# Mathematics Courses

**MATH 500 - Discrete Mathematics**

Hours: 4

Discrete Mathematics. Four semester hours. Study of formal logic; sets; functions and relations; principle of mathematical induction; recurrence relations; and introductions to elementary number theory; counting (basic combinatorics); asymptotic complexity of algorithms; graph theory; and NPcompleteness. This course is useful to those taking graduate classes in computer science. It may be taken for graduate credit towards a masters in mathematics only by consent of the department. Prerequisite: Consent of the instructor.

**MATH 501 - Mathematical Statistics**

Hours: 3

Mathematical Statistics. Six semester hours. Probability, distributions, moments, point estimation, maximum likelihood estimators, interval estimators, test of hypothesis. Prerequisite: Math 314

**MATH 502 - Mathematical Statistics**

Hours: 3

Mathematical Statistics. Six semester hours. Probability, distributions, moments, point estimation, maximum likelihood estimators, interval estimators, test of hypothesis. Prerequisite: Math 314.

**MATH 511 - Introduction to Real Analysis I**

Hours: 3

Intro Real Analysis. Three semester hours. Properties of real numbers, continuity, differentiation, integration, sequences and series of functions, differentiation and integration of functions of several variables. Prerequisite: Math 436 or 440.

**MATH 512 - Introduction to Real Analysis II**

Hours: 3

Intro Real Analysis II. Three semester hours. Properties of real numbers, continuity, differentiation, integration, sequences and series of functions, differentiation and integration of functions of several variables. Prerequisite: Math 436 or 440.

**MATH 515 - Dynamical Systems**

Hours: 3

Dynamical Systems. Three semester hours. Iteration of functions; graphical analysis; the linear, quadratic and logistic families; fixed points; symbolic dynamics; topological conjugacy; complex iteration; Julia and Mandelbrot sets. Computer algebra systems will be used. Recommended background; Math 192 and Math 331.

**MATH 517 - Calculus of Finite Differences**

Hours: 3

Calculus of Finite Differences. Three semester hours. Finite differences, integration, summation of series, Bernoulli and Euler Polynomials, interpolation, numerical integration, Beta and Gamma functions, difference equations. Prerequisite: Math 225.

**MATH 518 - Thesis**

Hours: 3-6

Thesis. Six semester hours. This course is required of all graduate students who have an Option I degree plan. Graded on a (S) satisfactory or (U) unsatisfactory basis. Prerequisite: Math 314

**MATH 522 - General Topology I**

Hours: 3

General Topology I - Three semester hours Ordinals and cardinals, topological spaces, identification topology, convexity, separation axioms, covering axioms. Pre-requisites : Math 440 or consent of instructor.

**MATH 523 - General Topology II**

Hours: 3

General Topology II - Three semester hours The course is a continuation of Math 522. Compact spaces, metric spaces, product spaces, convergence, function spaces, path connectedness, homotopy, fundamental group. Pre-requisites : Math 440 or consent of instructor.

**MATH 529 - Workshop in School Mathematics**

Hours: 3

Workshop in School Mathematics. Three semester hours. This course may be taken twice for credit. A variety of topics, taken from various areas of mathematics, of particular interest to elementary and secondary school teachers will be covered. Consult with instructor for topics.

**MATH 531 - Introduction to Theory of Matrices**

Hours: 3

Introduction to Theory of Matrices. Three semester hours. Vector spaces, linear equations, matrices, linear transformations, equivalence relations, metric concepts. Prerequisite: Math 334 or 335.

**MATH 532 - Fourier Analysis and Wavelets**

Hours: 3

Fourier And Wavelet Analysis and Applications - Three semester hours Inner Product Spaces; Fourier Series; Fourier Transform; Discrete Fourier Analysis; Haar Wavelet Analysis; Multiresolution Analysis; The Daubechies Wavelets; Applications to Signal Processing; Advanced Topics. Pre-requisites : Math 335 or the consent of the instructor

**MATH 533 - Optimization**

Hours: 3

Linear and Nonlinear Optimization - Three semester hours Graphical optimization, linear programming, simplex method, interior point methods, nonlinear programming, optimality conditions, constrained and unconstrained problems, combinatorial and numerical optimization, applications. Pre-requisites : Math 335 or the consent of the instructor

**MATH 536 - Cryptography**

Hours: 3

Cryptography. Three semester hours. (Same as CSci 568) The course begins with some classical cryptanalysis (Vigenere ciphers, etc). The remainder of the course deals primarily with number-theoretic and/or algebraic public and private key cryptosystems and authentication, including RSA, DES, AES and other block ciphers. Some cryptographic protocols are described as well. Prerequisites: Graduate standing in mathematics or consent of the instructor.

**MATH 537 - Theory of Numbers**

Hours: 3

Theory of Numbers. Three semester hours. Factorization and divisibility, diophantive equations, congruences, quadratic reciprocity, arithmetic functions, asymptotic density, Riemann's zeta function, prime number theory, Fermat's Last Theorem. Prerequisite: Consent of instructor.

**MATH 538 - Functions of a Complex Variable**

Hours: 3

Functions of a Complex Variable. Six semester hours. Geometry of complex numbers, mapping, analytic functions, Cauchy-Riemann conditions, complex integration. Taylor and Laurent series, residues. Prerequisite: Math 511.

