## Graduate Studies

### Mathematics - 2012-2013

Admission | Courses | Program | Requirements | Profile

**Chairperson:** Iraj Kalantari

**Committee Chairperson: **Dinesh Ekanayake

**Office:** Morgan Hall 476

**Telephone:** (309) 298-1054 or (309) 298-2467 **Fax:** (309) 298-1857

**E-mail:**
mathematics@wiu.edu

**Website:** wiu.edu/mathematics/

**Location of Program Offering: **Macomb

#### Graduate Faculty

Professors

- Samson A. Adeleke, Ph.D., Johns Hopkins University
- Iraj Kalantari, Ph.D., Cornell University
- James R. Olsen, Ph.D., University of Northern Colorado
- Nader Vakil, Ph.D., University of Washington
- 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

#### Assistant Professor

- Dinesh Ekanayake, Ph.D., Texas Tech University

#### Associate Graduate Faculty

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
- M. Koissi-Kouassi, Ph.D., Abo Akademi University
- 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
- Elizabeth Hansen, Ph.D., University of Iowa
- 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

##### Mathematics (MATH)

**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.*

**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.*

**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.*

**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.*

**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.*

**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.*

**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.*

**599 Special Topics. (1–3, repeatable to 6 under different titles)** 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 under different titles) **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 (STAT)**

**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.*

**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.*

**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.*

**Table of Contents2012-2013**

- 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

**Other**

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