Understanding Analysis

The choice of topics is a happy combination of the essential and the interesting, all truly leading to an understanding of what analysis is and what questions it addresses, aided by the author s extraordinarily lucid exposition. Summing Up: Highly recommended. Upper-division undergraduates. (D. Robbins, Choice, Vol. 53 (2), October, 2015)

This is the second edition of a text for an undergraduate course in single-variable real analysis. The topics covered in this book are the ones that have, by now, become standard for a one-semester undergraduate real analysis course . Overall, this book represents, to my mind, the gold standard among single-variable undergraduate analysis texts. (Mark Hunacek, MAA Reviews, June, 2015)

This is a dangerous book. Understanding Analysis is so well-written and the development of the theory so well-motivated that exposing students to it could well lead them to expect such excellence in all their textbooks. Understanding Analysis is perfectly titled; if your students read it, that s what s going to happen. This terrific book will become the text of choice for the single-variable introductory analysis course; take a look at it next time you re preparing that class.

Steve Kennedy, MAA Reviews

Each chapter begins with a discussion section and ends with an epilogue. The discussion serves to motivate the content of the chapter while the epilogue points tantalisingly to more advanced topics. I wish I had written this book! The development of the subject follows the tried-and-true path, but the presentation is engaging and challenging. Abbott focuses attention immediately on the topics which make analysis fascinating and makes them accessible to an inexperienced audience.

Scott Sciffer, The Australian Mathematical Society Gazette