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Rating: 
Summary: "The Weigh of Analysis" Would Be a Better Title for This!
Review: "The Way of Analysis" is intended for a heavy-duty one year course in Real Analysis at the undergraduate level, which may also be the first course some students will encounter rigorous proofs in. Strichartz's text, however, becomes hopelessly bogged down in its well intended efforts to be lucid and explanatory. What we end up with in the revised edition is a verbose, muddled, and poorly organized 600 page tome. The main fault of the text is the verbosity. Strichartz has a talent for taking simple ideas and brief proofs and turning them into long bloated discussions. For a book that claims to help readers learn rigorous proofs, the inclusion of meandering discussions and long comments about the intuition in the middle of a proof is a poor choice. The author is not even consistent in this approach, because some proofs are simply brushed off by appealing to similarity to another theorem, or given a quick informal "proof." In order to be able to effectively study from this text, the reader will need to either make her own comprehensive notes or take very good lecture notes. The book is typeset in the standard LaTeX style. The flow of the text is set up in a rather crowded manner. Unlike the usual visually pleasing mathematical publication, where all complicated expressions are displayed on their own line to make the text readable, Strichartz chooses to ram all but the most hideous into the normal paragraphs. I suppose a properly spaced version of this text would have had to take up another few hundred pages. The organization of the book is also harmed by the verbosity and giant paragraphs. Flipping through the chapters to find a particular fact is quickly seen to be futile. In a unique attempt to combat this problem, each chapter ends with a section that states all the definitions and theorems in the chapter. Strangely, this summary is at times the only place to find a precise statement of some of the definitions. Even the summary is not complete because many basic facts are stated and justified only within a paragraph discussion, and others are not even included. For example, nowhere in the text does Stricahrtz mention that the limit of a sum or product of functions is the sum or product of the limits, respectively. On the positive side, Strichartz does include a significant amount of heavy duty material in the sections marked with an asterisk. Unfortunately, it is just as muddled as the rest of the text. A positive example is his brief discussion of Dedekind Cuts as an alternative to the usual construction of the real numbers via the equivalence classes of rational Cauchy sequences. Many, but not all, of the exercises are of the routine variety. The selection is not particularly inspired, and doesn't help the reader extend the material or work out some significant applications or extensions herself. In conclusion, I would not recommend this text for independent study. Certain casual readers may appreciate the verbose introductions to the topics, but far better texts are dedicated to that. For a serious learner, I strongly recommend Serge Lang's "Undergraduate Analysis," published by Springer-Verlag and currently in the 2nd edition. Lang takes a much more concise and clean approach, and it gets the reader to the core of the material much faster.
Rating:
Summary: "The Weigh of Analysis" Would Be a Better Title for This!
Review: "The Way of Analysis" is intended for a heavy-duty one year course in Real Analysis at the undergraduate level, which may also be the first course some students will encounter rigorous proofs in. Strichartz's text, however, becomes hopelessly bogged down in its well intended efforts to be lucid and explanatory. What we end up with in the revised edition is a verbose, muddled, and poorly organized 600 page tome. The main fault of the text is the verbosity. Strichartz has a talent for taking simple ideas and brief proofs and turning them into long bloated discussions. For a book that claims to help readers learn rigorous proofs, the inclusion of meandering discussions and long comments about the intuition in the middle of a proof is a poor choice. The author is not even consistent in this approach, because some proofs are simply brushed off by appealing to similarity to another theorem, or given a quick informal "proof." In order to be able to effectively study from this text, the reader will need to either make her own comprehensive notes or take very good lecture notes. The book is typeset in the standard LaTeX style. The flow of the text is set up in a rather crowded manner. Unlike the usual visually pleasing mathematical publication, where all complicated expressions are displayed on their own line to make the text readable, Strichartz chooses to ram all but the most hideous into the normal paragraphs. I suppose a properly spaced version of this text would have had to take up another few hundred pages. The organization of the book is also harmed by the verbosity and giant paragraphs. Flipping through the chapters to find a particular fact is quickly seen to be futile. In a unique attempt to combat this problem, each chapter ends with a section that states all the definitions and theorems in the chapter. Strangely, this summary is at times the only place to find a precise statement of some of the definitions. Even the summary is not complete because many basic facts are stated and justified only within a paragraph discussion, and others are not even included. For example, nowhere in the text does Stricahrtz mention that the limit of a sum or product of functions is the sum or product of the limits, respectively. On the positive side, Strichartz does include a significant amount of heavy duty material in the sections marked with an asterisk. Unfortunately, it is just as muddled as the rest of the text. A positive example is his brief discussion of Dedekind Cuts as an alternative to the usual construction of the real numbers via the equivalence classes of rational Cauchy sequences. Many, but not all, of the exercises are of the routine variety. The selection is not particularly inspired, and doesn't help the reader extend the material or work out some significant applications or extensions herself. In conclusion, I would not recommend this text for independent study. Certain casual readers may appreciate the verbose introductions to the topics, but far better texts are dedicated to that. For a serious learner, I strongly recommend Serge Lang's "Undergraduate Analysis," published by Springer-Verlag and currently in the 2nd edition. Lang takes a much more concise and clean approach, and it gets the reader to the core of the material much faster.
