Geometry and Topology

Miles Reid, Balazs Szendroi

196 pages, parution le 28/11/2005

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Résumé

Geometry provides a whole range of views on the universe, serving as the inspiration, technical toolkit and ultimate goal for many branches of mathematics and physics. This book introduces the ideas of geometry, and includes a generous supply of simple explanations and examples. The treatment emphasises coordinate systems and the coordinate changes that generate symmetries. The discussion moves from Euclidean to non-Euclidean geometries, including spherical and hyperbolic geometry, and then on to affine and projective linear geometries. Group theory is introduced to treat geometric symmetries, leading to the unification of geometry and group theory in the Erlangen program. An introduction to basic topology follows, with the Möbius strip, the Klein bottle and the surface with g handles exemplifying quotient topologies and the homeomorphism problem. Topology combines with group theory to yield the geometry of transformation groups, having applications to relativity theory and quantum mechanics. A final chapter features historical discussions and indications for further reading. With minimal prerequisites, the book provides a first glimpse of many research topics in modern algebra, geometry and theoretical physics.
The book is based on many years' teaching experience, and is thoroughly class-tested. There are copious illustrations, and each chapter ends with a wide supply of exercises. Further teaching material is available for teachers via the web, including assignable problem sheets with solutions.

Exercises and practical illustrations introduce topics across maths and its applications

Prerequisites are minimal: ideally suited to beginner courses and newcomers to the subject

Further teaching material is available for teachers, including assignable problem sheets with solutions

Sommaire

List of figures
Preface
Euclidean geometry
Composing maps
Non-Euclidean
Affine geometry
Projective geometry
Geometry and group theory
Topology
Geometry of transformation groups
Concluding remarks
A: Metrics
B: Linear algebra
References
Index

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	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Miles Reid, Balazs Szendroi
Parution	28/11/2005
Nb. de pages	196
Format	17,5 x 24,5
Couverture	Broché
Poids	441g
Intérieur	Noir et Blanc
EAN13	9780521613255
ISBN13	978-0-521-61325-5