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Item Details
| Title:
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A MATHEMATICAL GIFT
THE INTERPLAY BETWEEN TOPOLOGY, FUNCTIONS, GEOMETRY, AND ALGEBRA |
| Volume: |
v. 1 |
| By: |
Kenji Ueno, Koji Shiga, Shigeyuki Morita |
| Format: |
Paperback |
| List price:
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£57.00 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
0821832824 |
| ISBN 13: |
9780821832820 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
15 October, 2003 |
| Series: |
Mathematical World v. 19 |
| Pages: |
136 |
| Description: |
Discusses 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). This book addresses various aspects of the concept of dimension, including the Peano curve and the Poincare approach. |
| 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. |
| Illustrations: |
Illustrations |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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