Applied and Computational Mathematics
Overview
There has never been a better time to be a mathematician. The combination of mathematics and computer modeling has transformed science and engineering, and is changing the nature of research in the biological sciences, data science and many other areas.
The minor in the Program in Applied and Computational Mathematics (PACM) is designed for students from engineering, from the physical, biological and social sciences, and from the humanities who wish to broaden their mathematical and computational skills. It is also an opportunity for mathematics majors whose primary focus is in pure mathematics to discover the challenges presented by applications from the sciences and engineering. The interaction between mathematical foundations and applications lies at the core of the program.
Princeton does not offer a separate major in Applied and Computational Mathematics. Students seeking to pursue an academic program whose primary focus lies in applied mathematics may either major in mathematics with a course of study geared toward applications, or major in another discipline and combine their major with the PACM minor.
Program Offerings
There has never been a better time to be a mathematician. The combination of mathematics and computer modeling has transformed science and engineering, and is changing the nature of research in the biological sciences, data science and many other areas.
The minor in the Program in Applied and Computational Mathematics (PACM) is designed for students from engineering, from the physical, biological and social sciences, and from the humanities who wish to broaden their mathematical and computational skills. It is also an opportunity for mathematics majors whose primary focus is in pure mathematics to discover the challenges presented by applications from the sciences and engineering. The interaction between mathematical foundations and applications lies at the core of the program.
Princeton does not offer a separate major in Applied and Computational Mathematics. Students seeking to pursue an academic program whose primary focus lies in applied mathematics may either major in mathematics with a course of study geared toward applications, or major in another discipline and combine their major with the PACM minor.
Goals for Student Learning
Mathematics is the language of science, and almost every discipline of science and engineering is ultimately founded on mathematics. At the same time, stateoftheart computational methods are enabling the study of increasingly complex systems. The aim of the Program in Applied and Computational Mathematics minor is to enable students from a broad range of disciplines to develop a stronger mathematical and computational foundation, and to promote dialogue between mathematics and its applications.
At the same time, the minor aims to encourage students whose primary concentration is in pure mathematics to explore the impact of mathematics on science, engineering and technology.
A core tenet of the PACM minor is the bilateral interaction between mathematical foundations and applications. A strong background in mathematics and computational methods provides students with powerful tools to address problems that arise in other disciplines, and may lead them to view these from a new perspective. Conversely, challenging mathematical and computational questions that arise in applications strongly motivate the study and development of mathematics. The PACM minor promotes such interactions:
 By requiring all students to take both mathematical foundations and applications courses;
 By requiring all students to perform an independent research project that connects mathematics with its applications;
 By requiring all students to attend and present their independent work in the minor seminar, where they are exposed to a broad range of applications of mathematics to different disciplines and have the opportunity to interact with students with applied mathematical interests from many different majors across campus.
At the same time, the flexible program is designed to allow each student to tailor their courses and independent work to their own interests, and to make mathematics as accessible as possible for students with diverse interests and backgrounds.
Prerequisites
The PACM minor has no formal prerequisites. However, the PACM course requirements (as detailed below) can be fulfilled only with 300+ level courses. While the PACM minor does not have any formal course requirements at the 200 level, students should note that most 300+ level mathematical foundations courses are likely to require either MAT 201 or MAT 202 as prerequisites.
Admission to the Program
Students interested in the PACM minor must contact the program's undergraduate representative on or before February 1 of their junior year to discuss their interests, and to lay out a plan for their course selection and research component.
Program of Study
The requirements for the PACM minor consist of:
 A total of five courses at 300 level or higher (requires letter grade; pass/D/fail not accepted), at least three of which are not included in the requirements for the candidate’s major.
 An independent research project consisting of a paper in one of the following formats: (a) a project that you are working on with a professor; or (b) a summer research project. The research project may not be used to satisfy any requirements of your major or of any other minor or certificate. Most (but not all) majors require a senior thesis and/or junior independent work, which therefore cannot be used as such for PACM; however, a significant extension of such independent work could be used for PACM subject to approval of the PACM undergraduate representative.
 Students are required to participate during the spring semester of their junior and senior years in a notforcredit colloquium offered by PACM. This will provide a forum for presentation and discussion of research projects among all students in the minor and will introduce them to a broad range of areas within applied mathematics.
The PACM course requirement may be satisfied by a broad range of courses that place a particular emphasis on applied mathematics, which are offered by the mathematics department as well as the science, engineering and economics departments. The five required courses must be distributed between the following two areas, with at least two from each area:
 Mathematical foundations and techniques, including differential equations, real and complex analysis, discrete mathematics, probability, numerical methods, etc.
 Mathematical applications in diverse areas offered by the applied and computational mathematics program and by science, engineering and economics departments.
An extensive list of courses that meet the minor requirements can be found on the program website. Courses that do not appear on this list may be approved by the PACM undergraduate representative. Specific programs should be tailored in consultation with the PACM undergraduate representative to meet the individual needs and interests of each student.
The PACM research project is typically done under the supervision of a PACM core or associated faculty member, but external advisers are regularly accommodated. In the latter case, a second reader from PACM is asked to verify that the paper contains enough applied mathematics to satisfy the minor requirements. In any case, plans for the research project must be approved by the undergraduate representative.
Additional Information
Normally, students may not pursue both the PACM minor and the minor offered by the mathematics department. However, students who believe they have a compelling curricular reason to pursue both minors may apply to the directors of both programs for permission to do so. Students who are majoring in mathematics are welcome to combine their studies with the PACM minor.
Faculty

