Department of Mathematics
- Associate Chair
- Departmental Representative
Jennifer M. Johnson
- Director of Graduate Studies
Javier Gómez Serrano
Michael Aizenman, also Physics
Noga M. Alon, also Applied and Computational Mathematics
Sun-Yung Alice Chang
Maria Chudnovsky, also Applied and Computational Mathematics
Fernando Codá Marques
Peter Constantin, also Applied and Computational Mathematics
Mihalis C. Dafermos
Weinan E, also Applied and Computational Mathematics
Charles L. Fefferman
Robert C. Gunning
Alexandru D. Ionescu
Nicholas M. Katz
Peter S. Ozsváth
John V. Pardon
Igor Y. Rodnianski
Peter C. Sarnak
Paul D. Seymour, also Applied and Computational Mathematics
Yakov G. Sinai
Amit Singer, also Applied and Computational Mathematics
Christopher M. Skinner
Allen M. Sly
Paul C. Yang
- Associate Professor
Zeev Dvir, also Computer Science
- Assistant Professor
Tristan J. Buckmaster
Gabriele Di Cerbo
Javier Gómez Serrano
Adam W. Marcus, also Applied and Computational Mathematics
Fabio G. Pusateri
Nicholas J. Sheridan
Nicolas A.S. Boumal
Daniel J. Ketover
Joseph A. Waldron
- Senior Lecturer
Jennifer M. Johnson
Mark W. McConnell
Christine J. Taylor
- Associated Faculty
Emmanuel A. Abbe, Electrical Engineering and Applied and Computational Mathematics
John P. Burgess, Philosophy
René A. Carmona, Operations Research and Financial Engineering
Bernard Chazelle, Computer Science
Hans P. Halvorson, Philosophy
William A. Massey, Operations Research and Financial Engineering
Frans Pretorius, Physics
Robert E. Tarjan, Computer Science
Ramon van Handel, Operations Research and Financial Engineering
Robert J. Vanderbei, Operations Research and Financial Engineering
Sergio Verdu, Electrical Engineering
Information and Departmental Plan of Study
Most freshmen and sophomores interested in science, engineering, or finance take courses from the standard calculus and linear algebra sequence 103-104-201-202, which emphasizes concrete computations over more theoretical considerations. Note that 201 and 202 can be taken in either order.
Students who are not prepared to begin with 103 may take 100, a rigorous precalculus/prestatistics refresher offered only in the fall semester and intended for students whose highest math SAT score is below 650.
Prospective economics majors can minimally fulfill their mathematics prerequisites with (100)-103-175. Note that 175 covers selected topics from 201, with biology and economics applications in mind. Prospective math-track economics/finance majors will need the standard sequence 103-104-201-202 instead of 175.
More mathematically inclined students, especially prospective physics majors, may opt to replace 201-202 with 203-204, for greater emphasis on theory and more challenging computational problems.
Prospective mathematics majors must take at least one course introducing formal mathematical argument and rigorous proofs. The recommended freshman sequence for prospective majors is 215-217. Prospective majors who already have substantial experience with university-level proof-based analysis courses may consider the accelerated sequence 216-218 instead. Other possible sequences for prospective majors include 214-204-203 and 203-204-215, although the latter two are relatively rare. Note that 203 and 204 can be taken in either order.
Placement. Students with little or no background in calculus are placed in 103, or in 100 if their SAT mathematics scores indicate insufficient background in precalculus topics. To qualify for placement in 104 or 175, a student should score 5 on the AB Advanced Placement Examination or a 4 on the BC Advanced Placement Examination. To qualify for placement into 201 or 202, a student should have a score of 5 on the BC Examination. Students who possess in addition a particularly strong interest in mathematics as well as a SAT mathematics score of at least 750 may opt for 203 or 214 or 215 or 216 instead. For more detailed placement information, consult the Department of Mathematics home page or placement officer.
One unit of advanced placement credit is granted when a student is placed in MAT 104 or 175. Two units of advanced placement credit are granted when a student is placed in MAT 201, 203, or 217.
Generally, either 215-217 or 216-218 or 203-204-215 are strongly recommended for admission to the department. Prospective mathematics majors should consult the department early and plan a program that includes as much of the 215-217 or 216-218 sequence as possible. Most majors begin taking courses at the 300-level by the second semester of the sophomore year, in preparation for their junior independent work.
Further information for prospective majors is available on the department home page.
Program of Study
Students must complete four core requirements:
- one course in real analysis (e.g. 320 or 325 or 425 or 385)
- one course in complex analysis (e.g. 330 or 335)
- one course in algebra (e.g. 340 or 345)
- one course in geometry or topology (e.g. 350 or 355 or 365 or 560)
It is recommended that students complete some of these core requirements by the end of the sophomore year. Completing these core courses early gives more options for junior and senior independent work.
Note: One course in discrete mathematics (e.g. 375, 377 or 378) can replace the geometry/topology core requirement, if desired.
In addition to the four core requirements, students must complete an additional four courses at the 300 level or higher, up to three of which may be cognate courses outside the mathematics department, with permission from the junior or senior advisers or departmental representative.
The departmental grade (the average grade of the eight departmental courses) together with grades and reports on independent work is the basis on which honors and prizes are awarded on graduation.
Students should refer to Course Offerings to check which courses are offered in a given term. Programs of study in various fields of pure mathematics and applied mathematics are available. Appropriate plans of study may be arranged for students interested in numerical analysis, discrete mathematics, optimization, physics, the biological sciences, probability and statistics, finance, economics, or computer science. For students interested in these areas, a coherent program containing up to three courses in a cognate field may be approved.
All departmental students engage in independent work, supervised by a member of the department chosen in consultation with a departmental adviser. The independent work of the junior year generally consists of participating actively in a junior seminar in both the fall and the spring semesters. Alternatively, a student may opt to replace one junior seminar with supervised reading in a special subject and then writing a paper based on that reading. The independent work in the senior year centers on writing a senior thesis. A substantial percentage of our majors work with faculty in other departments on their senior project.
Senior Departmental Examination
Each senior takes an oral examination based on the senior thesis and the broader subfield to which it contributes. A departmental committee conducts the examination in May.