# Undergraduate Course Descriptions

**Undergraduate Course Descriptions**

**092 DEVELOPMENTAL MATHEMATICS**

(Credit, 3 Hours). Algebra course designed especially for students who had little or no algebra in high school. Provides an extensive review as a prerequisite for College Algebra. Topics include operations on real numbers, variable expressions, linear equations and inequalities, polynomials, fractions, algebraic fractions, and sets.

Prerequisite: Students placed according to ACT/SAT scores.**130 COLLEGE MATHEMATICS I **(Credit, 3 Hours). An introduction to problem solving approaches, logic, the real number system, basic concepts of algebra including functions, graphs, systems of equations and inequalities, geometry, and topics in contemporary mathematics. Designed for students needing a maximum of six hours of mathematics.**131 COLLEGE MATHEMATICS II **(Credit, 3 Hours). An introduction to a variety of topics which permeate the field of mathematics. Topics include counting methods, probability, statistics, mathematical systems, problem solving, and contemporary mathematics. Designed for students needing a maximum of six hours of mathematics.**135 PRE-CALCULUS I: COLLEGE ALGEBRA** (Credit, 3 Hours). Topics include a review of the real numbers and their properties; operations with complex numbers; equations and inequalities; polynomial, rational, exponential and logarithmic functions and their graphs; and systems of equations and inequalities. Modeling is introduced and applications are emphasized. Designed for students in the business, scientific or engineering programs. Graphing calculators are required.

Prerequisite: Placement examination.**140 PRE-CALCULUS II: COLLEGE TRIGONOMETRY** (Credit, 3 Hours). Topics recommended include trigonometric equations and functions; trigonometric identities; right angle trigonometry; Laws of sines and cosines; and DeMoivre's Theorem. Modeling and applications are emphasized. Designed for science, engineering or architecture programs. Graphing calculators are recommended.

Prerequisite: A grade of C or better in **MATH 135** or by placement examination.**194 FRESHMAN HONORS MATHEMATICS** (Credit, 3 Hours). Course designed for freshmen with a good mathematical background who have been admitted to the Freshman Honors Program. It treats the elementary functions: algebraic, exponential, logarithmic, and trigonometric. Note: Course is a prerequisite to** MATH 264**.**200 FINITE MATHEMATICS** (Credit, 3 Hours). Designed for the business and social science major. Topics include systems of linear equations, vectors, matrices, and matrix Algebra; linear inequalities and linear Programming; counting techniques: permutations and combinations; probability, basic concepts in mathematics finance (annuities included) and introduction to statistics.

Prerequisite: **MATH 135** or its equivalent.**203 CALCULUS FOR BUSINESS AND SOCIAL SCIENCES** (Credit, 3 Hours). Topics include functions, limits, continuity, differentiation of algebraic, logarithmic, and exponential functions, introduction to maxima/minima, application of differential calculus, integral calculus, partial derivatives and probability.

Prerequisites: **MATH 135** or its equivalent and **MATH 200**.**204 CONCEPTS OF ELEMENTARY MATHEMATICS** (Credit, 3 Hours). Topics include the real numbers and their properties with special emphasis on whole numbers and place value; system with bases other than ten; integers; common and decimal fractions; ratio and proportion; percent; measurement, including the metric system; introduction to patterns; and problem solving. Applications to real life situations are emphasized. Designed for elementary education majors and nursing majors who must meet the requirements for certification by the State of Louisiana. A minimal background in mathematics required.**205 INFORMAL GEOMETRY** (Credit, 3 Hours). Intuitive study of points, angles, lines, perpendicularity, parallelism in the plane, basic constructions and proofs, including congruence and similarity, parallelism in the plane, basic area and volume problems. Designed for elementary school teachers. Hands-on activities, investigations to discover and make conjectures about properties of geometry are included.

Prerequisite: Consent of professor.**233 INTRODUCTION LINEAR ALGEBRA** (Credit, 3 Hours). An introductory study of elementary matrix algebra, systems of linear equations, determinants, vector spaces, eigenvectors and eigenvalues, and linear transformation is given.

