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A Topological Aperitif

4.3/5 ( ratings)

A guide to the calculation of elementary geometric topology, where geometry guides the calculation. The book starts with a wealth of examples of how to be mathematically certain whether two objects are the same from the point of view of topology. After introducing surfaces, such as the Klein bottle, the book explores the properties of polyhedra drawn on these surfaces. Even in the simplest case, of spherical polyhedra, there are good questions to be asked. More refined tools are developed in a chapter on winding number, and an appendix gives a glimpse of knot theory. There are many examples and exercises making this a useful textbook for a first undergraduate course in topology. For much of the book the prerequisites are slight, though, so anyone with curiosity and tenacity should be able to enjoy the book. As well as arousing curiosity, the book gives a firm geometrical foundation for further study.

Language: English

Pages: 166

Format: Paperback

Publisher: Springer

Release: January 01, 2001

ISBN: 1852333774

ISBN 13: 9781852333775

A Topological Aperitif

4.3/5 ( ratings)

A guide to the calculation of elementary geometric topology, where geometry guides the calculation. The book starts with a wealth of examples of how to be mathematically certain whether two objects are the same from the point of view of topology. After introducing surfaces, such as the Klein bottle, the book explores the properties of polyhedra drawn on these surfaces. Even in the simplest case, of spherical polyhedra, there are good questions to be asked. More refined tools are developed in a chapter on winding number, and an appendix gives a glimpse of knot theory. There are many examples and exercises making this a useful textbook for a first undergraduate course in topology. For much of the book the prerequisites are slight, though, so anyone with curiosity and tenacity should be able to enjoy the book. As well as arousing curiosity, the book gives a firm geometrical foundation for further study.

Language: English

Pages: 166

Format: Paperback

Publisher: Springer

Release: January 01, 2001

ISBN: 1852333774

ISBN 13: 9781852333775

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