# Graduate Courses in Mathematics

*Notes:*

- Courses numbered 400 to 499 are open to undergraduate and graduate students.
- Courses numbered 500 to 599 are open only to graduate students.
- MT 501 to MT 530 are not applicable to the Master of Science program.

**421. MATHEMATICAL STATISTICS 3 cr.** Prerequisites: MT 229, 233. Moment generating functions, transformations, properties of estimators, foundations of hypothesis tests, one- and two-factor analysis of variance, and nonparametric analyses.

**422. APPLIED STATISTICS 3 cr.** Prerequisites: MT 223 or 228 or 229 or chair permission. Multi-factor analysis of variance, interaction, serial correlation, time series, forecasting, multivariate data, categorical data, data reduction, simulation, analysis of large datasets; use of appropriate statistical software.

**424. APPLIED REGRESSION ANALYSIS 3 cr. **Prerequisite: MT 223 or 228 or 229 or chair permission. Multiple linear regression, colinearity, model diagnostics, variable selection, nonlinear models, logistic regression; use of appropriate statistical software.

**425. OPERATIONS RESEARCH 3 cr.** Prerequisite: MT 271. Linear programming, sensitivity analysis and duality, queuing theory, and topics from networks, decision making, game theory, Markov chains, dynamic programming, and simulation.

**431. INTRODUCTION TO REAL ANALYSIS 3 cr.** Prerequisites: MT 233, 271. Rigorous mathematical treatment of the fundamental ideas of calculus: sequences, limits, continuity, differentiation, and integration.

**432. ADVANCED CALCULUS OF SEVERAL VARIABLES 3 cr.** Prerequisites: MT 233, MT 271. Development of and motivation for vector-valued functions, calculus of functions of several variables, implicit functions and Jacobians, multiple integrals, and line integrals.

**436. INTRODUCTION TO COMPLEX ANALYSIS 3 cr.** Prerequisite: MT 271 or permission of department chair. Complex number plane, analytic functions, integration of complex functions, sequences and series. Residue theorem, and evaluation of real integrals.

**438. ORDINARY LINEAR DIFFERENTIAL EQUATIONS 3 cr.** Prerequisites: MT 233, MT 342. Linear equations and systems, existence and uniqueness theorems, oscillation theory. Autonomous equations and systems, their solutions and qualitative properties.

**441. INTRODUCTION TO ABSTRACT ALGEBRA 3 cr.** Prerequisite: MT 271. Groups, homomorphisms, permutations, quotient groups, rings, ideals, integral domains, fields, polynomial rings, and factorization.

**450. EUCLIDEAN AND NON-EUCLIDEAN GEOMETRY 3 cr.** Prerequisite: MT 271 or permission of department chair. Alternative ways of investigating the Euclidean plane, including transformational geometry; examination of the parallel postulate and how it can be changed to create new geometries; hyperbolic geometry.

**452. ELEMENTARY TOPOLOGY 3 cr.** Prerequisite: MT 271. Topological spaces, homeomorphisms, connected spaces, compact spaces, regular and normal spaces, metric spaces, and topology of surfaces.

**453. DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS 3 cr.** Prerequisite: MT 233. Introduction to the qualitative study of differential equations and related dynamical systems. Topics include first-order differential equations, planar systems and their dynamical classification, general nonlinear systems and their equilibria, closed orbits, limit sets, discrete systems, and applications to mechanics.

**468. THEORY OF NUMBERS 3 cr.** Prerequisite: MT 271. Divisibility theorems, number-theoretic functions, primitive roots, quadratic congruences and reciprocity, partitions.

**469. HISTORY OF MATHEMATICS 3 cr.** Prerequisite: MT 271. Study of mathematics from its origins to its present state. Topics include the development and impact of geometry, algebra, number theory, irrational numbers, analytic geometry, calculus, non-Euclidean geometry, and infinite sets.

**479. COMBINATORICS AND GRAPH THEORY 3 cr.** Prerequisite: MT 271. Pigeonhole principle, inclusion and exclusion, recurrence relations and generating functions, combinatorial designs, the theory of graphs, graphical optimization problems.

**480. SPECIAL TOPICS 1-3 cr.** Readings about, reports on, and investigation of selected material and topics.

**501. MATHEMATICAL STRUCTURES 3 cr.** Axiomatic and constructive approaches to the number systems, algebraic structures.

**502. DISCRETE MATHEMATICS 3 cr.** Matrices, graph theory, iterative processes, game theory, and applications.

**503. MODERN GEOMETRY 3 cr.** Euclidean and non-Euclidean geometries. Axiomatic, transformational, and metric approaches to geometry.

