MATH0999. Remedial Transfer Credit.10 Credit Hours.
This is not a course offered at the University of Oklahoma. It is used to denote remedial transfer credit for which there is no OU equivalent course.
MATH1471. Mathematics for Critical Thinking Corequisite.1 Credit Hour.
Prerequisite: A satisfactory score on the math placement examination; Corequisite: MATH1473. This course is designed as a corequisite supplement to MATH1473 (Math for Critical Thinking). It covers material that supports the learning of key arithmetic, algebra topics, and terminology needed to address common contextualized scenarios involving quantities and numeration (e.g., personal financial mathematics and interpretation of data representations found in media). The course also further emphasizes topics from MATH1473. (F, Sp, Su)
MATH1473. Mathematics for Critical Thinking.3 Credit Hours.
Prerequisite: "C" or better in DMAT0123 at OU, or satisfactory score on the math assessment. A study of the mathematics needed for the critical evaluation of quantitative information and arguments including logic, critical appraisal of graphs and tables; use of simple mathematical models and an introduction to elementary statistics. (F, Sp, Su) [I-M].
MATH1501. College Algebra Corequisite.1 Credit Hour.
Prerequisite: A satisfactory score on the math placement examination; Corequisite: MATH1503. This course is a corequisite supplement to MATH1503 (College Algebra), which is designed for students in preparation for engineering calculus. MATH1501 supports the learning of key algebra topics, including expanding and simplifying algebraic expressions (linear, quadratic, polynomial, rational, radical, exponential, and logarithmic); factoring techniques; and representations of mathematical information. The course also further emphasizes topics from MATH1503. (F, Sp, Su)
MATH1503. College Algebra.3 Credit Hours.
Prerequisite: "C" or better in DMAT0123, or satisfactory score on the math assessment. Study of equations, inequalities, functions (linear, absolute value, quadratic, polynomial, rational, radical, exponential, logarithmic). Includes systems of equations; recognizing, utilizing, creating, and converting between symbols, tables, graphs, models. Prerequisite for MATH1523. A student may not receive credit for this course and MATH1643. (F, Sp, Su) [I-M].
MATH1523. Precalculus and Trigonometry.3 Credit Hours.
Prerequisite: MATH1503 or satisfactory score on the math assessment. Primarily concentrates on trigonometric functions and their inverses, trigonometric identities, solutions of triangles, and applications. In addition, limits, vectors and some vector operations, polar coordinates and continuity are introduced. Suitable for students planning to take calculus; intended as prerequisite for MATH1823. (F, Sp, Su) [I-M].
MATH1641. Functions and Modeling Corequisite.1 Credit Hour.
Prerequisite: A satisfactory score on the math placement examination; Corequisite: MATH1643. This course is a corequisite supplement to MATH1643 (Functions & Modeling), which is designed to prepare students for business calculus, as well as other business, life, and social science courses. The 1641 course focuses on key algebra skills and improvement of academic study skills necessary for success in MATH1643. It also further emphasizes topics covered in MATH1643. (F, Sp, Su)
MATH1643. Functions and Modeling for Business, Life and Social Sciences.3 Credit Hours.
Prerequisite: "C" or better in DMAT0123 at OU, or satisfactory score on the math assessment. Study of equations and functions (linear, polynomial, rational, exponential, logarithmic) from various perspectives (symbolic, verbal, numerical, graphical); digital techniques for graphing functions, solving equations, and modeling data using regressions. This course is designed for students in agricultural, business, life/health sciences, or social science majors. A student may not receive credit for this course and MATH1503. (F, Sp, Su) [I-M].
MATH1743. Calculus I for Business, Life and Social Sciences.3 Credit Hours.
Prerequisite: MATH1523, MATH1643, or satisfactory score on the math assessment. Topics in differentiation of polynomial, exponential and logarithmic functions. Applications to the business, life and social sciences, including optimization. A student may not receive credit for this course and MATH1823. (F, Sp, Su) [I-M].
MATH1823. Calculus and Analytic Geometry I.3 Credit Hours.
Prerequisite: MATH1523 or satisfactory score on the math assessment. Topics include functions, limits, and continuity; differentiation; and applications of differentiation including related rates, maximum-minimum theory, curve sketching, and optimization. A student may not receive credit for this course and MATH1743; duplicates 3 hours of MATH1914. (F, Sp, Su) [I-M].
MATH1914. Differential and Integral Calculus I.4 Credit Hours.
Prerequisite: Satisfactory score on math assessment. Topics include limits and continuity; differentiation; applications of differentiation including related rates, maximum-minimum theory, curve sketching, and optimization; Fundamental Theorem of Calculus; substitution rule; and applications of integration to computation of areas and volumes. Duplicates three hours of MATH1823 and one hour of MATH2423. (F, Sp, Su) [I-M].
MATH2123. Calculus II for Business, Life and Social Sciences.3 Credit Hours.
