MATHEMATICS (MAT)
MAT 5125. History of Mathematics/(3).On Demand.
The history and development of
mathematical thought and theory from ancient to
modern times, with particular attention to the
history of geometry, algebra, calculus,
differential equations, linear algebra, and
statistics, and to the persons who made
significant contributions to these areas of
mathematics.
MAT 5160. Complex Variables/(3).On Demand.
An introduction to the study of complex variables
to include such topics as line integrals, the
Cauchy theorem, the Cauchy integral formula,
Morera's theorem, and the Laurent series.
MAT 5210. Abstract Algebra/(3).F.
A study of group theory including quotient groups,
the fundamental theorem of finite Abelian groups,
and the Sylow theorems. Includes an introduction
to rings with emphasis on Euclidean rings and
other principal ideal domains. Prerequisite: MAT
3110 (Modern Algebra) or permission of the instructor.
(Dual-listed with MAT 4720.)
MAT 5220. Ring Theory/(3).On Demand.
A study of rings including Euclidean and
polynomial rings. Modules on Euclidean rings will
be emphasized. Included will be an introduction to
fields and field extensions. Prerequisite: MAT 5210
or permission of instructor.
MAT 5230. Linear Algebra/(3).F.
A study of finite dimensional vector spaces. Among
the topics covered are matrices, linear
transformations, change of basis, eigenvalues,
canonical forms, quadratic forms and quasi-
inverses. Prerequisite: MAT 2240 (Linear Algebra) or
3110 (Modern Algebra).
MAT 5310. Numerical Analysis with Computer
Applications/(3).On Demand.
A study of methods of solving systems of linear
and non-linear equations, differential equations
and numerical integrations with emphasis on
convergence properties and error analysis. Prere-
quisites: MAT 3220 (Real Variables), CS 1440 (Computer
Programming)
Corequisite: 5610. (Same as CS 5310.)
MAT 5330. Mathematical Models/(3).S.Odd-numbered
years.
A problems oriented course. The student uses
mathematics to model a number of different
situations. Among the tools used will be
statistics, linear programming, differential
equations, and computer simulation. Prerequisites:
CS 1440 (Programming) and background in at least two of
the utilized tools.
MAT 5340. Introduction to Operations
Research/(3).On Demand.
A thorough study of linear
programming including duality theory and
sensitivity analysis. At least two other topics
related to mathematical applications in the
management sciences queuing theory, Markov
processes, game theory, decision analysis, network
analysis, etc. will be covered. Prerequisites:
MAT 2240 (Linear Algebra) and either STT 3850 or 4250
(Probability and Statistics).
MAT 5360. Methods of Applied Mathematics/(3).F.
On Demand.
The content may vary depending on the instructor.
Suggested topics are: Fourier series;
Sturm-Liouville problems; special functions and
transforms; partial differential and nonlinear
differential equations with applications;
numerical methods. Prerequisites: MAT 3130
(Differential Equations) with
MAT 3220 (Real Variables) recommended. Knowledge
of computers might be helpful. (Dual-listed with
MAT 4560.)
MAT 5370. Advanced Differential Equations/(3).F.
Even numbered years.
Usual topics include: power series solutions;
special functions; methods and theory of systems;
existence and uniqueness theorems and
continuations of solutions; Sturm theory;
nonlinear differential equations; numerical
methods. Prerequisites: MAT 2240 (Linear Algebra),
3130 (Differential Equations), with MAT 3220 (Real
Variables) recommended. (Dual-listed with MAT
4570.)
MAT 5380. Partial Differential
Equations/(3).On Demand
Topics include: classification and properties of
elliptic, hyperbolic, and parabolic equations;
separation of variables; Laplace and Fourier
transforms; initial and boundary value problems;
eigenfunction expansions; solution of Laplace,
wave and heat equations; and solitons.
Prerequisite: MAT 3130 (Differential Equations).
MAT 3220 (Real Variables) recommended.
(Dual-listed with MAT 4580.)
MAT 5390. Numerical Linear Algebra/(3).S.On
Demand.
Methods for solving systems of linear equations
with an emphasis on large, sparse systems. LU
factorization including storage schemes, graph
theory, ordering algorithms, and block
factorization. Iterative methods including
Jacobi, SOR, and conjugate gradient. Eigenvalue
methods including power method, QR factorization,
and Lanczos methods. Parallel matrix computations.
Prerequisite: MAT 4310 (Numerical Methods).
(Same as C S 5990). (Dual-listed with MAT 4990.)
MAT 5415. Seminar in the Pedagogy of
Mathematics/(1).F;S.
Topics from mathematics and pedagogy are examined,
such as research methods, recent advances in
mathematics, alternative learning styles, teaching
developmental and adult students, and teaching
with technology. Students will share their
experiences from the corequisite teaching
apprenticeship. This course may be repeated for a
total credit of three semester hours.
Corequisite: MAT 5420, Teaching Apprenticeship.
MAT 5420. Teaching Apprenticeship/(1).F;S.
This course provides a supervised
experience in college teaching through direct
participation in a classroom situation. Each
student will work closely with a faculty mentor
teaching an undergraduate course and will be
actively engaged in the development of activities
and assignments. Students will share their
experiences in the corequisite seminar. This
course may be repeated for a total credit of three
semester hours. Corequisite: MAT 5415, Seminar in
the Pedagogy of Mathematics.
MAT 5500. Independent Study/(1-3).F;S.
Prerequisite: 12 hours of graduate mathematics.
MAT 5525. Product of Learning/(1-3).F;S.On
Demand.
Graded on S/U basis only.
MAT 5530-5549. Selected Topics/(1-4).On Demand.
MAT 5610. Analysis I/(3).F.
