- Gebundene Ausgabe: 352 Seiten
- Verlag: Higher Math; Auflage: 3 Revised edition. (1. Februar 1976)
- Sprache: Englisch
- ISBN-10: 007054235X
- ISBN-13: 978-0070542358
- Größe und/oder Gewicht: 15,5 x 1,8 x 23,6 cm
- Durchschnittliche Kundenbewertung: 40 Kundenrezensionen
- Amazon Bestseller-Rang: Nr. 170.208 in Fremdsprachige Bücher (Siehe Top 100 in Fremdsprachige Bücher)
- Komplettes Inhaltsverzeichnis ansehen
Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics) (Englisch) Gebundene Ausgabe – 1. Februar 1976
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The third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first-year graduate students. The text begins with a discussion of the real number system as a complete ordered field. (Dedekind's construction is now treated in an appendix to Chapter I.) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included. This text is part of the Walter Rudin Student Series in Advanced Mathematics.
First, let me say right off that I like this book. I've seen better math textbooks though, so it doesn't get the five stars. The reason I like it is its utility as a reference. I can look up something to refresh my memory very easily. The style is concise, clearly outlined. Rudin also has some interesting proofs. I sometimes find myself looking up something pretty standard, and being enlightened at seeing familiar material in a new light.
But, and this is a big 'but', I wouldn't recommend this to a beginner. Mathematical 'maturity' is a funny thing. Some people have it; others don't. But most that do have it, get it by a long, arduous process of studying. Few are ready to immediately jump in and study the advanced textbooks. With this thought in mind, I think if you're reading this, wondering if this book is going to help you survive your first real math class, then Rudin will probably be tough. Not because it presumes some sort of secret knowledge. It doesn't. Just like any other intro analysis book, it doesn't assume you know analysis. But there are easier books. Like probably whatever your prof assigned for the class. 'Course, your prof could suck, and correspondingly, the book could suck. But if the faculty at your school is that inept, you're better off transferring.
Actually, I read with some surprise that some reviewers mentioned that the books they used had lots of useless pictures, etc. I don't recall ever reading an analysis book that had lots of pictures, period. So I guess I was lucky. But if your book is of that kind, then I guess I could recommend The Way of Analysis by Robert Strichartz. That's the book I first learned from. And it's the one used for the honors intro real analysis sequence(2 semesters) at my university here in Ithaca. The last half of the book is on applications of analysis to ODE's, Fourier series, Lebesgue integration. The style is very conversational, so it's definitely not a great reference book. I should add that the discussions are usually on motivating a definition, etc, rather than explaining something trivial, like a lot of similar books. Oh, and it has some pictures, but not many.
The book is divided in the three main parts, foundations, convergence, and integration. But in addition, it contains a good amount of Fourier series, approximation theory, and a little harmonic analysis.
I loved it when I was a student, and since then I have taught from it many times. It has stood the test of time over almost three decades, and it is still my favorite. I have to admit that it is not the favorite of everyone I know.
What I like is that it is concise, and that the material is systematically built up in a way that is both effective and exciting.
The exercises and just at the right level. They can be assigned in class, or students can work on them alone. I think that is good, and the exercises serve well as little work-projects. This approach to the subject is probably is more pedagogical as well.
I think students will learn things that stay with them for life.
Review by Palle Jorgensen, Septembr 2002.
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Nevertheless, very nice reading!