
Mathematics (MATH) 


MATH 400  History of Mathematics 3 Credit Hours Development of major ideas in mathematics from ancient to modern times and the influence of these ideas in science, technology, philosophy, art, and other areas. Includes at least one inclass essay examination and 3,000 words of writing outside classroom. (RE) Prerequisite(s): 251 or 257. (DE) Prerequisite(s): 300 or 307.



MATH 403  Mathematical Methods for Engineers and Scientists 3 Credit Hours Matrix computations, numerical methods, partial differential equations, SturmLiouville Theory and special functions as used in engineering and science. (RE) Prerequisite(s): 231; 241 or 247. Comment(s): Knowledge of highlevel programming language required.



MATH 404  Applied Vector Calculus 3 Credit Hours Topics from multivariable and vector calculus; line and surface integrals, divergence theorem and the theorems of Gauss and Stokes. (RE) Prerequisite(s): 241 or 247.



MATH 405  Models in Biology 3 Credit Hours Difference and differential equation models of biological systems. Crosslisted: (Same as Ecology and Evolutionary Biology 406.)
Credit Restriction: May not be applied toward a mathematics graduate degree. (RE) Prerequisite(s): 142 or 148 or 152.



MATH 411  Mathematical Modeling 3 Credit Hours Construction and analysis of mathematical models used in science and industry. Projects emphasized. (RE) Prerequisite(s): 231; 241 or 247; 200 or 251 or 257.



MATH 421  Combinatorics 3 Credit Hours Introduction to problems of construction and enumeration for discrete structures such as sequences, partitions, graphs, finite fields and geometries, and experimental designs. (RE) Prerequisite(s): 300 or 307.



MATH 423  Probability 3 Credit Hours Axiomatic probability, univariate and multivariate distributions, conditional distributions and expectations, moment generating functions, laws of large numbers and central limit theorem. (RE) Prerequisite(s): 241 or 247; 300 or 307. (DE) Prerequisite(s): 323.



MATH 424  Stochastic Processes 3 Credit Hours Markov chains, Poisson processes and Brownian motion. Other topics as selected by instructor. (RE) Prerequisite(s): 423.



MATH 425  Statistics 3 Credit Hours Standard statistical distributions, independence of mean and variance for a Gaussian sample, basic limit theorems; point and interval estimation, tests of statistical hypotheses, NeymanPearson theorem; likelihood ratio and other parametric and nonparametric tests. (RE) Prerequisite(s): 423.



MATH 431  Differential Equations II 3 Credit Hours A second course in ordinary differential equations. Linear systems of differential equations, Frobenius method, SturmLiouville eigenvalue problems, phase plane analysis. (RE) Prerequisite(s): 231; 200 or 251 or 257.



MATH 435  Partial Differential Equations 3 Credit Hours Separation of variables, Fourier series, solution of Laplace, wave, and heat equations. (RE) Prerequisite(s): 231; 241 or 247.



MATH 443  Complex Variables 3 Credit Hours Introduction to the theory of functions of a complex variable, including residue theory and contour integrals. (RE) Prerequisite(s): 241 or 247.



MATH 445  Advanced Calculus I 3 Credit Hours Introduction to the theory of sequences, series, differentiation, and Riemann integration of functions of one or more variables. (RE) Prerequisite(s): 241 or 247; 300 or 307.



MATH 446  Advanced Calculus II 3 Credit Hours Continuation of 445. (RE) Prerequisite(s): 445.



MATH 447  Honors: Advanced Calculus I 3 Credit Hours Honors version of 445. (RE) Prerequisite(s): 341.



MATH 448  Honors: Advanced Calculus II 3 Credit Hours Continuation of 447. (RE) Prerequisite(s): 447.



MATH 453  Matrix Algebra II 3 Credit Hours Advanced topics in matrix theory including Jordan canonical form. (RE) Prerequisite(s): 200 or 251 or 257.



