The University of Texas at Arlington®Undergraduate Catalog 2007-2008 Table of Contents - About the CatalogClass Schedules - Choose Your Majoremail: ugcatalog@uta.edu Catalogs on the Web: Current '06 - '07: Fall 2006 | '05-'06: Spring 2006, Fall 2005 '03-'05: Spring 2005, Fall 2004, Spring 2004, Fall 2003 2001-2003 | 1999-2001 Printed versions of earlier catalogs are available in the University Archives.

Fall 2007

# Undergraduate Course Descriptions for MATH

Choose a subject:

MATH 0301. THEA TEST PREPARATION (3-0) Review of topics covered on the Texas Higher Education Assessment (THEA) test (formerly the Texas Academic Skills Program [TASP] test), including algebra and geometry. Credit in this course does not fulfill any degree requirement.

MATH 0302. FUNDAMENTALS OF ALGEBRA (3-0) Basic algebraic operations, linear equations and inequalities, polynomials, rational expressions, factoring, exponents and radicals, and quadratic equations. Credit in this course does not fulfill any degree requirement. Prerequisite: MATH TASP score greater than 219.

MATH 1301. ELEMENTARY MATHEMATICAL MODELING (3-0) Intended for Liberal Arts majors to develop student capabilities in reasoning, analytical thinking, and problem solving. The majority of time and effort will be on solving word problems, with less emphasis on algebra than MATH 1302. Problems include growth projections, statistical modeling, optimization, and money problems, ie compound interest, amortization of loans. A graphing calculator, such as TI-83, is required. Business majors should enroll in MATH 1302 or 1315. Science/Engineering majors should enroll in Math 1322. Credit may be received for only one of MATH 1301, MATH 1302, or MATH 1315. Prerequisite: passing score on Math Placement Test. (For details on this placement test, contact the Mathematics department.)

MATH 1302. COLLEGE ALGEBRA (3-0) Linear, quadratic and higher order polynomial equations and inequalities solved algebraically, graphically and numerically; graphs and operations on relations and functions; real and complex zeros of polynomials and rational functions; exponential and logarithmic functions; systems of linear equations; matrices. Prerequisite: passing score on the Math Placement Test. Credit may be received for only one of MATH 1301, MATH 1302, or MATH 1315.

MATH 1303. TRIGONOMETRY (3-0) Trigonometric functions, radian measure, solution of triangles, graphs of trigonometric functions, trigonometric identities and equations, and complex numbers. Prerequisite: passing score on the Math Placement Test.

MATH 1308. ELEMENTARY STATISTICAL ANALYSIS (3-0) Descriptive statistics, relationships between variables, interpretation of data and graphs, rudiments of probability, elementary statistical models, hypothesis testing, inference, and estimation. Prerequisite: MATH 1301 or 1302 or 1315 or equivalent, or passing score on the Math Placement Test.

MATH 1313. LIBERAL ARTS HONORS MATHEMATICS (3-0) Topics include the development of the real number system, different orders of infinity, the idea of convergence and how this led to the development of calculus, the concept of a mathematical proof, the conceptual foundations of topology, networks, and knot theory, and modern applications of mathematics to the sciences.

MATH 1315. COLLEGE ALGEBRA FOR ECONOMICS & BUSINESS ANALYSIS (3-0) Presents material covered in a traditional algebra course but with emphasis toward business applications. Linear equations, systems of linear equations, systems of linear inequalities, elements of matrix algebra and probability. Credit may be received for only one of MATH 1301, MATH 1302, or math 1315.

MATH 1316. MATHEMATICS FOR ECONOMICS AND BUSINESS ANALYSIS (3-0) Presents some of the mathematical tools that are useful in the analysis of business and economic problems. Topics are: compound interest, annuities, differential and integral calculus. Prerequisite: C or better in MATH 1315 or MATH 1302.

MATH 1319. FORTRAN PROGRAMMING AND COMPUTER LITERACY (2-2) Computing techniques using the Fortran programming language. Word processing, spreadsheets, e-mail, Internet access, library search. This course will satisfy both the computer programming and computer literacy requirements for math majors. Prerequisite: MATH 1323 or 1426 or concurrent registration.

MATH 1322. PRECALCULUS I (3-0) This is the first semester of a two-semester sequence to prepare students for the study of calculus. An emphasis will be placed on introducing vocabulary, notation, and concepts encountered in calculus. Topics include: a review of fundamental algebra concepts, equations, inequalities, functions, graphs, polynomial functions, rational functions, exponential functions, and logarithmic functions. Prerequisite: a score of 17 or above on the Math Placement Test.

