Spring 2020

Archived:

Differential Geometry I

Core topics in differential and Riemannian geometry including Lie groups, curvature, relations with topology.

Partial Differential Equations II

This course covers the general mathematical theory of linear stationary and evolution problems plus selected topics chosen on the instructor's interests.

Real Analysis II

This course is a continuation of MATH 6337. It covers L^p and Hilbert spaces, and an introduction to operator theory and functional analysis.

This course is equivalent to MATH 6580. Students should not be able to obtain credit for both MATH 6580 and MATH 6338.

Real Analysis I

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.

Complex Analysis

Complex integration, including Goursat's theorem; classification of singularities, the argument principle, the maximum principle; Riemann Mapping theorem; analytic continuation and Riemann surfaces; range of an analytic function, including Picard's theorem.

Ordinary Differential Equations II

This sequence develops the qualitative theory for systems of differential equations. Topics include stability, Lyapunov functions, Floquet theory, attractors, invariant manifolds, bifurcation theory, and normal forms. (2nd of two courses)

Multivariate Statistical Analysis

Multivariate normal distribution theory, correlation and dependence analysis, regression and prediction, dimension-reduction methods, sampling distributions and related inference problems, selected applications in classification theory, multivariate process control, and pattern recognition.

Statistical Estimation

Basic theories of statistical estimation, including optimal estimation in finite samples and asymptotically optimal estimation. A careful mathematical treatment of the primary techniques of estimation utilized by statisticians.

Probability II

Develops the probability basis requisite in modern statistical theories and stochastic processes. (2nd of two courses)

Algebra II

Graduate level linear and abstract algebra including rings, fields, modules, some algebraic number theory and Galois theory. (2nd of two courses)