MAT

COURSE DESCRIPTIONS

MATHEMATICS

(MAT)

0103 TASP Review I
(3-0) 3 hours credit.
A course intended for students with minimal mathematical skills who need a comprehensive review before they can successfully complete an algebra course. Topics include the Fundamental Mathematics and Geometry objectives of the Texas Academic Skills Program (TASP), with an introduction to algebra. Intensive review and maintenance of computational skills with integers, fractions, decimals, percents, ratio, and proportions; reading and interpreting information presented in graphs, tables, and charts; solving word problems, elementary algebraic equations, and problems with two- and three-dimensional geometric figures; and inductive and deductive reasoning skills. Course does not count toward any degree at UTSA.

0113 TASP Review II
(3-0) 3 hours credit.
Introductory algebra course that includes the Texas Academic Skills Program (TASP) Algebra and Problem Solving objectives. Operations with algebraic expressions; solving one- and two-variable equations; solving word problems involving one and two variables; graphing numbers and number relationships; solving problems involving quadratic equations. Course does not count toward any degree at UTSA.

1023 College Algebra with Applications
(3-0) 3 hours credit. Prerequisite: Satisfactory performance on a placement examination.
Topics include algebraic expressions, equations, inequalities over the real numbers, relations, functions and graphs, polynomial and rational functions, systems of linear equations and inequalities, complex numbers, and matrices and determinants. A wide range of applications will be included in this course. Students majoring in areas that require MAT 1214, Calculus I are encouraged to take MAT 1073 instead of MAT 1023. [TCCN 1314.] (Formerly MAT 1063. Credit can be earned for only one of the following: MAT 1023, MAT 1063, or MAT 1073.)

1033 Algebra with Calculus for Business
(3-0) 3 hours credit. Prerequisite: Satisfactory performance on a placement examination.
An introduction to business calculus with an emphasis on the algebra of functions. Concentration is on the algebraic manipulations of functions and includes volume and profit functions, both linear and quadratic; root finding and graphical analysis; matrices; and differentiation and integration. [TCCN: MATH 1325.]

1043 Introduction to Mathematics
(3-0) 3 hours credit. Prerequisite: Satisfactory performance on a placement examination.
This course is designed primarily for the liberal arts major to satisfy the core curriculum mathematics requirement. Topics may include logic, proofs, deductive and inductive reasoning, number theory, fundamentals of statistics, basic statistical graphs, casual connections, financial management, functions, linear graphs and modeling, exponential growth and decay, logarithms, fundamentals of probability, fundamentals of geometry, and basic ideas from trigonometry, calculus, and discrete mathematics. [TCCN: MATH 1332]

1073 Algebra for Scientists and Engineers
(3-0) 3 hours credit. Prerequisite: Satisfactory performance on a placement examination.
This course is designed to prepare the student for MAT 1093 Precalculus and MAT 1214 Calculus. Topics and graphs include algebraic expressions, equations, inequalities over the real numbers, relations, functions, polynomials and rational functions, logarithmic and exponential functions, systems of linear equations and inequalities, matrices and determinants, complex numbers and polynomials, sequences, series, binomial expansion, mathematical induction, permutations, and combinations. (Credit can be earned for only one of the following: MAT 1023, MAT 1063, or MAT 1073.)

1093 Precalculus
(3-0) 3 hours credit. Prerequisite: MAT 1023 or MAT 1073, or the equivalent course or satisfactory performance on a placement examination.
Exponential functions, logarithmic functions, trigonometric functions, complex numbers, DeMoivre's theorem, and polar coordinates. [TCCN: MATH 2312.]

1143 Essential Elements in Mathematics
(3-0) 3 hours credit. Prerequisite: MAT 1023.
Numeration systems; properties of the systems of whole numbers, integers, rational numbers, and real numbers; problem solving; geometry and measurement; probability and statistics; logic. May not be applied toward a major in mathematics. [TCCN: MATH 1335.] (Credit cannot be earned for both MAT 1143 and MAT 1153).

1153 Essential Elements in Mathematics I
(3-0) 3 hours credit. Prerequisite: MAT 1023 or MAT 1073.
Numeration systems; properties of the systems of whole numbers, integers, rational numbers, and real numbers; problem solving; logic. May not be applied toward a major in mathematics. [TCCN: MATH 1350] (Credit cannot be earned for both MAT 1153 and MAT 1143.)

