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## 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.

## Real Analysis I

Lebesgue measure and integration, differentiation, abstract measure theory.

This course is equivalent to MATH 6579. Students should not be able to obtain credit for both MATH 6579 and MATH 6337.

## Probability I

Develops the probability basis requisite in modern statistical theories and stochastic processes. Topics of this course include measure and integration foundations of probability, distribution functions, convergence concepts, laws of large numbers and central limit theory. (1st of two courses)

## Probability Theory for Scientists and Engineers

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

The three course series MATH 6579, 6580, and 6221 is designed to provide a high level mathematical background for engineers and scientists.

Note that MATH 6221 is not equivalent to MATH 6421, and does not provide any credit towards completion of that course.

## Math Methods of Applied Sciences I

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

## 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.

## 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.

## Differential Topology

The differential topology of smooth manifolds.