100, E3010, E3210, E4140, E4500), or Prerequisites: None. An introductory course CHEN E3120y Transport phenomena, II instructor’s permission. The course emphasizes intended to expose students to Chemical 3 pts. Lect: 3. Professor Durning. active, experiment-based resolution of open- Engineering. Examines the ways in which Prerequisite: CHEN E3110. Corequisite: CHEN ended problems involving use, design, and chemical and biological sciences are interpreted E3220. Developments in Transport I are optimization of equipment, products, or materials. through analytical, design, and engineering extended to handle turbulence. Topics include: Under faculty guidance students formulate, frameworks to generate products that enhance Turbulent energy cascade, wall-bounded carry out, validate, and refine experimental human endeavor. Students are introduced to turbulent shear flow, time-averaging of the procedures, and present results in oral and the culture of chemical engineering and the equations of change, Prandtl’s mixing length written form. The course develops analytical, wide variety of chemical engineering practices, hypothesis for the Reynolds stress, the Reynolds communications, and cooperative problem- through lectures by department faculty and analogy, continuum modeling of turbulent flows solving skills in the context of problems that practicing chemical engineers, trips to industrial and heat transfer processes, friction factor, span from traditional, large scale separations facilities, reverse-engineering of chemical and Nusselt number correlations for turbulent and processing operations to molecular level products, and a chemical design competition. conditions. Then, macroscopic (system-level) design of materials or products. Sample projects mass, momentum, and energy balances for one- include: scale up of apparatus, process control, CHEE E3010x Principles of chemical component systems are developed and applied chemical separations, microfluidics, surface engineering thermodynamics to complex flows and heat exchange processes. engineering, molecular sensing, and alternative 3 pts. Lect: 3. Professor Castaldi. The final part focuses on mass transport in energy sources. Safety awareness is integrated Prerequisite: CHEM C1403. Corequisite: mixtures of simple fluids: Molecular-level origins throughout the course. CHEN E3020. Introduction to thermodynamics. of diffusion phenomena, Fick’s law and its multi- Fundamentals are emphasized: the laws of component generalizations, continuum-level CHEN E3900x and y Undergraduate research thermodynamics are derived and their meaning framework for mixtures and its application to project explained and elucidated by applications to diffusion dominated processes, diffusion with 1–6 pts. Members of the faculty. engineering problems. Pure systems are treated, chemical reaction, and forced/free convection Candidates for the B.S. degree may conduct followed by an introduction to mixtures and mass transport. an investigation of some problem in chemical phase equilibrium. engineering or applied chemistry or carry out

engineering 2011–2012 88 a special project under the supervision of the CHEE E4140x Engineering separations CHEN E4330y Advanced chemical kinetics staff. Credit for the course is contingent upon processes 3 pts. Lect: 3. Professor McNeill. the submission of an acceptable thesis or final 3 pts. Lect: 3. Professor Park. Prerequisite: CHEN E4230 or instructor’s report. No more than 6 points in this course may Prerequisites: CHEN E3100, E3120, and permission. Complex reactive systems. be counted toward the satisfaction of the B.S. E3210 or permission of instructor. Design Catalysis. Heterogeneous systems, with an degree requirements. and analysis of unit operations employed in emphasis on coupled chemical kinetics and chemical engineering separations. Fundamental transport phenomena. Reactions at interfaces CHEN E4010x Chemical process analysis aspects of single and multistaged operations (surfaces, aerosols, bubbles). Reactions in 3 pts. Lect: 3. Not offered in 2011–2012. using both equilibrium and rate-based methods. solution. Open to undergraduates only with the instructor’s Examples include distillation, absorption and permission. Application of selected mathematical CHEN E4500x Process and product design, I stripping, extraction, membranes, crystallization, methods to solution of chemical engineering 4 pts. Lect: 4. Professors Hill, Kumar, and bioseparations, and environmental applications. problems. Leshaw. CHEN E4201x Engineering applications of Prerequisites: CHEE E4140, CHEN E3100. An CHEN E4020x Protection of industrial and electrochemistry introduction to the process engineering function. intellectual property 3 pts. Lect: 3. Not offered in 2011–2012. The design of chemical process, process 3 pts. Lect: 3. Professor Pearlman. Prerequisites: Physical chemistry and a course equipment, and plants and the economic and To expose engineers, scientists and technology in transport phenomena. Engineering analysis ecological evaluation of the chemical engineering managers to areas of the law they are most of electrochemical systems, including electrode project. Use of statistics to define product quality likely to be in contact with during their career. kinetics, transport phenomena, mathematical is illustrated with case studies. Recitation section Principals are illustrated with various case modeling, and thermodynamics. Common required. studies together with active student participation. experimental methods are discussed. Examples CHEN E4510y Process and product design, II CHEE E4050y Principles of industrial from common applications in energy conversion 4 pts. Lect: 4. Professors Hill and Leonard. and metallization are presented. electrochemistry Prerequisite: CHEN E4500. Students carry out a 3 pts. Lect: 3. Not offered in 2011–2012. CHEN E4230y Reaction kinetics and reactor semester long process or product design course Prerequisites: CHEE E3010 or equivalent. A design with significant industrial involvement. The presentation of the basic principle underlying 3 pts. Lect: 3. Professor Leshaw. project culminates with a formal written design electrochemical processes. Thermodynamics, Prerequisites: CHEE E3010. Reaction report and a public presentation. Recitation electrode kinetics, and ionic mass transport. kinetics, applications to the design of batch section required. Examples of industrial and environmental and continuous reactors. Multiple reactions, applications illustrated by means of laboratory CHEE E4530y Corrosion of metals nonisothermal reactors. Analysis and modeling of experiments: electroplating, refining, and 3 pts. Lect: 3. Professor Duby. reactor behavior. Recitation section required. winning in aqueous solutions and in molten Prerequisite: CHEE E3010 or equivalent. The salts; electrolytic treatment of wastes; primary, CHEE E4252x Introduction to surface and theory of electrochemical corrosion, corrosion secondary, and fuel cells. colloid chemistry tendency, rates, and passivity. Application to 3 pts. Lect: 3. Professor Somasundaran. various environments. Cathodic protection and CHEN E4110x Transport phenomena, III Prerequisites: Elementary physical chemistry. coatings. Corrosion testing. 3 pts. Lect: 3. Professor Durning. Thermodynamics of surfaces, properties Prerequisite: CHEN E3120. Tensor analysis; CHEN E4600x Atmospheric aerosols of surfactant solutions and surface films, kinematics of continua; balance of laws for one- 3 pts. Lect: 3. Professor McNeill. electrostatic and electrokinetic phenomena at component media; constituitive laws for free Prerequisite: CHEN E3120 or instructor’s interfaces, adsorption; interfacial mass transfer energy and stress in one-component media; permission. Atmospheric aerosols and their and modern experimental techniques. exact and asymptotic solutions to dynamic effects on atmospheric composition and problems in fluids and solids; balance laws for CHEN E4300x Chemical engineering control climate. Major topics are aerosol sources and mixtures; constitutive laws for free energy, stress 2 pts. Lab: 2. Professors Bedrossian and West. properties, field and laboratory techniques and diffusion fluxes in mixtures; solutions to Prerequisites: Material and energy balances. for characterization, gas-aerosol interactions, dynamic problems in mixtures. Ordinary differential equations including Laplace secondary organic aerosols, aerosol direct and transforms. Reactor Design. An introduction to indirect effects on climate. CHAP E4120x Statistical mechanics process control applied to chemical engineering 3 pts. Lect: 3. Professor O’Shaughnessy. CHEN E4620x Introduction to polymers and through lecture and laboratory. Concepts include Prerequisites: CHEE E3010 or equivalent soft materials the dynamic behavior of chemical engineering thermodynamics course, or instructor’s 3 pts. Lect: 3. Professor Durning. systems, feedback control, controller tuning, and permission. Fundamental principles and Prerequisite: An elementary course in physical process stability. underlying assumptions of statistical mechanics. chemistry or thermodynamics. Organic Boltzmann’s entropy hypothesis and its CHEN E4320x Molecular phenomena in chemistry, statistics, calculus and mechanics restatement in terms of Helmholtz and Gibbs chemical engineering are helpful, but not essential. An introduction free energies and for open systems. Correlation 4 pts. Lect: 4. Professor O’Shaughnessy. to the chemistry and physics of soft material times and lengths. Exploration of phase space This course located strategically at the end of the systems (polymers, colloids, organized and observation timescale. Correlation functions. curriculum is intended to provide students with surfactant systems and others), emphasizing the Fermi-Dirac and Bose-Einstein statistics. a molecular basis for the engineering concepts connection between microscopic structure and Fluctuation-response theory. Applications to ideal covered in the curriculum. It is meant to both macroscopic physical properties. To develop gases, interfaces, liquid crystals, microemulsions validate the basic science and math foundations an understanding of each system, illustrative and other complex fluids, polymers, Coulomb developed earlier and to stimulate the student experimental studies are discussed along with gas, interactions between charged polymers and toward applying modern molecular concepts of basic theoretical treatments. High molecular charged interfaces, ordering transitions. chemical engineering that will define their future. weight organic polymers are discussed first Recitation section required. (basic notions, synthesis, properties of single polymer molecules, polymer solution and blend thermodynamics, rubber and gels). Colloidal

engineering 2011–2012 systems are treated next (dominant forces in Chemical and physical aspects of genome for engineering students to develop the hands-on 89 colloidal systems, flocculation, preparation and structure and organization, genetic information skills in conducting genomics research. manipulation of colloidal systems) followed by a flow from DNA to RNA to protein. Nucleic acid CHEN E4800x Protein engineering discussion of self-organizing surfactant systems hybridization and sequence complexity of DNA 3 pts. Lect: 3. Professor Banta. (architecture of surfactants, micelles and and RNA. Genome mapping and sequencing Prerequisite: CHEN E4230, may be taken surfactant membranes, phase behavior). methods. The engineering of DNA polymerase concurrently, or the instructor’s permission. for DNA sequencing and polymerase chain CHEN E4640y Polymer surfaces and Fundamental tools and techniques currently reaction. Fluorescent DNA sequencing and used to engineer protein molecules. Methods interfaces high-throughput DNA sequencer development. used to analyze the impact of these alterations 3 pts. Lect: 3. Not offered in 2011–2012. Construction of gene chip and micro array for on different protein functions with specific Prerequisite: CHEN E4620 or consent of gene expression analysis. Technology and emphasis on enzymatic catalysis. Case studies instructor. A fundamental treatment of the biochemical approach for functional genomics reinforce concepts covered, and demonstrate thermodynamics and properties relating to analysis. Gene discovery and genetics database the wide impact of protein engineering research. polymer surfaces and interfaces. Topics include search method. The application of genetic Application of basic concepts in the chemical the characterization of interfaces, theoretical database for new therapeutics discovery. modeling of interfacial thermodynamics and engineering curriculum (reaction kinetics, structure, and practical means for surface CHEN E4740x Biological transport and rate mathematical modeling, thermodynamics) modification. phenomena, II to specific approaches utilized in protein 3 pts. Lect: 3. Not offered in 2011–2012. engineering. CHEN E4645x Inorganic polymers, hybrid Prerequisites: Any two of the following: BMCH E4810y Artificial organs materials, and gels CHEN E3110; BIOL C2005; CHEN E3210 or 3 pts. Lect: 3. Professor Leonard. 3 pts. Lect: 3. Not offered in 2011–2012. BMCH E3500. Analysis of transport and rate Analysis and design of replacements for the Prerequisite: Organic chemistry. The focus of the phenomena in biological systems and in the heart, kidneys, and lungs. Specification and first art of the course, taught by Prof. Mark is on design of biomimetic transport-reaction systems realization of structures for artificial organ the preparation, characterization, and applications for technological and therapeutic applications. systems. of inorganic polymers, with a heavy emphasis on Modeling of homogeneous and heterogeneous those based on main-group elements. Main topics biochemical reactions. The Bases of biological CHEN E6050x Advanced electrochemistry are characterization methods, polysiloxanes, transport: roles of convection, ordinary diffusion, 3 pts. Lect: 3. Not offered in 2011–2012. polysilanes, polyphosphazenes, ferrocene- forced diffusion. Systems where reaction and Prerequisite: Instructor’s permission. An based polymers, other phosphorous-containing transport interact strongly. Applications to natural advanced overview of the fundamentals of polymers, boron-containing polymers, preceramic and artificial tissue beds, tumor modeling, electrochemistry, with examples taken from inorganic polymers, and inorganic-organic hybrid controlled release, natural and artificial organ modern applications. An emphasis is placed on composites. The focus of the second part of the function. mass transfer and scaling phenomena. Principles course, taught by Prof. Koberstein is on gels, are reinforced through the development of both physical and chemical. Topics will include CHEN E4750x The genome and the cell mathematical models of electrochemical gel chemistry, including epoxies, polyurethanes, 3 pts. Lect: 3. Not offered in 2011–2012. systems. Course projects will require computer polyesters, vinyl esters and hydrogels, as well as Prerequisites: BIOL C2005, MATH E1210 simulations. The course is intended for advanced theoretical methods used to characterize the gel The utility of genomic information lies in its graduate students, conducting research involving point and gel properties. capacity to predict the behavior of living cells in electrochemical technologies. physiological, developmental, and pathological CHEN E4660y Biochemical engineering situations. The effect of variations in genome CHEE E6220y Equilibria and kinetics in 3 pts. Lect: 3. Not offered in 2011–2012. structure between individuals within a species, hydrometallurgical systems Prerequisite: BMEN E4001 or the equivalent. including those deemed healthy or diseased, 3 pts. Lect: 3. Professor Duby. Engineering of biochemical and microbiological and among species, can be inferred statistically Prerequisite: Instructor’s permission. An reaction systems. Kinetics, reactor analysis, and by comparisons of sequences with behaviors, advanced overview of the fundamentals of design of batch and continuous fermentation and and mechanistically, by studying the action of electrochemistry, with examples taken from enzyme processes. Recovery and separations in molecules whose structure is encoded within modern applications. An emphasis is placed on biochemical engineering systems. the genome. This course examines known mass transfer and scaling phenomena. Principles CHEN E4680x Soft materials laboratory mechanisms that elucidate the combined effect are reinforced through the development of 3 pts. Lect/lab: 3. Not offered in 2011–2012. of environmental stimulation and genetic makeup mathematical models of electrochemical Prerequisites: Two years of undergraduate on the behavior of cells in homeostasis, disease systems. Course projects will require computer science courses and the instructors’ permission. states, and during development, and includes simulations. The course is intended for advanced Corequisites: Limited to 15 students. assessments of the probable effect of these graduate students, conducting research involving Covers modern characterization methods behaviors on the whole organism. Quantitative electrochemical technologies. for soft materials (polymers, complex fluids, models of gene translation and intracellular CHEE E6252y Applied surface and colloid biomaterials). Techniques include differential signal transduction will be used to illustrate scanning calorimetry, dynamic light scattering, switching of intracellular processes, transient and chemistry gel permeation chromatography, rheology, and permanent gene activation, and cell commitment, 3 pts. Lect: 2. Lab: 3. Professor Somasundaran. spectroscopic methods. Team-taught by several development, and death. Prerequisites: CHEN 4252. Applications of surface chemistry principles to wetting, faculty and open to graduate and advanced CHEN E4760y Genomics sequencing undergraduate students. Lab required. flocculation, flotation, separation techniques, laboratory catalysis, mass transfer, emulsions, foams, CHEN E4700x Principles of genomic 3 pts. Lect: 1. Lab: 2. Professor Ju. aerosols, membranes, biological surfactant technologies Prerequisites: Undergraduate level biology, systems, microbial surfaces, enhanced oil 3 pts. Lect: 3. Professor Ju. organic chemistry, and instructor’s permission. recovery, and pollution problems. Appropriate Prerequisites: Undergraduate-level biology, The chemical, biological and engineering individual experiments and projects. Lab organic chemistry, and instructor’s permission. principles involved in the genomics sequencing required. process will be illustrated throughout the course

engineering 2011–2012 90 CHEN E6620y Physical chemistry of in DNA. Polyelectrolytes, charged biopolymers, CHEN E9500x and y–S9500 Doctoral research macromolecules DNA charge-induced condensation. 1–15 pts. Members of the faculty. 3 pts. Lect: 3. Professor Koberstein. Prerequisites: The qualifying examinations for CHEN E8100y Topics in biology Prerequisite: CHEN E4620 or the instructor’s the doctorate. Open only to certified candidates 3 pts. Lect: 3. Professor O’Shaughnessy. permission. Modern studies of static and for the Ph.D. and Eng.Sc.D. degrees. Doctoral Prerequisites: Instructor’s permission. This dynamic behavior in macromolecular systems. candidates in chemical engineering are required research seminar introduces topics at the Topics include single-chain behavior adsorption, to make an original investigation of a problem forefront of biological research in a format and solution thermodynamics, the glass transition, in chemical engineering or applied chemistry, language accessible to quantitative scientists diffusion, and viscoelastic behavior. The the results of which are presented in their and engineers lacking biological training. molecular understanding of experimentally dissertations. No more than 15 points of credit Conceptual and technical frameworks from both observed phenomena is stressed. toward the degree may be granted when the biological and physical science disciplines are dissertation is accepted by the department. CHEN E6630x Special topics in soft utilized. The objective is to reveal to graduate condensed matter students where potential lies to apply techniques CHEN E9600x and y Advanced research 3 pts. Lect: 3. Not offered in 2011–2012. from their own disciplines to address pertinent problems Tutorial lectures on selected topics in soft biological questions in their research. Classes 2–10 pts. Members of the faculty. condensed matter. entail reading, criticism and group discussion of Prerequisites: Recommendation of the professor research papers and textbook materials providing concerned and approval of the master’s research CHEN E6910y Theoretical methods in overviews to various biological areas including: department. For postdoctoral students and other polymer physics evolution, immune system, development and cell qualified special students who wish to pursue 3 pts. Lect: 3. Not offered in 2011–2012. specialization, the cytoskeleton and cell motility, research under the guidance of members of the Prerequisite: CHAP 4120 or equivalent statistical DNA transcription in gene circuits, protein department. Not open to undergraduates or to mechanics course, or instructor’s permission. networks, recombinant DNA technology, aging, candidates for the degrees of Ch.E.,M.S., Ph.D., Modern methods for understanding polymeric and gene therapy. or Eng.Sc.D. liquids and critical phenomena are introduced and applied in detail. Scaling and universality. CHEN E9000x and y Chemical engineering CHEN E9800x and y Doctoral research Relationship of high polymer physics to critical colloquium instruction phenomena. Landau theory, self-consistent field 0 pts. Col: 1. Professor Banta. 3, 6, 9 or 12 pts. Members of the faculty. method. Scaling approach. Renormalization All graduate students are required to attend the A candidate for the Eng.Sc.D. degree in group theory. Epsilon expansion for polymer and department colloquium as long as they are in chemical engineering must register for 12 points other critical exponents. Applications to polymer residence. No degree credit is granted. of doctoral research instruction. Registration in statics and dynamics, and to other complex fluids. CHEN E9800 may not be used to satisfy the CHEN E9400x and y Master’s research minimum residence requirement for the degree. CHEN E6920y Physics of soft matter 1–6 pts. Members of the faculty. 3 pts. Lect: 3. Not offered in 2011–2012. Prescribed for M.S. and Ch.E. candidates; CHEN E9900x and y–S9900 Doctoral Prerequisites: Instructor’s permission. Physics elective for others with the approval of the dissertation of polymers, biopolymers (especially DNA), Department. Degree candidates are required 0 pts. Members of the faculty. membranes, gels, and other types of soft matter. to conduct an investigation of some problem in Open only to certified doctoral candidates. A Statistical mechanics, scaling theory, self- chemical engineering or applied chemistry and candidate for the doctorate in chemical engineering consistent field theory; experimental surveys. to submit a thesis describing the results of their may be required to register for this course in every Dilute, semidilute, and concentrated polymer work. No more than 6 points in this course may term after the student’s course work has been solutions. Mesophases and self-assembly in be counted for graduate credit, and this credit is completed, and until the dissertation has been soft matter. Polymers at interfaces, polymer- contingent upon the submission of an acceptable accepted. membrane interactions. Fluctuating double helix thesis. The concentration in pharmaceutical models of DNA, DNA melting, pattern recognition engineering requires a 2-point thesis internship.

engineering 2011–2012 civil engineering and engineering mechanics 91 610 S. W. Mudd, MC 4709 Phone: 212-854-3143 www.civil.columbia.edu

Chair Upmanu Lall, Earth Adjunct Staff Daniel Peterson Raimondo Betti and Environmental Ali Ashrafi Bettina Quintas Engineering William Becker Robert Ratay Departmental Hoe I. Ling Logan Brant Robert A. Rubin Administrator Richard W. Longman, Aine M. Brazil Vincent Tirolo Elaine MacDonald Mechanical Engineering Eli B. Gottlieb Richard L. Tomasetti Christian Meyer William M. Hart Pawel Woelke Professors Feniosky Peña-Mora Wilfred Laufs Bojidar Yanev Raimondo Betti Andrew Smyth Samuel A. Leifer Theodore P. Zoli Bruno A. Boley Rene B. Testa Elisabeth Malsch Patricia J. Culligan Aly M. Mohammad Staff Associate Gautam Dasgupta Assistant Professors Nasri Munfakh Adrian Brügger George Deodatis Haim Waisman Robert D. Mutch Jacob Fish Huiming Yin Mysore Nagaraja Information Morton B. Friedman Reza Nikain Technology Manager LecturerS in Gary F. Panariello King-Tung Chan discipline Thomas Panayotidi Julius Chang Tom Papachristos José I. Sánchez

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

engineering 2011–2012 92 Structures: dynamics, stability, and Facilities Florence Guggenheim Foundation. It design of structures, structural failure The offices and laboratories of the provides a base for graduate training and damage detection, fluid and soil department are in the S. W. Mudd in aerospace and aeronautical related structure interaction, ocean structures Building and the Engineering Terrace. applications of structural analysis and subjected to wind-induced waves, design. inelastic dynamic response of reinforced Computing concrete structures, earthquake- The department manages a substantial Center for Infrastructure Studies resistant design of structures. computing facility of its own in addition The Center was established in the to being networked to all the systems department to provide a professional Geotechnical engineering: soil operated by the University. The environment for faculty and students from behavior, constitutive modeling, department facility enables its users a variety of disciplines to join with industry reinforced soil structures, geotechnical to perform symbolic and numeric and government to develop and apply earthquake engineering, liquefaction computation, three-dimensional the technological tools and knowledge and numerical analysis of geotechnical graphics, and expert systems bases needed to deal with the massive systems. development. Connections to wide-area problems of the city, state, and regional networks allow the facility’s users to infrastructure. The Center is active in Structural materials: cement-based communicate with centers throughout major infrastructure projects through a materials, micro- and macromodels of the world. All faculty and student consortium of universities and agencies. fiber-reinforced cement composites, offices and department laboratories utilization of industrial by-products are hardwired to the computing facility, and waste materials, beneficiation of which is also accessible remotely to Undergraduate Programs dredged material. users. Numerous personal computers The Department of Civil Engineering and graphics terminals exist throughout and Engineering Mechanics offers Earthquake engineering: response of the department, and a PC lab is undergraduate programs in civil structures to seismic loading, seismic available to students in the department engineering and engineering mechanics. risk analysis, active and passive control in addition to the larger school-wide Both are intended to prepare students of structures subject to earthquake facility. with firm technical bases while nurturing excitation, seismic analysis of long-span decision-making and leadership cable-supported bridges. Laboratories potential. The Robert A. W. Carleton Strength of The civil engineering program is Flight structures: aeroelasticity, Materials Laboratory is a very large facility designed to enable the student, upon aeroacoustics, active vibration and equipped for research into all types of completion of the B.S. degree program, noise control, smart structures, engineering materials and structural to enter the profession—for example, in noise transmission into aircraft, and elements. The Heffner Laboratory industry, on a construction project, in a vibroacoustics of space structures. for Hydrologic Research is a newly consulting engineering office, through established facility for both undergraduate a government agency—or to begin Construction engineering and instruction and research in all aspects of graduate study, or both. The program management: contracting strategies; fluid mechanics and its applications. The is fully accredited by the Engineering alternative project delivery systems, such Eugene Mindlin Laboratory for Structural Accreditation Commission (EAC) of the as design-build, design-build-operate, Deterioration Research is a teaching and Accreditation Board for Engineering and design-build-finance-operate; research facility dedicated to all facets and Technology (ABET) and provides minimizing project delays and disputes; of the assessment of structures and the a broad traditional civil engineering advanced technologies to enhance processes of deterioration of structural background that focuses on basic productivity and efficiency; strategic performance. The concrete laboratory is theory and design. Technical electives decisions in global engineering and equipped to perform a wide spectrum of can be selected to obtain a strong construction markets. experimental research in cement-based technical base in a particular field of materials. The Donald M. Burmister Soil civil engineering or other engineering Mechanics Laboratory is used in both Infrastructure delivery and disciplines. undergraduate and graduate instruction management: decision support systems The engineering mechanics program for static and dynamic testing of soils for infrastructure asset management; provides a strong analytical background in and foundations. The 200G geotechnical assessing and managing infrastructure mechanics for students planning to con- centrifuge located in the Carleton assets and systems; capital budgeting tinue on to graduate school and to pursue Laboratory is used for geotechnical and processes and decisions; innovative research. Admission to the engineering geoenvironmental research. financing methods; procurement mechanics program requires a grade point strategies and processes; data average of B or better and maintenance of management practices and systems; The Institute of Flight Structures performance while in the program. indicators of infrastructure performance The Institute of Flight Structures was and service. established within the department through a grant by the Daniel and

engineering 2011–2012 Program Objectives selected in architecture, education, industry law, construction techniques, 93 In developing and continually updating economics, and any of the engineering managing civil infrastructure systems, our program to achieve the stated departments in the School. In the junior civil engineering and construction mission of the department, we seek to and senior years, 18 credits of technical entrepreneurship achieve the following objectives: electives are allocated. • Environmental engineering and The department offers a first-year water resources: transport of 1. To provide a firm foundation in the design course, CIEN E1201: The art of water-borne substances, hydrology, basic math, science, and engineering structural design, which all students are sediment transport, hydrogeology, sciences that underlie all technological required to take in the spring semester and geoenvironmental design of development so our graduates will be of the first year or later. An equivalent containment systems well equipped to adapt to changing course could be substituted for E1201. technology in the profession. Engineering Mechanics Minor in Architecture 2. To provide the broad and Programs in engineering mechanics Civil engineering program students may fundamental technical base needed offer comprehensive training in the want to consider a minor in architecture by graduates who will enter the principles of applied mathematics (see page 190). profession through the increasingly and continuum mechanics and in the common path of a specialized M.S., application of these principles to the but also provide suitable preparation Graduate Programs solution of engineering problems. The to those who choose to enter the The Department of Civil Engineering emphasis is on basic principles, enabling professional workforce with a B.S. to and Engineering Mechanics offers students to choose from among a wide develop specialized expertise by way graduate programs leading to the range of technical areas. Students may of apprenticeship. degree of Master of Science (M.S.), the work on problems in such disciplines as professional degrees Civil Engineer and systems analysis, acoustics, and stress 3. To provide the breadth and choices in Mechanics Engineer and the degrees analysis, and in fields as diverse as our programs that can accommodate of Doctor of Engineering Science (Eng. transportation, environmental, structural, and foster not only students with Sc.D.) and Doctor of Philosophy (Ph.D.). nuclear, and aerospace engineering. differing technical objectives, but also These programs are flexible and may Program areas include: those who will use their technical involve concentrations in structures, • Continuum mechanics: solid and background to follow other career construction engineering, reliability and fluid mechanics, theories of elastic paths. random processes, soil mechanics, and inelastic behavior, and damage fluid mechanics, hydrogeology, mechanics 4. To provide a basis for effective continuum mechanics, finite element • Vibrations: nonlinear and random writing and communication as well methods, computational mechanics, vibrations; dynamics of continuous as a background to foster awareness experimental mechanics, vibrations media, of structures and rigid bodies, of societal issues. and dynamics, earthquake engineering, and of combined systems, such as or any combination thereof, such as fluid-structure interaction; active, Engineering Mechanics fluid-structure interaction. The Graduate passive, and hybrid control systems The prerequisites for this program are Record Examination (GRE) is required for structures under seismic loading; the courses listed in the First Year– for admission to the department. dynamic soil-structure interaction Sophomore Program (see above), or effects on the seismic response of their equivalents, with the provision that structures Civil Engineering ENME E3105: Mechanics be taken • Random processes and reliability: By selecting technical electives, students in the sophomore year and that the problems in design against failure may focus on one of several areas of student have obtained a grade of B or under earthquake, wind, and wave concentration or prepare for future better. loadings; noise, and turbulent flows; endeavors such as architecture. Some analysis of structures with random typical concentrations are: properties Civil Engineering • Structural engineering: applications • Fluid mechanics: turbulent flows, The prerequisites for this program to steel and concrete buildings, two-phase flows, fluid-structure are the courses listed in the First bridges, and other structures interaction, fluid-soil interaction, flow in Year–Sophomore Program or their • Geotechnical engineering: soil porous media, computational methods equivalents. The civil engineering mechanics, foundation engineering, for flow and transport processes, and program offers three areas of tunneling, and geodisasters flow and transport in fractured rock concentration: civil engineering and • Construction engineering and under mechanical loading construction management, geotechnical management: capital facility planning • Computational mechanics: finite engineering or structural engineering, and financing, strategic management, element and boundary element and water resources/environmental managing engineering and techniques, symbolic computation, engineering. An optional minor can be construction processes, construction and bioengineering applications

engineering 2011–2012 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)

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

mechanics ENME-MECE E3105 (4) either semester

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

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

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

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

physical C1001 (1) C1002 (1) education

gateway lab E1102 (4) either semester

A flight structures program is CIEN E1201y The art of structural design CIEN E3004y Urban infrastructure systems designed to meet the needs of industry 3 pts. Lect: 3. Professor Deodatis. 3 pts. Lect: 3. Instructor to be announced. in the fields of high-speed and space An introduction to basic scientific and Introduction to: (a) the infrastructure engineering principles used for the design of systems that support urban socioeconomic flight. The emphasis is on mechanics, buildings, bridges, and other parts of the built activities, and (b) fundamental system mathematics, fluid dynamics, flight infrastructure. Application of these principles design and analysis methods. Coverage of structures, and control. The program to the analysis and design of a number of water resources, vertical, transportation, is a part of the Guggenheim Institute actual large-scale structures. Experimental communications and energy infrastructure. of Flight Structures in the department. verification of these principles through laboratory Emphasis upon the purposes that these Specific information regarding degree experiments. Coverage of the history of systems serve, the factors that influence their requirements is available in the major structural design innovations and of performance, the basic mechanisms that the engineers who introduced them. Critical govern their design and operation, and the department office. examination of the unique aesthetic/artistic impacts that they have regionally and globally. perspectives inherent in structural design. Student teams complete a semester-long Courses in Civil Consideration of management, socioeconomic, design/analysis project with equal emphasis and ethical issues involved in the design given to water resources / environmental Engineering (CIEN) and construction of large-scale structures. engineering, geotechnical engineering and See also Engineering Mechanics Introduction to some recent developments in construction engineering and management (ENME), at the end of this section. sustainable engineering, including green building topics. design and adaptable structural systems.

engineering 2011–2012 95 civil engineering: Third and Fourth Years

Semester V Semester VI Semester VII Semester VIII

CIEN E3125 (3) Structural design CIEN E4111 (3) ENME E3113 (3) Uncertainty and risk in Mech. of solids CIEN E3126 (1) infrastructure systems CIEN E3128 (4) core Required Computer-aided Courses Design projects ENME E3161 (4) struct. design CIEN E3129 (3) Fluid mech. Proj. mgmt. for CIEN E3141 (4) construction Soil mech.

CIEN E4332 (3) Finite element anal. geotech ENME E3114 (4) Exper. mech. of materials CIEN E3127 (3) eng. (GE) ENME E3106 (3) or Struct. design projects Dynamics and vibrations Struct. CIEN E3121 (3) (SE) Eng. (SE) Struct. anal. or CIEN E4241 (3) Geotech. eng. fund. (GE)

tech 3 points 3 points 12 points electives

ENME E3114 (4) Exper. mech. of materials CIEN E4133 (3) civil eng. Capital facility planning and CIEN E3121 (3) and financing CIEN E4131 (3) constr. Struct. anal. Princ. of constr. tech. mngmt. or CIEN E3127 (3) or CIEE E3250 (3) CIEN E4241 (3) Hydrosystems eng.

tech

c o ncentrati ns 6 points 3 points 9 points electives

CIEN E4250 (3) Waste containm. CIEE E3255 (3) design and practice Environ. control / pollution or CIEE E4163 (3) CIEN E4257 (3) water res./ CIEE E3250 (3) Environ. Environ. eng. contam. transport Hydrosystems eng. Eng. wastewater in subsurface sys. CIEN E3303 (1) EAEE E4006 (3) Independent studies Field methods for environ. eng.

tech 6 points 3 points 9 points electives

nontech 3 points 3 points electives

15 16 total points 16 17 (water res./environ. eng. 16) (water res./environ. eng. 15)

engineering 2011–2012 96 engineering mechanics program: first and second Years

Semester i Semester iI Semester iII Semester iV

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

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

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

mechanics ENME-MECE E3105 (4) any semester

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

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

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

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

physical C1001 (1) C1002 (1) education

gateway lab E1102 (4) either semester

CIEN E3121y Structural analysis CIEN E3127x Structural design projects CIEN E3129x Project management for 3 pts. Lect: 3. Professor Testa. 3 pts. Lect: 3. Professor Meyer. construction Methods of structural analysis. Trusses, arches, Prerequisites: CIEN E3125 and E3126 or the 3 pts. Lect: 3. Instructor to be announced. cables, frames; influence lines; deflections; instructor’s permission. Design projects with Prerequisite: Senior standing in Civil Engineering force method; displacement method; computer various structural systems and materials. or instructor’s permission. Introduction applications. to Project Management for design and CIEN E3128y Design projects construction processes. Elements of planning, CIEN E3125y Structural design 4 pts. Lect: 4. Professor Meyer. estimating, scheduling, bidding, and contractual 3 pts. Lect: 3. Professor Betti. Prerequisites: CIEN E3125 and E3126. relationships. Computer scheduling and cost Prerequisite: ENME 3113. Design criteria for Capstone design project in civil engineering. control. Critical path method. Design and varied structural applications, including buildings This project integrates structural, geotechnical construction activities. Field supervision. and bridges; design of elements using steel, and environmental/water resources design concrete, masonry, wood, and other materials. problems with construction management tasks CIEN E3141y Soil mechanics and sustainability, legal and other social issues. 4 pts. Lect: 3. Lab 3. Professor Ling. CIEN E3126y Computer-aided structural Project is completed in teams, and communication Prerequisite: ENME E3113. Index properties design skills are stressed. Outside lecturers will address and classification; compaction; permeability and 1 pt. Lect: 1. Lab: 1. Professor Betti. important current issues in engineering practice. seepage; effective stress and stress distribution; Corequisite: CIEN E3125. Introduction to Every student in the course will be exposed with shear strength of soil; consolidation; slope software for structural analysis and design with equal emphasis to issues related to geotechnical stability. lab. Applications to the design of structural engineering, water resources/environmental elements and connections. Lab required. engineering, structural engineering, and CIEE E3250y Hydrosystems engineering construction engineering and management. 3 pts. Lect: 3. Instructor to be announced. Prerequisites: CHEN E3110 or ENME E3161

engineering 2011–2012 97 engineering mechanics: Third and Fourth Years

Semester V Semester VI Semester VII Semester VIII

ENME E3113 (3) Mech. of solids ENME E3114 (4) CIEN E4332 (3) Experimental mech. Finite element ENME E3161 (4) Fluid mechanics Required CIEN E3121 (3) ENME E4113 (3) ENME E4202 (3) Courses Structural analysis Advanced solids Advanced mech. APMA E3101 (3) Applied math., I APMA E3102 (3) ENME E4215 (3) Applied math., II Theory of vibrations ENME E3106 (3) Dynamics and vibrations

tech 3 points 6 points 6 points 9 points

nontech 3 points 3 points E lectives

total points 16 16 18 15

or equivalent, SIEO W3600 or equivalent, of social, economical, and governance issues, CIEN E4022y Bridge design and management or the instructor’s permission. A quantitative and that can be implemented now or in the near 3 pts. Lect: 3. Professor Yanev. introduction to hydrologic and hydraulic systems, future. The course is open to all undergraduate Prerequisite: CIEN E3125 or the equivalent. with a focus on integrated modeling and engineering students. Multidisciplinary teamwork Bridge design history, methods of analysis, analysis of the water cycle and associated mass and approaches are stressed. Outside lecturers loads: static, live, dynamic. Design: allowable transport for water resources and environmental are used to address issues specific to developing stress, ultimate strength, load resistance engineering. Coverage of unit hydrologic communities and the particular project under factor, supply/demand. Steel and concrete processes such as precipitation, evaporation, consideration. superstructures: suspension, cable stayed, infiltration, runoff generation, open channel and prestressed, arches. Management of the assets, CIEN E3303x and y Independent studies in pipe flow, subsurface flow and well hydraulics life-cycle cost, expected useful life, inspection, in the context of example watersheds and civil engineering for juniors maintenance, repair, reconstruction. Bridge specific integrative problems such as risk-based 1–3 pts. By conference. Members of the faculty. inventories, condition assessments, data design for flood control, provision of water, and A project on civil engineering subjects approved acquisition and analysis, forecasts. Selected assessment of environmental impact or potential by the chairman of the department. Lab fee: case histories and field visits. for nonpoint source pollution. Spatial hydrologic $200. CIEN E4100y Earthquake and wind analysis using GIS and watershed models. Note: CIEN E3304x and y Independent studies in engineering This course is to be joint listed with CIEN and civil engineering for seniors replaces the previous CIEN 3250. 3 pts. Lect: 3. 1–3 pts. By conference. Members of the faculty. Prerequisite: ENME E3106 or the equivalent. CIEE E3255y Environmental control and A project on civil engineering subjects Basic concepts of seismology. Earthquake pollution reduction systems approved by the chairman of the department. characteristics, magnitude, response spectrum, 3 pts. Lect: 3. Professor Castaldi. Lab fee: $200. dynamic response of structures to ground Prerequisite: ENME E3161 or MECE E3100. motion. Base isolation and earthquake-resistant Review of engineered systems for prevention CIEN E4010y Transportation engineering design. Wind loads and aeroelastic instabilities. and control of pollution. Fundamentals of 3 pts. Lect: 3. Instructor to be announced. Extreme winds. Wind effects on structures and material and energy balances and reaction An overview of the planning, design, operation, gust factors. kinetics. Analysis of engineered systems to and construction of urban highways and CIEN E4111x Uncertainty and risk in address environmental problems, including solid mass transportation systems. Transportation and hazardous waste, and air, water, soil and planning and traffic studies; traffic and infrastructure systems noise pollution. Life cycle assessments and highway engineering; rapid transit and railroad 3 pts. Lect: 3. Professor Smyth. emerging technologies. engineering. Prerequisite: Working knowledge of calculus. Introduction to basic probability; hazard function; CIEE E3260y Engineering for developing CIEN E4021x Elastic and plastic analysis of reliability function; stochastic models of natural communities structures and technological hazards; extreme value Lect: 3. 3 pts. Professor Culligan. 3 pts. Lect: 3. Professor Meyer. distributions; Monte Carlo simulation techniques; Introduction to engineering problems faced Prerequisite: CIEN E3121 or the equivalent. fundamentals of integrated risk assessment and by developing communities and exploration of Overview of classical indeterminate structural risk management; topics in risk-based insurance; design solutions in the context of a real project analysis methods (force and displacement case studies involving civil infrastructure with a community client. Emphasis is on the methods), approximate methods of analysis, systems, environmental systems, mechanical and design of sustainable solutions that take account plastic analysis methods, collapse analysis, aerospace systems, construction management. shakedown theorem, structural optimization.

engineering 2011–2012 98 CIEN E4128y Civil engineering management value, innovation and private sector participation. and ethics of the forensic consultant and expert 3 pts. Available only on CVN. Fundamentals of engineering economy and witness. Students are assigned projects of actual Principles of engineering management with a project finance. Elements of life cycle cost cases of nonperformance or failure of steel, strong emphasis on planning of infrastructure estimation and decision analysis. Environmental, concrete, masonry, geotechnical, and temporary systems. The course stresses leadership, institutional, social and political factors. Case structures, in order to perform, discuss, and creativity, and management analysis. Program studies from transportation, water supply and report their own investigations under the planning with optimization under financial and wastewater treatment. guidance of the instructor. environmental constraints; project planning and CIEN E4134y Construction industry law scheduling using deterministic and stochastic CIEN E4212y Structural assessment 3 pts. Lect: 3. Professors Quintas and Rubin. network theories; production rate development and failure Prerequisite: Graduate standing or the and control using statistical, heuristic, simulation, 3 pts. Lect: 3. Not offered in 2011–2012. instructor’s permission. Practical focus upon and queuing theory approaches. Students Prerequisites: ENME E3113 and CIEN E3121. legal concepts applicable to the construction prepare and formally present term projects. Laboratory and field test methods in assessment industry. Provides sufficient understanding to of structures for rehabilitation and to determine CIEN E4129x or y Managing engineering and manage legal aspects, instead of being managed causes of failure; ASTM and other applicable construction processes by them. Topics include contractual relationships, standards; case histories of failures and 3 pts. Lect: 3. Instructor to be announced. contract performance, contract flexibility and rehabilitation in wood, steel, masonry, and Prerequisite: Graduate standing in Civil change orders, liability and negligence, dispute concrete structures. Engineering, or instructor’s permission. avoidance/resolution, surety bonds, insurance Introduction to the principles, methods and tools and site safety. CIEN E4213x Elastic and inelastic buckling of necessary to manage design and construction structures CIEN E4135y Strategic management global processes. Elements of planning, estimating, 3 pts. Lect: 3. Professor Laufs. design and construction scheduling, bidding and contractual relationships. Stability of framed structures in the elastic and 3 pts. Lect: 3. Instructor to be announced. Valuation of project cash flows. Critical path inelastic ranges. Lateral buckling of beams. Core concepts of strategic planning, method. Survey of construction procedures. Cost Torsional buckling of compression members. management and analysis within the construction control and effectiveness. Field supervision. Buckling of plates of plate-stiffener combinations. industry. Industry analysis, strategic planning Linear stability analysis of cylindrical shells and CIEN E4130x Design of construction systems models and industry trends. Strategies for discussion of its limitations. Discussion of the 3 pts. Lect: 3. Professor Tirolo. information technology, emerging markets and semiempirical nature of the elastoplastic relations Prerequisite: CIEN E3125 or the equivalent, or globalization. Case studies to demonstrate key used in the case of plates and shells. the instructor’s permission. Introduction to the concepts in real-world environments. design of systems that support construction CIEN E4226y Advanced design of steel CIEN E4136y Global entrepreneurship in civil activities and operations. Determination of structures design loads during construction. Design of engineering 3 pts. Lect: 3. Professor Woelke. excavation support systems, earth retaining 3 pts. Lect: 3. Instructor to be announced. Prerequisite: CIEN E3125 or equivalent. Review systems, temporary supports and underpinning, Capstone practicum where teams develop of loads and structural design approaches. concrete formwork and shoring systems. Cranes strategies and business plans for a new Material considerations in structural steel and erection systems. Tunneling systems. enterprise in the engineering and construction design. Behavior and design of rolled steel, Instrumentation and monitoring. Students industry. Identification of attractive market welded, cold-formed light-gauge, and composite prepare and present term projects. segments and locations; development of an concrete/steel members. Design of multistory entry strategy; acquisition of financing, bonding buildings and space structures. CIEN E4131x or y Principles of construction and insurance; organizational design; plans for techniques recruiting and retaining personnel; personnel CIEN E4232y Advanced design of concrete 3 pts. Lect: 3. Professor Hart. compensation/incentives. Invited industry structures Prerequisite: CIEN 4129 or equivalent. speakers. 3 pts. Lect: 3. Professor Panayotidi. Current methods of construction, cost-effective Prerequisite: CIEN E3125 or equivalent. Design CIEE E4163x Environmental engineering: designs, maintenance, safe work environment. of concrete slabs, deep beams, walls, and Design functions, constructability, site and wastewater other plane structures; introduction to design of environmental issues. 3 pts. Lect: 3. Professor Becker. prestressed concrete structures. Prerequisites: Introductory chemistry (with CIEN E4132x or y Prevention and resolution laboratory) and fluid mechanics. Fundamentals CIEE E4233x Design of large-scale bridges of construction disputes of water pollution and wastewater characteristics. 3 pts. Lect: 3. Professor Zoli. 3 pts. Lect: 3. Professor Nikain. Chemistry, microbiology, and reaction kinetics. Prerequisites: CIEN E3121 or equivalent, and Prerequisite: CIEN E 4129 or equivalent. Design of primary, secondary, and advanced CIEN E3127 or equivalent. Design of large-scale Contractual relationships in the engineering and treatment systems. Small community and and complex bridges with emphasis on cable- construction industry and the actions that result residential systems. supported structures. Static and dynamic loads, in disputes. Emphasis on procedures required to component design of towers, superstructures CIEN E4210x Investigation of structural/ prevent disputes and resolve them quickly and and cables; conceptual design of major bridge cost-effectively. Case studies requiring oral and construction failures types including arches, cable stayed bridges and written presentations. 3 pts. Lect: 3. Professor Ratay. suspension bridges. Prerequisite: CIEN E3125 or equivalent. Review CIEN E4234y Design of large-scale building CIEN E4133x or y Capital facility planning and of significant failures, civil/structural engineering financing design and construction practices, ethical structures 3 pts. Lect: 3. Professor Chang. standards and the legal positions as necessary 3 pts. Lect: 3. Professor Tomasetti. Prerequisite: CIEN E4129 or equivalent. Planning background to forensic engineering. Discussion Prerequisites: CIEN E3121 and E3127. Modern and financing of capital facilities with a strong of standard-of-care. Study of the process of challenges in the design of large-scale building emphasis upon civil infrastructure systems. engineering evaluation of structural defects structures will be studied. Tall buildings, large Project feasibility and evaluation. Design of and failures in construction and in service. convention centers, and major sports stadiums project delivery systems to encourage best Examination of the roles, activities, conduct present major opportunities for creative solutions

engineering 2011–2012 and leadership on the part of engineers. This CIEN E4246x Earth retaining structures Preservation (GSAPP) that explores solutions 99 course is designed to expose the students to 3 pts. Lect: 3. Professor Leifer. to problems of urban density. Engineering and this environment by having them undertake the Prerequisite: CIEN E3141. Retaining structures, GSAPP students will engage in a joint project complete design of a large structure from initial bulkheads, cellular cofferdams, and braced that address habitability and sustainability design concepts on through all the major design excavations. Construction dewatering and issues in an urban environment, and also decisions. The students work as members of a underpinning. Instrumentation to monitor actual provides community service. Emphasis will be design team to overcome the challenges inherent performances. Ground improvement techniques, on the integration of science, engineering and in major projects. Topics include overview of including earth reinforcement, geotextiles, and design within a social context. Interdisciplinary major projects, project criteria and interface with grouting. To alternate with CIEN E4243. approaches and communication will be stressed. architecture, design of foundations and structural CIEN E4250y Waste containment design systems, design challenges in the post 9/11 CIEN E6131x Quantitative infrastructure risk environment and roles, responsibilities and legal and practice management issues. 3 pts. Lect: 3. Not offered in 2011–2012. 3 pts. Lect: 3. Not offered in 2011–2012. Prerequisites: ENME E3161 and CIEN E3141, Prerequisites: IEOR E4003, CIEN E4133 or the CIEN E4241x Geotechnical engineering or equivalents. Strategies for the containment equivalent. Core concepts of risk analysis, risk fundamentals of buried wastes. Municipal and hazardous mitigation, and quantitative risk management 3 pts. Lect: 3. Professor Mohammad. waste landfill design; bioreactor landfills; applied to civil infrastructure systems. State Prerequisite: CIEN E3141 or instructor’s vertical barriers, evapotranspiration barriers of art of simulation applied to infrastructure permission. Bearing capacity and settlement of and capillary barriers; hydraulic containment; in risk management during construction and shallow and deep foundations; earth pressure situ stabilization and solidification techniques; operation. Public Private Partnership (PPP) theories; retaining walls and reinforced soil site investigation; monitoring and stewardship risk management: identification, quantification, retaining walls; sheet pile walls; braced excavation; of buried wastes; options for land reuse/ mitigation of risks in transportation and energy slope stability. redevelopment. PPP systems. Risk management during construction using the envelop method. CIEN E4242x Geotechnical earthquake CIEE E4252x Environmental engineering engineering 3 pts. Lect: 3. Professor Chandran. CIEN E6132y Advanced systems and 3 pts. Lect: 3. Professor Ling. Prerequisites: CHEM C1403 or equivalent; technologies for global project collaboration Prerequisite: CIEN E3141 or equivalent. ENME E3161 or the equivalent. Engineering 3 pts. Lect: 3. Not offered in 2011–2012. Seismicity, earthquake intensity, propagation aspects of problems involving human interaction Prerequisite: CIEN E4129 or the equivalent. of seismic waves, design of earthquake with the natural environment. Review of Systems and technologies that support motion, seismic site response analysis, in fundamentals principles that underlie the collaborative work in global projects. Information situ and laboratory evaluation of dynamic soil discipline of environmental engineering, i.e., technologies for design, visualization, project properties, seismic performance of underground constituent transport and transformation management, and collaboration in globally structures, seismic performance of port and processes in environmental media such distributed networks of design, fabrication, and harbor facilities, evaluation and mitigation of as water, air and ecosystems. Engineering construction organizations, including Web-based, soil liquefaction and its consequences. Seismic applications for addressing environmental parametric computer-aided modeling, project earth pressures, slopes stability, safety of dams problems such as water quality and treatment, organizational simulation, and other emerging and embankments, seismic code provisions and air pollutant emissions, and hazardous waster applications. Global team project with students at practice. To alternate with E4244. remediation. Presented in the context of collaborating universities abroad. current issues facing practicing engineers CIEN E4243x Foundation engineering and government agencies, including legal CIEN E6133y Advanced construction and 3 pts. Lect: 3. Professor Brant. and regulatory framework, environmental infrastructure risk management using real Prerequisite: CIEN E3141 or equivalent. impact assessments, and natural resource options Conventional types of foundations and foundation management. Not offered in 2011–2012. problems: subsurface exploration and testing. Prerequisite: CIEN E6131. Advanced concepts Performance of shallow and deep foundations CIEN E4253y Finite elements in geotechnical of risk analysis and management applied to civil and evaluation by field measurements. Case engineering engineering systems. Identifying and valuing histories to illustrate typical design and 3 pts. Lect: 3. Not offered in 2011–2012. flexibility in construction and operation. Tools to construction problems. To alternate with CIEN Prerequisites: CIEN E3141 and E4332. State- perform risk analysis in flexible civil infrastructure E4246. of-the-art computer solutions in geotechnical systems. Valuation methods for real options. engineering; 3D consolidation, seepage flows, Risk flexibility analysis; integrating real CIEN E4244x Geosynthetics and waste and soil-structure interaction; element and mesh options analysis with quantitative risk analysis. containment instabilities. To be offered in alternate years with Applications to case studies on construction 3 pts. Lect: 3. Professor Brant. CIEN E4254. management, life-cycle cost analysis for Prerequisite: CIEN E4241 or the equivalent. infrastructure assets, public-private partnerships Properties of geosynthetics. Geosynthetic design CIEE E4257x Contaminant transport in projects, real estate developments, and for soil reinforcement. Geosynthetic applications subsurface systems renewable energy infrastructure projects. in solid waste containment system. To alternate 3 pts. Lect: 3. Professor Mutch. with CIEN E4242. Prerequisites: CIEE E3250 or equivalent. Single CIEN E6232x Advanced topics in concrete and multiple phase transport in porous media; engineering CIEN C4245x Tunnel design and construction contaminant transport in variably saturated 3 pts. Lect: 3. Not offered in 2011–2012. 3 pts. Lect: 3. Professor Munfakh. heterogeneous geologic media; physically based Prerequisite: CIEN E3125 or the equivalent. Engineering design and construction of different numerical models of such processes. Behavior of concrete under general states of types of tunnel, including cut and cover tunnel, stress, numerical modeling of steel and concrete, rock tunnel, soft ground tunnel, immersed tub CIEN E4260x Urban ecology studio finite element analysis of reinforced concrete, tunnel, and jacked tunnel. The design for the 4 pts. Lect: 3. Lab: 3. Professor Culligan. design of slabs and their shell concrete structures. liner, excavation, and instrumentation are also Prerequisites: Graduate standing and instructor’s covered. A field trip will be arranged to visit the permission. Conjoint studio run with the tunneling site. Graduate School of Architecture, Planning and

engineering 2011–2012 100 CIEN E6246y Advanced soil mechanics doctoral research instruction. Registration in ENME E4114y Mechanics of fracture 3 pts. Lect: 2.5. Professor Ling. CIEN E9800 may not be used to satisfy the and fatigue Prerequisite: CIEN E3141. Stress-dilatancy of minimum residence requirement for the degree. 3 pts. Lect: 3. Professor Testa. sand; failure criteria; critical state soil mechanics; Prerequisite: Undergraduate mechanics of solids CIEN E9900x and y–S9900 Doctoral limit analysis; finite element method and case course. Elastic stresses at a crack; energy dissertation histories of consolidation analysis. and stress intensity criteria for crack growth; Members of the faculty. effect of plastic zone at the crack; fracture CIEN E6248x Experimental soil mechanics A candidate for the doctorate may be required testing applications. Fatigue characterization by 3 pts. Lect: 2.5. Not offered in 2011–2012. to register for this course every term after the stress-life and strain-life; damage index; crack Prerequisite: CIEN E3141. Advanced soil testing, student’s coursework has been completed and propagation; fail safe and safe life analysis. including triaxial and plane strain compression until the dissertation has been accepted. tests; small-strain measurement. Model testing; EMME E4115y Micromechanics of composite application (of test results) to design. materials Courses in Engineering 3 pts. Lect: 3. Professor Yin. CIEN E9101x and y–S9101 Civil engineering Mechanics Prerequisite: ENME E4113 or instructor’s research approval. An introduction to the constitutive 1–4 pts. Members of the faculty. See also Civil Engineering. modeling of composite materials: Green’s Advanced study in a specialized field under the ENME E3105x or y Mechanics functions in heterogenous media, Eshelby’s supervision of a member of the department staff. 4 pts. Lect: 4. Professors Hone and Testa. equivalent inclusion methods, eigenstrains, Before registering, the student must submit an Prerequisites: PHYS C1406 and MATH spherical and ellipsoidal inclusions, dislocations, outline of the proposed work for approval of the V1101-V1102 and V1201. Elements of statics; homogenization of elastic fields, elastic, supervisor and the department chair. dynamics of a particle and systems of particles; viscoelastic and elasto-plastic constitutive CIEN E9120x and y–S9120 Independent dynamics of rigid bodies. modeling, micromechanics-based models. studies in flight sciences ENME E3106x Dynamics and vibrations ENME E4202y Advanced mechanics 3 pts. By conference. 3 pts. Lect: 2. Professor Smyth. 3 pts. Lect: 3. Professor Smyth. Prerequisite: Instructor’s permission. This course Prerequisite: Math E1201. Corequisite: ENME Prerequisite: ENME E3105 or equivalent. is geared toward students interested in flight E3105. Kinematics of rigid bodies; momentum Differentiation of vector functions. Review sciences and flight structures. Topics related and energy methods; vibrations of discrete of kinematics. Generalized coordinates and to aerodynamics, propulsion, noise, structural and continuous systems; eigenvalue problems, constraint equations. Generalized forces. dynamics, aeroelasticity, and structures may be natural frequencies and modes. Basics of Lagrange’s equations. Impulsive forces. selected for supervised study. A term paper is computer simulation of dynamics problems using Collisions. Hamiltonian. Hamilton’s principle. required. MATLAB or Mathematica. ENME E4214y Theory of plates and shells CIEN E9130x and y–S9130 Independent ENME E3113x Mechanics of solids 3 pts. Lect: 3. Not offered in 2011–2012. studies in construction 3 pts. Lect: 3. Professor Deodatis. Prerequisite: ENME E3113. Static flexural 3 pts. By conference. Pre- or corequisite: ENME E3105 or equivalent. response of thin, elastic, rectangular, and Prerequisites: Permission by department chair and Stress and strain. Mechanical properties of circular plates. Exact (series) and approximate instructor. Independent study of engineering and materials. Axial load, bending, shear, and (Ritz) solutions. Circular cylindrical shells. construction industry problems. Topics related to torsion. Stress transformation. Deflection of Axisymmetric and nonaxisymmetric membrane capital planning and financing, project management, beams. Buckling of columns. Combined loadings. theory. Shells of arbitrary shape. contracting strategies and risk allocation, dispute Thermal stresses. mitigation and resolution, and infrastructure ENME E4215x Theory of vibrations assessment and management may be selected for ENME E3114y Experimental mechanics of 3 pts. Lect: 3. Professor Betti. supervised study. A term paper is required. materials Frequencies and modes of discrete and 4 pts. Lect: 2. Lab: 3. Professor Yin. continuous elastic systems. Forced vibrations- CIEN E9165x and y–S9165 Independent Prerequisite: ENME E3113. Material behavior steady-state and transient motion. Effect of studies in environmental engineering and constitutive relations. Mechanical properties damping. Exact and approximate methods. 4 pts. By conference. of metals and cement composites. Structural Applications. Prerequisite: CIEN E4252 or the equivalent. materials. Modern construction materials. Emphasizes a one-on-one study approach to Experimental investigation of material properties ENME E4332x Finite element analysis, I specific environmental engineering problems. and behavior of structural elements including 3 pts. Lect: 3. Professor Waisman. Students develop papers or work on design fracture, fatigue, bending, torsion, buckling. Prerequisites: Mechanics of solids, structural problems pertaining to the treatment of solid analysis, elementary computer programming and liquid waste, contaminant migration, ENME E3161x Fluid mechanics (MATLAB) is recommended, linear algebra and monitoring and sampling programs for 4 pts. Lect: 3. Lab: 3. Professor Waisman. and ordinary differential equations. Direct remediation design. Prerequisites: ENME E3105 and ordinary stiffness approach for trusses. Strong and differential equations. Fluid statics. Fundamental weak forms for one-dimensional problems. CIEN E9201x and y–S9201 Civil engineering principles and concepts of flow analysis. Galerkin finite element formulation, shape reports Differential and finite control volume approach to functions, Gauss quadrature, convergence. 1–4 pts. By conference. flow analysis. Dimensional analysis. Application Multidimensional scalar field problems (heat A project on some civil engineering subject of flow analysis: flow in pipes, external flow, flow conduction), triangular and rectangular elements, approved by department chair. in open channels. Isoparametric formulation. Multidimensional CIEN E9800x and y–S9800 Doctoral research ENME E4113x Advanced mechanics of solids vector field problems (linear elasticity). Practical instruction 3 pts. Lect: 3. Professor Yin. FE modeling with commercial software 3–12 pts. May be taken for 3, 6, 9, or 12 points, Stress and deformation formulation in two-and (ABAQUS). Computer implementation of the dependent on instructor’s permission. three-dimensional solids; viscoelastic and plastic finite element method. Advanced topics. A candidate for the Eng.Sc.D. degree in civil material in one and two dimension energy methods. engineering must register for 12 points of

engineering 2011–2012 ENME E4363y Multiscale computational ENME E6333y Finite element analysis, II Courses in Graphics 101 science and engineering 3 pts. Lect: 3. Professor Waisman. 3 pts. Lect: 3. Professor Fish. Prerequisite: ENME E4332. FE formulation GRAP E1115x and y Engineering graphics Prerequisites: ENME E4332, elementary for beams and plates. Generalized eigenvalue 3 pts. Lect: 1. Lab: 3. Professor Sánchez. computer programming, linear algebra. problems (vibrations and buckling). FE Open to all students. Visualization and simulation Introduction to multiscale analysis. Information- formulation for time-dependent parabolic and in virtual environments; computer graphics passing bridging techniques: among them, hyperbolic problems. Nonlinear problems, methods for presentation of data. 3-D modeling; generalized mathematical homogenization linearization, and solution algorithms. Geometric animation; rendering; image editing; technical theory, the heterogeneous multiscale method, and material nonlinearities. Introduction to drawing. Lab fee: $300. 1220 S. W. Mudd variational multiscale method, the discontinuous continuum mechanics. Total and updated Building. Galerkin method and the kinetic Monte Lagrangian formulations. Hyperelasticity and GRAP E2005y Computer-aided engineering Carlo–based methods. Concurrent multiscale plasticity. Special topics: fracture and damage graphics mechanics, extended finite element method. techniques: domain bridging, local enrichment, 3 pts. Lect: 1.5. Lab: 2.5. Professor Dasgupta. and multigrid-based concurrent multiscale EMME E6364x Nonlinear computational Prerequisite: MATH V1105. Basic concepts methods. Analysis of multiscale systems. mechanics needed to prepare and understand engineering ENME E6220x Random processes in 3 pts. Lect: 3. Professor Fish. drawings and computer-aided representations: mechanics Prerequisites: ENME 4332 or equivalent, preparation of sketches and drawings, 3 pts. Lect: 3. Professor Deodatis. elementary computer programming, linear preparation and transmission of graphic Prerequisites: CIEN E4111 and ENME E4215 algebra. The formulations and solution strategies information. Lectures and demonstrations, hands- (or equivalent). Review of random variables. for finite element analysis of nonlinear problems on computer-aided graphics laboratory work. Random process theory: stationary and ergodic are developed. Topics include the sources of Term project. processes, correlation functions, power spectra. nonlinear behavior (geometric, constitutive, GRAP E3115y Advanced computer modeling boundary condition), derivation of the governing Nonstationary and non-Gaussian processes. and animation discrete equations for nonlinear systems such Linear random vibration theory. Crossing rates, 3 pts. Lect: 1. Lab: 3. Professor Sánchez. as large displacement, nonlinear elasticity, rate peak distributions, and response analysis of Prerequisite: GRAP E1115 or instructor’s independent and dependent plasticity and other nonlinear structures to random loading. Major permission. Explores applications of 3D nonlinear constitutive laws, solution strategies emphasis on simulation of various types of modeling, animation, and rendering techniques in for nonlinear problems (e.g., incrementation, random processes. Monte Carlo simulation. the arts, architecture, engineering, entertainment iteration), and computational procedures for large and science. Visualization through conceptual ENME E6315x Theory of elasticity systems of nonlinear algebraic equations. modeling and animation techniques for product 3 pts. Lect: 2.5. Professor Dasgupta. ENME E8320y Viscoelasticity and plasticity design and realistic presentations. Lab fee: $300. Foundations of continuum mechanics. General 4 pts. Lect: 3. Professor Dasgupta. theorems of elasticity. Application to stress GRAP E4005y Computer graphics in Prerequisite: ENME E6315 or equivalent, or analysis and wave propagation. engineering instructor’s permission. Constitutive equations 3 pts. Lect: 3. Professor Dasgupta. of viscoelastic and plastic bodies. Formulation Prerequisites: Any programming language and methods of solution of the boundary value, and linear algebra. Numerical and symbolic problems of viscoelasticity and plasticity. (algebraic) problem solving with Mathematica. ENME E8323y Nonlinear vibrations Formulation for graphics application in civil, 3 pts. Lect: 2.5. Not offered in 2011–2012. mechanical, and bioengineering. Example of two- Prerequisite: ENME E4215 or equivalent. and three-dimensional curve and surface objects Free and forced motion of simple oscillators in C++ and Mathematica; special projects of interest to electrical and computer science. with nonlinear damping and stiffness. Exact, perturbation, iteration, and graphical methods of solution. Stability of motion. Chaotic vibrations.

engineering 2011–2012 102 Computer Engineering Program Administered by both the Electrical Engineering and Computer Science Departments through a joint Computer Engineering Committee. Student records are kept in the Electrical Engineering Department.

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

In Charge Martha A. Kim Kenneth L. Shepard Steven M. Nowick Assistant Professor of Computer Science Professor of Electrical Engineering and 508 Computer Science Vishal Misra Biomedical Engineering Associate Professor of Computer Stephen H. Unger Computer Engineering Committee Science Professor Emeritus of Computer Science Luca Carloni, Steven M. Nowick and Electrical Engineering Associate Professor of Computer Professor of Computer Science Charles A. Zukowski Science Daniel Rubenstein Professor of Electrical Engineering Stephen A. Edwards Associate Professor of Computer Associate Professor of Computer Science Science Simha Sethumadhavan Assistant Professor of Computer Science

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

engineering 2011–2012 103 computer engineering program: first and second Years early-starting students

Semester i Semester iI Semester iII Semester iV

MATH V1202 (3) mathematics MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) and APMA E2101 (3)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 C3045 or C1604 chemistry Lab C1500 (3) either semester or physics lab C1493 (3)

COMS W3137 (3) or W3139 (4) core required ELEN E1201 (3.5) ELEN E3801 (3.5) Data structures courses Intro. to elec. eng. (either semester) Signals and systems CSEE W3827 (3) Fund. of computer sys.

ELEN E3084 (1) ELEN E3082 (1) required labs Signals and systems lab Digital systems lab

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

HUMA C1001, HUMA C1002, COCI C1101, COCI C1102, required or Global Core (3–4) or Global Core (3–4) nontechnical electives1 HUMA W1121 or ECON W1105 (4) and W1123 (3)1 W1155 recitation (0)

COMS W1007 (3) or W3203 (3) computer COMS W1004 (3)2 science W1009 Discrete math.

physical C1001 (1) C1002 (1) education

gateway lab E1102 (4) either semester

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

engineering 2011–2012 104 computer engineering: Third and Fourth Years early-starting students

Semester V Semester VI Semester VII Semester VIII

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

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

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

Tech 15 points required; see details on pages 105–107

Complete 27-point requirement; see page 10 or www.seas.columbia.edu for details nontech (administered by the advising dean) E lecti v e s

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.

Technical Electives Starting Early such fields as digital computer design, The Computer Engineering Program Students are strongly encouraged to digital communications, and the design includes 15 points of technical electives. begin taking core computer engineering of embedded computer systems. Any 3000-level or higher courses listed courses as sophomores. They start with Applicants are generally expected to in the Computer Science or Electrical ELEN E1201: Introduction to electrical have a bachelor’s degree in computer Engineering sections of this bulletin engineering in the second semester engineering, computer science, or can be used for this requirement with of their first year and may continue electrical engineering with at least a 3.2 the following exceptions: ELEN E3000, with other core courses one semester GPA in technical courses. The Graduate EEHS E3900/4900, EEJR E4901, COMS after that. For sample “early-starting” Record Examination (GRE), General Test W3101, W4400, W4405, courses and “late-starting” programs, see only, is required of all applicants. used for other computer engineering these degree track charts. It must be Students must take at least 30 points requirements (including COMS W3203 emphasized that these charts present of courses at Columbia University at or and either CSEE W4840, EECS E4340, examples only; actual schedules may above the 4000 level. These must include or CSEE W4140), and courses that have be customized in consultation with at least 15 points from the courses significant overlap with other required academic advisers. listed below that are deemed core to or elective courses (e.g., COMS W3137 computer engineering. At least 6 points and W3139). Courses at the 3000 level must be included from each department. Graduate Program or higher in other areas of engineering, CSEE and EECS courses can count The Computer Engineering Program math, and science can be considered toward either department minimum. offers a course of study leading to the for approval, as long as they do not Other courses may be chosen with the degree of Master of Science (M.S.). significantly overlap with other required prior approval of a faculty adviser in the The basic courses in the M.S. program or elective courses. Economics courses Computer Engineering Program. come from the Electrical Engineering cannot be used as technical electives. and Computer Science Departments. Core Computer Engineering Courses Students completing the program are COMS W4115: P rogramming languages and prepared to work (or study further) in translators

engineering 2011–2012 105 computer engineering program: first and second Years late-starting students

Semester i Semester iI Semester iII Semester iV

MATH V1202 (3) mathematics MATH V1101 (3) MATH V1102 (3) MATH V1201 (3) and APMA E2101 (3)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 C3045 or C1604 chemistry Lab C1500 (3) either semester or physics lab C1493 (3)

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

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

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

COMS W1007 (3) or W3203 (3)2 computer COMS W1004 (3)1 science W1009 Discrete math.

physical C1001 (1) C1002 (1) education

gateway lab E1102 (4) either semester

1 Only required if needed to prepare for COMS W1007/W1009. 2 Transfer and combined-plan students are expected to have completed the equivalent of the first- and second-year program listed above before starting their junior year. Note that this includes some background in discrete math (see COMS W3203) and electronic circuits (see ELEN E1201). Transfer and combined-plan students are also expected to be familiar with Java before they start their junior year. If students must take the one-point Java course (COMS W3101-03) junior year, prerequisite constraints make it difficult to complete the remaining computer engineering program by the end of the senior year. 3 APMA E2101 may be replaced by MATH E1210 and either APMA E3101 or MATH V2010.

engineering 2011–2012 106 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 core Required Data structures Courses COMS W3261 (3)3 ELEN E3201 (3.5) Models of comp. CSEE W4119 (3) or CSEE W4823 (3) Circuit analysis Computer networks Advanced logic design CSEE W3827 (3) ELEN E3801 (3.5) Fund. of computer Signals and systems systems

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

Tech 15 points required; see details on pages 105–107.4

Complete 27-point requirement; see page 10 or www.seas.columbia.edu for details nontech (administered by the advising dean). E lecti v e s

total points5 15 17 15 18­

For a discussion about programming languages used in the program, please see www.compeng.columbia.edu. 1 SIEO W3600, STAT W4105, and SIEO W4150 can be used instead of IEOR E3658, but W3600 and W4150 may not provide enough probability background for elective courses such as ELEN E3701. Students completing an economics minor who want such a background can take IEOR E3658 and augment it with STAT W1211. 2 If possible, ELEN E3081 and ELEN E3084 should be taken along with ELEN E3201 and ELEN 3801 respectively, and ELEN E3083 and ELEN E3082 taken with ELEN E3331 and CSEE W3827 respectively. 3 COMS W3261 can be taken one semester later than pictured. 4 The total points of technical electives is reduced to 12 if APMA E2101 has been replaced by MATH E1210 and either APMA E3101 or MATH V2010. 5 Assuming technical electives taken Semesters VII and VIII, and 9 points of nontechnical electives taken Semesters VI, VII, and VIII.

