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. FOUNDATIONS OF ANALYSIS THE ARITHMETIC OF WHOLE, RATIONAL, IRRATIONAL AND COMPLEX NUMBERS A Supplement to Text-Books on the Differential and Integral Calculus BY EDMUND LANDAU Translated by F Steinhardt Columbia University CHELSEA PUBLISHING COMPANY 1951

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

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