BULLETIN 2018– 2019 UNDERGRADUATE ADMISSIONS Need more information? Office of Undergraduate Admissions You can find the contact information 212 Hamilton Hall, Mail Code 2807 for the people who know in the 1130 Amsterdam Avenue Columbia University Resource List New York, NY 10027 on pages 259–263 or visit the Columbia Engineering Phone: 212-854-2522 website, engineering.columbia.edu. Fax: 212-854-3393 For the most current information, visit our online E-mail: [email protected] bulletin at bulletin.engineering.columbia.edu. undergrad.admissions.columbia.edu GRADUATE ADMISSIONS Photography: Graduate Admissions, Financial Aid, and Student Affairs Confocal microscope image showing elongation of 530 S. W. Mudd, Mail Code 4708 a fruit fly embryo from the lab of Clare Boothe Luce 500 West 120th Street Assistant Professor Karen Kasza. Cell membranes New York, NY 10027 are labeled with GFP. Phone: 212-854-6438 Fax: 212-854-5900 Superimposed over this image is the emblem of E-mail: [email protected] the School’s new vision, Columbia Engineering for gradengineering.columbia.edu Humanity. FINANCIAL AID Office of Financial Aid and Educational Financing Office: 618 Lerner Hall Mailing: 100 Hamilton Hall, Mail Code 2802 1130 Amsterdam Avenue New York, NY 10027 Phone: 212-854-3711 Fax: 212-854-5353 E-mail: [email protected] cc-seas.financialaid.columbia.edu BULLETIN 2018 – 2019 Mission The mission of The Fu Foundation School of Engineering and Applied Science is to expand knowledge and advance technology through research, while educating students to become leaders and innovators informed by an engineering foundation. Enriched with the intellectual resources of a global university in the City of New York, we push disciplinary frontiers, confront complex issues, and engineer innovative solutions to address the grand challenges of our time. We create a collaborative environment that embraces interdisciplinary thought, creativity, integrated entrepreneurship, cultural awareness, and social responsibility, and advances the translation of ideas into innovations that impact humanity. Our mission can be encapsulated as "Transcending Disciplines, Education Leaders, Transforming Lives." ENGINEERING 2018–2019 A MESSAGE FROM THE DEAN elcome to Columbia University’s students are engaged in to create a more Fu Foundation School of sustainable, healthy, secure, connected, and W Engineering and Applied Science. creative world. As students here, you are among the very best This work is conducted in collaboration with and brightest of your generation. Together our world-class sister schools in medicine, with a talented group of students from around public health, architecture, science, business, the world, you are embarking on a course of policy, the social sciences, social work, study that will enable you to become the next journalism, even the arts and humanities. We generation of leaders. Engineering today is a also benefit from the resources of leading foundational degree that prepares you for a institutes such as the Zuckerman Mind Brain wealth of pursuits, and your education here will Behavior Institute, the Data Science Institute, serve you not only in fields of engineering and The Earth Institute, the Precision Medicine applied science, but in other disciplines as well. Initiative, and the Columbia Nano Initiative. You are joining a vibrant and intellectually Columbia Engineering is an exciting and challenging community, with a long history of stimulating community. I encourage you to take scientific and engineering breakthroughs that full advantage of the exceptional opportunities have impacted our world. From the School’s for learning and advancement that await you beginning in 1864 through today, the work here. of faculty, alumni, and students of Columbia Engineering has pushed disciplinary frontiers to With best wishes for the academic year, create, invent, and innovate devices, materials, and processes to make life better. Our first dean, Charles Frederick Chandler, served as president of New York City’s Metropolitan Board of Health. In this role, he crusaded to ensure the purity of food and drugs, the safety of milk, the availability of Mary C. Boyce clean water in the city, and the introduction of Dean of Engineering building codes. Today, our faculty and students Morris A. and Alma Schapiro Professor continue to develop innovative solutions to the world’s most challenging problems, and with entrepreneurial energy, translate their ideas into real-world solutions at an ever faster pace. You are coming to Columbia Engineering at an extraordinary moment. In the spring of 2017, we unveiled a new strategic vision for the School—Columbia Engineering for Humanity. This vision highlights the innovative and interdisciplinary work