2016-2017 Graduate

MATH 700 Advanced Seminar

Consent of Instructor. An advanced seminar in an active area of mathematical research. Content depends upon instructor's choice. Repeatable, may be taken two times, under different subtitles.

2

MATH 709 Abstract Algebra I

Prerequisite MATH 523 or equivalent. Groups and rings and their structure. Sylow theorems. Modules. History and applications.

3

MATH 723 Abstract Algebra II

Prerequisite MATH 709. Polynomial Noetherian rings and ideals. Fields and Galois theory. Structure of fields. History and applications.

3

MATH 727 Representation Theory

Introduction to Representation Theory of various mathematical structures. Emphasis is on group representations.

3

MATH 728 Topics in Discrete Mathematics

Prerequisite: MATH 778. A broad yet deep survey of current topics in combinatorics and graph theory essential for teachers K-16, including applications to probability, coding theory, sorting and matching algorithms and optimization.

3

MATH 732 Complex Variables

Prerequisite: A course in complex analysis. Analytic and meromorphic functions in the complex plane. Integration, conformal mapping and advanced topics.

3

MATH 733 Geometric Analysis

Prerequisites: MATH 525; MATH 540 recommended. Analysis of functions of several variables, unifying and extending ideas from calculus and linear algebra. Includes the implicit function theorem and Stokes' Theorem.

3

MATH 735 Real Analysis

Abstract spaces, Lebesque measure, continuity, integration and differentiation theorems, Baire category.

3

MATH 736 Real Analysis II

Prerequisite: MATH 735. Topics from real and functional analysis such as: measure theory, distributions, metric spaces and other topics of the instructor's choice.

3

MATH 744 Differential Geometry

Prerequisite: A course in Analysis. A course in the differential geometry of curves and surfaces. Both modern and classical aspects will be covered.

3

MATH 764 Difference Equations and Chaos

Applications of difference equations in problem solving and modeling, especially in the area of chaos.

3

MATH 778 Mathematical Logic

The notion of proof, first order logic, set theory, ordinals, cardinals and an overview of the most important recent results in the field.

3

MATH 791 Number Theory

Prerequisite: MATH 732. A survey of topics in arithmetic and analytic number theory, such as Eulers' function, quadratic reciprocity, continued fractions and the distribution of prime numbers.

3

MATH 795 Special Topics

Topics from various fields of mathematics, for example, algebraic topology, functional analysis, Lie groups and algebras or nonlinear analysis. Repeatable, under different subtitles.

3

MATH 797 Doctoral Proposal Research

Required of all doctoral students. Four hours of credit for doctoral dissertation proposal research must be earned in partial fulfillment of requirements before admission to candidacy. Repeatable, maximum of four credits.

1-4

MATH 799 Doctoral Dissertation

Required of all doctoral candidates. S/U graded. Repeatable, no limitations.

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