I am thinking about taking the thesis route to complete my master in pure math. In anticipation of these in the coming semesters, here are my questions:
- Do you know of any links to archives of master-level theses, especially in Group Theory? I would like to get a feeling. I found one here but looks like it is for PhD level.
- Do you have any suggestions as to the possible topics, especially in Finite Group Theory, that I can bring up for discussion with my prof next semesters? (Shy not from suggesting any plain vanilla topics, for my school is only a non-flagship plain vanilla state school, and I am just an average plain vanilla student too -- but eager to move ahead.)
Thank you very much.
I am not aware of anywhere one can submit a master's thesis for specifically archiving master's theses online. I would imagine some universities do this in-house just as you discovered that UCSD does for its PhD student's theses (where I went to grad school they archived my PhD thesis on their library's website).
If your university doesn't archive your thesis in a satisfactory way, you could consider using the preprint archive: http://arxiv.org/
It's primarily for preprints of research papers (I have several of my papers posted there), but I've seen theses posted there as well. It's doesn't cost anything and is open to anyone.
As for a project, your best option is to pick the brains of your committee. While it's your project, you would be wise to pick a topic that the faculty there can help you with!
Two interesting master thesis topics (related to group theory) that came to mind are:
(1) The word problem in group theory: Given a group presented using generators and relations, can you tell whether a random element is actually equal to the identity? Surprisingly the answer is "No." The "word problem" in group theory is unsolvable!
I did a term project on that in grad school while I was taking a computer science course. Here's my presentation and term project. A great book to look at if you go with such a project is Joseph Rotman's graduate Group Theory text. The last chapter (I think) is about the word problem.
Exploring what can and cannot be computed in group theory can be fascinating. There's a lot to survey and I think would make a great thesis.
(2) Another interesting project would be to survey the "inverse Galois problem". Given an irreducible polynomial (with rational coefficients), one can compute the Galois group of that polynomial (the group of it's splitting field). An open question is "Which groups can show up as a Galois group of a (rational) polynomial?" Exploring what's known and what's still open would make a great project as well.
I hope this helps!