# Course descriptions

*See explanation at bottom of page*

### MATHEMATICS (MAT)

**090. Developmental Mathematics.** 3 hrs. Basic arithmetic skills review and strong concentration on beginning algebra; open only to Development Educational Program students

**099. Intermediate Algebra.** 3 hrs. Required of all entering freshmen with a substandard ACT mathematics score; does not satisfy any university core or degree requirements; meets 250 contact minutes per week; arithmetic operations review, basic operations on polynominals, solving linear and quadraic equations and graphing linear and quadratic functions (CC 1233)

**100. Quantitative Reasoning. **3 hrs. Prerequisite: ACT Math subscore ≥20 or C or higher in MAT 99. Logic, probabilty, finance. Satisfies no prerequisite for any other math course.

**101. College Algebra.** 3 hrs. Prerequisite: Math ACT ≥ 20 or a grade of C or better in MAT 099. Functions and graphs, linear equations and inequalities, non-linear equations, including exponential and logarithmic equations (CC 1313)

**101E. Explorations in College Algebra.** 3 hrs. Prerequisite: Math ACT ≥ 20 or a grade of C or better in MAT 099. Functions and graphs, linear equations and inequalities, non-linear equations, including exponetial and logarithmic equations; taught using technology and group projects (CC 1313)

**102. Brief Applied Calculus.** 3 hrs. Prerequisite: Math ACT ≥ 24 or a grade of C or better in MAT 101. An introduction to differential and integral calculus with applications primarily related to business and finance (CC 1333, 1423, 1513)

**103. Plane Trigonometry.** 3 hrs. Prerequisite: Math ACT ≥ 24 or a grade of C or better in MAT 101. Trigonometric functions and their inverses, trigonomic identities and equations, and solutions of triangles (CC 1323)

**115. Elementary Statistics. **3 hrs. Prerequisite(s): Math ACT greater than or equal to 20 or a grade of C or better in MAT 099. Intro to statistics, elementary probability, point and interval estimates, hypothesis testing, linear regression.

**128. Precalculus Mathematics. **3 hrs. Prerequisite: Math ACT ≥ 24 or a grade of C or better in MAT 101. Functions, analytic geometry, roots of polynomials and basic concepts of trigonometry

**167. Calculus I with Analytic Geometry.** 3 hrs. Prerequisite: Math ACT ≥ 26 or a grade of C or better in MAT 103 or MAT 128. Limits, Derivatives, Applications of the Derivative. (CC 1613)

**168. Calculus II with Analytic Geometry.** 3 hrs. Prerequisite: MAT 167. Integration, Applications of Integration, Integration Techniques. (CC 1623)

**169. Calculus III with Analytic Geometry.** 3 hrs. Prerequisite: MAT 168. Sequences and Infinite Series, Power Series, Parametric and Polar Curves, Vectors and Vector-Valued Functions. (CC 2613)

**210. Mathematics for Elementary Teachers I.** 3 hrs. Prerequisite: MAT 101. Problem solving, sets, whole nimbers and whole numbers operations, number systems and operations including different bases and contributions from diverse cultures, number theory, integers and integer operations (Open only to elementary and special education majors.) (CC 1723)

**220. Explorations in the Mathematics Classroom. **1 hr. Ten hours of secondary classroom observations together with five hours of seminar under the direction of a mathematics faculty member

**280. Multivariable Calculus.** 3 hrs. Prerequisite: MAT 169. Functions of Several Variables, Multiple Integration, Vector Calculus. (CC 2623)

**285. Introduction to Differential Equations I.** 3 hrs. Prerequisite: MAT 168. Linear differential equations, nonlinear differential equations, systems of differential equations, Laplace transforms, and the Frobenius method (series solution).

**305. Mathematical Computing I.** 3 hrs. Prerequisite: MAT 280. Introduction to symbolic mathematical problem solving using computer based systems.

**308. Mathematics for Early Childhood Education.** 3 hrs. Prerequisite: MAT 210. Problem solving, ordering, comparing, classifying, numberless, money, time, measurement and geometry (Open only to elementary and special education majors.)

