Geometry from a Differentiable Viewpoint - Brossura

McCleary, John

Brossura

ISBN 10: 0521133114 ISBN 13: 9780521133111

Casa editrice: Cambridge University Press, 2012

Riassunto

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.

Su questo libro

Recensione

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

Descrizione del libro

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.

Dettagli dell?edizione

• Editore: Cambridge University Press
• Data di pubblicazione: 2012
• ISBN 10: 0521133114
• ISBN 13: 9780521133111
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero edizione: 2
• Numero di pagine: 374