proof background required for Courant's "Introduction to Calculus and Analysis"?

Question

I am considering reading Courant and John's famous Introduction to Calculus and Analysis as a reintroduction to, and to expand my understanding of, calculus. I was reading reviews on Amazon, and one reviewer said:

While Courant's insistence on proof does mean that the student needs to have a 
basic grounding in proof methods, this is usually a standard part of the 
undergraduate curriclum.

How much understanding of proofs do you think is necessary? I have read a few proofs in an introductory statistics textbook and seemed to understand them, but I don't have any sort of background in "formal proof theory," if there is such a thing.

Do you think any other books are a prerequisite and if so which ones?

Answer 1

You won't need much of a background. Books like that are designed to be first courses in proofs. If you want, you could use something like Richard Hammock's "The Book of Proof" to get a quick introduction to proof logic, and then head into Courant.

Answer 2

I think that one the best way to develop proof skills is to solve demonstrative problems. There are also good books like:

• Problem-Solving Strategies by Arthur Engel
• How to Solve it by George Pólya
• The Art And Craft of Problem Solving by Paul Zeitz

These books contain many challenging problems. Maybe you was searching for standard form of proofs but I think it's more important to fully understand the reasoning behind a solution. The formal writing is a conseguence of it.