Prerequisite: MATH1743. Integration of polynomial, exponential and logarithmic functions, including u-substitution. Applications of integrals to the business, life and social sciences, including probability. Partial derivatives including multivariable optimization, Lagrange multipliers, and least squares. A student cannot receive credit for this course and MATH2423. (Sp) [I-M].
MATH2213. Mathematical Systems.3 Credit Hours.
Prerequisite: plane geometry, intermediate algebra, enrollment in an appropriate elementary teachers' program. A systematic analysis of arithmetic and a presentation of intuitive algebra and geometry. Not open to students in the University College. (F, Sp, Su)
MATH2223. Data Analysis and Geometric Systems.3 Credit Hours.
Prerequisite: 0123 at OU or satisfactory score on math placement test and admission to 0802A, 0808A, or 0823A degree programs. Algebra and the structure of number systems, functional relationships, informal geometry. Course is not open to students in University College. (F, Sp)
MATH2423. Calculus and Analytic Geometry II.3 Credit Hours.
Prerequisite: MATH1823 or MATH1914. Topics include integration and its applications; calculus of transcendental functions; indeterminate forms; techniques of integration; and improper integrals. A student may not receive credit for this course and MATH2123; duplicates one hour of MATH1914 and two hours of MATH2924. (F, Sp, Su) [I-M].
MATH2433. Calculus and Analytic Geometry III.3 Credit Hours.
Prerequisite: MATH2423 or MATH2924. Polar coordinates, parametric equations, sequences, infinite series, vector analysis. (F, Sp, Su)
MATH2443. Calculus and Analytic Geometry IV.3 Credit Hours.
Prerequisite: 2433. Vector calculus; functions of several variables; partial derivatives; gradients, extreme values and differentials of multivariate functions; multiple integrals; line and surface integrals. (F, Sp, Su)
MATH2513. Discrete Mathematical Structures.3 Credit Hours.
Prerequisite: MATH2423 or MATH2924 or concurrent enrollment. A course for math majors or prospective math majors. Provides an introduction to discrete concepts such as finite sets and structures, and their properties and applications. Also exposes students to the basic procedures and styles of mathematical proof. Topics include basic set theory, functions, integers, symbolic logic, predicate calculus, induction, counting techniques, graphs and trees. Other topics from combinatorics, probability, relations, Boolean algebras or automata theory may be covered as time permits. (F, Sp, Su)
MATH2924. Differential and Integral Calculus II.4 Credit Hours.
Prerequisite: MATH1914 with a grade of C or better. Topics include calculus of transcendental functions; indeterminate forms; techniques of integration; improper integrals, parametric curves; polar coordinates, infinite sequences and series, vectors in two and three dimensions. Duplicates two hours of MATH2423 and two hours of MATH2433. (F, Sp, Su)
MATH2934. Differential and Integral Calculus III.4 Credit Hours.
Prerequisite: 2924 with grade of C or better. Vectors and vector functions, functions of several variables, partial differentiation and gradients, multiple integration, line and surface integrals, Green-Stokes-Gauss theorems. Duplicates one hour of 2433 and three hours of 2443. (F, Sp, Su)
MATH2970. Special Topics/Seminar.1-3 Credit Hours.
1 to 3 hours. Prerequisite: Permission of instructor. May be repeated; maximum credit nine hours. Special topics or seminar course for content not currently offered in regularly scheduled courses. May include library and/or laboratory research and field projects. (Irreg.)
MATH3113. Introduction to Ordinary Differential Equations.3 Credit Hours.
Prerequisite: MATH2423 or MATH2924. First order ordinary differential equations, linear differential equations with constant coefficients, two-by-two linear systems, Laplace transformations, phase planes and stability. Duplicates two hours of MATH3413. (F, Sp, Su)
MATH3333. Linear Algebra I.3 Credit Hours.
Prerequisite: MATH2123 or MATH1823 or MATH1914 or permission of instructor. Systems of linear equations, determinants, finite dimensional vector spaces, linear transformations and matrices, characteristic values and vectors. (F, Sp, Su)
MATH3401. Numerical Methods With Matlab.1 Credit Hour.
Prerequisite: 3413 or concurrent enrollment. Programming with MATLAB. Numerical solution of nonlinear equations. Matrices and linear algebraic equations, regression, interpolation, splines. Numerical integration. Numerical solution of systems of ordinary differential equations. Numerical solution of partial differential equation. Laboratory (F, Sp)
MATH3413. Physical Mathematics I.3 Credit Hours.
Prerequisite: MATH2443 or MATH2934 or concurrent enrollment. Complex numbers and functions. Fourier series, solution methods for ordinary differential equations and partial differential equations, Laplace transforms, series solutions, Legendre's equation. Duplicates two hours of MATH3113. (F, Sp)
MATH3423. Physical Mathematics II.3 Credit Hours.
