Spring 2019


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.


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