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Real Analysis: Modern Techniques and Their Applications [Hardcover]

Gerald B. Folland
4.2 out of 5 stars  See all reviews (26 customer reviews)

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Book Description

April 7, 1999 0471317160 978-0471317166 2
An in-depth look at real analysis and its applications-now expanded and revised.

This new edition of the widely used analysis book continues to cover real analysis in greater detail and at a more advanced level than most books on the subject. Encompassing several subjects that underlie much of modern analysis, the book focuses on measure and integration theory, point set topology, and the basics of functional analysis. It illustrates the use of the general theories and introduces readers to other branches of analysis such as Fourier analysis, distribution theory, and probability theory.

This edition is bolstered in content as well as in scope-extending its usefulness to students outside of pure analysis as well as those interested in dynamical systems. The numerous exercises, extensive bibliography, and review chapter on sets and metric spaces make Real Analysis: Modern Techniques and Their Applications, Second Edition invaluable for students in graduate-level analysis courses. New features include:
* Revised material on the n-dimensional Lebesgue integral.
* An improved proof of Tychonoff's theorem.
* Expanded material on Fourier analysis.
* A newly written chapter devoted to distributions and differential equations.
* Updated material on Hausdorff dimension and fractal dimension.

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Real Analysis: Modern Techniques and Their Applications + Abstract Algebra, 3rd Edition
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Editorial Reviews

From the Back Cover

An in-depth look at real analysis and its applications-now expanded and revised.

This new edition of the widely used analysis book continues to cover real analysis in greater detail and at a more advanced level than most books on the subject. Encompassing several subjects that underlie much of modern analysis, the book focuses on measure and integration theory, point set topology, and the basics of functional analysis. It illustrates the use of the general theories and introduces readers to other branches of analysis such as Fourier analysis, distribution theory, and probability theory.

This edition is bolstered in content as well as in scope-extending its usefulness to students outside of pure analysis as well as those interested in dynamical systems. The numerous exercises, extensive bibliography, and review chapter on sets and metric spaces make Real Analysis: Modern Techniques and Their Applications, Second Edition invaluable for students in graduate-level analysis courses. New features include:
* Revised material on the n-dimensional Lebesgue integral.
* An improved proof of Tychonoff's theorem.
* Expanded material on Fourier analysis.
* A newly written chapter devoted to distributions and differential equations.
* Updated material on Hausdorff dimension and fractal dimension.

About the Author

GERALD B. FOLLAND is Professor of Mathematics at the University of Washington in Seattle. He has written extensively on mathematical analysis, including Fourier analysis, harmonic analysis, and differential equations.

Product Details

  • Hardcover: 408 pages
  • Publisher: Wiley; 2 edition (April 7, 1999)
  • Language: English
  • ISBN-10: 0471317160
  • ISBN-13: 978-0471317166
  • Product Dimensions: 9.6 x 6.4 x 1.2 inches
  • Shipping Weight: 1.4 pounds (View shipping rates and policies)
  • Average Customer Review: 4.2 out of 5 stars  See all reviews (26 customer reviews)
  • Amazon Best Sellers Rank: #375,957 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews
38 of 44 people found the following review helpful
3.0 out of 5 stars Could have been great June 5, 2001
Format:Hardcover
I speak as a graduate student in applied math. I really like this book but was bothered by its flaws. Nevertheless, with a good instructor, this text can make for a good learning experience.
Positives: The book is well organized. It builds in a reasonable way so that I could focus on the material in the book and develop my understanding as I went. The book is reasonably well contained. Outside of a reasonable level of basics (a BA or BS in math) the proofs and most of the problems use material developed earlier in the text. I found the book very interesting -- I especially liked the topics presented in the last few chapters.
Negatives: Lots of typos - the author's errata sheet is woefully incomplete. Too few expamples. Too condensed - sometimes to the point of incomprehensibility or even error. The contents of a whole course may be condensed in to a single chapter or even a single section.
Things to be aware of: You should be comfortable with advanced calculus, topology, set theory, and algebra (linear and modern). It also helps to have had some basic real analysis. I highly recommend that you've seen Fourier transforms, Dirac deltas (distributions), and continuous probability. You aren't going to learn these here - you're going to see how measure theory is applied to them.
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14 of 14 people found the following review helpful
5.0 out of 5 stars I get it now September 26, 2009
By Kinga
Format:Hardcover|Verified Purchase
This is the second time I've re-reviewed this book.

First off, I am not a mathematician. I was trained as an engineer, and have recently started studying more advanced mathematics to apply it to my research. The only undergrad math course I'd taken before using this book was the standard analysis course. I initially used this book for a first graduate course in real analysis. Even with a professor, going through the book was incredibly difficult, and I had to resort to another book (Wheeden and Zygmund) as well as extensive notes provided by the professor. This experience made me loathe the book.

A few months after the course, having gained more exposure in this area, I returned to the book, and was surprised to find that I had finally started to understand why the author had organized it the way he had. Now, 6 months and another grad course in analysis later (operator theory), I think the book is worth its weight in gold.

