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Edmund Landau
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Foundations of Analysis Reprint Edition

by Edmund Landau (Author)
4.5 4.5 out of 5 stars 29 ratings
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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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  1. ISBN-10
    082182693X
  2. ISBN-13
    978-0821826935
  3. Edition
    Reprint
  4. Publisher
    Chelsea Pub Co
  5. Publication date
    January 1, 2001
  6. Part of series
    Ams Chelsea Publishing
  7. Language
    English
  8. Dimensions
    6 x 0.5 x 9 inches
  9. Print length
    136 pages
  10. See all details
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Product details

  • Publisher ‏ : ‎ Chelsea Pub Co; Reprint edition (January 1, 2001)
  • Language ‏ : ‎ English
  • Hardcover ‏ : ‎ 136 pages
  • ISBN-10 ‏ : ‎ 082182693X
  • ISBN-13 ‏ : ‎ 978-0821826935
  • Item Weight ‏ : ‎ 8.1 ounces
  • Dimensions ‏ : ‎ 6 x 0.5 x 9 inches
  • Customer Reviews:
    4.5 4.5 out of 5 stars 29 ratings

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Edmund Landau

Edmund Landau

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4.5 out of 5 stars
4.5 out of 5
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29 global ratings

Top reviews from the United States

Ariel Paisley
5.0 out of 5 stars Absolutely the best reference book for any advanced math student who plans ...
Reviewed in the United States on October 16, 2016
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Absolutely the best reference book for any advanced math student who plans to take calculus, or for any calculus survivor who want to actually understand why calculus works.
4 people found this helpful
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Juan Valverde
5.0 out of 5 stars Edmund Landau
Reviewed in the United States on December 29, 2013
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It is a very interesting book af a great Jewish mathematician from Germany. In fact, a good and relatively cheap edition.
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João Salvatti
5.0 out of 5 stars Great Book.
Reviewed in the United States on April 7, 2016
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Few pages, difficult content. It is not an introductory book.
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Paulo Argolo
5.0 out of 5 stars Five Stars
Reviewed in the United States on May 1, 2016
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Beautiful work! Required reading for those who like mathematics.
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Amazon Customer
5.0 out of 5 stars Five Stars
Reviewed in the United States on December 9, 2014
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The best and readable!
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Daniel Kian Mc Kiernan
5.0 out of 5 stars Classic and Unsurpassed
Reviewed in the United States on October 12, 2013
I acquired and worked my way through this book about 25 years ago. I remain very glad to have done so.

Landau begins with the system of the natural numbers as described by the Peano axioms, and from these constructs the system of the integers. Then, from the system of the integers, he constructs the system of the rational numbers. From the system of the rational numbers, he constructs the system of the real numbers. And, from the system of the real numbers, he constructs the system of the complex number.

Landau presented this book as something to be read in a very few days, and then held for possible future reference, by mathematics students who wanted to seee the real and complex number systems rigorously constructed `from scratch'.

Given exactly those ambitions, this book offers virtually nothing in the way of `intuition'. It's axiomata, theoremata, lemmata, and proofs. The spartan exposition will have different effects on different sorts of readers. For those whose intuitions would have closely but imperfectly matched the intuitions of the author, an intuitive discourse might have been a very good thing. But those whose intuitions perfectly matched those of the author would fall asleep were this much material surrounded by prose that offered no surprises. Those whose intuitions were poorly fit by the author would have found such discourse a source of misery. For my part, I doubt that I would have made it through this book had it ever slowed or cut away from the chase.

(I was not a young German mathematics student of the early 20th Century, but a young-ish American economist of the late 20th Century; it took me rather longer to work my way through this book that Landau apparently envisioned.)

I do think that there is one deficiency in exposition that ought to be corrected, and could be with an editorial footnote. As I say, Landau _constructs_ one number system from another. He does not treat the complex numbers as a superset of the reals numbers, the real numbers as a superset of the rational numbers, the rational numbers as a superset of the integers, nor the integers as a superset of the natural numbers. In fact, upon constructing each number system, he tells he reader to forget the system from which it were constructed. What is really needed is at least a mention of homomorphism. That is to say that, since there is a formal equivalence between a subset of the constructed system and the system from which it was constructed, and since numbers are formal in nature, that subset may be regarded as identical to the system used for construction. I think that Landau's telling the reader to set aside the prior system is meant to be taken as jocular, and I would guess that most readers would have enough background to recognize what was really being done; but I'm very sure that some readers crash-and-burn when they reach that point of transition.
10 people found this helpful
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Ricardo C. Martini
5.0 out of 5 stars Excelente
Reviewed in the United States on March 11, 2019
Este libro es uno de los primeros y mejores libros (sino el mejor) sobre el tema escrito por uno de los matemáticos mas importantes de principios del siglo XX (Edmund Landau). Todos los libros posteriores están basados en este libro
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Mark Flanagan
4.0 out of 5 stars The reals from the integers via Dedekind cuts.
Reviewed in the United States on April 16, 2008
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This book dates from 1951 but it's still a satisfactory place to see how the real (and even complex) numbers can be developed from the integers. A quick read.
2 people found this helpful
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Top reviews from other countries

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plinto
5.0 out of 5 stars Super Clássico Bem escrito Muito Citado
Reviewed in Brazil on August 23, 2020
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Excelente livro sobre construção dos números. É o tipo de livro que eu gosto
( teorema seguido da prova ) . Esse livro é um prato cheio para os estudiosos aficionados pelos fundamentos da matemática. Altamente recomendado por grandes matemáticos e professores. Chegou em ótimo estado e melhor do que eu esperava.
2 people found this helpful
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agingjb
5.0 out of 5 stars Classic
Reviewed in the United Kingdom on August 22, 2013
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The classic presentation of the development of the reals from the natural numbers. For mathematicians, but all mathematicians should read it at least once.
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