*MATH 3100/8015 Applied Combinatorics (3
hours)
Basic counting methods, generating functions, recurrence relations,
principle of inclusion-exclusion. Polya's theorem. Elements of graph theory,
trees and searching, network algorithms. Prerequisite: MATH 2030 or
MATH 2230. (Same as CSCI 3100/8105).
MATH 3230/8235 Introduction to Analysis (3
hours)
Provides a theoretical foundation for the concepts of elementary
calculus. Topics include the real number system, topology of the real line,
limits, functions of one variable, continuity, differentiation,
integration. Prerequisites: MATH 1970 and MATH 2230 or equivalent.
*MATH 3300/8305 Numerical Methods (3
hours)
Solving equations and systems of equations, interpolation, numerical
differentiation and integration, numerical solutions to ordinary
differential equations, numerical calculations of eigenvalues and
eigenvectors, analysis of algorithms and errors, computational
efficiency. Prerequisites: MATH 1960 and MATH 2050. (Same as CSCI
3300/8305).
MATH 3350/8355 Differential Equations (3
hours)
Solutions of linear and first-order non-linear differential equations with
applications. Also power series solutions, Fourier series, and Laplace
Transform. Prerequisites: MATH 1960.
3500/8505 Selected Topics in Mathematics (6
hours)
This is a variable content course with selected topics in the mathematical
sciences, which may be of interest to students in other disciplines such as
mathematics education, psychology, and business. The course may be taken
more than once for credit provided topics differ, with a maximum credit of
nine hours. Mathematics majors may apply no more than 3 hours of MATH 3500
toward the minimum major requirements. Prerequisites: Permission of
Instructor.
MATH 3640/8645 Modern Geometry (3 hours)
Axiomatic systems, finite geometries, modern foundations of Euclidean
geometry, hyperbolic and other non-Euclidean geometries, projective
geometry. Prerequisites: MATH 2230 or MATH 2030, or equivalent
mathematical maturity.
3850/8855 History of Mathematics (3
hours)
An overview of the historical development of mathematical concepts and
methods. Brief biographies of major mathematicians, descriptions of the
cultural context of selected major advances, and examples of the solution of
problems using the knowledge and methods appropriate for each time period
will be included. Prerequisites: MATH 1970 and MATH 2230.
MATH 4030/8036 Applied Modern Algebra (3
hours)
Review of sets, relations, and functions. Semigroups, groups, rings and
fields, lattices and Boolean algebra. Applications may include coding
theory, linear machines and finite automata. Prerequisites: MATH 2030
or MATH 2230. Recommended: MATH 4560/8566 (Cross-listed with MATH 8036)..
MATH 4050/8056 Linear Algebra (3 hours)
The theory of vectors, vector spaces, inner product spaces, linear
transformations, eigenvalues and canonical forms, complex vectors and
matrices and orthogonality. Unlike MATH 2050, this course emphasizes the
theoretical aspects of linear algebra. Prerequisites: MATH 2050; MATH
2030 or MATH 2230 or equivalent; or permission.
MATH 4110/8116 Abstract Algebra I (3
hours)
Advanced undergraduate (beginning graduate) course in abstract algebra to
include congruences, axioms for number systems, group axioms, group theory,
homorphisms, isomorphisms, quotient groups, and introduction to rings,
integral domains, and fields. Prerequisites: MATH 4510/8516 or MATH
4030/8036 or permission of instructor.
*MATH 4150/8156 Graph Theory and Applications
(3 hours)
Introduction to graph theory. Representations of graphs and graph
isomorphism. Trees as a special case of graphs. Connectivity, covering,
matching and coloring in graphs. Applications of graph theory in several
fields such as networks, social sciences, VLSI, chemistry, and parallel
processing. Prerequisites: MATH 2030 or MATH 2230 or permission of
instructor. (Same as CSCI 4150/8156).
MATH 4230/8236 Mathematical Analysis I (3
hours)
Provides a theoretical foundation for the concepts of elementary
calculus. Topics include ordered fields and the real number system, basic
properties of complex numbers, metric space topology, sequences and series
in Rk, limits and continuity in a metric space, monotonic
functions. Prerequisites: MATH 3230/8235 or equivalent.