1163 Essential Elements in Mathematics II
(3-0) 3 hours credit. Prerequisite: MAT 1153.
Algebra, statistics and probability; geometric shapes; measurement; coordinate and transformational geometry. May not be applied toward a major in mathematics. [TCCN: MATH 1351]

1203 Calculus Concepts and Applications
(3-0) 3 hours credit. Prerequisite: MAT 1093.
This course is primarily for students pursuing a degree in Interdisciplinary Studies and/or seeking Pre-K through 8 teacher certification. The course will include the following calculus concepts: functions, limits, derivatives, and integrals. Applications and the use of technology are incorporated throughout the course. This course may not be applied toward a major in mathematics and will not meet the prerequisite for MAT 1223 Calculus II.

1214 Calculus I
(4-0) 4 hours credit. Prerequisite: MAT 1093 or an equivalent course or satisfactory performance on a placement examination.
An introduction to the concepts of limit, continuity and derivative, mean value theorem, and applications of derivatives such as velocity, acceleration, maximization, and curve sketching; introduction to the Riemann integral and the fundamental theorem of calculus. [TCCN: MATH 2413.]

1223 Calculus II
(3-0) 3 hours credit. Prerequisite: MAT 1214.
Methods of integration, inverse trigonometric functions, and applications of the integral. [TCCN: MATH 2314.]

2213 Calculus III
(3-0) 3 hours credit. Prerequisite: MAT 1223.
Special areas of differential and integral calculus; includes Taylor series, power series, convergence tests, vectors, functions of several variables, partial derivatives, and multiple integrals. [TCCN: MATH 2315.]

2233 Linear Algebra
(3-0) 3 hours credit. Prerequisite: MAT 2213 or EGR 2323.
Vector spaces and matrix algebra, matrices and determinants, characteristic values of matrices, and reduction to canonical forms. Emphasis on applications. [TCCN: MATH 2318.]

3013 Foundations of Mathematics
(3-0) 3 hours credit. Prerequisite: MAT 1214.
Development of theoretical tools for rigorous mathematics. Topics may include mathematical logic, propositional and predicate calculus, set theory, functions and relations, cardinal and ordinal numbers, Boolean algebras, and construction of the natural numbers, integers, and rational numbers. Emphasis on theorem proving. (Formerly MAT 2243. Credit cannot be earned for MAT 3013 and MAT 2243.)

3123 Fundamentals of Geometry
(3-0) 3 hours credit. Prerequisites: MAT 1214 and MAT 3013.
A survey of geometric concepts, including axiomatic development of advanced Euclidean geometry, coordinate geometry, non-Euclidean geometry, three-dimensional geometry, and topology. May not be applied toward a major in mathematics other than the General Mathematical Studies Concentration of the B.S. in Mathematics.

3213 Foundations of Analysis
(3-0) 3 hours credit. Prerequisites: MAT 1214 and MAT 3013.
Axiomatic definition of real numbers, including order properties and completeness; infinite sequences and their convergence; basic notions related to series and their convergence; functions and function limits. Introduction to topology of the real line. Emphasis on theorem proving.

3223 Complex Variables
(3-0) 3 hours credit. Prerequisites: MAT 2213 and MAT 3013. An introduction to complex variables, including elementary functions, line integrals, power series, residues and poles, and conformal mappings.

3233 Modern Algebra
(3-0) 3 hours credit. Prerequisites: MAT 1214 and MAT 3013.
Topics will include the development of groups, integral domains, fields, and number systems, including the complex numbers. Divisibility, congruences, primes, perfect numbers, and some other problems of number theory will be considered.

3243 Calculus for Applications
(3-0) 3 hours credit. Prerequisite: MAT 2233.
Line vector differential and integral calculus, line integrals, Green's theorem, Stokes' theorem and Divergence theorem.

3253 Engineering Analysis
(3-0) 3 hours credit. Prerequisite: MAT 2213.
Ordinary differential equations, Laplace transforms, linear algebra, and matrix arithmetic. May not be applied to a major in mathematics.

3273 Applied Mathematics for Sciences and Engineering
(3-0) 3 hours credit. Prerequisite: MAT 3253 or MAT 3613.
Complex analysis, Fourier series, Fourier transforms, harmonic analysis, and partial differential equations. (Formerly MAT 3263. Credit cannot be earned for both MAT 3273 and MAT 3263.)

3613 Differential Equations I
3-0) 3 hours credit. Prerequisite: Completion of or concurrent enrollment in MAT 2233.
Basic notions of differential equations, solution of first-order equations and linear equations with constant coefficients, nth-order initial value problems, and power series solutions of differential equations.

