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## Math Graduate

## Definition of Prefixes

- MAA-Mathematics, Analysis;
- MAD-Mathematics, Discrete;
- MAP-Mathematics, Applied;
- MAS-Mathematics, Algebraic-Structures;
- MAT-Mathematics, General;
- MHF-Mathematics, History and Foundations;
- MTG- Mathematics, Topology and Geometry.

Courses with prefixes COT and STA are offered by the departments of Computer Science and Statistics respectively.

## Graduate Courses

**COT 5420**Theory of Computation I (3). Abstract models of computation; halting problem; decidability and undecidability; recursive function theory. Prerequisites: MAD 3512.**COT 6400**Analysis of Algorithms (3). Complexity behavior of algorithms is described for Set Manipulation, Graph Theory, and Matrix Manipulation problems, among others. P and NP classes of problems reveal an inherent difficulty in designing efficient algorithms. Prerequisites: COP 3530.**MAA 5406**Complex Analysis (3). Harmonic functions, normal families, Riemann mapping theorem, univalent functions, infinite products and entire functions, elliptic functions, analytic continuation. Prerequisites: MAA 4211 and MAA 4402.**MAA 5616**Introduction to Real Analysis (3). Lebesgue Measure and Integral with applications to Integral Transforms. Prerequisites: Any one of MAS 3105, MAA 4211, MAP 4401, or MAA4212.**MAD 5405**Numerical Methods (3). Advanced ideas and techniques of numerical analysis for digital computation. Topics include: linear and non-linear systems, ordinary differential equations, continuous system modeling techniques, and languages. Prerequisites: MAS 3105 and MAP 3302.**MAP 5236**Mathematical Techniques of Operations Research (3). This course surveys the mathematical methods used in operations research. Topics will be chosen from linear programming, dynamic programming, integer programming, network analysis, classical optimization techniques, and applications such as inventory theory. Prerequisites: MAP 5117 and MAS 3105 and either CGS 3420 or COP 2210.**MAP 5316**Ordinary Differential Equations (3). Existence and Uniqueness theorem, matrix formulation, physical applications, regular singular points, autonomous systems, Laplace transform, special topics. Prerequisites: MAA 3200, MAA 4402 and MAS 3105.**MAP 5317**Advanced Differential Equations for Engineers (3). Topics may include Bessel Functions and other special functions arising from classical differential equations, Sturm-Liouville problems, partial differential equations, transform techniques. Credit may not be counted for both MAP 4401 and MAP 5317. Credit for MAP 5317 may not be applied toward the Master's degree in Mathematical Sciences. Prerequisites: MAC 3313 and MAP 3302.**MAP 5326**Partial Differential Equations (3). Basic concepts of first and second order PDE's, application to optics and wave fronts, Cauchy problem, Laplace equation, Green's function, Dirichlet problem, heat equation. Prerequisites: MAA 4211.**MAP 5407**Methods of Applied Analysis (3). Convergence, fixed point theorems, application to finding roots of equations, normed function spaces, linear operators, applications to numerical integration, differential and integral equations. Prerequisites: MAA 4211, MAP 3302, and MAS 3105.**MAS 5145**Applied Linear Algebra (3). Concepts of finite dimensional vector spaces. Theorems that have infinite dimensional analogues and those with important applications are emphasized. Prerequisites: MAS 3105 and MAA 3200.**MAS 5311**Graduate Algebra (3). A study of the basic material on groups, rings and vector spaces. Topics include the Jordan-Holder theorem, structure of modules over Euclidean domains and canonical forms of matrices. Prerequisites: MAS 4301 or equivalent.**MAS 5312**Galois Theory (3). Extension fields, ruler and compass constructions, fundamental theorem of Galois Theory, cyclotomic and cyclic extensions, solutions of equations by radicals, selected topics. Prerequisites: MAS 5311 or permission of instructor.**MAT 5907**Independent Study (VAR). Individual conferences, assigned reading, and reports on independent investigations.**MAT 5921**Training in Mathematical Exposition (1). Students prepare and present supervised lectures on undergraduate mathematical topics to fellow students. Prerequisites: Graduate standing.**MAT 5970**Master's Research (1-6). Research toward preparation of master's project. Prerequisites: Permission of graduate committee.**MHF 5106**Graduate Set Theory (3). Zermelo-Frankel axioms, ordinals and cardinals, Godel's constructible universe, large cardinals, forcing and the independence of the Continuum Hypothesis and the Axiom of Choice. Prerequisites: MHF 4102 or MAA 4211 or permission of instructor.**MHF 5306**Graduate Mathematical Logic (3). First order languages, construction of models from constants, advanced construction of models, nonstandard models, recursion theory, RE sets, Turing degrees, oracle construction. Prerequisites: MHF 4302 or permission of instructor.**MTG 5326**Introduction to Algebraic Topology (3). Classification of surfaces, fundamental group, homotopy type, Van Kampen theorem, simplicial complexes, introduction to homology theory. Prerequisites: MAS 4301 and MTG 4302.**STA 5446-STA 5447**Probability Theory I and II (3-3). This course is designed to acquaint the student with the basic fundamentals of probability theory. It reviews the basic foundations of probability theory, covering such topics as discrete probability spaces, random walk, Markov Chains (transition matrix and ergodic properties), strong laws of probability, convergence theorems, and law of iterated logarithm. Prerequisites: MAC 3313.**STA 6807**Queuing and Statistical Models (3). Review of probability concepts, basic probability distributions, Poisson process, queuing models, statistical models. Prerequisites: Permission of Instructor, MAC 3312 and either STA 3033 or STA 3321.