Note: Multivariable calculus and a course in proof techniques
or its equivalent or permission of the mathematics
adviser are required prerequisites for all graduate mathematics
courses.
| MTH 5512 |
Discrete Mathematics (3) |
| |
This course covers sets, relations, functions,
counting, algorithms, Boolean algebra, and
graphs. |
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| MTH 5520 |
Introduction to Graph Theory (3) |
| |
The elements of the theory and algorithms of
graphs and hypergraphs with motivating
examples from computer science, networking,
scheduling, biology etc.: algorithms,
complexity, data structures, shortest paths,
spanning trees, depth-first search, planar
graphs, colorings of graphs and hypergraphs. Prerequisites: Linear Algebra, computer
programming course, or permission of instructor. |
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| 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. |
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|
| MTH 5524 |
Real Analysis I (3) |
| |
A study of the real number system, completeness,
limits, continuity, sequences,
differentiation, and the Riemann integral. |
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| 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. |
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|
| 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. |
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| MTH 5536 |
Number Theory (3) |
| |
This course covers divisibility, congruences,
prime numbers, Fermat’s theorem, Diophantine
equations, number theoretic functions,
quadratic reciprocity. |
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|
| 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. |
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|
| 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. |
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|
| 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. |
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|
| 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. |
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| MTH 5560 |
Topology (3) |
| |
An introduction to metric and topological
spaces and associated topics, separation
axioms, compactness, and connectedness. |
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| 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. |
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|
| 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. |
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|
| 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. |
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|
| MTH 6615 |
Advanced Topology (3) |
| |
Generalization of such topics as functions,
continuous functions, open, closed, compact
and connected sets, arbitrary topological
spaces. Prerequisites: MTH 4424 or 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. |
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|
| MTH 6620 |
Advanced Concepts of Algebra (3) |
| |
This course covers topics including rings
and fields, polynomial rings and factorization,
and Galois theory. Prerequisite: 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. |
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| MTH 6624 |
Applied Combinatorics (3) |
| |
A study of generating functions, Inclusion-Exclusion, Burnside’s Theorem and Polya’s
Enumeration Formula. |
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|
| MTH 6625, 6626, 6627 |
Specialized Study in Area of
Mathematics (3)
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. |
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|
| MTH 6632 |
Non-Euclidean Geometry (3) |
| |
A study of non-Euclidean geometries with
emphasis given to their logical development. |
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|
| 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. |
