2013-2014 Graduate Catalog

College of Natural and Health Sciences

School of Mathematical Sciences

MATH 508 Workshop

A variety of workshops on special topics within the discipline. Goals and objectives will emphasize the acquisition of general knowledge and skills in the discipline. Repeatable, under different subtitles.

1 - 3

MATH 510 Seminar in Mathematics

Study discussion and student presentation of topics in mathematics. S/U graded. Repeatable, under different subtitles.

1

MATH 513 Professional Renewal

Update skills and knowledge of professionals in the discipline. Goals and objectives will be specifically directed at individual professional enhancement rather than the acquisition of general discipline knowledge or methodologies. S/U or letter graded. Repeatable, under different subtitles.

1 - 3

MATH 520 Functions and Equations

Graduates only. Polynomial equations including DeMoivre's Theorem, the Fundamental Theorem of Algebra, methods of root extraction (e.g. Newton, Graffe) multiplicities, symmetric functions, matrices and determinants. Elementary computer applications.

3

MATH 522 Directed Studies

Individualized investigation under the direct supervision of faculty member. (Minimum of 37.5 clock hours required per credit hour.) Repeatable, maximum concurrent enrollment is two times.

1 - 3

MATH 523 Modern Algebra

A study of groups, rings and fields with a special emphasis on groups and fields.

3

MATH 525 Linear Algebra I

Prerequisite: MATH 321. Vector spaces, linear transformations, matrices, eigenvalues, canonical forms, quadratic forms and other selected topics.

3

MATH 528 Discrete Mathematics

Graduates only. Broad, deep, survey of topics in combinatorics, graph theory addressing existence, enumeration, optimization. Blend of mathematics, applications and development of mathematical reasoning skills, guided by the NCTM standards.

3

MATH 529 Mathematical Problem Solving

Graduates only. Techniques in problem solving applied to algebra, number theory, geometry, probability, discrete mathematics, logic and calculus. A study of Polya's heuristic rules of mathematical discovery.

3

MATH 531 Basic Analysis I

Prerequisite: MATH 233 with a grade of "C" or better (C- is not acceptable), and permission of instructor. Sequence of two courses to extend studies of calculus and analysis into the mathematical rigor and logic of analysis. Includes: real numbers, sequences, topology, limits, continuity, differentiation, series and integration.

3

MATH 532 Basic Analysis II

Prerequisite: MATH 531. Continuation of MATH 531.

3

MATH 534 Continuous Mathematics

Graduates only. Students will explore selected topics in mathematical analysis such as differential mappings and chaotic systems.

3

MATH 537 Mathematical Modeling

Graduates only. Introduction to the process of mathematical modeling and its use in teaching secondary school mathematics. Emphasizes development and communication of models.

3

MATH 540 Introduction to Topology

Point-set topology and the foundations of real analysis.

3

MATH 543 Modern Geometry

A survey of both traditional Euclidean geometry and contemporary geometries, in which applications of geometry are integrated into the study of the mathematical structure of geometrical systems.

3

MATH 545 Introductory Analysis

Prerequisite: MATH 540. Sequences, series, differentiation, Riemann-Stieltjes Integral, series of functions, special functions and functions of several variables.

3

MATH 550 Applied Probability and Statistics

Graduates only. Concepts include history, counting techniques, distributions and inference (confidence intervals, point estimation, testing, ANOVA, regression, non-parametrics). The Context focus is secondary level mathematics.

3

MATH 560 Introductory Complex Variables

Prerequisite: MATH 432 or equivalent. First course in complex variables, especially for potential calculus teachers. After preliminaries, proceed directly to power series, Laurent's series, contour integration, residue theory, polynomials and rational functions.

3

MATH 591 Abstract Algebra and Number Theory

Basic methods of problem solving in abstract algebra and number theory with applications in secondary school mathematics.

3

MATH 595 Topics in Mathematics

Topics from various fields of mathematics which reflect specific interests of instructors and students. Repeatable, under different subtitles.

1 - 3

MATH 599 Mathematics Action Research Project Seminar

Graduates only. Students research a mathematical problem relevant to their own teaching and write an expository paper on that topic. Repeatable without limitation.

3

MATH 622 Directed Studies

Individualized investigation under the direct supervision of a faculty member. (Minimum of 37.5 clock hours required per credit hour.) Repeatable, maximum concurrent enrollment is two times.

1 - 4

MATH 695 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 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.

1 - 12