Missouri State University

Graduate College

2013-14 Graduate Catalog

Preliminary Edition
published April 2013

Department of Mathematics

Cheek Hall, Room 10 M , Phone: (417) 836-5112, Fax: (417) 836-6966
Email: Mathematics@missouristate.edu
Website: http://math.missouristate.edu
Department Head: William O. Bray

Graduate faculty

Distinguished Professor:  Paula A. Kemp

Professor:  Richard G. Belshoff, William O. Bray, Yungchen Cheng, Kanghui Guo, Shouchuan Hu, J. Kurt Killion, Shelby J. Kilmer, George Mathew, Lynda S. Plymate, Gay A. Ragan, Jorge Rebaza, Les Reid, Kishor Shah, Clayton C. Sherman, Vera B. Stanojevic, Yingcai Su, Xingping Sun, Cameron Wickham

Associate Professor:   Mark W. Rogers

Assistant Professor:   Adam P. Harbaugh, Matthew Wright, Songfeng Zheng

Emeritus Professor:   Earl E. Bilyeu, James R. Downing, Frank S. Gillespie, Shirley M. Huffman, John D. Kubicek, David B. Lehmann, E. Rebecca Matthews, Neil C. Pamperien, Clyde A. Paul, Woodrow Sun, William Sutherlin, Joe L. Wise, Xiang Ming Yu, Liang-Cheng Zhang  

Programs

Master of Science, Mathematics

Entrance Requirements

Students seeking admission to the Master of Science program in mathematics must meet the general Graduate College requirements for admission as degree-seeking students.  In addition, students must have the following.

  1. Students must have credit for MTH 503 Advanced Calculus; MTH 532 Abstract Algebra; MTH 533 Linear Algebra; MTH 540 Statistical Theory I, or equivalent courses.
  2. Students must have a GPA, in upper division mathematics courses beyond the first calculus sequence, of 3.00 or higher on a 4.00 scale.

Students who do not meet conditions 1 and 2 above may be admitted conditionally.  Deficiencies must be made up with B grades or above in courses approved by the mathematics department.  Credit in such courses will not count toward the total hours required for the Master of Science in mathematics.

Degree Requirements  (minimum of 32 hours)
  1. A minimum of 18 semester hours of 700 level mathematics courses (except MTH 796).  At least one of the following four courses must be completed:

    MTH 702 Real and Abstract Analysis
    MTH 732 Abstract Algebra II
    MTH 722 Theory of Ordinary Differential Equat. II
    MTH 742 Statistical Inference II

    Students planning to continue to a Ph.D. degree are strongly advised to take the analysis and algebra sequences.
  2. Mathematics Electives.  From 4 to 15 elective hours in mathematics, dependent upon hours of research and other electives.
  3. Related Electives.  A maximum of 6 hours of elective courses in fields related to mathematics may be taken with the approval of the student's advisor.
  4. Research Requirements. 1-6 semester hours of course work from MTH 791, 792, 798, or 799, but a maximum of 6 semester hours may be applied toward the requirement for the M.S. degree.  This requirement will be met in one of the following ways:
    1. Option I:  Completion of a satisfactory thesis in the candidate's discipline.  Thesis credit shall be no more than 6 semester hours of the minimum 32 hours required for a master's degree.
    2. Option II:  Completion of a minimum of two seminars, each of which shall require an extensive paper or major creative work.
  5. Comprehensive Examination.  A comprehensive examination must be passed by the candidate before a degree will be granted.
Accelerated Master's Option

The Accelerated Master’s Program option in Mathematics provides an opportunity for outstanding undergraduate students to begin their graduate course work during their senior year.  To be eligible to apply for admission to this program, the student must have completed at least three of the courses MTH 503, MTH 532, MTH 533 and MTH 540; have a GPA of 3.5 or higher in all mathematics courses numbered MTH 261 or higher.  An eligible student may apply for admission during the second semester of the junior year. 

If accepted into the accelerated program, up to a maximum of 6 hours of 600/700 level mathematics courses taken after admission into the program may be given credit for both undergraduate and graduate programs.  The courses MTH 603, MTH 631, MTH 633, and MTH 640 will not be given credit in the graduate program.

A student is fully admitted to the Graduate College upon completion of the requirements for the baccalaureate degree.  All requirements for the master’s program should be met for graduation from the master’s program.

Before enrolling in a course to be counted as both undergraduate and graduate credit and to count the course toward the masters degree, an undergraduate student must be accepted into the accelerated program and receive prior approval from the graduate program advisor, department head of the undergraduate program, and the dean of the Graduate college.  Acceptance into the program and all approvals must be completed prior to the end of the Change of Schedule Period for the course(s).  See the Graduate College for further information.