COMS W4118: Operating systems, I CSEE E6847: Distributed embedded systems The overall program must include at COMS W4130: P rinciples and practice of parallel CSEE E6861: Computer-aided design of digital least 15 points of 6000-level ELEN, programming systems EECS, CSEE, or COMS courses ELEN E4321: Digital VLSI circuits COMS W6998: T opics in computer science: formal (exclusive of seminars). No more than verification of hardware/software ELEN E4332: VLSI design laboratory* 9 points of research may be taken systems EECS E4340: Computer hardware design CSEE W4119: Computer networks ELEN E4702: Digital communications for credit. No more than 3 points of a CSEE W4140: Networking laboratory ELEN E4810: Digital signal processing nontechnical elective (at or above the COMS W4180: Network security ELEN E4830: Digital image processing 4000 level) may be included. A minimum CSEE W4823: Advanced logic design ELEN E4896: Music signal processing GPA of at least 2.7 must be maintained, CSEE W4824: Computer architecture ELEN E6321: Advanced digital electronic circuits and all degree requirements must CSEE W4825: Digital systems design* ELEN E6488: Optical interconnects and be completed within five years of the CSEE W4840: Embedded systems interconnection networks beginning of the first course credited COMS E6118: Operating systems, II* ELEN E6761: Computer communication CSEE E6180: Modeling and performance evaluation networks, I toward the degree. COMS E6181: Advanced Internet services ELEN E6762: Computer communication networks, II* CSEE E6824: Parallel computer architecture ELEN E6850: Visual information systems CSEE E6831: Sequential logic circuits* ELEN E6860: Advanced digital signal processing CSEE E6832: Topics in logic design theory* * Occasionally offered

engineering 2011–2012 Computer Science 107 450 Computer Science, MC 0401 Phone: 212-939-7000 www.cs.columbia.edu

Chair Professors Associate Lecturer in Associate Research Shree Kumar Nayar Alfred V. Aho Professors Discipline Scientists 450 Computer Science Peter K. Allen Luca Carloni Adam Cannon Marta Arias* 212-939-7004 Peter Belhumeur Stephen A. Edwards Jiang Chen* Steven M. Bellovin Luis Gravano Associated Faculty Wei Chu* Vice Chair Michael Collins Eitan Grinspun Shih-Fu Chang Mona Diab* Vishal Misra Steven K. Feiner Tony Jebara Edward G. Coffman Jr. Nizar Habash* 512 Computer Science Jonathan L. Gross Angelos D. Keromytis Dana Pe’er Claire Monteleoni* 212-939-7061 Julia Hirschberg Tal Malkin Clifford Stein Anargyros Papageorgiou Gail E. Kaiser Vishal Misra Steven H. Unger, Cynthia Rudin* Associate Chair John R. Kender Jason Nieh Professor Emeritus Ansaf Salleb-Audissi* for Undergraduate Kathleen R. McKeown Itsik Pe’er Vladimir Vapnik* Education Shree Kumar Nayar Daniel S. Rubenstein Adam Cannon Steven M. Nowick Rocco Servedio Senior Research 459 Computer Science Kenneth A. Ross Scientists 212-939-7016 Henning G. Schulzrinne Assistant David L. Waltz* Salvatore J. Stolfo Professors Arthur G. Werschulz Departmental Joseph F. Traub Augustin Chaintreau Moti Yung Administrator Henryk Wozniakowski Xi Chen Patricia Hervey Mihalis Yannakakis Roxana Geambasu Research Yechiam Yemini Martha Allen Kim Scientists Simha Sethumadhavan Rebecca Passonneau Junfeng Yang Owen Rambow* *Columbia Center for Computational Learning Systems

he function and influence of such areas as artificial intelligence, with 6 servers and business process the computer is pervasive computational complexity and the servers, a large student laboratory, T in contemporary society. analysis of algorithms, combinatorial featuring 18 Windows machines and 33 Today’s computers process the daily methods, computer architecture, Linux towers each with 8 cores and 24GB transactions of international banks, the computer-aided digital design, memory; a remote Linux cluster with 17 data from communications satellites, the computer communications, databases, servers, a large Linux compute cluster images in video games, and even the mathematical models for computation, and a number of computing facilities for fuel and ignition systems of automobiles. optimization, and software systems individual research labs. In addition, the Computer software is as data center houses a compute cluster commonplace in education and Laboratory Facilities consisting of a Linux cloud with 43 servers recreation as it is in science and The department has well-equipped lab each with 2 Nehalem processors, 8 business. There is virtually no field or areas for research in computer graphics, cores and 24GB memory. This cloud can profession that does not rely upon computer-aided digital design, computer support approximately 5000 of VMware computer science for the problem- vision, databases and digital libraries, instances. solving skills and the production data mining and knowledge discovery, Research labs contain Puma 500 expertise required in the efficient distributed systems, mobile and and IBM robotic arms; a UTAH-MIT processing of information. Computer wearable computing, natural-language dexterous hand; an Adept-1 robot; three scientists, therefore, function in a wide processing, networking, operating mobile research robots; a real-time variety of roles, ranging from pure systems, programming systems, defocus range sensor; PC interactive theory and design to programming and robotics, user interfaces, and real-time 3-D graphics workstations with 3-D marketing. multimedia. position and orientation trackers; The computer science curriculum The computer facilities include a prototype wearable computers, wall- at Columbia places equal emphasis shared infrastructure of Sun and Linux sized stereo projection systems; on theoretical computer science and multiprocessor file servers, NetApp file see-through headmounted displays; mathematics and on experimental servers, a student interactive teaching a networking testbed with three computer technology. A broad range and research lab of high-end multimedia Cisco 7500 backbone routers, traffic of upper-level courses is available in workstations, a load balanced Web cluster generators, Ethernet switches, Sun Ray

engineering 2011–2012 108 thin clients, and a 17-node (34CPU) multicomputer design, user interfaces, is an accepted substitute for W4150). IBM Netfinity cluster. The department VLSI applications, artificial intelligence, Collectively these courses are called the uses a 3COM SIP IP phone system. combinatorial modeling, virtual CS Core Curriculum. The protocol was developed in the environments, and microprocessor Students who pass the Computer department. applications. Students are strongly Science Advanced Placement (AP) The department’s computers are encouraged to arrange for participation Exam, either A or AB, with a 4 or 5 will connected via a switched 1 Gb/s by consulting individual faculty receive 3 points of credit and exemption Ethernet network, which has direct members. from COMS W1004. connectivity to the campus OC-3 Most graduates of the computer Note: A maximum of one course Internet and Internet2 gateways. The science program at Columbia step worth no more than 4 points passed campus has 802.11a/b wireless LAN directly into career positions in computer with a grade of D may be counted coverage. science with industry or government, toward the major or minor. The servers have remote consoles or continue their education in graduate and remote power for easy maintenance degree programs. Many choose to Track 1: Foundations of CS Track after hours. combine computer science with a The foundations track is suitable for The research facility is supported by second career interest by taking students who plan to concentrate on a full-time staff of professional system additional programs in business theoretical computer science in graduate administrators and programmers, administration, medicine, or other school or in mathematical topics such aided by a number of part-time student professional studies. as communications security or scientific system administrators. For further information on the computation in their career plans. undergraduate computer science Register for track course COMS E0001. program, please see the home page Undergraduate Program Required: 9 points (www.cs.columbia.edu/education/ Computer science majors at Columbia undergrad) and the Quick Guide (www. CSOR W4231: Analysis of algorithms study an integrated curriculum, partially COMS W4236: Introduction to computational cs.columbia.edu/education/undergrad/ in areas with an immediate relationship complexity seasguide). to the computer, such as programming COMS W4241: Numerical algorithms and complexity languages, operating systems, and Breadth: 6 points Technical Electives computer architecture, and partially Any COMS 3000- or 4000-level courses except in theoretical computer science and All technical electives except those those countable toward the CS core or foundations mathematics. Thus, students obtain the noted in each track must be approved of CS track by the adviser. In every case, the background to pursue their interests Electives: 15 points from the following list: both in applications and in theoretical technical elective course must be at the 3000 level or higher. All technical COMS W4203: Graph theory developments. COMS W4205: Combinatorial theory electives should be taken in computer Practical experience is an essential COMS W4252: Computational learning theory component of the computer science science. With the adviser’s approval, COMS W4261: Introduction to cryptography program. Undergraduate students however, courses in other departments COMS W4281: Quantum computing are often involved in advanced faculty may be taken as technical electives; COMS W4444: Programming and problem solving COMS W4771: Machine learning research projects using state-of-the-art in every such case, the subject of the COMS W4772: Advanced machine learning computing facilities. Qualified majors course must have a strong and obvious connection with computer science. COMS W4995: Math foundations of machine learning sometimes serve as consultants at COMS E6232: Analysis of algorithms, II COMS W4400: Computers and society the Computer Center, which operates COMS E6261: Advanced crytography several labs with microcomputers and ELEN E4901: Telecommunication COMS E6717: Information theory and terminals available at convenient networks and applications are not COMS E6998: Approximation algorithms locations on the campus. acceptable as technical electives COMS W3902: Undergraduate thesis (with adviser approval; may be repeated for Upper-level students in computer and are the only advanced computer credit) science may assist faculty members science courses that cannot be taken as electives. COMS W3998: Projects in Computer Science (with with research projects, particularly adviser approval; may be repeated Students are encouraged to select in the development of software. for credit) Ongoing faculty projects include one of the following five preapproved COMS W4901: Projects in Computer Science (with algorithmic analysis, computational groupings of electives called “tracks.” adviser approval; may be repeated complexity, software tool design, An advanced version of each track for credit) COMS E6901: Projects in Computer Science (with distributed computation, modeling and is available by invitation for qualified adviser approval; may be repeated performance evaluation, computer students who wish an extra opportunity for advanced learning. for credit) networks, computer architecture, Note: No more than 6 units of project/thesis The following courses are required CAD for digital systems, computer courses (COMS W3902, W3998, W4901, and graphics, programming environments, as a preparation for all tracks: COMS E6901) can count toward the major. expert systems, natural language W1004, W1007, W3137, W3157, processing, computer vision, robotics, W3203, W3210, W3251, W3261, CSEE W3827, and SIEO W4150 (SIEO W3600

engineering 2011–2012 Track 2: Systems Track COMS W4165: Pixel processing science, I and II (with 109 The systems track is for students COMS W4252: Computational learning theory adviser approval) Any COMS W47xx course if not used as a COMS E6901: P rojects in computer science (with interested in the implementation of required course adviser approval; may be repeated software and/or hardware systems. COMS W4995: Special topics, I (with adviser for credit) or other COMS E69xx Register for track course COMS E0002. approval; may be repeated) course (with adviser approval) Required: 9 points COMS W4996: Special topics, II (with adviser Any COMS E69xx course (with adviser approval) approval; may be repeated) Note: No more than 6 units of project/thesis COMS W4115: Programming languages and Any COMS W67xx course courses (COMS W3902, W3998, W4901, E6901) translators COMS E6998: T opics in computer science, I (with can count toward the major. COMS W4118: Operating systems adviser approval) CSEE W4119: Networking COMS E6999: Topics in computer science, II (with Track 5: Vision and Graphics Track Breadth: 6 points adviser approval) Objective: The vision and graphics track Any COMS 3000- or 4000-level course except Up to 6 points from the following list: exposes students to interesting new those countable for the CS core or systems track COMS W3902: U ndergraduate thesis (with adviser fields and focuses on visual information Electives: 15 points from the following list: approval; may be repeated for credit) with topics in vision, graphics, human- COMS W3998: U ndergraduate projects in computer Any COMS W41xx course computer interaction, robotics, science (with adviser approval; may Any COMS W48xx course modeling, and learning. Students learn COMS W4444: Programming and problem solving be repeated for credit) about fundamental ways in which visual COMS W3902: Undergraduate thesis (with adviser COMS W4901: Projects in computer science (with approval; may be repeated for credit) adviser approval; may be repeated information is captured, manipulated, COMS W3998: Undergraduate projects in computer for credit) and experienced. Register for track science (with adviser approval; may COMS E6901: P rojects in computer science (with course COMS E0005. be repeated for credit) adviser approval; may be repeated Required: 6 points COMS W4901: Projects in computer science (with for credit) COMS W4731: Computer vision adviser approval; may be repeated Up to 3 points from the following list: for credit) COMS W4160: Computer graphics COMS W4111: Database systems COMS W4995-W4996: Special topics in computer COMS W4160: Computer graphics Breadth: 6 points science COMS W4170: User interface design Any COMS 3000- or 4000-level courses except COMS E6901: Projects in computer science (with COMS W4999: Computing and the humanities those countable toward the CS core or vision and adviser approval; may be repeated Note: No more than 6 units of project/thesis graphics track for credit) courses (COMS W3902, COMS W3998, COMS Any COMS E61xx E68xx course (with adviser Electives: 18 points from the following list: W4901, COMS E6901) can count toward the approval) major. COMS W4162: Advanced computer graphics Note: No more than 6 units of project/thesis courses COMS W4165: Pixel processing (COMS W3902, COMS W3998, COMS W4901, COMS W4167: Computer animation COMS E6901) can count toward the major. Track 4: Applications Track COMS W4170: User interface design The applications track is for students COMS W4172: 3D user interface design Track 3: Artificial Intelligence Track interested in the implementation of COMS W4701: Artificial intelligence COMS W4733: Computational aspects of robotics The artificial intelligence track is interactive multimedia applications for the Internet and wireless networks. COMS W4735: Visual interfaces to computers for students interested in machine COMS W4771: Machine learning Register for track course COMS E0004. learning, robots, and systems capable COMS W4995: Video game technology and design of exhibiting “human-like” intelligence. Required: 9 points COMS W3902: Undergraduate thesis (with adviser A total of ten required, breadth, and COMS W4115: Programming languages and approval; may be repeated for credit) elective courses are to be chosen from translators the following schedule. Register for track COMS W4170: User interface design COMS W3998: U ndergraduate projects in course COMS E0003. COMS W4701: Artificial intelligence computer science (with adviser Required: 3 points Breadth: 6 points approval; may be repeated for COMS W4701: Artificial intelligence Any COMS 3000- or 4000-level courses except credit) those countable toward the CS core or applications COMS W4901: Projects in computer science (with Plus any 6 points from tracks adviser approval; may be repeated COMS W4705: Natural language processing for credit) COMS W4731: Computer vision Electives: 15 points from the following list: COMS W4995-W4496: Special topics in computer COMS W4733: Computational aspects of robotics Any COMS W41xx course science, I and II (with COMS W4771: Machine learning Any COMS W47xx course adviser approval) COMS W3902: U ndergraduate thesis (with adviser COMS E6901: Projects in computer science (with Breadth: 6 points approval; may be repeated for credit) adviser approval; may be repeated Any 3-point COMS 3000- or 4000-level course COMS W3998: U ndergraduate projects in computer for credit) except those countable toward the CS core or science (with adviser approval; may Any COMS E691x course (with adviser approval) elective courses for the artificial intelligence track be repeated for credit) Note: No more than 6 units of project/thesis COMS W4901: P rojects in computer science (with Electives: Up to 15 points from the following courses (COMS W3902, W3998, W4901, E6901) adviser approval; may be repeated list: can count toward the major. for credit) Any COMS W40xx course with adviser approval COMS W4995-W4996: Special topics in computer

engineering 2011–2012 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)

Chemistry or physics lab: physics C1401 (3) C1402 (3) PHYS C1493 (3) or (three tracks, C1601 (3.5) C1602 (3.5) CHEM W3081 (2) or choose one) C2801 (4.5) C2802 (4.5) 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 (three tracks, Z1003 (0) C1010 (3) choose one) Z0006 (0) Z1003 (0) C1010 (3)

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

required Professional-level course (3) (see page 12) either tech electives semester

COMS W3137 (4) COMS W1007 (3) Data structures Object-oriented and COMS W1004 (3) programming COMS W3157 (4) computer Intro. to computer science science and Adv. programming either semester COMS W3203 (3) and Discrete math COMS W3210 (3) Scientific computation

physical C1001 (1) C1002 (1) education

gateway lab E1102 (4) either semester

Track 6: Advanced courses for that track, prior to entry into the Invitation The advanced track of the B.S. in Advanced Track. There are two or three courses, Only the top 20 percent of computer science depending on the designated area. Computer Science provides extra majors in course performance in computer science courses will be considered for invitation during the opportunity for advanced learning. Breadth Requirement junior year. (A student in the advanced track who 6 points of any COMS 3000- or 4000-level courses It comprises accelerated versions of does not maintain this status may be required to except those that count toward the CS core or the other five tracks. Entry is only by return to his or her previously selected track area.) collective faculty invitation, extended to designated track. students who have already completed Electives Graduate Programs the core courses and the required At least 6 points of 4000-level lecture courses from courses for one of those tracks. the menu for the designated track, plus 6 points of The Department of Computer Science 6000-level courses in the designated track area. offers graduate programs leading Required Track Courses to the degree of Master of Science, A student designates one of the five other track Thesis the professional degree of Computer areas and completes the set of required track There is a required 6-point senior thesis. Systems Engineer and the degree

engineering 2011–2012 111 computer science: Third and Fourth Years

Semester V Semester VI Semester VII Semester VIII

COMS W3251 (3) Computational lin. algebra SIEO W4150 (3) Required COMS W3261 (3) or Courses Computer sci. theory SIEO W3600 (4) Prob. and stat. CSEE W3827 (3) Fund. of computer sys.

nonTech 3 points 6 points 3 points

Tech 3 points 6 points 12 points 9 points ELECTI V E S

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/W3137 is Java. COMS W1004 is waived for students who have scored 4 or 5 on the AP computer science exam.

of Doctor of Philosophy. Both the members of the Department of Journalism School. In addition to Aptitude Test and Advanced Tests Computer Science are engaged in taking classes already offered at the of the Graduate Record Examination experimental and theoretical research journalism and engineering schools, (GRE) are required for admission to in most of the fields in which courses students will attend a seminar and the department’s graduate programs. are offered. The degree of doctor of workshop designed specifically for Applicants for September admission philosophy requires a dissertation based the joint program. The seminar will should take the GREs by October of the on the candidate’s original research, teach students about the impact of preceding year. Applicants for January which is supervised by a faculty member. digital techniques on journalism; the admission should take these exams by The professional degree program emerging role of citizens in the news April of the preceding year. also provides the student with the process; the influence of social media; The course requirements in all opportunity to specialize beyond the and the changing business models programs are flexible, and each student level of the Master of Science program. that will support newsgathering. In the is urged to design his or her own The program leading to the degree workshop, students will use a hands- program under the guidance of a faculty of Computer Systems Engineer is on approach to delve deeply into adviser. The student’s program should particularly suited to those who wish to information design, focusing on how focus on a particular field of computer advance their professional development to build a site, section, or application science. Among the fields of graduate after a period of industrial employment. from concept to development, study in computer science are analysis ensuring the editorial goals are kept uppermost in mind. of algorithms, artificial intelligence, Dual Degree Program in expert systems, natural language Journalism and Computer understanding, computer vision, Science courses in computer multicomputer design, VLSI applications, The Graduate School of Journalism science combinatorial modeling, combinatorial and the School of Engineering In the listing below, the designator optimization, computational complexity, and Applied Science offer a dual COMS (Computer Science) is computer architecture and design, degree program leading to the M.S. understood to precede all course computer communications networks, degree from the Graduate School of numbers for which no designator is computer graphics, database machines Journalism and the M.S. degree in indicated. NOTE: Students may receive and systems, microprocessors, Computer Science from the School of credit for only one of the following three parallel computation, programming Engineering and Applied Science. courses: COMS W1003, W1004, and environments, programming languages, Admitted students will enroll W1005. Likewise students may receive robotics, user interfaces, software for a total of five semesters— credit for only one of the following three design, computational biology, computer approximately three in The Fu courses: COMS W3133, W3134, and security, and machine learning. Foundation School of Engineering W3137. Graduate students are encouraged and Applied Science and two in the actively to pursue research. Faculty

engineering 2011–2012 112 COMS W1001x and y Introduction to organization, structure, function and manipulation searching, hashing, garbage collection. Storage information science of the biomolecular sequences of nucleic management. Design and analysis of algorithms. 3 pts. Lect: 3. Professor Cannon. acids and proteins. The role of enzymes and Taught in Java. Note: Due to significant overlap, Basic Introduction to concepts and skills gene regulatory elements in natural biological students may receive credit for only one of the in Information Sciences: human-computer functions as well as in biotechnology and following four courses: COMS W3133, W3134, interfaces, representing information digitally, genetic engineering. Recombination and W3137, and W3139. organizing and searching information on the other macromolecular processes viewed COMS W3157x and y Advanced programming World Wide Web, principles of algorithmic as mathematical operations with simulation 4 pts. Lect: 4. problem solving, introduction to database and visualization using simple computer Prerequisite: COMS W1007. Practical, hands-on concepts, introduction to programming in Python. programming. This course shares lectures with introduction to programming techniques and tools ECBM E4060, but the work requirements differ COMS W1003x or y Introduction to computer for professional software construction, including somewhat. science and programming in C learning how to write code to given specifications 3 pts. Lect: 3. COMS W3101x and y Programming languages as well as document the results. Provides A general introduction to computer science 1 pt. Lect: 1. introductory overview of C and C++ in a UNIX concepts, algorithmic problem-solving Prerequisite: Fluency in at least one environment, for students with Java background. capabilities, and programming skills in C. programming language. Introduction to a Also introduces scripting languages (Perl) and Columbia University students may receive credit programming language. Each section is basic web programming. UNIX programming for only one of the following three courses: 1003, devoted to a specific language. Intended only utilities are also covered. Lab required. 1004, and 1005. for those who are already fluent in at least one COMS W3203x and y Discrete mathematics: programming language. Sections may meet for COMS W1004x and y Introduction to introduction to combinatorics and graph one hour per week for the whole term, for three computer science and programming in Java theory hours per week for the first third of the term, or 3 pts. Lect: 3. Professor Cannon. 3 pts. Lect: 3. Professor Gross. for two hours per week for the first six weeks. A general introduction to computer science for Prerequisite: Any introductory course in May be repeated for credit if different languages science and engineering students interested in computer programming. Logic and formal proofs, are involved. majoring in computer science or engineering. sequences and summation, mathematical Covers fundamental concepts of computer COMS W3133x or y Data structures in C induction, binomial coefficients, elements science, algorithmic problem-solving capabilities, 3 pts. Lect: 3. of finite probability, recurrence relations, and introductory Java programming skills. Prerequisite: COMS W1003 or knowledge of equivalence relations and partial orderings, and Assumes no prior programming background. C. Not intended for computer science majors. topics in graph theory (including isomorphism, Columbia University students may receive credit Data types and structures: arrays, stacks, singly traversability, planarity, and colorings). for only one of the following three courses: 1003, and doubly linked lists, queues, trees, sets, and COMS W3210y Scientific computation 1004, and 1005. graphs. Programming techniques for processing 3 pts. Lect: 3. such structures: sorting and searching, hashing, COMS W1005x and y Introduction to Prerequisites: Two terms of calculus. Introduction garbage collection. Storage management. computer science and programming in to computation on digital computers. Design Rudiments of the analysis of algorithms. Taught MATLAB and analysis of numerical algorithms. Numerical in C. Note: Due to significant overlap, students 3 pts. Lect: 3. Professor Blaer. solution of equations, integration, recurrences, may receive credit for only one of the following Prerequisites: None. Corequisites: None. chaos, differential equations. Introduction to four courses: COMS W3133, W3134, W3137, A general introduction to computer science Monte Carlo methods. Properties of floating point and W3139. concepts, algorithmic problem-solving arithmetic. Applications to weather prediction, capabilities, and programming skills in MATLAB. COMS W3134x and y Data structures in Java computational finance, computational science, Assumes no prior programming background. 3 pts. Lect: 3. and computational engineering. Columbia University students may receive credit Prerequisite: COMS W1004 or knowledge of COMS W3251x Computational linear algebra for only one of the following three courses: 1003, Java. Not intended for computer science majors. 3 pts. Lect: 3. Professor Papageorgiou. 1004, and 1005. Data types and structures: arrays, stacks, singly Prerequisites: Two terms of calculus. and doubly linked lists, queues, trees, sets, and COMS W1007x and y Object-oriented Computational linear algebra, solution of linear graphs. Programming techniques for processing programming and design in Java systems, sparse linear systems, least squares, such structures: sorting and searching, hashing, 3 pts. Lect: 3. Professor Kender. eigenvalue problems, and numerical solution of garbage collection. Storage management. Prerequisite: COMS W1004 or AP Computer other multivariate problems as time permits. Science with a grade of 4 or 5. The second Rudiments of the analysis of algorithms. Taught COMS W3261x and y Computer science theory course for majors in computer science. in Java. Note: Due to significant overlap, 3 pts. Lect: 3. Professor Aho. A rigorous treatment of object-oriented students may receive credit for only one of the Prerequisite: COMS W3203. Corequisite: COMS concepts using Java as an example language. following four courses: COMS W3133, W3134, W3137. Regular languages: deterministic Development of sound programming and design W3137, and W3139. and nondeterministic finite automata, regular skills, problem solving and modeling of real COMS W3137x and y Data structures and expressions. Context-free languages: context- world problems from science, engineering, and algorithms free grammars, push-down automata. Turing economics using the object-oriented paradigm. 4 pts. Lect: 3. Professor Hershkop. machines, the Chomsky hierarchy, and the Prerequisite: COMS W1007. Corequisite: COMS ECBM E3060x Introduction to genomic Church-Turing thesis. Introduction to complexity W3203. Data types and structures: arrays, information science and technology theory and NP-completeness. 3 pts. Lect: 3. Professor Anastassiou. stacks singly and doubly linked lists, queues, Introduction to the information system trees, sets, and graphs. Programming techniques paradigm of molecular biology. Representation, for processing such structures: sorting and

engineering 2011–2012 CSEE W3827x and y Fundamentals of COMS W4111x and y Introduction to databases of the UNIX operating system. A programming 113 computer systems 3 pts. Lect: 3. Professor Biliris. project is required. 3 pts. Lect: 3. Professor Edwards. Prerequisites: COMS W3137 or W3134, fluency CSEE W4119x and y Computer networks Prerequisite: An introductory programming in Java; or permission of the instructor. The 3 pts. Lect: 3. Professor Yemini. course. Fundamentals of computer organization fundamentals of database design and application Corequisite: SIEO W3600 or IEOR E3658 or and digital logic. Boolean algebra, Karnaugh development using databases: entity-relationship equivalent. Introduction to computer networks maps, basic gates and components, flip-flops modeling, logical design of relational databases, and the technical foundations of the Internet, and latches, counters and state machines, basics relational data definition and manipulation of combinational and sequential digital design. languages, SQL, XML, query processing, including applications, protocols, local area Assembly language, instruction sets, ALUs, physical database tuning, transaction processing, networks, algorithms for routing and congestion single-cycle and multi-cycle processor design, security. Programming projects are required. control, security, elementary performance introduction to pipelined processors, caches, and evaluation. Several written and programming COMS W4112y Database system virtual memory. assignments required. implementation COMS W3902x and y Undergraduate thesis 3 pts. Lect: 2.5. COMS W4130x Principles and practice of 1–6 pts. Prerequisites: COMS W4111; fluency in Java parallel programming Prerequisite: Agreement by faculty member or C++. CSEE W3827 is recommended. The 3 pts. Lect: 2.5. Professor Kim. to serve as thesis adviser. An independent principles and practice of building large-scale Prerequisites: experience in Java, basic theoretical or experimental investigation by an database management systems. Storage understanding of analysis of algorithms. COMS undergraduate major of an appropriate problem methods and indexing, query processing and W1004 and W3137 (or equivalent). Principles in computer science carried out under the optimization, materialized views, transaction of parallel software design. Topics include supervision of a faculty member. A formal written processing and recovery, object-relational task and data decomposition, load-balancing, report is mandatory and an oral presentation may databases, parallel and distributed databases, reasoning about correctness, determinacy, also be required. May be taken over more than performance considerations. Programming safety, and deadlock-freedom. Application of one term, in which case the grade is deferred projects are required. techniques through semester-long design project until all 6 points have been completed. Consult implementing performance, parallel application in the department for section assignment. COMS W4115x and y Programming languages a modern parallel programming language. and translators COMS W3995x or y Special topics in 3 pts. Lect: 3. Professor Edwards. CSEE W4140x or y Networking laboratory computer science Prerequisites: COMS W3137 or equivalent, 4 pts. Lect: 3. Professor Zussman. 3 pts. Lect: 3. W3261, and CSEE W3827, or instructor’s Prerequisite: CSEE 4119 or equivalent. In this Prerequisite: Instructor’s permission. Consult the permission. Modern programming languages course, students will learn how to put “principles department for section assignment. Special topics and compiler design. Imperative, object-oriented, into practice,” in a hands-on networking lab arranged as the need and availability arise. Topics declarative, functional, and scripting languages. course. The course will cover the technologies are usually offered on a one-time basis. Since and proctocols of the Internet using equipment the content of this course changes each time it is Language syntax, control structures, data currently available to large Internet service offered, it may be repeated for credit. types, procedures and parameters, binding, scope, run-time organization, and exception providers such as CISCO routers and end COMS W3998x and y Undergraduate projects handling. Implementation of language translation systems. A set of laboratory experiments provides in computer science tools including compilers and interpreters. hands-on experience with engineering wide- 1–3 pts. Lexical, syntactic and semantic analysis; code area networks and will familiarize students with Prerequisite: Approval by a faculty member who generation; introduction to code optimization. the Internet Protocol (IP), Address Resolution agrees to supervise the work. Independent project Teams implement a language and its compiler. Protocol (ARP), Internet Control Message involving laboratory work, computer programming, Protocol (ICMP), User Datagram Protocol (UDP) analytical investigation, or engineering design. COMS W4117x or y Compilers and interpreters and Transmission Control Protocol (TCP), the May be repeated for credit, but not for a total of 3 pts. Lect: 3. Domain Name System (DNS), routing protocols more than 3 points of degree credit. Consult the Prerequisite: COMS W4115 or instructor’s (RIP, OSPF, BGP), network management department for section assignment. permission. Continuation of COMS W4115, protocols (SNMP, and application-level protocols with broader and deeper investigation into the ECBM E4060x Introduction to genomic (FTP, TELNET, SMTP). design and implementation of contemporary information language translators, be they compilers or COMS W4156x Advanced software engineering 3 pts. Lect: 3. Professor Anastassiou. interpreters. Topics include: parsing, semantic 3 pts. Lect: 3. Professor Kaiser. Introduction to the information system analysis, code generation and optimization, run- Prerequisite: Substantial software development paradigm of molecular biology. Representation, time environments, and compiler-compilers. A experience in Java, C++ or C# beyond the level organization, structure, function, and manipulation of COMS W3157. Recommended corequisite: of the biomolecular sequences of nucleic programming project is required. COMS W4111. Software lifecycle from the acids and proteins. The role of enzymes and COMS W4118x and y Operating systems, I viewpoint of designing and implementing N-tier gene regulatory elements in natural biological 3 pts. Lect: 3. Professor Nieh. applications (typically utilizing Web browser, functions as well as in biotechnology and Prerequisites: CSEE W3827 and knowledge of web server, application server, database). genetic engineering. Recombination and C and programming tools as covered in W3157 Major emphasis on quality assurance (code other macromolecular processes viewed as or W3101, or instructor’s permission. Design inspection, unit and integration testing, security mathematical operations with simulation and and implementation of operating systems. and stress testing). Centers on a student- visualization using simple computer programming. Topics include process management, process designed team project that leverages component This course shares lectures with ECBM E3060, synchronization and interprocess communication, services (e.g., transactions, resource pooling, but the work requirements differ somewhat. memory management, virtual memory, interrupt publish/subscribe) for an interactive multi-user handling, processor scheduling, device application such as a simple game. management, I/O, and file systems. Case study

engineering 2011–2012 114 COMS W4160y Computer graphics software support. 3D interaction devices and problems into complexity classes, reductions and 3 pts. Lect: 3. Professor Reed. displays. Virtual and augmented reality. Tangible completeness. Power and limitations of different Prerequisite: COMS W3137 or W3139; W4156 is user interfaces. Review of relevant 3D math. modes of computation such as nondeterminism, recommended. Strong programming background randomization, interaction and parallelism. COMS W4180x or y Network security and some mathematical familiarity including 3 pts. Lect: 3. COMS W4241y Numerical algorithms and linear algebra is required. Introduction to Prerequisites: COMS W3137 and W4119, or complexity computer graphics. Topics include 3D viewing instructor’s permission. Introduction to network 3 pts. Lect: 3. and projections, geometric modeling using spline security concepts and mechanisms. Foundations Prerequisite: Knowledge of a programming curves, graphics systems such as OpenGL, of network security and an in-depth review language. Some knowledge of scientific lighting and shading, and global illumination. of commonly-used security mechanisms and computation is desirable. Modern theory and Significant implementation is required: the final techniques, security threats and network- practice of computation on digital computers. project involves writing an interactive 3D video based attacks, applications of cryptography, Introduction to concepts of computational game in OpenGL. authentication, access control, intrusion detection complexity. Design and analysis of numerical COMS W4162x or y Advanced computer and response, security protocols (IPsec, SSL, algorithms. Applications to computational graphics Kerberos), denial of service, viruses and worms, finance, computational science, and 3 pts. Lect: 3. software vulnerabilities, Web security, wireless computational engineering. security, and privacy. Prerequisite: COMS W4160 or equivalent, or COMS W4252x or y Introduction to instructor’s permission. A second course in COMS W4187x or y Security architecture and computational learning theory computer graphics covering more advanced engineering 3 pts. Lect: 3. Professor Servedio. topics including image and signal processing, 3 pts. Lect: 3. Professor Cook. Prerequisites: CSOR W4231 or COMS W4236 geometric modeling with meshes, advanced Prerequisite: COMS W4118; W4180 and/or or W3203 and permission of instructor or image synthesis including ray tracing and global W4119 recommended. Secure programming. COMS W3261 and permission of instructor. illumination, and other topics as time permits. Cryptograhic engineering and key handling. Possibilities and limitations of performing Emphasis will be placed both on implementation Access controls. Trade-offs in security design. learning by computational agents. Topics include of systems and important mathematical and Design for security. computational models of learning, polynomial geometric concepts such as Fourier analysis, time learnability, learning from examples and mesh algorithms and subdivision, and Monte COMS W4203y Graph theory learning from queries to oracles. Computational Carlo sampling for rendering. Note: Course will 3 pts. Lect: 3. Professor Gross. and statistical limitations of learning. Applications be taught every two years. Prerequisite: COMS W3203. General introduction to Boolean functions, geometric functions, to graph theory. Isomorphism testing, algebraic COMS W4167x or y Computer animation automata. 3 pts. Lect: 3. Professor Grinspun. specification, symmetries, spanning trees, Prerequisites: COMS W3137 and W4156 is traversability, planarity, drawings on higher-order COMS W4261x or y Introduction to recommended. Previous familiarity with C is surfaces, colorings, extremal graphs, random cryptography recommended. Intensive introduction to computer graphs, graphical measurement, directed graphs, 3 pts. Lect: 2.5. Professor Malkin. animation, including: fundamental theory and Burnside-Polya counting, voltage graph theory. Prerequisites: Comfort with basic discrete math and probability. Recommended: COMS W3261 algorithms for computer animation, keyframing, COMS W4205x Combinatorial theory or CSOR W4231. An introduction to modern kinematic rigging, simulation, dynamics, free- 3 pts. Lect: 3. cryptography, focusing on the complexity- form animation, behavioral/procedural animation, Prerequisites: COMS W3203 and course in particle systems, post-production; small groups theoretic foundations of secure computation and calculus. Sequences and recursions, calculus of implement a significant animation project; communication in adversarial environments; a finite differences and sums, elementary number advanced topics as time permits. rigorous approach, based on precise definitions theory, permutation group structures, binomial and provably secure protocols. Topics include COMS W4170x User interface design coefficients, Stilling numbers, harmonic numbers, private and public key encryption schemes, 3 pts. Lect: 3. Professor Feiner. generating functions. digital signatures, authentication, pseudorandom Prerequisite: COMS W3137. Introduction to the CSOR W4231x Analysis of algorithms, I generators and functions, one-way functions, theory and practice of computer user interface 3 pts. Lect: 3. Professor Stein. trapdoor functions, number theory and design, emphasizing the software design of Prerequisites: COMS W3137 or W3139, and computational hardness, identification and zero graphical user interfaces. Topics include basic W3203. Introduction to the design and analysis knowledge protocols. interaction devices and techniques, human of efficient algorithms. Topics include models factors, interaction styles, dialogue design, and COMS W4281x or y Introduction to quantum of computation, efficient sorting and searching, software infrastructure. Design and programming computing algorithms for algebraic problems, graph projects are required. 3 pts. Lect: 3. algorithms, dynamic programming, probabilistic Prerequisite: Knowledge of linear algebra. Prior COMS W4172y 3D user interfaces and methods, approximation algorithms, and knowledge of quantum mechanics is not required augmented reality NP-completeness. 3 pts. Lect: 3. although helpful. Introduction to quantum Prerequisite: COMS W4160 or W4170 or COMS W4236y Introduction to computational computing. Shor’s factoring algorithm, Grover’s instructor’s permission. Design, development, complexity database search algorithm, the quantum and evaluation of 3D user interfaces. Interaction 3 pts. Lect: 3. summation algorithm. Relationship between techniques and metaphors, from desktop to Prerequisite: COMS W3261. Develops a classical and quantum computing. Potential immersive. Selection and manipulation. Travel quantitative theory of the computational difficulty power of quantum computers. and navigation. Symbolic, menu, gestural, and of problems in terms of the resources (eg., time, multimodal interaction. Dialogue design. 3D space) needed to solve them. Classification of

engineering 2011–2012 EECS E4340x Computer hardware design practices, determining the information needs of COMS W4731x or y Computer vision 115 3 pts. Lect: 2. Professor Sethumadhavan. health care providers and patients, developing 3 pts. Lect: 3. Professor Nayar. Prerequisites: ELEN E3331 plus ELEN E3910 interventions using computer technology, and Prerequisites: The fundamentals of calculus, or CSEE W3827. Practical aspects of computer evaluating the impact of those interventions. linear algebra, and C programming. Students without any of these prerequisites are advised hardware design through the implementation, COMS W4701x or y Artificial intelligence simulation, and prototyping of a PDP-8 3 pts. Lect: 3. Professor Pasik. to contact the instructor prior to taking the processor. High-level and assembly languages, Prerequisite: COMS W3137. Provides a broad course. Introductory course in computer vision. I/O, interrupts, datapath and control design, understanding of the basic techniques for Topics include image formation and optics, piplelining, busses, memory architecture. building intelligent computer systems. Topics image sensing, binary images, image processing Programmable logic and hardware prototyping include state-space problem representations, and filtering, edge extraction and boundary with FPGAs. Fundamentals of VHDL for register- problem reduction and and-or graphs, game detection, region growing and segmentation, transfer level design. Testing and validation of playing and heuristic search, predicate calculus, pattern classification methods, brightness and hardware. Hands-on use of industry CAD tools and resolution theorem proving, AI systems reflectance, shape from shading and photometric for simulation and synthesis. Lab required. and languages for knowledge representation, stereo, texture, binocular stereo, optical flow and machine learning and concept formation and motion, 2D and 3D object representation, object COMS W4444x Programming and problem other topics such as natural language processing recognition, vision systems and applications. solving may be included as time permits. 3 pts. Lect: 3. Professor Ross. COMS W4733x or y Computational aspects Prerequisites: COMS W3137 and CSEE W3827. COMS W4705x Natural language processing of robotics Hands-on introduction to solving open-ended 3 pts. Lect: 3. Professor Collins. 3 pts. Lect: 3. Professor Allen. computational problems. Emphasis on creativity, Prerequisite: COMS W3133, or W3134, or Prerequisite: COMS W3137. Introduction to cooperation, and collaboration. Projects W3137, or W3139, or instructor’s permission. robotics from a computer science perspective. spanning a variety of areas within computer Computational approaches to natural language Topics include coordinate frames and science, typically requiring the development of generation and understanding. Recommended kinematics, computer architectures for computer programs. Generalization of solutions preparation: Some previous or concurrent robotics, integration and use of sensors, world to broader problems, and specialization of exposure to AI or machine learning. Topics modeling systems, design and use of robotic complex problems to make them manageable. include information extraction, summarization, programming languages, and applications of Team-oriented projects, student presentations, machine translation, dialogue systems, and artificial intelligence for planning, assembly, and and in-class participation required. emotional speech. Particular attention is given to manipulation. COMS W4460x Principles of innovation and robust techniques that can handle understanding COMS W4735x or y Visual interfaces to entrepreneurship and generation for the large amounts of text on computers 3 pts. Lect: 3. Professor Yemini. the Web or in other large corpora. Programming 3 pts. Lect: 3. Prerequisites: COMS W3134, W3137, or exercises in several of these areas. Prerequisite: COMS W3137. Visual input as equivalent, or permission of instructor. Team COMS W4706y Spoken language processing data and for control of computer systems. project-centered course focused on principles 3 pts. Lect: 3. Not offered in 2011–2012. Survey and analysis of architecture, algorithms, of planning, creating, and growing a technology Prerequisite: COMS W3133, or W3134, and underlying assumptions of commercial venture. Topics include: identifying and and research systems that recognize and or W3137, or instructor’s permission. analyizing opportunities created by technology interpret human gestures, analyze imagery Computational approaches to speech generation paradigm shifts, designing innovative products, such as fingerprint or iris patterns, generate and understanding. Topics include speech protecting intellectual property, engineering natural language descriptions of medical or recognition and understanding, speech analysis innovative business models. map imagery. Explores foundations in human for computational linguistics research, and psychophysics, cognitive science, and artificial COMS W4560x Introduction to computer speech synthesis. Speech applications including intelligence. applications in health care and biomedicine dialogue systems, data mining, summarization, 3 pts. Lect: 3. and translation. Exercises involve data analysis COMS W4737x or y Biometrics Prerequisites: Experience with computers and and building a small text-to-speech system. 3 pts. Lect: 3. Professor Belhumeur. a passing familiarity with medicine and biology. Prerequisite: A background at the sophomore Undergraduates in their senior or junior years COMS W4725x or y Knowledge representation level in computer science, engineering, or like and reasoning may take this course only if they have adequate discipline. Corequisites: None. In this course we background in mathematics and receive 3 pts. Lect: 3. will explore the latest advances in biometrics as permission from the instructor An overview of Prerequisite: COMS W4701. General aspects well as the machine learning techniques behind the field of biomedical informatics, combining of knowledge representation (KR). The two them. Students will learn how these technologies perspectives from medicine, computer science, fundamental paradigms (semantic networks work and how they are sometimes defeated. and social science. Use of computers and and frames) and illustrative systems. Topics Grading will be based on homework assignments information in health care and the biomedical include hybrid systems, time, action/plans, and a final project. There will be no midterm or sciences, covering specific applications and defaults, abduction, and case-based reasoning. final exam. This course shares lectures with COMS general methods, current issues, capabilities and Throughout the course particular attention is E6737. Students taking COMS E6737 are required limitations of biomedical informatics. Biomedical paid to design trade-offs between language to complete additional homework problems and Informatics studies the organization of medical expressiveness and reasoning complexity, and undertake a more rigorous final project. Students information, the effective management of issues relating to the use of KR systems in larger will only be allowed to earn credit for COMS information using computer technology, and the applications. W4737 or COMS E6737 but not both. impact of such technology on medical research, education, and patient care. The field explores techniques for assessing current information

engineering 2011–2012 116 CBMF W4761x or y Computational genomics Advanced topics in digital logic: controller COMS W4996x or y Special topics in 3 pts. Lect: 3. synthesis (Mealy and Moore machines); adders computer science, II Prerequisites: Introductory probability and and multipliers; structured logic blocks (PLDs, 3 pts. Lect: 3. statistics and basic programming skills. PALs, ROMs); iterative circuits. Modern design Prerequisite: Instructor’s permission. A Provides comprehensive introduction to methodology: register transfer level modelling continuation of COMS W4995 when the special computational techniques for analyzing (RTL); algorithmic state machines (ASMs); topic extends over two terms. genomic data including DNA, RNA and protein introduction to hardware description languages COMS E6111y Advanced database Systems structures; microarrays; transcription and (VHDL or Verilog); system-level modelling and 3 pts. Lect: 2. Professor Gravano. regulation; regulatory, metabolic and protein simulation; design examples. Prerequisites: COMS W4111 and knowledge of interaction networks. The course covers CSEE W4824x or y Computer architecture Java or instructors permission. Continuation sequence analysis algorithms, dynamic 3 pts. Lect: 3. Professor Carloni. of COMS W4111, covers latest trends in both programming, hidden Markov models, Prerequisite: CSEE W3827 or equivalent. database research and industry: information phylogenetic analysis, Bayesian network Focuses on advanced topics in modern retrieval, web search, data mining, data techniques, neural networks, clustering computer architecture, illustrated by recent warehousing, OLAP, decision support, algorithms, support vector machines, Boolean case studies. Fundamentals of quantitative multimedia databases, and XML and databases. models of regulatory networks, flux based analysis. Pipelined, out-of-order, and speculative Programming projects required. analysis of metabolic networks and scale-free execution. Superscalar, VLIW, and vector network models. The course provides self- COMS E6113y Topics In database systems processors. Embedded processors. Memory contained introduction to relevant biological 3 pts. Lect: 2. Not offered in 2011–2012. hierarchy design. Multiprocessors and thread- mechanisms and methods. Prerequisite: COMS W4111. Concentration on level parallelism. Synchronization and cache some database paradigm, such as deductive, COMS W4771y Machine learning coherence protocols. Interconnection networks. heterogeneous, or object-oriented, and/or 3 pts. Lect: 3. CSEE W4840y Embedded systems some database issue, such as data modeling, Prerequisites: Any introductory course in linear 3 pts. Lect: 3. distribution, query processing, semantics, or algebra and any introductory course in statistics Prerequisite: CSEE W4823. Embedded system transaction management. A substantial project are both required. Highly recommended: design and implementation combining hardware is typically required. May be repeated for credit COMS W4701 or knowledge of artificial and software. I/O, interfacing, and peripherals. with instructor’s permission. intelligence. Topics from generative and Weekly laboratory sessions and term project on discriminative machine learning including least COMS E6117x or y Topics in programming design of a microprocessor-based embedded squares methods, support vector machines, languages and translators system including at least one custom peripheral. kernel methods, neural networks, Gaussian 3 pts. Lect: 2. Knowledge of C programming and digital logic distributions, linear classification, linear Prerequisite: COMS W4115 or instructor’s required. Lab required. regression, maximum likelihood, exponential permission. Concentration on the design and family distributions, Bayesian networks, Bayesian COMS W4901x and y Projects in computer implementation of programming languages, inference, mixture models, the EM algorithm, science and tools focused on advanced applications in graphical models and hidden Markov models. 1–3 pts. new areas in software verification, distributed Algorithms implemented in Matlab. Prerequisite: Approval by a faculty member who systems, programming in the large, and web agrees to supervise the work. A second-level computing. A substantial project is typically COMS W4772x Advanced machine learning independent project involving laboratory work, required. May be repeated for credit. 3 pts. Lect: 3. Professor Jebara. computer programming, analytical investigation, Prerequisites: COMS W4771 or permission COMS E6118y Operating systems, II or engineering design. May be repeated for of instructor; knowledge of linear algebra and 3 pts. Lect: 2. Not offered in 2011–2012. credit, but not for a total of more than 3 points of introductory probability or statistics is required. Prerequisite: COMS W4118. Corequisite: COMS degree credit. Consult the department for section An exploration of advanced machine learning W4119. Continuation of COMS W4118, with assignment. tools for perception and behavior learning. emphasis on distributed operating systems. Topics How can machines perceive, learn from, COMS W4910x and y Curricular practical include interfaces to network protocols, distributed and classify human activity computationally? training run-time binding, advanced virtual memory issues, Topics include appearance-based models, 1 pt. advanced means of interprocess communication, principal and independent components analysis, Prerequisites: Obtained internship and approval file system design, design for extensibility, security dimensionality reduction, kernel methods, from faculty adviser. Only for M.S. students in in a distributed environment. Investigation is manifold learning, latent models, regression, the Computer Science department who need deeper and more hands-on than in COMS W4118. classification, Bayesian methods, maximum relevant work experience as part of their program A programming project is required. entropy methods, real-time tracking, extended of study. Final report required. This course may COMS E6121x Reliable software Kalman filters, time series prediction, hidden not be taken for pass/fail credit or audited. 3 pts. Lect: 3. Professor Yang. Markov models, factorial HMMs, input-output COMS W4995x or y Special topics in Prerequisite: at least one of COMS W4118, HMMs, Markov random fields, variational computer science, I W4115, or W4117, or significant software methods, dynamic Bayesian networks, and 3 pts. Lect: 3. Professors Abrams, Chaintreau, development experiences. Topics include: Gaussian/Dirichlet processes. Links to cognitive Chen, Hirschberg, and Yee. automated debugging, automated software science. Prerequisite: Instructor’s permission. Special repair, concurrent software reliability, software CSEE W4823x or y Advanced logic design topics arranged as the need and availability arises. error detection, and more. 3 pts. Lect: 3. Professor Nowick. Topics are usually offered on a one-time basis. COMS E6123x or y Programming Since the content of this course changes each time Prerequisite: CSEE 3827, or a half-semester environments and software tools (PEST) it is offered, it may be repeated for credit. Consult introduction to digital logic, or equivalent. An 3 pts. Lect: 2. the department for section assignment. introduction to modern digital system design. Prerequisites: At least one COMS W41xx or

engineering 2011–2012 COMS E61xx course and/or COMS W4444, or orientation, motion, environmental context, COMS E6204x or y Topics in graph theory 117 instructor’s permission. Strongly recommended: and personal context. Applications and social 3 pts. Lect: 2. COMS W4156. Software methodologies and consequences. Prerequisite: COMS W4203 or instructor’s technologies concerned with development permission. Content varies from year to CSEE E6180x or y Modeling and performance and operation of today’s software systems. year. This course may be repeated for credit. 3 pts. Lect: 2. Reliability, security, systems management and Concentration on some aspect of graph theory, Prerequisites: COMS W4118 and SIEO W4150. societal issues. Emerging software architectures such as topological graph theory, algebraic graph Introduction to queuing analysis and simulation such as enterprise and grid computing. Term theory, enumerative graph theory, graphical techniques. Evaluation of time-sharing and paper and programming project. Seminar focus optimization problems, or matroids. multiprocessor systems. Topics include priority changes frequently to remain timely. queuing, buffer storage, and disk access, COMS E6206x or y Topics in combinatorial COMS E6125y Web-enhanced information interference and bus contention problems, and theory management (WHIM) modeling of program behaviors. 3 pts. Lect: 2. 3 pts. Lect: 2. Prerequisite: COMS W4203 or W4205, or COMS E6181x or y Advanced Internet Prerequisites: At least one COMS W41xx or instructor’s permission. Concentration on some services COMS E61xx course and/or COMS W4444, or aspect of combinatorial theory. Content varies 3 pts. Lect: 2. Professor Schulzrinne. instructor’s permission. Strongly recommended: from year to year. This course may be repeated In-depth survey of protocols and algorithms COMS W4111. History of hypertext, markup for credit. needed to transport multimedia information languages, groupware and the Web. Evolving across the Internet, including audio and video COMS E6232x or y Analysis of algorithms, II Web protocols, formats and computation encoding, multicast, quality-of-service, voice-over 3 pts. Lect: 2. paradigms such as HTTP, XML and Web IP, streaming media and peer-to-peer multimedia Prerequisites: CSOR W4231. Continuation of Services. Novel application domains enabled by systems. Includes a semester-long programming CSOR W4231. the Web and societal issues. Term paper and project. programming project. Seminar focus changes COMS E6253y Advanced topics in frequently to remain timely. COMS E6183x or y Advanced topics in computational learning theory network security 3 pts. Lect: 3. Not offered in 2011–2012. COMS E6160x or y Topics in computer 3 pts. Lect: 3. Prerequisite: CSOR W4231 or equivalent; COMS graphics Prerequisites: COMS W4180, CSEE 4119 W4252 or W4236 helpful but not required. 3 pts. Lect: 2. and COMS W4261 recommended. Review In-depth study of inherent abilities and limitations Prerequisite: COMS W4160 or instructor’s the fundamental aspects of security, including of computationally efficient learning algorithms. permission. An advanced graduate course, authentication, authorization, access control, Algorithms for learning rich Boolean function involving study of an advanced research topic confidentiality, privacy, integrity, and availability. classes in online, Probably Approximately in Computer Graphics. Content varies between Review security techniques and tools, and their Correct, and exact learning models. Connections offerings, and the course may be repeated applications in various problem areas. Study with computational complexity theory for credit. Recent offerings have included the state of the art in research. A programming emphasized. Substantial course project or term appearance models in graphics, and high quality project is required. paper required. real-time rendering. COMS E6184y Seminar on anonymity and COMS E6261x or y Advanced cryptography COMS E6174y Interaction design: a privacy 3 pts. Lect: 3. perceptual approach 3 pts. Lect: 3. Not offered in 2011–2012. Prerequisite: W4261. A study of advanced 3 pts. Lect: 3. Prerequisite: COMS W4261 or W4180 or cryptographic research topics such as: Prerequisite: COMS W4170 or instructor’s CSEE W4119 or instructor’s permission. This secure computation, zero knowledge, permission. Design methology for special- course covers the following topics: Legal and privacy, anonymity, cryptographic protocols. purpose user interfaces. Emphasis on how social framework for privacy. Data mining and Concentration on theoretical foundations, psychology and perception inform good design. databases. Anonymous commerce and Internet rigorous approach, and provable security. Interviewing and task modeling, participatory usage. Traffic analysis. Policy and national Contents varies between offerings. May be design, and low-fidelilty prototyping. Applications security considerations. Classes are seminars repeated for credit. of brain research, graphic design and art to with students presenting papers and discussing develop custom user interfaces components, COMS E6291x or y Theoretical topics in them. Seminar focus changes frequently to remain screen layouts, and interaction techniques for computer science timely. application-specific systems. 3 pts. Lect: 3. COMS E6185x or y Intrusion and anomaly Prerequisite: Instructor’s permission. COMS E6176x or y User interfaces for mobile detection systems Concentration on some theoretical aspect of and wearable computing 2 pts. Lect: 2. Professor Stolfo. computer science. Content varies from year to 3 pts. Lect: 2. Pre- or corequisite: COMS W4180 Network year. May be repeated for credit. Prerequisite: COMS W4170 or instructor’s security. The state of threats against computers, permission. Introduction to research on user COMS E6732x or y Computational imaging and networked systems. An overview of interfaces for mobile and wearable computing 3 pts. Lect: 3. computer security solutions and why they fail. through lectures, invited talks, student- Prerequisite: COMS W4731 or instructor’s Provides a detailedtreatment for network and led discussions of important papers, and permission. Computational imaging uses a host-based intrusion detection and intrusion programming projects. Designing and authoring combination of novel imaging optics and a prevention systems. Considerable depth is for mobility and wearability. Ubiquitous/ computational module to produce new forms provided on anomaly detection systems to detect pervasive computing. Collaboration with other of visual information. Survey of the state of new attacks. Covers issues and problems in users. Display, interaction, and communication art in computational imaging. Review of recent e-mail (spam, and viruses) and insider attacks technologies. Sensors for tracking position, papers on: omnidirectional and panoramic (masquerading and impersonation). imaging, catadioptric imaging, high dynamic

engineering 2011–2012 118 range imaging, mosaicing and superresolution. discipline. Corequisites: None In this course we of embedded software. Research challenges Classes are seminars with the instructor, guest will explore the latest advances in biometrics as such as design complexity, reliability, scalability, speakers, and students presenting papers and well as the machine learning techniques behind safety, and security. The course requires discussing them. them. Students will learn how these technologies substantial reading, class participation and a work and how they are sometimes defeated. research project. COMS E6733x or y 3D photography Grading will be based on homework assignments 3 pts. Lect: 2. CSEE E6861y Computer-aided design of and a final project. There will be no midterm Prerequisite: Experience with at least one of the digital systems or final exam. This course shares lectures with following topics: Computer graphics, computer 3 pts. Lect: 2. COMS W4737. Students taking COMS E6737 vision, pixel processing, robotics or computer- Prerequisites: (i) one semester of advanced are required to complete additional homework aided design, or permission of instructor. digital logic (CSEE W4823 or equivalent, problems and undertake a more rigorous final Programming proficiency in C, C++, or JAVA. or instructor’s permission); and (ii) a basic project. Students will only be allowed to earn credit 3D Photography—the process of automatically course in data structures and algorithms for COMS W4737 or COMS E6737 but not both. creating 3D, texture-mapped models of objects COMS W3133, 3134, 3137, 3139, or 3157, or in detail. Applications include robotics, medicine, CSEE E6824y Parallel computer architecture equivalent, and familiarity with programming. graphics, virtual reality, entertainment and digital 3 pts. Lect: 2. Introduction to modern digital CAD synthesis movies etc. Topics include 3D data acquisition Prerequisite: CSEE W4824. Parallel computer and optimization techniques. Topics include: devices, 3D modeling systems and algorithms principles, machine organization and design of modern digital system design (high-level to acquire, create, augment, manipulate, render, parallel systems including parallelism detection synthesis, register-transfer level modeling, animate and physically build such models. methods, synchronization, data coherence and algorithmic state machines, optimal scheduling interconnection networks. Performance analysis algorithms, resource allocation and binding, COMS E6734y Computational photography and special purpose parallel machines. retiming), controller synthesis and optimization, 3 pts. Lect: 3. exact and heuristic two-level logic minimization, Prerequisites: COMS W4160, W4731, CSEE E6831y Sequential logic circuits advanced multilevel logic optimization, optimal or a working knowledge of photography 3 pts. Lect: 3. Not offered in 2011–2012. technology mapping to library cells (for delay, are recommended. Students should have Prerequisite: CSEE W3827 or any introduction power and area minimization), advanced knowledge in any of three core areas: computer to logic circuits. Generation and manipulation data structures (binary decision diagrams), vision, computer graphics, or photography. of flow table descriptions to asynchronous SAT solvers and their applications, static Computational techniques are used to produce a sequential functions. Coding of flow tables to timing analysis, and introduction to testability. new level of images and visual representations. satisfy various design criteria. Delays, races, Includes hands-on small design projects using Topics include HDR imaging, feature matching hazards, metastability. Analysis of latches to and creating CAD tools. using RANSAC, image mosaics, image-based determine key parameters. Bounds of input rendering, motion magnification, camera lens rates. Clocking schemes for synchronous EECS E6870x or y Speech recognition arrays, programmable lighting, face detection, systems. Synthesis of self-timed systems using 3 pts. Lect: 3. single and multiview geometry, and more. 4-phase or 2-phase handshakes. Prerequisites: Basic probability and statistics. Theory and practice of contemporary COMS E6735y Visual databases CSEE E6832x or y Topics in logic design automatic speech recognition. Gaussian 3 pts. Lect: 3. Not offered in 2011–2012. theory mixture distributions, hidden Markov models, Prerequisites: COMS W3133, W3134, or W3137 3 pts. Lect: 3. pronunciation modeling, decision trees, finite- required. COMS W4731 and W4735 helpful but Prerequisite: CSEE W3827 or any introduction to state transducers, and language modeling. not required. Contact instructor if uncertain. logic circuits. A list of topics for each offering of Selected advanced topics will be covered in The analysis and retrieval of large collections the course is available in the department office more depth. of image and video data, with emphasis on one month before registration. May be taken visual semantics, human psychology, and more than once if topics are different Iterative COMS E6900x and y Tutorial in computer user interfaces. Low-level processing: features logic circuits applied to pattern recognition. Finite science and similarity measures; shot detection; key state machines; alternative representations, 1–3 pts. frame selection; machine learning methods information loss, linear circuits, structure theory. Prerequisite: Instructor’s permission. A reading for classification. Middle-level processing: Reliability and testability of digital systems. course in an advanced topic for a small number organizational rules for videos, including of students, under faculty supervision. CSEE E6847y Distributed embedded systems unedited (home, educational), semiedited 3 pts. Lect: 2. Not offered in 2011–2012. COMS E6901x Projects in computer science (sports, talk shows), edited (news, drama); Prerequisite: Any COMS W411X, CSEE W48XX, 1–12 pts. human memory limits; progressive refinement; or ELEN E43XX course, or permission of Prerequisite: Instructor’s permission. Software visualization techniques; incorporation of audio instructor. An interdisciplinary graduate-level or hardware projects in computer science. and text. High-level processing: extraction of seminar on the design of distributed embedded Before registering, the student must submit a thematic structures; ontologies, semantic filters, systems. System robustness in the presence written proposal to the instructor for review. and learning; personalization of summaries and of highly variable communication delays and The proposal should give a brief outline of the interfaces; detection of pacing and emotions. heterogeneous component behaviors. The project, estimated schedule of completion, and Examples and demonstrations from commercial study of the enabling technologies (VLSI computer resources needed. Oral and written and research systems throughout. Substantial circuits, communication protocols, embedded reports are required. May be taken over more course project or term paper required. processors, RTOSs), models of computation, than one semester, in which case the grade COMS E6737x or y Biometrics and design methods. The analysis of modern will be deferred until all 12 points have been 3 pts. Lect: 3. domain-specific applications including on-chip completed. No more than 12 points of COMS Prerequisite: Background at the sophomore micro-networks, multiprocessor systems, fault- E6901 may be taken. Consult the department for level in computer science, engineering, or like tolerant architectures, and robust deployment section assignment.

engineering 2011–2012 COMS E6902x and y Thesis COMS E6999x and y Topics in computer candidates holding GRA or TA appointments. 119 1–9 pts. science, II Note: It is NOT required that a student take Available to M.S. and CSE candidates. An 3 pts. Graduate research, I prior to taking Graduate independent investigation of an appropriate Prerequisite: COMS E6998. Continuation of COMS research, II. Consult the department for section problem in computer science carried out E6998. assignment. under the supervision of a faculty member. A COMS E9800x and y Directed research in COMS E9911x and y Graduate research, II formal written report is essential and an oral computer science 1-15 pts. presentation may also be required. May be 1–15 pts. Prerequisites: Submission of an outline of the taken over more than one semester, in which Prerequisites: Submission of outline of proposed proposed research for approval by the faculty case the grade will be deferred until all 9 points research for approval by faculty member who member who will supervise. The department have been completed. No more than 9 points will supervise. The department must approve the must approve the number of points. May be of COMS E6902 may be taken. Consult the number of points. May be repeated for credit. repeated for credit. This course is only for M.S./ department for section assignment. This course is only for Eng.Sc.D. candidates. Ph.D. track and Ph.D. students. Note: It is NOT COMS E6998x and y Topics in computer COMS E9910x and y Graduate research, I required that a student take Graduate research, I science 1–6 pts. prior to taking Graduate research, II. Consult the 3 pts. Members of the faculty. Prerequisites: Submission of an outline of the department for section assignment. Prerequisite: Instructor’s permission. Selected proposed research for approval by the faculty topics in computer science. Content varies from member who will supervise. The department year to year. May be repeated for credit. must approve the number of credits. May be repeated for credit. This course is only for M.S.

engineering 2011–2012 120 Earth and Environmental Engineering Henry Krumb School of Mines 918 S. W. Mudd, MC 4711 Phone: 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 Adjunct Assistant Senior Research Klaus Lackner Paul F. Duby Professors Professors Scientist Klaus Lackner Marco J. Castaldi Michael Bell Vasilis Fthenakis Vice Chair Upmanu Lall Pierre Gentine Pietro Ceccato Tuncel M. Yegulalp Ismail C.Noyan Ah-Hyung (Alissa) Park Scott Kaufman Associate Peter Schlosser Sri Rangarajan Research Departmental Ponisseril Adjunct Scientists Administrator Somasundaran Professors Instructor Irina Chernyshova Dawn Delvalle Nickolas J. Themelis William Becker Chris Gazze S. Murthy Khondrika Nicholas J. Turro Robert Farrauto Hyung Chul Kim Administrative Tuncel M. Yegulalp Yuri Gorokhovich Doherty Research Assistant Ian Morrison Scientist Adjunct Senior Gary S. Hill Associate Wade McGillis Research Scientist Professors Adjunct Associate Ray Farinato Kartik Chandran Professor Xi Chen Lei Zhang

Earth Resources and the department in the U.S. It became the of Applied Physics and Applied Environment foundation for Columbia’s School of Mathematics, is described in another The Earth and Environmental Engineering and Applied Sciences and section of this bulletin. Engineering program fosters education has been a pioneer in many areas of • The Earth Engineering Center and research in the development mining and metallurgy, including the first (www.seas.columbia.edu/earth). The and application of technology for the mining (Peele) and mineral processing current research areas include energy, sustainable development, use, and (Taggart) handbooks, flotation, chemical materials, and water resources. integrated management of Earth’s thermodynamics and kinetics, surface and colloid chemistry, and materials resources. Resources are identified Earth and Environmental science. as minerals, energy, water, air, Engineering (EEE) and land, as well as the physical, Nearly 100 years after its formation, Starting in 1996, the educational chemical, and biological components the School of Mines was renamed programs of Columbia University in of the environment. There is close Henry Krumb School of Mines (HKSM) mining and mineral engineering were collaboration with other engineering in honor of the generous Columbia transformed into the present program disciplines, the Lamont-Doherty Earth benefactor of the same name. The in Earth and Environmental Engineering Observatory, the International Research Henry Krumb School of Mines supports (EEE). This program is concerned with Institute for Climate Prediction, the three components: the environmentally sound extraction Center for Environmental Research and • The Department of Earth and and processing of primary materials Conservation, and other Columbia Earth Environmental Engineering (minerals, fuels, water), the management Institute units. (www.eee.columbia.edu) (EEE), and development of land and water one of Columbia Engineering’s nine resources, and the recycling or disposal departments. The Henry Krumb School of used materials. EEE offers the • Columbia’s interdepartmental of Mines at Columbia Bachelor of Science (B.S.) in Earth and program in Materials Science and Environmental Engineering, the Master University Engineering (www.seas.columbia. of Science (M.S.) in Earth Resources The School of Mines of Columbia edu/matsci) (MSE). This program, Engineering, the professional degrees University was established in 1864 and administered by the Department was the first mining and metallurgy of Engineer of Mines and Metallurgical

engineering 2011–2012 Engineer, and the doctorate degrees making, including the development management of wastes is most acute. 121 (Ph.D., Eng.Sc.D.) in EEE. of a forum, the Global Roundtable The Earth Engineering Center, in The EEE program welcomes on Water (GROW), to facilitate collaboration with the Department of Combined Plan students. An EEE minor international policy and technical Earth and Environmental Engineering, is offered to all Columbia engineering action to improve our collective water has already been engaged in this role, students who want to enrich their future. and some of our alumni are working in academic record by concentrating For more information: www.water. various parts of the waste management some of their technical electives on columbia.edu industry. There have been more than Earth/Environment subjects. There is twenty theses written on various aspects close collaboration between EEE and Center for Life Cycle Analysis (LCA). of waste management, including the Departments of Civil Engineering The Center for Life Cycle Analysis of in-depth studies of implementing and Earth and Environmental Sciences, Columbia University was formed in the advanced processes and methodologies including several joint appointments. spring of 2006 with the objective of in Chile, China, Greece, and India. For conducting comprehensive life cycle more information: www.surcenter.org analyses of energy systems. LCA Research Centers provides a framework for quantifying Earth Engineering Center. The Associated with Earth the potential environmental impacts of mission of the Earth Engineering and Environmental material and energy inputs and outputs Center is to develop and promote Engineering of a process or product from “cradle engineering methodologies that Columbia Water Center. The Columbia to grave.” The mission of the Center provide essential material to humanity Water Center, in collaboration with is to guide technology and energy in ways that maintain the overall other Earth Institute units and external policy decisions with data- based, well- balance between the constantly partners, is leading intellectual inquiry balanced, and transparent descriptions increasing demand for materials, the into an assessment, prediction, and of the environmental profiles of energy finite resources of the Earth, and solution of the potentially global crisis of systems. For more information: www. the need for clean water, soil, and freshwater scarcity. Goals are to: clca.columbia.edu air. The Center is dedicated to the • Develop multiscale predictive advancement of industrial ecology, i.e., capabilities (e.g., new data sets and Center for Sustainable Use of the reconfiguring of industrial activities modeling tools) for local, regional, and Resources (SUR). The Center for and products with full knowledge of global water resource assessment, Sustainable Use of Resources builds recognizing changing climate, the environmental consequences. on the strengths of past research at Research is being conducted on a demographic, and usage dynamics Columbia and North Carolina State on • Target analyses toward public and variety of geoenvironmental issues recycling, composting, waste-to-energy, private investment in future water with the intent to quantify, assess, and landfill engineering. Also, the Center resource development, local and and ultimately manage adverse human will clearly define the impacts of all solid regional ecosystem services provided effects on the environment. Research waste technologies and practices with by water and the essential life-support areas include management of water regard to greenhouse gas emissions and water needs of societies and energy resources, hydrology and will, on a case-by-case basis, establish • Identify and test appropriate hydrogeology, numerical modeling of and validate protocols that account for technologies for the storage, estuarine flow and transport processes, greenhouse gas emissions and savings treatment, and conveyance of water and integrated waste management. that may be easily replicated and to improve reliable, cost-efficient For more information, visit www.seas. access readily accepted. SUR will also identify columbia.edu/earth/index.html. • Identify and compare locally technologies that can replace some appropriate policy instruments that virgin feedstock with appropriate local Environmental Tracer Group (ETG). facilitate the implementation of waste streams. Through its publications, The Environmental Tracer Group uses selected incentives for higher-value, meetings, and Web page, SUR will natural and anthropogenic (frequently higher-efficiency water use, while disseminate information on the best transient) tracers, as well as deliberately promoting equity of use and life waste management technologies and released tracers, to investigate the support functions methods that, on a life-cycle basis, will physics and chemistry of transport in • Test and demonstrate the applicability result in reducing the impacts of waste environmental systems. The tracers of the policy and technology management on global climate change. include natural or anthropogenically developments in real-world settings, An equally important objective of the produced isotopes (e.g., tritium or working with local institutions and Center is to provide graduate-level radioactive hydrogen, helium and private-sector developers or users in training, at the participating universities, oxygen isotopes, or radiocarbon), as an open and public process in the ways and means of sustainable well as noble gases and chemical • Develop and disseminate the resource utilization to engineers and compounds (e.g., CFCs and SF6). knowledge base that results from scientists from the U.S. and around the The ETG analytical facilities include our activities to support global water world, in particular from the developing four mass spectrometric systems that resource development and decision world, where the need for modern can be used in the analysis of tritium

engineering 2011–2012 122 and noble gases in water, sediments, capability to understand, anticipate, and develop new sources, technologies, and and rocks. In addition to the mass manage the impacts of seasonal climate infrastructures. spectrometric systems, there are several fluctuations, in order to improve human The Lenfest Center focuses primarily gas chromatographic systems equipped welfare and the environment, especially in on the technological and institutional with electron capture detectors that developing countries. This mission is to be development of the three energy are used for measurements of SF6 in conducted through strategic and applied resources sufficient to support the continental waters and CFCs and SF6 research, education and capacity building, world’s projected population in 2100 in the atmosphere. GC/MS capability and provision of forecast and information without increased carbon emissions: is being added to the spectrum of products, with an emphasis on practical solar, nuclear, and fossil fuels combined analytical capabilities. and verifiable utility and partnerships. with carbon capture and storage. Although each of these options can, Industry/University Cooperative Langmuir Center for Colloids in theory, be developed on a scale to Research Center for Advanced and Interfaces (LCCI). This Center satisfy global demand, they each face Studies in Novel Surfactants (IUCS). brings together experts from mineral a combination of technological and IUCS was established in 1998 by engineering, applied chemistry, chemical institutional obstacles that demand the Henry Krumb School of Mines, engineering, biological sciences, and research and development before they Department of Chemical Engineering, chemistry to probe complex interactions can be deployed. and Department of Chemistry at of colloids and interfaces with The Center’s main activities are Columbia University. The Center surfactants and macromolecules. LCCI based within the range of natural encompasses detailed structure- activities involve significant interaction science and engineering disciplines. property assessment of several with industrial sponsors and adopt At the same time, it integrates classes of surface-active molecules, an interdisciplinary approach toward technological research with analysis including oligomeric, polymeric, and state-of-the-art research on interfacial of the institutional, economic, and bio-molecules. The aim of IUCS is phenomena. Major areas of research political context within which energy to develop and characterize novel at LCCI are thin films, surfactant and technologies are commercialized and surfactants for industrial applications polymer adsorption, environmental deployed. For more information: www. such as coatings, dispersions, problems, enhanced oil recovery, energy.columbia.edu deposition, gas hydrate control, personal computer tomography, corrosion and Waste to Energy Research and care products, soil decontamination, catalysis mechanisms, membrane Technology Council (WTERT). The waste treatment, corrosion prevention, technology, novel separations of Waste to Energy Research and flotation, and controlled chemical minerals, biocolloids, microbial surfaces, Technology Council brings together reactions. The proposed research thus and interfacial spectroscopy. engineers, scientists, and managers focuses on the design and development from industry, universities, and of specialty surfactants, characterization Lenfest Center for Sustainable Energy. government with the objective of of their solution and interfacial behavior, The mission of the Lenfest Center advancing the goals of sustainable and identification of suitable industrial for Sustainable Energy is to develop waste management globally. The applications for these materials. technologies and institutions to ensure mission of WTERT is to identify the The goals of IUCS are to perform a sufficient supply of environmentally best available technologies for the industrially relevant research to sustainable energy for all humanity. To treatment of various waste materials, address the technological needs in meet this goal, the Center supports conduct additional academic research commercial surfactant and polymer research programs in energy science, as required, and disseminate this systems; develop new and more engineering, and policy across Columbia information by means of its publications, efficient surface-active reagents for University to develop technical and policy the WTERT Web, and annual specific applications in the industry solutions that will satisfy the world’s meetings. In particular, WTERT strives and methodologies for optimizing future energy needs without threatening to increase the global recovery of their performance; promote the use of to destabilize Earth’s natural systems. energy and materials from used solids environmentally benign surfactants in a The mission of the Lenfest Center and to advance the economic and wide array of technological processes; is shaped by two global challenges. environmental performance of waste-to- and build a resource center to perform First, the Center seeks to reduce the energy (WTE) technologies in the U.S. and provide state-of-the-art facilities emission of carbon dioxide into the and worldwide. The guiding principle is for characterization of surface-active atmosphere and to forestall a disruption that responsible management of wastes reagents: www.columbia.edu/cu/iucrc. of global climate systems that would impose negative consequences for must be based on science and the International Research Institute for human welfare. Second, the Center best available technology and not what Climate Prediction (IRI). The IRI is seeks to create energy options that will seems to be inexpensive now but can the world’s leading institute for the meet the legitimate energy demands be very costly in the near future. For development and application of seasonal of a larger and increasingly wealthy more information: www.seas.columbia. to interannual climate forecasts. The world population. In order to meet these edu/earth/wtert mission of the IRI is to enhance society’s two challenges, the Center seeks to

engineering 2011–2012 Scholarships, Fellowships, 2. Graduates will be able to pursue Technical Elective Concentrations 123 and Internships careers in industry, government Students majoring in Earth and Environ­ The department arranges for agencies, and other organizations mental Engineering select one of the undergraduate summer internships concerned with the environment following three preapproved technical after the sophomore and junior years. and the provision of primary and elective concentrations. Note that Undergraduates can also participate in secondary materials and energy, the eight-course sequence for each graduate research projects under the as well as continue their education preapproved concentration includes two work-study program. Graduate research as graduate students in related science courses during sophomore year and teaching assistantships, as well as disciplines. (fall semester) and six technical elective fellowships funded by the Department, 3. Graduates will possess the basic skills courses during junior and senior years. are available to qualified graduate needed for the practice of Earth and Any deviations from a preapproved students. GRE scores are required of all Environmental Engineering, including concentration must be approved by applicants for graduate studies. measurement and control of material an undergraduate faculty adviser. flows through the environment; Alternatives for junior/senior electives assessment of environmental impact within each concentration are listed, and Undergraduate Program of past, present, and future industrial others may be considered among 3000- The Bachelor of Science (B.S.) degree activities; and analysis and design of to 4000-level courses of any Columbia in Earth and Environmental Engineering processes for remediation, recycling, Engineering department, as well as prepares students for careers in the and disposal of used materials. courses listed in the section “Courses in public and private sector concerned with 4. Graduates will practice their Other Divisions” in this bulletin. However, primary materials (minerals, fuels, water) profession with excellent written at least four of the six junior/senior and the environment. Graduates are and communication skills and electives must consist of engineering also prepared to continue with further with professional ethics and topics. Alternatives for sophomore-year studies in Earth/Environmental sciences responsibilities. science courses are shown in the EEE and engineering, business, public policy, program table. international studies, law, and medicine. The Curriculum A student may also choose to The EEE program is accredited as an The first two years of the EEE program develop an individual concentration environmental engineering program are similar to those of other engineering conforming to his/her specific interests, by the Engineering Accreditation programs. Students are provided with provided that it satisfies ABET Commission of ABET. a strong foundation in basic sciences engineering accreditation criteria. and mathematics, as well as the liberal Therefore, this must be developed in What Is Earth and Environmental arts core. Specific to the EEE program close consultation with and approved by Engineering? is an early and sustained introduction a faculty adviser. It is now recognized by the U.S. and to Earth science and environmental other nations that continuing economic engineering, and options for a number Water Resources and Climate Risks development must be accompanied by of science courses to meet the specific Concentration intelligent use of Earth’s resources and interests of each student. The junior Preapproved course sequence: that engineers can contribute much and senior years of the program PHYS C1403: Introduction to classical and quan- to the global efforts for sustainable consist of a group of required courses tum waves (SEM III) development. The technologies that in engineering science and a broad EESC V2100: Climate system (SEM III) EAEE E4006: Field methods for environmental have been developed for identifying, selection of technical electives organized extracting, and processing primary engineering (SEM VI) into three distinct concentrations, EAEE E4009: G IS for resource, environmental, materials are also being applied to representing major areas of focus within and infrastructure management the twenty-first-century problems of the department. (SEM VII) resource recovery from used materials, Several Columbia departments, EAEE E4350: Planning and management of urban pollution prevention, and environmental such as Civil Engineering, Mechanical hydrologic systems (SEM VII) remediation. The EEE undergraduate Engineering, and Earth and Environ- EAEE E4257: Environmental data analysis and modeling (SEM VIII) program encompasses these mental Sciences (Lamont-Doherty Earth technologies. ECIA W4100: Management and development of Observatory), as well as the Mailman water systems (SEM VIII) School of Public Health, contribute CIEE E4257: G roundwater contaminant transport Undergraduate Program Objectives courses to the EEE program. EEE and remediation 1. Graduates equipped with the students are strongly encouraged to Alternatives for junior/senior electives: necessary tools (mathematics, work as summer interns in industry or EAEE E4001: Industrial ecology of Earth resources chemistry, physics, Earth sciences, agencies on projects related to Earth CIEE E4260: Urban ecology studio and engineering science) will and environmental engineering. The CIEE E4163: E nvironmental engineering: wastewater understand and implement the department helps students get summer CIEN E4250: Waste containment design and practice underlying principles used in the internships. CIEN E4255: F low in porous media engineering of processes and APPH E4200: P hysics of fluids EESC W4008: Introduction to atmospheric science systems.

engineering 2011–2012 124 earth and environmental engineering program: first and second Years

Semester i Semester iI Semester iII Semester iV

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

C1401 (3) C1402 (3)

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

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

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

EESC W4001 (4) SIEO W3600 (4) or Introduction to EESC V2100 (4.5) probability and statistics required EAEE E1100 (3) A or profESSIONAL better planet by design EESC V2200 (4.5) and techNICAL or other departmental electives professional-level course EEAE E2002 (3) Alternative energy sources

computer Computer language: COMS W1003 (3) W1004 (3) any semester science or

physical C1001 (1) C1002 (1) education

gateway lab E1102 (4) either semester

EESC W4401: Quantitative models of climate- Sustainable Energy and Materials EAEE E4361: Economics of Earth resource sensitive natural and human Concentration industries (SEM VII) systems Preapproved course sequence: EAEE E4900: Applied transport and chemical rate EESC W4404: R egional dynamics, climate and CHEM C3443: O rganic chemistry (SEM III) phenomena (SEM VII) climate impacts EESC V2200: Solid earth system (SEM III) EAEE E4190: Photovoltaic systems engineering EESC W4001: Advanced general geology (SEM III) and sustainability (SEM VII) MECE E3311: H eat transfer (SEM VI) MECE E4302: A dvanced thermodynamics (SEM VIII) EAEE E4001: Industrial ecology of Earth EESC W3015: T he Earth’s carbon cycle (SEM VIII) resources (SEM VII) MECE E4211: E nergy: sources and conversion (SEM VIII)

engineering 2011–2012 125 earth and environmental engineering program: THIRD and FOURTH Years

Semester V Semester VI Semester VII Semester VIII

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

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

ENME E3161 (4) Fluid mechanics EAEE E4160 (3) EAEE E3801 (2) or Solid and hazardous Earth and environmental MECE E3100 (3) waste management engineering lab, II Required Introduction to mechanics Courses of fluids

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

TechNICAL 3 points 6 points 9 points ELECTIVES

NONTechNICAL 3 points 3 points 6 points ELECTIVES

total points 15–17 17 16 17

Alternatives for junior/senior electives: EHSC P6300: Environmental health sciences Graduate Programs CHEN E3110: T ransport phenomena, I (SEM VII) CHEN E3120: T ransport phenomena, II EAEE E4257: E nvironmental data analysis and M.S. in Earth Resources MSAE E3103: Elements of materials science modeling (SEM VIII) CHEM C3071: Introduction to organic chemistry EAEE E4150: A ir pollution prevention and control Engineering (M.S.-ERE) CHEM G4230: Statistical thermodynamics (SEM VIII) The M.S.-ERE program is designed EAEE E4550: Catalysis for emissions control EHSC P6309: Biochemistry basic to environmental for engineers and scientists who plan EESC W4008: Introduction to atmospheric science health (SEM VIII) to pursue, or are already engaged EAEE E4560: Particle technology Alternatives for junior/senior electives: in, environmental management/ EAEE E4001: Industrial ecology of Earth resources development careers. The focus of the Environmental Health Engineering EAEE E4900: Applied transport and chemical rate program is the environmentally sound Concentration phenomena mining and processing of primary EAEE E4950: Environmental biochemical Preapproved course sequence: materials (minerals, energy, and water) CHEM C3443: O rganic chemistry (SEM III) processes and the recycling or proper disposal EESC V2100: Climate system (SEM III) CIEE E4257: G roundwater contaminant transport EAEE E4006: Field methods for environmental and remediation of used materials. The program also engineering (SEM VI) CIEE E4163: Environmental engineering: includes technologies for assessment EAEE E4009: G IS for resource, environmental wastewater and remediation of past damage to the and infrastructure management environment. Students can choose a (SEM VII) pace that allows them to complete the

engineering 2011–2012 126 M.S.-ERE requirements while being Water Resources and Climate Risks are tightly coupled. Fossil fuel resources employed. Climate-induced risk is a significant are still plentiful, but access to energy is M.S.-ERE graduates are specially component of decision making for the limited by environmental and economic qualified to work for engineering, planning, design, and operation of water constraints. A future world population financial, and operating companies resource systems, and related sectors of 10 billion people trying to approach engaged in mineral processing ventures, such as energy, health, agriculture, the standard of living of the developed the environmental industry, environmental ecological resources, and natural nations cannot rely on today’s energy groups in all industries, and for city, hazards control. Climatic uncertainties technologies and infrastructures without state, and federal agencies responsible can be broadly classified into two areas: severe environmental impacts. Concerns for the environment and energy/resource (1) those related to anthropogenic over climate change and changes in conservation. At the present time, the climate change; (2) those related to ocean chemistry require reductions in U.S. environmental industry comprises seasonal- to century-scale natural carbon dioxide emissions, but most nearly 30,000 big and small businesses variations. The climate change issues alternatives to conventional fossil with total revenues of more than $150 impact the design of physical, social, fuels, including nuclear energy, are too billion. Sustainable development and and financial infrastructure systems to expensive to fill the gap. Yet access environmental quality has become a top support the sectors listed above. The to clean, cheap energy is critical for priority of government and industry in the climate variability and predictability providing minimal resources: water, United States and many other nations. issues impact systems operation, and food, housing, and transportation. This M.S. program is offered in hence design. The goal of the M.S. Concentration-specific classes will collaboration with the Departments concentration in water resources and sketch out the availability of resources, of Civil Engineering and Earth and climate risks is to provide (1) a capacity their geographic distribution, the Environmental Sciences. Many of for understanding and quantifying the economic and environmental cost of the teaching faculty are affiliated with projections for climate change and resource extraction, and avenues for Columbia’s Earth Engineering Center. variability in the context of decisions for increasing energy utilization efficiency, For students with a B.S. in water resources and related sectors such as cogeneration, district heating, engineering, at least 30 points (ten of impact; and (2) skills for integrated and distributed generation of energy. courses) are required. For students risk assessment and management Classes will discuss technologies with a nonengineering B.S. or a B.A., for operations and design, as well for efficiency improvement in the preferably with a science major, up as for regional policy analysis and generation and consumption sector; to 48 points (total of sixteen courses) management. Specific areas of interest energy recovery from solid wastes; may be required for makeup courses. include: alternatives to fossil fuels, including Students may carry out a research • Numerical and statistical modeling of solar and wind energy, and nuclear project and write a thesis worth 3–6 global and regional climate systems fission and fusion; and technologies for points. A number of areas of study are and attendant uncertainties addressing the environmental concerns available for the M.S.-ERE, and students • Methods for forecasting seasonal to over the use of fossil fuels and nuclear may choose courses that match their interannual climate variations and their energy. Classes on climate change, air interest and career plans. The areas of sectoral impacts quality, and health impacts focus on study include: • Models for design and operation of the consequences of energy use. Policy • Alternative energy and carbon water resource systems, considering and its interactions with environmental management climate and other uncertainties sciences and energy engineering will • Climate risk assessment and • Integrated risk assessment and be another aspect of the concentration. management management across water resources Additional specialization may consider • Environmental health engineering and related sectors region specific energy development. • Integrated waste management • Natural and mineral resource Sustainable Energy Integrated Waste Management (IWM) development and management Building and shaping the energy Humanity generates nearly 2 billion tons • Novel technologies: surficial and infrastructure of the twenty-first century of municipal solid wastes (MSW) annually. colloidal chemistry and is one of the central tasks for modern Traditionally, these wastes have been nanotechnology engineering. The purpose of the discarded in landfills that have a finite • Urban environments and spatial analysis sustainable energy concentration is lifetime and then must be replaced by converting more greenfields to landfills. Additionally, there are four optional to expose students to modern energy This method is not sustainable because concentrations in the program, in each technologies and infrastructures and to it wastes land and valuable resources. of which there are a number of required the associated environmental, health, Also, it is a major source of greenhouse specific core courses and electives. The and resource limitations. Emphasis gases and of various contaminants of concentrations are described briefly will be on energy generation and use air and water. In addition to MSW, the below; details and the lists of specific technologies that aim to overcome the U.S. alone generates billions of tons of courses for each track are available from limits to growth that are experienced industrial and extraction wastes. Also, the department. today. Energy and economic well-being the by-product of water purification is a

engineering 2011–2012 sludge or cake that must be disposed practitioners and engineers, who usually The qualifying examination will be an 127 in some way. The IWM concentration have very little understanding of the role oral exam administered by four faculty prepares engineers to deal with the of the other profession in this process. members. The adviser of the student will major problem of waste generation The goal is to train those specialists be a member of the exam committee by exposing them to environmentally collaboratively, through the Departments but may not be the chair. The students better means for dealing with wastes: of Earth and Environmental Engineering will be examined in their understanding waste reduction, recycling, composting, and Environmental Health Sciences. of fundamentals as they apply in the and waste-to-energy via combustion, four general areas of research of the anaerobic digestion, or gasification. Joint Degree Programs department: water resources, materials Students are exposed not only to the The Graduate School of Business and processing, energy, and chemical and technical aspects of integrated waste the School of Engineering and Applied biochemical processes. It is expected management but also to the associated Science offer a joint program leading to that each question period will last about economic, policy, and urban planning the M.B.A. degree from the Graduate 20 minutes, of which 15 minutes will issues. School of Business and the M.S. degree be led by the faculty member from the Since the initiation of the Earth and in Earth resources engineering from area and the remaining 5 minutes will be environmental engineering program in the School of Engineering and Applied open for questions by all faculty present 1996, there have been several graduate Science. The purpose of this program at the exam. There will be a final period research projects and theses that is to train students who wish to pursue of 20 minutes for general questions. exemplify the engineering problems Earth resource management careers. All graduate students are expected that will be encompassed in this Students are expected to register to have a background equivalent to concentration: full time for three terms in the Graduate the required core of our undergraduate • Of an automated materials recovery School of Business and for two terms in program. They have, of course, facility the School of Engineering and Applied an opportunity to make up for any • Analysis of the bioreactor landfill Science. It is possible, however, to deficiency in their master’s program. • Generation of methane by anaerobic study in the School of Engineering and In order to be prepared for the exam, digestion of organic materials Applied Science part time. Interested students can take at least one course • Design of corrosion inhibitors persons should contact Professor in each core area during their first two • Flocculation modeling Tuncel Yegulalp at 212-854-2984 or by semesters at Columbia (see website • Analysis of formation of dioxins in e-mail to: [email protected]. for up-to-date course listing). In case high-temperature processes the student declares an explicit minor • Combination of waste-to-energy and Doctoral Programs in another department, the qualifying anaerobic digestion exam requirements will be modified EEE offers two doctoral degrees: • Application of GIS in siting new WTE in consultation with the graduate (1) the Eng.Sc.D. degree, administered facilities committee. The minor has to be by Columbia Engineering; and (2) the • Corrosion phenomena in WTE approved by both departments. Ph.D. degree, administered by the • Combustion chambers The engineering objectives of EEE Graduate School of Arts and Sciences. • Mathematical modeling of transport research and education include: phenomena in a combustion chamber • Provision and disposal of materials: Doctoral Qualifying Examination and • Effect of oxygen enrichment on environmentally sustainable Research Proposal • Combustion of paper and other types extraction and processing of primary of solid wastes Before the end of the first semester in materials; manufacturing of derivative • Feasibility study and design of WTE the doctoral program, the student and products; recycling of used materials; facilities her/his adviser will set up an advisory management of industrial residues committee of two or three faculty and used products; materials-related Environmental Health Engineering members. This committee will meet application of industrial ecology. at least once a semester to assess The purpose of this concentration is to • Management of water resources: academic and research progress of the train professionals who can address understanding, prediction, and student and to recommend corrective both the public health and engineering management of the processes that action in case of emerging or existing aspects of environmental problems. govern the quantity and quality of deficiencies. The identification and evaluation of water resources, including the role Doctoral students are required environmental problems frequently of climate; development/operation of to pass a qualifying exam soon after revolve around the risks to human water resource facilities; management the completion of their first year into health, whereas the development of of water-related hazards. the program (spring or fall). They will remediation or prevention strategies • Energy resources and carbon submit and defend their research frequently involves engineering management: mitigation of proposal approximately one year after approaches. Currently, these two critical environmental impacts of energy successful completion of the qualifying steps in addressing environmental production; energy recovery from exam. Submission of the dissertation problems are handled by two separate waste materials; advancement of and thesis defense will follow general groups of professionals, public health energy efficient systems; new energy University rules.

