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Mathematics

Masters of Arts in Teaching Mathematics

General Description

This degree is designed for working mathematics teachers with a Single Subject Credential in Mathematics (from California or other state or nation), or mathematics teachers holding a Supplementary Authorization in Elementary Mathematics to a Single or Multiple Subject Credential. The purpose of the Master of Arts in Teaching Mathematics is to enable secondary and middle school mathematics teachers to increase their understanding of secondary school mathematics, its pedagogy, and related topics. The course of study is designed to deepen the participant’s mathematical knowledge and integrate it with his/her prior experiences and training.

Requirements for Admission

Admission to the graduate program leading to the Master of Arts in Teaching Mathematics requires the following:

• a baccalaureate degree with a relevant major (as determined by the Mathematics Graduate Program Committee) from an accredited college or university
• a 2.50 GPA (A=4.0) for the last (baccalaureate or postbaccalaureate) 90 quarter units (60 semester units) of college or university coursework attempted
• good academic standing at the last college or university attended
• submission of a letter of application to the Department of Mathematics.
• application to the university for graduate status.

Requirements for the Master of Arts in Teaching Mathematics

A minimum of 45 units is required for the MA in Teaching Mathematics; the following courses are required of all students:

• 1. MATH 520 Discrete Mathematical Models
• 2. MATH 521 Statistics and Data Analysis
• 3. MATH 522 Numerical Approach to Calculus and Differential Equations
• 4. MATH 523 Geometric Linear Algebra
• 5. MATH 524 Number Theory and Codes
• 6. MATH 525 Dynamical Geometry
• 7. MATH 526 History of Mathematics
• 8. MATH 540 Introduction to Mathematics Education Research
• 9. MATH 591 Culminating Project

Satisfaction of the CSU Graduation Writing Assessments Requirement (GWAR).

COURSE DESCRIPTIONS

NOTE: Students who have not attained graduate standing and who are interested in enrolling in a graduate class are encouraged to consult with the instructor and/ or members of the Mathematics Graduate Program Committee.

MATH 520 Discrete Mathematical Models (5)

Construction and analysis of difference models from physical, biological, social, and financial sciences. Cobweb analysis, convergence, stability and chaos in discrete dynamical systems. Phase plane analysis of systems of difference equations. Prerequisites: Graduate standing.

MATH 521 Statistics and Data Analysis (5)

Exploratory data analysis; statistical inference including estimation, testing hypotheses and confidence intervals; contingency tables and chi-squared tests; linear and non-linear statistical modeling; bootstrap and jackknife; smoothing histograms; nonparametric techniques; and Bayesian statistics. This courses makes use of statistical packages. Prerequisites: Graduate standing MATH 140.

MATH 522 Numerical Approach to Calculus and Differential Equations (5)

Use of numerical and algebraic techniques to study change. The use of forward, back, and symmetric differences in data analysis. Divided differences as average rates of change and as approximations to instantaneous rate of change. Difference equations and Euler’s method as numerical approximations to differential equations. Reimann sums, midpoint, trapezoid and Simpson’s method to approximate accumulated change. Error analysis for numerical approximations. Prerequisites: (1) Graduate standing and MATH 520 OR (2) Graduate standing and credit for MATH 300.

MATH 523 Geometric Linear Algebra (5)

The algebra and geometry of vectors in two and three dimensions. Complex numbers. Matrices as linear transformations of R2 and R3. Rigid motions in two and three dimensions: rotations, reflections, translations, glide reflections etc. Theory of perspective. Prerequisites: Graduate standing and MATH 300.

MATH 524 Number Theory and Cryptography (5)

Elementary theory of natural numbers, including prime numbers, divisibility, and modular arithmetic. These concepts will be applied to cryptographic systems, such as Caesar ciphers and RSA codes. A significant amount of calculator or computer programming is involved in these applications. Additional topics selected by the instructor. Prerequisites: Graduate standing and MATH 300.

MATH 525 Dynamical Geometry (5)

Classical and modern Euclidean geometry. Review of Euclid’s Book I. Theorems of Menelaus and Ceva and their consequences. Comparisons of synthetic and analytic methods. Additional topics selected from inversions, tessellations, complex analytic methods, and higher dimensional theories. Emphasis on exploration, conjecture and verification using modern dynamical geometry software. Prerequisites: Graduate standing and MATH 300.

MATH 526 History of Mathematics (5)

Development of mathematics from its empirical origins to its present form. Euclid’s Elements. Emphasis may vary with the instructor. Evaluation will include at least one substantial student paper. Prerequisites: (1) Graduate Standing; AND (2) MATH 300; AND (3) At least two mathematics courses numbered above 300.

MATH 540 Introduction to Mathematics Education Research (5)

Primary focus on introduction to research related to contemporary issues in mathematics education. Course includes understanding the ethics, confidentiality, and protection of human subjects involved in mathematics education research. Brief introduction to basic philosophies, key terms, and generally accepted strategies of both quantitative and qualitative research, such as the criteria and processes appropriate for establishing validity, reliability, credibility, trustworthiness, variables, sampling, and data collection. This course could provide the foundation for completing MATH 591. Prerequisites: Graduate standing.

MATH 577 Advanced Topics in Mathematics (1-5)

Topics and prerequisites to be announced. May be repeated for different topics. General prerequisite: Major or minor in Mathematics.

MATH 580 Advanced Research Participation (1-5)

Individual mathematical investigation, under supervision. (Experience as a research assistant does not count for credit.) Offered on a credit/no credit basis only. Prerequisite: Permission of instructor.

MATH 591 Culminating Project (5)

Design and implementation of a written report of mathematical or field research or similar activity. A final presentation of the project is made to a Culminating Activity Committe as determined by the supervising instructor. Prerequisites: Successful completion of 30 approved credits towards the Master of Arts in Teaching Mathematics.