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Title: Elementary Classical Analysis by Jerrold E. Marsden, Michael J. Hoffman ISBN: 0-7167-2105-8 Publisher: W.H. Freeman & Company Pub. Date: 01 April, 1993 Format: Hardcover Volumes: 1 List Price(USD): $118.75 |
Average Customer Rating: 3.71 (7 reviews)
Rating: 5
Summary: An excellent introduction to Real Analysis
Comment: Marsden and Hoffman have done an admirable job combining clarity and rigor in a book appropriate to the level of an advanced undergrad class at a good university. The organization and tone of the work set it apart from the alternatives. The authors proceed from lesser rigor to greater within each chapter, presenting definitions, theorems, and worked examples before the proofs, which are placed at the end of each chapter. The authors address this somewhat unusual organization in their introduction:
"We decided to retain the format of the first edition, which gives full technical proofs at the end of each chapter but presents some idea of the main point in the text. This seems to have been well-received by the majority of readers... and we still believe that it is a sound pedagogical device for a course like this. It is not meant as a way to shun the proofs; on the contrary it is intended to give to views of the proof: on in the way working mathematicians think about it, (the trade secrets, so to speak), and the other in the way mathematicians write out formal proofs."
Marsden Hoffman is written in a slightly more conversational tone than other rigorous introductions to analysis. However, as a math major at Stanford, I felt like this only made the text more readable.
A side note: Though Marsden and Hoffman do make light of Cantor's quaint, 19th century definition of a set in their intro to set theory, they ultimately do so only to motivate the exposition of a formal, axiomatic view.
Rating: 4
Summary: Reasonable textbook, some editions full of typos
Comment: The good part: The text contains the usual definitions, theorems and proofs in a spacious layout (LaTeX - what would you expect...), and also provides some intuition and insight (with pictures of open and closed sets, sin(1/x) etc). The main text is quite long (some find it too verbose, I liked it), and proofs are given after the main text, and don't clutter the exposition. There are also many worked examples, and exercises (with hints/solutions for odd numbered ones).
However, the book (in its 2nd edition, 7th printing) is riddled with typos. And these are not only the occasional harmless typo, no, there are errors at the heart of definitions and proofs. For example, when defining the limes inferior, the sign on infinity is wrong for degenerate cases. Confusing! The proof that Q is countable is wrong, too (though this is trivial to see, so no confusion here.)
Lamentably, this is no isolated case. There are about 36 (!) typos on the first 100 pages of the 7th printing (check the author's homepage for a list of errata). This is really too much for a such an expensive "elementary" textbook.
However, apparently there is a new printing as of May 2003 that fixes most of these problems. So, make sure you don't accidentally buy an old printing of this second edition.
Rating: 1
Summary: From a grad student's point of view
Comment: The book is poorly written. And the author tries to claim the credit for a lot of previous work, without mentioning when, where or who invented the proofs or solutions. He sometimes mocks and makes fun of other people's definitions calling them "pitiful!." The language used seems to be intended to sound fancy and sophisticated, but to me it's plain annoying.
The answers to most examples are not provided promptly, instead they are piled together at the end of the chapter.. leaving the student to wander around constantly looking for what the author is trying to say.
I would not recommend this book for use as a text book, for it is (unlike what some reviews say) not easy to read, in fact most proofs and explinations are not formatted well, they are written as in an essay.. long sentences and in text format ex: (1/2) instead of an actual math font for the number one half.
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Title: Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics) by Walter Rudin ISBN: 007054235X Publisher: McGraw-Hill Science/Engineering/Math Pub. Date: 01 January, 1976 List Price(USD): $147.70 |
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Title: Numerical Analysis by Richard L. Burden, J. Douglas Faires ISBN: 0534382169 Publisher: Brooks/Cole Publishing Company Pub. Date: 29 December, 2000 List Price(USD): $134.95 |
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Title: Complex Variables and Applications by James Ward Brown, Ruel Vance Churchill ISBN: 0072872527 Publisher: McGraw-Hill Science/Engineering/Math Pub. Date: 26 February, 2003 List Price(USD): $133.50 |
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Title: Mathematical Analysis (2nd Edition) by Tom M. Apostol ISBN: 0201002884 Publisher: Addison Wesley Publishing Company Pub. Date: 01 January, 1974 List Price(USD): $112.33 |
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Title: Topology (2nd Edition) by James Munkres ISBN: 0131816292 Publisher: Pearson Education Pub. Date: 28 December, 1999 List Price(USD): $101.33 |
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