Program in Applied and Computational Mathematics
Philip J. Holmes
A. Robert Calderbank, Electrical Engineering, Mathematics
René A. Carmona, Operations Research and Financial Engineering
Emily A. Carter, Mechanical and Aerospace Engineering
Ingrid C. Daubechies, Mathematics
Weinan E, Mathematics
Philip J. Holmes, Mechanical and Aerospace Engineering
Yannis G. Kevrekidis, Chemical and Biological Engineering
Paul D. Seymour, Mathematics
Amit Singer, Mathematics
James M. Stone, Astrophysical Sciences
Jeroen Tromp, Geosciences
Sergio Verdú, Electrical Engineering
Yacine Aït-Sahalia, Economics
Michael Aizenman, Physics, Mathematics
William Bialek, Physics, Lewis-Sigler Institute for Integrative Genomics
David M. Blei, Computer Science
Adam Burrows, Astrophysical Sciences
Carlos D. Brody, Molecular Biology, Princeton Neuroscience Institute
Roberto Car, Chemistry
Moses S. Charikar, Computer Science
Bernard Chazelle, Computer Science
Patrick Cheridito, Operations Research and Financial Engineering
Mung Chiang, Electrical Engineering
Erhan Çinlar, Operations Research and Financial Engineering
Iain D. Couzin, Ecology and Environmental Biology
Bradley W. Dickinson, Electrical Engineering
David P. Dobkin, Computer Science
Jianqing Fan, Operations Research and Financial Engineering
Jason W. Fleischer, Electrical Engineering
Christodoulos A. Floudas, Chemical and Biological Engineering
Mikko P. Haataja, Mechanical and Aerospace Engineering
Gregory W. Hammett, Plasma Physics Lab, Astrophysical Sciences
Isaac M. Held, Geosciences, Atmospheric and Oceanic Sciences
Sergiu Klainerman, Mathematics
Naomi Ehrich Leonard, Mechanical and Aerospace Engineering
Simon A. Levin, Ecology and Evolutionary Biology
Elliott H. Lieb, Mathematics, Physics
Luigi Martinelli, Mechanical and Aerospace Engineering
William A. Massey, Operations Research and Financial Engineering
Jeremiah P. Ostriker, Astrophysical Sciences
H. Vincent Poor, Electrical Engineering
Warren B. Powell, Operations Research and Financial Engineering
Frans Pretorius, Physics
Jean-Hervé Prévost, Civil and Environmental Engineering
Herschel A. Rabitz, Chemistry
Peter J. Ramadge, Electrical Engineering
Jennifer L. Rexford, Computer Science
Clarence W. Rowley, Mechanical and Aerospace Engineering
Robert E. Schapire, Computer Science
José A. Scheinkman, Economics
Yakov G. Sinai, Mathematics
Jaswinder P. Singh, Computer Science
K. Ronnie Sircar, Operations Research and Financial Engineering
Howard Stone, Mechanical and Aerospace Engineering
John D. Storey, Molecular Biology, Lewis-Sigler Institute for Integrative Genomics
Sankaran Sundaresan, Chemical and Biological Engineering
Salvatore Torquato, Chemistry
Olga G. Troyanskaya, Computer Science, Lewis-Sigler Institute for Integrative Genomics
Geoffrey K. Vallis, Geosciences, Atmospheric and Oceanic Sciences
Robert J. Vanderbei, Operations Research and Financial Engineering
Applied Mathematics at Princeton. 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. The requirements for the mathematics major are a minimum of eight upperclass courses in mathematics or applied mathematics including three basic courses on real analysis, complex analysis, and algebra. It is possible to design a course of undergraduate study aimed more strongly toward applications. Applied and computational mathematics/mathematics faculty have developed core courses in applied mathematics and several courses where the emphasis is mathematical modeling. The latter is central to applied mathematics where it is not only necessary to acquire mathematical techniques and skills, but also important to learn about the application domain.
The Undergraduate Certificate. The certificate is designed for students from engineering and from the physical, biological, and social sciences who are looking to broaden their mathematical and computational skills. It is also an opportunity for mathematically oriented students to discover the challenges presented by applications from the natural sciences and engineering. Students interested in the undergraduate certificate contact the program's undergraduate representative in the spring semester of their sophomore year to discuss their interests, and to lay out a plan for their course selection and research component.