Master of Science in Education, Secondary Education: Mathematics Area of Emphasis

Contact Dr. Lynda Plymate and see program requirements for the M.S.Ed., Secondary Education under Interdisciplinary Graduate Programs.

Prerequisite Mathematics Requirements 

MTH 315 or equivalent; and MTH 302 or equivalent.

Mathematics Requirements 

Mathematics courses selected with a minimum of 3 hours in courses numbered 700 or above to total 15 hours

Accelerated Master's Option

The Accelerated Master’s Program option in Secondary Education, Mathematics provides an opportunity for outstanding undergraduate students to begin their graduate course work during their senior year.  To be eligible to apply for admission to this program, the student must have completed MTH 460, MTH 532 and MTH 533; and have a GPA of 3.5 or higher in all mathematics courses numbered MTH 261 or higher.  An eligible student may apply for admission during the second semester of the junior year. 

If accepted into the accelerated program, up to a maximum of 6 hours of coursework from among MTH 603, MTH 636, MTH 640 and MTH 667 taken after admission into the program may be given credit for both undergraduate and graduate programs.  A student is fully admitted to the Graduate College upon completion of the requirements for the baccalaureate degree.  All requirements for the master’s program should be met for graduation from the master’s program.

Before enrolling in a course to be counted as both undergraduate and graduate credit and to count the course toward the masters degree, an undergraduate student must be accepted into the accelerated program and receive prior approval from the graduate program advisor, department head of the undergraduate program, and the dean of the Graduate college.  Acceptance into the program and all approvals must be completed prior to the end of the Change of Schedule Period for the course(s).  See the Graduate College for further information.

Master of Science in Education, Secondary Education: Natural Science Area of Emphasis

Contact Dr. Tamera Jahnke and see program requirements for the M.S.Ed., Secondary Education under Interdisciplinary Graduate Programs.

Natural Science Prerequisite and Requirements 

In this option, students complete a minimum of 15 hours with course work selected from two of the following disciplines:  Biology, Chemistry, Geography and/or Geology, Mathematics, and Physics.  A minimum of 3 hours of course work numbered 700 or above must be included. The prerequisite requirements are those listed in the departmental statements of both selected academic areas of emphasis.  

Courses from one of the above disciplines                      9 hrs
Courses from a second of the above disciplines             6 hrs
Total                                                                               15 hrs 

Mathematics Courses

MTH 603 Advanced Calculus I

Prerequisite: MTH 280 and MTH 315. Concepts of limit, continuity, differentiation, Riemann integration, sequences and series, other related topics. May be taught concurrently with MTH 503. Cannot receive credit for both MTH 503 and MTH 603.

MTH 604 Advanced Calculus II

Prerequisite: MTH 302; and MTH 503 or MTH 603. This is a continuation of MTH 603, including sequences and series of functions, uniform convergence, multivariate calculus, and other selected topics. May be taught concurrently with MTH 504. Cannot receive credit for both MTH 504 and MTH 604.

MTH 605 Theory of Functions of a Complex Variable

Prerequisite: MTH 280 and MTH 315. Theory of elementary functions-polynomial, trigonometric, exponential, hyperbolic, logarithmic-of a complex variable; their derivatives, integrals; power series; other selected topics. May be taught concurrently with MTH 506. Cannot receive credit for both MTH 506 and MTH 605.

MTH 607 Introduction to Partial Differential Equations

Prerequisite: MTH 302 and MTH 303 and MTH 315. Introduction to linear first and second order partial differential equations, including some formal methods of finding general solutions; the Cauchy problem for such equations, existence theorems, formal methods of finding the solution, and the role of characteristics; the classical boundary and initial value problems for the wave equation, heat equation and the boundary value problems for Laplace's equation. May be taught concurrently with MTH 507. Cannot receive credit for both MTH 507 and MTH 607.

MTH 631 Introduction to Abstract Algebra

Prerequisite: MTH 302 and MTH 315. Theory of groups, rings, integral domains, fields, polynomials. May be taught concurrently with MTH 532. Cannot receive credit for both MTH 532 and MTH 631.

MTH 633 Linear Algebra I

Prerequisite: MTH 280 and MTH 315. Vector spaces, linear independence, inner product spaces, linear transformations, Eigenvectors, diagonalization. May be taught concurrently with MTH 533. Cannot receive credit for both MTH 533 and MTH 633.

