# Undergraduate Program

## Undergraduate Course Descriptions

**MATH 0303: Intermediate Algebra**

A study of the real number system, fractions, decimals, absolute values, percentages, comparisons and proportional reasoning, signed numbers, solving linear equations and inequalities, simplifying expressions and functions. Does not count toward any degree program or electives.

**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. Prerequisite: Two years of high school algebra, satisfactory score on SAT, ACT, or THEA. Credit not given for both MATH 1314, MATH 1324, MATH 1332.

**MATH 1316: Trigonometry [TCCN: MATH 1316]**

A study of trigonometric functions of angles, degree and radian measure, circular functions, graphs, identities, inverse trigonometric functions, polar coordinates, solution of general triangles, complex numbers. Prerequisite: Two years of high school algebra, satisfactory score on SAT, ACT, or THEA.

**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. Prerequisite: Two years of high school algebra, satisfactory score on SAT, ACT, or THEA.. Credit not given for MATH 1324 and MATH 1314, MATH 1324 or MATH 1332.

**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. Prerequisite: MATH 1324 or MATH 1314. (Credit not given to mathematics majors, minors, or students using mathematics as a secondary teaching specialization.). Credit not given for MATH 1325 and MATH 1333.

**MATH 1332: Contemporary Mathematics I [TCCN: MATH 1332]**

Topics may include logic and mathematics reasoning, sets, problem solving, applications, networks, graphs, probability, statistics, geometry, mathematics of finance, and number theory. Prerequisite: Two years of high school algebra, one year of high school geometry, satisfactory score on SAT, ACT, or THEA.. Credit not given for MATH 1332 and MATH 1314 and MATH 1324.

**MATH 1333: Contemporary Mathematics II [TCCN: MATH 1333]**

Topics include statistics, probability, combinatorics, and game theory. Emphasis will be given to methods and models utilizing these topics in real world applications. Credit not given for both MATH 1333 and MATH 1325. Prerequisite: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: MATH 1314, MATH 1332 or MATH 1324. Credit not given for both MATH 1340 and 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. Prerequisite: MATH 1314 or equivalent. (Credit not given to mathematics majors or minors.)

**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. Prerequisite: MATH 1350 or equivalent. (Credit not given to mathematics majors or minors.)

**MATH 2113: Calculus I Computer Lab**

Calculus I concepts illustrated and expanded through the use of a computer algebra system. Graphing and symbolic and numerical computations will be emphasized. Corequisite: MATH 2413.

**MATH 2114: Calculus II Computer Lab**

Calculus II concepts illustrated and expanded through the use of a computer algebra system. Graphing and symbolic and numerical computations will be emphasized. Corequisite: MATH 2414.

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

**MATH 2412: Precalculus**

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 2412 and MATH 1314.

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

A study of functions, limit, continuity, differentiation of algebraic and trigonometric functions, applications of the derivative, definite and indefinite integrals with applications. Prerequisites: Minimum math score on SAT, ACT or THEA and "C" or better in MATH 1316, or passing score on departmental trigonometry test, or "C" or better in MATH 2412.

**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: MATH 2413.

**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 2414 or concurrent enrollment.

**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: 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. 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. Emphasis is given to real and complex number systems. Prerequisites: MATH 2414 and 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. Prerequisite: MATH 2414.

**MATH 3365: Geometric Systems**

Study of Euclidean and non-Euclidean geometries. Prerequisite: MATH 3425.

**MATH 3373: Applied Mathematics I**

This course explores topics in applied mathematics as they pertain to the physical sciences. Topics include linear and nonlinear systems, Laplace transforms and Fourier series with a focus on theoretical development and physical applications. Prerequisite: MATH 3305, MATH 3203 or MATH 3315, and MATH 3404.

**MATH 3380: Algorithms in Applied Mathematics**

Study of applications selected from descriptive statistics, combinatorics, numerical methods, and matrices utilizing the computer. Prerequisite: MATH 2414 or concurrent enrollment.

**MATH 3404: Multivariate Calculus**

Vector calculus in Euclidean n-space, functions of several variables, partial differentiation and multiple integration. Prerequisite: MATH 2414. Course fee $10.

**MATH 3104: Multivariate Calculus Computer Lab**

Multivariate Calculus concepts illustrated and expanded through the use a computer algebra system. Graphing and symbolic and numerical computations will be emphasized. Corequisite: MATH 3404.

**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. Prerequisite: MATH 2330. (Credit not given to mathematics majors or minors.)

**MATH 4336: Abstract Algebra II**

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

**MATH 4341: Introduction to Real Variables**

Study of real-valued functions of a real variable. Emphasis is given to continuity, differentiation, integration, series expansions. Prerequisite: MATH 3345.

**MATH 4342: Introduction to Complex Variables**

Study of functions of a complex variable. Emphasis is given to analytic functions, differentiation, integration, series expansions. Prerequisite: MATH 3345.

**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 2414 and 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 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 BS 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: MATH4160

**MATH 4373: Applied Mathematics II**

Continuation of MATH 3373. Development of mathematical ideas needed to solve problems in the physical sciences. Topics include heat, wave and Laplace equations, use of Fourier methods to solve boundary value problems and the development of Sturm-Liouville Theory. Prerequisite: MATH 3373.

**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 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.