Undergraduate Analysis_SergeLang

Undergraduate Analysis (Undergraduate Texts in Mathematics)
Serge Lang (Author)

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.

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.
It 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.

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

Product details

Paperback: 642 pages
Publisher: Springer; Softcover reprint of hardcover 2nd ed. 1997 edition (4 December 2010)
Language: English
ISBN-10: 1441928537
ISBN-13: 978-1441928535