The Real Analysis Lifesaver, by Raffi Grinberg, Princeton University Press, Princeton, New Jersey, 2017. 200 pp., $27.95(paper). ISBN 9780691172934.
Five out of five stars
For most students that take a class in real analysis, there is a rough beginning. They may have struggled a bit with the epsilons and deltas in calculus, but they ultimately triumphed. However, the bar of rigor and detail is dramatically raised in analysis, leading to frustration and uncertainty.
This book is designed to provide the reader some insight into the fundamental material of a real analysis course. As a veteran of that specific war, I certainly recognized the material, the general content was identical to what I worked through. The perspective is different, in the sense that it is a bit more chatty that the usual math book, although the attempts at humor are weak. For example, in the middle of the discussion of the Cantor set on page 119, there is the aside “It is real and perfect (just like you, you special snowflake) . . . “
The explanations are rigid in the sense that no formula is spared, from that perspective it is a typical math book. Detailed proofs of the theorems and lemmas are all included. Yet, there is a lightening of the prose that makes the book more readable than others in the field. It is not a traditional textbook in the sense of containing worked examples or any other exercises. If you are studying real analysis and are looking for another book to read in order to experience a different perspective, this book will serve you well.