Faculty
Professor and Chair, A. Genz; Professors, K. Ariyawansa, D. DeTemple, R. Gomulkiewicz, M. Jacroux, V. Jandhyala, M. Kallaher, A. Khapalov, D. Kent, V. Manoranjan, R. Mifflin, E. Pate, D. Watkins, W. Webb, D. Wollkind; Associate Professors, S. Cooper, R. Dillon, M. Hudelson, H. Li, J. McDonald, F. Pascual, M. Schumaker, D. Slavit, M. Tsatsomeros, H. Yin; Assistant Professors, B. Krishnamoorthy, A. Panchenko; Professors Emeriti, D. Barnes, D. Bushaw, J. Cochran, R. Johnson, J. Jordan, J. Kucera, C. Long, C. Millham, J. Nazareth, T. Newton, D. Ng, T. Ostrom, J. Robertson, S. Saunders, H. C. Wiser; Adjunct Professor, K. Cooper.
Program
Degrees Granted: Master of Science in Mathematics,; Doctor of PhilosophyGraduate programs leading to the degrees Master of Science in Mathematics (which also has an Applied Mathematics Option and a Mathematics Teaching Option) and Doctor of Philosophy are offered by the Department of Mathematics. Information on all degree programs in Mathematics can be found in the Department’s web site: www.math.wsu.edu.
Requirements for the MS in Mathematics include at least 31 credit hours of graduate work. Degree candidates take 6 hours of material from real analysis and introduction to functional analysis, and pass an oral examination on their course work plus the content of Mathematics 401-02 (analysis) and 420-21 (linear and abstract algebra). Each candidate for this degree must participate in a one-credit proseminar devoted to the problems of instruction in mathematics, carry out a four-credit special project, and be responsible for teaching at least one undergraduate class for a semester.
Requirements for the Applied Mathematics Option of the Master of Science in Mathematics include 35 credit hours of approved course work. This course work should include 2 graduate courses chosen from one of the three following areas: Numerical Analysis/Optimization; Modeling/Simulation; and Statistical Analysis. Each candidate for this degree must complete a two-credit group project supervised by at least two faculty members in different areas of applied mathematics or other application areas, and a two-credit individual project supervised by the candidate’s degree committee members.
Requirements for the Mathematics Teaching Option of the Master of Science in Mathematics include at least 35 credit hours of approved coursework. Degree candidates must satisfy this requirement by taking courses chosen from two specified lists of mathematics content courses and mathematics education courses. Each candidate for this degree must participate in a one-credit proseminar devoted to the problems of instruction in mathematics and carry out a four-credit special project. In addition, each candidate must pass a final oral examination that covers the candidate’s coursework plus the content of math 401-402 (analysis) and 420-421 (linear and abstract algebra), and includes an oral presentation on the candidate’s special project.
Requirements for the degree Doctor of Philosophy include 72 credit hours of approved course work; passing written examinations over material from real analysis in a single variable, functions of several variables, and linear algebra; demonstrating at least a minimal ability to read mathematical literature in two of the following foreign languages: French, German, and Russian; passing a preliminary examination over the student’s specialty; completing a doctoral thesis which in originality and importance is at least good enough to appear in a research journal; and passing a final oral examination.
Requirements for the proseminar and teaching experience are the same as those described above for the Master of Science degree.
The Department has masters and doctoral programs for
those who are interested in nonteaching careers in
mathematics. These programs have been designed with
extensive encouragement and advice from many experts on
applied mathematics education and from representatives
of many industrial and governmental organizations.
Special features of these programs include: courses and
seminars devoted to mathematical modeling, data
analysis, optimization, discrete mathematics and other
applications-related subjects;
a curriculum with recommended concentrations in
operations re-search, computational mathematics,
applied statistics, discrete mathematics and
mathematical modeling; a sequence of practical
experiences, including internships;
a PhD dissertation in which the emphasis is on using
powerful mathematical methods to solve problems outside
mathematics rather than on presenting new mathematical
discoveries as such.
At the same time, the Department continues to offer the traditional PhD with specialization in such areas as topology, number theory, finite geometry, algebra and analysis. The Department has a teaching emphasis option to its PhD program.
