**The Master of Arts and Master of Science in Mathematics requires 30 - 31 credit hours. **

**Degree Requirements:**

**Algebra, 6 credit hours**

MATH 511 - Abstract Algebra 1 (3)

MATH 512 - Abstract Algebra 2 (3)

If the undergraduate equivalent is not complete. Otherwise course substitutions in Algebra will be made in conjunction with the Program Advisor.

**Analysis, 6-7 credit hours**

MATH 571 - Real Analysis 1 (4)

MATH 572 - Real Analysis 2 (3)

If the undergraduate equivalent is not complete. Otherwise 3-credit hour course substitutions in analysis will be made in conjunction with the Program Advisor.

MATH 645 - Topology 1 (3)

MATH 675 - Measure Theory and Integration 1 (3)

MATH 677 - Complex Variables 1 (3)

**3-6 hours from:**

MATH 516 - Theory of Numbers (3)

MATH 556 - Introduction to Operations Research (3)

MATH 562 - Numerical Analysis 1 (3)

MATH 563 - Numerical Analysis 2 (3)

MATH 573 - Boundary Value Problems (3)

MATH 575 - Topics Partical Dif Equations (3)

MATH 625 - Probability Theory Application (3)

MATH 626 - Probability Stochastic Process (3)

MATH 646 - Topology 2 (3)

MATH 676 - Measure Theory and Integrations 2 (3)

MATH 678 - Complex Variables 2 (3)

**Research component, 3 - 6 credit hours for MA in Mathematics **

**Research component is 6 credit hours for MS in Mathematics**

MATH 689 - Research Methods in Mathematics and Statistics (3)

MATH 694 - Research Methods in Mathematics Education (3)

THES 698 - Thesis (1-6)

**Related Links**
Graduate Course Offering Schedule (PDF)

**511 Abstract Algebra 1 (3)**

The theory of groups, including subgroups, cyclic groups, normal subgroups, cosets, Lagrange's Theorem, quotient structures, homomorphism, automorphisms, group actions, Sylow's Theorems, structure of finite abelian groups, generators, and relations.

*Prerequisite: *MATH 311 or permission of the department chairperson.

*Not open to *students who have credit in MATH 411.

**512 Abstract Algebra 2 (3)**

An introduction to the theory of rings, including integral domains, divison rings, and fields. Quotient fields of integral domains. Homomorphisms, ideals and quotient structures. Factorization in commutative rings. Polynomial rings and field extensions. Aspects of Galois theory.

*Prerequisite: *MATH 411 or MATH 511, or permission of the department chairperson.

*Not open to *students who have credit in MATH 412.

**516 Theory of Numbers (3)**

Topics include the division algorithm; positional notation; divisibility; primes; congruences; divisibiilty criteria; the sigma, divisor, and phi functions; Diophantine equations; linear, polynomial, and simultaneous congruences; theorems of Fermat, Euler, Lagrange, and Wilson; quadratic reciprocity.

*Prerequisite: *MATH 215 or permission of the department chairperson.

*Not open to *students who have credit in MATH 416.

**556 Introduction to Operations Research (3)**

Optimization techniques of linear programming, dynamic programming, and integer programming. Optimal solutions of PERT-CPM networks. Optimal decision strategies.

*Prerequisite: *MATH 162 or MATH 166 and MATH 217 or permission of the department chairperson.

*Not open to *students who have credit in MATH 456.

**562 Numerical Analysis 1 (3)**

Topics include error analysis, locating roots of equations, interpolation, numerical differentiation and integration, spline functions, smoothing of data. Includes programming of numerical algorithms.

*Prerequisite: *MATH 162 or MATH 166; MATH 259 or CS 120; or permission of the departmetnt chairperson.

*Not open to *students who have credit in MATH 362.

**563 Numerical Analysis 2 (3)**

Topics include direct and iterative methods for solving systems of linear equations, eigenvalue problems; minimization of functions and linear programming. Includes programming of numerical algorithms.

*Prerequisite: *MATH 217 and MATH 362 or MATH 562.

*Not open to *students who have credit in MATH 363.

**571 Real Analysis 1 (4)**

Real and complex number systems: ordered sets, least upper bound property, fields, Archimedean property; Basic topology: cardinality, metric spaces, completeness, compactness, connectedness; Numerical sequences and series: convergence tests, upper-lower limits; Continuity: continuous functions, uniform continuity, Intermediate and Extreme Value Theorems: Differentiation: derivative, Mean Value Theorem, 1 'Hospital's Rule, Taylor's Theorem.

