Customer Reviews


6 Reviews
5 star:
 (5)
4 star:
 (1)
3 star:    (0)
2 star:    (0)
1 star:    (0)
 
 
 
 
 
Average Customer Review
Share your thoughts with other customers
Create your own review
 
 
Most Helpful First | Newest First

11 of 11 people found the following review helpful
5.0 out of 5 stars An excellent text and reference, 11 Jun 2001
By A Customer
This review is from: REAL & COMPLEX ANALYSIS 3E (5P) (Int'l Ed) (McGraw-Hill International Editions: Mathematics Series) (Paperback)
Rudin's book is a classic in analysis, and deservedly so. Unlike many analysis texts, he maintains as much generality as possible, working in locally compact, Hausdorff spaces and forgoing the reals when possible. He develops the standard measure and integration theory (Fubini's theorem, Lebesgue Dominated Convergence, etc) in these general cases. The proofs are basically the same (although Rudin likes slick proofs), and there is a massive gain in applicability. This book is inappropriate for a (US-level) undergraduate analysis course, but after a first introduction to the Riemann integral, I think this is an excellent way to explore measure theory and the Lebesgue integral. His treatment of complex analysis is also excellent and quite standard (Max Mod, Riemann Mapping, Mittag-Leffler, etc). In both parts, he proves nearly all his statements, but his proofs are quick enough to allow some detail-checking calisthenics for the interested reader. His exercises are generally excellent--they truly test understanding of the material, and even present some variant proofs (like an alternate proof of Riemann Mapping Theorem). At the very least, this is an excellent reference, but it also makes a very good text if you are ready for it.
Help other customers find the most helpful reviews 
Was this review helpful to you? Yes No


9 of 9 people found the following review helpful
5.0 out of 5 stars Excellent, often intriguing treatment of the subject, 26 Jun 1999
By A Customer
The first part of this book is a very solid treatment of introductory graduate-level real analysis, covering measure theory, Banach and Hilbert spaces, and Fourier transforms. The second half, equally strong but often more innovative, is a detailed study of single-variable complex analysis, starting with the most basic properties of analytic functions and culminating with chapters on Hp spaces and holomorphic Fourier transforms. What makes this book unique is Rudin's use of 20th-century real analysis in his exposition of "classical" complex analysis; for example, he uses the Hahn-Banach and Riesz Representation theorems in his proof of Runge's theorem on approximation by rational functions. At times, the relationship circles back; for example, he combines work on zeroes of holomorphic functions with measure theory to prove a generalization of the Weierstrass approximation theorem which gives a simple necessary and sufficient condition for a subset S of the natural numbers to have the property that the span of {t^n:n in S} is dense in the space of continuous functions on the interval. All in all, in addition to being a very good standard textbook, Real and Complex Analysis is at times a fascinating journey through the relationships between the branches of analysis.
Help other customers find the most helpful reviews 
Was this review helpful to you? Yes No