**309. Mathematics for Elementary Teachers II.** 3 hrs. Prerequisite: MAT 210. Problem solving, rational numbers and rational number operations, real numbers, ratios, proportions, percents, statistics and probability (Open only to elementary and special education majors and mathematics licensure majors.)

**310. Mathematics for Elementary Teachers III.** 3 hrs. Prerequisite: MAT 210. Problem solving, logic, basic concepts of 2-dimensional and 3-dimensional geometry, congruence and similarity of triangles and measurement (Open only to elementary and special education majors.)

**114. Calculus for the Arts and Sciences.** 3 hrs. Prerequisite: Math ACT ≥ 24 or a grade of C or better in MAT 101. An introduction to functions, graphs, continuity, differential and integral calculus, with applications to the arts and life sciences.

**320. Probability and Mathematical Statistics I.** 3 hrs. Prerequisite: MAT 169, 326, and 340. Discrete distributions, random variables, independence, moment generating functions, continuous distributions and multivariate distributions

**326. Linear Algebra.** 3 hrs. Prerequisite: MAT 340.Vector spaces, matrices, linear transformations, systems of linear equations, eigenvalues and eigenvectors.

**340. Discrete Mathematics. **3 hrs. Logic, set theory and selected topics from algebra, combinatorics and graph theory

**370. Introductory Geometry. **3 hrs. Prerequisite: MAT 326 and 340. Concepts and principles of Euclidean and non-Euclidean geometries in two and three dimensions, axiomatics and proof, coordinate geometry and vectors, congruence and similarity, transformations, concepts and formulas related to two and three-dimensional space. Reasoning and proof, communication, problem solving, connections, representations, and interactive geometry software are integrated throughout the course (Open only to those students preparing to teach mathematics in grades 7-12.)

**410. Mathematics for Teachers of Junior High School Mathematics.** 3 hrs. Prerequisite: MAT 310. The real number system and major subsystems, modular arithmetic, patterns, relations and functions, algebraic expressions and equations, counting techniques and probability; selected topics in geometry including coordinate geometry and transformations (Open only to elementary and special education majors.)

**415. Differential Equations and Special Functions.** 3 hrs. Prerequisite: MAT 285, 326. Sturm-Liouville theory-orthogonal functions, the Gamma and hypergeometric function, Bessel functions, Legendre, Hermite, Laguerre, and Chebyshev polynomials, and physical applications to partial differential equations.

**417. Introduction to Partial Differential Equations.** 3 hrs. Prerequisite: MAT 285, 326. Integrability conditions, quasilinear equations, applications of physics, classification of second order equations and canonical forms, and separation of variables

**418. Linear Programming. **3 hrs. Prerequisite: MAT 326 and 340. Convex sets, linear inequalities, extreme-point solutions, simplex procedure and applications

**419. Optimization in Mathematical Programming.** 3 hrs. Prerequisites: MAT 280. Selected topics in optimization from linear and nonlinear programming

**420. Probability and Mathematical Statistics II. **3 hrs. Prerequisites: MAT 320. Central limit theorem, estimation and hypothesis tests

**421. Number Theory. **3 hrs. Prerequisite: MAT 326 and 340. Induction, well-ordering, division algorithm, Euclidean algorithm, Fundamental Theorem of Arithmetic, number theoretic functions and congruences

**423. Modern Algebra I.** 3 hrs. Prerequisite: MAT 326 and 340. Elementary notions in groups, Fundamental Theorem of Finitely Generated Groups, permutation groups, quotient groups, isomorphism theorems and applications of transformation groups

**424. Modern Algebra II.** 3 hrs. Prerequisite: MAT 423. Survey of standard algebraic systems; rings, integral domains, fields, modules, polynomial rings and fields of quotients

**426. Advanced Linear Algebra.** 3 hrs. Prerequisite: MAT 326 and 340. Linear transformations and matrices, eigenvalues and similarity transformations, linear functionals, bilinear and quadratic forms, orthogonal and unitary transformations, normal matrices, applications of linear algebra.

**430. Advanced Engineering Mathematics I.** 3 hrs. Prerequisites: MAT 280 and 285. Introduction to Laplace transforms and Fourier series with emphasis on solving ordinary and simple partial differential equations (Does not count as an upper-level mathematics elective.)

