Math Explorations

Why do so many people like math? It's true! Many people actually enjoy the beauty of mathematics (besides using it every day in their work and life). Maybe it is because they see some "inner secrets," or perhaps they understand that math is so much more than just rearranging symbols on a piece of paper. This summer, we want to open your eyes to the "secret knowledge" of higher math. We plan problem solving, discussions, brainstorms, and independent and group investigations. We have picked a variety of the most intriguing and fun topics that mathematics can offer. The math that you already know is enough to start understanding these topics. As participants of Math Explorations, you can expect to enjoy new experiences, to become familiar with concepts of higher mathematics, and to see the connections between these concepts and their relations to other areas of life and science and the world around us.

Participants will work both in teams and individually in a supervised, highly interactive, hands-on learning environment. When appropriate for the topic, participants use laptop computers with a high-speed internet connection.

**Possible topics: **

- Paradoxes and math history. We present things that "just can't be true" but are, and things that appear to be true but aren't! The topics include Zeno's paradoxes and calculus, incongruency paradoxes and irrational numbers, Russell's paradoxes and set theory.
- Stories and graphs. Students will transform stories into graphs and graphs into stories. We plan to discuss slope, concavity, area under curve (as introduction to integration and differentiation).
- Museum of math abuse. Truth or Consequences! How can you tell when someone is lying with percents or lying with probability? We also plan to investigate data manipulation, misleading data representation, and interpreting information.
- Our favorite weird math objects. The unit is devoted to the objects such as Mobius strip, Sierpinski fractals, and the Cantor set.
- Math connections. We start from one problem and move to new topics from different domains of math, clearly showing the connections.
- Topics of students' choice. Students will help design some of the sessions, drawing from earlier topics that captured students' interest, as well as from new questions or puzzles they wish to discuss.

**Facilities and equipment:** All activities take place at the Shodor offices at 807 East Main Street, Building 7, in Durham,
NC. When appropriate for the topic, participants use high-speed laptop computers connected
directly to the Internet via a T1 line (about 50 times faster than a 28.8 K modem).

**Prerequisites:** Participants should be rising 6th to 8th graders (or the homeschool equivalent); younger or older
students who are interested may also be considered. Most topics only require the knowledge of very
basic arithmetic, yet lead to more advanced math. Students should have the desire to participate
in the course and to explore mathematics.