Elementary Classical Analysis

Rating:
Summary: great for readers who want to learn the material.
Review: It is always delightful and pleasure to read Marsden's book on such subject from his applied mathematics background: the author is always put readers perspective to understand important concepts and insights. This book will get the most benefit for those readers who are serious on the subject with non-traditional mathematical background. Although the book is over 700 pages, it covers more than enough a tradition real analysis course syllabi, the author put great efforts on informal illustations on the hardcore of the material (no-nonsense diagrams, layman's terms). I think if readers can follow this book thoroughlly, they will be more confident to attack Rudin's scholarly's work "Elementary Mathematical Analysis" and they should be feel very comfortable to Rudin's work as "cheat sheet" for this book, and for other scholarly quality works.

Rating:
Summary: This book is complete and yet easy to read.
Review: Marsden and Hoffman have created a superior text. Not only are virtually all of the proves provided for elementary analysis, but the text is easy to read and full of examples. If not the best book available, this is certainly one of the top two. It's real strength stems from versitility. This text is outstanding for new mathematicians learning analysis, and yet makes a solid reference text for graduate level studies. Elementary Classical Analysis is truly a rare find as a high quality, readable mathematical text.

Rating:
Summary: An excellent introduction to Real Analysis
Review: 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:
Summary: Well written introduction to mathematical analysis
Review: Marsden's new edition of his 1974 book features a more logical progression of topics and countless corrections. His use of illustrations certainly helps the newcomer grasp the concepts at hand, although a few of the practice problems are answered INCORRECTLY. This is the major drawback of the book. Although the book does not have as many errors as the first edition, again the publication of faulty solutions keeps this book from being the premiere book on the subject. I highly recommend the book to advanced undergraduates and graduate students, but caution instructors on the use of the answers provided in the text.

Rating:
Summary: From a grad student's point of view
Review: 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.

Rating:
Summary: Reasonable textbook, some editions full of typos
Review: 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:
Summary: Poorly written; to be avioded
Review: This book has been used as the text for an undergrad analysis class at Stanford for a number of years. It is overly verbose, poorly organized, and terribly written. The language is imprecise, and relies too much on intuition than solid reasoning. Furthermore, the proofs often lack elegance.

A much better text is Rudin's Principles of Mathematical Analysis. Concise and eleganty written. The language is precise, and the proofs are often full of beautiful and clever ideas.

Rating:
Summary: Not So Hot.
Review: Unevenly written. Full of typos. Some sections, like the one describing types of matrices, are so incompetently worded as to defy complete comprehension, even with repeated readings. Although some of the coverage of topological material is good, overall the informal explanations don't really do much to supplement the rigorous proofs -- they're just sort of... verbose. Not recommended. (Instead, try "Yet Another Introduction to Analysis" by Victor Bryant, as a fine introduction to the subject.)