Prerequisites: **MATH 135** and **140**. **MATH 233** may be taken concurrently with **MATH 264**.**250 TOPICS IN GEOMETRY **(Credit, 3 Hours). An axiomatic approach to Euclidean Geometry or to Absolute Geometry with a introduction to Euclidean and Hyperbolic geometries, including basic constructions. History of geometry is an assigned part of this course.

Prerequisite: Consent of professor.**264 CALCULUS I **(Credit, 4 Hours). The first course of the calculus sequence of three courses. Topics include revisit to some basic functions, the derivative at a point, the derivative function, higher derivatives, product and quotient rule of differentiation, chain rule of differentiation, and applications of derivatives.

Prerequisites: A grades of 'C' or better in** Math 134** and **140**, or consent of the department.**265 CALCULUS II **(Credit, 4 Hours). The second course of the calculus sequence of three courses. Topics include definite and indefinite Integrals, the Fundamental Theorem of Calculus, integration by substitution, integration by parts, improper integrals, and applications of the definite integrals.

Prerequisite: **MATH 264** with a grade of 'C' or better is strongly recommended.**274 ELEMENTARY STATISTICS I** (Credit, 3 Hours). An introduction to basic descriptive statistics and mathematical concepts commonly used in statistics. Topics discussed are percentiles, measures of central tendency and of dispersion, standard normal distribution, correlation, regression, and prediction. (Not applicable toward a major in mathematics).**275 ELEMENTARY STATISTICS II **(Credit, 3 Hours). An introduction to probability, hypothesis testing for both parametric and nonparametric statistics, statistics inference with continuous variables, two independent samples, and correlated samples. An introduction to analysis of variance (ANOVA) technique, and categorical data analysis are topics that are included. (Not applicable toward a major in mathematics).

Prerequisite: **MATH 274** or **MATH 200.****276 STATISTICS FOR THE MATHEMATICAL SCIENCES OR ENGINEERING MAJORS **(Credit, 3 Hours). An introduction to the basic concepts of statistics with emphasis placed on descriptive statistical analysis, probability, discrete random variables, continuous random variables, and sampling distributions.

Prerequisite: **MATH 265 **with a grade of 'C' or better.**330 MODERN ALGEBRA I** (Credit, 3 Hours). An introduction to the basic concepts of modern algebra is given. Topics include the nature of proofs, cosets, and Lagrange's theorem.

Prerequisites: **MATH 233** and **MATH 265** with a grade of 'C' on better or consent to the department.**346 SEMINAR FOR ACTUARIAL** EXAM 100 (Credit, 3 Hours). Study and discussion of concepts and problems from calculus and linear algebra are undertaken. Recent actuarial examinations will be used for the discussion.

Prerequisites: **MATH 233** and **MATH 365** with a grade of 'C' or better.**364 CALCULUS III** (Credit, 4 Hours). The third course of a three-course sequence. Topics include Taylor's polynomials, Taylor's series, contour diagrams, vectors, vector calculus, functions of several variables, partial derivatives, multiple integrals and optimization.

Prerequisite: **MATH 265** with a grade of 'C' or better.**365 ADVANCED CALCULUS** (Credit, 3 Hours). Advanced topics of calculus including vectors and vector calculus, linear approximations of vector valued functions of several variables, the derivative matrix, real values functions, multiple integrals, line integrals, surface integrals, and theorems of Green, and Stokes' divergence theorem are covered.

Prerequisite: **MATH 364 **with a grade of 'C' or better.**370 INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS (**Credit, 4 Hours). Elementary theory and methods of solutions of first order ordinary differential equations; series solutions of linear differential equations; methods of solutions of systems of differential equations; LaPlace transforms and applications; and selected methods of solving linear differential equations are covered.

