Das Kontinuum Und Andere Monographien (AMS Chelsea Publishing)

Das Kontinuum Und Andere Monographien (AMS Chelsea Publishing)

Hardback

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Description

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 Mobius 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.

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 Zusatze Literatur Namen- und Sachverzeichnis Darstellung und Begrundung einiger neuerer Ergebnisse d er Funktionentheorie by Edmund Landau: Uber beschrankte Potenzreihen Summabilitat hoherer Ordnung Umkehrungen des Abelschen Stetigkeitssatzes Uber einige Merkwurdigkeiten des Verhaltens von Potenzreihen a uf dem Rande Beziehungen der Koeffizienten einer Potenzreihe zu Singularitaten d er Funktion auf dem Rande Maximum und Mittelwert des absoluten Betrages einer analytischen Funktio n auf Kreisen Der Picardsche Ideenkries Schlichte Funktionen Literaturverzeichnis Uber die Hypothesen, welche der Geometrie zu Grunde lie gen by B. Riemann: Uber die Hypothesen, welche der Geometrie zugrunde liegen Plan der Untersuchung Ubersicht Erlauterungen (des Herausgebers).

Product Details

  • ISBN13: 9780821840979
  • Format: Hardback
  • ID: 9780821840979
  • ISBN10: 0821840975

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