GEOMETRY FROM A DIFFERENTIABLE VIEWPOINT by John McCleary ( 9780521133111 )

Item Details

Title:

GEOMETRY FROM A DIFFERENTIABLE VIEWPOINT

By:

John McCleary

Format:

Paperback

List price:

£44.99

Our price:

£39.37

Discount:

12.5% off

You save:

£5.62

ISBN 10:

0521133114

ISBN 13:

9780521133111

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Publisher:

CAMBRIDGE UNIVERSITY PRESS

Pub. date:

29 October, 2012

Edition:

2nd Revised edition

Pages:

368

Description:

A thoroughly revised second edition of a textbook for a first course in differential/modern geometry that introduces methods within a historical context.

Synopsis:

The development of geometry from Euclid to Euler to Lobachevsky, Bolyai, Gauss and Riemann is a story that is often broken into parts - axiomatic geometry, non-Euclidean geometry and differential geometry. This poses a problem for undergraduates: Which part is geometry? What is the big picture to which these parts belong? In this introduction to differential geometry, the parts are united with all of their interrelations, motivated by the history of the parallel postulate. Beginning with the ancient sources, the author first explores synthetic methods in Euclidean and non-Euclidean geometry and then introduces differential geometry in its classical formulation, leading to the modern formulation on manifolds such as space-time. The presentation is enlivened by historical diversions such as Huygens's clock and the mathematics of cartography. The intertwined approaches will help undergraduates understand the role of elementary ideas in the more general, differential setting. This thoroughly revised second edition includes numerous new exercises and a new solution key. New topics include Clairaut's relation for geodesics and the use of transformations such as the reflections of the Beltrami disk.

Illustrations:

164 b/w illus. 203 exercises

Publication:

Imprint:

Cambridge University Press

Returns:

Returnable

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