ULM Mathematics

Courses

Monroe, Louisiana

Contents:

Courses for Undergraduates Only
Courses for both Undergraduates and Graduates
Courses for Graduates Only

ULM offers the following mathematics courses:

For Undergraduates Only

Mathematics 091. Fundamentals of Mathematics. (3 cr.): Description: Addition, subtraction, multiplication of whole numbers, fractions, decimals, integers, and rational numbers and their applications; divisibility and primes; integer powers, roots and order of operations; applications of ratio, proportion, and percent; systems of measurement, perimeter, area, and volume; solving simple linear equations and their applications. Three semester hours will be added to the degree program of any student required to take this course.

Mathematics 093. Introductory Algebra. (3 cr.): Description: Review of fundamentals; operations and properties of rational and real numbers; solutions and linear equations and applications; graphing linear equations and inequalities in two variables; solving systems of linear equations; exponents and polynomials; factoring polynomials; simplifying rational and radical expressions; solving fractional, radical and quadratic equations. Three semester hours will be added to the degree program of any student required to take this course.

Mathematics 111. College Algebra. (3 cr.): Prerequisite: Proficiency in high school algebra or Math 093.; Description: Real number system, functions, linear equations and inequalities, systems of equations and inequalities, quadratics, complex numbers, polynomial equations, arithmetic and geometric series, permutations and combinations.

Mathematics 112. Trigonometry. (3 cr.): Prerequisite: A grade of C or better in Math 111.; Description: Trigonometric functions, trigonometric identities and equations, solutions of triangles, inverse trigonometric functions, logarithms, vectors, complex numbers.

Mathematics 113. Elementary Functions. (3 cr.): Prerequisite: Credit and/or proficiency in Math 093.; Description: A pre-calculus cousre emphasizing functions of algebraic, trigonometric, and trancendental nature. This course is designed for those students who intend to enroll in calculus.

Mathematics 114. Applied Calculus for the Life Sciences. (3 cr.): Prerequisite: Credit and/or proficiency in Math 093.; Description: A study of the concepts of differential and integral calculus with applications from the life sciences.

Mathematics 116. Elementary Statistics. (3 cr.): Prerequisite: A grade of C or better in 103, 107, 111, 113 or 114.; Description: Introduction to descriptive statistics, probability, binomial and normal distributions, hypothesis testing, correlation and regression. Not applicable to a major or minor in mathematics or computer science.

Mathematics 118. The Nature of Mathematics. (3 cr.): Prerequisite: A grade of C or better in Math 111, 113 or 114.; Description: Selected topics from logic, set theory, number theory, graph theory, combinatorics, and geometry. Intended for liberal arts degree programs.

Mathematics 131. Calculus. (4 cr.): Prerequisite: A grade of C or better in Math 113.; Description: Functions, limits, derivatives, applications of the derivative, the integral, conic sections.

Mathematics 132. Calculus. (4 cr.): Prerequisite: A grade of C or better in Math 131.; Description: Inverse functions, techniques of integration, applications of the integral, sequences and series.

Mathematics 201H. Honors Mathematics. (3 cr.): Prerequisite: Five hours of mathematics at the 111 level or higher and admission to the University Honors Program or permission of the University Honors Council.; Description: A course in the aesthetics of mathematics, including such studies as logic, the history of mathematics, famous impossibilities and unsolved problems.

Mathematics 202. Applied Linear Algebra. (3 cr.): Prerequisite: A grade of C or better in Math 131 or Math 114 and advanced standing.; Description: An introduction to the application of matrix algebra. Emphasis on the application of procedures and algorithms.

Mathematics 209. Dynamical Systems and Chaos. (3 cr.): Prerequisite: A grade of C or better in Math 131 or Math 114 or approval by the department head.; Description: Covers fractals, the historical perspectives of chaos, Koch Curves, Cantor, Julia, and Mandlebrot sets, time series, population studies, and how Chaos involves other branches of science.

Mathematics 232. Calculus. (4 cr.): Prerequisite: A grade of C or better in Math 132.; Description: Vectors, lines, and planes, vector valued functions, partial derivatives, multiple integrals, calculus of vector fields.

Mathematics 240. Foundations of Mathematics. (3 cr.): Prerequisite: A grade of C or better in Math 131.; Description: Introduction to logic and proofs, set theory, functions and structures relating to algebra and analysis.