engineering 2011–2012 128 sources; development of carbon EAEE E1100y A better planet by design and their impact on the environment and the sequestration strategies. 3 pts. Lect: 3. Professors Lau and Park. biogeochemical cycles; chemical extraction from • Sensing and remediation: Development of the infrastructure for providing mineral ores, and metallurgical processes for understanding of transport processes safe and reliable resources (energy, water and extraction of metals. In analogy to metallurgical at different scales and in different other materials, transportation services) to support processing, power generation and the refining human societies while attaining environmental of fuels are treated as extraction and refining media; containment systems; objectives. Introduction of a typology of problems processes. Large scale of power generation modeling flow and transport in surface by context, and common frameworks for address- and a discussion of its impact on the global and subsurface systems; soil/water ing them through the application of appropriate biogeochemical cycles. decontamination and bioremediation. technology and policy. An interdisciplinary perspec- MSAE E3111x Thermodynamics, kinetic tive that focuses on the interaction between human theory, and statistical mechanics The Professional Degrees and natural systems is provided. Alternatives for 3 pts. Lect: 3. Professor Billinge. resource provision and forecasts of their potential The department offers the professional An introduction to the basic thermodynamics environmental impacts through a context provided degrees of Engineer of Mines (E.M.) of systems, including concepts of equilibrium, by real-world applications and problems. and Metallurgical Engineer (Met.E.). In entropy, thermodynamic functions, and phase order to gain admission to both degree EAEE E2002x Alternative energy resources changes. Basic kinetic theory and statistical programs, students must have an 3 pts. Lect: 3. Professors Lackner and Walker. mechanics, including diffusion processes, undergraduate degree in engineering Unconventional, alternative energy resources. concept of phase space, classical and quantum and complete at least 30 credits of Technological options and their role in the world statistics, and applications thereof. energy markets. Comparison of conventional and graduate work beyond the M.S. degree, EAEE E3112y Introduction to rock mechanics unconventional, renewable and non-renewable or 60 credits of graduate work beyond 3 pts. Lect: 3. Not offered in 2011–2012. energy resources and analysis of the conse- the B.S. degree. These programs are Prerequisites: EAEE E3101 and ENME 3111, quences of various technological choices and planned for engineers who wish to do or their equivalents. Rock as an engineering constraints. Economic considerations, energy advanced work beyond the level of the material, geometry and strength of rock joints, availability, and the environmental consequences M.S. degree but who do not desire to geotechnical classification of rock masses, of large-scale, widespread use of each particular strength and failure of rock, field investigations emphasize research. technology. Introduction to carbon dioxide cap- prior to excavation in rock, rock reinforcement, The professional degrees are ture and carbon dioxide disposal as a means of analysis and support of rock slopes and tunnels, awarded for satisfactory completion of sustaining the fossil fuel option. and case histories. a graduate program at a higher level of EAEE E3101y Earth resource production course work than is normally completed MSAE E3141y Processing of metals and systems semiconductors for the M.S. degree. Students who 3 pts. Lect: 3. Not offered in 2011–2012. 3 pts. Lect: 3. Professor Duby. find it necessary to include master’s- Technologies and equipment common to a wide Prerequisite: MSAE E3103 or equivalent. level courses in their professional range of surface and subsurface engineering Synthesis and production of metals and degree program will, in general, take activities: mine reclamation, hazardous waste semiconductors with engineered microstructures such courses as deficiency courses. remediation, discovering and operating surface for desired properties. Includes high- A candidate is required to maintain a and underground mines, detection and removal temperature, aqueous, and electrochemical of hidden underground objects, waste disposal, grade-point average of at least 3.0. A processing; thermal and mechanical processing dredging and harbor rehabilitation, and tunneling student who, at the end of any term, of metals and alloys; casting and solidification; for transportation or water distribution systems. has not attained the grade-point average diffusion, microstructural evolution, and phase These methods and equipment are examined required for the degree may be asked to transformations; modification and processing of as they apply across the spectrum from mining withdraw. The final 30 credits required surfaces and interfaces; deposition and removal to environmental engineering projects. The for the professional degree must be of thin films. Processing of Si and other materials aim is to provide a broad background for completed in no more than five years. for elemental and compound semiconductor- earth and environmental engineers in careers based electronic, magnetic, and optical devices. Specific requirements for both involving minerals and industrial, large-scale professional degrees include a set of environmental projects. EAEE E3185y Summer fieldwork for earth and core courses and a number of electives environmental engineers EAEE E3103x Energy, minerals, and materials appropriate for the specific area of 0.5 pt. Not offered in 2011–2012. systems concentration. All course work must Undergraduates in Earth and Environmental 3 pts. Lect: 3. Professors Lackner and Yegulalp. lead to the successful completion of a Engineering may spend up to 3 weeks in the Prerequisites: MSAE E3111 or MECE E3301 field under staff direction. The course consists project in mining engineering. A list of and ENME E3161 or MECE E3100 or equivalent of mine, landfill, plant, and major excavation site core courses and electives is available at Corequisites: MSAE E3111 or MECE E3301 and visits and brief instruction of surveying methods. the department office. ENME E3161 or MECE E3100 or equivalent. A final report is required. Overview of energy resources, resource management from extraction and processing to EAEE E3221x Environmental geophysics courses in earth recycling and final disposal of wastes. Resources 3 pts. Lect: 3. Not offered in 2011–2012. and environmental availability and resource processing in the Introduction to applied and environmental engineering context of the global natural and anthropogenic geophysics methods. Overview of principles See also Chemical Engineering section material cycles; thermodynamic and chemical of geophysics, geophysical methods and for courses in applied chemistry. conditions including nonequilibrium effects that techniques (seismic, ground penetrating radar, shape the resource base; extractive technologies resistivity, frequency em, and magnetics), and

engineering 2011–2012 theory and practical aspects of data processing EAEE E3900x and y–S3900 Undergraduate scientific background for addressing problems 129 and inversion. Examination of geophysical research in Earth and environmental of aqueous pollution, water treatment, and case studies for engineering and environmental engineering sustainable production of materials with minimum purposes. 0–3 pts. Directed study. Members of the faculty. environmental impact. Hydrolysis, oxidation- This course may be repeated for credit, but reduction, complex formation, dissolution and CIEE E3250y Hydrosystems engineering no more than 3 points of this course may be precipitation, predominance diagrams; examples 3 pts. Lect: 3. Professor Lall. counted towards the satisfaction of the B. S. of natural water systems, processes for water Prerequisites: CHEN E3110 or ENME E3161 degree requirements. Candidates for the B.S. treatment and for the production of inorganic or equivalent, SIEO W3600 or equivalent, degree may conduct an investigation in Earth materials from minerals. or instructor’s permission. A quantitative and Environmental Engineering, or carry out a introduction to hydrologic and hydraulic EAEE E4004x Physical processing and special project under the supervision of EAEE systems, with a focus on integrated recovery of solids faculty. Credit for the course is contingent on modeling and analysis of the water cycle and 3 pts. Lect: 3. Not offered in 2011–2012. the submission of an acceptable thesis or final associated mass transport for water resources Generalized treatment of processes for solids report. This course cannot substitute for the and environmental engineering. Coverage separation. Applications to materials processing Undergraduate design project (EAEE E3999 or of unit hydrologic processes such as and handling; mining; solid waste, recycling, and EAEE E3999). precipitation, evaporation, infiltration, runoff resource recovery; construction materials and generation, open channel and pipe flow, EAEE E3901y Environmental microbiology debris; scrap materials, yard and park wastes. subsurface flow and well hydraulics in the 3 pts. Lect: 3. Professor Chandran. Economic considerations and context. Relevant context of example watersheds and specific Prerequisite: CHEM C1404 or equivalent. materials properties and bulk materials analyses. integrative problems such as risk-based Fundamentals of microbiology, genetics and Process system flow-sheets and analysis. Solid/ design for flood control, provision of water, molecular biology, principles of microbial solid, solid/liquid, and solid/gas separation and assessment of environmental impact nutrition, energetics and kinetics, application process. Liberation, concentration, and auxiliary or potential for non-point source pollution. of novel and state-of-the-art techniques in processes. Design of separation machines: types Spatial hydrologic analysis using GIS and monitoring the structure and function of microbial and intensities of force involved; scalling-up watershed models. communities in the environment, engineered factors. Laboratory demonstrations and a field processes for biochemical waste treatment and trip will be included. CIEE E3255y Environmental control and bioremediation, microorganisms and public pollution reduction systems EAEE E4005x Near-surface engineering health, global microbial elemental cycles. 3 pts. Lect: 3. Professor Castaldi. geophysics Prerequisite: ENME E3161 or MECE E3100. EAEE E3998x-E3999y Undergraduate design 3 pts. Lect: 3. Not offered in 2011–2012. Review of engineered systems for prevention project Geophysical methods as applicable to and control of pollution. Fundamentals of 2 pts. (each semester). Lect: 1. Lab: 2. engineering problems. Principles of geophysics material and energy balances and reaction Professors Lall and Park. and noninvasive imaging techniques (inversion kinetics. Analysis of engineered systems to Prerequisite: senior standing. Students must technology) and benefits and pitfalls of address environmental problems including solid enroll for both 3998x and 3999y during their geophysics vs. direct imaging methods. and hazardous waste, air, water, soil and noise senior year. Selection of an actual problem in Discussion of theory of each method. Discussion pollution. Life cycle assessments and emerging Earth and environmental engineering, and design of data acquisition, processing and interpretation technologies. of an engineering solution including technical, for each method. Treatment of several case economic, environmental, ethical, health and studies. Class-wide planning and execution of EAEE E3800y Earth and environmental safety, social issues. Use of software for design, small-scale geophysical survey. engineering laboratory, I visualization, economic analysis, and report 2 pts. Lect: 1. Lab: 3. Professors Castaldi and Duby. EAEE E4006y Field methods for preparation. Students may work in teams. Prerequisite: CHEE E3010. Corequisite: EAEE environmental engineering Presentation of results in a formal report and E3255. Experiments on fundamental aspects 3 pts. Lect: 1.5. Lab: 2. Professor McGillis. public presentation. of Earth and environmental engineering with Prerequisite: ENME E3161 or equivalent or emphasis on the applications of chemistry, EAEE E4001x Industrial ecology of earth instructor’s permission Principles and methods biology and thermodynamics to environmental resources for designing, building and testing systems processes: energy generation, analysis and 3 pts. Lect: 3. Professor Kaufman. to sense the environment. Monitoring the purification of water, environmental biology, Industrial ecology examines how to reconfigure atmosphere, water bodies and boundary and biochemical treatment of wastes. Students industrial activities so as to minimize the adverse interfaces between the two. Sensor systems for will learn the laboratory procedures and environmental and material resource effects on the monitoring heat and mass flows, chemicals, and use analytical equipment firsthand, hence planet. Engineering applications of methodology biota. Measurements of velocity, temperature, demonstrating experimentally the theoretical of industrial ecology in the analysis of current flux and concentration in the field. The class concepts learned in class. processes and products and the selection or will involve planning and execution of a study to design of environmentally superior alternatives. sense a local environmental system. EAEE E3801x Earth and environmental Home assignments of illustrative quantitative engineering laboratory, II EAEE E4007y Environmental geophysics field problems. 2 pts. Lect: 1. Lab: 3. Professors Castaldi and Duby. studies Prerequisite: EAEE E3800. Corequisite: EAEE EAEE E4003x Introduction to aquatic 3 pts. Lect: 3. Not offered in 2011–2012. E4003. A continuation of EAEE E3800, with chemistry Application of geophysical methods to emphasis on the principles underlying water 3 pts. Lect: 3. Professor Duby. noninvasive assessment of the near surface. analysis for inorganic, organic, and bacterial Prerequisite: CHEE E3010. Principles of First part consists of series of two-hour lectures contaminants. Lab required. physical chemistry applied to equilibria and of physics and math involved in instrumental kinetics of aqueous solutions in contact with methods and data acquisition and processing. minerals and anthropogenic residues. The

engineering 2011–2012 130 the field (nine field days) students plan surveys; waste loadings; (b) LCA of an existing industrial storage and disposal of solid and hazardous collect and analyze geophysical data in teams; or consumer product using a commercially waste. Impact on the environment and public learn how to integrate geophysical data established method. health. Government regulations. Recycling and with invasive data, hydrological, geological, resource recovery. CHEE E4050x Industrial and environmental engineering, and contaminant transport models; electrochemistry CIEE E4163x Environmental engineering: and develop a comprehensive and justifiable 3 pts. Lect: 3. Professor Duby. wastewater model of the subsurface. Geophysical methods Prerequisite: CHEN E3010 or equivalent. A 3 pts. Lect: 3. Professor Becker. include GPR (Ground Penetrating Radar), presentation of the basic principle underlying Prerequisites: Introductory chemistry (with conductivity, and magnetic and seismic methods. electrochemical processes. Thermodynamics, lab) and fluid mechanics. Fundamentals of Field applications include infrastructure/ electrode kinetics, and ionic mass transport. water pollution and wastewater characteristics. environmental assessment, archeological Examples of industrial and environmental Chemistry, microbiology, and reaction kinetics. studies, and high resolution geology. applications illustrated by means of laboratory Design of primary, secondary, and advanced EAEE E4009x Geographic information experiments: electroplating, refining, and treatment systems. Small community and systems (GIS) for resource, environmental winning in aqueous solutions and in molten residential systems. and infrastructure management salts; electrolytic treatment of wastes; primary, EAEE E4190x Photovoltaic systems 3 pts. Lect: 3. Professor Gorokhovich. secondary, and fuel cells. engineering and sustainability Prerequisite: Permission of the instructor. Basic ECIA W4100y Management and development 3 pts. Lect: 3. Professor Fthenakis. concepts of geomatics, spatial data representation of water systems Prerequisite: Senior standing or instructor’s and organization, and analytical tools that 3 pts. Lect: 3. Professor Lall. permission. Corequisites: N/A. A systems comprise GIS are introduced and applied to Decision analytic framework for operating, approach for intermittent renewable energy a variety of problems including watershed managing, and planning water systems, involving the study of resources, generation, protection, environmental risk assessment, considering changing climate, values and needs. demand, storage, transmission, economics material mass balance, flooding, asset Public and private sector models explored and politic. Study of current and emerging management, and emergency response to natural through US-international case studies on topics photovoltaic technologies, with focus on basic or man-made hazards. Technical content includes ranging from integrated watershed management sustainability metrics (e.g., cost, resource geography and map projections, spatial statistics, to the analysis of specific projects for flood availability, and life-cycle environmental database design and use, interpolation and mitigation, water and wastewater treatment, or impacts). The status and potential of first- and visualization of spatial surfaces and volumes from distribution system evaluation and improvement. second-generation photovoltaic technologies irregularly spaced data, and decision analysis in (e.g., crystalline and amorphous Si, CdTe, CIGS) an applied setting. Taught in a laboratory setting EAEE E4101y Introduction to particle and emerging third-generation ones. Storage using ArcGIS. Access to New York City and other technology options to overcome the intermittency constraint. standard databases. Term projects emphasize 3 pts. Lect: 3. Not offered in 2011–2012. Large scales of renewable energy technologies information synthesis towards the solution of a Prerequisite: Instructor’s permission. Size and plug-in hybrid electric cars. specific problem. reduction, theory of comminution. Small particle statistics, particle size measurement, properties EAEE E4200y Production of inorganic EAEE E4010y Remote sensing and of particle aggregates, behavior of particles in materials environmental change fluids, flow and retention of fluids in packings. 3 pts. Lect: 3. Professor Duby. 3 pts. Lect: 3. Professors Bell and Ceccato. Prerequisite: CHEE E3010 or equivalent. Prerequisite: EAEE E4009 or EESC W4050 or CHEE E4140x Engineering separations Production and recycling of inorganic materials instructor’s permission. Practical and theoretical processes in aqueous and high temperature systems. foundations for the application of remote sensing 3 pts. Lect: 3. Professor Park. Industrial and environmental applications techniques to identification and monitoring of Prerequisites: CHEN E3100, E3120, and of hydrometallurgy, pyrometallurgy, and environmental change. Designing and applying E3210 or permission of instructor. Design electrometallurgy. Reactor systems for, e.g., spectral indices for assessment and monitoring, and analysis of unit operations employed in leaching, precipitation, and solvent extraction, time series analysis of remote sensing data for chemical engineering separations. Fundamental bath and flash smelting reactors, rotary kilns, analyzing environmental problems. Discussions aspects of single and multistaged operations and fluid bed reactors. Thermodynamic and of published literature relevant to the central using both equilibrium and rate-based methods. kinetic factors and materials/energy balances topic covered in class. Analysis of remote Examples include distillation, absorption and involved in the design and performance of such sensing data using IRI data library. stripping, extraction, membranes, crystallization, reactors in typical applications. bioseparations, and environmental applications. EAEE E4011y Industrial ecology for EAIA E4200y Alternative energy resources manufacturing EAEE E4150y Air pollution prevention and 3 pts. Lect: 3. Professors Lackner and Walker. 3 pts. Lect: 3. Not offered in 2011–2012. control Unconventional, alternative energy resources. Prerequisite: EAEE E4001. Application of 3 pts. Lect: 3. Professor Fthenakis. Technological options and their role in the world industrial ecology to Design for Environment Adverse effects of air pollution, sources and energy markets. Comparison of conventional and (DFE) of processes and products using transport media, monitoring and modeling of unconventional, renewable and nonrenewable, environmental indices of resources consumption air quality, collection and treatment techniques, energy resources and analysis of the and pollution loads. Introduction of methodology pollution prevention through waste minimalization consequences of various technological choices for Life Cycle Assessment (LCA) of and clean technologies, laws, regulations, and constraints. Economic considerations, manufactured products. Analysis of several DFE standards, and guidelines. energy availability, and the environmental and LCA case studies. Term project required on EAEE E4160y Solid and hazardous waste consequences of large-scale, widespread use use of DFE/LCA on a specific product/process: management of each particular technology. Introduction to (a) product design complete with materials and 3 pts. Lect: 3. Professor Somasundaran. carbon dioxide disposal as a means of sustaining process selection, energy consumption, and Generation, composition, collection, transport, the fossil fuel option. Recitation section required.

engineering 2011–2012 EAEE E4241x Solids handling and transport Applications are developed using the ArcView or equivalent. Introduction to engineering 131 systems Geographical Information System (GIS), processes involving particulates and powders. 3 pts. Lect: 3. Not offered in 2011–2012. integrated with currently available statistical The fundamentals of particle characterization, Analysis and design of transportation systems packages. Team projects that lead to publication- multiphase flow behavior, particle formation, for bulk solids in tunnels, mines, and large quality analyses of data in various environmental processing and utilization of particles in various excavations. Design of hoisting, cable transport, fields of interest. An interdisciplinary perspective engineering applications with examples in rail and trackless haulage systems, conveyor is emphasized in this applications-oriented class. energy and environment related technologies. belts, selection of loaders, excavators, Engineering of functionalized particles and EAEE E4350x Planning and management of off-highway trucks, and draglines for large design of multiphase reactors and processing urban hydrologic systems excavations. units with emphasis on fluidization technology. 3 pts. Lect: 3. Professor Rangarajan. Particle technology is an interdisciplinary field. CHEE E4252x Introduction to surface and Prerequisite: ENME E3161 or equivalent. Due to the complexity of particulate systems, colloid chemistry Introduction to runoff and drainage systems in an particle technology is often treated as art rather 3 pts. Lect: 3. Professor Somasundaran. urban setting, including hydrologic and hydraulic than science. In this course, the fundamental Prerequisite: Elementary physical chemistry. analyses, flow and water quality monitoring, principles governing the key aspects of particle Thermodynamics of surfaces, properties common regulatory issues, and mathematical science and technology are introduced along of surfactant solutions and surface films, modeling. Applications to problems of climate with various industrial examples. electrostatic and electrokinetic phenomena at variation, land use changes, infrastructure interfaces, adsorption; interfacial mass transfer operation and receiving water quality, developed EAEE E4900x Applied transport and chemical and modern experimental techniques. using statistical packages, public-domain models, rate phenomena and Geographical Information Systems (GIS). 3 pts. Lect: 3. Professor Chen. CIEE E4252y Environmental engineering Team projects that can lead to publication quality Introduction to fluid dynamics, heat and mass 3 pts. Lect: 3. Professor Chandran. analyses in relevant fields of interest. Emphasis transfer, and some applications in heterogeneous Prerequisites: CHEM C1403, or equivalent; on the unique technical, regulatory, fiscal, policy, reaction systems. Effect of velocity, temperature, ENME E3161 or equivalent. Engineering aspects and other interdisciplinary issues that pose a and concentration gradients and material of problems involving human interaction with challenge to effective planning and management properties on fluid flow, heat and mass transfer the natural environment. Review of fundamental of urban hydrologic systems. and rate of chemical reactions; differential and principles that underlie the discipline of overall balance; engineering concepts and semi- environmental engineering, i.e., constituent EAEE E4361y Economics of earth resource empirical correlations; application to chemical transport and transformation processes in industries and materials processing and environmental environmental media such as water, air, and 3 pts. Lect: 3. Professor Yegulalp. problems. ecosystems. Engineering applications for Prerequisite: EAEE E3101 or instructor’s addressing environmental problems such permission. Definition of terms. Survey of EAEE E4901y Environmental microbiology as water quality and treatment, air pollution Earth resource industries: resources, reserves, 3 pts. Lect: 3. Professor Chandran. emissions, and hazardous waste remediation. production, global trade, consumption of mineral Basic microbiological principles; microbial Presented in the context of current issues commodities and fuels. Economics of recycling metabolism; identification and interactions facing the practicing engineers and government and substitution. Methods of project evaluation: of microbial populations responsible for the agencies, including legal and regulatory estimation of operating costs and capital biotransformation of pollutants; mathematical framework, environmental impact assessments, requirements, project feasibility, risk assessment, modeling of microbially mediated processes; and natural resource management. and environmental compliance. Cost estimation biotechnology and engineering applications using for reclamation/remediation projects. Financing microbial systems for pollution control. CIEE E4257y Groundwater contaminant of reclamation costs at abandoned mine sites transport and remediation EAEE E4950x Environmental biochemical and waste-disposal post-closure liability. 3 pts. Lect: 3. processes Prerequisite: CIEE E3250 or equivalent. Sources CHEE E4530y Corrosion of metals 3 pts. Lect: 3. Professor Chandran. and types of groundwater contamination. 3 pts. Lect: 3. Professor Duby. Prerequisite: EAEE 4901 or CIEE E4252 or Groundwater hydrology. Groundwater Prerequisite: CHEN E3010 or equivalent. The EAEE E4003 or instructor’s approval. Qualitative contaminant rate and transport. Flow and theory of electrochemical corrosion, corrosion and quantitative considerations in engineered transport in the unsaturated zone. Nonaqueous tendency, rates, and passivity. Application to environmental biochemical processes. phase liquids and multiphase flow. Physical various environments. Cathodic protection and Characterization of multiple microbial reactions and numerical models for contaminant coatings. Corrosion testing. in a community and techniques for determining transport. Characterization and assessment of associated kinetic and stoichiometric parameters. EAEE E4550x Catalysis for emissions control contaminated sites. Groundwater remediation Engineering design of several bioreactor 3 pts. Lect: 3. Professor Farrauto. alternatives. Regulations. configurations employed for biochemical waste Prerequisites: ENME E3161 and MSAE E3111 treatment. Mathematical modeling of engineered EAEE E4257y Environmental data analysis or equivalent. Fundamentals of heterogeneous biological reactors using state-of-the-art simulation and modeling catalysis including modern catalytic preparation packages. 3 pts. Lect: 3. Professor Yegulalp. techniques. Analysis and design of catalytic Prerequisite: SIEO W3600 or SIEO W4250 or emissions control systems. Introduction to EAEE E4980 Urban environmental technology equivalent. Statistical methods for the analysis current industrial catalytic solutions for controlling and policy of the space and time structure in environmental gaseous emissions. Introduction to future 3 pts. Lect: 3. Not offered in 2011–2012. data. Application to problems of climate catalytically enabled control technologies. Progress of urban pollution engineering via variation and change; hydrology; air, water and contaminant abatement technology, government EACE E4560y Particle technology soil pollution dynamics; disease propagation; policy, and public action in urban pollution. 3 pts. Lect: 3. Professor Park. ecological change; and resource assessment. Pollutant impact on modern urban environmental Prerequisites: ENME E3161 and MSAE E3111

engineering 2011–2012 132 quality, natural resources, and government, Prerequisite: EAEE E4900 or equivalent or technologies. Techniques used to treat municipal, and social planning and management instructor’s permission. The fundamentals hazardous materials in the environment, in situ programs. Strong emphasis on current and of combustion phenomena and the intrinsic and removal for treatment, focusing on those twentieth-century waste management in New chemistry of combustion processes. The theory aspects that are unique to the application of York City. of the essential combustion processes such as those technologies in an uncontrolled natural ignition, sustained reaction, stability and flame environment. Management, safety, and training EAEE E6132y Numerical methods in quenching. Processes that govern reactant issues. geomechanics consumption and product formation, in particular 3 pts. Lect: 3. Professor Chen. EAEE E6228y Theory of flotation by-products that are formed that result in pollutant Prerequisites: EAEE E3112 and CIEN E4241 3 pts. Lect: 3. Not offered in 2011–2012. emissions, and the impacts and implications or instructor’s permission. A detailed survey Prerequisite: CHEE E4252 or instructor’s that combustion has locally and globally on the of numerical methods used in geomechanics, permission. A detailed study of the environment. Detailed examination of the entire emphasizing the Finite Element Method (FEM). physicochemical principles of the flotation range of combustion systems from diffusion flame Review of the behavior of geological materials. process. processes to current developing technologies Water and heat flow problems. FEM techniques including millisecond catalytic combustion EAEE E6240x or y Physical hydrology for solving nonlinear problems, and simulating processes, noncarbon fueled combustion, fuel 3 pts. Lect: 3. Professor Lall. incremental excavation and loading on the cells, and plasma combustion. Prerequisite: Engineering hydrology or surface and underground. equivalent. Spatial/temporal dynamics of EAEE E6210x Quantitative environmental risk EAEE E6150y Industrial catalysis the hydrologic cycle and its interactions with analysis 3 pts. Lect: 3. Professor Farrauto. landforms and vegetation. Hydroclimatology 3 pts. Lect: 3. Professor Yegulalp. Prerequisite: EAEE E4550 or equivalent, or at regional to planetary scales, focusing on Prerequisite: EAEE E3101, SIEO W4150, or instructor’s permission. Fundamental principles mechanisms of organization and variation of equivalent. Comprises the tools necessary for of kinetics, characterization and preparation of water fluxes as a function of season, location, technical professionals to produce meaningful catalysts for production of petroleum products reservoir (ocean, atmosphere, land), and time risk analyses. Review of relevant probability and for conventional transportation fuels, specialty scale. Land-atmosphere interaction and the role statistics; incorporation of probability in facility chemicals, polymers, food products, hydrogen of vegetation and soil moisture. Topography as failure analysis. Availability, assessment, and and fuel cells and the application of catalysis an organizing principle for land water fluxes. incorporation of risk-related data. Contaminant in biomass conversion to fuel. Update of Geomorphology and the evolution of river transport to exposed individuals; uptake, the ever changing demands and challenges networks. Sedimentation, erosion and hill slope morbidity, and mortality. Computational tools in environmental applications, focusing on hydrology. Dynamics of water movement over necessary to risk modeling. Use and applicability advanced catalytic applications as described in land, in rivers and in the subsurface, with an of resulting measurements of risk, and their use modern literature and patents. emphasis on modeling interfaces. Integrated in public policy and regulation. models and the scale problem. Emphasis on EAEE E6151y Applied geophysics EAEE E6212y Carbon sequestration data-based spatial/temporal modeling and 3 pts. Lect: 3. Not offered in 2011–2012. 3 pts. Lect: 3. Professor Lackner. exploration of outstanding theoretical challenges. Potential field data, prospecting, wave equations. Prerequisite: EAEE E4900 or equivalent or Huygens’ principle, Green’s functions, Kirchoff CHEE E6252y Advanced surface and colloid instructor’s permission. New technologies for equation, WKB approximation, ray tracing. Wave chemistry capturing carbon dioxide and disposing of it away propagation, parameters. Computer applications. 3 pts. Lect: 2. Lab: 3. Professor Somasundaran. from the atmosphere. Detailed discussion of the Wavelet processing, filters and seismic data. Prerequisite: CHEE E4252. Applications extent of the human modifications to the natural Stratified Earth model, seismic processing and of surface chemistry principles to wetting, carbon cycle, the motivation and scope of future profiling. Radon transform and Fourier migration. flocculation, flotation, separation techniques, carbon management strategies and the role of Multidimensional geological interpretation. catalysis, mass transfer, emulsions, foams, carbon sequestration. Introduction of several aerosols, membranes, biological surfactant EAEE E6200y Theory and applications of carbon sequestration technologies that allow for systems, microbial surfaces, enhanced oil extreme value statistics in engineering and the capture and permanent disposal of carbon recovery, and pollution problems. Appropriate earth sciences dioxide. Engineering issues in their implementation, individual experiments and projects. Lab 3 pts. Lect: 3. Professor Yegulalp. economic impacts, and the environmental issues required. Prerequisite: STAT W4107 or equivalent raised by the various methods. background in probability and statistical EAEE E6255x-E6256y Methods and CHEE E6220y Equilibria and kinetics in inference, or instructor’s permission. Introduction applications of analytical decision making in hydrometallurgical systems of fundamental concepts in extreme value mineral industries 3 pts. Lect: 3. Professor Duby. statistics. The exact and asymptotic theory 3 pts. Lect: 3. Not offered in 2011–2012. Prerequisite: CHEE E4050 or EAEE E4003. of extremes. Development of statistical Prerequisites: Instructor’s permission. Advanced Detailed examination of chemical equilibria study of decision-making problems with critical methodology for estimating the parameters in hydrometallurgical systems. Kinetics and of asymptotic extremal distributions from mechanisms of homogeneous and heterogeneous survey and applications of quantitative decision- experimental data. Examples of applications of reactions in aqueous solutions. making techniques in mineral industries. extreme value statistics to regional and global Systematic development of methods of the earthquake forecasting, laboratory testing EAEE E6220x Remedial and corrective action formulation, analysis, and resolution of these of rocks and metals, fatigue failure, floods, 3 pts. Lect: 3. Not offered in 2011–2012. problems. droughts, extreme wind velocities, and rainfalls. Prerequisite: EAEE E4160 or equivalent. Integrates the engineering aspects of cleanup EAEE E8229x Selected topics in processing EAEE E6208y Combustion chemistry and of hazardous materials in the environment. minerals and wastes processes Site assessment/investigation. Site closure, 3 pts. Lect: 2. Lab: 3. 3 pts. Lect: 3. Professor Castaldi. containment, and control techniques and Prerequisite: CHEE E4252 or instructor’s

engineering 2011–2012 permission. Critical discussion of current EAEE E9271x and y–S9271 Earth and wastes. Through readings, research, and class 133 research topics and publications in the area environmental engineering thesis discussions, it engages students to critically of flotation, flocculation, and other mineral 0–6 pts. Members of the faculty. evaluate arguments both for and against nuclear processing techniques, particularly mechanisms Research work culminating in a creditable power. The course builds basic literacy in of adsorption, interactions of particles in dissertation on a problem of a fundamental nuclear technology and is open to students with solution, thinning of liquid films, and optimization nature selected in conference between student technical, policy, or economic backgrounds. techniques. and adviser. Wide latitude is permitted in choice EAEE E9302x and y Mining engineering of a subject, but independent work of distinctly EAEE E8231y Selected topics in hydro- and research graduate character is required in its handling. electrometallurgy 0–4 pts. Professor Yegulalp. 3 pts. Lect: 3. EAEE E9273x-E9274y Earth and Graduate research directed toward solution of Prerequisites: EAEE E4003 and CHEE environmental engineering reports technicoscientific problems in mining. E4050, or instructor’s permission. Review 0–4 pts. EAEE E9305x and y–S9305 Earth and of current research and literature in the May substitute for the formal master’s thesis, environmental engineering research field of hydrometallurgy, electrometallurgy, EAEE E9271, upon recommendation of the 0–12 pts. Members of the faculty. and corrosion. Topics will be selected by department. Graduate research directed toward solution of the instructor to illustrate the application of EAEE E9280x and y Earth and environmental a problem in mineral processing or chemical thermodynamics and rate phenomena to engineering colloquium metallurgy. the design and control of electrochemical 0–1 pt. Lect: 1.5. Professor Park. EAEE E9800x and y–S9800 Doctoral research engineering processes. All graduate students are required to attend the instruction EAEE E8233x and y Research topics in departmental colloquium as long as they are 3, 6, 9, or 12 pts. Members of the faculty. particle processing in residence. Advanced doctoral students may A candidate for the Eng.Sc.D. degree in mineral 0–1 pt. Professor Somasundaran. be excused after three years of residence. No engineering must register for 12 points of doc- Emergent findings in the interactions of degree credit is granted. toral research instruction. Registration in EAEE E9800 may not be used to satisfy the minimum particles with reagents and solutions, especially EAEE E9281x Prospects for nuclear energy– residence requirement for the degree. inorganics, surfactants, and polymers in earth and environmental engineering seminar solution, and their role in grinding, flotation, 0–1 pt. Lect: 1.5. Professors Gazze and Lackner. EAEE E9900x and y–S9900 Doctoral agglomeration, filtration, enhanced oil recovery, This seminar course examines the prospects dissertation and other mineral processing operations. for nuclear energy as a source of safe, secure, 0 pts. Members of the faculty. EAEE E8273x-E8274y Mining engineering and environmentally sustainable energy both A candidate for the doctorate may be required reports in the U.S. and internationally. In particular, it to register for this course every term after the analyzes the four key issues that limit the expan- 0–4 pts. Professor Yegulalp. student’s course work has been completed, and sion of nuclear energy: cost, safety, proliferation May substitiute for formal thesis, EAEE E9271, until the dissertation has been accepted. concerns, and long-term disposal of radioactive upon recommendation of the student’s adviser.

engineering 2011–2012 134 Electrical Engineering 1300 S. W. Mudd, MC 4712, 212-854-3105 www.ee.columbia.edu

Chair Steven Nowick, Senior Lecturer Adjunct Associate Associate Research Keren Bergman Computer Science David Vallancourt Professors ScientistS 805 CEPSR Richard M. Osgood Jr. Yves Baeyens William Andreopoulos Henning G. Schulzrinne, Adjunct Zhu Liu Nadia Pervez Vice Chair Computer Science Professors Deepak Turaga Vladimir Sokolov Charles Zukowski Amiya K. Sen Miron Abramovici Martin Roetteler 1026 Schapiro Kenneth L. Shepard Yuliv Baryshnikov Postdoctoral Yannis P. Tsividis Doru Calin Adjunct Assistant Research Departmental Wen I. Wang Young-Kai Chen Professors Scientists Administrator Xiaodang Wang David Gibbon Neda Cvijetic Ryan Davies Kevin Corridan Charles A. Zukowski Howard Huang Timothy Dickinson Cory Dean 1303 S. W. Mudd Irving Kalet Eran Fishler Jonathan Hodges Associate Ta-Hsin Li Sanjiv Kumar Rongrong Ji Professors Professors Thao Nguyen Ching-Yung Lin Zhenguo Li Dimitris Anastassiou Dan Ellis Krishnan Sabnani Eftychios Pnevmatikakis Dong Liu Keren Bergman Peter Kinget Mischa Schwartz Ali Tajer Yadong Mu Shih-Fu Chang Jacob Sharony Chao Tian Viktoria Rumjantseva Paul Diament Assistant Alexander Stolyar Vinay Varadan Siddharth Ramakrishnan Tony F. Heinz Professors Paul Solomon Kai Yang Brian Tull Andreas H. Hielscher, Dirk Englund Vinay Vaishampayan Eric Zavesky Liming Wang Biomedical Engineering Harish Krishnaswamy Anwar Walid Aurel A. Lazar Ioannis (John) Kymissis Shalom Wind Senior Research Predrag Jelenkovic Mingoo Seok Thomas Woo Scientist Nicholas Maxemchuk John Wright James Yardly Robert Laibowitz Gil Zussman

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

engineering 2011–2012 engineering. Details on those programs development of semi conductor light Measurement Laboratory, Ultrafast 135 can be found in the Computer sources such as LEDs and injection Optoelectronics Laboratory, Columbia Engineering section in this bulletin. lasers, fabrication and analysis of Integrated Systems Laboratory (CISL), quantum confined structures, photo Lightwave Communications Laboratory, Research Activities conductors, pin diodes, avalanche Photonics Laboratory, Plasma Physics The research interests of the faculty photodiodes, optical interconnects, and Laboratory (in conjunction with the encompass a number of rapidly growing quantum optics. A major effort is the Department of Applied Physics). areas, vital to the development of future picosecond optoelectronics program, Laboratory instruction is provided in technology, that will affect almost every focusing on the development of new the Introduction to Electrical Engineering aspect of society: communications devices and their applications to high- Laboratory, Marcellus-Hartley Electronics and information processing; solid-state speed optoelectronic measurement Laboratory, Microprocessor Laboratory, devices; ultrafast optics and photonics; systems, photonic switching, and optical Microwave Laboratory, Optical microelectronic circuits, integrated logic. In addition, research is being Electronics Laboratory, Solid-State systems and computer-aided design; performed in detection techniques for Laboratory, VLSI Design Laboratory, and systems biology; and electromagnetics optical communications and radar. Student Projects Laboratory, all on the and plasmas. Details on all of Members of the photonics group play twelfth floor of the S. W. Mudd Building. these areas can be found at www. a leading role in a multi-university ee.columbia.edu/research. consortium: The National Center for Undergraduate Program Integrated Photonics Technology. Communications research focuses The educational objectives of the Integrated systems research involves on wireless communication, multimedia Electrical Engineering program, in the analysis and design of analog, digital, networking, real-time Internet, support of the mission of the School, and mixed-signal microelectronic circuits lightwave (fiber optic) communication are to produce graduates who: and systems. These include novel signal networks, optical signal processing 1. Can identify and solve engineering processors and related systems, data and switching, service architectures, problems, drawing on a strong converters, radio frequency circuits, network management and control, foundation in the basic sciences and low noise and low power circuits, and the processing of image and video mathematics. fully integrated analog filters that share information, and media engineering. 2. Possess a solid foundation in the same chip with digital logic. VLSI Current studies include wireless and electrical engineering sufficient to architectures for parallel computation, mobile computing environments, enable careers and professional packet switching, and signal processing broadband kernels, object-oriented growth in electrical engineering or are also under investigation. Computer- network management, real-time related fields. aided design research involves the monitoring and control, lightwave 3. Can communicate effectively development of techniques for the network architectures, lightweight and contribute as members of analysis and design of large-scale protocol design, resource allocation and multidisciplinary teams. integrated circuits and systems. networking games, real-time Internet 4. Appreciate diversity of opinion, Electromagnetics research ranges services, future all-digital HDTV systems, consider ethical issues, and from the classical domains of microwave coding and modulation. understand the context of their generation and transmission and wave Solid-state device research profession. propagation in various media to modern is conducted in the Columbia 5. Understand the relationship applications involving lasers, optical Microelectronics Sciences Laboratories. between theory and practice based fibers, plasmas, and solid-state devices. This is an interdisciplinary facility, on significant engineering design Problems relevant to controlled thermo- involving aspects of electrical experience. nuclear fusion are under investigation. engineering and applied physics. It The B.S. program in electrical includes the study of semiconductor engineering at Columbia University physics and devices, optical electronics, Laboratory Facilities seeks to provide a broad and solid and quantum optics. The emphasis is Current research activities are fully foundation in the current theory and on laser processing and diagnostics supported by more than a dozen well- practice of electrical engineering, for submicron electronics, fabrication equipped research laboratories run by including familiarity with basic tools of compound semiconductor the department. Specifically, laboratory of math and science, an ability to optoelectronic devices by molecular research is conducted in the following communicate ideas, and a humanities beam epitaxy, physics of superlattices laboratories: Multimedia Networking background sufficient to understand and quantum wells, and interface Laboratory, Lightwave Communications the social implications of engineering devices such as Schottky barriers, Laboratory, Systems Laboratory, Image practice. Graduates should be qualified MOS transistors, heterojunctions, and and Advanced Television Laboratory, to enter the profession of engineering, to bipolar transistors. Another area of Laser Processing Laboratory, Molecular continue toward a career in engineering activity is the physics and chemistry of Beam Epitaxy Laboratory, Surface research, or to enter other fields microelectronics packaging. Analysis Laboratory, Microelectronics in which engineering knowledge is Research in photonics includes Fabrication Laboratory, Device essential. Required nontechnical courses

engineering 2011–2012 136 electrical engineering: FIRST and SECOND Years early-starting students

Semester i Semester iI Semester iII Semester iV

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

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

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

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

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

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

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

computer COMS W1007 (3) any semester1 science

physical C1001 (1) C1002 (1) education

gateway lab E1102 (4) either semester

1 COMS 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). 2 If possible, these labs should be taken along with their corresponding lecture courses. 3 APMA E2101 may be replaced by MATH E1210 and either APMA E3101 or MATH V2010.

cover civilization and culture, philosophy, computer knowledge is also included, courses on circuit theory and electronic economics, and a number of additional with an introductory course on using circuits, one course on semiconductor electives. English communication engineering workstations and two devices, one on electromagnetics, one skills are an important aspect of rigorous introductory computer science on signals and systems, one on digital these courses. Required science courses. Core electrical engineering systems, and one on communications courses cover basic chemistry and courses cover the main components or networking. Engineering practice is physics, whereas math requirements of modern electrical engineering and developed further through a sequence cover calculus, differential equations, illustrate basic engineering principles. of laboratory courses, starting with a probability, and linear algebra. Basic Topics include a sequence of two first-year course to introduce hands-

engineering 2011–2012 137 electrical engineering: Third and Fourth Years early-starting students

Semester V Semester VI Semester VII Semester VIII

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

ELEN E3401 (4) Electromagnetics

ee core ELEN E3106 (3.5) ELEN E3701 (3)2 required Solid-state devices and Intro. to courses materials communication systems or CSEE W4119 (3)2 Computer networks

ELEN E3043 (3) One capstone design Solid state, microwave, course3 (ELEN E3390, and fiber optics lab ELEN E4332, ee required labs EECS E4340, ELEN E3399 (1) or CSEE W4840) 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 courses background can take some of these courses in the sophomore year)

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

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

E lecti v e s other Additional technical electives (consisting of more depth or breadth courses, or further options listed at www. tech ee.columbia.edu/academics/undergrad) as required to bring the total points of technical electives to 185

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

total points6 16.5 17 16 18

1 Chemistry lab (CHEM 1500) may be substituted for physics lab, although this is not generally recommended. 2 These courses can be taken in the sophomore year if the prerequisites/corequisites are satisfied. 3 The capstone design course provides ELEN majors with a “culminating design experience.” As such, it should be taken near the end of the program and involve a project that draws on material from a range of courses. 4 SIEO W3600 and W4150 cannot generally be used to replace IEOR E3658 or STAT W4105. 5 The total points of technical electives is reduced to 15 if APMA E2101 has been replaced by MATH E1210 and either APMA E3101 or MATH V2010. 6 “Total points” assumes that 20 points of nontechnical electives and other courses are included.

on experience early and to motivate both within these lab courses and design course (capstone design theoretical work. Simple creative design in the parallel lecture courses, often course), which includes a significant experiences start immediately in this coupled with experimentation and design project that ties together the first-year course. Following this is a computer simulation, respectively. The core program, encourages creativity, sequence of lab courses that parallel culmination of the laboratory sequence explores practical aspects of engineering the core lecture courses. Opportunities and the design experiences introduced practice, and provides additional for exploring design can be found throughout earlier courses is a senior experience with communication skills in

engineering 2011–2012 138 electrical engineering program: first and second Years late-starting students

Semester i Semester iI Semester iII Semester iV

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

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

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

electrical ELEN E1201 (3.5) either semester1 engineering

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

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

computer COMS W1007 (3) either semester2 science

physical C1001 (1) C1002 (1) education

gateway lab E1102 (4) either semester

1 Transfer students and 3-2 Combined Plan students who have not taken ELEN E1201 prior to the junior year are expected to have taken a roughly equivalent course when they start ELEN E3201. 2 COMS 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). 3 APMA E2101 may be replaced by MATH E1210 and either APMA E3101 or MATH V2010. 4 Chemistry lab (CHEM C1500) may be substituted for physics lab, although this is not generally recommended.

an engineering context. Finally, several and the Departments of Computer These courses are shown on the charts in technical electives are required, chosen Science, Applied Physics and Applied Undergraduate Degree Tracks. A full cur- to provide both breadth and depth in a Mathematics, Industrial Engineering riculum checklist is also posted at www. specific area of interest. More detailed and Operations Research, Physics, and ee.columbia.edu/academics/undergrad. program objectives and outcomes Chemistry. are posted at www.ee.columbia.edu/ Technical Electives academics/undergrad. EE Core Curriculum The 18-point technical elective require- The program in electrical engineering All electrical engineering (EE) students ment for the electrical engineering leading to the B.S. degree is accredited must take a set of core courses, which program consists of three components: by the Engineering Accreditation collectively provide the student with depth, breadth, and other. A general out- Commission of the Accreditation Board fundamental skills, expose him/her to line is provided here, and more specific for Engineering and Technology (ABET). the breadth of EE, and serve as a spring- course restrictions can be found at www. There is a strong interaction between board for more advanced work, or for ee.columbia.edu/academics/undergrad. the Department of Electrical Engineering work in areas not covered in the core. For any course not clearly listed there,

engineering 2011–2012 139 electrical engineering: Third and Fourth Years1 late-starting students

Semester V Semester VI Semester VII Semester VIII

CSEE W3827(3) Fund. of computer sys.

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

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

E lecti v e s other Additional technical electives (consisting of more depth or breadth courses, or further options listed at tech www.ee.columbia.edu/academics/undergrad) as required to bring the total points of technical electives to 185

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

total points6 15.5 18 16 18

1 This chart shows one possible schedule for a student who takes most of his or her major program in the final two years. Please refer to the previous chart for a recommended earlier start. 2 If possible, these labs should be taken along with their corresponding lecture courses. 3 The capstone design course provides ELEN majors with a “culminating design experience.” As such, it should be taken near the end of the program and involve a project that draws on material from a range of courses. 4 SIEO W3600 and W4150 cannot generally be used to replace IEOR E3658 or STAT W4105. 5 The total points of technical electives is reduced to 15 if APMA E2101 has been replaced by MATH E1210 and either APMA E3101 or MATH V2010. 6 “Total points” assumes that 9 points of nontechnical electives are included. adviser approval is necessary. tronics; (c) signals and systems; and (d) that can be applied later to other disci- The depth component must consist communications and networking. The plines, if desired. of at least 6 points of electrical engineer- depth requirement provides an oppor- The breadth component must ing courses in one of four defined areas: tunity to pursue particular interests and consist of at least 6 additional points of (a) photonics, solid-state devices, and exposure to the process of exploring a engineering courses that are outside of electromagnetics; (b) circuits and elec- discipline in depth—an essential process the chosen depth area. These courses

engineering 2011–2012 140 can be from other departments within does not allow taking electives in that only) is required of all applicants except the School. The breadth requirement area; thus, such students cannot choose special students. An undergraduate precludes overspecialization. Breadth circuits and electronics as a depth area. grade point average equivalent to B or is particularly important today, as Plan 2: This plan is for students who better from an institution comparable to innovation requires more and more have taken a course equivalent to ELEN Columbia is expected. of an interdisciplinary approach, and E1201 at their school of origin, including Applicants who, for good reasons, exposure to other fields is known to help a laboratory component. See the bulletin are unable to submit GRE test results one’s creativity in one’s own main field. for a description of this course. Many by the deadline date but whose Breadth also reduces the chance of pre-engineering programs and physics undergraduate record is clearly superior obsolescence as technology changes. departments at four-year colleges offer may file an application without the GRE Any remaining technical elective such courses. Such students can start scores. An explanatory note should be courses, beyond the minimum 12 points taking circuits at Columbia immediately, added to ensure that the application will of depth and breadth, do not have to and thus can choose circuits and be processed even while incomplete. If be engineering courses (except for stu- electronics as a depth area. the candidate’s admissibility is clear, the dents without ELEN E1201 or approved decision may be made without the GRE It is stressed that ELEN E1201 or transfer credit for ELEN E1201) but must scores; otherwise, it may be deferred its equivalent is a key part of the EE be technical. Generally, math and sci- until the scores are received. curriculum. The preparation provided by ence courses that do not overlap with There are no prescribed course this course is essential for a number of courses used to fill other requirements requirements in any of the regular other core courses. are allowed. graduate degree programs. Students, in Sample programs for both Plan 1 consultation with their faculty advisers, and Plan 2 transfer students can be design their own programs, focusing on Starting Early found at www.ee.columbia.edu/ particular fields of electrical engineering. The EE curriculum is designed to allow academics/undergrad. students to start their study of EE in their Among the fields of graduate study are microelectronics, communications and first year. This motivates students early B.S./M.S. Program and allows them to spread nontechnical signal processing, integrated circuit The B.S./M.S. degree program is open requirements more evenly. It also makes and system analysis and synthesis, to a select group of undergraduate evident the need for advanced math and photonics, electromagnetic theory students. This double degree program physics concepts, and motivates the and applications, plasma physics, and makes possible the earning of both study of such concepts. Finally, it allows quantum electronics. the Bachelor of Science and Master of more time for students to take classes Graduate course charts for several Science degrees simultaneously. Up in a chosen depth area, or gives them focus areas can be found at www. to 6 points may be credited to both more time to explore before choosing ee.columbia.edu/academics/masters. degrees, and some graduate classes a depth area. Students can start with taken in the senior year may count ELEN E1201: Introduction to electrical Master of Science Degree toward the M.S. degree. Both degrees engineering in the second semester of Candidates for the M.S. degree in may be conferred at the same time. their first year, and can continue with electrical engineering must complete 30 Interested students can find further other core courses one semester after points of credit beyond the bachelor’s information at www.ee.columbia.edu/ that, as shown in the “early-starting stu- degree. A minimum of 15 points of academics/undergrad and can discuss dents” chart. It is emphasized that both credit must be at the 6000 level or options directly with their faculty adviser. the early- and late-starting sample pro- higher. No credit will be allowed for Students must be admitted prior to grams shown in the charts are examples undergraduate courses (3000 or lower). the start of their seventh semester at only; schedules may vary depending on At least 15 points must be taken in Columbia Engineering. Students in the student preparation and interests. EE courses (i.e., courses listed by the 3-2 Combined Plan undergraduate Electrical Engineering Department) or program are not eligible for admission to courses designated COMS, of which Transfer Students this program. at least 10 points must be EE courses. Transfer students coming to Courses to be credited toward the Columbia as juniors with sufficient Graduate Programs M.S. degree can be taken only upon general background can complete all requirements for the B.S. degree in The Department of Electrical Engineering prior approval of a faculty adviser in the electrical engineering. Such students fall offers graduate programs leading to Department of Electrical Engineering. into one of two categories: the degree of Master of Science (M.S.), This applies to the summer session as the graduate professional degree of well as the autumn and spring terms. Plan 1: Students coming to Columbia Electrical Engineer (E.E.), and the Certain 4000-level courses will not without having taken the equivalent of degrees of Doctor of Engineering be credited toward the M.S. degree, ELEN E1201 must take this course in Science (Eng.Sc.D.) and Doctor of and no more than 6 points of research their junior year. This requires postponing Philosophy (Ph.D.). The Graduate may be taken for credit. Up to 3 points the core courses in circuits and Record Examination (General Test of credit for approved graduate courses electronics until the senior year, and thus

engineering 2011–2012 outside of engineering and science applying for admission to the Eng.Sc.D. systems or COMS W4111: Database 141 may be allowed. The general school program or the Ph.D. program. Students systems. requirements listed earlier in this bulletin, who elect the Eng.Sc.D. degree register 4. COMS E6181: Advanced Internet such as minimum GPA, must also be in the School of Engineering and Applied services. satisfied. All degree requirements must Science; those who elect the Ph.D. With an adviser’s approval, any of the be completed within five years of the degree register in the Graduate School courses above can be replaced by the beginning of the first course credited of Arts and Sciences. following closely related subjects: CSEE toward the degree. Doctoral candidates must obtain a E4140: Networking laboratory; CSEE More details and a checklist for minimum of 60 points of formal course W4119: Computer networks; COMS adviser approvals can be found at www. credit beyond the bachelor’s degree. W4180: Network security; ELEN E6762: ee.columbia.edu/academics/masters. A master’s degree from an accredited institution may be accepted as Computer communication networks, II; ELEN E6850: Visual information Professional Degree equivalent to 30 points. A minimum of 30 points beyond the master’s degree systems; ELEN E6950: Wireless and The professional degree in electrical must be earned while in residence in the mobile networking, I; ELEN E6951: engineering is intended to provide doctoral program. Wireless and mobile networking, II. specialization beyond the level of More detailed information regarding the M.S. degree, in a focused area the requirements for the doctoral degree Concentration in Telecommunications of electrical engineering selected to may be obtained in the department Engineering meet the professional objectives of the office and at www.ee.columbia.edu/ Advisers: Prof. Henning Schulzrinne, candidate. A minimum of 30 points of academics/phd. Prof. Pedrag Jelenkovic, Prof. Ed credit is required. Coffman, Prof. Nicholas Maxemchuk, The prospective E.E. candidate Optional M.S. Concentrations Prof. Gil Zussman follows a program of study formulated Students in the electrical engineering 1. Satisfy M.S. degree requirements. in consultation with, and approved by, M.S. program often choose to use 2. One basic hardware or software a faculty adviser. At least three courses some of their electives to focus on course such as: ELEN E4321: will be in a specific, focused area of a particular field. Students may pick Digital VLSI circuits; ELEN E4411: electrical engineering, and at least one of a number of optional, formal Fundamentals of photonics; COMS two-thirds of the entire program will be concentration templates or design their W4118: Operating systems, I; COMS in electrical engineering or computer own M.S. program in consultation with W4111: Database systems. science. No thesis is required, but an adviser. These concentrations are not 3. One basic systems course such the program may optionally include a degree requirements. They represent as: ELEN E4702: Communication seminar or project or research for which suggestions from the faculty as to how theory; ELEN E4703: Wireless a report is produced; up to 6 points of one might fill one’s programs so as to communications; CSEE W4119: such projects may be credited toward focus on a particular area of interest. Computer networks; ELEN E6761: the degree. Students may wish to follow these Computer communication networks, I. The level of the courses will generally suggestions, but they need not. The 4. At least two approved courses from be higher than is typical of a master’s degree requirements are quite flexible a focus area such as Signal/Image degree program, although courses and are listed in the Master of Science Processing and Telecommunications/ at the 4000 level may be included to Degree section, above. All students, Multimedia Networks. prepare for more advanced work. A whether following a formal concentration candidate is required to maintain a template or not, are expected to include Concentration in Media Engineering grade-point average of at least 3.0. breadth in their program. Not all of the Advisers: Prof. Shi-Fu Chang, Prof. Dan All degree requirements must be elective courses listed here are offered Ellis, Prof. Xiaodong Wang completed within five years of the every year. For the latest information 1. Satisfy M.S. degree requirements. beginning of the first course credited on available courses, visit the Electrical 2. Both ELEN E4810: Digital signal toward the degree. Engineering home page at www. processing and ELEN E4830: Digital ee.columbia.edu. image processing. Doctoral Degree 3. Either ELEN E6761: Computer The requirements for the Ph.D. and Eng. Concentration in Multimedia communication networks, I or CSEE Sc.D. degrees are identical. Both require Networking W4119: Computer networks. a dissertation based on the candidate’s Advisers: Prof. Henning Schulzrinne, 4. At least two approved advanced original research, conducted under the Prof. Predrag Jelenkovic courses such as: ELEN E4896: Music supervision of a faculty member. The work 1. Satisfy M.S. degree requirements. signal processing; ELEN E6820: may be theoretical or experimental or both. 2. Both ELEN E6711: Stochastic Speech and audio processing and Students who wish to become signals and noise and ELEN E6761: recognition; ELEN E6850: Visual candidates for the doctoral degree in Computer communication networks, I. information systems; ELEN E6860: electrical engineering have the option of 3. Either COMS W4118: Operating Advanced digital signal processing; ELEN E688x: Topics in signal

engineering 2011–2012 142 processing; ELEN E6762: Computer mobile networking, II; ELEN E6761: physics; ELEN E6945: Nanoscale communication networks, II; ELEN Computer communication networks, fabrication and devices. E6717: Information theory; COMS I; ELEN E6712: Communication 4. At least two approved courses in E6181: Advanced internet services; theory; ELEN E6713: Topics in devices or a related area. ELEN E6950: Wireless and mobile communications; ELEN E6717: networking, I; or ELEN E6001-E6002: Information theory. Concentration in Systems Biology Advanced projects in electrical 4. At least two approved courses in Advisers: Prof. Dimitris Anastassiou, engineering with an appropriate wireless communications or a related Prof. Pedrag Jelenkovic, Prof. Aurel project. A cross-disciplinary project area. Lazar, Prof. Kenneth Shepard, Prof. in areas related to new media Xiaodong Wang, Prof. Charles Zukowski technology is especially encouraged. Concentration in Microelectronic 1. Satisfy M.S. degree requirements. Circuits 2. Take both ECBM E4060: Introduction Concentration in Lightwave Advisers: Prof. Yannis Tsividis, Prof. to genomic information science (Photonics) Engineering Charles Zukowski, Prof. Kenneth and technology and BMEB W4011: Advisers: Prof. Keren Bergman, Prof. Shepard, Prof. Peter Kinget Computational neuroscience, I: Paul Diament, Prof. Richard Osgood, 1. Satisfy M.S. degree requirements. circuits in the brain Prof. Amiya Sen, Prof. Tony Heinz 2. One digital course: ELEN E4321: 3. Take at least one course from CBMF 1. Satisfy M.S. degree requirements. Digital VLSI circuits or ELEN E6321: W4761: Computational genomics; 2. Take both ELEN E4411: Advanced digital electronic circuits. CHBC W4510: Molecular systems Fundamentals of photonics and ELEN 3. One analog course such as: ELEN biology, I; CHBC W4511: Molecular E6403: Classical electromagnetic E4312: Analog electronic circuits; systems biology, II; BIST P8139: theory (or an equivalent, such ELEN E4215: Analog filter synthesis Theoretical genetic modeling as APPH E4300: Applied and design; ELEN E6312: Advanced (Biostatistics); ELEN E6010: Systems electrodynamics or PHYS G6092: analog integrated circuits; ELEN biology; EEBM E6020: Methods Electromagnetic theory). E6316: Analog circuits and systems in computational neuroscience; 3. One more device/circuits/photonics in VLSI; ELEN E4314: Communication BMEE E6030: Neural modeling and course such as: ELEN E4401: circuits; ELEN E6314: Advanced neuroengineering; APMA E4400: Wave transmission and fiber optics; communication circuits. Introduction to biophysical modeling; ELEN E6412: Lightwave devices; 4. One additional course such as: CHEN E4700: Principles of genomic ELEN E6413: Lightwave systems; ELEN E4332: VLSI design laboratory; technologies; ELEN E4312: Analog ELEN E4405: Classical nonlinear ELEN E6211: Circuit theory; ELEN electronic circuits. optics; ELEN E6414: Photonic E6261: Computational methods of 4. Take at least one course from ELEN integrated circuits; ELEN E4314: circuit analysis; ELEN E6304: Topics E608x: Topics in systems biology; Communication circuits; ELEN E4501: in electronic circuits; ELEN E6318: ELEN E6717: Information theory; Electromagnetic devices and energy Microwave circuit design. ELEN E6201: Linear systems theory; conversion. 5. At least two additional approved EEME E6601: Introduction to control 4. At least two approved courses in courses in circuits or a related area. theory; ELEN E6711: Stochastic photonics or a related area. models in information systems; Concentration in Microelectronic ELEN E6860: Advanced digital signal Concentration in Wireless and Mobile Devices processing; EEBM E6090: Topics Communications Advisers: Prof. Wen Wang, Prof. Richard in computational neuroscience and Adviser: Prof. Gil Zussman Osgood, Prof. Ioannis (John) Kymissis neuroengineering; ELEN E6261: 1. Satisfy M.S. degree requirements. 1. Satisfy M.S. degree requirements. Computational methods of circuit 2. One basic circuits course such as: 2. One basic course such as: ELEN analysis. ELEN E4312: Analog electric circuits; E4301: Introduction to semiconductor ELEN E4314: Communication devices or ELEN E4411: courses in electrical circuits; ELEN E6314: Advanced Fundamentals of photonics. engineering communication circuits; ELEN E6312: 3. One advanced course such as: ELEN Advanced analog ICs. E4193: Modern display science ELEN E1101x or y The digital information age 3. Two communications or networking and technology; ELEN E4944: 3 pts. Lect: 3. Professor Vallancourt. An introduction to information transmission and courses such as: CSEE W4119: Principles of device microfabrication; storage, including technological issues. Binary Computer networks; ELEN E4702: ELEN E4503: Sensors, actuators, numbers; elementary computer logic; digital Digital communications; ELEN and electromechanical systems; speech and image coding; basics of compact E4703: Wireless communications; ELEN E6151: Surface physics and disks, telephones, modems, faxes, UPC bar ELEN E6711: Stochastic signals analysis of electronic materials; ELEN codes, and the World Wide Web. Projects and noise; ELEN E4810: Digital E6331: Principles of semiconductor include implementing simple digital logic systems signal processing; ELEN E6950: physics, I; ELEN E6332: Principles and Web pages. Intended primarily for students Wireless and mobile networking, of semiconductor physics, II; ELEN outside the School of Engineering and Applied I; ELEN E6951: Wireless and E6333: Semiconductor device Science. The only prerequisite is a working

engineering 2011–2012 knowledge of elementary algebra. E3331. Companion lab course for ELEN ELEN E3399x Electrical engineering practice 143 E3331. Experiments cover such topics as 1 pt. Professor Vallancourt. ELEN E1201x and y Introduction to electrical macromodeling of nonidealities of opamps Design project planning, written and oral engineering using SPICE; Schmitt triggers and astable technical communication, practical aspects of 3.5 pts. Lect: 3. Lab:1. Professor Vallancourt. multivibrations using opamps and diodes; logic Prerequisite: MATH V1101. Basic concepts of engineering as a profession, such as career inverters and amplifiers using bipolar junction electrical engineering. Exploration of selected development and societal and environmental transistors; logic inverters and ring oscillators topics and their application. Electrical variables, impact. Generally taken senior year. using MOSFETs; filter design using op-amps. circuit laws, nonlinear and linear elements, The lab generally meets on alternate weeks. ELEN E3401y Electromagnetics ideal and real sources, transducers, operational 4 pts. Lect: 3. Professor Diament. amplifiers in simple circuits, external behavior ELEN E3084x Signals and systems laboratory Prerequisite: MATH V1201, PHYS C1402 of diodes and transistors, first order RC and RL 1 pt. Lab: 3. Professor X. Wang. or PHYS C1602, or equivalents. Basic circuits. Digital representation of a signal, digital Corequisite: ELEN E3801. Companion lab field concepts. Interaction of time-varying logic gates, flip-flops. A lab is an integral part of course for ELEN E3801. Experiments cover electromagnetic fields. Field calculation of the course. Required of electrical engineering topics such as: introduction and use of MATLAB lumped circuit parameters. Transition from and computer engineering majors. for numerical and symbolic calculations; electrostatic to quasistatic and electromagnetic linearity and time invariance; continuous-time ELEN E3043x Solid state, microwave and regimes. Transmission lines. Energy transfer, convolution; Fourier-series expansion and signal fiber optics laboratory dissipation, and storage. Waveguides. Radiation. reconstruction; impulse response and transfer 3 pts. Lect: 1. Lab: 6. Professor W. Wang. function; forced response. The lab generally EEME E3601x Classical control systems Prerequisites: ELEN E3106 and ELEN E3401. meets on alternate weeks. 3 pts. Lect: 3. Professor Longman. Optical electronics and communications. Prerequisite: MATH E1210. Analysis and design Microwave circuits. Physical electronics. ELEN E3106x Solid-state devices and materials of feedback control systems. Transfer functions; 3.5 pts. Lect: 3. Recit: 1. Professor Kymissis. ECBM E3060x Introduction to genomic block diagrams; proportional, rate, and integral Prerequisite: MATH V1201 or equivalent. information science and technology controllers; hardware; implementation. Routh Corequisite: PHYS C1403 or PHYS C2601 or 3 pts. Lect: 3. Professor Anastassiou. equivalent. Crystal structure and energy band stability criterion, root locus, Bode and Nyquist Introduction to the information system paradigm of theory of solids. Carrier concentration and plots, compensation techniques. molecular biology. Representation, organization, transport in semiconductors. P-n junction and structure, function and manipulation of the ELEN E3701y Introduction to communication junction transistors. Semiconductor surface biomolecular sequences of nucleic acids and systems and MOS transistors. Optical effects and proteins. The role of enzymes and gene regulatory 3 pts. Lect: 3. Professor Kalet. optoelectronic devices. elements in natural biological functions as well Prerequisite: ELEN E3801. Corequisite: IEOR as in biotechnology and genetic engineering. ELEN E3201x Circuit analysis E3658. A basic course in communication Recombination and other macromolecular 3.5 pts. Lect: 3. Recit: 1. Professor Zukowski. theory, stressing modern digital communication processes viewed as mathematical operations with Prerequisite: ELEN E1201 or equivalent. systems. Nyquist sampling, PAM and PCM/ simulation and visualization using simple computer Corequisite: MATH V1201. A course on analysis DPCM systems, time division multipliexing, programming. This course shares lectures with of linear and nonlinear circuits and their high frequency digital (ASK, OOK, FSK, ECBM E4060, but the work requirements differ applications. Formulation of circuit equations. PSK) systems, and AM and FM systems. An somewhat. Network theorems. Transient response of first and introduction to noise processes, detecting signals second order circuits. Sinusoidal steady state- in the presence of noise, Shannon’s theorem on ELEN E3081x Circuit analysis laboratory analysis. Frequency response of linear circuits. channel capacity, and elements of coding theory. 1 pt. Lab: 3. Professor Zukowski. Poles and zeros. Bode plots. Two-port networks. Prerequisite: ELEN E1201 or equivalent. ELEN E3801x Signals and systems Corequisite: ELEN E3201. Companion lab course ELEN E3331y Electronic circuits 3.5 pts. Lect: 3. Professor X. Wang. for ELEN E3201. Experiments cover such topics 3 pts. Lect: 3. Professor Vallancourt. Corequisite: MATH V1201. Modeling, description, as: use of measurement instruments; HSPICE Prerequisites: ELEN E3201. Operational and classification of signals and systems. simulation; basic network theorems; linearization of amplifier circuits. Diodes and diode circuits. Continuous-time systems. Time domain analysis, nonlinear circuits using negative feedback; op-amp MOS and bipolar junction transistors. Biasing convolution. Frequency domain analysis, transfer circuits; integrators; second order RLC circuits. techniques. Small-signal models. Single-stage functions. Fourier series. Fourier and Laplace The lab generally meets on alternate weeks. transistor amplifiers. Analysis and design of transforms. Discrete-time systems and the Z CMOS logic gates. A/D and D/A converters. transform. ELEN E3082y Digital systems laboratory 1 pt. Lab: 3. Professor Shepard. ELEN E3390y Electronic circuit design CSEE W3827x and y Fundamentals of Corequisite: CSEE W3827. Recommended laboratory computer systems preparation: ELEN E1201 or equivalent. 3 pts. Lab: 6. Professor Vallancourt. 3 pts. Lect: 3. Professors Kim and Rubenstein. Companion lab course for CSEE W3827. Prerequisites: ELEN E3082, E3083, E3331, Prerequisites: An introductory programming Experiments cover such topics as logic gates; E3401, E3801. Advanced circuit design course. Fundamentals of computer organization flip-flops; shift registers; counters; combinational laboratory. Students work in teams to specify, and digital logic. Boolean algebra, Karnaugh logic circuits; sequential logic circuits; design, implement and test an engineering maps, basic gates and components, flipflops and programmable logic devices. The lab generally prototype. The work involves technical as latches, counters and state machines, basics meets on alternate weeks. well as non-technical considerations, such as of combinational and sequential digital design. Assembly language, instruction sets, ALUs, ELEN E3083y Electronic circuits laboratory manufacturability, impact on the environment, single-cycle and multi-cycle processor design, 1 pt. Lab: 3. Professor Vallancourt. and economics. The projects may change from introduction to pipelined processors, caches, and Prerequisite: ELEN E3081. Corequisite: ELEN year to year. virtual memory.

