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Mathematics

MAT 501
MATH FOR TEACHERS: ALGEBRA
3, 3/0

Prerequisite: 24 credit hours of undergraduate mathematics.

Operational systems, number systems, groups, rings, fields, ordered fields, functions over fields, algebraic properties of the trigonometric functions.

MAT 521
MATH FOR TEACHERS: GEOMETRY
3, 3/0

Formal and informal geometry; nonmetric geometry; congruence; measurement; constructions; similarity; coordinate geometry; trigonometric functions.

MAT 552
MATHEMATICS FOR TEACHERS: NUMBER THEORY
3, 3/0

Prerequisites: MAT 121 and MAT 122. 

Structure of the integers; divisibility; primes; congruence classes; linear congruences; Diophantine equations; Fibonacci numbers; selected topics.

MAT 581
MATHEMATICS FOR TEACHERS: PROBABILITY AND STATISTICS
3, 3/0

Prerequisites: Two semesters of calculus, MAT 325, MAT 311 or equivalent.

Probability, probability distributions, sampling, design of experiments, hypothesis testing, regression, analysis of variance, nonparametric statistics.

MAT 590
INDEPENDENT STUDY
3, 0/0

MAT 593
MATHEMATICS FOR TEACHERS: DISCRETE MATHEMATICS
3, 3/0

Prerequisites: MAT 121 and MAT 122. 

Partitions; permutations; probability measure; conditional probability; vectors; matrices; operations and properties; linear programming applications.

MAT 601
TOPICS IN MODERN ALGEBRA
3, 3/0

Prerequisite: Acceptance to the mathematics master’s degree program.

Groups, semigroups, and monoids; homomorphisms; subgroups and cosets;
Abelian groups; the symmetric group; actions and the Sylow theorems; rings, subrings, and ideals; ring homomorphisms; integral domains, division rings, and fields; ring and  field extensions; Galois theory.

MAT 603
THEORY OF MATRICES
3, 3/0

Prerequisite: 12 credit hours of mathematics coursework beyond calculus.

Algebra of matrices and determinants; equivalence, similarity, and congruence relations on matrices; vector spaces, linear transformations; characteristics, roots, and vectors; applications.

MAT 611
TOPICS IN REAL ANALYSIS
3, 3/0

Prerequisites: Three semesters of an undergraduate calculus sequence.

Real numbers; basic topology; continuous functions; differentiation; the Riemann-Stieltjes integral; sequence and series of functions; some special functions; the Lebesgue theory.

MAT 620
MODERN GEOMETRY: SELECTED TOPICS
3, 3/0

Prerequisite: MAT 322. 

Foundations; axiomatic projective geometry; real projective geometry; linear projective geometry; finite geometries; non-Euclidean geometries.

MAT 631
FOUNDATIONS OF MATHEMATICS
3, 3/0

Prerequisite: 12 credit hours of mathematics coursework beyond calculus.

Axiomatic method; theory of sets and infinite sets; real number system and linear continuum; the complex number system; groups and their significance for the foundations; development of various viewpoints on foundations.

MAT 651
THEORY OF NUMBERS
3, 3/0

Prerequisite: 12 credit hours of mathematics coursework beyond calculus.

Counting and recording of numbers; properties of numbers; Euclid’s algorithm; prime numbers; the aliquot parts; indeterminate problems and their theory; Diophantine problems; congruences; analysis of congruences; Wilson’s theorem; Euler’s theorem; theory of decimal expansions; the converse of Fermat’s theorem; the classical construction
problems.

MAT 670
DISCRETE MATHEMATICS AND FOUNDATIONS OF COMPUTER
SCIENCE
3, 3/0

Prerequisite: Acceptance to the mathematics master’s degree program.

Problems, theorems, and discrete structures commonly used in mathematics and computer science; mathematical analysis of algorithmic/computer solutions to problems in mathematics; mathematical problems that are not solvable by computer.

MAT 681
INTERMEDIATE PROBABILITY
3, 3/0

Prerequisite: MAT 381.

Advanced probability theory; combinatorial analysis; the laws of large numbers; theory of stochastic processes.

MAT 683
STATISTICAL THEORY
3, 3/0

Prerequisite: MAT 381.

Probability; estimation; confidence sets; tests of hypotheses; decision theory; Bayesian methods; linear models; nonparametric methods.

MAT 690
MASTER’S PROJECT
3, 3/0

Prerequisite: Written approval of the faculty member and the department chair.

Research study or investigation of a mathematical problem or topic, conducted under the guidance of a graduate faculty member of the Mathematics Department.

MAT 695
MASTER’S THESIS
3, 0/0

MAT 696
HISTORY OF MATHEMATICS
3, 3/0

Prerequisite: 12 credit hours of mathematics coursework beyond calculus.

Chronological study of the development of mathematics; contributions of nations, ages, or periods; selected biographies, appraisals, and critiques; problem studies.

MAT 699
SELECTED ADVANCED TOPICS
3, 3/0

Prerequisite: Instructor permission.

Seminar considering an advanced branch of contemporary mathematics such as combinatorics, game theory, automata theory, or intensive study of an advanced topic in mathematical research.

MAT 701
MODERN ALGEBRA I
3, 3/0

Prerequisite: MAT 301.

Cyclic groups; transformation groups; factor groups; groups with operators; isomorphism theorems; composition series; direct products of groups; Sylow theorems; residue class rings; operations on ideals; extensions of rings.

MAT 711
ANALYSIS I
3, 3/0

Prerequisite: MAT 417.

Graduate functions of several variables; topology of Euclidean space; continuity and uniform continuity; convergence and uniform convergence of sequences of functions; partial differentiation; chain rule; implicit functions theorems; Riemann-Stieltjes integration; multiple integrals; Fubini’s theorem; line integrals.

MAT 771
TOPOLOGY
3, 3/0

Topological spaces; bases and subbases; subspaces; continuous functions; product spaces; separation and countability; Urysohn’s Lemma; Tietz extension theorem; compactness; metrizability; connectedness; locally
compact spaces and compactification.

MAT 795
MASTER'S THESIS
6, 6/0

Individual investigation into an area of mathematics, under the guidance of a faculty member.

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Mathematics

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