Classical introduction to probability theory including expectation, notions of convergence, laws of large numbers, independence, large deviations, conditional expectation, martingales, and Markov chains.
Discrete time Markov chains, Poisson processes and renewal processes. Transient and limiting behavior. Average cost and utility measures of systems. Algorithm for computing performance measures. Modeling of inventories, and flows in manufacturing and computer networks. (Also listed as ISyE 6761)
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.
Geometry, convergence, and structure of linear operators in infinite dimensional spaces. Applications to science and engineering, including integral equations and ordinary and partial differential equations.