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 Mathem
atical Society Gazette