MATH 455  Abstract Algebra I 3 Credit Hours Introduction to algebraic structures such as groups, rings, fields, vector spaces, and linear transformations. (RE) Prerequisite(s): 251 or 257; 300 or 307.



MATH 456  Abstract Algebra II 3 Credit Hours Continuation of 455. (RE) Prerequisite(s): 455.



MATH 457  Honors: Abstract Algebra I 3 Credit Hours Honors version of 455. (RE) Prerequisite(s): 351.



MATH 458  Honors: Abstract Algebra II 3 Credit Hours Continuation of 457. (RE) Prerequisite(s): 457.



MATH 460  Geometry 3 Credit Hours Axiomatic and historical development of neutral, Euclidean, and hyperbolic geometry stressing proof technique and critical reasoning. Models of NonEuclidean geometries. (RE) Prerequisite(s): 300 or 307.



MATH 462  Differential Geometry 3 Credit Hours Classical differential geometry of curves and surfaces: Frenet frames, first and second fundamental forms, Gauss curvature and mean curvature, geodesics and parallel transport, the GaussBonet theorem, geometry of the hyperbolic plane. (RE) Prerequisite(s): 241 or 247.



MATH 467  Honors: Topology 3 Credit Hours Includes topology of line and plane, separation properties, compactness, connectedness, continuous functions, homeomorphisms, continua, and topological invariants. (RE) Prerequisite(s): 300 or 307. (DE) Prerequisite(s): 241 or 247.



MATH 471  Numerical Analysis 3 Credit Hours Introduction to computation, instabilities, and rounding. Interpolation and approximation by polynomials and piecewise polynomials. Quadrature and numerical solution of initial and boundary value problems of ordinary differential equations, stiff systems. Crosslisted: (Same as Computer Science 471.)
(RE) Prerequisite(s): 231; 200 or 251 or 257. (DE) Prerequisite(s): 371. Comment(s): Knowledge of a highlevel programming language required.



MATH 472  Numerical Algebra 3 Credit Hours Direct and iterative methods for systems of linear equations. Solution of single nonlinear equation and nonlinear systems. Orthogonal decomposition, least squares and algebraic eigenvalue problem. Crosslisted: (Same as Computer Science 472.)
(RE) Prerequisite(s): 231; 200 or 251 or 257. (DE) Prerequisite(s): 371. Comment(s): Knowledge of a highlevel programming language required.



MATH 475  Industrial Mathematics 3 Credit Hours Modeling, analysis, and computation applied to scientific/technical/industrial problems. (RE) Prerequisite(s): 231. Recommended Background: Familiarity with operating system and programming language.



MATH 490  Readings in Mathematics 13 Credit Hours Open to superior students. Independent study with faculty guidance. Repeatability: May be repeated. Maximum 9 hours. Comment(s): Consent of faculty mentor to supervise independent work required. Registration Permission: Consent of department head. 


MATH 499  Seminar in Mathematics 13 Credit Hours Topics vary. Requires outofclass projects and inclass presentations by students. Students must register for the number of credit hours announced for a particular seminar. Repeatability: May be repeated. Maximum 9 hours. Registration Permission: Consent of instructor. 


MATH 500  Thesis 115 Credit Hours Grading Restriction: P/NP only. Repeatability: May be repeated. Credit Level Restriction: Graduate credit only. Registration Restriction(s): Minimum student level – graduate.



MATH 502  Registration for Use of Facilities 115 Credit Hours Required for the student not otherwise registered during any semester when student uses university facilities and/or faculty time before degree is completed. Grading Restriction: Satisfactory/No Credit grading only. Repeatability: May be repeated. Credit Restriction: May not be used toward degree requirements. Credit Level Restriction: Graduate credit only. Registration Restriction(s): Minimum student level – graduate.



