Department of Mathematics

http://www.wku.edu/math

Bruce Kessler, Department Head
College High Hall 4124
(270) 745-3651
math@wku.edu

The Department of Mathematics offers the M.S. degree and the M.A. degree.  Both degrees have the thesis and non-thesis options, and both require 30 hours of graduate-level courses.

The M.S. has two options available. The M.S. (general option) provides knowledge in such traditional areas as analysis, algebra, topology, and applied mathematics, and is recommended for students who wish to obtain a Ph. D. degree, to teach in a community college, or to seek employment in industry with an emphasis on conceptual foundations. The M.S. (computational option) is designed for students seeking employment in industry with an emphasis on computational mathematics and/or computer science in addition to knowledge in traditional areas.

The M.A. degree is designed for students interested in careers in secondary education and will help students become more knowledgeable about the mathematics they will teach in high school and make connections and extensions of that knowledge to college and higher mathematics.

A more detailed description of the mathematics graduate programs can be found at www.wku.edu/math/grad_ms.php for the M.S. program and at www.wku.edu/math/grad_ma.php for the M.A. program.

Faculty

Professor

Ferhan Atici, PhD (Mathematics and Statistics), University of Nebraska-Lincoln, 1995

Claus D. Ernst, PhD (Mathematics), Florida State University, 1988

Nezam Iraniparast, PhD (Mathematics), University of California-Davis, 1984

Walter B. Kessler, PhD (Mathematics), Vanderbilt University, 1997

Dominic A. Lanphier, PhD (Mathematics), University of Minnesota-Twin Cities, 2000

David K. Neal, PhD (Mathematics), University of Florida, 1988

Thanh L. Nguyen, PhD (Mathematics), Ohio University Main Campus, 2002

Thomas A. Richmond, PhD (Mathematics), Washington State University, 1986

Mark P. Robinson, PhD (Mathematics), University of Kentucky, 1991

Associate Professor

Melanie A. Autin, PhD (Statistics), University of South Carolina - Columbia, 2007

Tilak Bhattacharya, PhD (Mathematics), Purdue University Main Campus, 1988

Molly Dunkum, PhD (Mathematics), University of Kentucky, 2005

Mikhail Khenner, PhD (Physico-Mathematical Sciences), Perm State University-Russia, 1999

Hope L. Marchionda, PhD (Curriculum and Instruction), Clemson University, 2006

Samangi Munasinghe, PhD (Mathematics), Texas A M University, 2006

Ngoc B. Nguyen, PhD (Mathematics), Bowling Green State University, 2010

Attila Por, PhD (Mathematics), Eotvos Lorand University-Hungary, 2003

Richard C. Schugart, PhD (Applied Mathematics), North Carolina State University, 2005

Assistant Professor

Daniel L. Clark, PhD (Mathematics Education), Michigan State University, 2016

Kanita K. Ducloux, PhD (Mathematics Education), University of Georgia, 2009

Natasha E. Gerstenschlager, PhD (Mathematics Science Educ), Middle Tennessee State University, 2015

Ahmet O. Ozer, PhD (Applied Mathematics), Iowa State University, 2011


Mathematics Courses

MATH 403G   Geometry for Elementary and Middle School Teachers    3 Hours

Both formal and informal methods are used to explain the basic concepts of Euclidean geometry. Emphasis is given to the investigative approach, organizational skills, and problem solving. (Not applicable for the M.S. degree in Mathematics or the M.A.E. degree in Secondary Education.)
Recent Term(s) Offered: spring 2015; fall 2015; fall 2016; fall 2017

MATH 405G   Numerical Analysis I    3 Hours

Computer arithmetic, roots of equations, polynomial approximation and interpolation, numerical differentiation and integration. Computer solutions of problems will be required.
Equivalent(s): CS 405G.
Recent Term(s) Offered: fall 2015; fall 2016; fall 2017

MATH 406G   Numerical Analysis II    3 Hours

The solution of linear systems by direct and iterative methods, matrix inversion, the calculation of eigenvalues and eigenvectors of matrices. Initial and boundary value problems in ordinary differential equations. Computer solution of problems will be required.
Recent Term(s) Offered: spring 2017