**MATH 539 - Functions of a Complex Variable**

Hours: 3

Functions of a Complex Variable. Six semester hours. Geometry of complex numbers, mapping, analytic functions, Cauchy-Riemann conditions, complex integration. Taylor and Laurent series, residues.

**MATH 543 - Abstract Algebra**

Hours: 3

Abstract Algebra. Three semester hours. Groups, isomorphism theorems, permutation groups, Sylow Theorems, rings, ideals, fields, Galois Theory. Prerequisite: Math 334.

**MATH 544 - Abstract Algebra**

Hours: 3

Abstract Algebra. Three semester hours. Groups, isomorphism theorems, permutation groups, Sylow Theorems, rings, ideals, fields, Galois Theory. Prerequisite: Math 334.

**MATH 546 - Numerical Analysis**

Hours: 3

Numerical Analysis - Three semester hours The course will include numerical methods for derivatives and integrals approximation, teach Euler's and Runge-Kutta methods for solving ordinary differential equations, and study methods for approximate solution of partial differential equations (PDE), including parabolic PDE. Students will learn also how to program the basic methods in MatLab, improving their skills in working with this software. Pre-requisite: Calculus III, Math 314

**MATH 550 - Foun Abstract Algebra**

Hours: 3

Foundations of Abstract Algebra - Three semester hours This course will cover the fundamental properties of algebraic structures such as properties of the real numbers, mapping, groups, rings, and fields. The emphasis will be on how these concepts can be related to the teaching of high school algebra. Note: This course will be helpful to secondary teachers by giving them a better understanding of the terms and ideas used in modern mathematics.

**MATH 560 - Euclidean and nonEuclidean geometry for teachers**

Hours: 3

Euclidean and non Euclidean Geometry - Three semester hours This course is specifically designed for middle- and high-school teachers. The National Council of Teachers of Mathematics (NCTM) explains in its Principles and Standards that the geometric skills students should be able to use possess by the time they are through high school are: (1) Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. (2) Specify locations and describe spatial relationships using coordinate geometry and other representational systems. (3) Apply transformations and use symmetry to analyze mathematical situations. (4) Use visualization, spatial reasoning, and geometric modeling to solve problems.

**MATH 561 - Statistical Computing and Design of Experiments**

Hours: 3

Statistical Computing and Design of Experiments. Three semester hours. A computer oriented statistical methods course which involves concepts and techniques appropriate to design experimental research and the application of the following methods and techniques on the digital computer: methods of estimating parameters and testing hypotheses about them, analysis of variance, multiple regression methods, orthogonal comparisons, experimental designs with applications. Prerequisite: Math 401 or 501.

**MATH 563 - Image Processing with Applications**

Hours: 3

Introduction to image processing, with applications to images from medicine, agriculture, satellite imagery, physics, etc. Students will learn techniques such as edge detection, 2D image enhancement using laplacian and gradient operators, fourier transforms and the FFT, filtering, and wavelets, as time allows. Students will acquire practical skills in image manipulation by implementing the above mentioned algorithms.

**MATH 571 - Higher Order Approximations for Teachers**

Hours: 3

Higher Order Approximations. 3 Semester Hours. This course, specifically for teachers, explores algedra-based techniques for powerful, highly accurate numerical approximations. Graphing calculators and some computer software will be used. Approximations for areas and volumes of regions, solutions to equations and systems of equations, sums of infinite series, values of logarithmic and trigonometric functions and other topics are covered.

**MATH 572 - Modern Applications of Mathematics for Teachers**

Hours: 3

Modern Applications of Mathematics - Three semester hours This course, specifically designed for teachers, covers a range of applications of mathematics. Specific topics may vary but have included classical (private key) encryption, data compression ideas, coding theory ideas (Hamming 7,4 code), private and public key cryptography, data compression including wavelets, difference equations (populations models, disease models) and stochastic difference equations (stocks), GPS systems, computer tomography (e.g. CAT scans), polynomial interpolation/Belier curves, and topics from student presentations.

**MATH 573 - Calculus of Real and Complex Functions for Teachers**

Hours: 3

Calculus of Real and Complex Functions - Three semester hours This course is designed for teachers, and explores similarities and differences between functions whose domain and range consist of sets of real numbers, and sets of complex numbers. Complex numbers are reviewed, with nontraditional applications to plane geometry. Alternate approaches to the meaning of the derivative are given so as to provide links between the notions of f (x) and f (z) (x real, z complex), and ways of understanding derivatives of inverse functions and composite functions. The geometry of functions of a complex number are explored. Cauchy-Riemann equations are derived and utilized. Power series in both the real and complex context are compared.

**MATH 580 - Topics from the History of Mathematics**

Hours: 3

Topics in history of mathematics - Three semester hours A chronological presentation of historical mathematics. The course presents historically important problems and procedures.

**MATH 589 - Independent Study**

Hours: 1-4

Independent Study - Hours: One to four Individualized instruction/research at an advanced level in a specialized content area under the direction of a faculty member. Prerequisites Consent of department head. Note May be repeated when the topic varies.

**MATH 595 - Research Literature and Techniques**

Hours: 3

Research Literature and Techniques. Three semester hours. This course provides a review of the research literature pertinent to the field of mathematics. The student is required to demonstrate competence in research techniques through a literature investigation and formal reporting of a problem. Graded on a (S) satisfactory or (U) unsatisfactory basis. Prerequisite: Consent of instructor.

**MATH 597 - Special Topics**

Hours: 3

Special Topics. One to four semester hours. Organized class. May be repeated when topics vary.