I will be adding to this list through the term. Although I have several ideas in mind, feel free to suggest your own topic. Let me know, to avoid duplications if possible (on the other hand, if you really want to work on a topic that somebody else has already chosen, that should be fine as well).
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.
Suggested topics:
- The Banach-Tarski paradox. (Chosen by two groups:
- K. Williams.
- J. Giudicelli, Ch. Kelly, and J. Kunz.
- Quaternions and Octonions.
- The 17 plane symmetry groups.
- The word problem.
- The Gordon game (See 5.5.2 on the book.)
- The Redfield–Pólya enumeration theorem.
- Character theory.
- Conway polynomials (See 12.2.3 on the book).
[...] addition, you will be assigned a project (to work in groups of two or at most three), to be turned in at the latest by the scheduled time of [...]