SUBJ	COURSE	TITLE	DECRIPTION
MATH	0113	Elementary Algebra	Prerequisite: completion of placement test. For students who score in the lowest bracket on the placement test. A review of beginning algebra including polynomial arithmetic, solving equations, graphing, inequalities, and the quadratic equation. Not acceptable for degree credit at the University of Oklahoma. (F, Sp, Su)
MATH	0115	Fundamental Algebra	Prerequisite: placement test. Combines the course content of Math 0113 and 0123. A review of beginning algebra including polynomial arithmetic, solving equations, graphing, inequalities, rational expressions, exponents and radicals, imaginary and complex numbers, quadratic equations, systems of linear equations. Not acceptable for degree credit at the University of Oklahoma. (F, Sp, Su)
MATH	0123	Intermediate Algebra	Prerequisite: 0113 at OU, or satisfactory score on the placement test, or satisfactory score on the ACT/SAT. Properties of real numbers, equations and inequalities, algebra of rational expressions, exponents and radicals, introduction to quadratic equations, functions and graphs, systems of linear equations. Not acceptable for degree credit at the University of Oklahoma. (F, Sp, Su)
MATH	0999	Remedial Transfer Credit	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.
MATH	1473	Mathematics for Critical Thinking	Prerequisite: "C" or better in DMAT 0123 at OU, or satisfactory score on the placement test, or, for incoming freshmen direct from high school, satisfactory score on the ACT/SAT. 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]
MATH	1503	College Algebra	Prerequisite: "C" or better in DMAT 0123 at OU, or satisfactory score on the placement test, or, for incoming freshmen direct from high school, satisfactory score on the ACT/SAT. Review of basic algebraic skills such as multiplying and factoring polynomials, rational expressions, linear equations and inequalities, exponents and radicals, absolute values. Other topics include the concept, notation, and algebra of functions, functions of linear, polynomial, rational, exponential, and logarithmic type, systems of equations. A student may not receive credit for this course and 1643. (F, Sp, Su) [I-M]
MATH	1523	Precalculus and Trigonometry	Prerequisite: 1503 at OU, or satisfactory score on the placement test, or, for incoming freshmen direct from high school, satisfactory score on the ACT/SAT. Review of function concepts. Topics covered include properties of functions, exponential and logarithmic functions, trigonometric functions and their inverses by unit circle and triangle approaches, trigonometric equations and identities, simple conic sections, polar coordinates, Demoivre's theorem, discrete algebra, induction, limits and continuity. (F, Sp, Su) [I-M]
MATH	1643	Precalculus for Business, Life, and Social Sciences	Prerequisite: "C" or better in DMAT 0123 at OU, or satisfactory score on the placement test, or, for incoming freshmen direct from high school, satisfactory score on the ACT/SAT. Review of basic algebra skills. Topics covered include linear functions, exponential and logarithmic functions, systems of linear equations and inequalities, matrices and operations on matrices, linear programming, introductory trigonometry, elementary probability and statistics. A student may not receive credit for this course and 1503. (F, Sp, Su) [I-M]
MATH	1743	Calculus I for Business, Life and Social Sciences	Prerequisite: 1523 or 1643 at OU, or satisfactory score on the placement test, or, forincoming freshmen direct form high school, satisfactory score on the ACT/SAT. Topics in differentiation and integration of polynomial, exponential and logarithmic functions. Applications to the business, life and social sciences. A student may not receive credit for this course and 1823. (F, Sp, Su) [I-M]
MATH	1823	Calculus and Analytic Geometry I	Prerequisite: 1523 at OU, or satisfactory score on the placement test, or, for incoming freshmen direct from high school, satisfactory score on the ACT/SAT. Topics covered include equations of straight lines; conic sections; functions, limits and continuity; differentiation; maximum-minimum theory and curve sketching. A student may not receive credit for this course and 1743. (F, Sp, Su) [I-M]
MATH	1914	Differential and Integral Calculus I	Prerequisite: satisfactory score on the placement test or, for incoming freshmen direct from high school, satisfactory score on the ACT/SAT. Duplicates three hours of 1823 and one hour of 2423. Limits and continuity, differentiation, applications of differentiation to optimization and curve sketching, integration, the fundamental theorem of calculus, the substitution rule, applications of integration to computation of areas. (F, Sp, Su) [I-M]
MATH	1999	Lower Division Transfer Credit	This is not a course offered at the University of Oklahoma. It is used to denote lower division transfer credit for which there is no OU equivalent course.
