**Mathematics Education**

**PROGRAM CONTACT INFORMATION**

John Beam, Program Coordinator

Office: Swart 110

Telephone: 920-424-1058

Website: uwosh.edu/mathematics/graduate-programs

E-mail: beam@uwosh.edu

**FACULTY**

Beam, Belap, Benzaid, Bullington, Edwards, Eroh, Ganapathy, Gundawardena, Hart, Kazmi, Koker, Kuennen, Moghadam, Moussavi, Muthuvel, Parrott, Penniston, Price, Szydlik, J., Szydlik, S., Winters, Zhang.

**PURPOSE**

The graduate program in Mathematics Education is designed to enhance the professional expertise of secondary and post secondary mathematics teachers. The program is structured to meet the needs of the individual graduate students.

**DEGREES/CERTIFICATES**

Completion of the program will lead to the degree: Master of Science (M.S.)

**ADDITIONAL ADMISSIONS REQUIREMENTS INFORMATION**

In addition to the requirements of the Office of Graduate Studies specified in the POLICIES section of this Bulletin, the program has established the following policies and procedures for admission:

**Admission with Deficiencies**

Applicants who lack adequate undergraduate preparation may be admitted with deficiencies and will be expected to take mathematics courses specified by the program coordinator.

**Grade-Point Average**

A grade-point average of 2.75 in all undergraduate mathematics courses is required.

**Undergraduate Coursework**

The applicant must have taken 30 credits of mathematics, which should include one year of calculus, two semesters of upper-level, abstract (proof-based) mathematics, and one semester of probability and statistics.

**Undergraduate Major**

Normally, the baccalaureate will have been taken in mathematics or a related discipline.

**SUMMARY**

**A. Structure**

The program is comprised of a set of electives subject to the requirements described below.

**B. Academic Plans of Study**

Mathematics Education is the description for the Mathematics Education plan of study.

**C. Minimum Credit Requirements**

30 graduate credits applicable to the graduate degree, which must include at least 18 upper-level (700) credits, are required for all students seeking the MS.

**D. Admission to Candidacy**

Students must satisfy fully the Office of Graduate Studies requirements for advancement to candidacy as stated in the POLICIES section of this Bulletin. Students must confer with their program coordinator/advisor to plan and receive program approval for their admission to candidacy. Students should apply for Admission to Candidacy after completing 9-21 credits. The Office of Graduate Studies gives final approval to Admission to Candidacy.

**E. Graduation Requirements**

Candidates must satisfy all program and Office of Graduate Studies academic, culminating, and degree requirements to be eligible for graduation and degree conferral.

**DEGREE REQUIREMENTS**

Students must successfully complete 30 credits from the list below. These courses must be chosen so as to meet the following requirements:

- At least 15 credits must be numbered 700 or above;
- At least 15 credits must have a MATH prefix;
- At least two courses must be chosen from among the following courses:
- No more than one Educational Leadership course may be counted among the 30 credits.
- Math 712
- Math 714
- Math 716
- Math 718
- Sec Ed 715
- Sec Ed 739
- Sec Ed 791
- Ed Found 770

**Mathematics**

546 3 Linear Algebra

547 3 Introduction to Group Theory

548 3 Introduction to Ring Theory

549 3 Introduction to Number Theory

575 3 Vector & Complex Analysis

601 3 Mathematical Statistics

667 3 Introduction to Real Analysis

680 3 Introduction to Topology

701 3 Workshop in Computing Mathematics

702 3 Statistics Workshop

712 3 Problem Solving for Teachers

714 3 Developing Problem Solving in Teaching

716 3 Research in Teaching and Learning Mathematics

717 3 Nonlinear Dynamics and Chaos

718 3 Historical and Philosophical Foundations of Mathematics

720 3 Combinatorial Mathematics

722 3 Discrete Structures

730 3 Advanced Euclidean Geometry

742 3 Algebra

746 3 Workshop on Current Topics

757 3 Advanced Topics in Mathematics

795 1-6 Mathematics Thesis

796 1-3 Independent Study in Mathematics**Secondary Education **

715 1-3 Current Trends in Curriculum and Instruction

739 3 Mathematics Curriculum

791 1-4 Improving Classroom Practice**Educational Foundations**

770 3 Foundations in Educational Research**Educational Leadership**

725 3 Evaluation of Educational Research

730 3 Leadership in Educational Systems

754 3 Integrating Technology into the Curriculum

760 3 Teaching from a Distance

762 3 Nontraditional Higher and Post-Secondary Education

763 3 Understanding and Facilitating Learning in Adulthood

Any course not on the above list must be approved by the Graduate Coordinator.

