5
$\begingroup$

want to study math as a hobby. I find it very interesting, but I made a lot of twists and turns in college which lead me on a different path. Plus, I'm not really sure I'm gifted enough to hack it at the grad school level. I have taken Calc one and I have taken applied math classes for my economics major which involve some work with differential equations. I was wondering where I should go from here if I'm interested in Number theory and Combinatorics? I was also wondering how important Calc II and CalcIII are with regards to these areas of mathematics? What lower level maths should I read up on? Linear? Set theory? What books to people recommend? Should I get a tutor, or do you guys think it is conceivable to cover such advanced topics being an autodidact? Any answers would be helpful.

Thanks a bunch!

| cite | improve this question | |
$\endgroup$
4
$\begingroup$

You can start learning combinatorics with what you already have; any undergraduate discrete math text will have at least some of the basics, but I especially like Edward A. Scheinerman, Mathematics: A Discrete Introduction. Going beyond that, there is Miklós Bóna, A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory. I’ve also heard very good things about Arthur T. Benjamin & Jennifer Quinn, Proofs that Really Count: The Art of Combinatorial Proof. The last one requires a little more mathematical sophistication than the first two, but still not much in the way of technical background.

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ Thanks! Yeah I just wasn't sure what sort of background I needed because I had heard that combinatorics was kind of a broad field and it could really shoot up in terms of difficulty. If I wanted to look at the more difficult stuff, would it be enough to simply go through some of these texts you have recommended as a base, or would I have to learn other maths? $\endgroup$ – matt Oct 15 '13 at 13:01
3
$\begingroup$

Since you know some basic mathematics,i recommend ''Topics in the Theory of Numbers'' by Erdos and Suranyi.
It is a nice, simple book which studies Number Theory in a combinatorial way.
The arguments are simple and they start from the beggining.
I believe it will inspire you. Calculus might be helpfull, but what you really need is to be able to handle limits,equations and some polynomial identities.

Good luck!

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ Thanks! I'll certainly check it out! $\endgroup$ – matt Oct 15 '13 at 0:32

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.