MATH	2123	Calculus II for Business, Life and Social Sciences	Prerequisite: 1743. Differentiation and integration of exponential and logarithmic functions; simple differential equations; partial derivatives; double integrals, probability. Applications to the business, life and social sciences. A student may not receive credit for this course and 2423. (F, Sp, Su) [I-M]
MATH	2213	Mathematical Systems	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)
MATH	2223	Data Analysis and Geometric Systems	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)
MATH	2423	Calculus and Analytic Geometry II	Prerequisite: 1823. Integration and its applications; the calculus of transcendental functions; techniques of integration; and the introduction to differential equations. A student may not receive credit for this course and 2123. (F, Sp, Su) [I-M]
MATH	2433	Calculus and Analytic Geometry III	Prerequisite: 2423. Polar coordinates, parametric equations, sequences, infinite series, vector analysis. (F, Sp, Su)
MATH	2443	Calculus and Analytic Geometry IV	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)
MATH	2513	Discrete Mathematical Structures	Prerequisite: MATH 2423 or MATH 2924 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)
MATH	2924	Differential and Integral Calculus II	Prerequisite: 1914 with a grade of C or better. Duplicates two hours of 2423 and two hours of 2433. Further applications of integration, the natural logarithmic and exponential functions, indeterminate forms, techniques of integration, improper integrals, parametric curves and polar coordinates, infinite sequences and series. (F, Sp, Su)
MATH	2934	Differential and Integral Calculus III	Prerequisite: 2924 with grade of C or better. Duplicates one hour of 2433 and three hours of 2443. Vectors and vector functions, functions of several variables, partial differentiation and gradients, multiple integration, line and surface integrals, Green-Stokes-Gauss theorems. (F,Sp,Su)
MATH	3113	Introduction to Ordinary Differential Equations	Prerequisite: MATH 2423 or MATH 2924. Duplicates two hours of 3413. First order ordinary differential equations, linear differential equations with constant coefficients, two-by-two linear systems, Laplace transformations, phase planes and stability. (F, Sp, Su)
MATH	3333	Linear Algebra I	Prerequisite: MATH 2433 or MATH 2934 or permission of instructor. Systems of linear equations, determinants, finite dimensional vector spaces, linear transformations and matrices, characteristic values and vectors. (F, Sp, Su)
MATH	3401	Numerical Methods With Matlab	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)
MATH	3413	Physical Mathematics I	Prerequisite: MATH 2443 or MATH 2934 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 3113. (F)
MATH	3423	Physical Mathematics II	Prerequisite: MATH 2443 or MATH 2934, MATH 3413. The Fourier transform and applications, a survey of complex variable theory, linear and nonlinear coordinate transformations, tensors, elements of the calculus of variations. (F, Sp)
MATH	3613	Modern Geometry	Prerequisite: MATH 1743 or MATH 1823 or MATH 1914. An introduction to geometry including axiomatics, finite geometry, convexity, and classical Euclidean and non-Euclidean geometry. (F, Sp)
MATH	3960	Honors Reading	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)
MATH	3980	Honors Research	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)
MATH	3990	Independent Study	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)
MATH	3999	Upper Division Transfer Credit	This is not a course offered at the University of Oklahoma. It is used to denote upper division transfer credit for which there is no OU equivalent course.
MATH	4073	Numerical Analysis I	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)
MATH	4093	Applied Numerical Methods	Prerequisite: 2443, 3113 or 3413, 3333 or 4373, or permission of the 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.)
MATH	4103	Introduction to Functions of a Complex Variable	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)
MATH	4113	Topics in Applied Mathematics	(Slashlisted with 5113) Prerequisite: permission of instructor. May be repeated with change of content; maximum credit nine hours. Algebraic coding theory, linear finite state workings, numerical analysis of differential equations, asymptotic analysis, game theory or other subjects. No student may earn credit for both 4113 and 5113. (Irreg.)
MATH	4123	Fourier Transforms	(Slashlisted with 5123) Prerequisite: MATH 2443, MATH 3113 or MATH 3413, MATH 3333, 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)
MATH	4163	Introduction to Partial Differential Equations	Prerequisite: 2443, 3113 or 3413. Physical models, classification of equations, Fourier series and boundary value problems, integral transforms, the method of characteristics. (F, Sp, Su)
MATH	4193	Introductory Mathematical Modeling	Prerequisite: 3113 or 3413, 3333, 4733 or 4753, 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. (F)
MATH	4232	Specialized Topics and Methods--a Teachers' Course	Prerequisite: 2433. Selected specialized topics and methods relevant to the secondary school mathematics curriculum. Content will vary, but will include problem solving, use of computers in teaching secondary school mathematics, specialized methods for teaching algebra and geometry, teaching probability and statistics at the secondary level, or other appropriate content and methods not covered in EDMA 4242. For major credit only for those in teacher certification programs. (F)
MATH	4313	Introduction to Number Theory	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.)
