Spring 2018


Numerical Methods for Ordinary Differential Equations

Analysis and implementation of numerical methods for initial and two point boundary value problems for ordinary differential equations.

Advanced Numerical Methods for Partial Differential Equations

Analysis and implementation of numerical methods for nonlinear partial differential equations including elliptic, hyperbolic, and/or parabolic problems.

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.


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