Fall 2016

Archived:

## Partial Differential Equations I

Introduction to the mathematical theory of partial differential equations covering the basic linear models of science and exact solution techniques.

## Real Analysis I

Measure and integration theory

## Ordinary Differential Equations I

This sequence develops the qualitative theory for systems of ordinary differential equations. Topics include stability, Lyapunov functions, Floquet theory, attractors, invariant manifolds, bifurcation theory, normal forms. (1st of two courses)

## Linear Statistical Models

Basic unifying theory underlying techniques of regression, analysis of variance and covariance, from a geometric point of view. Modern computational capabilities are exploited fully. Students apply the theory to real data through canned and coded programs.

## Testing Statistical Hypotheses

Basic theories of testing statistical hypotheses, including a thorough treatment of testing in exponential class families. A careful mathematical treatment of the primary techniques of hypothesis testing utilized by statisticians.

## Probability I

Develops the probability basis requisite in modern statistical theories and stochastic processes. Topics of this course include measure and integration foundations of probability, distribution functions, convergence concepts, laws of large numbers and central limit theory. (1st of two courses)

## Stochastic Processes in Finance II

This is the second of a two-semester sequence that develops basic probability concepts and models for working with financial markets and derivative securities. Continuous-time parameter stochastic processes are emphasized in this course. Mathematical concepts are introduced as needed.

## Algebra I

Graduate level linear and abstract algebra including groups, rings, modules, and fields. (1st of two courses)

## Graph Theory

Fundamentals, connectivity, matchings, colorings, extremal problems, Ramsey theory, planar graphs, perfect graphs. Applications to operations research and the design of efficient algorithms.