Suggested Projects for Math 640: EXPERIMENTAL MATHEMATICS, Spring 2013

First posted: March 18, 2013

Last Update: April 22, 2013

First draft due May 6, 2013, 10:00pm . It should be in the same public-secret directory (em13) where your homework resides. As with the homework, please indicate whether you give me permission to post it for the whole world to see.

Feel free to propose your own project! As long as it uses Maple (or even Mathematica, or SAGE) in a non-trivial way it is fine. I prefer that it would involve Games, but you are welcome to do it on anything mathematical. After all, the whole of math is a game!

NOTE: Any project can be done by n people, with 1 ≤ n ≤ 2 .

Untaken Projects

• Study Conway-style games abstractly, and enumerative aspects.

• Pick any (interesting) game and write programs for finding its Conway values (if it is partizan) and its Sprague-Grundy function if it is non-partizan

• Study gambling trees and Black-Scholes from a symbolic-computational point of view
  

Taken Projects

• Jake Baron's Proposal to study the triangle-free process.

• Philip Benjamin's proposal to study Abstract Solitaire Games .

• Ross Berkowitz's proposal to study the Shepp Urn .

• Patrick Devlin's proposal to study randomly chosen determinstic games (as in class 6)

• Tim Naumowitz's proposal to study the Wythoff game.

• Viraj Pandya's proposal for "space exploration".

• Joey Reichert and Vaibhav Verma's proposal to study Tic-Tac-Toe and variants.

• Matthew Russell will explore Iterated Prisoner's Dilemma

• Nathaniel Shar's proposal Develop a toolbox for automatic construction of bijective proofs to combinatorial identities

• Thom Tyrrell's proposal to study some diophantine questions.

• Tomas Vyskocil will write a program that tells you how to play Backgammon optimally, for a general board with b points and house-size h, and any arrangement of pieces. (For the usual one, b=24, h=6).

• Study the centepede game [Claimed by Alex Weiner]

  Alex's plan:
  "For my project, I would like to make a model of the quasi-centipede game as discussed in the paper "The Evolution of Cooperation in the Centipede Game with Finite Populations" by Rory Smead. It is a variation on the centipede game where both player make the decision simultaneously."