MATH 409G   History of Mathematics    3 Hours

History of mathematics from ancient times through the development of calculus with emphasis on famous problems. Provides knowledge and appreciation useful in the classroom. Term papers will be required. (Not applicable to the M.S. degree in Mathematics).
Prerequisite(s): Graduate standing with at least 6 hours of undergraduate mathematics or permission of instructor.
Recent Term(s) Offered: summer 2015; summer 2016; summer 2017

MATH 411G   Problem Solving for Elementary and Middle School Teachers    3 Hours

Integrates concepts developed in algebra, geometry, logic, statistics, probability, and elementary number theory. Students are encouraged to use problem-solving strategies, models, and technologies, and to create problems of their own. (Not applicable to the M.S. degree in Mathematics or the M.A.E. in Secondary Education.)
Recent Term(s) Offered: spring 2015; fall 2015; spring 2016; fall 2016; spring 2017; fall 2017

MATH 413G   Algebra and Technology for Middle Grades Teachers    3 Hours

The use of graphing calculators and computer software to explore algebraic ideas including patterns, functions, equations, inequalities, linear programming, curve fitting, and practical applications of algebra and technology. (Not applicable to the M.S. degree in Mathematics or the M.A.E. degree in Secondary Education.)
Recent Term(s) Offered: spring 2015; fall 2015; spring 2016; spring 2017; fall 2017

MATH 415G   Algebra and Number Theory    3 Hours

Survey of modern algebra and number theory. Includes number systems, divisibility, congruences, groups and their application to number theory.
Recent Term(s) Offered: None

MATH 417G   Algebraic Systems    3 Hours

The theory of finite groups and related algebraic systems. Lagrange's Theorem, Sylow Theorems, and the structure of finite groups are studied. Applications of group theory to the study of algebraic problems and symmetry.
Recent Term(s) Offered: spring 2015; spring 2017

MATH 421G   Problem Solving for Secondary Teachers    3 Hours

Utilizes various techniques and technology to solve mathematical problems. Integrates concepts from algebra, geometry, trigonometry, probability, statistics, number theory, discrete mathematics, linear algebra, and calculus. (Not applicable to the M.S. degree in mathematics).
Recent Term(s) Offered: spring 2015

MATH 423G   Geometry II    3 Hours

An axiomatic development of plane hyperbolic geometry which presupposes a development of absolute geometry.
Recent Term(s) Offered: None

MATH 431G   Intermediate Analysis I    3 Hours

Topics in analysis chosen from inverse and implicit function theorems, differentiation, integration, infinite series, series of functions, and introductory functional analysis.
Recent Term(s) Offered: fall 2015; spring 2016; fall 2016; fall 2017

MATH 435G   Partial Differential Equations    3 Hours

Equations of first and second order; elliptic, hyperbolic and parabolic equations of mathematical physics using separation of variables and Fourier series.
Recent Term(s) Offered: spring 2015; spring 2016; spring 2017

MATH 439G   Topology I    3 Hours

Introduction to topology including topics selected from: topological spaces, mappings, homeomorphisms, metric spaces, surfaces, knots, manifolds, separation properties, compactness and connectedness.
Recent Term(s) Offered: fall 2015; fall 2016; fall 2017

MATH 450G   Complex Variables    3 Hours

Complex number plane, analytic functions of a complex variable, integration, power series, calculus of residues, conformal representation, applications of analytic function theory.
Recent Term(s) Offered: spring 2015; spring 2016; spring 2017

MATH 470G   Introduction to Operations Research    3 Hours

Principles and techniques of operations research including linear programming, integer programming, quality theory, sensitivity analysis, and dynamic programming.
Recent Term(s) Offered: summer 2016

MATH 482G   Probability & Statistics II    3 Hours

Multivariate probability distributions; sampling distributions, statistical inference; point and interval estimation, properties of estimators; hypothesis testing; regression and correlation; analysis of variance; non-parametric methods.
Recent Term(s) Offered: None

MATH 500   Readings in Mathematics    1-3 Hours (repeatable max of 6 hrs)

Students read and present papers that have appeared in (or have been accepted by) mathematical journals. Topics covered are determined by areas of interest.
Prerequisite(s): Undergraduate major in mathematics.
Recent Term(s) Offered: summer 2015