6 of 6 people found the following review helpful
5.0 out of 5 stars Welcome to the self-service analysis center!, 5 Feb 2004
By 
This year we have been using Walter Rudin's treatise as the main text for a standard first-year graduate sequence on real analysis, backed up by Wheeden/Zygmund's book on Measure and Integral, and the two seem to complement each other quite nicely. Rudin writes in a very user-friendly yet concise manner, and at the same time he masterfully manages to maintain the high level of formality required from a graduate mathematics text. To be totally honest, a few years ago my very first attempt at learning graduate-level real analysis in a classroom setting (via Folland's book) was unsuccessful, as I found the exposition in Folland very dense and rigid, and the homework problems too difficult to do. Rudin's book however, is a lot more accessible for the beginning graduate students who may not have had any more than some basic exposure to measure theory in their upper division analysis classes. One point to keep in mind is that, Rudin developes the measure in the more formal axiomatic way, instead of the more concrete (constructive) approach. In the constructive approach, one first introduces the "subadditive" outer measure as a set function which is defined on the power set P(X) of a nonempty set X. One then proceeds by showing that the restriction of the domain of the outer measure to a smaller class of subsets of X (a sigma algebra M), obtained via applying the Caratheodory's criterion, results in a "countably additive" set function that is called a measure on (X,M). (The latter is the approach taken in both H.L. Royden and Wheeden/Zygmund). The formal axiomatic approach is not very intuitive and is less natural for the readers who have not yet developed a certain level of mathematical maturity. Also, Rudin does not discuss some of the more advanced or interdisciplinary topics such as distribution theory (Sobolev spaces, weak derivatives, etc.), or applications of measure theory to the probability theory, both explored in the book by Folland. (Please also note that contrary to the common practice, Folland gives many end-of-chapter notes outlining the historical development of the topics, as well as a good few references and suggestions for further study). All said, I can recommend taking up Royden as your very first approach to measure theory, then based on how well you think you have learned the first course, move on to either Rudin or Folland for a more advanced treatment. Rudin also does a great job on the complex analysis part, a subject not discussed in the other books mentioned above. There are however a few other equally well-written complex analysis books to pick from, for example try John B. Conway's and L.V. Ahlfors's classics, to name just a couple.
Help other customers find the most helpful reviews 
Was this review helpful to you? Yes No


6 of 7 people found the following review helpful
5.0 out of 5 stars A start in mathematical analysis., 4 Dec 2004
By 
Palle E T Jorgensen "Palle Jorgensen" (Iowa City, Iowa United States) - See all my reviews
(REAL NAME)   
This review is from: REAL & COMPLEX ANALYSIS 3E (5P) (Int'l Ed) (McGraw-Hill International Editions: Mathematics Series) (Paperback)
I am a fan of Rudin's books. This one "Real and Complex Analysis" has served as a standard textbook in the first graduate course in analysis at lots of universities in the US, and around the world.
The book is divided in the two main parts, real and complex analysis. But in addition, it contains a good amount of functional and harmonic analysis; and a little operator theory.
I loved it when I was a student, and since then I have taught from it many times. It has stood the test of time over almost three decades, and it is still my favorite. I have to admit that it is not the favorite of everyone I know.
What I like is that it is concise, and that the material is systematically built up in a way that is both effective and exciting.
Some of the exercises are notoriously hard, but I think that is good: It simply means that they serve as work-projects when the students use the book. And this approach probably is more pedagogical as well.
After surviving some of the hard exercises in Rudin's Real and Complex, I think we learn things that stay with us for life; you will be "marked for life!"
Review by Palle Jorgensen, December 2004.
Help other customers find the most helpful reviews 
Was this review helpful to you? Yes No


3 of 5 people found the following review helpful
4.0 out of 5 stars An Excellent Read, 3 Sep 1998
By A Customer
A terrific book for all Mathematicians, Rudin's books sometimes feel like they have plot, if you know what I mean. Maybe thats because often his proofs rely on trickery. Rather than sense the "natural" connections between the topics, you get the impression that Rudin is more interested in performing magic. You read a proof, and instead of saying "that really SEEMS to be why this theorem is true" you instead say "Wow! Good thing we had that little tool to use." If you do not take my meaning, I suggest you pick apart his proofs of the Complex and Positive versions of the Reiss Representation Theorem.
Mind you, I recommend the book highly, with or without the "tricks." Rudin, as always, is informative and entertaining. And the tricks may not even be tricks to you. As a graduate student, "I am only an egg."
Help other customers find the most helpful reviews 
Was this review helpful to you? Yes No


0 of 8 people found the following review helpful
5.0 out of 5 stars Joining real analysis and complex analysis, 26 Sep 1998
By A Customer
This book presents a large part of the classical real and complex analysis. The good thing is that the two diciplins is joint.
Help other customers find the most helpful reviews 
Was this review helpful to you? Yes No


Most Helpful First | Newest First

This product

Only search this product's reviews