# Mathematics

### Courses

MATH 504 Linear Algebra & Matrix Analysis 3.0 Credits

Course topics include the QR decomposition, Schur's triangularization theorem, the spectral decomposition for normal matrices, the Jordan canonical form, the Courant-Fisher theorem, singular value and polar decompositions, the Gersgorin disc theorem, the Perron-Frobenius theorem, and other current matrix analysis topics. Applications of the material are outlined as well.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 505 Principles of Analysis I 3.0 Credits

Metric spaces, compactness, connectedness, completeness. Set theory and cardinality, continuity, differentiation, Riemann integral.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 506 Principles of Analysis II 3.0 Credits

A continuation of MATH 505. Uniform convergence, Fourier series, Lebesque integral in Euclidean spaces, differential calculus in Euclidean spaces, inverse and implicit functions theorems, change of variables in multiple integrals.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 505 [Min Grade: C]

MATH 507 Applied Mathematics I 3.0 Credits

Covers matrix theory, linear transformations, canonical forms, matrix decompositions, and factorizations, including the singular value decomposition, quadratic forms, matrix least squares problems, and fast unitary transforms. Introduces computational linear algebra.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 508 Applied Mathematics II 3.0 Credits

Covers the techniques of mathematical modeling in the physical and biological sciences using discrete and combinatorial mathematics, probabilistic methods, variational principles, Fourier series and integrals, integral equations, calculus of variations, asymptotic series and expansions, and eigenvalue problems associated with Sturm-Liouville boundary value problems. Topics vary from year to year.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 507 [Min Grade: C]

MATH 509 Applied Mathematics III 3.0 Credits

Continues the theme of MATH 508. Topics vary from year to year.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 508 [Min Grade: C]

MATH 510 Applied Probability and Statistics I 3.0 Credits

Covers basic concepts in applied probability; random variables, distribution functions, expectations, and moment generating functions; specific continuous and discrete distributions and their properties; joint and conditional distributions; discrete time Markov chains; distributions of functions of random variables; probability integral transform; and central limit theorem.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 511 Applied Probability and Statistics II 3.0 Credits

Covers probability plots and graphical techniques for determining distribution of data, including sampling and sampling distributions, law of large numbers, parametric point estimation, maximum likelihood estimation, Bayes estimation, properties of estimators, sufficient statistics, minimum variance unbiased estimators, and parametric interval estimation. Introduces hypothesis testing.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 510 [Min Grade: C]

MATH 512 Applied Probability and Statistics III 3.0 Credits

Covers hypothesis testing, analysis of variance, multiple regression, and special topics. Introduces linear models.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 511 [Min Grade: C]

MATH 520 Numerical Analysis I 3.0 Credits

Covers polynomial interpolation, numerical solutions of nonlinear equations, numerical integration (Newton-Cotes, Gauss quadrature), error estimates of various numerical methods, and function approximation (polynomial, Fourier, Pade).

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 521 Numerical Analysis II 3.0 Credits

Covers numerical linear algebra and matrix computation, direct and iterative methods for solving linear systems and eigenvalue problems, least square problems, various matrix factorizations (QR, singular value decomposition, LU and Cholesky), and Krylov subspace methods.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 522 Numerical Analysis III 3.0 Credits

Covers numerical solutions of ordinary and partial differential equations.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 520 [Min Grade: C]

MATH 523 Computer Simulation I 3.0 Credits

Covers computer simulation of pseudo-random variables, including Monte Carlo methods.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 510 [Min Grade: C]

MATH 524 Computer Simulation II 3.0 Credits

Covers discrete and continuous event simulation models and techniques.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 523 [Min Grade: C]

MATH 525 Topics in Computer Simulation 3.0 Credits

Covers statistical analysis of simulation data, variance reduction techniques, and advanced topics in simulation.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 524 [Min Grade: C]

MATH 530 Combinatorial Mathematics I 3.0 Credits

Covers graphs and networks, with an emphasis on algorithms. Includes minimum spanning trees, shortest path problems, connectivity, network flows, matching theory, Eulerian and Hamiltonian tours, graph coloring, and random graphs.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 531 Combinatorial Mathematics II 3.0 Credits

Covers mathematical tools for the analysis of algorithms, including combinatorics, recurrence relations and generating functions, elementary asymptotics, and probabilistic methods.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 530 [Min Grade: C]

MATH 532 Topics in Combinatorial Math 3.0 Credits

Covers topics in discrete mathematics, including asymptotic enumeration, number theory, probabilistic combinatorics, and combinatoric algorithms.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 531 [Min Grade: C]

MATH 533 Abstract Algebra I 3.0 Credits

Covers groups, transformation groups and group actions, isomorphism and homomorphism theorems, Sylow theorems, symmetric groups, rings, and fields.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 534 Abstract Algebra II 3.0 Credits

Covers factorization domains, Euclidean domains, and polynomial rings, and modules, vector spaces, and linear transformations.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 533 [Min Grade: C]

MATH 535 Topics in Abstract Algebra 3.0 Credits

This third course in the Abstract Algebra sequence covers a selection of topics in advanced modern algebra such as symmetries, representation theory, algebraic geometry, homological algebra, Galois Theory and coding theory.