MATH 4270/8276 Complex Variables (3
hours)
Differentiation, integration, and power series expansions of analytic
functions, conformal mapping, residue calculus and
applications. Prerequisites: MATH 3230/8235 or
equivalent.
*MATH 4300/8306 Operations Research I (3
hours)
Basic concepts and linear programming including convex sets, hyperplanes,
polytopes, mathematical modeling, formulation and geometry of linear
programming, primal simplex method, dual simplex method, revised simplex
method, sensitivity analysis and problem solving using computer
packages. Prerequisites: MATH 2050. (Same as CSCI 4300/8306).
*MATH 4310/8316 Operations Research II (3
hours)
Basic concepts of integer programming, network programming and related
topics. Content includes the mathematical foundations and solution
algorithms of discrete optimization problems including transportation
problems, network problems, and integer programming. Prerequisites:
MATH 2050, MATH/CSCI 4300/8306. (Same as CSCI 4310/8316).
MATH 4330/8336 Introduction to Partial Differential
Equations (3 hours)
Heat conduction, vibrating membranes, boundary value problems,
Strum-Liouville systems, Fourier series, Fourier integrals, Bessel
functions, Legendre polynomials. Prerequisites: MATH 1970 and MATH
3350/8355.
MATH 4510/8516 Theory of Numbers (3
hours)
Congruences, quadratic reciprocity, diophantine equations, continued
fractions, and prime number distribution. Prerequisites: MATH 2030 or
MATH 2230.
MATH 4580/8586 Tensor Analysis (3 hours)
Review of vector spaces and matrix theory. Tensor algebra, the metric tensor
and Riemannian curvature. Geodesics, applications to geometry, mechanics,
relativity and continuous media. Prerequisites: MATH 1970, MATH 2050,
and MATH 3350.
MATH 4600/8606 Differential Geometry (3
hours)
Tensor algebra, differential forms, Lie groups, surface theory, curvature,
sympletic geometry. Applications to classical mechanics and
relativity. Prerequisites: MATH 1970 and MATH 3350/8355.
MATH 4610/8616 Elementary Topology (3
hours)
Sets and functions, metric spaces, topological spaces, continuous functions
and homeomorphisms, connectedness, compactness. Prerequisites: MATH
3230/8235 or equivalent.
MATH 4650/8656 Transform Methods and Applications
(3 hours)
Laplace transform and the inversion integral. Fourier transform. Other
transforms and special techniques. Applications to differential equations,
boundary value problems of mathematical physics, and signal
analysis. Prerequisites: MATH 3350/8355 and MATH 4270/8276.
*MATH 4660/8666 Automata, Computability and Formal
Language (3 hours)
This course presents a sampling of several important areas of theoretical
computer science. Definition of formal models of computation and important
properties of such models, including finite automata and Turing
machines. Definition and important properties of formal grammars and their
languages. Introduction to the formal theories of computability and
complexity. Prerequisites: MATH 2030 or MATH 2230; Recommended: CSCI
3320. (Same as CSCI 4660/8666)
MATH 4740/8746 Intro to Probability and Statistics
I (3 hours)
A mathematical introduction to probability theory including the properties
of probability; probability distributions, expected values and moments,
specific discrete and continuous distributions; and transformations of
random variables. Prerequisites: MATH 2030 or MATH 2230 and MATH
1970.
MATH 4750/8756 Introduction to Probability and
Statistics II (3 hours)
Theory and methods of statistical inference including estimators,
statistical hypotheses, multivariate estimation, chi-square tests, analysis
of variance, and statistical software. Prerequisites: MATH
4740/8746.
MATH 4760/8766 Topics in Modeling (3 hours)
Selection of such topics as formulation and analysis of various models
involving Markov chains, Markov processes (including birth and death
processes), queues, cellular automata, difference and differential
equations, chaotic systems and fractal geometries. Prerequisites:
MATH 3350/8355 and MATH 4740/8746.
