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Mathematics Education
PROGRAM CONTACT INFORMATION
John Beam, Program Coordinator
Office: Swart 110
Telephone: 920-424-1058
Website: https://www.uwosh.edu/mathematics/graduate/
E-mail: beam@uwosh.edu
FACULTY/GRADUATE INSTRUCTIONAL ACADEMIC STAFF
Beam, Belnap, Bullington, Eroh, Hart, Hussein, Kazmi, Koker, Kuennen, Lavrentiev, Liang, Mohammad, Parrott, Penniston, Price, Szydlik, J., Szydlik, S., Tirel, Winters, Zaiden, Zhang.
PURPOSE
The graduate certificate program in Mathematics for Teachers is designed for practicing high school math teachers and others who wish to enrich their content knowledge, mathematical practices, and pedagogy. It offers 18 credits of graduate math courses. Completion of this certificate fulfills the HLC requirement for dual enrollment instructors (18 graduate credits in the content area).
DEGREES/CERTIFICATES
Completion of the program will lead to the certificate: Graduate Certificate in Mathematics for Teachers
ADDITIONAL ADMISSIONS REQUIREMENTS INFORMATION
In addition to the requirements of the Graduate School specified in the POLICIES section of this Bulletin, the program has established the following policies and procedures for admission:
Admission with Deficiencies
Probationary or conditional admissions may be considered based upon individual merit.
Grade-Point Average
A grade-point average of 2.75 in all undergraduate mathematics courses is required.
Undergraduate Coursework
The applicant must have taken 24 credits of mathematics, including the equivalent of two semesters of calculus and two proof-based courses with a minimum grade point average of 2.75.
Undergraduate Major
Normally, the baccalaureate will have been taken in mathematics or a related discipline.
SUMMARY
A. Structure
The program is comprised of a 6 (six) required courses from the Mathematics Department.
B. Academic Plans of Study
Graduate Certificate in Mathematics for Teachers is the description of the plan of study.
C. Minimum Credit Requirements
18 graduate credits constitute the minimum credit requirement for all students in the certificate program.
D. Graduation Requirements
Candidates must satisfy all program and Graduate School academic requirements to be eligible for graduation.
CERTIFICATE REQUIREMENTS
Students must successfully complete 18 credits from the list below:
Mathematics
- 702 Statistics Workshop for Teachers
- 714 Developing a Problem-Solving Focus in Teaching
- 716 Research in Teaching and Learning Math
- 718 Historical and Philosophical Foundations of Math
- 732 Calculus Workshop for Teachers
- 742 Algebra Workshop for Teachers
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 Abstract Algebra | |
| This course offers an introduction to groups and rings, which are formed by associative operations on sets. A group has one operation, an identity, and inverses exist. Groups covered in this class include permutation, symmetric, alternating, and dihedral groups. Rings, which have addition and multiplication operations, arise naturally as generalized number systems. Rings covered in this class include matrices, integers modulo n, and polynomial rings. These algebraic systems have applications in art, biology, chemistry, combinatorics, computer science, geometry, linguistics, music, physics, and topology.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 256. 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 | |
| Designed to build one’s understanding of topics in probability and statistics through active exploration, problem solving and discussion. It is intended for secondary and post-secondary teachers of statistics. Topics broadly include descriptive statistics; probability, random trials, and limit theorems; and inferential statistics. Special attention will be given to developing conceptually intuitive approaches, both theoretical and through simulations, to content that is commonly misunderstood by students. Prerequisite: Admission into the Online Graduate Certificate in Mathematics for Teachers program, 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 is for teachers of secondary and post-secondary 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. In this course, we will engage in various aspects of the problem-solving process. The specific types of problems considered will depend on the interest and background of the class. This course will also discuss curricular and pedagogical practices which can help students become powerful problem solvers. Prerequisite: Admission into the Online Graduate Certificate for Teachers program, or 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: Admission into the Online Graduate Certificate for Teachers program, or 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. Prerequisite: Admission into the Online Graduate Certificate for Teachers program, or consent of instructor. | |
| 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 732 | 3 (crs.) |
| Calculus Workshop for Teachers | |
| This course is designed to build an understanding of topics in calculus through active exploration, problem solving and discussion, and is intended for secondary and post-secondary teachers of calculus. This course will explore a variety of topics in real analysis, including infinity, convergence of sequences and series, limits and continuity, the derivative, the Riemann integral, the Fundamental Theorem of Calculus, and power series. Special attention will be given to developing conceptually intuitive approaches, both theoretical and through experimentation, to content that is commonly misunderstood by students. Prerequisites: Admission into the Online Graduate Certificate in Mathematics for Teachers program, or consent of instructor. | |
| Mathematics 742 | 3 (crs.) |
| Algebra Workshop for Teachers | |
| Designed to build one’s understanding of topics in algebra through active exploration, problem solving and discussion. It is intended for secondary and post-secondary teachers of algebra and pre-calculus. This course introduces selected abstract algebra topics from the theory of groups, rings and fields. Students will explore how the algebraic concepts and techniques taught in secondary school fit into the framework of abstract algebra. Prerequisites: Admission into the Online Graduate Certificate in Mathematics for Teachers program, 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. | |