engineering 2011–2012 144 ELEN E3998x and y Projects in electrical course. The technologies and protocols of the demodulators; phase-locked loops. An extensive engineering Internet are covered, using equipment currently design project is an integral part of the course. 0 to 3 pts. available to large Internet service providers ELEN E4321x Digital VLSI circuits May be repeated for credit, but no more than such as CISCO routers and end-systems. A set 3 pts. Lect: 3. Professor Shepard. 3 total points may be used for degree credit. of laboratory experiments provides hands-on Recommended preparation: ELEN E3331, CSEE Prerequisite: approval by a faculty member experience with engineering wide-area networks W3827, and ELEN E3106. Design and analysis who agrees to supervise the work. Independent and familiarizes students with the Internet of high speed logic and memory. Digital CMOS project involving laboratory work, computer Protocol (IP), Address Resolution Protocol and BiCMOS device modeling. Integrated circuit programming, analytical investigation, or (ARP), Internet Control Message Protocol fabrication and layout. Interconnect and parasitic engineering design. (ICMP), User Datagram Protocol (UDP) and elements. Static and dynamic techniques. Transmission Control Protocol (TCP), the BMEB W4020x Computational neuroscience: Worst-case design. Heat removal and I/O. Yield Domain Name System (DNS), routing protocols circuits in the brain and circuit reliability. Logic gates, pass logic, (RIP, OSPF, BGP), network management 3 pts. Lect: 3. Professor Lazar. latches, PLAs, ROMs, RAMs, receivers, drivers, protocols (SNMP), and application-level protocols Prerequisite: ELEN E3801 or BIOL W3004. repeaters, sense amplifiers. (FTP, TELNET, SMTP). The biophysics of computation: modeling EECS E4340x Computer hardware design biological neurons, the Hodgkin-Huxley neuron, ELEN E4193x or y Modern display science 3 pts. Lect: 2. Lab: 3. Professor Sethumadhavan. modeling channel conductances and synapses and technology Prerequisites: ELEN E3331 and CSEE W3827. as memristive systems, bursting neurons and 3 pts. Lect: 3. Professor Kymissis. Practical aspects of computer hardware design central pattern generators, I/O equivalence Prerequisites: Linear algebra, differential through the implementation, simulation, and and spiking neuron models. Information equations, and basic semiconductor physics. prototyping of a PDP-8 processor. High-level and representation and neural encoding: stimulus Introduction to modern display systems in assembly languages, I/O, interrupts, datapath representation with time encoding machines, the an engineering context. The basis for visual and control design, pipelining, busses, memory geometry of time encoding, encoding with neural perception, image representation, color architecture. Programmable logic and hardware circuits with feedback, population time encoding space, metrics of illumination. Physics of prototyping with FPGAs. Fundamentals of VHDL machines. Dendritic computation: elements luminescence, propagation and manipulation for register-transfer level design. Testing and of spike processing and neural computation, of light in anisotropic media, emissive displays, validation of hardware. Hands-on use of industry synaptic plasticity and learning algorithms, and spatial light modulators. Fundamentals CAD tools for simulation and synthesis. unsupervised learning and spike time-dependent of display addressing, the Alt-Pleshko plasticity, basic dendritic integration. Projects in theorem, multiple line addressing. Large area ELEN E4401x Wave transmission and fiber Matlab. electronics, fabrication, and device integration of optics commercially important display types. A series of 3 pts. Lect: 3. Professor Diament. ECBM E4060x Introduction to genomic short laboratories will reinforce material from the Prerequisite: ELEN E3401 or equivalent. Waves information science and technology lectures. Enrollment may be limited. and Maxwell’s equations. Field energetics, 3 pts. Lect: 3. Professor Anastassiou. dispersion, complex power. Waves in dielectrics Introduction to the information system ELEN E4301y Introduction to semiconductor and in conductors. Reflection and refraction. paradigm of molecular biology. Representation, devices Oblique incidence and total internal reflection. organization, structure, function and manipulation 3 pts. Lect: 3. Professor Laibowitz. Transmission lines and conducting waveguides. of the biomolecular sequences of nucleic Prerequisite: ELEN E3106 or equivalent. Planar and circular dielectric waveguides; acids and proteins. The role of enzymes and Semiconductor physics. Carrier injection and integrated optics and optical fibers. Hybrid and gene regulatory elements in natural biological recombination. P-n junction and diodes: Schottky LP modes. Graded-index fibers. Mode coupling; functions as well as in biotechnology and barrier and heterojunctions, solar cells and light- wave launching. genetic engineering. Recombination and emitting diodes. Junction and MOS field-effect other macromolecular processes viewed as transistors, bipolar transistors. Tunneling and ELEN E4411x Fundamentals of photonics mathematical operations with simulation and charge-transfer devices. 3 pts. Lect: 3. Professor Osgood. visualization using simple computer programming. Prerequisite: ELEN E3401 or equivalent. Planar ELEN E4312x Analog electronic circuits This course shares lectures with ECBM E3060, resonators. Photons and photon streams. 3 pts. Lect: 3. Professor Tsividis. but the work requirements differ somewhat. Photons and atoms: energy levels and band Prerequisites: ELEN E3331 and ELEN E3801. structure; interactions of photons with matter; CSEE W4119x and y Computer networks Differential and multistage amplifiers; small- absorption, stimulated and spontaneous 3 pts. Lect: 3. Professor Misra. signal analysis; biasing techniques; frequency emission; thermal light, luminescence light. Corequisite: IEOR E3658 or SIEO W3600 or response; negative feedback; stability criteria; Laser amplifiers: gain, saturation, and phase equivalents. Introduction to computer networks frequency compensation techniques. Analog shift; rate equations; pumping. Lasers: theory of and the technical foundations of the Internet, layout techniques. An extensive design project is oscillation; laser output characteristics. Photons including applications, protocols, local area an integral part of the course. in semiconductors: generation, recombination, networks, algorithms for routing and congestion ELEN E4314y Communication circuits and injection; heterostructures; absorption control, security, elementary performance 3 pts. Lect: 3. Professor Tsividis. and gain coefficients. Semiconductor photon evaluation. Several written and programming Prerequisite: ELEN E4312. Principles of sources: LEDs; semiconductor optical amplifiers; assignments required. electronic circuits used in the generation, homojunction and heterojunction laser diodes. CSEE W4140x or y Networking laboratory transmission, and reception of signal waveforms, Semiconductor photon detectors: p-n, p-i-n, 4 pts. Lect: 3. Professor Zussman. as used in analog and digital communication and heterostructure photo diodes; avalanche Prerequisite: CSEE W4119 or equivalent. In this systems. Nonlinearity and distortion; power photodiodes. course, students learn how to put “principles amplifiers; tuned amplifiers; oscillators; into practice,” in a hands-on-networking lab multipliers and mixers; modulators and

engineering 2011–2012 ELEN E4488x Optical systems EEME E4601y Digital control systems (RTL); algorithmic state machines (ASMs); 145 3 pts. Lect: 3. Professor Bergman. 3 pts. Lect: 3. Professor Longman. introduction to hardware description languages Prerequisite: ELEN E3401 or equivalent. Prerequisite: ELEN E3801 or EEME E3601, (VHDL or Verilog); system-level modeling and Introduction to optical systems based on physical or equivalent. Real-time control using digital simulation; design examples. design and engineering principles. Fundamental computers. Solving scalar and state-space CSEE W4824x or y Computer architecture geometrical and wave optics with specific difference equations. Discrete equivalents of 3 pts. Lect: 3. Professor Carloni. emphasis on developing analytical and numerical continuous systems fed by holds. Z-transfer Prerequisite: CSEE W3827 or equivalent. tools used in optical engineering design. Focus functions. Creating closed-loop difference Focuses on advanced topics in modern on applications that employ optical systems and equation models by Z-transform and state computer architecture, illustrated by recent networks, including examples in holographic variable approaches. The Nyquist frequency case studies. Fundamentals of quantitative imaging, tomography, Fourier imaging, confocal and sample rate selection. Classical- and analysis. Pipelined, out-of-order, and speculative microscopy, optical signal processing, fiber optic modern-based digital control laws. Digital system execution. Superscalar, VLIW and vector communication systems, optical interconnects identification. processors. Embedded processors. Memory and networks. ELEN E4702x or y Digital communications hierarchy design. Multiprocessors and thread- ELEN E4501x Electromagnetic devices and 3 pts. Lect: 3. Professor Cvijetic. level parallelism. Synchronization and cache energy conversion Prerequisite: ELEN E3701 or equivalent. Digital coherence protocols. Interconnection networks. 3 pts. Lect: 3. Professor Sen. communications for both point-to-point and ELEN E4830y Digital image processing Prerequisite: ELEN E3401. Linear and nonlinear switched applications is further developed. 3 pts. Lect: 3. magnetic circuits. Electric and magnetic energy Optimum receiver structures and transmitter Introduction to the mathematical tools and storage, loss, and transfer. Circuit behavior of signal shaping for both binary and M-ary signal algorithmic implementation for representation energy storage and transfer devices. Field theory transmission. An introduction to block codes and and processing of digital pictures, videos, and of moving bodies. Dynamical equations of an convolutional codes, with application to space visual sensory data. Image representation, electromechanical system. Electromechanical communications. filtering, transform, quality enhancement, and thermo-electric sensors and actuators. ELEN E4703y Wireless communications restoration, feature extraction, object Rotating electric energy converters. 3 pts. Lect: 3. Professor Diament. segmentation, motion analysis, classification, Superconductivity and applications. Prerequisite: ELEN E3701 or equivalent. and coding for data compression. A series of ELEN E4503x Sensors, actuators and Wireless communication systems. System design programming assignments reinforces material electromechanical systems fundamentals. Trunking theory. Mobile radio from the lectures. 3 pts. Lect: 3. propagation. Reflection of radio waves. Fading CSEE W4840y Embedded systems Prerequisites: ELEN E3201 and ELEN E3401, and multipath. Modulation techniques; signal 3 pts. Lect: 3. or equivalents. Electromagnetic energy space; probability of error, spread spectrum. Prerequisite: CSEE W4823 or equivalent. storage, loss, and transfer. Dynamics of Diversity. Multiple access. Embedded system design and implementation electromechanical systems. Linearization ELEN E4810x Digital signal processing combining hardware and software. I/O, of nonlinear coupled dynamical equations 3 pts. Lect: 3. Professor Ellis. interfacing, and peripherals. Weekly laboratory and equivalent circuits. Electromechanical Prerequisite: ELEN E3801. Digital filtering in sessions and term project on design of a actuators: acoustic, IC processed time and frequency domain, including properties microprocessor-based embedded system micromachines. Electromechanical sensors: of discrete-time signals and systems, sampling including at least one custom peripheral. acoustic, pressure, and acceleration. Thermal theory, transform analysis, system structures, Knowledge of C programming and digital logic sensors: polysilicon thermopiles and bipolar IIR and FIR filter design techniques, the Discrete required. transistor temperature sensors. Electro-optic Fourier Transform, Fast Fourier Transforms. sensors: visible light, infrared, and X-ray. ELEN E4896y Music signal processing ELEN E4815y Random signals and noise 3 pts. Lect: 3. ELEN E4510x or y Solar energy and smart 3 pts. Lect: 3. Prerequisite: ELEN E3801, E4810, or the grid power systems Prerequisite: IEOR E3658 or equivalent. equivalent. An investigation of the applications 3 pts. Lect: 3. Professors Kymissis and Schwartz. Characterization of stochastic processes as of signal processing to music audio, spanning Prerequisite: Background in circuits. Inorganic models of signals and noise; stationarity, the synthesis of musical sounds (including solar cell semiconductor physics. Single and ergodicity, correlation functions, and power frequency modulation [FM], additive sinusoidal tandem junction design. Measures of spectral spectra. Gaussian processes as models of synthesis, and linear predictive coding and energy efficiency. Introduction to organic noise in linear and nonlinear systems; linear and [LPC]), the modification of real and synthetic solar cells and thin film inorganic cells. nonlinear transformations of random processes; sounds (including reverberation and time/ Batteries and other energy storage systems. orthogonal series representations. Applications pitch scaling), and the analysis of music Introduction to legacy power networks: Single to circuits and devices, to communication, audio to extract musical information (including phase equivalents to three-phase networks. control, filtering, and prediction. pitch tracking, chord transcription, and music Reactive and real power. Equivalent circuits matching). Emphasis on practical, hands-on of synchronous machines, transformers, and CSEE W4823x or y Advanced logic design experimentation, with a wide range of software transmission lines. Smart grid technology: 3 pts. Lect: 3. Professor Nowick. implementations introduced and modified within Control and management of distributed solar Prerequisite: CSEE W3827 or equivalent. An the class. energy and other intermittent renewable power introduction to modern digital system design. sources connected to legacy power networks. Advanced topics in digital logic: controller ELEN E4944x or y Principles of device Microgrid concept. “Small world” networks and synthesis (Mealy and Moore machines); adders microfabrication fault management. Communication over power and multipliers; structured logic blocks (PLDs, 3 pts. Lect: 3. Professor Yardley. lines. Smart metering. PALs, ROMs); iterative circuits. Modern design Science and technology of conventional and methodology: register transfer level modeling advanced microfabrication techniques for

engineering 2011–2012 146 electronics, integrated and discrete components. computation. Synaptic plasticity and learning ELEN E6312y Advanced analog integrated Topics include diffusion; ion implantation, algorithms. Major project(s) in Matlab. circuits thin-film growth including oxides and metals, 3 pts. Lect: 2. BMEE E6030y Neural modeling and molecular beam and liquid-phase epitaxy; optical Prerequisite: ELEN E4312. Integrated circuit neuroengineering and advanced lithography; and plasma and wet device characteristics and models; temperature- 3 pts. Lect: 3. Professor Sajda. etching. and supply-independent biasing; IC operational Prerequisites: APMA E3101, ELEN E3801, and amplifier analysis and design and their ELEN E4998x or y Intermediate projects in BMEB W4020, or equivalent, or instructor’s applications; feedback amplifiers, stability and electrical engineering permission. Engineering perspective on the study frequency compensation techniques; noise in 0–3 pts. of multiple levels of brain organization, from circuits and low-noise design; mismatch in circuits Prerequisites: Instructor’s permission. May be single neurons to cortical modules and systems. and low-offset design. Computer-aided analysis repeated for credit, but no more than 3 total Mathematical models of spiking neurons, neural techniques are used in homework or a design points may be used for degree credit. Substantial dynamics, neural coding, and biologically- project. independent project involving laboratory work, based computational learning. Architectures computer programming, analytical investigation, and learning principles underlying both artificial ELEN E6314x Advanced communication or engineering design. and biological neural networks. Computational circuits models of cortical processing, with an emphasis 3 pts. Lect: 2. ELEN E6001x-E6002y Advanced projects in on the visual system. Applications of principles Prerequisites: ELEN E4314 and ELEN E6312. electrical engineering in neuroengineering; neural prostheses, Overview of communication systems, modulation 1–4 pts. Members of the faculty. neuromorphic systems and biomimetics. Course and detection schemes. Receiver and transmitter May be repeated for up to 6 points of credit. will include a computer simulation laboratory. architectures. Noise, sensitivity, and dynamic Graduate-level projects in various areas of range. Nonlinearity and distortion. Low-noise electrical engineering and computer science. ELEN E6080–6089x or y Topics in systems RF amplifiers, mixers, and oscillators. Phase- In consultation with an instructor, each student biology locked loops and frequency synthesizers. designs his or her project depending on the 3 pts. Lect: 2. Typical applications discussed include wireless student’s previous training and experience. Prerequisite: Instructor’s permission. Selected RF transceivers or data links. Computer-aided Students should consult with a professor in their advanced topics in systems biology. Content analysis techniques are used in homework(s) or area for detailed arrangements no later than the varies from year to year, and different topics a design project. last day of registration. rotate through the course numbers 6080 to 6089. ELEN E6316y Analog systems in VLSI ELEN E6010y Systems biology: design EEBM E6090–6099x or y Topics in computational 3 pts. Lect: 3. principles for biological circuits neuroscience and neuroengineering Prerequisite: ELEN E4312. Analog-digital 4.5 pts. Lect: 3. 3 pts. Lect: 2. interfaces in very large scale integrated circuits. Prerequisite: ECBM E4060 or instructor’s Prerequisite: Instructor’s permission. Selected Precision sampling; A/D and D/A converter permission. Beyond bioinformatics, cells as advanced topics in computational neuroscience architectures; continuous-time and switched systems. Metabolic networks, transcription and neuroengineering. Content varies from year capacitor filters; system considerations. A design regulatory networks, signaling networks. to year, and different topics rotate through the project is an integral part of this course. Deterministic and stochastic kinetics. course numbers 6090 to 6099. Mathematical representation of reconstructed ELEN E6318x or y Microwave circuit design CSEE E6180x or y Modeling and performance networks. Network motifs. Signal transduction 3 pts. Lect: 3. evaluation and neuronal networks. Robustness. Prerequisites: ELEN E3331 and E3401, 3 pts. Lect: 2. Bacterial chemotaxis and patterning in fruit fly or equivalents. Introduction to microwave Prerequisites: COMS W4118 and SIEO W4150 or development. Kinetic proofreading. Optimal permission of the instructor. Introduction to queuing engineering and microwave circuit design. gene circuit design. Rules for gene regulation. analysis and simulation techniques. Evaluation of Review of transmission lines. Smith chart, Random networks and multiple time scales. time-sharing and multiprocessor systems. Topics S-parameters, microwave impedance matching, Biological information processing. Numerical include priority queuing, buffer storage, and disk transformation and power combining networks, and simulation techniques. Major project(s) in access, interference and bus contention problems, active and passive microwave devices, Matlab. and modeling of program behaviors. S-parameter-based design of RF and microwave amplifiers. A microwave circuit design project EEBM E6020y Methods of computational ELEN E6201x Linear system theory (using microwave CAD) is an integral part of the neuroscience 3 pts. Lect: 3. Professor Fishler. course. 4.5 pts. Lect: 3. Prerequisites: ELEN E3801 and APMA E3101, Prerequisite: BMEB W4020 or instructor’s or equivalents. Abstract objects, the concepts of ELEN E6320x or y Millimeter-wave IC design permission. Formal methods in computational state. Definition and properties of linear systems. 3 pts. Lect: 3. Professor Krishnaswamy. neuroscience including methods of signal Characterization of linear continuous-time and Prerequisites: ELEN E3401 or equivalent, processing, communications theory, information discrete-time, fixed, and time-varying systems. ELEN E4314 and E6312. Principles behind the theory, systems and control, system identification State-space description; fundamental matrix, implementation of millimeter-wave (30GHz- and machine learning. Molecular models of calculation by computer and matrix methods. 300GHz) wireless circuits and systems in silicon- transduction pathways. Robust adaptation and Modes in linear systems. Adjoint systems. based technologies. Silicon-based active and integral feedback. Stimulus representation and Controllability and observability. Canonical passive devices for millimeter-wave operation, groups. Stochastic and dynamical systems forms and decompositions. State estimators. millimeter-wave low-noise amplifiers, power models of spike generation. Neural diversity and Lyapunov’s method and stability. amplifiers, oscillators and VCOs, oscillator phase ensemble encoding. Time encoding machines noise theory, mixers and frequency dividers for and neural codes. Stimulus recovery with time PLLs. A design project is an integral part of the decoding machines. MIMO models of neural course.

engineering 2011–2012 ELEN E6321y Advanced digital electronic switches; bistable optical devices. Introduction networks on-chip. 147 circuits to fiber-optic communications: components of EEME E6601x Introduction to control theory 4.5 pts. Lect: 3. the fiber-optic link; modulation, multiplexing 3 pts. Lect: 3. Professor Longman. Prerequisite: ELEN E4321. Advanced topics in and coupling; system performance; receiver Prerequisite: MATH E1210. A graduate-level the design of digital integrated circuits. Clocked sensitivity; coherent optical communications. introduction to classical and modern feedback and non-clocked combinational logic styles. ELEN E6413y Lightwave systems control that does not presume an undergraduate Timing circuits: latches and flip-flops, phase- 3 pts. Lect: 2. background in control. Scalar and matrix locked loops, delay-locked loops. SRAM and Prerequisites: ELEN E4411. Recommended differential equation models, and solutions in DRAM memory circuits. Modeling and analysis preparation: ELEN E6412. Fiber optics. Guiding, terms of state transition matrices. Transfer of on-chip interconnect. Power distribution dispersion, attenuation, and nonlinear properties functions and transfer function matrices, block and power-supply noise. Clocking, timing, and of fibers. Optical modulation schemes. Photonic diagram manipulations, closed-loop response. synchronization issues. Circuits for chip-to-chip components, optical amplifiers. Semiconductor Proportional, rate, and integral controllers, electrical communication. Advanced technology laser transmitters. Receiver design. Fiber optic issues that affect circuit design. The class may and compensators. Design by root locus and telecommunication links. Nonregenerative include a team circuit design project. frequency response. Controllability, observability. transmission using erbium-doped fiber amplifier Luenberger observers, pole placement, and ELEN E6331y Principles of semiconductor chains. Coherent detection. Local area networks. linear-quadratic cost controllers. physics, I Advanced topics in light wave networks. 3 pts. Lect: 2. EEME E6602y Modern control theory ELEN E6414y Photonic integrated circuits Prerequisite: ELEN E4301. Designed for 3 pts. Lect: 3. 3 pts. Lect: 3. students interested in research in semiconductor Prerequisite: EEME E6601 or E4601 or ELEN Photonic integrated circuits are important materials and devices. Topics include energy E6201, or instructor’s permission. Singular value subsystem components for telecommunications, bands: nearly free electron and tight-binding decomposition. ARX model and state-space optically controlled radar, optical signal approximations, the k.p. method, quantitative model system identification. Recursive least processing, and photonic local area networks. calculation of band structures and their squares filters and Kalman filters. LQR, H, linear An introduction to the devices and the design of applications to quantum structure transistors, robust control, predictive control. Learning control, these circuits. Principle and modelling of dielectic photodetectors, and lasers; semiconductor repetitive control, adaptive control. Liapunov waveguides (including silica on silicon and InP statistics, Boltzmann transport equation, and Popov stability. Nonlinear adaptive control, based materials), waveguide devices (simple and scattering processes, quantum effect in transport nonlinear robust control, sliding mode control. star couplers), and surface diffractive elements. phenomena, properties of heterostructures. Discussion of numerical techniques for modelling ELEN E6711x Stochastic models in Quantum mechanical treatment throughout. circuits, including beam propagation and finite information systems ELEN E6332y Principles of semiconductor difference codes, and design of other devices: 4.5 pts. Lect: 3. Professor Baryshnikov. physics, II optical isolators, demultiplexers. Prerequisite: IEOR E3658. Foundations: 3 pts. Lect: 2. probability review, Poisson processes, discrete- ELEN E6430x or y Applied quantum optics Prerequisites: ELEN E6331. Optical properties 3 pts. Lect: 2. time Markov models, continuous-time Markov including absorption and emission of radiation, Prerequisites: Background in electromagnetism models, stationarity, and ergodicity. The course electron-phonon interactions, radiative and (ELEN E3401, E4401, E4411, or PHYS G6092) presents a sample-path (time domain) treatment phonon-mediated processes, excitons, plasmons, and quantum mechanics (APPH E3100, of stochastic models arising in information polaritons, carrier recombination and generation, E4100, or PHYS G402x). An introduction to systems, including at least one of the following and related optical devices, tunneling phenomena, fundamental concepts of quantum optics and areas: communications networks (queueing superconductivity. Quantum mechanical treatment quantum electrodynamics with an emphasis systems), biological networks (hidden Markov throughout, heavy use of perturbation theory. on applications in nanophotonic devices. models), Bayesian restoration of images (Gibbs ELEN E6333y Semiconductor device physics The quantization of the electromagnetic field; fields), and electric networks (random walks). 3 pts. Lect: 2. coherent and squeezed states of light; interaction ELEN E6712x Communication theory Prerequisites: ELEN E4301 or equivalent. between light and electrons in the language 3 pts. Lect: 3. Physics and properties of semiconductors. of quantum electrodynamics (QED); optical Prerequisite: ELEN E4815, or equivalent, or Transport and recombination of excess carriers. resonators and cavity QED; low-threshold lasers; instructor’s permission. Representation of Schottky, P-N, MOS, and heterojunction diodes. and entangled states of light. bandlimited signals and systems. Coherent Field effect and bipolar junction transistors. ELEN E6488y Optical interconnects and and incoherent communications over Gaussian Dielectric and optical properties. Optical devices interconnection networks channels. Basic digital modulation schemes. including semiconductor lamps, lasers, and 3 pts. Lect: 2. Professor Bergman. Intersymbol inference channels. Fading multipath detectors. Prerequisite: ELEN E4411 or E4488 or an channels. Carrier and clock synchronization. ELEN E6412y Lightwave devices equivalent photonics course. Introduction ELEN E6713y Topics in communications 3 pts. Lect: 2. to optical interconnects and interconnection 3 pts. Lect: 3. Prerequisites: ELEN E4411. Electro-optics: networks for digital systems. Fundamental Prerequisite: ELEN E6712 or E4702 or E4703 or principles; electro-optics of liquid crystals and optical interconnects technologies, optical equivalent, or instructor’s permission. Advanced photo-refractive materials. Nonlinear optics: interconnection network design, characterization, topics in communications, such as turbo codes, second-order nonlinear optics; third-order and performance evaluation. Enabling photonic LDPC codes, multiuser communications, network nonlinear optics; pulse propagation and solitons. technologies including free-space structures, coding, cross-layer optimization, cognitive radio. Acousto-optics: interaction of light and sound; hybrid and monolithic integration platforms for Content may vary from year to year to reflect the acousto-optic devices. Photonic switching photonic on-chip, chip-to-chip, backplane, and latest development in the field. and computing: photonic switches; all-optical node-to-node interconnects, as well as photonic

engineering 2011–2012 148 ELEN E6717x Information theory methods, synchronization, data coherence and (COMS W3133, 3134, 3137, 3139 or 3157, or 3 pts. Lect: 2. interconnection networks. Performance analysis equivalent, and familiarity with programming. Prerequisite: IEOR E3658 or a course in stochastic and special purpose parallel machines. Introduction to modern digital CAD synthesis processes. Corequisite: ELEN E4815. Mutual and optimization techniques. Topics include: CSEE E6847y Distributed embedded systems information and entropy. The source coding modern digital system design (high-level 3 pts. Lect: 2. theorem. The capacity of discrete memoryless synthesis, register-transfer level modeling, Prerequisite: Any COMS W411X, CSEE channels and the noisy channel coding theorem. algorithmic state machines, optimal scheduling W48XX, or ELEN E43XX course, or instructor’s The rate distortion function. Discrete memoryless algorithms, resource allocation and binding, permission. An interdisciplinary graduate-level sources and single-letter distortion measures. retiming), controller synthesis and optimization, Bhattacharya bounds, convolutional codes, and seminar on the design of distributed embedded exact and heuristic two-level logic minimization, the Viterbi algorithm. systems. System robustness in the presence advanced multi-level logic optimization, optimal of highly variable communication delays and technology mapping to library cells (for delay, ELEN E6718y Algebraic coding theory heterogeneous component behaviors. The power and area minimization), advanced data 3 pts. Lect: 2. study of the enabling technologies (VLSI structures (binary decision diagrams), SAT Prerequisite: IEOR E3658. Elementary concepts circuits, communication protocols, embedded solvers and their applications, static timing of error control codes. Linear block codes. processors, RTOSs), models of computation, analysis, and introduction to testability. Includes Elements of algebra: Galois fields. Cyclic and design methods. The analysis of modern hands-on small design projects using and codes: BCH, Reed Solomon, Goppa codes. domain-specific applications including on-chip creating CAD tools. Coder, decoder implementation. Decoding micro-networks, multiprocessor systems, fault- algorithms based on spectral techniques. EECS E6870x or y Speech recognition tolerant architectures, and robust deployment Convolutional codes. 3 pts. Lect: 2. of embedded software. Research challenges Prerequisites: Basic probability and statistics. ELEN E6761x Computer communication such as design complexity, reliability, scalability, Theory and practice of contemporary networks I safety, and security. The course requires automatic speech recognition. Gaussian 3 pts. Lect: 3. Professor Maxemchuk. substantial reading, class participation and a mixture distributions, hidden Markov models, Prerequisites: IEOR E3658 and CSEE W4119 or research project. pronunciation modeling, decision trees, finite- equivalent, or instructor’s permission. Focus on ELEN E6850x Visual information systems state transducers, and language modeling. architecture protocols and performance evaluation 3 pts. Lect: 2. Selected advanced topics will be covered in of geographically distributed and local area data Prerequisite: ELEN E4830 or instructor’s more depth. networks. Emphasis on layered protocols. Data permission. Introduction to critical image link layer. Network layer: flow and congestion ELEN E6873x or y Detection and estimation technologies in advanced visual information control routing. Transport layer. Typical Local and theory systems, such as content-based image Metropolitan Area Network standards: Ethernet, 3 pts. Lect: 2. databases, video servers, and desktop video DQDB, FDDI. Introduction to Internetting. Review Prerequisite: ELEN E4815. Introduction to editors. Intended for graduate students. of relevant aspects of queueing theory to provide the fundamental principles of statistical signal Topics include visual data representation and the necessary analytical background. processing related to detection and estimation. compression, content-based visual indexing and Hypothesis testing, signal detection, parameter ELEN E6770–6779x or y Topics in retrieval, storage system design (data placement, estimation, signal estimation, and selected telecommunication networks scheduling, and admission control), compressed advanced topics. Suitable for students doing 3 pts. Lect: 2. video editing, and synchronization issues of research in communications, control, signal Further study of areas such as communication stored video/audio signals. Programming projects processing, and related areas. protocols and architectures, flow and congestion and final presentations are required. ELEN E6880-6889x or y Topics in signal control in data networks, performance evaluation ELEN E6860y Advanced digital signal processing in integrated networks. Content varies from year processing 3 pts. Lect: 2. to year, and different topics rotate through the 3 pts. Lect: 2. Professor Nguyen. Prerequisite: ELEN E4810. Advanced topics course numbers 6770 to 6779. Prerequisite: ELEN E4810. This course is in signal processing, such as multidimensional ELEN E6820y Speech and audio processing designed as an extension to ELEN E4810, with signal processing, image feature extraction, and recognition emphasis on emerging techniques in the area image/video editing and indexing, advanced 4.5 pts. Lect: 3. of digital signal processing. Topics include digital filter design, multirate signal processing, Prerequisite: ELEN E4810 or instructor’s multirate signal processing, multidimensional adaptive signal processing, and wave-form permission. Fundamentals of digital speech signal processing, short-time Fourier transform, coding of signals. Content varies from year to processing and audio signals. Acoustic and signal expansion in discrete and continuous time, year, and different topics rotate through the perceptual basics of audio. Short-time Fourier filter banks, multiresolution analysis, wavelets, course numbers 6880 to 6889. analysis. Analysis and filterbank models. Speech and their applications to image compression and EECS E6890-6899x or y Topics in information and audio coding, compression, and reconstruction. understanding. Other topics may be included to processing Acoustic feature extraction and classification. reflect developments in the field. 3 pts. Lect: 2. Recognition techniques for speech and other Advanced topics spanning electrical CSEE E6861y Computer-aided design of sounds, including hidden Markov models. engineering and computer science such as digital systems speech processing and recognition, image and CSEE E6824y Parallel computer architecture 3 pts. Lect: 2. multimedia content analysis, and other areas 3 pts. Lect: 2. Prerequisites: (i) one semester of advanced drawing on signal processing, information theory, Prerequisite: CSEE W4824. Parallel computer digital logic (CSEE W4823 or equivalent, machine learning, pattern recognition, and principles, machine organization and design of or instructor’s permission); and (ii) a basic related topics. Content varies from year to year, parallel systems including parallelism detection course in data structures and algorithms

engineering 2011–2012 and different topics rotate through the course Prerequisite: submission of an outline of the ELEN E3999x or y Electrical engineering 149 numbers 6890 to 6899. proposed research for approval by the faculty design challenge member who is to supervise the work of the 1 pt. ELEN E6900–6909x or y Topics in electrical student. The research facilities of the department Prerequisite: Approval by a faculty member who and computer engineering are available to qualified students interested in agrees to supervise the work. May be repeated 3 pts. Lect: 2. advanced study. for credit, but no more than 3 total points may be Prerequisite: Instructor’s permission. Selected used for degree credit. Short-term design project topics in electrical and computer engineering. ELEN E9011x and y–E9012 Doctoral research organized as a faculty-led team competition. Content varies from year to year, and different 0–6 pts. Particular design targets are set that vary by topics rotate through the course numbers 6900 Points of credit to be approved by the semester. A set of hardware and software to 6909. department. Open only to doctoral students constraints is specified. The project takes place who have passed the qualifying examinations. ELEN E6945x or y Device nanofabrication over an advertised subset of the semester, Submission of an outline of the proposed 3 pts. Lect: 3. beginning around the third week. research for the approval of the faculty member Prerequisites: ELEN E3106 and E3401, or who is to supervise the work of the student. ELEN E4215y Analog filter synthesis and equivalents. Recommended: ELEN E4944. design This course provides an understanding of ELEN E9800x and y Doctoral research 3 pts. Lect: 3. the methods used for structuring matter on instruction Prerequisites: ELEN E3201 and ELEN E3801, the nanometer length: thin-film technology; 3, 6, 9 or 12 pts. or equivalent. Approximation techniques for lithographic patterning and technologies including A candidate for the Eng.Sc.D. degree in magnitude, phase, and delay specifications , photon, electron, ion and atom, scanning probe, electrical engineering must register for 12 points transfer function realization sensitivity, passive LC soft lithography, and nanoimprinting; pattern of doctoral research instruction. Registration filters, active RC filters, MOSFET-C filters, Gm-C transfer; self-assembly; process integration; and in ELEN E9800 may not be used to satisfy the filters, switched-capacitor filters, automatic tuning applications. minimum residence requirement for the degree. techniques for integrated filters. Filter noise. A ELEN E6950x Wireless and mobile networking, I ELEN E9900x and y–9900 Doctoral dissertation design project is an integral part of the course. 4.5 pts. Lect: 2. Lab: 1. Professor Jelenkovic. 0 pts. ELEN E4302x or y Magnetic sensors and Corequisite: ELEN E6761 or instructor’s A candidate for the doctorate may be required instruments for medical imaging permission. Overview of mobile and wireless to register for this course every term after the 3 pts. Lect: 2.5, Lab: 0.5. networking. Fundamental concepts in mobile student’s course work has been completed, and Prerequisite: ELEN E3106, ELEN E3401, or wireless systems: propagation and fading, until the dissertation has been accepted. instructor’s permission. Physics of nuclear cellular systems, channel assignment, power magnetic resonance (NMR) and superconducting control, handoff. Examples of second-generation quantum interference device (SQUID). Design circuits-switched systems and standards. Courses in Electrical and operation of superconducting DC magnet, Quantitative homework assignments may require Engineering Offered RF receiver, Josephson junction, and integrated use of a mathematical software package. Occasionally SQUID. Principles of biomedical sensoring systems ELEN E6951y Wireless and mobile networking, II EEHS E3900y History of telecommunications: including Magnetic Resonance Imaging (MRI), 3 pts. Lect: 2. Lab: 1. Professor Zussman. from the telegraph to the Internet SQUID magnetometer, and NMR spectroscopy. Prerequisite: CSEE W4119, ELEN E6761, or 3 pts. Lect: 3. Medical image formation and processing. instructor’s permission. Third-generation packet Historical development of telecommunications ELEN E4332y VLSI design laboratory switched systems, wireless LANs, mobile from the telegraphy of the mid-1800s to 3 pts. Lab: 3. computing and communications. Study of some the Internet at present. Included are the Prerequisite: ELEN E4321 or E6316 or EECS current research topics. Quantitative homework technologies of telephony, radio, and computer E4340. Design of a large-scale deep submicron assignments may require use of a mathematical communications. The coverage includes both CMOS integrated circuit. The class may divide software package. A project based on readings the technologies themselves and the historical up into teams to work on different aspects of from the literature will be required. events that shaped, and in turn were shaped by, a single mixed-signal circuit. The chip(s) is the technologies. The historical development, ELEN E6999 Curricular practical training fabricated for testing the following term. Lectures both the general context and the particular 1–3 pts. cover use of computer-aided design tools, events concerning communications, is presented Prerequisites: Obtained internship and approval design issues specific to the project(s), and chip chronologically. The social needs that elicited from a faculty adviser. Only for Electrical integration issues. new technologies and the consequences of their Engineering and Computer Engineering graduate adoption are examined. Throughout the course, ELEN E4405x Classical nonlinear optics students who include relevant off-campus work relevant scientific and engineering principles 3 pts. Lect: 3. experience as part of their approved program of are explained as needed. These include, Prerequisite: ELEN E4401. Waves in anisotropic study. Final report required. May not be taken for among others, the concept and effective use media. Maxwell’s equations and constitutive pass/fail credit or audited. of spectrum, multiplexing to improve capacity, relations. Fresnel equations. Optical waves in EEME E8601y Advanced topics in control digital coding, and networking principles. There anisotropic crystals. Birefringence. Waves in theory are no prerequisites, and no prior scientific or nonlinear media. Plasma model. Electro-optic, 3 pts. Lect: 3. engineering knowledge is required. Engineering Pockels, and Kerr effects. Second harmonic See entry under “Courses in Mechanical students may not count this course as a generation and phase matching. Parametric Engineering” for description. technical elective. The course shares lectures amplification. Backward-wave oscillator. Acousto- with EEHS E4900, but the work requirements optic beam deflection and light modulation. ELEN E9001x and y–E9002 Research differ somewhat. 0–6 pts. Points of credit to be approved by the department.

engineering 2011–2012 150 ELEN E4420x Topics in electromagnetics photoemission, photo stimulated desorption, Objectives of optimal control. Continuous and 3 pts. Lect: 3. and low energy electron diffraction), physical discrete control problems. Calculus of variations: Prerequisites: Undergraduate electromagnetic principles of each approach. Mayer and Bolza; Pontryagin’s maximum principle. theory. Selected topics in the theory and practice Bang-bang and singular controls. Existence ELEN E6211x or y Circuit theory of electromagnetics, varying from year to year. of optimal control. Hamilton-Jacobi theory and 3 pts. Lect: 3. Topic for current term will be available in the dynamic programming. Numerical methods. Prerequisites: ELEN E3331 and ELEN E3801. department office one month before registration. Optimal feedback control regulatory problems. An axiomatic development of circuit theory. This course may be taken more than once when Linear-quadratic-Gaussian estimation. Applications. Circuit theorems, circuit topology, general topics are different. Possible topics: microwave methods of circuit analysis. Normal form EEME E6612x or y Control of nonlinear theory and design (generalized waveguides, characterizations. Scattering characterization dynamic systems excitation and coupling of waveguides, junctions, and sensitivity function. Basic network synthesis 3 pts. Lect: 3. microwave networks, periodic structures, optical methods: immittance and transfer function Prerequisites: EEME E6601 or ELEN E6201 and fibers); antennas (filamentary antennas, arrays, realization, multiport realization, approximation an undergraduate controls course. Fundamental aperture radiation, system properties, pattern techniques. properties of nonlinear systems; qualitative synthesis); electrodynamics (special relativity, analysis of nonlinear systems; nonlinear radiation by charged particles, relativistic beams, ELEN E6261y Computational methods of controllability and observability; nonlinear stability; free electron lasers). circuit analysis zero dynamics and inverse systems; feedback 3 pts. Lect: 3. ELEN E4741x Introduction to biological stabilization and linearization; sliding control Prerequisites: ELEN E3331 and APMA E3101. sensory systems theory; nonlinear observers; describing functions. Computational algorithms for DC, transient, 3 pts. Lect: 3. and frequency analysis of linear and nonlinear ELEN E6731y Satellite communication Corequisite: IEOR E3658. Introduction to vision circuits. Formulation of equations: state systems and hearing using engineering principles. equations, hybrid equations, sparse tableaux. 3 pts. Lect: 2. Not offered in 2011–2012. Nature of sound and light; minimum detectable Solution techniques: iterative methods to solve Prerequisite: ELEN E4702. Introduction to energy for human observers; excitation of the nonlinear algebraic equations; piecewise linear satellite communication, with emphasis on visual and hearing systems; rods, cones, and methods; sparse matrix techniques; numerical characterization and systems engineering of the hair-cell receptors; the experiment of Hecht, integration of stiff, nonlinear differential transmission channel. Power budgets, antennas, Shlaer, and Pirenne; Poisson counting statistics; equations, companion network models; waveform transponders, multiple access, and frequency stimulus-based modeling; detection and false- relaxation. re-use techniques. Noise, intermodulation, alarm probabilities; de Vries-Rose square-root interference, and propagation effects. Modulation law; Weber’s law; relation of sensory and ELEN E6302x or y MOS transistors methods, earth terminals, and standards. Digital communication systems. 3 pts. Lect: 2. transmission and advanced systems. Prerequisite: ELEN E3106 or equivalent. CSEE W4825y Digital systems design Operation and modelling of MOS transistors. ELEN E6762y Computer communication 3 pts. Lect: 3. MOS two- and three-terminal structures. The networks, II Prerequisite: CSEE W3827. Dynamic logic, MOS transistor as a four-terminal device; general 3 pts. Lect: 2. field programmable gate arrays, logic design charge-sheet modelling; strong, moderate, Prerequisite: ELEN E6761. Broadband languages, multipliers. Special techniques for and weak inversion models; short-and-narrow- ISDN, services and protocols; ATM. Traffic multilevel NAND and NOR gate circuits. Clocking channel effects; ion-implanted devices; scaling characterization and modeling: Markov- schemes for one- and two-phase systems. Fault considerations in VLSI; charge modelling; large- modulated Poisson and Fluid Flow processes; checking: scan method, built-in-test. Survey of signal transient and small-signal modelling for application to voice, video, and images. Traffic logic simulation methods. Other topics to be quasistatic and nonquasistatic operation. Management in ATM networks: admission added as appropriate. and access control, flow control. ATM switch ELEN E6304x or y Topics in electronic ELEN E6140x Gallium arsenide materials architectures; input/output queueing. Quality of circuits processing service (QoS) concepts. 3 pts. Lect: 3. 3 pts. Lect: 3. Prerequisite: Instructor’s permission. State-of- ELEN E6763y Digital circuit switched networks Prerequisite: ELEN E4301 or instructor’s the-art techniques in integrated circuits. Topics 3 pts. Lect: 2. permission. Materials and device aspects of may change from year to year. Prerequisite: ELEN E6761 or instructor’s GaAs and compound technologies, electronic permission. Current topics in digital circuit properties of GaAs, growth techniques (bulk ELEN E6403y Classical electromagnetic theory switching: introduction to circuit switching, and epitaxial), surface and etching properties, 4.5 pts. Lect: 3. comparison with packet switching, elements implantation, MESFETS, transferred electron Prerequisite: One term of undergraduate of telephone traffic engineering, space and devices, Impatt diodes, HEMTS, HBTs. electromagnetic theory. A mathematical physics time switching, call processing in digital approach to electromagnetic phenomena. ELEN E6151y Surface physics and analysis of circuit-switched systems, overload control Poisson, Laplace equations; Green’s functions. electronic materials mechanisms, nonhierarchical routing, common Theorems of electrostatics. Multipole expansions. 3 pts. Lect: 2. channel signaling, introduction to integrated Energy relations and stress tensor. Maxwell’s Prerequisite: Instructor’s permission. Basic services digital networks. Examples of current equations in stationary and moving media. physical principles of methods of surface systems are introduced throughout. Emphasis on The wave equation, energy and momentum analysis, surfaces of electronic materials modeling and quantitative performance analysis. theorems, potentials, choice of gauge. including structure and optical properties (auger Queueing models introduced where possible. electron spectroscopy, x-ray photoemission, EEME E6610x Optimal control theory ultraviolet photoelectron spectroscopy, 3 pts. Lect: 3. electron energy loss spectroscopy, inverse Prerequisite: ELEN E6201 or EEME E6601.

engineering 2011–2012 ELEN E6781y Topics in modeling and the theory of innovations, state estimate ELEN E9402x or y Seminar in quantum 151 analysis of random phenomena for queues. Markovian queueing networks. electronics 3 pts. Lect: 3. Hypothesis testing, the separation between 3 pts. Lect: 2. Prerequisite: ELEN E6711. Recommended filtering and detection. Mutual information and Open to doctoral candidates, and to qualified preparation: a course on real analysis capacity for the Poisson-type channel. Stochastic M.S. candidates with instructor’s permission. and advanced probability theory. Current control, dynamic programming for intensity control. Recent experimental and theoretical methodology in research in stochastic processes developments in various areas of quantum ELEN E9060x or y Seminar in systems biology applied to communication, control, and signal electronics research. Examples of topics that 3 pts. Lect: 2. processing. Topics vary from year to year to may be treated include novel nonlinear optics, Open to doctoral candidates, and to qualified reflect student interest and current developments lasers, transient phenomena, and detectors. M.S. candidates with instructor’s permission. in the field. Study of recent developments in the field of ELEN E9403x or y Seminar in photonics CSEE E6831y Sequential logic circuits systems biology. 3 pts. Lect: 2. 3 pts. Lect: 3. Prerequisite: ELEN E4411. Open to doctoral EEBM E9070x or y Seminar in computational Prerequisite: CSEE W3827 or any introduction candidates, and to qualified M.S. candidates neuroscience and neuroengineering to logic circuits. Generation and manipulation of with instructor’s permission. Recent experimental 3 pts. Lect: 2. flow table descriptions to asynchronous sequential and theoretical developments in various areas of Open to doctoral candidates and qualified functions. Coding of flow tables to satisfy photonics research. Examples of topics that may M.S. candidates with instructor’s permission. various design criteria. Delays, races, hazards, be treated include squeezed-light generation, Study of recent developments in computational metastability. Analysis of latches to determine quantum optics, photon detection, nonlinear neuroscience and neuroengineering. key parameters. Bounds of input rates. Clocking optical effects, and ultrafast optics. schemes for synchronous systems. Synthesis ELEN E9101x or y Seminar in physical ELEN E9404x or y Seminar in lightwave of self-timed systems using 4-phase or 2-phase electronics communications handshakes. 3 pts. Lect: 2. 3 pts. Lect: 2. Prerequisites: Quantum electronics and ELEN CSEE E6832x or y Topics in logic design Open to doctoral candidates, and to qualified E4944, or instructor’s permission. Advanced theory M.S. candidates with instructor’s approval. topics in classical and quantum phenomena 3 pts. Lect: 3. Recent theoretical and experimental that are based on ion and electron beams, Prerequisite: CSEE W3827 or any introduction to developments in light wave communications gas discharges, and related excitation logic circuits. A list of topics for each offering of research. Examples of topics that may be sources. Application to new laser sources and the course is available in the department office treated include information capacity of light microelectronic fabrication. one month before registration. May be taken wave channels, photonic switching, novel light more than once if topics are different. Iterative ELEN E9201x or y Seminar in circuit theory wave network architectures, and optical neural logic circuits applied to pattern recognition. Finite 3 pts. Lect: 2. networks. state machines; alternative representations, Open to doctoral candidates, and to qualified ELEN E9701x or y Seminar in information and information loss, linear circuits, structure theory. M.S. candidates with instructor’s permission. communication theories Reliability and testability of digital systems. Study of recent developments in linear, 3 pts. Lect: 2. nonlinear, and distributed circuit theory and ELEN E6920x or y Topics in VLSI systems Open to doctoral candidates, and to qualified analysis techniques important to the design of design M.S. candidates with instructor’s permission. very large scale integrated circuits. 3 pts. Lect: 2. Recent developments in telecommunication Prerequisite: ELEN E4321. Design automation: ELEN E9301x or y Seminar in electronic networks, information and communication layout, placement, and routing. Circuit simulation devices theories, and related topics. algorithms and optimization of performance 3 pts. Lect: 2. ELEN E9801x or y Seminar in signal and area. Multiprocessor computing systems. Open to doctoral candidates, and to qualified processing Verification of testing. Topics may change from M.S. candidates with instructor’s permission. 3 pts. Lect: 2. year to year. Theoretical and experimental studies of Open to doctoral candidates, and to qualifies semiconductor physics, devices, and technology. ELEN E8701y Point processes in information M.S. candidates with instructor’s approval. and dynamical systems ELEN E9303x or y Seminar in electronic Recent developments in theory and applications 3 pts. Lect: 3. circuits of signal processing, machine learning, content Prerequisite: ELEN E6711 or equivalent. 3 pts. Lect: 2. analysis, and related topics. Recommended preparation: Course in measure Open to doctoral candidates, and to qualified theory or advanced probability theory. Probability M.S. candidates with instructor’s permission. and point processes. Random intensity rate, Study of recent developments in electronic martingales, and the integral representation of circuits. point process martingales. Recursive estimation,

engineering 2011–2012 152 Industrial Engineering and Operations Research 313 S. W. Mudd, MC 4704 Phone: 212-854-2941 www.ieor.columbia.edu

Chair Director: Master Professors Ward Whitt Adjunct Faculty Clifford Stein of Science Daniel Bienstock Vlihalis Yannakakis, David DeRosa 326 S. W. Mudd Programs Mark Broadie, Computer Science Leon S. Gold Soulaymane Kachani Business School David D. Yao David Gulley Director: Edward M. Coffman Jr., Mark Higgins Administration, Director: Financial Electrical Engineering Associate Ali Hirsa Academic and Engineering Emanuel Derman Professors Iraj Kani Professional Program Awi Federgruen, Maria Chudnovsky Alexander Kuznetsov Development Emanuel Derman Business School Rama Cont William J. Latzko Jenny S. Mak Guillermo Gallego Soulaymane Kachani Michael D. Lipkin 324 S. W. Mudd Director: Doctoral Paul Glasserman, Jay Sethuraman Hanan Luss Programs Business School Allan Malz Student Affairs Daniel Bienstock Donald Goldfarb Assistant Peter V. Norden Manager Garud Iyengar Professors Lucius J. Riccio Director: Adina Berrios Brooks Iannis Karatzas, Jose Blanchet Moshe Rosenwein Executive Mathematics Vineet Goyal Ali Sadighian Director: Education Peter J. Kolesar, Xuedong He Alexander Stanton Undergraduate Soulaymane Kachani Business School Tim Leung Leon Tatevossian Programs S. G. Steven Kou Mariana Olvera-Cravioto Leo Tilman Garud Iyengar Karl Sigman Van Anh Truong Sheldon Weinig Clifford Stein Larry Wright M. Suresh Sundaresan, Lecturers in Business School Discipline Garrett van Ryzin, Martin Haugh Business School Anthony Webster

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

engineering 2011–2012 Current Research Activities of research done by members of the to participate in teams, understand 153 In industrial engineering, research is Center. and practice interpersonal and conducted in the area of logistics, The Computational Optimization organizational behaviors, and routing, scheduling, production and Research Center (CORC) at Columbia communicate their solutions and supply chain management, inventory University is an interdisciplinary group recommendations effectively control, revenue management, and of researchers from a variety of through written, oral, and electronic quality control. departments on the Columbia campus. presentations; In operations research, new Its permanent members are Professors 3. To familiarize students with the developments are being explored Daniel Bienstock, Don Goldfarb, Garud historical development of industrial in mathematical programming, Iyengar, Jay Sethuraman, and Cliff engineering tools and techniques and combinatorial optimization, stochastic Stein, from the Industrial Engineering with the contemporary state of the modeling, computational and and Operations Research Department, art, and to instill the need for lifelong mathematical finance, queueing and Professor David Bayer, from learning within their profession; and theory, reliability, simulation, and both the Department of Mathematics at 4. To instill in our students an deterministic and stochastic network Barnard College. Researchers at understanding of ethical issues flows. CORC specialize in the design and and professional and managerial In engineering and management implementation of state-of-the-art responsibilities. systems, research is conducted in algorithms for the solution of large-scale the areas of logistics, supply chain optimization problems arising from a B.S. in Operations Research optimization, and revenue and risk wide variety of industrial and commercial The operations research program management. applications. is one of several applied science In financial engineering, research programs offered at the School. At is being carried out in portfolio undergraduate programs the undergraduate level, it offers management; option pricing, including basic courses in probability, statistics, exotic and real options; computational applied mathematics, simulation, B.S. in Industrial Engineering finance, such as Monte Carlo simulation and optimization as well as more The undergraduate program is and numerical methods; as well as data professionally oriented operations designed to develop the technical mining and risk management. research courses. The curriculum is well skills and intellectual discipline needed Projects are sponsored and suited for students with an aptitude for by our graduates to become leaders supported by leading private firms mathematics applications. in industrial engineering and related and government agencies. In addition, It prepares graduates for professional professions. The program is distinctive our students and faculty are involved employment as operations research in its emphasis on quantitative, in the work of three research and analysts, e.g., with management economic, computer-aided approaches educational centers: the Center for consultant and financial service to production and service management Applied Probability (CAP), the Center organizations, as well as for graduate problems. It is focused on providing for Financial Engineering (CFE), and studies in operations research or an experimental and mathematical the Computational and Optimization business. It is flexible enough to be problem-formulating and problem- Research Center (CORC). These centers adapted to the needs of future medical solving framework for industrial are supported principally by grants from and law students. the National Science Foundation. engineering work. The curriculum provides a broad foundation in the The Center for Applied Probability B.S. in Operations Research: current ideas, models, and methods of (CAP) is a cooperative center involving Engineering Management Systems the School of Engineering and Applied industrial engineering. It also includes a substantial component in the humanities This operations research option is Science, several departments in the designed to provide students with Graduate School of Arts and Sciences, and social sciences to help students understand the societal implications of an understanding of contemporary and the Graduate School of Business. technology and management. It is Its interests are in four applied areas: their work. The industrial engineering program for students who are interested in a mathematical and computational finance, technical-management background stochastic networks, logistics and objectives are: 1. To provide students with the requisite rather than one in a traditional distribution, and population dynamics. engineering field. It consists of required The Center for Financial Engineering analytical and computational skills to assess practical situations and courses in industrial engineering and (CFE) at Columbia University operations research, economics, encourages interdisciplinary research on academic problems, formulate models of the problems represented business, and computer science, financial engineering and mathematical intended to provide a foundation modeling in finance and promoting or embedded therein, design potential solutions, and evaluate their for dealing with engineering and collaboration between Columbia faculty management systems problems. and financial institutions, through the impact; 2. To prepare students for the Elective courses are generally intended organization of research seminars, to provide a substantive core in at least workshops, and the dissemination workplace by fostering their ability

engineering 2011–2012 154 one technology area and at least one to participate. Students are invited to Tests of the Graduate Record management area. apply to the track upon the completion Examination. M.S./M.B.A. candidates Due to the flexibility of this option, it of their sophomore year. Advanced are also required to take the Graduate can incorporate the varied educational track students are required to take Management Admissions Test. needs of preprofessional students higher-level IEOR courses, including the A minimum grade point average interested in law, medicine, business, following: of 3.0 (B) or its equivalent in an and finance. In addition, most students undergraduate engineering program IEOR E4004 instead of IEOR E3608 are encouraged to add a minor in is required for admission to the M.S. IEOR E4106 instead of IEOR E3106 economics or computer science to their and professional degree programs. At IEOR E4403 instead of IEOR E4003 standard course schedules. a minimum, students are expected, and MATH V2500 on entry, to have completed courses B.S. in Operations Research: Students successfully completing in ordinary differential equations, linear Financial Engineering the requirements of the undergraduate algebra, probability, and a programming The operations research concentration advanced track will receive recognition language such as C or Java. in financial engineering is designed to on their academic record. provide students with an understanding M.S. in Management Science and of the application of engineering Minors Engineering methodologies and quantitative A number of minors are available for The Master of Science program methods to finance. Financial students wishing to add them to their in Management Science and engineering is a multidisciplinary programs. These minors are described Engineering (MS&E), offered by the field integrating financial theory with starting on page 190 of this bulletin. IEOR Department in conjunction with economics, methods of engineering, IEOR program students may want Columbia Business School, is the tools of mathematics, and practice of to consider minors in economics first such program between Columbia programming. Students graduating with or computer science. In addition, Engineering and Columbia Business this concentration are prepared to enter operations research and engineering School. It reflects the next logical step careers in securities, banking, financial and management systems majors may in the longstanding close collaboration management, and consulting industries, elect to minor in industrial engineering, between the IEOR Department at the and fill quantitative roles in corporate and industrial engineering majors may Engineering School and the Decision, treasury and finance departments of elect to minor in operations research. Risk, and Operations (DRO) Division at general manufacturing and service firms. The department does not offer a the Business School. Students who are interested in minor in engineering management This program was formed and pursuing the rigorous concentration in systems or financial engineering. structured following many interactions financial engineering must demonstrate with corporations, alumni, and students. proficiency in calculus, computer Graduate Programs It emphasizes both management and programming, linear algebra, ordinary engineering perspectives in solving The Department of Industrial differential equations, probability, problems, making decisions, and Engineering and Operations Research and statistics. Applications to the managing risks in complex systems. offers courses and M.S. programs concentration are accepted during Students pursuing this degree program in (1) industrial engineering and (2) the fall and spring semesters of the are provided with a rigorous exposure operations research on either a full- sophomore year, and students will be to optimization and stochastic modeling, or part-time basis and (3) financial notified of the departmental decision by and a deep coverage of applications in engineering on a full-time basis only. the end of that spring semester. The the areas of operations engineering and The Department is launching the new department is seeking students who management. M.S. program in Management Science demonstrate strength and consistency The MS&E program is a three- and Engineering in conjunction with in all the above-mentioned areas. semester program (36 points) that can the Columbia Graduate School of Application to this concentration is be completed in a single calendar year. Business. Graduate programs leading available online: www.ieor.columbia. Students enter in the fall term and can to a Ph.D. or Eng.Sc.D. in industrial edu/pages/undergraduate/financial_eng/ either finish their course work at the end engineering or operations research, as bsfe_app.html. of the following August, or alternatively, well as one leading to the professional have the option to take the summer degree of Industrial Engineer, are also term off (e.g., for an internship) and Undergraduate Advanced Track available. In addition, the department complete their course work by the end The undergraduate advanced and the Graduate School of Business of the following fall term. Students are track is designed for advanced offer combined M.S./M.B.A. degree required to take the equivalent of 12 undergraduate students with the desire programs in industrial engineering, in 3-point courses (36 points), provided to pursue further higher education financial engineering, and in operations they have adequate preparation in the after graduation. Students with a research. areas of probability/statistics. In the minimum cumulative GPA of 3.4 and All degree program applicants absence thereof, they are required to faculty approval have the opportunity are required to take the Aptitude

engineering 2011–2012 take one additional 3-point course. 155 Students must take at least 6 M.S. in Management Science and Engineering (36 points) courses within the IEOR Department, 4 to 6 courses at the Business School, Required Core IEOR E4004 Intro to OR: deterministic models (first [fall] semester) and the remaining courses (if any) within Courses IEOR E4106 Intro to OR: stochastic models (fall or spring semester) the School of Engineering, the School IEOR E4111 Operations consulting (first [fall] semester, of International and Public Affairs, continues in the spring semester till May) the Law School, or the Departments (SIEO W4150 Intro to probability and statistics must be taken if student has of Economics, Mathematics, and not taken the equivalent previously. first [fall] semester) Statistics. Students in residence during Semi Core Courses FINC B6302 Capital markets and investments (fall semester) the summer term take 2 to 4 Business Management FINC B8301 Advanced corporate finance (spring semester) School courses in the third (summer) Electives IEME E4310 The manufacturing enterprise (fall semester) semester in order to complete their At least two of the IEOR E4505 Operations research in public policy (spring semester) program. following: IEOR E4510 Project management (spring semester) Graduates from this program are IEOR E4550 Entrepreneurial business creation for engineers expected to assume positions as ana- (fall or spring semester) lysts and associates in consulting firms, IEOR E4705 Studies in OR (fall semester) business analysts in logistics, supply IEOR E4721 Global capital markets (fall semester) chain, operations, or revenue manage- IEOR E4998 Managing technological innovation and entrepreneurship ment departments of large corporations, (fall or spring semester) and as financial analysts in various func- tions (e.g., risk management) of invest- Analysis Electives IEOR E4000 Production and operations management (fall semester) ment banks, hedge funds, credit-card At least two of the IEOR E4403 Advanced engineering and corporate economics (fall semester) companies, and insurance firms. following: IEOR E4404 Simulation (fall or spring semester) IEOR E4405 Production scheduling (spring semester) M.S. in Financial Engineering IEOR E4407 Game theoretic models of operations (fall semester) The department offers a full-time IEOR E4418 Logistics and transportation management (spring semester) only M.S. in Financial Engineering. IEOR E4601 Dynamic pricing and revenue optimization (spring semester) This program is intended to provide DRAN B9801/IEOR E4520 Computing for business research a unique technical background for (taught alternately each year by DRO and IEOR faculty) students interested in pursuing career Decision, Risk, and OPMN B8833 Managerial negotiations (with game theoretical analysis) opportunities in financial analysis and Operations Electives (fall or spring semester) risk management. At least three of the OPMN B8811 Service operations (summer semester) In addition to the basic requirements following: MRKT B8617 Marketing research (summer semester) for graduate study, students are DRAN B8834/OPMN B5201 Decision models, II/Operations strategy expected, on entry, to have attained a (summer semester) high level of mathematical and computer DRAN B8832 Applied multivariate statistics (summer semester) programming skills, particularly in DRAN B8840 Enterprise risk management (fall semester) probability, statistics, linear algebra, and OPMN B8815/IEOR E4210 Supply chain management (spring semester) the use of a programming language DRAN B8839/IEOR E4220 Demand and supply anlytics (spring semester) such as C or JAVA. Work experience is desirable but not required. Other Electives: The program consists of 36 points The remaining electives can be selected from the Business School, the School of Engineering, the School of (12 courses), which can be taken over International and Public Affairs, the Law School, or the Departments of Economics, Mathematics, and Statistics. a 12-month period of full-time studies, starting with a Part II six-week summer session (July 5–August 26, 2011). IEOR website: www.ieor.columbia.edu. The department requires that Students may elect to complete the The eight required core courses for students achieve grades of B– or higher program in May, August, or December the financial engineering program are in each of the four fundamental core of the following year. The requirements IEOR E4007, IEOR E4701, IEOR E4702, courses offered in the first summer. include eight required core courses and IEOR E4703, IEOR E4706, IEOR E4707, Poor performance in these courses is additional elective courses chosen from IEOR E4709, and IEOR E4729. indicative of inadequate preparation a variety of departments or schools In addition, students select two and is very likely to lead to serious at Columbia including the Graduate semicore courses from a group of problems in completing the program. School of Business, International Affairs, specialized offerings in the spring term. As a result, students failing to meet Computer Science, Statistics, and Electives are chosen with the approval this criterion may be asked to withdraw Economics. A sample schedule is available of an adviser. from the program. in the department office and on the

engineering 2011–2012 156 M.S. in Industrial Engineering 1 The department’s graduate program M.S. in Financial Engineering—May 2012 Completion (36 points) in industrial engineering are generally intended to enable students with Summer Semester Fall Semester Spring Semester industrial engineering bachelor’s degrees (9 points)2 (12 points)2 (15 points)2 to enhance their undergraduate training with studies in special fields such as Required core courses: Required core courses: Required core course: production planning, inventory control, scheduling, and industrial economics. IEOR E4701 Stochastic models IEOR E4007 Optimization for IEOR E4703 Monte Carlo for financial engineering financial engineering simulation However, the department also offers broader master’s and professional IEOR E4702 Statistical inference IEOR E4707 Continuous time Choose four from the courses degree programs for engineers whose for financial engineering (1.5) finance below, plus one other course in consultation with faculty adviser3: undergraduate training is not in industrial IEOR E4706 Foundations of IEOR E4709 Data analysis for engineering. financial engineering financial engineering IEOR E4500 Applications pro- M.S. degree candidates are required gramming for financial engineering to satisfy a core program of graduate IEOR E4729 Financial markets, Elective institutions, and risk (1.5) IEOR E4602 Quantitative risk courses in production management, management probability theory, statistics, simulation, and operations research. Students with IEOR E4630 Asset allocation B.S. degrees in industrial engineering will IEOR E4708 Seminar on usually have satisfied this core in their important papers in financial undergraduate programs. All students engineering must take at least 18 points of graduate IEOR E4710 Term structure work in industrial engineering and at modeling least 30 points of graduate studies at Columbia. Master’s degree programs IEOR E4718 Intro to implied may include concentrations in: volatility smile engineering and management systems IEOR E4731 Credit risk and production and operations management credit derivatives manufacturing DRAN B8835 Security pricing industrial regulation studies models Additional details regarding these concentrations are available 1 Students may conclude the program in May, August, or December 2011. Please visit the departmental in the department office. A thesis website (www.ieor.columbia.edu/pages/graduate/ms_financial_eng/index.html) for more information. is not required. Students who plan 2 All courses listed are for 3 points, unless stated otherwise. post–master’s degree studies 3 Other courses include experimental finance, foreign exchange and related derivative instruments, hedge should give due consideration to the fund management, structured products, etc. Specific offerings may vary each term. course, examination, and admission requirements of these programs. 60-point program includes (a) 30 points students with engineering or other The department requires that completed in ten core courses, (b) a undergraduate majors that include strong students in the program achieve concentration of at least four courses, mathematics preparation to complete grades of B– or higher in each of the (c) other electives and (possibly) defi- work in two terms of full-time study. fundamental core courses (IEOR E4004 ciencies. A minimum of twelve courses, M.S. degree candidates are required and IEOR E4106). Poor performance providing 36 points of credit, must be to satisfy a core set of graduate courses in these courses is indicative of industrial engineering courses taken in probability, statistics, linear program- inadequate preparation and is very from departmental course offerings or at ming, and simulation. All students must likely to lead to serious problems in other institutions where advanced stand- complete at least 18 points of opera- completing the program. In addition, ing is given. A thesis is not required. tions research courses and at least 30 students must maintain a cumulative points of graduate work at Columbia. GPA equivalent to a B– during every The department considers it desir- term enrolled. A student failing to meet M.S. in Operations Research able that students construct balanced these criteria may be asked to withdraw The graduate program in this area is programs involving deterministic and from his/her program. designed to enable students to concen- stochastic models, as well as substan- The professional degree of Industrial trate their studies in methodological areas tive areas for application. Engineer requires a minimum of 60 such as mathematical programming, sto- The M.S. degree program may be points of graduate credit with at least chastic models, and simulation. However, constructed to include the following 30 points beyond the M.S. degree in the department also has a broadly based areas of focus: industrial engineering. The complete master’s degree program that enables

engineering 2011–2012 optimization 157 applied probability M.S. in Operations Research (30 points) financial and managerial application of operations research Required Core SIEO W4150 Intro to Probability and Statistics (3) Additional details regarding these Courses IEOR E4004 Intro to OR: Deterministic Models (3) (12 points) concentrations are available in the IEOR E4106 Intro to OR: Stochastic Models (3) department office. A thesis is not IEOR E4004 Simulation (3) required. Students who plan to continue their studies beyond the master’s degree level should give due consideration to Electives The department suggests a number of elective courses depending on areas of the course, examination, and grade-point (18 points) focus. The areas of focus include optimization, applied probability, and financial and managerial applications of operations research. requirements of doctoral programs. The M.S. degree program can be taken on a part-time basis or completed in one year Optimization IEOR E4000 Production and operations management of full-time study. Students planning to The department IEOR E4210 Supply chain management recommends taking complete this program in one year are at least three of the IEOR E4405 Production scheduling expected, on entry, to have completed following elective IEOR E4418 Logistics and transportation management courses in ordinary differential equations, courses: IEOR E4600 Applied integer programming in linear algebra, and in a programming language such as C or Java. IEOR E4630 Asset allocation The department requires that students in the program achieve Applied Probability IEOR E4000 Production and operations management grades of B– or higher in each of the The department IEOR E4210 Supply chain management fundamental core courses (IEOR E4004 recommends taking at least three of the IEOR E4220 Demand and supply analytics and IEOR E4106). Poor performance in following elective IEOR E4407 Game theoretic models of operation these courses is indicative of inadequate courses: IEOR E4601 Dynamic pricing and revenue management preparation and is very likely to lead to serious problems in completing the IEOR E4602 Quantitative risk management program. In addition, students must IEOR E4700 Intro to financial engineering maintain a cumulative GPA equivalent to a B– during every term enrolled. A Students interested Corporate Finance Derivatives Pricing Management student failing to meet these criteria in financial and Courses Courses Courses may be asked to withdraw from his/her managerial applications of operations research program. IEOR E4403 Advanced IEOR E4700 Intro to At least one of: should consider taking: engineering & corporate financial engineering IEOR E4505 Joint M.S. and M.B.A. economics And at least one of: OR in public policy The department and the Graduate And at least one of: IEOR E4602 IEOR E4510 School of Business offer joint master’s FINC B6302 Capital mar- Quantitative risk Project management programs in financial engineering, kets and investments management IEOR E4550 industrial engineering, and operations FINC B8301 Advanced IEOR E4630 Entrepreneurial research. Prospective students for corporate finance Asset allocation business creation for these special programs must submit ECIE W4280 Corporate IEOR E4620 engineers separate applications to the School of finance Pricing models IEOR E4705 Engineering and Applied Science and IEOR E4721 Global Studies in OR the Graduate School of Business and be capital markets IEOR E4998 Managing admitted to both schools for entrance technological innovation into the joint program. Admissions requirements are the same as those for the regular M.S. of their first year of study. Students in Doctoral Studies programs and for the M.B.A. These joint the IE or OR joint program should take The requirements for the Ph.D. in indus- programs are coordinated so that both IEOR E4000, IEOR E4004, and SIEO trial engineering and operations research degrees can be obtained after five terms W4150. If a substantial equivalent has are identical. Both require the student of full-time study (30 points in two terms been completed during undergraduate to pass two qualifying examinations— while registered in SEAS and 45 points studies, students should consult with respectively covering stochastic and in three terms while registered in the a faculty adviser in order to obtain deterministic models—as well as submit Graduate School of Business). exemption from a required course. and defend a dissertation based on Students in joint programs must the candidate’s original research, con- complete certain courses by the end ducted under the supervision of a faculty

engineering 2011–2012 158 industrial engineering: first and second Years

Semester i Semester iI Semester iII Semester iV

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

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

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

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

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

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

COMS W1004 (Java) (3) or COMS W1007 (Java) (3)2 computer science and COMS W3134 (3) or COMS W3137 (4)2

physical C1001 (1) C1002 (1) education

gateway lab E1102 (4) either semester

1 The linear algebra requirement may be filled by either MATH V2010 or APMA E3101. 2 If taking IEOR E3658, students must take STAT W3107 or W4107 to complete the SIEO W3600 requirement.

member. The dissertation work may be equivalent to 30 points. A minimum of IEOR E2261x and y Introduction to theoretical or computational or both. 30 points beyond the master’s degree accounting and finance Doctoral students are also required to must be earned while in residence in 3 pts. Lect: 3. Professor Webster. select a concentration for their stud- the doctoral program. Detailed informa- Prerequisite: ECON W1105 Principles of ies and complete a certain amount of tion regarding the requirements for the economics. For undergraduates only. This course is required for all undergraduate students majoring course work in one of the following doctoral degree may be obtained in the in IE, OR:EMS, OR:FE, and OR. This course fields: applied probability, mathematical department office or online at www.ieor. examines the fundamental concepts of financial programming, financial engineering, or columbia.edu/phd_ieor.html. accounting and finance, from the perspective supply chain management and logis- of both managers and investors. Key topics tics. Doctoral candidates must obtain a covered include: principles of accrual accounting; Courses in industrial minimum of 60 points of formal course recognizing and recording accounting transactions; engineering and credit beyond the bachelor’s degree. preparation and analysis of financial statements; operations research ratio analysis; pro-forma projections; time value of A master’s degree from an accred- For up-to-date course offerings, please money (present values, future values and interest/ ited institution may be accepted as visit www.ieor.columbia.edu. discount rates); inflation; discounted-cash-flow

engineering 2011–2012 159 industrial engineering: Third and Fourth Years

Semester V Semester VI Semester VII Semester VIII

MATH E1210 (3) Ordinary diff. equations IEOR E4003 (3) IEOR E4405 (3) Industrial econ. Prod. scheduling IEOR E3106 (3) IEOR E3402 (4) Stochastic models Production planning IEOR E4207 (3) IEOR E4412 (3) Required Human factors Courses1 Quality control and IEOR E3608 (4) IEOR E4404 (4) management Mathematical prog. Simulation IEOR E4705 (3) Studies in operations IEOR E4510 (3) COMS W4111 (3) research Project management Database systems

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

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

Industrial Engineering Choose two (6 pts.): IEOR E4210, IEOR E4418, or IEME E4310 Electives

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

(DCF) project evaluation methods; deterministic planning of production, inventory, and work force. planning applications. IEOR E3608 must be and probabilistic measures of risk; capital Multi-echelon integrated production-inventory completed by the fifth term. Only students with budgeting. systems. Production scheduling. Term project. special academic circumstances may be allowed Recitation section required. to take these courses in alternative semesters IEOR E3106x Introduction to operations with the consultation of CSA and Departmental research: stochastic models SIEO W3600y Introduction to probability advisers. Recitation section required. 3 pts. Lect: 3. Professor Whitt. and statistics Prerequisite: SIEO W3600. For undergraduates 4 pts. Lect: 3. Recit: 1. Instructor to be announced. IEOR E3658x Probability only. This course is required for all undergraduate Prerequisite: Calculus. For undergraduates only. 3 pts. Lect: 3. Professor Olvera-Cravioto. students majoring in IE, OR:EMS, OR:FE, and OR. This course is required for undergraduate students Prerequisite: Calculus. For undergraduates This class must be taken during (or before) the majoring in IE, OR:EMS, and OR. This class must only. This course is required for the OR:FE fifth semester. Some of the main stochastic models be taken during the fourth semester. Fundamentals concentration. This class must be taken during used in engineering and operations research of probability and statistics used in engineering (or before) the third semester. Fundamentals of applications: discrete-time Markov chains, Poisson and applied science. Probability: random variables, probability theory. Distributions of one or more processes, birth and death processes and other useful distributions, expectations, law of large random variables. Moments, generating functions, continuous Markov chains, renewal reward numbers, central limit theorem. Statistics: point and law of large numbers and central limit theorem. processes. Applications: queueing, reliability, confidence interval estimation, hypothesis tests, IEOR E3900x and y Undergraduate research inventory, and finance. IEOR E3106 must be linear regression. SIEO W3600 must be completed or project completed by the fifth term. Only students with by the fourth term. Only students with special 1–3 pts. Members of the faculty. special academic circumstances may be allowed academic circumstances may be allowed to take Prerequisite: Approval by a faculty member who to take these courses in alternative semesters these courses in alternative semesters with the agrees to supervise the work. Independent work with the consultation of CSA and Departmental consultation of CSA and Departmental advisers. involving experiments, computer programming, advisers. Recitation section required. analytical investigation, or engineering design. IEOR E3402y Production inventory planning IEOR E3608x Introduction to mathematical IEOR E4000x Production and operations and control programming management 4 pts. Lect: 3. Recit: 1. Professor Truong. 4 pts. Lect: 3. Recit: 1. Professor Chudnovsky. 3 pts. Lect: 3. Professor Goyal. Prerequisites: SIEO W3600 Probability and Prerequisite: MATH V2010 Linear algebra. Prerequisites or Corequisite: Probability theory Statistics and IEOR E3608 Introduction to OR: Corequisite: COMS W3134 (or COMS W3137 and linear programming. Required course for Mathematical programming. For undergraduates Data structures). For undergraduates only. MSIE. An introduction to production management only. This course is required for all undergraduate This course is required for all undergraduate for students not having an industrial engineering students majoring in IE, OR:EMS, OR:FE, and students majoring in IE, OR:EMS, OR:FE, and bachelor’s degree. Topics include deterministic OR. This class must be taken during (or before) OR. This class must be taken during (or before) inventory models, aggregate production planning, the sixth semester. Inventory management and the fifth semester. Introduction to mathematical material requirements planning, forecasting, production planning. Continuous and periodic programming models and computational stochastic inventory models and supply chain review models: optimal policies and heuristic techniques. Linear programming and the management. Emphasis is on modeling and its solutions, deterministic and probabilistic demands. simplex method, dynamic programming, implicit implications for managerial decisions. Material requirements planning. Aggregate enumeration for integer programs; production

engineering 2011–2012 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: PHYS C1493 (3) or C1401 (3) C1402 (3) physics PHYS W3081 (2) or (three tracks, C1601 (3.5) C1602 (3.5) CHEM C1500 (3) or choose one) C2801 (4.5) C2802 (4.5) CHEM C2507 (3) or CHEM C3085 (4) or

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

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

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

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

COMS W1004 (Java) (3) or COMS W1007 (Java) (3)2 computer science and COMS W3134 (3) or COMS W3137 (4)2

physical C1001 (1) C1002 (1) education

gateway lab E1102 (4) either semester

1 The linear algebra requirement may be filled by either MATH V2010 or APMA E3101. 2 If taking IEOR E3658, students must take STAT W3107 or W4107 to complete the SIEO W3600 requirement.

IEOR E4001y Design and management of economic evaluation of industrial projects. IEOR E4007x Optimization models and production and service systems Economic equivalence and criteria. Deterministic methods for financial engineering 3 pts. Lect: 3. Professor Riccio. approaches to economic analysis. Multiple projects 3 pts. Lect: 3. Professor Bienstock. Prerequisite: IEOR E4000 or E3402. This course and constraints. Analysis and choice under risk and Prerequisite: Linear algebra. This course is for is required for undergraduate students majoring in uncertainty. MSFE students only. Linear, quadratic, nonlinear, OR:EMS. Design and management problems in dynamic, and stochastic programming. Some IEOR E4004x and y Introduction to operations production and service systems: process design discrete optimization techniques will also be research: deterministic models and capacity management, inventory system introduced. The theory underlying the various 3 pts. Lect: 3. Professor Sethuraman. design and management, aggregate planning, staff optimization methods is covered. The emphasis This is a required course for MSEMS, MSIE, and scheduling, and quality control system design. is on modeling and the choice of appropriate MSOR students. This is also required for students optimization methods. Applications from financial IEOR E4003x Industrial economics in the Undergraduate Advanced Track. For engineering are discussed. 3 pts. Lect: 3. Professor Sadighian. students who have not studied linear programming. Prerequisites or corequisites: Probability theory Some of the main methods used in IEOR CSOR E4010y Graph theory: a combinatorial view and linear programming. This course is required applications involving deterministic models: linear 3 pts. Lect: 3. Professor Chudnovsky. for all undergraduate students majoring in IE, programming, the simplex method, nonlinear, Prerequisites: Linear algebra, or instructor’s OR:EMS, OR:FE, and OR. Introduction to the integer and dynamic programming. permission. An introductory course in graph theory

engineering 2011–2012 161 operations research: Third and Fourth Years

Semester V Semester VI Semester VII Semester VIII

MATH E1210 (3) Ordinary diff. equations IEOR E4003 (3) IEOR E3402 (4) Industrial econ. Production planning IEOR E3106 (3) Stochastic models IEOR E4700 (3) Required IEOR E4404 (4) IEOR E4405 (3) Intro to FE Courses1 Simulation Prod. scheduling IEOR E3608 (4) Mathematical prog. IEOR E4407 (3) IEOR E4600 (3) Game theoretic models of Applied integer prog. COMS W4111 (3) operations Database systems

operations Choose four OR electives (12 pts. total): research electives Please consult the list on the departmental website: www.ieor.columbia.edu

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

1 Taking required courses later than the prescribed semester is not permitted. with emphasis on its combinatorial aspects. Basic IEOR E4208y Seminar in human factors design IEOR E4307x Applied statistical models in definitions, and some fundamental topics in graph 3 pts. Lect: 3. Professor Gold. operations research theory and its applications. Topics include trees Prerequisite: IEOR E4207 or instructor’s 3 pts. Lect: 3. Professor Wright. and forests graph coloring, connectivity, matching permission. This course is an elective Prerequisites: probability, linear algebra. theory and others. undergraduate students majoring in IE. An in-depth Descriptive statistics, central limit theorem, exploration of the application potential of human parameter estimation, sufficient statistics, IEOR E4106x and y Introduction to operations factor principles for the design of products and hypothesis testing, regression, logistic regression, research: stochastic models processes. Applications to industrial products, goodness-of-fit tests, applications to operations 3 pts. Lect: 3. Professor Yao. tools, layouts, workplaces, and computer displays. research models. Prerequisites: SIEO W4150 or probability theory. Consideration to environmental factors, training IEOR E4308x Industrial budgeting and This is a required course for MSEMS, MSIE, and and documentation. Term project. MSOR students. This is also required for students financial control in the Undergraduate Advanced Track. Some of IEOR E4210y Supply chain management 3 pts. Lect: 3. Professor Luss. the main stochastic models used in engineering 3 pts. Lect: 3. Professor Truong. Prerequisite: ENGI W2261 or accounting and and operations research applications: discrete-time Prerequisite: IEOR E3402, E4000, or finance. Management control via the budgeting and Markov chains, Poisson processes, birth and death permission of instructor. This is a IE elective for financial processes. Topics include the preparation, evaluation, and implementation of operating and processes and other continuous Markov chains, undergraduate students majoring in IE. Major capital budgets and review of their performance. renewal reward processes. Applications: queueing, issues in supply chain management, including, Examples from contemporary practice. reliability, inventory, and finance. definition of a supply chain; role of inventory; supply contracts; bullwhip effect and information IEME E4310x The manufacturing enterprise SIEO W4150x and y Introduction to probability sharing; vendor-managed inventories and 3 pts. Lect: 3. Professor Weinig. and statistics other distribution strategies; third-party logistics The strategies and technologies of global 3 pts. Lect: 3. Professor Wright. providers; managing product variety; information manufacturing and service enterprises. technology and supply chain management; Prerequisite: Calculus. Fundamentals of probability Connections between the needs of a global international issues. Emphasis on quantitative theory and statistical inference used in engineering enterprise, the technology and methodology models and analysis. and applied science. Probabilistic models, random needed for manufacturing and product variables, useful distributions, expectations, law IEOR E4220y Demand and supply analytics development, and strategic planning as currently of large numbers, central limit theorem. Statistical 3 pts. Lect: 3. Not offered in 2011–2012. practiced in industry. inference: point and confidence interval estimation, Prerequisites: IEOR E4004 (or E3608), IEOR IEOR E4403x Advanced engineering and hypothesis tests, linear regression. E4106 (or E3608). Tools to efficiently manage corporate economics supply and demand networks. Topics include IEOR E4207x Human factors: performance 3 pts. Lect: 3. Professor Sadighian. service and inventory trade-offs, stock allocation, 3 pts. Lect: 3. Professor Gold. Prerequisites: Probability theory and linear pricing, markdown management and contracts, This course is required for undergraduate programming This course is required for students timely product distribution to market while avoiding students majoring in IE. Sensory and cognitive in the Undergraduate Advanced Track. Key excess inventory, allocating adequate resources to (brain) processing considerations in the design, measures and analytical tools to assess the the most profitable products and selling the right development, and operations of systems, products, financial performance of a firm and perform product to the right customer at the right price and and tools. User or operator limits and potential in the economic evaluation of industrial projects. at the right time. sensing, perceiving decision making, movement Deterministic mathematical programming models coordination, memory, and motivation. for capital budgeting. Concepts in utility theory, game theory and real options analysis.

engineering 2011–2012 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: PHYS C1493 (3) or C1401 (3) C1402 (3) physics PHYS W3081 (2) or (three tracks, C1601 (3.5) C1602 (3.5) CHEM C1500 (3) or choose one) C2801 (4.5) C2802 (4.5) CHEM C2507 (3) or CHEM C3085 (4) or

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

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

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

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

COMS W1004 (Java) (3) or COMS W1007 (Java) (3)2 computer science and COMS W3134 (3) or COMS W3137 (4)2

physical C1001 (1) C1002 (1) education

gateway lab E1102 (4) either semester

1 The linear algebra requirement may be filled by either MATH V2010 or APMA E3101. 2 If taking IEOR E3658, students must take STAT W3107 or W4107 to complete the SIEO W3600 requirement.

IEOR E4404x and y Simulation 4 points. NOTE: Students who have taken IEOR IEOR E4407x Game theoretic models of 4 pts. Lect: 3. Recit: 1. Professors Blanchet and E4703 Monte Carlo simulation may not register for operations Olvera-Cravioto. this course for credit. Recitation section required. 3 pts. Lect: 3. Professor Sethuraman. Prerequisites: SIEO W3600 or SIEO W4150, Prerequisites: IEOR E4004 (or E3608), IEOR IEOR E4405y Production scheduling computer programming. Corequisite: IEOR E3106 E4106 (or E3106), familiarity with differential 3 pts. Lect: 3. Professor Sethuraman. or IEOR E4106. This course is required for all equations and computer programming; or Prerequisites: SIEO W3600, IEOR E3608, undergraduate students majoring in IE, OR:EMS, instructor’s permission. This course is required computer programming. This course is required OR:FE, and OR. This course is also required for undergraduate students majoring in for undergraduate students majoring in IE and for MSIE and MSOR. Generation of random OR:FE and OR. A mathematically rigorous OR. Job shop scheduling: parallel machines, numbers from given distributions; variance study of game theory and auctions, and their machines in series; arbitrary job shops. Algorithms, reduction; statistical output analysis; introduction application to operations management. Topics complexity, and worst-case analysis. Effects to simulation languages; application to financial, include introductory game theory, private value of randomness: machine breakdowns, random telecommunications, computer, and production auction, revenue equivalence, mechanism processing time. Term project. systems. Graduate students must register for 3 design, optimal auction, multiple-unit auctions, points. Undergraduate students must register for

engineering 2011–2012 163 OPERATIONS RESEARCH: engineering management systems: Third and Fourth Years

Semester V Semester VI Semester VII Semester VIII

MATH E1210 (3) IEOR E4001 (3) Ordinary diff. equations Design and mgmt. of prod. IEOR E3402 (4) and service systems Production planning IEOR E3106 (3) IEOR E4003 (3) Stochastic models Industrial econ. IEOR E4550 Required ECON W3213 (3) Entrepren. bus. creation Courses1 Macroeconomics IEOR E3608 (4) IEOR E4404 (4) for engrs. Mathematical prog. Simulation or COMS W4111 (3) IEOR E4998 Database systems ECON W3211 (3) Managing technol. innov. Microeconomics and entrepreneurship

tech Technical electives (12 pts. total)2

Management electives (9 pts. total): management Please consult lists posted on IEOR website: www.ieor.columbia.edu E le c ti v es Nontech Complete 27-point requirement; see page 10 or www.engineering.columbia.edu for details.

