This book outlines an elementary, one-semester course that exposes students to both the process of rigor, and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. -Scott Sciffer, The Australian Mathematical Society Gazette, 29:3, 2002. and makes them accessible to an inexperienced audience.
Abbott focuses attention immediately on the topics which make Analysis fascinating ...
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. ...
The discussion serves to motivate the content of the chapter while the epilogue points tantalisingly to more advanced topics. -Steve Kennedy, The Mathematical Association of America, 2001 Each chapter begins with a discussion section and ends with an epilogue.
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.
Understanding Analysis is perfectly titled; if your students read it that\'s what\'s going to happen. ...
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.
Reviews from the first edition: This is a dangerous book.
New features include a discussion of infinite products, and expanded sections on metric spaces, the Baire category theorem, multi-variable functions, and the Gamma function.
In addition to the inclusion of extra exercises, the quality and focus of the exercises in this book has improved, which will help motivate the reader.
This new edition is extensively revised and updated with a refocused layout.
The philosophy of this book is to focus attention on questions which give Analysis its inherent fascination.
The aim of a course in real Analysis should be to challenge and improve mathematical intuition rather than to verify it.
This book outlines an elementary, one-semester course that exposes students to both the process of rigor, and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable
