# Undergraduate Mathematical Courses

## MA 0003. Developmental Mathematics. (3)

(MA 0003 is a developmental course designed to prepare a student for university mathematics courses at the level of MA 1313 College Algebra: credit received for this course will not be applicable toward a degree). Three hours lecture. Real numbers fractions, decimal fractions, percent, algebraic expressions, factoring, algebraic fractions, linear equations/inequalities, integral exponents, quadratic equations.

## MA 0103. Intermediate Algebra. (3)

(MA 0103 is designed to prepare a student for MA 1313 College Algebra) Two hours lecture. Two hours laboratory. Real numbers, algebraic expressions, factoring, algebraic fractions, linear equations/inequalities, quadratic equations, Pythagorean Theorem. Does not count toward any degree.

## MA 1313. College Algebra. (3)

(Students with credit in MA 1713 will not receive credit for this course. Prerequisite: ACT Math subscore 20, or grade of C or better in MA 0103). Two hours lecture. Two hours laboratory. Review of fundamentals; linear and quadratic equations; inequalities; functions; simultaneous equations; topics in the theory of equations.

## MA 1323. Trigonometry. (3)

(Students with credit in MA 1713 will not receive credit for this course. Prerequisite: ACT Math subscore 24, or grade of C or better in MA 1313). Three hours lecture. The trigonometric functions: identities; trigonometric equations: applications.

## MA 1413. Structure of the Real Number System. (3)

(Prerequisite: a C or better in MA 1313 or an ACT Math sub-score of 24). Three hours lecture. The nature of mathematics; introductory logic; structure and development of the real number system. (Course is meant primarily for Elementary and Special Education majors).

## MA 1423. Problem Solving with Real Numbers. (3)

(Prerequisite: a C or better in MA 1413). Three hours lecture. Proportions, percent problems, probability, counting principles, statistics. (Course is meant primarily for Elementary or Special Education majors).

## MA 1433. Informal Geometry and Measurement. (3)

(Prerequisites: a C or better in both MA 1413 and MA 1423). Three hours lecture. Measurements and informal geometry. (Course is meant primarily for Elementary and Special Education majors).

## MA 1453. Precalculus with Graphing Calculators. (3)

(Prerequisites: Math ACT 24 or C or better in MA 1323 or score of at least 70 on the Precalculus Qualifying Exam). Three hours lecture. Properties, applications, and graphs of linear, quadratic, polynomial, exponential, logarithmic, and trigonometric functions; trigonometric identities, equations and inverses; inequalities. (Degree credit will not be granted for MA 1453 and either MA 1313 or MA 1323. This course is intended to prepare students to take MA 1713 Calculus I).

## MA 1463. Finite Mathematics and Introduction to Calculus.

(Prerequisite: ACT Math subscore 24, or grade of C or better in MA 1313). Three hours lecture. Matrices and systems of linear equations; introduction to calculus.

## MA 1613. Calculus for Business and Life Sciences I. (3)

(Prerequisite: ACT Math subscore 24, or grade of C or better in MA 1313). Three hours lecture. Algebraic and some transcendental functions, solutions of systems of linear equations, limits, continuity, derivatives, applications.

## MA 1623. Calculus for Business and Life Sciences II. (3)

(Prerequisite: MA 1613). Three hours lecture. Anti-derivatives, the definite integral, applications of the definite integral, functions of two or more variables, partial derivatives, maxima and minima, applications.

## MA 1713. Calculus I. (3)

(Prerequisite: ACT Math subscore 26, or grade of C or better in MA 1323 or MA 1453). Three hours lecture. Analytic geometry; functions; limits; continuity; derivatives of algebraic functions. Application of the derivative. Honors section available through invitation.

## MA 1723. Calculus II. (3)

(Prerequisite: Grade of C or better in MA 1713). Three hours lecture. Antidifferentiation; the definite integral; applications of the definite integral; differentiation and integration of transcendental functions. Honors section available through invitation.

## MA 2113. Introduction to Statistics. (3)

(Prerequisite: ACT Math subscore 24, or a grade of C or better in MA 1313). Two hours lecture. Two hours laboratory. Introduction to statistical techniques: descriptive statistics, random variables, probability distributions, estimation, confi dence intervals, hypothesis testing, and measurement of association. Computer instruction for statistical analysis. (Same as ST 2113).

