Customer Reviews

Introduction to Analysis

5 star:		(3)
4 star:		(2)
3 star:		(2)
2 star:		(2)
1 star:		(1)

 

 

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.

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.

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.

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.

I can't believe this is the book my advanced calc 1 class used at university. They sold it to me for $114.50+tax! This is a deal here. This class was the hardest class I took for undergrad. The book was no help. I learned everything I knew from the teacher and from the Internet/study groups. I do like how organized the book is, but the information was impossible for me to learn from the book.

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.

I had to get this book for my advanced calculus class. There are 3 issues I have with this book. First, that the material in any given chapter gives what is needed to work most, BUT NOT ALL, of the problems at the end of the given chapter. Second, having solutions to selected exercises is a good tool to have, and if an instructor disagrees, he or she can just assign problems that don't have solutions given. Not all students would use those solutions, but it's nice to have to verify one is on the right track. Third, the author does not explain things as clearly as other authors do. He (assuming Edward is male) could have explained things much better without adding a single word to the text. I find myself frequently referring to 'How To Prove It' by Velleman, since Velleman explains things much better. In short, this book is not the worst I've seen, and I would give this book 3 stars, were it not for the price.

As a math major, I am of course interested in the subject of Real Analysis. But I cannot agree with the other reviews in that the book is very UNACCESSIBLE to undergraduates! I have poured through the first 3 chapters until I almost have them memorized and the concepts are NOT CLEAR. Instead of explaining what is going on, the author rambles on about the "beauty" of his subject and how "we" as students should "carefully" digest the ideas. The examples and proofs are NOT clear and are NOTHING like the HW problems! In fact the proofs are so incomplete, that proving them in the fashion that the author does, does not convince my professor??? This book is a BIG waste of over $100 and a class that I might have enjoyed if the author could see outside of his ego and stop trying to show off to undergraduates who do not know the subject yet!

In my college days ,i found Edward D gaughan's 'Introduction to Analysis',amidst pile of other books.I read the preface countless times.With his words of encouragement and admonishment ,writer makes you more comfortable ,in your long journey of Mathematics which is real and abstract at once!! I liked this book;After a decade still i fondly remember this book !!I recommend this book whole heartedly, to any one who is sincere in his approach and wants to become first rate mathematician.

I believe the author has given students a wonderful text for the beginning of analysis. I disagree with the student who stated that the proofs are unclear. When I took this class last fall, all of the proofs were not clear in the beginning but with a little clarifying by my professor, they quickly became understandable. The problems at the end of the sections are designed to help students fully understand the chapter and while some of the problems require a lot of extra work, they are not impossible. It seems to me if you gave this book a bad review, it was because you were unwilling to put forth the time and effort to fully understand the material. This book was extremely helpful and guided the class in a clear and concise manner.