The University of Texas at Arlington Undergraduate Catalog
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Bachelor’s Degrees in Mathematics The Bachelor of Science (no option) is primarily intended for students wishing to pursue graduate work in mathematics. The industrial and applied mathematics option is aimed at students seeking careers as mathematicians in the emerging high-tech industries. The computer science option is intended for those students who wish to seek employment relating to mathematical computing. The statistics and management science/operations research options are intended for students with an interest in a career involving various applications of mathematics to the world of business. The Bachelor of Arts is intended for those students desiring to teach mathematics at the elementary and secondary school level and for those seeking a traditional liberal arts education with an emphasis on mathematics. All students seeking a bachelor’s degree in mathematics must take at least two mathematics sequences. A sequence is defined as a 3300-level course followed by a 4300-level course in the same general area of mathematics. The approved sequences are as follows: MATH 3321-4321 (Abstract Algebra), MATH 3335 and 4335 or 4334 (Analysis), MATH 3345 and 4345 (Numerical Analysis), MATH 3313-4313 (Probability and Statistics), MATH 3313-4311 (Probability and Random Processes), MATH 3314-4314 (Discrete Mathematics), MATH 3318-4320 or MATH 3318-4324 (Differential Equations), MATH 3318-4318 (Mathematical Methods for Sciences), and MATH 3301-4342 (Contemporary Geometry). For the computer science option, the second sequence must be MATH 3345-4345. For the statistics option, the second sequence must be MATH 3313-4313. It is strongly recommended that mathematics majors take MATH 3330 (Intro to Matrices and Linear Algebra) as early as possible, since this course is a prerequisite for many other 3000/4000-level courses. It is suggested to take MATH 3330 simultaneously with Calculus III. Mathematics majors may want to consider taking MATH 3300 (Intro to Proofs) before attempting the required courses MATH 3321 and MATH 3335. It is also strongly recommended that mathematics majors with little or no computer programming experience satisfy the computer programming requirements as early as possible with MATH 1319, CSE 1306, 1310, or 1320. Teacher Certification Requirements for
a Bachelor of Science Degree in Mathematics Area Minor:
24 hours including at least nine hours of 3000/4000 level courses.
The areas permitted are natural sciences (biology, chemistry, geology,
physics), and engineering (all courses). Requirements
for a Bachelor of Science Degree in Mathematics Requirements
for a Bachelor of Science Degree in Mathematics Requirements
for a Bachelor of Science Degree in Mathematics Computer Programming Senior Year Requirements
for a Bachelor of Science Degree in Mathematics Option Second Major Admission Requirements • Minimum GPA of 2.25 in at least nine hours
of mathematics courses in residence at the level of MATH 1325 or
above. Students currently enrolled at the University may qualify to change their major to mathematics by meeting the requirements listed above depending on their current status. Academic Probation (College of Science): Majors whose overall GPA or GPA in major courses falls below 2.0 will be placed on probation and, in addition to counseling by the University Advising Center, must consult with the Department Advisor prior to enrolling in additional courses.Satisfactory Academic Standard
Requirement Graduation Requirement Transitional Graduation
Requirement Non-Credit Courses Pre-Actuarial Program Department of Mathematics
Faculty
0302. FUNDAMENTALS
OF ALGEBRA (3-0) 3 hours credit. 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. 1302. COLLEGE ALGEBRA
(3-0) 3 hours credit (MATH 1314). 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; compound interest
and annuities; systems of linear equations; matrices; permutations,
combinations and probability. Prerequisite: passing score on the
mathematics placement test (for details, contact the Mathematics
Department). Credit cannot be received for both MATH 1302 and MATH
1315. 1303. TRIGONOMETRY
(3-0) 3 hours credit (MATH 1316). Trigonometric functions,
radian measure, solution of triangles, graphs of trigonometric functions,
trigonometric identities and equations, and complex numbers. Prerequisite:
passing score on the mathematics placement test (for details, contact
the Mathematics Department). 1308. ELEMENTARY STATISTICAL
ANALYSIS (3-0) 3 hours credit (MATH 1342). Descriptive statistics,
relationships between variables, interpretation of data and graphs,
rudiments of probability, elementary statistical models, hypothesis
testing, inference, and estimation. Prerequisites: MATH 1302 or
MATH 1315 or equivalent and passing score on the mathematics placement
test (for details, contact the Mathematics Department). 1313. LIBERAL ARTS
HONORS MATHEMATICS (3-0) 3 hours credit. 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. 1315. COLLEGE ALGEBRA
FOR ECONOMICS AND BUSINESS ANALYSIS (3-0) 3 hours credit (MATH 1324).
