Real and Complex Analysis (McGraw-Hill International Editions: Mathematics Series)

Author - Walter Rudin ... [Goo?] [Posters]

This Paperback Book item from McGraw-Hill Publishing Co. was reviewed on 26-Oct-2008.

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1) Paperback Book Real and Complex Analysis (McGraw-Hill International Editions: Mathematics Series) by McGraw-Hill Publishing Co.. 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.¤

2) Paperback Book Real and Complex Analysis (McGraw-Hill International Editions: Mathematics Series) by McGraw-Hill Publishing Co.. 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.¤

3) Paperback Book Real and Complex Analysis (McGraw-Hill International Editions: Mathematics Series) by McGraw-Hill Publishing Co.. 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.¤

4) Paperback Book Real and Complex Analysis (McGraw-Hill International Editions: Mathematics Series) by McGraw-Hill Publishing Co.. 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.¤

5) Paperback Book Real and Complex Analysis (McGraw-Hill International Editions: Mathematics Series) by McGraw-Hill Publishing Co.. While I would not recommend this text to someone wishing to teach herself real and complex analysis, having this book in your personal mathematics library is a must for anyone seeking to further her education in higher mathematics. It´s one of the most commonly used undergraduate texts, referred to by some as the "Bible". If you can afford it though, I would recommend that you pick up a copy of Baby Rudin to use as a reference.

The first two chapters in combination with Bartle´s text on Lebesgue Integration and Measure makes for a killer introductory course in Measure Theory.

Oh, and if you can solve the problems in Rudin´s book, you can do pretty much anything, so it´s a major confidence booster!¤

6) Paperback Book Real and Complex Analysis (McGraw-Hill International Editions: Mathematics Series) by McGraw-Hill Publishing Co.. 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.¤

Page Updated: Robert N. Goolsby, 23-Nov-2008, 00710027669780071002769, 130-5X0-680-660-920-530-8

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