Georgia Institute of Technology College of Sciences

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.

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.

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.

Approximation of the dynamical structure of a differential equation and preservation of dynamical structure under discretization.

Theoretical and computational aspects of polynomial, rational, trigonometric, spline and wavelet approximation.

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.