Fall 2016

## 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.

## Modeling and Dynamics

Mathematical methods for solving problems in the life sciences. Models-based course on basic facts from the theory of ordinary differential equations and numerical methods of their solution. Introduction to the control theory, diffusion theory, maximization, minimization and curve fitting.

## Math Methods of Applied Sciences I

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

## 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.

## Industrial Mathematics I

Applied mathematics techniques to solve real-world problems. Topics include mathematical modeling, asymptotic analysis, differential equations and scientific computation. Prepares the student for MATH 6515. (1st of two courses)

## 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.