Mathematical Perspectives

Essays on Mathematics and Its Historical Development

1st Edition - October 28, 1981
Editor: Joseph W. Dauben
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 2 - 6 2 5 7 - 4

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… Read more

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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.

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