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. Prerequisite: passing score on
the mathematics placement test (for details, contact the Mathematics
Department). Credit cannot be received for both MATH 1302 and MATH
1315. 1316. MATHEMATICS
FOR ECONOMICS AND BUSINESS ANALYSIS (3-0) 3 hours credit (MATH 1325).
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:
MATH 1315 or equivalent. 1319. FORTRAN PROGRAMMING
AND COMPUTER LITERACY (2-2) 3 hours credit. Computing techniques
using the FORTRAN 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 1325 or concurrent registration. 1323. PRE-CALCULUS
(3-0) 3 hours credit. This course provides requisite knowledge
and skills for success in MATH 1426 (Calculus I). An emphasis will
be placed on introducing vocabulary, notation and concepts that
are basic to the study of first year calculus. Course topics include:
Review of fundamental algebraic concepts, equations, and inequalities,
functions and graphs, polynomial and rational functions, sequences
and summation, trigonometric functions, vectors in two dimensions.
Prerequisites: MATH 1302 and 1303; or MATH 1324 or equivalent. Students
without either MATH 1302 and 1303, or MATH 1324, must take the math
placement test and obtain permission from a mathematics department
advisor before enrolling in this course. 1324. ALGEBRA AND
TRIGONOMETRY (3-0) 3 hours credit. A fast-paced summary study
of the topics of MATH 1302 and 1303 and intended for calculus-track
students. Credit cannot be received for MATH 1324 and MATH 1302
or 1303. Prerequisite: Equivalent of at least two years high school
algebra and trigonometry. 1330. ARITHMETICAL
PROBLEM SOLVING (3-0) 3 hours credit. 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 consent of instructor. 1331. GEOMETRICAL
INFERENCE AND REASONING (3-0) 3 hours credit. 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
consent of instructor. 1332. FUNCTIONS, DATA,
AND APPLICATIONS (3-0) 3 hours credit. 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 consent of instructor. 1426. CALCULUS I (3-2)
4 hours credit (MATH 2413). Concepts of limit, continuity,
differentiation and integration; applications of these concepts.
The laboratory work will include a computer algebraic system. Prerequisite:
MATH 1323, MATH 1325 or concurrent registration with major advisor’s
approval. 2325. CALCULUS II
(3-0) 3 hours credit (MATH 2314). Applications of integration,
techniques of integration, parametric equations, polar coordinates,
sequences and series. Prerequisite: MATH 1426. 2326. CALCULUS III
(3-0) 3 hours credit (MATH 2315). Partial differentiation,
multiple integrals (with applications), line integrals, Green’s
Theorem, surface integrals, Stokes’ Theorem, divergence theorem.
Prerequisite: MATH 2325. 3300. INTRODUCTION
TO PROOFS (3-0) 3 hours credit. 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.
Prerequisite: MATH 1426. 3301. INTRODUCTION
TO THE FOUNDATIONS OF GEOMETRY (3-0) 3 hours credit. A development
of the foundations of geometry. Prerequisite: MATH 1426. 3302. MULTIVARIATE
STATISTICAL METHODS (3-0) 3 hours credit. Topics in multivariate
data analysis with applications in various areas of interest including
business research. Multiple regression, introduction to econometric
models, discriminant analysis, cluster analysis, factor analysis,
and the use of standard multivariate statistical packages. Prerequisite:
MATH 3313 or MATH 3316. 3303. MATHEMATICAL
GAME THEORY (3-0) 3 hours credit. 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. 3304. LINEAR OPTIMIZATION
APPLICATIONS (3-0) 3 hours credit. 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. 3307. ELEMENTARY NUMBER
THEORY (3-0) 3 hours credit. Various topics in elementary
number theory. Divisibility, congruences, quadratic reciprocity,
and multiplicative functions. Prerequisite: nine hours of college
mathematics. 3313. INTRODUCTION
TO PROBABILITY AND MATHEMATICAL STATISTICS (3-0) 3 hours credit.
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. 3314. DISCRETE MATHEMATICS
(3-0) 3 hours credit. 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. 3315. MATHEMATICAL
MODELS (3-0) 3 hours credit. 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 the instructor. 3316. STATISTICAL
INFERENCE (3-0) 3 hours credit. A comprehensive treatment
of statistical methodology in various areas of applications. Elementary
probability, descriptive statistics, discrete and continuous distributions,
estimation, testing hypothesis, linear regression, and analysis
of variance. Prerequisite: six hours of mathematics. 3318. DIFFERENTIAL
EQUATIONS (3-0) 3 hours credit. 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. 3319. DIFFERENTIAL
EQUATIONS AND LINEAR ALGEBRA (3-0) 3 hours credit. Introductory
course with emphasis on solution techniques. Ordinary differential
equations, vector spaces, linear transformations, matrix/vector
algebra, eigenvectors, Laplace Transform, and systems of equations.
