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A Mathematical Gift, 1: The Interplay Between Topology, Functions, Geometry, and Algebra - Couverture souple

Livre 17 sur 25: Mathematical World

American Mathematical Society

 
9780821832820: A Mathematical Gift, 1: The Interplay Between Topology, Functions, Geometry, and Algebra
Couverture souple
ISBN 10 : 0821832824 ISBN 13 : 9780821832820
Editeur : American Mathematical Society, 2003

Synopsis

This book will bring the beauty and fun of mathematics to the classroom. It offers serious mathematics in a lively, reader-friendly style. Included are exercises and many figures illustrating the main concepts. The first chapter presents the geometry and topology of surfaces. Among other topics, the authors discuss the Poincare-Hopf theorem on critical points of vector fields on surfaces and the Gauss-Bonnet theorem on the relation between curvature and topology (the Euler characteristic).The second chapter addresses various aspects of the concept of dimension, including the Peano curve and the Poincare approach. Also addressed is the structure of three-dimensional manifolds. In particular, it is proved that the three-dimensional sphere is the union of two doughnuts. This is the first of three volumes originating from a series of lectures given by the authors at Kyoto University (Japan). It is suitable for classroom use for high school mathematics teachers and undergraduate mathematics courses in the sciences and liberal arts. The second volume is available as Volume 20 in the AMS series, ""Mathematical World"". A third volume is forthcoming.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Éditeur
American Mathematical Society
Date d'édition
2003
Langue
anglais
ISBN 10 
0821832824
ISBN 13 
9780821832820
Reliure
Broché
Coordonnées du fabricant
non disponible
Personne responsable
non disponible