<p>The 2+2=4 stuff is just to get used to a few basic properties given in the introduction of the book. There’s no proving 1+1=2 in the sense of rigorous mathematical foundation (i.e. Principia Mathematica by Russell & Whitehead).</p>
<p>I’m willing to bet the class entails quite a bit of set theory. Naive Set Theory by Halmos is therefore a great complimentary text, I think. In fact, it’s recommended by Spivak at the end of Calculus.</p>
<p>EDIT:
I’ve talked to a grad student who said that most of his mathematical knowledge was learned independent of the classroom. My conclusion is that if you have the passion for the subject, you will succeed. At least, that’s what I’m hoping.</p>