# Mathematics (MATH) Course Descriptions

**1191 Research.** Individual research problems. May be repeated for a total of four credits.

**1314/MATH 1314 College Algebra (3-0).** Exponents and radicals, logarithms, factoring, algebraic quotients, systems of equations, inequalities, absolute value, complex numbers, quadratic equations, binomial theorem, progressions, theory of equations, and determinants.

Prerequisite: Completion of Mathematics Texas Success Initiative (TSI) requirements.

**1316/MATH 1316 Trigonometry with Analytic Geometry (3-0).** Trigonometric functions, radian measure, solutions of triangles, graphs of trigonometric functions, trigonometric identities, trigonometric equations, polar coordinates, vectors, and conic sections.

Prerequisite: Mathematics 1314 or 1324, or a suitable score on a placement exam.

**1324/MATH 1324 Finite Mathematics I (3-0).** Topics include basic algebra, linear equations, quadratic equations, functions and graphs, inequalities, logarithms and exponential functions, mathematics of finance, linear programming, matrices, systems of linear equations, and applications to management, economics, and business.

Prerequisite: Completion of Mathematics Texas Success Initiative (TSI) requirements.

**1332/MATH 1332 Introduction to Contemporary Mathematics (3-0).** A survey of ideas in contemporary mathematics. Topics may include graphs and networks, theory of elections and apportionment, statistics, and mathematical models. Recommended for students who wish to satisfy their core mathematics requirement but do not plan to take additional mathematics coursework.

Prerequisite: Completion of Mathematics Texas Success Initiative (TSI) requirements.

**1342/MATH 1342 Elementary Statistics (3-0).** A survey of basic statistical methods from an elementary standpoint. Topics include distributions, central tendency, variability, inferential procedures for one population; brief introduction to sampling techniques and nonparametric methods.

Prerequisite: Completion of Mathematics Texas Success Initiative (TSI) requirements.

**1350/MATH 1350 Fundamental Mathematics for Elementary and Middle School Teachers (3-0).** The system of whole numbers, numeration systems, the system of integers, elementary number theory, fractions, and rational numbers, decimals and real numbers, and the properties of mathematical operations. In-class activities include making and using math manipulatives, comparing different problem-solving techniques, making interdisciplinary connections, and experiencing math concepts through auditory, visual, and kinesthetic approaches to inquiry-bashed activities.

Prerequisite: Completion of Mathematics Texas Success Initiative (TSI) requirements.

**1351/MATH 1351 Geometry for Elementary and Middle School Teachers (3-0).** The fundamentals of plane and solid geometry, including measurement, area, volume, motion, and construction. In-class activities will include making and using math manipulatives, comparing different problem-solving techniques, making interdisciplinary connections, and experiencing math concepts through auditory, visual, and kinesthetic approaches to inquiry-based activities.

Prerequisite: Mathematics 1350.

**1352 Algebraic Reasoning for Elementary and Middle School Teachers (3-0).** Ratio and proportion, elementary number theory, the fundamentals of algebra, statistics, and probability, and the application of these topics in the contest of elementary and middle school. In-class activities will include making and using math manipulatives, comparing different problem-solving techniques, making interdisciplinary connections, and experiencing math concepts through auditory, visual, and kinesthetic approaches to inquiry-based activities.

Prerequisite: Mathematics 1350.

**1391 Research.** Individual research problems.

**2305/MATH 2305 Discrete Mathematics I (3-0).** An introduction to discrete mathematics including counting principles, combinatorics, discrete probability, sequences, series, and binomial theorem.

Prerequisite: Completion of Mathematics Texas Success Initiative (TSI) requirements.

**2312/MATH 2312 Precalculus (3-0).** Review of algebra, solving equations and inequalities, study of functions and inverse functions, vectors in the plane and space, parametric equations, and lines and planes in space.

Prerequisite: Mathematics 1314 or a suitable score on a placement exam.

**2412/MATH 2412 Precalculus (4-0).** An overview of topics from algebra, trigonometry, and analytic geometry that are needed for calculus, including equations and inequalities, functions and inverse functions, trigonometric functions, and applications.

Prerequisite: Mathematics 1314 or a suitable score on a placement exam.

**2413/MATH 2413 Calculus I (4-0).** Calculus of functions of one variable including a study of limits, continuity, differentiation of different classes of functions, applications of the derivative, introduction to the integral, the relationship between the derivative and integral, and the Fundamental Theorem of Calculus.

Prerequisites: Mathematics 1316 and 2312; or a suitable score on a placement exam.

**2414/MATH 2414 Calculus II (4-0).** A continued study of calculus of functions of one variable including techniques of integration, improper integrals, applications of the integral, sequences and series, power series, and differentiation and integration of parametric and polar curves.

Prerequisite: Mathematics 2413.

**3300 Introduction to Abstract Mathematics (3-0).** Logic, set operations, equivalence relations, properties of the real number system, cardinality of sets, and related topics, with an emphasis throughout on developing the necessary skills to read and construct formal mathematical arguments.

Prerequisite: Mathematics 2413.

**3301 Linear Algebra (3-0).** The algebra and geometry of finite dimensional vector spaces; determinants; linear transformations and matrices; characteristic values and vectors of linear transformations.

Prerequisite: Mathematics 2413.

**3305 Discrete Mathematics II (3-0).** Graphs, matrices, computational methods, and other discrete structures.

Prerequisite: Mathematics 2305.

**3307 Probability and Statistics (3-0).** Mathematical models of random processes; probability spaces; random variables; dependence and independence; mean values and moments of random variables; density and distribution functions; laws of large numbers.

Prerequisites: Mathematics 2305, 3415.

