# Mathematics (MATH)

### Courses

**MATH 92. Algebra Prep II. 2 Credits.**

This course continues the development of the fundamental skills required for the successful completion of studies in college level mathematics courses. Topics include the solutions of linear equations and inequalities, formula manipulation, Cartesian geometry and the graphing of linear equations and inequalities, systems of equations, and an introduction to functions. Study skills will be incorporated throughout the course. Credit earned does not count toward any degree, nor does it transfer. Prerequisite: Placement by appropriate ACT Math sub-score or Math Placement Exam score. F,S,SS.

**MATH 93. Algebra Prep III. 2 Credits.**

This course continues the development of the fundamental skills required for the successful completion of studies in college level mathematics courses. Topics include exponents and radicals, algebraic manipulation involving polynomial and rational forms, and unit analysis. Study skills will be incorporated throughout the course. Credit earned does not count towards any degree, nor does it transfer. Prerequisite: MATH 92 or Placement by appropriate ACT Math sub-score or Math Placement Exam score. F,S,SS.

**MATH 103. College Algebra. 3 Credits.**

Polynomial and rational functions, inverse functions, exponential and logarithmic functions, simple conics, systems of equations, determinants, arithmetic and geometric sequences, the Binomial Theorem. Sections meeting 5 days per week are offered for students determined eligible by the Math Department. Prerequisite: Appropriate score in the Placement Testing Program or MATH 93. F,S,SS.

**MATH 105. Trigonometry. 2 Credits.**

Angles, trigonometric functions and their inverses, solving triangles, trigonometric identities. Prerequisite: One year of high school geometry and either an appropriate score in the Placement Testing Program or MATH 93. S.

**MATH 107. Precalculus. 4 Credits.**

Equations and inequalities; polynomial rational, exponential, logarithmic and trigonometric functions; inverse trigonometric functions; algebraic and trigonometric methods commonly needed in calculus. Prerequisite: MATH 93 or an appropriate score in the Placement Testing Program. F,S,SS.

**MATH 112. Transition to Calculus. 1 Credit.**

This course is designed for students intending to take MATH 165, Calculus I who have mastered most of, but not all, the material covered in MATH 107, Pre-Calculus. Emphasis is therefore on topics such as inverse functions, partial fraction expansion, trigonometric identities, and applications of trigonometry, which are deemed most difficult for pre-calculus students. Prerequisite: MATH 107 or MATH 146 or an appropriate score in the Placement Testing Program. S/U grading. F.

**MATH 115. Introduction to Mathematical Thought. 3 Credits.**

The course will focus on analysis and interpretation of common types of mathematical arguments as well as having students construct their own arguments. A combination of topics will be included, such as: elementary combinatorics, probability, statistics, set theory, number theory, geometry and topology, mathematical logic, the mathematics of voting, etc. F.

**MATH 146. Applied Calculus I. 3 Credits.**

A nonrigorous introduction to differential and integral calculus. Topics include limits, continuity, differentiation and integration techniques, and applications. Prerequisites: MATH 103 or an appropriate score in the Placement Testing Program. F,S,SS.

**MATH 165. Calculus I. 4 Credits.**

Limits, continuity, differentiation, Mean Value Theorem, integration, Fundamental Theorem of Calculus. Prerequisite: an appropriate score in the Placement Testing Program or MATH 112 or completion of MATH 107 with a grade of C or better. F,S,SS.

**MATH 166. Calculus II. 4 Credits.**

Techniques and applications of integration, exponential and logarithmic functions, parametric equations, infinite sequences and series. Prerequisites: Completion of MATH 165 with a grade of C or better; or permission of the Mathematics Department. F,S,SS.

**MATH 207. Introduction to Linear Algebra. 2 Credits.**

A computational treatment of systems of linear equations, finite dimensional vector spaces, linear transformations, determinants, matrices, eigenvalues, eigenvectors, and diagonalizability. Prerequisite: MATH 165. F,S.

**MATH 208. Discrete Mathematics. 3 Credits.**

Introduction to Set Theory, Functions and Relations, Permutations and Combinations, Logic, Boolean Algebra, Induction, Difference Equations. Other topics from Graphs, Finite Automata and Formal Languages. Prerequisite: an appropriate score in the Placement Testing Program or MATH 103 or MATH 107. F,S,SS.