MATH 504  Discrete Mathematics for Teachers 3 Credit Hours Mathematical logic and methods of argument, sets, functions and relations, combinatorics. Normally, the first graduate course for students seeking Master of Mathematics degree. Credit Restriction: May not apply toward mathematics major (Master of Science). Recommended Background: 1 year of calculus or equivalent. Comment(s): For students in Master of Mathematics program and for students in graduate programs in the College of Education, Health, and Human Sciences.



MATH 505  Analysis for Teachers 3 Credit Hours Development of differential and integral calculus, proofs of basic theorems. Credit Restriction: May not apply toward mathematics major (Master of Science). Recommended Background: 1 year of calculus or equivalent. Comment(s): For students in Master of Mathematics program and for students in graduate programs in the College of Education, Health, and Human Sciences.



MATH 506  Algebra for Teachers 3 Credit Hours Algebraic structures: integral domains and fields and their applications to algebra of integers and polynomials. Credit Restriction: May not apply toward mathematics major (Master of Science). Recommended Background: 1 year of calculus or equivalent. Comment(s): For students in Master of Mathematics program and for students in graduate programs in the College of Education, Health, and Human Sciences.



MATH 507  Probability and Statistics for Teachers 3 Credit Hours Probability models. Discrete random variables. Binomial, hypergeometric, and Poisson distributions. Credit Restriction: May not apply toward mathematics major (Master of Science). Recommended Background: 1 year of calculus or equivalent. Comment(s): For Students in Master of Mathematics program and for students in graduate programs in the College of Education, Health, and Human Sciences.



MATH 509  Seminar for Teachers 3 Credit Hours Repeatability: May be repeated. Maximum 12 hours. Credit Restriction: May not apply toward mathematics major (Master of Science). Comment(s): For Students in Master of Mathematics program and for students in graduate programs in the College of Education, Health, and Human Sciences. Registration Permission: Consent of instructor. 


MATH 511  Methods in Applied Mathematics I 3 Credit Hours Fundamentals and techniques associated with discrete models of physical, engineering and biological systems: difference equations, networks and graphs, optimization, and other topics. Recommended Background: Courses in advanced calculus and linear algebra.



MATH 512  Methods in Applied Mathematics II 3 Credit Hours Fundamentals and techniques associated with continuous models of physical, engineering, and biological systems: development, solution and qualitative analysis of ordinary and partial differential equations, and calculus of variations. (DE) Prerequisite(s): 511.



MATH 513  Mathematical Principles of Fluid Mechanics I 3 Credit Hours Equations of motion, incompressible and compressible potential flow, shock waves, viscous flows. NavierStokes equations. Recommended Background: Advanced courses in ordinary and partial differential equations and advanced calculus.



MATH 514  Mathematical Principles of Fluid Mechanics II 3 Credit Hours Continuation of 513. (DE) Prerequisite(s): 513.



MATH 515  Analytical Applied Mathematics I 3 Credit Hours Analysis of advanced techniques in modern context for applied problems: dimensional analysis and scaling, perturbation theory, variational approaches, transform theory, wave phenomena and conservation laws, stability and bifurcation, distributions, integral equations. Recommended Background: Courses in advanced calculus, linear algebra, and either advanced differential equations or 512.



MATH 516  Analytical Applied Mathematics II 3 Credit Hours Continuation of 515. (DE) Prerequisite(s): 515.



MATH 517  Mathematical Methods in Physics I 3 Credit Hours Crosslisted: (See Physics 571.)



MATH 518  Mathematical Methods in Physics II 3 Credit Hours Crosslisted: (See Physics 572.)



MATH 519  Seminar in Applied Mathematics 13 Credit Hours Repeatability: May be repeated. Maximum 12 hours.



MATH 521  Enumerative Combinatorics I 3 Credit Hours Sieve methods, recursion, generating functions, and permutation groups applied to enumeration of discrete structures. Incidence algebras and combinatorics of partially ordered sets.



MATH 522  Enumerative Combinatorics II 3 Credit Hours Continuation of 521. (DE) Prerequisite(s): 521.



