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Grundlagen der Analysis: Fourth Edition
 
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Softcover ISBN:  978-0-8284-0141-8
Product Code:  CHEL/141
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $62.10
eBook ISBN:  978-1-4704-7845-2
Product Code:  CHEL/141.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $58.50
Softcover ISBN:  978-0-8284-0141-8
eBook: ISBN:  978-1-4704-7845-2
Product Code:  CHEL/141.B
List Price: $134.00 $101.50
MAA Member Price: $120.60 $91.35
AMS Member Price: $120.60 $91.35
Click above image for expanded view
Grundlagen der Analysis: Fourth Edition
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Softcover ISBN:  978-0-8284-0141-8
Product Code:  CHEL/141
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $62.10
eBook ISBN:  978-1-4704-7845-2
Product Code:  CHEL/141.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $58.50
Softcover ISBN:  978-0-8284-0141-8
eBook ISBN:  978-1-4704-7845-2
Product Code:  CHEL/141.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: 1411951; 173 pp
    MSC: Primary 26; 01; Secondary 00

    Landau's classic book on the foundations of analysis is presented in its original German, with a German-English dictionary as an appendix. One intent of this edition is to provide the English-speaking mathematician with an opportunity to learn some mathematical German. Of course, a pleasant by-product is having Landau's exposition on the construction of the real numbers from the natural numbers using Dedekind cuts. The book is written in an extremely telegraphic style, with few words outside the “Theorem-Proof” motif, making the German notably simpler than in more advanced texts. Thus, the student who begins this book with little or no knowledge of German will gain the experience of successfully reading an entire book in mathematics and with it a feeling for the language and a well-ingrained mathematical vocabulary. (Note: The English edition of the book is available as Foundations of Analysis).

  • Table of Contents
     
     
    • Front Cover
    • lnhaltsverzeichnis.
    • Preface for the Student
    • Preface for the Teacher
    • Vorwort für den Lernenden.
    • Vorwort für den Kenner.
    • Kapitel 1. Natürliche Zahlen.
    • § 1. Axiome.
    • § 2. Addition.
    • § 3. Ordnung.
    • § 4. Multiplikation.
    • Kapitel 2. Brüche.
    • § 1. Definition und Äquivalenz.
    • § 2. Ordnung.
    • § 3. Addition.
    • § 4. Multiplikation.
    • § 5. Rationale Zahlen und ganze Zahlen.
    • Kapitel 3. Schnitte.
    • § 1. Definition.
    • § 2. Ordnung.
    • § 3. Addition.
    • § 4. Multiplikation.
    • § 5. Rationale Schnitte und ganze Schnitte.
    • Kapitel 4. Reelle Zahlen.
    • § 1. Definition.
    • § 2. Ordnung.
    • § 3. Addition.
    • § 4. Multiplikation.
    • § 5. Dedekindscher Hauptsatz.
    • Kapitel 5. Komplexe Zahlen.
    • § 1. Definition.
    • § 2. Addition.
    • § 3. Multiplikation.
    • § 4. Subtraktion.
    • § 5. Division.
    • § 6. Konjugierte Zahlen.
    • § 7. Absoluter Betrag.
    • § 8. Summen und Produkte.
    • § 9. Potenzen.
    • § 10. Einordnung der reellen Zahlen.
    • German-English Vocabulary
    • Back Cover
  • Additional Material
     
     
  • Reviews
     
     
    • A famous book by one of the most distinguished pure mathematicians of recent times ... can be read by anyone with almost no knowledge of German.

      British Journal for the Philosophy of Science
  • 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: 1411951; 173 pp
MSC: Primary 26; 01; Secondary 00

Landau's classic book on the foundations of analysis is presented in its original German, with a German-English dictionary as an appendix. One intent of this edition is to provide the English-speaking mathematician with an opportunity to learn some mathematical German. Of course, a pleasant by-product is having Landau's exposition on the construction of the real numbers from the natural numbers using Dedekind cuts. The book is written in an extremely telegraphic style, with few words outside the “Theorem-Proof” motif, making the German notably simpler than in more advanced texts. Thus, the student who begins this book with little or no knowledge of German will gain the experience of successfully reading an entire book in mathematics and with it a feeling for the language and a well-ingrained mathematical vocabulary. (Note: The English edition of the book is available as Foundations of Analysis).

  • Front Cover
  • lnhaltsverzeichnis.
  • Preface for the Student
  • Preface for the Teacher
  • Vorwort für den Lernenden.
  • Vorwort für den Kenner.
  • Kapitel 1. Natürliche Zahlen.
  • § 1. Axiome.
  • § 2. Addition.
  • § 3. Ordnung.
  • § 4. Multiplikation.
  • Kapitel 2. Brüche.
  • § 1. Definition und Äquivalenz.
  • § 2. Ordnung.
  • § 3. Addition.
  • § 4. Multiplikation.
  • § 5. Rationale Zahlen und ganze Zahlen.
  • Kapitel 3. Schnitte.
  • § 1. Definition.
  • § 2. Ordnung.
  • § 3. Addition.
  • § 4. Multiplikation.
  • § 5. Rationale Schnitte und ganze Schnitte.
  • Kapitel 4. Reelle Zahlen.
  • § 1. Definition.
  • § 2. Ordnung.
  • § 3. Addition.
  • § 4. Multiplikation.
  • § 5. Dedekindscher Hauptsatz.
  • Kapitel 5. Komplexe Zahlen.
  • § 1. Definition.
  • § 2. Addition.
  • § 3. Multiplikation.
  • § 4. Subtraktion.
  • § 5. Division.
  • § 6. Konjugierte Zahlen.
  • § 7. Absoluter Betrag.
  • § 8. Summen und Produkte.
  • § 9. Potenzen.
  • § 10. Einordnung der reellen Zahlen.
  • German-English Vocabulary
  • Back Cover
  • A famous book by one of the most distinguished pure mathematicians of recent times ... can be read by anyone with almost no knowledge of German.

    British Journal for the Philosophy of Science
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
Please select which format for which you are requesting permissions.