Prerequisite: MATH2443 or MATH2934, MATH3413. The Fourier transform and applications, a survey of complex variable theory, linear and nonlinear coordinate transformations, tensors, elements of the calculus of variations. (F)
MATH3440. Mentored Research Experience.3 Credit Hours.
0 to 3 hours. Prerequisites: ENGL1113 or equivalent, and permission of instructor. May be repeated; maximum credit 12 hours. For the inquisitive student to apply the scholarly processes of the discipline to a research or creative project under the mentorship of a faculty member. Student and instructor should complete an Undergraduate Research & Creative Projects (URCP) Mentoring Agreement and file it with the URCP office. Not for honors credit. (F, Sp, Su)
MATH3960. Honors Reading.1-3 Credit Hours.
1 to 3 hours. Prerequisite: admission to Honors Program. May be repeated; maximum credit six hours. Consists of topics designated by the instructor in keeping with the student's major program. Covers materials not usually presented in the regular courses. (F, Sp, Su)
MATH3970. Honors Seminar.1-3 Credit Hours.
1 to 3 hours. Prerequisite: admission to Honors Program. May be repeated; maximum credit six hours. Projects covered will vary. The content will deal with concepts not usually presented in regular coursework. (F, Sp)
MATH3980. Honors Research.1-3 Credit Hours.
1 to 3 hours. Prerequisite: admission to Honors Program. May be repeated; maximum credit six hours. Will provide an opportunity for the gifted Honors candidate to work at a special project in the student's field. (F, Sp, Su)
MATH3990. Independent Study.1-3 Credit Hours.
1 to 3 hours. Prerequisite: one course in general area to be studied; permission of instructor and department. Overall grade point average of 2.50 or better. May be repeated; maximum credit six hours. Contracted independent study for topic not currently offered in regularly scheduled courses. Independent study may include library and/or laboratory research and field projects. (F, Sp, Su)
MATHG4073. Numerical Analysis I.3 Credit Hours.
Prerequisite: 3113 or 3413. Solution of linear and nonlinear equations, approximation of functions, numerical integration and differentiation, introduction to analysis of convergence and errors, pitfalls in automatic computation, one-step methods in the solutions of ordinary differential equations. (F)
MATH4093. Applied Numerical Methods.3 Credit Hours.
(Slashlisted with MATH5093) Prerequisite: MATH2443 or MATH2934, MATH3113 or MATH3413, MATH3333 or MATH4373, or permission of instructor. Numerical treatment of ordinary differential equations, numerical linear algebra and applications, basic numerical methods for partial differential equations. No student may earn credit for both 4093 and 5093. (Alt. Sp.)
MATHG4103. Introduction to Functions of a Complex Variable.3 Credit Hours.
Prerequisite: 3113. Complex analytic functions, conformal mappings, complex integrals. Taylor and Laurent series, integration by the method of residues, complex analytic functions and potential theory. (Sp)
MATH4123. Fourier Transforms.3 Credit Hours.
(Slashlisted with MATH5123) Prerequisite: MATH2443 or MATH2934, MATH3113 or MATH3413, MATH3333, or permission of instructor. Fourier series, classical Fourier transform, discrete Fourier transform, distributions and Fourier transforms. Sampling and Shannon's Theorem. No student may earn credit for both 4123 and 5123. (F)
MATHG4163. Introduction to Partial Differential Equations.3 Credit Hours.
Prerequisite: MATH2443 or MATH2934, MATH3113 or MATH3413. Physical models, classification of equations, Fourier series and boundary value problems, integral transforms, the method of characteristics. (F, Sp, Su)
MATH4193. Introductory Mathematical Modeling.3 Credit Hours.
Prerequisite: MATH3113 or MATH3413, MATH3333, MATH4733 or MATH4753, or permission of instructor. Mathematics models are formulated for problems arising in various areas where mathematics is applied. Techniques are developed for analyzing the problem and testing validity of proposed model. (Sp)
MATHG4313. Introduction to Number Theory.3 Credit Hours.
Prerequisite: 2513 and 3333 or permission of instructor. Topics include factorization and prime numbers, congruence, quadratic residues and reciprocity, continued fractions and approximations, Diophantine equations, arithmetic functions, and selected applications. (Irreg.)
MATHG4323. Introduction to Abstract Algebra I.3 Credit Hours.
Prerequisite: MATH3333 and MATH2513, or permission of instructor. Concepts from set theory; the system of natural numbers, extension from the natural numbers to the integers; semigroups and groups; rings, integral domain and fields. (F, Sp)
MATHG4333. Introduction to Abstract Algebra II.3 Credit Hours.
Prerequisite: 4323. Extensions of rings and fields, elementary factorization theory; groups with operators; modules and ideals; lattices. (Sp)
MATH4373. Abstract Linear Algebra.3 Credit Hours.
