ENGLISH

A mathematical gift, 1, interplay between topology, functions, geometry, and algebra

By Kenji Ueno , Shigeyuki Morita , Koji Shiga

Book information

Publisher
American Mathematical Society
Year
2003
ISBN
0821832824, 9780821832820
LCC
QA445 .U3613 2003
Open Library ID
OL18919694M
Language
english
Format
DJVU
Filesize
2 MB (2443145 bytes)
Series
Mathematical World
Edition
AMS
Pages
137\137
Library
Kolxo3
DPI
400
Time added
2009-07-20 03:45:11
Математика;Прочие разделы математики

Description

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 Poincaré-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 Poincaré 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).

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