MATH 523  Probability I 3 Credit Hours Probability spaces and random variables, expectation, characteristic functions, convergence of random variables. Recommended Background: One year of advanced calculus and 323.



MATH 524  Probability II 3 Credit Hours Continuation of 523. Law of large numbers, central limit theorem, conditional expectation, martingales. Other topics as selected by instructor. (DE) Prerequisite(s): 523.



MATH 525  Statistics I 3 Credit Hours Formulation of statistical models, sufficiency; methods of estimation and optimal theory, asymptotic efficiency; the confidence procedures and hypothesis testing, uniformly most powerful tests; Bayesian statistics. Recommended Background: One year of advanced calculus and 425.



MATH 526  Statistics II 3 Credit Hours Continuation of 525. Estimation and tests in general linear models; nonparametric models, rank methods for comparison, robust tests. Other topics as selected by instructor. (DE) Prerequisite(s): 525.



MATH 527  Stochastic Modeling 3 Credit Hours Variable topics in probability applied to real world situations. Topics may include queuing theory, branching processes, Monte Carlo simulation, stochastic finance and other topics as selected by instructor. Recommended Background: One year of advanced calculus and one year of undergraduate probability or mathematical statistics.



MATH 529  Seminar in Stochastics 13 Credit Hours Repeatability: May be repeated. Maximum 12 hours.



MATH 531  Ordinary Differential Equations I 3 Credit Hours Existence, uniqueness, extendibility, and dependence on parameters for solutions of differential equations. The theory of linear systems of differential equations including boundary value problems and series methods. Recommended Background: One year of advanced calculus and undergraduate differential equations.



MATH 532  Ordinary Differential Equations II 3 Credit Hours Continuation of 531. The nonlinear theory of differential equations including Liapunov stability, critical point analysis, and PoincareBendixson theory. (DE) Prerequisite(s): 531.



MATH 534  Calculus of Variations 3 Credit Hours Necessary and sufficient conditions for weak and strong extrema in onedimensional variation problems; Lagrangian mechanics. Multiple integrals. Basic elements of direct methods. Recommended Background: At least one seniorlevel course in differential equations or advanced calculus. Mathematical maturity.



MATH 535  Partial Differential Equations I 3 Credit Hours First order partial differential equations, classification of second order partial differential equations, properties of elliptic, parabolic and hyperbolic partial differential equations. Recommended Background: One year of advanced calculus.



MATH 536  Partial Differential Equations II 3 Credit Hours Continuation of 535. Properties and representation formulas for elliptic, parabolic and hyperbolic partial differential equations. (DE) Prerequisite(s): 535.



MATH 537  Mathematical Principles of Continuum Mechanics I 3 Credit Hours Conservation principles, equations of equilibrium and motion for fluids and elastic solids, constitutive relations and stress, convexity properties, bifurcation phenomena, existence theory. Recommended Background: Courses in advanced calculus and advanced differential equations.



MATH 538  Mathematical Principles of Continuum Mechanics II 3 Credit Hours Continuation of 537. (DE) Prerequisite(s): 537.



MATH 539  Seminar in Differential Equations 13 Credit Hours Repeatability: May be repeated. Maximum 12 hours.



MATH 545  Real Analysis 3 Credit Hours Measure theory, Lebesgue integration, Holder and Minkowski inequalities, RadonNikodym theorem, Fubini’s theorem. Recommended Background: One year of advanced calculus.



MATH 546  Complex Analysis 3 Credit Hours Holomorphic functions, Cauchy’s theorem, Maximum Modulus theorem, Schwarz’s lemma, normal families, Riemann mapping theorem. (DE) Prerequisite(s): 545.



MATH 547  Applied Linear Analysis 3 Credit Hours Banach and Hilbert spaces, linear operators and spectral theory, Sobolev spaces, applications. (DE) Prerequisite(s): 545.



MATH 549  Seminar in Analysis 13 Credit Hours Repeatability: May be repeated. Maximum 12 hours.



