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The Way of Analysis (Jones and Bartlett Books in Mathematics) (Englisch) Taschenbuch – 2. Juni 2000


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Amazon.com: 31 Rezensionen
80 von 84 Kunden fanden die folgende Rezension hilfreich
The best book out there for UNDERSTANDING the material 19. Januar 2001
Von Kevin C. - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
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.
36 von 38 Kunden fanden die folgende Rezension hilfreich
Good for novices in mathematics 27. September 1998
Von Chan-Ho Suh - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
Strichartz's book contains many clear explanations, and most importantly, contains informal discussions which reveal the motivations for the definitions and proofs. I believe the "informalness" of the book with the insights make this book a very appropriate text for those taking their first rigorous mathematics class. And this text is definitely much better than many of the texts that target that audience.
The format of the book is more disorganized than the standard texts like Rudin, but makes it more likely that it will be read and thoroughly digested, instead of sitting on the shelf. That said, one will probably never want to look at the book again after one has learned the material. If one does so, like I did, one will gasp in horror at the lack of conciseness, brevity, etc., and then rewrite one's Amazon review, like I am.
While trying to do the homeworks, I noticed that because not every result was made into a lemma or theorem, this made it somewhat difficult in finding the necessary info; however, the bulk of the definitions and theorems are listed in the chapter summaries.
The proofs in the book are fairly standard and repetitive. If you want to see cleverness that makes one gasp, see Rudin.
26 von 28 Kunden fanden die folgende Rezension hilfreich
nice analysis book to start with 31. August 2001
Von Cobalt78 - Veröffentlicht auf Amazon.com
Format: Taschenbuch
This is certainly the most intuitive Analysis book on the market. It is well written and the author presents the proofs in a way that should be accessable to most readers. He usually tries to use similiar proof techniques over and over again giving the student the practice he needs and seldom uses the rabbit in a hat style some other authors seem to prefer. Although these arguments make this book well suited for self-study, lack of solutions to the exercises is annoying for the "home-learner". As a text for a course the book is somewhat too cosy - given a lecture on a topic, you don't want to read 15 pages of anecdotes at home before the relevant theorems come up, at least that is my opinion. In any case this book offers a nice change of pace to the standard terse presentation of most Analysis books. For people with a backround in rudimentary Analysis who want some insights into Functional Analysis too, Rudins or Kolmogorov's books are probably the wiser choice.
34 von 38 Kunden fanden die folgende Rezension hilfreich
All mathematics books should be like this. 14. März 2004
Von Ein Kunde - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
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...
10 von 10 Kunden fanden die folgende Rezension hilfreich
From one who saw the embryo develop 9. November 2009
Von Allan D. Bennett - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe Verifizierter Kauf
OK, so what does that title mean? I was a graduate student in math at Cornell in the early 1980's and a TA for Bob Strichartz when he used a set of original lecture notes--which eventually developed as "The Way of Analysis"--for an undergraduate analysis course there. The "standard" book for that course at the time was Rudin's "Principles of Mathematical Analysis" a.k.a. "Baby Rudin".

Looking through my copy of the 1995 edition of the finished book, I recognize Strichartz's method of showing students "the way" to think about--and eventually try to discover for themselves--what theorems might be true, what definitions might be useful, what arguments might be fruitful, etc. As the grader for the course, I had an opportunity to see how many students (not all of whom were math majors) were able to benefit from the motivation provided in the notes to get a real feel for the subject. Moreover, even as (at that time) a third-year graduate student specializing in analysis myself, I found that the notes provided a context that I had not seen before in other analysis books.

One criticism appearing in some of the other reviews is that the exposition in the book is often verbose--thus not providing a useful reference book. I do agree with this to some extent--a few definitions are not clearly marked as such in boldface type when the reader first encounters them. Nonetheless, the chapter summaries do provide lists of definitions and theorems presented in each chapter. And for those interested mainly in a reference text for undergraduate analysis, choices such as Baby Rudin and Apostol's "Mathematical Analysis" are readily available.

However, for an advanced undergraduate level analysis course--particularly for students who have not already had an introduction to reading and writing proofs--this book is to be highly recommended.
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