Mathematics provides a language and tools for understanding the physical world around us and the abstract world within us. MIT's Mathematics Department is one of the strongest in the world. It offers a broad spectrum of fields ranging from the traditional areas of pure mathematics, such as analysis, algebra, geometry, and topology, to applied mathematics areas such as combinatorics, computational biology, fluid dynamics, theoretical computer science, and theoretical physics.
The Mathematics Department offers a choice of two undergraduate degrees: a Bachelor of Science in Mathematics and a Bachelor of Science in Mathematics with Computer Science. Undergraduate students may elect one of three options leading to the degree in mathematics: applied mathematics, theoretical mathematics, or general mathematics. The general mathematics option provides a great deal of flexibility and allows students to design their own programs in conjunction with their advisors. The Mathematics with Computer Science degree is offered for students who want to pursue interests in mathematics and theoretical computer science within a single undergraduate program. Nearly 40 percent of the graduating seniors in mathematics are double majors. Popular second majors include computer science, physics, and economics.
There are a variety of opportunities available to our students after graduation. Some students go on to graduate school in mathematics, computer science, and other fields such as medicine, finance, and engineering. Many begin careers in consulting, actuarial science, software engineering, and investment banking.
At the graduate level, the department offers the PhD in mathematics where students learn to conduct original research.
For more information, visit http://www-math.mit.edu/.
An undergraduate degree in mathematics provides an excellent basis for graduate work in mathematics or computer science, or for employment in such mathematics-related fields as systems analysis, operations research, finance, or actuarial science.
Because the career objectives of undergraduate mathematics majors are diverse, each undergraduate's program is individually arranged through collaboration between the student and his or her faculty advisor. Students are encouraged to explore the various branches of mathematics, both pure and applied.
Undergraduates in mathematics are encouraged to elect an upper-level mathematics seminar during their junior or senior year. The experience gained from active participation in a seminar conducted by a research mathematician is particularly valuable for a student planning to pursue graduate work. These seminars additionally provide training in communicating mathematics effectively.
This option is the one followed by most students who major in mathematics. In addition to the General Institute Requirements, the requirements consist of 18.03 Differential Equations, or 18.034 Differential Equations, and eight 12-unit subjects in Course 18 of essentially different content, including at least six advanced subjects (first decimal digit one or higher). This leaves available 84 units of unrestricted electives. The requirements are flexible in order to accommodate several categories of students: students who pursue programs that combine mathematics with a related field (such as physics, economics, or management); students who are interested in both theoretical and applied mathematics; and students who choose mathematics as a general Institute major.
Applied mathematics is the mathematical study of general scientific concepts, principles, and phenomena that, because of their widespread occurrence and application, relate or unify various disciplines. The core of the program at MIT concerns the following principles and their mathematical formulations: propagation, equilibrium, stability, optimization, computation, statistics, and random processes.
Sophomores interested in applied mathematics typically survey the field by enrolling in 18.310 or 18.310C, and 18.311 Principles of Applied Mathematics. Subjects 18.310 and 18.310C, offered only in the first term, are devoted to the discrete aspects of applied mathematics and may be taken concurrently with 18.03. Subject 18.311, given only in the second term, is devoted to continuous aspects and makes considerable use of differential equations.
The subjects in Group I of the program correspond roughly to those areas of applied mathematics that make heavy use of discrete mathematics, while Group II emphasizes those subjects that deal mainly with continuous processes. Some subjects, such as probability or numerical analysis, have both discrete and continuous aspects.
Students planning to go on to graduate work in applied mathematics also should take some basic subjects in analysis and algebra.
Theoretical mathematics (or "pure" mathematics) is the study of the basic concepts and structures that underlie the mathematical tools used in science and engineering. Its purpose is to search for a deeper understanding and an expanded knowledge of mathematics itself.