MATH 8010 Statistical Research for Mathematics Teachers
(3 hours)
This course is designed for graduate students in the MAT program who select
the statistics option to complete their degree. The student will do a
literature review, design a study involving mathematics education, gather
and analyze the data, and prepare a manuscript for submission to a refereed
journal. (The course will not count toward a major in the M.A. or M.S.)
Prerequisites: STAT 8015 and TED 8010.
MATH 8020 Topics in Geometry and Topology
(3 hours)
Selection from the following topics: Straight line and compass
constructions; geometries and transformations - complex numbers and
stereographic projection, non-Euclidean geometries; graph theory; topology
of the plane; two dimensional manifolds; theory of dimension. (This course
will not count toward a major in the M.A. or M.S. programs.)
Prerequisites: Has secondary teacher certification or is working
toward it or permission of instructor.
MATH 8040 Topics in Computer Science (3
hours)
An introduction to digital computers and programming techniques. Brief
history of the development of computing, a survey of the applications of
computers, and the implications of the use of computers in education. (This
course will not count toward a major in the M.A. or M.S. programs.)
Prerequisites: Has teacher certification or is working toward it or
permission of instructor.
*MATH 8050 Algorithmic Graph Theory (3
hours)
Review of the basic concepts of graph theory. Introduction to perfect graphs
and their characterizations. Main classes of perfect graphs and their
properties. Algorithms for main problems of perfect graphs. Applications of
perfect graphs in several fields such as scheduling, VLSI and communication
networks. Prerequisites: CSCI 3320/8325 and MATH/CSCI
4150/8156. (Same as CSCI 8050).
*MATH 8060 Algorithmic Combinatorics (3
hours)
Classical combinatorial analysis, graph theory, trees, network flow,
matching theory, extremal problems, block designs. Prerequisites:
MATH/CSCI 3100/8105. (Same as CSCI 8060).
*MATH 8080 Design and Analysis of Algorithms (3 hours)
The study of algorithms important in computer programming. Principles and
underlying concepts of algorithm design, fundamental techniques of algorithm
analysis, typical types of algorithms. Related topics such as algorithms and
computer architecture. Prerequisites: MATH/CSCI 3320/8325 or
equivalent. (Same as CSCI 8080).
MATH 8120 Abstract Algebra II (3 hours)
Beginning graduate course in abstract algebra to include rings, integral
domains, fields, vector spaces, ideals, algebraic number fields, finite
fields, and introduction to Galois Theory. Prerequisites: MATH
4110/8116.
MATH 8240 Mathematical Analysis II (3 hours)
Provides a theoretical foundation for the concepts of elementary
calculus. Topics include differentiation and Riemann-Stieltjes integration,
sequences and series of functions, uniform convergence, power series,
functions of several variables, and Implicit Function
Theorem. Prerequisites: MATH 4230/8236.
MATH 8250 Partial Differential Equations (3
hours)
Linear and nonlinear first order equations, classification of second order
linear equations, elliptic, hyperbolic, and parabolic equations and boundary
value problems, Green’s functions. Prerequisites: MATH 4230/8236
or MATH 4330/8336.
MATH 8450 Calculus of Variations (3
hours)
Functionals, the Euler-Lagrange Equation, the Brachistochrone, minimum
surface of revolution, isoperimetric problem, Fermat’s Principle,
Hamilton’s Principle, least action, the vibrating string and membrane,
max-min characterization of eigenvalues, further
applications. Prerequisites: MATH 3230/8235 and MATH 3350/8355.
MATH 8490 Applied Complex Variables (3
hours)
Applications of complex variables to potential theory, Fourier and Laplace
transforms, ordinary and partial differential equations, number theory,
chaotic dynamical systems, etc. Prerequisites: MATH
4270/8276.
*MATH 8500 Advanced Numerical Methods I (3
hours)
Error propagation, solutions of linear equations by various schemes. Matrix
norms and conditioning, computation of eigenvalues and
eigenvectors. Additional topics such as nonlinear systems, and least square
problems, etc. The computer algebra system Maple will be
used. Prerequisites: MATH/CSCI 3300/8305. (Same as CSCI
8500).