## MA 2733. Calculus III. (3)

(Prerequisite: Grade of C or better in MA 1723). Three hours lecture. Further methods of integration; polar coordinates; vectors; infinite series. Honors section available through invitation.

## MA 2743. Calculus IV. (3)

(Prerequisite: Grade of C or better in MA 2733). Three hours lecture. Differential calculus of functions of several variables; multiple integration; vector calculus. Honors section available through invitation.

## MA 3053. Foundations of Mathematics. (3)

(Prerequisite: MA 1723). Three hours lecture. The logical structure of mathematics; the nature of a mathematical proof; applications to the basic principles of algebra and calculus.

## MA 3113. Introduction to Linear Algebra. (3)

(Prerequisite: MA 1723). Three hours lecture. Vector spaces; matrices; linear transformations; systems of linear equations; characteristic values and characteristic vectors.

## MA 3123. Introduction to Statistical Inference. (3)

(Prerequisite: ACT Math subscore 24, or grade of C or better in MA 1313). Two hours lecture. Two hours laboratory. Basic concepts and methods of statistics, including descriptive statistics, probability, random variables, sampling distribution, estimation, hypothesis testing, introduction to analysis of variance, simple linear regression. (Same as ST 3123).

## MA 3163. Introduction to Modern Algebra. (3)

(Prerequisite: MA 3113 and MA 3053). Three hours lecture. Rings, integral domains, and fields with special emphasis on the integers, rational numbers, real numbers and complex numbers; theory of polynomials.

## MA 3253. Differential Equations I. (3)

(Prerequisite: MA 2743 or co-registration in MA 2743). Origin and solution of differential equations; series solutions; Laplace Transform methods; applications.

## MA 3353. Differential Equations II. (3)

(Prerequisite: MA 3253). Three hours lecture. Systems of differential equations; matrix representations; infinite series solution of ordinary differential equations; selected special functions; boundary-value problems; orthogonal functions: Fourier series.

## MA 3463. Foundations of Geometry. (3)

(Prerequisite: MA 1723 and MA 3053). Three hours lecture. The structural nature of geometry; modern methods in geometry: finite geometrics.

## MA 3513. History of Mathematics. (3)

(Prerequisite: MA 2733 or co-registration in MA 2733). Three hours lecture. A historical development of mathematicians and their most important contributions will be emphasized.

## MA 4133/6133. Discrete Mathematics. (3)

(Prerequisites: MA 3163 or consent of instructor). Three hours lecture. Sets, relations, functions, combinatorics, review of group and ring theory, Burnside’s theorem, Polya’s counting theory, group codes, finite fields, cyclic codes, and error-correcting codes.

## MA 4143/6143. Graph Theory. (3)

(Prerequisites: MA 3113 or consent of instructor). Three hours lecture. Basic concepts, graphs, and matrices, algebraic graph theory, planarity and nonplanarity, Hamiltonian graphs, digraphs, network flows, and applications.

## MA 4153/6153. Matrices and Linear Algebra. (3)

(Prerequisites: MA 3113 and MA 3253). Three hours lecture. Linear transformations and matrices; eigenvalues and similarity transformations; linear functionals, bilinear and quadratic forms; orthogonal and unitary transformations; normal matrices; applications of linear algebra.

## MA 4163/6163. Group Theory. (3)

(Prerequisite: MA 3163 or consent of the instructor). Three hours lecture. Elementary properties: normal subgroups; factor groups; homomorphisms and isomorphisms; Abelian groups; Sylow theorems; composition series; solvable groups.

## MA 4173/6173. Number Theory. (3)

(Prerequisite: MA 3113). Three hours lecture. Divisibility: congruences; quadratic reciprocity; Diophantine equations; continued fractions.

## MA 4213. Senior Seminar in Mathematics. (3)

(Prerequisites: MA 3163 and MA 3253 and MA 4633). Three hours lecture. Students explore topics in current mathematical research, write expository articles, and give oral presentations. Refinement of specialized writing skills needed for effective mathematical communication.

## MA 4243/6243 Data Analysis I. (3)

(Prerequisite: MA 2743. Co-requisite: MA 3113). Three hours lecture. Data description and descriptive statistics, probability and probability distributions, parametric one-sample and two-sample inference procedures, simple linear regressions, one-way ANOVA. Use of SAS. (Same as ST 4243/6243.)

