MATH
0301
THEA TEST PREPARATION
(30)
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
(30)
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 THEA score greater than 219.

MATH
1301
TOPICS IN CONTEMPORARY MATHEMATICS
(30)
Intended for Liberal Arts majors. This course will survey realworld applications of mathematics. Topics may include the mathematics of dimensional analysis, population growth, optimization, voting theory, graph theory, networks, probability, statistics, and finance. A graphing calculator is required. Credit may be received for only one of MATH 1301, MATH 1302, or MATH 1315. The Math Aptitude Test (MAT) is required to register for this course. See http://www.uta.edu/math/pages/main/mpt.htm for test details.

MATH
1302
COLLEGE ALGEBRA
(30)
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. A calculator in the TI30 series is required for this course. Business majors should enroll in Math 1315. The Math Aptitude Test (MAT) is required to register for this course. See http://www.uta.edu/math/pages/main/mpt.htm for test details.

MATH
1303
TRIGONOMETRY
(30)
Trigonometric functions, radian measure, solution of triangles, graphs of trigonometric functions, trigonometric identities and equations, and complex numbers. This course is not intended for Science majors. The Math Aptitude Test (MAT) is required to register for this course. See http://www.uta.edu/math/pages/main/mpt.htm for test details.

MATH
1308
ELEMENTARY STATISTICAL ANALYSIS
(30)
Descriptive statistics, relationships between variables, interpretation of data and graphs, rudiments of probability, elementary statistical models, hypothesis testing, inference, and estimation. The Math Aptitude Test (MAT) is required to register for this course. See http://www.uta.edu/math/pages/main/mpt.htm for test details.

MATH
1313
LIBERAL ARTS HONORS MATHEMATICS
(30)
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
(30)
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. The Math Aptitude Test (MAT) is required to register for this course. See http://www.uta.edu/math/pages/main/mpt.htm for test details.

MATH
1316
MATHEMATICS FOR ECONOMICS AND BUSINESS ANALYSIS
(30)
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
(22)
Computing techniques using the Fortran programming language. Word processing, spreadsheets, email, 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
(30)
This is the first semester of a twosemester 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. systems of equations, exponential functions, and logarithmic functions. The Math Aptitude Test (MAT) is required to register for this course. See http://www.uta.edu/math/pages/main/mpt.htm for test details.

MATH
1323
PRECALCULUS II
(30)
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 trigonometry, trigonometric identities, trigonometric functions and their graphs, trigonometric equations, and topics from analytic geometry. Prerequisite: C or better in MATH 1322 or the Math Aptitude Test (MAT) is required to register for this course. See http://www.uta.edu/math/pages/main/mpt.htm for test details.

MATH
1324
ALGEBRA AND TRIGONOMETRY
(30)
A fastpaced 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. The Math Aptitude Test (MAT) is required to register for this course. See http://www.uta.edu/math/pages/main/mpt.htm for test details.

MATH
1325
ANALYTIC GEOMETRY
(30)
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. The Math Aptitude Test (MAT) is required to register for this course. See http://www.uta.edu/math/pages/main/mpt.htm for test details.

MATH
1327
ARCHITECTURAL CALCULUS
(30)
Topics from Calculus I and II that are pertinent to architecture. Prerequisite: Major or intended major in Architecture and C or better in Math 1325. This course will not substitute for Math 1426.

MATH
1330
ARITHMETICAL PROBLEM SOLVING
(30)
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: C or better in MATH 1302 and enrollment as an education major.

MATH
1331
GEOMETRICAL INFERENCE AND REASONING
(30)
A discoveryoriented exploration of twoand threedimensional geometry, with emphasis on reasoning and writing. Topics include constructions, polygons, tessellations, polyhedra, symmetry, rigid motions in the plane, measurement, and discovering theorems. Prerequisite: C or better in MATH 1330 and enrollment as an education major.

MATH
1332
FUNCTIONS, DATA, AND APPLICATIONS
(30)
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: C or better in MATH 1330 and enrollment as an education major.