MTH 634 Linear Algebra II

Prerequisite: MTH 533 or MTH 633. Topics include eigenvalue problems; Jordan normal form, linear functionals, bilinear forms, quadratic forms, orthogonal and unitary transformations, Markov processes, and other topics selected by the instructor. May be taught concurrently with MTH 534. Cannot receive credit for both MTH 534 and MTH 634.

MTH 636 Theory of Numbers

Prerequisite: MTH 302 and MTH 315. Factorization, Euler totient function, congruences, primitive roots, quadratic residues and reciprocity law. May be taught concurrently with MTH 536. Cannot receive credit for both MTH 536 and MTH 636.

MTH 637 Applied Abstract Algebra

Prerequisite: MTH 532 or MTH 632 or MTH 533 or MTH 633. Topics typically include finite fields, block designs, error-correcting codes (nonlinear, linear, cyclic, BCH, and Reed-Solomon codes), cryptography, and computer implementation of these applications. May be taught concurrently with MTH 537. Cannot receive credit for both MTH 537 and MTH 637.

MTH 640 Statistical Theory I

Prerequisite: MTH 302 and MTH 315. Random variables, discrete and continuous probability functions, expectation, moment-generating functions, transformation of variables. May be taught concurrently with MTH 540. Cannot receive credit for both MTH 540 and MTH 640.

MTH 643 Statistical Theory II

Prerequisite: MTH 540 or MTH 640 or equivalent. Estimation, complete and sufficient statistics, maximum likelihood estimation, hypothesis testing, nonparametric statistics. May be taught concurrently with MTH 541. Cannot receive credit for both MTH 541 and MTH 643.

MTH 645 Applied Statistics

A course on statistical concepts, methods and data analysis with emphasis on assumptions and effects on violating those assumptions. Computer statistical packages will be used. Topics include statistical models, random sampling, normal distribution, estimation, confidence intervals, tests and inferences in single and two populations, and n-way analysis of variance. May be taught concurrently with MTH 545. Cannot receive credit for both MTH 545 and MTH 645.

MTH 646 Analysis of Variance and Design of Experiments

Prerequisite: MTH 345 or MTH 541 or MTH 643 or MTH 545 or MTH 645. Topics include analysis of variance, estimation of variance components, randomized incomplete blocks, Latin squares, factorial nested, split-plot designs, fixed, random and mixed models. May be taught concurrently with MTH 546. Cannot receive credit for both MTH 546 and MTH 646.

MTH 647 Applied Regression Analysis

Prerequisite: MTH 345 or MTH 541 or MTH 643 or MTH 545 or MTH 645. Topics include fitting a straight line, matrix models, residuals, selecting best equation, multiple regression, and nonlinear estimation. May be taught concurrently with MTH 547. Cannot receive credit for both MTH 547 and MTH 647.

MTH 648 Applied Time Series Analysis

Prerequisite: MTH 540 or MTH 640; and MTH 345 or MTH 541 or MTH 643 or MTH 545 or MTH 645. This course will study the analysis of data observed at different points of time. Topics include stationary and non-stationary time series models, linear time series models, autoregressive models, autocorrelations, partial autocorrelations, moving average models, ARMA models, ARIMA models, forecasting, prediction limits, model specification, least square estimation, and seasonal time series models. Computer statistical packages will be used. May be taught concurrently with MTH 548. Cannot receive credit for both MTH 548 and MTH 648.

MTH 653 Stochastic Modeling

Prerequisite: MTH 540 or MTH 640. This course will study applications of probability and statistics from a modeling point of view. Topics include generating functions, branching processes, discrete time Markov chains, classification of states, estimation of transition probabilities, continuous time Markov Chains, Poisson processes, birth and death processes, renewal theory, queuing systems, Brownian motion, and stationary processes. Computer statistical packages will be used. May be taught concurrently with MTH 543. Cannot receive credit for both MTH 543 and MTH 653.

MTH 667 Introduction to Non-Euclidean Geometry

Prerequisite: MTH 302 and MTH 315. Development of non-Euclidean geometries; intensive study of hyperbolic geometry. May be taught concurrently with MTH 567. Cannot receive credit for both MTH 567 and MTH 667.

MTH 670 Combinatorial Analysis

Prerequisite: MTH 280 and MTH 315. An introduction to combinatorial analysis including enumeration methods, combinatorial identities with applications to the calculus of finite differences and difference equations. May be taught concurrently with MTH 570. Cannot receive credit for both MTH 570 and MTH 670.

MTH 675 History of Mathematics

Prerequisite: MTH 302 and MTH 315. Development of mathematics through the calculus; solution of problems of historical interest, problems which use historically significant techniques; problems whose solutions illuminate significant mathematical characteristics of elementary mathematics. May be taught concurrently with MTH 575. Cannot receive credit for both MTH 575 and MTH 675.

