Fall 2019

## Probability Theory

This course is a mathematical introduction to probability theory, covering random variables, moments, multivariate distributions, law of large numbers, central limit theorem, and large deviations.

## Probability and Statistics with Applications

Introduction to probability, probability distributions, point estimation, confidence intervals, hypothesis testing, linear regression and analysis of variance.

## A Second Course on Linear Algebra

This course will cover important topics in linear algebra not usually discussed in a first-semester course, featuring a mixture of theory and applications.

## Introduction to Discrete Mathematics

Mathematical logic and proof, mathematical induction, counting methods, recurrence relations, algorithms and complexity, graph theory and graph algorithms.

## Foundations of Mathematical Proof

An introduction to proofs in advanced mathematics, intended as a transition to upper division courses including MATH 4107, 4150 and 4317.

## Classical Mathematical Methods in Engineering

Fourier series, Fourier integrals, boundary value problems for partial differential equations, eigenvalue problems

## Dynamics and Bifurcations I

A broad introduction to the local and global behavior of nonlinear dynamical systems arising from maps and ordinary differential equations.

## Differential Geometry

The theory of curves, surfaces, and more generally, manifolds. Curvature, parallel transport, covariant differentiation, Gauss-Bonet theorem

## Introduction to Topology

Point set topology, topological spaces and metric spaces, continuity and compactness, homotopy and covering spaces

## Partial Differential Equations I

Method of characteristics for first and second order partial differential equations, conservation laws and shocks, classification of second order systems and applications.