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7 Reviews
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27 of 29 people found the following review helpful
5.0 out of 5 stars Great intro to real analysis with logical format
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...
Published on July 22, 1999 by Roger Peng

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27 of 40 people found the following review helpful
2.0 out of 5 stars okay
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...
Published on March 12, 2002


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27 of 29 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.
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19 of 20 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
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.
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7 of 7 people found the following review helpful
4.0 out of 5 stars Solid Text - Complete Solutions Manual Available, March 27, 2011
This review is from: Undergraduate Analysis (Undergraduate Texts in Mathematics) (Hardcover)
If you are considering purchasing this book for self-study it's worth it because as far as I know it's the only Analysis text available that gives you the option of purchasing an additional complete solutions manual, Rami Shakarchi's "Problems and Solutions for Undergraduate Analysis." Attempting to learn Analysis on your own is especially difficult if you do not get feedback on attempts at proofs. I would think that I had correctly proven theorems in class only to find out that I was overlooking something critical as pointed out by the professor. So if you have no professor, Shakarchi's text can give you the feedback that you need, though you have to consider if it's worth it to purchase both texts. I just want to make sure that people are aware that the complimentary text exists. It's worked well for me to have both.

As for Lang's Analysis itself, it's quite terse, though I enjoy Lang's writing style myself. Quite a bit is left to the reader, but that's a good thing as it gets you thinking. Also, this book is quite thick and goes pretty deep into analysis. You can learn much more than you would in one semester at school. If you can get through this text, you are well on your way...
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10 of 12 people found the following review helpful
4.0 out of 5 stars Just like every other Lang text, February 17, 2004
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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.
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7 of 9 people found the following review helpful
5.0 out of 5 stars A beauty, July 12, 2005
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This review is from: Undergraduate Analysis (Undergraduate Texts in Mathematics) (Hardcover)
I learned this material years ago but when I need to

look things up, this book has everything, well written.

For example the Taylor expansion with multinomial notation

is given here. The writer treats the undergraduate student's

intellect with respect. This is a serious book.
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27 of 40 people found the following review helpful
2.0 out of 5 stars okay, March 12, 2002
By A Customer
This review is from: Undergraduate Analysis (Undergraduate Texts in Mathematics) (Hardcover)
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)
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1 of 2 people found the following review helpful
1.0 out of 5 stars Book is excellent, but print is horrible, March 30, 2013
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Book is excellent, but print is horrible. The print is very unclear and some of the equations are hard to read (at least for me). Hope the publisher consider to reprint the book.
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Undergraduate Analysis (Undergraduate Texts in Mathematics)
Undergraduate Analysis (Undergraduate Texts in Mathematics) by Serge A. Lang (Hardcover - July 28, 2005)
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