The degree Doctor of Philosophy with teaching emphasis certifies completion of a graduate program designed to provide exceptionally strong preparation for teaching mathematics to undergraduates. It differs from the traditional PhD in its objectives but not in the expected degree of competence in the “core” areas of mathematics and in foreign languages. This program also requires or strongly recommends study in: the history and philosophy of mathematics; disciplines where applications of mathematics frequently occur; computing; and the craft of teaching generally, and in mathematics particularly. In connection with this last, each candidate serves a term as a full-time teaching intern at an undergraduate college. To offset these additional requirements, the traditional PhD research thesis requirement is replaced by requiring a thesis that does not necessarily make an original contribution to mathematics itself but is a piece of mathematical scholarship that may serve a prospective college teacher even better.
In general the requirements have been so chosen that transfer from the Doctor of Philosophy with teaching emphasis to the Doctor of Philosophy or vice versa, when approved, should be feasible with as little difficulty as possible.
Interested persons are urged to request detailed information about these programs and the supporting staff and facilities from the Chair of the Graduate Studies Committee.
Students anticipating graduate study in mathematics should ideally have an extensive knowledge of undergraduate mathematics including, beyond the calculus, at least two years of analysis and one year of algebra. They should have studied also computer programming. Moreover, some acquaintance with applied mathematics (e.g., or some other area which makes extensive use of mathematics) is highly desirable, as is at least a moderate reading knowledge of French, German, or Russian.
Mathematics
500 Proseminar 1 May be repeated for credit; cumulative maximum 2 hours. S, F grading.
501 Real Analysis 3 Prereq Math 402. Metric spaces, convergence, continuous functions, infinite series, differentiation and integration of functions of one and several variables.
502 Introduction to Functional Analysis 3 Prereq Math 420, 501. Normed linear spaces Banach spaces, introduction to Hilbert space, linear operations.
503 Complex Analysis 3 Prereq Math 501. Analytic functions, complex integration, Taylor and Laurent series, conformal mapping, Riemann surfaces and analytic continuation. Cooperative course taught jointly by WSU and UI (Math 531).
504 Measure and Integration 3 Prereq Math 501. Lebesque measure, Lebesque integration, differentiation, L spaces general measure and integration, Radon-Nikodym Theorem, outer measure and product measures. Cooperative course taught jointly by WSU and UI (Math 571).
505 Abstract Algebra 3 Prereq Math 421. Groups, rings, fields and homological algebra.
506 Abstract Analysis 3 Prereq Math 502. Generalized measure and integration, topological vector spaces, duality, advanced topics in functional analysis. Cooperative course taught jointly by WSU and UI (Math 572).
507 Advanced Theory of Numbers 3 May be repeated for credit, cumulative maximum 6 hours. Analytic and algebraic number theory. Cooperative course taught by WSU, open to UI students (Math 507).
508 Topics in Applied Analysis 3 Prereq Math 502. Advanced treatment of applications using techniques from fundamental analysis, convexity, analytic function theory, asymptotics, differential equations. Cooperative course taught by WSU, open to UI students (Math 508).
509 Foundations of Mathematics 3 The basis of mathematics in logic and set theory; continuum hypothesis; Godel’s theorems, recent developments. Cooperative course taught by WSU, open to UI students (Math 509).
510 Topics in Probability and Statistics 3 Prereq stat course. Same as Stat 510. Credit not granted for both Math 410 and 510.
511 (554) Advanced Linear Algebra 3 Prereq Math 420. Vector spaces, unitary equivalence, similarity, Jordan forms, inner products, spectral theory, singular value decomposition, norms and inequalities. Cooperative course taught jointly by WSU and UI (Math 550).
512 Ordinary Differential Equations 3 Prereq Math 402. Existence of solutions; linear systems; qualitative behavior, especially stability; periodic solutions. Cooperative course taught jointly by WSU and UI (Math 539).
515 Statistical Packages 3 (2-3) Same as Stat 515.
516 Simulation Methods 3 Model formulation and simulation in business, industry, and government; simulation languages; analysis of simulation output; applications. Graduate level counterpart of Math 416; additional requirements. Credit not granted for both Math 416 and 516.
518 Mathematical and Scientific Visualization 3 Prereq graduate standing. Three-dimensional computer imaging of scientific, engineering, and mathematical phenomena using modern techniques for curve and surface display in computer-aided design. Graduate level counterpart of Math 418; additional requirements. Credit not granted for both Math 418 and 518.
