**The Master of Arts in Mathematics Education: Option 2 (Secondary mathematics)** **requires 31 credit hours**.

**Content knowledge for teaching mathematics, 10 hours **

MATH 641 - Topics in Geometry (3)

**Take each of the following unless the undergraduate equivalent is completed.**

MATH 511 - Abstract Algebra 1 (3)

MATH 571 - Real Analysis 1 (4)

**Electives in content knowledge for teaching mathematics, 6-13 hours (as approved by advisor) from the following (If undergraduate equivalent is not completed)**

MATH 512 - Abstract Algebra 2 (3)

MATH 516 - Theory of Numbers (3)

MATH 560 - History of Mathematics (3)

MATH 572 - Real Analysis 2 (3)

MATH 620 - Mathematical Theory of Statistics 1 (4)

MATH 621 - Mathematical Theory of Statistics 2 (4)

MATH 623 - Data Analysis and Probability for Teachers (3)

MATH 645 - Topology 1 (3)

MATH 675 - Measure Theory and Integration 1 (3)

MATH 677 - Complex Variables 1 (3)

**Research and pedagogical knowledge for teaching mathematics, 12 hours**

MATH 690 - Curriculum & Instruction in Mathematics Education (3)

MATH 693 - Teaching Mathematics through Problem Solving (3)

MATH 694 - Research Methods in Mathematics Education (3)

MATH 696 - Action Research in Mathematics Education (3)

**Electives in pedagogical knowledge for teaching mathematics, 3 hours (as approved by advisor) from the following:**

MATH 631 - Technology for Mathematics Teachers (3)

MATH 632 - Assessment in Mathematics Education (3)

MATH 695 - Mathematics Learners and Learning (3)

MATH 697 - Mathematics Teacher Leadership 1 (3)

**Related Links**Graduate Course Offering Schedule (PDF)

**511** **Abstract Algebra 1 (3)**

The theory of groups, including subgroups, cyclic groups, normal subgroups, cosets, Lagrange's Theorem, quotient structures, homomorphism, automorphisms, group actions, Sylow's Theorems, structure of finite abelian groups, generators, and relations.

*Prerequisite: *MATH 311 or permission of the department chairperson.

*Not open to *student who have credit in MATH 411.

**512 Abstract Algebra 2 (3)**

An introduction to the theory of rings, including integral domains, division rings, and fields. Quotient fields of integral domains. Homomorphisms, ideals, and quotient structures. Factorization in commutative rings. Polynomial rings and field extensions. Aspects of Galois theory.

*Prerequisite: *MATH 411 or MATH 511, or permission of the department chairperson.

*Not open to *students who have credit in MATH 412.

**516 Theory of Numbers (3)**

Topics include the division algorithm; positional notation; divisibility; primes; congruences; divisibility criteria; the sigma, divisor, and phi functions; Diophantine equations; linear, polynomial, and simultaneous congruences; theorems of Fermat, Euler, Lagrange, and Wilson; quadratic reciprocity.

*Prerequisite: *MATH 215 or permission of the department chairperson.

*Not open to *students who have credit in MATH 416.

**560 History of Mathematics (3)**

The development of mathematics from pre-history to the seventeeth century. Topics may include number concepts and numeration, algebra, geometry, trigonometry, analytic geometry, and calculus.

*Prerequisite: *MATH 161 or MATH 165.

*Not open to *students who have credit in MATH 460.

**571 Real Analysis 1 (4)**

Real and complex number systems; ordered sets, least upper bound property, fields, Archimedean property; Basic topology; cardinality, metric spaces, completeness, compactness, connectedness; Numerical sequences and series; convergence tests, upper-lower limits; Continuity; continuous functions, uniform continuity, Intermediate and Extreme Value Theorems; Differentiation: derivative, Mean Value Theorem, 1 'Hospital's Rule, Taylor's Theorem.

*Prerequisite: *MATH 215 and MATH 267; or permission of the department chairperson.

*Not open to *students who have credit in MATH 471.

**572 Real Analysis 2 (3)**

The Reimann-Stieltjes integral and Fundamental Theorem of Calculus. Sequences and series of functions. Differential calculus of functions of several variables. Inverse and implicit function theorems. Extremum problems. Lebesgue integration and comparison with the Riemann integral.

*Prerequisite: *MATH 471 and MATH 571.

*Not open to *students who have credit in MATH 472.

**620 Mathematical Theory of Statistics 1 (4)**

Probability set functions, random variables, density and distribution functions, mathematical expectations, marginal and conditional distributions, sampling distributions, and limiting distributions. The mathematical rigor requires a strong background in calculus.