**504. CURVES, SURFACES AND SPACE 3 cr.** Examination of the topology and geometry of two-, three-, and four-dimensional spaces. Visualization and classification of mathematical spaces. Shape and curvature of the universe.

**505. ADVANCED TOPICS IN CALCULUS 3 cr.** Advanced approach to the calculus with emphasis on its topological and analysis underpinnings. Designed to give the necessary background to teach calculus at the introductory college level.

**507. STATISTICAL LITERACY 3 cr.** Graphical approach to data analysis, probability, art and techniques of simulation, surveys and information from samples, confidence intervals and tests of hypotheses. Emphasizes material applicable to the high school curriculum.

**509. GREAT MOMENTS IN MATHEMATICS 3 cr.** Survey of some of the more important historical developments in the history of mathematics, with emphasis on those with connections to the secondary curriculum.

**510. MATHEMATICAL POTPOURRI 3 cr.** Selected topics in and about mathematics to be used as course enrichment material and to foster an appreciation of mathematics as a creative endeavor. Includes readings about mathematics from various viewpoints.

**512. TECHNOLOGY IN THE TEACHING OF MATHEMATICS 3 cr.** Seminar/lab course in the use of graphing calculators and computer software in teaching mathematics. Students will collaborate in developing classroom and laboratory activities.

**513. COMPUTER SCIENCE FOR HIGH SCHOOL TEACHERS 3 cr.** Exploration of the content areas outlined in the new Advanced Placement Computer Science Principles course: computing as a creativity that facilitates the creation of knowledge; societal and global impact of computing and the internet; computer principles of abstraction, programming, database and website content management; graphical programming languages and software tools.

**514. PROBLEMS IN MATHEMATICS 3 cr.** Old and new problems from various areas of mathematics, chosen to be applicable to co-curricular high school activities such as mathematics clubs and contests.

**517. MATHEMATICAL MODELING IN THE HIGH SCHOOL CLASSROOM 3 cr.** Exploration of mathematical modeling for use within high school classroom contexts. Topics include theory of measurement, dynamical systems, probability, network analysis. Applications include population growth, biomechanics, financial models, social networks and ecology. Emphasis on the use of modeling as a necessary and sufficient requirement for excellent mathematical pedagogy.

**519. SPECIAL TOPICS IN MATHEMATICS cr. TBA** Supervised study of special topics.

**531. REAL ANALYSIS I 3 cr.** Topics on Lebesgue integration theory, including measure, integration, integrable functions. Relation between Lebesgue integral and Riemann integral. Functions of bounded variation, absolute continuity, generalized Fundamental Theorem of Calculus.

**532. REAL ANALYSIS II 3 cr.** Prerequisite: MT 531. Topics to be selected from: Borel sets, Baire functions, ordinal numbers, Lebesgue measure, absolute continuity, Lebesgue-Stieljes integral, signed measures, Radon-Nikodym theorem, product measures, and Fubini’s theorem.

**536. COMPLEX ANALYSIS 3 cr.** Prerequisite: MT 431. Topology of the complex plane, analytic functions, integration theory, Riemann Mapping Theorem, analytic continuation, Riemann surfaces, harmonic functions.

**538. FUNCTIONAL ANALYSIS 3 cr.** Prerequisite: MT 452. Topics to be selected from: normed spaces, linear functionals, Hahn-Banach theorem, dual space, inner-product space, Riesz-Fischer theorem, linear operators.

**541. ALGEBRA I 3 cr.** Groups, homomorphism, group actions, Sylow theorems, rings and ideals, polynomials, and p.i.d.s.

**542. ALGEBRA II 3 cr.** Prerequisite: MT 541. Topics to be selected from: projective and injective modules, structure of semigroups, rings, radicals, and Galois Theory.

**552. GENERAL TOPOLOGY 3 cr.** Prerequisite: MT 452. Topics to be selected from: topological spaces and mappings, topological and homotopic invariants, product and quotient spaces, topological constructions, separation axioms, metrization, generalized convergence, fundamental group.

**553. ALGEBRAIC AND GEOMETRIC TOPOLOGY 3 cr.** Prerequisite: MT 552. Elements of algebraic topology, including homology and cohomology theory. Topology of smooth manifolds.

**557. DIFFERENTIAL GEOMETRY 3 cr.** Prerequisite: MT 431. Local and global properties of curves and surfaces; Gauss map, curvature, Theorema Egregium, covariant derivative, geodesics, Gauss-Bonnet Theorem, generalizations to manifolds.

**580. SPECIAL TOPICS 1-3 cr.** Reading, reports on, and investigation of selected material and topics.

**599. INDEPENDENT STUDY 1-3 cr.** Independent study under the supervision of a faculty member. Requires approval of the faculty member and permission of the department chair.