Rating: 
Summary: All mathematics books should be like this.
Review: Many people might agree that other books may serve as a text for intro to analysis course better than 'The Way' . However, i find that the writing is very motivated (albeit sometimes he got carried away) and the math is, at least, comprehensible. I sometimes use this as a source of some challenging analysis problems. I am not really sure about using it as a main text, though (I used it as a supplementary text during my freshman year).
Rating:
Summary: Very lucid and ideal material for learning real analysis
Review: Most books on mathematics simply dump concepts,equations and examples and let you figure out what to do. Not this one. The book is written in a passionate manner where the author takes pains to explain why we are going in a particular direction and the goals. The style is extremely lucid and informal, something unusual for a subject that is steeped in formal mathematics. Yet the author presents, explains and covers all the formal theorems, concepts etc . The book also has excellent exercises. A truly noteworthy achievement. I would highly recommend this to anyone (especially self-study) trying to learn this subject.
Rating:
Summary: The best book out there for UNDERSTANDING the material
Review: There are many fine books on analysis out there. If you're just looking for something for reference, those by Rudin, or Kolmogorov, or others would work just fine. But if you want to LEARN analysis, if you want to actually understand the motivation behind it, then this is, simply put, the best book out there. I've used this book along with Kolmogorov's for about a term and a half now in my classical analysis class. As an example of the difference between them, consider their coverage of the implicit function theorem, one of the most fundamental theorems of behind the study of surfaces. Strichartz devoted two sections to this theorem, explaining what it was, what it's motivation was, and even how the proof related to the Newton's Method of First-Year Calculus. I came away from the text feeling I actually understood what the theorem meant and how it fit into the rest of Analysis. Kolmogorov left it as an exercise to the reader. This is the kind of textbook you can bring with you on a car trip and easily study along the way. It takes an informal writing style and from the beginning is focused on making sure you, as the reader, understand not just the theorems and proofs, but the concepts of real analysis as well. Every new idea is given not only with a What or a How, but with a Why as well, preparing the reader to ask themselves the same questions as they progress further. This is not to say the book is without rigor though. The theorems and the proofs are still there, just enriched by the other material contained within the book, and anyone mastering this book will be well prepared for future analysis courses, both mathematically and in their way of thinking about the subject.
Rating:
Summary: All mathematics books should be like this.
Review: This book is terrible for reference but EXCELLENT for LEARNING real analysis, certainly the best I have ever seen. The main issue that divides most readers is one of style, should mathematics books be succinct and clean or should they contain some "entertainment" as well? Should there be some extra explanation or not. As a student, the answer to this question can be given easily: The more explanation, the better. Just as the title suggests, the author leads you to understand analysis, to understand how things fit together, why certain things need to be proved and why other things are obvious. If a book just states theorems and proofs, it is unclear to me how that makes you better at mathematics because the question is, could you have thought of these proofs yourself? Given the theorems, can you come up with the proofs? Do you have a feeling for what's going on? After reading Strichartz you might not remember all the proofs but given any theorem, one should be able to reconstruct the proof from the understanding of the material. One should have a feeling for the concepts and that is something NO OTHER ANALYSIS BOOK seeks to develop. Also, Strichartz lays things out in a very natural way, not a single topic just comes out of nowhere. There is a flow to the text. Overall assessment: I love this book, made me get an A+ in the analysis, which I had already given up on, thought I would never get it...
Rating:
Summary: The best to understand and do Analysis
Review: This is the best Analysis book I ever read, you can learn not only the subject, but how to do Math, the introductive paragraph in each chapter gives the motivation of the topic, for example the introduction to the Lebesgue integral is memorable, many people "learn" the Lebesgue theory passively, some think it is a play to integrate strange functions, instead Prof. Strichartz treats estensively the PRACTICAL weaknesses of the Riemann theory.
For important theorems it is underlined the importance of every hypotheses, often from many points of view, the errors of the past are cited, I think one can learn more from explanations and errors than from a crystallized theory.
The notation is not standard and the printing is not good, however these are light faults.
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