Director
 Amit Singer

Director of Undergraduate Program
 Paul Seymour

Executive Committee
 Noga M. Alon, Mathematics
 René A. Carmona, Oper Res and Financial Eng
 Emily Ann Carter, Mechanical & Aerospace Eng
 Maria Chudnovsky, Mathematics
 Peter Constantin, Mathematics
 Guillermo Sapiro, Electrical & Comp Engineering
 Amit Singer, Mathematics
 Howard A. Stone, Mechanical & Aerospace Eng
 Romain Teyssier, Astrophysical Sciences
 Jeroen Tromp, Geosciences
 Ramon van Handel (on leave), Oper Res and Financial Eng

Associated Faculty
 Ryan P. Adams, Computer Science
 Amir Ali Ahmadi, Oper Res and Financial Eng
 Michael Aizenman, Physics
 Yacine AïtSahalia, Economics
 William Bialek, Physics
 Mark Braverman, Computer Science
 Carlos D. Brody, Princeton Neuroscience Inst
 Adam S. Burrows, Astrophysical Sciences
 Roberto Car, Chemistry
 Bernard Chazelle, Computer Science
 Jianqing Fan, Oper Res and Financial Eng
 Jason W. Fleischer, Electrical & Comp Engineering
 Mikko P. Haataja, Mechanical & Aerospace Eng
 Gregory W. Hammett, PPPL Theory
 Isaac M. Held, Atmospheric & Oceanic Sciences
 Sergiu Klainerman, Mathematics
 Naomi E. Leonard, Mechanical & Aerospace Eng
 Simon A. Levin, Ecology & Evolutionary Biology
 Luigi Martinelli, Mechanical & Aerospace Eng
 William A. Massey, Oper Res and Financial Eng
 Assaf Naor, Mathematics
 Jonathan W. Pillow, Princeton Neuroscience Inst
 H. Vincent Poor, Electrical & Comp Engineering
 Frans Pretorius, Physics
 Herschel A. Rabitz, Chemistry
 Peter J. Ramadge, Electrical & Comp Engineering
 Jennifer Rexford, Computer Science
 Clarence W. Rowley, Mechanical & Aerospace Eng
 Szymon M. Rusinkiewicz, Computer Science
 Frederik J. Simons, Geosciences
 Jaswinder P. Singh, Computer Science
 Ronnie Sircar, Oper Res and Financial Eng
 Mete Soner, Oper Res and Financial Eng
 John D. Storey, Integrative Genomics
 Sankaran Sundaresan, Chemical and Biological Eng
 Ludovic Tangpi, Oper Res and Financial Eng
 Robert E. Tarjan, Computer Science
 Corina E. Tarnita, Ecology & Evolutionary Biology
 Salvatore Torquato, Chemistry
 Olga G. Troyanskaya, Computer Science
 Matt Weinberg, Computer Science

Professor
 Noga M. Alon
 Maria Chudnovsky
 Peter Constantin
 Amit Singer
 Romain Teyssier
 Jeroen Tromp

Associate Professor
 Ramon van Handel

Lecturer
 Henry F. Schreiner

Visiting Professor
 Ehud Yariv
For a full list of faculty members and fellows please visit the department or program website.