MATH	4323	Introduction to Abstract Algebra I	Prerequisite: MATH 3333 and MATH 2513, 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)
MATH	4333	Introduction to Abstract Algebra II	Prerequisite: 4323. Extensions of rings and fields, elementary factorization theory; groups with operators; modules and ideals; lattices. (Sp)
MATH	4373	Abstract Linear Algebra	(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)
MATH	4383	Applied Modern Algebra	(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)
MATH	4413	Intermediate Ordinary Differential Equations	Prerequisite: 3113 or 3413; 3333. Duplicates one hour of 4323. Topics selected from: linear systems of equations, integral equations, stability theory, existence and uniqueness criteria, perturbation theory, dynamical systems, boundary-value problems, numerical methods. (Irreg.)
MATH	4433	Introduction to Analysis I	Prerequisite: 2433 and 2513 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)
MATH	4443	Introduction to Analysis II	(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)
MATH	4513	Senior Mathematics Seminar	Prerequisite: MATH 2443 or MATH 2934; MATH 2513; MATH 3113 or MATH 3413; MATH 3333; 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]
MATH	4623	Convexity Theory I	(Slashlisted with 5623) Prerequisite: 2513 and 3333, or permission of instructor. An introduction to the theory of convex sets. Topics include basic definitions and properties, separating and supporting hyperplanes, and combinatorial theorems of Caratheodory, Radon and Helly. No student may earn credit for both 4623 and 5623. (F)
MATH	4643	Topics in Geometry and Combinatorics	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)
MATH	4653	Introduction To Differential Geometry I	(Slashlisted with 5653) Prerequisite: 2433 and 3333, 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)
MATH	4663	Introduction to Differential Geometry II	(Slashlisted with 5663) Prerequisite: 4653 or 5653. Intermediate theory of surfaces, covariant differentiation, geodesics, Gauss-Bonnet Theorem. Further topics may include: rigidity theorems, minimal surfaces, the Hopf-Rinow Theorem, the Hadamard Theorem, index of vector fields. No student may earn credit for both 4663 and 5663. (Sp)
MATH	4673	Graph Theory I	(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)
MATH	4733	Mathematical Theory of Probability	Prerequisite: MATH 2443 or MATH 2934 or concurrent enrollment. Probability spaces, counting techniques, random variables, moments, special distributions, limit theorems. (F)
MATH	4743	Introduction to Mathematical Statistics	(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)
MATH	4753	Applied Statistical Methods	Prerequisite: MATH 2123 or MATH 2423 or MATH 2924 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)
MATH	4773	Applied Regression Analysis	(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)
MATH	4793	Advanced Applied Statistics	(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)
MATH	4803	Topics in Mathematics	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)
MATH	4853	Introduction to Topology	Prerequisite: MATH 2433 or MATH 2924; and MATH 2513; or permission of instructor. Metric spaces and topological spaces, continuity, connectedness, compactness and related topics. (Sp)
MATH	4960	Directed Readings	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.)
MATH	4970	Special Topics/Seminar	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.)
MATH	4990	Independent Study	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)
MATH	5093	Applied Numerical Methods	Prerequisite: 2443, 3113 or 3413, 3333 or 4373, or permission of the 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.)
MATH	5103	Mathematical Models	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)
MATH	5113	Topics in Applied Mathematics	(Slashlisted with 4113) Prerequisite: permission of instructor. May be repeated with change of content;maximum credit fifteen hours. Algebraic coding theory, linear finite state workings, numerical analysis of differential equations, asymptotic analysis, game theory or other subjects. No student may earn credit for both 4113 and 5113. (Irreg.)
MATH	5123	Fourier Transforms (Slashlisted with 4123)	Slashlisted with 4123. Prerequisite: MATH 2443, MATH 3113 or MATH 3413, MATH 3333, 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)
MATH	5163	Partial Differential Equations	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)
MATH	5173	Advanced Numerical Analysis I	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)
MATH	5183	Advanced Numerical Analysis II	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)
MATH	5253	Introduction to Mathematics Pedagogy Research	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)
MATH	5263	Issues and Problems in Mathematics Pedagogy
MATH	5303	Topics in Group Theory	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.)
