Foundations of Analysis (Graduate Studies in Mathematic) [Hardcover]

Edmund Landau (Author)

Book Description

ISBN-10: 082182693X | ISBN-13: 978-0821826935 | Publication Date: May 2001 | Edition: 3rd Revised edition

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.

Product Details

• Hardcover: 136 pages
• Publisher: Chelsea Pub Co; 3rd Revised edition edition (May 2001)
• Language: English
• ISBN-10: 082182693X
• ISBN-13: 978-0821826935
• Product Dimensions: 9.2 x 6 x 0.2 inches
• Shipping Weight: 12 ounces (View shipping rates and policies)
• Average Customer Review: 4.1 out of 5 stars  See all reviews (14 customer reviews)
• Amazon Best Sellers Rank: #346,287 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

29 of 29 people found the following review helpful:

5.0 out of 5 stars The beggining of it all, April 17, 2002

By 

Guilherme (Brazil) - See all my reviews

This review is from: Foundations of Analysis (Graduate Studies in Mathematic) (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'".

16 of 19 people found the following review helpful:

5.0 out of 5 stars one of a kind treasure, April 22, 2003

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"seriousthinker" (USA) - See all my reviews

This review is from: Foundations of Analysis (Graduate Studies in Mathematic) (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!

4 of 4 people found the following review helpful:

5.0 out of 5 stars Very nice book., January 16, 2007

By 

nightowl03d "nightowl03d" (Lexington, MA, USA) - See all my reviews

This review is from: Foundations of Analysis (Graduate Studies in Mathematic) (Hardcover)

Ever wonder how many of those field axioms in the front of your calculus/analysis book were redundant and what were essential? Are you a skeptic, who is not sure that you can really derive the complex numbers from Peano's axioms? Are you someone who does not know what the hell Peano's axioms are, even though you do know what an Axiom is? Then this book is for YOU!

This book proves the properties of the complex numbers and some of their subsets, (positive integers, integers, rationals, and reals). The proofs are quite rigorous, and provide an excellent foundation for which to study calculus, real or complex analysis. I thought it was a wonderfull read, and surprisingly accessible, given its hieroglyphic initial appearance.

If you decide to read this book in several sittings, I recommend being sure you cover each of the small sections. If you can't finish a full section, restart the section. I think that if you do it that way the results will seem more cohesive.