- General Information
- Campus and Facilities
- University Services
- Special Programs
- Admission
- Academic Guidelines
- Graduate School Policies
- Fees and Financial Assistance
- Fields of Study
- Post-Bacc. Certificates
- Other Departments Offering Courses for Graduate Credit
- Index

Admission | Courses | Program | Requirements

Department Chairperson: Iraj Kalantari

Graduate Committee Chairperson: Khodr
M. Shamseddine

Department Office: Morgan Hall 476

Department Telephone:
309/298-1054 or 309/298-2467

Fax: 309/298-1857

Department E-mail: mathematics@wiu.edu

WWW Address: www.wiu.edu/mathematics/

Location of Program Offering: Macomb

**Graduate Faculty**

**Professors**- Samson A. Adeleke, Ph.D., Johns Hopkins University
- Don B. Campbell, Ph.D., University of Delaware
- Iraj Kalantari, Ph.D., Cornell University
- Marko Kranjc, Ph.D., University of California-Los Angeles
- Nader Vakil, Ph.D., University of Washington
- David A. Voss, Ph.D., Iowa State University
- Galen Weitkamp, Ph.D., Pennsylvania State University
- Lawrence V. Welch, Ph.D., University of Illinois

**Associate Professors**- Robert Mann, Ph.D., University of Nebraska-Lincoln
- James R. Olsen, Ph.D., University of Northern Colorado
- Mei Yang, Ph.D., University of Canterbury

**Assistant Professor**- Khodr M. Shamseddine, Ph.D., Michigan State University

** ****Associate Graduate Faculty**

**Associate Professors**- Fedor Andreev, Ph.D., St. Petersburg Steklov Mathematical Institute
- John Chisholm, Ph.D., University of Wisconsin
- Kimberly Hartweg, Ph.D., University of Iowa

**Assistant Professors**- Victoria Baramidze, Ph.D., University of Georgia–Athen
- J. Thomas Blackford, Ph.D., Ohio State University
- Rumen Dimitrov, Ph.D., George Washington University
- Boris Petracovici, Ph.D., University of Illinois
- Lia Petracovici, Ph.D., University of Illinois
- Ioana Sirbu, Ph.D., SUNY State University
- Feridun Tasdan, Ph.D., Western Michigan University
- Anna Valeva, Ph.D., University of California-Santa Barbara
- Zhihui Yang, Ph.D., University of Maryland

The graduate program in the Department of Mathematics prepares students for needed professions in the region and nationwide. The program provides students with a solid graduate level training in the central and fundamental methods of continuous and discrete mathematics. Both the theoretical framework and the applications of these methods will be covered in the core courses. The 500-level core courses have a significant lean toward applications but theory is present; while the 600-level core courses have a significant lean toward theory and mathematical foundation but applications are not abandoned.

Students entering the program should normally have completed an undergraduate degree program including course work equivalent to a major in mathematics. Other students may be admitted at the discretion of the Departmental Graduate Committee with admission usually conditional upon the student completing specified deficiencies. Applicants are strongly encouraged to take the general part of the Graduate Record Examination and it is a requirement for an assistantship.

Degree requirements of this 36-semester hour program consist of 21 semester hours of core courses, 3 semester hours of mathematics directed electives, and 12 semester hours of focus area courses that will allow for focus in a single area of applied or pure mathematics, as well as other areas of study outside the Department of Mathematics, as sanctioned by the Department Graduate Committee. For example, the focus area courses may be in statistics, numerical analysis, teaching of mathematics, Ph.D. pursuit, biology, business, chemistry, computer science, economics, financial mathematics, or physics. Focus area courses (12 semester hours) will share a common thread with the first 6 semester hours taken in MATH 599 and/or MATH 596; or through directed electives from another department. The second 6 semester hours of the focus area courses may also be earned through directed electives; or in special topics (MATH 699) and/or thesis (MATH 600), and/or project (MATH 601), and/or internship (MATH 602). All directed electives used to satisfy focus area requirements must be taken within the same academic department.

The program consists of two steps. The first step requires 18 semester hours that lead to a post-baccalaureate certificate in Applied Mathematics. Please go to www.wiu.edu/grad/catalog/certificate.php for more specific information. The second step includes an additional 18 semester hours of coursework leading to the Master of Science degree in Mathematics.