**Other Requirements**

All students must register for MATH 799 (0 credits) and pass a comprehensive exam that assesses three courses at the 600-level or above with a MATH prefix. The set of courses will be chosen by the student in consultation with, and subject to the approval of, the Graduate Coordinator. A goal of the exam is to assess both mathematics and mathematics education topics. The exam may be taken as soon as the approved set of three courses has been completed.

**COURSE OFFERING(S)**

Mathematics 546

3 (crs.)

Linear Algebra

This course is a proof-oriented, abstract approach to the study of finite dimensional vector spaces and linear transformations. Linear Algebra is central in mathematics and used heavily in other areas, such as computer science, economics, and physics. Topics include bases and dimension, matrices, determinants, inner product spaces, and characteristic values and characteristic vectors. Additional topics may include the Jordan canonical form, the spectral theorem, and quadratic forms. Prerequisite: Math 222 and Math 256 each with a grade of C or better. 346/546 (Fall)

Mathematics 547

3 (crs.)

Introduction to Group Theory

A group is an algebraic system described by a set equipped with one associative operation. Groups contain an identity element and every element has an inverse. Group theory has applications in diverse areas such as art, biology, geometry, linguistics, music, and physics. The types of groups covered in this class include permutation, symmetric, alternating, and dihedral groups. Some of the important theorems covered are Cayley’s Theorem, Fermat’s Little Theorem, Lagrange’s Theorem and the Fundamental Theorem of Finite Abelian Groups. Prerequisite: Math 222 with a grade of C or better. 347/547

Mathematics 548

3 (crs.)

Introduction to Ring Theory

A ring is an algebraic system described by a set equipped with addition and multiplication operations. Rings arise naturally as generalized number systems. The integers, for example, form a ring with the usual addition and multiplication operations. Ring theory has applications in diverse areas such as biology, combinatorics, computer science, physics, and topology. Topics include rings of matrices, integers modulo n, polynomials, and integral domains. Some of the important theorems covered are the Fundamental Theorem of Algebra, the Division and Euclidean Algorithms, and Eisenstein’s Criterion. Prerequisite: Math 222 with a grade of C or better. 348/548

Mathematics 549

3 (crs.)

Introduction to Number Theory

Number Theory is a branch of mathematics that involves the study of properties of the integers. Topics covered include factorization, prime numbers, continued fractions, and congruencies as well as more sophisticated tools such as quadratic reciprocity, Diophantine equations, and number theoretic functions. However, many results and open questions in number theory can be understood by those without an extensive background in mathematics. Additional topics might include Fermat’s Last Theorem, twin primes, Fibonacci numbers, and perfect numbers. Prerequisite: Math 222 with a grade of C or better. 349/549

Mathematics 575

3 (crs.)

Vector & Complex Analyses

Topics in mathematics applicable to the physical sciences: Vector analysis, Green’s theorem and generalizations, analytic function theory. Prerequisite: Mathematics 273. 375/575

Mathematics 586

3 (crs.)

Linear Statistical Models

A unified approach to the application of linear statistical models in analysis of variance (ANOVA) and experimental design. In ANOVA topics from single-factor ANOVA and multifactor ANOVA will be considered. Experimental design will include, randomized blocks, Latin squares, and incomplete block designs. Prerequisites: Mathematics 256 and Mathematics 302. 386/586

Mathematics 601

3 (crs.)

Mathematical Statistics

A mathematical treatment of advanced statistical methods, beginning with probability. Discrete and continuous, univariate, and multivariate distributions; functions of random variables and moment generating functions, transformations, the theory of estimation and hypothesis testing. Prerequisites: Mathematics 273 and 301 with a grade of C or better. 401/601 (Fall)

Mathematics 667

3 (crs.)

Introduction to Real Analysis

This course offers a proof-oriented, abstract approach to many of the concepts covered in Calculus. Topics include real number properties, the topology of the real numbers, functions, limits of functions, continuity, uniform continuity, differentiation, integration, sequences, series, pointwise and uniform convergence of sequences of functions, and series of functions. Reading and writing proofs are an integral part of the course. Prerequisites: Mathematics 222 and 273. 467/667

Mathematics 680

3 (crs.)

