Georgia Institute of Technology College of Sciences

An introduction to the Ito stochastic calculus and stochastic differential equations through a development of continuous-time martingales and Markov processes. (2nd of two courses in sequence)

Applications of probabilistic techniques in discrete mathematics, including classical ideas using expectation and variance as well as modern tools, such as martingale and correlation inequalities.

Fundamental combinatorial structures including hypergraphs, transversal sets, colorings, Sperner families, intersecting families, packings and coverings, perfect graphs, and Ramsey theory. Algebraic and topological methods, applications.

Selection of topics vary with each offering.

Description, institutional features, and mathematical modeling of fixed income securities. Use of both deterministic and stochastic models. Crosslisted with ISYE 6769.

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.

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.

Introduction to the numerical solution of the classic problems of linear algebra including linear systems, least squares, SVD, eigenvalue problems. Crosslisted with CSE 6643.