## Edmund Landau: *Foundations of Analysis* Contents

In 1930 Edmund Landau's Grundlagen der Analysiswas 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, wasFoundations 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.

## FOUNDATIONS OF ANALYSIS

## THE ARITHMETIC OF

WHOLE, RATIONAL, IRRATIONAL AND COMPLEX NUMBERSA Supplement to Text-Books on the

Differential and Integral Calculus

BY

## EDMUND LANDAU

Translated by

F Steinhardt

Columbia University

CHELSEA PUBLISHING COMPANY

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

JOC/EFR August 2007

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