Understanding Analysis
  • Understanding Analysis
  • Understanding Analysis
  • Understanding Analysis
ISBN: 1493927116
EAN13: 9781493927111
Language: English
Release Date: Aug 22, 2016
Pages: 312
Dimensions: 0.94" H x 9.29" L x 6.46" W
Weight: 1.41 lbs.
Format: Hardcover
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Book Overview

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. The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination.

This new edition is extensively revised and updated with a refocused layout. 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. 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.

Reviews from the first edition:

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 Read More chevron_right

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Book Reviews (16)

5
  |   16  reviews
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5
   Amazing
By far the best introductory analysis book and one of the best introductory math books around. One of the few math - texts books so well written that it is easy to learn and study from even a non-math major while also being rigorous and concise.
 
5
   Actually readable, while still conveying the core ideas of analysis
We used it for the first semester for real-world analysis for over a decade, targeted at an audience that includes math majors, minors and mathecon concentrators. It is perhaps the only textbook I ever used for any math course that students say they like on course evaluations. It is readable and approachable. It is not as intense as quite a few other classics, and when you dig it, you get the sense that it is missing some key idea, but when you skim it, this idea is actually there, at least at an introductory level. The old issue was probably a little light on good HW problems -- we added some -- but the new issue has made substantial revisions to the problems, so that quite possibly further supplementation would not be necessary. If you are looking for the most advanced introduction to real analysis, this is probably not the book for you.
 
5
   I wasn't disappointed. Dr
I was not disappointed. Dr. Abbott does an excellent job of explaining the concepts.
 
5
   Amazing book
When I began reading the analysis, I was disappointed that I was asked to start with Rudin's book. But this book was probably inexcessible because I come from an engineering background. I started reading Apostol in search of more readable books. It was pleasant, but I was not readable on the subject. I recently came across Abbott's book and was completely blowing away. It is just amazing. It makes the analysis exciting and you learn a lot at the same time.
 
5
   A Joy to Read
This is my first book of analysis. I have therefore no basis for using it as an analysis book. But as a math book, it is honestly the most readable and enjoyable book I have ever read.
 
1
   A book which is too unfocused for beginners
I have tried to teach from this book, and my students found it difficult because many of its exercises are not properly prefaced in the sections for which they were intended. The order of the ideas is also random and the general presentation assumes far more mathematical knowledge and familiarity with basic concepts than can be gleaned alone from its pages. An extension to the initial section on specific theory and mappings would be helpful in presenting the presentation. In the wrong places, many sections are unfocused and unnecessarily chatty. It is an expensive book, but the masterful introduction by Bartle and Sherbert is well worth the 5 times its price.
 
3
   Adequate, but missing solutions is frustrating.
It is a good introductory book, but it leaves a prodigious amount of the theorems as exercises. This makes studying the book in a time crunch very difficult. Still, it is easy to understand the explanations given.
 
4
   I recommend this book if your goal is to understand analysis.
In fact, this is the whole reason I bought the book. I needed a book where I can learn many basic topics of real analysis by myself. If you want to paint a clear picture, go for this book. The only reason this book did not receive 5 stars is because the problems, which are good problems, did not provide hints for more challenging ones. Taking this course with others could make this perspective very different, though. In all, a good book.
 
5
   A MUST for anyone being introduced into the world of Real Analysis!
Real analysis begins when mathematics becomes truly complicated for the aspiring student when you have to start looking beyond the linearity of mathematics and take a step back to see the big picture for what it is really. There are plenty of other books on this topic by other authors, e.g. Rudin, Gaughan, Wade, etc... But for anyone who doesn 't understand what is going on, these books will make you think that mathematics is impossible. Part of the problem with other books on this subject is that they assume that the reader understands and follows their every move, and if not, that they can work it out by themselves. This is, however, a terrible mistake and Abbot makes no assumptions other than the absolute necessary basics. He realizes he is not writing his book for teachers and other scholars, but writing for the student.
 
2
   The book's examples and exercises are a stumbling block.
I have been studying math for about 5 years and now I am self-studying analysis. But I found that the examples that Abbott presents are not transparent at all. Just the opposite, I have to find other sources that explained the exact same examples in a much clearer fashion. This is a flaw in learning this subject, which could have been corrected if the author had chosen to do so. While the text is clear and well-written, mathematics is a significant stumbling block.
 
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