MATH 1323. PRECALCULUS II (3-0) This is the second semester of a two semester sequence to prepare students for the study of calculus. An emphasis will be placed on introducing vocabulary, notation and concepts that are basic to the study of first year calculus. Course topics include: right angle trigonometry, unit circle trigonometric, trigonometric identities, trigonomic functions and their graphs, trigonometric equations, systems of linear equations and topics from analytic geometry. Prerequisite: C or better in MATH 1322 or a score of 7 on the Calculus Readiness Test (CRT) Algebra.

MATH 1324. ALGEBRA AND TRIGONOMETRY (3-0) A fast-paced summary study of the topics of MATH 1302 and 1303. This course is not intended for calculus track students; those students should take MATH 1322 AND 1323. Credit cannot be received for MATH 1324 and MATH 1302 or 1303. Prerequisite: sufficient score on Math Placement Test.

MATH 1325. ANALYTIC GEOMETRY (3-0) Vectors, lines in two dimensions, circles, conics, transformation of coordinates, polar coordinates, parametric equations, and the solid analytic geometry of vectors, lines, planes, cylinders, spherical and cylindrical coordinates. Prerequisite: Math Placement Test score of 17 or higher.

MATH 1330. ARITHMETICAL PROBLEM SOLVING (3-0) This is a course in small and large group problem solving, with emphasis on reasoning and writing. Topics include problem solving, sets, operations and relations, arithmetic, place value and bases, propositional logic, fractions, number theory, number systems and estimation. Prerequisite: MATH 1302 and enrollment as an education major.

MATH 1331. GEOMETRICAL INFERENCE AND REASONING (3-0) A discovery-oriented exploration of two-and three-dimensional geometry, with emphasis on reasoning and writing. Topics include constructions, polygons, tessellations, polyhedra, symmetry, rigid motions in the plane, measurement, and discovering theorems. Prerequisite: MATH 1330 and enrollment as an education major.

MATH 1332. FUNCTIONS, DATA, AND APPLICATIONS (3-0) An exploration of interpreting data, using cooperative groups, spreadsheets and mathematical models. Topics include graphs, applications to economics and natural sciences, function concepts, counting principles, and basic probability and statistics. Prerequisite: MATH 1330 and enrollment as an education major.

MATH 1426. CALCULUS I (3-2) Concepts of limit, continuity, differentiation and integration; applications of these concepts. Prerequisite: C or better in MATH 1323 or passing score on the Calculus Readiness Test.

MATH 2326. CALCULUS III (3-0) Partial differentiation, multiple integrals (with applications), line integrals, Green's Theorem, surface integrals, Stokes' Theorem, divergence theorem. Prerequisite: C or better in MATH 2425.

MATH 2425. CALCULUS II (3-2) Applications of integration, techniques of integration, parametric equations, polar coordinates, sequences, series vectors, dot product, cross product, planes and quadric surfaces. Prerequisite: C or better in MATH 1426.

MATH 3300. INTRODUCTION TO PROOFS (3-0) Techniques for constructing proofs for various propositions. The propositions chosen exhibit properties of functions, relations, sets, cardinality, and other ideas in mathematics. An axiomatic approach to some areas in mathematics. Oral presentations of proofs are required. Prerequisite: MATH 1426.

MATH 3301. FOUNDATIONS OF GEOMETRY (3-0) A development of the foundations of geometry. Prerequisite: MATH 2425.

MATH 3302. MULTIVARIATE STATISTICAL METHODS (3-0) Topics in multivariate data analysis with applications in various areas of interest, including multiple regression, analysis of experimental designs, covariate adjustment, non-linear regression and the use of standard multivariate statistical packages. Prerequisite: MATH 3316 or consent of instructor.

MATH 3303. MATHEMATICAL GAME THEORY (3-0) Two-person zero-sum games, solving matrix games by linear programming, two-person non-zero sum games, noncooperative n-person games, Nash equilibrium points and refinements, cooperative n-person games, core, Shapley value, and other concepts of solution. Applications to cost allocation, fair division, and voting power. Prerequisite: MATH 3330.

MATH 3304. LINEAR OPTIMIZATION APPLICATIONS (3-0) An introduction to basic methods of optimization with applications to optimal resource application, minimal cost allocation and interpersonal decision making in noncooperative and cooperative environments. Includes simplex method, duality, zero sum games, transportation and assignment. Prerequisite: MATH 3330.

