# Undergraduate Program

## Undergraduate Course Descriptions

**MATH 1314: College Algebra [TCCN: MATH 1314]**

Study of linear and quadratic equations and inequalities, logarithmic and exponential functions, graphs, systems of equations, matrices, partial fractions, binomial theorem, theory of equations. Credit not given for both MATH 1314 and MATH 1324 or MATH 1332.

Prerequisite: Appropriate score on SAT, ACT, or TSI.

**MATH 1324: Mathematics for Business and Economics I [TCCN: MATH 1324]**

Topics include review of basic algebraic concepts, linear equations and inequalities, mathematics of finance, matrices, introduction to linear programming, topics in probability. Credit not given for both MATH 1324 and MATH 1314 or MATH 1332.

Prerequisite: Appropriate score on SAT, ACT, or TSI.

**MATH 1325: Mathematics for Business and Economics II [TCCN: MATH 1325]**

Study of the real number system, sets, functions, graphs, linear equations, linear inequalities, differential and integral calculus. Credit not given to mathematics majors, minors, or students using mathematics as a secondary teaching specialization.

Prerequisite: MATH 1324 or MATH 1314.

**MATH 1332: Math for Liberal Arts Majors I [TCCN: MATH 1332]**

Topics may include logic and mathematical reasoning, sets, problem solving, applications, networks, graphs, probability, statistics, geometry, mathematics of finance, and number theory. Credit not given for both MATH 1332 and MATH 1314 or MATH 1324.

Prerequisite: Appropriate score on SAT, ACT, or TSI.

**MATH 1333: Math for Liberal Arts Majors II [TCCN: MATH 1333]**

Topics include statistics, probability, combinatorics, game theory, voting theory, and mathematics of finance.

Prerequisite: MATH 1314, MATH 1324, or MATH 1332.

**MATH 1342: Statistics [TCCN: MATH 1342]**

Measures of central tendency and dispersion, sampling, probability, testing of hypothesis, correlation and regression, and analysis of variance.

Prerequisite: Appropriate score on SAT, ACT, or TSI.

MATH 1343: Statistics II

A second course in statistics covering a variety of topics in statistical inference, including: inference of means, proportions, regression, and both one- and two-way analysis of variance. Additional topics may be included.

Prerequisite: A grade of C or better in MATH 1342.

**MATH 1350: Concepts of Modern Mathematics I [TCCN: MATH 1350]**

Study of topics in logic, set theory, and conceptual foundations of elementary number systems. Course intended for Interdisciplinary Studies majors only. Credit not given to mathematics majors or minors.

Prerequisite: MATH 1314 or equivalent.

**MATH 1351: Concepts of Modern Mathematics II [TCCN: MATH 1351]**

Study of geometry and elementary probability and statistics. Course intended for Interdisciplinary Studies majors only. Credit not given to mathematics majors or minors.

Prerequisite: MATH 1350 or equivalent.

MATH 2312: Precalculus [TCCN: MATH 2312]

A survey of college algebra, trigonometry and analytical geometry to prepare student for calculus. Topics include algebraic functions and their graphs, exponential and logarithmic functions, trigonometric functions and identities, two and three dimensional analytical geometry. Credit not given for both MATH 2312 and MATH 1316.

Prerequisite: Appropriate score on SAT, ACT, or TSI.

**MATH 2325: Functions and Modeling**

Modeling using families of functions (including linear, exponential, polynomial, and trigonometric functions), conic sections, parametric equations and polar equations. Use of multiple representations, transformations, data analysis techniques, and interconnections among geometry, probability, and algebra.

Prerequisite: MATH 2413.

**MATH 2330: Discrete Structures**

Study of mathematical logic, sets, combinations, relations, functions, graphs and trees, Boolean algebra, and algebraic structures. Students may not receive credit for both MATH 2330 and MATH 3425.

Prerequisite: MATH 1325 or MATH 2413 or equivalent, and one high-level computer language.

**MATH 2413: Calculus I [TCCN: MATH 2413]**

A study of functions, limits, continuity, differentiation of algebraic and trigonometric functions, applications of the derivative, definite and indefinite integrals with applications.

Prerequisites: Appropriate math score on SAT, ACT or TSI and a grade of C or better in MATH 1316, a passing score on departmental placement exam, or a grade of C or better in MATH 2312.

**MATH 2414: Calculus II [TCCN: MATH 2414]**

A study of differentiation and integration of transcendental functions, polar coordinates, techniques of integration, sequences, series, indeterminate forms, improper integrals.

Prerequisite: A grade of C or better in MATH 2413.

MATH 2415: Multivariate Calculus [TCCN: MATH 2415]

Vector calculus in Euclidean n-space, functions of several variables, partial differentiation and multiple integration.

Prerequisite: A grade of C or better in MATH 2414.

**MATH 3203: Matrix Methods in Science and Engineering**

Matrices and matrix algebra, determinants, systems of linear equations, Gaussian elimination, eigenvalues and eigenvectors, linear transformation, applications in science and engineering.

Prerequisite: MATH 2413.

**MATH 3305: Ordinary Differential Equations**

Study of ordinary differential equations. Emphasis is given to equations of the first order, linear equations, and solution by series.

Prerequisite: A grade of C or better in MATH 2414.

**MATH 3315: Linear Algebra and Matrix Theory**

Study of finite dimensional vector spaces and linear transformations. Emphasis is given to basic theory of matrices. Students may not receive credit for both MATH 3315 and MATH 3203.