(Slashlisted with 5373) Prerequisite: 3333. Vector spaces over arbitrary fields, bases, dimension, linear transformations and matrices, similarity and its canonical forms (rational, Jordan), spectral theorem and diagonalization of quadratic forms. No student may earn credit for both 4373 or 5373. (F, Sp)
MATH4383. Applied Modern Algebra.3 Credit Hours.
(Slashlisted with 5383) Prerequisite: 3333. Topics from the theory of error correcting codes, including Shannon's theorem, finite fields, families of linear codes such as Hamming, Golay, BCH, and Reed-Solomon codes. Other topics such as Goppa codes, group codes, and cryptography as time permits. No student may earn credit for both 4383 and 5383. (Sp)
MATHG4433. Introduction to Analysis I.3 Credit Hours.
Prerequisite: MATH2433 or MATH2924, and MATH2513 or permission of instructor. Review of real number system. Sequences of real numbers. Topology of the real line. Continuity and differentiation of functions of a single variable. (F, Sp, Su)
MATH4443. Introduction to Analysis II.3 Credit Hours.
(Slashlisted with 5443) Prerequisite: 4433. Integration of functions of a single variable. Series of real numbers. Series of functions. Differentiation of functions of more than one variable. No student may earn credit for both 4443 and 5443. (Sp)
MATH4513. Senior Mathematics Seminar.3 Credit Hours.
Prerequisite: MATH2443 or MATH2934; MATH2513; MATH3113 or MATH3413; MATH3333; and senior standing. Capstone course which synthesizes ideas from different areas of mathematics with emphasis on current topics of interest. The course will involve student presentations, written projects and problem solving. (F, Sp) [V].
MATHG4643. Topics in Geometry and Combinatorics.3 Credit Hours.
Prerequisite: 3333. May be repeated with permission of instructor; maximum credit six hours. Topics may include convexity (convex sets, combinatorial theorems in finite dimensional Euclidean space), graph theory, finite geometries, foundations of geometry. (F, Sp)
MATH4653. Introduction To Differential Geometry I.3 Credit Hours.
(Slashlisted with MATH5653) Prerequisite: MATH2443 or MATH2934, and MATH3333, or permission of instructor. Elementary theory of curves and surfaces in three-dimensional Euclidean space, differentiable manifolds, Riemannian geometry of two dimensions, Gauss Theorem Egregium. No student may earn credit for both 4653 and 5653. (F)
MATH4673. Graph Theory I.3 Credit Hours.
(Slashlisted with 5673) Prerequisite: 2513 or permission of instructor. An introduction to the theory of graphs. Topics include basic definitions, cutpoints, blocks, trees, connectivity and Menger's theorem. No student may earn credit for both 4673 and 5673. (F)
MATHG4733. Mathematical Theory of Probability.3 Credit Hours.
Prerequisite: MATH2443 or MATH2934 or concurrent enrollment. Probability spaces, counting techniques, random variables, moments, special distributions, limit theorems. (F)
MATH4743. Introduction to Mathematical Statistics.3 Credit Hours.
(Slashlisted with 5743) Prerequisite: 4733. Mathematical development of basic concepts in statistics: estimation, hypothesis testing, sampling from normal and other populations, regression, goodness-of-fit. No student may earn credit for both 4743 and 5743. (Sp)
MATHG4753. Applied Statistical Methods.3 Credit Hours.
Prerequisite: MATH2123 or MATH2423 or MATH2924 or permission of instructor. Estimation, hypothesis testing, analysis of variance, regression and correlation, goodness-of-fit, other topics as time permits. Emphasis on applications of statistical methods. (F, Sp, Su)
MATH4773. Applied Regression Analysis.3 Credit Hours.
(Slashlisted with 5773) Prerequisite: 3333, 4733 or 4753 or any statistical probability course at an equivalent level. The general regression problem of fitting an equation involving a single dependent variable and several independent variables, estimation and tests of regression parameters, residual analysis, selecting the "best" regression equation. No student may earn credit for both 4773 and 5773. (Alt. F)
MATH4793. Advanced Applied Statistics.3 Credit Hours.
(Slashlisted with 5793) Prerequisite: 4743 or 4753 or equivalent. Survey of advanced applied statistical methods other than applied regression, including exploratory data analysis, analysis of multivariate data (principal components: analysis, multiple analysis of variance, cluster analysis, etc.), and introduction to non-parametric methods. No student may earn credit for both 4793 and 5793. (Alt. F)
MATH4803. Topics in Mathematics.3 Credit Hours.
Prerequisite: permission of instructor. May be repeated with change of content; maximum credit nine hours. Topics may include any area of mathematics; these will be substantial and fundamental subjects not offered in regular courses. (F, Sp, Su)
MATHG4853. Introduction to Topology.3 Credit Hours.
Prerequisite: MATH2433 or MATH2924; and MATH2513; or permission of instructor. Metric spaces and topological spaces, continuity, connectedness, compactness and related topics. (Sp)
MATH4960. Directed Readings.1-4 Credit Hours.
