Undergraduate Level Mathematics Courses
The department offers courses which are slashlisted so undergraduate students may take an undergraduate 4000-level course while graduate students may take a graduate 5000-level course. The lectures in a slashlisted course are the same. However, students in the 5000-level course have substantial additional requirements beyond those for students in the 4000-level course. These additional requirements are listed in the slashlisted course syllabus. ACT/SAT scores are valid for placement during a freshman's entry year only.
Explanation of Course Numbers
In the Department of Mathematics the second digit indicates the area within the department: 1—miscellaneous; 2—mathematics education; 3—algebra; 4—analysis; 5—foundations and logic; 6—geometry; 7—probability and statistics; 8—topology; 9—research. The third digit identifies the course within the level and area.
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)
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)
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)
1473 Mathematics for Critical Thinking. Prerequisite: 0123 at OU, or satisfactory score on the placement test, or 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]
1503 Introduction to Elementary Functions. Prerequisite: 0123 at OU, or satisfactory score on the placement test, or 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]
1523 Elementary Functions. Prerequisite: 1503 at OU, or satisfactory score on the placement test, or 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]
1643 Precalculus for Business, Life and Social Sciences. Prerequisite: 0123 at OU, or satisfactory score on the placement test, or 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]
1743 Calculus I for Business, Life and Social Sciences. Prerequisite: 1523 or 1643 at OU, or satisfactory score on the placement test, or 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]
1823 Calculus and Analytic Geometry I. Prerequisite: 1523 at OU, or satisfactory score on the placement test, or 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]
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]
2213 Mathematical Systems. Prerequisite: plane geometry, intermediate algebra, enrollment in 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)
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]
2433 Calculus and Analytic Geometry III. Prerequisite: 2423. Polar coordinates, parametric equations, sequences, infinite series, vector analysis. (F, Sp, Su)
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)
2513 Discrete Mathematical Structures. Prerequisite: 2423 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)
†G3113 Introduction to Ordinary Differential Equations. Prerequisite: 2443 or concurrent enrollment. Duplicates two hours of 3413. First order ordinary differential equations, linear differential equations with constant coefficients, Laplace transformations, power-series solutions of differential equations, Bessel functions. (F, Sp, Su)
3213 Data Analysis and Geometric Systems. Prerequisite: plane geometry, intermediate algebra, 2213, enrollment in elementary teacher's program. Algebra and the structure of number systems, functional relationships, informal geometry. (F, Sp)
†G3333 Linear Algebra I. Prerequisite: 2433 or permission of instructor. Systems of linear equations, determinants, finite dimensional vector spaces, linear transformations and matrices, characteristic values and vectors. (F, Sp, Su)
†G3343 Linear Algebra II. Prerequisite: 3333. Diagonalization, inner product spaces, applications, and other advanced topics in finite and infinite dimensional vector spaces. No student may earn credit for this course and 4373 or 5373. (F, Sp, Su)
†G3413 Physical Mathematics I. Prerequisite: 2443 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)
†3423 Physical Mathematics II. Prerequisite: 2443, 3413. The Fourier transform and applications, a survey of complex variable theory, linear and nonlinear coordinate transformations, tensors, elements of the calculus of variations. Duplicates one hour of 3333 and one hour of 4103. (Sp)
†G3513 Foundations of Analysis. Prerequisite: 2433 or concurrent enrollment. The real number system, sequences of numbers, series of numbers, limits and continuity of functions, topology and continuity on the real line. (F, Sp, Su)
†G3613 Modern Geometry. Prerequisite: 1823 or 1743. An introduction to geometry including axiomatics, finite geometry, convexity, and classical Euclidean and non-Euclidean geometry. (F, Sp)
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)
3970 Honors Seminar. 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)
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)
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)
G4033 Applied Matrix Models. Prerequisite: 3333 and either a programming course or permission of instructor. Solution of systems of m linear equations in m unknowns; solution of m linear equations in k unknowns; linear programming; eigenvalue and vector problems; matrix models selected from various areas such as ecology, voting systems, city street sweeping, infectious diseases, population, predator prey systems, heat transfer in frozen soil, network analysis, psychology, sociology, Markov processes. (F)
G4073 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)
G4083 Numerical Analysis II. Prerequisite: 3113 or 3413; 4073 or Electrical Engineering 3793; 3333 or 4373 or Biostatistics and Epidemiology 5563. Matrix inversion and related topics; numerical solution of ordinary differential equations, partial differential equations, integral equations and functional equations; numerical solution of eigenvalue problems and applications of functional analysis. (Alt. Sp)
G4103 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)
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.)
G4163 Introduction to Partial Differential Equations. Prerequisite: 3113. Physical models, classification of equations, Fourier series and boundary value problems, integral transforms, the method of characteristics. (F, Sp)
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)
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)
G4323 Introduction to Abstract Algebra I. Prerequisite: 3333 and 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. Duplicates one hour of 4383. (F, Sp)
G4333 Introduction to Abstract Algebra II. Prerequisite: 4323. Extensions of rings and fields, elementary factorization theory; groups with operators; modules and ideals; lattices. (Sp)
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 3343 and 4373 or 5373, or for both 4373 and 5373. (F, Sp, Su)
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)
G4413 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.)
G4433 Introduction to Analysis I. Prerequisite: 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)
4443 Introduction to Analysis II (Slashlisted with 443). 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)
4513 Senior Mathematics Seminar. Prerequisite: senior standing or permission of instructor. 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]
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)
G4643 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)
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)
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)
4673 Graph Theory I (Slashlisted with 5673). Prerequisite: 2513 (or 3513) 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)
G4733 Mathematical Theory of Probability. Prerequisite: 2443 or concurrent enrollment. Probability spaces, counting techniques, random variables, moments, special distributions, limit theorems. (F)
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)
G4753 Applied Statistical Methods. Prerequisite: 2123 or 2423 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)
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)
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)
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)
G4853 Introduction to Topology. Prerequisite: 2433, 2513 or permission of instructor. Metric spaces and topological spaces, continuity, connectedness, compactness and related topics. (Sp)
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)
4991 Mathematics Capstone Course. Prerequisite: senior standing and concurrent or previous enrollment of one of 4083, 4193, 4333, 4443, 4653, 4853, or any topics course at the 4000 level. Students will write a senior thesis showing an understanding of a substantial area of modern mathematics. The thesis will be either an essay, the result of a computation, or a combination thereof. (F, Sp) [V]
Updated: August 15, 2003