Ideas and Their Reception - 1st Edition - ISBN: 9780125996617, 9781483266213

Ideas and Their Reception

1st Edition

Proceedings of the Symposium on the History of Modern Mathematics, Vassar College, Poughkeepsie, New York, June 20-24, 1989

Editors: David E. Rowe John McCleary
eBook ISBN: 9781483266213
Imprint: Academic Press
Published Date: 28th December 1989
Page Count: 470
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Description

The History of Modern Mathematics, Volume I: Ideas and their Reception documents the proceedings of the Symposium on the History of Modern Mathematics held at Vassar College in Poughkeepsie, New York on June 20-24, 1989.

This book is concerned with the emergence and reception of major ideas in fields that range from foundations and set theory, algebra and invariant theory, and number theory to differential geometry, projective and algebraic geometry, line geometry, and transformation groups. Other topics include the theory of reception for the history of mathematics and British synthetic vs. French analytic styles of algebra in the early American Republic. The early geometrical works of Sophus Lie and Felix Klein, background to Gergonne's treatment of duality, and algebraic geometry in the late 19th century are also elaborated.

This volume is intended for students and researchers interested in developments in pure mathematics.

Table of Contents


Table of Contents for Volume II

Contributors List

Preface

The Context of Reception

A Theory of Reception for the History of Mathematics

Riemann's Habilitationsvortrag and the Synthetic A Priori Status of Geometry

Foundations of Mathematics

Cantor's Views on the Foundations of Mathematics

Kronecker's Views on the Foundations of Mathematics

Toward a History of Cantor's Continuum Problem

National Styles in Algebra

British Synthetic vs. French Analytic Styles of Algebra in the Early American Republic

Toward a History of Nineteenth-Century Invariant Theory

Geometry and the Emergence of Transformation Groups

The Early Geometrical Works of Sophus Lie and Felix Klein

Line Geometry, Differential Equations, and the Birth of Lie's Theory of Groups

Projective and Algebraic Geometry

The Background to Gergonne's Treatment of Duality: Spherical Trigonometry in the Late 18th Century

Algebraic Geometry in the Late Nineteenth Century

Abel's Theorem

Abel's Theorem

Number Theory

Heinrich Weber and the Emergence of Class Field Theory

Notes on the Contributors

Details

No. of pages:
470
Language:
English
Copyright:
© Academic Press 1989
Published:
Imprint:
Academic Press
eBook ISBN:
9781483266213

About the Editor

David E. Rowe

John McCleary

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