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Professors: J. Barksdale, B. Brunson, R. Crawford, C. Ernst,
P. Hamburger, N. Iraniparast,
B. Kessler, D. Neal,
B. Richmond, T. Richmond, M. Robinson, J. Spraker, W. Weidemann
Associate Professor: F. Atici, D. Lanphier, V. Moody, L. Nguyen
Assistant Professors: M. Autin, T. Bhattacharya, B. Csaba, M. Dunkum, J. Gishe,
H. Marchionda, A. Por, J. Quiton,
R. Schugart, D. Wu
The Department of Mathematics offers the Master of Science (M.S.) degree and the Master of Arts (M.A.) degree. Both degrees have thesis and non-thesis options, and both require 30 semester hours of graduate-level courses. The M.S. degree is designed for students who wish to: obtain a Ph.D. degree, teach in a community college, or to seek employment in industries
needing mathematical or computational expertise. On the other hand, the M.A. is designed
for secondary teachers and includes courses that will help them become more knowledgeable about the mathematics they teach in high school while exploring the connections and
extensions of that knowledge to college and higher mathematics. The required courses for the M.A. degree program
are offered through online courses.
Master of Science in Mathematics (Ref. # 085)
The M.S. program has two options: the "General Option " and the "Computational Option." The M.S. General Option requires traditional courses in analysis, algebra, topology, and applied mathematics, and is recommended for students who wish to obtain a Ph.D. degree, plan a teaching career at the community college level, or to seek employment in industry. This option is based to a large extent on traditional course work from applied and pure mathematics. The M.S. Computational Option is designed for students seeking employment in industry with an emphasis on computational mathematics and/or computer science. The option contains a large component of computer science graduate courses and has entry requirements that are tailored to meet the needs of this option. Many high-end positions in
industry, financial sector, or government require hands-on mathematical expertise that goes beyond what is provided by a bachelor's degree and is different in flavor from the "General Option." All students in the M.S. program must develop a working knowledge of a high-level programming language or computer algebra system.
I. The General Option
The General Option requires a minimum of 30 semester hours of graduate-level mathematics courses. The following are required:
1. Algebra: MATH 417G -- Algebraic Systems
Analysis: MATH 431G -- Intermediate Analysis I
Topology: MATH 439G -- (point-set) Topology
If equivalent courses were taken at the undergraduate level, then the student must substitute appropriate graduate mathematics courses selected in consultation with a Mathematics Department graduate advisor.
2. An applied Mathematics course selected from MATH 529, 531, 535, 536, 540, 541, 542, 550,
570, STAT 549, or as approved by the Departmental Graduate Committee.
3. MATH 532
4. One of the following two-course sequences: MATH 417G-517, 439G-539, 450G-550, 405G-406G, 435G-535, MATH 470G-570, 529-540, 435G-531, or 535-536. The sequence 405G-406G can be taken by students who have substituted a 500-level course for at least one of the three courses listed in (1).
5. The remaining mathematics courses in the student's program must be chosen from MATH 405G, 406G, 415G, 423G, 435G, 450G, 470G, 504, 517, 523, 529, 531, 535, 536, 539, 540, 541, 542, 550, 560, 570, 590 or STAT 549.
6. A maximum of 12 hours at the 400G-level may be included in the entire program. Graduate students are required to complete additional problem sets and/or papers to receive graduate credit for these courses, which are also open to undergraduate students.
7. Students who choose to write a thesis are required to complete 6 hours of MATH 599 -- Thesis Research and Writing and to give an oral defense of the thesis.
8. A student may, upon prior approval of the Mathematics Department Graduate Committee, include in his/her program a maximum of 6 hours of coursework from a related field.
A Research Tool is required and may entail coursework beyond the 30 hours of mathematics. The research tool must be completed during the first 15 hours of coursework and may be fulfilled by: a mathematics reading course, a computer science course, a foreign language examination, or another option approved by the Mathematics Department graduate advisor. The choice of a research tool will be discussed in the graduate committee and must be approved by the Mathematics Department graduate advisor in advance or at the latest at the time when the student files the degree program form.
Comprehensive Exams: A student electing to write a thesis is required to present an oral defense of the thesis and to complete comprehensive written exams over four courses (normally including on year-long sequence) approved by the departmental Graduate Committee. Non-thesis students must complete comprehensive written exams based on six courses (normally including two year-long sequences) approved by the departmental Graduate Committee.