**3310 Introduction to Problem Solving (3-0).** Designed to help the student develop analytical skills through exposure to a variety of problem solving techniques utilizing algebra, geometry, trigonometry, and other areas of precalculus mathematics. Includes graphing calculator and instructional software applications. For students pursuing secondary teacher certification in mathematics.

Prerequisites: Mathematics 1316, 2312, 2413.

**3321 Statistics (3-0).** A survey of statistical methods, including distributions, central tendency, variability, inferential procedures for two or more populations; one-way ANOVA, inferential methods for regression and correlation.

Prerequisites: Mathematics 1314, 1316, 1324, 1342, 2312, or 2413.

**3324 Applied Mathematics for Engineering (3-0).** Application of mathematical principles to the analysis of engineering problems using linear algebra and ordinary differential equations (ODE’s). Topics include: mathematical modeling of engineering problems; separable ODE’s; first-, second-, and higher-order linear constant coefficient ODE”s; characteristic equation of an ODE; non-homogeneous equations; matrix addition and multiplication; solution of a linear system of equations; rank, determinant, and inverse of a matrix; eigenvalues and eigenvectors; solution to system of ODE’s by diagonalization; Fourier transforms. This course also introduces the use of scientific computing for the solution of differential equations and linear algebra problems.

Prerequisites: Mathematics 2413 and 2414.

**3335 Differential Equations (3-0).** Solution of differential equations, with geometric and physical applications.

Prerequisite: Mathematics 3415.

**3415 Calculus III (4-0).** Calculus of multivariable functions including partial differentiation, multiple integrals, vector functions, line integrals, Green’s Theorem, and Stoke’s Theorem.

Prerequisite: Mathematics 2414.

**4091 Research: 1 to 6.** May be repeated for a total of 12 credits.

Prerequisite: Consent of the department chair.

**4171, 4271, 4371 Internship.** Supervised internship with an approved cooperating business or government agency encompassing duties directly related to the mathematical sciences. Grading will be either pass or fail. (May be repeated for credit.)

**4181 Seminar in Mathematics (1-0).** Presentations and discussions on selected topics to encourage an exchange among mathematics majors and faculty members. (May be taken at most twice for credit.)

**4301 Abstract Algebra (3-0).** Elementary number theory including integer congruences and modular arithmetic, equivalence relations, basic topics in ring and group theory including the fundamental homomorphism theorems, structure and basic properties of fields.

Prerequisite: Mathematics 3300.

**4311 Numerical Analysis (3-0).** Number representations, error analysis; roots of equations; numerical integration, approximation, and differentiation; systems of equations; approximation by spline functions; ordinary differential equations; Monte Carlo methods and simulation.

Prerequisites: Mathematics 2414.

**4321 College Geometry (3-0).** A study of Euclidean, non-Euclidean, and transformational geometry.

Prerequisite: Mathematics 2413.

**4322 A Survey of Mathematics with Applications (3-0).** Logic and set theory, algebraic and transcendental functions, inverse functions, limits, the derivative and integral, sequences and series, linear systems, vectors, geometry, probability and statistics. Emphasis on applications utilizing the graphics calculator.

Prerequisites: Mathematics 1316, 2305, 2312, 2413, 3301, 3307 or 3321, 3310, 4321; 2.75 GPA, with no grade lower than “C” in all required mathematics courses attempted, cumulative and in residence; admission to the Educator Preparation Program.

**4331 Analysis (3-0).** The real number system, functions, limits, continuity, differentiation, Riemann integration, sequences.

Prerequisites: Mathematics 2414, 3300.

**4335 Partial Differential Equations (3-0).** A survey of partial differential equations, including classification, qualitative features, methods of solution, and applications.

Prerequisite: Mathematics 3324 or 3335.

**4351 Topology (3-0).** Sets and functions, metric spaces, topological spaces, compactness, separation, connectedness, approximation.

Prerequisite: Mathematics 3300.

**4355 Topics in Abstract Mathematics (3-0).** Selected topics from number theory, field theory, or other areas of higher mathematics, with an emphasis on understanding and constructing proofs of theorems. (May be repeated for credit when the topic varies.)

Prerequisite: Consent of the instructor.

**4361 Complex Variables (3-0).** Complex numbers, analytic functions, complex integration, power series, residues, conformal mapping, and applications.

Prerequisite: Mathematics 2414.

## Developmental Mathematics Program

**Texas Success Initiative (TSI) Requirements.** A student who fails to meet the minimum passing standard on the mathematics section of the TSIA must complete an appropriate developmental option determined by the Department of Mathematics. TSI requirements may be satisfied by one of the options specified under Developmental Education.

**Non-course-based Option.** Certain students as determined by the Department of Mathematics may be eligible to participate in non-course-based activities to complete TSI requirements. Contact the department for information about this option.

**Course-based Option.** Specially designated sections of freshman mathematics courses (“T-sections,” whose section number begins with a “T”) are designed to provide additional support for students who are not TSI complete. Students who are required to participate in developmental activities must enroll in these sections, which are identified by section numbers T10, T20, etc.

The “T-sections” meet for six hours weekly, however, “T-sections” only count three hours toward a student’s bill, course load, and GPA. A passing grade in mathematics “T-section” will both complete the student’s TSI requirements in mathematics and also earn the student credit for the appropriate college-level mathematics course. Students should choose the appropriate course in conjunction with their academic advisor to align with their degree programs.

**130C Developmental Mathematics (3-0).** An introductory course designed to remediate identified deficiencies and provide a review of fundamental operations in mathematics based on the student’s mastery of the College and Career Readiness Standards. Topics may include elementary algebra and functions; intermediate algebra and functions; geometry and measurement; and data analysis, statistics, and probability. Software will be used to customize the course to fit individual students’ needs.