**First-Year Core Courses: 12 s.h.**- MATH 551 Methods of Classical Analysis (3)
- MATH 552 Scientific Computing with MATLAB (3)
- STAT 553 Applied Statistical Methods (3)
- MATH 554 Methods of Symmetry in Algebra, Geometry, and Topology (3)

**Second-Year Core Courses: 9 s.h.**- MATH 651 Elements of Modern Analysis (3)
- MATH 652 Computational Differential Equations (3)
- STAT 653 Elements of Statistical Inference (3)

**Focus Courses: 12 s.h.**

The focus courses must be approved by the Department Graduate Committee. Students must select 6 s.h. from A. and 6 s.h. from B.

A. MATH 599 Special Topics (1–6), and/or MATH 596 Project in Applied Mathematics (3–6) or Directed Electives from any department but in a single focus area (6 )

B. MATH 699 Advanced Special Topics (3–6), and/or MATH 600 Thesis (3), and/or MATH 601 Advanced Project in Applied Mathematics (3–6), and/or MATH 602 Internship in Applied Mathematics (3–6) or Directed Electives from any department but in the same single focus area as selected above in A.

**Directed Electives: 3 s.h.**- Must be in mathematics or statistics.

**TOTAL PROGRAM: 36
s.h. **

**Post-Baccalaureate Certificate Program **

The department offers a post-baccalaureate certificate in Applied Mathematics. For program details, please go to www.wiu.edu/grad/catalog/certificate.php .

**402G Investigations in School Geometry. (3)** A conceptual
development of geometry through the investigation of geometric relationships
and informal understandings leading to formal deductions. Middle and junior
high school emphasis. *Prerequisite: Permission of the instructor.*

**406G Mathematical Reasoning in School Mathematics. (3)** Problem
solving using a variety of reasoning patterns, proof in mathematics, the
concept of mathematical groups, and related topics. Open only to students
majoring in an elementary education program. *Prerequisite: MATH 128
or equivalent.*

**407G Number Theory Concepts in School Mathematics. (3)** Divisibility,
prime numbers, perfect numbers, modular arithmetic, linear Diophantine
equations, and related topics. Open only to students majoring in an elementary
education program. *Prerequisite: MATH 128 or equivalent.*

**408G Computers in Elementary/Middle School Mathematics. (3)** The
study of special topics in mathematics utilizing microcomputers through
an introduction to Logo and the effective use of selected software. *Prerequisites:
MATH 206 and some computer experience, or permission of the instructor*.

**421G Abstract Algebra. (3)** An introduction to the basic
properties of groups, rings, and fields. *Prerequisite: MATH 341.*

**424G Advanced Linear Algebra. (3)** Matrix algebra, vector
spaces, linear independence, basis, linear transformations, canonical
forms, inner product spaces. *Prerequisite: MATH 421 or permission
of the instructor.*

**430G Multivariable Calculus. (3)** The algebra of functions,
continuity, differentiation and integration of n-place functions,
and related topics. *Prerequisites: MATH 231 and 311.*

**435G Introduction to Real Variables I. (3)** Topology
of the real line, limits, derivatives, integrals, improper integrals,
sequences, series, and introduction to calculus of functions of several
variables. *Prerequisites: MATH 231 and MATH 341.*

**436G Introduction to Real Variables II. (3) **A continuation
of Math 435. *Prerequisite: MATH 435. *

* ***441G Mathematical Logic. (3) **Introduction
to some of the principal topics of mathematical logic. Topics include
Propositional Calculus, Quantification Theory, the Completeness Theorem,
Formal Theories, Models of Theories and Recursion Theory. *Prerequisite:
MATH 341. *

* ***456G Theory of Numbers. (3) **Divisibility,
congruences, periodic decimals, Fermat =s Theorem, Wilson's Theorem,
Diophantine equations, primitive roots, and other topics. *Prerequisite:
MATH 341.*

**461G Introductory Topology. (3)** Basic properties of
topological spaces. Open and closed sets, compactness, the intermediate
value theorem, metric spaces, completeness, and uniform continuity. *Prerequisite:
MATH 341 or permission of the instructor.*

**481G Numerical Analysis ****I.**** (3)** A
survey of current methods in numerical analysis. Error analysis, solution
of nonlinear equations and systems of linear equations, polynomial interpolation
and approximations, and related topics. *Prerequisites: CS 211 and
212 (or 245), Math 231 and 311, or permission of the instructor. *