*Prerequisite: *MATH 166 and MATH 215.

**621 Mathematical Theory of Statistics 2 (4)**

Estimation theory and statistical tests of hypothesis. Topics include: classical and Bayesian estimation, sufficiency, completeness, uniqueness, likelihood function, exponential families, Rao-Blackwell Theorem, Rao-Cramer inequality, hypothesis testing, Neyman-Pearson Lemma, likelihood ratio tests, goodness-of-fit, contingency tables, nonparametric tests, distribution of quadratic forms, and correlation and regression, bootstrapping.

*Prerequisite: *MATH 620.

**623 Data Analysis and Probability for Teachers (3)**

Students will select and use appropriate statistical methods to analyze data, develop, and evaluate inferences and predictions that are based on data, and understand and apply the basic concepts of probability.

*Prerequisite: *at least one year of teaching experience or permission of the department chairperson.

**631 Technology for Mathematics Teachers (3)**

Modeling, computational, and communication tools used in teaching mathematics.

*Prerequisite: *at least one year of teaching experience or permission of the department chairperson.

**632 Assessment in Mathematics Education (3)**

Issues related to assessment in mathematics education and the relationship of assessment to curriculum and instruction. Examination of various types of assessments administered in mathematics classrooms, as well as large-scale local, national, and international assessments.

*Prerequisite: *at least one year of teaching experience or permission of the department chairperson.

**641 Topics in Geometry (3)**

A survey of topics in contemporary geometry from various perspectives, including conjecture and exploration, formal analysis, and application beyond geometry.

*Prerequisite: *at least one year of teaching experience or permission of the department chairperson.

**645 Topology 1 (3)**

Introduction to point-set topology. Topics include set-theoretic preliminaries, topological spaces, continuous functions, metric spaces, product and quotient spaces, connectedness, compactness, countability and separation axioms. Urysohn's Metrization Theorem, Tietze's Extension Theorem, and Tychonoff's Theorem.

*Prerequisite: *MATH 471 or MATH 571.

**675 Measure Theory and Integration 1 (3)**

The concept of measurability, simple functions, properties of measures, integration of positive as well as complex functions, sets of measure zero, Riesz representation theorem, Borel and Lebesgue measures, LP-spaces, approximation by continuous functions, elementary Hilbert space theory.

*Prerequisite: *MATH 472 or MATH 572.

**677 Complex Variables 1 (3)**

Complex number systems, differentiation and integration, functions (analytic, entire, meromorphic) of one complex variable, singularities, complex integration, Cauchy's theorem, Cauchy's integral formula, power series, Laurent series, calculus of residues.

*Prerequisite; *MATH 471 or MATH 571

**690 Curriculum and Instruction in Mathematics Education (3)**

Focuses on the mathematics curriculum, with emphasis on current issues and trends, on teaching strategies, and standards-based teaching. Looking at mathematics curriculum from a K-12 perspective, students will work on understanding these recommendations in light of previous mathematics curriculum experiences.

*Prerequisite: *at least one year of teaching experience or permission of the department chairperson.

**693 Teaching Mathematics through Problem Sovling (3)**

Knowledge and skills for teaching and learning mathematics through problem solving using multiple representations and orchestrating mathematical discourse to promote mathematical reasoning in student-centered mathematics classrooms. Design, select/adapt, and solve worthwhile mathematical tasks to support teaching through problem solving.

*Prerequisite; *at least one year of teaching experience or permission of the department chairperson.

**694 Research Methods in Mathematics Education (3)**

Research analysis and methodology in mathematics education.

*Prerequisite: *at least one year of teaching experience, and 18 hours of graduate credit in mathematics or mathematics education, including MATH 690 and either MATH 632 or MATH 695, or permission of the department chairperson.

**695 Mathematics Learners and Learning (3)**

In-depth look at mathematics learners and learning as related to learning trajectories, cultural differences, and social learning contexts while building upon learners' existing knowledge/skills.

*Prerequisite: *at least one year of teaching experience or permission of the department chairperson.

**696 Action Research in Mathematics Education (3)**

Teachers conduct an action research project in a mathematics classroom and present their findings in a written report.

*Prerequisite*: MATH 694 or permission of the department chairperson.

**697 Mathematics Teacher Leadership 1 (3)**

An introduction to the development of strategies and skills for teacher leadership in mathematics education, with a focus on models for professional development of mathematics teachers.

*Prerequisite: *MATH 690.

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