|
MTH |
5512 |
Discrete
Mathematics (3) |
| |
|
This course covers sets,
relations, functions, counting, algorithms, Boolean algebra,
and graphs. |
|
MTH |
5522 |
Numerical
Analysis (3) |
| |
|
This course covers
topics including finite
differences, interpolation, numerical integration and
differentiation, solutions of equations of one variable,
linear systems, and numerical solutions of ordinary
differential equations. |
|
MTH |
5524 |
Real
Analysis I (3) |
| |
|
A study of the real number
system, completeness, limits, continuity, sequences,
differentiation, and the Riemann integral. |
|
MTH |
5525 |
Real
Analysis II (3) |
| |
|
A study of sequences and series
of functions, series, and a continuation of the integral to
include the Fundamental Theorem of Calculus.
Prerequisite: MTH 4424 or MTH 5524. |
|
MTH |
5526 |
Complex Analysis (3) |
| |
|
A study of
complex numbers,
elementary functions and their mappings, complex limits and
power series, analytic functions, integrals, contour
integral, and Cauchy integral formula. |
|
MTH |
5536 |
Number
Theory (3) |
| |
|
This course covers
divisibility, congruences, prime numbers, Fermat’s theorem,
Diophantine equations, number theoretic functions, quadratic
reciprocity. |
|
MTH |
5541 |
Abstract
Algebra I (3) |
| |
|
A study of
properties of the
integers, modular arithmetic. Elementary theory of groups,
finite groups, subgroups, cyclic groups, permutation groups.
Group isomorphisms and homomorphisms. |
|
MTH |
5542 |
Abstract
Algebra II (3) |
| |
|
This course covers
the elementary theory of
rings, polynomial rings, divisibility, unique factorization
domains. Integral domains, ideals, factor rings,
divisibility in integral domains. Elementary theory of
fields. Extension fields.
Prerequisite: MTH 4441 or MTH 5541. |
|
MTH |
5551 |
Mathematical
Statistics I (3) |
| |
|
A study of probability theory,
sample spaces, random variables, mutual exclusion,
independence, conditional probability, permutations and
combinations, common discrete and continuous distributions,
expected value, mean, variance, multivariate distributions,
covariance, Central Limit Theorem. |
|
MTH |
5552 |
Mathematical
Statistics II (3) |
| |
|
A study of the
fundamentals of the
theory of statistics, the Central Limit Theorem, point
estimation, sufficiency, consistency, hypothesis testing,
sampling distributions, confidence intervals, linear
regression models, interpretation of experimental results,
Bayesian Estimation.
Prerequisite: MTH 4451 or MTH 5551. |
|
MTH |
5560 |
Topology (3) |
| |
|
An introduction to metric and
topological spaces and associated topics, separation axioms,
compactness, and connectedness. |
|
MTH |
6600 |
Modern Topics
in Mathematics (3) |
| |
|
An investigation of current
topics in mathematics that are generally not covered in
regularly offered graduate courses in the mathematics
graduate curriculum.
Prerequisites will be determined by the topic under
investigation. |
|
MTH |
6601 |
Metric Education for Elementary
Teachers (3) |
| |
|
A study of the materials and
methods program of instruction with workshops in selected
school systems.
Prerequisite: Admission by permission of
instructor. |
|
MTH |
6610 |
History of Mathematics (3) |
| |
|
The course is designed to
acquaint the secondary mathematics teacher with the
historical development of mathematics with particular
attention given to the techniques of the period studied. |
|
MTH |
6612 |
Advanced Discrete Mathematics (3) |
| |
|
This course covers trees,
network models and Petri nets, Boolean algebra and
combinatorial circuits, automata, grammars, and languages.
Prerequisite: MTH 4412, MTH 5512 or permission of
instructor. |
|
MTH |
6615 |
Advanced Topology (3) |
| |
|
Generalization of such topics
as functions, continuous functions, open, closed, compact
and connected sets, arbitrary topological spaces.
Prerequisites: MTH 4424or 5524, MTH 4426 or 5526 or
permission of instructor. |
|
MTH |
6616 |
Mathematical Models (3) |
| |
|
An introduction to the modeling
process. Students will practice creative
and empirical model constructions, analyze
models and do independent model research.
Application using paired data will be included. |
|
MTH |
6620 |
Advanced Concepts of Algebra (3) |
| |
|
This course covers topics
including rings and fields, polynomial rings and
factorization, and Galois theory.
Prerequisites: MTH 4442 or 5542 or permission of
instructor. |
|
MTH |
6621 |
Foundations of Mathematics (3) |
| |
|
A study of
the axiomatic nature of mathematics, theory of sets,
cardinal and ordinal numbers, continuum hypothesis and axiom
of choice. |
|
MTH |
6624 |
Applied Combinatorics
(3) |
| |
|
A study of generating
functions, Inclusion-Exclusion, Burnside’s Theorem and
Polya’s Enumeration Formula. |
|
MTH |
6625, |
Specialized Study in Area of
Mathematics (3) |
| |
6626,
6627 |
A study of a problem or
problems using research techniques. Selection of problem
must be approved by student’s adviser, instructor under whom
the study is to be made, and the appropriate director of the
Graduate School or Dean of Arts and Sciences.
Note:
Total credit for any combination of enrollments in these
courses may not exceed six semester hours.
See semester hour limits listed
under Course Restrictions in General Regulations section. |
|
MTH |
6632 |
Non-Euclidean Geometry (3) |
| |
|
A study of non-Euclidean
geometries with emphasis given to their logical development. |
|
MTH |
6633 |
Advanced Linear Algebra (3) |
| |
|
A study of linear and
orthogonal transformations, orthogonal and unitary matrices,
numerical linear algebra, and applications. Spectral theory
and duality.
Prerequisite: MTH 3331 or permission of instructor. |
|
MTH |
6640 |
Advanced Concepts of Analysis (3) |
| |
|
A study
from the classical theory of point sets in Euclidean space
and the theory of functions of one or more real variables to
topology, continuous functions, and Lebesgue integral and
the Henstock integral.
Prerequisites: MTH 4425 or MTH 5525. |
|
MTH |
6650 |
Trends in Technology and
Problem Solving in Secondary Mathematics
Instruction (3) |
| |
|
A
comprehensive study of contemporary teaching strategies that
incorporate current technologies and effective problem
solving approaches for use by the mathematics educator in
the modern secondary school mathematics program. Emphasis
will be placed upon the effective use of calculators,
writing, and computer software in the mathematics
curriculum. |
|
MTH |
6691 |
Research in Education (3) |
| |
|
A study of a
variety of research and evaluations methods in the teaching
of mathematics. |
