Georgia Institute of Technology College of Sciences

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

Iterative methods for linear and nonlinear systems of equations including Jacobi, G-S, SOR, CG, multigrid, fixed point methods, Newton quasi-Newton, updating, gradient methods. Crosslisted with CSE 6644.

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

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

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

Continuation of MATH 6421.

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

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 may not obtain credit for both MATH 6580 and MATH 6338.

Lebesgue measure and integration, differentiation, abstract measure theory.

This course is equivalent to MATH 6579. No student may obtain credit for both MATH 6579 and MATH 6337. 

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.