MATH 3307. ELEMENTARY NUMBER THEORY (3-0) Various topics in elementary number theory. Divisibility, congruences, quadratic reciprocity, and multiplicative functions. Prerequisite: nine hours of college mathematics.

MATH 3313. INTRODUCTION TO PROBABILITY AND MATHEMATICAL STATISTICS (3-0) Permutations, combinations, events and their probabilities, Bayes formula, random variables, probability distributions, expected value, functions of random variables, moment generating functions, central limit theorem and its role in statistics. Prerequisite: MATH 2326.

MATH 3314. DISCRETE MATHEMATICS (3-0) An introduction into discrete structures. Propositional calculus, sets and operations, functions, induction, counting, relations and matrices, equivalences and partial orders, graphs and shortest path algorithms, trees and minimal spanning trees, tree traversal, elements of boolean algebra. Prerequisite: MATH 1426.

MATH 3315. MATHEMATICAL MODELS (3-0) Methods for solving, by means of mathematics, problems which occur in other disciplines such as physics, engineering, biology, and economics. Basic mathematical tools are chosen from areas such as optimization, probability, differential equations, and computer-oriented mathematics. Problems arising in other disciplines or industrial applications are emphasized. Subject matter will depend on the instructor. Prerequisite: MATH 2326 or permission of instructor.

MATH 3316. STATISTICAL INFERENCE (3-0) A comprehensive study of basic statistical methods. Topics include descriptive statistics, numeracy, report writing, basic probability, experimental design and analysis. Prerequisite: six hours of math.

MATH 3318. DIFFERENTIAL EQUATIONS (3-0) Ordinary differential equations with emphasis on the solutions and analysis of first and higher order differential equations drawn from fields of physics, chemistry, geometry, and engineering. Prerequisite: math 2326 or concurrent registration.

MATH 3319. DIFFERENTIAL EQUATIONS & LINEAR ALGEBRA (3-0) Introductory course with emphasis on solution techniques. Ordinary differential equations, vector spaces, linear transformations, matrix/vector algebra, eigenvectors, Laplace Transform, and systems of equations. Math majors will not receive credit for this course. Prerequisite: MATH 2326 or concurrent enrollment.

MATH 3321. ABSTRACT ALGEBRA I (3-0) Groups including Lagrange's Theorem, Cauchy's Theorem, the homomorphism theorems, and symmetric groups. Prerequisite: MATH 3300.

MATH 3330. INTRODUCTION TO MATRICES AND LINEAR ALGEBRA (3-0) Solving systems of linear equations, matrix operations, determinants, vector spaces, linear transformation, orthogonality, Gram-Schmidt process, projections, and eigenvalues and eigenvectors. Prerequisite: MATH 1426.

MATH 3335. ANALYSIS I (3-0) Real numbers, sequences, series, limits of functions, continuity. Prerequisite: MATH 2326, 3300.

MATH 3345. NUMERICAL ANALYSIS AND COMPUTER APPLICATIONS (2-2) Elementary error analysis, numerical solutions of nonlinear equations, numerical integration and differentiation, polynomial interpolation, solutions of linear systems, and an introduction to spline functions. The laboratory work will include use of the computer in solving the problems. Prerequisite: MATH 2326, 3330.

MATH 4180. ORAL COMMUNICATION OF MATHEMATICS (1-0) This course trains students in giving effective oral presentations of mathematics and topics involving mathematics. Students will give presentations to the class and evaluate the presentations of their classmates. Topics may be chosen from mathematics and science journals at a level suitable for undergraduates, from books and articles on the history and development of mathematics, or from previous course material.

MATH 4191. SPECIAL TOPICS IN MATHEMATICS (0-0) Special topics in mathematics are assigned to individuals or small groups. Faculty members closely supervise the projects and assign library reference material. Small groups will hold seminars at suitable intervals. May be repeated for credit. Prerequisite: senior standing and written permission of the instructor & department chair.

MATH 4291. SPECIAL TOPICS IN MATHEMATICS (0-0) Special topics in mathematics are assigned to individuals or small groups. Faculty members closely supervise the projects and assign library reference material. Small groups will hold seminars at suitable intervals. May be repeated for credit. Prerequisite: senior standing and written permission of the instructor & department chair.

MATH 4303. INTRODUCTION TO TOPOLOGY (3-0) A first course in topology from the axiomatic point of view. Prerequisite: C or better in MATH 3335.

