
Geometry and Topology
Cambridge University Press
Published on 10. November 2005
Book
Paperback/Softback
216 pages
978-0-521-61325-5 (ISBN)
Description
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 Moebius 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.
Reviews / Votes
?A welcome addition to the undergraduate library. Highly recommended.? --ChoiceMore details
Language
English
Place of publication
Cambridge
United Kingdom
Target group
College/higher education
Professional and scholarly
Product notice
Paperback (trade)
Illustrations
Worked examples or Exercises; 1 Halftones, unspecified; 92 Line drawings, unspecified
Dimensions
Height: 244 mm
Width: 170 mm
Thickness: 12 mm
Weight
382 gr
ISBN-13
978-0-521-61325-5 (9780521613255)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions

Miles Reid | Balazs Szendroi
Geometry and Topology
E-Book
02/2006
1st Edition
Cambridge University Press
€54.49
Available for download

Miles Reid | Balazs Szendroi
Geometry and Topology
Book
11/2005
Cambridge University Press
€77.99
Article exhausted; check for reprint
Previous edition

Miles Reid | Balazs Szendroi
Geometry and Topology
Book
11/2005
Cambridge University Press
€77.99
Article exhausted; check for reprint
Persons
Miles Reid is a Professor of Mathematics at the Mathematics Institute, University of Warwick. Balazs Szendroei 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.
Content
Introduction; 1. Euclidean geometry; 2. Composing maps; 3. Non-Euclidean; 4. Affine geometry; 5. Projective geometry; 6. Geometry and group theory; 7. Topology; 8. Geometry of transformation groups; 9. Concluding remarks; A. Metrics; B. Linear algebra; References; Index.