Basic Real Analysis and Advanced Real Analysis Set (Cornerstones) [Hardcover]

Anthony W. Knapp (Author)

Book Description

Publication Date: August 9, 2005 | ISBN-10: 0817644075 | ISBN-13: 978-0817644079 | Edition: 1

Basic Real Analysis and Advanced Real Analysis systematically develop those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. These works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics. Key topics and features: * The development proceeds from the particular to the general, often introducing examples well before a theory that incorporates them * Incorporates, in the text and especially in the problems, material in which real analysis is used in algebra, in topology, in complex analysis, in probability, in differential geometry, and in applied mathematics of various kinds * The texts include many examples and hundreds of problems, and each provides a lengthy separate section giving hints or complete solutions for most of the problems Because they focus on what every young mathematician needs to know about real analysis, the books are ideal both as course texts and for self-study, especially for graduate students preparing for qualifying examinations. Their scope and approach will appeal to instructors and professors in nearly all areas of pure mathematics, as well as applied mathematicians working in analytic areas such as statistics, mathematical physics, and differential equations. Indeed, their clarity and breadth make them a welcome addition to the personal library of every mathematician.

Editorial Reviews

Review

"Basic Real Analysis and Advanced Real Analysis are two companion volumes of a comprehensive treatment unifying numerous branches of classical and functional analysis that can, with more or less assurance, be named as Real Analysis... Summing I can repeat that this volume is useful and interesting for all who deal with Analysis and its applications.  I suppose, any mathematical library must have a copy of this book and can recommend it for students and lecturers." ---Zentrablatt MATH

From the Back Cover

Basic Real Analysis and Advanced Real Analysis (available separately or together as a Set) systematically develop those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. These works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics. Key topics and features of Basic Real Analysis: * Early chapters treat the fundamentals of real variables, sequences and series of functions, the theory of Fourier series for the Riemann integral, metric spaces, and the theoretical underpinnings of multivariable calculus and differential equations * Subsequent chapters develop the Lebesgue theory in Euclidean and abstract spaces, Fourier series and the Fourier transform for the Lebesgue integral, point-set topology, measure theory in locally compact Hausdorff spaces, and the basics of Hilbert and Banach spaces * The subjects of Fourier series and harmonic functions are used as recurring motivation for a number of theoretical developments * The development proceeds from the particular to the general, often introducing examples well before a theory that incorporates them * The text includes many examples and hundreds of problems, and a separate 55-page section gives hints or complete solutions for most of the problems Basic Real Analysis requires of the reader only familiarity with some linear algebra and real variable theory, the very beginning of group theory, and an acquaintance with proofs. It is suitable as a text in an advanced undergraduate course in real variable theory and in most basic graduate courses in Lebesgue integration and related topics. Because it focuses on what every young mathematician needs to know about real analysis, the book is ideal both as a course text and for self-study, especially for graduate students preparing for qualifying examinations. Its scope and approach will appeal to instructors and professors in nearly all areas of pure mathematics, as well as applied mathematicians working in analytic areas such as statistics, mathematical physics, and differential equations. Indeed, the clarity and breadth of Basic Real Analysis make it a welcome addition to the personal library of every mathematician. --This text refers to an alternate Hardcover edition.

Product Details

• Hardcover: 1224 pages
• Publisher: Birkhäuser Boston; 1 edition (August 9, 2005)
• Language: English
• ISBN-10: 0817644075
• ISBN-13: 978-0817644079
• Product Dimensions: 9.5 x 6.6 x 2.4 inches
• Shipping Weight: 1.8 pounds
• Average Customer Review: 3.7 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #1,739,244 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

15 of 15 people found the following review helpful:

5.0 out of 5 stars Great book for real analysis, March 14, 2006

By 

Fadi (Denver, CO) - See all my reviews

This review is from: Basic Real Analysis and Advanced Real Analysis Set (Cornerstones) (Hardcover)

This is a fabulous book for learning real analysis. I've never taken a course in the subject (High school doesn't have one) but I have used the book for an independent study. After a fair study of point-set topology, this book can take you in and out of real analysis with ease. It's comprehensive and provides interesting insight into fields you thought you knew. It first tackles the problem of axiomatizing basic calculus, then it gives some background on metric spaces before hitting calculus of several variables and ordinary differential equations. The chapter on metric spaces was far more comprehensive than any I've read, and I've never seen a book that develops the theory of differential equations from an abstract perspective (none to this degree at least).

After this, it hits the meat of real analysis: Measure theory (and Lebesgue integration). Again, the author does an excellent job explaining and elaborating on this powerful theory. Euclidean spaces, topological spaces, L^p spaces, and Hilbert/Banach spaces take up the rest of this book. It even includes a very interesting chapter on Fourier transforms for Euclidean spaces. Overall, it's definitely worth the buy.

8 of 22 people found the following review helpful:

1.0 out of 5 stars Kindle edition is unreadable, February 11, 2010

By 

Dave "Dave" (Melbourne Beach, Fl United States) - See all my reviews

Amazon Verified Purchase

This review is from: Basic Real Analysis (Cornerstones) (Kindle Edition)

The kindle edition has many unreadable equations in it.
I don't know the root cause (translation to kindle format, etc.)
The bottom line is some of the equations are worthless.
Don't buy this book in this format.

5 of 17 people found the following review helpful:

5.0 out of 5 stars Basic Real Analysis and Advanced Real Analysis Set, January 21, 2007

By 

Mr7 (cali) - See all my reviews

Amazon Verified Purchase

This review is from: Basic Real Analysis and Advanced Real Analysis Set (Cornerstones) (Hardcover)

I have only scanned the book very quickly but the book appears to be well written which is why i purchased the books. They appear very clear and easy to follow for self study. I like the fact that everything is explained including "standard" notation. Unfortunately, I have only scratched the surface in each book; however, they seem perfectly suited for a non mathematician interested in becoming one.