## Graduate Studies

### Teaching Mathematics

2023-2024

Admission | Courses | Program | Requirements | Profile

**Chairperson:** Victoria Baramidze

**Committee Chairperson: **Dinesh Ekanayake

**Graduate Coordinator:** Robert Mann

**Office:** Morgan Hall 476

**Telephone:** (309) 298-1054

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

**Website:** wiu.edu/mathphil

**Location of Program Offering: **Online

#### Graduate Faculty

**Professors**

- Fedor Andreev, Ph.D., St. Petersburg Steklov Mathematical Institute
- Victoria Baramidze, Ph.D., University of Georgia–Athens
- Amy Ekanayake, Ph.D., Texas Tech University
- Dinesh Ekanayake, Ph.D., Texas Tech University
- Douglas LaFountain, Ph.D., University at Buffalo, The State University of New York
- Susan Martinelli-Fernandez, Ph.D., University of Chicago
- Gordon Pettit, Ph.D., University of Notre Dame
- Christopher A. Pynes, Ph.D., Florida State University

**Associate Professors**

- Robert Mann, Ph.D., University of Nebraska-Lincoln
- Seyfi Turkelli, Ph.D., University of Wisconsin-Madison
- Mei Yang, Ph.D., University of Canterbury

#### Associate Graduate Faculty

**Professors**

- J. Thomas Blackford, Ph.D., Ohio State University
- Rumen Dimitrov, Ph.D., George Washington University
- Clifton Ealy, Ph.D., University of California-Berkeley
- Kimberly Hartweg, Ph.D., University of Iowa
- Brian Powell, Ph.D., University of Virginia
- Feridun Tasdan, Ph.D., Western Michigan University

**Associate Professors**

- Susan Brooks, Ph.D., University of Iowa
- Elizabeth Hansen, Ph.D., University of Iowa
- Boris Petracovici, Ph.D., University of Illinois
- Lia Petracovici, Ph.D., University of Illinois

#### Learning Outcomes

For student learning outcomes, please see wiu.edu/provost/learningoutcomes.

#### Program Description

The fully online Master of Science in Teaching Mathematics prepares students for career advancement in Mathematics Education, such as obtaining dual-credit endorsement in mathematics and/or teaching mathematics courses at community colleges. The degree is designed to primarily serve current secondary teachers who already have both their Bachelors in Mathematics and their Secondary Teaching License. The program provides coursework in mathematics content that includes topics from and advanced perspectives of Statistics, Analysis, Algebra, and Geometry. The program includes a capstone sequence of courses that allows students to research topics from mathematics education, conduct action research in their classrooms, and generate research papers, projects, or a thesis. To provide flexible pathways to the MSTM the program combines core content with a mixture of graduate courses from various topics and disciplines.

#### Admission Requirements

- A minimum cumulative GPA of 2.75
__OR__3.0 or higher GPA for the last two years (60 s.h.) of undergraduate work

Students admitted on probationary status must complete six semester hours of mathematics or statistics graduate coursework with a B or better and must complete all undergraduate deficiency courses before eligible for regular admission.

#### Degree Requirements

**I. Core Courses: 12 s.h.**

MATH 552 Scientific Computing (3)

MATH 554 Symmetry, Algebra, Geometry, Topology (3)

MATH 656 Advanced Perspective of Secondary School Mathematics (3)

STAT 553 Applied Statistical Methods (3)

**II. General Electives: 12 s.h.**

Graduate coursework related to mathematics or teaching at the secondary college levels and must be approved by the graduate committee. Courses from mathematics, statistics, educational studies, or education leadership may be included. Courses may include:

MATH 406G Problem Solving and the History of Mathematics (3)

MATH 407G Number Theory Concepts in School Mathematics (3)

MATH 430G Multivariate Calculus (3)

STAT 471G Introduction to Mathematical Statistics I (3)

STAT 474G Regression and Correlation Analysis (3)

**III. Capstone: 9 s.h.**

A. MATH 504 Research in Secondary Mathematics Education (3)

MATH 607 Practicum in Mathematics Education (6)

B. MATH 504 Research in Secondary Mathematics Education (3)

MATH 607 Practicum in Mathematics Education (3)