MATH 501   Introduction to Probability and Statistics I    3 Hours

Interpreting, analyzing, and simulating univariate and bivariate data; probability and sampling distributions; regression and chi-squared procedures from traditional and randomization approaches.
Recent Term(s) Offered: spring 2015; spring 2016; spring 2017

MATH 502   Introduction to Probability and Statistics II    3 Hours

Review of linear algebra, Markov chains, decision theory, linear programming and game theory.
Recent Term(s) Offered: None

MATH 503   Introduction to Analysis    3 Hours

Theoretical examination of selected topics in real analysis including sequences, series, limits, continuity, derivatives, and integration.
Prerequisite(s): Admission to the Master of Arts in Mathematics program or permission of instructor.
Recent Term(s) Offered: fall 2015; fall 2016; summer 2017; fall 2017

MATH 504   Application of Technology to Problems in Mathematics    3 Hours

Integration of technology to solve problems in areas of mathematics including calculus, applied statistics, probability, geometry, and algebra.
Prerequisite(s): Admission to the Master of Arts in Mathematics Program or permission of instructor.
Recent Term(s) Offered: fall 2015; fall 2016; fall 2017

MATH 506   Mathematical Applications for Middle Grades Teachers    3 Hours

Sets, logic, dimensional analysis, functions and modeling, and discrete mathematics with a focus on real-world applications. Not applicable for MS and MA in Mathematics.
Prerequisite(s): Middle Grades Mathematics Certification or permission of instructor.
Recent Term(s) Offered: summer 2017

MATH 507   Mathematics Concepts for Elementary Teachers    3 Hours

Course intended for graduate students in Elementary Education only. Focuses on mathematics and strategies to effectively teach Kentucky Mathematics Core Content in grades K-5.
Recent Term(s) Offered: summer 2015; summer 2017

MATH 508   Number Concepts for Elementary and Middle Grades Teachers    3 Hours

Mathematical structures of integers and rational numbers; numeration systems; elementary number theory; special sequences and numerical of relationships; applications of fractions, decimals, percents, ratio, proportion, exponents, and scientific notation. (Not applicable to M.S. degree in Mathematics or M.A.E. degree in Secondary Education.)
Recent Term(s) Offered: summer 2016

MATH 510   Intermediate Statistics    3 Hours

Extended coverage of experimental design and data collection, statistical inference including confidence intervals, estimation, tests of significance, comparison of population parameters, and multiple regression.
Prerequisite(s): MATH 501.
Recent Term(s) Offered: summer 2015; summer 2016; summer 2017

MATH 511   Algebra from an Advanced Perspective    3 Hours

Topics in algebra from an advanced perspective including analysis of functions and polynomials, number theory, and fields.
Prerequisite(s): Admission to the Master of Arts in Mathematics program or permission of instructor.
Recent Term(s) Offered: fall 2015; fall 2016; fall 2017

MATH 512   Geometry from an Advanced Perspective    3 Hours

Topics in geometry from an advanced perspective including a theoretical examination of transformations in real and complex plane; distance congruence, and similarity in a variety of contexts; connections and applications between geometry, trigonometry, and calculus.
Prerequisite(s): Math 511 with a "C" or better or permission of instructor.
Recent Term(s) Offered: spring 2015; spring 2016; spring 2017

MATH 514   Mathematical Modeling and Applications    3 Hours

Uses mathematical modeling to describe and explore real world problems using algebraic, geometric, and statistical approaches.
Prerequisite(s): Admission to the Master of Arts in Mathematics program or permission of instructor.
Recent Term(s) Offered: spring 2015; spring 2016; spring 2017

MATH 517   Topics from Algebra    3 Hours

Theory of rings, fields, and vector spaces. Topics include: polynomial rings, principal ideal domains, unique factorization domains, field extensions, Galois theory.
Recent Term(s) Offered: None

MATH 529   Applied Probability    3 Hours

Axiomatic development of the theory of probability. Introduction to Markov chains, random variables, distributions, transformations. Limit theorems and various modes of convergence.
Recent Term(s) Offered: fall 2016