MATH
1421
CONSOLIDATED PRECALCULUS
(40)
A onesemester coverage of the topics of MATH 1322 and MATH 1323. This course is intended for calculus track students who are unable to qualify for MATH 1426 (Calculus I) but are able to address the necessary prerequisites in one semester. Credit cannot be received for MATH 1421 and 1322 or 1323. Permission of a math undergraduate advisor is required.

MATH
1426
CALCULUS I
(32)
Concepts of limit, continuity, differentiation and integration; applications of these concepts. Prerequisite: C or better in MATH 1323 or MATH 1421 or the Math Aptitude Test (MAT) is required to register for this course. See http://www.uta.edu/math/pages/main/mpt.htm for test details.

MATH
2326
CALCULUS III
(30)
Partial differentiation, multiple integrals (with applications), line integrals, Green's Theorem, surface integrals, Stokes' Theorem, divergence theorem. Prerequisite: C or better in MATH 2425 or HONRSC 2425

MATH
2330
FUNCTIONS AND MODELING
(30)
Students engage in explorations and lab activities designed to strengthen and expand their knowledge of the topics found in secondary mathematics. Students collect data and explore a variety of situations that can be modeled using linear, exponential, polynomial, and trigonometric functions. Activities are designed to have them take a second, deeper look at topics they should have been exposed to previously; illuminate the connections between secondary and college mathematics; illustrate good, as opposed to typically poor, sometimes counterproductive, uses of technology in teaching; illuminate the connections between various areas of matheamtics; and engage them in serious (i.e., nonroutine) problem solving, problembased learning, and applications of mathematics. While there is some discussion of how the content relates to secondary mathematics instruction, the course primarily emphasizes mathematics content knowledge and content connections, as well as applications of the mathematics topics covered. Prerequisite: C or better in MATH 2425 and acceptance into UTeach Arlington.

MATH
2350
MATHEMATICAL MODELING IN ECOLOGY
(30)
An introductory course in modeling techniques in biology with emphasis on construction and interpretation of models in ecology and epidemiology. Computational tools will allow students to work with mathematical models based on difference and differential equations. The goals of this course will include teaching programming skills and illustrating how biological knowledge is used in this computational approach. Offered as BIOL 2350 and MATH 2350. Credit will be granted only once. Prerequisite: C or better in BIOL 1441 and MATH 1426 or HONRSC 1426.

MATH
2425
CALCULUS II
(32)
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 or HONRSC 1426.

MATH
3300
INTRODUCTION TO PROOFS
(30)
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 major or math intended major. B or better in MATH 1426 or HONRSC 1426; OR C or better in MATH 2425 or HONRSC 2425.

MATH
3301
FOUNDATIONS OF GEOMETRY
(30)
A development of the foundations of geometry. Prerequisite: C or better in MATH 2425 or HONRSC 2425.

MATH
3302
MULTIVARIATE STATISTICAL METHODS
(30)
Topics in multivariate data analysis with applications in various areas of interest, including multiple regression, analysis of experimental designs, covariate adjustment, nonlinear regression and the use of standard multivariate statistical packages. Prerequisite: C or better in MATH 3316 or STATS 3316 or MATH 3351 or BIOL 3351 or consent of the instructor.

MATH
3303
MATHEMATICAL GAME THEORY
(30)
Twoperson zerosum games, solving matrix games by linear programming, twoperson nonzero sum games, noncooperative nperson games, Nash equilibrium points and refinements, cooperative nperson games, core, Shapley value, and other concepts of solution. Applications to cost allocation, fair division, and voting power. Prerequisite: C or better in MATH 3330 or MATH 3319, or consent of the instructor.

MATH
3304
LINEAR OPTIMIZATION APPLICATIONS
(30)
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: C or better in MATH 3330 or MATH 3319.

