Free PDF Undergraduate Analysis (Undergraduate Texts in Mathematics), by Serge Lang
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Undergraduate Analysis (Undergraduate Texts in Mathematics), by Serge Lang
Free PDF Undergraduate Analysis (Undergraduate Texts in Mathematics), by Serge Lang
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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
- Sales Rank: #806096 in Books
- Published on: 2005-06-28
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x 1.56" w x 6.14" l, 2.41 pounds
- Binding: Hardcover
- 642 pages
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
Most helpful customer reviews
8 of 10 people found the following review helpful.
A beauty
By stochasticmind
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.
13 of 13 people found the following review helpful.
Solid Text - Complete Solutions Manual Available
By Publicagent
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...
21 of 22 people found the following review helpful.
Solid, complete reference to basic analysis topics
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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