*Prerequisite: *MATH 215 and MATH 267; or permission of the department chairperson.

*Not open to *students who have credit in MATH 471.

**572 Real Analysis 2 (3)**

The Reimann-Stieltjes integral and Fundamental Theorem of Calculus. Sequences and series of functions. Differential calculus of functions of several variables. Inverse and implicit function theorems. Extremum problems. Lebesgue integration and comparison with the Riemann integral.

*Prerequisite: *MATH 471 or MATH 571.

*Not open to *students who have credit in MATH 472.

**573 Boundary Value Problems (3)**

Fourier Series and integrals, heat and wave equations in one dimension, Laplace equation in two dimensions, problems in higher dimensions, and numerical methods of solving boundary value problems.

*Prerequisite: *MATH 374

*Not open to *students who have credit in MATH 473.

**575 Topics in Partial Differential Equations (3)**

Classical solution techniques for linear PDEs. Topics include first-and second-order equations, method of characteristics, special functions, orthogonal polynomials, transforms, Green's functions, and fundamental solutions. A computer algebra system is utilized.

*Prerequisite: *MATH 267 and MATH 374, or permission of the department chairperson.

*Not open to *students who have credit in MATH 475.

**625 Probability Theory and Applications (3)**

Basic probability theory, random variables, conditional probability and conditional expectation, Poisson process, interarrival time, and waiting time distributions.

*Prerequisite: *MATH 166 or equivalent.

**626 Probability and Stochastic Processes (3)**

Discrete and continuous time Markov chains, queuing theory, renewal theory.

*Prerequisite: *MATH 625 or equivalent.

**645 Topology 1 (3)**

Introduction to point-set topologoy. Topics include set-theoretic preliminaries, topological spaces, continuous functions, metric spaces, product and quotient spaces, connectedness, compactness, countability and separation axioms. Urysohn's Metrization Theorem, Tietze's Extension Theorem, and Tychonoff's Theorem.

*Prerequisite: *MATH 471 or MATH 571

**646 Topology 2 (3)**

A second semester course in point-set topology. Stone-Cech compactification, paracompactness, metrization theorems, Ascoli's Theorem, Baire's Category Theorem, introduction to homotopy theory, Jordan Curve Theorem, Invariance of Domain, Brouwer Fixed-Point Theorem.

*Prerequisite: *MATH 645.

**675 Measure Theory and Integration 1 (3)**

The concept of measurability, simple functions, properties or measures, integration of positive as well as complex functions, sets of measure zero, Riesz representation theorem, Borel and Lebesgue measures, LP-spaces, approximation by continuous functions, elementary Hilbert space theory.

*Prerequisite: *MATH 472 or MATH 572.

**676 Measure Theory and Integration 2 (3)**

Banach spaces, Baire's theorem, Hahn-Banach theorem, complex measures, total variation, absolute continuity, Radon-Nikodym theorem, bounded linear functionals on LP, the Riesz representation theorem, differentiation of measures, the fundamental theorem of calculus, integration on product spaces, the Fubini theorem, completion of product measures, convolutions, distribution functions.

*Prerequisite: *MATH 675.

**677 Complex Variables 1 (3) **

Complex number systems, differentiation and integration, functions (analytic, entire, meromorphic) of one complex variable, singularities, complex integration, Cauchy's theorem, Cauchy's integral formula, power series, Laurent series, calculus of residues.

*Prerequisite: *MATH 471 or MATH 571.

**678 Complex Variables 2 (3)**

Analytic continuation, Riemann surfaces, theorems of Weierstrass and Mittag-Leffler, solution of two-dimensional potential problem, conformal mapping, Schwartz-Christoffel transformations and their applications.

*Prerequisite: *MATH 677

**689 Research Methods in Mathematics and Statistics (3)**

The scientific method in mathematical research. Location of relevant journal articles, reference books, and reviews. Development of research and problem-solving techniques. Each student will write a mathematical paper. The instructor will assist students whose work is of exceptional quality in submitting their results for publication.

**694 Research Methods in Mathematics Education (3)**

Research analysis and methodology in mathematics education.

*Prerequisite: *at least one year of teaching experience, and 18 hours of graduate credit in mathematics or mathematics education, including MATH 690 and either MATH 632 or MATH 695, or permission of the department chairperson.

**Thesis (THES)**

**698 Thesis**

This plan requires the candidate to present a thesis embodying the results of a study of some subject directly related to the area of specialization. The thesis must show that the candidate possesses the abilities to pursue a research problem successfully and to draw valid and significant conclusions from the data. The student must have a committee of three faculty members seleced in consultation with the department chairperson.

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