II. The Computational Option
The Computational Mathematics Option requires a minimum of 30 hours of graduate-level mathematics and computer science courses. The following are required:
1. MATH 405G Numerical Analysis I
MATH 406G Numerical Analysis II
STAT 549 Statistical Methods I
MATH 470G Introduction to Operations Research
CS 549 Algorithms Analysis
2. At least two courses from the list below are required:
CS 562 Parallel and Distributed Computing
CS 565 Data Mining Techniques and Tools
CS 595 Advanced Topics in computer science (with permission of advisor regarding content)
3. The remaining courses will be chosen from the list below:
MATH 431G Intermediate Analysis I
MATH 541 Graph Theory
MATH 570 Topics in Operations Research
MATH 504 Computer Applications to Problems in Mathematics
MATH 540 Stochastic Processes
MATH 542 Advanced Topics in Discrete Mathematics
MATH 590 Advanced Topics in Mathematics (with permission of advisor regarding content)
4. A maximum of 12 hours at the 400G-level may be included in the entire program. Graduate students are required to complete additional problem sets and/or papers to receive graduate credit for these courses, which are also open to undergraduate students.
5. Comprehensive exams are required.
6. The research tool requirement is satisfied by the computer science classes.
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Master of Arts in Mathematics (Ref. # 049))
The M.A. degree is designed specifically to accomodate the busy schedules of secondary mathematics teachers. All required courses are offered online so that teachers have flexibility to complete the coursework at nontraditional times. Access to the internet is neccesary. Simply CLICK on the following LINK to learn more about this flexibility option: e-Math @ WKU .
The M.A. in Mathematics requires a minimum of 30 semester hours of graduate-level courses, including the following:
CORE Mathematics Courses
A student must complete at least FOUR of the following:
MATH 501 -- Introduction to Probability and Statistics I
MATH 503 -- Introduction to Analysis
MATH 511 -- Secondary Mathematics from an Advanced Perspective I
MATH options: MATH 512 -- Secondary Mathematics from an Advanced Perspective II, or
MATH 423G -- Geometry II, or
MATH 523 -- Topic from Geometry
MATH 514 -- Modeling and Applications fro Secondary Teachers
CORE Education Courses
PSY 510 -- Advanced Ed. Psychology, or PSY 511 Psychology of Learning
SEC 580 -- The Curriculum
EDU 544 -- Classroom Teaching Strategies
SEC 534 -- Seminar in Mathematics Education
Elective Courses
Six hours of mathematics courses chosen from those listed above, or chosen from the following list:
MATH 405G, 406G, 409G, 415G, 421G,423G, 429G, 431G, 432G, 435G, 439G, 450G, 470G, 475G, or
MATH 500, 504, 509, 517, 531, 532, 535, 536, 539, 540, 541, 542, 550, 560, 590, 599.
A maximum of 9 hours at the 400G level may be included in the entire program. Graduate students are required to complete additional problem sets and/or papers to receive graduate credit for these courses, which are also open to undergraduate students.
A thesis student is required to complete 6 hours of MATH 599 (Thesis Research and Writing) and to give an oral defense of the thesis.
Comprehensive exams are required.
Rank II Certification
A student may receive Rank II Certification from the Kentucky Department of Education by earning a Master of Arts in Mathematics or a Master of Science in Mathematics. In addition to satisfying the degree requirements, such a student must develop and submit a professional portfolio consistent with the Experience Teacher Standards. A teaching component of at least one semester (either in a secondary school or as a graduate teaching assistant) is also required.
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Graduate Courses in Mathematics
500 Readings in Mathematics. 1 to 3 hours.
Prerequisite: Undergraduate major in mathematics.
Students read and present papers that have appeared in (or have been accepted by)
mathematical journals. Topics covered are determined by areas of interest.
501 Introduction to Probability and Statistics I. 3 hours.
Prerequisite: Permission of instructor.
Interpreting and analyzing univariate and bivariate data; data collection; planning
and conducting
experiments; probability and sampling distributions; statistical in
ference. (Not applicable to the
M.S. degree in Mathematics.)
502 Introduction to Probability and Statistics II. 3 hours.
Prerequisite: MATH 203 or 329 or 501; or permission of instructor.