Prerequisite: MATH 2326 or concurrent registration. 3321. ABSTRACT ALGEBRA
I (3-0) 3 hours credit. Groups including Lagrange’s
Theorem, Cauchy’s Theorem, the homomorphism theorems, and symmetric
groups. Prerequisite: MATH 3330 or MATH 3314. 3330. INTRODUCTION
TO MATRICES AND LINEAR ALGEBRA (3-0) 3 hours credit. Solving
systems of linear equations, matrix operations, determinants, vector
spaces, linear transformation, orthogonality, Gram-Schmidt process,
projections, and eigenvalues and eigenvectors. Prerequisite: MATH
1426. 3335. ANALYSIS I (3-0)
3 hours credit. Real numbers, sequences, series, limits of
functions, continuity, and differentiation. Prerequisite: MATH 2326
and MATH 3314 or MATH 3330. 3345. NUMERICAL ANALYSIS
AND COMPUTER APPLICATIONS (2-2) 3 hours credit. 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. Prerequisites: MATH 2326, MATH 3330, and a knowledge of
FORTRAN, C, or PASCAL. 4180. ORAL COMMUNICATION
OF MATHEMATICS (1-0) 1 hour credit. 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. 4191, 4291, 4391.
SPECIAL TOPICS IN MATHEMATICS (variable credit from 1 to
3 semester hours as arranged). 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. Prerequisites: senior standing and written permission
of the instructor and chair. 4303. INTRODUCTION
TO TOPOLOGY (3-0) 3 hours credit. A first course in topology
from the axiomatic point of view. Prerequisite: MATH 3335. 4311. ELEMENTARY RANDOM
PROCESSES (3-0) 3 hours credit. A continuation of MATH 3313.
Topics: Markov chains, Poisson process, birth and death processes,
Brownian motion. Has applications to physics, biology, engineering,
business. Prerequisite: MATH 3313 or equivalent. 4313. APPLICATIONS
OF MATHEMATICAL STATISTICS (3-0) 3 hours credit. A continuation
of MATH 3313. Sampling distributions, estimation of parameters,
confidence intervals, testing of hypotheses, regression, correlation,
and selected topics. Prerequisite: MATH 3313. 4314. ADVANCED DISCRETE
MATHEMATICS (3-0) 3 hours credit. Finite automata, Turing
machines, formal languages, graph theory, combinatorial optimization,
complexity of algorithms, P versus NP, and decidable versus undecidable
problems. Prerequisite: MATH 3314. 4318. MATHEMATICAL
METHODS FOR SCIENCES (3-0) 3 hours credit. Infinite series:
complex variables; determinants; matrices; tensor analysis; Fourier
analysis; differential equations; special functions. Prerequisites:
MATH 3318 or 3319 and eight hours in the discipline of appropriate
department. 4320. ADVANCED DIFFERENTIAL
EQUATIONS (3-0) 3 hours credit. The existence and properties
of solution of differential equations. Prerequisite: MATH 3318 or
3319. 4321. ABSTRACT ALGEBRA
II (3-0) 3 hours credit. Rings and field theory, including
polynomial rings and field extensions. Prerequisite: MATH 3321.
4322. INTRODUCTION
TO COMPLEX VARIABLES (3-0) 3 hours credit. 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: MATH 2326. 4324. INTRODUCTION
TO PARTIAL DIFFERENTIAL EQUATIONS (3-0) 3 hours credit. Methods
of solutions of selected elliptic, parabolic, and hyperbolic partial
differential equations with reference to physical applications.
Prerequisite: MATH 3318 or 3319. 4334. ADVANCED MULTIVARIABLE
CALCULUS (3-0) 3 hours credit. 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: MATH 3335. 4335. ANALYSIS II
(3-0) 3 hours credit. Integration, sequences and series of
functions, and metric spaces. Prerequisite: MATH 3335. 4342. COMPUTATIONAL
GEOMETRY (2-2) 3 hours credit. A survey of the mathematical
elements for computer graphics. Topics included are: affine, perspective
and projective transformations, Bezier and B-spline curves and surfaces.
Prerequisites: MATH 3301 or permission of instructor and a knowledge
of a technical programming language. 4345. NUMERICAL ANALYSIS
AND COMPUTER APPLICATIONS II (2-2) 3 hours credit. Numerical
solutions for ordinary differential equations, boundary value problems,
minimizations of multivariate functions, and methods of least squares.
Prerequisites: MATH 3345 and 3318 or 3319. 4381. MATHEMATICS
RESEARCH (3-0) 3 hours credit. 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. 4392. ADVANCED TOPICS
IN MATHEMATICS (3-0) 3 hours credit. 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. 4393. HONORS THESIS/SENIOR PROJECT (3-0) 3 hours credit. 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. --- |