523 Statistical Methods for Engineers and Scientists 3 Same as Stat 523. Credit not granted for both Math 423 and 523.
525 General Topology 3 Prereq Math 402. Sets, metric spaces, topological spaces; continuous mappings, compactness, connectedness, local properties, function spaces, and fundamental groups. Cooperative course taught jointly by WSU and UI (Math 511).
526 Advanced Topology 3 Prereq Math 421, 525. General topology; basic ideas of algebraic topology. Cooperative course taught jointly by WSU and UI (Math 512).
527 Algebraic Topology I 3 Prereq Math 526. Basic homotopy theory and application. Cooperative course taught by UI (Math 523) open to WSU students.
528 Algebraic Topology II 3 Prereq Math 527. Continuation of Math 527. Cooperative course taught by UI (Math 524), open to WSU students.
531 Intersections of Culture and Mathematics 3 (2-2) May be repeated for credit. Graduate-level counterpart of Math 431; additional requirements. Credit not granted for both Math 431 and 531.
532 Mathematics for College and Secondary Teachers 2 Prereq graduate standing. Pre-algebra and algebra from a mature point of view; properties of systems; open sentences; equations; functions and graphs. Graduate level counterpart of Math 432; additional requirements. Credit not granted for both Math 432 and 532.
534 Approaches to Mathematics Teaching 3 Prereq Math 531, 532. Instruction and curricula of mathematics content for community college and high school, covering basic arithmetic through calculus.
536 Statistical Computing 3 (2-3) Same as Stat 536.
540 Applied Mathematics I 3 Prereq graduate standing. Partial differential equations; Fourier series and integrals; Bessel functions; calculus of variations; vector calculus; application. Graduate level counterpart of Math 440; additional requirements. Credit not granted for both Math 440 and 540.
541 Applied Mathematics II 3 Prereq graduate standing complex variable theory including analytical functions, infinite series, residues, and conformal mapping; Laplace transforms; applications. Graduate level counterpart of Math 441; additional requirements. Credit not granted for both 441 and 541.
543 Approximation Theory 3 Prereq Math 448. Univariate polynomial and rational approximation techniques; approximation using splines and wavelets; selected topics in multivariate approximation; algorithms for approximation. Cooperative course taught by WSU, open to UI students (Math 543).
544 Advanced Matrix Computations 3 Prereq Math 548. Advanced topics in the solution of linear systems and eigenvalue problems, including parallel matrix computations. Cooperative course taught by WSU, open to UI students (Math 548).
545 Numerical Analysis of Evolution Equations 3 Prereq Math 448. Discretization and numerical solution of partial differential equations of evolution; stability, consistency, and convergence; shocks; conservation of forms. Cooperative course taught by WSU, open to UI students (Math 545).
546 Numerical Analysis of Elliptic PDEs 3 Prereq Math 448. Methods of discretizing elliptic partial differential equations and solving the resulting systems of equations; error analysis. Cooperative course taught by WSU, open to UI students (Math 547).
548 Numerical Analysis 3 Prereq graduate standing. Fundamentals of numerical computation; finding zeroes of functions, approximation and interpolation; numerical integration (quadrature); numerical solution of ordinary differential equations. Graduate level counterpart of Math 448; additional requirements. Credit not granted for both Math 448 and 548.
550 Advanced Topics in Geometry 3 Projective, affine, and non-Euclidean geometries and their relation to abstract algebra and differential geometry. (a/y) Cooperative course taught by WSU, open to UI students (Math 554).
551 Ring Theory 3 Ideals quotient rings, modules, radicals, semi-simple Artinian rings, Noetherian rings. (a/y) Cooperative course taught by UI (Math 551), open to WSU students
552 Galois Theory 3 Field extension, automorphisms, normality, splitting fields, radical extension, finite fields, separability. Cooperative course taught by UI (Math 552), open to WSU students.
553 Graph Theory 3 Prereq graduate standing. Graphs and their applications, directed graphs, trees, networks, Eulerian and Hamiltonian paths, matrix representations, construction of algorithms. Graduate level counterpart of Math 453, additional requirements. Credit not granted for both Math 453 and 553.