MATH	5333	Topics in Number Theory	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.)
MATH	5353	Abstract Algebra I	Prerequisite: 4323, permission of instructor. Groups, Sylow theorems, group actions, group presentations. Rings, ideals, polynomial rings, unique factorization. Fields, algebraic and transcendental extensions. (F)
MATH	5363	Abstract Algebra II	Prerequisite: 5353. Galois theory, solvability. Modules over a principal ideal domain. Noetherian ideal theory. Group representations, semisimple rings. Classical groups. (Sp)
MATH	5373	Abstract Linear Algebra	(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)
MATH	5383	Applied Modern Algebra	(Slashlisted with 4383) 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. Duplicates one hour of 4323. (Sp)
MATH	5403	Calculus of Variations	Prerequisite: 4433 or 3423 or 4163. Linear spaces, global and local theories of optimization, necessary conditions for relative extrema of integrals. (Irreg.)
MATH	5423	Complex Analysis I	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)
MATH	5433	Complex Analysis II	Prerequisite: 5423. Selected topics from classical and modern function theory such as geometric theory, univalent functions, Hardy spaces and Nevanlinna theory. (Alt. Sp)
MATH	5443	Introduction To Analysis II	(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)
MATH	5453	Real Analysis I	Prerequisite: 4433 or permission of instructor. Lebesgue measure and integration theory, absolutely continuous functions, metric spaces. (F)
MATH	5463	Real Analysis II	Prerequisite: 5453. General measure and integration theory, Banach spaces, topics from related areas. (Sp)
MATH	5483	Wavelets	Prerequisite: 3113 or 3413 and 3333. Fourier analysis on a finite cyclic group, the group of integers, and the real line. The matching pursuit algorithm. The Poisson summation formula and sampling. Multi-resolution analysis, various wavelet constructions (including those of Daubechies and Meyer) and filter banks. An introduction to the MATLAB wavelet toolbox. (F)
MATH	5623	Convexity Theory I	(Slashlisted with 4623) Prerequisite: 3333, 2513 or permission of instructor. An introduction to the theory of convex sets. Topics include basic definitions and properties, separating and supporting hyperplanes, and combinatorial theorems of Caratheodory, Radon and Helly. No student may earn credit for both 4623 and 5623. (F)
MATH	5633	Convexity Theory II	Prerequisite: 5623 or permission of instructor. A continuation of the study of convex sets. Topics include Helly-type theorems, the Blaschke selection theorem, alternate characterizations of convex sets, convex polytopes and Eveler's formula. (Sp)
MATH	5653	Introduction To Differential Geometry I	(Slashlisted with 4653) Prerequisite: 2433 and 3333, 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)
MATH	5663	Introduction to Differential Geometry II	(Slashlisted with 4663) Prerequisite: 4653 or 5653. Intermediate theory of surfaces, covariant differentiation, geodesics, Gauss-Bonnet Theorem. Further topics may include: rigidity theorems, minimal surfaces, the Hopf-Rinow Theorem, the Hadamard Theorem, index of vector fields. No student may earn credit for both 4663 and 5663. (Sp)
MATH	5673	Graph Theory I	(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)
MATH	5683	Graph Theory II	Prerequisite: 5673 or permission of instructor. A continuation of the study of graphs. Topics include partitions, Eulerian and Hamiltonian graphs, planarity and colorability. (Sp)
MATH	5693	Topics in Geometry and Combinatorics I	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)
MATH	5743	Introduction to Mathematical Statistics	(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)
MATH	5763	Introduction to Stochastic Processes	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.)
MATH	5773	Applied Regression Analysis	(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)
MATH	5783	Topics in Mathematical Statistics	Prerequisite: 4743. May be repeated with change of content; maximum credit 15 hours. Topics may include stochastic processes, linear models, non-parametric methods, experimental design, sequential analysis, decision theory, etc. (Irreg.)
