

Mathematics (20032004)Admission  Courses  Program  Requirements Department Chairperson: Iraj Kalantari Graduate Faculty
Associate Graduate Faculty
The Department of Mathematics offers a program of graduate study leading to the Master of Science degree with a variety of courses in pure and applied mathematics and statistics. The requirements are highly flexible, allowing a student to arrange a program of study which will serve as a basis for further graduate study, meet the immediate and changing needs of teachers of mathematics and other educators, or prepare the candidate for a position in industry, business, or government. Students entering the program should normally have completed an undergraduate
degree program including course work equivalent to a major in mathematics.
Other students may be admitted at the discretion of the Departmental Graduate
Committee with admission usually conditional upon the student completing
specified deficiencies. The Graduate Record Examination is not required. The M.S. degree in mathematics may be earned under one of three plans. In each plan the student will have successfully completed the following four core courses:
Oral Examination Plan. (30 semester hours) Under this plan, the student must earn 30 graduate semester hours in approved course work, including the core courses, and pass an oral examination. Of the 30 semester hours, at least 15 must be in 500level courses. The oral examination is over a portion of the student's course work. Students may choose this portion with the approval of their advisory committee. Thesis Plan. (33 semester hours) Including the core courses, the student must earn 30 semester hours in approved course work and three semester hours of MATH 600, Thesis. Of the 30 semester hours in course work, at least 15 must be in 500level courses. The thesis may be either expository, historical, critical, or original and must be approved by the student's advisory committee. The student will present his/her thesis to the mathematics department faculty in a colloquium. Course Work Plan. (36 semester hours) The student must earn 36 semester hours in approved course work including the core courses. Of these, at least 18 semester hours must be in 500level courses. A student who has completed a course equivalent to any of the core courses as a part of the undergraduate program would, of course, be exempted from that course requirement. Also, candidates who hold secondary school teaching certification may, with permission of the Graduate Committee, substitute course work in geometry for any one of the courses mentioned above except MATH 435G, Introduction to Real Variables I. Students may, with approval of the Graduate Committee, include up to six semester hours in a cognate area such as biology, chemistry, physics, economics, computer science, etc. If education is chosen as a cognate area, no more than nine semester hours of the program may be completed in mathematics methods and education courses. A student may receive credit for the maximum number of transfer and extension hours allowed by the School of Graduate Studies. Each graduate assistant is required to complete at least nine semester hours in Mathematics in each semester of the first year. Any exception to this policy must be approved in writing by the Graduate Committee. 402G Investigations in School Geometry. (3) A conceptual development of geometry through the investigation of geometric relationships and informal understandings leading to formal deductions. Middle and junior high school emphasis. Prerequisite: Consent of the instructor. 406G Mathematical Reasoning in School Mathematics. (3) Problem solving using a variety of reasoning patterns, proof in mathematics, the concept of mathematical groups, and related topics. Open only to students majoring in an elementary education program. Prerequisite: MATH 128 or equivalent. 407G Number Theory Concepts in School Mathematics. (3) Divisibility, prime numbers, perfect numbers, modular arithmetic, linear Diophantine equations, and related topics. Open only to students majoring in an elementary education program. Prerequisite: MATH 128 or equivalent. 408G Computers in Elementary/Middle School Mathematics. (3) The study of special topics in mathematics utilizing microcomputers through an introduction to Logo and the effective use of selected software. Prerequisites: MATH 206 and some computer experience, or consent of instructor. 421G Abstract Algebra. (3) An introduction to the basic properties of groups, rings, and fields. Prerequisite: MATH 341. 424G Advanced Linear Algebra. (3) Matrix algebra, vector spaces, linear independence, basis, linear transformations, canonical forms, inner product spaces. Prerequisite: MATH 421 or consent of the instructor. 430G Multivariable Calculus. (3) The algebra of functions, continuity, differentiation and integration of nplace functions, and related topics. Prerequisite: MATH 231 and 311. 