Mathematics Graduate Courses

Some courses may not be offered every year. Check with the college or department office for current information about when specific courses are offered.  

 

For course syllabi, see the departmental website.

 

MAT  500 REFLECTIONS ON/IN MATH EDUCATION      (3)

This course facilitates reflections regarding effective mathematics education and presents a powerful framework for collaboratively researching and revitalizing the mathematics teaching and learning.  Cannot be used for the M.S. degree.  Instructor's consent required.  

 

MAT  501 HISTORY AND PHILOSOPHY OF MATHEMATICS EDUCATION       (3)

Historical underpinnings of the field of mathematics education; identifying issues and forces which influence curricular and philosophical change in mathematics education.  Cannot be used for the M.S. degree.  Instructor's consent required.

 

MAT  502 PROBLEM SOLVING:  THEORY AND PRACTICE      (3)

Theoretical and pedagogical aspects of problem solving; curricular materials, teaching strategies, and evaluation techniques.  Instructor's consent required.

 

MAT  504 CONNECTIONS - ALGEBRA AND NUMBER THEORY      (3)

This course will address the teaching and learning of the following content areas:  rings, fields and groups, arithmetic and congruence within the integers and isomorphisms.  Cannot be used for the M.S. degree.  Co-convenes with MAT 411C.  Letter grade only.  Prerequisite:  MAT 320W

 

MAT  505 CONNECTIONS - CALCULUS      (3)

This course will address the teaching and learning of the following content areas:  functions, sequences and series, limits, continuity, derivatives, integrals, introductory differential equations and introductory analysis in the real number system.  Cannot be used for the M.S. degree.  Prerequisite:  MAT 320W

 

MAT  506 CONNECTIONS - GEOMETRY      (3)

This course will address the teaching and learning of the following content areas:  axiomatic foundation of Euclidean and non-Euclidean geometry, transformations, geometric applications of trigonometry, visualization, geometric modeling and graphs.  Cannot be used for the M.S. degree.  Prerequisite:  MAT 320W

 

MAT  507 CONNECTIONS - PROBABILITY AND STATISTICS      (3)

This course will address the teaching and learning of the following content areas:  collecting and displaying data, descriptive statistics, counting techniques, discrete and geometric probability, conditional probability, simulation, random variables, expected value and variance of a random variable, probability distributions, correlation, regression, and estimation.  Cannot be used for the M.S. degree.  Prerequisite: MAT 137

 

MAT  508 TECHNOLOGY IN MATHEMATICS EDUCATION      (3)

Examines current technology used in secondary school mathematics; use of software packages to explore variety of topics.  Instructor's consent required.  Letter grade only.  Course fee required.  

 

MAT  511 ABSTRACT ALGEBRA I      (3)

Groups through the Sylow theorems, rings, and fields. Assumes familiarity with definitions and elementary properties of basic algebraic structures.  Prerequisite: MAT 411C with a grade greater than or equal to C

 

MAT  516 LINEAR ALGEBRA      (3)

Vector spaces, linear mappings, dual spaces, matrix theory, invariants, spectral theory, canonical forms, factorizations, lambda matrices, bilinear forms.  Prerequisite: MAT 316 with a grade greater than or equal to C

 

MAT  526 TOPICS IN COMBINATORICS      (3)

Topics in enumerative, algebraic, and geometric combinatorics, chosen at instructor's discretion; may include advanced counting techniques, graph theory, combinatorial designs, matroids, and error-correcting codes.  Prerequisite: MAT 226, MAT 316 and MAT 411C with grades greater than or equal to C

 

MAT  531 REAL ANALYSIS      (3)

Metric spaces, limits, sequences and series, continuity, differentiation, Riemann-Stielties integration, uniform convergence of sequences of functions.  Prerequisite: MAT 238 and 431C with grades greater than or equal to C

 

MAT  535 COMPLEX ANALYSIS      (3)

Complex numbers, analytic functions, Cauchy integral theorems, calculus of residues, Taylor and Laurent expansions, applications.  Prerequisite: MAT 431C with grade greater than or equal to C

 

MAT  542 WILDLIFE POPULATION MODELING      (3)

Application and analysis of deterministic and simulation models in ecology, emphasizing conservation and management of wildlife. Co-taught by a mathematician and an ecologist. Letter grade or pass-fail.  Prerequisite: (MAT 136 or MAT 136H) or MAT 316 with grade greater than or equal to C

 

MAT  543 POPULATION ECOLOGY LAB       (1-2)

Building and using population models using calculus and matrix algebra. Letter grade or pass-fail.  Instructor's consent required.  Corequisite: MAT 542

 

MAT  562 INTEREST THEORY FOR ACTUARIAL SCIENCE      (3)

Theory and applications of interest, or the time value of money. Topics include measurement of interest, annuities certain, yield rates, amortization schedules and sinking funds, bonds, and related securities.  Prerequisite: MAT 137 with a grade greater than or equal to C

