Undergraduate Catalog - University of Louisiana at Monroe

2012-2013 UNDERGRADUATE CATALOG
3003. ELEMENTARY MATHEMATICAL STATISTICS. 3 cr. Random
variables, probability, distribution functions, mathematical
models, testing hypotheses, frequency distributions, correlations,
regression, goodness of fit, derived distributions, non-parametric
methods. Prerequisite: MATH 1031.
3007. COLLEGE GEOMETRY. 3 cr. Selected topics from finite,
projective, or non-Euclidean geometries. Advanced topics in
Euclidean geometry, including constructions. Prerequisite: A
grade of “C” or better in MATH 2040. Sp
3050. GEOMETRY AND MEASUREMENT FOR ELEMENTARY
TEACHERS. 3 cr. Students will analyze Euclidian geometry
and measurement among and between the English and metric
systems. Emphasis is placed on applying the processes of
problem solving, reasoning, and proof, connections,
communications, and representation by combining discussion,
modeling, manipulatives, cooperative learning and technology.
For Elementary Education majors only. Prerequisite: A grade of
“C” or better in MATH 2055.
3073. NUMERICAL METHODS. 3 cr. Numerical algorithms
fundamental to scientific work including discussion or error.
Prerequisite: CSCI 2003, a grade of “C” or better in MATH 2002,
and MATH 1032. (Dual listed as CSCI 3073).
3080. REAL ANALYSIS. 3 cr. Sequences and series of real numbers
and their convergence; continuity, differentiation, and integration
of real valued functions of one real variable. Prerequisites: A
grade of “C” or better in MATH 1032, MATH 2040.
3086. MODERN ALGEBRA. 3 cr. Axioms and the nature of proof,
groups, rings, integral domains, fields, homomorphisms and
isomorphisms. Prerequisite: A grade of “C” or better in MATH
2002 and MATH 2040.
4011. FUNDAMENTALS OF MIDDLE SCHOOL MATHEMATICS
I. 3 cr. 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.
4012. FUNDAMENTALS OF MIDDLE SCHOOL MATHEMATICS II.
3 cr. 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.
4017. ADVANCED REAL ANALYSIS. 3 cr. Sequences and series
of vector-valued functions of several real variables and their
convergence; continuity, differentiation, and integration of vectorvalued
functions of several real variables. Prerequisite: A grade of
“C” or better in MATH 3080.
4020. INTRODUCTION TO BIOSTATISTICS I. 3 cr. An introduction
to the discipline of statistics and its application to problems of
biology, including human biology, medicine, and public health.
Topics include Bayesian inferences, estimation techniques,
hypothesis testing, goodness of fit, and analysis of variance.
Prerequisite: MATH 1014 or MATH 1031 or permission of the
department head and junior standing or above. (Same as
Computer Science 4020).
4021. INTRODUCTION TO BIOSTATISTICS II. 3 cr. A continuation
of 420. Topics include linear and multiple regression, logistics
regression, longitudinal data analysis, nonparametric methods
and principle component techniques. Prerequisite: MATH 4020
or CSCI 4020 and junior standing or above. (Same as Computer
Science 4021).
4031. FUNDAMENTALS OF HIGH SCHOOL MATHEMATICS I. 3 cr.
Emphasis is on teaching at the high school level. Topics include,
but are not restricted to, number concepts and relationships,
geometry and measurement. Not applicable toward a major
or minor in mathematics. Applies to middle and high school
certification.
MATHEMATICS 213
4032. FUNDAMENTALS OF HIGH SCHOOL MATHEMATICS II. 3 cr.
Emphasis is on teaching at the high school level. Topics include,
but are not restricted to, algebra, algebraic structures, data
analysis, basic statistics. Not applicable toward a major or minor
in mathematics. Applies to middle and high school certification.
4042. MATHEMATICAL MODELS. 3 cr. University capstone course.
Development and analysis of mathematical models for physical,
biological, and social science. Prerequisites: MATH 3001, 3003
or approval by department head.
For Undergraduates and Graduates
4001. DIFFERENTIAL EQUATIONS. 3 cr. Series solutions to ordinary
differential equations, Laplace transforms, systems of differential
equations, numerical methods and applications which arise in
geometry, chemistry, and physics. Prerequisite: MATH 3001.
4002. LINEAR SPACES. 3 cr. A study of abstract vector spaces
including function spaces, linear transformations, operators,
functionals and duality, bilinear and quadratic forms. Prerequisite:
MATH 2002, 1032.
4003-4004. MATHEMATICAL STATISTICS. 3 cr. each. Probability,
discrete and continuous random variables, expected values
and moments, special continuous distributions, sampling,
point estimation, multivariate normal,interval estimation, tests
of hypothesis, regression and linear hypothesis, experimental
design models, sequential tests, and nonparametric methods.
Prerequisite: MATH 3003.
4005. PARTIAL DIFFERENTIAL EQUATIONS. 3 cr. Fourier series,
boundary value problems, partial differential equations, special
functions, with an emphasis on applications. Prerequisite: MATH
3001.
4006. THEORY OF FUNCTIONS OF A COMPLEX VARIABLE. 3
cr. 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. Prerequisite: MATH 2032.
4007. HISTORY OF MATHEMATICS. 3 cr. 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. Prerequisites: A grade of “C” or
better in MATH 2040 and either MATH 3080 or MATH 3086.
4009. CRYPTOLOGY. 3 cr. Introduction to modern applications of
mathematics. Private key ciphers, including shift, affine and
vigenere; attacks on these ciphers. Modern public key ciphers
including RSA and Knapsack. Prerequisite: A grade of “C” or
better in Math 2040 or permission of the instructor.
4019. TOPOLOGY. 3 cr. Point sets, axiomatic bases, topology of the
line and the plane. Emphasis on connectedness, compact sets
and continuous transformations. Prerequisite: MATH 2040 and
1032.
4025. ADVANCED MODERN ALGEBRA. 3 cr. Continuation of Math
386; Euclidean domains, unique factorization domains, principal
ideal domains, Galois theory and related topics. Prerequisite: A
grade of “C” or better in MATH 3086.
4094. RESEARCH: ALGEBRA. 1-3 cr. Maximum, 6 cr. Research.
Open to advanced undergraduates who are capable of
developing a problem independently. Prerequisite: approval of
department head. (Formerly MATH 498A)
4095. RESEARCH: ANALYSIS. 1-3 cr. Maximum, 6 cr. Research.
Open to advanced undergraduates who are capable of
developing a problem independently. Prerequisite: approval of
department head. (Formerly MATH 498B)
4096. RESEARCH: TOPOLOGY. 1-3 cr. Maximum, 6 cr. Research.
Open to advanced undergraduates who are capable of
developing a problem independently. Prerequisite: approval of
department head. (Formerly MATH 498C)