Enter your mobile number or email address below and we'll send you a link to download the free Kindle App. Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required.

  • Apple
  • Android
  • Windows Phone
  • Android

To get the free app, enter your email address or mobile phone number.

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

4.7 out of 5 stars 37 customer reviews
ISBN-13: 978-0070542341
ISBN-10: 0070542341
Why is ISBN important?
ISBN
This bar-code number lets you verify that you're getting exactly the right version or edition of a book. The 13-digit and 10-digit formats both work.
Scan an ISBN with your phone
Use the Amazon App to scan ISBNs and compare prices.
Sell yours for a Gift Card
We'll buy it for $29.14
Learn More
Trade in now
Have one to sell? Sell on Amazon
Rent On clicking this link, a new layer will be open
$19.48 - $19.49 On clicking this link, a new layer will be open
Buy used On clicking this link, a new layer will be open
$55.13 On clicking this link, a new layer will be open
Buy new On clicking this link, a new layer will be open
$126.02 On clicking this link, a new layer will be open
More Buying Choices
31 New from $99.60 31 Used from $46.89
Free Two-Day Shipping for College Students with Amazon Student Free%20Two-Day%20Shipping%20for%20College%20Students%20with%20Amazon%20Student


Save Up to 90% on Textbooks Textbooks
$126.02 FREE Shipping. Only 12 left in stock (more on the way). Ships from and sold by Amazon.com. Gift-wrap available.

Frequently Bought Together

  • Real and Complex Analysis (Higher Mathematics Series)
  • +
  • Principles of Mathematical Analysis (International Series in Pure and Applied Mathematics) (International Series in Pure & Applied Mathematics)
  • +
  • Abstract Algebra, 3rd Edition
Total price: $378.72
Buy the selected items together
NO_CONTENT_IN_FEATURE



Product Details

  • 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: 6.6 x 1.1 x 9.5 inches
  • Shipping Weight: 1.7 pounds (View shipping rates and policies)
  • Average Customer Review: 4.7 out of 5 stars  See all reviews (37 customer reviews)
  • Amazon Best Sellers Rank: #107,514 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Top Customer Reviews

Format: Hardcover
Rudin's Real and Complex Analysis is an excellent book for several reasons. Most importantly, it manages to encompass a whole range of mathematics in one reasonably-sized volume. Furthermore, its problems are not mere extensions of the proofs given in the text or trivial applications of the results- many of the results are alternate proofs to major theorems or different theorems not proved. With that in mind, this book is not appropriate for a course where the instructor wants students to merely understand the theorems well enough to develop applications- the structure of the book is far better suited for a more theoretical course.
For example, the construction of Lebesgue measure is considered one of the most important topics in graduate analysis courses. After this construction, more abstract measures are developed, and then one proves the Riesz Representation Theorem for positive functionals later.
Conversely, Rudin develops a few basic topological tools, such as Urysohn's Theorem and a finite partition of unity, to construct the Radon measure needed in a sweeping proof of Riesz's Theorem. From this, results about regularity follow clearly, and the construction of Lebesgue measure involves little more than a routine check of its invariance properties.
Another example of where Rudin takes a more theoretical approach to provide a more elegant, yet less intuitive proof, is the Lebesgue-Radon-Nikodym theorem. Other books generally introduce signed measures with several examples, and use this result, along with properties of measures to derive the proof. On the other hand, since the first half of the book contains an intermission on Hilbert Space, Rudin uses the completeless of L^2 and the Riesz Representation Theorem for a more sweeping proof.
Read more ›
Comment 125 of 127 people found this helpful. Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback.
Sorry, we failed to record your vote. Please try again
Report abuse
Format: Hardcover
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.
Comment 33 of 34 people found this helpful. Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback.
Sorry, we failed to record your vote. Please try again
Report abuse
Format: Hardcover
This Book of Rudin, Like Principles, rewards perhaps above all else, persistence; a virtue that, if we are to believe some professional Mathematicians, is indispensable for the study of Mathematics.
Its true that it is terse and efficient. However, this "short-coming" is to me not a short-coming at all for the simple reason that Rudin makes up for it. How? The problems. Once you get through the proofs, a TON of challenging questions will be waiting at the other end to hammer out of you any illusions about you depth of understanding. In my opinion, this is the greatest strenghth of Rudin's book. STICK with the problems, attack them relentlessly and at the end of it all, you will have learned, a little perhaps, how to think for yourself in Analysis.
As regards the section on Complex Variables, I found it fruitful to read it while supplementing the problems with those of Ahlfors, which is more computational (E.g. Although Rudin discusses complex int., he scarcely provides any problems for this, and the same goes for expansion in Power Series).
Stick with the book, and soon it will be like a classic novel. (At least it is for me)
Comment 31 of 32 people found this helpful. Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback.
Sorry, we failed to record your vote. Please try again
Report abuse
Format: Hardcover
This text is a model of mathematical style. The usual Rudin stuff: concise and elegant proofs, great chanllenging exercises and that undefinable sense of quality -mathematical taste- pervading all the book.
The book covers the standard material on 'real variable' (measure theory') in a masterful and compact way; then it goes through the standard complex analysis to a level deeper than usual and showing in a very original way its intertwining with real variable. The final third of the book is devoted to more specialized topics.
Just a warning: the construction of Lebesgue measure is based on Riesz representation theorem, whose lengthy proof is imposed to the reader in chapter 2. It is really tough, and makes this chapter much harder to read than the rest of the book.
If you want to learn REAL mathematics, this is the book for you, you'll learn not only the subject matter, but a great style as well.
Comment 36 of 41 people found this helpful. Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback.
Sorry, we failed to record your vote. Please try again
Report abuse

Most Recent Customer Reviews

Set up an Amazon Giveaway

Amazon Giveaway allows you to run promotional giveaways in order to create buzz, reward your audience, and attract new followers and customers. Learn more
Real and Complex Analysis (Higher Mathematics Series)
This item: Real and Complex Analysis (Higher Mathematics Series)
Price: $126.02
Ships from and sold by Amazon.com