1 to 4 hours. Prerequisite: good standing in University; permission of instructor and dean. May be repeated; maximum credit four hours. Designed for upper-division students who need opportunity to study a specific problem in greater depth than formal course content permits. (Irreg.)
MATH4970. Special Topics/Seminar.1-3 Credit Hours.
1 to 3 hours. Prerequisite: Senior standing or permission of instructor. May be repeated; maximum credit nine hours. Special topics or seminar course for content not currently offered in regularly scheduled courses. May include library and/or laboratory research and field projects. (Irreg.)
MATH4990. Independent Study.1-3 Credit Hours.
1 to 3 hours. Prerequisite: three courses in general area to be studied, permission of instructor and department. May be repeated; maximum credit six hours. Contracted independent study for topic not currently offered in regularly scheduled courses. Independent study may include library and/or laboratory research and field projects. (Sp)
MATH5093. Applied Numerical Methods.3 Credit Hours.
(Slashlisted with MATH4093) Prerequisite: graduate standing and MATH2443 or MATH2934, MATH3113 or MATH3413, MATH3333 or MATH4373, or permission of instructor. Numerical treatment of ordinary differential equations, numerical linear algebra and applications, basic numerical methods for partial differential equations. No student may earn credit for both MATH4093 and MATH5093. (Alt. Sp.)
MATH5103. Mathematical Models.3 Credit Hours.
Prerequisite: permission of instructor or admission to the M.S. program. May be repeated with change of content; maximum credit six hours. Mathematical models are formulated for problems arising in various areas in which mathematics has been applied. In each case, techniques are developed for analyzing the resulting mathematical problem, and this analysis is used to test the validity of the model. (Sp)
MATH5123. Fourier Transforms.3 Credit Hours.
(Slashlisted with MATH4123) Prerequisite: graduate standing and MATH2443 or 2934, MATH3113 or MATH3413, MATH3333, or permission of the instructor. Fourier series, classical Fourier transform, discrete Fourier transform, distributions and Fourier transforms. Sampling and Shannon's Theorem. No student may earn credit for both 4123 and 5123. (F)
MATH5163. Partial Differential Equations.3 Credit Hours.
Prerequisite: 4163 or permission of instructor. First order equations, Cauchy problem for higher order equations, second order equations with constant coefficients, linear hyperbolic equations. (Sp)
MATH5173. Advanced Numerical Analysis I.3 Credit Hours.
Prerequisite: 4433, 4443 or permission of instructor. Topics may include: error analysis of numerical methods for optimization and initial value problems, numerical approximation of aspects of control problems. (Alt. F)
MATH5183. Advanced Numerical Analysis II.3 Credit Hours.
Prerequisite: 4433, 4443 or permission of instructor. Topics may include: analysis of spline approximations as a basis of the finite element method, error analysis for finite element approximation of elliptic and parabolic boundary value problems. (Alt. Sp)
MATH5253. Introduction to Mathematics Pedagogy Research.3 Credit Hours.
Prerequisite: Graduate standing in mathematics or permission of the instructor. This course is intended for students who will be consumers of mathematics education research as well as those who will be producers of this research. The course offers an overview of the mathematics pedagogy research process and a detailed survey of selected aspects of this process. Particular topics including reviewing existing mathematics teaching research literature, designing research studies, gathering research data, analyzing research data, and reporting pedagogical research. (F)
MATH5263. Issues and Problems in Mathematics Pedagogy.3 Credit Hours.
Prerequisite: graduate standing in mathematics or permission of instructor. May be repeated with change of content; maximum credit 12 hours. Considers current issues and perennial problems in undergraduate mathematics teaching. Potential topics include, but are not limited to, use of technology in mathematics instruction, use of group work and other instructional strategies actively engaging students in Mathematics learning, the nature of mathematics learning, research-based practices in teaching undergraduate mathematics, issues of gender and diversity in undergraduate mathematics, the nature of the undergraduate mathematics curriculum. (Sp)
MATH5303. Topics in Group Theory.3 Credit Hours.
Prerequisite: 4323 or permission of instructor. May be repeated with change of content; Maximum credit 15 hours. Topics may include permutation groups, invariant subgroups, prime power groups, abelian groups, generators and relations, free groups, solvable and nilpotent groups, semi-direct products and extensions, automorphism groups, reflection groups, coxeter groups, crystallographic groups, matrix groups and representation group actions. (Irreg.)
MATH5333. Topics in Number Theory.3 Credit Hours.
Prerequisite: at least one mathematics course numbered above 3000, other than 4232. May be repeated with change of content; maximum credit nine hours. Topics may include congruencies, arithmetic functions, quadratic reciprocity, continued fractions, diophantine equations, primality testing, factorization methods, cryptography, quadratic forms and quadratic fields, computational number theory, additive number theory, coding theory, p-adic numbers. (Irreg.)
MATH5353. Abstract Algebra I.3 Credit Hours.
