What Independent Math Study Topics Should I Explore This Summer?

[papernail]

Hey everyone,

I've been thinking about my summer, and I would like to do some sort of research. I applied for some REUs, but it doesn't look like I've gotten into any. However, I would still like to learn something this summer.

I've taken DE, Linear Algebra, Abstract Algebra, and Statistics. I really enjoy Abstract Algebra, so I would perhaps like to learn something more about group theory or something like that. I've talked to a few professors about their plans for the summer, and it looks like I may be able to do a little with them, but I don't know that I'll have the time available to go to Nashville and do full time research.

So, I'd like to perhaps see some interesting problems I could work on over the summer, or just to learn more about Algebra.

I'm planning on taking Number Theory, Intro to Logic, and History of Math next semester, so I've considered trying to get an introduction to number theory by reading some textbook. I don't think that's my best option, so I'd like to try and do some sort of independent study instead.

Do you guys have any ideas?

Thanks

 

[owlpride]

I've considered trying to get an introduction to number theory by reading some textbook. I don't think that's my best option, so I'd like to try and do some sort of independent study instead.

Aehm... Isn't Independent Study a.k.a. reading a textbook on your own? Or are you looking for suggestions for an independent study topic that is not part of your regular coursework?

 

[Jacobpm64]

if you like algebra, pick up something like hungerford's graduate algebra textbook and work through it

 

[papernail]

Aehm... Isn't Independent Study a.k.a. reading a textbook on your own? Or are you looking for suggestions for an independent study topic that is not part of your regular coursework?

Yeah, when I said independent study, I more meant topics that aren't a part of my regular coursework, rather than just trying to get ahead on my courses for next year.

 

[qspeechc]

Well, real analysis looks conspicuously absent from the list of things you have studied so far, maybe you want to read up on that?

 

[papernail]

Well, real analysis looks conspicuously absent from the list of things you have studied so far, maybe you want to read up on that?

At my school, real analysis is only offered in the spring, so I'll be taking it Spring 2010. On a related note, I'm not planning on taking complex analysis. Is that a bad idea, or should I be ok to avoid it?