# Guide Fourier Series and Integrals (Probability and Mathematical Statistics)

Duplicates two hours of and two hours of 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. Prerequisite: with grade of C or better.

Duplicates one hour of and three hours of Vectors and vector functions, functions of several variables, partial differentiation and gradients, multiple integration, line and surface integrals, Green-Stokes-Gauss theorems.

• Fourier Series and Integrals (Probability and Mathematical Statistics).
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• Thinking about Inequality: Personal Judgment and Income Distributions.
• Courses in Mathematics and Statistics.

Introduction to Ordinary Differential Equations. Duplicates two hours of First order ordinary differential equations, linear differential equations with constant coefficients, two-by-two linear systems, Laplace transformations, phase planes and stability.

## Mathematics Courses

Systems of linear equations, determinants, finite dimensional vector spaces, linear transformations and matrices, characteristic values and vectors. Prerequisite: or concurrent enrollment. Numerical solution of nonlinear equations. Matrices and linear algebraic equations, regression, interpolation, splines. Numerical integration.

### by H. Dym, Henry P. McKean

Numerical solution of systems of ordinary differential equations. Numerical solution of partial differential equation. Laboratory F, Sp. Complex numbers and functions. Fourier series, solution methods for ordinary differential equations and partial differential equations, Laplace transforms, series solutions, Legendre's equation. The Fourier transform and applications, a survey of complex variable theory, linear and nonlinear coordinate transformations, tensors, elements of the calculus of variations.

An introduction to geometry including axiomatics, finite geometry, convexity, and classical Euclidean and non-Euclidean geometry.

## Fourier Series and Integrals

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. Will provide an opportunity for the gifted Honors candidate to work at a special project in the student's field. Prerequisite: one course in general area to be studied; permission of instructor and department. Overall grade point average of 2.

Contracted independent study for topic not currently offered in regularly scheduled courses. It is used to denote upper division transfer credit for which there is no OU equivalent course. Prerequisite: or 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.

Prerequisite: , or , or , 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 and Introduction to Functions of a Complex Variable.

Complex analytic functions, conformal mappings, complex integrals. Taylor and Laurent series, integration by the method of residues, complex analytic functions and potential theory. Slashlisted with 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. Fourier series, classical Fourier transform, discrete Fourier transform, distributions and Fourier transforms.

Sampling and Shannon's Theorem. Introduction to Partial Differential Equations. Prerequisite: , or Physical models, classification of equations, Fourier series and boundary value problems, integral transforms, the method of characteristics.

Prerequisite: or , , or , 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. Specialized Topics and Methods--a Teachers' Course. 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 For major credit only for those in teacher certification programs.

Prerequisite: and 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.

Convolution of Two Functions

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. Extensions of rings and fields, elementary factorization theory; groups with operators; modules and ideals; lattices. Slashlisted with Prerequisite: 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 or 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.

Intermediate Ordinary Differential Equations. Prerequisite: or ; Duplicates one hour of Topics selected from: linear systems of equations, integral equations, stability theory, existence and uniqueness criteria, perturbation theory, dynamical systems, boundary-value problems, numerical methods. Review of real number system. Sequences of real numbers. Topology of the real line.

Continuity and differentiation of functions of a single variable. Integration of functions of a single variable. Series of real numbers. Series of functions. Differentiation of functions of more than one variable. 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]. Slashlisted with Prerequisite: and , 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. 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.

Elementary theory of curves and surfaces in three-dimensional Euclidean space, differentiable manifolds, Riemannian geometry of two dimensions, Gauss Theorem Egregium. Slashlisted with Prerequisite: or 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.

Slashlisted with Prerequisite: or permission of instructor. An introduction to the theory of graphs. Topics include basic definitions, cutpoints, blocks, trees, connectivity and Menger's theorem. Probability spaces, counting techniques, random variables, moments, special distributions, limit theorems. Mathematical development of basic concepts in statistics: estimation, hypothesis testing, sampling from normal and other populations, regression, goodness-of-fit.