sp16

Spring 2016

Archived: 

Algebraic Topology I

The fundamental group, covering spaces, core topics in homology and cohomology theory including CW complexes, universal coefficients, and Poincare duality.

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.

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.

Algebra II

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

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