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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 choose one of three options leading to the Bachelor of Science 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 receive training and gain experience in the teaching of mathematics.

The CLE 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://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 fields as finance, business, or consulting. Students' programs are arranged through consultation with their faculty advisors.

Undergraduates in mathematics are encouraged to elect an undergraduate 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 as well as for those going on to other careers. 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 take 18.821 Project Laboratory in Mathematics, which fulfills both the Institute's Laboratory Requirement and Communication Requirement.

[see degree chart]

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 or 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 focuses on the mathematical concepts and techniques applied in science, engineering, and computer science. Particular attention is given to 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 and 18.311 Principles of Discrete and Continuum Applied Mathematics. Subject 18.310 is 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 should also take some basic subjects in analysis and algebra.

Theoretical (or "pure") mathematics is the study of the basic concepts and structure of mathematics. 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 Algebra I 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 Real Analysis, or 18.700 Linear Algebra.

[see degree chart]

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.

The purpose of this program is to allow students to study a combination of these mathematical areas and potential areas of application 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 software construction (6.005 or 6.033) where 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.

For further information, see http://math.mit.edu/academics/undergrad/ or contact Math Academic Services, 617-253-2416.

The Mathematics Department offers programs covering a broad range of topics leading to the Doctor of Philosophy or Doctor of Science degree. Candidates are admitted to either the Pure or Applied Mathematics programs but are free to pursue interests in both groups. Of the roughly 110 doctoral students, about two thirds are in Pure Mathematics, one third in Applied Mathematics.

The programs in Pure and Applied Mathematics offer basic and advanced classes in analysis, algebra, geometry, Lie theory, logic, number theory, probability, statistics, topology, astrophysics, combinatorics, fluid dynamics, numerical analysis, theoretical physics, and the theory of computation. In addition, many mathematically oriented subjects are offered by other departments. Students in Applied Mathematics are especially encouraged to take subjects in engineering and scientific subjects related to their research.

All students pursue research under the supervision of the faculty and are encouraged to take advantage of the many seminars and colloquia at MIT and in the Boston area.

The requirements for these degrees are described on the department's website at http://math.mit.edu/academics/grad/timeline/. In outline, they consist of a language requirement, an oral qualifying examination, a thesis proposal, completion of a minimum of 132 units (11 graduate subjects), and a thesis containing original research in mathematics.

Financial support is guaranteed for up to five years to students making satisfactory academic progress. Financial aid after the first year is usually in the form of a teaching or research assistantship.

For further information, see http://math.mit.edu/academics/grad/ or contact Math Academic Services, 617-253-2416.

Michael Sipser, PhD

Professor of Applied Mathematics

Department Head

Interim Dean, School of Science

Gigliola Staffilani, PhD

Abby Rockefeller Mauzé Professor of Mathematics

Associate Department Head

Martin Z. Bazant, PhD

Professor of Chemical Engineering and Applied Mathematics

Bonnie A. Berger, PhD

Professor of Applied Mathematics and Computer Science

Associate Member, Broad Institute

(On leave, spring)

Roman Bezrukavnikov, PhD

Professor of Mathematics

(On leave, spring)

Alexei Borodin, PhD

Professor of Mathematics

John W. Bush, PhD

Professor of Applied Mathematics

Hung Cheng, PhD

Professor of Applied Mathematics

Tobias H. Colding, PhD

Levinson Professor of Mathematics

(On leave, fall)

Richard Mansfield Dudley, PhD

Professor of Mathematics

Alan Edelman, PhD

Professor of Applied Mathematics

(On leave, spring)

Pavel I. Etingof, PhD

Professor of Mathematics

Michel X. Goemans, PhD

Leighton Family Professor of Applied Mathematics

Chairman, Committee on Applied Mathematics

Victor William Guillemin, PhD

Professor of Mathematics

Alice Guionnet, PhD

Professor of Mathematics

Larry Guth, PhD

Professor of Mathematics

Sigurdur Helgason, PhD

Professor of Mathematics

Anette E. Hosoi, PhD

Professor of Mechanical Engineering and Applied Mathematics

MacVicar Faculty Fellow

David S. Jerison, PhD

Professor of Mathematics

MacVicar Faculty Fellow

Victor G. Kac, PhD

Professor of Mathematics

Ju-Lee Kim, PhD

Professor of Mathematics

(On leave, spring)

Steven Kleiman, PhD

Professor of Mathematics

F. Thomson Leighton, PhD

Professor of Applied Mathematics

(On leave)

George Lusztig, PhD

Abdun-Nur Professor of Mathematics

James McKernan, PhD

Norbert Weiner Professor of Mathematics

(On leave)

Richard Burt Melrose, PhD

Simons Professor of Mathematics

Haynes R. Miller, PhD

Professor of Mathematics

MacVicar Faculty Fellow

(On leave, spring)

William P. Minicozzi II, PhD

Professor of Mathematics

Tomasz S. Mrowka, PhD

Singer Professor of Mathematics

Chairman, Committee on Pure Mathematics

(On leave)