Mathematics 301. Differential Equations. (3 cr.): Prerequisite: A grade of C or better in Math 132.; Description: An introduction to ordinary differential equations, emphasizing equations of first order and first degree, linear differential equations of higher order, and applications of equations which arise in geometry, chemistry, and physics.

Mathematics 303. Elementary Mathematical Statistcs. (3 cr.): Prerequisite: A grade of C or better in Math 132.; Description: Descriptive statistics, probability theory, discrete and continuous probability distribution functions, expected values, moments and moment generating functions, bivariate probablity distributions, and sampling distributions. Introduction to SAS and Minitab statistical packages.

Mathematics 307. College Geometry. (3 cr.): Prerequisite: A grade of C or better in Math 240.; Description: Selected topics from finite, projective, or non-Euclidean geometries. Advanced topics in Euclidean geometry, including constructions.

Mathematics 311. Fundamental Concepts of Modern Mathematics. (3 cr.): Prerequisite: A grade of C or better in Math 117.; Description: Euclidean geometry for the elementary teacher, both intuitive and deductive, with emphasis on its use in teaching elementary school mathematics. Not applicable to a major or minor in mathematics.

Mathematics 312. Data, Patterns and Structures for Elentary Teachers. (3 cr.): Prerequisite: A grade of C or better in Math 311.; Description: Descriptive statistics, probability, algebraic patterns and functions. Not applicable to a major or minor in mathematics. For Elementary Education majors only.

Mathematics 373. Numerical Methods. (3 cr.): Prerequisite: CSCI 203; a grade of C or better in Math 202 and Math 132.; Description: Numerical algorithms fundamental to scientific work including discussion or error. (Dual listed as CSCI 373.)

Mathematics 380. Real Analysis. (3 cr.): Prerequisite: A grade of C or better in Math 232 and Math 240.; Description: Sequences and series of real numbers and their convergence; continuity, differentiation and integration of real valued functions of one real variable.

Mathematics 386. Modern Algebra. (3 cr.): Prerequisite: A grade of C or better in Math 202 and Math 240.; Description: Axioms and the nature of proof, groups, rings, integral domains, fields, homomorphisms and isomorphisms.

Mathematics 407. History of Mathematics. (3 cr.): Prerequisite: A grade of C or better in Math 240 and either Math 380 or 386.; Description: Selected topics on the development of mathematics as a human endeavor; numeration systems; growth of algebra, trigonometry, geometry and the calculus; contributions from various cultures; selected biographies of mathematicians.

Mathematics 417. Real Analysis. (3 cr.): Prerequisite: A grade of C or better in Math 380.; Description: Sequences and series of vector-valued functions of several real variables and their convergence; continuity, differentiation and integration of vector valued functions of several real variables.

Mathematics 425. Modern Algebra. (3 cr.): Prerequisite: A grade of C or better in Math 386.; Description: Continuation of 386; Euclidian Domains, unique factorization domains, principal ideal domains; Galois theory and related topics.

For Undergraduates and Graduates

Mathematics 401. Differential Equations. (3 cr.): Prerequisite: Math 301.; Description: Series solutions to ordinary differential equations. Laplace transforms, systems of differential equations, numerical methods and applications which arise in geometry, chemistry, and physics.

Mathematics 402. Linear Spaces. (3 cr.): Prerequisite: Math 202 and Math 231.; Description: A study of abstract vector spaces including function spaces, linear transformations. operators, functionals and duality, bilinear and quadratic forms.

Mathematics 403-404. Mathematical Statistics. (3 cr. each): Prerequisite: Math 303.; Description: Probability, discrete and continuous random variables, expected values and moments, special continuous distributions, sampling, point estimation, multivariate normal, interval estimation, tests of hypothesis, regression andd linear hypothesis, experimental design models, sequential tests, and nonparametric methods.

Mathematics 405. Partial Differential Equations. (3 cr.): Prerequisite: Math 301.; Description: Fourier series, boundary value problems, partial differential equations, special functions, witha n emphasis on applications.

Mathematics 406. Theory of Functions of a Complex Variable. (3 cr.): Prerequisite: Math 232.; Description: Real and complex numbers, differentiation and integration of functions of a complex variable, mapping by elementary functions, transformations, infinite series, and theory of residues and poles.

