Graduate Catalog 2021-2022

Department of Mathematics

Department website: http://www.wku.edu/math

Kanita Ducloux, (Interim) Chair
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 three concentrations available. The M.S. (general mathematics) 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 mathematics) 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.S. (mathematical economics) is for students that have completed WKU’s mathematical economics major or want to work as an mathematical economist in industry, and want to complete their thesis under the direction of a math faculty member.

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.

Faculty

Professor

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

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

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

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

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

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

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

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

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

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

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

Nicholas C. Fortune PhD (Mathematics Education), North Carolina State University, 2018

Lukun Zheng PhD (Applied Mathematics), University North Carolina Charlotte, 2015

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.

Restriction(s): Students cannot enroll who are in Secondary Ed Teacher Leader (0435) or Mathematics (085)

Recent Term(s) Offered: None

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.

Prerequisite(s): (MATH 307 or MATH 310 or MATH 237) and (CS 180 or CS 146) or permission of instructor

Equivalent(s): CS 405G

Recent Term(s) Offered: fall 2019; fall 2020; fall 2021

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 2019; spring 2020; spring 2021

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. Note: 6 hours of undergraduate mathematics required.

Prerequisite(s): permission of instructor

Restriction(s): Students cannot enroll who are in Mathematics (085)

Recent Term(s) Offered: summer 2019

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.

Restriction(s): Students cannot enroll who are in Secondary Ed Teacher Leader (0435) or Mathematics (085)

Recent Term(s) Offered: spring 2019; fall 2019; spring 2020; fall 2020; fall 2021

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.

Restriction(s): Students cannot enroll who are in Secondary Ed Teacher Leader (0435) or Mathematics (085)

Recent Term(s) Offered: None

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: None

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.

Restriction(s): Students cannot enroll who are in Mathematics (085)

Recent Term(s) Offered: None

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 2020

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 2019; spring 2020; spring 2021; fall 2021

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 2021

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 2019; spring 2020; spring 2021

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: fall 2019

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: spring 2019; spring 2020; spring 2021

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. Note: Undergraduate major in mathematics required.

Prerequisite(s): permission of instructor

Recent Term(s) Offered: spring 2019; summer 2019; summer 2021

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 2019; spring 2020; spring 2021

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.

Restriction(s): Enrollment is limited to students in Mathematics (049)

Recent Term(s) Offered: fall 2019; fall 2020; fall 2021

MATH 504    Application of Technology to Problems in Mathematics    3 Hours

Problem solving via non-routine problems from various branches of mathematics, including, but not limited to number theory, discrete math, linear algebra, calculus, probability, and statistics.

Restriction(s): Enrollment is limited to students in Mathematics (049)

Recent Term(s) Offered: fall 2019; summer 2020; fall 2020; summer 2021

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. Note: Middle grades math certification required.

Prerequisite(s): permission of instructor

Restriction(s): Students cannot enroll who are in Mathematics (049) or Mathematics (085)

Recent Term(s) Offered: None

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 2019; summer 2021

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.

Restriction(s): Students cannot enroll who are in Secondary Ed Teacher Leader (0435) or Mathematics (085)

Recent Term(s) Offered: summer 2020

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 2019; summer 2020; summer 2021

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.

Restriction(s): Enrollment is limited to students in Mathematics (049)

Recent Term(s) Offered: fall 2019; fall 2020; fall 2021

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 or permission of instructor

Recent Term(s) Offered: spring 2019; spring 2020; spring 2021

MATH 514    Mathematical Modeling and Applications    3 Hours

Uses mathematical modeling to describe and explore real world problems using algebraic, geometric, and statistical approaches.

Restriction(s): Enrollment is limited to students in Mathematics (049)

Recent Term(s) Offered: spring 2019; spring 2020; spring 2021

MATH 515    Introduction to Number Theory    3 Hours

An introduction to number theory, including, but not limited to, divisibility, congruences, quadratic reciprocity, theory of primes, Fermat’s Theorem, Euler’s Theorem, application problems

Restriction(s): Enrollment is limited to students in Mathematics (049)

Recent Term(s) Offered: None

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: None

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 2019; fall 2021

MATH 532    Real Analysis    3 Hours

Function spaces, additive set functions, outer measure; measurable functions, integration.

Recent Term(s) Offered: None

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 2020

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: None

MATH 539    Topology II    3 Hours

Homotopy, homology theory.

Recent Term(s) Offered: None

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. Note: Undergraduate major in mathematics required.

Prerequisite(s): permission of instructor

Recent Term(s) Offered: spring 2021

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: spring 2019

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 585    Advanced Mathematical Thinking I    3 Hours

Students will explore and identify connections between research in mathematics education and the mathematics content, from an advanced perspective, they are teaching in their courses.

Prerequisite(s): (MATH 501 and MATH 503 and MATH 511 and MATH 512 and MATH 515 (may be taken concurrently))

Restriction(s): Enrollment is limited to students in Mathematics (049)

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: spring 2019; summer 2019; fall 2020; spring 2021; fall 2021

MATH 595    Advanced Mathematical Thinking II    3 Hours

Students will conduct their own research project regarding secondary students’ mathematical thinking, applying what was learned in MATH 585 (Adv Mathematical Thinking I).

Prerequisite(s): MATH 585

Restriction(s): Enrollment is limited to students in Mathematics (049)

Recent Term(s) Offered: None

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 2019; spring 2021

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

Thesis research and writing directed by faculty committee.

Recent Term(s) Offered: spring 2019; summer 2019; fall 2019; spring 2020; fall 2020; spring 2021; summer 2021; fall 2021

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

Continued enrollment for thesis completion.

Recent Term(s) Offered: spring 2019; summer 2019

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 2020

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 minimum grade of B or permission of instructor

Recent Term(s) Offered: None