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## High-dimensional probability

The goal of this PhD level graduate course is to provide a rigorous introduction to the methods of high-dimensional probability.

## College Algebra

Study of the properties of algebraic, exponential, and logarithmic functions as needed for pre-calculus and calculus.

## Statistical Theory

This course is an introduction to theoretical statistics for students with a background in probability. A mathematical formalism for inference on experimental data will be developed.

## 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.

## 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.

## 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.

## Stochastic Processes I

Simple random walk and the theory of discrete time Markov chains

## Analysis I

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