Bjorn Poonen, PhD

Shannon Professor of Mathematics

Igor Rodnianski, PhD

Professor of Mathematics

(On leave)

Rodolfo Ruben Rosales, PhD

Professor of Applied Mathematics

Paul Seidel, PhD

Professor of Mathematics

(On leave, spring)

Scott Sheffield, PhD

Professor of Mathematics

(On leave, fall)

Peter W. Shor, PhD

Morss Professor of Applied Mathematics

Richard P. Stanley, PhD

Professor of Applied Mathematics

(On leave, spring)

W. Gilbert Strang, PhD

MathWorks Professor of Mathematics

David Alexander Vogan, Jr., PhD

Professor of Mathematics

Mark J. Behrens, PhD

Cecil and Ida B. Green Career Development Associate Professor of Mathematics

Steven G. Johnson, PhD

Associate Professor of Applied Mathematics

Jonathan A. Kelner, PhD

Associate Professor of Applied Mathematics

Abhinav Kumar, PhD

Associate Professor of Mathematics

(On leave, spring)

Alexander Postnikov, PhD

Associate Professor of Applied Mathematics

(On leave, fall)

Lie Wang, PhD

Associate Professor of Mathematics

Katrin Wehrheim, PhD

Associate Professor of Mathematics

(On leave)

Clark Barwick, PhD

Assistant Professor of Mathematics

Laurent Demanet, PhD

Assistant Professor of Applied Mathematics

Jacob Fox, PhD

Assistant Professor of Applied Mathematics

Sug Woo Shin, PhD

Assistant Professor of Mathematics

(On leave, fall)

Charles Smart, PhD

Assistant Professor of Mathematics

Jared Speck, PhD

Assistant Professor of Mathematics

Gonçalo Tabuada, PhD

Assistant Professor of Mathematics

Henry Cohn, PhD

Adjunct Professor of Applied Mathematics

Benjamin Elias, PhD

Vyacheslav Gerovitch, PhD

Jeremy M. Orloff, PhD

Thomas Bitoun, PhD

Jonathan Bloom, PhD

Emanuele Dotto, PhD

Vadim Gorin, PhD

Philip Isett, PhD

Joseph Lauer, PhD

Yifeng Liu, PhD

Jonathan Luk, PhD

Jason McGibbon, PhD

Emmy Murphy, PhD

Nathaniel Stapleton, PhD

Vesna Stojanoska, PhD

Chelsea Walton, PhD

Hao Wu, PhD

Ting Zhou, PhD

Eric Baer, PhD

Joseph Hirsh, PhD

Holly Krieger, PhD

Michael McBreen, PhD

Laura Rider, PhD

Vidya Venkateswaran, PhD

Joshua Zahl, PhD

Peter Csikvari, PhD

Romain Lagrange, PhD

Choongbum Lee, PhD

Jonathan Novak, PhD

Lorenzo Orecchia, PhD

Richard Yang Peng, PhD

Homer Reid, PhD

Thomas Rothvoss, PhD

Norbert Stoop, PhD

Andrew Suk, PhD

Vladislav Voroninski, PhD

Aaron Welters, PhD

Ivan Corwin, PhD

Kiril Datchev, PhD

Paul Hand, PhD

Stephen James Kleene, PhD

Jason Miller, PhD

Kyle Ormsby, PhD

Tomer Schlank, PhD

Vivek Shende, PhD

Michael Artin, PhD

Professor of Mathematics, Emeritus

David J. Benney, PhD

Professor of Applied Mathematics, Emeritus

Herman Chernoff, PhD

Professor of Applied Mathematics, Emeritus

Daniel Z. Freedman, PhD

Professor of Applied Mathematics and Physics, Emeritus

Harvey Philip Greenspan, PhD

Professor of Applied Mathematics, Emeritus

Louis Norberg Howard, PhD

Professor of Applied Mathematics, Emeritus

Daniel Marinus Kan, PhD

Professor of Mathematics, Emeritus

Daniel J. Kleitman, PhD

Professor of Applied Mathematics, Emeritus

Bertram Kostant, PhD

Professor of Mathematics, Emeritus

Willem V. R. Malkus, PhD

Professor of Applied Mathematics, Emeritus

Arthur Paul Mattuck, PhD

Professor of Mathematics, Emeritus

James Raymond Munkres, PhD

Professor of Mathematics, Emeritus

Hartley Rogers, PhD

Professor of Mathematics, Emeritus

Gerald E. Sacks, PhD

Professor of Mathematical Logic, Emeritus

Richard Donald Schafer, PhD

Professor of Mathematics, Emeritus

Isadore Manual Singer, PhD

Professor of Mathematics, Emeritus

Institute Professor, Emeritus

Harold Stark, PhD

Professor of Mathematics, Emeritus

Daniel W. Stroock, PhD

Professor of Mathematics, Emeritus

Alar Toomre, PhD

Professor of Applied Mathematics, Emeritus