Ideas and Their Reception : Proceedings of the Symposium on the History of Modern Mathematics, Vassar College, Poughkeepsie, New York, June 20-24, 1989

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. Content: Inside Front Cover, Page ii Front Matter, Page iii Copyright, Page iv Contents for Volume II, Pages vii-viii Contributors List, Pages ix-x Preface, Pages xi-xvi, David E. Rowe, John McCleary A Theory of Reception for the History of Mathematics, Pages 2-14, John McCleary Riemann's Habilitationsvortrag And the Synthetic A Priori Status of Geometry, Pages 15-46, Gregory Nowak Cantor's Views on the Foundations of Mathematics, Pages 48-65, Walter Purkert Kronecker's Views on the Foundations of Mathematics, Pages 65-77, Harold M. Edwards Towards A History of Cantor's Continuum Problem, Pages 78-121, Gregory H. Moore British Synthetic vs. French Analytic Styles of Algebra In the Early American Republic, Pages 124-154, Helena M. Pycior Toward a History of Nineteenth-Century Invariant Theory, Pages 155-206, Karen Hunger Parshall The Early Geometrical Works of Sophus Lie and Felix Klein, Pages 208-273, David E. Rowe Line Geometry, Differential Equations And the Birth of Lie's Theory of Groups, Pages 274-327, Thomas Hawkins The Background to Gergonne's Treatment of Duality: Spherical Trigonometry in the late 18th Century, Pages 330-359, Karine Chemla Algebraic Geometry in the late Nineteenth Century, Pages 360-385, J.J. Gray Abel's Theorem, Pages 388-421, Roger Cooke Heinrich Weber and the Emergence of Class Field Theory, Pages 424-450, Günther Frei Notes on the Contributors, Pages 451-453 This volume contains nine essays dealing with historical issues of mathematics. The topics covered span three different approaches to the history of mathematics that may be considered both representative and vital tothe field. The first section, Images of Mathematics, addresses the historiographical and philosophical issues involved in determining the meaning of mathematical history. The second section, Differential Geometry and Analysis, traces the convoluted development of the ideas of differential geometry and analysis. The third section, Research Communities and International Collaboration, discusses the structure and interaction of mathematical communities through studies of the social fabric of the mathematical communities of the U.S. and China. Please provide. Addresses the historiographical and philosophical issues involved in determining the meaning of mathematical history. This book traces the development of the ideas of differential geometry and analysis and discusses structure and interaction of mathematical communities. The first mathematician to explicitly utilize the group concept in a geometrical setting was Camille Jordan (1838-1922). v. 1. Ideas and their reception v. 2. Institutions and applications v. 3. Images, ideas, and communities.