305 – Projects

[Edited, April 3, 2012.]

As mentioned on the syllabus,

I expect groups of two or three per project. The deadline for submission is the scheduled time of the final exam. This will constitute 20% or your total grade. Your final project must be typeset; I encourage you to consult with me through the semester in terms of how it looks and its contents.

What I expect is a paper where you explain the topic, and present its history and a few results on it with complete proofs. Work out a few examples. If relevant, do some numerical simulations. List all the references you consult. (Of course, do not plagiarize.) Some of the topics may end up being too ambitious, and if that occurs, let me know. In that case, it would be better to restrict your presentation (to some aspects of the topic at hand) rather than trying to be comprehensive.

I’ll give you a list of references you may find useful once you pick your topic, but of course if you find additional references, use those instead.

Topics:

1. The Banach-Tarski paradox. Chosen by two groups:
   • K. Williams.
   • J. Giudicelli, Ch. Kelly, and J. Kunz.
2. The 17 plane symmetry groups. Chosen by two groups:
   • S. Burns, C. Fletcher, and A. Zell.
   • A. Nelson, H. Newman, and M. Shipley.
3. Quaternions and Octonions. Chosen by:
   • K. Mcallister.
4. The Gordon game (See 5.5.2 on the book.) Chosen by:
   • J. Thompson
5. The Rubik cube. Chosen by:
   • M. Mesenbrink, and N. Stevenson.