Professors:  J. Barksdale, D. Biles, B. Brunson, C. Ernst, J. Gishe, P. Hamburger, N. Iraniparast,
B. Kessler, D. Neal, B. Richmond, T. Richmond, M. Robinson, J. Spraker, W. Weidemann

Associate Professor:  F. Atici, C. Edwards, L. Nguyen

Assistant Professors: M. Autin, D. Benko, T. Bhattacharya, B. Csaba, M. Dunkum, J. Gishe,
D. Lanphier, H. Marchionda, A. Por, J. Quiton, D. Wu

Master of Science in Mathematics (Ref. # 085)

The M.S. in Mathematics 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
     Topology:  MATH 439G -- (point-set) Topology
     Computer Applications (3 hours): MATH 504 - Computer Applications to Problems in Mathematics.

     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.

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.  

The remaining mathematics courses in the student's program must be chosen from:  MATH 405G, 406G, 415G, 432G, 435G, 450G, 470G, 504, 517, 523, 529, 531, 535, 536, 539, 540, 541, 542, 550, 560, 570, 590, or STAT 549.

A maximum of 12 hours at the 400G-level may be included in the entire program. 

A research tool is required and may entail coursework beyond the 30 hours of mathematics.  The research too 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.  In addition, all students in the M.S. program must have a working knowledge of a high-level programming language or computer algebra system.

With prior approval of the Mathematics Department Graduate Committee, a student may include (toward the M.S. in Mathematics) a maximum of 6 hours of coursework chosen from a related discipline.

Master of Arts in Mathematics (Ref. # 049)

The M.A. in Mathematics requires a minimum of 30 semester hours of graduate-level mathematics courses. The following are required:

CORE:

Mathematics:  (4 of the following 5 courses)
MATH 501 -- Introduction to Probability and Statistics I
MATH 503 -- Introduction to Analysis
MATH 511 -- Secondary Mathematics from an Advanced Perspective
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

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,
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.

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 exam are required.  Students must develop and submit a professional portfolio to demonstrate mastery of the Kentucky Experienced Teacher Standards.

Rank II Certification

  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.

  509     History of Modern 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, and permission of a              mathematics gradu­ate advisor.
 
             History and development of mathematics since the 18th century with an emphasis on important              problems and famous mathematicians.

  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     Mathematical Statistics I.  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.

  530     Mathematical Statistics II.  3 hours.
             Prerequisite:  Math 529.

             Statistical inference.  Point estimates and their proper­ties; Bayes estimates; Cramer-Rao
             inequality; interval estimates; hypothesis testing; linear models; analysis of variance; non-                          parametric inference.

  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.

  550     Complex Analysis.  3 hours.
             Prerequisites:  Math 432, 450.

             Analytic continuation; conformal mapping; Riemann surfaces; and uni-valent 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.

Additional 500-level Math courses acceptable for the Master of Arts in Education

  501     Introduction to Probability and Statistics I.  3 hours.
             Prerequisite:  Permission of instructor.

             Combinations and permutations; basic theorems or probability; mathematical expectations;              random variable and basic probability distributions; central limit theorem.

  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.

  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.

  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.     

These 400-level math courses may be taken for graduate credit.  Graduate students are required to complete additional problem sets and/or papers to receive graduate credit.

  403G  Geometry for Elementary Teachers.  3 hours.
             Prerequisites:  Math 211 and 212, or equivalent.  (For students enrolled in elementary or middle              grades graduate programs.)

             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.

  405G  Numerical Analysis I (CS 405).  3 hours.
             Prerequisites:  Math 327, CS 245 FORTRAN 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 (CS 406).  3 hours.
             Prerequisites:  Math 307, 331, and 405.

  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.

  411G  Problem Solving for Elementary and Middle School Teachers.  3 hours.
             Prerequisites:  CS 230, and Math 403 or 323.

             Integration of concepts developed in algebra, geome­try, computer science, logic, statistics,
             probability, and  elementary number theory.  Students will be encour­aged to use various
             problems solving strate­gies and models and to create related problems of their own.

  413G  Algebra and Computing for Elementary Teachers.  3 hours.
             Prerequisite:  Math 212 or equivalent.

             Algebraic properties and relationships of our number systems, algebraic functions, introduction
             to computing including programming in BASIC, applications of computing in algebra.  (For
             elementary or middle school education majors only.)

  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.

  423G  Geometry II.  3 hours.
             Prerequisite:  Math 323.

             An axiomatic development of plane hyperbolic geome­try which presupposes a development of
             absolute 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
             mathematicalphysics 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; con-formal 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.  (on demand)

  475G  Selected Topics in Mathematics.  1 to 3 hours.
             Prerequisite:  Permission of instructor.

             Significant problems and developments of current interest.

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