Independent branch of Mathematics?

[1mmorta1]

I have done well in undergraduate mathematics, and would like to do some self study in something more advanced and stimulating.

I am interested in concepts such as number theory and set theory, or any type of mathematics that can be used to study systems of information, behavior...anything beyond your "daily" mathematical calculations.

The problem is that I've noticed I often don't understand some of the basic concepts in advanced mathematics books. I recognize that this just means I have more learning to do before I can begin studies in those areas :)

My question is if there are any advanced areas of mathematics that are self-contained, that I could study from the ground up without having to understand some of the more advanced undergrad subjects. (i.e. can I study [insert branch here] without mastering lie groups, or having taking coursework on mathematical proofs, and so on and so on)

I am certainly not mathematicaly incompetent, but I'm also not a graduate student. I was thinking perhaps number theory or game theory could be prime candidates, but don't want to purchase any materials only to find out they are beyond me.

Does anyone have any recommendations?

(This question may need to be moved from this thread, I wasn't sure where the best place to post it would be)

 

[mathman]

Number theory is probably your best bet. Game theory might need calculus. If you have had calculus, there is much more open.

 

[Bacle]

I think combinatorics is also a pretty good bet.

 

[1mmorta1]

Thank you guys. Calculus won't be a problem :) Wow, there is an awful lot to combinatorics.