- 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

2007/2008 Graduate Catalog

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

Website: 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
- 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-Athens
- J. Thomas Blackford, Ph.D., Ohio State University
- Rumen Dimitrov, Ph.D., George Washington University
- Elizabeth Hansen, Ph.D., University of Iowa
- 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
- 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 CS 225
or equivalent, 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.*

**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 or CS 225 or equivalent,
or CS 240, 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 366 or MATH 367.*

**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 6)** 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. *Prerequisite: Permission of the instructor.*

**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.*

**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.*