Prerequisite: 4323, permission of instructor. Groups, Sylow theorems, group actions, group presentations. Rings, ideals, polynomial rings, unique factorization. Fields, algebraic and transcendental extensions. (F)
MATH5363. Abstract Algebra II.3 Credit Hours.
Prerequisite: 5353. Galois theory, solvability. Modules over a principal ideal domain. Noetherian ideal theory. Group representations, semisimple rings. Classical groups. (Sp)
MATH5373. Abstract Linear Algebra.3 Credit Hours.
(Slashlisted with 4373) Prerequisite: 3333. Vector spaces over arbitrary fields, bases, dimension, linear transformations and matrices, similarity and its canonical forms (rational, Jordan), spectral theorem and diagonalization of quadratic forms. No student may earn credit for both 4373 and 5373. (F, Sp)
MATH5383. Applied Modern Algebra.3 Credit Hours.
(Slashlisted with MATH4383) Prerequisite: MATH3333. Topics from the theory of error correcting codes, including Shannon's theorem, finite fields, families of linear codes such as Hamming, Golay, BCH, and Reed-Solomon codes. Other topics such as Goppa codes, group codes, and cryptography as time permits. No student may earn credit for both 4383 and 5383. (Sp)
MATH5403. Calculus of Variations.3 Credit Hours.
Prerequisite: 4433 or 3423 or 4163. Linear spaces, global and local theories of optimization, necessary conditions for relative extrema of integrals. (Irreg.)
MATH5423. Complex Analysis I.3 Credit Hours.
Prerequisite: 4433. The complex numbers, topologies of the extended plane and related sphere, elementary functions, power series, properties of general holomorphic functions. The integral of a complex-valued function over an oriented rectifiable curve, the classical theorems on integrals, Taylor and Laurent expansions, analytic continuation, introduction to Riemann surfaces. (Alt. F)
MATH5443. Introduction To Analysis II.3 Credit Hours.
(Slashlisted with 4443) Prerequisite: 4433. Integration of functions of a single variable. Series of real numbers. Series of functions. Differentiation of functions of more than one variable. No student may earn credit for both 4443 and 5443. (Sp)
MATH5453. Real Analysis I.3 Credit Hours.
Prerequisite: 4433 or permission of instructor. Lebesgue measure and integration theory, absolutely continuous functions, metric spaces. (F)
MATH5463. Real Analysis II.3 Credit Hours.
Prerequisite: 5453. General measure and integration theory, Banach spaces, topics from related areas. (Sp)
MATH5653. Introduction To Differential Geometry I.3 Credit Hours.
(Slashlisted with MATH4653) Prerequisite: graduate standing and MATH2443 or MATH2934, and MATH3333, or permission of instructor. Elementary theory of curves and surfaces in three-dimensional Euclidean space, differentiable manifolds, Riemannian geometry of two dimensions, Gauss Theorem Egregium. No student may earn credit for both 4653 and 5653. (F)
MATH5673. Graph Theory I.3 Credit Hours.
(Slashlisted with 4673) Prerequisite: 2513 or permission of instructor. An introduction to the theory of graphs. Topics include basic definitions, cutpoints, blocks, trees, connectivity and Menger's theorem. No student may earn credit for both 4673 and 5673. (F)
MATH5693. Topics in Geometry and Combinatorics I.3 Credit Hours.
Prerequisite: permission of instructor. May be repeated with permission of instructor; maximum credit 12 hours. Topics may include convexity, combinatorial geometry, graph theory, or Riemannian geometry. (F, Sp, Su)
MATH5743. Introduction to Mathematical Statistics.3 Credit Hours.
(Slashlisted with 4743) Prerequisite: 4733. Mathematical development of basic concepts in statistics: estimation, hypothesis testing, sampling from normal and other populations; regression, goodness of fit. No student may earn credit for both 4743 and 5743. (Sp)
MATH5763. Introduction to Stochastic Processes.3 Credit Hours.
Prerequisite: 4733 or permission of instructor. Stochastic processes in discrete time including random walks, recurrent events, Markov chains and branching processes. Processes in continuous time including linear and nonlinear birth-death processes and diffusions. Applications taken from economics, engineering, operations research. (Irreg.)
MATH5773. Applied Regression Analysis.3 Credit Hours.
(Slashlisted with 4773) Prerequisite: 3333, 4733 or 4753 or any statistical probability course at an equivalent level. The general regression problem of fitting an equation involving a single dependent variable and several independent variables, estimation and tests of regression parameters, residual analysis, selecting the "best" regression equation. No student may earn credit for both 4773 and 5773. (Alt. F)
MATH5793. Advanced Applied Statistics.3 Credit Hours.
(Slashlisted with 4793) Prerequisite: 4743 or 4753 or equivalent. Survey of advanced applied statistical methods other than applied regression, including exploratory data analysis, analysis of multivariate data (principal components: analysis, multiple analysis of variance, cluster analysis, etc.), and introduction to non-parametric methods. No student may earn credit for both 4793 and 5793. (Alt. F)
MATH5803. Topics in Mathematics.3 Credit Hours.
