Discrete Mathematics
A course description will be
available soon.
Session 2 (July 14 - August 2)
Prerequisite(s): Parrticipants must have completed math courses
through pre-calculus.
Age and grade requirements: 9th 10th or 11th grade
in Spring 2008, and age 14 - 17 on July 14, 2008.
Top
Mathematical Logic and Problem Solving
This course is for those who
delight in solving challenging math problems and who would like to further
develop both their problem-solving and their logical-reasoning skills. Problem
solving is the activity of the mathematician, and logical reasoning is the
framework for this activity. Here we give an introductory course in logic,
drawing from examples outside of mathematics but focusing on the use of logic
within mathematics. Students are introduced to the basics of propositional and
first-order logic, and this gives them access to formal notions of familiar
logical methods. Additionally, students discover how their formal understanding
can be used directly to help solve certain mathematical problems. But logical
reasoning is not all there is to problem solving. Good problem-solving skills
include ingenuity, creativity, and the ability to apply a variety of strategies
and techniques. In this course, students are taught fundamental tools and
standard techniques for problem solving, and they are given the opportunity to
develop their mathematical ingenuity through practice on problems in a wide
range of difficulty. The mathematical subject areas that the problems are drawn
from include set theory, number theory, and combinatorics - none of which
require more background than algebra.
Session 1 (June 22 - July 11)
Session 2 (July 14 - August 2)
Prerequisite(s): Completion of an algebra course.
Age and grade requirements: 8th or 9th grade
in Spring 2008, and age 13 and age 15 at start of session. Students will be
assigned to sections according to age and grade.
Top
Math Olympiad Problem Solving
Mathematics contests have been
gaining popularity in recent years, now with over half a million students in the
U.S. participating in the American Mathematics Competition (AMC) exams each
year. In the way that participation in sports provides an opportunity to build
fitness through an enjoyable activity, math contests provide the opportunity to
build mathematical knowledge and skills through an activity that many find
pleasurable, exciting and fun. This course is for those who enjoy finding a
solution to a difficult problem, as well as for those who simply want to improve
their performance on the AMC or similar exams. The course draws problems from a
variety of sources and spends time developing mathematical material that is
commonly found on math contest exams at different levels.
Session 2 (July 14 - August 2)
Prerequisite(s): Completion of an algebra course. Students who have
taken second year algebra, pre-calculus, or other courses beyond algebra may be
placed in a more advanced section.
Age and grade requirements: 9th or 10th grade
in Spring 2008, and age 14 - 16 on July 14, 2008.
Top
Non-Euclidean Geometry
This course is for students who
have completed a course in geometry and would like to learn more. Taught
at the advanced undergraduate level, Mathematical Investigations: Geometries
challenges students to stretch their logical, mathematical, and creative
abilities. Topics include a review of the axiomatic development of Euclidean
geometry, advanced problem solving, and an introduction to non-Euclidean
geometries, including elliptic geometry and hyperbolic geometry. The discovery
of non-Euclidean geometries in the late 1800s shattered the traditional
conception of geometry as the true description of physical space. This discovery
was fundamental in Einstein's development of the theory of relativity, and it
has played an essential role in modern theories of the universe. This course
provides an excellent opportunity to reinforce a solid foundation in geometry,
build geometry problem-solving skills, and gain a taste of some of the most
fascinating developments in the field.
Session 2E (July 14 - August 9)
Prerequisite(s): Completion of courses in algebra and geometry.
Age and grade requirements: 10th or 11th
grade in Spring 2008, and age 16 - 17 on July 14, 2008.
Top
Number Theory
Number theory, the study of
properties of integers, has attracted the interest of mathematicians for over
4000 years. This branch of mathematics continues to be an area of intrigue and
active research. For some, the attraction is the possibility of solving a
problem that has remained unsolved for hundreds of years; for others it is the
pure beauty of a branch of mathematics where the basic concepts are easy to
understand, yet the techniques are deep and intricate. Number Theory is also
important for its applications in cryptography, which are routinely applied to
insure the secure transmission of information over the internet. In this course,
students learn about unique factorization, the Euclidean Algorithm, congruence
arithmetic, the Fermat/Euler Theorem, Diophantine Equations, Fibonacci Numbers,
and other topics.
Session 1 (June 22 - July 11)
Prerequisite(s): Completion of an algebra course. Students who have
taken second year algebra, pre-calculus, or other courses beyond algebra may be
placed in a more advanced section.
Age and grade requirements: 9th, 10th or 11th
grade in Spring 2008, and age 14 - 17 on June 22, 2008.
Top
Topology: Knots and Surfaces
A course description will be
available soon.
Session 1 (June 22 - July 11)
Prerequisite(s): Completion of an algebra, geometry, and
trigonometry course.
Age and grade requirements: 10th or 11th grade
in Spring 2008, and age 15 - 17 on June 22, 2008.
Top
|
