A new math circle for middle school and high schools students is starting up today in Princeton, New Jersey! The legendary Professor John Conway is going to be giving a talk and Albany Area Math Circle founding member Alison Miller, now a math grad student at Princeton, will lead a problem session afterwards.
AAMC high school students who are leading middle school math circles may not be able to get John Conway to appear in person, but that doesn't mean you can't introduce the mathematical excitement of his work to your students.
Here's a video of John Conway talking about his work on cellular automata and The Game of Life:
If you don't know about his work on cellular automata and The Game of Life, you and your students are in for a treat. Visit this link to learn more about the concept and play an interactive version of the game.
Understanding the real world policy applications:
Conway's Game of Life relates very nicely to some extremely influential work done by economist Tom Schelling, who won a Nobel Prize for his work applying game theory to real life. Schelling's books are extremely well-written, lucid and thought-provoking. They don't require a lot of background. Micromotives and Macrobehavior is a good place to start. Schelling started working on models of racial segregation patterns in the 1950s and 1960s by creating simple cellular automata rules with pennies on a chessboard. Another great Schelling book has a title that I love and can (deeply!) relate to: Choices and Consequences: Perspectives of an Errant Economist. Here's a video from economist Tim Harford briefly presenting and discussing Schelling's model, using eggs to demonstrate cellular automata:
To explore the math more deeply:
Check out the links on this page at Wolfram demonstrations. The first page allows you to change parameters and visualize different ways that his Game of Life will play out, but make sure to check out the links on the right side of the page as well.
John Conway is co-author, along with Richard Guy and John Berlekamp, of a great series of books on mathematical game theory, called Winning Ways for Your Mathematical Plays. It's in the fun but deep and sometimes hard category--highly recommended for those who want to delve more deeply into this subject. Google Books also offers a limited preview of volume 2 of the series which I've linked below. If you follow the google books link, you can find what local libraries near you own the book.