Courses for Advanced Undergraduates and Graduate Students
601. Vector Analysis. (1.5) Vector functions, partial derivatives, line and multiple integrals, Green's theorem, Stokes' theorem, divergence theorem. Not to be counted toward any major offered by the department, except for the major in mathematical business.
602. Matrix Algebra. (1.5) Matrices, determinants, solutions of linear equations, special matrices, eigenvalues and eigenvectors of matrices. Not to be counted toward any major offered by the department, except for the major in mathematical business. Credit not allowed for both Mathematics 121 and 602.
603. Complex Variables. (1.5) Topics in analytic function theory, Cauchy's theorem, Taylor and Laurent series, residues. Not to be counted toward any major offered by the department. Credit not allowed for both 603 and 617.
604. Applied Partial Differential Equations. (1.5) The separation of variables technique for the solution of the wave, heat, Laplace, and other partial differential equations with the related study of special functions and Fourier series. Not to be counted toward any major offered by the department.
610. Advanced Calculus. (3) A rigorous proof-oriented development of important ideas in calculus. Limits and continuity, sequences and series, pointwise and uniform convergence, derivatives and integrals. Credit not allowed for both Mathematics 610 and 611. May not be used toward any graduate degree offered by the department.
611, 612. Introductory Real Analysis I, II. (3,3) Limits and continuity in metric spaces, sequences and series, differentiation and Riemann-Stieltjes integration, uniform convergence, power series and Fourier series, differentiation of vector functions, implicit and inverse function theorems. Credit not allowed for both Mathematics 610 and 611.
617. Complex Analysis I. (3) Analytic functions. Cauchy's theorem and its consequences, power series, and residue calculus. Credit not allowed for both 603 and 617.
622. Modern Algebra II. (3) A continuation of modern abstract algebra through the study of additional properties of groups, rings, and fields.
624. Linear Algebra II. (3) A thorough treatment of vector spaces and linear transformations over an arbitrary field, canonical forms, inner product spaces, and linear groups.
626. Numerical Linear Algebra. (3) Numerical methods for solving matrix and related problems in science and engineering. Topics include systems of linear equations, least squares methods, and eigenvalue computations. Special emphasis given to parallel matrix computations. Beginning knowledge of a programming language such as Pascal, FORTRAN, or C is required. Credit not allowed for both Mathematics 626 and Computer Science 652.
631. Geometry. (3) An introduction to axiomatic geometry including a comparison of Euclidean and non-Euclidean geometries.
634. Differential Geometry. (3) Introduction to the theory of curves and surfaces in two and three dimensional space including such topics as curvature, geodesics, and minimal surfaces.
645, 646. Elementary Theory of Numbers I, II. (3,3) Properties of integers, including congruences, primitive roots, quadratic residues, perfect numbers, Pythagorean triples, sums of squares, continued fractions, Fermat's Last Theorem, and the Prime Number Theorem.
647. Graph Theory. (3) Paths, circuits, trees, planar graphs, spanning trees, graph coloring, perfect graphs, Ramsey theory, directed graphs, enumeration of graphs and graph theoretic algorithms.
648, 649. Combinatorial Analysis I, II. (3,3) Enumeration techniques, generating functions, recurrence formulas, the principle of inclusion and exclusion, Polya theory, graph theory, combinatorial algorithms, partially ordered sets, designs, Ramsey theory, symmetric functions, and Schur functions.
652. Partial Differential Equations. (3) A detailed study of partial differential equations, including the heat, wave, and Laplace equations, using methods such as separation of variables, characteristics, Green's functions, and the maximum principle.
653. Mathematical Models. (3) Development and application of probabilistic and deterministic models. Emphasis given to constructing models that represent systems in the social, behavioral, and management sciences.
655. Introduction to Numerical Methods. (3) Numerical computations on modern computer architectures; floating point arithmetic and round-off error. Programming in a scientific/engineering language (C or FORTRAN). Algorithms and computer techniques for the solution of problems such as roots of functions, approximation, integration, systems of linear equations and least squares methods. Credit not allowed for both Mathematics 655 and Computer Science 655.
656. Statistical Methods. (3) A study of statistical methods that have proven useful in many different disciplines. These methods include tests of model assumptions, regression, general linear models, nonparametric alternatives, and analysis of data collected over time. Knowledge of matrix algebra is desirable but not necessary.
657, 658. Mathematical Statistics I, II. (3,3) Probability distributions, mathematical expectation, sampling distributions, estimation and testing of hypotheses, regression, correlation, and analysis of variance.