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

combinatorial auctions, incentives, and supply IEOR E4500x and y Applications for undergraduate students majoring in OR:EMS. chain coordination with contracts. No previous programming for financial engineering Introduces the basic concepts and methodologies knowledge of game theory is required. 3 pts. Lect: 3. Professor Bienstock. that are used by the non-engineering part of the Prerequisite: Computer programming or world in creating, funding, investing in, relating to, IEOR E4412y Quality control and management instructor’s approval. This course is required for and operating entrepreneurial ventures. The first 3 pts. Lect: 3. Professor Latzko. undergraduate students majoring in OR:FE. In half of the course focuses on the underpinning Prerequisite: SIEO W3600 or W4150. This course this course we will take a hands-on approach to principles and skills required in recognizing, is required for undergraduate students majoring developing computer applications for Financial analyzing, evaluating, and nurturing a business idea. in IE. Statistical methods for quality control and Engineering. Special focus will be placed on The second half focuses on basic legal knowledge improvement: graphical methods, introduction to high-performance numerical applications that necessary in creating a business entity, defending experimental design and reliability engineering and interact with a graphical interface. In the course your business assets, and in promoting effective the relationships between quality and productivity. of developing such applications we will learn how interaction with other individuals and organizations. Contemporary methods used by manufacturing to create DLLs, how to integrate VBA with C/ and service organizations in product and process C++ programs, and how to write multithreaded IEOR E4600y Applied integer programming design, production and delivery of products and programs. Examples of problems settings that 3 pts. Lect: 3. Professor Iyengar. services. we consider include simulation of stock price Prerequisites: Linear programming, linear algebra, and computer programming. This course is IEOR E4418y Logistics and transportation evolution, tracking, evaluation and optimization of required for undergraduate students majoring in management a stock portfolio; optimal trade execution. In the OR. Applications of mathematical programming 3 pts. Lect: 3. course of developing these applications, we review techniques, especially integer programming, with Prerequisite: IEOR E3608 or E4404 or permission topics of interest to OR:FE in a holistic fashion. emphasis on software implementation. Typical of instructor. Introduces quantitative techniques IEOR E4510y Project management applications: capacity expansion, network design, and state-of-the-art practice of operations research 3 pts. Lect: 3. Professor Rosenwein. and scheduling. relevant to the design and both the tactical Prerequisites: IEOR E4004 (or IEOR E3608). and strategic management of logistical and Management of complex projects and the tools IEOR E4601y Dynamic pricing and revenue transportation systems. Discusses a wide variety of that are available to assist managers with such management passenger and freight systems, including air, urban projects. Topics include: project selection, 3 pts. Lect: 3. Professor Gallego. and highway traffic, rail, and maritime systems. project teams and organizational issues, Prerequisites: SIEO W4150 and IEOR E4004. Explores the practice of revenue management and project monitoring and control, project risk Focus on capacity allocation, dynamic pricing and dynamic pricing. Through case studies, analyzes management, project resource management, revenue management. Perishable and/or limited successes and failures in third-party logistics, and managing multiple projects. product and pricing implications. Applications to postal, truck and rail pickup and delivery systems. various industries including service, airlines, hotel, IEOR E4550x and y Entrepreneurial business Investigates large-scale integrated logistics and resource rentals, etc. creation for engineers transportation systems and studies the underlying 3 pts. Lect: 3. Professor Gulley. principles governing transportation planning, Prerequisite: ENGI W2261. This course is required investment and operations.

engineering 2011–2012 164 OPERATIONS RESEARCH: FINANCIAL engineering: first and second Years

Semester i Semester iI Semester iII Semester iV

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

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

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

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

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

first- and IEOR E2261 (4) Second-Year Professional-level course (3) (see pages 12–13) and IEOR E3658 (3) or STAT W4105 (3) Dept. 3 Requirements and IEOR E4307 (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

1 The linear algebra requirement may be filled by either MATH V2010 or APMA E3101. 2 Computer programming should be taken consecutively with data structures. 3 Students may also take STAT W3107 or W4107; however, the department strongly recommends IEOR E4307 in the spring term.

IEOR E4602y Quantitative risk management IEOR E4611y Decision models and IEOR E4620x Pricing models for financial 3 pts. Lect: 3. Professor Haugh. applications engineering Prerequisites: SIEO W4150 and IEOR E4106. 3 pts. Lect: 3. Professor Webster. 3 pts. Lect: 3. Professor DeRosa. Risk management models and tools; measure risk Prerequisites: For undergraduates: SIEO W3600/ Prerequisite: IEOR E4700. This course is using statistical and stochastic methods, hedging SIEO W4150 or equivalent and IEOR E3608/ required for undergraduate students majoring in and diversification. Examples include insurance IEOR E4004 or equivalent. For graduate students: OR:FE. Characteristics of commodities or credit risk, financial risk, and operational risk. Topics Instructor’s permission required. Corequisite: IEOR derivatives. Case study and pricing of structures covered include VaR, estimating rare events, E4404 or equivalent. Introduction to deterministic and products. Topics covered include swaps, extreme value analysis, time series estimation of and stochastic decision tools used by leading credit derivatives, single tranche CDO, hedging, extremal events; axioms of risk measures, hedging corporations and applied researchers. Real- convertible arbitrage, FX, leverage leases, debt using financial options, credit risk modeling, and world problems in engineering and finance are markets, and commodities. various insurance risk models. discussed.

engineering 2011–2012 165 OPERATIONS RESEARCH: FINANCIAL engineering: Third and Fourth Years

Semester V Semester VI Semester VII Semester VIII

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

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

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

IEOR E4630y Asset allocation students only, offered during the summer session. IEOR E4705x Studies in operations research 3 pts. Lect: 3. Professor Iyengar. Review of elements of probability theory, Poisson 3 pts. Lect: 3. Professor Riccio. Prerequisite: IEOR E4700. Models for pricing processes, exponential distribution, renewal theory, Prerequisites: IEOR E4004 (or E3608) and IEOR and hedging equity, fixed-income, credit- Wald’s equation. Introduction to discrete-time E4106 (or E3106). Analysis and critique of current derivative securities, standard tools for hedging Markov chains and applications to queueing theory, operations research studies. Blood bank inventory, and risk management, models and theoretical inventory models, branching processes. fire departments, police departments, and housing foundations for pricing equity options (standard operations research studies are considered. IEOR S4702 Statistical inference for financial European, American equity options, Asian engineering IEOR S4706 Foundations of financial options), standard Black-Scholes model (with 1.5 pts. Lect: 1.5. Professor Kou. engineering multiasset extension), asset allocation, portfolio Corequisites: IEOR E4701 and E4706. This 3 pts. Lect: 3. Professor Cont. optimization, investments over longtime course is for MSFE students only, offered during Prerequisites: IEOR E4701, E4702, and linear horizons, and pricing of fixed-income derivatives the summer session. The course covers basic algebra. This course is for MSFE students only, (Ho-Lee, Black-Derman-Toy, Heath-Jarrow- tools of statistical inference relevant to financial offered during the summer session. Discrete-time Morton interest rate model). engineering. The statistical topics covered include models of equity, bond, credit, and foreign- IEOR E4700x and y Introduction to financial point estimation, maximum likelihood estimators, exchange markets. Introduction to derivative engineering confidence intervals, the delta method, markets. Pricing and hedging of derivative 3 pts. Lect: 3. Professors He and Yao. hypothesis testing, and goodness of fit tests. securities. Complete and incomplete markets. Introduction to portfolio optimization and the Prerequisite: IEOR E4106 or E3106. This course The financial examples include selection bias in capital asset pricing model. is required for undergraduate students majoring finance, estimation of drift and volatility in the in OR:FE. Introduction to investment and financial geometric Brownian motion model, the leptokurtic IEOR E4707x Financial engineering: instruments via portfolio theory and derivative feature, and difficulties in estimating the tail continuous-time asset pricing securities, using basic operations research/ distributions of asset returns. 3 pts. Lect: 3. Professor Haugh. engineering methodology. Portfolio theory, IEOR E4703y Monte Carlo simulation Prerequisites: IEOR E4701. This course is for arbitrage; Markowitz model, market equilibrium, 3 pts. Lect: 3. Members of the faculty. MSFE students only. Modeling, analysis, and and the capital asset pricing model. General Prerequisite: IEOR E4701. This course is for computation of derivative securities. Applications models for asset price fluctuations in discrete MSFE students only. Multivariate random number of stochastic calculus and stochastic differential and continuous time. Elementary introduction to generation, bootstrapping, Monte Carlo simulation, equations. Numerical techniques: finite-difference, Brownian motion and geometric Brownian motion. efficiency improvement techniques. Simulation binomial method, and Monte Carlo. Option theory; Black-Scholes equation and call output analysis, Markov-chain Monte Carlo. IEOR E4708y Seminar on important papers in option formula. Computational methods such as Applications to financial engineering. Introduction financial engineering Monte Carlo simulation. to financial engineering simulation software and 3 pts. Lect: 3. Professor Derman. exposure to modeling with real financial data. IEOR E4701 Stochastic models for financial Prerequisites: IEOR E4703, E4706, probability NOTE: Students who have taken IEOR E4404 engineering and statistics. Selected topics of special interest to Simulation may not register for this course for credit. 3 pts. Lect: 3. Instructor to be announced. Financial Engineering M.S. students. If topics are Prerequisite: SIEO W4105. This course is for MSFE different then this course can be taken more than once for credit.

engineering 2011–2012 166 IEOR E4709x Data analysis for financial schema, organize tests via options/stock as part of their program of study. Final reports engineering databases and carry out tests efficiently and required. This course may not be taken for pass/ 3 pts. Lect: 3. Professor Kou. accurately. It exposes students to the striking fail credit or audited. Prerequisites: Probability and IEOR E4702. differences between static, thermodynamic/ MSIE W6408y Inventory theory Corequisites: IEOR E4706, E4707. This course is SDE model solutions and real (time-of-flight) 3 pts. Lect: 3. for MSFE students only. Empirical analysis of asset pricing. They become familiar with computational prices: heavy tails, test of the predictability of stock techniques for modeling and testing proposals for Prerequisites: Probability theory, dynamic returns. Financial time series: ARMA, stochastic trading strategies. programming. Construction and analysis of volatility, and GARCH models. Regression models: mathematical models used in the design and linear regression and test of CAPM, nonlinear IEOR E4729 Financial markets, risk, and analysis of inventory systems. Deterministic and regression and fitting of term structures. institutions stochastic demands and lead times. Optimality 1.5 pts. Lect: 1.5. of (s, S) policies. Multiproduct and multiechelon IEOR E4710y Term structure models Corequisites: IEOR E4701, E4702, E4706. systems. Computational methods. 3 pts. Lect: 3. Professor Haugh. This course is for MSFE students only, offered Prerequisites: IEOR E4706, E4707, and computer during the summer session. This core curriculum IEOR E6602y Nonlinear programming programming. Interest rate models and numerical course introduces students pursuing a graduate 3 pts. Lect: 3. techniques for pricing and hedging interest rate degree in financial engineering to the main Prerequisite: Ph.D.-level linear programming. contracts and fixed income securities areas and concepts of modern finance. Topics Convex sets and functions, convex duality and optimality conditions. Computational methods: IEOR E4718y Introduction to the implied include financial analytics; fixed income and steepest descent, Newton and quasi-newton volatility smile equity markets; macroeconomic aspects of methods for unconstrained problems, active set, 3 pts. Lect: 3. Professor Derman. investment decisions; portfolio and utility penalty set, interior point, augmented Lagrangian Prerequisites: IEOR E4706, knowledge of theories; introduction to risk management; and sequential quadratic programming methods derivatives valuation models. During the past 15 financial crises. The course’s objective is to provide the broadest possible perspective for constrained problems. Introduction to years the behavior of market options prices have on how financial theory and real-life practice nondifferentiable optimization and bundle methods. shown systematic deviations from the classic interact, preparing students for successful Black-Scholes model. The course examines IEOR E6613x Optimization, I careers in the financial industry and paving the the empirical behavior of implied volatilities, in 4.5 pts. Lect: 3. Professor Goldfarb. way for in-depth studies that follow. particular the volatility smile that now characterizes Prerequisite: Linear algebra. Theory and geometry most markets, the mathematics and intuition IEOR E4731y Credit risk modeling and credit of linear programming. The simplex method. behind new models that can account for the smile, derivatives Duality theory, sensitivity analysis, column and their consequences for hedging and valuation. 3 pts. Lect: 3. Instructor to be announced. generation and decomposition. Interior point Prerequisites: IEOR E4701 and E4707. IEOR E4720x and y–E4729 Topics in methods. Introduction to nonlinear optimization: Introduction to quantitative modeling of credit risk, quantitative finance convexity, optimality conditions, steepest descent, with a focus on the pricing of credit derivatives. 1.5–3 pts. Lect: 2–2.5. Members of the faculty. and Newton’s method, active set, and barrier Focus on the pricing of single-name credit methods. Prerequisites: IEOR E4700; additional pre- derivatives (credit default swaps) and collateralized requisites will be announced depending on debt obligations (CDOs). Detail topics include IEOR E6614y Optimization, II offering. Selected topics of interest in the area default and credit risk, multiname default barrier 4.5 pts. Lect: 3. Professor Stein. of quantitative finance. Offerings vary each models and multiname reduced form models. Prerequisite: Linear algebra. An introduction to year; some topics include: energy derivatives, combinatorial optimization, network flows and experimental finance, foreign exchange IEOR E4900x and y Master’s research or discrete algorithms. Shortest path problems, and related derivative instruments, inflation project maximum flow problems. Matching problems, 1–3 pts. Members of the faculty. derivatives, hedge fund management, modeling bipartite and cardinality nonbipartite. Introduction Prerequisite: Approval by a faculty member who equity derivatives in Java, mortgage-backed to discrete algorithms and complexity theory: agrees to supervise the work. Independent work securities, numerical solutions of partial differential NP-completeness and approximation algorithms. equations, quantitative portfolio management, risk involving experiments, computer programming, management, trade and technology in financial analytical investigation, or engineering design. IEOR E6703y Advanced financial engineering 3 pts. Lect: 2. Not offered in 2011–2012. markets. IEOR E4998x and y Managing technological Prerequisites: Probability theory and advanced innovation and entrepreneurship IEOR E4725y Topics in quantitative finance: stochastic models at the SIEO W6501 level. 3 pts. Lect: 3. Professor McGourty. numerical solutions of partial differential Review of basic mathematics, including renewal This is a required course for undergraduate equation theory and stochastic calculus. Martingale students majoring in OR:EMS. Focus on the 3 pts. Lect: 3. Not offered in 2011–2012. approach to Black-Scholes formula. Optimal management and consequences of technology- Prerequisites: IEOR E4706 and E4707. stopping and American options. Pricing of based innovation. Explores how new industries The course covers derivations and solutions continuous and discrete exotic options. Term of partial differential equations under variety of are created, how existing industries can be structure models and pricing of bond options. underlying stochastic price processes. Students transformed by new technologies, the linkages Jump diffusion models. Applications, including will gain exposure to applications of partial between technological development and the pricing of real and electricity options and hedging differential equations to security pricing in different creation of wealth and the management challenges of real options. financial markets (i.e. equity derivatives, fixed of pursuing strategic innovation. income securities and credit derivative markets). IEOR E6711x Stochastic models, I IEOR E4999x and y Curricular practical 4.5 pts. Lect: 3. Professor Olvera-Cravioto. IEOR E4726y Topics in quantitative finance: training Prerequisite: SIEO W4105 or equivalent. Advanced experimental finance 1–2 pts. Professor Derman. treatment of stochastic modeling in the context 3 pts. Lect: 3. Professors Lipkin and Stanton. Prerequisites: Obtained internship and approval of queueing, reliability, manufacturing, insurance Prerequisites: IEOR E4706 and E4707. The from faculty adviser. Only for IEOR graduate risk, financial engineering and other engineering course introduces concepts to propose trading students who need relevant work experience

engineering 2011–2012 applications. Review of elements of probability stochastic comparisons; martingales; introduction This course may be repeated for credit. 167 theory; exponential distribution; renewal to stochastic calculus. IEOR E9800x and y Doctoral research theory; Wald’s equation; Poisson processes. IEOR E8100x and y Advanced topics in IEOR instruction Introduction to both discrete and continuous-time 1–3 pts. Members of the faculty. 3, 6, 9, or 12 pts. Members of the faculty. Markov chains; introduction to Brownian motion. Prerequisite: Faculty adviser’s permission. A candidate for the Eng.Sc.D. degree in IEOR E6712y Stochastic models, II Selected topics of current research interest. May industrial engineering or operations research 4.5 pts. Lect: 3. Professor Yao. be taken more than once for credit. must register for 12 points of doctoral research Prerequisite: IEOR E6711 or equivalent. instruction. Registration in IEOR E9800 may IEOR E9101x and y Research Continuation of IEOR E6711, covering further not be used to satisfy the minimum residence 1–6 pts. Members of the faculty. topics in stochastic modeling in the context of requirement for the Ph.D. degree. Before registering, the student must submit an queueing, reliability, manufacturing, insurance outline of the proposed work for approval by risk, financial engineering, and other engineering the supervisor and the chair of the Department. applications. Topics from among generalized Advanced study in a specialized field under the semi-Markov processes; processes with a supervision of a member of the department staff. nondiscrete state space; point processes;

engineering 2011–2012 168 Materials Science and Engineering Program Program in the Department of Applied Physics and Applied Mathematics, sharing teaching and research with the faculty of the Henry Krumb School of Mines.

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

In Charge of Committee on Louis E. Brus James S. Im Ponisseril Somasundaran Materials Science and Materials Science and Professor of Chemistry Professor of Materials Professor of Mineral Engineering Engineering/ Solid-State Siu-Wai Chan Science Engineering Professor James S. Im Science and Engineering Professor of Materials Chris A. Marianetti Yasutomo Uemura 1106 S. W. Mudd William E. Bailey Science Assistant Professor of Professor of Physics Associate Professor of Paul F. Duby Materials Science Wen I. Wang In Charge of Solid- Materials Science Professor of Mineral Richard M. Osgood Jr. Professor of Electrical State Science and Katayun Barmak Engineering Professor of Electrical Engineering Engineering Professor of Materials Christopher J. Durning Engineering Chee Wei Wong Professor Siu-Wai Chan Science Professor of Aron Pinczuk Associate Professor of 1136 S. W. Mudd Simon J. Billinge Chemical Engineering Professor of Applied Physics Mechanical Engineering Professor Irving P. Herman Professor of Materials Irving P. Herman and Physics 208 S. W. Mudd Science Professor of Applied Physics

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

engineering 2011–2012 Current Research Activities Undergraduate Program two may be in the Type B category. 169 Current research activities in the in materials science and The Type B electives are listed under materials science and engineering engineEring different materials subdisciplines for program at Columbia focus on thin films This program provides the basis for guidance. Still, some courses listed and electronic materials that enable developing, improving, and under- under different categories may appeal to significant advances in information standing materials and processes for students interested in a given area. For technologies. Specific topics under electronic, structural, and other appli- example, CHEE E4252: Intro to surface investigation include interfaces, stresses, cations. It draws from physics, chem- and colloidal chemistry should also be and grain boundaries in thin films; istry, and other disciplines to provide considered by students interested in lattice defects and electrical properties a coherent background for immediate biomaterials and environmental materials. of semiconductors; laser processing application in engineering or for subse- Type A electives are: and ultrarapid solidification of thin films; quent advanced study. The emphasis CHEE E4530: Corrosion of metals nucleation in condensed systems; is on fundamentals relating atomic- to MSAE E4207: L attice vibrations and crystal optical and electric properties of wide- microscopic-scale phenomena to mate- defects band semiconductors; synthesis of rials properties and processing, includ- MSAE E4250: Ceramics and composites nanocrystals, carbon nanotubes, and ing design and control of industrially ELEN E4944: Principles of device microfabrication nanotechnology-related materials; important materials processes. Core deposition, in-situ characterization, courses and electives combine rigor Type B electives are: electronic testing, and ultrafast with flexibility and provide opportunities BIOMATERIALS spectroscopy of magnetoelectronic for focusing on such areas as electronic BMEN E4300: Solid biomechanics ultrathin films and heterostructures. In materials, polymers, ceramics, bioma- BMEN E4301: Structure, mechanics, and addition, there is research in surface terials, structural materials, and metals adaptation of bone and colloid chemistry involving both and mineral processing. There are also BMEN E4501: T issue engineering, I inorganic and organic materials such opportunities for combining materials ELECTRONIC MATERIALS as surfactants, polymers, and latexes, science and engineering with interests APPH E3100: Intro to quantum mechanics with emphasis on materials/environment in areas such as medicine, business, APPH E3300: Applied electromagnetism interactions. law, or government. APPH E4100: Quantum physics of matter The research activities in solid-state The unifying theme of understanding APPH E4110: Modern optics science and engineering are described and interrelating materials synthesis, ELEN E4301: Intro to semiconductor devices later in this section. processing, structure, and properties ELEN E4411: Fundamentals of photonics forms the basis of our MSE program ENVIRONMENTAL MATERIALS Laboratory Facilities and is evident in the undergraduate EAEE E4001: Industrial ecology of Earth resources curriculum and in faculty research EAEE E4160: Solid and hazardous waste mgmt Facilities and research opportunities activities. These activities include also exist within the interdepartmental MECHANICAL PROPERTIES OF MATERIALS work on polycrystalline silicon for Nanoscale Science and Engineering ENME E3114: Experimental mechanics of solids flat panel displays; high-temperature Center (NSEC), and Energy Frontier ENME E4113: Advanced mechanics of solids superconductors for power transmission ENME E4114: Mechanics of fracture and fatigue Research Center (EFRC), which and sensors; semiconductors for laser MECE E4608: Manufacturing processes focus on complex films formed from and solar cell applications; magnetic nanoparticles, molecular electronics, and SOFT MATERIALS AND SURFACES heterostructures for information storage solar energy conversion, respectively. CHEE C3443: O rganic chemistry and novel computation architectures; Modern clean room facilities with (note that C3444 is not allowed) electronic ceramics for batteries, gas optical and e-beam lithography, thin CHEE E4252: Intro to surface and colloid chemistry sensors, and fuel cells; electrodeposition APMA E4400: Intro to biophysical modeling film deposition, and surface analytical and corrosion of metals; and the probes (STM, SPM, XPS) are available. OTHER analysis and design of high-temperature More specialized equipment exists in MSAE E3900: U ndergrad research in materials reactors. Through involvement with our individual research groups in solid state science research groups, students gain valuable engineering and materials science and Alternative courses can be taken hands-on experience and are often engineering. The research facilities in as electives with the approval of the engaged in joint projects with industrial solid-state science and engineering undergraduate adviser. Of the 24 and government laboratories. are listed in the sections for each host points of elective content in the third The MSE undergraduate curriculum department. Facilities, and research and fourth years, at least 12 points requires 16 courses in the third and opportunities, also exist within the of restricted electives approved by fourth years, of which four are restricted interdepartmental clean room, shared the adviser must be taken. Of the electives. This program allows students materials characterization laboratories, remaining 12 points of electives to specialize in a subdiscipline of MSE and electron microscopy facility. allotted, a sufficient number must if they so choose. Students must actually be taken so that no fewer take twelve required courses and four than 64 points of courses are credited electives. At least two electives must to the third and fourth years. Those be in the Type A category, and at most

engineering 2011–2012 170 materials science and engineering: first and second Years

Semester i Semester iI Semester iII Semester iV

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

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

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

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

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

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

computer 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

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

remaining points of electives are The following 5 courses (18 points) which may be Type I or Type II: intended primarily as an opportunity are required for the degree: • Type I Electives: to complete the four-year, 27-point 12 points: nontechnical requirement, but any type MSAE E4101: Structural analysis of materials MSAE E4090: Nanotechnology of course work can satisfy them. MSAE E4206: Electronic and magnetic properties MSAE E4132: F undamentals of polymers and of solids ceramics MSAE E4202: T hermodynamics and reactions MSAE E4207: L attice vibrations and crystal Graduate Programs in in solids defects Materials Science and MSAE E4215: Mechanical behavior of structural MSAE E4250: Ceramics and composites MSAE E4990: Special topics in materials science Engineering materials 6 points: and engineering MSAE E6273: Materials science reports MSAE E6091: Magnetism and magnetic materials Master of Science Degree MSAE E6225: T echniques in X-ray and neutron Candidates for the Master of Science If a candidate has already taken one diffraction MSAE E6229: E nergy and particle beam degree in Materials Science and or more of these courses at Columbia processing of materials Engineering will follow a program of University, substitutions from the Type I Elective list may be approved. MSAE E6230: Kineticsof phase transformations study formulated in consultation with MSAE E6251: Thin films and layers The remaining 12 points will be and approved by a faculty adviser. MSAE E8235: Selected topics in materials science Thirty points of credit are required at a chosen from elective courses, 6 points MSAE E4000-, 6000- or 8000-level courses not minimum. of which must be Type I and 6 points of listed here

engineering 2011–2012 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

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

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

engineering 2011–2012 172 being developed for oxide thin films, understanding these properties in calculations of materials (Professor including uncooled IR focal plane arrays terms of the atomic and electronic Marianetti, Applied Physics and and integrated fuel cells for portable structure of the materials in question. Applied Mathematics); and optical equipment. Long-range applications Insulators (dielectrics), semiconductors, nanostructures (Professor Wong, of high-temperature superconductors ceramics, and metallic materials are all Mechanical Engineering). include efficient power transmission and studied from this viewpoint. Quantum highly sensitive magnetic field sensors. and statistical mechanics are key Program of Study Thin film synthesis and processing background subjects. The engineering The applicant for the graduate specialty in this program include evaporation, aspects deal with the design of materials must be admitted to one of the sputtering, electrodeposition, and to achieve desired properties and the participating programs: applied physics plasma and laser processing. For assembling of materials into systems to and applied mathematics, or electrical analyzing materials structures and produce devices of interest to modern engineering. A strong undergraduate properties, faculty and students employ technology, e.g., for computers and for background in physics or chemistry and electron microscopy, scanning probe energy production and utilization. in mathematics is important. microscopy, cathodoluminescence The doctoral student must meet the and electron beam–induced current Areas of Research formal requirements for the Eng.Sc.D. or imaging, photoluminescence, dielectric The graduate specialty in solid-state Ph.D. degree set by the department in and anelastic relaxation techniques, science and engineering includes which he or she is registered. However, ultrasonic methods, magnetotransport research programs in the nonlinear the bulk of the program for the specialty measurements, and X-ray diffraction optics of surfaces (Professor Heinz, will be arranged in consultation with techniques. Faculty members have Electrical Engineering/Physics); a member of the interdepartmental research collaborations with Lucent, semiconductor nanocrystals (Professor Committee on Materials Science and Exxon, IBM, and other New York area Brus, Chemistry/Chemical Engineering); Engineering/ Solid-State Science and research and manufacturing centers, optics of semiconductors, including Engineering. At the end of the first year as well as major international research at high pressure (Professor Herman, of graduate study, doctoral candidates centers. Scientists and engineers from Applied Physics and Applied are required to take a comprehensive these institutions also serve as adjunct Mathematics); chemical physics of written examination concentrating on faculty members at Columbia. The surfaces and photoemission (Professor solid-state science and engineering. National Synchrotron Light Source at Osgood, Electrical Engineering/Applied The following are regarded as core Brookhaven National Laboratory is used Physics and Applied Mathematics); courses of the specialty: for high-resolution X-ray diffraction and molecular beam epitaxy leading to absorption measurements. semi-conductor devices (Professor APPH E4100: Quantum physics of matter Entering students typically have Wang, Electrical Engineering/Applied APPH E4112: Laser physics APPH-MSAE E6081-E6082: Solid state physics, undergraduate degrees in materials Physics and Applied Mathematics); I and II science, metallurgy, physics, chemistry, and inelastic light scattering in CHEM G4230: Statistical thermodynamics or other science and engineering low-dimensional electron gases or disciplines. First-year graduate courses within semiconductors (Professor provide a common base of knowledge CHAP E4120: Statistical mechanics Pinczuk, Applied Physics and Applied ELEN E4301: Intro to semiconductor devices and technical skills for more advanced Mathematics/Physics); large-area ELEN E4944: Principles of device microfabrication courses and for research. In addition electronics and thin-film transistors ELEN E6331-E6332: Principles of semiconductor to course work, students usually (Professor Im, Henry Krumb School physics begin an association with a research of Mines/Applied Physics and Applied ELEN E6403: Classical electromagnetic theory group, individual laboratory work, and Mathematics); structural analysis and or participation in graduate seminars during high Tc superconductors (Professor PHYS G6092: Electromagnetic theory, I their first year. Chan, Henry Krumb School of MSAE E4206: E lectronic and magnetic properties Mines/Applied Physics and Applied of solids Mathematics); X-ray microdiffraction MSAE E4207: L attice vibrations and crystal Graduate Specialty in defects and stresses (Professor Noyan, Henry Solid-State Science and MSAE E6220: Crystal physics Engineering Krumb School of Mines/Applied MSAE E6240: Impurities and defects in Physics and Applied Mathematics); Solid-state science and engineering semiconductor materials electronic and magnetic metal thin is an interdepartmental graduate MSAE E6241: Theory of solids films (Professor Barmak, Applied PHYS G6018: Physics of the solid state specialty that provides coverage of an Physics and Applied Mathematics); PHYS G6037: Quantum mechanics important area of modern technology magnetic properties of thin films that no single department can provide. It (Professor Bailey, Applied Physics encompasses the study of the full range Courses in Materials and Applied Mathematics); the of properties of solid materials, with Science and Engineering structure of nanomaterials (Professor special emphasis on electrical, magnetic, For related courses, see also Applied Billinge, Applied Physics and Applied optical, and thermal properties. The Physics and Applied Mathematics, Mathematics); electronic structure science of solids is concerned with Chemical Engineering and Applied

engineering 2011–2012 Chemistry, Earth and Environmental Established and novel methods involved in the MSAE E4132y Fundamentals of polymers and 173 Engineering, and Electrical Engineering. processing of polymers and ceramics. The funda- ceramics mental aspects of the structure and properties of 3 pts. Lect: 3. Not offered in 2011–2012. MSAE E1001y Atomic-scale engineering of polymers and ceramic materials; strategy in the Prerequisite: MSAE E3103 or instructor’s permis- new materials preparatory, synthesis,, and processing methods sion. The science and engineering of polymer, 3 pts. Lect: 3. Instructor to be announced. for obtaining them. Topics include polymer synthe- ceramic and composite inorganic materials. An introduction to the nanoscale science and sis, elastomers, thermoplastics, thermoset materi- Fundamental aspects of structure, processing and engineering of new materials. The control and als, design and molding processes. Ceramics: properties. Polymers: classification, synthesis, manipulation of atomic structure can create new inorganic glasses and composites, materials elastomers, thermoplastics, thermosets; ceram- solids with unprecedented properties. Computer production and principle inorganic chemistry. ics: Crystal structure, morphology, classification, hard drives, compact disc players, and liquid Processing methodology, conditioning, drying, oxides, nitrides, carbides, silicates. Electrical, crystal displays (LCDs) are explored to understand forming, sintering, and microstructure develop- mechanical, thermal and optical properties. the role of new materials in enabling technolo- ment. Relevant aspects of transport phenomena, Common and advanced technological applications, gies. Group problem-solving sessions are used to colloid and sol-gel science, contemporary issues electrical/optical devices, catalytic and environmen- develop understanding. in modern polymer and ceramic processing. tal applications. MSAE E3103x Elements of materials science MSAE E3156x-E3157y Design project 3 pts. Lect: 3. Professor Marianetti. MSAE E4202y Thermodynamics and reactions Prerequisites: CHEM C1404 and PHYS C1011. 3 pts. Members of the faculty. in solids Atomic and crystal structures, structural defects, Prerequisite: Senior standing. May be repeated with 3 pts. Lect: 3. Professor Im. alloying and phase diagrams. The influence of the permission of the undergraduate adviser. E3156: Prerequisite: Instructor’s permission. Free energy microstructure on the strength and physical proper- A design problem in materials science or metallurgi- of phases, the relationship between phase dia- ties of metals and alloys, semiconductors, ceram- cal engineering selected jointly by the student and grams and metastability. Thermodynamics of ics, glasses, and polymers. a professor in the department. The project requires surfaces and interfaces, effect of particle size research by the student, directed reading, and regu- on phase equilibria, Gibbs adsorption of solute MSAE E3104y Laboratory in materials science lar conferences with the professor in charge. E3157: at interfaces, grain boundaries, surface energy. 3 pts. Lect: 1. Lab: 4. Professor Marianetti. Completion of the research, directed reading, and Nucleation and growth, spinodal decomposi- Corequisite: MSAE E3103. Metallographic speci- conferences, culminating in a written report and an tion of phases. Diffusion in metals, intermetallic men preparation, optical microscopy, quantitative oral presentation to the department. compounds and ionic crystals. Diffusion along metallography, hardness and tensile testing, plastic interfaces. deformation, annealing, phase diagrams, brittle MSAE E3900x and y Undergraduate research fracture of glass, temperature and strain rate in materials science MSAE E4206x Electronic and magnetic dependent deformation of polymers, written and 0–4 pts. Members of the faculty. properties of solids oral reports. This course may be repeated for credit, but no 3 pts. Lect: 3. Professor Bailey. more than 6 points of this course may be counted Prerequisite: PHYS C1401-3 or equivalent. A MSAE E3111x Thermodynamics, kinetic toward the satisfaction of the B.S. degree require- survey course on the electronic and magnetic theory and statistical mechanics ments. Candidates for the B.S. degree may con- properties of materials, oriented towards materi- 3 pts. Lect: 3. Professor Bailey. duct an investigation in materials science or carry als for solid state devices. Dielectric and mag- An introduction to the basic thermodynamics of out a special project under the supervision of the netic properties, ferroelectrics and ferromagnets. systems, including concepts of equilibrium, entro- staff. Credit for the course is contingent upon the Conductivity and superconductivity. Electronic py, thermodynamic functions, and phase changes. submission of an acceptable thesis or final report. band theory of solids: classification of metals, Basic kinetic theory and statistical mechanics, insulators, and semiconductors. Materials in including diffusion processes, concept of phase MSAE E4090x Nanotechnology devices: examples from semiconductor lasers, space, classical and quantum statistics, and appli- 3 pts. Lect: 3. Instructor to be announced. cellular telephones, integrated circuits, and mag- cations thereof. Prerequisites: APPH E3100 and MSAE E3103 or netic storage devices. Topics from physics are their equivalents with instructor’s permission. The MSAE E3141y Processing of metals and introduced as necessary. science and engineering of creating materials, semiconductors functional structures and devices on the nanometer MSAE E4207y Lattice vibrations and crystal 3 pts. Lect: 3. Professor Duby. scale. Carbon nanotubes, nanocrystals, quantum defects Prerequisite: MSAE E3103 or the equivalent. dots, size dependent properties, self-assembly, 3 pts. Lect: 3. Professor Chan. Synthesis and production of metals and semi- nanostructured materials. Devices and applica- An introductory course in topics of solid state phys- conductors with engineered microstructures for tions, nanofabrication. Molecular engineering, ics other than electronics and magnetic properties. desired properties. Includes high-temperature, bionanotechnology. Imaging and manipulating at Elastic waves in solids. Phonons and lattice vibra- aqueous, and electrochemical processing; the atomic scale. Nanotechnology in society and tions. Brillouin zones. Thermal properties of solids. thermal and mechanical processing of metals industry. Offered in alternate years. Defects, such as point defects in metals, ionic and alloys; casting and solidification; diffusion, crystals, semiconductors, and ceramics. microstructural evolution, and phase transforma- MSAE E4101x Structural analysis of materials tions; modification and processing of surfaces 3 pts. Lect: 3. Professor Chan. MSAE E4215y Mechanical behavior of and interfaces; deposition and removal of thin Prerequisites or corequisite: MSAE E3103 or the structural materials films. Processing of Si and other materials for instructor’s permission. Geometry of crystals, basic 3 pts. Lect: 3. Professor Lee. elemental and compound semiconductor-based diffraction theory. X-ray diffraction. Techniques and Prerequisite: MSAE E3103. Recommended electronic, magnetic, and optical devices. theory of electron microscopy. Analysis of crystal preparation: A course in mechanics of materi- structures and orientations. Microstructure charac- als. Review of states of stress and strain and MSAE E3142y Processing of ceramics and terization and analysis of crystalline defects. their relations in elastic, plastic, and viscous polymers materials. Dislocation and elastic-plastic concepts 3 pts. Lect: 3. Instructor to be announced. introduced to explain work hardening, various Prerequisite: MSAE E3103 or equivalent. materials-strengthening mechanisms, ductility,

engineering 2011–2012 174 and toughness. Macroscopic and microstructural odic, nearly periodic, and more advanced analysis of MSAE E6225y Techniques in X-ray and aspects of brittle and ductile fracture mechanics, electron band structure. neutron diffraction creep and fatigue phenomena. Case studies used 3 pts. Lect: 3. Not offered in 2011–2012. MSAE E6082y Solid state physics, II throughout, including flow and fracture of struc- Prerequisite: MSAE E4101. Crystal symmetry, 3 pts. Lect: 3. Professor Kim. tural alloys, polymers, hybrid materials, composite diffraction, reciprocal space and Ewald sphere con- Prerequisite: MSAE E6081 or instructor’s permis- materials, ceramics, and electronic materials struction, radiation sources, analytical representa- sion. Semiclassical and quantum mechanical elec- devices. Materials reliability and fracture preven- tion of diffraction peaks, diffraction line broadening, tron dynamics and conduction; dielectric properties tion emphasized. Fourier analysis of peak shape, texture analysis, of insulators; semiconductors; defects; magnetism; diffraction analysis of stress and strain, diffraction MSAE E4250x Ceramics and composites superconductivity; low-dimensional structures; and analysis of order-disorder thermal diffuse scat- 3 pts. Lect: 3. Not offered in 2011–2012. soft matter. tering, small angle scattering, instrumentation in Prerequisites or corequisites: MSAE E3142 and MSAE E6085x Computing the electronic diffraction experiments, error analysis. E3104, or instructor’s permission. The course structure of complex materials MSAE E6229x Energy and particle beam will cover some of the fundamental processes of 3 pts. Lect: 3. Offered in alternate years. atomic diffusion, sintering and microstructural evo- processing of materials Prerequisite: APPH E3100 or equivalent. Basics 3 pts. Lect: 3. Not offered in 2011–2012. lution, defect chemistry, ionic transport, and electri- of density functional theory (DFT) and its appli- Prerequisites: MSAE E4202 or instructor’s permis- cal properties of ceramic materials. Following this, cation to complex materials. Computation of sion. Laser-, electron-, and ion-beam modification we will examine applications of ceramic materials, electronics and mechanical properties of materi- specifically, ceramic thick and thin film materials in als. Group theory, numerical methods, basis of materials to achieve unique microstructures and the areas of sensors and energy conversion/stor- sets, computing, and running open source DFT metastable phases for electronic and structural age devices such as fuel cells, and batteries. The codes. Problem sets and a small project. applications. Fundamentals of energy deposition course work level assumes that the student has and heat flow during laser- and electron-beam MSAE E6091y Magnetism and magnetic already taken basic courses in the thermodynam- irradiation. Atomic displacement processes in ion- materials irradiated materials. Beam-induced microstructural ics of materials, diffusion in materials, and crystal 3 pts. Lect. 3. Professor Bailey. structures of materials. evolution, crystallization, surface alloying, rapid Prerequisite: MSAE E4206, APPH E6081, or solidification, and metastable phase formation. MSAE E4301x and y Materials science equivalent. Types of magnetism. Band theory of fer- Review of current industrial applications. laboratory romagnetism. Magnetic metals, insulators, and semi- 1–3 pts. Members of the faculty. conductors. Magnetic nanostructures: ultrathin films, MSAE E6230y Kinetics of phase transformations Prerequisite: Instructor’s permission. Materials superlattices, and particles. Surface magnetism and 3 pts. Lect: 3. Professor Im. science laboratory work so conducted as to fulfill spectroscopies. High speed magnetization dynamics. Prerequisite: MSAE E4202 or instructor’s permis- particular needs of special students. Spin electronics. Offered in alternate years. sion. Principles of nonequilibrium thermodynamics; stochastic equations; nucleation, growth, and MSAE E4990x and y Special topics in MSAE E6120x Grain boundaries and interfaces coarsening reactions in solids; spinodal decompo- materials science and engineering 3 pts. Lect: 2. Not offered in 2011–2012. sition; eutectic and eutectoid transformations. 1–3 pts. Instructor to be announced. Prerequisites: the instructor’s permission. Prerequisite: Instructor’s permission. This course Suggested background: basic knowledge of MSAE E6251y Thin films and layers may be repeated for credit. Topics and instructors materials science, dislocations and point defects. 3 pts. Lect: 3. Professor Chan. change from year to year. For advanced under- The course gives an overview of the classic Vacuum basics, deposition methods, nucleation graduate students and graduate students in engi- approaches in studying grain boundaries. Topics and growth, epitaxy, critical thickness, defects neering, physical sciences, and other fields. include boundary geometry and structure, bound- properties, effect of deposition procedure, ary interactions with crystal defects, boundaries mechanical properties, adhesion, interconnects, MSAE E4999x or y–S4999 Curricular as short-circuit diffusion paths, applications of and electromigration. practical training boundary concepts to interfaces, and roles of grain 1 pt. Members of the faculty. MSAE E6273x and y–S6273x Materials boundaries in material properties and in kinetic science reports Prerequisite: Internship and approval from phenomena in polycrystalline materials. adviser must be obtained in advance. Only for 0 to 6 pts. Members of the faculty. master’s students in the Department of Applied MSAE E6220x Crystal physics Formal written reports and conferences with the Physics and Applied Mathematics who may need 3 pts. Lect: 3. Not offered in 2011–2012. appropriate member of the faculty on a subject of relevant work experience as part of their program Prerequisite: MSAE E4206 or instructor’s permis- special interest to the student but not covered in of study. Final report required. This course may not sion. The course develops the idea of a tensor and the other course offerings. be taken for pass/fail or audited. applies it to stress and, together with considerations MSAE E8235x and y Selected topics in of crystal symmetry, to the study of the physical materials science MSAE E6020y Electronic ceramics constants of crystals, such as diamagnetic and 3 pts. Lect: 3. Not offered in 2011–2012. 3 pts. Lect: 3. x: Professor Marianetti. paramagnetic susceptibility, dielectric constants, This course may be repeated for credit. Selected Structure and bonding of ceramics and glasses. thermal expansivity, piezoelectric constants, and Point defects and diffusion. Electronic and ionic topics in materials science. Topics and instruc- others. The physical properties are also studied tors change from year to year. For students in conduction. Dielectric, ferroelectric, magnetic, and against the background material of MSAE E4206. optical ceramics. engineering, physical sciences, biological sciences, MSAE E6221x Introduction to dislocation and related fields. MSAE E6081x Solid state physics, I theory MSAE E8236y Anelastic relaxations in 3 pts. Lect: 3. Professor Pinczuk. 3 pts. Lect: 3. Not offered in 2011–2012. Prerequisite: APPH E3100 or equivalent. Knowledge crystals Prerequisite: MSAE E4215 or course in theory of of statistical physics on the level of MSAE E3111 or 3 pts. Lect: 3. Not offered in 2011–2012. elasticity, or instructor’s permission. Point and line PHYS G4023 strongly recommended. Crystal struc- Prerequisite: Instructor’s permission. Formal theory imperfections. Theory of dislocations. Relation ture; reciprocal lattices; classification of solids; lattice of anelastic relaxation phenomena. Detailed study of between imperfections and structure-sensitive dynamics; anharmonic effects in crystals; stress and the mechanisms of anelasticity and internal friction properties. strain; classical electron models of metals; and peri- in crystals, including the role of point defects, dislo-

engineering 2011–2012 cations, grain boundaries, electron-phonon interac- MSAE E9301x-S9301 Doctoral research MSAE E9800x and y–S9800 Doctoral research 175 tions, and ferromagnetic domain effects. 0–15 pts. Members of the faculty. instruction Prerequisite: Qualifying examination for doctorate. 3, 6, 9, or 12 pts. Professor Im. MSAE E9000x and y Materials science and Required of doctoral candidates. A candidate for the Eng.Sc.D. degree must register engineering colloquium for 12 points of doctoral research instruction. 0 pts. Professor Im. MSAE E9309x and y–S9309 Proposal of Registration in MECE E9800 may not be used to Speakers from industry are invited to speak on the Research for the Doctorate satisfy the minimum residence requirement for the recent impact of materials science and engineering 0–3 pts. Members of the faculty. degree. innovations. A written report prepared by the prospective doc- toral candidate defining the proposed research for MSAE E9900x and y–S9900 Doctoral MSAE E9259x-E9260y Research topics the dissertation, and oral defense of the proposal dissertation in materials science and metallurgical at the time of the qualifying examinations. 0 pts. Members of the faculty. engineering A candidate for the doctorate may be required to 1 pt. Lect: 1. Members of the faculty. register for this course every term after the course Discussion of a group of technical papers related work has been completed and until the dissertation to a topic of current research interest. has been accepted.

engineering 2011–2012 176 Mechanical Engineering 220 S. W. Mudd, MC 4703 Phone: 212-854-2965 www.columbia.edu/cu/mechanical

Chair Professors Assistant Adjunct faculty Manager of Gerard H. A. Ateshian Gerard H. A. Ateshian Professors Pejman Akbari Instructional 248 S. W. Mudd Jeffrey W. Kysar Jung-Chi Liao Ines Basalo Laboratories Richard W. Longman Kristin Myers Kai Kang Robert G. Stark Departmental Vijay Modi Arvind Narayanaswamy Michael McGough Administrator Y. Lawrence Yao Elon Terrell Mohammad H. N. Sandra Morris Naraghi 220 S. W. Mudd Associate senior Lecturer Elias Panides Professors Fred Stolfi V. T. Rajan James Hone Graham Walker Qiao Lin Chee Wei Wong

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

engineering 2011–2012 Biomechanics and Mechanics of precision pointing, particle accelerators, of nanoscale radiation transport is 177 Materials. Some of the current etc. Time optimal control of robots is measured using a novel heat transfer research in biomechanics is concerned being studied for increased productivity measurement technique based on with the application of continuum on assembly lines through dynamic the deflection of a bimaterial atomic theories of mixtures to problems of motion planning. Research is also force microscope cantilever. Numerical electromechanical behavior of soft being conducted on improved system simulations are also performed to biological tissues, contact mechanics, identification, making mathematical confirm these measurements. The lubrication of diarthrodial joints, and models from input-output data. The measurements are also used to infer cartilage tissue engineering. (Ateshian) results can be the starting point for extremely small variations of van der In the area of the mechanics of designing controllers, but they are Waals forces with temperature. This materials, research is performed to better also studied as a means of assessing enhancement of radiative transfer will understand material constitutive behavior damage in civil engineering structures ultimately be used to improve the power at the micro- and mesolength scales. from earthquake data. (Longman) density of thermophotovoltaic energy This work is experimental, theoretical, and In the area of advanced conversion devices. (Narayanaswamy) computational in nature. The ultimate goal manufacturing processes and systems, Research in the area of tribology—the is to formulate constitutive relationships current research concentrates on laser study of friction, lubrication, and wear— that are based on physical concepts materials processing. Investigations focuses on studying the wear damage rather than phenomenology, as in the are being carried out in laser and energy loss that is experienced in case of plasticity power-law hardening. micromachining; laser forming of sheet power generation components such In addition, the role that the constitutive metal; microscale laser shock-peening, as piston rings, fuel injection systems, relations play in the fracture and failure of material processing using improved geartrains, and bearings. Next-generation materials is emphasized. (Kysar) laser-beam quality. Both numerical and lubricants, additives, surface coatings, In the area of molecular mechanics in experimental work is conducted using and surface finishes are being studied in biology, mechanical effects on stem cell state-of-the-art equipment, instruments, order to determine their effects on friction differentiation is studied to understand and computing facilities. Close ties and wear. Additionally, environmentally the underlying molecular mechanisms. with industry have been established for friendly lubricants are also being identified The molecular motion in living cells is collaborative efforts. (Yao) and characterized. (Terrell) monitored to examine how the dynamics of molecules determine the specificity of Energy, Fluid Mechanics, and Heat/ MEMS and Nanotechnology. In these stem cell differentiation. Mechanics of Mass Transfer. In the area of energy, areas, research activities focus on power molecular motors is studied to correlate one effort addresses the design of generation systems, nanostructures for their functions with cell differentiation. (Liao) flow/mass transport systems for the photonics, fuel cells and photovoltaics, Other areas of biomechanics extraction of carbon dioxide from and microfabricated adaptive cooling include characterizing the structure- air. Another effort addresses the skin and sensors for flow, shear, and function behavior of the cervix during development of distributed sensors for wind speed. Basic research in fluid the remodeling events of pregnancy use in micrositing and performance dynamics and heat/mass transfer and characterizing the mechanical evaluation of energy and environmental phenomena at small scales also support properties of the eye-wall in relation to systems. The design and testing these activities. (Hone, Lin, Modi, glaucoma. Research in our lab includes of components and systems for Narayanaswamy, Wong) the mechanical testing of biological soft micropower generation is part of the We study the dynamics of tissues, the biochemical analysis of tissue thermofluids effort as well as part of the microcantilevers and atomic force microstructure, and material modeling MEMS effort. (Modi) microscope cantilevers to use them based on structure-mechanical property In the area of fluid mechanics, study as microscale thermal sensors based relationships. In collaboration with of low-Reynolds-number chaotic flows on the resonance frequency shifts clinicians, our goal is to understand the is being conducted both experimentally of vibration modes of the cantilever. etiologies of tissue pathology and disease. and numerically, and the interactions Bimaterial microcantilever-based (Myers) with molecular diffusion and inertia are sensors are used to determine the presently being investigated. Other thermophysical properties of thin films. Control, Design, and Manufacturing. areas of investigation include the fluid (Narayanaswamy) Control research emphasizes iterative mechanics of inkjet printing, drop on Research in the area of learning control (ILC) and repetitive demand, the suppression of satellite nanotechnology focuses on control (RC). ILC creates controllers droplets, shock wave propagation, and nanomaterials such as nanotubes that learn from previous experience remediation in high-frequency printing and nanowires and their applications, performing a specific command, systems. (Modi) especially in nanoelectromechanical such as robots on an assembly line, In the area of nanoscale thermal systems (NEMS). A laboratory is available aiming for high-precision mechanical transport, our research efforts center on for the synthesis of carbon nanotubes motions. RC learns to cancel repetitive the enhancement of thermal radiation and semiconductor nanowires using disturbances, such as precision motion transport across interfaces separated by chemical vapor deposition (CVD) through gearing, machining, satellite a nanoscale gap. The scaling behavior techniques and to build devices using

engineering 2011–2012 178 electron-beam lithography and various design and create MEMS and micro/ and to correlate their mechanical etching techniques. This effort will seek nanofluidic systems to control the characteristics with the process of stem to optimize the fabrication, readout, motion and measure the dynamic cell differentiation. (Liao) and sensitivity of these devices for behavior of biomolecules in solution. Microelectromechanical systems numerous applications, such as sensitive Current efforts involve modeling and (MEMS) are being exploited to enable detection of mass, charge, and magnetic understanding the physics of micro/ and facilitate the characterization and resonance. (Hone, Wong, Modi) nanofluidic devices and systems, manipulation of biomolecules. MEMS In the area of nanoscale imaging in exploiting polymer structures to technology allows biomolecules to biology, a superresolution microscopy enable micro/nanofluidic manipulation, be studied in well-controlled micro/ (nanoscopy) system is built to break and integrating MEMS sensors with nanoenvironments of miniaturized, the diffraction limit of light. The microfluidics for measuring physical integrated devices, and may enable superresolution microscopy system is to properties of biomolecules. (Lin) novel biomedical investigations not be used to observe molecular dynamics attainable by conventional techniques. in living cells. A high-speed scanning Biological Engineering and The research interests center on the system is designed and implemented Biotechnology. Active areas of research development of MEMS devices and to track molecular dynamics in a video in the musculoskeletal biomechanics systems for label-free manipulation rate. Control of sample motion in laboratory include theoretical and and interrogation of biomolecules. nanometer resolution is achieved by experimental analysis of articular Current research efforts primarily involve integrating single photon detection and cartilage mechanics; theoretical and microfluidic devices that exploit specific nanopositioning systems. (Liao) experimental analysis of cartilage and reversible, stimulus-dependent Research in the area of optical lubrication, cartilage tissue engineering, binding between biomolecules and nanotechnology focuses on devices and bioreactor design; growth and receptor molecules to enable selective smaller than the wavelength of light, remodeling of biological tissues; cell purification, concentration, and for example, in photonic crystal mechanics; and mixture theory for label-free detection of nucleic acid, nanomaterials and NEMS devices. biological tissues with experiments and protein, and small molecule analytes; A strong research group with computational analysis (Ateshian). miniaturized instruments for label-free facilities in optical (including ultrafast) The Hone group is involved in a characterization of thermodynamic characterization, device nanofabrication, number of projects that employ the and other physical properties of and full numerical intensive simulations tools of micro- and nanofabrication biomolecules; and subcutaneously is available. Current efforts include toward the study of biological implantable MEMS affinity biosensors for silicon nanophotonics, quantum systems. With collaborators in biology continuous monitoring of glucose and dot interactions, negative refraction, and applied physics, the group has other metabolites. (Lin) dramatically enhanced nonlinearities, developed techniques to fabricate Mass radiological triage is critical and integrated optics. This effort seeks metal patterns on the molecular scale after a large-scale radiological event to advance our understanding of (below 10 nanometers) and attach because of the need to identify nanoscale optical physics, enabled now biomolecules to create biofunctionalized those individuals who will benefit by our ability to manufacture, design, nanoarrays. The group is currently from medical intervention as soon as and engineer precise subwavelength using these arrays to study molecular possible. The goal of the ongoing NIH- nanostructures, with derived recognition, cell spreading, and protein funded research project is to design applications in high-sensitivity sensors, crystallization. Professor Hone is a co-PI a prototype of a fully automated, ultra high-bandwidth data communications, of the NIH-funded Nanotechnology high throughput biodosimetry. This and biomolecular sciences. Major Center for Mechanics in Regenerative prototype is supposed to accommodate ongoing collaborations across national Medicine, which seeks to understand multiple assay preparation protocols laboratories, industrial research centers, and modify at the nanoscale force- and that allow the determination of the and multiuniversities support this geometry-sensing pathways in health levels of radiation exposure that a research. (Wong) and disease. The Hone group fabricates patient received. The input to this fully Research in the area of many of the tools used by the center to autonomous system is a large number microtribology—the study of measure and apply force on a cellular of capillaries filled with blood of patients friction, lubrication, and wear at the level. (Hone) collected using finger sticks. These microscale—analyzes the surface In the area of molecular capillaries are processed by the system contact and adhesive forces between bioengineering, proteins are engineered to distill the micronucleus assay in translating and rotating surfaces in to understand their mechanical effects lymphocytes, with all the assays being MEMS devices. Additionally, the on stem cell differentiation. Molecular carried out in situ in multi-well plates. tribological behavior between sliding motors are designed and engineered The research effort on this project micro- and nano-textured surfaces is computationally and experimentally involves the automation system design also of interest, due to the prospects to identify key structural elements of and integration including hierarchical of enhanced lubrication and reduced motor functions. Fluorescent labels control algorithms, design and control friction. (Terrell) are added to the molecules of interest of custom built robotic devices, and Research in BioMEMS aims to to follow their dynamics in living cells automated image acquisition and

engineering 2011–2012 processing for sample preparation and setups for the understanding and research section of the department 179 analysis. (Yao) performance evaluation of a complete website. The students and staff of the A technology that couples the small steam power generation system, department can, by prior arrangement, power of multidimensional microscopy a heat exchanger, a solar cell system, use much of the equipment in these (three spatial dimensions, time, and a fuel cell system, and a compressor. research facilities. Through their multiple wavelengths) with that of Part of the undergraduate laboratory is participation in the NSF-MRSEC DNA array technology is investigated a staffed machine shop with machining center, the faculty also have access to in an NIH-funded project. Specifically, tools such as standard vertical milling shared instrumentation and the clean a system is developed in which machines, engine and bench lathes, room located in the Schapiro Center individual cells selected on the programmable surface grinder, band for Engineering and Physical Science basis of optically detectable multiple saw, drill press, tool grinders, and a Research. Columbia University’s features at critical time points in power hacksaw. The shop also has a extensive library system has superb dynamic processes can be rapidly tig welder. scientific and technical collections. and robotically micromanipulated into A mechatronics laboratory affords E-mail and computing services are reaction chambers to permit amplified the opportunity for hands-on experience maintained by Columbia University DNA synthesis and subsequent array with microcomputer-embedded control Information Technology (CUIT) (http:// analysis. Customized image processing of electromechanical systems. Facilities www.columbia.edu/cuit). and pattern recognition techniques for the construction and testing of are developed, including Fisher’s analog and digital electronic circuits undergraduate program linear discriminant preprocessing with aid the students in learning the basic The objectives of the undergraduate neural net, a support vector machine components of the microcomputer program in mechanical engineering are with improved training, multiclass cell architecture. The laboratory is divided as follows: detection with error correcting output into work centers for two-person The Mechanical Engineering coding, and kernel principal component student laboratory teams. Each work Department at Columbia University is analysis. (Yao) center is equipped with several power dedicated to graduating mechanical supplies (for low-power electronics engineers who: Facilities for Teaching and Research and higher power control), a function 1. Practice mechanical engineering in a The undergraduate laboratories, generator, a multimeter, a protoboard broad range of industries occupying an area of approximately for building circuits, a microcomputer 2. Pursue advanced education, research 6,000 square feet of floor space, are circuit board (which includes the and development, and other creative the site of experiments ranging in microcomputer and peripheral and innovative efforts in science, complexity from basic instrumentation components), a microcomputer engineering, and technology, as well and fundamental exercises to advanced programmer, and a personal computer as other professional careers experiments in such diverse areas as that contains a data acquisition board. 3. Conduct themselves in a responsible, automatic controls, heat transfer, fluid The data acquisition system serves professional, and ethical manner mechanics, stress analysis, vibrations, as an oscilloscope, additional function 4. Participate as leaders in their fields of microcomputer-based data acquisition, generator, and spectrum analyzer for expertise and in activities that support and control of mechanical systems. the student team. The computer also service and economic development Equipment includes microcomputers contains a complete microcomputer nationally and throughout the world and microprocessors, analog-to-digital software development system, including and digital-to-analog converters, editor, assembler, simulator, debugger, Highly qualified students are lasers and optics for holography and C compiler. The laboratory permitted to pursue an honors course and interferometry, a laser-Doppler is also equipped with a portable consisting of independent study under velocimetry system, a Schlieren oscilloscope, an EPROM eraser (to the guidance of a member of the faculty. system, dynamic strain indicators, a erase microcomputer programs from the Upon graduation the student may servohydraulic material testing machine, erasable chips), a logic probe, and an wish to enter employment in industry a photoelastic testing machine, analog filter bank that the student teams or government, or continue with an internal combustion engine, a share, as well as a stock of analog and graduate study. Alternatively, training in dynamometer, subsonic and supersonic digital electronic components. mechanical engineering may be viewed wind tunnels, a cryogenic apparatus, The department maintains a modern as a basis for a career in business, computer numerically controlled vertical computer-aided design laboratory patent law, medicine, or management. machine centers (VMC), a coordinate equipped with fifteen Silicon Graphics Thus, the department’s undergraduate measurement machine (CMM), and workstations and software tools. The program provides a sound foundation a rapid prototyping system. A CNC research facilities are located within for a variety of professional endeavors. wire electrical discharge machine individual or group research laboratories The program in mechanical (EDM) is also available for the use of in the department, and these facilities engineering leading to the B.S. degree specialized projects for students with are being continually upgraded. To view is accredited by the Engineering prior arrangement. The undergraduate the current research capabilities please Accreditation Commission of the laboratory also houses experimental visit the various laboratories within the Accreditation Board for Engineering and

engineering 2011–2012 180 mechanical engineering program: first and second Years standard track

Semester i Semester iI Semester iII Semester iV

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

physics C1401 (3) C1402 (3) C1403 (3)3 (three tracks, C1601 (3.5) C1602 (3.5) C2601 (3.5)3 choose one) 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 (three tracks, Z1003 (0) C1010 (3) choose one) Z0006 (0) Z1003 (0) C1010 (3)

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

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

computer Computer language: W1003 (3) W1004 (3) any semester science or

physical C1001 (1) C1002 (1) education

gateway lab E1102 (4) either semester

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

Technology (ABET). Fundamentals of Engineering (FE) some years of experience and a second Of the 21 points of elective content Exam examination, which tests knowledge in the third and fourth years, at least 12 The FE exam is a state licensing exam gained in engineering practice. For more points of technical courses, including at and the first step toward becoming information, please see www.columbia. least 6 points from the Department of a Professional Engineer (P.E.). P.E. edu/cu/mechanical/misc-pages/ Mechanical Engineering, must be taken. licensure is important for engineers FE_Exam.html. Those remaining points of electives are to obtain—it shows a demonstrated The Mechanical Engineering Depart- intended primarily as an opportunity commitment to professionalism and ment strongly encourages all seniors to complete the four-year, 27-point an established record of abilities that to take this exam and offers a review nontechnical requirement. Consistent will help a job candidate stand out in course covering material relevant to with professional accreditation the field. Ideally, the FE exam should the exam, including a practice exam to standards, courses in engineering be taken in the senior year while the simulate the testing experience. The FE science and courses in design must technical material learned while pursuing exam is given in the fall and spring of have a combined credit of 48 points. the undergraduate degree is still fresh in each year. The review course is offered Students should see their advisers for the student’s mind. In addition to the FE in the spring semester, concluding details. exam, achieving P.E. licensure requires before the spring exam.

engineering 2011–2012 181 mechanical engineering: third and fourth Years standard track

Semester V Semester VI Semester VII Semester VIII

MECE E3018 (3) MECE E3028 (3) Lab I Lab II

MECE E3100 (3) MECE E3408 (3) MECE E3038 (3) Fluids I Graphics and design Lab III

Required MECE E3301 (3) MECE E3311 (3) MECE E3409 (3) MECE E3410 (4) Courses Thermodynamics Heat transfer Machine design Engineering design

ENME E3105 (4)1 MECE E4608 (3) MECE E3601 (3) Mechanics Manufacturing proc. Classical control sys.

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

technical 6 points 6 points Electives

NONTECH 3 points 6 points Electives

total points2 15 15.5 15 16

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

Integrated B.S./M.S. Program graduate programS from a set of predefined concentrations, The Integrated B.S./M.S. Program is or special tracks. open to a select group of Columbia Master of Science Degree Program Typical choices of concentration juniors (excluding 3-2 combined plan The program leading to the Master in the standard track include such students) and makes possible the of Science degree in mechanical subjects as mechanics of solids and earning of both a B.S. and an M.S. engineering requires completion of a fluids, thermodynamics, heat transfer, degree simultaneously. Benefits of this minimum of 30 points of approved manufacturing engineering, robotics, program include optimal matching of course work consisting of no fewer kinematics, dynamics and vibrations, graduate courses with corresponding than ten courses. A thesis based on controls, and power generation. undergraduate prerequisites, greater either experimental, computational, or Nevertheless, the following guidelines ability to plan ahead for most analytical research is optional and may must be adhered to: advantageous course planning, be counted in lieu of up to 6 points of 1. The sequence of courses selected opportunities to do research for credit course work. In general, attainment of must not be haphazard but rather during the summer after senior year, and the degree requires one academic year show a clearly discernible specialty. up to 6 points of 4000-level technical of full-time study, although it may also 2. All courses must be at the graduate electives from the B.S. requirement be undertaken on a part-time basis level, i.e., numbered 4000 or higher, may count toward the fulfillment of over a correspondingly longer period. A with some 6000-level courses the point requirement of the M.S. minimum grade point average of 2.5 is included. degree. Additional benefits include required for graduation. 3. Every program must contain at least simplified application process, no GRE The M.S. degree in mechanical one course in mathematics (APMA or is required, and no reference letters are engineering requires a student to take MATH designators) or their equivalent, required. To quality for this program, a sequence of courses that shows covering material beyond what the your cumulative GPA should be at least a “clearly discernible specialty or student has taken previously. It 3.4. This program is not applicable to concentration.” In consultation with his/ should appear early in the sequence 3-2 students. For more information her adviser an M.S. student can develop in order to serve as a basis for the on requirements and access to an a concentration specifically tailored to technical course work. application form, please visit http://www. his/her interests and objectives, and 4. Out-of-department study is me.columbia.edu/pages/academics/ we refer to this as the standard track. encouraged, but at least five courses Integrated_BSMS/index.html. Alternatively, M.S. students can pick should be in mechanical engineering.

engineering 2011–2012 182 mechanical engineering program: first and second Years early decision track

Semester i Semester iI Semester iII Semester iV

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

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

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

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

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

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

computer Computer language: W1003 (3) W1004 (3) any semester science or

physical C1001 (1) C1002 (1) education

gateway lab E1102 (4) either semester

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

Rather than apply for the standard track, M.S. in Mechanical Engineering with preparation for careers in energy students can apply for a special track Concentration in Energy Systems production and energy consultation. in either energy systems or in micro/ Advisers: Profs. Vijay Modi and Arvind Requirements: While satisfying nanoscale engineering. The require- Narayanaswamy the general mechanical engineering ments for a special track are identical requirements, take at least five courses The concentration in energy systems to those of the standard track, with one from: provides the M.S. candidate with a exception: a special track student must global understanding of current energy MECE E4210: Energy infrastructure planning take at least 15 of his/her points from a challenges. Advanced thermofluidic MECE E4211: Energy: sources and conversion list determined by a special track adviser MECE E4302: Advanced thermodynamics knowledge is provided to design in consultation with a special track MECE E4304: Turbomachinery and optimize energy systems, with advisory committee. The name of the MECE E4305: Mechanics and thermodynamics a strong emphasis on renewable special track will be listed on a student’s propulsion energies. Courses related to energy and transcript. The currently available special MECE E4312: Solar thermal engineering environmental policy, two strong areas MECE E4314: Energy dynamics of green buildings tracks are listed below. of Columbia as a global university, can MECE E6100: Advanced mechanics of fluids be integrated into the course sequence. MECE E6104: Case studies in computational fluid This concentration is a suitable dynamics

engineering 2011–2012 183 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) Lab I Lab II Lab III

Required MECE E3100 (3) MECE E3311 (3) MECE E3409 (3) MECE E3410 (4) Courses Fluids I Heat transfer Machine design Engineering design

MECE E3301 (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 3 points 3 points 6 points Electives

total points1 15 16 15 16

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

MECE E6313: Advanced heat transfer MECE E4212: Microelectromechanical systems reference letters are required. To qualify APPH E4130: Physics of solar energy MECE E4213: BioMEMS for this program, your cumulative EAEE E6126: Carbon sequestration MECE E6105: T ransport phenomena in the GPA should be at least 3.4. For more presence of interfaces EAEE E6208: Combustion chemistry or processes information on requirements and access INTA W4200: Alternative energy resources MECE E6700: Carbon nanotubes to an application, please visit www. ARCH A4684: Sustainable design MECE E6710: Nanofabrication laboratory SIPA U4727: Environmental politics and policy MECE E6720: Nano/microscale thermal transport me.columbia.edu/pages/academics/ management processes Express_MS/index.html. SIPA U6060: International energy systems and MECE E8990: Small scale mechanical behavior business structures ELEN E4503: Sensors, actuators, and Doctoral/Professional Degree electromechanical systems Programs M.S. in Mechanical Engineering with ELEN E6945: Device nanofabrication BMEN E4590: BioM EMS: cellular and molecular Students who wish to continue their Concentration in Micro/Nanoscale applications studies beyond the master’s degree Engineering MSAE E4090: Nanotechnology level but are unwilling to embark upon a Advisers: Profs. James Hone and Jeff program of research of the kind required Kysar Express M.S. Program for a doctoral degree may continue in a program leading to the professional The concentration in micro/nanoscale The Express M.S. Program is offered to degree of Mechanical Engineer (MECE). engineering provides the M.S. candidate current seniors, including 3-2 students, The course of study consists of a with an understanding of engineering who are enrolled in the BS program. In minimum of 30 points of work beyond challenges and opportunities in micro- the Express M.S. Program, a master’s the master’s degree, combining courses and nanoscale systems. The curriculum degree can be earned seamlessly. of an analytical nature with those addresses fundamental issues of Graduate classes are available for emphasizing the applied aspects of one mechanics, fluid mechanics, optics, heat seniors to apply toward their M.S. or more fields in mechanical engineering. transfer, and manufacturing at small-size degree and the advanced courses that For the professional degree, the student scales. Application areas include MEMS, will be taken have been designed to must have a grade point average of 3.0 bio-MEMS, microfluidics, thermal have the exact prerequisites completed or better. systems, and carbon nanostructures. as an undergraduate. Other advantages When a student becomes a Requirements: While satisfying include the opportunity for better course prospective candidate for either the the general mechanical engineering planning and creating a streamlined set Doctor of Engineering Science (Eng. requirements, take at least five courses of courses more possible. Additional Sc.D.) or Doctor of Philosophy (Ph.D.) from: benefits include simplified application process, no GRE is required and no degree, a faculty adviser is assigned

engineering 2011–2012 184 whose task is to help choose a recommend modifications or additions. Continuity equation. Two-dimensional kinematics. program of courses, provide general This is the last formal requirement until Equation of motion. Bernoulli’s equation and advice on academic matters, and the dissertation is submitted for approval. applications. Equations of energy and angular momentum. Dimensional analysis. Two- monitor academic performance. All doctoral students are required to dimensional laminar flow. Pipe flow, laminar, and The doctoral candidate is expected successfully complete four semesters turbulent. Elements of compressible flow. to attain a level of mastery in some of the mechanical engineering seminar area of mechanical engineering, and MECE E9500. ENME E3105x and y Mechanics must therefore choose a field and 4 pts. Lect: 4. Professor Hone. Prerequisites: PHYS C1401 and MATH V1101, concentrate in it by taking the most courseS in mechanical V1102, and V1201. Elements of statics, dynamics advanced courses offered. This choice engineering of a particle, systems of particles, and rigid bodies. of specialty is normally made by the time the student has completed 30 points of MECE E1001x Mechanical engineering: ENME E3113x Mechanics of solids 3 pts. Lect: 3. Professor Deodatis. credit beyond the bachelor’s degree, at micromachines to jumbo jets Pre- or corequisite: ENME E3105 or equivalent. which time a complete course program 3 pts. Lect: 3. Professor Myers. Stress and strain. Mechanical properties of is prepared and submitted to the Corequisite: MATH V1101 Calculus I. This introductory course explores the role of Mechanical materials. Axial load, bending, shear, and departmental doctoral committee for Engineering in developing many of the fundamental torsion. Stress transformation. Deflection of approval. The student must maintain a technological advances on which today’s society beams. Buckling of columns. Combined loadings. grade point average of 3.2 or better in depends. Students will be exposed to several Thermal stresses. graduate courses. mature and emerging technologies through a MECE E3301x Thermodynamics series of case studies. Topics include: airplanes, The department requires the 3 pts. Lect: 3. Professor Basalo. automobiles, robots, modern manufacturing prospective candidate to pass a Classical thermodynamics. Basic properties and methods as well as the emerging fields of qualifying examination. Given once a concepts, thermodynamic properties of pure microelectromechanical machines (MEMS) and year, in January, it is usually taken after substances, equation of state, work, heat, the first nanotechnology. The physical concepts that govern and second laws for flow and nonflow processes, the student has completed 30 points the operation of these technologies will be developed energy equations, entropy, and irreversibility. beyond the bachelor’s degree. However, from basic principles and then applied in simple Introduction to power and refrigeration cycles. it may not be delayed past the next design problems. Students will also be exposed to examination given after completion of state-of-the art innovations in each case study. MECE E3311y Heat transfer 3 pts. Lect: 3. Professor Narayanaswamy. 45 points. The examination comprises MECE E3018x Mechanical engineering Steady and unsteady heat conduction. Radiative a written test, given in two parts over laboratory, I heat transfer. Internal and external forced and free two days, in which questions may be 3 pts. Lect: 3. Professor Kysar. convective heat transfer. Change of phase. Heat selected from a broad set in all areas Experiments in instrumentation and measurement: exchangers. of mechanical engineering and applied optical, pressure, fluid flow, temperature, stress, mathematics, devised to test the and electricity; viscometry, cantilever beam, digital MECE E3401x Mechanics of machines data acquisition. Probability theory: distribution, candidate’s ability to think creatively. 3 pts. Lect: 3. Professor Lin. functions of random variables, tests of significance, Prerequisites: ENME E3105 and MECE E3408. There is also an oral examination based correlation, ANOVA, linear regression. A lab fee of Introduction to mechanisms and machines, on some research project the student $50.00 is collected. analytical and graphical synthesis of mechanism, has undertaken. A candidate who fails displacement analysis, velocity analysis, MECE E3028y Mechanical engineering the examination may be permitted to acceleration analysis of linkages, dynamics of laboratory, II repeat it once in the following year. mechanism, cam design, gear and gear trains, and 3 pts. Lect: 3. Professor Wong. computer-aided mechanism design. After passing the qualifying Experiments in engineering and physical examination, the student chooses a phenomena: aerofoil lift and drag in wind tunnels, MECE E3408y Computer graphics and design faculty member in the pertinent area laser Doppler anemometry in immersed fluidic 3 pts. Lect: 3. Instructor to be announced. of specialization who then serves as channels, supersonic flow and shock waves, Introduction to drafting, engineering graphics, the research adviser. This adviser Rankine thermodynamical cycle for power computer graphics, solid modeling, and mechanical helps select a research problem and generation, and structural truss mechanics and engineering design. Interactive computer graphics analysis. A lab fee of $50.00 is collected. and numerical methods applied to the solution supervises the research, writing, and of mechanical engineering design problems. A MECE E3038x Mechanical engineering defense of the dissertation. Once a laboratory fee of $175 is collected. specific problem has been identified laboratory, III and a tentative plan for the research 3 pts. Lect: 3. Professor Stolfi. MECE E3409x Machine design Mechatronic control of mechanical and 3 pts. Lect: 3. Professor Ateshian. prepared, the student submits a electromechanical systems. Control of various Prerequisite: MECE E3408. Computer-aided research proposal and presents it to thermodynamic cycles, including internal analysis of general loading states and deformation a faculty committee. The committee combustion engine (Otto cycle). Reverse of machine components using singularity functions considers whether the proposed engineering of an electromechanical product. A lab and energy methods. Theoretical introduction to problem is suitable for doctoral fee of $50.00 is collected. static failure theories, fracture mechanics, and research, whether the plan of attack is fatigue failure theories. Introduction to conceptual MECE E3100x Introduction to mechanics design and design optimization problems. Design well formulated and appropriate to the of fluids of machine components such as springs, shafts, problem, and whether the student is 3 pts. Lect: 3. Professor Liao. fasteners, lead screws, rivets, welds. Modeling, adequately prepared. It may approve Prerequisite: ENME E3105. Basic continuum analysis, and testing of machine assemblies for the plan without reservation, or it may concepts. Liquids and gases in static equilibrium.

