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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!

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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.

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  • $\begingroup$ 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, 2013 at 13:01
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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!

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  • $\begingroup$ Thanks! I'll certainly check it out! $\endgroup$
    – matt
    Oct 15, 2013 at 0:32

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