**MATH 217. Introduction to Cultural Mathematics. 3 Credits.**

This course covers mathematical concepts within the context of cultures. Mathematical ideas are investigated in topics such as number systems, calendars, art, kinship relations, divination, and games. Examples are taken from cultures in many parts of the world. The main emphasis in the course is on learning how cultural activities can be considered mathematical and often include non-trivial mathematical ideas. One or more case studies of particular cultures will also be included. The case studies will consist of investigations into several cultural aspects that have mathematical connections. Prerequisite: A grade of C or better in MATH 103. S, odd years.

**MATH 265. Calculus III. 4 Credits.**

Multivariate and vector calculus including partial derivatives, multiple integration, line and surface integrals, Green's Theorem, Stokes' Theorem, the Divergence Theorem. Prerequisite: MATH 166. F,S,SS.

**MATH 266. Elementary Differential Equations. 3 Credits.**

Solution of elementary differential equations by elementary techniques. Laplace transforms, introduction to matrix theory and systems of differential equations. Prerequisites: MATH 265 and proficiency in a programming language. F,S,SS.

**MATH 277. Mathematics for Elementary School Teachers. 3 Credits.**

Development of the number systems used in elementary schools. Includes some methods and work with laboratory materials. For elementary education majors only. Prerequisites: Admission to Teacher Education and either an appropriate score in the Placement Testing Program or MATH 103. F,S.

**MATH 308. History of Mathematics. 3 Credits.**

This is a course on the conceptual and chronological history of mathematics. The course involves the interpretation and analysis of how and why mathematical ideas have developed over time, including political and cultural considerations. Topics include: numbers and counting systems, non-Western developments, mathematics of Egypt, Babylonia and Greece, early European developments, the Renaissance, the Scientific Revolution and the development of calculus, women in mathematics, twentieth century mathematics. Prerequisite: MATH 166 or equivalent, or consent of instructor. S.

**MATH 315. Topics in Computational Mathematics. 1-3 Credits.**

An introduction to mathematical methods useful in the computational analysis of problems in applied mathematics. Topics may include numerical methods, numerical simulation, symbolic computation, and theory of computation. May be repeated for credit with consent of instructor up to six credits. Prerequisites: MATH 266 and proficiency in a programming language, or consent of instructor. Repeatable to 6 credits. On demand.

**MATH 321. Applied Statistical Methods. 3 Credits.**

Introductory statistics for students with a background in single-variable calculus. Topics include descriptive statistics, continuous and discrete probability density functions, sampling distributions, point and interval estimation, and tests of hypotheses. Prerequisite: MATH 166. F,S.

**MATH 330. Set Theory and Logic. 3 Credits.**

Axioms and operations on sets, mathematical logic, relations and functions, development of the natural and real number systems, including field axioms and the completeness axiom for the real numbers. Prerequisite: MATH 166 or consent of instructor. F,S.

**MATH 352. Introduction to Partial Differential Equations. 3 Credits.**

Partial differential equations, Fourier series, special functions, series solutions to ordinary differential equations. Prerequisite: MATH 266. S.

**MATH 377. Geometry Elementary Teachers. 1-3 Credits.**

Experimental and inductive discovery in building geometric concepts at the elementary school level. Prerequisite: For elementary education majors only. On demand.

**MATH 397. Cooperative Education. 1-8 Credits.**

A practical work experience with an employer closely associated with the student's academic area. 1-8 credits repeatable to 18. Arranged by mutual agreement among student, department, and employer. A maximum of 6 cooperative education credits may be applied against requirements for a Math major. Prerequisites: 15 completed credits in math including MATH 165, MATH 166, and MATH 265, in addition to standard co-op requirements (see department for approval). Repeatable to 18 credits. S/U grading. F,S,SS.

**MATH 399. Methods for Secondary Teachers: Mathematical Content Knowledge. 3 Credits.**

National and State Standards for teaching and learning secondary mathematics. Secondary mathematics content from an advanced perspective. Technology for learning mathematics. Current issues and recent developments in mathematics curriculum and in effective instructional practices. Prerequisite: 9 hours of upper division mathematics, excluding MATH 377 and MATH 477. S.

