The following are descriptions of all mathematics courses offered via the eMath program. Please visit the Department of Teacher Education’s website or consult WKU’s Graduate Catalog for a complete description of education courses required for eMath.

405G Numerical Analysis I (CS 405G) 3 hours.
Prerequisites:  MATH 307, Math 310, or Math 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, Math 327, and Math 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 solutions of problems will be required

409G History of Mathematics  3 hours.
Prerequisite: At least 6 hours of upper division undergraduate mathematics, or permission of instructor. History of mathematics from ancient times through the development of calculus with  em-phasis 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.

421G Problem Solving for Secondary Teachers  3 hours.
Prerequisites: MATH 307 and MATH 310; MATH 329 and MATH 323, or permission of instructor. 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.

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.

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 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. Signifcant problems and developments of current interest.

Courses numbered 500 and above are for graduate students only.

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:  Admission to the Master of Arts in Mathematics program or permission of instructor.  
Interpreting and analyzing univariate and bivariate data; probability and sampling distributions simulation.  (Not applicable to the M.S. degree in Mathematics.)

503 Introduction to Analysis  3 hours.
Prerequisite:  Admission to the Master of Arts in Mathematics program or permission of instructor. 
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.

504 Computer Applications to Problems
in Mathematics  3 hours.
Prerequisite: Admission to the Master of Arts in Mathematics program or permission of instructor.
Integration of technology to solve problems in areas of mathematics including calculus, applied statistics, probability, geometry, and 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.

510  Intermediate Statistics 3 hours.
Prerequisite: MATH 501 
Extended coverage of experimental design and data collection. Statistical inference including confidence intervals, estimation, tests of significance, comparison of population parameters, and chi-square procedures.

511 Secondary Mathematics from an Advanced Perspective I 3 hours.
Prerequisite: Admission to the Master of Arts in Mathematics program 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 applicable to the M.S. degree in Mathematics.)

512 Secondary Mathematics from an Advanced Perspective II  3 hours.
Prerequisite: Admission to the Master of Arts in Mathematics program 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 
Teachers  3 hours.
Prerequisite: Admission to the Master of Arts in Mathematics program 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 teachers. Not applicable to the M.S. degree in Mathematics.

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.

531 Advanced Differential Equations  3 hours.
Prerequisites: MATH 331, 431. Power series solutions, existence and uniqueness theorems, stability and Lia-
punov's 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.

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.

590 Special Topics in Mathematics  3 hours.
Prerequisite: Permission of instructor.

599 Thesis Research and Writing  6 hours.