MATH 551  Modern Algebra I 3 Credit Hours Groups and rings. Recommended Background: One year of undergraduate abstract algebra.



MATH 552  Modern Algebra II 3 Credit Hours Continuation of 551; modules, fields and Galois theory. (DE) Prerequisite(s): 551.



MATH 555  Number Theory I 3 Credit Hours Introduction to algebraic number theory. Recommended Background: One year of undergraduate abstract algebra.



MATH 556  Number Theory II 3 Credit Hours Continuation of 555. (DE) Prerequisite(s): 555.



MATH 559  Seminar in Algebra 13 Credit Hours Repeatability: May be repeated. Maximum 12 hours.



MATH 561  Topology I 3 Credit Hours Topological spaces and continuous functions, separation axioms, product and quotient topologies, connectedness, compactness, complete metric spaces. Recommended Background: One year of advanced calculus.



MATH 562  Topology II 3 Credit Hours Continuation of 561. Fundamental group and covering spaces. (DE) Prerequisite(s): 561.



MATH 567  Riemannian Geometry I 3 Credit Hours Riemannian and Lorentzian manifolds. Variations of arc length, Jacobi fields, comparison theorems. Constant curvature spaces. Curvature and topology of manifolds. Recommended Background: One year of advanced calculus.



MATH 568  Riemannian Geometry II 3 Credit Hours Continuation of 567. (DE) Prerequisite(s): 567.



MATH 569  Seminar in Topology and Geometry 13 Credit Hours Repeatability: May be repeated. Maximum 12 hours.



MATH 571  Numerical Mathematics I 3 Credit Hours Direct and iterative methods for linear systems. The algebraic eigenvalue problem and the singular decomposition theorem. Newton and quasiNewton methods for systems of nonlinear equations. Crosslisted: (Same as Computer Science 571.)
Recommended Background: Courses in advanced calculus and basic numerical analysis.



MATH 572  Numerical Mathematics II 3 Credit Hours Numerical techniques for initial value problems of ordinary differential equations. Twopoint boundary value problems. Finite difference and finite element methods for selected partial differential equations. Fast Poisson solvers. Crosslisted: (Same as Computer Science 572.)
(DE) Prerequisite(s): 571.



MATH 574  Finite Element Methods 3 Credit Hours Finite element techniques for solution of boundary and initialboundary value problems. Variational formulation. Finite dimensional subspaces and their approximating properties; rates of convergence. Computer implementation. Crosslisted: (Same as Computer Science 574.)
Recommended Background: Courses in partial differential equations, linear algebra and numerical analysis.



MATH 577  Optimization 3 Credit Hours Mathematical foundations of constrained and unconstrained optimization. Lagrange multipliers, the Farkas lemma, the KuhnTuckerKarush theorem. Analysis of major algorithms and applications to real world problems. Recommended Background: Courses in numerical algorithms, linear algebra and advanced calculus.



MATH 578  Numerical Methods for Partial Differential Equations 3 Credit Hours Numerical approximation of solutions of partial differential equations including conservation laws and hyperbolic, parabolic, and elliptic problems. Derivation, physical meaning, and implementation of schemes. Recommended Background: A course in partial differential equations or 512 or 515, and familiarity with an operating system and a programming language.



MATH 579  Seminar in Numerical Mathematics 13 Credit Hours Repeatability: May be repeated. Maximum 12 hours.



MATH 581  Mathematical Ecology I 3 Credit Hours Deterministic and stochastic models of populations, communities, and ecosystems. Crosslisted: (Same as Ecology and Evolutionary Biology 581.)
(DE) Prerequisite(s): 431 and 453.



MATH 582  Mathematical Ecology II 3 Credit Hours Continuation of 581. Crosslisted: (Same as Ecology and Evolutionary Biology 582.)
(DE) Prerequisite(s): 581.