Traditionally, pure mathematics has been classified into three general fields: analysis, which deals with continuous aspects of mathematics; algebra, which deals with discrete aspects; and geometry. The undergraduate program is designed so that students become familiar with each of these areas. Students also may wish to explore other topics such as logic, number theory, complex analysis, and subjects within applied mathematics.
The subject 18.100B Analysis I is basic to the program. Since this subject is strongly proof oriented, many students find an intermediate subject such as 18.06 Linear Algebra or 18.700 Linear Algebra useful as preparation.
The subject 18.701 Algebra I is more advanced and should not be elected until the student has had some experience with proofs (as in 18.100B or 18.700).
Mathematics and computer science are closely related fields. Problems in computer science are often formalized and solved with mathematical methods. It is likely that many important problems currently facing computer scientists will be solved by researchers skilled in algebra, analysis, combinatorics, logic and/or probability theory, as well as computer science.
This program allows students to study a combination of these mathematical areas and potential application areas in computer science. Required subjects include linear algebra (18.06 or 18.700) because it is so broadly used; discrete mathematics (18.062J or 18.310) to give experience with proofs and the necessary tools for analyzing algorithms; and complex systems (6.033 or 6.170) in which mathematical issues may arise. The required subjects covering complexity (18.404J or 18.400J) and algorithms (18.410J) provide an introduction to the most theoretical aspects of computer science.
Some flexibility is allowed in this program. In particular, students may substitute the more advanced subject 18.701 Algebra I for 18.06 and, if they already have strong theorem-proving skills, may substitute 18.314 for 18.062 or 18.310.
The requirements for a Minor in Mathematics are as follows:
Six 12-unit subjects in mathematics, beyond the Institute calculus requirement, of essentially different content, including at least four advanced subjects (first decimal digit one or higher).
For a general description of the minor program, see Undergraduate Education in Part 1.
Inquiries regarding academic programs may be addressed to Joanne Jonsson, Undergraduate Mathematics Office, Room 2-108, MIT, 617-253-2416.
Additionally, the following information sheets are available in Room 2-108 and online at http://www-math.mit.edu/undergraduate/:
What Math Subject Shall I Take?
Careers in Mathematics
Thinking of Majoring in Mathematics?
The Mathematics Department offers programs covering a broad range of topics leading to the Doctor of Philosophy and the Doctor of Science degrees. Numerous formal and informal seminars, as well as a joint weekly mathematics colloquium sponsored alternately by MIT, Brandeis, Harvard, and Northeastern, supplement the subject offerings.
Students are expected to have one year of college-level natural science in addition to an undergraduate mathematics program approximating that of mathematics majors at MIT. Students may enter the applied mathematics program from any undergraduate field of concentration; however, special consideration is given to students with a strong scientific background.
The Institute requirements for these degrees are given under Graduate Education in Part 1. The details of the departmental requirements are explained on the department's website at http://math.mit.edu/graduate/. In outline, the requirements include a general qualifying examination to be taken in the third semester of registration in the program and completion of a minimum of 132 units (registration in at least 11 graduate subjects). The decisive requirement is conducting original research in mathematics and summarizing the results of that research in a thesis.
For students in the pure mathematics program, the oral part of the general examination covers three areas chosen by the student in consultation with the chairperson of the Committee on Graduate Students. One of the three areas is examined in greater depth and normally becomes the field of specialization. The examiner in this area normally becomes the thesis advisor.
For students electing the applied mathematics program, the basic objective is a proper balance of specialization and diversity. A range of subjects is required, including at least one in discrete and one in continuous applied mathematics. By the end of the first year of study, each student must submit a plan of study for approval by the chairperson of the Applied Mathematics Committee. The general oral examination in applied mathematics tests the student's competence in the area chosen for thesis research.
Most graduate students in mathematics are supported in full or in part by teaching assistantships, fellowships, or research assistantships. This support is renewed for students who are progressing satisfactorily, so that they are supported for a total of four years.
