90/100. First Year Seminar. (Syllabus for Kuzmanovich, Parsley, Warrington.)
105. Fundamentals of Algebra and Trigonometry. (1.5h, 2.5h, or 3h) A review of the essentials of algebra and trigonometry. Admission by permission only (generally, a student must have taken fewer than three years of high school mathematics to be eligible for admission). Not to be counted toward the major or minor in mathematics.
107. Explorations in Mathematics. (4h) An introduction to mathematical reasoning and problem solving. Topics vary by instructor and may include one or more of the following: knot theory, Euclidean and non-Euclidean geometry, set theory, cryptography, discrete models, number theory, discrete mathematics, chaos theory, probability, and MAPLE programming. (D, QR) (Syllabus for Parsley, Robinson.)
109. Elementary Probability and Statistics. (4h or 3h) Probability and distribution functions, means and variances, and sampling distributions. (D, QR) (Syllabus for Blackburn, Cotwright, Connolly, Erway , Jiang, Norris, Seurken, Wilson.)
111. Calculus with Analytic Geometry I. (4h) Functions, trigonometric functions, limits, continuity, differentiation, applications of derivatives, introduction to integration, the fundamental theorem of calculus. (D, QR) (Syllabus for Allen, Berenhaut, Blackburn, Connolly, Cotwright, Erway, Jiang, Kuzmanovich, Lockridge, Norris, Seurken, Wilson.)
112. Calculus with Analytic Geometry II. (4h) Techniques of integration, indeterminate forms, improper integrals, transcendental functions, sequences, Taylor’s formula, and infinite series, including power series. (D, QR) (Syllabus for Allen, Dometrus, Howards, Jiang, Kirkman, Parsley.)
113. Multivariable Calculus. (4h) The calculus of vector functions, including geometry of Euclidean space, differentiation, extrema, line integrals, multiple integrals, and Green’s, Stokes’, and divergence theorems. Credit not allowed for both MTH 113 and 205. (D, QR) (Syllabus for Carmichael, Jiang, Raynor, Robinson, Warrington. )
117. Discrete Mathematics. (4h) Introduction to various topics in discrete mathematics applicable to computer science including sets, relations, Boolean algebra, propositional logic, functions, computability, proof techniques, graph theory, and elementary combinatorics. (D, QR) (Syllabus for Allen, Berenhaut, Kuzmanovich, Plemmons, Warrington.)
121. Linear Algebra I. (3h) Vectors and vector spaces, linear transformations and matrices, determinants, eigenvalues, and eigenvectors. Credit not allowed for both 121 and 205. (D, QR) (Syllabus for Allen, Howards, Kirkman, Kuzmanovich, Robinson.)
165. Problem Solving Seminar. (1h) Weekly seminar designed for students who wish to participate in mathematical competition such as the annual Putnam examination. Not to be counted toward any major or minor offered by the department. May be repeated for credit. Pass/Fail only. (Syllabus for Raynor, Robinson.)
205. Applied Multivariable Mathematics. (3h) Introduction to several topics in applied mathematics including complex numbers, probability, matrix algebra, multivariable calculus, and ordinary differential equations. Not to be counted toward any major offered by the department except for the major in mathematical business. Credit not allowed for both 205 and 121, or for both 205 and 113. P—MTH 112.
211. Advanced Calculus. (3h) 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 211 and 311. (D) (Syllabus for Carmichael, Raynor.)
243. Codes and Cryptography. (3h) Essential concepts in coding theory and cryptography. Congruences, cryptosystems, public key, Huffman codes, information theory, and other coding methods. (D) (Syllabus for Allen.)
251. Ordinary Differential Equations. (3h) Linear equations with constant coefficients, linear equations with variable coefficients, and existence and uniqueness theorems for first order equations. P--Mathematics 112. (D, QR) (Syllabus for Carmichael, Howard, Raynor.)
253. Operations Research. (3h) Mathematical models and optimization techniques. Studies in allocation, simulation, queuing, scheduling, and network analysis. P--Mathematics 111. (D, QR)
254. Optimization Theory. ( l.5h) Unconstrained and constrained optimization problems; Lagrange multiplier methods; sufficient conditions involving bordered Hessians; inequality constraints; Kuhn-Tucker conditions; applications primarily to problems in economics. P-Mathematics 113 and Mathematics 121. (Syllabus for Jiang.)
