# Department of Mathematics

Department website: 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

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

John S. Spraker, PhD (Mathematics), Indiana Uni Bloomin-USE 601401, 1987

### Associate Professor

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

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

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

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

Nicholas C. Fortune, PhD, North Carolina State University, 2018

Natasha 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.

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

*Recent Term(s) Offered: fall 2016; fall 2017; spring 2018*

**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 2016; fall 2017; fall 2018*

**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.

**Equivalent(s): **CS 406G

*Recent Term(s) Offered: spring 2017; spring 2018*

**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 2016; summer 2017; summer 2018*

**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 2016; fall 2016; spring 2017; fall 2017; spring 2018; fall 2018*

**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: 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 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.

**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: spring 2016; fall 2016; fall 2017; fall 2018*

**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 2016; spring 2017; spring 2018*

**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 2016; fall 2018*

**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 2016; spring 2017; spring 2018*

**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: spring 2018*

**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: None*

**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 2016; spring 2017; spring 2018*

**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 2016; summer 2017; fall 2017; fall 2018*

**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.

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

*Recent Term(s) Offered: fall 2016; fall 2017; fall 2018*

**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: 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 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.

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

*Recent Term(s) Offered: summer 2016; summer 2018*

**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 2016; summer 2017; summer 2018*

**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 2016; fall 2017; fall 2018*

**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 2016; spring 2017; spring 2018*

**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 2016; spring 2017; spring 2018*

**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: 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 2016; spring 2018*

**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. Note: Undergraduate major in mathematics required.

**Prerequisite(s): **permission of instructor

*Recent Term(s) Offered: spring 2017; fall 2018*

**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 2016; fall 2017; spring 2018*

**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 2016; fall 2016; spring 2017; spring 2018; fall 2018*

**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 2016; fall 2016; spring 2017; fall 2017; spring 2018; summer 2018; fall 2018*

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

Continued enrollment for thesis completion.

*Recent Term(s) Offered: summer 2016; fall 2017; spring 2018; summer 2018*

## 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 2016; fall 2018*

**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: spring 2016; spring 2017*