Edmund Landau: Foundations of Analysis Contents
In 1930 Edmund Landau's Grundlagen der Analysis was published by the Akademische Verlagsgesellschaft M.B.H., Leipzig. In 1951 an English translation of Landau's work by F Steinhardt of Columbia University in New York was published by the Chelsea Publishing Company. The full title, including subtitles, was Foundations of Analysis: the Arithmetic of Whole, Rational, Irrational and Complex Number: A Supplement to Text-Books on the Differential and Integral Calculus. Below is a list of the Contents of this interesting book.
For the two Prefaces see Landau's Foundations.
THE ARITHMETIC OF
For the two Prefaces see Landau's Foundations.
FOUNDATIONS OF ANALYSIS
THE ARITHMETIC OF
WHOLE, RATIONAL, IRRATIONAL AND COMPLEX NUMBERS
A Supplement to Text-Books on the
Differential and Integral Calculus
Differential and Integral Calculus
BY
EDMUND LANDAU
Translated by
F Steinhardt
Columbia University
F Steinhardt
Columbia University
CHELSEA PUBLISHING COMPANY
1951
1951
TABLE OF CONTENTS
Preface for the Student
Preface for the Scholar
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
Last Updated August 2007