Mathematical Perspectives

Mathematical Perspectives

Essays on Mathematics and Its Historical Development

1st Edition - October 28, 1981

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  • Editor: Joseph W. Dauben
  • eBook ISBN: 9781483262574

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Description

Mathematical Perspectives: Essays on Mathematics and its Historical Development is a collection of 13 biographical essays on the historical advances of science. This collection is originally meant to comprise an issue of the journal Historia Mathematica in honor of Professor Kurt R. Biermann’s 60th birthday. This 12-chapter text includes essays on studies and commentaries on the problem of “figures of equal perimeter” by various authors in antiquity, including Zenodorus, Theon, and Pappus. Other essays explore the comparison of the areas of polygons with equal perimeter; the concept of function; history of mathematics; the development of mathematical physics in France; and the history of Logicism and Formalism. The remaining chapters deal with essays on an early version of Gauss’ Disquisitiones Arithmeticae, ideal numbers, a mathematical-philosophilica theory of probability, and historical examples of problem of number sequence interpolation. This book will be of value to mathematicians, historians, and researchers.

Table of Contents


  • List of Contributors

    Preface

    Kurt-Reinhard Biermann

    Adrianus Romanus and Giovanni Camillo Glorioso on Isoperimetric Figures

    Notes

    References

    Des Fonctions Comme Expressions Analytiques Aux Fonctions Représentables Analytiquement

    La Notion Eulérienne de Fonction

    La Fonction Continue au Sens de Bolzano

    Cauchy et la Conservation de la Continuité par des Opérations de l'analyse

    Dirichlet et les "Fonctions qui ne sont Assujetties á Aucune loi Analytique"

    Weierstrass et les "Expressions Analytiques" des Functions Continues

    Dedekind et l'Application Comme Fondement des Mathematiques

    Cantor, la topologie générale, et le Transfini

    Baire et les Fonctions Représentables Analytiquement

    Bibliographie

    August Leopold Crelle und die Berliner Akademie der Wissenschaften

    Notes

    Hermite-Weber-Neumann: Kleine Briefgeschichte Eines Grossen Irrtums

    Notes

    Mittelalterliche Mathematische Handschriften in Westlichen Sprachen in der Berliner Staatsbibliothek. Ein Vorläufiges Verzeichnis

    Anmerkungen

    Beschreibungen

    Literaturverzeichnis

    Namen- und Sachregister

    Verzeichnis der Initien

    Mathematical Physics in France, 1800-1840: Knowledge, Activity, and Historiography

    1. Introduction

    2. An Outline of Developments from 1800 to 1840

    3. Institutional Aspects: The Académie des Sciences, and Outside

    4. Educational Aspects: The Ecole Polytechnique, and Outside

    5. Mathematical Procedure

    6. The Use of Mathematics in Physics: A Spectrum of Modes

    7. Some Companion Philosophical Aspects

    8. The French Community in Mathematical Physics, 1800-1840

    9. Some Remarks on the Social History of Science

    10. On the Decline of French Mathematical Physics

    11. On Mathematical Physics outside France, 1800-1840

    12. Bibliographical Statement

    Bibliography

    Symbolik und Formalismus im Mathematischen Denken des 19. und Beginnenden 20. Jahrhunderts

    Einleitung

    1. Heuristik und Ordnungsprinizipien

    2. Symbolische Algebra und formale Mathematik

    3. Hamilton und die Quaternionentheorie

    4. Operationenkalkül

    5. Algorithmisierung

    6. Universalisierung

    Anmerkungen

    An Early Version of Gauss's Disquisitiones Arithmeticae

    Provenance

    Description

    Contents

    Creation of the AR

    Creation of the DA

    Conclusion

    Notes

    References

    Über die Anstöße zu Kummers Schöpfung der "Idealen Complexen Zahlen"

    1. Zielstellung

    2. Über Einige Aüsserungen Hensels

    3. Kummer und die Fermatsche Vermutung

    4. Kummers Weg zu den "idealen complexen Zahlen"

    Zitierte Literatur

    Leibniz on the Probable

    1. Introduction

    2. Leibniz's Interests in Jurisprudence as His Starting Point

    3. Leibniz's Attempt to Mathematize the Probable, to Estimate the Uncertain

    4. Leibniz's Influence on the Theory of Probability in the Early Eighteenth Century

    5. Conclusion

    Abbreviations

    Notes

    Von Pascals Dreieck zu Eulers Gamma-Funktion. Zur Entwicklung der Methodik der Interpolation

    Literatur

    Neue Geometrische Texte aus Byzanz

    Anmerkungen

    Deutsche Mathematiker—Auswärtige Mitglieder der Akademie der Wissenschaften der UdSSR

    Literaturverzeichnis

    Bibliographie: Veröffentlichungen von Prof. Dr. rer. nat. habil. Kurt-R. Biermann

    Index zur Bibliographie

Product details

  • No. of pages: 288
  • Language: English
  • Copyright: © Academic Press 1981
  • Published: October 28, 1981
  • Imprint: Academic Press
  • eBook ISBN: 9781483262574

About the Editor

Joseph W. Dauben

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