**MATH 400. Methods for Teaching Middle and Secondary Mathematics; Pedagogical Content Knowledge. 3 Credits.**

National and State Standards for teaching and learning secondary mathematics. Teaching methods, strategies and materials for effective standards-based teaching and learning of mathematics in middle and secondary schools. Preparation/evaluation of assessments, unit plans, and materials of instruction. Appropriate use of technology for mathematics instruction. Prerequisites: T&L 250 and T&L 345. Corequisite: T&L 486. F.

**MATH 403. Theory of Probability. 3 Credits.**

Sets, sample spaces, discrete probability, distribution functions, density functions, characteristic functions, study of normal, Poisson, binomial and other distributions with applications. Prerequisite: MATH 265. S, odd years.

**MATH 405. Selected Topics in Mathematics. 1-3 Credits.**

May be repeated to maximum of six credits. Prerequisite: Permission of the Mathematics Department. Repeatable to 6 credits. On demand.

**MATH 408. Combinatorics. 3 Credits.**

Introduction to the techniques and reasoning needed in combinatorial problem-solving. The course may include topics related to combinatorics, such as graph theory. Prerequisites: MATH 166 and MATH 208. S.

**MATH 409. Geometry. 3 Credits.**

Metric and synthetic approach to Euclidean geometry. The usual topics in elementary geometry treated in a mathematically logical way. Topics include congruence, inequalities, parallelism, similarity, area, solid geometry and the circle. Prerequisite: MATH 208 or MATH 330. F.

**MATH 412. Differential Equations. 3 Credits.**

Basic types of ordinary differential equations. Existence and uniqueness of solutions. Prerequisite: MATH 266. F, odd years.

**MATH 415. Topics in Applied Mathematics. 1-3 Credits.**

An introduction to selected areas in applied mathematics chosen from a variety of topics including: Applied algebra, difference equations, linear programming, modeling and simulation, operations research, optimization, partial differential equations and computers in mathematics. Topics to be considered will be illustrated with examples and practical applications. May be repeated for credit with consent of instructor up to a maximum of six credits. Prerequisites: MATH 265 and consent of instructor. Repeatable to 6 credits. On demand.

**MATH 416. Topics in Statistics. 1-3 Credits.**

An introduction to a variety of topics in statistics including: Linear models in categorical analysis, Bayesian methods, decision theory, ridge regression, Non parametric techniques, stochastic games and models. The number of topics to be considered during a semester will be limited to permit greater depth of coverage and sufficient practical illustrations. May be repeated for credit with consent of instructor up to six credits. Prerequisites: MATH 265 and MATH 321 or consent of instructor. Repeatable to 6 credits. On demand.

**MATH 421. Statistical Theory I. 3 Credits.**

Discrete and continuous random variables, expectation, moments, moment generating functions, properties of special distributions, introduction to hypothesis testing, sampling distributions, Central Limit Theorem, curve of regression, correlation, empirical regression by least squares, maximum likelihood estimation, Neyman-Pearson lemma, likelihood ratio test, power function, chi-square tests, change of variable, "t" and "F" tests, one and two-way ANOVA, nonparametric methods. Prerequisite: MATH 265. F.

**MATH 422. Statistical Theory II. 3 Credits.**

Discrete and continuous random variables, expectation, moments, moment generating functions, properties of special distributions, introduction to hypothesis testing, sampling distributions, Central Limit Theorem, curve of regression, correlation, empirical regression by least squares, maximum likelihood estimation, Neyman-Pearson lemma, likelihood ratio test, power function, chi-square tests, change of variable, "t" and "F" tests, one and two-way ANOVA, nonparametric methods. Prerequisite: MATH 421. S.

**MATH 425. Cryptological Mathematics. 3 Credits.**

This course develops the math behind elementary symmetric-key cryptoschemes and a variety of public-key schemes. Modern block ciphers may be discussed. Prerequisite: MATH 208. F, odd years.

**MATH 431. Introduction to Analysis I. 3 Credits.**

Development of the real number system, functions, sequences, limits, continuity, and differentiation. Prerequisite: MATH 330 or consent of instructor. F.

**MATH 432. Introduction to Analysis II. 3 Credits.**

A continuation of MATH 431, topics in the second semester include integration, partial differentiation, infinite series, power series and vector analysis. Prerequisite: MATH 431. S.

