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Principles, techniques, and issues in the teaching of mathematics in other cultural and national settings. Study tour of schools and institutions in various nations.

Cognitive development and learning strategies for teaching and the use of instructional materials. Current research in mathematics education. Required for pre-service students.

Historical/comparative study of mathematical education programs in the United States and abroad. Current research in mathematics education.

Content, methods, and instructional models for teaching exceptional students, including LED, LD, and MT students.

A review of teaching methods and curricular innovations in computing and computer mathematics.

The role of applications in mathematics curriculum. Mathematical models, use of calculators and computers. Applications in the natural and social sciences.

Primes, composites, divisibility and factorization, congruence, historical topics.

For students who are preparing to teach in secondary school. The mathematical content of advanced secondary school mathematics and the development and application of fundamental ideas in mathematics.

Statements, propositions, and sets; vectors and matrices; probability. Applications: finite Markov chains, game theory.

Permission required. Prerequisite: MSTM 5011. Open only to students enrolled in the pre-service program. Students do supervised teaching in metropolitan area schools.

Permission required from the instructor with whom the student wishes to work. Independent study in selected areas.

Problems, issues, and methods in the teaching and supervision of elementary school mathematics.

Problems, issues, and methods in the teaching and supervision of secondary school mathematics. Includes field experiences. Required for preservice students.

Taxonomy of games, two-person zero-sum games, transferable and non-transferable utility, equilibrium concepts, two-sided markets, elections and voting, bankruptcy, apportionment, combinatorial games. Game theory and the K-12 curriculum.

Survey of mathematical topics, methods, and issues related to teaching and learning as represented in popular culture and media, including literature, film, art, advertising, and the press.

Survey of mathematical topics and methods appropriate for multicultural and bilingual programs.

Principles, strategies, and techniques for curriculum development and textbook preparation in mathematics.

Theories and methods of mathematical problem solving with applications to classroom instruction.

Simple, compound, and conditional probabilities and applications. Doctoral students should register for MSTM 6030.

Propositional and predicate calculi, set theory, axiomatics, order types, the linear continuum, and Goedel's theorem.

Foundation of geometry/topology. Emphasis upon the relationship between topology and geometry and other mathematical areas.

Groups, rings, fields. Doctoral students should register for MSTM 6033.

Real or complex functions and their properties. Doctoral students should register for MSTM 6034.

Simulation, information theory and coding, stochastic models, probabilistic systems, simple harmonic motion. Topics vary between natural sciences and behavioral sciences.

Discrete mathematics, combinatorics, graph theory.

Historical development of major ideas in mathematics. Contributions of noteworthy mathematicians. Analysis of mathematical classics.

Prepositional calculus, Church-Turing thesis, Goedel's incompleteness theorem.

A review and comparison of mathematics education in other nations.

Theory and methods of evaluating pupils and programs in the cognitive and affective domains. The roles of research and policy in evaluation of mathematics outcomes.

Prerequisite: MSTM 5030 or MSTM 6030. Estimation, hypothesis testing, and tests based on the chi-square distribution. The normal distribution and its applications. Analysis of variance and regression. Doctoral students should register for MSTM 6126.

Permission required. Open only to doctoral students. Guided field experience in supervising student teachers.

Current issues in undergraduate mathematics. Examination of relations between elementary and advanced mathematics.

Lecture series featuring presentations by distinguished guest speakers.

Lecture series featuring presentations by distinguished guest speakers.

Open only to doctoral students. Advanced study of game theory.

Open only to doctoral students. Emphasis on proof and advanced applications.

Open only to doctoral students. Advanced study of axiom systems and 19th – 20th century developments in the logical foundations of mathematics.

Foundation of geometry/topology. Emphasis upon the relationship between topology and geometry and other mathematical areas.

Open only to doctoral students. Advanced study of groups, rings, and fields.

Open only to doctoral students. Advanced study of real or complex functions.

Open only to doctoral students. Advanced study of mathematical modeling.

Open only to doctoral students. Advanced study of discrete mathematics, combinatorics, and graph theory.

Topics will vary

A review and comparison of mathematics education in other nations.

Open only to doctoral students. Prerequisite: MSTM 5030 or MSTM 6030. Advanced topics including hypothesis testing, distribution theory, and analysis of variance and regression.

Permission required. Supervised intern service in a variety of field settings including classroom teaching at various levels, supervision, curriculum development, and inservice education.

Permission required. Research oriented seminars dealing with a variety of issues and leading to preparation of preliminary proposals for the doctoral dissertation. Required for doctoral students.

Permission required. Research oriented seminars dealing with a variety of issues and leading to preparation of preliminary proposals for the doctoral dissertation. Required for doctoral students.

Permission required. Guided independent study leading to the preparation of a major project or paper. May be taken repeatedly by doctoral candidates engaged in research.

Development of final doctoral dissertation proposals and presentation of proposals for departmental review.

Individual advisement on doctoral dissertations. Fee to equal 3 points at current tuition rate for each term. For requirements, see section in catalog on Continuous Registration for Ed.D./Ph.D. degrees.

*Program Director:* Professor Alexander Karp

*Box:* 210-M

Teachers College, Columbia University

323 Thompson

*Email:* tcmath@tc.edu