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Fall 2020

Archived:

## Undergraduate Seminar

Pass/fail basis.

This course provides students with a broad exposure to areas of mathematics research through weekly speakers.

## 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. 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.

## Stochastic Processes I

Simple random walk and the theory of discrete time Markov chains

## 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.

## Analysis I

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

## Abstract Algebra I

This course develops in the theme of "Arithmetic congruence, and abstract algebraic structures." There will be a very strong emphasis on theory and proofs.

## 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.