Review of linear algebra, Markov chains, decision theory, linear programming and
game theory.
(Not applicable to the M.S. degree in Mathematics.)
503 Introduction to Analysis. 3 hours.
Examination of selected topics in elementary calculus including sequences, series,
limits, continuity,
the derivative, and the Riemann integral. Introductory material
includes logic, set theory, and
functions. (Not applicable to the M.S. degree in
Mathematics.)
504 Computer Applications to Problems in Mathematics. 3 hours.
Computer techniques and solutions of problems in mathematics including calculus,
applied
statistics, simulation, linear programming, game theory and linear algebra.
509 History of Modern Mathematics. 3 hours.
Prerequisite: Math 227 or permission of instructor.
History and development of mathematics since the 18th century with an emphasis on important
problems and famous mathematicians. (Not applicable to the M.S. degree in Mathematics.)
511 Secondary Mathematics from an Advanced Perspective I. 3 hours.
Prerequisite: Mathematics major or minor, or permission of instructor.
Intended for teachers
wishing to develop a deeper understanding of underlying concepts of algebra and calculus.
Examines links among different fields of mathematics
and connections among high school, college,
and higher mathematics. (Not appli
cable to the M.S. degree in Mathematics.)
512 Secondary Mathematics from an Advanced Perspective II. 3 hours.
Prerequisite: Mathematics major or minor, or permission of instructor.
Intended for teachers wishing to develop a deeper understanding of underlying concepts of
geometry. Examines relationships among different fields of mathematics
and connections among
high school, college, and higher mathematics. (Not applicable to the M.S. degree in Mathematics.)
514 Applications and Modeling for Secondary Teachers. 3 hours.
Prerequisite: Mathematics major or minor, or permission of instructor.
Utilizes concepts from
many fields of mathematics to explore how high school and college
mathematics is used in real
world settings. Intended for secondary teachers (Not applicable
to the M.S. degree in athematics).
517 Topics from Algebra. 3 hours.
Prerequisite: Math 417.
Theory of rings, fields, and vector spaces. Topics include: polynomial rings; principal ideal
domains; unique factorization domains; field extensions; Galois theory.
523 Topics from Geometry. 3 hours.
Prerequisite: Undergraduate geometry and permission of instructor.
Geometry of special lines and points; isometrics; similarities; inversion; applications.
529 Applied Probability. 3 hours.
Prerequisites: Math 431 or Math 327, and permission of instructor.
Axiomatic development of the theory of probability. Introduction to Markov chains; random
variables, distributions, transformations. Limit theorems and various modes of convergence.
531 Advanced Differential Equations. 3 hours.
Prerequisites: Math 331, 431.
Power series solutions; existence and uniqueness theorems; stability and Liapunovs method;
regular singular points; perturbations of periodic solutions.
532 Real Analysis. 3 hours.
Prerequisite: Math 432.
Function spaces, additive set functions; outer measure; measurable functions; integration.
535 Advanced Applied Mathematics I. 3 hours.
Prerequisites: Math 331, 431.
Eigenvalue and boundary value problems; orthogonal expansions in function spaces; classical
polynomials; Sturm-Liouville theory; Fourier and Laplace transforms.
536 Advanced Applied Mathematics II. 3 hours.
Prerequisite: Math 535.
Integral equations; calculus of variations; maximation of linear functionals; maximum gradient
method.
539 Topology II. 3 hours.
Prerequisite: Math 439.
Homotopy; homology theory.
540 Stochastic Processes. 3 hours.
Prerequisite: Permission of instructor.
Theory and application of stochastic processes, random walks, Markov chains, Poisson
processes; birth and death processes, queues, renewal and branching.
541 Graph Theory. 3 hours.
Prerequisite: Undergraduate major in mathematics or permission of instructor.
Introduction to the basic concepts of graph theory. Topics include Eulerian circuits,
Hamiltonian
cycles, coloring problems and planar graphs.
542 Advanced Topics in Discrete Mathematics. 3 hours.
Prerequisites: Math 310 and Math 317.
Combinatorics, ordered sets and lattice theory, modeling with difference equations,
discrete
calculus, dynamic equations on time scales.
STAT 549 Statistical Methods I. 3 hours.
Prerequisite: Permission of instructor.