Prerequisite: **MATH 364 **with a grade of 'C' or better.**390 CO-OP PROGRAM FOR MATHEMATICS MAJORS** (Credit, 3 Hours). Co-op students may be given up to nine semester hours of credit. A maximum of three semester hours may be applied to the mathematics requirement for graduation with the approval of the department. Prerequisite: Consent of instructor.**395 CALCULUS III and DIFFERENTIAL EQUATIONS for ENGINEERING MAJORS **(Credit, 4 Hours). This course combines selective topics normally covered in both calculus III and differential equations courses. Major focus is on application of fundamental mathematical principles to investigate realistic design elements. Topics include: vector differential and integral calculus; power series (Bessel and Legendre functions, and Fourier), partial fractions, Fourier and LaPlace transforms of derivatives; modeling of and solutions to DE's (ordinary, linear, and homogeneous) with constant coefficients, initial values, and Free and forced oscillations.

Prerequisites:** MATH 265 **with a grade of 'C' or better and junior standing in engineering.**401 HISTORY OF MATHEMATICS** (Credit, 3 Hours). Topics includes the evolution of the number concept, numeration systems, number theory, the history of computation, the roots of algebra, the origin and extensions of geometry, extension on number concepts, the nature of infinity, and the history of calculus from Archimedes to Weierstrauss.

Prerequisite: Consent of professor.**432 ELEMENTARY THEORY OF NUMBERS **(Credit, 3 Hours). An introductory study of number theory. Topics studied are divisibility, congruencies, quadratic reciprocity, numerical functions, Diophantine equations, simple continued fractions, and indices.

Prerequisite: Consent of the department.**433 LINEAR ALGEBRA** (Credit, 3 Hours). Topics includes an advanced study of vector spaces, subspaces and dimension; inner products; elementary matrices, the inverse of a matrix and rank of a matrix; linear transformations; rank, nullity, and inverse of a linear transformation; eigenvalues and eigenvectors; similarity and Cayley-Hamilton Theorem. A good mixture of proofs and computations is given.

Prerequisite: Consent of professor.**435 MODERN ALGEBRA II **(Credit, 3 Hours). A continuation of **MATH 330**. Topics include permutation groups, factor groups, homomorphism theorems, rings and ideals, including integral domains, and fields.

Prerequisite: **MATH 330 **with a grade of 'C' or better.**445 MATHEMATICS OF COMPOUND INTEREST** (Credit, 3 Hours). A detailed study of the theory of interest. Topics include nominal and effective rates of interest and discount; force of interest at; general annuities; amortization schedules and sinking funds; including determination of outstanding principal and split of payments into principal and interest; determination of fund yield rates and pricing of bonds and related securities.

Prerequisite: **MATH 265** or equivalent with a grade of 'C' or better.**446 SEMINAR IN ACTUARIAL EXAM 110** (Credit, 3 Hours). Study and discussion of concepts and problem in probability and statistics. Recent actuarial examinations will be used for discussion.

Prerequisites: **MATH 276** and **MATH 475 **with a grade of 'C' or better.**450 TOPICS IN GEOMETRY** (Credit, 3 Hours). Topics will be chosen from compass and ruler construction, theorems of Menelaus and Ceva, projective geometry, lattice theory, Boolean geometry, hyperbolic geometry, or Euclidean geometry.**462 REAL ANALYSIS** (Credit, 3 Hours). A theoretical study of real numbers. Topics included are limits, continuity limit superior and limit inferior, metric spaces, open and closed sets, Heine-Borel theorem, theorems of differentiation, and Riemann integration.

Prerequisite: **MATH 364** with a grade of 'C' or better.**463 INTRODUCTION TO COMPLEX VARIABLES** (Credit, 3 Hours). A theoretical study of complex numbers. Topics include complex numbers, functions of a complex variable, differentiation and integration (Cauchy-Riemann equations, Cauchy's theorem), and conformal mapping.

