Math Thesis

i need some ideas for my undergrad math thesis, i'm gonna end up writing it some time in this next school year but i want to start some work this summer.

topics of interest (in order of interest):
galois theory
rings & modules
groups and group representations
number theory & group theory interactions
combinatorics

stuff i want to stay away from:
dynamical systems
numerical analysis
fractals!
goemetry

the only idea i've had so far, is maybe making explicit a specific galois correspondence for a particular group.

also, for those interested in some open math problems here is a nice website, although largely graph theory problems, and mostly grad level+
http://garden.irmacs.sfu.ca/

Britfag here. What kind of work does a "thesis" generally comprise? Is it supposed to involve original research, or what?

my school defines it as "substantial research effort and analytical thought" as defined by thesis advisor. i assume it should be somewhat original, but it is usually left unpublished, so the originality isn't as much of a concern as in a phd thesis.

This one looks pretty cool

http://garden.irmacs.sfu.ca/?q=op/what_is_the_largest_graph_of_positive_curvature

It sounds like you already have a strong preference for algebra over analysis.  Nullstellensatz maybe:

http://en.wikipedia.org/wiki/Hilbert's_Nullstellensatz

Do you have to give a talk?  Is the paper required for your major?

giving a talk isn't part of the requirement, but i do need to do write the paper to graduate.

another option is a seminar type research paper, but i feel like i need to do a good thesis to get into a good graduate school because my grades werent all that great my first two years (3.0 gpa after busting my ass this year).