Program in Applied and Computational Mathematics

Academic Unit

Program Information

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.

Program of Study

The requirements for the undergraduate certificate in applied and computational mathematics 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 candidate's major concentration; and

2. Independent work consisting of a paper in one of the following formats: (a) a course project/computational laboratory (possibly in the context of a course offered by Program in Applied and Computational Mathematics [PACM] faculty); (b) a project that you are working on with a professor; or (c) a summer research project that you are planning on undertaking. However, you may not use your junior paper or senior thesis to satisfy the independent work for the certificate program. Your paper should have a significant applied mathematics component (subject to approval of the PACM undergraduate representative). The independent work may not be used to satisfy the requirements of any other certificate. Students interested in the PACM certificate program must apply on or before December 31 of their junior year.

Regardless of which option is selected in (2), students will also be required to participate during their junior and senior years in a not-for-credit colloquium offered by PACM. 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, and optimization, mathematical economics, typically offered by the economics, science, and engineering departments.

Specific choices must be approved by the PACM 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. These courses should be taken in your junior year if you intend to use them as a paper for your independent work. Four courses developed and staffed by applied and computational mathematics faculty and offered regularly are the following:

CBE 448/MAT 481 Introduction to Nonlinear Dynamics
MAT323/APC 323 Topics in Mathematical Modeling
MAE 541/APC 571 Applied Dynamical Systems

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.

Certificate of Proficiency

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.