**MATH 435. Theory of Numbers. 3 Credits.**

Basic properties of numbers, including divisibility, primes, congruences, Diophantine equations and residue theory. Prerequisite: MATH 208 or 330. S.

**MATH 441. Abstract Algebra. 3 Credits.**

Rings, integral domains, fields, elements of group theory. Prerequisite: MATH 330 or consent of instructor. F.

**MATH 442. Linear Algebra. 3 Credits.**

A theoretical treatment of systems of linear equations, matrices, vector spaces, linear transformations and elementary canonical forms. Prerequisites: MATH 207 and MATH 330 or consent of instructor. S.

**MATH 460. Mathematical Modeling. 3 Credits.**

The primary goal of the course is to present the mathematical analysis provided in scientific modeling. Topics may include population modeling, mechanical vibrations, traffic flow, epidemic modeling, queues and decay processes. Prerequisites: MATH 266 and MATH 207 or consent of instructor. F, even years.

**MATH 461. Numerical Analysis. 3 Credits.**

Numerical techniques for: the solution of equations in one or several unknowns, approximate integration, differential equations, approximation theory, optimization theory and matrix analysis. Corresponding error analysis will be investigated. Prerequisites: MATH 266 and a scientific programming language. F, odd years.

**MATH 471. Introduction to Complex Variables. 3 Credits.**

The complex plane, analytic functions, complex integration, power series, the theory of residues and contour integration, conformal mapping, Fourier and Laplace transformations, and applications. Prerequisite: MATH 265. F, even years.

**MATH 477. Topics in Elementary School Mathematics. 1-3 Credits.**

Selected topics from mathematical concepts appropriate to the elementary school curriculum. May be repeated for credit up to six credits. Prerequisite: Elementary education majors only. Repeatable to 6 credits. On demand.

**MATH 479. Topics in Mathematics Education. 1-3 Credits.**

Selected topics from mathematical concepts appropriate for K-12 educators. May be repeated for up to six credits. Prerequisite: Instructor consent. Repeatable to 6 credits. On demand.

**MATH 488. Senior Capstone. 3 Credits.**

This course is designed to help students transition into working mathematicians. Thus the course will address 1) written and oral expression of mathematical material and concepts, 2) research and problem solving in mathematics, and 3) technology in mathematics, and its appropriate use. Material will build on the core areas of calculus, linear algebra, and differential equations. Prerequisites: Senior standing with a major in mathematics. F.

**MATH 494. Reading Course in Mathematics. 1-3 Credits.**

Directed individual reading on selected topics not developed in other courses. Repeatable to six credits. Prerequisites: Consent of instructor. Repeatable to 6 credits. F,S,SS.

**MATH 495. Readings in Mathematics. 1-3 Credits.**

Directed individual reading on selected topics not developed in other courses. Repeatable to six credits. Prerequisite: Consent of instructor. Repeatable to 6 credits. F,S,SS.

**MATH 505. Seminar in Mathematics. 1-3 Credits.**

Repeatable.

**MATH 512. Modern Analysis I. 3 Credits.**

Algebras and ó - algebras, Borel sets, measures, measurable sets and Lebesgue measure, non-measurable sets, measurable functions, the definition and basic properties of the Lebesgue integral, Fatou's lemma, the monotone convergence theorem, and Lebesgue's dominated convergence theorem. Prerequisite: MATH 432.

**MATH 513. Modern Analysis II. 3 Credits.**

Product measures, Fubini's theorem, the Radon Nikodym theorem, inequalities of Hölder and Minkowski, definitions and basic properties of normed spaces and Banach spaces, some classical Banach spaces such as Lp and lp, bounded linear operators, and dual spaces. Prerequisite: MATH 512.

**MATH 515. Applied Mathematics. 3 Credits.**

The content of the course varies but includes current topics in applied mathematics such as: (1) ordinary or partial differential equations, (2) approximation theory and perturbation techniques, (3) modeling and computer simulation, (4) special functions, (5) numerical analysis, (6) variational methods, (7) transforms, (8) integral equations. Prerequisite: MATH 266 or consent of instructor.

**MATH 516. Applied Mathematics. 3 Credits.**

The content of the course varies but includes current topics in applied mathematics such as: (1) ordinary or partial differential equations, (2) approximation theory and perturbation techniques, (3) modeling and computer simulation, (4) special functions, (5) numerical analysis, (6) variational methods, (7) transforms, (8) integral equations. Prerequisite: MATH 266 or consent of instructor.