*MATH 8510 Advanced Numerical Methods II (3
hours)
Numerical solutions of partial differential equations. The computer algebra
system Maple will be used. Prerequisites: MATH/CSCI 8500 and MATH
1970. (Same as CSCI 8510).
*MATH 8520 Advanced Topics in Operations Research
(3 hours)
Topics selected from dynamic programming, multi-objective optimization,
optimization in vector spaces, optimal management in bioeconomics, and
optimal control. May be repeated for credit with the permission of graduate
adviser, and instructor. Prerequisites: MATH/CSCI 4300/8306 or MATH
4310/8316, and MATH 3230/8235 or permission by instructor. (Same as CSCI
8520).
MATH 8620 General Topology (3 hours)
The concepts of MATH 4610/8616 are studied at an advanced level in
conjunction with ordinal and cardinal numbers, open and closed maps,
separation axioms and countable compactness. Prerequisites: MATH
4610/8616 or permission of instructor.
MATH 8650 Introduction to Probability Models
(3 hours)
An introduction to probability modeling including Poisson Processes, Markov
chains, birth-death processes, queuing models and renewal theory.
Applications will be an important part of the course. Prerequisites:
MATH 4740/8746 or MATH/CSCI 4760 or STAT 3800.
*MATH 8850 Advanced Automata and Formal Languages
(3 hours)
A continuation of MATH/CSCI 4660/8666. The course will be an introduction to
computational complexity. Topics that will be covered include space and time
complexities of Turing Machines, deterministic versus non-deterministic
machines, NP-complete problems, alternating Turing Machines, and concepts of
reducibility. Prerequisites: MATH/CSCI 4660/8666. (Same as CSCI
8850).
MATH 8880 Advanced Placement Institute: Calculus
(3 hours)
A workshop for teachers planning to offer an advanced placement course in
calculus. Objectives include increasing teacher competencies in
single-variable calculus, discussion and study of AP calculus exams,
implementations of AP courses in calculus, and development and presentation
of projects for graduate credit. (This course will not count toward a major
in the M.A. or M.S. programs.) Prerequisites: Graduate in mathematics
or mathematics education.
MATH 8970 Independent Graduate Studies
(1-3 hours)
Under this number a graduate student may pursue studies in an area that is
not normally available to him/her in a formal course. The topics studied
will be a graduate area in mathematics to be determined by the
instructor. Prerequisites: Permission of instructor and graduate
classification.
MATH 8980 Graduate Seminar (1-3 hours)
A graduate seminar in mathematics.
MATH 8990 Thesis (1-6 hours)
MATH 9110 Advanced Topics in Applied Mathematics
(3 hours)
Topics selected from applied algebra, applied linear algebra, coding theory,
graph theory, differential equations, numerical; analysis, etc. May be
repeated for credit with permission for the graduate
advisor. Prerequisites: Permission of instructor.
MATH 9230 Theory of Functions of Real Variables
(3 hours)
Real number system, convergence, continuity, bounded variation,
differentiation, Lebesque-Stieltjes integration, abstract measure theory,
the Lp spaces. Prerequisites: MATH 4230/8236 and
MATH 8240, or equivalent.
STAT 3000/8005 Statistical Methods I (3
hours)
Distributions, introduction to measures of central value and dispersion,
population and sample, the normal distribution, inference: Single
population, inference: Two populations, introduction to analysis of
variance. Statistical packages on the computer will also be utilized in the
course. Prerequisites: MATH 1310 or equivalent.
STAT 3010/8015 Statistical Methods II (3
hours)
Regression and correlation, analysis of covariance, chi-square type
statistics, more analysis of variance, questions of normality, introduction
to nonparametric statistics. Statistical packages are used when
appropriate. Prerequisites: STAT 3000/8005 or equivalent.
STAT 3800/8805 Applied Engineering Probability and
Statistics (3 hours)
An introduction to the application of probabilistic and statistical
techniques to the solution of engineering and industrial design
problems. Credit for both MATH 4740 and STAT 3800 will be given, only with
permission, for dual majors. Prerequisites: MATH 1970
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