Department of Mathematics

Mathematics RET Description: Participating teachers will raise their level of understanding of relevant mathematics by engaging important topics in a “hands on” way in the workshop. They will be able to transform what they have learned into new curricular materials that will improve the mathematics abilities of their students and hopefully stimulate them to consider a career in science. Each of the proposed topics is accessible to high school mathematics teachers, but each also leads naturally to many substantial and interesting mathematical issues. The teaching assistant and mentors will introduce the topics, providing background and initial exercises as necessary, but the goal will be to shift the focus to the teachers who will pose and investigate questions according to their own interests and abilities. The mentors and assistant will serve as catalysts and advisors in the process. Teachers will engage one or more topics of relevant, horizon expanding, mathematics. Below is a list of possibilities. Final choices will be made in consultation with the participating teachers. Teachers will be able to choose from the following projects.

Project Descriptions: ARCHIVES

1. Elementary Coding Theory (ISBN code, constructing good codes).
2. Strange Curves (A curve constructed with tiles, Peano curves, related computer programs).
3. Some Elementary Number Theory (Fermat’s Little Theorem, modular arithmetic, RSA encryption).
4. Some Probability Theory (Shared birthdays, normal bell curves). 
5. Rational and Irrational Numbers (p and e, and Euler’s argument). 
6. Fibonacci Sequences and the Golden Ratio (Occurrences of Fibonacci in art and nature, some of the theory).
7. Population Models, Fractals, and Dynamical Systems (applications of elementary calculus).
8. Elementary Calculus and the Flight Paths of Spacecraft (The full set of procedures of basic one variable calculus in action, combined with NASA data from the Voyagers and Cassini).

These mathematics projects will be directed by Professors Diller and Hahn, and Teaching Assistant Margaret Doig.

Further Information. Applications are due April 15, 2005. Teacher stipends are in the amount of $1500 for this 4 week, 3 hours per day research experience.