**431. Advanced Engineering Mathematics II.** 3 hrs. Prerequisite: MAT 430. Vector calculus and an introduction to complex variables with emphasis on integral theorems and integration (Does not count as an upper-level mathematics elective.)

**436. Theory of Functions of a Complex Variable.** 3 hrs. Prerequisite: MAT 280, 326, and 340. Complex numbers and functions, limits, continuity, differentiation, analytic functions, branches, contour integration, and series

**437. Graph Theory.** 3 hrs. Prerequisite: MAT 326 and 340. An introduction to graphs and a sampling of their numerous and diverse applications

**439. Combinatorics.** 3 hrs. Prerequisites: MAT 169, 326, and 340. Counting and enumeration techniques, inversion formulas and their applications, and counting schemata relative to permutations of objects

**441. Real Analysis I.** 3 hrs. Prerequisites: MAT 168, 326, and 340. The real numbers, sequences and series, limits, continuous functions, differentiation.

**442. Real Analysis II.** 3 hrs. Prerequisite: MAT 441. The Riemann integral, sequences of functions, infinite series, the generalized Riemann Integral, and a glimpse into topology.

**457. Methods in Mathematics-Secondary.** 3 hrs. Prerequisites: CIS 313, MAT 280, 285, 326, and 340, PSY 374. A course designed to give the students a knowledge of the objectives, curriculum problems and organization and methods of teaching secondary school mathematics (Does not count as an upper-level mathematics elective.)

**457L. Methods in Mathematics-Secondary Laboratory.** 1 hr. Corequisite: MAT 457. A practicum with a minimum of 15 contact hours in a school setting (Does not count as an upper-level mathematics elective.)

**460. Numerical Analysis I.** 3 hrs. Prerequisites: MAT 280, 326, and knowledge of a programming language. Methods of solving equations and systems of equations, error analysis and difference equations

**461. Numerical Analysis II.** 3 hrs. Prerequisites: MAT 285 and 460. Interpolating polynomials, numerical differentiation and integration, numerical solutions of differential equations, and roundoff error

**472. Modern Geometry.** 3 hrs. Prerequisites: MAT 280, 326, and 340. Heuristic and analytic treatment of a branch of modern geometry, such as projective or differential geometry

**475. General Topology. **3 hrs. Prerequisites: MAT 169, 326, and 340. General topological spaces, bases and subbases, and continuity

**481. History of Mathematics.** 3 hrs. Prerequisites: MAT 169, 326, and 340. Historical development of number and number systems, measurement, algebra, Euclidean and non-Euclidean geometries, calculus, discrete mathematics, statistics and probability including contributions from diverse cultures to each of these mathematical branches. Reasoning and proof, communication, problem solving, connections, representations are integrated throughout the course (Does not count as an upper-level mathematics elective.)

**485. Mathematical Modeling. **3 hrs. Prerequisites: MAT 280, 285, 326, and a programming language. An introduction to mathematical modeling using case studies; projects and presentations are required

**+489. Student Teaching in Mathematics I.** 6 hrs. Prerequisite: Approval of the director of student teaching. Corequisite: MAT 490

**+490. Student Teaching in Mathematics II.** 6 hrs. Prerequisite: Approval of the director of student teaching. Corequisite: MAT 489

**492. Special Problems I, II. **1-3 hrs. Prerequisite: Approval of department chair. Students undertaking a Senior Honors Project will enroll in MAT H492

**494. Undergraduate Mathematics Seminars I, II.** 1 hr. Prerequisite: Consent of instructor. Topics of current interest

### EXPLANATION

The semester credit hours are listed after the title of each course.

*Example:*

**100. Introduction to the Arts.** 3 hrs. A team-taught investigation of the music, visual and theatrical arts designed for students who are not otherwise academically involved with these arts (CC 1233)

Southern Miss courses for which there are acceptable junior/community college courses are marked as (CC ____). It should be noted that there is a variance in course sequence between the junior/community colleges and Southern Miss. In addition, courses with the same junior/community college numbers vary from college to college. An adviser should be consulted before course scheduling.

The plus (+) sign in front of a course indicates that a special fee is charged for that course. (All labs are subject to a usage fee.)