Additional information regarding academic or research programs in mathematics, admissions, or financial aid, may be obtained from Linda Okun, Graduate Mathematics Office, Room 2-233, MIT, 617-253-2689.
Michael Sipser, PhD
Professor of Applied Mathematics
Department Head
Tomasz S. Mrowka, PhD
Simons Professor of Mathematics
Chairman, Committee on Pure Mathematics
Alar Toomre, PhD
Professor of Applied Mathematics
Chairman, Committee on Applied Mathematics
Michael Artin, PhD
Professor of Mathematics
David J. Benney, PhD
Professor of Applied Mathematics
Bonnie A. Berger, PhD
Professor of Applied Mathematics
(On leave, fall)
Roman Bezrukavnikov, PhD
Professor of Mathematics
Hung Cheng, PhD
Professor of Applied Mathematics
Tobias H. Colding, PhD
Professor of Mathematics
Richard Mansfield Dudley, PhD
Professor of Mathematics
Alan Edelman, PhD
Professor of Applied Mathematics
(On leave, fall)
Pavel I. Etingof, PhD
Professor of Mathematics
Daniel Z. Freedman, PhD
Professor of Applied Mathematics
(On leave)
Michel X. Goemans, PhD
Professor of Applied Mathematics
(On leave)
Victor William Guillemin, PhD
Professor of Mathematics
(On leave, fall)
Sigurdur Helgason, PhD
Professor of Mathematics
David S. Jerison, PhD
Professor of Mathematics
MacVicar Faculty Fellow
Victor Kac, PhD
Professor of Mathematics
Steven Kleiman, PhD
Professor of Mathematics
Daniel J. Kleitman, PhD
Professor of Applied Mathematics
F. Thomson Leighton, PhD
Professor of Applied Mathematics
(On leave)
George Lusztig, PhD
Norbert Wiener Professor of Mathematics
(On leave, spring)
Arthur Paul Mattuck, PhD
Professor of Mathematics
James McKernan, PhD
Professor of Mathematics
Richard Burt Melrose, PhD
Simons Professor of Mathematics
Haynes R. Miller, PhD
Professor of Mathematics
MacVicar Faculty Fellow
Hartley Rogers, Jr., PhD
Professor of Mathematics
Rodolfo Rubén Rosales, PhD
Professor of Applied Mathematics
Paul Seidel, PhD
Professor of Mathematics
Peter W. Shor, PhD
Morss Professor of Applied Mathematics
Isadore Manual Singer, PhD
Professor of Mathematics
Institute Professor
Gigliola Staffilani, PhD
Abby Rockefeller Mauze Professor of Mathematics
Richard P. Stanley, PhD
Levinson Professor of Applied Mathematics
(On leave, spring)
W. Gilbert Strang, PhD
Professor of Mathematics
Daniel W. Stroock, PhD
Simons Professor of Mathematics
David Alexander Vogan, Jr., PhD
Professor of Mathematics
Denis S. Auroux, PhD
Associate Professor of Mathematics
Martin Z. Bazant, PhD
Associate Professor of Applied Mathematics
(On leave)
John W. Bush, PhD
Associate Professor of Applied Mathematics
Lars Hesselholt, PhD
Associate Professor of Mathematics
Kiran S. Kedlaya, PhD
Associate Professor of Mathematics
Ju-Lee Kim, PhD
Associate Professor of Mathematics
Jacob A. Lurie, PhD
Associate Professor of Mathematics
Igor Pak, PhD
Associate Professor of Applied Mathematics
(On leave)
Dmitry A. Panchenko, PhD
Associate Professor of Mathematics
