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Real and Complex Analysis (International Series in Pure and Applied Mathematics)

by Walter Rudin

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(23 votes)

Edition: Hardcover

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• Principles of Mathematical Analysis, Third Edition
• Functional Analysis
• Counterexamples in Analysis (Dover Books on Mathematics)
• Real Analysis: Modern Techniques and Their Applications (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)
• Real Analysis (3rd Edition)

Product Description:

This is an advanced text for the one- or two-semester course in analysis taught primarily to math, science, computer science, and electrical engineering majors at the junior, senior or graduate level.

Customer Reviews:

Great Learning Experience
Review date: 2010-01-28

This is truly a well-crafted book. The organization is tight and the book is largely self-sufficient, really only calling upon material covered in his previous book, Principles of Mathematical Analysis. Rudin only proves such lemmas as he needs to get to the major results; peripheral facts and theorems are left to the exercises, which are far from routine and require a lot of thought and patience to get through. The book is rather terse, but there's a powerful elegance behind it. The proofs are rigorous and avoid hand-waving, albeit Rudin intentionally leaves gaps for the reader to fill. Working carefully through this book and doing as many exercises as possible, one can get a good grasp of the material.

However, this is not a book I would recommend for people who have not had prior experience with measure theory or complex analysis. Rudin provides little motivation. His arguments are elegant, but his methods are designed to give the quickest route to the results, which is seldom the most intuitive one. For example, where other authors explicitly construct Lebesgue measure, Rudin opts for a difficult proof of the Riesz Representation Theorem from which he pulls Lebesgue measure as a magician might pull a rabbit out of a hat. A lot of the material has a lot of geometric intuition behind it, but Rudin seldom goes out of his way to point it out. The beginner would be much better served getting an introduction to the material elsewhere before tackling Rudin. It will enable one to get much more out of the book than slogging through it blindly. It's one thing to know the definitions and be able to follow the proofs, and another thing to understand what it all means; Rudin doesn't hold the reader's hand where the latter is concerned.

For those with adequate preparation and sufficient daring, this book makes for a great learning experience and I daresay is even fun in places.

One of a Kind
Review date: 2008-03-13

I normally don't review books that already have this many reviews, especially when I agree so much with the reviews that already exist. But I'm teaching out of green Rudin for the first time this semester, 20 years after getting to know the book well as a student, and I find myself so enthusiastic about it again, that I just had to chime in with an "Amen" to the other positive reviews. When it comes to mathematical writing, it doesn't get any more exquisitely elegant than this.

Probably all our reviews are irrelevant, however, because there are probably very few discretionary purchases of this book: There will be nearly a one-to-one correspondence between buyers of the book and students in classes for which it is required. For them, I can only recommend skipping the outrageously expensive hardback (which even at its high price is pretty cheaply constructed nowadays) and opting for the more reasonable international paperback edition.

Rewards you again and again
Review date: 2007-12-09

A few words for the person thinking of buying and using this book.

First, go for it. Don't be scared. But you need to be prepped a little on how it all fits together. Roughly, it breaks up into a course on real analysis (with quite a lot of supplementary material, especially on Fourier analysis), and then breaks into complex analysis in chapter 10.

Now on the first part--You might be tempted to ask "what am I learning?" as you start on the first chapter. It seems like Rudin is taking you the longest way possible. Is he torturing me?, you wonder. Can't you make this more concrete?, you ask. Keep going, and you will begin to see what he's up to. The reason he wrote chapter 1 the way he does is because (note) it involves no structure *except* the space X and the sigma algebra M. He's showing you, in other words, what you can rely on no matter *where* you are, no matter what measure you are using. That taken care of, it's off to chapter 2, where he stirs in a topology T. Two main goals: the Riesz Representation theorem (version 1) and the construction of Lebesgue measure. Try hard to make it through this and see what Rudin is doing. Make some time to read through it, and you will really gain some insight into what Lebesgue measure on R^k does to the study of analysis, extending it beyond Riemann. Personally, I'm still not sure it's 100 percent the best way to do things, but--like I said--it's pretty cool stuff after the hard work is finally over.

Next, he goes through some chapters on different sorts of function spaces that are more or less self contained (all in good time, m'boy), and then he comes back around in Complex Measures (chapter 6) to really hammer in some important things--especially the Radon-Nikodym theorem. Now you're ready to learn about differentiation in chapter 7. By now, you will have seen for yourself what I am talking about--the book really gives it to you straight, and best of all, when you're done learning out of it, it continues to be valuable as a reference because of the meticulous organization of each chapter.

I love this book!
Review date: 2006-11-07

I love this book, even though I have not absorbed more than a small portion of it yet. I find this to be a much better book than the "baby Rudin", which struck me as dry, overly concise, and without motivation. This book provides ample motivation, and although it proceeds in great generality, proceeds at a reasonable pace.

The best thing about this book, however, is the spirit of it--the integrated approach to analysis that Rudin takes is unique and greatly appreciated--Rudin is, like Lang, a testimony to the fact that the best mathematicians do not draw artificial lines between different areas within mathematics. Rudin presents the material in ways that connect to other areas of mathematics and will help the reader become a better mathematician, even if she never directly uses any of the material contained in this volume.

I would not recommend this book as a first exposure to measure theory or complex analysis--it is advanced and requires a great deal of background to fully understand and appreciate. But I think this is a book that any serious mathematician should add to their collection and eventually work through. People wanting to learn measure theory might look to the book by Inder K. Rana, or to the classic book by Royden. For more elementary treatments of complex analysis I would recommend the classic by Ahlfors, Theodore Gamelin's book, or the book by Greene and Krantz.

My 2 cents
Review date: 2006-10-11

There are some excellent reviews here for this outstanding book, so I will try to avoid repetition. In preparation for my qualifying exams in graduate school, two of my colleagues and I did all of the exercises in Rudin (give or take a couple, no more). What I found striking at the time was how Rudin took three subjects -- measure theory, functional analysis, and complex analysis -- and weaved them together seamlessly. It is not that I believed them to be separate subjects, but until then I hadn't realized just how they all fit together. Really, this book is superb.

A word of warning, though. Rudin's prose is concise, and his proofs leave you wondering if you'd ever be able to reproduce them on your own. It is what we in the business are used to call 'elegant'. It pays to work in groups, persevere, and go over everything twice or more. Good luck.

Product Details/Specifications:

Authors:
Walter Rudin

Recording label: McGraw-Hill Science/Engineering/Math
Publishers:
McGraw-Hill Science/Engineering/Math

Manufacturer: McGraw-Hill Science/Engineering/Math
EAN: 9780070542341
Binding: Hardcover
Dewey decimal number: 515
ISBN: 0070542341
Number of items: 1
Number of pages: 483
Publication date: 1986-05-01