Fall 2018

## Probability and Statistics with Applications

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

## 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. 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.

## Quantum Information and Quantum Computing

Introduction to quantum computing and quantum information theory, formalism of quantum mechanics, quantum gates, algorithms, measurements, coding, and information. Physical realizations and experiments. Crosslisted with PHYS 4782

## 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