MATH 583  Mathematical Evolutionary Theory 3 Credit Hours Population genetics and evolutionary ecology. Crosslisted: (Same as Ecology and Evolutionary Biology 585.)
(DE) Prerequisite(s): 431 and 453.



MATH 585  Optimal Control Theory 3 Credit Hours Deterministic optimal control. Examples involving calculus of variations, optimal trajectories, and engineering control problems. Introduction to stochastic control. Recommended Background: One year of advanced calculus and undergraduate differential equations.



MATH 589  Seminar in Mathematical Ecology 13 Credit Hours Repeatability: May be repeated. Maximum 12 hours.



MATH 590  Seminar in Teaching College Mathematics 13 Credit Hours Selected topics in research, theory, and techniques for teaching collegiate mathematics. Repeatability: May be repeated. Maximum 12 hours. Credit Restriction: May not be applied toward mathematics major (Master of Science). Registration Permission: Consent of department head. 


MATH 593  Independent Study 112 Credit Hours Repeatability: May be repeated. Maximum 12 hours.



MATH 598  Graduate Reading in Mathematics 13 Credit Hours Independent study with faculty guidance. Repeatability: May be repeated. Maximum 6 hours. Comment(s): Graduate standing required. Registration Permission: Consent of instructor. 


MATH 599  Seminar in Mathematical Presentations 1 Credit Hours



MATH 600  Doctoral Research and Dissertation 315 Credit Hours Grading Restriction: P/NP only. Repeatability: May be repeated. Registration Restriction(s): Minimum student level – graduate.



MATH 619  Seminar in Applied Mathematics 13 Credit Hours Repeatability: May be repeated. Maximum 12 hours. Registration Restriction(s): Minimum student level – graduate.



MATH 623  Advanced Probability I 3 Credit Hours Selected topics in modern theory of probability and stochastic processes. Repeatability: May be repeated. Maximum 12 hours. (DE) Prerequisite(s): 523 and 524. Registration Restriction(s): Minimum student level – graduate.



MATH 624  Advanced Probability II 3 Credit Hours Continuation of 623. Repeatability: May be repeated. Maximum 12 hours. (DE) Prerequisite(s): 623. Registration Restriction(s): Minimum student level – graduate.



MATH 635  Advanced Partial Differential Equations I 3 Credit Hours Selected topics in classical and modern theoretical partial differential equations. Repeatability: May be repeated. Maximum 12 hours. (DE) Prerequisite(s): 535 and 536. Registration Restriction(s): Minimum student level – graduate.



MATH 636  Advanced Partial Differential Equations II 3 Credit Hours Continuation of 635. Repeatability: May be repeated. Maximum 12 hours. (DE) Prerequisite(s): 635. Registration Restriction(s): Minimum student level – graduate.



MATH 641  Functional Analysis I 3 Credit Hours Topological vector spaces, distributions, and Banach algebras with applications to Fourier analysis and differential equations: theorems of KreinMilman, PaleyWiener, Lax, MalgrangeEhrenpreis, GelfandNaimark, and spectral theory of normal operators. Repeatability: May be repeated. Maximum 6 hours. (DE) Prerequisite(s): 545. (DE) Corequisite(s): 546 or 443. Registration Restriction(s): Minimum student level – graduate.



MATH 642  Functional Analysis II 3 Credit Hours Continuation of 641. Repeatability: May be repeated. Maximum 6 hours. (DE) Prerequisite(s): 641. Registration Restriction(s): Minimum student level – graduate.



MATH 645  Advanced Analysis I 3 Credit Hours Selected topics in real, complex, or discrete analysis. Repeatability: May be repeated. Maximum 12 hours. (DE) Prerequisite(s): 545 and 546. Registration Restriction(s): Minimum student level – graduate.



MATH 646  Advanced Analysis II 3 Credit Hours Continuation of 645. Repeatability: May be repeated. Maximum 12 hours. (DE) Prerequisite(s): 645. Registration Restriction(s): Minimum student level – graduate.


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