Math Research

Math Research is a one-term math elective that can be taken in the winter or spring term by sophmores and freshmen. This class covers both topics taught and not taught in the Integrated Algebra, Integrated Geometry, and Algebra II and Trigonometry curriculums. It is currently taught by Mr. Rubinstein.

Homework is regularly given and a few quizzes will be given. However, the homework and quizzes are generally easy since Mr. Rubinstein gives a practice quiz very similar to the real quiz right before the quiz and he collects homework on a specified day, giving ample time to do it. Some topics may be taught in a few days or one to two weeks and the topics are generally interesting and easy to learn. Students will be given a month to complete tasks on Geometer's Sketchpad, a mathematical drawing program specially designed for creating geometric constructions and are required to submit a 12-page feedback. Tasks to be finished by Geometer's Sketchpad include creating fractals, reconstructing geometric proofs of the Pythagorean theorem and other theorems, reconstructing classic geometric constructions, squaring the circle, and constructing inscribed polygons. In the last month of the course, class-time is entirely devoted to working on a 12- page research paper about a mathematical topic approved by Mr. Rubinstein.

Possible Class Topics

 * Fermat's Last Theorem
 * Solving Rubik's Cube
 * RSA encryption
 * Chinese Remainder Theorem
 * Proving the Pythagorean Theorem
 * Pythagorean Triples
 * Pascal's Triangle
 * Combinations and Permutations
 * Continued Fractions
 * Amicable Numbers
 * Algorithms to Estimate Square Root Values
 * Euclidean Algorithm
 * Modules
 * Finding Functions for Geometric Series
 * Geometric Constructions