Prerequisite: **MATH 364 **with a grade of 'C' or better.**470 DIFFERENTIAL EQUATIONS **(Credit, 3 Hours). Course consists of advanced topics in differential equations. They include series solutions of linear ordinary differential equations about ordinary and singular points, theory and methods of solution of linear systems of ordinary differential equations, Sturm-Liouville boundary value problems and Fourier series, stability of autonomous systems, and numerical methods applications.

Prerequisites: **MATH 370 **and **MATH 233**, or the equivalent with a grade of 'C' or better.**472 BOUNDARY VALUE PROBLEMS** (Credit, 3 Hours). Topics include ordinary differential equations and boundary value problems, Fourier series and integrals; classical equations of mathematical physics; and heat, wave, and potential equations.

Prerequisites: **MATH 370 **and **MATH 233**, or the equivalent with a grade of 'C' or better.**474 NUMERICAL ANALYSIS** (Credit, 3 Hours). Numerical solutions and iterative solutions of equations, interpolation, and polynomial approximations of functions, numerical differentiation and integration, numerical solution of ordinary differential equations, derivation of numerical methods; error, stability, and convergence of numerical procedures are included. Prerequisites: **MATH 370 **and **MATH 233**, or the equivalent with a grade of 'C' or better.**475 PROBABILITY AND STATISTICS I** (Credit, 3 Hours). Probability distribution, combinational analysis, random variables, laws of large numbers, moment generating function, Markov chain, and Poisson process are covered.

Prerequisites: **MATH 364** and **MATH 276 **with a grade of 'C' or better.**476 PROBABILITY AND STATISTICS II **(Credit, 3 Hours). Sampling distributions, distribution of function of random variables, limiting distributions, estimations, methods of estimation, hypothesis testing; linear models, and estimation by least squares are included.

Prerequisite: **MATH 475 **with a grade of 'C' or better.**477 MATHEMATICAL MODELING** (Credit, 3 Hours). Construction, development, and study of mathematical models for real situations; basic examples; models construction; models for linear optimization; and selected case studies are included.**480 MATHEMATICS AND CRITICAL THINKING** (Credit, 3 Hours). The art of making, testing, and modifying conjectures and making logical arguments in support of a conjecture is repeated throughout the course. The mathematical experiences include a subset of the curriculum found in National Standards, grades 5-12. The appropriate use of manipulative, estimation, number sense, calculators, critical thinking, and problem solving will be integrated into the course. Of particular importance are the communication and connections standards from the NCTM Standards.**481 PRINCIPLES OF ALGEBRA I **(Credit, 3 Hours). An investigation of the algebraic structure of arithmetic and other algebras, including a look at defining axioms for an algebra; geometric models for introducing algebra (algebra tiles); issues of transitional mathematics, research on the teaching of algebra and the structure of finite fields and rings are undertaken.**482 PRINCIPLES OF GEOMETRY **(Credit, 3 Hours). Basic geometric experiences including those found in the NCTM Standards of Curriculum for grades 5-12, with an emphasis on informal geometry and making and modifying of conjectures are covered. Appropriate experience designed to contrast measurement experience at the concept as well as the algorithm level is shared. Finally, experiences designed to show the need and procedures used to develop geometry at the deductive system level will be given.**483 PRINCIPLES OF ANALYSIS I** (Credit, 3 Hours). An introduction of the study of functions, including all functions found in NCTM Standards of Curriculum for grades 5-12 is shared. The second course includes an introduction to differential and integral calculus. A review of all algebraic and numerical experiences which are prerequisite for success in calculus, including use of graphing calculators will be integrated into the course.**492 INTRODUCTION TO POINT-SET TOPOLOGY** (Credit, 3 Hours). An introduction to the study of topological spaces, continuous functions, homomorphism, and various topological properties including compactness and connectedness is given.

Prerequisite: **MATH 364 **with a grade of 'C' or better.**499 SEMINAR IN MATHEMATICS **(Credit, 1-3 Hours). Selected topics in mathematics are covered. The course content varies with the professor who emphasizes topics in his or her particular area. The student may receive credit for this course for up to six hours under two different headings.

Prerequisite: Consent of the professor.