MST Course Descriptions
A selected set of the following courses is offered each summer, in a sequence which allows all program participants to pursue in-depth study of the major areas of algebra, analysis, and geometry over a three-summer period.
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Math 901. An Introduction to Programming and the Internet for Teachers
An Introductory course covering the basics of
programming using Java applets on the Internet that can be used as mathematics
teaching tools. Topics include programming concepts and techniques, the
definition and use of classes and basic graphical user interface
components. Necessary Internet topics will also be covered, such as the
World Wide Web and HTML. 3 credits
Math 903-904. Higher
Algebra for Teachers, I-II
Integers, integral domains, topics from number
theory, equivalence relations, congruences, real
numbers, complex numbers, fields, polynomials, group theory, matrix theory,
vectors, vector spaces, rings, and Boolean algebra. 6
credits.
Math 905-906. Higher Geometry for Teachers, I-II
Systems of
postulates of various geometries, geometric invariants, synthetic and analytic
projective geometry, and an introduction to non-Euclidean geometry. 6 credits.
Math 907-908. Higher
Analysis for Teachers, I-II
The real number system, functions and limits,
elements of set theory, numerical sequences and series, continuity, the
derivative and the Riemann integral, maxima and minima.
6 credits.
Math
909. Probability
and Statistics for Teachers
Permutations
and combinations; finite sample spaces, random variables, binomial
distributions, and statistical applications. 3 credits.
Math 910. Topics in Mathematics Education
Mathematics Education-Teaching Strategies
Current developments and issues in mathematics methods, psychology of teaching, and psychology of learning mathematics. Emphasis on 7-12 curriculum. 1 credit.Mathematics Education-Software
A survey of mathematical software (e.g., Maple, Geometer's Sketchpad) and word processing software which is useful for writing mathematics (e.g., Scientific Notebook, MS Word with Equation Editor) with an emphasis on the software's use in the secondary curriculum. 1 credit.Mathematics Education-Assessment
Current developments and issues in assessment. Emphasis on 7-12 curriculum. 1 credit.
Math
911. Technology
in Teaching Mathematics
Consideration
of the role of technology in teaching mathematics, preparation of classroom
materials for the Macintosh, and IBM, and exchange of ideas and software. 3 credits.
Math
912. Exploring Data and
Planning Investigations.
Covers the basic concepts and methodologies
behind exploratory statistics and design of
experiments, and provides background for teaching AP Statistics.
Graphical displays, distributions, summary measures and their distributions,
confidence intervals, hypothesis tests, factorial and fractional factorial
designs, randomization, blocking, response surface methods. JMP software
will be used extensively. 3 credits.
Math
914. Topology
for Teachers
Fundamental
concepts of elementary topology, network problems, map problems, sets, spaces,
and transformations. 3 credits.
Math
916. Theory of Numbers for
Teachers
Divisibility, primes, congruences,
quadratic reciprocity, number theoretic functions, Diophantine equations,
perfect and amicable numbers. 3 credits.
Math
917. Mathematical
Proof and Problem Solving
Introduction
to abstract mathematics with an emphasis on problem solving and proof
structure, methods, and techniques. Content includes logic, set theory, and basic number
theory. 3 credits.
Math
919. The
Real Number System
A postulational approach to fundamental aspects of algebraic
structure; sequences, limits, and continuity. 3 credits.
Math
920. History of Mathematics
A problem-study approach to mathematical problems from the
period of Greek mathematics until the modern era. 3 credits.
Math
921. A Modern Approach to
Geometry
The foundations and development of Euclidean geometry, with
emphasis on recent recommendations for high school geometry. 3
credits.
Math
925. Problem
Solving Seminar
A study of
a variety of problem solving strategies and techniques in the context of
solving mathematical problems.
Problems will emphasize the connections between the core areas of Algebra,
Geometry, and Analysis. Other mathematical topics may also be
included. Typically, taken in conjunction with Concluding
Experience Problem Set. 3 credits.
(Pass/Fail)
Math 928. Selected Topics in Mathematics for Teachers
Selected
Topics in Mathematics - Knot Theory
VStudents will study simple, closed curves (knots) in three-dimensional
space, identifying and classifying them by using techniques that
analyze
two-dimensional representation of knots. We will focus on knots
invariants such as crossing number, unknotting number, tricolorability,
and the
Jones polynomial (1984). 1
credit.
Selected
Topics in Mathematics - Spherical Geometry
Through
proofs and problem solving, participants in this course will explore
concepts in spherical geometry including: Straightness, Vertical Angle
Theorem, Triangles and
Congruencies, Area and Holonomy, and Sum of the Angles of a
Triangle. 1
credit.
Math
929. Directed Reading
A directed reading project on a selected topic in mathematics
or mathematics education, planned in collaboration with a faculty member. 3 credits.
Back to the MST homepage
View the Summer 2008 class
schedule