engineering 2011–2012 prescribed design problems. Problems will be Systems explored include on/off systems, separation and detection; sample preparation; 185 drawn from statics, kinematics, dynamics, solid solenoids, stepper motors, DC motors, thermal micro bioreactors and temperature control; modeling, stress analysis, and design optimization. systems, magnetic levitation. Use of analog and implantable MEMS, including sensors, actuators digital electronics and various sensors for control. and drug delivery devices. MECE E3410y Engineering design Programming microcomputers in Assembly and C. 4 pts. Lect: 4. Professor Stolfi. MECE E4302y Advanced thermodynamics A lab fee of $75.00 is collected. Lab required. Prerequisite: Senior standing. Elements of the 3 pts. Lect: 3. Professor Kang. design process: concept formulation, systems MECE E4100y Mechanics of fluids Prerequisite: MECE E3301. Advanced classical synthesis, design analysis optimization. Selection 3 pts. Lect: 3. Instructor to be announced. thermodynamics. Availability, irreversibility, and execution of a project involving the design Prerequisite: MECE E3100 or equivalent. Fluid generalized behavior, equations of state for of an actual engineering device or system. A dynamics and analyses for mechanical engineering nonideal gases, mixtures and solutions, phase and laboratory fee of $125 is collected. and aerospace applications: boundary layers chemical behavior, combustion. Thermodynamic MECE E3411y Fundamentals of engineering and lubrication, stability and turbulence, and properties of ideal gases. Applications to 1 pt. Lect: 3. Professor Stolfi. compressible flow. Turbomachinery as well as automotive and aircraft engines, refrigeration and Prerequisite: Senior standing. Review of core additional selected topics. air conditioning, and biological systems. courses in mechanical engineering, including MECI E4210x Energy infrastructure planning MECE E4304x Turbomachinery mechanics, strength of materials, fluid mechanics, 3 pts. Lect: 3. Professor Modi. 3 pts. Lect: 3. Professor Akbari. thermodynamics, heat transfer, materials and Prerequisites: One year each of college level This course will introduce you to the basics processing, control, and mechanical design and physics, chemistry, and mathematics. Energy of theory, design, selection and applications analysis. Review of additional topics, including infrastructure planning with specific focus on of turbomachinery. Turbomachines are widely engineering economics and ethics in engineering. countries with rapidly growing infrastructure used in many engineering applications such as The course culminates with a comprehensive needs. Spatiotemporal characteristics, scale, and energy conversion, power plants, air-conditioning, examination, similar to the Fundamentals of environmental footprints of energy resources, pumping, refrigeration and vehicle engines, Engineering examination. This course meets the power generation and storage, modeling as there are pumps, blowers, compressors, first 4.5 weeks only. demand growth, technology choices and learning gas turbines, jet engines, wind turbines etc. EEME E3601x Classical control systems for planning. Computer-assisted decision Applications are drawn from energy conversion 3 pts. Lect: 3. Professor Longman. support and network design/optimization tools. technologies, HVAC and propulsion. The course Prerequisite: MATH E1210. Analysis and design Similarities, differences and interactions among provides a basic understanding of the different of feedback control systems. Transfer functions; electricity, gas, information, transportation and kinds of turbomachines. block diagrams; proportional, rate, and integral water distribution networks. Penetration of MECE E4305y Mechanics and controllers; hardware, implementation. Routh renewable and/or decentralized technologies thermodynamics of propulsion stability criterion, root locus, Bode and Nyquist into existing or new infrastructure. Special guest 3 pts. Lect: 3. Professor Akbari. plots, compensation techniques. lectures on infrastructure finance, regulation and Prerequisites: MECE E3301x Thermodynamics public-private partnerships. MECE E3900x-E3901y Honors tutorial in and MECE E3311y Heat transfer; MECE mechanical engineering MECE E4211x Energy: sources and E4304x Turbomachinery (or instructor approval). Principles of propulsion. Thermodynamic cycles 3 pts. Lect: 3. Members of the faculty. conversion of air breathing propulsion systems including Individual study; may be selected after the first 3 pts. Lect: 3. Professor Modi. ramjet, scramjet, turbojet, and turbofan engine term of the junior year by students maintaining a Prerequisite: MECE E3301. Energy sources such and rocket propulsion system concepts. Turbine 3.2 grade-point average. Normally not to be taken as oil, gas, coal, gas hydrates, hydrogen, solar, engine and rocket performance characteristics. in a student’s final semester. Course format may and wind. Energy conversion systems for electrical Component and cycle analysis of jet engines and vary from individual tutorial to laboratory work power generation, automobiles, propulsion and turbomachinery. Advanced propulsion systems. to seminar instruction under faculty supervision. refrigeration. Engines, steam and gas turbines, Columbia Engineering interdisciplinary course. Written application must be made prior to wind turbines; devices such as fuel cells, registration outlining proposed study program. thermoelectric converters, and photovoltaic cells. IEME E4310x The manufacturing enterprise Projects requiring machine-shop use must be Specialized topics may include carbon-dioxide 3 pts. Lect: 3. Professor Weinig. approved by the laboratory supervisor. sequestration, cogeneration, hybrid vehicles and The strategies and technologies of global MECE E3998x and y Projects in mechanical energy storage devices. manufacturing and service enterprises. Connections between the needs of a global engineering MECE E4212x or y Microelectromechanical 1-3 pts. Members of the faculty. enterprise, the technology and methodology systems needed for manufacturing and product Prerequisite: Approval by faculty member who 3 pts. Lect: 1.5. Lab: 3. Professor Wong. agrees to supervise the work. Normally not to be development, and strategic planning as currently MEMS markets and applications; scaling laws; practiced in industry. taken in a student’s final semester. Independent silicon as a mechanical material; Sensors and project involving theoretical, computational, actuators; micromechanical analysis and design; MECE E4312x Solar thermal engineering experimental or engineering design work. May substrate (bulk) and surface micromachining; 3 pts. Lect: 3. Professor Narayanaswamy. be repeated, but no more than 3 points may be computer aided design; packaging; testing and Prerequisite: MECE E3311 (Heat transfer). counted toward degree requirements. Projects characterization; microfluidics. Fundamentals of solar energy transport: requiring machine-shop use must be approved by radiation heat transfer, convention, conduction the laboratory supervisor. MECE E4213y Biomicroelectromechanical and phase change processes. Heat exchangers systems (BioMEMS): design, fabrication, and MECE E4058x and y Mechatronics and and solar collectors: basic methods of thermal analysis embedded microcomputer control design, flow arrangements, effects of variable 3 pts. Lect: 3. Professor Lin. 3 pts. Lect: 3. Professor Stolfi. conditions, rating procedures. Solar energy Prerequisites: MECE E3100 and E3311, course in Prerequisite: ELEN E1201. Recommended: concentration. Piping Systems: series and transport phenomena, or instructor’s permission. ELEN E3000. Enrollment limited to 12 students. parallel arrangements, fluid movers. Thermal Silicon and polymer micro/nanofabrication Mechatronics is the application of electronics and response and management of photovoltaic techniques; hydrodynamic microfluidic control; microcomputers to control mechanical systems. energy conversion. Solar energy storage. Solar electrokinetic microfluidic control; microfluidic

engineering 2011–2012 186 cooling, solar thermal power and cogeneration. MEBM E4439x Modeling and identification of MECE E4604x Product design for Applications to the design of solar thermal dynamic systems manufacturability engineering systems. 3 pts. Lect: 3. Professor Chbat. 3 pts. Lect: 3. Professor Walker. Prerequisite: APMA E2101, ELEN E3801, or Prerequisites: Manufacturing process, computer MECE E4314y Energy dynamics of green corequisite EEME E3601, or permission of graphics, engineering design, mechanical design. buildings instructor. Generalized dynamic system modeling General review of product development process; 3 pts. Lect: 3. Professor Naraghi. and simulation. Fluid, thermal, mechanical, market analysis and product system design; Prerequisites: MECE E3301 and E3311. diffusive, electrical, and hybrid systems are principles of design for manufacturing; strategy Introduction to analysis and design of heating, considered. Nonlinear and high order systems. for material selection and manufacturing process ventilating and air-conditioning systems. Heating System identification problem and Linear choice; component design for machining; casting; and cooling loads. Humidity control. Solar gain and Least Squares method. State-space and noise molding; sheet metal working and inspection; general passive solar design. Global energy implications. representation. Kalman filter. Parameter estimation assembly processes; product design for manual Green buildings. Building-integrated photovoltaics. via prediction-error and subspace approaches. assembly; design for robotic and automatic assembly; Roof-mounted gardens and greenhouses. Financial Iterative and bootstrap methods. Fit criteria. Wide case studies of product design and improvement. assessment tools and case studies. Open to applicability: medical, energy, others. MATLAB and MECE E4608y Manufacturing processes Mechanical Engineering graduate students only. Simulink environments. 3 pts. Lect: 3. Professor Yao. MECE E4400x and y Computer laboratory access MECE E4501y Geometrical modeling Prerequisite: ENME E3113 or equivalent. Processes 0 pts. Professor Ateshian. 3 pts. Lect: 3. Professor Rajan. and materials of manufacture: metal cutting, forming, Sign up for this class to obtain a computer account Prerequisite: COMS W1005. Relationship between stamping, forging, welding, powder metallurgy; and access to the Department of Mechanical 3D geometry and CAD/CAM; representations classification and fabricating characteristics of Engineering Computer Laboratory. of solids; geometry as the basis of analysis, metals and composites; plastics, adhesives. design, and manufacturing; constructive solid MECE E4404x Tribology: friction, lubrication, MECE E4609y Computer-aided manufacturing geometry and the CSG tree; octree representation and wear 3 pts. Lect: 3. Professor Walker. and applications; surface representations and 3 pts. Lect: 3. Professor Terrell. intersections; boundary representation and Prerequisites: Introductory course on manufacturing Prerequisites: MECE E3100, E3311, and ENME boundary evaluation; applied computational processes and knowledge of computer-aided design, E3113, or permission of the instructor. Friction, geometry; analysis of geometrical algorithms and mechanical design or instructor’s permission. lubrication, and wear between sliding surfaces. and associated data structures; applications of Computer-aided design, free-form surface modeling, Surface metrology, contact mechanics, and sliding geometrical modeling in vision and robotics. tooling and fixturing, computer numeric control, friction. Deformation, wear, and temperature rapid prototyping, process engineering, fixed and rise of non-lubricated, liquid-lubricated, and MECE E4502x Computational geometry for programmable automation, industrial robotics. solid-lubricated rolling and sliding materials. CAD/CAM MECE E4610x Advanced manufacturing The theories of boundary, elastohydrodynamic, 3 pts. Lect: 3. Professor Rajan. processes hydrodynamic, hydrostatic, and solid-phase Prerequisite: COMS W1005 FORTRAN or 3 pts. Lect: 3. Not offered in 2011–2012. lubrication. Lubricant flow and load-carrying PASCAL. Analysis of geometric problems and Prerequisites: Introductory course on capacity in bearings. Special applications such as the design of efficient methodologies to obtain manufacturing processes, and heat transfer, geartrains, cam/tappets, and micro- and nanoscale solutions to these problems. Algorithms to be knowledge of engineering materials, or tribological interfaces. studied include geometric searching, convex hulls, triangulations, Voronoi diagrams, intersections, instructor’s permission. Principles of nontraditional MECE E4430y Automotive dynamics hidden surfaces. Emphasis will be on practical manufacturing, nontraditional transport and media. 3 pts. Lect: 3. Not offered in 2011–2012. aspects of these algorithms, and on applications of Emphasis on laser assisted materials processing, Prerequisite: ENME 3105 or equivalent; the solutions in computer-aided product design and laser material interactions with applications to recommended: ENME 3106 or equivalent. manufacturing. laser material removal, forming, and surface Automobile dynamic behavior is divided into three modification. Introduction to electrochemical subjects: vehicle subsystems, ride, and handling. EEME E4601y Digital control systems machining, electrical discharge machining and 3 pts. Lect: 3. Professor Longman. Vehicle subsystems include: tire, steering, abrasive water jet machining. mechanisms, suspensions, gearbox, engine, Prerequisite: EEME E3601 or ELEN E3201. Real- time control using digital computers. Solving scalar MEBM E4702x Advanced musculoskeletal clutch, etc. Regarding ride, vibrations and ride and state-space difference equations. Discrete biomechanics comfort are analyzed, and suspension optimization equivalents of continuous systems fed by holds. 3 pts. Lect: 3. Not offered in 2011–2012. of a quarter car model is treated. Regarding Z-transer functions. Creating closed-loop difference Advanced analysis and modeling of the handling, vehicle dynamic behavior on the road is equation models by Z-transform and state variable musculoskeletal system. Topics include analyzed, with emphasis on numerical simulations approaches. The Nyquist frequency and sample advanced concepts of 3D segmental kinematics, using planar as well as roll models. rate selection. Classical and modern based digital musculoskeletal dynamics, experimental MECE E4431 Space vehicle dynamics and control laws. Digital system identification. measurements of joints kinematics and anatomy, control MECE E4602y Introduction to robotics modeling of muscles and locomotion, multibody 3 pts. Lect: 3. Not offered in 2011–2012. 3 pts. Lect: 3. Instructor to be announced. joint modeling, introduction to musculoskeletal Prerequisite: ENME-MECE E3105; ENME E4202 Overview of robot applications and capabilities. surgical simulations. recommended. Space vehicle dynamics and Linear algebra, kinematics, statics, and control, rocket equations, satellite orbits, initial MEBM E4703y Molecular mechanics in dynamics of robot manipulators. Survey of trajectory designs from earth to other planets, biology sensor technology: force, proximity, vision, satellite attitude dynamics, gravity gradient 3 pts. Lect: 3. Professor Liao. compliant manipulators. Motion planning and stabilization of satellites, spin-stabilized satellites, Prerequisite: ENME E3105, APMA E2101, or artificial intelligence; manipulator programming dual-spin satellites, satellite attitude control, instructor’s permission. Mechanical understanding requirements and languages. modeling, dynamics, and control of large flexible of biological structures including proteins, DNA spacecraft. and RNA in cells and tissues. Force response of protenis and DNA, mechanics of membranes,

engineering 2011–2012 biophysics of molecular motors, mechanics MECE E6105y Transport phenomena in the and strain. Formulation of the problem of elastic 187 of protein-protein interactions. Introduction to presence of interfaces equilibrium. Torsion and flexure of prismatic bars. modeling and simulation techniques, and modern 3 pts. Lect: 3. Not offered in 2011–2012. Problems in stress concentration, rotating disks, biopohysical techniques such as single molecule Prerequisites: MECE E3301 Thermodynamics shrink fits, and curved beams; pressure vessels, FRET, optical traps, AFM, and superresolution and MECE E3311 Heat transfer; MECE E4100 contact and impact of elastic bodies, thermal imaging, for understanding molecular mechanics Mechanics of fluids, or equivalent or instructor’s stresses, propagation of elastic waves. and dynamics. permission; CHEE E4252 Introduction to surface MECE E6424x Vibrations in machines, I and colloid chemistry, or the equivalent, or the MECE E4990x or y Special topics in 3 pts. Lect: 3. Professor Stolfi. instructor’s permission. Surface energy and mechanical engineering Prerequisite: MECE E3401. Review of vibration capillary phenomena. Wetting and spreading 3 pts. Lect: 3. Instructor to be announced. analysis of systems and mechanisms with one of liquids, wetting line pinning and hysteresis, Prerequisites: Permission of the instructor. Topics degree of freedom. Natural frequencies. Forced dynamics of wetting. Surfactants. Bubbles: and Instructors change from year to year. For vibrations. Effects of dry and viscous friction. nucleation, stability, dynamics, microstreaming. advanced undergraduate students and graduate Energy methods of Rayleigh and Ritz. Suppression Jets and Drops: generation, dynamics, stability and students in engineering, physical sciences, and and elimination of vibration. Vibration isolation. impact with surfaces. Measurement of transport other fields. Measuring instruments. Critical speeds in machinery. phenomena involving interfaces. Interfacial Synchronous whirl. Half-frequency whirl. Influence of MECE E4999x, y or s Curricular practical training transport phenomena involvng thermal, chemical bearing characteristics on critical speeds. Effect of 1 pt. Professor Ateshian. or electrical gradients. Applications in microfluidic gyroscopic moments. Systems with multiple degrees Prerequisite: Instructor’s written approval. Only for systems. of freedom. Dynamic vibration absorbers. Self-tuning ME graduate students who need relevant intern MECE E6200y Turbulence absorbers of pendulum and roller types. Lagrangian or field-work experience as part of their program equations of motion as applied to vibrating systems. 3 pts. Lect: 3. Not offered in 2011-2012. of study as determined by the instructor. Written General equations for transverse critical speeds of Prerequisite: MECE E6100. Introductory concepts application must be made prior to registration shafts. Surging of helical springs. and statistical description. Kinematics of random outlining proposed study program. Final reports velocity fields, dynamics of vorticity, and scalar EEME E6601x Introduction to control theory required. This course may not be taken for pass/ quantities. Transport processes in a turbulent 3 pts. Lect: 3. Professor Longman. fail credit or audited. International students must medium. Turbulent shear flows: deterministic Prerequisite: MATH E1210. A graduate-level also consult with the International Students and and random structures. Experimental techniques, introduction to classical and modern feedback Scholars Office. prediction methods, and simulation. control that does not presume an undergraduate MECE E6100x Advanced mechanics of fluids background in control. Scalar and matrix MEBM E6310x-E6311y Mixture theories for 3 pts. Lect: 3. Professor Panides. differential equation models and solutions in terms biological tissues, I and II Prerequisites: MATH E1210 and MECE E3100. of state transition matrices. Transfer functions 3 pts. Lect: 3. Not offered in 2011-2012. Eulerian and Lagrangian descriptions of motion. and transfer function matrices, block diagram Prerequisites: MECE E6422 and APMA E4200 or manipulations, closed loop response. Proportional, Stress and strain rate tensors, vorticity, integral equivalent. Development of governing equations rate, and integral controllers, and compensators. and differential equations of mass, momentum, for mixtures with solid matrix, interstitial fluid, Design by root locus and frequency response. and energy conservation. Potential flow. and ion constituents. Formulation of constitutive Controllability and observability. Luenberger models for biological tissues. Linear and nonlinear MECE E6102y Computational heat transfer observers, pole placement, and linear-quadratic models of fibrillar and viscoelastic porous matrices. and fluid flow cost controllers. 3 pts. Lect: 3. Not offered in 2011–2012. Solutions to special problems, such as confined Prerequisites: MECE E3100 and E3311; COMS and unconfined compression, permeation, EEME E6602y Modern control theory W1005 FORTRAN. Mathematical description of indentation and contact, and swelling experiments. 3 pts. Lect: 3. Not offered in 2011-2012. Prerequisite: EEME E6601 or E4601 or ELEN pertinent physical phenomena. Basics of finite- MECE E6313x Advanced heat transfer E6201, or instructor’s permission. Singular value difference methods of discretization, explicit 3 pts. Lect: 3. Professor Naraghi. decomposition. ARX model and state space and implicit schemes, grid sizes, stability, and Prerequisites: MECE E3311. Corequisites: MECE model system identification. Recursive least convergence. Solution of algebraic equations, E6100. Application of analytical techniques to the squares filters and Kalman filters. LQR, Hlinear relaxation. Heat conduction. Incompressible solution of multidimensional steady and transient robust control, predictive control, adaptive fluid flow, stream function-vorticity formulation. problems in heat conduction and convection. control. Liapunov and Popov stability. Nonlinear Forced and natural convection. Use of primitive Lumped, integral, and differential formulations. adaptive control, nonlinear robust control, sliding variables, turbulence modeling, and coordinate Topics include use of sources and sinks, laminar/ mode control. transformations. turbulent forced convection, and natural convection in internal and external geometries. EEME E6610y Optimal control theory MECE E6104y Case studies in computational 3 pts. Lect: 3. Not offered in 2011–2012. fluid dynamics MECE E6400y Advanced machine dynamics Prerequisite: EEME E6601 or E4601 or instructor’s 3 pts. Lect: 3. Professor Panides. 3 pts. Lect: 3. Instructor to be announced. permission. Covers topics in calculus of variations, Prerequisites: APAM E4200 and MECE E6100. Prerequisite: MECE E3401. Review of classical Pontryagin maximum principle, quadratic cost dynamics, including Lagrange’s equations. Corequisites: APAM E4300 and MECE E4400. optimal control, predictive control, dynamic Analysis of dynamic response of high-speed Hands-on case studies in computational fluid programming for optimal control, Kalman filtering, machine elements and systems, including dynamics, including steady and transient numerical methods for solution. Some applications mass-spring systems, cam-follower systems, flows, heat and mass transfer, turbulence, discussed include: minimum energy subway and gearing; shock isolation; introduction to compressible flow and multiphase flow. Identifying operation (our solution saved 11% in tests on the gyrodynamics. assumptions, computational domain selection, Flushing Line, and the method was adopted by the model creation and setup, boundary conditions, MECE E6422x–E6423y Introduction to the transit authority, saving many millions of dollars per choice of convergence criteria, visualization and theory of elasticity, I and II year), minimum time robot optimal control allowing interpretation of computed results. Taught in the 3 pts. Lect: 3. Professor Ateshian. one to run assembly lines faster for increased Mechanical Engineering Computer Laboratory with Corequisite: APMA E4200. Analysis of stress productivity. Computational Fluid Dynamics software.

engineering 2011–2012 188 MECE E6614y Advanced topics in robotics MECE E6710x or y Nanofabrication laboratory MECE E8990x and y Special topics in and mechanism synthesis 3 pts. Lect: 3. Not offered in 2011–2012. mechanical engineering 3 pts. Lect: 3. Not offered in 2011–2012. Prerequisite: ELEN E6945 or instructor’s 3 pts. Lect: 3. Instructor to be announced. Prerequisites: APMA E2101, E3101, MECE permission. Laboratory in techniques for Prerequisite: Instructor’s permission. This course E4602 (or COMS W4733). Recommended: MECE fabrication at the nanometer scale. Electron- may be taken for credit more than once. The instruc- E3401 or instructor’s permission. Kinematic beam lithography. Plasma etching and 3D tor from the Mechanical Engineering Department modeling methods for serial, parallel, redundant, nanofabrication. Thin film deposition. Self- and the topics covered in the course will vary from wire-actuated robots and multifingered hands with assembly and “bottom up” nanofabrication. year to year. This course is intended for students discussion of open research problems. Introduction Fabrication of and testing of complete with graduate standing in Mechanical Engineering to screw theory and line geometry tools for nanodevices. A lab fee of $300 is required. and other engineering and applied sciences. kinematics. Applications of homotropy continuation MECE E6720x Nano/microscale thermal Topic for Spring 2012: Small-scale methods and symbolic-numerical methods for direct kinematics of parallel robots and synthesis of transport process mechanical behavior mechanisms. Course uses 3 pts. Lect: 3. Not offered in 2011–2012. 3 pts. Lect: 3. Instructor to be announced. textbook materials as well as a collection of recent Nano- and microscale origins of thermal Prerequisites: ENME E3105 or equivalent; research papers. transport phenomena by molecules, electrons, APMA E4200 or equivalent. Introduction to the phonons, and photons. Quantum mechanics mechanical behavior of small scale components, MECE E6620x or y Applied signal recognition and statistical physics. Density of states. structures and devices. Review of variational and classification Kinetic theory of gases. Boltzmann transport calculus as used to derive governing equations 3 pts. Lect: 3. Not offered in 2011–2012. equation (BTE), classical and quantum size of beam and plate theory. Deformation and Prerequisites: MATH E1210, APMA E3101, effects. Landauer formalism for transport vibration of beams and plates. Stress, deformation, knowledge of a programming language, or via nanostructures. Macroscopic constitutive and substrate curvature in thin films. Fracture, permission of instructor. Applied recognition equations from BTE. Application to electronics delamination, bulging, and classification of signals using a selection cooling, thermoelectric and thermophotovoltaic buckling and of thin films. Equilibrium and of tools borrowed from different disciplines. devices, and energy conversion. stability of surfaces. Small scale mechanical Applications include human biometrics, imaging, characterization including: nanoindentation, thin geophysics, machinery, electronics, networking, MECE E8020x-E8021y Master’s thesis film bulge test, and electron microscopy methods. languages, communications, and finance. 1–3 pts. Members of the faculty. MECE E9000x-E9001y and E9002s Graduate Practical algorithms are covered in signal Interpretive research in graduate areas in generation, modeling, feature extraction, metrics mechanical engineering and engineering science. research and study 1–3 pts. Members of the faculty. for comparison and classification, parameter MECE E8100y Advanced topics in fluid Theoretical or experimental study or research in estimation, supervised, unsupervised and mechanics hierarchical clustering and learning, optimization, graduate areas in mechanical engineering and 3 pts. Lect: 3. Not offered in 2011–2012. engineering science. scaling and alignment, signals as codes emitted Prerequisite: MECE E6100. This course may from natural sources, information, and extremely be taken more than once, since its content has MECE E9500x and y Graduate seminar large-scale search techniques. minimal overlap between consecutive years. 0 pts. Pass/fail only. Instructor to be announced. MECE E6700y Carbon nanotube science and Selected topics from viscous flow, turbulence, All doctoral students are required to complete technology compressible flow, rarefied gas dynamics, successfully four semesters of the mechanical 3 pts. Lect: 3. Professor Hone. computational methods, and dynamical systems engineering seminar MECE E9500. theory, non-Newtonian fluids, etc. Prerequisite: Knowledge of introductory solid MECE E9800x and y Doctoral research state physics (e.g., PHYS G4018, APPH E6081, EEME E8601y Advanced topics in control theory instruction or MSAE E3103) or instructor’s permission. 3 pts. Lect: 3. Not offered in 2011–2012. 3, 6, 9, or 12 pts. Members of the faculty. Basic science of solid state systems. Crystal Prerequisites: EEME E6601 and E4601 or A candidate for the Eng.Sc.D. degree in structure, electronic and phonon band structures instructor’s permission This course may be taken mechanical engineering must register for 12 points of nanotubes. Synthesis of nanotubes and other more than once, since the content changes from of doctoral research instruction. Registration in nanomaterials. Experimental determination year to year, electing different topics from control MECE E9800 may not be used to satisfy the of nanotube structures and techniques for theory such as learning and repetitive control, minimum residence requirement for the degree. nanoscale imaging. Theory and measurement of adaptive control, system identification, Kalman MECE E9900x and y Doctoral dissertation mechanical, thermal, and electronic properties of filtering, etc. nanotubes and nanomaterials. Nanofabrication and 0 pts. Members of the faculty. nanoelectronic devices. Applications of nanotubes. A candidate for the doctorate may be required to register for this course every term after his/her course work has been completed and until the dissertation has been accepted.

engineering 2011–2012 Undergraduate Minors 190 undergraduate minors

ndergraduate minors are Minor in Applied 4. APPH E3300: Applied electromagnetism (3) designed to allow engineering Mathematics 5. MSAE E3111: Thermodynamics, kinetic theory, U and applied science students Prospective students should consult and statistical mechanics (3) to study, to a limited extent, a discipline the first- and second-year requirements 6. Two of the following courses other than their major. Besides for applied mathematics majors to APPH E4010: Intro to nuclear science (3) engineering minors offered by Columbia ensure that prerequisites for the applied APPH E4100: Quantum physics of matter (3) Engineering departments, liberal arts mathematics minor are satisfied in the APPH E4110: Modern optics (3) minors are available. first two years. APPH E4112: Laser physics (3) A minor requires at least 15 points Course work counting toward the APPH E4300: Applied electrodynamics (3) APPH E4301: Intro to plasma physics (3) of credit, and no more than one course applied mathematics minor may not can be taken outside of Columbia include advanced placement credits. or met through AP or IB credit. This Any substitutions for the courses listed Minor in Architecture includes courses taken through study below require the approval of the applied 1. Studio: One of the following courses abroad. In Engineering departments mathematics program adviser. ARCH V1020: Intro to architectural design and with more than one major program, visual culture (3) 1. APMA E3101: Linear algebra (3) ARCH V3101: Abstraction (4) a minor in the second program may or MATH V2010: Linear algebra (3) be permitted, if approved by the ARCH V3103: Perception (4) department. 2. APMA E3102: Partial differential equations (3) 2–4. History/theory courses (see Note below) or MATH V3028: Partial differential equations (3) No substitutions or changes of any 5. Elective: must be either an approved second kind from the approved minors are 3–5. Three of the following courses: design studio or an additional history/theory permitted (see lists below). No appeal APMA E4300: Intro to numerical methods (3) course APMA E4204: Func of complex variable (3) for changes will be granted. Please APMA E4101: Intro to dynamical systems (3) Note: A list of the approved history/theory note that the same courses may not be MATH V2500: Analysis and optimization (3) courses is available at the departmental used to satisfy the requirements of more SIEO W4105: Intro to probablity and statistics (3) office each semester. than one minor. No courses taken for STAT W4107: Statistical inference (3) pass/fail may be counted for a minor. or any other course designated APMA, MATH, Minor in Art History Minimum GPA for the minor is 2.0. STAT, IEOR, or COMS that is approved by the Departments outside the Engineering applied mathematics program adviser 1–7. Seven courses in art history, covering School have no responsibility for four of the following areas: (a) ancient nonengineering minors offered by Minor in Applied Physics Mediterranean, (b) medieval Europe, Engineering. Prospective students should consult the (c) Renaissance and baroque, (d) 18th, For a student to receive credit for first- and second-year requirements for 19th, and 20th century, and (e) non- a course taken while studying abroad, applied physics majors to ensure that Western the department offering the minor must prerequisites for the applied physics approve the course in writing, ahead of minor are satisfied in the first two years. Minor in Biomedical the student’s study abroad. Course work counting toward the Engineering Students must expect a course load applied physics minor may not include The Biomedical Engineering program that is heavier than usual. In addition, advanced placement credits. offers a minor in one of three tracks: (I) unforeseen course scheduling changes, 1. APPH E4901: Problems in applied physics (1) cellular engineering, (II) biomechanics, problems, and conflicts may occur. The and (III) biosignals and biomedical 2. PHYS W3003: Mechanics (3) School cannot guarantee a satisfactory imaging. Students who wish to get a completion of the minor. 3. APPH E3100: Intro to quantum mechanics (3) minor in biomedical engineering should

engineering 2011–2012 take the core BME requirements, as well or MSAE E3111: Thermodynamics, kinetic 1. COMS W1004: Intro to computer science and 191 as select courses from one of the three theory, and statistical mechanics (3) programming in Java (3) or MECE E3301: Thermodynamics (3) tracks, described below. Participation in 2. COMS W1007: Obj-oriented prog and design (3) the minor is subject to the approval of 3. CHEN E3110: Transport phenomena, I (3) 3. COMS W3133: Data structures in C (3) or EAEE E4900: Applied transport and the major program adviser. or COMS W3134: Data structures in Java (3) chemical rate phenomena (3) or COMS W3137: Data structures and Core BME Requirements or MECE E3100: Intro to mech of fluids (3) algorithms (4) 1. BIOL C2005: Intro biology, I (4) or ENME E3161: Fluid mechanics (4) 4. COMS W3157: Advanced programming (4) 2. BMEN E4001: Quantitative physiology, I (3) 4. CHEN E4230: Reaction kinetics and or BMEN E4002: Quantitative physiology, II (3) reactor design (3) 5. COMS W3203: Discrete mathematics (3) I. Cell and Tissue Engineering Track 5–6. Two of the following courses: 6. COMS W3261: Comp science theory (3) Any 3000-level or higher BMCH, CHEN, CHAP, 7. CSEE W3827: Fund of computer systems (3) 3. CHEE E3010: Prin of chemical engineering or CHEE course or a 4000-level COMS technical elective thermodynamics (4) APMA E3101: Linear algebra (3) or BMEN E4210: Thermodyn of bio systems (4) APMA E3102: Partial differential equations (3) 4. BMEN E4501: Tissue engineering, I (3) BMEN E3320: Fluid biomechanics (3) Minor in Dance BMEN E4001: Quantitative physiology, I (3) The dance minor consists of five 5. BMEN E4502: Tissue engineering, II (3) BMEN E4002: Quantitative physiology, II (3) 3-point courses. Please note that no ELEN E3201: Circuit analysis (3.5) 6. One of the following courses: performance/choreography courses ELEN E3331: Electronic circuits (3) BMEN E3320: Fluid biomechanics (3) below count toward the nontech BMEN E4570: Sci and eng of body fluids (3) SIEO W3600: Intro to probability and statistics (4) requirement for Engineering students. ECBM E3060: Intro to genomic info (3) IEOR W4105: Probability (3) CHEN E3110: Transport phenomena, I (3) IEOR W4106: Stochastic models (3) 1–2. History/criticism: Two of the following: CHEN E4700: Prin of genomic technologies (3) MSAE E3103: Elements of mat sci (3) DNCE BC2565: World dance history MSAE E3103: Elements of mat sci (3) MSAE E3142: Ceramics and polymers (3) DNCE BC2570: Dance in New York City DNCE BC2575: Choreography for the American II. Biomechanics Track Minor in Civil Engineering musical 3. BMEN E4300: Solid biomechanics (3) DNCE BC3000: From the page to the 1. CIEN E3121: Structural analysis (3) dance stage 4. BMEN E3320: Fluid biomechanics (3) or ENME E3161: Fluid mechanics (4) DNCE BC3001: Western theatrical dance from 5–6. Two from the following course groups: or MECE E3100: Intro to mech of fluids (3) the Renaissance to the 1960s ENME E3113: Mechanics of solids (3) 2. ENME E3105: Mechanics (4) DNCE BC3200: Dance in film ENME E3161: Fluid mechanics (4) DNCE BC3567: Dance in Asia or MECE E3301: Thermodynamics (3) 3. ENME E3113: Mechanics of solids (3) DNCE BC3570: Latin American and Caribbean or MSAE E3111: Thermodynamics, kinetic 4–6. Electives: Three of the following courses: dance theory, and statistical mechanics (3) CIEN E1201: Design of buildings, bridges, and DNCE BC3574: Seminar on contemporary spacecraft (3) choreographers and their works III. biosignals and Biomedical Imaging ENME E3161: Fluid mechanics (4) DNCE BC3576: Dance criticism Track ENME E3114: Exp mechanics of materials (4) DNCE BC3577: Performing the political MECE E3414: Adv strength of materials (3) DNCE BC3578: Traditions of African-American 3. BMEN E4894: Biomedical imaging (3) ENME E4332: Finite element analysis, I (3) dance 4–5. Two of the following courses: CIEN E3125: Structural design (3) 3–4. Performance/choreography: Two of the BMEN E4430: Prin of magnetic resonance CIEN E4241: Geotech eng fundamentals (3) following: imaging (3) CIEE E3250: Hydrosystems engineering (3) DNCE BC2563: Dance composition: form BMEE E4400: Wavelet applications in CIEE E4163: Environ eng: wastewater (3) DNCE BC2564: Dance composition: content biomedical image and signal processing (3) CIEN E3129: Project mgmt for construction (3) DNCE BC2567: Music for dance BMEN E4898: Biophototonics (3) CIEN E4131: Prin of construction tech (3) DNCE BC2580: Tap as an American art form BMEN E4410: Ultrasound in diagnostic Note: At least three of the courses must DNCE BC3565: Composition: collaboration and imaging (3) be courses that are not required in the the creative process BMEN E4420: Biomedical signal processing and DNCE BC3590: Rehearsal and performance signal modeling (3) student’s major. in dance 6. One of the following courses: Minor in Computer Science 5. One elective ELEN E3801: Signals and systems (3.5) ELEN E4810: Digital signal processing (3) Students who pass the Computer ELEN E4830: Digital image processing (3) Science Advanced Placement Exam, Minor in Earth and either A or AB, with a 4 or 5 will receive Environmental Minor in Chemical 3 points and exemption from COMS Engineering Engineering W1004. An additional elective is to 1–3. Three of the following courses: Of the six courses required, at least be recommended but not required. EAEE E3103: Energy, minerals, and mat syst (3) three must have the CHEN, CHEE, or Participation in the minor is subject to the EAEE E3255: Environmental control and CHAP designator: approval of the major program adviser. pollution reduction systems (3) For further information, please see the EAEE E4001: Industrial ecology of Earth res (3) 1. CHEN E3100: Mat and energy balances (4) QuickGuide at www.cs.columbia.edu/ EAEE E4003: Intro to aquatic chemistry (3) EAEE E4004: Physical processing and recovery 2. CHEE E3010: Prin of chemical engineering education/undergrad/seasguide. thermodynamics (3) of solids (3)

engineering 2011–2012 192 EAEE E4006: Field methods for environ eng (3) ECON W2257: Global economy requirement, please consult the non-tech EAEE E4009: GIS for resource, environment, ECON W4280: Corporate finance elective section of this bulletin for further and infrastructure management (3) ECON V3025: Financial economics details. EAEE E4150: Air pollution prevention and ECON V3265: Econ of money and banking • Students with AP credit for economics control (3) ECON W4020: Econ of uncertainty and info and an exemption for W1105 may use EAEE E4160: Solids and hazardous waste ECON W4080: Globalization, incomes and the credit toward the minor. management (3) inequality • Transfer or study abroad credits may not EAEE E4190: Photovoltaic systems eng and ECON W4211: Advanced microeconomics be applied to fulfill the requirements of sustainability (3) ECON W4213: Advanced macroeconomics the economics minor. EAEE E4200: Prod of inorganic materials (3) ECON W4228: Urban economics EAEE E4257: Environ data analysis and ECON G4235: Historical foundations of modern Minor in Electrical modeling (3) economics Engineering EAEE E4361: Econ of Earth res industries (3) ECON W4251: Industrial organization EAEE E4560: Particle technology (3) ECON G4301: Economic growth and develop 1. ELEN E1201: Intro to electrical eng (3.5) ECON W4321: Economic development 4–6. Three of the following courses: (May be replaced by a similar course or roughly ECON W4329: Economics of sustainable develop CHEE E4252: Intro to surface and colloid chem equivalent experience) ECON W4345: World economic problems CHEE E3010: Prin of chemical engineering ECON W4370: Political economy 2. ELEN E3201: Circuit analysis (3.5) thermodynamics (3) ECON W4400: Labor economics CHEE E3110: Transport phenomena, I (3) 3. CSEE W3827: Fund of computer systems (3) ECON W4412: Advanced econometrics CHEN E4410: Environmental control technology (3) ECON W4415: Game theory 4. ELEN E3081 and ELEN E3082: CIEE E3250: Hydrosystems engineering (3) ECON W4438: Economics of race in the US Electrical engineering labs (2) CIEE E4163: Environ eng: wastewater (3) ECON W4457: Industrial organization of art, CIEE E4252: Environmental engineering (3) 5. ELEN E3801: Signals and systems (3.5) entertainment and communications CIEE E4257: Groundwater contaminant ECON W4465: Public economics 6. ELEN E3106: Solid-state dev and mat (3.5) transport and remediation (3) ECON W4480: Gender and applied economics or ELEN E3401: Electromagnetics (4) CIEE E4260: Urban ecology studios (3) ECON W4490: Economics of the Internet CIEN E3141: Soil mechanics (3) Note: Not available to computer ECON W4500: International trade CIEN E4250: Waste contain design and prac (3) engineering majors ECON W4505: Int’l monetary theory and policy EAEE E4190: Photovoltaic systems eng (3) ECON W4615: Law and economics ECIA W4100: Mgmt and dev of water systems (3) ECON W4625: Economics of the environment Minor in Engineering MECE E4211: Energy: sources and conv (3) ECON W4750: Globalization and its risks SIEO W3600: Intro to probability and statistics (4) Mechanics Note: Electives may be taken only after 1. ENME E3105: Mechanics (4) Minor in East Asian Studies the completion of both W3211 and W3213, with the exception of W2257, 2. ENME E3113: Mechanics of solids (3) 1–5. Any two of the survey courses on which may be taken after completion of Chinese, Japanese, Korean, or Tibetan 3. ENME E3161: Fluid mechanics (4) W1105. Some of the elective courses civilization (ASCE V2359, V2361, V2363, or MECE E3100: Intro to mech of fluids (3) listed above have additional prerequisites. V2365), plus three elective courses 4–6. Electives: Two of the following dealing with East Asia. The elective Courses may be taken only after the completion of all prerequisites. Please ENME E3106: Dynamics and vibrations (3) courses may be taken in departments ENME E3114: Exp mechanics of materials (4) outside of East Asian Languages and see the Columbia College bulletin for or MECE E3414: Adv strength of materials (3) Cultures. The minor does not include course descriptions and complete lists of CIEN E3121: Structural analysis (3) a language requirement. However, one prerequisites. ENME E4202: Advanced mechanics (3) semester of an East Asian language ENME E4113: Advanced mechanics of solids (3) class may be used to fulfill one of the 7. Statistics: One of the following courses ENME E4114: Mech of fracture and fatigue (3) three electives, as long as at least two (or sequence of courses): ENME E4214: Theory of plates and shells (3) semesters of that language have been STAT W1211: Intro to statistics (with calculus) ENME E4215: Theory of vibrations (3) taken. Placement exams may not be SIEO W3600: Intro to probability and statistics MECE E3301: Thermodynamics (3) used in place of these courses. IEOR W3658: Probability and STAT W3659 or W4107: Stat inference Note: At least three of the courses must Minor in Economics SIEO W4150: Intro to probability and statistics be courses that are not required in the Notes: student’s major. 1. ECON W1105: Principles of economics • T he statistics course must be finished 2. ECON W3211: Intermediate microeconomics before taking W3412, and it is Minor in English and recommended that students take W3412 3. ECON W3213: Intermediate macroeconomics Comparative Literature in the semester following the statistics 4. ECON W3412: Introduction to econometrics course. 1–5. Any five courses in the English • Some courses done as part of the Department with no distribution Note: W1105 is a prerequisite for W3211, economics minor nay count towards requirement. No speech courses, only one W3213, and W3412. Students must have fulfilling the School’s nontechnical writing course as above and excluding completed Calculus I before taking W3213, requirements. However, other courses, ENGL C1010, may be taken; total 15 points. Calculus III before taking W3211, and one such as W3412: Intro to econometrics, of the introductory statistics courses (see may not be applied toward satisfaction list) before taking W3412. of the nontechnical course requirements. To determine which economic class can 5–6. Electives: Two of the following courses: count towards the non-tech elective

engineering 2011–2012 MINOR IN Entrepreneurship Minor in Hispanic Studies CHEN E4620: Polymers and soft materials (3) 193 and Innovation CHEN E4630: Polymer laboratory (3) 1. SPAN W3300: Adv language through content (3) CHEM C3443-C3444: Organic chemistry (3.5) Minimum: 15 points 2. SPAN W3330: Intro to the study of Hispanic ELEN E4411: Fundamentals of photonics (3) 1–2. Required courses: cultures (3) ELEN E4301: Intro to semiconductor devices (3) IEOR E2261: Intro to acct and finance (3) ELEN E4944: Prin of dev microfabrication (3) and IEOR E4998: Managing technological 3-4. SPAN W3349 and W3350: Hispanic cultures, ENME E4113: Adv mechanics of solids (3) innovation and entrepreneurship (3) I and II (3, 3) ENME E4114: Mech of fracture and fatigue (3) MECE E4608: Manufacturing processes (3) 3–5. Electives: Three of the following courses: 5. One additional 3000-level elective course MECE E4701: Introductory biomechanics (3) BMEN E3998: Projects in biomedical eng (3) in the Department of Latin American and BUSI W3021: Marketing management (3) Iberian Cultures CHEN E4020: Protection of industrial and Note: Please see the director of Minor in Mechanical intellectual property (3) undergraduate studies in the Department Engineering CIEN E4136: Global entrepreneurship in civil of Latin American and Iberian Cultures for 1–4. Four of the following courses: engineering (3) more information and to declare the minor. MECE E3100: Intro to mechanics of fluids (3) COMS W4444: Program and problem solving (3) or ENME E3161: Fluid mechanics (4) ECON E4280: Corporate finance (3) or CHEN E3110: Transport phenomena, I (3) IEOR E4003: Industrial economics (3) Minor in History or EAEE E4900: App transport and chemical IEOR E4308: Industrial budgeting and finance 1–5. Minimum 15 points in the History rate phenomena (3) control (3) Department with no distribution or seminar ENME E3105: Mechanics (4) IEOR E4403: Adv eng and corporate econ (3) requirements. Transfer or study-abroad MECE E3301: Thermodynamics (3) IEOR E4510: Project management (3) credits may not be applied. or CHEE E3010: Principles of chemical IEOR E4550: Entrepreneurial business creation engineering thermodynamics (3) for engineers (3) or MSAE E3111: Thermodynamics, kinetic IEOR E4705: Studies in operations research (3) Minor in Industrial theory, and statistical mechanics (3) IEME E4310: The manufacturing enterprise (3) Engineering ENME E3113: Mechanics of solids (3) SCNC W3010: Science, tech, and society (3) MECE E3408: Comp graphics and design (3) or URBS V3310: Sci/tech in urban environ (3) 1. SIEO W3600: Intro to probability and statistics (4) MECE E3311: Heat transfer (3) 2. IEOR E3608: Intro to math programming (4) MECE E4608: Manufacturing processes (3) Minor in French 3. IEOR E3402: Production inventory planning and MECE E3409: Machine design (3) 1–2. FREN W3333: Major literary works to 1800 (3) control (3) EEME E3601: Classical control systems (3) and W3334: Major literary works since 1800 (3) 4. IEOR E4003: Industrial economics (3) 5–6. Electives: Two additional mechanical engineering courses from either the above 3–5. Three additional courses in French 5–6. Electives: Two IEOR courses of interest list or the following (not all courses in this beyond satisfaction of the language and approved by a faculty adviser requirement list are given every year): Note: In addition to the required courses, MECE E3401: Mechanics of machines (3) students majoring in operations research MECE E4058: Mechatronics and embedded Minor in French and and its concentrations (EMS or FE) microcomputer control (3) Francophone Studies minoring in industrial engineering must take MECE E4100: Mechanics of fluids (3) Required: 15 points beyond second-year French three industrial engineering courses that MECE E4211: Energy: sources and conversion (3) are not used to satisfy the requirements of MECE E4212: Microelectromechanical sys (3) 1–2. FREN W3420 and W3421: Intro to French MECE E4302: Advanced thermodynamics (3) and francophone studies, I and II (3, 3) their major. MECE E4404: Tribology (3) 3–5. Three additional courses in French MECE E4501: Geometrical modeling (3) beyond satisfaction of the language Minor in Materials Science MECE E4502: Comp geometry for CAD/CAM (3) requirement and Engineering EEME E4601: Digital control systems (3) MECE E4602: Intro to robotics (3) 1. MSAE E3103: Elements of mat sci (3) Minor in German MECE E4604: Product design for manufact (3) 2–3. Two of the following courses: MECE E4609: Computer-aided manufacturing (3) Required: 15 points beyond second-year German MSAE E3111: Thermodynamics, kinetic theory, MECE E4610: Adv manufacturing processes (3) 1. GERM V3001 or V3002: Adv German, I or II (3) and statistical mechanics (3) MSAE E3141: Metals and semiconductors (3) Minor in Middle Eastern, 2. GERM W3333: Intro to German literature (3) MSAE E3142: Ceramics and polymers (3) South Asian, and African 3. One of the period survey courses in MSAE E4090: Nanotechnology (3) German literature and culture, GERM MSAE E4101: Struc analysis of materials (3) Studies W3442, W3443, W3444, W3445 MSAE E4206: Electronic and magnetic 1–5. Five courses, to be chosen with the approval properties of solids (3) 4–5. Two courses taken from any 3000/4000- of the MESAAS Director of Undergraduate MSAE E4215: Mech behavior of materials (3) level German or CompLit-German courses MSAE E4250: Ceramics and composites (3) Studies; no elementary or intermediate taught in German or English language courses may be counted. 4–6. Three of the following courses Minor in Greek or Latin (other materials-related courses may be acceptable): Minor in Music 1–4. A minimum of 13 points in the chosen APPH E4100: Quantum physics of matter (3) 1. MUSI V2318-V2319: Diatonic harmony, I and II (3, 3) language at the 1200 level or higher CHEE E4050: Industrial electrochemistry (3) CHEE E4252: Intro to surface and colloid chem (3) 2. MUSI V1312-V1313: Intro ear training (1) 5. 3 points in ancient history of the CHEE E4530: Corrosion of metals (3) appropriate civilization 3. MUSI V2314: Ear training, I (1) engineering 2011–2012 194 4. One of the following courses: Minor in Psychology MINOR IN SUSTAINABLE MUSI V3128: History of Western music, I (3) ENGINEERING MUSI V3129: History of Western music, II (3) Minimum: 15 points Total of six courses from the following 5–6. Any two electives at the 3000 or 4000 1. PSYC W1001: The science of psychology (3) lists required with no substitutions level. See also the Engineering-approved 2–5. Any four courses from, at a minimum, two allowed: nontechnical electives in music (page 12). of the three groups below: 1–4. Four of the following courses: Notes: I. PERCEPTION AND COGNITION EAEE E1101: Better planet by design • Students must successfully place out of Courses numbered in the 2200s, 3200s, or EAEE E2002: Alternative energy sources MUSI V1002: Fundamentals of Western 4200s. Also PSYC W1420, W1480, or W1490 music (3.0 points). CIEE/EAEE 3260: Eng for developing comm • Steps 4 and 5 must be completed II. PSYCHOBIOLOGY AND NEUROSCIENCE EAEE E3901: Environmental microbiology to fulfill the nontechnical elective PSYC W1010: Mind, brain, and behavior (3) EAEE E4001: Industrial ecology requirement for graduation. Courses numbered in the 2400s, 3400s, or EAEE W4100: Mgmt and dev of water systems • Students are strongly encouraged to 4400s; also PSYC W1440 APPH E4130: Physics of solar energy EAEE E4190: Photovoltaic systems eng and take HUMA W1123: Masterpieces of III. SOCIAL, PERSONALITY, AND ABNORMAL sustainability Western music (3.0 points) from the list Courses numbered in the 2600s, 3600s, or MECE E4211: Energy sources and conversion of nontechnical electives. 4600s; also PSYC W1450 or W1455 CIEE E4260: Urban ecology studio MECE E4312: Solar thermal engineering Minor in Operations Minor in Religion MECE E4314: Dynamics of green buildings Research EESC W4404: Regional climate and climate 1–5. Five courses (total 15 points), one of impacts 1. IEOR E3106: Stochastic models (3) which must be at the 2000 level 5. One of the following courses: 2. SIEO W3600: Intro to probability and statistics (4) ECON W2257: Global economy Minor in Sociology 3. IEOR E3608: Intro to math programming (4) PLAN 4151: Found of urban economic analysis PLAN 4304: Intro to housing 1. SOCI W1000: The social world (3) 4. IEOR E4404: Simulation (3) ECON 4321: Economic development 5–6. Electives: Two IEOR courses of interest 2. SOCI W2200: Evaluation of evidence (3) PLAN 4501: Local econ development planning Econ org and develop of China and approved by a faculty adviser. IEOR 3. SOCI W3000: Social theory (3) ECON G4527: E3402: Production-inventory planning and PLAN 4540: Interdisciplinary planning for health control 3.0 points is strongly recommended. 4–5. Any two 2000-, 3000-, or 4000-level PLAN 4579: Environmental planning courses offered by the Department of PLAN 4609: Intro to international planning Note: In addition to the required courses, Sociology; total 6 points ECON W4625: Economics of the environment students majoring in industrial engineering must take three operations research 6. One of the following courses: courses that are not used to satisfy the Minor in Statistics SOCI V2230: Food and the social order SCNC W3010: Science, technology, and society requirements of their major. 1. STAT W1001: Intro to statistical reason (3) SOCI W3235: Social movements or W1111: Intro to statistics (w/o calculus) (3) ANTH V3950: Anthropology of consumption or W1211: Intro to statistics (w/calculus) (3) Minor in Philosophy SOCI W3960: Law, science, and society 1–5. Any five courses in the Philosophy 2. STAT W2024: App linear regression analysis (3) INAF U4763: Policy analysis of development (seniors only) Department with no distribution 3. STAT W2025: App statistical methods (3) requirement; total 15 points. See also the list of exceptions under Elective 4. STAT W2026: Stat appl and case studies (3) Nontechnical Courses. 5. STAT W3026: Applied data mining (3) Note: Please be aware that some 6. STAT W3997: Independent research philosophy courses may not count as or any Statistics Department offering numbered nontechnical electives. 4201 or above.

Notes: Minor in Political Science • The curriculum is designed for students 1–2. Two of the following courses: seeking practical training in applied POLS W1201: American govt and politics (3) statistics; students seeking a foundation POLS V1501: Comparative politics (3) for advanced work in probabilty and POLS V1601: International politics (3) statistics should consider substituting W3105, W3107, W3315, and W4606. 3–5. Any three courses in the Political Science • Students may, with permission of the Department with no distribution requirement; Director of Undergraduate Studies total 9 points in Statistics, substitute for courses. Students may count up to two courses toward both the Statistics minor and another Engineering major.

engineering 2011–2012 Interdisciplinary Courses and Courses in Other Divisions of the University 196 Interdisciplinary Engineering Courses

f the following courses, cash-flow (DCF) project evaluation methods; social needs that elicited new technologies and some may be requirements deterministic and probabilistic measures of risk; the consequences of their adoption are examined. for degree programs, and capital budgeting. Throughout the course, relevant scientific and O engineering principles are explained as needed. others may be taken as electives. See SCNC W3010x and y Science, technology These include, among others, the concept and your departmental program of study and society effective use of spectrum, multiplexing to improve or consult with an adviser for more 3 pts. Lect: 3. Professor McGourty. capacity, digital coding, and networking principles. information. Prerequisite: Students must have declared their There are no prerequisites, and no prior scientific concentration/major. By investigating the scientific or engineering knowledge is required. Engineering ENGI E1102x and y Design fundamentals and technical evolution and subsequent diffusion of students may not count this course as a technical using advanced computer technologies contemporary technological innovations, students elective. 4 pts. Lect: 4. Professors Stolfi and Vallancourt. learn how science and technology fit into the Core requirement for all entering Engineering bigger picture; i.e., how technologies technically CHEN E4020x Protection of industrial and students. Students attend design lectures and develop from concept to diffusion into society, how intellectual property work on “real engineering” projects with socially they work, and how they are bidirectionally related 3 pts. Lect: 3. Professor Pearlman. responsible themes. Students learn how math and to social forces, cultural values, economic trends, To expose engineers, scientists, and technology science integrate into design solutions. Aligned environmental factors, and political influences. An managers to areas of the law they are most likely with the technical components of design, students essential part of the course work is participation in to be in contact with during their career. Principles develop collaboration, communication, problem- a community-based learning project, working with are illustrated with various case studies together solving, and project management skills. Lab fee: local not-for-profit organizations. with active student participation. $325. URBS V3310x Science and technology in IEOR E4998x and y Managing technological SCNC E1820y Topics in community urban environments innovation and entrepreneurship engagement 3 pts. Lect: 3. Professor McGourty. 3 pts. Lect: 3. Professor McGourty. 1 pt. Professors McGourty and Montás. Prerequisite: Students must have declared Focus on the management and consequences of Prerequisite: instructor approval. This colloquium their concentration/major. Examines the role of technology-based innovation. Explores how new prepares students for community-based science and technology in urban settings, using industries are created, how existing industries internships. With a focus on problem-solving, it examples from modern cities. Explores how can be transformed by new technologies, the examines the theoretical paradigms and principles technology shapes towns and cities, and how linkages between technological development underlying community engagement efforts and urban environments, including politics, economics, and the creation of wealth, and the management provides students with some of the practical skills culture, and the natural environment, have challenges of pursuing strategic innovation. necessary to make these efforts successful. The influenced the development, acceptance, and specific context and challenges posed by the city application of technology. An essential part of the of New York are addressed through readings and course work is participation in a community-based discussions with local community leaders. Class learning project, working with local not-for-profit meets biweekly. Enrollment limited to 15 students. organizations. IEOR E2261x Introduction to accounting EEHS E3900y History of telecommunications: and finance from the telegraph to the internet 3 pts. Lect: 3. Professor Webster. 3 pts. Lect: 3. Prerequisite: ECON W1105. For undergraduates Historical development of telecommunications from only. This course examines the fundamental the telegraphy of the mid-1800s to the Internet concepts of financial accounting and finance, from at present. Included are the technologies of the perspective of both managers and investors. telephony, radio, and computer communications. Key topics covered include: principles of accrual The coverage includes both the technologies accounting; recognizing and recording accounting themselves and the historical events that shaped, transactions; preparation and analysis of financial and in turn were shaped by, the technologies. statements; ratio analysis; pro-forma projections; The historical development, both the general time value of money (present values, future values context and the particular events concerning and interest/discount rates); inflation; discounted- communications, is presented chronologically. The

engineering 2011–2012 Courses in Other Divisions of the University 197

his listing of courses (at BIOC C3501 Biochemistry: structure and Chemistry left) has been selected with metabolism Placement Exam specific engineering program 4 pts. Professors Stockwell and Tong. T Prerequisites: BIOL W2001 or C2005 and one requirements in mind. For information All students must take the placement year of organic chemistry. Lecture and recitation. on these courses and additional courses exam during Orientation week. The Students wishing to cover the full range of results of the placement exam are offered by these departments, please modern biochemistry should take both BIOC used to advise students which track to consult the bulletins of Columbia C3501 and C3512. C3501 covers subject matters pursue. College, the School of Continuing in modern biochemistry, including chemical Education, the School of General biology and structural biology, discussing the Studies, and the Graduate School of structure and function of both proteins and small Courses of Instruction molecules in biological systems. Proteins are the Arts and Sciences. Pre-engineering students should primary class of biological macromolecules and refer to the First Year–Sophomore serve to carry out most cellular functions. Small Program to determine the chemistry Biological Sciences organic molecules function in energy production and creating building blocks for the components requirements for admission to particular BIOL C2005 Introductory biology, I: of cells and can also be used to perturb the Junior-Senior Programs. Special biochemistry, genetics, and molecular biology functions of proteins directly. The first half of the attention should be given to the 4 pts. Professors Chasin and Mowshowitz. course covers protein structure, enzyme kinetics requirements for admission to chemical Prerequisite: one year of college chemistry, or a and enzyme mechanism. The second half of the engineering, biomedical engineering, strong high school chemistry background. Lecture course explores how small molecules are used materials science and metallurgical and recitation. Recommended as the introductory endogenously by living systems in metabolic engineering, and other related fields. biology course for biology and related majors, and and catabolic pathways; this part of the course for premedical students. Fundamental principles focuses on mechanistic organic chemistry of biochemistry, molecular biology, and genetics. involved in metabolic pathways. Laboratory Fee Website: www.columbia.edu/cu/biology/courses/ The laboratory fee covers the cost of c2005/ nonreturnable items, chemicals, and Business BIOL C2006 Introductory biology, II: cell reasonable breakage. In addition, biology, development, and physiology BUSI W3021x or y Marketing management students may be charged for lab 4 pts. Professor Mowshowitz. 3 pts. Lect: 3. handouts and excessive breakage, for Prerequisite: EEEB W2001 or BIOL C2005, or Designed to provide students with an cleaning of equipment returned dirty, the instructor’s permission. Lecture and recitation. understanding of the fundamental marketing and for checking out late. Recommended second term of biology for majors concepts and their application by business in biology and related majors, and for premedical and non-business organizations. The goal CHEM C1403x-C1404y General chemistry students. Cellular biology and development; is to expose students to these concepts as 3.5 pts. Members of the faculty. physiology of cells and organisms. Website: www. they are used in a wide variety of settings, Prerequisites: for C1403: concurrent registration columbia.edu/cu/biology/courses/c2006/ including consumer goods firms, manufacturing in MATH V1101; for C1404: CHEM C1403 or W1403. Preparation equivalent to one year of high BIOL W2501x or y Contemporary biology and service industries, and small and large school chemistry is assumed. Students lacking laboratory businesses. The course gives an overview such preparation should plan independent study of 3 pts. Professor Hazen. of marketing strategy issues, elements of a chemistry over the summer or take CHEM F0001 Strongly recommended prerequisite or corequisite: market (company, customers, and competition), before taking C1403. Topics include stoichiometry, BIOL C2005 or F2401. Enrollment limited to 24 as well as the fundamental elements of the states of matter, chemical equilibria, acids and students per section. Attendance at the first class marketing mix (product, price, placement/ bases, chemical thermodynamics, nuclear is mandatory. Fee $150. Topics covered include distribution, and promotion). properties, electronic structures of atoms, periodic both mammalian anatomy and experiments in a properties, chemical bonding, molecular geometry, variety of biological fields, with an emphasis on introduction to organic and biological chemistry, data analysis. solid state and materials science, polymer science

engineering 2011–2012 198 and macromolecular structures, chemical kinetics, chemistry of selected main group elements, CHEM W3543x and y Organic chemistry coordination chemistry, and electrochemistry. transition metal chemistry, metal clusters, laboratory Although C1403 and C1404 are separate metal carbonyls, and organometallic chemistry. 3 pts. Lab: 3. Professors Ghurbanyan, Ng, and courses, students are expected to take both terms Recitation section required. Schacherer. sequentially. The order of presentation of topics may Prerequisite: CHEM C1500 or W1500. Corequisite: CHEM C3079x-C3080y Physical chemistry, differ from the order presented here, and from year CHEM C3443 or W3343. Fee: $125. Students I and II to year. Recitation section required. planning to take a full year of laboratory should 4 pts. Professors Cacciuto and Reichman. enroll in CHEM C3543 and C3546. Techniques of CHEM W1500x or y General chemistry Prerequisites: CHEM C1403 and C1404, or C1604, experimental organic chemistry, with emphasis on laboratory or C3045 and C3046; PHYS V1201-V1202 is understanding fundamental principles underlying 3 pts. Lab: 3. Professors Hansen and Ulichny. acceptable, PHYS C1401-C1402 is recommended, the experiments in methodology of solving Corequisite: CHEM C1403 or W1403. Fee: $140. or the equivalent; and MATH V1101-V1102 or laboratory problems involving organic molecules. An introduction to basic techniques of modern V1207-V1208. Recommended corequisite: CHEM experimental chemistry, including quantitative C3085-C3086. Elementary but comprehensive CHEM W3545x Organic chemistry laboratory procedures and chemical analysis. treatment of the fundamental laws governing the 3 pts. Lab: 3. Professor Ng. behavior of individual atoms and molecules and Prerequisites: CHEM C3045 and C3046 and CHEM C1604x Second semester general collections of them. C3079: The thermodynamics C2507. Fee: $125. The course covers the same chemistry of chemical systems at equilibrium and the material as CHEM C3543, but is intended for 3.5 pts. Professor Flynn. chemical kinetics of nonequilibrium systems. those students who have taken Intensive Organic Prerequisite: A grade of “B” or better in CHEM C3080: The quantum mechanics of atoms and Chemistry for First-Year Students, CHEM C1403 or W1403 or acceptable performance on molecules, the quantum statistical mechanics of C3045-C3046. the Department placement exam. Corequisite: chemical systems, and the connection of statistical Calculus II. Topics include gases (kinetic mechanics to thermodynamics. Recitation section CHEM W3546y Advanced organic chemistry theory of gases); binary collision model for required. laboratory chemical reactions; chemical kinetics; acid-base 3 pts. Lab: 3. Professor Ng. equilibria; thermochemistry (Thermodynamics CHEM C3085x-C3086y Physical and analytical Prerequisite: CHEM C3543 or W3543 or C3545. I); spontaneous processes (Thermodynamics chemistry laboratory Corequisite: CHEM C3444 or W3444. Fee: $125. II); chemical bonding in polyatomic molecules. 4 pts. Lab: 4. Professor Avila. A project laboratory with emphasis on complex Recitation section required. Prerequisite: CHEM C3085 is prerequisite for synthesis and advanced techniques including C3086. Corequisites: CHEM C3079 for CHEM qualitative organic analysis and instrumentation. CHEM W2507y Intensive general chemistry C3085 and C3080 for C3080. Fee: $125 per laboratory term. Techniques of experimental physical 3 pts. Lab: 3. Professor Avila. chemistry and instrumental analysis, including Earth and Environmental Prerequisite: CHEM C1604 or C3045. Fee: $140. infrared and ultraviolet spectrophotometry, Sciences An introduction to basic techniques and practices magnetic resonance, electroanalytical methods, Undergraduates in the four-year course of modern experimental chemistry, including calorimetry, reaction kinetics, hydrodynamic qualitative procedures and chemical analysis. This of study in the School of Engineering methods, and applications of digital computers to and Applied Science may take courses course differs from CHEM C1500 in its emphasis the analysis of experimental data. on instrumentation and methods. numbered up to 4999 but may enter CHEM C3098x and y Supervised independent courses of higher numbers only if CHEM C3045x-C3046y Intensive organic research chemistry for first-year students (lecture) (1) the course is expressly included in 4 pts. Lab: 4. Professor Valentini. the prescribed curriculum or 3.5 pts. Professors Breslow and Snyder. Prerequisite: Permission of the professor in charge (2) special permission is obtained Prerequisites: A grade of 5 on the Chemistry for entrance and permission of the departmental Advanced Placement exam and an acceptable representative for aggregate points in excess from the Department of Earth and grade on the Department placement exam. Not of 12 or less than 4. Laboratory fee: $105 per Environmental Sciences. open to students who have taken other courses term. This course may be repeated for credit (see in college-level chemistry. Premedical students EESC V1011x Earth: origin, evolution, major and concentration requirements). Individual processes, future may take CHEM C3045, C3046, and W3545 to research under the supervision of a member of the meet the minimum requirements for admission 4 pts. Lect: 3. Lab: 1. Professors Kelemen and staff. Research areas include organic, physical, Mutter. to medical school. This course covers the inorganic, analytical, and biological chemistry. same material as CHEM C3443-C3444, but Students who wish to take only the lectures should is intended for students who have learned CHEM C3443x-C3444y Organic chemistry register for V1411. What is the nature of our the principles of general chemistry in high (lecture) planet and how did it form? From geochemical school. The level of instruction is appropriate 3.5 pts. Professors Cornish, Lambert, Sames, and geophysical perspectives we explore for those who have not had a college course and Turro. Earth’s internal structure, its dynamical character in general chemistry. Students enrolled in Prerequisites: CHEM C1404 or W1404 or expressed in plate tectonics, and ask if its future CHEM C3045-C3046 are expected to enroll C1604, and C1500 or W1500. The principles of behavior can be known. concurrently in CHEM W2507. Recitation organic chemistry. The structure and reactivity EESC V1030x Oceanography section required. of organic molecules are examined from the 3 pts. Lect: 3. Professor Hoenisch. standpoint of modern theories of chemistry. Topics CHEM C3071y Introduction to inorganic Explore the geology of the sea floor, understand include stereochemistry, reactions of organic what drives ocean currents and how ocean chemistry molecules, mechanisms of organic reactions, 3 pts. Lect: 3. Professor Owen. ecosystems operate. Case studies and discussions syntheses and degradations of organic molecules, centered on ocean-related issues facing society. Corequisite: CHEM C3444 or C3046. Principles and spectroscopic techniques of structure governing the structure and reactivity of inorganic determination. Recitation section required. compounds surveyed from experimental and theoretical viewpoints. Topics include inorganic solids, aqueous and nonaqueous solutions, the

engineering 2011–2012 EESC V1201y Environmental risks and EESC W4001x Advanced general geology optical properties of minerals, mineral associations, 199 disasters 4 pts. Lect: 3. Lab: 1. Professors Anders and economic minerals. Laboratory: identification 3 pts. Lect: 3. Not offered in 2011–2012. Scholz. of minerals in hand specimens and use of the Prerequisites: high school science and math. Prerequisites: one semester of college-level petrographic microscope. An introduction to risks and hazards in the calculus, physics, and chemistry. A concentrated EESC W4230y Crustal deformation environment. Different types of hazards are introduction to the solid Earth, its interior, and 3 pts. Lect: 3. Professors Anders and Scholz. analyzed and compared: natural disasters, such near-surface geology. Intended for students with Prerequisites: introductory geology and one year of as tornados, earthquakes, and meteorite impacts; good backgrounds in the physical sciences but calculus. Recommended preparation: higher levels acute and chronic health effects caused by none in geology. Laboratory and field trips. of mathematics. Introduction to the deformation exposure to radiation and toxic substances such processes in the Earth’s crust. Fundamental as radon, asbestos, and arsenic; long-term societal EESC W4008x Introduction to atmospheric theories of stress and strain; rock behavior effects due to environmental change, such as sea science in both brittle and ductile fields; earthquake level rise and global warming. Emphasizes the 3 pts. Lect: 3. Professor Del Genio. processes; ductile deformation; large-scale crustal basic physical principles controlling the hazardous Prerequisites: advanced calculus and general physics, or the instructor’s permission. Basic contractional and extensional events. phenomena and develops simple quantitative physical processes controlling atmospheric methods for making scientifically reasoned EESC W4300x The earth’s deep interior structure: thermodynamics; radiation physics assessments of the threats (to health and 3 pts. Lect: 3. Not offered in 2011–2012. and radiative transfer; principles of atmospheric wealth) posed by various events, processes, and Prerequisites: calculus, differential equations, dynamics; cloud processes; applications to Earth’s exposures. Discusses methods of risk mitigation one year of college physics, and EESC W4950 atmospheric general circulation, climatic variations, and sociological, psychological, and economic or its equivalent. An introduction to properties and the atmospheres of the other planets. aspects of risk control and management. of the Earth’s mantle, fluid outer core, and solid EESC W4009x. Chemical geology inner core. Current knowledge of these features is EESC V1600x Earth resources and 4 pts. Offered in alternate years. Not offered in explored, using observations of seismology, heat sustainable development 2011–2012. flow, gravity, and geomagnetism, plus information 3 pts. Lect: 3. Professor Kelemen. Prerequisite: physical chemistry or the instructor’s on the Earth’s bulk composition. Prerequisites: none. High school chemistry permission. Thermodynamics as applied to earth EESC W4600x Earth resources and recommended. Survey of the origin and extent systems. of mineral resources, fossil fuels, and industrial sustainable development materials, that are non-renewable, finite EESC W4050x Global assessment and 3 pts. Lect: 3. Professor Kelemen. resources, and the environmental consequences monitoring using remote sensing Prerequisites: none. High school chemistry of their extraction and use, using the textbook 3 pts. Offered in alternate years. Professor Small. recommended. Survey of the origin and extent Earth Resources and the Environment, by James Prerequisite: instructor’s permission. of mineral resources, fossil fuels, and industrial Craig, David Vaughan and Brian Skinner. This Recommended preparation: some college- materials, that are nonrenewable, finite resources, course provides an overview but includes focus level physics or math. Enrollment limited to 24 and the environmental consequences of their on topics of current societal relevance, including students. General introduction to fundamentals of extraction and use, using the textbook Earth Resources and the Environment, by James estimated reserves and extraction costs for remote sensing and image processing. Example Craig, David Vaughan and Brian Skinner. This fossil fuels, geological storage of CO , sources applications in the Earth and environmental 2 course provides an overview, but includes focus and disposal methods for nuclear energy fuels, sciences are explored through the analysis of on topics of current societal relevance, including sources and future for luxury goods such as gold remote sensing imagery in a state-of-the-art estimated reserves and extraction costs for and diamonds, and special, rare materials used in visualization laboratory. Lab required. fossil fuels, geological storage of CO2, sources consumer electronics (e.g., “Coltan,” mostly from EESC W4076y Geologic mapping and disposal methods for nuclear energy fuels, Congo) and in newly emerging technologies such 3 pts. Lect: 3. Professors Anders and Walker. sources and future for luxury goods such as gold as superconducting magnets and rechargeable Fieldwork on weekends in April and for two weeks and diamonds, and special, rare materials used in batteries (e.g., heavy rare earth elements, mostly in mid-May, immediately following the end of consumer electronics (e.g., “Coltan,” mostly from from China). Guest lectures from economists, examinations. Estimated expenses: $250. The Congo) and in newly emerging technologies such commodity traders and resource geologists will principles and practices of deciphering geologic as superconducting magnets and rechargeable provide “real world” input. history through the observation of rocks in the batteries (e.g., heavy rare earth elements, mostly field, mapmaking, construction of geological cross- EESC W3018y Weapons of mass destruction from China). Guest lectures from economists, sections, and short written reports. 3 pts. Lect: 3. Professor Richards. commodity traders and resource geologists will Prerequisites: high school science and math. EESC W4085x Geodynamics provide “real world” input. Required recitation A review of the history and environmental 3 pts. Lect: 3. Offered in alternate years. Not session. consequences of nuclear, chemical, and biological offered in 2011–2012. EESC W4701 Introduction to igneous weapons of mass destruction (WMD); of how Prerequisites: calculus, differential equations, petrology these weapons work, what they cost, how they introductory physics. An introduction to how the 4 pts. Offered in alternate years. have spread, how they might be used, how they Earth and planets work. The focus is on physical Prerequisite: introductory geology or the are currently controlled by international treaties processes that control plate tectonics and the equivalent. Recommended preparation: EESC and domestic legislation, and what issues of policy evolution of planetary interiors and surfaces; W4113 and knowledge of chemistry. Students not and technology arise in current debates on WMD. analytical descriptions of these processes; weekly enrolled in terrestrial geology may elect to write What aspects of the manufacture of WMD are physical model demonstrations. a substantial term paper in lieu of the laboratory easily addressed, and what aspects are technically EESC W4113 Introduction to mineralogy course. Compositional characteristics of igneous challenging? It may be expected that current 4 pts. Offered in alternate years. and metamorphic rocks and how they can be events/headlines will be discussed in class. Prerequisites: introductory geology or the used as tools to investigate earth processes. equivalent, elementary college physics and Development of igneous and metamorphic rocks in chemistry, or the instructor’s permission. a plate-tectonic framework. Elementary crystallography and crystal structures,

engineering 2011–2012 200 EESC W4885 The chemistry of continental analysis of the plate-tectonic cycle. Driving discuss a range of published essays, complete waters forces and mantle convection, plate kinematics, regular reading and writing exercises, write several 3 pts. Lect: 3. Offered in alternate years. magmatism, structure, thermal and chemical longer essays, and undertake a collaborative Recommended preparation: a solid background in evolution of mid-ocean ridges and subduction research and writing project designed by the class. basic chemistry. Introduction to geochemical cycles zones, continental rifts and collisions, and hot spots. Students placed in C1010 whose names fall in the involving the atmosphere, land, and biosphere; Includes literature readings of great debates, and first part of the alphabet must take the course in chemistry of precipitation, weathering reactions, emphasizes integration of geophysical, geological the fall. Students whose names fall in the second rivers, lakes, estuaries, and groundwaters; stable and geochemical observations and processes. part of the alphabet take the course in the spring. isotopes and radioactive tracers of transport The alphabet will be split somewhere between K EESC W4949x Introduction to seismology processes in continental waters. 3 pts. Lect: 3. Offered in alternate years. Not and O. The exact place for the split will be posted EESC W4924 Introduction to atmospheric offered in 2011–2012. before fall registration. chemistry Prerequisites: elementary college physics and Global Core 3 pts. Lect: 3. Offered in alternate years. Not mathematics (including calculus). Basic methods The Global Core requirement consists of courses offered in 2011–2012. of seismogram analysis. Classification of seismic that examine areas not the primary focus A survey of trace gas photochemistry important waves and elementary theory of body waves of Literature Humanities and Contemporary in the Earth’s atmosphere. Major topics are and normal modes. Elementary aspects of Civilization and that, like other Core courses, composition, including biogenic and anthropogenic seismic prospecting, earthquake source theory, are broadly introductory, interdisciplinary, and inputs, and chemical processes, including instrumentation, discrimination between explosions temporally or spatially expansive. Courses in reaction kinetics and photochemistry. Specific and earthquakes, inversion of seismic data to infer the Global Core are organized around a set of applications to tropospheric air quality, including Earth structure, earthquake engineering, earthquake primary texts or artifacts, which may range from smog, acid rain, and stratospheric ozone, including insurance and hazards mitigation, estimation of texts of literate traditions to media (e.g. film), seismic risk, and earthquake prediction. the Antarctic ozone hole, are covered, with an ritual performances or oral sources, produced in emphasis on the response to anthropogenic the regions of the world in question. Global Core pollutants and climate change. Humanities and Social courses fall into two categories: those that focus EESC W4925x Principles of physical Sciences on a specific culture or civilization, tracing its oceanography appearance and/or existence across a significant For listings of additional courses of 3 pts. Lect: 3. Professor Gordon. span of time and sometimes across more than Recommended preparation: a solid background interest to engineering students, consult one present-day country or region; and those in mathematics, physics, and chemistry. Physical the bulletins of Columbia College; the that address several world settings or cultures properties of seawater, water masses and their School of General Studies; the Graduate comparatively (and may include Europe and distribution, sea-air interaction influence on the ocean School of Architecture, Planning, and the West), in terms of a common theme, a set structure, basic ocean circulation pattern, relation of Preservation; the Graduate School of of analytic questions, or interactions between diffusion and advection with respect to distribution Business; and the Graduate School of different world regions. Students must complete of ocean properties, ocean tides and waves, two courses from the Global Core List of Approved Arts and Sciences. turbulence, and introduction to ocean dynamics. Courses for a letter grade. COCI C1101x-C1102y Introduction to EESC W4926y Principles of chemical HUMA C1001x-C1002y Masterpieces of contemporary civilization oceanography Western literature and philosophy 4 pts. Lect: 4. Instructor to be announced. 3 pts. Offered in alternate years. Not offered in 4 pts. Lect: 4. Instructor to be announced. Taught by members of the Departments of 2011–2012. Taught by members of the Departments of Anthropology, Classics, English and Comparative Recommended preparation: Solid background Classics, English and Comparative Literature, Literature, French, German, History, Middle East in mathematics, physics, and chemistry. Factors French, German, Italian, Middle East and Asian and Asian Languages and Cultures, Philosophy, controlling the concentration and distribution Languages and Cultures, Philosophy, Religion, Political Science, Religion, Slavic Languages, of dissolved chemical species within the sea. Slavic Languages, and Spanish; and members of and Sociology; and members of the Society of Application of tracer and natural radioisotope the Society of Fellows in the Humanities. Major Fellows. A study in their historical context of major methods to large-scale mixing of the ocean, the works by over twenty authors, ranging in time, contributions to the intellectual traditions that geological record preserved in marine sediments, theme, and genre from Homer to Virginia Woolf. underpin contemporary civilization. Emphasis is the role of ocean processes in the global carbon Students are expected to write at least two papers, on the history of political, social, and philosophical cycle, and biogeochemical processes influencing to complete two examinations each semester, and thought. Students are expected to write at least the distribution and fate of elements in the ocean. to participate actively in class discussions. three papers to complete two examinations, and to EESC W4930y Earth’s oceans and participate actively in class discussions. HUMA W1121x or y Masterpieces of atmosphere Western art ECON W1105x and y Principles of economics 3 pts. Lect: 3. Offered in alternate years. 3 pts. Lect: 3. Instructor to be announced. 4 pts. Professors Desai, Musatti, and Salanie. Professor Gordon. Discussion and analysis of the artistic qualities Corequisites: ECON W1155 recitation section Recommended preparation: a good background and significance of selected works of painting, in the physical sciences. Physical properties of with the same instructor. How a market economy sculpture, and architecture from the Parthenon in water and air. Overview of the stratification and determines the relative prices of goods, factors of Athens to works of the 20th century. circulation of Earth’s oceans and atmosphere and production, and the allocation of resources and their governing processes; ocean-atmosphere the circumstances under which it does it efficiently. HUMA W1123x or y Masterpieces of interaction; resultant climate system; natural and Why such an economy has fluctuations and how Western music anthropogenic forced climate change. they may be controlled. Recitation section required. 3 pts. Lect: 3. Instructor to be announced. Popularly known as “Music Hum,” this course aims EESC W4947y Plate tectonics ENGL C1010x or y University writing to instill in students a basic comprehension of the 3 pts. Lect: 3. Professor Abers. 3 pts. Members of the faculty. many forms of the Western musical imagination. Prerequisite: physical geology. Prepares students Teaches general techniques and strategies for The course involves students actively in the for research and oral exams with cross-disciplinary academic reading and writing. Students read and

engineering 2011–2012 process of critical listening, both in the classroom MATH E1210x or y Ordinary differential MATH W4061x-W4062y Introduction to 201 and in concerts. Although not a history of Western equations modern analysis music, the course is taught in chronological 3 pts. Lect: 3. Professors Munteanu and Fang. 3 pts. Lect: 3. Professor Gallagher. format and includes masterpieces by Josquin Prerequisite: MATH V1201 or the equivalent. The second term of this course may not be taken des Prez, Monteverdi, Bach, Handel, Mozart, Special differential equations of order one. Linear without the first. Prerequisite: MATH V1202 or the Haydn, Beethoven, Verdi, Wagner, Schoenberg, differential equations with constant and variable equivalent. Real numbers, metric spaces, elements Stravinsky, Louis Armstrong, and Duke Ellington, coefficients. Systems of such equations. Transform of general topology. Continuous and differentiable among others. and series solution techniques. Emphasis on functions. Implicit functions. Integration, change of applications. variables. Function spaces. Further topics chosen by the instructor. Mathematics MATH V2010 x and y Linear algebra 3 pts. Lect: 3. Professors Stein, Vela-Vick, and MATH W4065x Honors complex variables Courses for First-Year Students Zheng. 3 pts. Lect: 3. Professor Friedman. Depending on the program, completion Prerequisite: MATH VI201 or the equivalent. Prerequisite: MATH V1207, V1208, or W4061. of Calculus III or IV satisfies the basic Vector spaces, linear transformations, matrices, A theoretical introduction to analytic functions. mathematics requirement. Normally quadratic and hermitian forms, reduction to Holomorphic functions, harmonic functions, power students who have taken an AP canonical forms. series, Cauchy-Riemann equations, Cauchy’s integral formula, poles, Laurent series, residue Calculus course begin with either MATH V2500x or y Analysis and optimization theorem. Other topics as time permits: elliptic 3 pts. Lect: 3. Professors Pinkham and Hongler. Calculus II or Calculus III. Refer to the functions, the gamma and zeta functions, the Prerequisites: MATH V1102 and V1201 or the AP guidelines on page 14 for placement Riemann mapping theorem, Riemann surfaces, equivalent, and MATH V2010. Mathematical information. The sequence ends with Nevanlinna theory. methods for economics. Quadratic forms, Hessian, MATH E1210: Ordinary differential implicit functions. Convex sets, convex functions. equations. Optimization, constrained optimization, Kuhn- Physics Students who wish to transfer Tucker conditions. Elements of the calculus of The general four-term preengineering from one calculus course to another variations and optimal control. are allowed to do so beyond the date physics sequence consists of PHYS MATH V3007y Complex variables specified on the Academic Calendar. C1401, C1402, C1403, and C1494 3 pts. Lect: 3. Professor Phong. They are considered to be adjusting (laboratory); or PHYS C1601, C1602, Prerequisite: MATH V1202. An elementary course C2601, and C2699 (laboratory). their level, not changing their program. in functions of a complex variable. Fundamental They must, however, obtain the approval properties of the complex numbers, differentiability, PHYS C1401x Introduction to mechanics and of the new instructor and the Center for Cauchy-Riemann equations, Cauchy integral thermodynamics Student Advising before reporting to the theorem, Taylor and Laurent series, poles, and 3 pts. Lect: 2.5. Professors Hailey and Pasupathy. Registrar. essential singularities. Residue theorem and Corequisite: MATH V1101 or the equivalent. conformal mapping. Fundamental laws of mechanics, kinematics and MATH V1101 Calculus, I dynamics, work and energy, rotational dynamics, MATH V3027x Ordinary differential equations 3pts. Lect: 3. oscillations, gravitation, fluids, temperature and 3 pts. Lect: 3. Professor Daskalopoulos. Functions, limits, derivatives, introduction to heat, gas laws, the first and second laws of Prerequisite: MATH V1201 or the equivalent. integrals. thermodynamics. Equations of order one, linear equations, series MATH V1102 Calculus, II solutions at regular and singular points, boundary PHYS C1402y Introduction to electricity, 3 pts. Lect: 3. value problems. Selected applications. magnetism, and optics Prerequisite: Calculus I or the equivalent. Methods 3 pts. Lect: 2.5. Professors Hailey and Hughes. MATH V3028y Partial differential equations of integration, applications of integrals, series, Prerequisite: PHYS C1401. Corequisite: MATH 3 pts. Lect: 3. Professor Savin. including Taylor’s series. V1102 or the equivalent. Electric fields, direct Prerequisite: MATH V3027 or the equivalent. currents, magnetic fields, alternating currents, MATH V1201 Calculus, III Introduction to partial differential equations. First- electromagnetic waves, polarization, geometrical 3 pts. Lect: 3. order equations. Linear second-order equations, optics, interference and diffraction. Prerequisite: Calculus II or the equivalent. Vector separation of variables, solution by series algebra, complex numbers and exponential, vector expansions. Boundary value problems. PHYS C1403x Introduction to classical and differential calculus. quantum waves MATH W4032x Fourier analysis 3 pts. Lect: 2.5. Professor Dodd. MATH V1202 Calculus, IV 3 pts. Lect: 3. Professor Lipyanskiy. Prerequisite: PHYS C1402. Corequisite: MATH 3 pts. Lect: 3. Prerequisites: MATH V1201 and linear algebra, or V1201 or the equivalent. Classical waves and the Prerequisite: Calculus II and III. Multiple integrals, MATH V1202. Fourier series and integrals, discrete wave equation, Fourier series and integrals, normal line and surface integrals, calculus of vector fields, analogues, inversion and Poisson summation, modes, wave-particle duality, the uncertainty Fourier series. formulae, convolution, Heisenberg uncertainty principle, basic principles of quantum mechanics, principle. Emphasis on the application of Fourier MATH V1207x-V1208y Honors math A-B energy levels, reflection and transmission analysis to a wide range of disciplines. 4 pts. Lect and recit. Professor Savin. coefficients, applications to atomic physics. Prerequisite: Score of 5 on the Advanced MATH W4041x-W4642y Introduction to PHYS C1493x Introduction to experimental Placement BC calculus exam. The second term modern algebra physics of this course may not be taken without the first. 3 pts. Lect: 3. Professor Friedman. 3 pts. Lab: 3. Multivariable calculus and linear algebra from a The second term of this course may not be taken Prerequisites: PHYS C1401 and C1402. rigorous point of view. without the first. Prerequisites: MATH V1202 and Laboratory work associated with the two V2010 or the equivalent. Groups, homomorphisms, prerequisite lecture courses. Experiments rings, ideals, fields, polynominals, and field in mechanics, thermodynamics, electricity, extensions. Galois theory.