Mathematics 411. Fundamentals of Middle School Mathematics I. (3 cr.): Description: For the middle-school teacher; number concepts and relationships; geometry and measurement; algebra and algebraic structures. Emphasis is on teaching mathematics at the middle-school level. Not applicable toward a major nor minor in mathematics at undergraduate or graduate level. Applies to elementary and middle school certification.

Mathematics 412. Fundamentals of Middle School Mathematics II. (3 cr.): Description: Probability and Statistics for the middle school teacher. Topics include, but are not restricted to, data analysis and basic concepts of probability and statistics. Not applicable toward a major nor minor in mathematics at undergraduate or graduate level. Applies to elementary and middle school certification.

Mathematics 419. Topology. (3 cr.): Prerequisite: Math 202 and Math 232.; Description: Point sets, axiomatic bases, topology of the line and the plane. Emphasis on connectedness, compact sets and continuous transformations.

Mathematics 436. Introduction to Mathematical Concepts in Operations Research. (3 cr.): Prerequisite: Math 303 and CSCI 436.; Description: A mathematical approach to concepts in advanced linear and nonlinear programming, dynamic programming, game theories, queuing theory and other standard topics in operations research.

Mathematics 498. Research. (3 cr.): Prerequisite: Approval of department head; Description: Open to advanced undergraduates who are capable of developing a problem independently. Available topics: A. Algebra B. Analysis C. Topology D. Statistics

For Graduates Only

Mathematics 501. Basic Concepts of Elementary Mathematics. (3 cr.): Prerequisite: N/A; Description: In depth study of various mathematical concepts requisite to current backgrounds in teaching elementary school mathematics.

Mathematics 503. Foundations. (3 cr.): Prerequisite: A grade of C or better in Math 113 or advanced standing.; Description: Rudimentary topics from algebra and analysis for junior high and high school mathematics teachers.

Mathematics 504. Geometry for Secondary Teachers. (3 cr.): Prerequisite: A grade of C or better in Math 113 or advanced standing.; Description: The real number system, elementary functions and their graphs and an introduction to differential and integral calulus and its applications.

Mathematics 505. Geometry for Secondary Teachers. (3 cr.): Prerequisite: A grade of C or better in Math 307 or advanced standing.; Description: Incidence geometry in planes and space, congruence, separation in planes and space, geometric inequalities, synthetic postulation, similarities, constructions, rigid motion and metrization. For high school and junior high school teachers.

Mathematics 506. Elementary Number Theory. (3 cr.): Prerequisite: Approval of department head.; Description: Prime numbers and their distribution, divisibility of numbers, Pythagorean triples, Diophantine equations and their applications.

Mathematics 508. Introduction to Modern Algebra for Secondary Teachers. (3 cr.): Prerequisite: A grade of C or better in Math 113 or advanced standing.; Description: The logical structure of mathematics presented through the development of the properties of rings and fields. Intensive investigation of the real and complex number systems.

Mathematics 511. Introduction to Analysis. (3 cr.): Prerequisite: A grade of C or better in Math 416 or Math 419.; Description: Real and Complex number systems, elements of set theory, linear and linear metric spaces including function spaces.

Mathematics 515. Theory of Functions of a Real Variable. (3 cr.): Prerequisite: A grade of C or better in Math 416 or Math 419.; Description: Cardinality, measurable sets, measurable functions and the Lebesque integral.

Mathematics 520-521. Statistical Methods for the Experimenter. (3 cr.): Prerequisite: Only a high school background in mathematics and no prior knowledge of statistics is assumed.; Description: Data description, probability and probability distributions, estimation and tests of hypothesis, linear regression nad correlation, multiple comparisons, multiple regression; analysis of variance for completely randomized, randomized block, Latin square, factorial and k-way classification, and unbalanced designs; expected mean squaresm, analysis of covariance. The use of SAS and Minitab statistical computer packages. Emphasis is on methodoligy. Credit can not be earned in both 437-438 and 520-521.

Mathematics 525. Modern Algebra. (3 cr.): Prerequisite: A grade of C or better in Math 413.; Description: Semi-groups, rings, integral domains, fields, groups with operators, modules, ideals, and lattices.

Mathematics 591. Directed Study. (1-6): Prerequisite: Approval of department head.; Description: Directed study in one of the following topics: A. Algebra B. Analysis C. Topology D. Statistics

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