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Foundations of Analysis: Third Edition
 
Foundations of Analysis
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Softcover ISBN:  978-1-4704-7057-9
Product Code:  CHEL/79.S
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $62.10
eBook ISBN:  978-1-4704-7061-6
Product Code:  CHEL/79.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $58.50
Softcover ISBN:  978-1-4704-7057-9
eBook: ISBN:  978-1-4704-7061-6
Product Code:  CHEL/79.S.B
List Price: $134.00 $101.50
MAA Member Price: $120.60 $91.35
AMS Member Price: $120.60 $91.35
Foundations of Analysis
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Foundations of Analysis: Third Edition
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Softcover ISBN:  978-1-4704-7057-9
Product Code:  CHEL/79.S
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $62.10
eBook ISBN:  978-1-4704-7061-6
Product Code:  CHEL/79.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $58.50
Softcover ISBN:  978-1-4704-7057-9
eBook ISBN:  978-1-4704-7061-6
Product Code:  CHEL/79.S.B
List Price: $134.00 $101.50
MAA Member Price: $120.60 $91.35
AMS Member Price: $120.60 $91.35
  • Book Details
     
     
    AMS Chelsea Publishing
    Volume: 791966; 136 pp
    MSC: Primary 26; 01;

    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.

  • Table of Contents
     
     
    • PREFACE FOR THE STUDENT
    • PREFACE FOR THE TEACHER
    • TABLE OF CONTENTS
    • CHAPTER I: NATURAL NUMBERS
    • §1 Axioms
    • §2 Addition
    • §3 Ordering
    • §4 Multiplication
    • CHAPTER II: FRACTIONS
    • §1 Definition and Equivalence
    • §2 Ordering
    • §3 Addition
    • §4 Multiplication
    • §5 Rational Numbers and Integers
    • CHAPTER III: CUTS
    • §1 Definition
    • §2 Ordering
    • §3 Addition
    • §4 Multiplication
    • §5 Rational Cuts and Integral Cuts
    • CHAPTER IV: REAL NUMBERS
    • §1 Definition
    • §2 Ordering
    • §3 Addition
    • §4 Multiplication
    • §5 Dedekind's Fundamental Theorem
    • CHAPTER V: COMPLEX NUMBERS
    • §1 Definition
    • §2 Addition
    • §3 Multiplication
    • §4 Subtraction
    • §5 Division
    • §6 Complex Conjugates
    • §7 Absolute Value
    • §8 Sums and Products
    • §9 Powers
    • §10 Incorporation of the Real Numbers into the System of Complex Numbers
    • INDEX
    • Blank Page
  • Additional Material
     
     
  • Reviews
     
     
    • Certainly no clearer treatment of the foundations of the number system can be offered ... one can only be thankful to the author for this fundamental piece of exposition, which is alive with his vitality and genius.

      American Mathematical Monthly
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 791966; 136 pp
MSC: Primary 26; 01;

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.

  • PREFACE FOR THE STUDENT
  • PREFACE FOR THE TEACHER
  • TABLE OF CONTENTS
  • CHAPTER I: NATURAL NUMBERS
  • §1 Axioms
  • §2 Addition
  • §3 Ordering
  • §4 Multiplication
  • CHAPTER II: FRACTIONS
  • §1 Definition and Equivalence
  • §2 Ordering
  • §3 Addition
  • §4 Multiplication
  • §5 Rational Numbers and Integers
  • CHAPTER III: CUTS
  • §1 Definition
  • §2 Ordering
  • §3 Addition
  • §4 Multiplication
  • §5 Rational Cuts and Integral Cuts
  • CHAPTER IV: REAL NUMBERS
  • §1 Definition
  • §2 Ordering
  • §3 Addition
  • §4 Multiplication
  • §5 Dedekind's Fundamental Theorem
  • CHAPTER V: COMPLEX NUMBERS
  • §1 Definition
  • §2 Addition
  • §3 Multiplication
  • §4 Subtraction
  • §5 Division
  • §6 Complex Conjugates
  • §7 Absolute Value
  • §8 Sums and Products
  • §9 Powers
  • §10 Incorporation of the Real Numbers into the System of Complex Numbers
  • INDEX
  • Blank Page
  • Certainly no clearer treatment of the foundations of the number system can be offered ... one can only be thankful to the author for this fundamental piece of exposition, which is alive with his vitality and genius.

    American Mathematical Monthly
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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