## Introduction

The teaching
and research programs of the Department of Applied Mathematics and Statistics
span modern applied mathematics. The
department's curriculum in Probability/Statistics covers probability
theory, stochastic processes, and applied and theoretical statistics.
Its Operations Research/Optimization program includes continuous
and discrete optimization, numerical optimization, network programming,
and game theory. Its curriculum in Discrete Mathematics includes combinatorics,
graph theory and cryptology and coding. Its
program in Scientific Computing includes computing, numerical analysis,
matrix analysis, and mathematical modeling of systems. The
programs of the department together emphasize mathematical reasoning,
mathematical modeling and computation, abstraction from the particular,
innovative application of mathematics, and development of new methodology.

## Philosophy

The objective of the department's Ph.D. program is to produce graduates who are broadly educated in Applied Mathematics and Statistics and who can work at the current research frontiers of their specialized disciplines. Follow this link for information about admission to the AM&S graduate program.

A student should demonstrate mathematical comprehension in **two
stages**:

- general mathematical proficiency (breadth), measured by an Introductory Exam on the following topics: real analysis, linear algebra, and probability; and
- qualification for advance research (depth), measured by a Ph.D. Candidacy Exam covering in-depth knowledge of the student’s proposed research area.

A main objective is to help those students with the desire and background
to do so, to get an earlier start on initial research-type activities. These
activities would not necessarily be in the same area as the ultimate
doctoral research, and typically would not have the same degree of intensity
and commitment as that later work; for example they would involve interaction
with the student’s faculty “mentor” rather than an
official “dissertation advisor.” One role of the Introductory
Exam is to gauge readiness for such activity.