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A Mathematical Gift I: The Interplay between Topology, Functions, Geometry, and Algebra

A Mathematical Gift I: The Interplay between Topology, Functions, Geometry, and Algebra -

A Mathematical Gift I: The Interplay between Topology, Functions, Geometry, and Algebra (ISBN10: 0821832824; ISBN13: 9780821832820)
ISBN13: 978-0821832820
ISBN10: 0821832824
Cover: Paperback
Publisher: American Mathematical Society
Published: 12/31/2003
International: No

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Brand new. We distribute directly for the publisher. This book will bring the beauty and fun of mathematics to the classroom. It offers serious mathematics in a lively, reader-friendly style. Include ...show mored 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 Poincar??-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 Poincar?? 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. ...show less
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