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.
550 Complex Analysis. 3 hours.
Prerequisites: Math 432, 450.
Analytic continuation; conformal mapping; Riemann surfaces; and univalent functions.
560 Functional Analysis. 3 hours.
Prerequisite: Math 432.
Theory of abstract linear spaces. Topics include: normed vector spaces; inner product spaces;
Hilbert spaces; open mapping and closed graph theorems; Banach-Steinhaus theorem; weak
and weak*- topologies.
570 Advanced Topics in Operations Research. 3 hours.
Prerequisites: Math 432, 470, or consent of instructor.
Specific area(s) of operations research.
590 Special Topics in Mathematics. 3 hours.
Prerequisite: Permission of instructor.
599 Thesis Research and Writing. 6 hours.
600 Maintaining Matriculation. 1 to 6 hours.
No more than 12 hours of 400G-level Math Courses may be applied toward the M.S.,
and no more than 9 hours of these courses may be applied toward the M.A.
Graduate students are required to complete additional problem sets and/or papers to receive graduate credit for these 400G-level courses.
405G Numerical Analysis I (CS 405). 3 hours.
Prerequisites: Math 307 or 310 or 327; and CS 230 or CS 240 or permission of instructor.
Computer arithmetic, roots of equations, polynomial approximation and interpolation, numerical
differentiation and integration. Computer solutions of problems will be required.
406G Numerical Analysis II. 3 hours.
Prerequisites: Math 307, 327 and 331, and either MATH 405 or CS 405.
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.
409G History of Mathematics. 3 hours.
Prerequisite: Acceptance into a graduate degree program leading to the Master of Arts in
Education with a mathematics major, minor, or emphasis component, or permission of
instructor.
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. This course may not be applied to the Master of Science in Mathematics
degree.
415G Algebra and Number Theory. 3 hours.
Prerequisite: Math 315 or 317.
Survey of modern algebra and number theory. Includes number systems, divisibility,
congruences, groups and their application to number theory.
417G Algebraic Systems. 3 hours.
Prerequisite: Math 317.
Theory of groups.
421G Problem Solving for Secondary Teachers. 3 hours.
Prerequisite: Math 307 and Math 310; Math 329 and Math 323, or permission of instructor.
Utilizes various techniques and technology to solve mathematical problems. Inte grates concepts
from algebra, geometry, trigonometry, probability, statistics, num ber theory, discrete
mathematics, linear algebra, and calculus. Not applicable to the M.S. degree in Mathematics.
423G Geometry II. 3 hours.
Prerequisite: Math 323.
An axiomatic development of hyperbolic geometry based on the hyperbolic parallel postulate and
the absolute geometry developed in MATH 323, including an emphasis on contrasts
with Euclidean geometry.
429G Probability and Statistics II. 3 hours.
Prerequisite: Math 329.
Sampling distributions, statistical inference; point and interval estimation, properties of
estimators;hypothesis testing; regression and correlation; analysis of variance; and non-
parametric methods.
431G Intermediate Analysis I. 3 hours.
Prerequisite: Math 317.
Topics chosen from cardinality, limits, continuity, elementary topological concepts, sequences
and series, differentiation and integration, elementary functional analysis.
432G Intermediate Analysis II. 3 hours.
Prerequisite: Math 431.
Continuation of Math 431.
435G Partial Differential Equations. 3 hours.
Prerequisites: Math 307, 327, and 331.
Equations of first and second order; elliptic, hyperbolic and parabolic equations of
mathematical physics using separation of variables and Fourier series.
439G Topology. 3 hours.
Prerequisite: Math 317 or permission of instructor.
Topological spaces; mappings; separation of axioms; compactness; connectedness; arcwise
connectedness; metric spaces.
450G Complex Variables. 3 hours.
Prerequisite: Math 327.
Complex number plane; analytic functions of a complex variable; integration; power series;
calculus of residues; conformal representation; applications of analytic function theory.
470G Introduction to Operations Research. 3 hours.
Prerequisite: Math 307 and 327 or permission of instructor.
Principles and techniques of operations research including linear programming, integer
programming, quality theory, sensitivity analysis, and dynamic programming.
475G Selected Topics in Mathematics. 1 to 3 hours.
Prerequisite: Permission of instructor.
Significant problems and developments of current interest.
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