MATH 531   Advanced Differential Equations    3 Hours

Power series solutions, existence and uniqueness theorems, stability and Liapunov's method, regular singular points, perturbations of periodic solutions.
Recent Term(s) Offered: fall 2017

MATH 532   Real Analysis    3 Hours

Function spaces, additive set functions, outer measure; measurable functions, integration.
Recent Term(s) Offered: spring 2015

MATH 535   Advanced Applied Mathematics- I    3 Hours

Eigenvalue and boundary value problems, orthogonal expressions in function spaces, classic polynomials, Sturm-Liouville theory, Fourier and Laplace transforms.
Recent Term(s) Offered: spring 2016

MATH 536   Advanced Applied Mathematics- II    3 Hours

Integral equations, calculus of variations, maximation of linear functionals, maximum gradient method.
Prerequisite(s): MATH 535.
Recent Term(s) Offered: fall 2016

MATH 539   Topology II    3 Hours

Homotopy, homology theory.
Recent Term(s) Offered: fall 2017

MATH 540   Stochastic Processes    3 Hours

Theory and application of stochastic processes; random walks; Markov chains; Poisson processes; birth and death processes; queues; renewal and branching processes; computer simulations.
Recent Term(s) Offered: None

MATH 541   Graph Theory    3 Hours

Introduction to the basic concepts of graph theory. Topics include Eulerian circuits, Hamiltonian cycles, coloring problems and planar graphs.
Prerequisite(s): Undergraduate major in mathematics or permission of instructor.
Recent Term(s) Offered: spring 2017

MATH 542   Advanced Topics in Discrete Mathematics    3 Hours

Combinatorics, ordered sets and lattice theory, modeling with difference equations, discrete calculus, dynamic equations on time scales.
Recent Term(s) Offered: None

MATH 550   Complex Analysis    3 Hours

Analytic continuation, conformal mapping, Riemann surfaces, and univalent functions.
Recent Term(s) Offered: None

MATH 570   Topics in Operations Research    3 Hours

Specific area(s) of operations research.
Recent Term(s) Offered: None

MATH 590   Special Topics in Mathematics    3 Hours (repeatable max of 6 hrs)

No course description is available.
Prerequisite(s): Permission of instructor.
Recent Term(s) Offered: fall 2015; fall 2016; fall 2017

MATH 598   Graduate Seminar: Communicating Mathematics and Technical Writing    3 Hours

This course will familiarize graduate students in mathematics with the many different areas of mathematics and active research topics in the field as well as give them an opportunity to practice effective oral presentation skills. Students will also learn mathematical typesetting with LaTeX.
Recent Term(s) Offered: spring 2015; fall 2015; spring 2016; fall 2016; spring 2017; fall 2017

MATH 599   Thesis/Research    1-6 Hours (repeatable max of 6 hrs)

Thesis research and writing directed by faculty committee.
Grade Mode: Pass/Fail
Recent Term(s) Offered: spring 2015; fall 2015; spring 2016; fall 2016; spring 2017; fall 2017

MATH 600   Maintaining Matriculation    1-6 Hours (repeatable max of 6 hrs)

Continued enrollment for thesis completion.
Grade Mode: Non-graded
Recent Term(s) Offered: summer 2015; summer 2016; fall 2017

Statistics Courses

STAT 549   Statistical Methods I    3 Hours

Principles of applied statistical research. Elements of data collection and experimental design. Parametric and nonparametric methods for analyzing interval, ordinal and categorical data, including confidence intervals and hypothesis testing, single factor ANOVA, simple and multiple linear regression and correlation. Emphasis will be placed on analyzing real data.
Prerequisite(s): Permission of instructor.
Recent Term(s) Offered: fall 2015; fall 2016

STAT 550   Statistical Methods II    3 Hours

Continuation of STAT 549. Topics include multiple linear regression, generalized linear model, two-way ANOVA and more general factorial design, block and nested design, mixed and random effect models, analysis of covariance. Emphasis on analyzing real data using statistical software packages, such as SAS, SPSS, or R.
Prerequisite(s): STAT 549 with a grade of B or better; or permission of instructor.
Recent Term(s) Offered: spring 2016; spring 2017