that our faculty and ENGINEERING 2018–2019 TABLE OF CONTENTS About the School and 1 Faculty and Administration 35 Campus and Student Life 217 University CAMPUS LIFE 218 HISTORY OF THE SCHOOL 2 Departments and Academic 47 STUDENT SERVICES 223 RESOURCES AND FACILITIES 5 Programs KEY TO COURSE LISTINGS 48 Scholarships, Fellowships, 227 Undergraduate Studies 9 APPLIED PHYSICS AND 50 Awards, and Prizes THE UNDERGRADUATE 10 APPLIED MATHEMATICS Named Scholarships and Grants 228 PROGRAMS Named Fellowships 234 Policy on Degree Requirements 10 BIOMEDICAL ENGINEERING 64 Outside Fellowship 236 The First-Year/Sophomore Program 10 CHEMICAL ENGINEERING 77 Medals and Prizes 236 Study Abroad 13 Residence Hall Scholarships 240 Combined Plan Programs 15 CIVIL ENGINEERING AND 87 The Junior-Senior Programs 16 ENGINEERING MECHANICS University and School 241 Programs in Preparation for 17 Policies, Procedures, and Other Professions COMPUTER ENGINEERING 100 Regulations Joint Programs 19 PROGRAM Undergraduate Admissions 19 ACADEMIC PROCEDURES 242 COMPUTER SCIENCE 105 AND STANDARDS UNDERGRADUATE TUITION, 20 EARTH AND ENVIRONMENTAL 120 FEES, AND PAYMENTS ACADEMIC STANDING 246 ENGINEERING FINANCIAL AID FOR 22 POLICY ON CONDUCT AND 249 ELECTRICAL ENGINEERING 135 UNDERGRADUATE STUDY DISCIPLINE INDUSTRIAL ENGINEERING 155 ESSENTIAL POLICIES FOR THE 252 Graduate Studies 23 AND OPERATIONS RESEARCH COLUMBIA COMMUNITY THE GRADUATE PROGRAMS 24 MATERIALS SCIENCE AND 175 OFFICIAL UNIVERSITY 253 The Master of Science Degree 24 ENGINEERING PROGRAM Doctoral Degrees: Eng.Sc.D. 25 REGULATIONS and Ph.D. MECHANICAL ENGINEERING 185 STUDENT GRIEVANCES, 256 Nondegree Students 26 ACADEMIC CONCERNS, AND Undergraduate Minors 201 COLUMBIA VIDEO NETWORK 27 COMPLAINTS GRADUATE ADMISSIONS 28 Interdisciplinary Courses 207 Directory of University 259 and Courses in Other GRADUATE TUITION, FEES, 30 Resources Divisions of the University AND PAYMENTS COLUMBIA UNIVERSITY 260 INTERDISCIPLINARY 208 RESOURCE LIST FINANCIAL AID FOR GRADUATE 32 ENGINEERING COURSES STUDY MAPS 264 Financing Graduate Education 32 COURSES IN OTHER DIVISIONS 209 INDEX 266 Instructions for Financial Aid 32 OF THE UNIVERSITY Applicants Applied Science and Applied 209 Academic Calendar (see inside back Graduate School Departmental 32 Mathematics cover) Funding Biological Sciences 209 Alternative Funding Sources 33 Business 209 Other Financial Aid—Federal 33 Chemistry 209 and Private Programs Earth and Environmental Sciences 211 Veteran's Benefits 33 Humanities and Social Sciences 212 Employment 33 Mathematics 213 Contact Information 34 Physics 213 Statistics 215 About the School and University 2 HISTORY OF THE SCHOOL A COLONIAL CHARTER Working around the globe, William industry. Working with Pupin, an Since its founding in 1754, as King’s Barclay Parsons, Class of 1882, was engineering student named Edwin College, Columbia University has always an engineer on the Chinese railway and Howard Armstrong was conducting been an institution both of and for the the Cape Cod and Panama Canals. experiments with the Audion tube in the City of New York. And it has always Most importantly for New York, he was basement of Philosophy Hall when he been an institution of and for engineers. chief engineer of the city’s first subway. discovered how to amplify radio signals In its original charter, the college stated Opened in 1904, the subway’s electric through regenerative circuits. Armstrong, that it would teach, among other things, cars took passengers from City Hall Class of 1913, was stationed in France “the arts of Number and Measuring, to Brooklyn, the Bronx, and the newly during the First World War, where he of Surveying and Navigation, . the renamed and relocated Columbia invented the superheterodyne circuit knowledge of . Meteors, Stones, University in Morningside Heights. to tune in and detect the frequencies Mines and Minerals, Plants and Animals, of enemy aircraft ignition systems. After the war, Armstrong improved his and everything useful for the Comfort, A MODERN SCHOOL method of frequency modulation (FM), the Convenience and Elegance of Life.” FOR MODERN TIMES and by 1931, had both eliminated The School of Mines became the School the static and improved the fidelity of EARLY ENGINEERS of Mines, Engineering, and Chemistry in radio broadcasting forever. The historic 1896, and its professors—now called An early and influential graduate from significance of Armstrong’s contributions the Faculty of Engineering and Applied the School was John Stevens, Class of was recognized by the U.S. government Science—included Michael Idvorsky 1768. Instrumental in the establishment when the Philosophy Hall laboratory was Pupin, a graduate of the Columbia of U.S. patent law, Stevens procured designated a National