The Real Analysis Lifesaver: All the Tools You Need to Understand Proofs (Princeton Lifesaver Study Guides)

I simply cannot recommend this book highly enough. The material is presented in a friendly, approachable manner that illustrates the concepts very lucidly with examples and engaging dialogue between the author and reader. One of the main difficulties that math students have with proofs is that proofs are often given as a final draft; the thought process and reasoning that went into tying the assumption(s) and conclusion(s) together are often omitted and this leaves the student perplexed on how to approach proofs. This book gives you a firm grounding in proof analysis as well as propositional and quantificational logic to become proficient in developing your own proofs. I genuinely feel that after using this book, a student will have a much easier time approaching proofs in other math classes. Using this book as a prerequisite to, or concurrently with, a real analysis course will be beneficial to you if you are struggling or just need a little extra intuitive help. Either way, you will not regret purchasing this book.

This book starts with familiar math topics, explains clearly the various methods of proofs, and then provides very clearly worked examples of each of those. I have a number of books on proofs, but this is the one I would most recommend for an introduction to the subject. (Note: I also have the Calculus Lifesaver, and it is also excellent.)

The book is very well written and very engaging. But it doesn't cover much material. It starts with basic proof methods and theory and stops at sequences. It would almost be better for a introductory general proof class instead of a real analysis class.

Excellent quality!

Before buying this, I thought the topics covered will include something like Arsela Ascoli theorem, or to the extent on Hausdorff measure. However, it's baby Rudin. The name for baby Rudin is principal of mathematical analysis, and the second book is called real and complex analysis! I don't know why the author write life savor for Real analysis...

A friendly presentation that is ideal for a basic introduction to analysis. An excellent supplement.

Using this book to apply to Real Analysis problems

How is a student supposed to know if they have filled in the blanks correctly if there are no answers in the book? The given examples are not closely related to the exercises (as claimed by the descriptions). The author smugly states that answers were not included because that would be too tempting. Well, I would rather know that I was writing the proof correctly and would not call it temptation. Produce an answer book, so the rest of us can earn a degree in math, not just enrich Princeton and its alum.