255. Dynamical Systems. (1.5h) Introduction to optimal control, including the Pontryagin maximum principle, and systems of nonlinear differential equations, particularly phase space methods. Applications to problems in economics, including optimal management of renewable resources. P--Mathematics 113 and Mathematics 121. (Syllabus for Jiang.)
256. Statistical Methods. (3h) A study of statistical methods that have proved 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. (D, QR) (Syllabus for Norris.)
601. Vector Analysis. (1.5h) 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. (Syllabus for Carmichael.)
602. Matrix Algebra. (1.5h) 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 121 and 602. (Syllabus for Carmichael, Robinson.)
603. Complex Variables. (1.5h) 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. P--Mathematics 112. (Syllabus for Carmichael.)
604. Applied Partial Differential Equations. (1.5h) 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. (Syllabus for Carmichael, Robinson. )
306. Advanced Mathematics for the Physical Sciences. (3h) Advanced topics in linear algebra, special functions, integral transforms, and partial differential equations. Not to be counted toward any major offered by the department except for the major in mathematical business. P—MTH 205.
610. Advanced Calculus. (3h) A rigorous proof-oriented development of important ideas in calculus. Limits and continuity, sequences and series, pointwise and uniform convergence, derivatives and integrals. (No student allowed credit for both Mathematics 610 and 611. May not be used toward any graduate degree offered by the department.
311/611, 312/612. Introductory Real Analysis I, II. (3h,3h) 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 211 and 311. (D) (311/611 Syllabus for Carmichael, 311 Kuzmanovic, 611 Kuzmanovich, Robinson. )
317/617. Complex Analysis I. (3h) Analytic functions, Cauchy's theorem and its consequences, power series, and residue calculus. Credit not allowed for both 303 and 317. P --Mathematics 113. (D) (Syllabus for Carmichael, Jiang.)
321/621.Modern Algebra I. (3h) Introduction to modern abstract algebra through the study of groups, rings, integral domains, and fields. P--Mathematics 121. (D) (Syllabus forHoward, Howards, Kirkman, Warrington. )
322/622. Modern Algebra II. (3h) Continuation of modern abstract algebra through the study of additional properties of groups, rings, and fields. P--Mathematics 321. (D)
324/624. Linear Algebra II. (3h) Thorough treatment of vector spaces and linear transformations over an arbitrary field, canonical forms, inner product spaces, and linear groups. P--Mathematics 121 and Mathematics 321. (D) (Syllabus for Kirkman.)
326/626. Numerical Linear Algebra. (3h) Numerical methods for solving matrix and related problems in science and engineering. Topics will include systems of linear equations, least squares methods, and eigenvalue computations. Special emphasis given to parallel matrix computations. Beginning knowledge of a high level programming language is required. Credit not allowed for both Mathematics 326 and Computer Science 326. P--Mathematics 112 and Mathematics 121 or 205. (D) (Syllabus for Plemmons.)
331/631. Geometry. (3h) An introduction to axiomatic geometry including a comparison of Euclidean and non-Euclidean geometries. (D) (Syllabus for Allen, Jiang, Parsley. )
334/634. Differential Geometry. (3h) Introduction to the theory of curves and surfaces in two and three dimensional space, including such topics as curvature, geodesics, and minimal surfaces. P--Mathematics 113. (D) (Syllabus for Parsley, Robinson.)
345/645, 346/646. Elementary Theory of Numbers I, II. (3h,3h) 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. (D) (Syllabus for Howard.)
347/647. Graph Theory. (3h) Paths, circuits, trees, planar graphs, spanning trees, graph coloring, perfect graphs, Ramsey theory, directed graphs, enumeration of graphs, and graph theoretic algorithms. (D) (Syllabus for Warrington.)
348/648, 349/649. Combinatorial Analysis I, II. (3h,3h) 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. (D) (348/648 Syllabus for Howard. 349/649 Syllabus for Warrington.)