College/Department: College of Arts and Sciences
Repeat Status: Can be repeated 3 times for 9 credits
Prerequisites: MATH 533 [Min Grade: C] and MATH 534 [Min Grade: C]

MATH 536 Topology I 3.0 Credits

Covers general topological spaces, metric spaces, and function spaces; open sets, limit points, limits of sequences, convergence, separation axioms, compactness, connectedness, continuity, homeomorphisms, and product of N-spaces; and specialized applications to the real line, Euclidean N-space, and well-known function spaces.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 537 Topology II 3.0 Credits

Continues MATH 536.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 538 Manifolds 3.0 Credits

Topics will be selected from the following: Differential structures, immersion theorems, tangent bundles, vector fields and distributions, integral manifolds, integration on manifolds, differential forms, general Stokes Theorem, applications to physics and engineering.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 540 Numerical Computing 3.0 Credits

Intended to introduce students to contemporary computing environments and the associated tools. Uses contemporary software tools and specific applications from science and engineering to illustrate numerical and visualization methods.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 544 Advanced Engineering Mathematics I 3.0 Credits

Covers solution techniques for ordinary differential equations, including series techniques, Legendre and Bessel functions, Sturm-Liouville theory, and Laplace and Fourier techniques. Introduces symbolic computation as time permits.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 545 Advanced Engineering Mathematics II 3.0 Credits

Covers partial differential equations, including separation of variables and its applications to standard equations. Introduces Green's functions for differential equations.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 544 [Min Grade: C]

MATH 546 Advanced Engineering Mathematics III 3.0 Credits

Covers complex analysis, including complex differentiation and integration, Cauchy's theorems and residue theory, and their applications; conformal maps; and applications to fluid flow.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 545 [Min Grade: C]

MATH 553 Sci Comp & Visualization I 3.0 Credits

Covers scientific computing, with an emphasis on numerical computing and visualization techniques. Includes techniques of computational geometry, including an introduction to methods used to describe the shapes of free-form curves, surfaces, and volumes, and applications to computer-aided design and other areas of scientific computing.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 540 [Min Grade: C]

MATH 554 Sci Comp & Visualization II 3.0 Credits

Covers scientific visualization, using a computational environment that includes high-performance workstations and supercomputers, and application in science and engineering. Includes applications to finite element and difference methods.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 553 [Min Grade: C]

MATH 555 Topics in Sci Comp & Visualiz 3.0 Credits

Covers special topics chosen from contemporary problem areas in scientific computing and visualization, including digital image processing, wavelet transforms and their numerical treatment, numerical conformal mapping, and contemporary problem areas in scientific computing and visualization.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 554 [Min Grade: C]

MATH 572 Financial Mathematics: Fixed Income Securities 3.0 Credits

The course is a mathematical introduction to interest rates and interest rates related instruments including loans, bonds, mortgages and swaps. The course emphasizes the mathematical aspects of the subject and computational implementation.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 610 Probability Theory I 3.0 Credits

Covers basics of modern probability theory: properties of probability measures, independence, Borel-Cantelli lemma, zero-one law, random variables, distribution theory, and expectations.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 633 [Min Grade: C]

MATH 611 Probability Theory II 3.0 Credits

Covers further development of modern probability theory, including modes of convergence of random variables, series of random variables, weak and strong laws of large numbers, characteristics functions, inversion formula and continuity theorem, and central limit theorem.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 610 [Min Grade: C]

MATH 612 Topics in Probability Theory 3.0 Credits

This third course in the probability sequence covers a selection of topics in modern probability theory. Topics may include: theory of sums of independent random variables, inequalities, martingale theory, combinatorial probability.

College/Department: College of Arts and Sciences
Repeat Status: Can be repeated 2 times for 6 credits
Prerequisites: MATH 611 [Min Grade: C]

MATH 613 Stochastic Processes I 3.0 Credits

Covers conditional probabilities, expectations, Markov chains, classification of states, recurrence and absorption probabilities, asymptotic behavior, random walk, birth and death processes, and ruin problems.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 510 [Min Grade: C] and MATH 611 [Min Grade: C]

MATH 614 Stochastic Processes II 3.0 Credits

Covers queuing theory, waiting line models, embedded Markov chain method, and optimization problems. Includes applications and simulation.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 613 [Min Grade: C]

