<p>I'm going to be taking a class that covers a lot of topics that Calc III covers, but with much more theory. I thought it might be nice to get acquainted with theory before taking the class since I've never done any proofs or anything like that before.</p>
<p>What books do you guys suggest?</p>
<p>"How To Prove It: A Structured Approach by Daniel J. Velleman"
Definitely recommend this one. It is user-friendly and starts you off with simple techniques and proofs.
"The nuts and bolts of proofs by Antonella Cupillari". Personally haven't tried this one, but plenty of friends have recommended it and said it was just as good as Daniel's. </p>
<p>Now, if you're looking for a real and more rigorous challenge:
Spivak's Calculus 4th edition.</p>
<p>Thank you :)</p>
<p>i liked Apostol's calc book more than Spivak. Although, I've never read the second volume of Apostol's book.</p>
<p>I second Spivak! Used it in my freshman year math class- its amazing! (but a bit challenging)</p>
<p>Mmm not sure if the above posters are leading you in the right direction. If you really want to look into math theory you need more of an analysis book as opposed to a classic calculus text. In my basic real class we used a book by William Wade called "An Introduction to Analysis". The book covers calc I, II and III topics and their proofs. I honestly wouldn't recommend the book, but if you want gritty math theory, analysis type books are what you want to look at.</p>
<p>well, if you want an analysis book, then introduction to analysis by maxwell rosenlicht is very good and its cheap. </p>
<p>if you want something in between calc and analysis, then apostol is the book for you.</p>
<p>Fundamentally, proofs are just applying the definitions in order to make a sound reasoning. If you understand the concept inside and out and can write coherent sentences, then "doing" proofs shouldn't be a problem.</p>