MATH 4313. APPLICATIONS OF MATHEMATICAL STATISTICS (3-0) A continuation of MATH 3313. Sampling distributions, estimation of parameters, confidence intervals, testing of hypotheses, regression, correlation, and selected topics. Prerequisite: C or better in MATH 3313.

MATH 4314. ADVANCED DISCRETE MATHEMATICS (3-0) Finite automata, Turing machines, formal languages, graph theory, combinatorial optimization, complexity of algorithms, P versus NP, and decidable versus undecidable problems. Prerequisite: C or better in MATH 3314.

MATH 4318. MATHEMATICAL METHODS FOR SCIENCES (3-0) Infinite series: complex variables; determinants; matrices; tensor analysis; Fourier analysis; differential equations; special functions. Prerequisite: MATH 3318 or 3319 and eight hours in the discipline of appropriate department.

MATH 4320. ADVANCED DIFFERENTIAL EQUATIONS (3-0) The existence and properties of solution of differential equations. Prerequisite: C or better in MATH 3318 or 3319.

MATH 4321. ABSTRACT ALGEBRA II (3-0) Rings and field theory, including polynomial rings and field extensions. Prerequisite: C or better in MATH 3321.

MATH 4322. INTRODUCTION TO COMPLEX VARIABLES (3-0) An introduction to the theory of functions of a complex variable and also an introduction to applications including uses of the residue theory, contour integration and conformal mapping. Prerequisite: C or better in MATH 2326.

MATH 4324. INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS (3-0) Methods of solutions of selected elliptic, parabolic, and hyperbolic partial differential equations with reference to physical applications. Prerequisite: C or better in MATH 3318 or MATH 3319.

MATH 4334. ADVANCED MULTIVARIABLE CALCULUS (3-0) The properties of continuous mappings from N-dimensional Euclidean space to M-dimensional Euclidean space; an introduction to differential forms and vector calculus, based upon line integrals, surface integrals, and the general Stokes theorem. Prerequisite: C or better in MATH 3335.

MATH 4335. ANALYSIS II (3-0) Integration, sequences and series of functions, and metric spaces. Prerequisite: C or better in MATH 3335.

MATH 4345. NUMERICAL ANALYSIS & COMPUTER APPLICATIONS II (2-2) Numerical solutions for ordinary differential equations, boundary value problems, minimizations of multivariate functions, and methods of least squares. Prerequisite: C or better in MATH 3345.

MATH 4381. MATHEMATICS RESEARCH (3-0) Formulation and definition of research problems, the formulation and execution of strategies of solution, and the presentation of results. Prerequisite: consent of instructor. Recommendation by other faculty encouraged.

MATH 4391. SPECIAL TOPICS IN MATHEMATICS (0-0) Special topics in mathematics are assigned to individuals or small groups. Faculty members closely supervise the projects and assign library reference material. Small groups will hold seminars at suitable intervals. May be repeated for credit. Prerequisite: senior standing and written permission of the instructor & department chair.

MATH 4392. ADVANCED TOPICS IN MATHEMATICS (3-0) Varies from semester to semester. New developments in mathematics, in-depth study of a topic not covered in other courses, or a special faculty expertise made available to undergraduates. May be repeated for credit as topic varies. Prerequisite: permission of instructor.

MATH 4393. HONORS THESIS/SENIOR PROJECT (0-0) Required of all students in the University Honors College. During the senior year the student must complete a thesis or a project under the direction of a faculty member in the math department. Prerequisite: enrollment in the University Honors College and written permission of the instructor and chair.

MATH 4394. UNDERGRADUATE RESEARCH EXPERIENCES (3-0) Research under faculty supervision and mentorship involving collaboration within a small group. The topic varies from semester to semester, is determined by the faculty teaching the course, and is announced in advance. The course promotes active learning based on inquiry, development of higher-order thinking skills, and meaningful scientific research. Prerequisite: consent of instructor.

MATH 4411. SIMULATION OF RANDOM PROCESS (4-0) A study of processes, whose outcomes are governed by chance, through a combination of lectures and computer lab sessions. Experiments include random number generation, coin tossing and other games of chance, random walks, Markov Chains, Poisson processes, birth-death processes, branching processes, and Brownian Motion. A foundation for modeling random phenomena in sciences, engineering and business. Prerequisite: C or better in MATH 2326 and knowledge of basic probability (MATH 3313 or equivalent).

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