 

MAT  563 NUMERICAL ANALYSIS      (3)

Error analysis, approximation theory and application, numerical solution of equations, ordinary and partial differential equations and systems, numerical integration.  Letter grade only.  Course fee required.  Prerequisite: MAT 239 with a grade greater than or equal to C

 

MAT  565 ACTUARIAL MATHEMATICS I      (3)

Theory and applications of contingency mathematics: life and health insurance, annuities and pensions using probabilistic and deterministic models.  Prerequisite: STA 473C with grade greater than or equal to C

 

MAT  567 RISK THEORY      (3)

Risk theory applied to insurance, especially with respect to compound Poisson and negative binomial processes.  Prerequisite: STA 473C with grade greater than or equal to C

 

MAT  587 PROFESSIONAL DEVELOPMENT SEMINAR      (1)

Designed to assist you in preparing for entry into your professional arena. Pass-fail only. Prerequisite: graduate status.  

 

MAT  593 PUBLIC SCHOOL IN-SERVICE WORKSHOP       (1-3)

Topical instruction involving exchange of ideas, practical methods, skills, and principles. Normally you may count up to 6 hours of 593 toward your graduate program. Pass-fail only.

 

MAT  597 READING FOR COMPREHENSIVE EXAM      (1-9)

Preparation for comprehensive examination.  Pass-fail only.  Department consent required.  

 

MAT  599 CONTEMPORARY DEVELOPMENTS      (1-3)

Examines recent trends and investigations in a selected area of a particular field of study.  May be offered no more than three times before being submitted for a permanent course number.  May be repeated for credit.  Pass-fail or letter grade.  

 

MAT  601 SEMINAR IN MATHEMATICS EDUCATION      (3)

Investigates special topics in mathematical education. Department consent required.

 

MAT  602 RESEARCH IN MATHEMATICS EDUCATION       (3)

Research within the field of mathematics education; types of research and their contributions and limitations; articulation of research and classroom practice.  Cannot be used for the M.S. degree.  Letter grade only.

 

MAT  608 FIELDWORK EXPERIENCE      (1-12)

Pass-fail only.  Department consent required.  

 

MAT  612 ABSTRACT ALGEBRA II      (3)

Continuation of MAT 511. Rings and modules, field extensions and Galois theory, and advanced topics at instructor's discretion.  Prerequisite: MAT 511 with grade greater than or equal to C

 

MAT  618 THEORY OF NUMBERS      (3)

Divisibility, congruences, continued fractions, Fermat's theorem, quadratic residues.  Prerequisite:  MAT 412C or 511 with grade greater than or equal to C

 

MAT  632 MEASURE AND INTEGRATION      (3)

Measure theory, the Lebesgue integral, convergence theorems, absolute continuity, differentiation, Lebesgue function spaces.  Prerequisite: MAT 531 with grade greater than or equal to C

 

MAT  641 TOPOLOGY      (3)

Topological spaces, metric spaces, homeomorphism, compactness, connectedness, separation axioms, product and quotient spaces, local properties, elementary algebraic, and geometric topology.  Prerequisite: MAT 411C and 531 with grades greater than or equal to C

 

MAT  661 APPLIED MATHEMATICS      (3)

Analytical tools of mathematical physics, including the calculus of variations, eigenfunction expansions, and perturbation methods.  Prerequisite: MAT 431C and 461 with grades greater than or equal to C

 

MAT  665 ORDINARY DIFFERENTIAL EQUATIONS      (3)

Existence and uniqueness of solutions, continuous dependence, maximal interval of existence, linear systems, stability, nonlinear autonomous systems in the plane.  Prerequisite: MAT 239 and 431C with grades greater than or equal to C

 

MAT  667 DYNAMICAL SYSTEMS      (3)

Discrete dynamical systems and nonlinear differential equations, emphasizing structural stability, bifurcation theory, and chaos. Includes such examples as the logistic map, solenoid, Smale horseshoe, and Lorenz equations.  Prerequisite: MAT 239 and 431C with grades greater than or equal to C

 

MAT  685 GRADUATE RESEARCH      (1-6)

Letter grade or pass-fail.  Department consent required.  

 

MAT  690 ADVANCED TOPICS IN MATHEMATICS      (3)

Investigates specific advanced topics in mathematics. May be repeated for up to 6 hours of credit. Instructor's consent required.  

 

MAT  697 INDEPENDENT STUDY      (1-3)

Letter grade or pass-fail.  Department consent required.  

 

MAT  698 GRADUATE SEMINAR      (1-3)

Letter grade or pass-fail.  Department consent required.  

 

MAT  699 THESIS      (1-9)

Individualized directed research, writing, and oral defense of selected thesis topic.  May be repeated as needed.  Department consent required.  Prerequisite: GPA of at least 3.3 in MS mathematics program coursework