**Graduate Course Descriptions**

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**500 FOUNDATION OF MATHEMATICS **(Credit, 3 hours). Properties of axiom systems, axiomatic set theory ordinal and cardinal arithmetic; and first and second order predicate calculus.

Prerequisite: Consent of professor

**501 HISTORY OF MATHEMATICS **(Credit, 3 hours). Experiences in the history of arithmetic, algebra, geometry, trigonometry calculus, probability, statistics, and other experiences (will be covered). A major theme of the course is to develop insights into how the modern curriculum evolved. Applications to the classroom will be emphasized.

**530 ABSTRACT ALGEBRA I** (Credit, 3 hours). Topics covered in this course include equivalence relations, mappings, integers, and groups. Emphasis is placed on properties and examples.

**531 ABSTRACT ALGEBRA II** (Credit, 3 hours). Topics covered in this course include rings, integral domains, fields, polynomial over a field, and factorization. Emphasis is placed on properties and examples.

Prerequisite: **MATH 530** **or equivalent**

**533- 534 COMPUTATIONAL LINEAR ALGEBRA I, II **(Credit, 3 hours). Complex numbers, theory of equations, linear equations, matrices, determinants, vector spaces, linear transformations, matrix norms, the Gram-Schmidt orthogonalization process, orthogonal polynomials, eigenvalues and eigenvectors, diagonalization, quadratic forms, positive definite matrices, non-negative matrices, applications: least square problems, differential equations; numerical linear algebra: Gaussian elimination, pivoting strategies, iterative methods, and the eigenvalue problem are covered.

Prerequisite: **MATH 364** **or equivalent**

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**551 HIGHER GEOMETRY** (Credit, 3 hours). This course covers absolute geometry, elements of Euclidean, hyperbolic, and projective geometries. Also includes a discussion of the consistency of Euclid fifth postulate.

Prerequisite: Consent of professor

**565- 566 REAL ANALYSIS I, II** (Credit, 6 hours). Axioms of the real numbers, supremum, infinum, upper limits, lower limits, open and closed sets in Rp, compactness, the Bolzano-Weierstrass and Heine-Borel Theorems, the Cantor Theorem, uniform continuity, uniform convergence, Riemann and Riemann-Stieltjes integration, and metric spaces are shared.

**571- 572 NUMERICAL ANALYSIS I, II** (Credit, 6 hours). Some general principles of numerical calculation, estimating accuracy in numerical calculations, numerical uses of series, approximation of functions, numerical integration, differentiation and interpretation, differential equations, Fourier methods, optimization, Monte Carlo method, and stimulation are offered.

Prerequisite:** MATH 370 ****or equivalent**

**577- 578 OPERATIONAL MATHEMATICS I, II** (Credit, 3 hours). The LaPlace transformation, elementary application, problems in partial differential equations, functions of a complex variable, the inversion integral, problems in heat conduction, problems in mechanical vibrations, generalized Fourier series, general integral transfers, Fourier transforms on the half line, Hankel transforms, Legendre, and other integral transforms are covered.

Prerequisite: **MATH 370**** or equivalent**

**579 TOPICS IN DISCRETE MATHEMATICAL MODULES** (Credit, 1-6 hours). This course offers various methods of attacking discrete mathematical problems with emphasis on enumerative analysis, graph theory, modern and Boolean algebra. It develops both practical and theoretical topics systematically.

Prerequisite: **MATH 364**** or equivalent**

**585- 586 COMPUTERS, STATISTICS AND PROBABILITY **(Credit, 3 hours). This sequence provides experiences in statistics, probability, computer literacy, the use of descriptive and inferential statistics, and computers in mathematics education research and in the classroom.

**595 TOPICS IN APPLIED MATHEMATICS (formerly MATH 598) **(Credit, 1-6 hours). Selected topics in mathematics from probability and statistics, differential equations, linear programming, mathematical modeling, modern or applied algebra, graph theory, or analysis are covered. Credit is up to six hours for the course under different headings. Course used only for an extension of topics beyond the scope of the courses already in the catalog. Courses offered under this number will appear on the transcripts under a heading which specifies the topic to be discussed.

**596 GRADUATE SEMINAR **(Credit, 3 hours) Selected topics in algebra and analysis, geometry, applied mathematics, are determined by instructor and students. Credit for this course is under different headings.

**597 SEMINAR IN MATHEMATICS FOR TEACHERS **(Credit, 3 – 6 hours) This course may include experiences in any one of the following: number theory, algebra, geometry, calculus, analysis, linear algebra, theory of problem solving, curriculum materials to supplement the teaching and learning of mathematics in grades 5 – 12 (in line with NCTM Standards). Mathematics 597 is to be used by the students as a primer to a research project. Credit for this course is under different headings.

**599 THESIS** (Credit, 0-6 Hours). This is for those students writing a thesis. Six hours credit is given only upon completion of an acceptable thesis.

**600 COMPREHENSIVE** (Credit, 0 hours). Must be completed and passed by all persons applying for the Master of Science degree who do not write a thesis.