Can anybody give me a pure math honours thesis idea?

Question

So far I've looked at something on elliptic curves, but my profs say that those are too advanced to do anything interesting with at this level. Any ideas? (Oh, no analysis please. Anything else is fine).

Perhaps I should mention that I shouldn't do a topic in analysis because I've done quite a few courses in that area already and I want to try something different.

Answer 1

Presuming you took group theory, how about the transfer map? It looks a little complicated at first, but once you get by through a bit of notation it is extremely powerful and allows you to prove that all sorts of groups are solvable (a key part of the classification of finite simple groups).

For a quick intro to the transfer map (it does not contain the history), try Chapter 10 of the lecture notes by Boltje:

http://math.ucsc.edu/~boltje/courses/f99/m214.pdf


Or maybe you could do an introduction to category theory, defining adjoint functors and showing their relavance to many different areas of mathematics, including algebra, analysis and logic.

Of course, knot theory and graph theory are nice too, but they are terribly overused as thesis topics.

Answer 2

Sure. Get a copy of "A Course in Arithmetic" by Serre. Read up to Theorem 8 (Hasse-Minkowski), and then reprove everything for local fields of characteristic p>2 (finite laurent series over F_q). Can you say anything about the case p=2? Anything about non-finite fields? If you write it up nicely, send me a copy. Have fun.

Answer 3

If this is for undergrad, you could try knot theory or game theory. Both topics are easy to understand at the begining and you could easily pick a topic from them.

Answer 4

Why does taking the derivitive of the equation for the volume of a sphere give the equation for the area of a sphere ?

Answer 5

Altruism can't be shown. you may't be attentive to the authentic motives of yet another (or maybe possibly your self.) case in point, if somebody spends their existence giving, how can or no longer this is prevalent that that individual is appearing in basic terms out of compassion for others? the guy must be appearing on the basis that their movements will deliver approximately eternal salvation, or yet another advantages. additionally, it may look contradictory that a individual could improve a trait that did no longer earnings him/her. If a individual did improve the type of trait it ought to nonetheless be considered self serving. it may be self-serving in that it aspects what that individual needs -the survival of others. yet, while that's broken down, that's considered self-serving. it continues to be what the guy needs. truthfully, how do you define "organic compassion"? in case you mean "no longer out of self interest," then i could say that's impossible. no count how a individual acts they could act of their very own self-interest. whether it seems to be self-sacrificing. no count how self-sacrificing an act seems to be, it continues to be completed out of self-interest. Altruism is considered "selfless subject for the welfare of others." yet, evaluate the occasion of Christ. He knew that he could be crucified. yet his fee device precluded determination kinds of action. He does no longer have been waiting to stay with himself if he acted in a selfish way (averting dying.) via dying on the circulate he ensured the survival of his thought device which will properly be considered an extension of the self. i do no longer inevitably have faith the this, even with the undeniable fact that that's a valid argument. that's the place faith steps in. It can't be conclusively shown that altruism exists. yet human beings have confidence that it does.

Answer 6

Why pi (which describes the circle) has a nonrepeating, endless number stream associated with it.

Answer 7

If you are afraid of analysis you shouldn't be in maths.

Answer 8

How about efficient partitioning algorithms ?

Answer 9

http://web.maths.unsw.edu.au/~danielch/honthesis.html