MATH 615 Topics in Stochastic Processes 3.0 Credits

Covers topics including branching processes, Brownian motion, renewal processes, compounding stochastic processes, martingales, and decision-making under uncertainty.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 613 [Min Grade: C]

MATH 620 Partial Differential Equations I 3.0 Credits

Covers derivation and classification of partial differential equations; elementary methods of solution, including Fourier series and transform techniques; linear and equilinear equations of the first order; hyperbolic, elliptic, and parabolic type equations; maximum principles; existence, uniqueness, and continuous dependence theorems; Riemann's method; method of characteristics; Green's functions; and variational and numerical methods.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 621 Partial Differential Equations II 3.0 Credits

Continues MATH 620.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 622 Partial Differential Equations III 3.0 Credits

Continues MATH 621.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 623 Ordinary Differential Equations I 3.0 Credits

Covers existence and uniqueness theorems, properties of solutions, adjoint equations, canonical forms, asymptotic behavior, phase space, method of isocline, classification of singular points, linear two-dimensional autonomous systems, non-linear systems, stability theory, Lyapunov's methods, quadratic forms, construction of Lyapunov's function, boundedness, limit sets, applications to controls, linear equations with periodic coefficients, Floquet theory, characteristic multipliers and exponents, existence of periodic solutions to weakly non-linear systems, jump phenomena, subharmonic resonance, and stability of periodic solutions.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 624 Ordinary Differential Equations II 3.0 Credits

Continues MATH 625.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 625 Ordinary Differential Equations III 3.0 Credits

Continues MATH 626.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 630 Complex Variables I 3.0 Credits

Covers Cauchy's theorem, Morera's theorem, infinite series, Taylor and Laurent explanations, residues, conformal mapping and applications, analytic continuation, and Riemann mapping theorem.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 631 Complex Variables II 3.0 Credits

Covers entire functions, Picard's theorem, series and product developments, Riemann Zeta function, and elliptic functions.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 630 [Min Grade: C]

MATH 632 Topics in Complex Variables 3.0 Credits

Covers topics including global analytic functions, algebraic functions, and linear differential equations in the complex plane.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 631 [Min Grade: C]

MATH 633 Real Variables I 3.0 Credits

Covers algebra of sets, topology of metric spaces, compactness, completeness, function spaces, general theory of measure, measurable functions, integration, convergence theorems, and applications to classical analysis and integration.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 634 Real Variables II 3.0 Credits

Covers Fubini's theorem, Radon-Nikodym theorem, LP-spaces, linear functionals on LP-spaces, Riesz-representation theorem, topological integration, Riesz-Markoz theorem, Luzin's theorem, basic complex functions, analytic functions, and complex-integration.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 633 [Min Grade: C]

MATH 635 Real Variables III 3.0 Credits

Covers topics including differentiation theory, Fourier series and transforms, and singular integrals.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 634 [Min Grade: C]

MATH 640 Functional Analysis 3.0 Credits

An introduction to abstract linear spaces, including normed linear spaces, Hilbert spaces, Banach spaces, and their duals. Fundamental theorems such as the Hahn-Banach theorem, open mapping and closed graph theorems will be covered, along with possible applications to differential and integral equations and fundamentals of distribution theory.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 504 [Min Grade: C] and MATH 506 [Min Grade: C]

MATH 641 Harmonic Analysis 3.0 Credits

Covers modern techniques and applications of harmonic analysis, including Fourier series, Fourier transforms and related topics.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 640 [Min Grade: C]

MATH 642 Operator Theory 3.0 Credits

An introduction to basic spectral theory of linear operators, theory of compact operators, and theory of unbounded operators.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 640 [Min Grade: C]

MATH 643 Integral Equations I 3.0 Credits

Covers theory and application of linear integral equations, including the Hilbert-Schmidt theory. Introduces non-linear and singular integral equations and numerical methods.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 645 Transform Theory I 3.0 Credits

Covers selected topics from wavelet transforms, including properties; asymptotic analyses; and applications of the integral transforms of Laplace, Fourier, Mellin, and Radon.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 640 [Min Grade: C]

MATH 646 Transform Theory II 3.0 Credits

Covers selected topics from wavelet transforms and applications, convolution equations, and the calculus of distributions.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 640 [Min Grade: C] and MATH 645 [Min Grade: C]

MATH 660 Lie Groups and Lie Algebras I 3.0 Credits

Covers matrix groups, topological groups, locally isomorphic groups, universal covering groups, analytic manifolds, Lie groups; the Lie algebra of a Lie group, differential forms, and Lie's three theorems; analytic subgroups of a Lie group and compact Lie groups; and semisimple Lie algebras, general structure of Lie algebras, Cartan subalgebras, modules and representation, and computational techniques in representation theory.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 661 Lie Groups and Lie Algebras II 3.0 Credits

Continues MATH 660.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 662 Lie Groups/Algebras III 3.0 Credits

