Math Explorations at Sigma Xi

**Please Note:**

This workshop is held at the Sigma Xi facility in RTP. Participants staying the whole day are expected to bring a packed lunch. There are no microwaves available for workshop participant use. Pick up is at 4:00pm. Participants that remain after 4:20pm will be charged a $25 dollar fee that will be added to the cost of the workshop. ALL participants must be picked up by 5:00pm when the Sigma Xi facility closes.

**Location:**

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. Students will engage in 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.

**Facilities and equipment:** All activities take place at the Sigma Xi offices. When appropriate for the topic, participants
use high-speed laptop computers.

Participants will work both in teams and individually in a supervised, highly interactive, hands-on learning environment.

**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 objects such as the 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.

**Prerequisites:** Participants should be 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.