sp19

Spring 2019

Archived: 

Math Methods of Applied Sciences II

Review of vector calculus and and its application to partial differential equations.

Numerical Methods in Finance

This course contains the basic numerical and simulation techniques for the pricing of derivative securities.

Differential Geometry I

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

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.

Real Analysis II

Topics include L^p, Banach and Hilbert spaces, basic functional analysis.

Real Analysis I

Measure and integration theory

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)

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.

Pages

Subscribe to RSS - sp19