engineering 2011–2012 202 magnetism, optics, wave motion, atomic and mathematics, or the equivalent, and the instructor’s laboratory capacity. Experiments (classical and nuclear physics. (Students cannot receive credit for permission. (A special placement meeting is modern) cover topics in electricity, magnetism, both PHYS C1493 and C1494.) held during Orientation.) This accelerated two- optics, atomic physics, and nuclear physics. semester sequence covers the subject matter of PHYS C1494y Introduction to experimental PHYS W3083y Electronics laboratory PHYS C1601, C1602, and C2601 and is intended physics 3 pts. Lab: 3. Professor Parsons. for students who have an exceptionally strong 3 pts. Lab: 3. Registration is limited to the capacity of the background in both physics and mathematics. The Prerequisites: PHYS C1401 and C1402. laboratory. Corequisite or prerequisite: PHYS course is preparatory for advanced work in physics Laboratory work associated with the two W3003 or W3007. A sequence of experiments in and related fields. There is no accompanying prerequisite lecture courses. Experiments solid-state electronics, with introductory lectures. laboratory; however, students are encouraged to in mechanics, thermodynamics, electricity, take the intermediate laboratory, PHYS W3081, in PHYS G4003y Advanced mechanics magnetism, optics, wave motion, atomic and the following year. 3 pts. Lect: 2.5. Professor Nicolis. nuclear physics. (Students cannot receive credit for Prerequisites: Differential and integral calculus, both PHYS C1493 and C1494.) PHYS W3002y From quarks to the cosmos: differential equations, and PHYS W3003 or the applications of modern physics PHYS C1601x Physics, I: mechanics and equivalent. Lagrange’s formulation of mechanics, 3.5 pts. Lect: 3.5. relativity calculus of variations and the Action Principle, Prerequisite: PHYS C2601 or C2802. This course 3.5 pts. Lect: 2.5. Professor Millis. Hamilton’s formulation of mechanics, rigid body reinforces basic ideas of modern physics through Corequisite: MATH V1102 or the equivalent. motion, Euler angles, continuum mechanics, applications to nuclear physics, high-energy Fundamental laws of mechanics, kinematics and Introduction to chaotic dynamics. physics, astrophysics, and cosmology. The dynamics, work and energy, rotational dynamics, ongoing Columbia research programs in these PHYS G4018y Solid-state physics oscillations, gravitation, fluids, introduction to 3 pts. Lect: 2.5. Professor Uemura. fields are used as practical examples. The course special relativity and relativistic kinematics. The Prerequisites: PHYS G4021 and G4023, or the is preparatory for advanced work in physics and course is preparatory for advanced work in physics equivalent. Introduction to solid-state physics: related fields. and related fields. crystal structures, properties of periodic lattices, PHYS W3003x Mechanics electrons in metals, band structure, transport PHYS C1602y Physics, II: thermodynamics, 3 pts. Lect: 2.5. Professor Weinberg. properties, semiconductors, magnetism, and electricity, and magnetism Prerequisites: General physics; differential superconductivity. 3.5 pts. Lect: 2.5. Professor Dodd. and integral calculus. Newtonian mechanics, Prerequisite: PHYS C1601. Corequisite: PHYS G4019x Mathematical methods of oscillations and resonance, conservative forces MATH V1201 or equivalent. Temperature physics and potential energy, central forces, noninertial and heat, gas laws, the first and second laws 3 pts. Lect: 3. Not offered in 2011–2012. frames of reference, rigid body motion, an of thermodynamics, kinetic theory of gases, Prerequisite: Differential and integral calculus. introduction to Lagrange’s formulation of electric fields, direct currents, magnetic fields, Highlights of complex analysis, differential mechanics, coupled oscillators, and normal modes. alternating currents, electromagnetic waves. equations, integral equations, Green’s functions, The course Is preparatory for advanced work in PHYS W3007y Electricity and magnetism special functions, Fourier and other transforms, physics and related fields. 3 pts. Lect: 2.5. Professor Pasupathy. approximation methods, group theory and Prerequisite: General physics; differential representations, differential geometry and PHYS C2601x Physics, III: classical and manifolds. Emphasis is placed on applications to and integral calculus. Electrostatics and quantum waves physical problems. magnetostatics, Laplace’s equation and boundary- 3.5 pts. Lect: 2.5. Rec: 1 hour weekly to be value problems, multipole expansions, dielectric arranged. Professor Kim. PHYS G4021x-G4022y Quantum mechanics, and magnetic materials, Faraday’s law, AC Prerequisite: PHYS C1602 or C1402. Corequisite: I and II circuits, Maxwell’s equations, Lorentz covariance, MATH V1202 or equivalent. Classical waves 3 pts. Lect: 2.5. Professors Greene and Weinberg. and special relativity. Prerequisite: PHYS C2601 or C2802, or the and the wave equation, geometrical optics, equivalent. The formulation of quantum mechanics interference and diffraction, Fourier series and PHYS W3008x Electromagnetic waves and in terms of state vectors and linear operators, integrals, normal modes, wave-particle duality, optics three-dimensional spherically symmetric potentials, the uncertainty principle, basic principles of 3 pts. Lect: 2.5. Professor Heinz. the theory of angular momentum and spin, time- quantum mechanics, energy levels, reflection and Prerequisite: PHYS W3007. Maxwell’s equations independent and time-dependent perturbation transmission coefficients, the harmonic oscillator. and electromagnetic potentials, the wave theory, scattering theory, identical particles. The course is preparatory for advanced work in equation, propagation of plane waves, reflection Selected phenomena from atomic physics, nuclear physics and related fields. and refraction, geometrical optics, transmission physics, and elementary particle physics are lines, wave guides, resonant cavities, radiation, PHYS C2699y Experiments in classical and described and then interpreted using quantum interference of waves, and diffraction. modern physics mechanical models. 3 pts. Lab: 3. PHYS W3081x or y Intermediate laboratory PHYS G4023x Thermal and statistical physics Prerequisites: PHYS C1601 (or C1401), C1602 (or work 3 pts. Lect: 2.5. Professor Ruderman. C1402), and C2601. Laboratory work associated 2 pts. Lab: 2. Professors Aprile and May. Prerequisite: PHYS G4021 or equivalent. with the three prerequisite lecture courses. Primarily for junior and senior physics majors. Thermodynamics, kinetic theory, and methods Experiments in mechanics, thermodynamics, Other majors require the instructor’s permission. of statistical mechanics; energy and entropy; electricity, magnetism, optics, wave motion, atomic May be repeated for credit by performing different Boltzmann, Fermi, and Bose distributions; ideal and nuclear physics. experiments. The laboratory has 13 individual and real gases; blackbody radiation; chemical experiments available, of which two are required equilibrium; phase transitions; ferromagnetism. PHYS C2801x-C2802y Accelerated physics, per 2 points. Each experiment is chosen by I and II PHYS G4040x General relativity the student in consultation with the instructor. 4.5 pts. Lect: 3.5. Rec: 1 hour weekly to be 3 pts. Lect: 2.5. Professor Marka. Each section meets one afternoon per week, arranged. Professor Christ. Prerequisites: PHYS W3003 and W3007, or equiv- with registration in each section limited by the Prerequisite: Advanced placement in physics and alent. Tensor algebra, tensor analysis, introduction

engineering 2011–2012 to Riemann geometry. Motion of particles, fluid, STAT W2024x Applied linear regression comprehensive background should consider replacing 203 and fields in curved spacetime. Einstein equation. analysis this course with MATH V1102 and V2010, and one of Schwarzschild solution; test-particle orbits and light 3 pts. Professor Lindquist. COMS W1003, W1004, or W1007. bending. Introduction to black holes, gravational Prerequisite: One of STAT W1001, W1111, STAT W3105x Introduction to probability waves, and cosmological models. or W1211. Develops critical thinking and data 3 pts. Professor Lo. analysis skills for regression analysis in science Prerequisites: MATH V1101 and V1102 or the and policy settings. Simple and multiple linear equivalent. A calculus-based introduction to Statistics regression, nonlinear and logistic models, probability theory. A quick review of multivariate Engineering students interested in a random-effects models, penalized regression calculus is provided. Topics covered include methods. Implementation in a statistical package. survey of the mathematical theory of random variables, conditional probability, Optional computer-lab sessions. Emphasis on probability and statistics should consider expectation, independence, Bayes’ rule, important real-world examples and on planning, proposing, the pair STAT W3105: Probability distributions, joint distributions, moment generating implementing, and reporting. theory and W3107: Statistical inference. functions, central limit theorem, laws of large Students seeking a quicker overview STAT W2025y Applied statistical methods numbers and Markov’s inequality. 3 pts. Professor Whalen. that focuses more on probability theory STAT W3107y Introduction to statistical Prerequisite: STAT W2024. Classical should consider SIEO W4150. STAT inference nonparametric methods, permutation tests; W4105 and W4107 are the equivalent 3 pts. Instructor to be announced. contingency tables, generalized linear models, Prerequisite: STAT W3105 or W4105, or the of W3105 and W3107, respectively; but missing data, causal inference, multiple equivalent. Calculus-based introduction to the graduate students may not register for comparisons. Implementation in statistical theory of statistics. Useful distributions, law of W3105 and W3107. STAT W4109 (6 software. Emphasis on conducting data analyses large numbers and central limit theorem, point pts) covers the same material as W3105 and reporting the results. Optional weekly estimation, hypothesis testing, confidence computer-lab sessions. and W3107 in a single semester. STAT intervals maximum likelihood, likelihood ratio tests, W4315: Linear regression models takes STAT W2026x Statistical applications and nonparametric procedures, theory of least squares, W3105 and W3107 as prerequisites; like case studies and analysis of variance. other advanced offerings in statistics, 3 pts. Professor Lindquist. STAT W3315x Linear regression models Prerequisite: STAT W2025. A sample of topics it covers both theory and practical 3 pts. Instructor to be announced. and application areas in applied statistics. aspects of modeling and data analysis. Prerequisites: STAT W3107 (or W4150) and STAT Topic areas may include Markov processes and W3103 (or MATH V1101, V1102, and V2110). Advanced offerings in probability theory, queuing theory; meta-analysis of clinical trial Theory and practice of regression analysis. Simple stochastic processes, and mathematical research; receiver-operator curves in medical and multiple regression, testing, estimation, finance generally take STAT W3105 as diagnosis; spatial statistics with applications in prediction, and confidence procedures, modeling, a prerequisite; advanced offerings in geology, astronomy, and epidemiology; multiple regression diagnostics and plots, polynomial comparisons in bio-informatics; causal modeling statistical theory and methods generally regression, colinearity and confounding, model with missing data; statistical methods in genetic take STAT W4107 and, in several cases, selection, geometry of least squares. Extensive epidemiology; stochastic analysis of neural spike use of the computer to analyze data. Equivalent to W4315 as prerequisites; an exception train data; graphical models for computer and STAT W4315 except that enrollment is limited to is STAT W4220: Data mining, which social network data. has a course in computer programming undergraduate students. STAT W3026x Applied data mining as prerequisite and STAT W3107 as STAT W3997x and y Independent Research 3 pts. Professor Emir. Instructor to be announced. corequisite. STAT 4201 is a high-level Data mining is a dynamic and fast growing field at Prerequisites: The permission of a member of the survey of applied statistical methods. the interface of Statistics and Computer Science. department. May be repeated for credit. The student Please note that STAT W3000 The emergence of massive datasets containing participates in the current research of a member of millions or even billions of observations provides has been renumbered as W3105 and the department and prepares a report on the work. STAT W3659 has been renumbered as the primary impetus for the field. Such datasets arise, for instance, in large-scale retailing, W3107. For a description of the following STAT W4201x and y Advanced data analysis telecommunications, astronomy, computational 3 pts. Professors Alemayehu and Liu. course offered jointly by the Departments and statistical challenges. This course will provide Prerequisite: STAT W4315. At least one of of Statistics and Industrial Engineering an overview of current practice in data mining. W4290, W4325, W4330, W4437, W4413, W4543 and Operations Research, see “Industrial Specific topics covered with include databases is recommended. This is a course on getting the Engineering and Operations Research.” and data warehousing, exploratory data analysis most out of data. The emphasis will be on hands- and visualization, descriptive modeling, predictive on experience, involving case studies with real SIEO W4150x and y Introduction to modeling, pattern and rule discovery, text mining, data and using common statistical packages. The probability and statistics Bayesian data mining, and causal inference. The course covers, at a very high level, exploratory 3 pts. Professors Gallego, Hueter, and Wright. use of statistical software will be emphasized. data analysis, model formulation, goodness of Prerequisites: MATH V1101 and V1102 or the fit testing, and other standard and non-standard STAT W3103x Mathematical methods for equivalent. A quick calculus-based tour of the statistical procedures, including linear regression, statistics fundamentals of probability theory and statistical analysis of variance, nonlinear regression, 6 pts. Professor Rabinowitz. inference. Probabilistic models, random variables, generalized linear models, survival analysis, time Prerequisite: MATH V1101. A fast-paced coverage of useful distributions, expectations, laws of large series analysis, and modern regression methods. those aspects of the differential and integral calculus numbers, central limit theorem. Statistical inference: Students will be expected to propose a data set of of one and several variables and of the linear algebra point and confidence interval estimation, hypothesis their choice for use as case study material. tests, linear regression. Students seeking a more required for the core courses in the Statistics major. thorough introduction to probability and statistics The mathematical topics are integrated with an should consider STAT W3105 and W3107. introduction to computing. Students seeking more

engineering 2011–2012 204 STAT W4240x Data mining STAT W4325y Generalized linear models STAT W4543y Survival analysis 3 pts. Professors Madigan and Wood. 3 pts. Professor Sobel. Professor Shnaidman. Prerequisite: COMS W1003, W1004, W1005, Prerequisite: STAT W4315. Statistical methods Prerequisite: STAT W4315. Survival distributions, W1007, or the equivalent. Corequisites: Either for rates and proportions, ordered and nominal types of censored data, estimation for various STAT W3105 or W4105, and either STAT W3107 categorical responses, contingency tables, odds- survival models, nonparametric estimation of or W4107. Data Mining is a dynamic and fast ratios, exact inference, logistic regression, Poisson survival distributions, the proportional hazard growing field at the interface of Statistics and regression, generalized linear models. and accelerated lifetime models for regression Computer Science. The emergence of massive analysis with failure-time data. Extensive use of STAT W4330x Multilevel models datasets containing millions or even billions of the computer. Professor Chen. observations provides the primary impetus for the Prerequisites: STAT W4315. Theory and practice, STAT W4606x and y Elementary stochastic field. Such datasets arise, for instance, in large- including model-checking, for random and mixed- scale retailing, telecommunications, astronomy, processes effects models (also called hierarchical, multi- computational and statistical challenges. This 3 pts. Professors Brown and Hogan. level models). Extensive use of the computer to course will provide an overview of current Prerequisite: STAT W3105, W4105, or equivalent. analyze data. research in data mining and will be suitable for Review of elements of probability theory. Poisson processes. Renewal theory. Wald’s equation. graduate students from many disciplines. Specific STAT W4335x Sample surveys Introduction to discrete and continuous time topics covered with include databases and data 3 pts. Professor Sobel. Markov chains. Applications to queueing theory, warehousing, exploratory data analysis and Prerequisite: STAT W3107 or W4107. Introductory inventory models, branching processes. visualization, descriptive modeling, predictive course on the design and analysis of sample modeling, pattern and rule discovery, text mining, surveys. How sample surveys are conducted, STAT W4635y Stochastic Processes for Bayesian data mining, and causal inference. why the designs are used, how to analyze survey Finance results, and how to derive from first principles STAT W4290y Statistical methods in finance 3 pts. Professor Vecer. the standard results and their generalizations. 3 pts. Professor Pospisil. Prerequisite: STAT W3105, W4105, or equivalent. Examples from public health, social work, opinion Prerequisite: STAT W3107 or W4107. A fast- This course covers theory of stochastic polling, and other topics of interest. paced introduction to statistical methods used in processes applied to finance. It covers concepts of Martingales, Markov chain models, Brownian quantitative finance. Financial applications and STAT W4413y Nonparametric statistics motion. Stochastic Integration, Ito’s formula statistical methodologies are intertwined in all 3 pts. Professor Sen. as a theoretical foundation of processes used lectures. Topics include regression analysis and Prerequisite: STAT W3107 or W4107. Statistical in financial modeling. It also introduces basic applications to the Capital Asset Pricing Model and inference without parametric model assumption. discrete and continuous time models of asset price multifactor pricing models, principal components Hypothesis testing using ranks, permutations, and evolutions in the context of the following problems and multivariate analysis, smoothing techniques order statistics. Nonparametric analogs of analysis in finance: portfolio optimization, option pricing, and estimation of yield curves statistical methods of variance. Non-parametric regression, smoothing spot rate interest modeling. for financial time series, value at risk, term and model selection. structure models and fixed income research, and STAT W4840x Theory of interest STAT W4437x and y Time series analysis estimation and modeling of volatilities. Hands-on 3 pts. Professor Rajah. 3 pts. Professors Davis, Hernandez-del-Valle, experience with financial data. Prerequisite: MATH V1101 or equivalent. and Hueter. Introduction to the mathematical theory of interest STAT W4315x and y Linear regression models Prerequisite: STAT W4315 or equivalent. Least as well as the elements of economic and financial 3 pts. Instructor to be announced. squares smoothing and prediction, linear systems, theory of interest. Topics include rates of interest Prerequisites: STAT W3107 or equivalent, MATH Fourier analysis, and spectral estimation. Impulse and discount; simple, compound, real, nominal, V2110 or the equivalent. Corequisites: MATH response and transfer function. Fourier series, the effective, dollar (time)-weighted; present, current, V1101, V1102, and V2110. Simple and multiple fast Fourier transform, autocorrelation function, and future value; discount function; annuities; stocks regression, including testing, estimation and spectral density. Univariate Box-Jenkins modeling and other instruments; definitions of key terms confidence procedures, modeling, regression and forecasting. Emphasis on applications. of modern financial analysis; yield curves; spot diagnostics and plots, polynomial regression, fixed Examples from the physical sciences, social (forward) rates; duration; immunization; and short effects ANOVA and ANCOVA models, nonlinear sciences, and business. Computing is an integral sales. The course will cover determining equivalent regression, multiple comparisons, colinearity part of the course. and confounding, model selection. Emphasis on measures of interest; discounting; accumulating; geometric approach to the theory and the use of a determining yield rates; and amortization. statistical package to analyze data.

engineering 2011–2012 Campus and Student Life 206 campus life

olumbia Engineering attracts small enough to promote the close of its students and by creating a and admits an exceptionally interaction among students, faculty, and developmental, diverse, and open C interesting, diverse, and administration that has created a strong learning environment. Individually and multicultural group of students, and sense of community on campus. collaboratively, each advising dean: it takes steps to provide a campus With its mission of providing a wide • provides individual and group environment that promotes the range of services designed to enhance academic advisement, exploration, continued expansion of each student’s the student experience from the time and counseling ideas and perspectives. Starting with of admission through graduation, the • provides information on the residence halls, in which nearly all Division of Student Affairs is the hub of preprofessional studies, study abroad, first-year undergraduate students live, undergraduate student life. Admissions, and major declaration and completion, the University assigns rooms to both Financial Aid and Educational Financing, as well as various leadership, career, Engineering and Columbia College Center for Student Advising, Residential graduate school, and research undergraduate students, ensuring that Programs, Office of Multicultural Affairs, opportunities all students will live either with or near a Parent and Family Programs, Office • designs and facilitates programming student attending the other program. of Judicial Affairs and Community to meet the unique developmental Once students have moved into Standards, Student and Alumni needs of each class and to enhance their new campus home they will find Programs, Student Development and community among students, faculty, themselves part of a residential system Activities, and Office of Civic Action and and administrators that offers undergraduates a network Engagement are integral components • interprets and disseminates of social and academic support. of the Division. The integrated efforts information regarding University Designed to make students aware of of these units assures that individual polices, procedures, resources, and the vast number of social and academic students receive support in both their programs opportunities available to them at the academic and cocurricular pursuits. The • educates and empowers students to University, these networks provide an Division of Student Affairs is responsible take responsibility in making informed umbrella of comprehensive advising for assisting students in all matters decisions to help students articulate and realize beyond actual course instruction, • refers students to additional campus their goals while at Columbia. More helping to create a special spirit on resources information about the residence halls campus and a sense of community for can be found in the chapter “Housing students. Each student is assigned to an and Residence Life” in this bulletin. advising dean who advises in his or her academic area of interest. When Center for a student declares a major, a faculty Division of Student Advising member is appointed to guide him or her Student Affairs 403 Lerner Hall, MC 1201 for the next two years. Depending on Undergraduate life is not confined to Phone: 212-854-6378 their chosen major, students may also be the classroom. A blend of academic, E-mail: [email protected] assigned to work with the CSA liaison to educational, social, and cocurricular www.studentaffairs.columbia.edu/csa their major’s department. Advising deans activities contributes to the Columbia regularly refer students to their academic experience. While The Fu Foundation The Center for Student Advising (CSA) departments to receive expert advice School of Engineering and Applied reflects the mission of the University about their engineering course selections. Science is large enough to support in striving to support and challenge a wide variety of programs, it is also the intellectual and personal growth

engineering 2011–2012 Preprofessional Advising Engineering. Its members represent social, religious, cultural, academic, 207 The Office of Preprofessional Advising student interests on committees and athletic, political, literary, professional, works closely with the Center for projects addressing a wide range of public service, and other organizations. Student Advising and with the Center issues facing the Columbia community At SEAS, graduate students are for Career Education to provide and help shape the quality of life for encouraged to become active information for students who plan a Columbia students. members of the Engineering Graduate career in law or the health professions. Working in conjunction with the Student Council (EGSC). The EGSC The Office advises and assists students Student Council, the Activities Board is a recognized group that consists of throughout their four years, but works at Columbia (ABC), Student Governing representatives from each of the nine most closely with students during their Board (SGB), InterGreek Council (IGC), academic departments at SEAS. The application year and with alumni who Community Impact (CI), Club Sports, objectives of the EGSC are to foster apply for admission after graduation. and Interschool Governing Board (IGB) interaction among graduate engineering Information sheets, forms, and helpful oversee the management and funding of students, to serve as a voice for graduate resources are available in the Office more than 300 student organizations. engineering students, and to sponsor of Preprofessional Advising. Students The ABC provides governance for social and educational events of interest will work with their advising deans more than 160 recognized student to the graduate engineering community. as primary preprofessional advisers; organizations, including cultural these advisers will be instrumental in organizations, performance-based Office of Student Development writing committee evaluations for some and theatrical groups, media and and Activities professional schools. publications groups, competition and The Office of Student Development and special interests groups and pre- Activities (SDA) provides programs and professional organizations and societies. Community Development services designed to support a wide The pre-professional organizations range of co-curricular activities that help The Community Development team and societies are of special interest build a sense of community, support works to foster a vibrant and welcoming to engineering students. These responsible student governance and undergraduate community through societies reflect the range of academic student group involvement, and further organizational advising, leadership disciplines and interests to be found students’ leadership development and development, advocacy, diversity among students and include the personal growth. education, civic engagement, and Asian-American Society of Engineers, Student Development and Activities community programming. The National Society of Black Engineers, staff members advise student team includes the Office of Student the Society of Women Engineers, organizations recognized through the Development and Activities, the Office the American Institute of Aeronautics Activities Board of Columbia (ABC), as of Multicultural Affairs, the Office of Civic and Astronautics, and the Biomedical well as the student governments of The Action and Engagement, and the Office Engineering Society, just to name a few. Fu Foundation School of Engineering of Residential Programs. Knowing that The SGB provides governance and Applied Science and Columbia students’ learning continues beyond the for approximately 100 recognized College. SDA serves as resources classroom, Columbia University strongly student organizations that are faith- for event planning, organizational encourages students to become based, spiritual, political, activist, and leadership, and budgeting. The Office involved in programs and activities to humanitarian and that encourage open of Student Development and Activities enhance their educational experience interreligious and political dialogue at offers leadership training workshops and personal growth. A wide array of Columbia University’s Morningside and helps networking among student student organizations addresses both campus. The Interschool Governing leaders and administrative offices. In student interests and professional Board recognizes student organizations addition, the SDA administers the Urban concerns, including the arts, politics, whose membership spans across the New York Program, the New Student identity, culture, and religion. Joining various undergraduate and graduate Orientation Program, the Columbia such groups offers an exciting and schools. Urban Experience Program, and the dynamic opportunity to develop For more information on the InterGreek Columbia Outdoor Orientation Program. leadership skills that will serve students Council (IGC), see Fraternities and well throughout their lives. Sororities, below. For more information on Orientation Club Sports, see Intercollegiate Athletics All new students are required to Student Organizations Program (page 209), and for more participate in an orientation program Programs and activities at Columbia information on Community Impact see that is designed to acquaint them with are shaped primarily by students who Office of the University Chaplain (page the University and its traditions, the assume leadership and volunteer 215). All the governing groups provide administration and faculty of The Fu positions in hundreds of organizations networking, leadership, and professional Foundation School of Engineering and across the campus. The Engineering development opportunities for students. Applied Science, upperclass students, Student Council and its associated class Columbia University graduate and New York City. The New Student councils are the elected representative students can participate in and enjoy Orientation Program (NSOP) for new body of undergraduates at Columbia hundreds of diverse, University-affiliated

engineering 2011–2012 208 undergraduate students begins the among student groups. The Office of community within the student body. week prior to the start of the fall Civic Action and Engagement works to These contributions form an integral semester. NSOP is intended to assist enhance the undergraduate educational part of a Columbia education by all new students with the transition to experience by fostering a dynamic stimulating mutual understanding and college life. and enriching University community, by fostering an atmosphere based on Orientation is busy, exciting, and a supporting responsible student the appreciation of the differences and lot of fun, but it is also a week in which governance and co-curricular activities, similarities characterizing such a diverse important academic decisions are and offering programs and opportunities cultural community. made. Scheduled into the program are focused on civic and community The undergraduate student information sessions and opportunities to engagement. Through advising, the staff, resident advisers (RAs), and meet with academic advisers. Through office encourages critical thinking and community advisers (CAs) serve as large group programs and small group the free exchange of ideas by all of the role models for their residents. They activities, students will be introduced student organizations it supports. facilitate discussions about community to faculty members, deans, resident standards, provide community building advisers, and other students. NSOP Office of Multicultural Affairs programs, and serve as a resource for includes walking tours of New York City, The Office of Multicultural Affairs is the residents. Their RAs/CAs serve as social events, and information sessions devoted to promoting a just society the front line of a layered on-call system on University services and co-curricular and exploring issues of interculturalism and are trained to respond to the variety opportunities. During NSOP, new and diversity within and beyond the of issues that emerge in community life. students have the campus to themselves. Columbia University community. By The Faculty-in-Residence Program This provides students with a unique promoting forums that address diversity allows students, alumni, and faculty to opportunity to make friends and settle issues, self-discovery takes place meet formally and informally throughout into life at Columbia before classes begin. along with a greater awareness and the year. Faculty members who reside Undergraduate students may e-mail appreciation of cultural history within and in three residence halls invite students [email protected] or call 212-854- between communities on campus. We to dine in their apartments; organize 5808 for additional information on NSOP. endeavor to empower students, faculty, special programs around issues of Orientation for graduate students is and staff with the tools to be able to interest; provide opportunities for scheduled during the week prior to the successfully navigate their environments academic growth and challenges within beginning of each semester. For more and thus be able to positively change the residence halls; and help students information on orientation for graduate and impact the community at large. establish links with major cultural, students, contact the Office of Graduate Programs and services provided political, and professional institutions in Student Services. by Multicultural Affairs include the New York City. In addition, the faculty Columbia Mentoring Initiative, a member in residence partners with the Office of Civic Action and program connecting incoming Engineering alumni office to provide Engagement students with returning students, opportunities for students to network The Office of Civic Action and and returning students with alumni; and gain exposure to a variety of Engagement (CAE) is committed to Respecting Ourselves and Others careers. supporting the programming of our faith- Through Education (ROOTED), a peer Begun in fall 2006, the Gateway based, spiritual, political, activist, and diversity faciliation program; Dessert Residential Initiative allows Engineering humanitarian student organizations. In and Discussion, the signature lecture first-years, sophomores, juniors, and reaching to fulfill this commitment, CAE series; and the Intercultural House (ICH), seniors to live together clustered in the provides programming in leadership a unique residential experience that is Living Learning Center (LLC) housed in skills, program development, and supportive of Multicultural Affairs’ social Hartley and Wallach Halls. This initiative organizational management to all justice goals. seeks to bridge the academic and undergraduate student organizations co-curricular experience for Engineering recognized by the Student Governing Residential Programs students. Mentorship between students, connection among the class years, and Board (SGB) and organizations The Residential Programs staff, alumni interaction are the foundations for recognized by the Interschool Governing supervised by the Assistant Dean of the success of the program. Board (IGB). CAE assists students Community Development and Residential in their development as individuals, Programs, includes 8 professional community members, and leaders. staff, 13 graduate students, and 130 Fraternities and Sororities Issues of social responsibility undergraduates who contribute to the Fraternities and sororites have and civic engagement are central to growth, well-being, and personal and brownstones near the campus and the mission of CAE and the student intellectual development of students. some of the organizations without organizations that CAE supports. CAE The staff strives to enhance the quality brownstones have a suite within the strives to encourage open dialogue of residential life by cultivating an residence halls. at Columbia University’s Morningside atmosphere conducive to educational The InterGreek Council (IGC) is the Campus and seeks to find connections pursuits and the development of self-governing student organization that provides guidelines and support to the

engineering 2011–2012 three Greek councils: The Interfraternity and intercultural awareness. Residential Programs, Judicial Affairs, 209 Council (IFC), Panhellenic Council, The University Chaplain is available Multicultural Affairs, Office of Civic Action and Multicutural Greek Council (MGC). for confidential pastoral counseling to and Engagement, Center for Student There are thirty-three recognized Greek individuals, couples, and families in the Advising, Financial Aid, and Educational organizations whose membership totals Columbia University community. The Financing). These offices also include over one thousand undergraduates. Office of the University Chaplain may Student Development and Activities, Fraternity and sorority members share also assist with private ceremonies such the Double Discovery Center, Columbia in service, scholastic, philanthropic, as weddings, christenings, and memorial TV, WKCR, Disability Services, and cultural, and leadership experiences. This services. We warmly welcome your Counseling and Psychological Services. active and vibrant community adds to interest, questions, and participation. the diversity of the residential experience. For more information, please call the Office of Graduate Earl Hall Center at 212-854-1474 or Student Services 212-854-6242 or visit www.columbia. Office of Judicial Affairs The Office of Graduate Student edu/cu/earl/. and Community Standards Services at The Fu Foundation School The Office of Judicial Affairs and of Engineering and Applied Science Community Standards was created Lerner Hall is integral to the School’s teaching, to assist students in the maintenance Columbia’s student center, Lerner Hall, research, and service mission, and of a safe, honest, and responsible officially opened in the fall of 1999. works to enhance the educational campus community. To achieve this Located on the southwest corner of opportunities available to students. goal, the Office of Judicial Affairs and campus, this 225,000-square-foot This Office provides leadership for the Community Standards partners with student center was designed by Bernard integration of educational programs administrators and faculty to create Tschumi, the former Dean of Columbia’s and services that enhance recruitment, programs designed to educate students Graduate School of Architecture, retention, and quality of campus life regarding the potential impact of their Planning and Preservation. Architectural for graduate students at Columbia actions on both their individual lives and features of Lerner Hall, such as the glass Engineering. It strives to demonstrate the community at large. In addition, the facade and ramps, allow the campus sensitivity and concern in addressing the Office of Judicial Affairs and Community to clearly view the activities within the needs of the School’s population. The Standards works with student groups building, and offer those within Lerner Office is dedicated to providing service to facilitate the development of skills scenic views of the campus. to prospective, new, and continuing and processes students can use to Undergraduate students are likely to students pursuing a graduate education hold each other accountable when they visit Lerner to check the mail from the in engineering or applied science. encounter inappropriate behavior. The 7,000 student mailboxes located along Office of Judicial Affairs and Community the ramps. Students may check their Intercollegiate Athletics Standards also holds students e-mail in Lerner’s computer center or Program accountable for inappropriate behavior by plugging in their laptop computers through the Dean’s Discipline process at one of Lerner’s Ethernet-outfitted Columbia has a long tradition of success when necessary. lounges. Students will also visit Lerner in intercollegiate athletics, and The Fu to interact with one another in various Foundation School of Engineering and ways. They may strategize and plan Applied Science has always been an Office of the events with their student organizations in active participant in these programs. University Chaplain one of the student club offices, or in the While Columbia’s intercollegiate athletics Columbia is home to a community meeting rooms designated for student program is governed by Ivy League of scholars, students, and staff from club usage. Students may also meet regulations, Columbia is also a member many different religious backgrounds. friends in one of Lerner’s two dining of the National Collegiate Athletic The Office of the University Chaplain locations, for an event in the auditorium, Association. Columbia sponsors men’s ministers to their individual faiths and in various lounges, or in one of the varsity teams in baseball, basketball, supports individual spirituality, while building’s multipurpose spaces that are cross-country, fencing, football, golf, promoting interreligious understanding. ideal for exercise classes. rowing (heavyweight and lightweight), The University Chaplain oversees the In addition to providing spaces for soccer, squash, swimming and diving, work of the United Campus Ministries—a student interaction, Lerner is home to tennis, track and field (indoor and fellowship of more than twenty religious the Columbia University Bookstore. outdoor), and wrestling. life advisers representing specific faith Lerner also features retail services, Women in all undergraduate divisions traditions. The University Chaplain also including a travel agency, a copy center, of Columbia and in Barnard College fosters learning through spiritual, ethical, and an electronic banking center. compete together as members of religious, political, and cultural exchanges Included in the building are orchestra/ University-wide athletic teams. The and hosts programs on matters of band rehearsal and art exhibition spaces, arrangement, called a consortium under justice, faith, and spirituality. Through and various administrative offices (Dean NCAA rules, is one of only three in the these and other means, the Office of the of Student Affairs, Student Services, nation and the only one on a Division University Chaplain cultivates interfaith I level. Currently, there are women’s

engineering 2011–2012 210 varsity teams in archery, basketball, pool with three diving boards; a fully sports. Individual activities function cross-country, fencing, field hockey, equipped three-level exercise and through tournaments, while team golf, lacrosse, rowing, soccer, softball, weight room facility; two aerobic dance/ activities feature both league and squash, swimming and diving, tennis, martial arts rooms; a fencing room; a tournament competition. Club sports are track and field (indoor and outdoor), and wrestling room; an indoor running track; designed to allow groups of individuals volleyball. and two fully equipped saunas. who share a common athletics interest Columbia’s commitment to success to organize and collectively pursue in intercollegiate sporting competition Eligibility for Intercollegiate Athletics this activity. Clubs are organized has been matched by the determination Any student in the Engineering School on recreational, instructional, and of alumni and administrators to upgrade who is pursuing the undergraduate competitive levels. Activities range from the University’s athletic facilities. The program or an approved combined organized instruction to intercollegiate Baker Field Athletics Complex, a few program toward a first degree is eligible and tournament competition. A list of miles up the Hudson River on the for intercollegiate athletics. To be eligible the intramural activities and sports clubs northern tip of Manhattan, has been for athletic activities, the student must: as well as all information regarding the completely rebuilt and expanded. • Be a candidate for a bachelor’s degree program can be obtained in the Office of The complex features Robert K. Kraft • Be registered for at least 12 points of Intramurals and Club Sports, 331 Dodge Field at Lawrence A. Wien Stadium, credit Fitness Center or on the website at a 17,000-seat football and lacrosse • Make appropriate progress toward the www.gocolumbialions.com. facility; Robertson Field at Satow degree as defined by the NCAA, the Stadium, home of the baseball program; Ivy League, and Columbia University. Campus Safety softball and field hockey venues; and These criteria are monitored by the and Security an Olympic-quality synthetic track. At Director of Compliance and certified Columbia University prepares an annual Columbia’s Dick Savitt Tennis Center at by the Office of the Registrar. security report, which is available to the Baker Athletics Complex there are • Have attended the University for not all current and prospective employees six cushioned hard tennis courts, all of more than eight terms and students. The report includes which are covered by a state-of-the-art • Not have completed the requirements statistics for the three previous years air dome for winter use. The Remmer for the bachelor’s degree concerning reported crimes that and 1929 Boathouse includes a three- occurred on campus, in certain off bay shell house, complete with an upper Questions about athletic eligibility should campus buildings or property owned or level that includes an erg and weight be referred to the appropriate academic controlled by Columbia University, and room. adviser or the Director of Compliance on public property within, or immediately Columbia’s Dodge Physical Fitness in the Department of Intercollegiate adjacent to and accessible from, the Center draws thousands of students Athletics and Physical Education. campus. The report also includes each day for recreation, physical institutional policies concerning campus education classes, intramural play, club Recreational Programs security, such as policies concerning competition, and varsity sport contests In addition to the required physical sexual assault, and other matters. You and practices. The Center houses education courses (see page 13), the can obtain a copy of this report by most indoor sports and is available to Department of Intercollegiate Athletics contacting the Director of Administration all registered students. Major athletic and Physical Education offers a and Planning, Public Safety at 212- facilities on campus include two full-size comprehensive Intramural and Club 854-3815 or by accessing the following gymnasiums for basketball, volleyball, Sports Program. Through intramurals, website: and badminton; eight squash and students have the opportunity to www.columbia.edu/cu/publicsafety/ handball courts; the eight-lane Uris participate in both individual and team SecurityReport.pdf.

engineering 2011–2012 student services 211

university housing each floor. East Campus, 47 Claremont, campus. For further information, see Hartley-Wallach Living Learning Center, UAH’s website at www.columbia.edu/ Undergraduate Housing Hogan, River, Ruggles, 600 West 113th cu/ire. International House, a privately The residence halls are an important Street, Watt, and Woodbridge offer owned student residence near the focus for campus life outside the suite-style living, and all have kitchens. campus, has accommodations for about classroom, with the University All residence hall rooms are either single five hundred graduate students, both housing more than 95 percent of the or double. Single and double rooms international and American, who attend undergraduate population in residence are available in all halls except Carman, various area colleges and universities. halls on or near the campus. A trained which has only doubles, and Hogan, It provides a supportive and cross- Residential Programs staff lives with which is all singles. cultural environment with many activities the students in the halls. They work The residence halls are also and resources, and it is conveniently to create an atmosphere conducive home to a variety of Special Interest located two blocks from the Engineering to educational pursuits and the Communities. These communities building. For more information, write or development of community among the provide an opportunity for students call: International House, 500 Riverside diverse student body. Throughout the with a common interest to live together Drive, New York, NY 10027; 212-316- year the Residential Programs staff and develop programs in their area of 8400; or check their website at www. presents programs in the residence halls interest. The themes may vary from ihouse-nyc.org. and off campus that are both social and year to year. First-year students are There are also a number of off- educational. not eligible to live in Special Interest campus housing opportunities. The Columbia guarantees housing for Communities but are welcome to attend University operates Off-Campus all undergraduate students (except events. Housing Assistance (OCHA), which transfers) who have filed their intent Upperclass Columbia students also lists rooms and apartments in rental to reside on campus by the stated have the option of living in Brownstones, properties not owned or operated deadline and who have continuously Greek organizations, and certain by the University. Only students with registered as full-time students. Each Barnard College halls. Rooms are a valid ID or admission acceptance spring, continuing students participate chosen by a room selection process, letter are permitted to use the facility. in a room-selection process to select which takes place each spring. OCHA is open throughout the winter their accommodations for the next For more information, please visit and summer vacation periods except academic year. Students who take the housing website at academic holidays. Students should call an unauthorized leave of absence are www.columbia.edu/cu/housing 212-854-2773 for office hours. OCHA placed on the non-guaranteed wait list also operates a Web page at www. upon their return and are on the wait list Graduate Housing columbia.edu/cu/ire/ocha. There is also for each subsequent year. Graduate students have a number of a list of alternative housing opportunities A variety of residence hall housing opportunities in the Morningside maintained by the Office of Graduate accommodations are available to Heights neighborhood. The three main Student Services in 524 S. W. Mudd. Columbia students. Carman, John sources are University Apartment Students are sent the Alternative Jay, Wien, Furnald, McBain, Schapiro, Housing (UAH), International House, Housing flyer in their orientation packets. Harmony and Broadway Residence and off-campus listings. UAH operates UAH applications are sent along with Halls are traditional corridor-style Columbia-owned apartments and acceptance packets from the Office of residence halls, and all but Wien, John dormitory-style suites in the Morningside Graduate Student Services. They are also Jay, and Carman have kitchens on area within walking distance of the available in the Office of Graduate Student Services and the UAH Office. You can

engineering 2011–2012 212

also seek additional information on the Graduate Orientation and Registration, Meals Columbia Students Page: www.columbia. which are generally held the week before The meals portion of the dining plan edu/cu/students. Graduate housing the first day of class. If a student needs enables students to help themselves through UAH is processed for the fall and to move in earlier, proper documentation to unlimited servings of food served spring terms only. Summer sublets are from the department in support of the in John Jay Dining Hall, Ferris Booth also available through individual referrals. request is necessary. Commons, or JJ’s Place. The hours The UAH Office maintains an active listing of operations for these locations offers for those interested. Dining Services dining options for breakfast, lunch, Due to the growing demand for dinner, and late-night, with continuous housing, graduate housing is no longer dining from 7:30 a.m. to midnight. guaranteed, but every effort is made First-Year Students All first-year students in residence are to accommodate you. It is critical that Dining Dollars required to enroll in one of two dining you submit your housing application as In addition to meals, Dining Dollars plans, each of which is comprised of a soon as possible and that you follow the comprise the other portion of the first- varying number of meals served in John instructions in your acceptance packet. year dining plan. Each Dining Dollar is Jay Dining Hall, Ferris Booth Commons, Housing applications received after the equal to one dollar and operates as a or JJ’s Place, and Dining Dollars, which set date are not guaranteed housing. declining balance account, much like a can be used at the 12 dining locations The order of priority for selection is: debit card. on campus. graduate fellowship recipients, Zone 1 Columbia Dining Services maintains students (those who live further than First-Year Dining Plans twelve dining facilities conveniently 250 miles from campus), and then Zone 1. 19 meals per week and 75 Dining located on campus. Each of the 2 students (those who live between Dollars per term, plus 15 floating locations accepts Dining Dollars, 50 and 250 miles from campus). All meals and 6 faculty meals an alternative to cash payment that continuing students and applications 2. 15 meals per week and 125 Dining is accessed by the Columbia Card from Zone 3 areas (within 50 miles) are Dollars per term, plus 10 floating (student ID card). automatically placed on a waiting list. meals and 6 faculty meals With Dining Dollars, students will UAH-approved students can begin The dining plans are transacted through enjoy the ease and flexibility of cashless viewing apartments and moving in during transactions as well as the savings of the last week of August for the fall term, Columbia’s ID Card, called the Columbia Card, which serves as a convenient way sales tax on all food purchases. Dining and early January for the spring term. Dollars will roll over from year to year Students will be properly notified of to enjoy dining all over campus without carrying cash. until graduation.

engineering 2011–2012 Upperclass and Graduate Students Columbia health support services including assistive 213 Many upperclass and graduate students Phone: 212-854-2284 technology, networking groups, who dine on campus open a Dining After-hours Urgent Health academic skills workshops, and learning Dollars account; however, some choose Concerns: 212-854-9797 specialists. to enroll in an upperclass/graduate www.health.columbia.edu student dining plan. Alice! Health Promotion Dining Services offers four plans—all Columbia Health is an integrated Wien Hall, 1st Floor are accessed by the Columbia Card program providing extensive on- and off- Phone: 212-854-5453 and can be used for meals in John Jay campus health care and services for you www.health.columbia.edu/alice Dining Hall, Ferris Booth Commons, or while you are enrolled at the University. Alice! Health Promotion connects JJ’s Place.The hours of operations for The Columbia Health Program and an students with information and resources, these locations offers dining options for accepted medical insurance plan work and supports healthy attitudes and breakfast, lunch, dinner, and late-night, together to meet your health care needs. behaviors within the campus community. with continuous dining from 7:30 a.m. Columbia requires all full-time students to midnight. to enroll in both. To meet the insurance Sexual Violence Response requirement, you must either confirm Lerner Hall, 3rd Floor Upperclass, GS, and Graduate Dining your enrollment in the Columbia Student Phone: 212-854-3500 Plans Medical Insurance Plan (Columbia Plan) www.health.columbia.edu/svprp A. 14 meals per week and 200 Dining or provide proof of alternate coverage Dollars per term, plus 15 floating Sexual Violence Response supports that meets the established criteria listed meals and 6 faculty meals students in healing from sexual and on the Columbia Health website. Part- B. 175 meals and 200 Dining Dollars per relationship violence, as well as time students may also enroll in the term, plus 6 guest meals educates students about consent and Columbia Health Program and Columbia C. 100 meals and 125 Dining Dollars per coercion to promote a respectful and Plan. term, plus 4 guest meals safe campus. D. 75 meals and 75 Dining Dollars per Benefits and Services of the term, plus 2 guest meals Student Health Insurance Columbia Health Program Wien Hall, 1st Floor Kosher Dining Plan The Columbia Health Program Phone: 212-854-3286 compromises five departments and All students who participate in a dining more than 120 individuals to meet your All full-time students are automatically plan, including first-year, upperclass, health needs on campus. enrolled in the Basic level of the General Studies, or graduate students, Columbia Plan. To request a waiver are eligible for the Columbia Kosher Medical Services from automatic enrollment, you must Dining Plan. Signing up for this dining John Jay Hall, 3rd and 4th Floors submit a request at www.health. plan allows access to a restricted Phone: 212-854-7426 columbia.edu before September 30 kosher area within John Jay Dining www.health.columbia.edu/pcms (February 1 for new spring enrollment, Hall as well as Express Meals to go. or June 14 for newly arrived full-time CU kosher meals can also, for an Medical Services provides routine and trimester students). All waiver requests additional charge, be exchanged for urgent medical care, as well as sexual are considered but approval is not a kosher meal at Barnard’s Hewitt health, reproductive and gynecological guaranteed. Hall (kosher to kosher only). To sign services, travel medicine, LGBTQ health Optional coverage for early arrival, up, the student selects a plan from care, confidential HIV testing, and eligible dependents of insured students, either the First Year Dining Plan or immunizations. and a separate dental plan is available the Upperclass Dining Plan options, through Aetna Student Health. according to the student’s status, then Counseling and Psychological Services For more information, go to www. elects to enroll in the Kosher Dining Lerner Hall, 8th Floor aetnastudenthealth.com/columbiadirect. Plan. The addition of the Kosher Phone: 212-854-2878 html. Dining Plan adds 10 percent to the www.health.columbia.edu/cps cost of the selected plan. Visit the Counseling and Psychological Services Immunization Compliance H&D Customer Service Center in 118 offers short-term individual counseling, Hartley Hall (enrollment allowed at any couples counseling, student life support Wien Hall, 1st Floor point throughout the term) to sign up. groups, and medication consultation. Phone: 212-854-7210 There are two immunization Locations/Menus/Hours Disability Services requirements that all new students must Locations, menus, and hours of all Lerner Hall, 7th Floor meet before arrival on campus: campus dining facilities can be found at Phone: 212-854-2388 www.health.columbia.edu/ods Meningococcal Meningitis Vaccination www.columbia.edu/cu/dining. New York State public health law Disability Services coordinates requires that students receive reasonable accommodations and

engineering 2011–2012 214 information from their institutions about Documentation of Immunity to Measles, Please visit our website at www.health. meningococcal meningitis and the Mumps, and Rubella (MMR) columbia.edu. If you have questions, vaccine that protects against most All Columbia students taking six or please contact us. strains of the disease that can occur on more points of credit must document university campuses. Columbia students their immunity to measles, mumps, and must make an informed decision about rubella. Instructions and the Columbia being vaccinated and certify their University MMR Form are available decision online. Full instructions are at www.health.columbia.edu. This given at www.health.columbia.edu and documentation is also required by New the process takes two to three minutes York State public health law. to complete. You must formally indicate Deadline: Completed forms must your decision about being vaccinated be mailed or faxed before registering before you will be permitted to register for classes (August 1 for fall students, for classes. January 15 for new spring students). Deadline: Decisions must be recorded online before classes begin. Students will not be permitted to register until a decision is recorded.

engineering 2011–2012 Scholarships, Fellowships, Awards, and Prizes 216 Scholarships, Fellowships, Awards, and Prizes

Endowed Scholarships Frank and Harriet Ayer Scholarship Cornelius A. Boyle Scholarship (1962) and Grants (1977) Bequest of Cornelius A. Boyle. Bequest of Frank A. Ayer. Graduates Cvi Abel Memorial Scholarship (2003) of Deerfield Academy are given first Lauren Breakiron Fund (1999) Gift of Jack Abel. preference. For a student continuing in Columbia Engineering. Preference given to Aigrain Family Scholarship (2008) Cesare Barbieri Scholarship (1953) United States citizens. Gift of Lauren P. Gift of Jacques and Nicolleta Aigrain P’08. Gift of Cesare Barbieri Fund. Breakiron ’56.

Walter H. Aldridge (1936) William S. Barstow Scholarship (1935) Edwin W. and Mary Elizabeth Gift of Walter H. Aldridge. Gift of William S. Barstow. Bright Scholarship in Mechanical Engineering (1985) Alvey-Ferguson Company Edwin D. Becker Scholarship Fund Gift of Edwin W. ’42 and Mary Elizabeth Scholarship (1948) (1993) Bright. Awarded to a deserving Gift of the Alvey-Ferguson Company. Gift of Edwin D. Becker ’56. Preference mechanical engineering student who is a is given to students from the Rocky native-born U.S. citizen. Erwin H. Amick Memorial Scholarship Mountain states. (1970) Lewis G. Burnell Memorial Gift of various donors for students John E. Bertram Memorial Scholarship (2001) in chemical engineering and applied Scholarship (1990) Gift of Roger W. Burnell in memory of chemistry. Gift of Mrs. Lucy Bertram and friends his father, Lewis G. Burnell. Income to in honor of John E. Bertram. Awarded award an annual scholarship to a needy Nathaniel Arbiter Scholarship (1985) to students in electrical engineering or and deserving undergraduate. Gift of various donors in honor of computer science. Professor Nathaniel Arbiter for graduate Burns and Roe, Arthur J. Fiehn and undergraduate students in the Jerry and Evelyn Bishop Scholarship Scholarship (1989) following specializations in order of (1984) Gifts from various donors in memory of preference: mineral beneficiation, mines, Gift of Jerry ’42 and Evelyn Bishop for Arthur J. Fiehn ’46. and physical metallurgy. students in the Combined Plan Program. Preference is given to students in Byron Fellowship (1980) Attardo Scholarship (1999) the program who attended Columbia Bequest of Verna and Oscar Byron 1914. For needy and deserving students in College. Columbia Engineering. Gift of Michael J. Samuel J. Clarke Scholarship (1960) Attardo ’63. Paul H. Blaustein Scholarship (1994) Bequest of Agnes Robertson Clarke. Gift of Barbara Blaustein, Stacey Jee Yin and Choi Heung Au Blaustein Divack, and Joshua Divack. Class of 1885 (1910) Scholarship Fund (2002) Gift of the Class of 1885 School of Gift of Michael M. Au ’90 to support Philip P. Bonanno Scholarship (1999) Mines in commemoration of the twenty- undergraduate scholarships at Columbia Donated by Philip P. Bonanno ’55, fifth anniversary of their graduation. Engineering, with a preference to be Fidelity Investments Charitable Gift Fund. given to needy and deserving students Awarded to a deserving undergraduate. Class of 1889 (1939) who have graduated from Stuyvesant Gift of the Class of 1889 College and High School in New York City. Engineering.

engineering 2011–2012 Class of 1900 (1940) Herbert J. Cooper Scholarship (1999) Jack B. Freeman Scholarship (1994) 217 Gift of the Class of 1900 College and Gift of Mrs. Deborah Cooper and Supports a Columbia Engineering Engineering. the Estate of Herbert J. Cooper ’46. undergraduate who also plays varsity Awarded to a deserving undergraduate. baseball. Gift of Jack B. Freeman ’55. Class of 1902 (1952) Gift of the Class of 1902 College and Milton L. Cornell Scholarship (1958) Pier-Luigi Focardi Scholarship (1964) Engineering. Gift of various donors in memory of Bequest of Clara G. Focardi. Milton L. Cornell. Class of 1906 (1940) Ford/EEOC Scholarship Gift of the Class of 1906 in honor of Paul and Lillian Costallat Scholarship Designated for minorities and women. Frank D. Fackenthal 1906. (1972) Preference is given to Ford employees, Gift of Paul and Lillian Costallat. their spouses, or children. Class of 1907 (1937) Gift of the Class of 1907. Preference is Frederick Van Dyke Cruser Z. Y. Fu Scholarship (1993) given to sons and descendants of class Scholarship (1980) Gift of The Fu Foundation for members. Bequest of Maude Adelaide Cruser. For undergraduate scholarship support. students in chemical engineering with Class of 1909 (1959) financial need. General Motors Scholarship Gift of the Class of 1909 in honor of Designated for minorities and women. John J. Ryan. Cytryn Family Scholarship (2002) Preference is given to General Motors Gift of the Cytryn Family Fund to provide employees, their spouses, or children. Class of 1913 (1963) financial aid to deserving undergraduates. Gift of the Class of 1913 in Ben and Ethelyn Geschwind commemoration of the fiftieth Frank W. Demuth Scholarship (1965) Endowed Scholarship (2004) anniversary of their graduation. Bequest of Frank W. Demuth 1914. Gift of Benjamin and Ethelyn ’84 Geschwind. Awarded to a deserving Class of 1914 (1937) Freda Imber Dicker Endowed undergraduate. Gift of the Class of 1914 College and Scholarship Fund (2000) Engineering for a pre-engineering or Gift of Dr. Stanley Dicker ’61 in honor Alger C. Gildersleeve Scholarship prearchitecture student. of the hundredth anniversary of his (1955) mother’s birth (March 5, 1900). Bequest of Josephine M. Gildersleeve, in Class of 1950 Endowed Scholarship honor of Alger G. Gildersleeve 1889. (2000) Jack Dicker Endowed Scholarship Gift of members of the Class of 1950 (2003) Frederick A. Goetze Scholarship (1960) in commemoration of the fiftieth Gift of Dr. Stanley Dicker ’61 in honor Gift of William A. Baum, in honor of the anniversary of their graduation. Awarded of his father, to support a deserving former Dean of Columbia Engineering. to a deserving undergraduate. junior or senior in the Department of Biomedical Engineering. Sarah E. Grant Memorial Scholarship Class of 1951 Endowed Scholarship (1997) (2001) James and Donna Down Scholarship Gift of Geoffrey T. ’82 and Annette M. Gift of members of the Class of 1951 (1997) Grant in memory of their daughter, in commemoration of the fiftieth Gift of James ’73 and Donna Down to Sarah, to be awarded annually to a anniversary of their graduation. Awarded be awarded annually to a deserving deserving undergraduate who has to a deserving undergraduate. minority undergraduate who has demonstrated academic achievement. demonstrated academic achievement. Class of 1952 Endowed Scholarship Adam R. Greenbaum Memorial (2002) Stancliffe Bazen Downes Scholarship Scholarship Fund Established by Alexander Feiner to be (1945) Established in memory of Adam R. awarded to a deserving undergraduate. Bequest of Bezena Treat Downes Greenbaum by his parents, relatives, Merriman in honor of her brother, for a and friends following his death in Hugo Cohn Scholarship (1984) student in civil engineering. February 2001, when he was a Awarded annually with preference given sophomore. The scholarship is given to to electrical engineering students. Gift of Brooke Lynn Elzweig Scholarship (2002) a SEAS sophomore who was named to Hugo Cohn 1909. Gift of Gary Elzweig ’77. Income to the Dean’s List as a first-year, as Adam support an annual scholarship for a was, with a preference to students from deserving undergraduate student with New Jersey and New York. high financial need.

engineering 2011–2012 218 Luther E. Gregory Scholarship (1963) Edward Gurnee Hewitt Scholarship Stanley A. and Minna Kroll Bequest of Luther E. Gregory 1893. (1980) Scholarship for Engineering and Bequest of Mary Louise Cromwell. Computer Science (1987) Robert Gross Fund (1999) Gift of Stanley A. Kroll ’28. For Gifts of friends of Robert Gross for an Prentice Hiam Memorial Scholarship undergraduates who are studying applied physics student. (2007) electrical engineering or computer Gift of Atul Khanna ’83. Preference given science. Wallace K. Grubman-Graham to international students. Scholarship (1998) Henry Krumb Scholarship (1945) Gift of Wallace Grubman ’50 and James T. Horn Scholarship (1938) Gift of Henry Krumb for annual the Grubman Graham Foundation to Gift of Sarah L. and Mary T. Horn, in scholarships in mining engineering, support an undergraduate student in memory of their brother, James T. Horn metallurgy, and ore dressing. chemical engineering. 1884. Jacob Kurtz Memorial Scholarship Lawrence A. Gussman Scholarship Richard and Janet Hunter Scholarship (1982) (1987) (2000) Gift of Kulite Semiconductor Products, Gift of Lawrence Gussman ’38. Gift of Richard ’67 and Janet Hunter. Inc., and Kulite Tungsten, for Awarded annually to students studying Scholarship awarded to 3-2 program undergraduates, preferably studying in computer science. participants entering Columbia the fields of metallurgy or solid-state Engineering, with prefereces given to physics. In memory of Jacob Kurtz 1917. Haight Family Scholarship (2004) graduates from Whitman College. Gift of Deborah E. Haight ’00. Ronald A. Kurtz Scholarship Fund Awarded to a talented and deserving Jonathan Lewis Isaacs Memorial (1990) undergraduate. Scholarship (2001) Gift of Kulite Tungsten. This scholarship was endowed in 2001 Ralph W. Haines Scholarship (2002) by Gary F. Jonas ’66 and Jonathan L. Lahey Scholarship (1932) Gift of Ralph W. Haines ’69 for needy Isaacs ’66 as the Future Entrepreneurs Bequest of Richard Lahey. and deserving students in Columbia Scholarship to acknowledge the thirty- Engineering. fifth anniversary of their graduation from Charles and Sarah Lapple Columbia Engineering. On April 30, Scholarship (2004) A. A. Halden Scholarship (1962) 2003, Mr. Isaacs died at the young age Bequest from the Estate of Charles E. Established by bequests from Dorothy of fifty-seven, and the scholarship was Lapple and Sarah V. Lapple to be used C. Halden and Barbara Schwartz in then renamed in his memory by Gary F. to provide scholarships to deserving memory of Alfred A. Halden. Jonas, with the support of Jon’s wife, undergraduate students. Charlotte Isaacs. The Hamann Scholarship (1970) Frank H. Lee Memorial Scholarship Bequest of Adolf M. Hamann 1910. Sheldon E. Isakoff Endowed for Combined Plan Students (1986) Scholarship Fund (2000) Awarded annually to a student in the Alfred M. and Cornelia H. Haring Gift of Sheldon E. ’45 and Anita Isakoff. Combined Plan Program in honor of Scholarship (1965) Awarded to a deserving chemical Professor Frank H. Lee. Gift of the Aeroflex Foundation for an engineering undergraduate. annual scholarship in the School of Mines. Leung Endowed Scholarship (2006) Alfred L. Jaros Memorial Scholarship Gift of Lawrence Leung P’10, P’15. H. Field Haviland Scholarship Fund (1967) Awarded annually to a deserving (1988) Gift of various donors, in memory of undergraduate. Scholarships to be awarded equally Alfred L. Jaros 1911. between Columbia Engineering and James F. Levens Scholarship (1973) Columbia College. Bequest of Henry F. Cavalier Hargrave Jouet Scholarship Bequest of Ola Levens Poole for Haviland 1902. (1941) students in chemical engineering and Bequest of Belinda Hearn Jouet, in applied chemistry. Harold T. Helmer Scholarship (1965) memory of C. H. Jouet 1882. Bequest of Harold T. Helmer. George J. Lewin Scholarship (1965) Alfred E. Kadell Scholarship (1995) Gift of George J. Lewin 1917 and family. David Bendel Hertz College/Engineering Bequest of the Estate of Alfred E. Kadell Preference given to hearing-impaired Interschool Scholarship (1989) 1921. students. Gift of David B. Hertz ’39. Awarded in alternate years to the College and to the Wayne Kao Scholarship (1988) Alvin and Richard H. Lewis Engineering School to a student electing Awarded annually to undergraduate Scholarship to receive a B.A. from Columbia College students. Gift of Mabel C. Kao in Gift of Alvin and Helen S. Lewis in and a B.S. from Columbia Engineering. memory of Wayne Kao ’49. memory of their son, Richard Lewis ’63.

engineering 2011–2012 James M. and Elizabeth S. Li John K. Mladinov Scholarship (1994) Brainerd F. Phillipson Scholarship (1936) 219 Endowed Scholarship (2006) Gift of Barbara P. Mladinov in honor Gift of an anonymous donor in memory Gift of James ’68, ’70, ’76 and Elizabeth of her husband, John K. Mladinov ’43. of Brainerd F. Phillipson. Li. Awarded to students majoring in Awarded to a deserving undergraduate industrial engineering and operations. with a minor in liberal arts. Andre Planiol Scholarship (1967) Bequest of Andre Planiol for a student Robert D. Lilley Memorial Scholarship Frank C. Mock and Family from France. (1988) Scholarship (1987) For students who are in their final year Bequest of Frank C. Mock 1913. For Roy Howard Pollack Scholarship (1998) of the 3-2 Combined Plan Program and students in electrical engineering with Bequest of Roy Howard Pollack to be who have a commitment to community financial need. used for scholarships for junior or senior service. students. New Hope Foundation Scholarship Bruce and Doris Lister Endowed (2006) Polychrome-Gregory Halpern Scholarship (2000) Gift of Lee and Margaret Lau P’09 Scholarship Gift of Bruce A. Lister ’43, ’47 to P’10CC. Awarded to a deserving For graduate and undergraduate support a needy and deserving undergraduate with preference to students in chemical engineering and undergraduate student. students from Ontario, Canada, or applied chemistry. mainland China. Anna Kazanjian and Guy Longobardo Professor William H. Reinmuth Scholarship (2007) A. Peers Montgomery Memorial Scholarship (1988) Gift of Anna Kazanjian ’49, ’52 and Guy Scholarship (1990) Gift of Curtis Instruments, Inc., awarded ’49, ’50, ’62 Longobardo. Preference Gift of the family of A. Peers in alternate years to Columbia College given to students studying mechanical Montgomery ’26. and Columbia Engineering. Preference engineering. will be given to college students John J. Morch Scholarship (1963) studying chemistry and to engineering Donald D. MacLaren Scholarship Bequest of John J. Morch. students studying electrochemistry. (1995) Established in honor of Professor William For an undergraduate student who Seeley W. Mudd Scholarship (1958) H. Reinmuth. is studying biochemical engineering. Gift of the Seeley W. Mudd Foundation. Established by Donald D. MacLaren ’45. Several awarded annually for Brenda and Dave Rickey Endowed maintenance, not for tuition. Recipient Scholarship Fund (2008) Manelski Family Scholarship (2004) must be a U.S. citizen, and his or her Gift of David ’79 and Brenda Rickey Gift of Darren E. Manelski ’91 to support grandfather must have been born a U.S. P’08 to benefit undergraduate students needy and deserving students. citizen. Special application required. from California.

Ernest Marquardt Scholarship (1968) Mary Y. Nee Endowed Scholarship Kevin T. Roach Endowed Scholarship Bequest of Ernest Marquardt 1912. (2008) (2003) Gift of Mary Yuet-So Nee ’84. Gift of Kevin T. Roach ’77. Income Louis F. Massa Scholarship (1952) to provide tuition assistance to Bequest of Louis F. Massa 1890. Frederick Noel Nye Scholarship undergraduate students in engineering. (1971) Ralph Edward Mayer Scholarship Bequest of Frederick Noel Nye ’27. The Frederick Roeser Fund for (1924) Student Aid (1934) Contributed by friends in memory of Parker Family Endowed Scholarship An annual loan to help pay educational Professor Ralph Edward Mayer. (2001) expenses, which is awarded to students Gift of Peter D. Parker ’72, ’74. Income chosen by the Committee on Scholar- Henry Michel Scholarship (2005) to award an annual scholarship to a ships. The amount is individually Gift of Mrs. Mary-Elizabeth Michel needy and deserving undergraduate determined and is to be repaid only if in memory of Henry Michel ’49. student. and when the student can do so without Scholarship awarded to deserving personal sacrifice. Repayments go into undergraduate students with preference Robert I. Pearlman Scholarship (1989) the Frederick Roeser Research Fund for given to civil engineering majors. Gift of Robert I. Pearlman ’55. research in physics and chemistry. Preference is given to students from Stuart Miller Endowed Scholarship in single-parent households. Edgar Lewisohn Rossin Scholarship Engineering (2003) (1949) Gift of Stuart Miller, to be used to Robert Peele Scholarship (1925) Bequest of Edgar L. Rossin, to provide provide support for an undergraduate Gift of E. E. Olcott 1874. a scholarship for students in mining engineering student. engineering.

engineering 2011–2012 220 Harry B. Ryker (1947) Jared K. Shaper Scholarship Upton Fellowship Bequest of Miss Helen L. Ryker in For deserving and qualified candidates For the children of employees of D. memory of her brother, Harry Benson for degrees in engineering. C. Heath and Company of Lexington, Ryker 1900. Massachusetts. Edith Shih Interschool Scholarship Thomas J. Sands Endowed Fund (2008) Valeiras Family Scholarship (2009) Scholarship Fund (2001) Gift of Edith Shih, Esq. (Teachers Gift of Horacio and Amy Valeiras Gift of Thomas J. Sands to support a College 1977–1978). P’09 to support needy and deserving scholarship for a needy and deserving undergraduate students. undergraduate student. Silent Hoist and Crane Company (1950) Kenneth Valentine Memorial Peter K. Scaturro Scholarship Fund Gift of the Silent Hoist and Crane Scholarship (1986) (1997) Company. Bequest of Julia H. Valentine, in memory Gift of Peter K. Scaturro ’82, ’85 to of Kenneth Valentine 1914. Awarded be used to support scholarships to David W. Smyth Scholarship (1957) annually with preference given to students in Columbia Engineering or Bequest of Mrs. Millicent W. Smyth, students in chemical engineering. Columbia College, with preference given in memory of her husband, David W. to scholar-athletes from Archbishop Smyth 1902. Frank Vanderpoel Scholarship (1936) Molloy H.S. in Briarwood, Queens, NY. Bequest of Frank Vanderpoel. Gene F. Straube Fund (2007) Norman A. Schefer Scholarship (1999) Gift of Gene F. Straube ’50, ’49 CC. William E. Verplanck Scholarship Gift of Norman A. Schefer ’50 and Fay The fund shall provide scholarships to (1957) J. Lindner Foundation. Awarded annually undergraduate students who graduated Gift of Mrs. T. Bache Bleecker and to a deserving and talented student at from a high school or prep school Edward F. Verplanck 1912 in memory of the School of Engineering. in northern California, and who are their father, William E. Verplanck 1876. pursing studies in electrical engineering, Samuel Y. Sheng Scholarship (2007) computer engineering, or computer Arnold Von Schrenk Scholarship (1943) Gift of Samuel Y. Sheng ’51, Lauren science. Bequest of Mrs. Helen von Schrenk in Wong Sheng ’76, Kent Sheng, and memory of her husband, Arnold von Jean Sheng. Awarded to students who Steve Tai and Kin-Ching Wu Schrenk. demonstrate academic excellence. Endowed Scholarship Fund (2001) Gift of Steve Tai ’80 for an annual George Wascheck Scholarship Mark Schlowsky-Fischer Scholarship scholarship to a needy and deserving Bequest of George Wascheck ’26. (2005) undergraduate student. Gift of George Schlowsky ’65 in J. Watumull Scholarship (1989) memory of Mark Schlowsky-Fischer Tai Family Scholarship (2003) For students in the Graduate School ’97. Scholarship awarded to deserving Gift of Timothy Tai P’06 to be used to of Arts and Sciences and in the undergraduate students with preference support Asian students demonstrating Engineering School who are of East given to computer science majors. financial need and outstanding academic Indian ancestry. potential, with preference given to Hong Ralph J. Schwarz Scholarship (1993) Kong, Taiwanese, mainland Chinese, Wells and Greene Scholarship Gift of the Class of 1943 and other and Chinese-American applicants for Bequest of Josephine Wells Greene. donors in memory of Ralph J. Schwarz admission. A T. Tai Family Scholar will ’43. To be awarded to academically be named in a first-year class, and with Herbert A. Wheeler Scholarship (1923) outstanding students who require suitable academic achievement and Gift of Herbert A. Wheeler. financial aid. continuing need, would retain that honor Frederick C. Winter Scholarship until graduation. David C. and Gilbert M. Serber (1966) Memorial Scholarship (1950) Grace C. Townsend Scholarship Gift of various donors in memory of Gift of the Serber family, for a student (1941) Frederick C. Winter ’43. in civil engineering, in honor of David Bequest of Miss Grace C. Townsend. William F. Wurster Scholarship (1974) Serber 1896. Theodosios and Ekaterine Typaldos Awarded to a student of chemical Varsha H. Shah Scholarship (2003) Endowed Scholarship Fund (2000) engineering and applied chemistry. Gifts Gift of Hemant and Varsha Shah to Gift of Andreas ’69 and Renee Typaldos of William F. Wurster 1913. support undergraduate female minority and the Community Foundation of Robert H. and Margaret H. Wyld students. New Jersey. Awarded to deserving Scholarship undergraduates. Preference is given to Gift of Robert H. 1904 and Margaret H. Greek-American students. Wyld.

engineering 2011–2012 Max Yablick Memorial Scholarship Chiang Chen Fellowship (2004) Daniel and Florence Guggenheim 221 (1986) Chiang Chen Industrial Charity Fellowships Bequest of Max Yablick 1914. Awarded Foundation. Awarded to students in Two fellowships for the study of annually with preference given to mechanical engineering. engineering mechanics in the Institute of graduates of Hebrew day schools Flight Structures. and to students in the Combined Plan Professor Bergen Davis Fellowship Program with Yeshiva University. Gift of Dr. Samuel Ruben. To be M. D. Hassialis Memorial Fellowship awarded to a student in chemical (2002) Theresa Ann Yeager Memorial engineering and applied chemistry Gift of former students of the late Krumb Scholarship (1983) upon the recommendation of the senior Professor Emeritus Hassialis. Awarded to Gift of the family of Theresa Ann Yeager professor in chemical engineering active graduate students of the Henry Krumb ’81 to support a woman who is enrolled in electrochemistry research. School of Mines in the field of Earth Columbia Engineering. resources economics and management. George W. Ellis Fellowships Awarded annually for graduate study in Higgins Fellowships Endowed Fellowships any division of the University. Open to Fellowships awarded annually to first- graduate students who are residents of year graduate students. H. Dean Baker Fellowship (1982) the state of Vermont or who have been Awarded to support deserving graduate graduated from a Vermont college or Leta Stetter Hollingworth Fellowship students in mechanical engineering. university. Awarded annually to women who are graduates of the University of Nebraska, Boris A. Bakhmeteff Research Michael Frydman Endowed with preference given to those who were Fellowship in Fluid Mechanics Fellowship (2000) born in Nebraska or received their earlier Provides a stipend for the academic To support a fellowship to a deserving education there. Holders are eligible to year, with tuition exemption to be master’s student in the financial engineering apply for reappointment for one year. A arranged by the recipient’s department, program of the Department of Industrial gift of Harry L. Hollingworth in memory to a candidate for a doctoral degree in Engineering and Operations Research. of his wife. any department at Columbia University whose research is in fluid mechanics. Robert F. Gartland Fellowship Edward J. Ignall Research Fellowship Awarded annually for graduate study in Awarded annually to encourage and Quincy Ward Boese Fellowships the Department of Industrial Engineer-ing help support the research activities of a Predoctoral fellowships awarded annually and Operations Research. Preference is graduate student in the Department of to students studying under the Faculty of given to students who are native-born Industrial Engineering and Operations Engineering and Applied Science. U.S. citizens and who intend to pursue a Research who is selected by the career in business or finance. department chair. Gift of family, friends, Roy S. Bonsib Memorial Fellowship and former students in memory of (1957) GEM Fellowship Professor Edward J. Ignall. Awarded to worthy students for advanced The GEM fellowship provides African- study or research in engineering. Americans, Hispanic Americans, and George M. Jaffin Fellowship Native Americans access to graduate Awarded for graduate study and Arthur Brant Fellowship (1997) education. The fellowship includes research leading to the Ph.D. degree Gift of Arthur Brant. Awarded to graduate tuition, fees, a stipend, and a paid in orthopedic biomechanics by the students of the Henry Krumb School of summer internship. Applicants for this Department of Bioengineering of the Mines in the field of applied geophysics. fellowship must be engineering or Hospital for Joint Diseases, Orthopedic Samuel Willard Bridgham-William applied science majors. Institute, and the Department of Petit Trowbridge Fellowship Mechanical Engineering. It carries tuition Governor’s Committee on A combined fellowship awarded annually exemption and a twelve-month stipend Scholarship Achievement for research. of up to $10,000. One year awards based on financial William Campbell Fellowships for need. Renewal is based on academic Herbert H. Kellogg Fellowship (1988) Encouraging Scientific Research progress, financial need, and availability Funded by former students and friends Four or five fellowships awarded annually of funds. The student applies directly to of Professor Emeritus H. H. Kellogg and for research in the general field of metals. the GCSA; the awards are matched by the generous contribution of Professor the School and are not in supplement to Kellogg. Awarded to graduate students Robert A.W. and Christine S. Carleton initial School awards. of the Henry Krumb School of Mines Fellowships in Civil Engineering in the field of mineral engineering and Fellowships awarded to graduate Carl Gryte Fellowship (2007) chemical metallurgy. students in the Department of Civil Gift from friends of Professor Carl Engineering and Engineering Mechanics. Campbell Gryte. Awarded to needy and deserving graduate students.