* ***482G Numerical Analysis II. (3) ** A continuation
of MATH 481G. Numerical differentiation and integration, numerical solution
of ordinary and partial differential equations, function approximation
in various norms. *Prerequisite: Math 481 or permission of the instructor.*

**485G Linear Programming. (3) **The theory and computational
techniques of the regular and revised simplex algorithms, duality, degeneracy
problem, and application of these techniques. *Prerequisites: CS 211
and CS 212, MATH 311, or permission of the instructor. *

**488G Models in Applied Mathematics. (3)** Theory and computer
exploration of mathematical models using difference equations, differential
equations, and dynamical systems. Applications from the sciences. *Prerequisites:
MATH 231, MATH 311, and one of CS 211 and CS 212, CS 240 or CS 245, or
permission of the instructor.*

**500 Teaching of Elementary Mathematics. (3)** A study
of current trends and problems in the teaching of elementary and junior
high school mathematics. *Prerequisite: Permission of the instructor.*

**501 Elementary Mathematics I. (3)** A study of sets, logic,
real number system, open sentences, relations, and functions as they apply
to the elementary and junior high school curriculum. *Prerequisite:
Permission of the instructor.*

**502 Geometry for Teachers. (3)** A study of geometric
concepts as they pertain to the elementary and junior high school curriculum.
Topics will be chosen from coordinate, synthetic, and transformational
geometry. *Prerequisite: Permission of the instructor.*

**503 Methods of ****Teaching****Secondary
School**** Mathematics. (3)** A study of current
trends and problems in the teaching of secondary school mathematics. *Prerequisite:
Permission of the instructor.*

**504 Research in Secondary Mathematics Education. (3)** A
survey, evaluation, and application of recent research relative to the
teaching of secondary school math. *Prerequisite: Permission of the
instructor.*

**505 The Teaching of Mathematics in Middle Grades and Junior High.
(3)** A study of teaching strategies and current trends in mathematics
as they apply to the curriculum of the middle school and the junior
high school. *Prerequisites: MATH 106 and 206 (C grade or better)
or equivalent.*

**507 Research in Elementary Mathematics Education. (3)** A
survey, evaluation, and application of recent research relative to the
teaching of elementary and junior high school math. *Prerequisite:
Permission of the instructor.*

**508 Special Topics in Elementary Mathematics. (3, repeatable
to 15)** Topics will be available on demand in the areas of probability,
statistics, computer science, number theory, and history of math. *Prerequisite:
Permission of the instructor.*

**509 Diagnostic and Prescriptive Teaching of School Mathematics.
(3)** The assessment of strengths and weaknesses of students
in school mathematics with the development of appropriate prescriptive
remediation materials and strategies. *Prerequisites: Teacher certification,
MATH 360 or MATH 361.*

**521 Algebra. (3)** An introduction to higher algebra.
Topics to be included are groups, homomorphisms, Sylow theorems, rings
and ideals, fields, field extensions, and Galois theory. *Prerequisite:
MATH 424 or permission of the instructor.*

**531 Real Variables. (3)** An introduction to measure and
integration. *Prerequisite: MATH 435 or permission of the instructor.*

**533 Complex Variables. (3)** Topics to be studied include
the topology of the complex plane, analytic functions, complex integration,
and singularities. *Prerequisite: MATH 436 or permission of the instructor.*

**536 Ordinary Differential Equations. (3)** The initial
value problem, existence and uniqueness theorems, linear systems, asymptotic
behavior of solutions, two-dimensional systems. *Prerequisites:
MATH 333 and 435, or permission of the instructor.*

**537 Numerical Solutions of Ordinary Differential Equations. (3)** One-step
methods for initial value problems, one-step methods for systems,
multistep methods, boundary value problems. Examples using University
computers. *Prerequisites: MATH 536 and some programming experience,
or permission of the instructor.*

**541 Set Theory. (3)** A formal development of the theory
of sets, to include operations on sets, mapping, order types, cardinal
and ordinal number theory, and transfinite induction. *Prerequisite:
Permission of the instructor.*

**550 Workshop in School Mathematics. (1-****6, repeatable)** (Degree
candidates may receive credit toward program requirements only with the
permission of the student's Graduate Committee.) Workshops focusing on
specific topics may be organized as required to meet the identified needs
and interests of in-service teachers or specific school districts. *Prerequisite:
Graduate standing. *