555 Topics in Combinatorics 3 May be repeated for credit; cumulative maximum 6 hours. Combinatorics, generating functions, recurrence relations, inclusion-exclusion, coding theory; experimental design, graph theory.
556 Introduction to Statistical Theory 3 Same as Stat 556. Credit not granted for both Math 456 and 556.
560 Partial Differential Equations I 3 Prereq Math 402. Partial differential equations and other functional equations: general theory, methods of solution, applications. Cooperative course taught by WSU, open to UI students (Math 540).
561 Partial Differential Equations II 3 Prereq Math 560. Continuation of Math 560. Cooperative course taught by WSU, open to UI students (Math 542).
563 Mathematical Genetics 3 Prereq MbioS 301; Stat 412, 430, or 443; Math 273. Mathematical approaches to population genetics and genome analysis; theories and statistical analyses of genetic parameters.
564 Topics in Optimization 3 May be repeated for credit. Prereq advanced multivariable calculus and a programming language, Rec Math 464, 544. Advanced topics in the theory and computing methodology in optimization with emphasis on real-life algorithmic implementations. Cooperative course taught by WSU, open to UI students (Math 564).
565 Nonlinear Optimization II 3 Prereq Math 273, 564; programming language. Theory and algorithms for constrained linear and nonlinear optimization including interior point, quadratic programming, penalty, barrier and augmented Lagragian methods.
566 Optimization in Networks 3 Prereq graduate standing. Formulation and solution of network optimization problems including shortest path, maximal flow, minimum cost flow, assignment, covering, postman and salesman. Credit not granted for both 466 and 566.
568 Statistical Theory I 3 Same as Stat 548.
569 Statistical Theory II 3 Same as Stat 549.
570 Mathematical Foundations of Continuum Mechanics I 3 Prereq advanced calculus and differential equations. The basic mathematical theory of continuum mechanics and its relation to perturbation techniques and stability methods. Cooperative course taught by WSU, open to UI students (Math 570).
571 Mathematical Foundations of Continuum Mechanics II 3 Prereq Math 570. Continuation of Math 570. Cooperative course taught by WSU, open to UI students (Math 573).
572 Quality Control 3 Prereq Stat/Math 360 or 443. Same as Stat 572.
573 Reliability Theory 3 Same as Stat 573.
574 (564) Topics in Optimization 3 Prereq advanced multivariable calculus and a programming language; Rec Math 464, 544. Advanced topics in the theory and computing methodology in optimization with emphasis on real-life algorithmic implementations. May be repeated for credit. Cooperative course taught by WSU, open to UI students (Math 564).
581 Seminar in Analysis V 1-3 May be repeated for credit. Cooperative course taught jointly by WSU and UI (Math 541).
582 Seminar in Algebra V 1-3 May be repeated for credit. Cooperative course taught jointly by WSU and UI (Math 561).
583 Seminar in Applied Mathematics V 1-3 May be repeated for credit. Cooperative course taught by WSU, open to UI students (Math 583).
584 Seminar in Topology and Geometry V 1-3 May be repeated for credit. Cooperative course taught by WSU, open to UI students (Math 584).
585 Seminar in Number Theory V 1-3 May be repeated for credit. Cooperative course taught by WSU, open to UI students (Math 587).
586 Mathematical Modeling in the Natural Sciences 3 Graduate level counterpart of Math 486; additional requirements. Credit not granted for both 486 and 586.
591 Seminar in the History of Mathematics I 1 Topics in the history of mathematics to 1800.
592 Seminar in the History of Mathematics II 1 Topics in the history of mathematics from 1800 to present.
597 Mathematics Instruction Seminar 1 May be repeated for credit; cumulative maximum 5 hours. prereq graduate standing
600 Special Projects or Independent Study Variable credit. S, F grading.
602 Internship V 2-12 May be repeated for credit. Prereq 40 hrs graduate work. A structured internship from 3-9 months; teaching at the postsecondary level or applied work in a non-academic environment. S, F grading.
700 Master's Research, Thesis and/or Examination Variable credit. S, F grading.
702 Master's Special Problems, Directed Study, and/or Examination Variable credit. S, F grading.
800 Doctoral Research, Dissertation, and/or Examination Variable credit. S, F grading.