Prerequisite: permission of instructor. May be repeated with change of content; maximum credit fifteen hours. Topics may include any area of mathematics; these will be substantial and fundamental subjects not offered in regular courses. (F, Sp, Su)
MATH5853. Topology I.3 Credit Hours.
Prerequisite: 2433 and 2513. Set theory, separation axioms, connectedness, compactness, continuity, metric spaces, nets and sequences. (F)
MATH5863. Topology II.3 Credit Hours.
Prerequisite: 5853. Metrization, product and quotient spaces, function spaces, dimension theory, Hilbert spaces, hom*otopy, simplicial complexes, continua. (Sp)
MATH5900. Graduate Mathematics Readings.1-3 Credit Hours.
1 to 3 hours. Prerequisite: six-hour mathematics sequence at the 5000+ level. May be repeated with change of content; maximum credit fifteen hours. Special background readings in advanced mathematical topics as preparation for later dissertation work. (F, Sp, Su)
MATH5920. Seminar--Algebra and Theory of Numbers.1-2 Credit Hours.
1 to 2 hours. Prerequisite: permission of instructor. May be repeated with change of content; maximum credit 12 hours. (F, Sp)
MATH5930. Seminar--Geometry and Topology.1-2 Credit Hours.
1 to 2 hours. Prerequisite: permission of instructor. May be repeated with change of content; maximum credit 12 hours. (F, Sp)
MATH5950. Seminar-Undergraduate Mathematics Curriculum & Pedagogy.1-2 Credit Hours.
1 to 2 hours. May be repeated with change of content; maximum credit 12 hours. This seminar will explore the current research literature on undergraduate mathematics curriculum and pedagogy. (F, Sp)
MATH5960. Directed Readings.1-3 Credit Hours.
1 to 3 hours. Prerequisite: graduate standing and permission of department. May be repeated; maximum credit twelve hours. Directed readings and/or literature reviews under the direction of a faculty member. (F, Sp, Su)
MATH5970. Special Topics/Seminar.1-3 Credit Hours.
1 to 3 hours. Prerequisite: Graduate standing or permission of instructor. May be repeated; maximum credit nine hours. Special topics or seminar course for content not currently offered in regularly scheduled courses. May include library and/or laboratory research and field projects. (Irreg.)
MATH5980. Research for Master's Thesis.2-9 Credit Hours.
Variable enrollment, two to nine hours; maximum credit applicable toward degree, four hours. (F, Sp)
MATH5990. Special Problems in Mathematics.1-2 Credit Hours.
1 to 2 hours. An option for all candidates for the master's degree who do not present theses. (F, Sp, Su)
MATH6303. Literacy in Algebra.3 Credit Hours.
Prerequisite: Graduate standing and MATH5363; May be repeated with change of content; maximum credit 15 hours. This course will cover three independent advanced topics in the general area of Algebra. Some past topics have included: plane curves and singularities; introduction to buildings; invariant theory; representation stability; Morita theorems and Tannaka duality; computational commutative algebra; quiver representations; friezes; p-adic and motivic integration; introduction to algebraic analysis. (Irreg.)
MATH6333. Lie Theory I.3 Credit Hours.
Prerequisites: 5363 and 5863 or permission of the instructor. Basic properties of Lie algebras, nilpotent and solvable Lie algebras, semi-simple Lie algebras, root systems and classification theorems. (Irreg.)
MATH6343. Lie Theory II.3 Credit Hours.
Prerequisite: 6333 or permission of the instructor. Representation theory of semi-simple Lie algebras, Lie groups, connections between Lie groups and Lie algebras, structure theory and representation theory of compact Lie groups. (Irreg.)
MATH6373. Commutative Algebra.3 Credit Hours.
Prerequisite: 4323, 4333, 5333 or permission of instructor. Commutative rings and their modelus, ideals, prime ideals, Noetherian modules and rings, localization, principal and factorial rings, discrete valuation domains, Dedekind domains, integral ring extensions, dimension theory, tensor products, flat modules, the hom*ofunctor, injective and projective modules, regular rings, Cohen-Macauley rings. (Irreg.)
MATH6383. Algebraic Geometry.3 Credit Hours.
Prerequisite: 6373. Hilbert's Nullstellensatz, the correspondence between ideals and algebraic sets, Zariski topology, irreducible algebraic sets, ringed spaces, morphisms, affine varieties, algebraic varieties, regular maps, sub-varieties and products, bi-rational equivalence, local rings and tangent spaces, differentials, non-singular points. (Irreg.)
MATH6393. Topics in Algebra.3 Credit Hours.
Prerequisite: 5353 or permission of instructor. May be repeated with change of content; maximum credit 15 hours. Topics of modern research interest in algebra. (Irreg.)
MATH6403. Literacy in Analysis.3 Credit Hours.
