Probability Theory for Science and Engineering

Classical introduction to probability theory including expectation, notions of convergence, laws of large numbers, independence, large deviations, conditional expectation, martingales, and Markov chains.

Stochastic Processes I

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)

Stochastic Processes in Finance I

Mathematical modeling of financial markets, derivative securities pricing, and portfolio optimization. Concepts from probability and mathematics are introduced as needed. Crosslisted with ISYE 6759.

Math Methods of Applied Sciences I

Review of linear algebra and ordinary differential equations, brief introduction to functions of a complex variable.

Iterative Methods for Systems of 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.

Numerical Linear Algebra

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

Introduction to Numerical Methods for Partial Differential Equations

Introduction to the implementation and analysis of numerical algorithms for the numerical solution of the classic partial differential equations of science and engineering.

Introduction to Hilbert Spaces

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.

Differential Topology

The differential topology of smooth manifolds.

Partial Differential Equations I

Introduction to the mathematical theory of partial differential equations covering the basic linear models of science and exact solution techniques.


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