3623 Differential Equations II
(3-0) 3 hours credit. Prerequisite: MAT 3613.
Continuation of MAT 3613. Stability, partial differential equations, and boundary value problems.

3633 Numerical Analysis
(3-0) 3 hours credit. Prerequisites: MAT 2233, MAT 3213, and either CS 1073, CS 2073, or CS 1713.
Solution of linear and nonlinear equations, curve-fitting, and eigenvalue problems.

3653 Stochastic Calculus
(3-0) 3 hours credit. Prerequisite: STA 3513
Probability, random walk, Brownian motion, stationary and evolutionary processes and stochastic differential equations.

4013 Graphing Calculator Topics
(3-0) 3 hours credit. Prerequisites: MAT 1223 and MAT 3233.
Mathematical topics from algebra, trigonometry, calculus, modeling, and probability and statistics will be investigated using the graphing calculator. Assessment and evaluation techniques using technology will also be included. May not be applied toward a major in mathematics other than the General Mathematics Studies Concentration of the B.S. in Mathematics.

4113 Computer Mathematical Topics
(3-0) 3 hours credit. Prerequisites: MAT 3233 and either MAT 3123 or MAT 4263.
Mathematical topics from consumer mathematics, algebra, geometry, number theory, and probability and statistics will be investigated using the computer. Course will also include some instruction in BASIC programming language. May not be applied toward a major in mathematics other than the General Mathematical Studies Concentration of the B.S. in Mathematics.

4123 History of Mathematics
(3-0) 3 hours credit. Prerequisites: MAT 3233 and either MAT 3123 or MAT 4263.
Selected subjects in mathematics developed through historical perspectives and biographies. May not be applied toward a major in mathematics other than the General Mathematical Studies Concentration of the B.S. in Mathematics.

4213 Real Analysis I
(3-0) 3 hours credit. Prerequisite: MAT 3213.
Continuous functions, uniform continuity; theory of differentiation; applications of the derivative to properties of functions; antiderivatives; Riemann integral; connection between differentiation and integration.

4223 Real Analysis II
(3-0) 3 hours credit. Prerequisite: MAT 4213.
Lebesgue integral on the real line; n-dimensional spaces; vectors; calculus of functions of several variables; multidimensional integration.

4233 Modern Abstract Algebra
(3-0) 3 hours credit. Prerequisite: MAT 3213.
An in-depth study of groups and rings.

4253 Number Theory
(3-0) 3 hours credit. Prerequisite: MAT 3213.
The theory of primes, congruences, and related subjects.

4263 Geometry
(3-0) 3 hours credit. Prerequisite: MAT 3013.
Projective, affine, and non-Euclidean geometry.

4273 Topology
(3-0) 3 hours credit. Prerequisite: MAT 3213.
Set theory, including cardinal and ordinal numbers. Topological properties of the real-line and metric spaces.

4313 Applied Combinatorics
(3-0) 3 hours credit. Prerequisite: MAT 1223.
Permutations, combinations, arrangements, selections, distributions, generating functions, inclusion-exclusion principle.

4323 Applied Graph Theory
(3-0) 3 hours credit. Prerequisite: MAT 1223.
Isomorphism, planarity, computer representation of graphs, covering circuits and graph colorings, Euler and Hamiltonian graphs, trees and searching network algorithms (shortest paths, connectivity, traveling salesman, network flow, matching, sorting, etc.).

4803 Statistical Quality Control
(3-0) 3 hours credit. Prerequisite: STA 1993 or STA 3513.
Statistical methods are introduced in terms of problems that arise in manufacturing and their applications to the control of manufacturing processes. Topics include control charts and acceptance sampling plans. (Same as STA 4803. Credit cannot be earned for both MAT 4803 and STA 4803.)

4913 Independent Study
3 hours credit. Prerequisite: Permission in writing (form available) of the instructor, the student's advisor, the Department Chair and Dean of the College in which the course is offered.
Independent reading, research, discussion, and/or writing under the direction of a faculty member. May be repeated for credit, but not more than 6 semester credit hours, regardless of discipline, will apply to a bachelor's degree.

4953 Special Studies in Mathematics
(3-0) 3 hours credit. Prerequisite: Consent of instructor.
An organized course offering the opportunity for specialized study not normally or not often available as part of the regular course offerings. May be repeated for credit when the topics vary, but not more than 6 semester credit hours, regardless of discipline, will apply to a bachelor's degree.

4993 Honors Research
3 hours credit. Prerequisite: Enrollment limited to candidates for College Honors during their last two semesters; approval by the College Honors Committee. Supervised research and preparation of an honors thesis.