Fall 2017

Archived:

## 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. Fundamentals of mathematical abstraction including sets, logic, equivalence relations, and functions. Thorough development of the basic proof techniques: direct, contrapositive, existence, contradiction, and induction. Introduction to proofs in analysis and algebra.

## Analysis I

Real numbers, topology of Euclidean spaces, Cauchy sequences, completeness, continuity and compactness, uniform continuity, series of functions, Fourier series

## Topics in Linear Algebra

Linear algebra in R^n, standard Euclidean inner product in R^n, general linear spaces, general inner product spaces, least squares, determinants, eigenvalues and eigenvectors, symmetric matrices.

## Introduction to Graduate Mathematics

This course includes topics on professional development and responsible conduct of research. The course satisfies the GT RCR Academic Policy for Doctoral Students to complete in-person RCR training.

## 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.

## Complex Analysis

Topics from complex function theory, including contour integration and conformal mapping

## Pages 