Real and Complex Analysis (Higher Mathematics Series) 3rd Edition

by Walter Rudin (Author)

40 customer reviews

ISBN-13: 978-0070542341

ISBN-10: 0070542341

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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. The basic techniques and theorems of analysis are presented in such a way that the intimate connections between its various branches are strongly emphasized. The traditionally separate subjects of 'real analysis' and 'complex analysis' are thus united in one volume. Some of the basic ideas from functional analysis are also included. This is the only book to take this unique approach. The third edition includes a new chapter on differentiation. Proofs of theorems presented in the book are concise and complete and many challenging exercises appear at the end of each chapter. The book is arranged so that each chapter builds upon the other, giving students a gradual understanding of the subject.

This text is part of the Walter Rudin Student Series in Advanced Mathematics.

Real and Complex Analysis (Higher Mathematics Series)

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Series: Higher Mathematics Series
Hardcover: 483 pages
Publisher: McGraw-Hill Education; 3 edition (May 1, 1986)
Language: English
ISBN-10: 0070542341
ISBN-13: 978-0070542341
Product Dimensions: 6.8 x 0.8 x 9.5 inches
Shipping Weight: 1.7 pounds (View shipping rates and policies)
Average Customer Review: 40 customer reviews
Amazon Best Sellers Rank: #306,968 in Books (See Top 100 in Books)
- #225 in Books > Science & Math > Mathematics > Mathematical Analysis
- #3846 in Books > Textbooks > Science & Mathematics > Mathematics

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Rewarding, but if I had to choose one book...this would not be it

ByLucius Schoenbaumon December 9, 2007

Format: HardcoverVerified Purchase

This is a very nice book. However in my opinion it is not the best of Rudin's three well-known books on analysis (Principles, Real and Complex, and Functional). The third, Functional Analysis, is a better representation of the subject, covering distribution theory alongside Fourier analysis, and containing applications of analysis to other areas of mathematics, such as number theory and PDE.

The first chapter and the chapter on Hilbert spaces are favorites of mine. It makes a good reference, but one should be sure to study other authors as well. The organization of the book is innovative and for that it is stimulating.

It's good, but frustrating at times, when one is drawn in by an elegantly stated theorem only to be inexplicably let down by a proof which does the job, but leaves out the motivating ideas. Rudin has a talent for making difficult things clear, but one should exercise caution, because he also has a talent for making simple things appear difficult.

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This Real and complex analysis text by Walter Rudin is a useful addition to my reference library

ByDr. Ronald Cutburthon August 30, 2017

Format: PaperbackVerified Purchase

This Real and complex analysis text by Walter Rudin is a useful addition to my reference library

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Welcome to the self-service analysis center!

ByMark Arjomandion January 31, 2004

Format: HardcoverVerified Purchase

This year we have been using the 1987 third edition of 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 not successful, 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. (I will inevitably be making a few comparisons between the two texts in the following.) One point to keep in mind though, is that Rudin developes the measure in a more formal axiomatic direction, instead of in 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 which is called a measure on (X, M) (The latter is the approach also taken in both H.L. Royden and Wheeden/Zygmund). The formal approach is not very intuitive and is less natural for a beginning graduate student who might not have developed some level of mathematical maturity yet.

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. Last but not least, it's worth noting that contrary to the common practice, Folland includes many end-of-chapter notes where he outlines some important historical aspects of the development of the topics, and also gives a few references for further study. For example, in the notes section at the end of the chapter on Lebesgue integration, he mentions --and briefly outlines-- the basics of the theory of "gauge integration" (aka Henstock-Kurzweil theory) which serves to construct a more powerful integral than that of the Lebesgue's. As another instance, having already defined and used "nets" within the chapter on topology, in the end-notes Folland also introduces "filters" and "ultrafilters". These are all machineries which have been developed to play the role of the metric space sequences in general (locally Hausdorff) topological spaces, but for some historical reasons, ultrafilters have nowadays taken a backseat to the nets (the older general topology books usually prove the Tychonoff theorem using ultrafilters). 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. Please note that the other books I have mentioned above do not discuss complex analysis, a subject which is also masterfully presented in Rudin. There are however a few other equally well-written complex analysis books to pick from, for example John B. Conway's classic from the Springer-Verlag graduate text series, or L.V. Ahlfors's wonderful monograph, to name just a couple.

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Rudin versus Royden and Fitzpatrick

ByGary Bowerson December 22, 2013

Format: HardcoverVerified Purchase

Continuing on in the Rudin versus Royden debate, to be fair when Rudin gets compared to "Royden" the comparison really should be to this book and not "The Principles of Mathematical Analysis". If you want to include complex analysis, for example if you are interested in the characteristic function of the terminal node of a stochastic process, then you should consider this book over "Royden". However, Royden and Fitzpatrick is also very nicely written and is ultimately easier for the reader to understand.

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A new aquaintance

ByRolf M. Mjeldeon August 24, 2015

Format: PaperbackVerified Purchase

One problem: The cover of my received book is another than the one pictured on your website and has a golden yellow colour. On the front cover is the title and a small, coloured small disc in which the word NEW is printed. A tiny square at the bottom reads McGrawHill. The book was sent from Novatech in Mumbai in India, not Eva Port as printed in the specific list of books for sale I made my choice from, but maybe Novatech is a book store belonging to the Eva Port group. The book contained the expected text, except for not having any page having data about publisher, name, addresses, year, edition, ISBN No. and copyright statements. The book looks like a printed-on-demand issue where also any index or bibliography is lacking. .

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Five Stars

ByAmalia Banueloson April 9, 2015

Format: HardcoverVerified Purchase

Excellent book!!

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Thank you

ByKhazamon January 26, 2016

Format: PaperbackVerified Purchase

I like it, but the papers was not thick enough. Nothing wrong with the product, but it's papers are very thin that I can see the page behind each.

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What I can say... classic is classic

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complex analysis part

I took a graduate level course in complex analysis and Rudin's book was the textbook we used in the course. He made the proofs amazingly simple. I liked it 5 stars

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superb framework for basic analysis

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