**MATH 518. Algebra I. 3 Credits.**

Group theory, rings and fields, vector spaces, Galois theory and finite fields. Prerequisites: MATH 441 and MATH 442.

**MATH 519. Algebra II. 3 Credits.**

Group theory, rings and fields, vector spaces, Galois theory and finite fields. Prerequisites: MATH 441 and MATH 442.

**MATH 520. Topology I. 3 Credits.**

Point set topology, including metric spaces and such topics as homeomorphisms, separation axioms, compactness, connectedness, general convergence, compactification and metrizability. Prerequisite: MATH 431.

**MATH 521. Topology II. 3 Credits.**

Point set topology, including metric spaces and such topics as homeomorphisms, separation axioms, compactness, connectedness, general convergence, compactification and metrizability. Prerequisite: MATH 431.

**MATH 541. Linear Statistical Models. 3 Credits.**

Distributions of quadratic forms, general linear hypotheses of full rank, least squares, Gauss-Markoff theorem, estimability, parametric transformations, Cochran's theorem, projection operators and conditional inverses in generalized least squares, applications to ANOVA and experimental design models. Prerequisite: MATH 422 or consent of instructor.

**MATH 542. Advanced Topics in Statistics and Probability. 3 Credits.**

The content of the course varies but may include (but is not restricted to) current topics in statistics and probability such as (1) time series, (2) sampling, (3) nonparametric statistics, (4) experimental design, (5) probability theory, (6) statistical theory, (7) multivariate statistical analysis. Prerequisite: MATH 541 or consent of instructor.

**MATH 576. Algebra and Geometry for Middle School Teachers. 3 Credits.**

Algebra and Geometry course intended for middle school teachers: a) planning to qualify to teach middle school mathematics; or b) teachers looking to enrich their content knowledge in mathematics. Topics may include: rational number system, introduction to number theory, algebraic thinking, spatial reasoning and representation, introduction to Euclidean and non-Euclidean geometry, problem solving and pedagogical issues. May not be used in Ph.D. or Master's programs. Prerequisites: Licensed K-12 teacher, College Algebra, and instructor consent.

**MATH 577. Calculus Concepts for Middle School Teachers. 3 Credits.**

Calculus course intended for middle school teachers: a) planning to qualify to teach middle school mathematics; or b) teachers looking to enrich their content knowledge in mathematics. Topics may include: analysis of functions, mathematical modeling, limits, continuity, differentiation, integration, and pedagogical issues. May not be used in Ph.D. or Master's programs. Prerequisites: Licensed K-12 teacher, College Algebra, and instructor consent.

**MATH 578. Probability and Statistics for Middle School Teachers. 3 Credits.**

Probability and statistics course intended for middle school teachers: a) planning to qualify to teach middle school mathematics; or b) teachers looking to enrich their content knowledge in mathematics. Topics may include: counting, empirical and theoretical probabilities, simulation of probabilistic events, conditional probability, expected value, data and variables, random sampling, measures of central tendency and spread, least squares regression, and pedagogical issues. May not be used in Ph.D. or Master's programs. Prerequisites: Licensed K-12 teacher, College Algebra, and instructor consent.

**MATH 579A. Practicum in Middle School Mathematics. 2 Credits.**

Teachers will use their content and pedagogical knowledge to plan lesson(s) and develop and implement an action research project in their school. May be repeated for up to 6 credits. May not be used in Ph.D. or Master's programs. Prerequisites: Licensed K-12 teacher, Math 276, 577 or 578 and instructor consent. Repeatable to 6 credits.

**MATH 579B. Practicum in Middle School Mathematics. 2 Credits.**

Teachers will use their content and pedagogical knowledge to plan lesson(s) and develop and implement an action research project in their school. May be repeated for up to 6 credits. May not be used in Ph.D. or Master's programs. Prerequisites: Licensed K-12 teacher, Math 276, 577 or 578 and instructor consent.

**MATH 996. Continuing Enrollment. 1-12 Credits.**

Repeatable. S/U grading.

**MATH 997. Independent Study. 2 Credits.**

**MATH 998. Thesis. 1-9 Credits.**

Repeatable to 9 credits.