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I am looking for suggestions on books to use for self study over the summer. I'm just finishing my first year calculus class intended for math majors. We've used Stewart, and I've enjoyed it. I've also taken statistics for economics, and a mathematical economics class.

With what I've learned so far, what would be a good next step? I will be taking Linear Algebra in the fall. I've bought How to Prove It: A Structured Approach, and I will be reading it and going through it carefully. What else is open to me based on my current knowledge? It's mainly for interest, but anything that can help me be a better mathematician would be great.

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Number theory!!!!! Try MIT open courseware or Stein's book (with sage) and this site for questions. – bgins Mar 30 '12 at 8:51
Stein's book is here and a website for a recent course he taught with it is here. Number theory is an effective bridge between the elementary math courses you've taken until now and the higher levels of abstraction that await you. There are tons of materials available for self-study. Learning proofs, learning sage, and learning some number theory will work together synergistically and provide you with an excellent springboard for future success in and enjoyment of mathematics. – bgins Mar 30 '12 at 9:20
I would recommend "Proofs from the book" by Martin Aigner, Günter M. Ziegler, Karl H. Hofmann. – Kirthi Raman Mar 30 '12 at 11:57

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