MATH
3307
ELEMENTARY NUMBER THEORY
(30)
Various topics in elementary number theory. Divisibility, congruences, quadratic reciprocity, and multiplicative functions. Prerequisite: 2.0 or better in nine hours of college mathematics.

MATH
3313
INTRODUCTION TO PROBABILITY
(30)
Basic concepts in probability, random variables, probability distributions, functions of random variables, moment generating functions, central limit theorem and its role in statistics, joint probability functions and joint probability density functions, joint cumulative distribution functions, conditional and marginal probability distributions, covariance and correlation coefficients, transformation and order statistics. Prerequisite: C or better in MATH 2326.

MATH
3314
DISCRETE MATHEMATICS
(30)
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: C or better in MATH 1426 or HONRSC 1426.

MATH
3315
MATHEMATICAL MODELS
(30)
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 computeroriented mathematics. Problems arising in other disciplines or industrial applications are emphasized. Subject matter will depend on the instructor. Prerequisite: C or better in MATH 2326, or permission of instructor.

MATH
3316
STATISTICAL INFERENCE
(30)
A comprehensive study of basic statistical methods. Topics include descriptive statistics, numeracy, report writing, basic probability, experimental design and analysis. Prerequisite: C or better in 6 hours from the following: MATH 1302, 1308, 1322, 1323, 1330, 1331, 1332, 1421,1426, 2425, 2326, 3300, 3307, 3314, 3319, or 3330; HONRSC 1426, 2425.

MATH
3318
DIFFERENTIAL EQUATIONS
(30)
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: C or better in MATH 2326 or concurrent registration.

MATH
3319
DIFFERENTIAL EQUATIONS & LINEAR ALGEBRA
(30)
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: C or better in MATH 2326 or concurrent enrollment.

MATH
3321
ABSTRACT ALGEBRA I
(30)
Groups including Lagrange's Theorem, Cauchy's Theorem, the homomorphism theorems, and symmetric groups. Prerequisite: C or better in MATH 3300 and MATH 3330.

MATH
3330
INTRODUCTION TO MATRICES AND LINEAR ALGEBRA
(30)
Solving systems of linear equations, matrix operations, determinants, vector spaces, linear transformation, orthogonality, GramSchmidt process, projections, and eigenvalues and eigenvectors. Prerequisite: C or better in MATH 1426 or HONRSC 1426. MATH 2425 is strongly encouraged.

MATH
3335
ANALYSIS I
(30)
Real numbers, sequences, series, limits of functions, continuity. Prerequisite: Grade of C or better in both MATH 2326 and MATH 3300.

MATH
3345
NUMERICAL ANALYSIS AND COMPUTER APPLICATIONS
(30)
Numerical solutions of nonlinear equations, numerical integration and differentiation, polynomial interpolation, solutions of linear systems, and an introduction to spline functions. C or better in MATH 2326, and C or better in one of MATH 3330 or MATH 3319.

MATH
3350
DYNAMICAL SYSTEMS IN BIOLOGY
(30)
An introductory course in the existence and properties of solutions of differential and difference equations, qualitative analysis methods, and numerical solutions of differential equations using finitedifference methods. Offered as BIOL 3350 and MATH 3350: credit will be granted only once. Prerequisite: C or better in BIOL/MATH 2350 or consent of the instructor.

MATH
3351
PROBABILITY AND RANDOM PROCESSES IN BIOLOGY
(30)
Introduction to random processes arising in biological modeling. Topics include introduction to probability, Poisson processes, birthdeath processes, Markov chains, and Markov processes. Course taught as BIOL 3351 and MATH 3351; credit will be granted only once. Prerequisite: C or better in BIOL 3350 or MATH 3350 or consent of the instructor.

MATH
4150
SEMINAR IN MATHEMATICAL BIOLOGY
(10)
Formulation and definition of interdisciplinary research problems in Mathematical Biology, the formulation and execution of strategies of solution, and the presentation of results. Research under faculty supervision and mentorship involving collaboration within a small group. Prerequisite: Consent of the instructor.

