Undergraduate Analysis (Undergraduate Texts in Mathematics) [Hardcover]

Serge Lang (Author)

Book Description

ISBN-10: 0387948414 | ISBN-13: 978-0387948416 | Publication Date: December 5, 1996 | Edition: 2nd

This logically self-contained introduction to analysis centers around those properties that have to do with uniform convergence and uniform limits in the context of differentiation and integration.

From the reviews: "This material can be gone over quickly by the really well-prepared reader, for it is one of the book’s pedagogical strengths that the pattern of development later recapitulates this material as it deepens and generalizes it." --AMERICAN MATHEMATICAL SOCIETY

Editorial Reviews

Review

Second Edition

S. Lang

Undergraduate Analysis

"[A] fine book . . . logically self-contained . . . This material can be gone over quickly by the really well-prepared reader, for it is one of the book’s pedagogical strengths that the pattern of development later recapitulates this material as it deepens and generalizes it."—AMERICAN MATHEMATICAL SOCIETY

Product Details

• Hardcover: 683 pages
• Publisher: Springer; 2nd edition (December 5, 1996)
• Language: English
• ISBN-10: 0387948414
• ISBN-13: 978-0387948416
• Product Dimensions: 9.1 x 6.6 x 1.7 inches
• Shipping Weight: 2.4 pounds (View shipping rates and policies)
• Average Customer Review: 4.2 out of 5 stars  See all reviews (6 customer reviews)
• Amazon Best Sellers Rank: #436,069 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

21 of 23 people found the following review helpful:

5.0 out of 5 stars Great intro to real analysis with logical format, July 22, 1999

By 

Roger Peng (Baltimore, MD USA) - See all my reviews
(REAL NAME)   

This review is from: Undergraduate Analysis (Undergraduate Texts in Mathematics) (Hardcover)

Lang's book is an excellent introduction to real analysis that tries to build the reader's knowledge from the ground up. Lang starts with fundamental ideas from calculus and then proceeds in a logical way. Having taken Lang's course, for which this book was designed, it is clear to me that this book is a result of Lang's many years of experience teaching undergrads. I highly recommend this book to anyone who wants a solid foundation in analysis.

14 of 15 people found the following review helpful:

5.0 out of 5 stars Solid, complete reference to basic analysis topics, April 14, 2003

By A Customer

This review is from: Undergraduate Analysis (Undergraduate Texts in Mathematics) (Hardcover)

Serge Lang's "Undergraduate Analysis" offers an impeccable selection of topics and exercises for the student wishing to broaden his/her knowledge of analysis. The proofs of theorems can be terse at times, but a hardworking student will gain much through a thorough reading of the text. Also, Lang concentrates many of his exercises on estimates, which is an art form that is slowly dying among undergraduates (and graduate students as well, sad to say). Many of his problems require only the triangle inequality (the basic tool of estimation) and ingenuity (and hard work) from the student. I would strongly recommend this text for anyone who wishes to fully understand and appreciate the results and techniques of basic real analysis.

8 of 9 people found the following review helpful:

4.0 out of 5 stars Just like every other Lang text, February 17, 2004

By 

"vietulooj" (Austin, TX) - See all my reviews

This review is from: Undergraduate Analysis (Undergraduate Texts in Mathematics) (Hardcover)

This book typifies Lang's style. If you enjoyed any of his other books you'll enjoy this too. Like seemingly all of his texts, it has a section on the inverse function theorem and makes quite a deal out of it. Overall, it is quite comprehensive, but there's little motivation for the proofs so things can be a bit boring. Both Rudin and Browder cover the same amout of material in far fewer pages, and they have better excerises too.