659. Multivariate Statistics. (3) Multivariate and generalized linear methods for classification, modeling, discrimination, and analysis. P—Mathematics 602 and 656; or POI. Berenhaut, Norris
661. Selected Topics. (1,1.5,2, or 3) Topics in mathematics that are not considered in regular courses. Content varies.
681. Individual Study. (1 or 2) A course of independent study directed by a faculty adviser. By prearrangement.
682. Reading in Mathematics. (1,2, or 3) Reading in mathematical topics to provide a foundational basis for more advanced study in a particular mathematical area. Topics vary and may include material from algebra, analysis, combinatorics, computational or applied mathematics, number theory, topology, or statistics. May not be used to satisfy any requirement in the mathematics MA degree with thesis. No more than three hours may be applied to the requirements for the mathematics MA degree without thesis. Staff
For Graduate Students
711, 712. Real Analysis. (3,3) Measure and integration theory, elementary functional analysis, selected advanced topics in analysis. Carmichael, Hayashi, Robinson
715, 716. Seminar in Analysis. (1,1) Baxley
717. Optimization in Banach Spaces. (3) Banach and Hilbert spaces, best approximations, linear operators and adjoints, Frechet derivatives and nonlinear optimization, fixed points and iterative methods. Applications to control theory, mathematical programming, and numerical analysis. Baxley
718. Topics in Analysis. (3) Selected topics from functional analysis or analytic function theory. Baxley, Robinson
721, 722. Abstract Algebra. (3,3) Groups, rings, fields, extensions, Euclidean domains, polynomials, vector spaces, Galois theory. Kirkman, Kuzmanovich
723, 724. Seminar on Theory of Matrices. (1,1) Plemmons
725, 726. Seminar in Algebra. (1,1) John, Kirkman
728. Topics in Algebra. (3) Topics vary and may include algebraic coding theory, algebraic number theory, matrix theory, representation theory, non-commutative ring theory. Kirkman, Kuzmanovich
731, 732. General Topology. (3,3) An axiomatic development of topological spaces. Includes continuity, connectedness, compactness, separation axioms, metric spaces, convergence, embedding and metrization, function and quotient spaces, and complete metric spaces. Staff
733. Topics in Topology and Geometry. (3) Topics vary and may include knot theory, non-Euclidean geometry, combinatorial topology, differential topology, minimal surfaces and algebraic topology. Howards
735, 736. Seminar on Topology. (1,1) May
737, 738. Seminar on Geometry. (1,1) Staff
744. Topics in Number Theory. (3) Topics vary and are chosen from the areas of analytic, algebraic, and elementary number theory. Topics may include Farey fractions, the theory of partitions, Waring's problem, prime number theorem, and Dirichlet's problem. Hayashi, Howard
745, 746. Seminar on Number Theory. (1,1) Hayashi, Howard
747. Topics in Discrete Mathematics. (3) Topics vary and may include enumerative combinatorics, graph theory, algebraic combinatorics, combinatorial optimization, coding theory, experimental designs, Ramsey theory, Polya theory, representation theory, set theory and mathematical logic. Allen, Howard, John
748, 749. Seminar on Combinatorial Analysis. (1,1) Allen, Howard
750. Dynamical Systems. (3) Introduction to modern theory of dynamical systems. Linear and nonlinear autonomous differential equations, invariant sets, closed orbits, Poincare maps, structural stability, center manifolds, normal forms, local bifurcations of equilibria, linear and non-linear maps, hyperbolic sets, attractors, symbolic representation, fractal dimensions. P—Mathematics 611. Baxley, Jiang
752. Topics in Applied Mathematics. (3) Topics vary and may include computational methods in differential equations, optimization methods, approximation techniques, eigenvalue problems. Baxley, Plemmons, Robinson
753. Nonlinear Optimization. (3) The problem of finding global minimums of functions is addressed in the context of problems in which many local minima exist. Numerical techniques are emphasized, including gradient descent and quasi-Newton methods. Current literature is examined and a comparison made of various techniques for both unconstrained and constrained optimization problems. Credit not allowed for both Mathematics 753 and Computer Science 753. P—Mathematics 113 and Mathematics (or Computer Science) 655. Plemmons
754. Numerical Methods for Partial Differential Equations. (3) Numerical techniques for solving partial differential equations (including elliptic, parabolic and hyperbolic) are studied along with applications to science and engineering. Theoretical foundations are described and emphasis is placed on algorithm design and implementation using either C, FORTRAN or MATLAB. Credit not allowed for both Mathematics 754 and Computer Science 754. P-Mathematics 113 and either Computer Science 655 or Mathematics 655. Baxley, Jiang, Plemmons, Robinson
758. Topics in Statistics. (3) Topics vary and may include linear models, nonparametric statistics, stochastic processes. Kirkman, Norris
761. Stochastic Processes. (3) Discrete time and continuous time Markov chains, Poisson processes, general birth and death processes, renewal theory. Applications, including general queuing models. Norris
791, 792. Thesis Research. (1-9) Staff
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