Continues MATH 661.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 670 Methods of Optimization I 3.0 Credits

Provides a rigorous treatment of theory and computational techniques in linear programming and its extensions, including formulation, duality theory, simplex and dual-simplex methods, and sensitivity analysis; network flow problems and algorithms; systems of inequalities, including exploiting special structure in the simplex method and use of matrix decompositions; and applications in game theory and integer programming.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 671 Methods of Optimization II 3.0 Credits

Covers necessary and sufficient conditions for unconstrained and constrained optimization. Includes computational methods including quasi-Newtonian and successive quadratic programming, and penalty and interior methods.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 672 Methods of Optimization III 3.0 Credits

Covers advanced topics in mathematical programming, including interior point methods in linear programming; stochastic optimization; multi-objective optimization; and global minimax, functional, and non-linear least squares optimization methods.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 670 [Min Grade: C] and MATH 671 [Min Grade: C]

MATH 673 Calculus of Variations 3.0 Credits

Introduction to calculus of variations. Covers applications to geometry, classical mechanics and control theory, Euler-Lagrange equations, problems with constraints, canonical equations, Hamiltonian mechanics, symmetries and Noether's theorem, Hamilton-Jacobi theory, introduction to optimal control, maximum principle, and Hamilton-Jacobi-Bellman equations.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 701 Algebraic Combinatorics 3.0 Credits

This course covers methods of Abstract Algebra that can be applied to various combinatorial problems and conversely, combinatorial methods to approach problems in representation theory, algebraic geometry, and homological algebra.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit
Prerequisites: MATH 533 [Min Grade: C] and MATH 534 [Min Grade: C]

MATH 723 Mathematical Neuroscience 3.0 Credits

This is an introduction to mathematical and computational techniques for analyzing neuronal models. Topics include conductance based models, neuronal excitability, bursting, neural networks, and compartmental models, as well as phase plane analysis, slow-fast systems, elements of applied bifurcation theory, and simulating differential equation models using MATLAB.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 898 Master's Thesis 0.5-20.0 Credits

Master's thesis.

College/Department: College of Arts and Sciences
Repeat Status: Not repeatable for credit

MATH 997 Research 1.0-12.0 Credit

Research.

College/Department: College of Arts and Sciences
Repeat Status: Can be repeated multiple times for credit

MATH 998 Ph.D. Dissertation 1.0-12.0 Credit

Ph.D. dissertation.

College/Department: College of Arts and Sciences
Repeat Status: Can be repeated multiple times for credit

MATH I599 Independent Study in MATH 0.0-12.0 Credits

Self-directed within the area of study requiring intermittent consultation with a designated instructor.

College/Department: College of Arts and Sciences
Repeat Status: Can be repeated multiple times for credit

MATH I699 Independent Study in MATH 0.5-6.0 Credits

Self-directed within the area of study requiring intermittent consultation with a designated instructor.

College/Department: College of Arts and Sciences
Repeat Status: Can be repeated multiple times for credit

MATH I799 Independent Study in MATH 0.0-6.0 Credits

Self-directed within the area of study requiring intermittent consultation with a designated instructor.

College/Department: College of Arts and Sciences
Repeat Status: Can be repeated multiple times for credit

MATH I899 Independent Study in MATH 0.0-12.0 Credits

Self-directed within the area of study requiring intermittent consultation with a designated instructor.

College/Department: College of Arts and Sciences
Repeat Status: Can be repeated multiple times for credit

MATH I999 Independent Study in MATH 0.0-12.0 Credits

Self-directed within the area of study requiring intermittent consultation with a designated instructor.

College/Department: College of Arts and Sciences
Repeat Status: Can be repeated multiple times for credit

MATH T580 Special Topics in Mathematics 0.0-9.0 Credits

Topics decided upon by faculty will vary within the area of study.

College/Department: College of Arts and Sciences
Repeat Status: Can be repeated multiple times for credit

MATH T680 Special Topics in Mathematics 0.0-9.0 Credits

Covers special topics of interest to students and faculty.

College/Department: College of Arts and Sciences
Repeat Status: Can be repeated multiple times for credit

MATH T780 Special Topics in Mathematics 0.0-9.0 Credits

Topics decided upon by faculty will vary within the area of study.

College/Department: College of Arts and Sciences
Repeat Status: Can be repeated multiple times for credit

MATH T880 Special Topics in Mathematics 0.0-9.0 Credits

Topics decided upon by faculty will vary within the area of study.

College/Department: College of Arts and Sciences
Repeat Status: Can be repeated multiple times for credit

MATH T990 Special Topics in Mathematics 0.0-9.0 Credits

Topics decided upon by faculty will vary within the area of study.

College/Department: College of Arts and Sciences
Repeat Status: Can be repeated multiple times for credit