352/652. Partial Differential Equations. (3h) 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. P--Mathematics 113 and Mathematics 251. (D) (Syllabus for Warrington .)
353/653. Mathematical Models. (3h) Development and application of probabilistic and deterministic models. Emphasis given to constructing models which represent systems in the social, behavioral, and management sciences. (D)
355/655. Introduction to Numerical Methods. (3h) Numerical computations on modern computer architectures; floating point arithmetic and round-off error. Programming in a scientific/engineering language such as MATLAB, 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 355 and Computer Science 355. P--Mathematics 112, Mathematics 121 or 205, and Computer Science 111. (D) (Syllabus for Plemmons.)
656. Statistical Methods. (3) 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.
357/657, 358/658. Mathematical Statistics I, II. (3h,3h) Probability distributions, mathematical expectation, sampling distributions, estimation and testing of hypotheses, regression, correlation, and analysis of variance.MTH 357 prepares students for Actuarial exam #1. C-Mathematics 112, or P--Permission of instructor. (D) (Syllabus for Berenhaut, Kirkman. )
359/659. Multivariate Statistics. (3h) Multivariate and generalized linear methods for classification, modeling, discrimination and analysis. P--MTH 112, MTH 121 or 205, and MTH256. (D) (Syllabus for Norris.)
361/661. Selected Topics. (1.5h, 2.5h, or 3h) Topics in mathematics which are not considered in regular courses or which continue study begun in regular courses. Content varies. (Syllabus for Norris, Robinson.)
381. Individual Study. (l.5h, 2.5h, or 3h) Independent study directed by a faculty adviser. By prearrangement.
681. Individual Study. (lh or 2h) A course of independent study directed by a faculty adviser. By prearrangement.
682. Reading in Mathematics. (1h, 2h, or 3h) Reading in mathematical topics which is meant to provide a foundation basis for more advanced study in a particular mathematical area. Topics will 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 may be applied to the requirements for the mathematics MA degree without thesis.
391. Senior Seminar Preparation. (1h) Independent study or research directed by a faculty advisor by prearrangement with the adviser.
392. Senior Seminar Presentation. (1h) Preparation of a paper, followed by a one-hour oral presentation based upon work in Mathematics 391.
711, 712. Real Analysis. (3,3) Measure and integration theory, elementary functional analysis, selected advanced topics in analysis. Carmichael, Robinson. (711 Syllabus for Carmichael, Robinson; 712 Syllabus for Robinson.)
715, 716. Seminar in Analysis. (1,1)
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.
718. Topics in Analysis. (3) Selected topics from functional analysis or analytic function theory. Robinson
721, 722. Abstract Algebra. (3,3) Groups, rings, fields, extensions, Euclidean domains, polynomials, vector spaces, Galois theory. Kirkman, Kuzmanovich (721 Syllabus for Kirkman, Kuzmanovich ; 722 Syllabus for Kirkman.)
723, 724. Seminar on Theory of Matrices. (1,1) (Syllabus for Howards, Plemmons.)
725, 726. Seminar in Algebra. (l,l) 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. (Syllabus for Howards, Raynor.)
733. Topics in Topology and Geometry. (3) Topics will 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 will vary and will be 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. (Syllabus for Howard.)
745, 746. Seminar on Number Theory. (1,1) 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. (Syllabus for Berenhaut.)
748, 749. Seminar on Combinatorial Analysis. (1,1) Allen, Howard
750. Dynamical Systems. (3) Introduction to modern theory of dynamical systems. Linear and non-linear 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 121 and Mathematics 611. (Syllabus for Jiang.)
752. Topics in Applied Mathematics. (3) Topics will vary and may include computational methods in differential equations, optimization methods, approximation techniques, eigenvalue problems. Plemmons, Robinson. (Syllabus for Plemmons.)
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 will be 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 (or Computer Science) 655. (Syllabus for 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- Computer Science 655 or Mathematics 655. Jiang, Plemmons, Robinson
758. Topics in Statistics. (3) Topics will 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. (Syllabus for Bernehaut, Norris.)
791, 792. Thesis Research. (1-9) Staff