Georgia Institute of Technology College of Sciences

Continuation of MATH 6421.

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

Continuous time Markov chains. Uniformization, transient and limiting behavior. Brownian motion and martingales. Optional sampling and convergence. Modeling of inventories, finance, flows in manufacturing and computer networks. (Also listed as ISyE 6762)

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

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

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.

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

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