The Advanced Calculus by Gilbert Weinstein was published in 1996 first. In the course you will learn Analysis, that is the theory of differentiation and integration of functions. However, you will also learn something more fundamental than Analysis.

You will learn what is a mathematical proof. You may have seen some proofs earlier, but here, you will learn how to write your own proofs. You will also learn how to understand someone else’s proof, find a flaw in a proof, fix a deficient proof if possible and discard it if not. In other words you will learn the trade of mathematical exploration.