Geometry from a Differentiable Viewpoint

John McCleary author

Format:Paperback

Publisher:Cambridge University Press

Published:29th Oct '12

Currently unavailable, and unfortunately no date known when it will be back

This paperback is available in another edition too:

Geometry from a Differentiable Viewpoint cover

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

This text, for a first course in differential or modern geometry, introduces methods within a historical context that is familiar to students from high school. The thoroughly revised second edition has been reorganized for greater clarity and includes numerous new exercises and topics such as Euclid's geometry of space.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.

Review of the first edition: '… an unusual and interesting account of two subjects and their close historical interrelation.' The Mathematical Gazette
'… the author has succeeded in making differential geometry an approachable subject for advanced undergraduates.' Andrej Bucki, Mathematical Reviews

ISBN: 9780521133111

Dimensions: 253mm x 175mm x 18mm

Weight: 630g

368 pages

2nd Revised edition