Ideas and Their Reception
Proceedings of the Symposium on the History of Modern Mathematics, Vassar College, Poughkeepsie, New York, June 20-24, 1989
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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
Product details
- No. of pages: 470
- Language: English
- Copyright: © Academic Press 1989
- Published: December 28, 1989
- Imprint: Academic Press
- eBook ISBN: 9781483266213