* ***551 Methods of Classical Analysis. (3) ** Introduction
to complex and multivariable analysis with a significant lean toward applications.
Topics include sequences and series, conformal mappings, complex integration,
geometry and topology of R^n, Newton ’s method and Taylor polynomials,
extreme values of functions on R^n, manifolds and their tangent spaces. *Prerequisites:
MATH 231 and MATH 311, or equivalents. *

* ***552 Scientific Computing with MATLAB. (3) ** Design,
analysis, and MATLAB implementation of algorithms for solving problems
of continuous mathematics involving linear and nonlinear systems of equations,
interpolation and approximation, numerical differentiation and integration,
and ordinary differential equations with a significant lean toward applications. *Prerequisites:
MATH 311 and MATH 333, or equivalents. *

** ****554 Methods of symmetry in Algebra, Geometry,
and Topology. (3) **A
study of symmetry in algebra, geometry, and topology with a significant
lean toward applications. Topics of study include group of Euclidean transformations,
symmetries of planar sets, topological classification of compact surfaces,
crystallographic patterns and classification of their symmetry groups. *Prerequisite:
MATH 424 or permission of the instructor. *

**560 Advanced Topology. (3)** Product and quotient spaces,
path-connectedness, local compactness, homotopy, fundamental group. Additional
topics may include Baire category, function spaces, Brouwer Fixed Point
Theorem. *Prerequisites: MATH 421 and MATH 461, or permission of the
instructor.*

**581 Approximation Theory. (3)** The theory behind numerical
algorithms. Remainder theory, convergence theorems, best approximation
in various norms, the theory of matrices in numerical analysis including
the eigenvalue problem. *Prerequisites: MATH 435 and 481, or permission
of the instructor.*

**583 Nonlinear Unconstrained Optimization. (3)** Unconstrained
optimization of nonlinear functions of one or more variables. Necessary
and sufficient conditions, gradient methods. *Prerequisites: MATH 481
and 424, or permission of the instructor.*

**589 Mathematical Modeling. (1-****3)** A
development of the group approach in applications of techniques used in
applied mathematics, numerical analysis, operations research, and statistics
to real problems from other disciplines. May be repeated up to six hours. *Prerequisite:
Permission of the instructor.*

**590 Independent Study. (1-****3, repeatable to
6)*** Prerequisite: Approval of the Department Chair. *

* ***596 Project in Applied Mathematics. (3, repeatable
to 6) ** A
project in applied mathematics or statistics, or with a professional institution,
which will be presented in a final paper or portfolio, demonstrating entry
into an applied mathematics field. Graded S/U. *Prerequisite: Permission
of the Graduate Committee.*

**598 Seminar in Teaching Methods. (1) ***Prerequisite:
Graduate standing.*

**599 Special Topics. (1-****3, repeatable to 9)** Special
topics in mathematics or statistics with a lean towards application. May
be repeated with a change in topic. *Prerequisite: Permission of the
instructor.*

**600 Thesis. (3) ** The thesis may be either expository,
historical, critical, or original and must be approved by the student’s
advisory committee. The student must present his/her thesis to the mathematics
department faculty in a colloquium.* Prerequisite: Permission of the
graduate adviser. *

* ***601 Advanced Project in Applied Mathematics. (3, repeatable
to 6) ** Project in an advanced topic of mathematics or statistics,
which will be presented in a final paper or portfolio, demonstrating
advanced proficiency in an applied mathematics field. Graded S/U. *Prerequisite:
Permission of the Graduate Committee.*

**602 Internship in Applied Mathematics. (3, repeatable to 6) **Mathematical
work or training conducted at a professional institution, university or
government organization, which will be presented in a final paper or portfolio,
demonstrating advanced proficiency in an applied mathematics field. Graded
S/U. *Prerequisite: Permission of the Graduate Committee. *

**607 Practicum in Mathematics Education. (3)** Direct internship
experience for action research in mathematics education (K-8) under
guidance of qualified faculty. *Prerequisites: MATH 500 or 505 and
approval of degree plan, completion of over half of candidate's course
work, including EIS 500. Modifications in the above requirements are subject
to the approval of the candidate's adviser. *