First off, let's outline the cons. At first sight, the book takes brevity to the brink of lunacy. A (very) respectable first graduate course in analysis is covered in the first 100 pages. Dense doesn't even begin to cover it. Major results are relegated to the exercises, whole topics are compressed into a section (sometimes two or three are crammed into one), and even the proofs are presented with the barest minimum of explanation. The whole book is about 370 pages, and has enough material for about 4-5 courses. The exercises range from doable to extremely difficult. You also have chapters on everything from point set topology to harmonic analysis (abstract and otherwise) to probability to functional analysis. Heck, even fractals and manifolds pop up by the end.

The truth, however, is that all of these cons are actually pros in disguise.
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26 of 31 people found the following review helpful
5.0 out of 5 stars Great book January 23, 2000
Format:Hardcover
What I like most about the book is its concise but broad coverage of the fundamentals of real and functional analysis. Although I am not a mathematician, my main interest is solving various engineering problems using numerical methods. A solid background in real and functional analysis would be necessary for deeper understanding of various numerical methods. I wish I had known this book the first time I felt the need to study basic modern analysis. This books has exactly the material I wanted to learn.
In addition to the theorems and proofs, the author tells you why some theorems are important and how they can be used (of course also in a concise way). I found this type of "hints" are extremely helpful. The historical notes at the end of each chapter are also interesting to read.
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25 of 30 people found the following review helpful
4.0 out of 5 stars TOO MANY TYPOS. May 17, 2001
Format:Hardcover
Strictly from a student's perspective, this is a good textbook in real analysis. The way the material is presented is logical, whatever that means, and consistent. The author doesn't assume a student knows much and you can never go wrong with this assumption. However, this book has TOO MANY typos, so if you've never seen this stuff before, it's not easy to follow. Don't trust this book. Hopefully, next edition will fix this problem. This is a good book and it can become a classic, but, first, they have to correct all the typos. For those, who want a really good book in Analysis which has no typos, I recommend Rudin, "Real and Complex Analysis".
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8 of 8 people found the following review helpful
4.0 out of 5 stars good book... September 8, 2006
Format:Hardcover
My knowledge of this book originates from a course in measure and integration theory a couple of years ago. Back then I honestly didn't like the book very much. It is very terse, sometimes tending towards incomprehensible. The exercises were great though - hard. Exercises should be hard - that's the best way to learn mathematics.

Anyway - since then i have come to like the book more and more. Whenever I'm wondering of a definition or theorem I often find it in this book presented in a precise and rigorous manner. No redundant or unnecessary information is given - just exactly what I'm looking for. The book is perfect if you have a basic knowledge of a subject and want to fresh your memory or expand your mathematical horizon.

BUT as first time reading the book is almost useless. This, in particular, is the case for chapters 5,6,7,...,12. These chapters are close to incomprehensible if you haven't got a basic knowledge of the subjects allready.
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Most Recent Customer Reviews
5.0 out of 5 stars Five Stars
Nice quality, fast shipping
Published 5 days ago by David Neal
5.0 out of 5 stars My favorite analysis textbook
I first encountered this textbook when I used it to study for the analysis prelim at UT the summer after my first year of graduate school. Read more
Published 20 days ago by Keenan J. Kidwell
4.0 out of 5 stars No.1 Reference for Real analysis
The best book you can have in your library. Probably it is not the best to learn from it, since it does not include motivations, but It has pretty much everything you need for a... Read more
Published 1 month ago by Dimitris Ntalampekos
5.0 out of 5 stars Classic go-to for insight into methods of real analysis
About me:
Education level: Ph.D applied mathematics
Occupation: Systems Engineer

This book provides a great introduction to the methods of proof in real... Read more
Published 1 month ago by Joe Dinius
4.0 out of 5 stars Great introductory Real Analysis book
I like this book because is a really nice and complete introduction to Real Analysis. Besides, their explenations are always clear and precise.
Published 5 months ago by Felipe Negreira
5.0 out of 5 stars Good book
It was fast, and the book is in good condition.
I needed it for class.
A fairly manageable read. Recommended for people who wish to learn about higher level math
Published 8 months ago by Harry Song
2.0 out of 5 stars I am not very satisfied with the printing condition.
I have seen some copies printed excellently. I
do not understand why the company who printed it
save money on the quality of the appearance in the
case that it is... Read more
Published 13 months ago by Ronggang Shi
5.0 out of 5 stars Comprehensive and challenging
While trying to review and strengthen my foundations in measure theory and integration, I found this book. Read more
Published 17 months ago by Justin Bost
5.0 out of 5 stars Very decent book
I am taking measure theory and this is the required text. I was surprised by how conversational the author is at times, as most analysis books I have read were VERY dry. Read more
Published 22 months ago by Nick
5.0 out of 5 stars written at a graduate level
This book does not provide a lot of detail. At first this made me very annoyed, but if you are going to be successful in mathematics, you need to be able to work out details on... Read more
Published on April 3, 2012 by John W.
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