engineering 2011–2012 222 Otto Kress Fellowship (1990) Presidential Distinguished Fellowships Nickolas and Liliana Themelis Bequest of Mrs. Florence T. Kress in These fellowships are awarded annually Fellowship in Earth and memory of her husband, Otto Kress. to selected incoming Ph.D., Eng. Environmental Engineering (2000) Awarded to postgraduate students. Sc.D., and master’s/Ph.D. students. Gift of Nickolas and Liliana Themelis. Fellowships include tuition plus an Henry Krumb Fellowships annual stipend of $24,000 for up to Theodore and Jennifer Tsung Annual fellowships in mining engineering, four years, including three months of Fellowship metallurgy, and ore dressing. summer research. All applications for Gift of Theodore T. Tsung ’82. Awarded admission are considered for these new for graduate study in the Department of John F. T. Kuo Fellowship (1992) fellowships. Electrical Engineering. Established by Dr. I. J. Won and other students of Professor Emeritus Kuo Queneau Fellowship Fund Erwin S. and Rose F. Wolfson for the support of graduate students in Donated by Bernard R. Queneau. Memorial Engineering Fellowship applied geophysics. Awarded to a deserving graduate (1979) student in the Department of Earth and Gift of Erwin S. and Rose F. Wolfson. Charles and Sarah Lapple Fellowship Environmental Engineering. (2004) outside fellowship Bequest of Charles ’36, ’37 and Sarah David M. Rickey Endowed Fellowship Lapple. Awarded to support deserving (2000) Wei Family Private Foundation students in the Department of Chemical Gift of David M. Rickey ’79. Awarded to Fellowship Engineering. students studying electrical engineering The Wei Family Private Foundation under the holder of the David M. Rickey is a 501(c)(3) nonprofit organization Kuo and Grace Li Memorial Professorship. Fellowship (1993) established to honor the memory of Dr. Chung Kwai Lui Wei and Mr. Hsin Hsu Gift from the Li Foundation Inc. Awarded Lydia C. Roberts Graduate Wei. The purpose of the foundation is to deserving graduate students Fellowships to award scholarship grants to students interested in mining, mineral resources, Awarded annually. Open to persons of Chinese heritage with high academic metallurgy, and materials science. born in Iowa who have been graduated credentials who are pursuing a graduate from an Iowa college or university. degree in Electrical Engineering. Visit Ralph H. McKee Fellowship (1979) In addition to the stipend, the fellow www.wfpf888.org for more information. Bequest of Ralph H. Mckee. Income is reimbursed the cost of traveling to be used for fellowships and/or once from Iowa to New York City and scholarships in the fields of mathematics back. Special provisions: holders may Medals and Prizes or chemical engineering. not concentrate their studies in law, medicine, dentistry, veterinary medicine, American Society of Civil Engineers— Benjamin Miller Memorial Fellowship or theology, and each holder must, The Robert Ridgway Award Awarded to a graduate student in the when accepting the award, state that it Awarded to the senior showing the most Department of Industrial Engineering and is his or her purpose to return to Iowa promise for a professional career in civil Operations Research. Preference will be for at least two years after completing engineering. given to students concerned with work studies at Columbia; holders are eligible in government-industry regulatory policy, for reappointment. American Society of Civil Engineers— procurement procedures and trade Younger Member Forum Award regulations. Leo Rubinstein Endowed Fellowship Awarded annually to that member of the (2005) graduating class in civil engineering who Nichoplas Fellowship Bequest of Leo Rubinstein ’63 and gift has been most active in promoting the Designated for male students of Greek of Frederick Rubinstein. Awarded to aims of the Society. extraction or born in Greece and deserving students studying applied graduated from any Greek college or mathematics or industrial design. American Society of Mechanical university. Recipients will be eligible to Engineers receive benefits for not more than two Frank E. Stinchfield Fellowship in In recognition of outstanding efforts years. Orthopedic Biomechanics and accomplishments on behalf of the Awarded for graduate study and American Society of Mechanical Engineers Anthony Pesco Fellowship (2006) research in the Department of Student Section at Columbia University. Gift of Dr. Anthony Pesco ’82, ’83, ’87 Mechanical Engineering through the to support graduate students in the Orthopedic Research Laboratory of Applied Mathematics Faculty Award Chemical Engineering Department who the Department of Orthopedic Surgery, Awarded to an outstanding senior in the wish to pursue careers in academia. College of Physicians and Surgeons, it applied mathematics program. carries tuition exemption and a twelve- month stipend of up to $15,000.

engineering 2011–2012 Applied Physics Faculty Award Computer Science Department Award most improves engineering student life 223 Awarded to an outstanding graduating of Excellence during the academic year. Established senior in the applied physics program. A $200 cash prize to the student who in honor of Zvi Galil, dean of the School has demonstrated outstanding ability in from 1995 to 2007. The Edwin Howard Armstrong the field of computer science. Memorial Award The Jewell M. Garrelts Award Awarded by the Faculty of Electrical The Edward A. Darling Prize in Awarded to an outstanding graduating Engineering to one outstanding Mechanical Engineering senior who will pursue graduate study graduating senior and one outstanding Established in 1903 by a gift from in the department that was so long and candidate for the M.S. degree, to honor the late Edward A. Darling, formerly successfully shepherded by Professor the late Edwin Howard Armstrong, superintendent of Buildings and Jewell M. Garrelts. This award is made professor of electrical engineering Grounds; a certificate and $100 cash possible by gifts from alumni and friends and noted inventor of wideband prize awarded annually to the most of Professor Garrelts and from the FM broadcasting, the regenerative faithful and deserving student of Garrelts family in honor of an outstanding circuit, and other basic circuits of the graduating class in mechanical engineer, educator, and administrator. communications and electronics. engineering. The Carl Gryte Prize The Theodore R. Bashkow Award The Adam J. Derman Memorial Award Awarded annually to an undergraduate A cash award presented to a computer Established in 1989 by family and student for service to the Department of science senior who has excelled in friends in memory of Adam J. Derman Chemical Engineering. independent projects. This is awarded ’89 and graduate student in the in honor of Professor Theodore R. Department of Industrial Engineering The Stephen D. Guarino Memorial Bashkow, whose contributions as a and Operations Research. A certificate Award in Industrial Engineering and researcher, teacher, and consultant and cash prize awarded annually by the Operations Research have significantly advanced the art of Department of Industrial Engineering A certificate and cash prize established computer science. and Operations Research to a member by a gift from Roger Guarino (1951) in of the graduating class who has memory of his son. To be awarded to The Charles F. Bonilla Medal demonstrated exceptional ability to one outstanding senior in the Industrial The Bonilla Medal is an award for make computer-oriented contributions Engineering and Operations Research outstanding academic merit. It is to the fields of industrial engineering and Department who, in the opinion of presented annually to that student in operations research. the faculty and Board of Managers the graduating class in the Department of the Columbia Engineering School of Chemical Engineering who best Electrical Engineering Department Alumni Association, has been active exemplifies the qualities of Professor Research Award in undergraduate activities and has Charles F. Bonilla. Awarded by the faculty of Electrical displayed leadership, school spirit, and Engineering to one outstanding scholarship achievement. The Tullio J. Borri ’51 Award in Civil graduating senior who has Engineering demonstrated outstanding passion and The Wlliam A. Hadley Award in A certificate and cash prize presented accomplishment in research. Mechanical Engineering annually by the Department of Civil Established in 1973 by Lucy Hadley in Engineering and Engineering Mechanics Electrical Engineering Department memory of her husband. The award to a senior for outstanding promise of Service Award is made annually in the form of a scholarly and professional achievement Awarded by the faculty of Electrical certificate and cash to that student in civil engineering. This award has Engineering to one outstanding in the graduating class in mechanical been made possible by gifts from the graduating senior who has made engineering who has best exemplified stockholder/employees and the board significant contributions to the the ideals of character, scholarship, and of directors of the Damon G. Douglas department and community at large. service of Professor William A. Hadley. Company, a New Jersey-based general contractor, in appreciation of Mr. Borri’s The William L. Everitt Student Awards The Thomas “Pop” Harrington Medal many years of dedicated service and of Excellence Presented annually to the student who visionary leadership as chairman and Given to two students in the Department best exemplifies the qualities of character president. of Electrical Engineering who rank in the that Professor Harrington exhibited during top 10 percent of their class, have an his forty years of teaching. The medal is Computer Engineering Award of active interest in telecommunications, made possible by Dr. Myron A. Coler. Excellence and are active in a professional Awarded each year by vote of the organization. The Yuen-huo Hung and Chao-chin computer engineering faculty to an Huang Award in Biomedical outstanding senior in the computer Zvi Galil Award for Improvement in Engineering engineering program. Engineering Student Life This award has been endowed to Given annually to the student group that honor the grandfathers of Professor

engineering 2011–2012 224 Clark T.Hung in the Department of of Civil Engineering and Engineering outstanding teaching assistants for the Biomedical Engineering. His paternal Mechanics, 1999–2003. A certificate academic year. grandfather,Yuen-huo Hung, was a and cash prize awarded annually surgeon in Taipei who was renowned by the department to a doctoral The Russell C. Mills Award for his practice of medicine and for his student specializing in geotechnical/ Presented to a computer science major compassion toward patients. Professor geoenvironmental engineering and of for excellence in computer science in Hung’s maternal grandfather, Chao-chin outstanding promise for a career in memory of Russell C. Mills, a Ph.D. Huang, was a famous politician in Taiwan research and academia. candidate in computer science who who dedicated his life to the citizens of exemplified academic excellence by his his country, serving as mayor of Taipei, The Sebastian B. Littauer Award boundless energy and intellectual curiosity. speaker ofthe Taiwan Provincial Assembly, Established in 1979 in honor of Professor and consul general to the United States. Littauer, a certificate and cash prize The Mindlin Scholar in Civil This award is given to a graduating presented annually by the Department Engineering and Engineering doctoral student in the Department of of Industrial Engineering and Operations Mechanics Biomedical Engineering who embodies Research to a senior for outstanding This award will be made each year to the collective attributes of these promise of scholarly and professional a graduate student in the Department distinguished individuals.This student will achievement in operations research. of Civil Engineering and Engineering have demonstrated great potential for Mechanics in recognition of outstanding making significant contributions to the Mechanical Engineering Certificate promise of a creative career in research fields of biomedical engineering and public of Merit and/or practice. This award is made health, and for serving as an ambassador In recognition of excellence in possible by gifts of friends, colleagues, of biomedical engineering. undergraduate studies. and former students of Professor Raymond D. Mindlin, and, above all, The Illig Medal The Henry L. Michel Award in Civil by the Mindlin family. It is intended to Established in 1898 by a bequest Engineering honor the Mindlin brothers, Raymond, from William C. Illig, E.M., 1882, and Established by the Columbia Engineering Eugene, and Rowland, who excelled awarded by the faculty to a member of School Alumni Association in memory in their respective scientific fields of the graduating class for commendable of Henry M. Michel ’49, who built engineering research, engineering proficiency in his or her regular studies. Parsons Brinkerhoff and MacDonald into practice, and medical practice. one of the world’s leading engineering Eliahu I. Jury Award companies. A certificate and cash prize The Moles’ Student Award in Civil Established 1991 for outstanding is presented annually by the Department Engineering achievement by a graduate student in of Civil Engineering and Engineering Awarded to the student in engineering the areas of systems communication or Mechanics to a student or group whose academic achievement signal processing. of students in the Civil Engineering and enthusiastic application show Department who demonstrate outstanding promise of personal Charles Kandel Award outstanding promise of leadership and development leading to a career Medal and cash prize presented professional achievement in civil and in construction engineering and annually by the Columbia Engineering construction engineering. The award is management. School Alumni Association to that in support of a project with emphasis on member of the graduating class who the construction industry in which the The James F. Parker Memorial Award has best promoted the interests of students participate. (Mechanical Engineering Design Award) the School through participation in James F. Parker served and represented extracurricular activities and student- Paul Michelman Award for Exemplary Columbia engineering students as alumni affairs. Service to the Computer Science their dean from 1975 to 1984. He also Department distinguished himself in the pursuit Andrew P. Kosoresow Memorial This award is given to a Ph.D. and analysis of two-dimensional art. In Award for Excellence in Teaching, student in computer science who recognition of his special combination of TA-ing, and Service has performed exemplary service to talents and their integration, the School Awarded each year by the Department the department, devoting time and of Engineering and Applied Science of Computer Science to up to three effort beyond the call to further the salutes the graduate student who has computer science students for department’s goals. It is given in distinguished her- or himself as a designer. outstanding contributions to teaching in memory of Dr. Paul Michelman ’93, A person of creative and innovative the department and exemplary service who devoted himself to improving inclination receives the James Parker to the department and its mission. our department through service while Medal, as evidenced by outstanding excelling as a researcher. performance in courses integrating Dongju Lee Memorial Award engineering analysis and design. Established in 2005 by family and Millman Award friends in memory of Dongju Lee (DJ), A certificate and prize, in honor of Jacob The Robert Peele Prize graduate student in the Department Millman, awarded to two of the most A prize of $500 awarded from time to

engineering 2011–2012 time to that member of the graduating Robert Simon Memorial Prize Residence Hall 225 class in mining engineering who has The Robert Simon Memorial Prize was Scholarships shown the greatest proficiency in his or established in 2001 to honor Robert her course of studies. Simon, a Columbia alumnus who spent Class of 1887 Mines Residence a lifetime making valuable contributions Scholarship The Claire S. and Robert E. Reiss to computational and mathematical Awarded annually to a third-year degree Prize sciences, and is awarded annually by candidate, with preference given to Gift of Robert Reiss, InterVentional the Department of Applied Physics and descendants of members of the Class of Technologies Inc. Awarded to a Applied Mathematics to the doctoral 1887 Mines. graduating senior in biomedical student who has completed the most engineering judged by faculty most likely outstanding dissertation. Should no Class of 1896 Arts and Mines to contribute substantially to the field. dissertation qualify in a given year, the Scholarship prize may be awarded to either the most Awarded annually to a degree candidate The Robert Edward Reiss Award in outstanding student who has completed in Columbia College, Columbia Chemical Engineering a Master of Science degree in the Engineering, or the Graduate School Awarded annually to the student in the department or to the most outstanding of Architecture and Planning, with Department of Chemical Engineering graduating senior in the department. preference given to descendants of who shows the greatest promise of members of the Class of 1896 Arts and success in applying the discipline The Richard Skalak Memorial Prize Mines. of chemical engineering to the The Richard Skalak Memorial Prize improvement of biological products and was founded in recognition of the Class Of 1916 College and medical devices. pioneering contributions of Richard Engineering Fund Skalak to the development of the Gift of the Class of 1916 College and The Francis B. F. Rhodes Prize biomedical engineering program at Engineering. Established in 1926 by Eben Erskine Columbia University. Dr. Skalak was Olcott 1874, in memory of his an inspirational teacher and scholar classmate, Francis Bell Forsyth Rhodes, who taught students and colleagues School of Mines, 1874, and awarded to appreciate the value of broad from time to time to the member of the interactions between engineering and graduating class in materials science medicine, particularly in the fields and metallurgical engineering who has of cardiovascular mechanics, tissue shown the greatest proficiency in his or engineering, and orthopedics. The her course of study. Richard Skalak Memorial Prize is awarded annually to a senior biomedical School of Engineering and Applied engineering student who exemplifies Science Scholar Athlete Award the qualities of outstanding engineering Presented from time to time by the scholarship and breadth of scientific Office of the Dean to that graduating curiosity that form the basis for lifelong student who has distinguished himself or learning and discovery. herself as a varsity athlete and scholar. The George Vincent Wendell School of Engineering and Applied Memorial Medal Science Student Activities Award Established in 1924 by the friends in the This award is presented to an alumni and faculty of the late Professor undergraduate degree candidate in George Vincent Wendell to honor and Columbia Engineering who by virtue perpetuate his memory; a certificate of his or her willingness, energy, and and medal awarded annually by choice leadership has significantly contributed of the class and the faculty to that to the co-curricular life of the School. member of the graduating class who best exemplifies his ideals of character, scholarship, and service.

engineering 2011–2012

University and School Policies, Procedures, and Regulations 228 Academic Procedures and Standards

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

engineering 2011–2012 undergraduate registration is defined be making normal progress if at the Transfer Credits 229 as at least 12 semester credits per completion of 9 credits, he or she Undergraduate students may obtain term. However, in order to complete has earned a cumulative GPA of 2.5. academic credit toward the B.S. degree the degree, students must be averaging Candidates in the Doctor of Engineering by completing course work at other 16 points per term. Students may not Science (Eng.Sc.D.) and professional accredited institutions. Normally, this register for point loads greater than 21 programs are expected to achieve a 3.0 credit is earned during the summer. To points per term without approval from grade point average at the completion of count as credit toward the degree, a the Committee on Academic Standing. 9 points of course work. course taken elsewhere must have an To be eligible to receive the Bachelor Thereafter, graduate students are equivalent at Columbia and the student of Science degree, a student must considered to be making minimum must achieve a grade of at least B. complete the courses prescribed in a satisfactory progress if they successfully The institution must be an accredited faculty-approved major/program (or complete at least 75 percent of all four-year college. To transfer credit, a faculty-authorized substitutions) and courses they have registered for as student must obtain prior approval from achieve a minimum cumulative grade- candidates for the degree with grades his or her adviser and the department point average (GPA) of 2.0. While the of C– or better. Students placed on before taking such courses. A course minimum number of academic credits academic probation because of their description and syllabus should be is 128 for the B.S. degree, some grades are nonetheless considered furnished as a part of the approval programs of the School require a greater to be making minimum satisfactory process. Courses taken before the number of credits in order to complete progress for their first term on probation receipt of the high school diploma may all the requirements. Undergraduate (see chapter “Academic Standing,” not be credited toward the B.S. degree. engineering degrees are awarded only following). Degree requirements for A maximum of 6 credits may be credited to students who have completed at least master’s and professional degrees toward the degree for college courses 60 points of course work at Columbia. must be completed within five years; taken following the receipt of a high No credit is earned for duplicate courses, those for the doctoral degrees must school diploma and initial enrollment. including courses that are taken pass/fail be completed within seven years. Master degree students are not the first time and the final grade is a P. A minimum cumulative grade-point eligible for transfer credits. Undergraduates in the programs average of 2.5 (in all courses taken as Students possessing a conferred accredited by the Engineering a degree candidate) is required for the M.S. degree may be awarded 2 Accreditation Commission of the ABET M.S. degree; a minimum GPA of 3.0 is residence units toward their Ph.D., as (chemical engineering, civil engineering, required for the professional degree and well as 30 points of advanced standing Earth and environmental engineering, the Doctor of Engineering Science (Eng. toward their Ph.D. or Eng.Sc.D. with electrical engineering, and mechanical Sc.D.) degree. The minimum residence departmental approval. engineering) satisfy ABET requirements requirement for each Columbia degree by taking the courses in prescribed is 30 points of course work completed Examinations programs, which have been designed at Columbia. Midterm examinations: Instructors by the departments so as to meet the generally schedule these in late October ABET criteria. Changes in Registration and mid-March. A student who wishes to drop or add Final examinations: These are given Attendance courses or to make other changes in his at the end of each term. The Master Students are expected to attend or her program of study after the add/ University Examination Schedule is their classes and laboratory periods. drop period must obtain the signature available online and is confirmed by Instructors may consider attendance in of his or her adviser. A student who November 1 for the fall term and April assessing a student’s performance and wishes to drop or add a course in his 1 for the spring term. This schedule is may require a certain level of attendance or her major must obtain department sent to all academic departments and for passing a course. approval. The deadline for making is available for viewing on the Columbia program changes in each term is shown website. Students should consult with Graduate in the Academic Calendar. After this their instructors for any changes to the Graduate students are required date, undergraduate students must exam schedule. Examinations will not to complete the School’s degree petition their Committee on Academic be rescheduled to accommodate travel requirements as outlined on pages 30–33 Standing; graduate students must plans. (The Graduate Programs). Full-time petition the Office of Graduate Student Note: If a student has three final graduate registration is defined as at least Services. For courses dropped after examinations scheduled during one 12 credits per term. Students may not these dates, no adjustment of fees calendar day, as certified by the register for point loads greater than 21 will be made. Failure to attend a class Registrar, an arrangement may be made credits per term. without officially dropping the class will with one of the student’s instructors A graduate student who has result in a grade indicating permanent to take that examination at another, matriculated in an M.S. program or unofficial withdrawal (UW). mutually convenient time during the is a special student is considered to final examination period. This refers to a

engineering 2011–2012 230 calendar day, not a 24-hour time period. R, or who, with the approval of the grade. The privilege is granted only Undergraduate students unable to make instructor, file written notice of change when there is a wide discrepancy suitable arrangements on their own of intention with the Registrar not later between the quality of the student’s should contact their adviser. Graduate than the last day for change of program. work during the term and his or her students should contact the Office of Students wishing to change to R credit performance on the final examination, Graduate Student Services. after this date are required to submit the and when, in the instructor’s judgment, Dean’s written approval to the Registrar. the reasons justify a make-up Transcripts and Certifications A course which has been taken for R examination. A student may be granted For information on the Federal Family credit may not be repeated later for the mark of MU in only two courses in Education Rights and Privacy Act examination credit. The mark of R is one term, or, alternatively, in three or (FERPA) of 1974, please visit http:// automatically given in Doctoral Research more courses in one term if their total facets.columbia.edu—Essential Policies Instruction courses. point value is not more than 7 credits. for the Columbia Community. Information The mark of UW: given to students The student must remove MU by taking on obtaining University transcripts and who discontinue attendance in a course a special examination administered as certifications will be found as a subhead but are still officially registered for it, soon as the instructor can schedule it. under Essential Resources. or who fail to take a final examination The mark of P/F (pass/fail): this without an authorized excuse. grading option is designed to allow Report of Grades The mark of INC (incomplete): students to extend their academic granted only in the case of inquiry into new areas of study. No Students are notified by e-mail when incapacitating illness as certified by the course taken for pass/fail may be grades are submitted. Grades can then Health Services at Columbia, serious used to satisfy a student’s program be viewed the following day by using family emergency, or circumstances and degree requirements. The P/F the Student Services Online feature of comparable gravity. Undergraduate option does not count toward degree located on the Student Services home students request on INC by filling out requirements for graduate students. page at www.columbia.edu/students. If the Incomplete Request Form with you need an official printed report, you their advising dean. The deadline is must request a transcript (please see Credit for Internships the last day of class in the semester of Transcripts and Certifications above). Students who participate in non- enrollment. Students requesting an INC All graduate students must have a compensated off-campus internships must gain permission from both the current mailing address on file with the may have the internships noted on their Committee on Academic Standing (CAS) Registrar’s Office. transcripts. Approval for this notation and the instructor. Graduate students may be obtained from your adviser. should contact their instructor. If granted Transcript Notations Formal notification from the employer an INC, students must complete the is required. Graduate students may The grading system is as follows: A, required work within a period of time petition the office of Graduate Student excellent; B, good; C, satisfactory; stipulated by the instructor but not to Services for this notation. D, poor but passing; F, failure (a final exceed one year. After a year, the INC grade not subject to re-examination). will be automatically changed into an F Name Changes Occasionally, P (Pass) is the only or contingency grade. Students may change their name of passing option available. The grade- The mark of YC (year course): a mark record only while currently enrolled in point average is computed on the basis given at the end of the first term of a the University. There is no charge for of the following index: A=4, B=3, C=2, course in which the full year of work this service, but students must submit D=1, F=0. Designations of + or – (used must be completed before a qualitative a name change affidavit to the Student only with A, B, C) are equivalent to 0.33 grade is assigned. The grade given at Service Center. Affidavits are available (i.e., B+=3.33; B–=2.67). Grades of P, the end of the second term is the grade from this office. When you graduate or INC, UW, and MU will not be included for the entire course. cease to enroll in the University, your in the computation of the grade-point The mark of CP (credit pending): name of record is considered final and average. given only in graduate research courses may not be changed unless you enroll The mark of R (registration credit; no in which student research projects again at the University. qualitative grade earned): not accepted regularly extend beyond the end of for degree credit in any program. R the term. Upon completion, a final credit is not available to undergraduate qualitative grade is then assigned and Graduation students. In some divisions of the credit allowed. The mark of CP implies Columbia University awards degrees University, the instructor may stipulate satisfactory progress. three times during the year: in February, conditions for the grade and report The mark of MU (make-up May, and October. There is one a failure if those conditions are not examination): given to a student who commencement ceremony in May. satisfied. The R notation will be given has failed the final examination in a Only students who have completed only to those students who indicate, course but who has been granted the their requirements for the degree may upon registration and to the instructor, privilege of taking a second examination participate in graduation ceremonies. their intention to take the course for in an effort to improve his or her final

engineering 2011–2012 Application or Renewal of General deadlines for applying for Diplomas 231 Application for the Degree graduation are November 1 for February, There is no charge for the preparation In general, students pick up and file an December 1 for May, and August 1 for and conferral of an original diploma. application for a degree at their schools October. (When a deadline falls on a If your diploma is lost or damaged, or departments, but there are several weekend or holiday, the deadline moves there will be a charge of $100 for exceptions. Candidates for Master of to the next business day.) Doctoral a replacement diploma. Note that Science and professional degrees may students must deposit their dissertations replacement diplomas carry the pick up and file their application for the two days before the above conferral signatures of current University officials. degree with the Diploma Division, 210 dates in order to graduate. Applications for replacement diplomas Kent Hall, or through the Registrar’s Students who fail to earn the degree are available on our website: http:// website: http://registrar.columbia.edu/ by the conferral date for which they registrar.columbia.edu/registrar-forms/ registrar-forms/application-degree- applied must file another application for application-replacement-diploma. or-certificate. Candidates for doctoral a later conferral date. Any questions regarding graduation and Master of Philosophy degrees or diploma processing should be should inquire at their departments but addressed to [email protected]. must also follow the instructions of the Dissertation Office, 107 Low Library.

engineering 2011–2012 232 Academic standing

Academic Honors The Office of Graduate Student stated in their sanction letter Services will monitor the academic • Strict Probation: Students who are Dean’s List progress of graduate students in already on probation, fail to meet the To be eligible for Dean’s List honors, an consultation with the departments. minimum requirements as stated in undergraduate student must achieve a Academic performance is reviewed their sanction letter, and are far below grade-point average of 3.5 or better and by advisers at the end of each semester. minimum expectations; this action is complete at least 15 graded credits with The Committee on Academic Standing, typically made when there are signs of no unauthorized incompletes, UWs, or in consultation with the departments, severe academic difficulty. grades lower than C. meets to review undergraduate grades • Dismissal: Students who have a and progress toward the degree. history of not meeting minimum Indicators of academic well-being are requirements will be dismissed from Honors Awarded with the Degree grades that average above 2.0 each Columbia Engineering. At the end of the academic year, a term, in a coordinated program of study, select portion of the candidates for with no incomplete grades. the Bachelor of Science degree who Medical Leave of Absence Possible academic sanctions include: have achieved the highest academic A medical leave of absence for an • Warning: C– or below in any core cumulative grade-point average are undergraduate student is granted by the science course or in a required course accorded Latin honors. Latin honors are Committee on Academic Standing to a for their major; low points toward awarded in three categories (cum laude, student whose health prevents him or her degree completion magna cum laude, and summa cum from successfully pursuing full-time study. • Academic Probation: Students will be laude) to no more than 25 percent of the Undergraduates who take a medical leave placed on academic probation if they graduating class, with no more than 5 of absence are guaranteed housing upon meet any of the conditions below: percent summa cum laude, 10 percent their return. A medical leave of absence for – fall below a 2.0 GPA in a given magna cum laude, and 10 percent a graduate student is granted by the Office semester cum laude. Honors are awarded on of Graduate Student Services, so please – have not completed 12 points the overall record of graduating seniors consult with this office for more information. successfully in a given semester who have completed a minimum of four Documentation from a physician or – are a first-year student and have semesters at Columbia. Students may counselor must be provided before such not completed chemistry, physics, not apply for honors. a leave is granted. In order to apply for University Writing, Gateway Lab, readmission following a medical leave, a and calculus during the first year student must submit proof of recovery from Academic Monitoring – receive a D, F, UW, or unauthorized a physician or counselor. A medical leave The Fu Foundation School of Engineering Incomplete in any first-year/ is for a minimum of one year and cannot and Applied Science Committee on sophomore required courses be longer than two years. If the student Academic Standing determines academic – receive a D, F, UW, or unauthorized does not return within the two-year time policies and regulations for the School Incomplete in any course required frame, they will be permanently withdrawn except in certain instances when decisions for the major from the School. During the course of the are made by the faculty as a whole. – receive straight C’s in the core leave, students are not permitted to take The Committee on Academic Standing science courses (chemistry, any courses for the purpose of transferring is expected to uphold the policies and calculus, physics) credit and are not permitted to be on the regulations of the Committee on Instruction • Continued Probation: Students who campus. For more information about the and determine when circumstances are already on probation and fail to medical leave of absence policy, consult warrant exceptions to them. meet the minimum requirements as your advising dean.

engineering 2011–2012 Voluntary Leave Leave for Military Duty Readmission 233 of Absence Please refer to Military Leave of Students seeking readmission to The Fu A voluntary leave of absence may be Absence Policy in Essential Policies Foundation School of Engineering and granted by the Committee on Academic for the Columbia Community (http:// Applied Science must submit evidence Standing to undergraduate students facets.columbia.edu) for recent updates that they have achieved the purposes for who request a temporary withdrawal regarding leave for military duty. which they left. Consequently, specific from Columbia Engineering for a non- readmission procedures are determined medical reason. Students considering a by the reasons for the withdrawal. Further Involuntary Leave voluntary leave must discuss this option information for undergraduate students of Absence Policy in advance with their advising dean. is available in the Center for Student Please refer to Involuntary Leave of Voluntary leaves are granted for a period Advising. Graduate students should see Absence Policy in Essential Policies for of one year (12 months) only; VLOAs the Office of Graduate Student Services. the Columbia Community (http://facets. will not be granted for one semester, Students applying for readmission columbia.edu). or for more than one year. Students should complete all parts of the must be in good academic standing at appropriate readmission procedures by the time of the leave, and must be able Required Medical Leave June 1 for the autumn term or October to complete their major and degree for Students with 1 for the spring term. in eight semesters. Students may not Eating Disorders take courses for transferable credit Please refer to Required Medical Leave while on leave. Finally, students who for Students with Eating Disorders in choose to take voluntary leaves are not Essential Policies for the Columbia guaranteed housing upon return to the Community (http://facets.columbia.edu). University. International students should contact the International Students and Scholars Office to ensure that a leave will not jeopardize their ability to return to Columbia Engineering.

engineering 2011–2012 234 Policy on Conduct and Discipline

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

engineering 2011–2012 Most violations of rules concerning step in the process. At the hearing, at Office of Graduate Student Services 235 fraternities or sororities as organizations least two members of the staff of the website (www.engineering.columbia. are handled by the Associate Director Dean of Student Affairs present the edu/graduate-student-services). of Greek Life and Leadership. Some accused student with the information serious offenses are referred directly that supports the allegation that he/she Confidentiality to the Office of Judicial Affairs and has violated Columbia Engineering or In general, under University policy Community Standards. University policy(ies). The student is then and federal law, a student’s record, In matters involving rallies, picketing, asked to respond and will be given an including information about Dean’s and other mass demonstrations, the Rules opportunity to present information on his Discipline proceedings, is confidential; of University Conduct outlines procedures. or her behalf. however, there are certain exceptions The Office of Judicial Affairs and At the conclusion of the hearing, to this rule. One exception to this Community Standards (located within the hearing officers will make a principle is that the outcome of Dean’s the Division of Student Affairs) is determination, based on all of the Disciplinary proceedings alleging a crime responsible for all disciplinary affairs information available to them, regarding of violence may be disclosed both to concerning undergraduate students that whether the accused student is the accuser and the accused. To read are not reserved to some other body. responsible for the violation(s). The more about the exceptions that apply The Office of Graduate Student Services standard of proof used to make this to the disclosure of student records is responsible for all disciplinary affairs determination is the preponderance of information, please visit http://facets. concerning graduate students that are the evidence standard. This standard columbia.edu/policy-access-student- not reserved to some other body. allows for a finding of responsibility if records-ferpa. the information provided shows that it Dean’s Discipline Process for is more likely than not that a violation Academic Integrity Undergraduate and Graduate of Columbia policy(ies) occurred. If the Students student is found responsible, the degree Academic integrity defines a university and is essential to the mission of The purpose of the Dean’s Discipline of seriousness of the offense and the education. At Columbia students are process is twofold. First, it is used student’s previous disciplinary record, expected to participate in an academic to determine the accused student’s if any, will determine the severity of the community that honors intellectual work responsibility for the alleged violation(s) sanction that will be issued. The student and respects its origins. In particular, of Columbia Engineering or University will be notified of the outcome of the the abilities to synthesize information policy(ies). In addition, it is an hearing in writing. and produce original work are key opportunity for the student to engage A student found responsible after components in the learning process. As in a meaningful conversation regarding a hearing has the right to request an such, academic dishonesty is one of his or her role as a member of the appeal of the decision and the resulting the most serious offenses a student can Columbia community. The Dean’s sanctions. There are three grounds upon commit at Columbia and can result in Discipline process is not an adversarial which an appeal of the decision may dismissal. process, nor is it a legalistic one, and be made. A student found responsible Students rarely set out with the intent therefore the technical rules of evidence for the violation of Columbia policy(ies) of engaging in academic dishonesty. applicable to civil and criminal court may request a review of the decision But classes are challenging at Columbia, cases do not apply. if: (1) the student has new information, and students will often find themselves In a situation requiring immediate unavailable at the time of the hearing; pressed for time, unprepared for an action, a student may be removed from (2) the student has concerns with the assignment or exam, or feeling that the housing, if applicable, and/or placed on process that may change or affect risk of earning a poor grade outweighs interim suspension by the Student Affairs the outcome of the decision; or (3) the need to be thorough. Such staff if it is determined that the student’s the student feels that the sanction circumstances lead some students to behavior makes his or her presence issued is too severe. The request for behave in a manner that compromises on campus a danger to the normal review must be made in writing to the the integrity of the academic community, operations of the institution, or to the individual indicated in the decision disrespects their instructors and safety of himself or herself or others or to letter and must be received within ten classmates, and deprives them of an the property of the University or others. (10) calendar days (or as indicated in opportunity to learn. In short, they cheat. When a complaint is received, the the hearing outcome letter) after the Students who find themselves in such Office of Judicial Affairs and Community student receives notice of the hearing circumstances should immediately Standards or Office of Graduate outcome. For more information about contact their instructor and adviser for Student Services determines whether the discipline process for undergraduate advice. Dean’s Discipline is an appropriate students, please visit the Office The easiest way to avoid the response or if the complaint should of Judicial Affairs and Community temptation to cheat in the first place is be referred elsewhere. If a Dean’s Standards website (www.studentaffairs. to prepare yourself as best you can. Discipline hearing is to occur, a student columbia.edu/judicialaffairs). For more Here are some basic suggestions to is informed in writing of the complaint information about the discipline process help you along the way: made against him/her and of the next for graduate students, please visit the

engineering 2011–2012 236 • Understand what instructors deem as cited just like any other source. If you are including faculty and staff members. academic dishonesty and their policy uncertain how to properly cite a source Common types of academic on citation and group collaboration. of information that is not your own, dishonesty: • Clarify any questions or concerns whether from the Internet or elsewhere, • Plagiarism: the use of words, phrases, about assignments with instructors as it is critical that you do not hand in your or ideas belonging to another, without early as possible. work until you have learned the proper properly citing or acknowledging the • Develop a timeline for drafts and way to use in-text references, footnotes, source final edits of assignments and begin and bibliographies. Faculty members • Self-plagiarism: the submission of preparation in advance. are available to help as questions arise one piece of work in more than one • Avoid plagiarism: acknowledge about proper citations, references, course without the explicit permission people’s opinions and theories by and the appropriateness of group of the instructors involved carefully citing their words and always work on assignments. You can also • Falsification or misreprensentation indicating sources. check with the Undergraduate Writing of information in course work or lab • Utilize the campus’s resources, Program. Ignorance of proper citation work; on any application, petition, or such as the advising centers and methods does not exonerate one from forms submitted to the School Counseling and Psychological responsibility. • Fabrication of credentials in materials Services, if feeling overwhelmed, submitted to the University for burdened, or pressured. Personal Responsibility, Finding administrative or academic review • Assume that collaboration in the Support, and More Information • Violating the limits of acceptable completion of assignments is A student’s education at Columbia collaboration in course work set by a prohibited unless specified by the University is comprised of two faculty member or department instructor. complementary components: a mastery • Facilitating academic dishonesty by over intellectual material within a enabling another to engage in such Plagiarism and discipline and the overall development behavior Acknowledgment of Sources of moral character and personal ethics. • Cheating on examinations, tests, or Columbia has always believed that Participating in forms of academic homework assignments writing effectively is one of the most dishonesty violates the standards • Unauthorized collaboration on an important goals a college student can of our community at Columbia and assignment achieve. Students will be asked to do severely inhibits a student’s chance to • Receiving unauthorized assistance on a great deal of written work while at grow academically, professionally, and an assignment Columbia: term papers, seminar and socially. As such, Columbia’s approach • Copying computer programs laboratory reports, and analytic essays to academic integrity is informed by its • Unauthorized distribution of of different lengths. These papers play explicit belief that students must take full assignments and exams a major role in course performance, but responsibility for their actions, meaning • Lying to a professor or University officer more important, they play a major role you will need to make informed choices • Obtaining advance knowledge of in intellectual development. Plagiarism, inside and outside the classroom. exams or other assignments without the use of words, phrases, or ideas Columbia offers a wealth of resources permission belonging to another, without properly to help students make sound decisions A student alleged to have engaged in citing or acknowledging the source, regarding academics, extracurricular academic dishonesty will be subject to is considered one of the most serious activities, and personal issues. If you the Dean’s Discipline process. violations of academic integrity and don’t know where to go, see your Students found responsible for is a growing problem on university advising dean. academic dishonesty may face campuses. reports of such offenses on future One of the most prevalent forms Academic Dishonesty recommendations for law, medical, or graduate school. The parents or of plagiarism involves students using Academic dishonesty includes, but is guardians of students found responsible information from the Internet without not limited to, intentional or unintentional may also be notified. proper citation. While the Internet can dishonesty in academic assignments provide a wealth of information, sources or in dealing with University officials, obtained from the Web must be properly

engineering 2011–2012 Essential Policies for the Columbia Community 237

his bulletin is intended for the Policies for the Columbia Community • University Event Management Policies guidance of persons applying on the following website: http://facets. • Policy on Partisan Political Activity T for or considering application columbia.edu, including information on • Campus Safety and Security for admission to Columbia University the following: • Crime Definitions in Accordance with and for the guidance of Columbia • Student E-mail Communication Policy the Federal Bureau of Investigation’s students and faculty. The bulletin sets • CUIT Computer and Network Use Uniform Crime Reporting Program forth in general the manner in which Policy • Morningside Campus: Required the University intends to proceed with • Social Security Number Reporting Medical Leave for Students with respect to the matters set forth herein, • Policy on Access to Student Records Eating Disorders but the University reserves the right to under the Federal Family Educational • Voluntary Leave of Absence Policy depart without notice from the terms of Rights and Privacy Act (FERPA) of • Involuntary Leave of Absence Policy this bulletin. The bulletin is not intended 1974, as Amended • Military Leave of Absence Policy to be and should not be regarded as a • University Regulations (including Rules • Essential Resources: contract between the University and any of University Conduct) – Disability Services student or other person. • Policies on Alcohol and Drugs – Ombuds Office Valuable information to help students, • Equal Opportunity and – Transcripts and Certifications faculty, and staff understand some Nondiscrimination Policies • Additional Policy Sources for the of the policies and regulations of the • Sexual Assault Policy and Disciplinary Columbia Community University can now be found in Essential Procedure

engineering 2011–2012 238 Student Grievances, Academic Concerns, and Complaints

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

engineering 2011–2012 follow will depend upon the school to submit a written response. The to make his or her decision on the 239 within which the faculty member Committee reviews both statements appeal. is appointed and the nature of the and is given access to any other written The Provost will inform both the alleged misconduct. documents relevant to the complaint. It student and the faculty member of his will normally interview both the grievant or her decision in writing. If the Provost If the faculty member holds an and the faculty member and may, at decides that the faculty member should appointment in Columbia Engineering, its discretion, ask others to provide be dismissed for cause, the case is the student may use the procedures testimony. The merits of the grievance subject to further review according to described below to address the issues are evaluated within the context of the procedures in Section 75 of the listed below. If the faculty member University and Engineering school policy. University Statutes, as noted above. belongs to another school, students The investigative committee serves Otherwise the decision of the Provost is must use the procedure of that school. in an advisory capacity to the Dean of final and not subject to further appeal. They may, however, ask for help from the School. It is expected to complete All aspects of an investigation of a the departmental faculty mediator, chair, its investigation in a timely manner and student grievance are confidential. The and the School’s deans in identifying submit a written report to the Dean, who proceedings of the grievance committee and understanding the appropriate may accept or modify its findings and are not open to the public. Only the procedures. any recommendations it may have made student grievant and the faculty member Conduct that is subject to formal to remedy the student’s complaint. The accused of misconduct receive copies grievance procedure includes: Dean will inform both the student and the of the decisions of the Dean and the • failure to show appropriate respect in faculty member of his decision in writing. Provost. Everyone who is involved with the an instructional setting for the rights of The committee ordinarily convenes investigation of a grievance is expected to others to hold opinions differing from within 10 working days of receiving respect the confidentiality of the process. their own; the complaint from the Vice Dean and • misuse of faculty authority in an ordinarily completes its investigation B. Disputes over grades or instructional setting to pressure and sends the Dean its report within other academic evaluations students to support a political or 30 working days of convening. The The awarding of grades and all other social cause; and Dean normally issues his or her decision academic evaluations rests entirely with • conduct in the classroom or another within 30 working days of receiving the the faculty. If students have a concern instructional setting that adversely committee’s report. relating to a particular grade or other affects the learning environment. The Dean may discipline faculty assessment of their academic work, members who are found to have the student first should speak with the Formal grievance procedure at committed professional misconduct. Any instructor of the class to understand Columbia Engineering sanctions will be imposed in a manner how the grade or other evaluation was If the informal mediation mentioned that is consistent with the University’s derived and to address the student’s above failed, the student should policies and procedures on faculty specific concern. compose and submit to the Vice Dean discipline. In particular, if the Dean If the students do not feel of the School a written statement believes that the offense is sufficiently comfortable speaking with the class documenting the grievance and should serious to merit dismissal, he or she can instructor about the matter, they should also include a description of the remedy initiate the procedures in Section 75 of then bring the issue to the attention sought. This should be done no later the University Statutes for terminating of their class dean (undergraduate than 30 working days after the end of tenured appointments, and nontenured students) or department chair (graduate the semester in which the grievance appointments before the end of their students). occurred. stated term, for cause. If the students are unable thus to The Vice Dean will review the Either the student or the faculty resolve the matter to their satisfaction complaint to determine if a grievance member may appeal the decision of and believe that a procedural issue is hearing is warranted. If so, the Vice the Dean to the Provost. Findings involved, they should bring the matter to Dean will convene an ad hoc committee of fact, remedies given the student, the attention of the Vice Dean. The Vice consisting of the Assistant Dean for and penalties imposed on the faculty Dean will work with the student and the Graduate Student Services (graduate member are all subject to appeal. A faculty to determine whether there has students) or the Associate Dean written appeal must be submitted to the been a procedural breach and if so, take of Student Affairs (undergraduate Provost within 15 working days of the immediate steps to remedy the matter. If students), who acts as chair; a faculty date of the letter informing them of the the Vice Dean, together with appropriate member chosen by the Vice Dean; Dean’s decision. faculty other than the instructor, decides and a student chosen by one of the Normally, the Provost will take that there is no need for further action, student councils (an undergraduate or a no longer than 30 working days to the student will be informed and the graduate student to correspond to the evaluate an appeal. The Provost usually decision will be final. status of the student grieving). confines his or her review to the written The faculty member is given the record but reserves the right to collect student’s letter of complaint and invited information in any manner that will help

engineering 2011–2012 240 C. Discrimination and D. Scientific or sexual harassment scholarly misconduct If the alleged misconduct involves Complaints against the School’s discrimination and sexual harassment, faculty that allege scientific or scholarly a student should file a complaint misconduct are evaluated using other with the Associate Provost for Equal procedures. These are contained in the Opportunity and Affirmative Action. The Columbia University Institutional Policy procedures for handling such complaints on Misconduct in Research. are described in the statement Discrimination and Sexual Harassment Policy and Procedure.

engineering 2011–2012 Directory of University Resources 242 columbia university resource list

Admissions (Undergraduate) A. Alex España, [email protected] Brad Garton, [email protected] Office of Undergraduate Admissions Assistant Dean, Community Outreach Director of Undergraduate Studies 212 Hamilton, MC 2807 Robert Ferraiuolo, [email protected] Contemporary Civilization 212-854-2522 Assistant Dean, Advising Specialites 514 Fayerweather, MC 2811 www.studentaffairs.columbia.edu/ 212-854-2421 admissions Megan Rigney, [email protected] [email protected] Assistant Dean, Preprofessional Advising Professor Matthew Jones, Chair

Jessica Marinaccio Nathaniel Wood Jr., [email protected] Literature Humanities Dean of Undergraduate Admissions Assistant Dean 202 Hamilton, 212-854-2453 Mail Code 2811 Peter Johnson, [email protected] Center for Career Education Director of Admissions All inquiries concerning Lit Hum should East Campus, Lower Level, MC 5727 be directed to the Center for Core Joanna May, [email protected] 212-854-5609 Curriculum (listed above). Director of Outreach and Admissions www.careereducation.columbia.edu Operations [email protected] Undergraduate Writing Program 310 Philosophy, MC 4995 Meaghan McCarthy, [email protected] Columbia College 212-854-3886 Director of Visitor Relations 208 Hamilton, MC 2805 [email protected] Alice Huang Protas, [email protected] 212-854-2441 Nicole Wallack, Director Senior Associate Director Michele M. Moody-Adams Diane McKoy, [email protected] Dean of Columbia College Columbia Video Network Senior Associate Director 540 S. W. Mudd, MC 4719 Kathryn Yatrakis, [email protected] 212-854-8210 James Minter, [email protected] Dean of Academic Affairs Grace Chung, Executive Director Senior Associate Director Core Curriculum Program COMMUNITY DEVELOPMENT Advising (Undergraduate) Offices Office of Civic Action and Engagement Center for Student Advising Center for the Core Curriculum 510–515 Lerner, MC 2601 403 Lerner Hall, MC 1201 202 Hamilton, MC 2811 212-854-3611 212-854-6378 212-854-2453 www.studentaffairscolumbia.edu/csa Todd Smith, [email protected] Roosevelt Montás, [email protected] [email protected] Associate Dean of Student Affairs Director of the Center for the Core Monique Rinere Curriculum Peter Cerneka, [email protected] Dean of Advising Associate Director Art Humanities Andrew Plaa, [email protected] 826 Schermerhorn, MC 5517 Walter Rodriguez, [email protected] Associate Dean of Advising 212-854-4505 Associate Director

Lavinia Lorch, [email protected] Zoë Strother, [email protected] Office of Multicultural Affairs Senior Assistant Dean and Director of Undergraduate Studies 510 Lerner, MC 2607 212-854-0720 Director of Scholars Program Music Humanities Sunday Coward, [email protected] 621 Dodge, MC 1813 Intercultural Resource Center (IRC) Assistant Dean, Academic Success Program 212-854-3825 552 West 114th Street, MC 5755 212-854-7461

engineering 2011–2012 Melinda Aquino, [email protected] The earl hall center Office of graduate Student 243 Associate Dean of Multicultural Affairs Office of the University Chaplain Services Office: W710 Lerner 524 S. W. Mudd, MC 4708 Marta Esquilin, [email protected] Mailing: 202 Earl Hall, MC 2008 212-854-6438 Senior Associate Director/Manager of IRC 212-854-6242, 212-854-1493 Tiffany M, Simon, [email protected] Office of Residential Programs Jewelnel Davis, [email protected] Associate Dean 515 Lerner, MC 4205 University Chaplain Jonathan Stark, jrs@[email protected] 212-854-6805 Assistant Dean of Graduate Student and office of equal Opportunity Cristen Scully Kromm, [email protected] Post-Doctoral Affairs Assistant Dean of Community and Affirmative Action Development and Residential Programs 103 Low Library, MC 4333 Jocelyn Morales, [email protected] 212-854-5511 Assistant Director Stephanie Nixon, [email protected] Susan Rieger, [email protected] Director of Residential Programs columbia Health Associate Provost Darleny Cepin, [email protected] General Info: 212-854-2284 Associate Director (West Campus) After-hours Urgent Health Concerns: Financial Aid (Undergraduate) 212-854-9797 Adam Fertmann, [email protected] Office of Undergraduate Financial Aid www.health.columbia.edu Associate Director (The Block) & Educational Financing Scott Helfrich, [email protected] Office: 618 Lerner CU-EMS (Ambulance) Associate Director (Living Learning Center) Mailing: 100 Hamilton, MC 2802 212-854-5555 or 99 from a campus phone 212-854-3711 Deb Pawlikowski, [email protected] Insurance and Immunization [email protected] Associate Director (South Field) Compliance Office Laurie Schaffler Wien Hall, First Floor Kristen Sylvester, [email protected] Dean of Financial Aid Immunization Office: 212-854-7210 Associate Director (East Campus) Insurance Inquiries: 212-854-3286 Kathryn Tuman Victoria Lopez-Herrara, [email protected] Director of Financial Aid Student Medical Insurance Plan Associate Director of Greek Life and Administrators: Aetna Student Health Leadership Development Pamela Mason, [email protected] 1-800-859-8471 Senior Associate Director Student Development and Activities www.aetnastudenthealth.com/ 515 Lerner, MC 2601 José Carlos Rivera, [email protected] columbiadirect.html 212-854-3611 Associate Director Alice! Health Promotion Robert Taylor, [email protected] Leah Bestmann, [email protected] Wien Hall, Suite 108, MC 3711 Executive Director Assistant Director 212-854-5453 Cynthia Jennings, [email protected] www.alice.columbia.edu Financial Aid (Graduate) Director of New Student Orientation and Federal Financial Aid (Loans, Work Study) Counseling and Psychological Class Year Programming Financial Aid and Educational Financing Services Tailisha Gonzalez, [email protected] 615 Lerner, 212-854-3711 Lerner, 8th floor, MC 2606 Manager of SDA Leadership Programs Mail Code 2802 212-854-2878

Benjamin Young, [email protected] Jacqueline Perez, Associate Director Disability Services Director of Broadcasting and Operations [email protected] Lerner, 7th floor, MC 2605 Voice/TTY: 212-854-2388 David Milch, [email protected] Marjorie Ortiz, [email protected] Manager of Media, Performing Arts, and Assistant Director Disciplinary Procedure for Sexual Publications Production Assault Office Institutional Financial Aid Wien Hall, Suite 108C computing support center (Grants, Fellowships, Assistantships) 212-854-1717 Office of Graduate Student Services Client Services HelpDesk Melissa Tihinen, [email protected] 524 S. W. Mudd, MC 4708 202 Philosophy, MC 4926 Senior Manager 212-854-1919 212-854-6438 [email protected]

engineering 2011–2012 244 Medical Services Engineering Library (Monell) Public Safety Office John Jay Hall, 3rd and 4th Floors 422 S. W. Mudd, MC 4707 111 Low Library, MC 4301 212-854-7426 (Appointments) 212-854-2976 212-854-2797 (24 hours a day) 212-854-6655 (Gay Health Advocacy [email protected] Science & Engineering Library Project) 401 Northwest Corner CAMPUS EMERGENCIES: Sexual Violence Response 212-851-2950 212-854-5555 (4-8555) 112 Hewitt (Barnard Quad) Escort Service: 212-854-HELP (4357) Math/Science Departments 212-854-SAFE (4-7233) Biological Sciences Housing and Dining 600 Fairchild, MC 2402 James F. McShane Customer Service Center 212-854-4581 Vice President for Public Safety 118 Hartley Deborah Mowshowitz, [email protected] 212-854-2775 Registrar Director of Undergraduate Programs 210 Kent, MC 9202 Office of Dining Services Chemistry 102 Wallach, MC 3001 Barry Kane, [email protected] 344 Havemeyer, MC 3174 212-854-2782 University Registrar 212-854-2202 [email protected] Jennifer Caplan, [email protected] James J. Valentini, [email protected] Associate Registrar Office of Housing Services Director of Undergraduate Studies 125 Wallach, MC 3003 Sheila Serrano, [email protected] Earth and Environmental Sciences 212-854-2946 Associate Registrar [email protected] 106 Geoscience, Lamont-Doherty Earth Observatory, 845-365-8550 James Cunha, [email protected] Assistant Registrar Intercollegiate Athletics and Nicholas Christie-Blick, Physical Education [email protected] Lenore Hubner, [email protected] Dodge Physical Fitness Center Codirector of Undergraduate Studies Assistant Registrar 212-854-3439 Walter C. Pitman, [email protected] George Voorhis, [email protected] Ken Torrey, [email protected] Codirector of Undergraduate Studies Technical Specialist for Degree Audit Director of Undergraduate Studies Mathematics student affairs Jacqueline Blackett, [email protected] 410 Mathematics, MC 4426 Office of the Dean Senior Associate Athletics Director/SWA 212-854-2432 601 Lerner, MC 2607 Panagiota Daskalopoulos, International Students and 212-854-2446 [email protected] Scholars Office Director of Undergraduate Studies Kevin G. Shollenberger 524 Riverside Drive, Suite 200 Dean of Student Affairs, Columbia College/ 212-854-3587 Physics Columbia Engineering and Associate Vice Mailing: 2960 Broadway, MC 5724 704 Pupin, Mail Code 5255 President for Undergraduate Student Life, 212-854-3348 Sarah Taylor Arts and Sciences Acting Director Jeremy Dodd, [email protected] Susan Tucker, [email protected] Director of Undergraduate Studies Assistant Manager to the Dean office of Judicial Affairs and Statistics community standards Kathryn Wittner, [email protected] 1255 Amsterdam Avenue 609 Lerner, MC 4205 Senior Associate Dean of Student Affairs Room 1005 SSW, MC 4690 212-854-6872 212-851-2132 student Service Center Jeri Henry, [email protected] Daniel Rabinowitz, [email protected] 205 Kent, MC 9202 Senior Assistant Dean Director of Undergraduate Studies 212-854-4400 Cashiering: 212-854-1518 Libraries Ombuds Office Butler Library Information For quick answers to your questions, 600 Schermerhorn Ext., MC 5558 535 W 114th Street visit: askus.columbia.edu 212-854-1234 212-854-7309 Melbourne Francis, [email protected] Associate Director

engineering 2011–2012 Columbia University 245 The Morningside Campus & Environs

engineering 2011–2012 246 The Morningside Heights Area of New York City

engineering 2011–2012 index 247

A Alice! Columbia University’s Health B Promotion program, 213, 243 academic advising. See Center for Bachelor of Science degree (B.S.), Alumni Representative Committee, 22 Student Advising 16–17 Ambrose Monell Engineering Library, 7 academic calendar, inside back cover Baker Field Athletics Complex, 210 American College Testing (ACT) academic community, conduct Barnard Education Program, 18 examinations, 22 expected in, 234 bioinductive and biomimetic materials, American Language Program (ALP), 35 academic concerns, grievances, and program in, 87 applications complaints, student, 238–240 Biological Sciences, Department of, 244 for degrees, 231 academic discipline, 234–236 courses for engineering students, 197 graduate, 35 academic dishonesty, 236 biomedical engineering prerequisite tests, 21–22 academic honors, 232 courses in, 73–79 process for, 20 academic integrity, 235–236 minor in, 190–191 undergraduate, 20–21 academic monitoring, 232 Biomedical Engineering, Department applied chemistry. See Chemical academic procedures and standards, of, 69–79 Engineering, Department of 228–231 graduate programs, 72–73 applied mathematics academic progress, satisfactory, undergraduate program, 70–72 courses in, 66–68 25–26, 228–230 biophysics and soft matter physics, minor in, 190 academic standing, 232–233 program in, 86 applied physics Accreditation Board for Engineering Bookstore, Columbia University, 209 courses in, 64–66 and Technology (ABET), 17, 83, Botwinick Multimedia Learning minor in, 190 138, 179–180 Laboratory, 6 Applied Physics and Applied Activities Board at Columbia (ABC), Business, Graduate School of Mathematics, Department of, 56–68 207 courses for engineering students, current research activities, 56–57 addresses of Columbia University 197 graduate programs, 62–64 departments and resources, 242–244 joint programs with, 31, 127, 157 laboratory facilities, 57–58 administrative officers, lists of, Business/farm information, 27 44, 51–52 specialty areas, 60–62 admissions undergraduate programs, 58–62 graduate, 35–36. See also Graduate architecture, minor in, 190 C art history, minor in, 190 Student Services cable TV service, 7 assault, sexual, policy on, 237 undergraduate, 20–22, 242 calendar assistantships, 40 advanced placement, 13, 14, 21 academic, inside back cover Associate Provost for Equal advanced standing, of transfer for graduate admissions, 35–36 Opportunity and Affirmative Action, students, 21–22 campus life, 206–210 243 advising centers. See Center for campus safety and security, 210 athletic programs, 13, 209–210 Student Advising career counseling, 7–8 attendance, 229 Center for Applied Probability (CAP), 153

engineering 2011–2012 248 Center for Career Education (CCE), Columbia College and engineering computer labs and clusters, 7 7–8, 42, 242 students, 206–210 computer science Center for Financial Engineering, 153 Columbia Comprehensive Educational courses in, 115–119 Center for Infrastructure Studies, 92 Financing Plan, 42 minor in, 191 Center for Life Cycle Analysis (LCA), 121 Columbia Dining Dollars, 212 Computer Science, Department of, Center for Student Advising, Columbia Experience Overseas (CEO), 8 107–119 206–207, 242 Columbia Genome Center (CGC), 82 laboratory facilities, 107–108 Center for Sustainable Use of Columbia Health, 213–214, 243–244 graduate programs, 110–111 Resources (SUR), 121 Columbia Microelectronic Sciences undergraduate program, 108–110 Certificate of Professional Achievement Laboratories, 135 computer security resources, 7 program, 34, 63 Columbia Student Enterprises (CSE), 8 computing facilities, University, 6–7 certification of enrollment, 230 Columbia University Computing Support Center, 243 Chaplain, University, Office of the, 209, campuses, schools, affiliations, and conduct 243 research facilities, 5–8 expected in the academic chemical engineering history of, 2–4 community, 234 courses in, 87–90 maps of campus, 245, 246 unacceptable, subject to discipline, minor in, 191 new York City roots of, 5 234–236 Chemical Engineering, Department of, policy, procedures, and regulations, Core Curriculum of Columbia 80–90 228–240 University, 4 current research activities, 81 Provost, 239 program offices, 242 facilities and laboratories, 81–82 reservation of rights, 237 Counseling and Psychological Services graduate programs, 83–87 resources, phone numbers, and (CPS), 213, 243 undergraduate program, 82–83 e-mail addresses, list of, 242–244 courses Chemistry, Department of, 244 visits and tours, 22 for professions­ other than courses for engineering students, website, 6 engi­neering, 17–18 197–198 Columbia University Bookstore, 209 interdisciplinary engineering, 196 facilities and laboratories, 82 Columbia University Grant (CUG) key to listings, 54–55 Civic Action and Engagement, Office program, 26 in other divisions of the University, of, 207 Columbia University Information of interest to engineering students, civil engineering Technology (CUIT), 6–7 197–204 courses in, 94–100 Columbia University Libraries, 7 in Engineering School departments. minor in, 191 Columbia University’s Health Promotion See individual departments Civil Engineering and Engineering Program (Alice!), 213, 243 CourseWorks, 7 Mechanics, Department of, Columbia University Tutoring and credit, points of, required for degree 91–101 Translation Agency, 8 graduate, 30–33, 229 current research activities, 91–92 Columbia Video Network (CVN), undergraduate, 10–18, 228–229 facilities and laboratories, 92 33, 34, 242 graduate programs, 93–94 application to, 34 D undergraduate programs, 92–93 Columbia Water Center, 121 classes Combined Plan programs, 15–16, 22 damages, payment for, 24, 38 attendance at, 229 commencement ceremony, 230 dance, minor in, 191 registration and enrollment in, Committee on Academic Standing, Davis Scholars, C. Prescott, 21 228 228, 232 Dean’s discipline, 235 classrooms, electronic, 7 Committee on Instruction, 232 Dean’s List, 232 Club Sports, 207, 210 Community Impact, 207 Degree Audit Reporting System College Scholarship Service (CSS) complaints, academic concerns, and (DARS), 16 PROFILE Form, 27 grievances, student, 238–240 degrees colleges and universities in Combined Computational and Optimization application for, 231 Plan program, 16 Research Center (CORC), 153 doctoral, requirements, 32–33, Columbia Arts Experience, 8 computer accounts, obtaining, 6 229, 231 Columbia Bartending Agency and Computer Engineering Program, 102–106 See also individual degrees School of Mixology, 8 graduate program, 104–106 Dining Dollars, 212 Columbia Card (ID card), 212 undergraduate program, 102–104 dining facilities, locations, 213 computer kiosks, public, 7 Dining Services, 212–213, 244

engineering 2011–2012 diplomas, 231 economics See also Civil Engineering 249 direct loans, 41 minor in, 192 and Engineering Mechanics, Disability Services, University Office of, Egleston Scholars, 21 Department of 213, 237, 243 electrical engineering engineering societies, 207 discipline, academic, 234–236 courses in, 142–151 engineering students Dean’s, 235 minor in, 192 and campus life, 206–210 procedures for administering, 234 Electrical Engineering, Department of, courses for, offered by other discrimination 134–151 University divisions, 197–204 and sexual harassment policy and B.S./M.S. program, 140 interdisciplinary courses for, 196 procedure, 240 concentration options in the M.S. See also students dishonesty, academic, 236 program, 141–142 Engineering Student Council, 207 disputes over grades or other academic graduate programs, 140–142 English and comparative literature, evaluations, 239 laboratory facilities, 135 minor in, 192 distance education. See Columbia research activities, 135 English proficiency requirement, 35 Video Network undergraduate program, 135–140 enrollment, 228 Division of Student Affairs, 206, 235, electronic classrooms, 7 certification of, 230 243 Electronic Data Service, 7 entrepreneurship and innovation, minor Doctor of Engineering Science (Eng. e-mail in, 193 Sc.D.), 32–33 addresses of Columbia University environmental health engineering, Doctor of Philosophy (Ph.D.), 32–33 resources and staff, 242–244 concentration in, 125, 127 Dodge Physical Fitness Center, 210 as service of CUIT, 6 Environmental Tracer Group, 121–122 dual degree emergency resources, 243, 244 Equal Opportunity and Affirmative with the School of Journalism, in emeriti and retired officers, list of, 50–51 Action, Office of, 243 computer science, 31, 111 employment, student, 26, 42 Equal Opportunity and See also joint programs endowed fellowships, list of, 221 Nondiscrimination Policies, 237 endowed scholarships and grants, examinations, midterm and final, 229–230 list of, 216–221 E Engineer of Mines (professional F Earl Hall Center, 209, 243 degree), 128 Early Decision program, 20 Engineering Accreditation Commission faculty Earth and environmental engineering (EAC), 17 and staff academic misconduct, courses in, 128–133 engineering courses, interdisciplinary, complaints about, 238–239 minor in, 191–192 196 lists of, 44–51 Earth and Environmental Engineering, Engineering, School of members-at-large, list of, 50 Department of (DEEE), 120–133 courses. See individual departments Faculty in Residence, 208 graduate programs, 125–128 Dean of, 234 family contributions to educational joint degree programs, 127 department and course codes, 54–55 costs, 25 research centers, 121–122 departments and programs, 56–189 Family Educational Rights and Privacy scholarshihps, fellowships, and faculty and administration, 44–52 Act (FERPA), 230, 237 internships, 123 history of, 2–4 federal financial aid, 26–27, 39–42 undergraduate program, 123–125 resources and facilities, 5–8 Federal Graduate PLUS Loan, 41 See also Henry Krumb School of Vice Dean of, 239 federal income tax returns, 27–28 Mines See also Columbia University Federal Pell Grants, 26 Earth and Environmental Engineering Engineering Graduate Student Council Federal Perkins Loan, 41 (EEE) program, 120–121 (EGSC), 207 Federal Stafford Loan, 41 Earth and Environmental Sciences, engineering management science Federal Subsidized Student Loan, 41 Department of (Columbia College), graduate program in, 154–155 Federal Supplemental Educational 244 undergraduate program in, 153–154 Opportunity Grants (SEOG), 26 courses for engineering students, engineering mechanics Federal Unsubsidized Loan, 41 198–200 courses in, 100–101 Federal Work-Study Program (FWS), 26 Earth Engineering Center, 121 graduate program in, 93–94 fees Earth resources engineering program, minor in, 192 graduate, 37–38 125–127 undergraduate program in, 93–94 refunds of, 24, 38 East Asian studies, minor in, 192 undergraduate, 23–24

engineering 2011–2012 250 See also payments graduate courses, taking as an I fellowships, 40 undergraduate, 16 immunization requirements, 213–214 endowed, list of, 221–222 Graduate Engineering Student Loan income tax returns, 27–28 outside, 222 Request Form, 39 industrial engineering financial aid graduate programs, 30–33 courses in, 158–167 award packages, 26–27 admission to, 35–36 graduate programs in, 154–158 eligibility for, 25–26 applying to, 35–36 joint programs, 31, 157 employment and, 26, 42 planning and approval, 30 minor in, 193 federal, 26–27, 39–42 prerequisites for admission to, 30 undergraduate programs in, to graduate students, 39–42, 243 See also individual programs 153–154 how to apply for, 26–27 Graduate Record Examination (GRE), 35 Industrial Engineering and Operations private programs, 42 Graduate Student Services, Office of, Research, Department of, 152–167 state, 41 234, 235, 243 current research activities, 153 tax withholding from, for nonresident graduate students graduate programs, 154–158 aliens, 27–28 degree requirements for, 229, 231 undergraduate programs, 153–154 to undergraduate students, 25–28, discipline process for, 235 Inside New York, 8 243 financial aid for, 39–42, 243 Institute of Flight Structures, 92 Financial Aid and Educational housing, 211–212 institutional grants, 40 Financing, Office of, 25, 39, 42, 243 special students as, 33, 36 Insurance, Student Medical Plan, 23, financial engineering tuition and fees, 37–38 37, 213 graduate program in, 155 graduation, 230 integrated waste management, joint programs in, 157 grants and scholarships, 26 concentration in, 126 undergraduate program in, 154 endowed, list of, 216–222 integrity, academic, 235–236 First Year–Sophomore Program course graphics, courses in, 101 Intercollegiate Athletics requirements Greek or Latin, minor in, 193 eligibility for, 210 nontechnical, 10–12 grievance procedures, 239 program in, 209–210 professional-level, 12–13 grievances, academic concerns, and interdisciplinary engineering courses, 196 technical, 12 complaints, student, 238–240 interfacial engineering and electro- 4-2 Combined Plan B.S. program, chemistry, program in, 86–87 16, 22 H Inter-Greek Council, 207 4-2 Combined Plan M.S. program, International and Public Affairs, 16, 22, 31 harassing or threatening behavior, 240 School of, joint programs with, 18 fraternities and sororities, 208–209 harrassment International English Language Testing Free Application for Federal Student discriminatory, 240 System, 21 Aid (FAFSA), 27, 41–42, 43 sexual, 240 International Research Center for French Harriman Institute, Special Studies Climate Prediction (IRI), 122 and francophone studies, minor in, with, 31 International Students and Scholars 193 health insurance, 23, 37, 213 Office (ISSO), 8, 244 minor in, 193 health service. See Columbia Health Internet access, 6 Fu Foundation School of Engineering Henry Krumb School of Mines (HKSM), Interschool Governing Board, 207, 208 and Applied Science, The. See 120. See also Earth and Environ- internships, 230 Engineering, School of mental Engineering, Department of interviews, of undergraduate Fundamentals of Engineering (FE) Higher Education Opportunity Program applicants, 22 exam, 180 (HEOP), 21 Intramural and Club Sports Program, Hispanic studies, minor in, 193 210 history, minor in, 193 G honors, academic, 232 Gateway Residential Initiative, 208 housing, University and off-campus, J genomic engineering, program in, 86 211–212. See also residence halls John Jay Dining Hall, 212 German, minor in, 193 Humanities and Social Sciences, joint programs grade-point average (GPA), 230 Department of, courses for with the Graduate School of grades, report of, 230 engineering students, 200–201 Business, in Earth resources grading system, explained, 230 engineering, 31, 127

engineering 2011–2012 with the Graduate School of graduate programs, 170–172 Multicultural Affairs, Office of, 208, 243 251 Business, in financial engineering, 157 graduate specialty in solid-state multimedia networking, concentration with the Graduate School of science and engineering, 172 in, 141 Business, in industrial engineering, interdepartmental committee and, 168 music 31, 157 laboratory facilities, 169 instruction courses, 13 with the Graduate School of undergraduate program, 169–170 minor in, 193–194 Business, in operations research, Mathematics, Department of, 244 31, 157 courses for engineering students, 201 N with the School of International and meal plans. See dining plans Public Affairs, 18 Mechanical Engineer (professional names, student, change of, 230 with the School of Law, 18 degree), 183–184 National Opportunity Program (NOP), See also dual degree. mechanical engineering 21 Judicial Affairs and Community courses in, 184–188 New Student Orientation Program Standards, Office of, 209, 234–235 minor in, 193 (NSOP), 207–208 Junior-Senior programs, 16–17 Mechanical Engineering, Department New York City, 5 of, 176–188 New York State current research activities, 176–179 initial certification in adolescence L facilities for teaching and research, education, 18 laboratory charges, 23–24, 38 179 Tuition Assistance Program (TAP), Langmuir Center for Colloids and graduate programs, 181–184 26, 39–41 Interfaces (LCCI), 122 undergraduate program, 179–180 Noncustodial Parent’s Profile Form, 27 Latin, Greek or, minor in, 193 medals and prizes, list of, 222–225 nondiscriminatory policies, equal Law, School of, joint programs with, 18 media engineering, concentration in, educational opportunity and leave(s) of absence 141–142 student, 237 involuntary, 233 medical care and insurance, 23, 39, nontechnical requirements, 10–12 medical, 229, 232, 233 213–214, 243–244 military, 233 Medical College Admissions Test O voluntary, 229, 233 (MCAT), 17 Lenfest Center for Sustainable Energy, medical leave of absence, Off-Campus Housing Assistance 122 229, 232, 233 (OCHA), 211 Lerner Hall, 209 medical physics, graduate program officers of Columbia Engineering Library, Science & Engineering, 7, 244 in, 63 list of, 44, 50–52 Libraries, Columbia University, 7, 244 medical services and Columbia Health retired, list of, 50–51 lightwave (photonics) engineering, program, 213–214, 243–244 Ombuds Office, 237, 238 concentration in, 142 Mentoring, Columbia Initiative, 208 Ombuds Officer, 238 LionSHARE, 7–8 Metallurgical Engineer (professional operations research loans, student, 39, 41, 42 degree), 128 courses in, 158–167 microelectronic circuits, concentration graduate program in, 154–158 in, 142 joint programs with the Graduate M microelectronic devices, concentration School of Business, 31, 157 Manager of the Disciplinary Procedure in, 142 minor in, 194 for Sexual Assault, 244 Middle Eastern, South Asian, and undergraduate programs in, 153–154 maps of Columbia Morningside Heights African Studies, minor in, 193 See also Industrial Engineering and campus, 245, 246 military leave of absence, 233 Operations Research, Department of marks. See grading system minors, academic, 17, 190–194 optical and laser physics, graduate Master of Science degree (M.S.), misconduct program in, 64 30–31 academic, complaints about faculty orientation, 207–208 materials science and engineering and staff, 238–239 courses in, 173–175 scientific or scholarly, 240 P minor in, 193 sexual. See assault, sexual Materials Science and Engineering monthly payment plan, 26 Parent Loans for Undergraduate program (MSE), 120, 168–175 Morningside Heights campus, 6 Students (PLUS), 26 current research activities, 169 maps of, 245, 246

engineering 2011–2012 252 parents changes in, 229 sports, 13, 209–210 contributions to educational costs, 25 regulations, University, official, staff, romantic relationships with noncustodial, financial profile of, 27 228, 234, 237 students, 240 payments religion, minor in, 194 Stafford Loans, 41 financing options, 26 report of grades, 230 Statistics, Department of, 244 timely and overdue, 23, 37 residence hall scholarships, list of, 225 courses for engineering students, See also fees residence halls, 208–209, 211–212 203–204 Pell Grants, 26 violation of rules of, 234 statistics, minor in, 194 Perkins Loans, 41 Residence Units, and the Ph.D., 32 Student Advising, Center for, 206–207 personal expenses of students, 23, Residential Programs, 208 Student Affairs, Division of, 206, 235, 37–38 resources, Columbia University, list of, 244 philosophy, minor in, 194 242–244 Student Development and Activities physical education, 13 Respecting Ourselves and Others (SDA), 207 and intercollegiate athletics, 209–210 Through Education (ROOTED), 208 Student Financial Services. See Physical Education, Intercollegiate Rules of University Conduct, 234, 237 Student Service Center Athletics and, Department of, 210 Student Governing Board (SGB), 207 Physics, Department of, 244 student grievances, academic S courses for engineering students, concerns, and complaints, 238–240 201–203 safety and security, campus, 210 student loans, 39, 41, 42 plagiarism, 236 sanctions, for academic dishonesty, Student Medical Insurance Plan, 23, plasma physics, graduate program in, 64 236 37, 213 Plasma Physics Laboratory, 57–58 SAT tests, 21 student organizations, 207 political science, minor in, 194 Scholars programs student records, rights pertaining to, 230 polymers and soft materials, science C. Prescott Davis, 21 Student Service Center, 244 and engineering of, program in, 85–86 egleston, 21 student services, 211–214 pre-law program, 18 scholarships students pre-med program, 17 and grants, 26 and campus life, 206–210 preprofessional advising, 17–18, 207 and grants, endowed, list of, 216–222 contributions of, to educational printing facilities, 7 residence hall, list of, 225 costs, 25 prizes, medals and, list of, 222–225 School of Engineering. See Engineering employment and earnings of, 26, 42 professional degree programs, 31–32 School international, 8, 40–41 professions other than engineering, Science & Engineering Library, 7, 244 name changes of, 230 Engineering programs in preparation science and engineering of polymers new, orientation for, 207–208 for, 17–18 and soft materials, program in, 85–86 personal expenses of, 23, 37–38 psychological services, counseling and, secondary school preparation, recom- special, status, 33, 36 213 mended for first-year students, 21 transfer, 21–22, 36 psychology, minor in, 194 security resources, computer, 7 See also engineering students; Public Safety, Office of, 210 Sexual Assault, Manager of the graduate students; undergraduates Disciplinary Procedure for, 244 study abroad, 13–15 sexual assault policy and procedures, summer courses at other institutions, 229 R 237, 244 summer earnings, 25 Rape Crisis/Anti-Violence Support Sexual Violence Response, 213, 244 sustainable energy Center, See Sexual Violence Social Security number, registration and materials, concentration in, Response and, 228 125–126 readmission, 233 sociology, minor in, 194 sustainable engineering, minor in, 194 recreational programs, 210 solid-state physics, graduate program systems biology, concentration in, 142 refunds of tuition and fees, 24, 39 in, 64 registered programs (with New York solid-state science and engineering T State Department of Education), areas of research, 172 18–19 graduate specialty in, 172 Tau Beta Pi, 16 registrar, 244 sororities, fraternities and, 208–209 tax withholding, on tuition aid to See also Student Service Center Special Interest Communities, 211 nonresident alien students, 27–28 registration, 228 special student status, 33, 36 teacher certification, obtaining, 18

engineering 2011–2012 telecommunications engineering, U V 253 concentration in, 141 Undergraduate Research Involvement Veteran Affairs, Department of, 41 telephone and cable TV services, 7 Program (URIP), 10 veterans, educational benefits for, 41 telephone Helpdesk, 6 undergraduates Vice Dean, 239 telephone numbers of Columbia applications and admissions of, visual arts courses, 13 University departments and 20–22 resources, 242–244 degree requirements for, 10, 228– Test of English as a Foreign Language W 230 (TOEFL), 22, 37 financial aid for, 25–28 Waste to Energy Research and tests, preadmission, 20–21 housing for, 211 Technology Council, 122 3-2 Combined Plan B.A./B.S. minor programs for, 190–194 water resources and climate risks, program, 16, 22 programs in Engineering School for, concentration in, 126 transcripts, 230 10–20 wireless and mobile communications, transfer credits, 229 tuition and fees of, 23–24 concentration in, 142 transfer students, 21–22, 36 See also students wireless network, 6–7 tuition United Campus Ministries, 209 women’s athletics, 209–210 graduate, 37–38 University Apartment Housing (UAH), Work-Study Payroll Office, 26 refunds of, 24, 38 211–212 undergraduate, 23–24 University Chaplain, Office of the, 209, Tuition Assistance Program (TAP), 243 New York State, 26, 39–41 University regulations, official, tutoring, 7 228, 237

engineering 2011–2012 254 notes

engineering 2011–2012 255

engineering 2011–2012 256 notes

engineering 2011–2012 Academic Calendar 2011–2012 The following Academic Calendar was correct and complete when complied; however, the University reserves the right to revise or amend it, in whole or in part, at any time. Information on the current Academic Calendar may be obtained in the Student Service Center, 205 Kent, 212-854-4330, or visit the Registrar’s website at www.columbia.edu/cu/registrar.

AUTUMN TERM 2011 SPRING TERM 2012

August January 29–Sept. 5 New student orientation program. 10–13 Registration by appointment for all classes. 16 Birthday of Martin Luther King Jr. University holiday. September 17 First day of classes. 2 Registration by appointment for first-year 17–20, 23–27 Change of program by appointment. students. 27 Last day to (1) register for academic credit, 5 Labor Day. University holiday. (2) change course programs, (3) submit 6 First day of classes. written notice of withdrawal from the spring term to the Dean of Student Affairs Undergraduate Admissions Need more information? 6–9, 12–16 Change of program by appointment. 16 Last day to (1) register for academic credit, for full refund of tuition and special fees. You can find the contact information Office of Undergraduate Admissions (2) change course programs, (3) submit No adjustment of fees for individual 212 Hamilton Hall, Mail Code 2807 for the people who know in the written notice of withdrawal from the courses dropped after this date. 1130 Amsterdam Avenue Columbia University Resource List autumn term to the Dean of Student February New York, NY 10027 on pages 242–244 or visit the Columbia Engineering Affairs for full refund of tuition and special fees. No adjustment of fees for individual 1 Last day to confirm, update, or request a Phone: 212-854-2522 website, www.engineering.columbia.edu. courses dropped after this date. waiver from the Student Medical Fax: 212-854-3393 For the most current information, visit our online 30 Last day to confirm, update, or request a Insurance Plan. E-mail: [email protected] waiver from the Student Medical 8 February degrees conferred. bulletin at www.bulletin.engineering.columbia.edu. www.studentaffairs.columbia.edu/admissions Insurance Plan.

Financial Aid March October 5 Midterm date. Office of Financial Aid and Educational Financing 19 October degrees conferred. 12–16 Spring holiday. Office: 618 Lerner Hall 20 Midterm date. 22 Last day to drop Engineering courses Mailing: 100 Hamilton Hall, Mail Code 2802 without academic penalty. Last day 1130 Amsterdam Avenue to change grading option. New York, NY 10027 November Phone: 212-854-3711 1 Last day to apply for February degrees. April Fax: 212-854-5353 7 Academic holiday. 9–13 Registration by appointment for fall 2012. 8 Election Day. University holiday. 30 Last day of classes. Undergraduate Inquiry E-mail: [email protected] 14–18 Registration by appointment for spring Graduate Inquiry E-mail: [email protected] 2012. May www.studentaffairs.columbia.edu/finaid 17 Last day to drop Engineering courses 1–3 Study days. without academic penalty. Last day to 4–11 Final examinations. Graduate Student Services change a grading option. 5 Last day for continuing students to 24–25 Thanksgiving holiday. Graduate Admissions, Financial Aid, and Student Affairs apply for financial aid for the 2012–2013 academic year. 524 S. W. Mudd, Mail Code 4708 13 Baccalaureate Service. 500 West 120th Street December 14 Engineering Class Day. New York, NY 10027 1 Last day to apply for May degrees. 16 2012 University Commencement. Phone: 212-854-6438 12 Last day of classes. Fax: 212-854-5900 13–15 Study days. E-mail: [email protected] 16–23 Final examinations. www.engineering.columbia.edu 24–Jan. 16 Winter holiday. Bulletin Bulletin -2012 2011

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