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### Mathematics - 2010-2011

Admission | Courses | Program | Requirements | Profile

**Department
Chairperson:** Iraj Kalantari

**Graduate
Committee Chairperson: **Fedor Andreev

**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:** wiu.edu/mathematics/

**Location of Program Offering: **Macomb

####
**Graduate
Faculty**

Professors

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
- James R. Olsen, Ph.D., University of Northern Colorado
- Nader Vakil, Ph.D., University of Washington
- Galen Weitkamp, Ph.D., Pennsylvania State University
- Lawrence V. Welch, Ph.D., University of Illinois

####
**Associate
Professors**

- Fedor Andreev, Ph.D., St. Petersburg Steklov Mathematical Institute
- Victoria Baramidze, Ph.D., University of Georgia–Athens
- Robert Mann, Ph.D., University of Nebraska-Lincoln
- Mei Yang, Ph.D., University of Canterbury

####
**Associate
Graduate Faculty**

Associate
Professors

Associate Professors

- J. Thomas Blackford, Ph.D., Ohio State University
- John Chisholm, Ph.D., University of Wisconsin
- Rumen Dimitrov, Ph.D., George Washington University
- Kimberly Hartweg, Ph.D., University of Iowa
- Boris Petracovici, Ph.D., University of Illinois
- Lia Petracovici, Ph.D., University of Illinois
- Feridun Tasdan, Ph.D., Western Michigan University

####
**Assistant Professors**

- Clifton Ealy, Ph.D., University of California-Berkeley
- Amy Ekanayake, Ph.D., Texas Tech University
- Dinesh Ekanayake, Ph.D., Texas Tech University
- Elizabeth Hansen, Ph.D., University of Iowa
- M. Koissi-Kouassi, Ph.D., Abo Akademi University
- Jana Marikova, Ph.D., University of Illinois at Urbana-Champaign

####
**
Program
Description**

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.

####
**
Admission
Requirements**

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**

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 refer to the post-baccalaureate certificate section for more specific information. The second step includes an additional 18 semester hours of coursework leading to the Master of Science degree in Mathematics.

**I. 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)

**II. 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)

**III. 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.

**IV. 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, go to the post-baccalaureate certificates page.

####
**
Course Descriptions**

**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:
MATH 123 or MATH 128 or equivalent.*

**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 123 or MATH 128 or
equivalent.*

**408G Mathematical Topics and Technology for Middle School.
(3) **The study of programming,
algorithms, and technology resources to investigate concepts and connections in
the content areas of middle school mathematics. *Prerequisite: MATH 123 or MATH 128 or equivalent.*

**409G Probability and
Statistics for Middle School Teachers. (3) **Probability laws, random
variables, probability distributions, estimation and inference, sampling and
data analysis, emphasis on concepts and connections of probability and
statistical content to the challenges of teaching statistics for middle school
teachers. *Prerequisite: Math 123 or 128
or equivalent.*

**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 for Teachers. (3)** A study
of mathematical concepts of number and operation, algebra, geometry,
measurement, and data analysis and probability as they pertain to the
elementary and middle school curriculum.

**502 Algebraic Mathematical Modeling for Middle School
Teachers. (3)** Case study analyses of mathematical models of real-world
problems, using algebraic, graphical, and numerical representations. Students
will use algebra and technology to model, analyze, and solve real-world
problems.

**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.*

**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.

**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.*

**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)**

**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: 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: 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.*

#### 2010-2011 Graduate Catalog

##### Table of Contents

- General Information
- Campus and Facilities
- University Services
- Special Programs
- Admission
- Academic Guidelines
- Graduate School Policies
- Costs and Financial Assistance
- Programs of Study
- Integrated Baccalaureate/Master's Degrees
- Post-Baccalaureate Certificates
- Other Departments Offering Courses for Graduate Credit
- Index