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 |
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 |
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Book DetailsAMS Chelsea PublishingVolume: 79; 1966; 136 ppMSC: 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.
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Table of Contents
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PREFACE FOR THE STUDENT
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PREFACE FOR THE TEACHER
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TABLE OF CONTENTS
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CHAPTER I: NATURAL NUMBERS
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§1 Axioms
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§2 Addition
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§3 Ordering
-
§4 Multiplication
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CHAPTER II: FRACTIONS
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§1 Definition and Equivalence
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§2 Ordering
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§3 Addition
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§4 Multiplication
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§5 Rational Numbers and Integers
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CHAPTER III: CUTS
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§1 Definition
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§2 Ordering
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§3 Addition
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§4 Multiplication
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§5 Rational Cuts and Integral Cuts
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CHAPTER IV: REAL NUMBERS
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§1 Definition
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§2 Ordering
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§3 Addition
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§4 Multiplication
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§5 Dedekind's Fundamental Theorem
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CHAPTER V: COMPLEX NUMBERS
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§1 Definition
-
§2 Addition
-
§3 Multiplication
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§4 Subtraction
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§5 Division
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§6 Complex Conjugates
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§7 Absolute Value
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§8 Sums and Products
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§9 Powers
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§10 Incorporation of the Real Numbers into the System of Complex Numbers
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INDEX
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Blank Page
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Additional Material
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Reviews
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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
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
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