431G Partial differential Equations. (3) Fourier series, partial differential equations. Bessel and Legendre functions, and transform methods. Numerical techniques illustrated using the computer. Prerequisite: MATH 333 or consent of instructor. 435G Introduction to Real Variables I. (3) Topology of the real line, limits, derivatives, integrals, improper integrals, sequences, series, and introduction to calculus of functions of several variables. Prerequisite: MATH 231 and MATH 341. 436G Introduction to Real Variables II. (3) A continuation of Math 435. Prerequisite: MATH 435. 441G Mathematical Logic. (3) Introduction to some of the principal topics of mathematical logic. Topics include Propositional Calculus, Quantification Theory, the Completeness Theorem, Formal Theories, Models of Theories and Recursion Theory. Prerequisite: MATH 341. 456G Theory of Numbers. (3) Divisibility, congruences, periodic decimals, Fermat’s Theorem, Wilson’s Theorem, Diophantine equations, primitive roots, and other topics. Prerequisite: MATH 341. 461G Introductory Topology. (3) Basic properties of topological spaces. Open and closed sets, compactness, the intermediate value theorem, metric spaces, completeness, and uniform continuity. Prerequisite: MATH 341 or consent of instructor. 481G Numerical Analysis I. (3) A survey of current methods in numerical analysis. Error analysis, solution of nonlinear equations and systems of linear equations, polynomial interpolation and approximations, and related topics. Prerequisite: CS 211 and 212 (or 245), Math 231 and 311, or consent of the instructor. 482G Numerical Analysis II. (3) A continuation of MATH 481. Numerical differentiation and integration, numerical solution of ordinary and partial differential equations, function approximations in various norms. Prerequisite: Math 481 or consent of instructor. 488G Models in Applied Mathematics. (3) Theory and computer exploration of mathematical models using difference equations, differential equations, and dynamical systems. Applications from the sciences. Prerequisite: MATH 231, MATH 311, and one of CS 211 and CS 212, CS 240 or CS 245, or consent of the instructor. 500 Teaching of Elementary Mathematics. (3) A study of current trends and problems in the teaching of elementary and junior high school mathematics. Prerequisite: Permission of the instructor. 501 Elementary Mathematics I. (3) A study of sets, logic, real number system, open sentences, relations, and functions as they apply to the elementary and junior high school curriculum. Prerequisite: Permission of the instructor. 502 Geometry for Teachers. (3) A study of geometric concepts as they pertain to the elementary and junior high school curriculum. Topics will be chosen from coordinate, synthetic, and transformational geometry. Prerequisite: Permission of the instructor. 503 Methods of Teaching Secondary School Mathematics. (3) A study of current trends and problems in the teaching of secondary school mathematics. Prerequisite: Permission of the instructor. 504 Research in Secondary Mathematics Education. (3) A survey, evaluation, and application of recent research relative to the teaching of secondary school math. Prerequisite: Permission of the instructor. 505 The Teaching of Mathematics in Middle Grades and Junior High. (3) A study of teaching strategies and current trends in mathematics as they apply to the curriculum of the middle school and the junior high school. Prerequisites: MATH 106 and 206 (C grade or better) or equivalent. 507 Research in Elementary Mathematics Education. (3) A survey, evaluation, and application of recent research relative to the teaching of elementary and junior high school math. Prerequisite: Permission of the instructor. 508 Special Topics in Elementary Mathematics. (3, repeatable to 15) Topics will be available on demand in the areas of probability, statistics, computer science, number theory, and history of math. Prerequisite: Permission of the instructor. 509 Diagnostic and Prescriptive Teaching of School Mathematics. (3) The assessment of strengths and weaknesses of students in school mathematics with the development of appropriate prescriptive remediation materials and strategies. Prerequisite: Teacher certification, MATH 360 or MATH 361. 511 Modern Geometry. (3) Topics to be chosen to reflect current trends in geometry. Prerequisite: Permission of the instructor. 512 Projective Geometry. (3) Theorems of Desargues and Pappus, transformations, and basic properties of the projective plane. Prerequisite: Permission of the instructor. 521 Algebra. (3) An introduction to higher algebra. Topics to be included are groups, homomorphisms, Sylow theorems, rings and ideals, fields, field extensions, and Galois theory. Prerequisite: MATH 424 or permission of the instructor. 531 Real Variables. (3) An introduction to measure and integration. Prerequisite: MATH 435 or permission of the instructor. 533 Complex Variables. (3) Topics to be studied include the topology of the complex plane, analytic functions, complex integration, and singularities. Prerequisite: MATH 436 or permission of the instructor. 