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Das Kontinuum und andere Monographien
H. Weyl, E. Landau, and B. Riemann
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AMS Chelsea Publishing
1973; 400 pp; hardcover
Volume: 134
ISBN-10: 0-8218-4097-5
ISBN-13: 978-0-8218-4097-9
List Price: US$41
Member Price: US$36.90
Order Code: CHEL/134.H
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The present volume is a reprint, under one cover, of four short books written by outstanding German mathematicians.

The first book, The Continuum by Hermann Weyl, is the study of the continuum, particularly its role in the foundations of analysis.

The second piece is Mathematical Analysis of Space Problems, also by Weyl. The two main topics are infinitesimal geometry and the use of group theory in the analysis of space problems. These are followed by a selection of twelve additional topics, such as Möbius transformations, computing Riemannian curvature, and elements of Lie theory.

Next in the collection is Edmund Landau's short book Statement and Proof of Some New Results in Function Theory. In eight short chapters, Landau considers a variety of topics, such as Tauberian theorems, Hadamard's three circle theorem, and Koebe's distortion theorem for schlicht functions. In his preface, Landau writes that he has chosen the topics for their great elegance.

The final piece of this volume is Bernard Riemann's ground-breaking lecture On the Hypotheses Which Lie at the Foundations of Geometry. In this one remarkable lecture, Riemann laid out the foundations of what became Riemannian geometry, particularly the notion of curvature for arbitrary manifolds. The story is told that, of the audience, only Gauss fully appreciated the depth of what Riemann was saying.

Table of Contents

Das Kontinuum by Hermann Weyl
  • Menge und Funktion. (Analyse der mathematischen Begriffsbildung)
  • Zahlbegriff und Kontinuum. (Grundlagen der Infinitesimalrechnung)
Mathematische Analyse des Raumproblems by Hermann Weyl
  • Einleitung
  • Infinitesimalgeometrie
  • Gruppentheoretische Analyse des Raumproblems
  • Zusätze
  • Literatur
  • Namen- und Sachverzeichnis
Darstellung und Begründung einiger neuerer Ergebnisse d er Funktionentheorie by Edmund Landau
  • Über beschränkte Potenzreihen
  • Summabilität höherer Ordnung
  • Umkehrungen des Abelschen Stetigkeitssatzes
  • Über einige Merkwürdigkeiten des Verhaltens von Potenzreihen a uf dem Rande
  • Beziehungen der Koeffizienten einer Potenzreihe zu Singularitäten d er Funktion auf dem Rande
  • Maximum und Mittelwert des absoluten Betrages einer analytischen Funktio n auf Kreisen
  • Der Picardsche Ideenkreis
  • Schlichte Funktionen
  • Literaturverzeichnis
Über die Hypothesen, welche der Geometrie zu Grunde lie gen by B. Riemann
  • Über die Hypothesen, welche der Geometrie zugrunde liegen
  • Plan der Untersuchung
  • Übersicht
  • Erläuterungen (des Herausgebers)
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