Georgia Institute of Technology College of Sciences

An advanced course in Linear Algebra and applications.

Spectral theory of bounded and unbounded operators, major theorems of functional analysis, additional topics.

Fourier analysis on the torus and Euclidean space.

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.

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.

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

Lebesgue measure and integration, differentiation, abstract measure theory.

This course is equivalent to MATH 6579. Students should not be able to obtain credit for both MATH 6579 and MATH 6337.

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)

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)

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