Geometry

Popular undergraduate textbook revealing the beauty of geometry. Second edition includes chapter summaries, tougher exercises and an online Instructors' Manual.

David A. Brannan (Author), Matthew F. Esplen (Author), Jeremy J. Gray (Author)

9781107647831, Cambridge University Press

Paperback / softback, published 22 December 2011

602 pages, 750 b/w illus. 200 exercises
24.1 x 18.8 x 3 cm, 1.28 kg

'… an excellent and precisely written textbook that should be studied in depth by all would-be mathematicians.' Hans Sachs, American Mathematical Society

This richly illustrated and clearly written undergraduate textbook captures the excitement and beauty of geometry. The approach is that of Klein in his Erlangen programme: a geometry is a space together with a set of transformations of the space. The authors explore various geometries: affine, projective, inversive, hyperbolic and elliptic. In each case they carefully explain the key results and discuss the relationships between the geometries. New features in this second edition include concise end-of-chapter summaries to aid student revision, a list of further reading and a list of special symbols. The authors have also revised many of the end-of-chapter exercises to make them more challenging and to include some interesting new results. Full solutions to the 200 problems are included in the text, while complete solutions to all of the end-of-chapter exercises are available in a new Instructors' Manual, which can be downloaded from www.cambridge.org/9781107647831.

Preface
Introduction: geometry and geometries
1. Conics
2. Affine geometry
3. Projective geometry: lines
4. Projective geometry: conics
5. Inversive geometry
6. Hyperbolic geometry: the disc model
7. Elliptic geometry: the spherical model
8. The Kleinian view of geometry
Special symbols
Further reading
Appendix 1. A primer of group theory
Appendix 2. A primer of vectors and vector spaces
Appendix 3. Solutions to the problems
Index.

Subject Areas: Geometry [PBM]