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Spring 2019

Archived:

## Introduction to Algebraic Topology

Introduction to algebraic methods in topology. Includes homotopy, the fundamental group, covering spaces, simplicial complexes. Applications to fixed point theory and group theory.

## Complex Analysis

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

## Analysis II

Differentiation of functions of one real variable, Riemann-Stieltjes integral, the derivative in R^n and integration in R^n

## 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 Information Theory

The measurement and quantification of information. These ideas are applied to the probabilistic analysis of the transmission of information over a channel along which random distortion of the message occurs.

## Mathematical Statistics II

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

## Abstract Algebra II

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

## 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.

## Applied Combinatorics

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