Elective (3)

**TOTAL PROGRAM: 33 s.h.
**

#### 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. Topics include proofs, transformations, measurement, and coordinate geometry. Middle school mathematics standards will be emphasized. *Prerequisite: MATH 123 or MATH 128 or equivalent.*

**406G Problem Solving and the History of Mathematics. (3)** Various problems, their solutions, related mathematical concepts and their historical significance are analyzed through investigation of classic problems and their connection to middle school mathematics. Contributions by Archimedes, Descartes, Eratosthenes, Euler, Gauss, Pascal, Pythagoras and others are studied. *Prerequisite: MATH 123 or 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 311 & MATH 341, or equivalent.*

**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, sequences, limits, and series. Rigorous introduction to the study of one-variable functions, continuity and differentiability, based on the epsilon-delta method. *Prerequisites: MATH 231 and MATH 341.*

**439G Teaching and Assessment in Secondary School Mathematics. (4) **A study of teaching strategies and current trends in secondary mathematics education. Students will focus on curriculum, lesson-planning and assessment, and will learn to effectively incorporate technology into the teaching and learning of mathematics. Open to teacher education majors only. *Prerequisites: 2.5 GPA or higher in Mathematics; MATH 304, MATH 341, and co-registration in EDS 304; or permission of the department chair.*

**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 214 and 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: CS 214, MATH 231 and 311; 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 School Mathematics. (3)** A study of current trends and issues in the teaching and learning of K-12 mathematics. *Prerequisite: Permission of the instructor.*

**504 Research in 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. *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 Standards and Assessment in School Mathematics. (3)** An analysis of the current state and national standards for school mathematics and their corresponding assessments. Other assessment instruments and strategies for implementing the standards and improving student achievement for all learners will also be investigated. *Prerequisites: Teacher certification.*

**510 (cross-listed with DS 510) Foundations of Business Analytics. (3) **A survey of topics in calculus, applied linear algebra, probability and statistics useful for business decision making. The main objective is to lay the foundation required for advanced studies in applied statistics and business analytics.

*Prerequisite: Graduate standing.*

**511 Modern Geometry. (3) **Topics to be chosen to reflect current trends in geometry. *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.*

**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.*

**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 geometry of Rⁿ, differential calculus in Rⁿ, line and surface integrals; conformal mappings, complex integration, Laurent series, calculus of residues; and applications. *Prerequisites: MATH 231 and MATH 311, or equivalents.*

**552 Scientific Computing. (3) **Design, analysis, and MATLAB or Mathematica 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 Optimization. (3)** Unconstrained optimization; equality constrained optimization; convex optimization; optimality conditions; algorithms and applications using software such as Mathematica. *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.*

**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 advisor.*

**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. (1-3, repeatable to 6)** Direct internship experience for action research in mathematics education under guidance of qualified faculty. *Prerequisites: Permission of the instructor.*

**651 Elements of Modern Analysis. (3) **A study of elements of modern analysis with a significant lean toward developing theory. Topics include Riemann integrability; metric spaces; pointwise and uniform convergence; Hilbert and normed vector spaces; Banach fixed point theorem, Weierstrass approximation theorem; and applications. *Prerequisites: MATH 435 or equivalent.*

**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 Topics from Secondary School Mathematics. (3, repeatable to 6) **An advanced study of the topics from the secondary school mathematics curriculum for 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, Statistics, Geometry, and Calculus. *Prerequisites: Permission of the instructor.*

**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)**

**471G Introduction to Mathematical Statistics I. (3)** The mathematical foundations of probability and statistics, principals of probability, sampling, distribution, moments, and hypothesis testing. *Prerequisite: MATH 138 or MATH 231 or equivalent.*

**473G Nonparametric Statistical Methods. (3) **Systematic development of nonparametric statistical methods. Topics include order statistics, ranks, empirical distribution functions, point and interval estimations, hypothesis tests such as sign rank test, Mann-Whitney-Wilcoxen, Kruskal-Wallis, Kolmogorov-Smirnov, permutation and bootstrap methods. *Prerequisites: STAT 276 or STAT 471 or permission of the instructor.*

**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.*

**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.*

**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 or equivalent.*

## Connect with us: