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.
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.
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.
Repeat Status: Not repeatable for credit
Prerequisites: MATH 505 [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.
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.
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.
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).
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.
Repeat Status: Not repeatable for credit
MATH 522 Numerical Analysis III 3.0 Credits
Covers numerical solutions of ordinary and partial differential equations.
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.
Repeat Status: Not repeatable for credit
Prerequisites: MATH 510 [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.
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.
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.
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.
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.
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.
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.
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.
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.
Repeat Status: Not repeatable for credit
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.
Repeat Status: Not repeatable for credit
MATH 604 Topics in Matrix Analysis 3.0 Credits
Advanced matrix analysis, including topics such as inequalities involving eigenvalues and/or singular values, norms and their duals, operator monotone and convex functions, spectral variation and spectral perturbation, matrix inequalities, numerical range and its variations.
Repeat Status: Not repeatable for credit
Prerequisites: MATH 504 [Min Grade: C]
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.
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.
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.
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.
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.
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.
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.
Repeat Status: Not repeatable for credit
MATH 621 Partial Differential Equations II 3.0 Credits
Continues MATH 620.
Repeat Status: Not repeatable for credit
MATH 622 Partial Differential Equations III 3.0 Credits
Continues MATH 621.
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.
Repeat Status: Not repeatable for credit
MATH 624 Ordinary Differential Equations II 3.0 Credits
Continues MATH 625.
Repeat Status: Not repeatable for credit
MATH 625 Ordinary Differential Equations III 3.0 Credits
Continues MATH 626.
Repeat Status: Not repeatable for credit
MATH 626 Dynamical Systems 3.0 Credits
Dynamical systems, including topics on phase portraits, invariant sets, one-dimensional and higher-dimensional flows, the study of equilibrium and other dynamical phenomena such as periodic orbits, homoclinic orbits and heteroclinic orbits, linear and structural stabilities of equilibrium, Poincaré maps of dynamical systems, bifurcations of equilibrium and periodic orbits, the normal forms of bifurcations, the existence of invariant manifolds, the persistence and differentiability of invariant manifolds under perturbation.
Repeat Status: Not repeatable for credit
Prerequisites: MATH 623 [Min Grade: C]
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.
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.
Repeat Status: Not repeatable for credit
Prerequisites: MATH 630 [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.
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.
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.
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.
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.
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.
Repeat Status: Not repeatable for credit
Prerequisites: MATH 640 [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.
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.
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.
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.
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.
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.
Repeat Status: Not repeatable for credit
Prerequisites: MATH 533 [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.
Repeat Status: Not repeatable for credit
MATH 898 Master's Thesis 0.5-20.0 Credits
Master's thesis.
Repeat Status: Not repeatable for credit
MATH 997 Research 1.0-12.0 Credit
Research.
Repeat Status: Can be repeated multiple times for credit
MATH 998 Ph.D. Dissertation 1.0-12.0 Credit
Ph.D. dissertation.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Repeat Status: Can be repeated multiple times for credit
