Archived:

## Mathematical Statistics II

Hypothesis testing, likelihood ratio tests, nonparametric tests, bivariate and multivariate normal distributions

## Introduction to Number Theory

Primes and unique factorization, congruences, Chinese remainder theorem, Diophantine equations, Diophantine approximations, quadratic reciprocity. Applications such as fast multiplication, factorization and encryption.

## Abstract Algebra II

Continuation of Abstract Algebra I, with emphasis on Galois theory, modules, polynomial fields, and the theory of linear associative algebra.

## 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.

## Combinatorial Analysis

Combinatorial problem-solving techniques including the use of generating functions, recurrence relations, Polya theory, combinatorial designs, Ramsey theory, matroids, and asymptotic analysis.

## Introduction to Probability and Statistics

This course is a problem oriented introduction to the basic concepts of probability and statistics, providing a foundation for applications and further study.

MATH 3215, MATH 3235, and MATH 3670 are mutually exclusive; students may not hold credit for more than one of these courses.

## Applied Combinatorics

Elementary combinatorial techniques used in discrete problem solving: counting methods, solving linear recurrences, graph and network models, related algorithms, and combinatorial designs.

## Introduction to Operator Theory

Theory of linear operators on Hilbert space; spectral theory of bounded and unbounded operators; applications

## Stochastic Processes and Stochastic Calculus II

An introduction to the Ito stochastic calculus and stochastic differential equations through a development of continuous-time martingales and Markov processes. (2nd of two courses in sequence)

## Probabilistic Methods in Combinatorics

Applications of probabilistic techniques in discrete mathematics, including classical ideas using expectation and variance as well as modern tools, such as martingale and correlation inequalities.