Geometry and Topology
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Geometry and Topology by Miles Reid
Book DescriptionGeometry 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 Mobius 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.
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Book DetailsISBN: 9780521613255
(247mm x 174mm x 12mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 10-Nov-2005
Country of Publication: United Kingdom
Books By Author Miles Reid
Number Theory and Algebraic Geometry, Paperback (January 2004)
This volume honors Sir Peter Swinnerton-Dyer's mathematical career spanning more than 60 years' of amazing creativity in number theory and algebraic geometry.
Explicit Birational Geometry of 3-folds, Paperback (July 2000)
This volume, first published in 2000, is an integrated suite of papers centred around applications of Mori theory to birational geometry.
Undergraduate Commutative Algebra, Paperback (November 1995)
For those looking for an introduction to the area of commutative algebra, this book opens all the right doors and provides a clarity of understanding that all will welcome.
Commutative Ring Theory, Paperback (May 1989)» View all books by Miles Reid
This book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.
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Author Biography - Miles Reid
Miles Reid is a Professor of Mathematics at the Mathematics Institute, University of Warwick. Bal...zs Szendroi is a Tutor and Martin Powell Fellow in Pure Mathematics at St Peter's College, and a Faculty Lecturer in the Mathematical Institute, University of Oxford.
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