MTH 680 Applied Mathematics

Prerequisite: MTH 303; and MTH 533 or MTH 633. An introduction to several areas of applied mathematics including control theory, optimization, modeling of population dynamics, modeling of mathematical economics, minimax and game theory, and calculus of variations. May be taught concurrently with MTH 580. Cannot receive credit for both MTH 580 and MTH 680.

MTH 682 Introductory Topology

Prerequisite: MTH 302 and MTH 315. Properties of abstract metric and topological spaces; discussion of concepts of compactness and connectedness. May be taught concurrently with MTH 582. Cannot receive credit for both MTH 582 and MTH 682.

MTH 696 Readings

Prerequisite: permission of department head. Periodic conferences with an advisor are required. May be repeated to a total of 6 hours. May be taught concurrently with MTH 596. Cannot receive credit for both MTH 596 and MTH 696.

MTH 701 Real Analysis

Prerequisite: MTH 503 or MTH 603. Topics include countable and uncountable sets, convergence, Lebesgue measure on the real line, the development of the Lebesgue integral, the fundamental theorem of calculus and Lp spaces.

MTH 702 Real and Abstract Analysis

Prerequisite: MTH 701. A study of the theory of abstract measures and integration, and an introduction to functional analysis.

MTH 706 Complex Analysis

Prerequisite: MTH 503 or MTH 603. Analytic functions, power series, Cauchy's theorem and its applications, residues. Selected topics from conformal mapping, analytic continuation, harmonic functions, Fourier series, and Dirichlet problems.

MTH 710 Contemporary Mathematics for Secondary Teachers

Prerequisite: MTH 460; and MTH 533 or MTH 633. Reports, research, and recent trends in secondary mathematics; recently developed programs in algebra and geometry.

MTH 721 Theory of Ordinary Differential Equations I

Prerequisite: MTH 303; and MTH 503 or MTH 603. Existence and uniqueness theorems for first order differential equations; system of linear and nonlinear differential equations; continuous dependence of solutions on initial conditions and parameters; behavior of solutions of equations with constant coefficients, study of Lyapunov's theorems on stability; introduction to boundary value problems.

MTH 722 Theory of Ordinary Differential Equations II

Prerequisite: MTH 721. Theory and application of boundary value problems; periodic solutions; linear systems with periodic coefficients (Floquet theory); two dimensional (autonomous) systems limit cycles. Differential equations under Caratheodory conditions; theory of differential and integral inequalities and other selected topics, if time permits.

MTH 730 Abstract Algebra I

Prerequisite: MTH 532 or MTH 631; and MTH 533 or MTH 633. Topics from group theory will include Cayley's Theorem, finite abelian groups, Cauchy's Theorem, the Sylow Theorems, and free groups.

MTH 732 Abstract Algebra II

Prerequisite: MTH 730. Topics from ring theory will include the Chinese Remainder Theorem, Euclidean domains, rings of fractions, PID's and UFD's, and polynomial rings. Topics from field theory will include splitting fields, Galois Theory, separability, normality, and finite fields.

MTH 741 Statistical Inference I

Prerequisite: MTH 540 or MTH 640 or equivalent. Formulation of statistical models, sufficiency and exponential families, methods of estimation, optimality theory. Uniformly minimum variance unbiased estimators, Fisher information, Cramer/Rao inequality, large sample theory, Bayes procedures and minimax procedures.

MTH 742 Statistical Inference II

Prerequisite: MTH 741. Confidence intervals and regions, hypothesis testing, the Neyman-Pearson framework, uniformly most powerful tests, likelihood ratio criteria, power functions, similar regions, invariant tests, distribution free tests.

MTH 781 Topology

Point set topology in abstract spaces.

MTH 791 Seminar I

Seminar in Mathematics.

MTH 792 Seminar II

Seminar in Mathematics.

MTH 796 Science Internship

Completion of an internship project (at least 80 hours per credit hour) at a discipline-related business, nonprofit organization, or government agency, approved and supervised by both the departmental and internship advisors. Includes a formal report in the appropriate professional format, and an oral presentation at an approved venue. Graded Pass/Not Pass only. No more than 6 hours may count toward a masters degree. This course may only be counted toward the PSM designation of the MNAS degree.

MTH 797 Topics

Prerequisite: permission of department head. Material covered determined by the interests and backgrounds of the students. May be repeated for a maximum of 6 hours.

MTH 798 Research

Supervised research in special areas of mathematics. May be repeated. May not be counted toward the Master of Science in Education degree.

MTH 799 Projects

Independent research for thesis preparation.