* ***651 Elements of Modern Analysis. (3) ** A
study of elements of modern analysis with a lean toward developing the
theory. Topics include topology in normed linear spaces; inner product
spaces, Hilbert space, Fourier series; equicontinuity and Arzela-Ascoli
theorem, Banach contraction principle, Picard’s theorems, Peano’s
theorem; Gateaux differential and the Euler-Lagrange equation; compact
operators and existence of solutions of Fredholm integral equations. *Prerequisites:
MATH 435 and MATH 551, or equivalents. *

* ***652 Computational Differential Equations. (3) ** A
study of elements of computational mathematics of differential equations
with a lean toward developing the theory. Topics include adaptive one-step
and multi-step methods of ordinary differential equations, the method
of lines for evolutionary problems, and direct and iterative methods for
sparse linear systems. *Prerequisites: MATH 435 or MATH 551, and MATH
552 or MATH 481. *

* ***654 Applications of Logic and Computability Theory.
(3) ** A
study of elements of modern logic and computability with a lean toward
developing the theory. Topics include the mathematics of computability
and incomputability, introduction to computational complexity, and additional
applications of logic.

**655 Technology and the Secondary School Mathematics Curriculum.
(3) ** Strategies for using technology such as calculators, computers,
and Internet resources for teaching algebra, geometry, probability,
and statistics in the secondary mathematics curriculum, including research
on the use of the technology for mathematics teaching and learning. *Prerequisites:
Graduate standing and permission of the instructor. *

* ***656 Advanced Perspective of Secondary School
Mathematics. (3) ** An
advanced study of the mathematics of secondary school curriculum for the
purpose of developing deeper connection and representations for all students.
Focus is on rigorous conceptual context knowledge, methods of inquiry,
and investigative problem-solving. Topics include Algebra, Geometry, and
Statistics. *Prerequisites: Graduate standing and permission of the
Department Chair. *

* ***699 Advanced Special Topics. (3, repeatable to 6) ** Advanced
special topics in mathematics or statistics with a lean towards theory.
May be repeated with change of topic. *Prerequisite: Permission of
the instructor. *

**Statistics **

**471G Introduction to ****Mathematical****Statistics****I.**** (3)** The
mathematical foundations of probability and statistics, principles of
probability, sampling, distribution, moments, and hypothesis testing. *Prerequisite:
MATH 231 or equivalent.*

**472G Introduction to Mathematical Statistics II. (3)** Continuation
of Statistics 471, including further topics in estimation and hypothesis
testing. *Prerequisite: STAT 471.*

**474G Regression and Correlation Analysis. (3)** Least
squares theory, correlation theory, simple, multiple, and stepwise regression,
computer-assisted model building, and applied problems. *Prerequisite:
STAT 276 or equivalent.*

**478G Analysis of Variance. (3)** A study of analysis of
variance and covariance. Includes experimental design with applications. *Prerequisite:
STAT 276 or equivalent.*

**490G Topics in Statistics. (1-****6)** General
topics in statistics. *Prerequisite: Permission of the instructor. *

* ***553 Applied Statistical Methods. (3) ** Introduction
to probability and statistics with a significant lean toward applications.
Topics include probability, probability distributions, Central Limit Theorem,
sampling distributions (t, F, Chi-Square), parameter estimation, hypothesis
testing, nonparametric statistics, ANOVA, and linear regression. *Prerequisites:
MATH 231 and STAT 276, or equivalents.*

**570 Probability Theory and Stochastic Processes. (3)** Nature
of probability theory, sample space, combinatorial analysis, fluctuations
in random events, stochastic independence, random variables, generating
functions, Markov chains, and simple time-dependent stochastic processes. *Prerequisite:
STAT 471 or equivalent.*

**572 Mathematical Statistics ****I.**** (3)** The
study of statistical inference including topics in probability, estimation,
hypothesis testing and sampling. *Prerequisite: STAT 471 or equivalent.*

**573 Mathematical Statistics II. (3)** A continuation of
Statistics 572. *Prerequisite: STAT 572.*

**574 Linear Models and Experimental Designs. (3)** General
linear models, Gauss-Markov Theorem, experimental design model confounding,
and types of experimental designs and their analysis. *Prerequisite:
STAT 472 or permission of the instructor. *

* ***653 Elements of Statistical Inference. (3) ** A
study of elements of statistical inference with a lean toward developing
the theory. Topics include probability theory, random variables, probability
distribution functions, limit theorems, estimation, testing, sufficiency,
robust statistical methods, bootstrap, and linear models. *Prerequisites:
STAT 471 and STAT 553. *