536 Ordinary Differential Equations. (3) The initial value problem, existence and uniqueness theorems, linear systems, asymptotic behavior of solutions, twodimensional systems. Prerequisite: MATH 333 and 435, or permission of the instructor. 537 Numerical Solutions of Ordinary Differential Equations. (3) Onestep methods for initial value problems, onestep methods for systems, multistep methods, boundary value problems. Examples using University computers. Prerequisite: MATH 536 and some programming experience, or permission of the instructor. 541 Set Theory. (3) A formal development of the theory of sets, to include operations on sets, mapping, order types, cardinal and ordinal number theory, and transfinite induction. Prerequisite: Permission of the instructor. 550 Workshop in School Mathematics. (1–6, repeatable) (Degree candidates may receive credit toward program requirements only with the permission of the student's Graduate Committee.) Workshops focusing on specific topics may be organized as required to meet the identified needs and interests of inservice teachers or specific school districts. Prerequisite: Graduate Standing. 560 Advanced Topology. (3) Product and quotient spaces, pathconnectedness, local compactness, homotopy, fundamental group. Additional topics may include Baire category, function spaces, Brouwer Fixed Point Theorem. Prerequisites: MATH 421 and MATH 461, or permission of the instructor. 581 Approximation Theory. (3) The theory behind numerical algorithms. Remainder theory, convergence theorems, best approximation in various norms, the theory of matrices in numerical analysis including the eigenvalue problem. Prerequisites: MATH 435 and 481, or permission of the instructor. 583 Nonlinear Unconstrained Optimization. (3) Unconstrained optimization of nonlinear functions of one or more variables. Necessary and sufficient conditions, gradient methods. Prerequisites: MATH 481 and 424, or permission of the instructor. 589 Mathematical Modeling. (1–3) A development of the group approach in applications of techniques used in applied mathematics, numerical analysis, operations research, and statistics to real problems from other disciplines. May be repeated up to six hours. Prerequisite: Permission of the instructor. 590 Independent Study. (1–3, repeatable to 6) Prerequisite: Approval of Department Chairperson. 597 Mathematics Seminar. (1–2, repeatable to 6) Prerequisite: Permission of the instructor. 598 Seminar in Teaching Methods. (1) Prerequisite: Graduate standing. 599 Special Topics. (1–3, repeatable to 9) Prerequisite: Permission of the instructor. 600 Thesis. (3) Prerequisite: Permission of the graduate adviser. 607 Practicum in Mathematics Education. (3) Direct internship experience for action research in mathematics education (K8) under guidance of qualified faculty. Prerequisites: MATH 500 or 505 and approval of degree plan, completion of over half of candidate's course work, including EIS 500. Modifications in the above requirements are subject to the approval of the candidate's adviser. Statistics 470G Statistical Methods for Experimental Sciences. (3) (No credit for math majors) Statistical applications to laboratory problems, field experiments, analysis of designed experiments, including regression, correlation, and analysis of variance methods. Prerequisite: High school advanced algebra or MATH 100. 471G Introduction to Mathematical Statistics I. (3) The mathematical foundations of probability and statistics, principles of probability, sampling, distribution, moments, and hypothesis testing. Prerequisite: MATH 231 or equivalent. 472G Introduction to Mathematical Statistics II. (3) Continuation of Statistics 471, including further topics in estimation and hypothesis testing. Prerequisite: STAT 471. 474G Regression and Correlation Analysis. (3) Least squares theory, correlation theory, simple, multiple, and stepwise regression, computer assisted model building, and applied problems. Prerequisites: STAT 276 or equivalent. 478G Analysis of Variance. (3) A study of analysis of variance and covariance. Includes experimental design with applications. Prerequisites: STAT 276 or equivalent. 490G Topics in Statistics. (1–6) General topics in statistics. Prerequisite: Consent of instructor. 570 Probability Theory and Stochastic Processes. (3) Nature of probability theory, sample space, combinatorial analysis, fluctuations in random events, stochastic independence, random variables, generating functions, Markov chains, and simple timedependent stochastic processes. Prerequisite: STAT 471 or equivalent. 572 Mathematical Statistics I. (3) The study of statistical inference including topics in probability, estimation, hypothesis testing and sampling. Prerequisite: STAT 471 or equivalent. 573 Mathematical Statistics II. (3) A continuation of Statistics 572. Prerequisite: STAT 572. 574 Linear Models and Experimental Designs. (3) General linear models, GaussMarkov Theorem, experimental design model confounding, and types of experimental designs and their analysis. Prerequisite: STAT 472 or permission of the instructor. 

