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**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.

Buffalo, NY 14222 • Phone: (716) 878-5621 • Fax: (716) 878-6107

brusehm@buffalostate.edu

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