- Hardcover: 136 pages
- Publisher: American Mathematical Society; 3 edition (May 2001)
- Language: English
- ISBN-10: 082182693X
- ISBN-13: 978-0821826935
- Product Dimensions: 23.4 x 15.2 x 0.5 cm
- Shipping Weight: 340 g
- Average Customer Review: 5.0 out of 5 stars See all reviews (3 customer reviews)
- Amazon Bestsellers Rank: #496,900 in Books (See Top 100 in Books)
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Product Details |
Product Description
Book Description
Why does $2 \times 2 = 4$? What are fractions? Imaginary numbers? Why do the laws of algebra hold? And how do we prove these laws? What are the properties of the numbers on which the Differential and Integral Calculus is based? In other words, What are numbers? And why do they have the properties we attribute to them? Thanks to the genius of Dedekind, Cantor, Peano, Frege and Russell, such questions can now be given a satisfactory answer. This English translation of Landau's famous Grundlagen der Analysis-also available from the AMS-answers these important questions.
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Most helpful customer reviews
5.0 out of 5 stars
A classic that should remain in print,
By galloamericanus "galloamericanus" (Podunk, Iowa) - See all my reviews
This review is from: Foundations of Analysis (Hardcover)
Dover, please put this classic back into print!!This does for numbers what Suppes (1960) did for ZF set theory.
5.0 out of 5 stars
one of a kind treasure,
By "seriousthinker" (USA) - See all my reviews
This review is from: Foundations of Analysis (Hardcover)
The book is very good for people who want to be a high-school teacher of math, or be a mathematician. Even if you don't take a class with this book, read it on your own before taking real analysis. It will make your thought and logic complete and precise. A really nice training and practical preparation to do analysis.The book is very simple and short. It deals with number system from natural to complex, gently. Simple things are usually not easy, though. I took real analysis twice long time ago, but this book still improved my thinking of numbers very effectively. I recommend this book to those who want to be precise and correct, no matter you are math or theoretical physics people. And also for high-school students who want to know what pure mathematicians really do. And also for independent thinkers of mathematical science, and would-be philosophers!
5.0 out of 5 stars
The beggining of it all,
By Guilherme (Brazil) - See all my reviews
This review is from: Foundations of Analysis (Hardcover)
Landau's most known book is this little masterpiece. If you want to see everything about numbers proved, from the beggining, assuming just logical and set-theoretical principles and the five Peano axioms, you will find it here. You will see the proof of why 1+1=2, for instance, or why a+b=b+a. Usually people learn analysis with a lot of pictures and assumptions, and every once in a while one asks himself: how does it all begin? Because sometimes you see something which ought to be evident proved, and something which ought to be proved assumed. I recall that when I first met this book I became amazed and read it through with a lot of willing. It is difficult reading, so be prepared. That's because Landau wanted to follow the axiomatic Euclidean style in its most pure way. So the book is in the non-merciful telegram style of presenting everything in terms of "Axioms", "Definitions", "Propositions". Few books before and after strove to reach such pure and clear presentation of arithmetic. Thank God some one had once the patience to write such careful and complete text! In this book the words of Edgar Allan Poe are more than anywhere true: "What I here propound is true:-therefore it cannot die:-or if by any means it be now trodden down so that it die, it will 'rise again to the Life Everlasting'".
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