Prerequisite: Math 3425 or concurrent enrollment.

**MATH 3336: Abstract Algebra I**

Study of algebraic structures. Emphasis is given to groups, rings, and fields.

Prerequisite: MATH 3425.

**MATH 3345: Real Analysis I**

Study of metric spaces, sequences, series, and continuous functions, differentiation, and integration.

Prerequisite: MATH 3425.

**MATH 3351: Probability and Statistics for Engineers and Scientists**

Fundamentals of probability and statistics with relevant engineering and science applications. Discrete and continuous random variables, statistical inference, parameter estimation, regression, experimental design, and model verification. Students may not receive credit for both MATH 3351 and MATH 4350.

Prerequisite: MATH 2414.

**MATH 3365: Geometric Systems**

Study of Euclidean and non-Euclidean geometries.

Prerequisite: MATH 3425.

**MATH 3373: Advanced Ordinary Differential Equations**

This course explores topics in applied mathematics as they pertain to the physical sciences. Topics include linear and nonlinear systems, phase plane analysis, study of bifurcations, transform methods, mechanics, and chaos, with a focus on theoretical development and physical application.

Prerequisite: MATH 3305, MATH 3203 or MATH 3315, and MATH 3425.

**MATH 3380: Algorithms in Applied Mathematics**

Study of applications selected from descriptive statistics, combinatorics, numerical methods, and matrices utilizing the computer.

Prerequisite: MATH 2413.

**MATH 3425: Foundations of Mathematics**

Study of elementary logic, intermediate set theory, relations, functions and countable number systems.

Prerequisite: Math 2414.

**MATH 3452: Advanced Concepts of Mathematics**

Study of geometry, probability and counting, number theory and math history. Course for Interdisciplinary Studies majors only. Credit not given to mathematics majors or minors.

Prerequisite: MATH 2330.

MATH 4160: Senior Seminar I

Reviews and integrates concepts from different branches of mathematics in the curriculum.

Prerequisite: The student must be within 3 semesters of graduation with a B.S. in mathematics.

MATH 4161: Senior Seminar II

This "capstone" course is designed to evaluate what the student has learned as a math major at UT Tyler and to give the student an opportunity to explore additional mathematical ideas from start to finish outside the classroom with a faculty mentor.

Prerequisite: MATH 4160.

MATH 4301: Number Theory

A study of the theory of numbers including divisibility, prime numbers, factorization, the Euclidean algorithm, congruences, the Chinese Remainder Theorem, Diophantine equations, quadratic residues, quadratic reciprocity, and other topics to be selected by the instructor.

Prerequisite: MATH 3425 and MATH 3315.

MATH 4306: Topology

Study of metric spaces and topological spaces with emphasis on compactness, connectedness, covering properties, separation, and metrization.

Prerequisite: MATH 3345.

MATH 4321: Combinatorics/Graph Theory

Study of combinatorial structures and techniques. Topics may include: graph theory, coloring problems, planarity, paths and cycles, networks, permutations, combinations, recursion, inclusion-exclusion, ordered sets, partial orders, and directed graphs.

Prerequisite: A grade of C or better in MATH 3425.

**MATH 4336: Abstract Algebra II**

A continuation of MATH 3336 focusing on rings, fields, and vector spaces.

Prerequisite: MATH 3336.

**MATH 4341: Real Analysis II**

Continuation of MATH 3345. Study of metric spaces, sequences, series, continuous functions, differentiation, and integration.

Prerequisite: MATH 3345.

**MATH 4342: Introduction to Complex Variables**

Study of geometry of the complex plane and functions of a single complex variable, with particular emphasis given to analytic functions, differentiation, and integration. Topics covered will include the Cauchy-Riemann equations, harmonic functions, Cauchy's theorem and the Cauchy integral formula, Taylor and Laurent series expansions, and residue calculus. Special topics may include conformal mappings and applications to partial differential equations.

Prerequisite: MATH 3425 and MATH 2415.

**MATH 4350: Theory of Probability**

Study of mathematical probability theory. Emphasis is given to combinatorial analysis, axioms of probability, conditional probability, random variables, density functions, distribution functions, moments, and limit theorems.

Prerequisite: MATH 3425.

**MATH 4351: Applied Statistics**

Emphasis on statistical thinking and real world applications. Topics include: experimental design, sampling distributions, confidence intervals, hypothesis testing, regression and correlation, analysis of variance, chi-squared tests, and non-parametric methods.

Prerequisite: MATH 4350.

**MATH 4373: Partial Differential Equations**

Development of mathematical ideas needed to solve problems in the physical sciences involving partial differential equations. Topics include heat conduction, wave propagation, and Laplace equations, use of separation of variables and transform methods to solve boundary value problems, and the development of Sturm-Liouville Theory.

Prerequisite: MATH 3305, MATH 3203 or MATH 3315, and MATH 2415.

**MATH 4380: Modeling and Numerical Analysis**

Study of the development of mathematical models focusing on the numerical analysis which forms the basis for the models.

Prerequisite: MATH 3380.

MATH 4195–4395: Undergraduate Research

Directed mathematical research on a problem of mutual interest to a student and a mathematics faculty member. An oral presentation and a written report are required at the conclusion of this course. May be repeated for a maximum of six credit hours.

Prerequisite: Approval of department chair.

**MATH 4199–4399: Independent Study**

Independent study in specific areas of mathematics not covered by organized undergraduate courses. A maximum of six credit hours for independent study courses may be applied toward an undergraduate degree.

Prerequisite: Consent of department chair.