Undergraduate Analysis (Undergraduate Texts in Mathematics)

Rating:
Summary: okay
Review: I personally don't care much for this book. It's too terse, and there are nowhere near enough examples. I have about 6 analysis books and this is the one I look in the least. It seems to cover a lot of stuff, but maybe too much-- it wouldve been better to focus more on some more elementary topics. For instance, he spends about one and a half pages introducing the derivative. So if you want a book that glosses over more elementary concepts and leans heavily toward a graduate level, this book's for you. At my school we were supposed to learn advanced calculus from this and it is not good for that at all. For advanced calc try robert stritchart's Way of Analysis (the best book on analysis I've ever read) and for analysis Intro to real analysis by kolmogrov (only 10 bucks or so and actually better than most books costing a 100)

Rating:
Summary: Solid, complete reference to basic analysis topics
Review: 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.

Rating:
Summary: Solid, complete reference to basic analysis topics
Review: 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.

Rating:
Summary: Just like every other Lang text
Review: 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.