(On leave)
Alexander Postnikov, PhD
Associate Professor of Applied Mathematics
Mark J. Behrens, PhD
Assistant Professor of Mathematics
Benjamin B. Brubaker, PhD
Assistant Professor of Mathematics
Steven G. Johnson, PhD
Assistant Professor of Applied Mathematics
Jonathan A. Kelner, PhD
Assistant Professor of Applied Mathematics
Abhinav Kumar, PhD
Assistant Professor of Mathematics
Eric Lauga, PhD
Assistant Professor of Applied Mathematics
(On leave)
Katrin Wehrheim, PhD
Rockwell International Career Development Assistant Professor of Mathematics
Tewodros Amdeberhan, PhD
Assistant Professor of Mathematics
Christophe Clanet, PhD
Professor of Applied Mathematics
Darren Crowdy, PhD
Associate Professor of Applied Mathematics
Jeffry Kahn, PhD
Professor of Mathematics
Bjorn Poonen, PhD
Professor of Mathematics
Eric B. Rosen, PhD
Assistant Professor of Mathematics
Yongbin Ruan, PhD
Professor of Mathematics
Richard Shore, PhD
Professor of Mathematics
John B. Lewis, PhD
Dan Gutfreund, PhD
Pierre Albin, PhD
Sami H. Assaf, PhD (On leave)
Aliaa Barakat, PhD
Alina Ioana Bucur, PhD
Scott Carnahan, PhD
Pokman Cheung, PhD
Hans P. Christianson, PhD
David Jeremy Copeland, PhD
Marco E. Gualtieri, PhD
Matthew E. Hedden, PhD
Wenchuan Hu, PhD
Vera Mikyoung Hur, PhD
Youngmi Hur, PhD
Todd A. Kemp, PhD
Liat Kessler, PhD
Brett L. Kotschwar, PhD
Kobi A. Kremnizer, PhD
Ralf-Enno Lenzmann, PhD
Grace K. Lyo, PhD
Karl E. Mahlburg, PhD
Yi Ni, PhD (On leave)
Yaron Ostrover, PhD
Brett D. Parker, PhD
Thomas A. Putman, PhD (On leave, fall)
Martin Reiris, PhD
Junecue Suh, PhD
Ilya Tyomkin, PhD
Craig Van Coevering, PhD
Benjamin T. Webster, PhD
David J. Whitehouse, PhD
Yossi Farjoun, PhD
Morris R. Flynn, PhD
Matthew J. Hancock, PhD
Sunghwan Jung, PhD
Aslan R. Kasimov, PhD
Avshalom Manela, PhD
Gregg Musiker, PhD
Jean-Christophe Nave, PhD
Per-Olof Persson, PhD
Pedro Miguel Reis, PhD
Benjamin Seibold, PhD
Clifford D. Smyth, PhD
Jerome Waldispuhl, PhD
Josephine Yu, PhD
Yuuji Tanaka, PhD
Daniel Freund, PhD
Thierry Savin, PhD
Mohammed Abouzaid, PhD
Matthew Fayers, PhD
Kay Kirkpatrick, PhD
Alvaro Pelayo, PhD
David Speyer, PhD
Herman Chernoff, PhD
Professor of Applied Mathematics, Emeritus
Harvey Philip Greenspan, PhD
Professor of Applied Mathematics, Emeritus
Kenneth Myron Hoffman, PhD
Professor of Mathematics, Emeritus
Louis Norberg Howard, PhD
Professor of Applied Mathematics, Emeritus
Daniel Marinus Kan, PhD
Professor of Mathematics, Emeritus
Bertram Kostant, PhD
Professor of Mathematics, Emeritus
Chia-Chiao Lin, PhD
Institute Professor, Emeritus
Professor of Applied Mathematics, Emeritus
Willem V. R. Malkus, PhD
Professor of Applied Mathematics, Emeritus
James Raymond Munkres, PhD
Professor of Mathematics, Emeritus
Gerald E. Sacks, PhD
Professor of Mathematical Logic, Emeritus
Richard Donald Schafer, PhD
Professor of Mathematics, Emeritus
Harold Stark, PhD
Professor of Mathematics, Emeritus