The Department of Mathematics offers training at the undergraduate, graduate, and postgraduate levels. Its expertise covers 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.
Course 18 includes 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.
At the graduate level, the Mathematics Department offers the PhD in Mathematics, which culminates in the exposition of original research in a dissertation. Graduate students also are given training and experience in the teaching of mathematics.
The C.L.E. Moore instructorships and Applied Mathematics instructorships bring mathematicians at the postdoctoral level to MIT and provide them with training in research and teaching.
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 finance, physics, business, consulting, systems analysis, or actuarial science.
Because the career objectives of undergraduate mathematics majors are diverse, each student's program is arranged through collaboration with his or her faculty advisor.
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 has proven to be valuable for students planning to pursue graduate work and for those going on to other careers as well. These seminars also provide training in the verbal and written communication of mathematics and may be used to fulfill the Communication Requirement.
Many mathematics majors elect 18.821 Project Laboratory in Mathematics, which fulfills both the Institute's Laboratory Requirement and Communication Requirement.
In addition to the General Institute Requirements, the requirements consist of 18.03 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). One of these eight subjects must be 18.06 Linear Algebra, 18.700 Linear Algebra, or 18.701 Algebra I. This leaves available 84 units of unrestricted electives. The requirements are flexible in order to accommodate students who pursue programs that combine mathematics with a related field (such as physics, economics, or management) or students who are interested in both theoretical and applied mathematics.
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 enroll in 18.310 or 18.310C Principles of Applied Mathematics, and 18.311 Principles of Applied Mathematics. Subjects 18.310 and 18.310C, offered in the fall term, are devoted to the discrete aspects of applied mathematics and may be taken concurrently with 18.03. Subject 18.311, given in the spring 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 goal is to arrive at 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 subjects 18.701 and 18.901 Introduction to Topology are more advanced and should not be elected until a student has had experience with proofs, as in 18.100 Analysis I or 18.700 Linear Algebra.
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 Mathematics for Computer Science or 18.310) to give experience with proofs and the necessary tools for analyzing algorithms; and complex systems (6.033 Computer System Engineering or 6.170 Laboratory in Software Engineering) in which mathematical issues may arise. The required subjects covering complexity (18.404J Theory of Computation or 18.400J Automata, Computability, and Complexity) and algorithms (18.410J Design and Analysis of Algorithms) provide an introduction to the most theoretical aspects of computer science.
Some flexibility is allowed in this program. In particular, if students already have strong theorem-proving skills, they may substitute the more advanced subject 18.701 for 18.06, and 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, 617-253-2416.
Additionally, the following information sheets are available in Room 2-108 and on the department website 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 described 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 original research in mathematics that is described 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 it becomes the field of specialization. The examiner in this area usually becomes the thesis advisor.
For students choosing the applied mathematics program, the basic objective is a proper balance of specialization and diversity. A range of subjects is required, including some in discrete and some 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 chair of the Applied Mathematics Committee. The general oral examination in applied mathematics tests the student's competence in the area chosen for thesis research.
Nearly all 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, 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
Michel X. Goemans, PhD
Leighton Family 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
Pavel I. Etingof, PhD
Professor of Mathematics
Daniel Z. Freedman, PhD
Professor of Applied Mathematics
Victor William Guillemin, PhD
Professor of Mathematics
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
George Lusztig, PhD
Norbert Wiener Professor of Mathematics
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
Bjorn Poonen, PhD
Professor of Mathematics
Hartley Rogers, Jr., PhD
Professor of Mathematics
Rodolfo Ruben Rosales, PhD
Professor of Applied Mathematics
(On leave, spring)
Paul Seidel, PhD
Professor of Mathematics
Scott Sheffield, 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
W. Gilbert Strang, PhD
Professor of Mathematics
(On leave, spring)
Daniel W. Stroock, PhD
Professor of Mathematics
Alar Toomre, PhD
Professor of Applied Mathematics
David Alexander Vogan, Jr., PhD
Professor of Mathematics
Denis S. Auroux, PhD
Associate Professor of Mathematics
John W. Bush, PhD
Associate Professor of Applied Mathematics
Lars Hesselholt, PhD
Associate Professor of Mathematics
(On leave, fall)
Kiran S. Kedlaya, PhD
Cecil and Ida B. Green Career Development Associate Professor of Mathematics
Ju-Lee Kim, PhD
Associate Professor of Mathematics
Jacob A. Lurie, PhD
Associate Professor of Mathematics
Alexander Postnikov, PhD
Associate Professor of Applied Mathematics
(On leave, fall)
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
KDD Career Development Assistant Professor of Applied Mathematics
Abhinav Kumar, PhD
Assistant Professor of Mathematics
Lie Wang, PhD
Assistant Professor of Mathematics
Katrin Wehrheim, PhD
Rockwell International Career Development Assistant Professor of Mathematics
Soren Galatius, PhD
Assistant Professor of Mathematics
Mikio Furuta, PhD
Professor of Mathematics
Jeffry Kahn, PhD
Professor of Mathematics
John B. Lewis, PhD
Dan Gutfreund, PhD
Aslan Kasimov, PhD
Sami H. Assaf, PhD
Alina Ioana Bucur, PhD
Scott Carnahan, PhD
Pokman Cheung, PhD
Hans P. Christianson, PhD (On leave, fall)
David Jeremy Copeland, PhD
Michael Eichmair, PhD
Wenchuan Hu, PhD
Vera Mikyoung Hur, PhD
Todd A. Kemp, PhD
Liat Kessler, PhD
Brett L. Kotschwar, PhD
Ralf-Enno Lenzmann, PhD
Lionel Levine, PhD
Ivan Loseu, PhD
Grace K. Lyo, PhD
Karl E. Mahlburg, PhD
Mia Minnes, PhD
Yi Ni, PhD
Yaron Ostrover, PhD
Thomas Andrew Putman, PhD
Martin Reiris, PhD
Travis Schedler, PhD
Junecue Suh, PhD
Craig Van Coevering, PhD
Benjamin T. Webster, PhD
David J. Whitehouse, PhD
Chenyang Xu, PhD (On leave)
Yossi Farjoun, PhD
Sunghwan Jung, PhD
Avshalom Manela, PhD
Gregg Musiker, PhD
Jean-Christophe Nave, PhD
Pedro Miguel Reis, PhD
Benjamin Seibold, PhD
Daniel See-Wai Tam, PhD
Jerome Waldispuhl, PhD
Josephine Yu, PhD
Cameron Freer, PhD
Sikimeti Ma'u, PhD
Matthew Hedden, PhD
Mohammed Abouzaid, PhD
Pierre Albin, PhD
Spyridon Alexakis, PhD
Aliaa Barakat, PhD
Kay Kirkpatrick, PhD
Thomas Kragh, PhD
Davesh Maulik, PhD
David Speyer, PhD
Shannon Wieland, 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