A rigorous treatment of sequences, series, basic
topology, continuity, and differentiation.
Prerequisite: MAT 4220 (Real Analysis) or permission
of instructor.
MAT 5620. Analysis II/(3).S.
A continuation of MAT 5610, including a rigorous
development of the Riemann-Stieltjes integral,
sequences and series of functions, functions of
several variables, and Lebesgue theory.
Prerequisite: MAT 5610 or permission of
instructor.
MAT 5710. Introduction to Topology/(3).F.
A study of the basic concepts of general
topological space including such topics as
compactness, connectedness, product spaces, metric
spaces, and continuous functions. Prerequisite:
MAT 3110 (Modern Algebra). (Dual-listed with MAT
4710.)
MAT 5720. Topology/(3).On Demand.
A study of topology to include such topics as
general product spaces, complete metric spaces,
compatifications, embedding, metrization theorems,
and quotient spaces. Prerequisite: MAT 5710.
MAT 5910. Investigation in the Teaching of
Mathematics/(2).SS.
An examination of recent research and experimental
programs in the teaching of secondary school
mathematics. Students are encouraged to write
experimental designs for potential research
problems. Prerequisite: Undergraduate mathematics
major or permission of the instructor.
MAT 5920. Linear Algebra for Teachers/(4).SS.
(Odd numbered years).
Elementary concepts of linear algebra extending to
a rigorous level of algebraic proof are studied.
Prerequisite: Undergraduate major in mathematics.
MAT 5930. Analysis for Teachers/(4).SS.(Even
numbered years.)
This course is a rigorous study of elementary
calculus extending to a treatment of fundamental
concepts of analysis involving functions of a real
variable. Prerequisite: Undergraduate major in
mathematics.
MAT 5935. Basic Concepts of Probability and
Statistics/(3).On Demand.
This course examines the concepts underlying the
elementary and middle school curriculum in
probability and statistics. Probability models
will be studied using both mathematical approaches
and simulations. Statistics will be presented as a
problem solving process involving question
formulation, data collection, data analysis and
the interpretation of results. Prerequisite: MAT
3910 or 3920 (Logic and Structure of Math)
or permission of instructor. (Dual-listed with MAT
4930.)
MAT 5941. Technology for Secondary School
Mathematics/(3).On Demand.
The use of current computer and calculator
technology in various mathematics content areas
will be studied. Technology use in these areas
will involve problem solving, exploring patterns,
experimentation, conjecturing and generalization
of findings. Appropriate use of technology will be
stressed. Prerequisite: Undergraduate major in
mathematics, or permission of the instructor.
MAT 5950. Mathematical Modeling-Analytical
Models/(2).On Demand.
This course is an introduction to the mathematical
modeling of phenomena from business and science
with an emphasis on analytical models. Topics to
be covered include the modeling process, modeling
using functions and differential equations, linear
programming, optimization, population growth,
discrete versus continuous models. The course will
be project-based, with both team and individual
written and oral presentations an integral part of
the grading scheme. Prerequisites: Knowledge of
college algebra, calculus and linear algebra.
MAT 5951. Mathematical Modeling-Empirical
Models/(2).On Demand.
This course is an introduction to the mathematical
modeling of phenomena from business and science
with an emphasis on empirical and stochastic
models. Topics covered in this course include the
modeling process, modeling using data, regression,
curve fitting, probability and simulation,
population growth, Markov chains. The course will
be project-based, with both team and individual
written and oral presentations as an integral part
of the grading scheme. Prerequisites: Knowledge of
college algebra, calculus and linear algebra.
MAT 5952. Problem Solving/(3).On Demand.
Problem solving is the focus of this course. There
is an emphasis on building new mathematical
knowledge through work with problems and applying
a wide variety of strategies to solve problems and
adapt the strategies to new situations. Problems
may be drawn from algebra, geometry, number
theory, calculus, probability and statistics.
Prerequisites: Knowledge in all the areas from
which the problems will be drawn.
MAT 5961. Foundations of Geometry/(2).SS.
A treatment of projective geometry including both
the synthetic and the analytic approach. Also to
be considered is a study of the relation of
Euclidean, affine and hyperbolic geometries to
projective geometry. Prerequisites: MAT 2240
(Linear Algebra) and 3610 (Geometry). (Dual-listed
with MAT 4610.)
MAT 5965. Informal Geometry/(3).F.
An informal treatment of all aspects of geometry.
The topics considered include congruence, measure
of segments and angles, constructions, parallels
and parallelograms, similarity, space geometry,
areas and volumes, and measurements related to
circles. Prerequisite: MAT 3910 or 3920 (Logic and
structure of Math) or permission of the instructor.
(Dual-listed with MAT 4910.)
MAT 5970. Number Theory Concepts/(3).SS.
Designed primarily for secondary teachers, this
course is a study of the traditional number theory
concepts and theorems with special attention to
those of significance to the high school
curriculum. Emphasis will be on the historical as
well as the theoretical development of the
subject. Prerequisites: Undergraduate major in
mathematics; MAT 3250, or permission of
instructor.
MAT 5980. Special Topics in Mathematics Education/
(1-3).F;S.
A flexible program of reading, study, planning,
and writing designed to meet the needs of
individual teachers or groups of teachers in the
field of secondary school mathematics.
Prerequisite: Undergraduate major in mathematics
and recommendation of graduate advisor. May be
taken up to a total of fifteen semester hours.
MAT 5989. Graduate Research/(1-9).F;S.
This course is designed to provide access to
University facilities for continuing graduate
research at the master's and specialist's levels.
It is graded on an S/U basis and does not count
toward a degree.
MAT 5999. Thesis/(1-6).F;S.
Graded on an S/U basis only.