MATH	5793	Advanced Applied Statistics	(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)
MATH	5803	Topics in Mathematics	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)
MATH	5853	Topology I	Prerequisite: 2433 and 2513. Set theory, separation axioms, connectedness, compactness, continuity, metric spaces, nets and sequences. (F)
MATH	5863	Topology II	Prerequisite: 5853. Metrization, product and quotient spaces, function spaces, dimension theory, Hilbert spaces, homotopy, simplicial complexes, continua. (Sp)
MATH	5900	Graduate Mathematics Readings	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)
MATH	5910	Seminar--Analysis	1 to 2 hours. Prerequisite: permission of instructor. May be repeated with change of content; maximum credit 12 hours. (F, Sp)
MATH	5920	Seminar--Algebra and Theory of Numbers	1 to 2 hours. Prerequisite: permission of instructor. May be repeated with change of content; maximum credit 12 hours. (F, Sp)
MATH	5930	Seminar--Geometry and Topology	1 to 2 hours. Prerequisite: permission of instructor. May be repeated with change of content; maximum credit 12 hours. (F, Sp)
MATH	5940	Seminar--Applied Mathematics and Statistics	1 to 2 hours. May be repeated with change of content; maximum credit 12 hours. (F, Sp)
MATH	5950	Seminar-Undergraduate Mathematics Curriculum & Pedagogy	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)
MATH	5960	Directed Readings	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)
MATH	5970	Special Topics/Seminar	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.)
MATH	5980	Research for Master's Thesis	Variable enrollment, two to nine hours; maximum credit applicable toward degree, four hours. (F, Sp)
MATH	5990	Special Problems in Mathematics	1 to 2 hours. An option for all candidates for the master's degree who do not present theses. (F, Sp, Su)
MATH	5999	Graduate Level Transfer Credit	This is not a course offered at the University of Oklahoma. It is used to denote graduate level transfer credit for which there is no OU equivalent course.
MATH	6333	Lie Theory I	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.)
MATH	6343	Lie Theory II	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.)
MATH	6373	Commutative Algebra	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 homofunctor, injective and projective modules, regular rings, Cohen-Macauley rings. (Irreg.)
MATH	6383	Algebraic Geometry	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.)
MATH	6393	Topics in Algebra	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.)
MATH	6443	Topics in Differential Equations	Prerequisite: permission of instructor. May be repeated with change of content; maximum credit 15 hours. Topics include, but are not limited to, dynamical systems, nonlinear boundary value problems, parameter identification theory, wave theory, nonlinear functional analysis. (F, Sp)
MATH	6473	Functional Analysis I	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)
MATH	6483	Functional Analysis II	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)
MATH	6493	Topics in Analysis	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)
MATH	6673	Differential Geometry I	Prerequisite: 5853 or permission of instructor. Multilinear algebra, differential manifolds, exterior differential forms, affine connections, Riemannian manifolds. (F)
MATH	6683	Differential Geometry II	Prerequisite: 6673. Riemannian manifolds, theory of connections, bundles with classical groups as structure groups, curvature and Betti numbers, complex manifolds. (Sp)
MATH	6693	Topics in Geometry and Combinatorics II	Prerequisite: permission of instructor. May be repeated with permission of instructor; maximum credit 12 hours. Topics may include convexity, combinatorial geometry, graph theory, linear topological spaces, metric geometry, differential geometry or Riemannian geometry. (F, Sp)
MATH	6813	Algebraic Topology I	Prerequisite: 5863. Introduction to homology theory of spaces, fundamental group and covering spaces, higher homotopy groups, CW-complexes and cellular homology, Whitehead and Hurewicz theorems, Eilenberg-Steenrod axioms. (F)
MATH	6823	Algebraic Topology II	Prerequisite: 6813. Topics in cohomology and homology theory, universal coefficient theorems, orientation and duality on manifolds. Further topics may include: obstruction theory, cohomology operations, fibre bundles and characteristic classes, theory of sheaves, Eilenberg-MacLane spaces and Postnikov systems, spectral sequences. (Sp)
MATH	6833	Topics in Topology I	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)
MATH	6843	Topics in Topology II	Prerequisite: 6833. 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)
MATH	6910	Seminar--Analysis	1 to 2 hours. Prerequisite: permission of the instructor. May be repeated with change of content; maximum credit 15 hours. (F, Sp)
MATH	6920	Seminar--Algebra	1 to 2 hours. Prerequisite: permission of the instructor. May be repeated with change of content; maximum credit 12 hours. (F, Sp)
MATH	6930	Seminar--Geometry and Topology	1 to 2 hours. Prerequisite: permission of the instructor. May be repeated with change of content; maximum credit 12 hours. (F, Sp)
MATH	6960	Directed Readings	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.)
MATH	6970	Special Topics/Seminar	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 currenty offered in regularly scheduled courses. May include library and/or research and field projects. (Irreg.)
MATH	6980	Research for Doctoral Dissertation	(F, Sp, Su)
MATH	6990	Independent Study	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.)