# Undergraduate Program

### Certificate Program Overview

In engineering and science today there is a trend toward the use of modern, sophisticated mathematical techniques of both computational and theoretical types. One reason for this is the revolutionary development of computational resources. Modern engineers and scientists have at their disposal user-friendly, powerful computers with sophisticated graphics to display results. Such modeling and simulation techniques are also increasingly used in the biological and social sciences, especially economics. With these tools, interdisciplinary problems that are complex and nonlinear have become the norm in contemporary science and engineering. The engineer/scientist must learn to use such tools wisely, accurately, and to their full power. A natural time to be introduced to such skills is as an undergraduate. During these formative years the modern engineer or scientist should learn the use of mathematical and computational techniques in an interactive, interdisciplinary environment. At Princeton, the Program in Applied and Computational Mathematics offers a small group of undergraduate students the unique opportunity to learn to perform accurate and controlled numerical studies and, perhaps most important, exposes them to the philosophy and tools of interdisciplinary applied mathematics in a very personal and individualized manner. Students who complete the prescribed requirements are awarded a certificate in Applied and Computational Mathematics. Recently a new option has become available to undergraduate math majors who intend to pursue the PACM certificate, the applied math track.

### Applying

Formal application to the program typically occurs toward the beginning of the junior year of study, although sophomores who display high aptitude may be considered as well. Before December 31 of their junior year, students should submit a one-page proposal outlining their course selection and giving some idea of their choice of independent work (paper/ course project/ computational laboratory) or thesis. Proposals should be addressed to the undergraduate representative and sent in care of Gina Holland, Room 205 Fine Hall. Students accepted into the program will be notified by means of a formal acceptance letter. Students interested in more information about the program should contact the undergraduate representative, Prof. Paul Seymour, for a meeting.

## Applied Mathematics Track

The Applied Mathematics Track provides undergraduates with a new reason to major in mathematics. It includes courses in applied mathematics that emphasize mathematical modeling where you will learn about an application domain as you master new mathematical techniques. An example of such a course is given below.

**MAT 351 / APC 351: Topics in Mathematical Modeling. **This is an upper division course developed by Philip Holmes. It draws problems from the sciences and engineering for which mathematical models have been developed and analyzed in order to describe, understand and predict natural and man-made phenomena. Topics will change from year to year, such as Classical Mechanics and Chaos or Mathematical Neuroscience. The continuing theme is how applications motivate mathematical developments and how mathematical techniques influence the questions that science is able to address. The new course assumes familiarity with the application domain at the high school or freshman level and describes strategies for building models, including the level of detail and selection of an appropriate mathematical language.