Prerequisite: Graduate standing and MATH5463; May be repeated with change of content; maximum credit 15 hours. This course will cover three independent advanced topics in the general area of Analysis. Some past topics have included: Sobolev spaces; C*-algebras; analysis of partial differential operators; distributions; holomorphic functional calculus; interpolation spaces; symbolic dynamics; Hardy spaces; perturbation theory and fixed point theorems; regularity theory for elliptic PDE. (Irreg.)
MATH6473. Functional Analysis I.3 Credit Hours.
Prerequisite: 5463 or permission of instructor. Vector spaces with topology or norm, dual space, theorems on linear operators, spectral theory in Hilbert space, spectral decomposition of operators, convex sets and weak topologies, fixed point theorems. (Alt. F)
MATH6483. Functional Analysis II.3 Credit Hours.
Prerequisite: 6473. Banach algebras and harmonic analysis, representations of symmetric rings, unitary representations of a group, rings of operators in Hilbert space, decomposition of ring operators. Introduction to the theory of distributions. (Alt. Sp)
MATH6493. Topics in Analysis.3 Credit Hours.
Prerequisite: 5453 or permission of instructor. May be repeated with change of course content; maximum credit 15 hours. Topics of modern research interest in analysis. (F, Sp)
MATH6673. Differential Geometry I.3 Credit Hours.
Prerequisite: 5853 or permission of instructor. Multilinear algebra, differential manifolds, exterior differential forms, affine connections, Riemannian manifolds. (F)
MATH6683. Differential Geometry II.3 Credit Hours.
Prerequisite: 6673. Riemannian manifolds, theory of connections, bundles with classical groups as structure groups, curvature and Betti numbers, complex manifolds. (Sp)
MATH6803. Literacy in Topology.3 Credit Hours.
Prerequisite: Graduate standing and MATH5863; May be repeated with change of content; maximum credit 15 hours. This course will cover three independent advanced topics in the general area of Topology. Some past topics have included: Mostow rigidity; group cohom*ology; curvature and topology; Morse theory; ergodicity of geodesic flow; Bass-Serre theory; deRham cohom*ology; introduction to mapping class groups; K-theory; geometry of metric spaces; the homeomorphism group of the circle; topology of 3-manifolds. (Irreg.)
MATH6813. Algebraic Topology I.3 Credit Hours.
Prerequisite: 5863. Introduction to hom*ology theory of spaces, fundamental group and covering spaces, higher hom*otopy groups, CW-complexes and cellular hom*ology, Whitehead and Hurewicz theorems, Eilenberg-Steenrod axioms. (F)
MATH6823. Algebraic Topology II.3 Credit Hours.
Prerequisite: 6813. Topics in cohom*ology and hom*ology theory, universal coefficient theorems, orientation and duality on manifolds. Further topics may include: obstruction theory, cohom*ology operations, fibre bundles and characteristic classes, theory of sheaves, Eilenberg-MacLane spaces and Postnikov systems, spectral sequences. (Sp)
MATH6833. Topics in Topology I.3 Credit Hours.
Prerequisite: 5863. May be repeated with permission of instructor; maximum credit 15 hours. Topics may include algebraic topology, combinatorial topology, linear topological spaces, dimension theory, metrization, continua, decomposition spaces, topology of flat spaces. (F, Sp)
MATH6910. Seminar--Analysis.1-2 Credit Hours.
1 to 2 hours. Prerequisite: permission of the instructor. May be repeated with change of content; maximum credit 15 hours. Seminar on analysis and applied mathematics topics. (F, Sp)
MATH6930. Seminar--Geometry and Topology.1-2 Credit Hours.
1 to 2 hours. Prerequisite: permission of the instructor. May be repeated with change of content; maximum credit 12 hours. (F, Sp)
MATH6960. Directed Readings.1-3 Credit Hours.
1 to 3 hours. Prerequisite: graduate standing or permission of instructor. May be repeated; maximum credit six hours. Directed readings and/or literature review under the direction of a faculty member. (Irreg.)
MATH6970. Special Topics/Seminar.1-3 Credit Hours.
1 to 3 hours. Prerequisite: graduate standing or permission of instructor. May be repeated; maximum credit 12 hours. Special topics or seminar course for content not currently offered in regularly scheduled courses. May include library and/or research and field projects. (Irreg.)
MATH6980. Research for Doctoral Dissertation.2-16 Credit Hours.
2 to 16 hours. Prerequisite: Graduate standing and permission of instructor; may be repeated. Directed research culminating in the completion of the doctoral dissertation. (F, Sp, Su)
MATH6990. Independent Study.1-3 Credit Hours.
1 to 3 hours. Prerequisite: Graduate standing and permission of instructor. May be repeated; maximum credit nine hours. Contracted independent study for a topic not currently offered in regularly scheduled courses. Independent study may include library and/or laboratory research and field projects. (Irreg.)
