Fall 2020

## 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.

## 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.

## Ordinary Differential Equations I

This sequence develops the qualitative theory for systems of ordinary differential equations. Topics include stability, Lyapunov functions, Floquet theory, attractors, invariant manifolds, bifurcation theory, normal forms. (1st of two courses)

## 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)

## Algebra I

Graduate level linear and abstract algebra including groups, rings, modules, and fields. (1st of two courses)