MAIN CONTENT

**MTH 1750. College Algebra (I, II; 3) **

Topics include functions, rational expressions, systems of linear equations, Factor and Remainder Theorem, operations on functions, radical equations, inequalities, matrices, variations and exponential and logarithmic functions, sequences, series, and the binomial theorem. Equivalent to TAG TMM001.

**MTH 2001. Probability and Statistics I (I; 3) **

Topics include measures of central tendency, measures of dispersion, probability models, conditional probability, combinations, distributions, estimation and hypothesis testing. Prerequisite: MTH 1750.

**MTH2002. Probability and Statistics II (II;3) **

Topics include testing populations, means, proportions, variances, contingency tables, regression, ANOVA, computer applications, and non-parametric statistics. Prerequisite: MTH2001.

**MTH2500. Precalculus. (I, II; 4) **

This is an accelerated course in College Algebra and Trigonometry. Topics include linear, quadratic, polynomial, rational, radical, root, piecewise, exponential, logarithmic, trigonometric and inverse trigonometric functions; graphs and transformations; equations and inequalities; systems of equations; sequences and series; vectors and applications. Prerequisite: Placement exam.

**MTH2501. Trigonometry (I,II; 3) **

Topics include conic sections, exponential and logarithmic functions, trigonometric functions, inverse trigonometric functions, identities and equations, lines, polar coordinates, vectors in the plane, application problems, and complex numbers. Prerequisite: MTH 1750 or placement exam. Equivalent to TAG TMM003.

**MTH2502. Calculus I (I,II; 4) **

Topics include limits of functions, infinite limits, derivative and techniques of differentiation, implicit differentiation, higher derivatives, graphing, maxima and minima, plane curves, motion, antiderivatives, indefinite and definite integrals, and the Fundamental Theorem of Calculus. Prerequisite: MTH2501 or MTH2500. Equivalent to TAG TMM005.

**MTH 2503. Calculus II (I, II; 5) **

Topics include the fundamental theorem of calculus, the definite integral, techniques and applications of integration. Evaluation of improper integrals, indeterminate forms, graphs of polar equations, area in polar coordinates and parametric equations. Differentiation and integration a power series, Taylor and MacLaurin series. Calculation and application of the dot and cross products of vectors. Prerequisite: MTH 2502. Equivalent to TAG OMT006.

**MTH2540. Foundations in Mathematics (I,II; 3) **

This course is an introduction to mathematical proof, symbolic logic, induction, set theory, relations, functions, countability, and selected topics in number theory. Prerequisite: MTH 2502.

**MTH2002. Probability and Statistics II (II; 3) **

Topics include testing populations, means, proportions, variances, contingency tables, regression, ANOVA, computer applications, and non-parametric statistics. Prerequisite: MTH2001.

**MTH3000. Geometry for Teachers (II; 3) **

Topics include definitions, axioms, plane figures, triangle theorems, similar triangles, areas, computation of areas, solids, volumes, computation of volumes, and history of geometry. Prerequisite: MTH 1750.

**MTH3001. Linear Algebra (I; 3) **

Topics include matrices, determinants, linear systems, vector spaces, linear transformations, eigenvalues and eigenvectors. Prerequisite: MTH2503. Equivalent to TAG OMT008.

**MTH 3002. Calculus III (II; 4) **

Topics include the theory of infinite series, analytic geometry of space, vectors in space, partial derivatives, and multiple integrals. Prerequisite: MTH 2503.

**MTH3110. Differential Equations and Discrete Dynamical Systems (I; 4) **

First and second order, linear, simultaneous equations with descriptions of solution methodology. Laplace transforms, applications, and solutions methodology for nonlinear differential equations and nonlinear difference equations. Prerequisite: MTH 2502. Equivalent to OMT009.

**MTH3310. Numerical Methods (II; 3) **

This course is offered during odd years only. Solutions of equations, successive approximations, Newton-Raphson Method, roots of polynomials, error analysis and process graphs; simultaneous linear and non-linear equations, factorization methods, iterative methods for solving linear systems; description and solution of eigenvector problems, interpolation methods with and without spline functions; numerical solutions for ordinary differential equations, numerical solutions for partial differential equations, and applications of Monte Carlo methods. Prerequisites: MTH3001.

**MTH3430. Operations Research (I; 3) **

This course is offered during odd years only. Topics include stochastic processes, linear programming, transportation problems, inventory control, and network theory. Prerequisite: MTH3001.

**MTH3520. Abstract Algebra I (I; 3) **

Topics include properties of integers, groups, subgroups, quotient groups, group actions, products, homomorphisms, isomorphisms, and finite abelian groups. Prerequisite: MTH 2540.

**MTH3521. Abstract Algebra II (II; 3) **

Topics include rings, ideals, integral domains, fields, Euclidean domains, principal ideal domains, vector spaces, polynomial rings, and field extensions. Prerequisite: MTH 3520.

**MTH3530. Mathematical Writing and Research (II; 2) **

Topics include the mathematical research process, technical writing, and communications in mathematics. Prerequisite: MTH 2540.

**MTH3610. Introduction to Discrete Structures (I; 3) **

This course is offered in even years only. Topics include review of set algebra including mappings and relations, elements of the theory of directed and undirected grams, symbolic logic and applications of these structures to various areas of the computer. Prerequisite: MTH 2540. MTH3620. Seminar (II; 2) Topics include the nature of mathematics, topics from history of mathematics, problem-solving techniques, mathematical induction, and others. Prerequisite: MTH2503.

**MTH 4030. History of Mathematics (I; 3) **

The development of mathematics from ancient times to the twentieth century. Prerequisite: Junior standing. MTH4120. Introduction to Real Analysis (I; 3) Topics include the system of real numbers, functions, sequences, limits, the theory of continuity, differentiation, Riemann integration; sequences of functions, and infinite series. Prerequisites: MTH 2540.

**MTH4600. Capstone: Selected Topics in Mathematics (II; 3) **

This course is designed to meet the needs of advanced students as a preparation for graduate study or employment in mathematics related fields. Possible topics include, but are not limited to, topology, group theory, projective geometry, real analysis, probability and statistics, combinatorial analysis, and operations research.

**MTH4730. Functions of a Complex Variable (II; 3) **

This course is offered during even years only. Topics include complex numbers, elementary functions, power series, analytic functions, integrals, residues, Cauchy’s Theorem, and Moreara’s Theorem. Prerequisites: MTH 4120 and permission of the instructor.

## CESTA

## DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE

## EXTENSION