Introduction to Topology

An introduction to the fundamental concepts of point set topology. Topics may include: general topological spaces, functions and continuity, open and closed sets, neighborhoods, homeomorphism, properties of topological spaces, subspaces, products, and quotients. Emphasis will be placed on proofs and examples, with particular attention given to metric spaces. Prerequisites: Mathematics 222 and Mathematics 273. 480/680

Mathematics 701

3 (crs.)

Workshop in Computing Mathematics

Areas of mathematics which have direct applications in the secondary schools and which can be advantageously analyzed on digital computers. Prerequisite: Prior computing experience or concurrent registration in a programming course.

Mathematics 702

3 (crs.)

Statistics Workshop

For teachers of mathematics and other individuals interested in using examples from various topics with practical applications in algebra, probability, statistics, and computers. Prerequisite: One or more courses in statistics or consent of instructor.

Mathematics 712

3 (crs.)

Problem Solving for Teachers

This course is for teachers of middle and high school mathematics who are interested in improving their own problem solving skills and are looking for ideas on how to implement more problem solving into their classrooms. The first part of the course will engage the student in problem solving and mathematical modeling. The specific types of problems considered will depend on the interest and background of the class. The remainder of the course will focus on curricular issues and ways teachers can teach via problem solving. Prerequisite: Consent of instructor.

Mathematics 714

3 (crs.)

Developing Problem Solving Focus in Teaching

This course will focus on ways teachers can help their students become powerful problem solvers. As part of the class, we will create and identify mathematically rich tasks for use in middle, secondary and post-secondary settings. Prerequisite: Consent of instructor.

Mathematics 716

3 (crs.)

Research in Teaching and Learning Math

In this course, we will explore the research literature on teaching and learning in mathematics. We will focus on both theoretical concerns and practical applications of a variety of influential studies in mathematics education. Prerequisite: Consent of instructor.

Mathematics 717

3 (crs.)

Nonlinear Dynamics and Chaos

This course deals with the theory and applications of dynamical systems in one, two and three dimensions. Topics such as fixed points, linearization, bifurcation theory, attractors, limit cycles and nonlinear dynamics are covered.

Mathematics 718

3 (crs.)

Historical and Philosophical Foundations of Math

A survey of the historical development and corresponding philosophical pressures on mathematics from the Babylonians to the present.

Mathematics 720

3 (crs.)

Combinatorial Mathematics

Fundamentals of combinatorial mathematics including permutations, combinations, recurrence relations, the principle of inclusion-exclusion, graph theory, and selected topics. Prerequisite: Consent of instructor.

Mathematics 722

3 (crs.)

Discrete Structures

A survey of mathematical structures useful in theoretical computer science. Structures studied will include Boolean algebra, monoids, graphs and finite machines. Boolean algebra as applied to rating networks, structures, homomorphic structures and quotient structures are considered. Finite machines, their homeomorphisms and their use as recognizers are considered. This theory is the basis for the introduction of some fundamentals of machine design and construction. As time permits, additional topics in coding theory, computability and formal languages may be considered. Prerequisite: A course in abstract algebra or consent of instructor.

Mathematics 730

3 (crs.)

Advanced Euclidean Geometry

A survey of advanced Euclidean geometric results concerning concurrency, collinearity, symmetric points, cyclic quadrilaterals, equicircles and the nine-point circle. The study of course topics will employ deductive, analytic and transformational techniques.

Mathematics 742

3 (crs.)

Algebra

An advanced study of topics selected from groups, rings, and fields. Prerequisite: Mathematics 342, or consent of instructor.

Mathematics 746

3 (crs.)

Workshop on Current Topics

A workshop in special topics of interest. This course may be repeated for credit with different topics. Prerequisite: Consent of instructor.

Mathematics 757

3 (crs.)

Advanced Topics in Mathematics

Advanced topics selected from such fields as: algebra, analysis, topology, number theory, geometry, statistics, and applied mathematics. May be repeated for a maximum of 6 credits. Prerequisite: Consent of instructor.

Mathematics 795

1 – 6 (crs.)

Mathematics Thesis

Each registration accumulating to a maximum of 3 cr. Pass/Fail course.

Mathematics 796

1 – 3 (crs.)

Independent Study

Registration for qualified MS Mathematics Education students who submit an approved Independent Study Topic and Instructor Approval Form at or prior to registration. The combination of Mathematics 757 and Mathematics 796 may not exceed 6 cr.

Mathematics 799

0 (crs.)

Registration for Comprehensive Examination

Pass/Fail course.