The requirements for the undergraduate certificate in applied and computational mathematics (ACM) consist of:
1. A total of five courses normally 300 level or higher (requires letter grade; pass/D/fail not accepted), at least two of which are not included in the usual requirements for the candidates' major concentration; and
2. Independent work consisting of a paper/course project/computational laboratory, possibly in the context of a course offered by ACM faculty or a senior thesis in the major department with a significant applied mathematics component (subject to approval of the ACM undergraduate representative). This independent work may not be used to satisfy the requirements of any other certificate.
Regardless of which option is selected in (2), students will also be required to participate during their junior and senior year in a not-for-credit colloquium offered by ACM. This will provide a forum for presentation and discussion of independent work among all certificate students and will introduce them to other areas of applied mathematics.
The five required courses may vary widely from department to department in order to include a broad spectrum of science and engineering students throughout the University. These courses should fit readily within the degree requirements of the respective departments of the engineering school or the economics, mathematics, physics, chemistry, molecular biology, and ecology and evolutionary biology, or other relevant departments, but will require a particular emphasis in applied mathematics.
The five required courses must be distributed between the following two areas, with at least two from each area:
1. Mathematical foundations and techniques, including differential equations, real and complex analysis, discrete mathematics, probability, and statistics, typically offered by the Department of Mathematics.
2. Mathematical applications, including signal processing, control theory, optimization, mathematical economics, typically offered by the economics, science, and engineering departments.
Specific choices must be approved by the ACM undergraduate representative.
The paper/course project/computational laboratories can be done as part of a course offered by applied and computational mathematics faculty or associated faculty on a wide range of topics of current interest in applied mathematics. Such courses vary from year to year and are designated to satisfy automatically the independent work requirement. Four courses developed and staffed by applied and computational mathematics faculty and offered regularly are the following:
CBE 448/MAT 448 Introduction to Nonlinear Dynamics
MAE 541/APC 571 Applied Dynamical Systems
MAT 594/APC 584 Wavelets: Applications of Wavelets in Mathematics and Other Fields
MAT 595/APC 586 Topics in Discrete Mathematics: Discrete Math
Any other course that students might use to satisfy the independent work requirement must have prior approval from the applied and computational mathematics undergraduate representative. Students may satisfy the independent work requirement outside of a course after consultation with and approval by the undergraduate representative. If the senior thesis option is selected, attempts will be made to coordinate it with departmental requirements.
Students who fulfill all requirements of the program will receive a certificate of proficiency in applied and computational mathematics upon graduation.
Relevant Advanced Courses. A list of representative advanced undergraduate and some graduate courses that meet the certificate requirements can be found on the program website. This list is primarily illustrative and is by no means complete. Specific programs should be tailored by the program undergraduate representative in consultation with the student to meet individual and/or departmental needs.
APC 150 Introduction to Statistics QR
This course is an introduction to probability and statistical methods, and covers topics in probability, random variables, sampling, descriptive statistics, probability distributions, estimation and hypotheses testing, introduction to the regression model. The course emphasizes the practice, and students will learn how to perform data analysis using modern computational tools. L. Martinelli
APC 199 Math Alive (also MAT 199) QR
An exploration of some of the mathematical ideas behind important modern applications, from banking and computing to listening to music. Intended for students who have not had college-level mathematics and are not planning to major in a mathematically based field. The course is organized in independent two-week modules focusing on particular applications, such as bar codes, CD-players, population models, and space flight. The emphasis is on ideas and mathematical reasoning, not on sophisticated mathematical techniques. Two 90-minute classes, one computer laboratory. I. Daubechies, S. Hughes
APC 307 Combinatorial Mathematics (see MAT 307)
APC 350 Introduction to Differential Equations (also CEE 350/MAT 350) QR
An introduction to differential equations, covering both applications and fundamental theory. Basic second-order differential equations (including the wave, heat, and Poisson equations); separation of variables and solution by Fourier series and Fourier integrals; boundary value problem and Green's function; variational methods; normal mode analysis and perturbation methods; nonlinear first order (Hamilton-Jacobi) equations and method of characteristics; reaction-diffusion equations. Application of these equations and methods to finance and control. Prerequisites: MAT 102, 103, and 202. Two 90-minute lectures. W. E
APC 351 Topics in Mathematical Modeling (see MAT 351)
APC 441 Computational Geophysics (see GEO 441)