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) [IM] 
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) [IM] 
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) [IM] 
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) [IM] 
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) [IM] 
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; maximumminimum theory and curve sketching. A student may not receive credit for this course and 1743. (F, Sp, Su) [IM] 
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) [IM] 
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) [IM] 
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) [IM] 
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, GreenStokesGauss 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, twobytwo 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 nonEuclidean 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, onestep 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 Methodsa 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 ReedSolomon 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, boundaryvalue 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 threedimensional 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, GaussBonnet Theorem. Further topics may include: rigidity theorems, minimal surfaces, the HopfRinow 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, goodnessoffit. 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, goodnessoffit, 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 nonparametric 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 upperdivision 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 
Prerequisite: Graduate standing in mathematics of permission of the instructor. This course 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, researchbased practices in teaching undergraduate mathematics, issues of gender and diversity in undergraduate mathematics, the nature of the undergraduate mathematics curriculum. (Sp) 
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, semidirect 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, padic 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 ReedSolomon 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 complexvalued 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. Multiresolution 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 Hellytype 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 threedimensional 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, GaussBonnet Theorem. Further topics may include: rigidity theorems, minimal surfaces, the HopfRinow 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 birthdeath 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, nonparametric 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 nonparametric 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: sixhour 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 
SeminarAnalysis 
1 to 2 hours. Prerequisite: permission of instructor. May be repeated with change of content; maximum credit 12 hours. (F, Sp) 
MATH 
5920 
SeminarAlgebra 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 
SeminarGeometry 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 
SeminarApplied Mathematics and Statistics 
1 to 2 hours. May be repeated with change of content; maximum credit 12 hours. (F, Sp) 
MATH 
5950 
SeminarUndergraduate 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, semisimple Lie algebras, root systems and classification theorems. (Irreg.) 
MATH 
6343 
Lie Theory II 
Prerequisite: 6333 or permission of the instructor. Representation theory of semisimple 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, CohenMacauley 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, subvarieties and products, birational equivalence, local rings and tangent spaces, differentials, nonsingular 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, CWcomplexes and cellular homology, Whitehead and Hurewicz theorems, EilenbergSteenrod 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, EilenbergMacLane 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 
SeminarAnalysis 
1 to 2 hours. Prerequisite: permission of the instructor. May be repeated with change of content; maximum credit 15 hours. (F, Sp) 
MATH 
6920 
SeminarAlgebra 
1 to 2 hours. Prerequisite: permission of the instructor. May be repeated with change of content; maximum credit 12 hours. (F, Sp) 
MATH 
6930 
SeminarGeometry 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.) 