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13 of 15 people found the following review helpful
on May 16, 2002
At first glance, the book appears too thin. But once you've delved a few pages into it, you immediately recognize that the author has simply mastered the art of brevity - while remainining eminently readable. The book covers all the material needed for an undergraduate analysis course - and covers it extremely well. The proofs are easy to follow and extremely instructive, so that the book can also be used in a "Bridge to Advanced Mathematics" or "How to do Proofs" that some schools offer to their math majors to ease the transition from problem-based lower-division courses to proof-based upper-division courses.
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4 of 4 people found the following review helpful
on March 14, 2012
This book broke me into analysis. It gives the reader a gentle introduction to the subject. The proofs are rigorous and easy to follow. Before embarking upon an analysis class, a person should take an introduction to proof class. Without such a class, the language of analysis will make no sense to the reader. For example, if you do not know how to do proof by induction, then you will struggle in analysis. The negative reviews for this book likely stem from readers who did not take such a class. Thanks to this book and Munkres' topology, I am now able to read and enjoy Baby Rudin. Baby Rudin is good, but I would not have liked it without first using Munkres and Gaughan. Note that Gaughan is not a complete substitute for Rudin. Rudin is general whereas Gaughan focuses mainly on the real line. Albeit, Gaughan is much easier on a reader who is new to the subject. Gaughan's treatment of sequences sets the stage for the book. He then goes into continuity and uniform continuity. The definitions and theorems are lucid. Gaughan then delves into differentiation, integration, and power series. The ordering of the topics allows the reader to move from topic to topic without having to flip back and forth through the book.
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6 of 7 people found the following review helpful
on December 7, 1998
The proofs are well structured and easy to follow. The techniques used in the proofs lend themselves for use in other situations. A lot of information is embeded in the exercises which keep the students alert and focused and at the same time saves time and space. A good book for undergraduates in mathematical analysis.
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2 of 2 people found the following review helpful
on December 20, 2013
I greatly appreciate the fluency of the logic and discussion found in this book. It was fantastic. I've attempted this course at another school using the professors notes (it was death). This book is so much easy to use and understand; it was a night and day difference. There seem to be a lot of different methods for proving these basic theorems inherent to the concepts and principles underlying calculus and this book is very clear and smart about accomplishing this task. I would recommend this book and I am not going to sell it. It is great.
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8 of 12 people found the following review helpful
on March 3, 2006
Although this text has quite a few good projects and problems, it is a bit too concise particularly for the student who is new to anaylsis. While all the major theorems are presented with proofs, some of the proofs are quite difficult to follow and many involve "hand-waving" in the proof. For the new student, this may cause a bit of confusion. Also, when a student goes to complete the homework, they may not be as clear and rigorous as necessary. It could also do a bit more in ways of visual arguments to help clarify the concepts being proved. The projects are probably the best part of the text because they have some of the classic calculus concepts built up by the student. I would have also appreciated a selected solutions or more helpful hints on some of the more difficult homework problems.
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on June 14, 2014
Though I don't like bringing in the atmosphere in which the book is used, intro to analysis really suggests that this is going to be a students first exposure to rigorously enforced proofs. The book, therefore, is probably going to be hard to understand, and with a book that's so concise about it's explanations really can only be used in a setting where the teacher is going to provide the foundations of understanding the symbols and logic behind the proofs the book tends to breeze through. The class I was in took so long to understand the concepts we hardly made it anywhere in this book. So in a class where you're lectures expose you to the terminology and general shape of the proofs so that you can decipher the book I'm sure this could be used. If you're not getting that in your class maybe you'll want to find some additional reference material that will walk through it a bit slower.

Mindless complaint: Really wish authors wouldn't start with a Chapter 0. It makes it feel so unimportant.
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3 of 5 people found the following review helpful
on August 21, 2011
I was introduced to this book in my junior-year analysis course called Adv Calc 1. At the time I found it to be very fun to read, mostly very clear in its presentation, and well-motivated. One drawback of this book is that the material covers only single-variable analysis, and then the reader who wants to learn multivariable calculus has to go to another book where he has to get used to different notation, different emphases, different definitions of continuity, etc. This is unfortunate for someone who wants a unified perspective.

(As an aside, for Adv Calc II, my class used Friedman's Advanced Calculus, which I found impenetrable. I would not recommend this book.)

Then I discovered Fitzpatrick's text Advanced Calculus, which covers both single- and multi-variable calculus. What's more, it outdoes Gaughan's text in terms of clarity, motivation, simplicity, and everything else. I can't recommend Fitzpatrick's book enough.
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on November 1, 2014
Good textbook. Not expensive, and easy to read. Not enough pictures and explanation though
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3 of 5 people found the following review helpful
on February 5, 2000
I used this book for an undergraduate course in Analysis and was pleased with it. It is well-organized with poignant examples. The physical construction of the book, however, proved not to be as good as the content and it is quite worn.
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on January 12, 2015
Shipped on time and in condition as stated. Would buy again. Thank you!
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