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## Introduction to Topology

Point set topology, topological spaces and metric spaces, continuity and compactness, homotopy and covering spaces

## Complex Analysis

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

## 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.

## Mathematical Statistics I

Sampling distributions, Normal, t, chi-square and F distributions. Moment generating function methods, Bayesian estimation and introduction to hypothesis testing

## Introduction to Graph Theory

The fundamentals of graph theory: trees, connectivity, Euler torus, Hamilton cycles, matchings, colorings and Ramsey theory.

## 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.

## Applied Combinatorics

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

## Functional Analysis

Spectral theory of bounded and unbounded operators, major theorems of functional analysis, additional topics.

## Harmonic Analysis

Fourier analysis on the torus and Euclidean space.

## Real Analysis II

This course is a continuation of MATH 6337. It covers L^p and Hilbert spaces, and an introduction to operator theory and functional analysis.

This course is equivalent to MATH 6580. Students should not be able to obtain credit for both MATH 6580 and MATH 6338.