MATH
4180
ORAL COMMUNICATION OF MATHEMATICS
(10)
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
(10)
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
(20)
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
(30)
A first course in topology from the axiomatic point of view. Prerequisite: C or better in MATH 3335.

MATH
4311
STOCHASTIC MODELS AND SIMULATION
(30)
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, birthdeath 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/STATS 3313 or MATH/BIOL 3351 or equivalent), or consent of instructor

MATH
4312
PROBABILITY
(30)
Basic probability theory, random variables, expectation, probability models, generating functions, transformations of random variables, limit theory. Prerequisite: C or better in MATH/STATS 3313.

MATH
4313
APPLICATIONS OF MATHEMATICAL STATISTICS
(30)
A continuation of MATH 3313. Sampling distributions, estimation of parameters, confidence intervals, testing of hypotheses, linear regression, linear time series models, moving average, autoregressive and/or autoregressive integrated moving average (ARIMA) models, estimation, data analysis and forecasting with time series models and forecast errors and confidence intervals. Prerequisite: C or better in MATH 3313 or STATS 3313.

MATH
4314
ADVANCED DISCRETE MATHEMATICS
(30)
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
(30)
Infinite series: complex variables; determinants; matrices; tensor analysis; Fourier analysis; differential equations; special functions. Prerequisite: C or better in MATH 3318 or MATH 3319 and eight hours in the discipline of appropriate department.

MATH
4320
ADVANCED DIFFERENTIAL EQUATIONS
(30)
The existence and properties of solution of differential equations. Prerequisite: C or better in MATH 3318 or 3319.

MATH
4321
ABSTRACT ALGEBRA II
(30)
Rings and field theory, including polynomial rings and field extensions. Prerequisite: C or better in MATH 3321.

MATH
4322
INTRODUCTION TO COMPLEX VARIABLES
(30)
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
(30)
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
(30)
The properties of continuous mappings from Ndimensional Euclidean space to Mdimensional 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
(30)
Differentiation, integration, and selected topics in sequences and series of functions and metric spaces. Prerequisite: C or better in MATH 3335.

MATH
4345
NUMERICAL ANALYSIS & COMPUTER APPLICATIONS II
(30)
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
4350
PRECALCULUS FOR MIDLEVEL MATHEMATICS TEACHERS
(30)
This course serves to bridge the gap between algebra and calculus for middle level teachers. It will develop a firm understanding of the concept of function, how to graphically represent various functions, analyze their behavior and create new functions from old. Functions will be used to model reallife situations.
The course will focus on the essential elements of precalculus, as given by the TEKS. It will develop the foundations for functions and explore functions as a unifying theme. This includes transformations, inverses, and solving equations. These foundational ideas will be explored and applied to specific functions, including exponential, logarithmic, power, polynomial, rational, and trigonometric functions. There will be an emphasis on multiple representations of mathematical ideas: verbal, concrete, pictorial, tabular, symbolic and graphical. Throughout, the mathematical connections between precalculus and school mathematics will be highlighted. Prerequisite: C or better in MATH 1302,1308, 1330, 1331 and 1332
This course does not count toward a degree in mathematics.

MATH
4351
CALCULUS FOR MIDLEVEL MATHEMATICS TEACHERS
(30)
This course serves to introduce the basic concepts of calculus to middle level teachers. The primary goal is to help teachers develop a fundamental understanding of the key mathematical ideas in calculus in order to broaden their mathematical perspective and gain insight into the topics in the middle level curriculum which are related and foundational to its development. Participants will develop conceptual knowledge of the processes of differentiation and integration, and understanding of their applications and an understanding of the relationship between the two processes. Prerequisite: C or better in MATH 4350. This course does not count toward a degree in mathematics.

MATH
4381
MATHEMATICS RESEARCH
(30)
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
(30)
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
(30)
Varies from semester to semester. New developments in mathematics, indepth 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
(30)
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
(30)
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 higherorder thinking skills, and meaningful scientific research. Prerequisite: consent of instructor.