## MA 4253/6253 Data Analysis II. (3)

(Prerequisites: MA 4243/6243 and MA 3113). Three hours lecture. Multiple linear regression; fixed, mixed and random effect models; block designs; two-factor analysis of variance; three-factor analysis of variance; analysis of covariance. Use of SAS. (Same as ST 4253/6253.)

## MA 4313/6313. Numerical Analysis I. (3)

(Prerequisites: CSE 1213, MA 3113, and MA 2743). Three hours lecture. Matrix operations; error analysis; norms of vectors and matrices; transformations; matrix functions; numerical solutions of systems of linear equations; stability; matrix inversion; eigen value problems; approximations.

## MA 4323/6323. Numerical Analysis II. (3)

(Prerequisites: CSE 1213 or equivalent. MA 3113 and MA 3253). Three hours lecture. Numerical solution of equations; error analysis; finite difference methods; numerical differentiation and integration; series expansions; difference equations; numerical solution of differential equations.

## MA 4373/6373. Introduction to Partial Differential Equations. (3)

(Prerequisite: MA 3253). Three hours lecture. Linear operators: linear first order equations; the wave equation; Green’s function and Sturm—Liouville problems; Fourier series; the heat equation; Laplace’s equation.

## MA 4513/6513. Applied Probability and Statistics for Secondary Teachers. (3)

(Prerequisite: MA 1723). Three hours lecture. (Credit not available for students with credit in MA-ST 4543/6543). Graphical methods of presenting data; analysis of data; probability, binomial distribution, normal distribution; random sampling; linear regression and correlation.

## MA 4523/6523. Introduction to Probability. (3)

(Prerequisite: MA 2733). Three hours lecture. Basic concepts of probability, conditional probability, independence, random variables, discrete and continuous probability distributions, moment generating function, moments, special distributions, central limit theorem. (Same as ST 4523/6523).

## MA 4533/6533. Introductory Probability and Random Processes. (3)

(Prerequisites: MA 3113 and MA 2743). Three hours lecture. Probability, law of large numbers, central limit theorem, sampling distributions, confi dence intervals, hypothesis testing, linear regression, random processes, correlation functions, frequency and time domain analysis. (Credit can not be earned for this course and MA/ST 4523/6523.)

## MA 4543/6543. Introduction to Mathematical Statistics I. (3)

(Prerequisite: MA 2743.) Three hours lecture. Combinatorics; probability, random variables, discrete and continuous distributions, generating functions, moments, special distributions, multivariate distributions, independence, distributions of functions of random variables. (Same as ST 4543/6543.)

## MA 4573/6573. Introduction to Mathematical Statistics II. (3)

(Prerequisite: MA 4543/6543.) Three hours lecture. Continuation of MA-ST 4543/6543. Transformations, sampling distributions, limiting distributions, point estimation, interval estimation, hypothesis testing, likelihood ratio tests, analysis of variance, regression, chi-square tests. (Same as ST 4573/6573.)

## MA 4633/6633. Advanced Calculus I. (3)

(Prerequisite: MA 2743 and MA 3053). Three hours lecture. Theoretical investigation of functions; limits; differentiability and related topics in calculus.

## MA 4643/6643. Advanced Calculus II. (3)

(Prerequisite: MA 4633/6633). Three hours lecture. Rigorous development of the defi nite integral; sequences and series of functions; convergence criteria; improper integrals.

## MA 4733/6733. Linear Programming. (3)

(Prerequisites: MA 3113). Three hours lecture. Theory and application of linear programming; simplex algorithm, revised simplex algorithm, duality and sensitivity analysis, transportation and assignment problem algorithms, integer and goal programming. (Same as IE 4733/6733).

## MA 4753/6753. Applied Complex Variables. (3)

(Prerequisite: MA 2743). Three hours lecture. Analytic functions: Taylor and Laurent expansions; Cauchy theorems and integrals; residues; contour integration; introduction to conformal mapping.

## MA 4933/6933. Mathematical Analysis I. (3)

(Prerequisite: MA 4633/6633 or equivalent). Three hours lecture. Metric and topological spaces; functions of bounded variation and differentiability in normed spaces.

## MA 4943/6943. Mathematical Analysis II. (3)

(Prerequisite: MA 4933/6933). Three hours lecture. Riemann-Stieltjes integration, sequences and series of functions; implicit function theorem; multiple integration.

## MA 4953/6953. Elementary Topology. (3)

(Prerequisite: MA 4633/6633). Three hours lecture. Definition of a topological space, metric space, continuity in metric spaces and topological spaces; sequences; accumulation points.