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Following are capsule descriptions of the courses in the
Master of Arts in Mathematics Education program. The standard program
consists of twelve of the following courses: 606, 609, 610, 611, 612, 620,
630, 631, 640, 650, 651, 660, and 670.
606 Mathematical Software for Teachers.
Introduction to various mathematics software packages for
the investigation of significant mathematical ideas. Emphasis will be on the
use of software in the high school classroom for the enhancement of students'
discovery and understanding of fundamental mathematical concepts.
609 Teaching and Learning Secondary School
Mathematics.
Theories, methods, materials and techniques for teaching
and learning mathematics in secondary and upper elementary schools.
610 Calculus and Analysis for Mathematics Teachers I.
Real numbers, exponentials and logarithms trigonometric
functions, limits, the derivative and its applications. Introduction to
graphics calculators and some applications to classroom teaching.
611 Calculus and Analysis for Mathematics
Teachers II.
Concave and convex functions, optimization, the integral
and its applications. Study of some numerical algorithms and
implementation using graphing calculators
612 Calculus and Analysis for Mathematics
Teachers III.
Methods of integration, first and second order
differential equations and Taylor
series. Applications to numerical analysis and approximation with
graphics calculators.
620 Geometry for Secondary School Mathematics Teachers.
Axiom systems, types of reasoning used in proofs,
Euclidean geometry results with concentration on triangles and circles,
introduction to non-Euclidean geometry, and introduction to geometry
classroom software.
630 History of Mathematics Through Problem
Solving I.
Classical problems and techniques in number theory,
algebra and geometry from a historical point of view. Stress on both
historical aspects of mathematics and on solutions of concrete
problems.
631 History of Mathematics Through Problem
Solving II.
Continuation of MAT 63O. Topics include the development of
calculus, probability theory, number theory, non-Euclidean geometry, and set
theory.
640 Multivariable Calculus for Teachers.
Functions of several variables, vectors, dot products and
cross products, partial differentiation, directional derivatives,
optimization, Lagrange multipliers, multiple integrals, polar spherical
coordinates. Use of graphics calculators and computers to illustrate concepts..
650 Probability and Statistics for Mathematics Teachers
I.
Combinatorics, sets, probability, random variables,
distribution and density functions, standard probability laws, jointly
distributed random variables. Use of graphics calculators and computers to
illustrate concepts..
651 Probability and Statistics for Mathematics Teachers
II.
Central limit theorem, point and interval estimation of
parameters, hypothesis testing, least squares and regression.
660 Discrete Structures for Mathematics Teachers.
Logic and proof, number
theory, sequences and mathematical induction, sets and function, equivalence
relations, and introduction to combinatorics.
670 Abstract Algebra for Teachers.
Number systems, polynomial rings, fields, vector spaces,
and groups. This course provides the theoretical foundation for many topics covered
in high school mathematics courses.
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