2011-2012 Bulletin –

Columbia | Engineering Columbia Bulletin 2011 -2012 2 011 - 2 012 500 West 120th Street New York, New York 10027 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

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