Ebook Free Understanding Analysis (Undergraduate Texts in Mathematics)

Ebook Free Understanding Analysis (Undergraduate Texts in Mathematics)

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Understanding Analysis (Undergraduate Texts in Mathematics)

Ebook Free Understanding Analysis (Undergraduate Texts in Mathematics)

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Review

“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 â€¦ and makes them accessible to an inexperienced audience.”― Scott Sciffer, The Australian Mathematical Society Gazette             

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Product details

Series: Undergraduate Texts in Mathematics

Hardcover: 312 pages

Publisher: Springer; 2nd ed. 2015, Corr. 2nd printing 2016 edition (August 22, 2016)

Language: English

ISBN-10: 1493927116

ISBN-13: 978-1493927111

Product Dimensions:

6.1 x 0.8 x 9.2 inches

Shipping Weight: 1.2 pounds (View shipping rates and policies)

Average Customer Review:

4.3 out of 5 stars

92 customer reviews

Amazon Best Sellers Rank:

#38,576 in Books (See Top 100 in Books)

By far the best introductory analysis book, and one of the best introductory math books around. One of the few math texts books that is so well written it is easy for even a non-math major to learn and study from, while also being rigorous and concise.

This is the most beautifully written book I have ever laid my eyes on. Abbot sent us a gift from above with this book. There never has been, and very well may never be, another textbook so well written as this one. I used this book in my first semester of real analysis as an undergrad and can confidently say that I understand the bulk of what analysis is about after having read this book. The reason I love this book is that Abbot presents an introduction at the beginning of each chapter that motivates what is about to come. Then after completing each section, he caps off the chapter with some sort of mind-blowing conclusion that builds on what you have been just studying for the last 3-4 sections. The definitions are consistent throughout the book as well. The definitions for convergence of a sequence, functional limit, continuity, uniform continuity, convergence of a sequence of functions, etc are all written with intimately close language and symbolic representation making it easy to see the similarities and differences between the definitions. Sorry Rudin, but this is the one true way to learn analysis. I highly recommend this to any professor who is thinking about using this text for their class. Anyone who attempts to use a text other than Abbot as the first exposure to analysis is doing their students a huge disservice.

If you want to learn analysis than this is the book you should buy. I have read many analysis books and this one is the best at explaining it with a wide range of problems to practice from easy to hard. My background in math is a BA from Rutgers Unversity.

A brilliant introduction to this often intimidating course! Abbott provides context and an authorial voice that brings the subject alive. Real Analysis is often thought to be the driest of math courses; in Abbott's hands, it is as provocative as it is necessary. We really do need epsilon and delta, because our intuition can lead us terribly astray when we encounter the infinite and the infinitesimal! What's the best use of this text? I'm not sure: I teach high school, so I am not burdened with having to make it stand in for a college text. If the goal is to create a lasting understanding of this foundational topic, then this is the book for you. I will never teach Calculus the same after reading this.

We've used this as a textbook for over a decade for first-semester real analysis, targeted at an audience that includes math majors, minors, and math/econ concentrators. It's maybe the only textbook I've ever used for any math course that the students say they like on course evaluations. It's readable and approachable. It's not as intense as quite a few other "classics", and when you skim it, you get the sense that maybe it's missing some key idea, but then when you dig into it, that idea is actually there, at least at an introductory level. The old edition was probably a little light on good HW problems -- we routinely added some -- but the new edition has made substantial revisions to the problems, so that quite possibly further supplementation would not be needed.If you're looking for the most advanced introduction to real analysis, this is probably not the book for you. If you want a book that students can actually understand, I think this is the one.

Once in a while, a book comes along that is so wonderfully written, the reader reflexively searches for other books by its author. Understanding Analysis is a prime example of this rare breed (Unfortunately, this is Abbott's only book as far as I know: write more!).Undergraduates often begin analysis courses with dread and finish in a state of utter confusion,knowing the definitions of key phrases, and sometimes even being able to supply proofs for some elementary results, but having no intution as to why the main theorems are pertinent.But it does not have to be so. 'Understanding Analysis' has the distinction of being so readable, it is sometimes difficult to pry oneself away from its pages and attempt the exercises. On multiple occasions I found myself skimming through the book and reading the various 'special topics' (e.g. Cantor Sets, Integration, Fourier Series) interspersed throughout the book to pique the readers' interest. But most importantly, a reader will come away with an understanding of many theorems in analysis. He or she will begin to develop a vocabulary of results that make sense both mathematically and intuitively, be able to use the results to complete the exercises (which are by no means simple 'plug-and-chug' problems), and be excellently prepared for study at a more advanced level.Bottom line: Abbott's book may not be encyclopedaic in content, but it, without a doubt covers a sufficient amount of material to warrant its use for a one-semester course in analysis. My only concern is that after such a fantasticly lucid treatment, students may have difficulty adapting to the vast selection of more advanced, less pedagogical texts available. I sincerely hope Abbott writes a sequel.

I bought this book to complement Steven Lay's text on the same topic. Abbott is clearer in the early chapters (with more motivation and background, too), which was a big help. But by the time you get to differentiation and integration, they're about the same in understandability.

The cover of this book is in fair shape but when I opened it pages literally fell out! They must have fallen out and then someone randomly stuffed them back into the book at random spots. For example I have pages from Chapter 4 randomly placed in Chapter 2 as you can see from the pictures.

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