Groups
A Path to Geometry

R. P. Burn (Author)

9780521347938, Cambridge University Press

Paperback, published 3 September 1987

256 pages
22.9 x 15.1 x 1.9 cm, 0.349 kg

'… the author is encouraging throughout and patiently leads his audience to an understanding of the interplay between group theory and the classical geometry of two and three dimensions … the author is a knowledgeable and considerate guide.' Mathematical Gazette

This book follows the same successful approach as Dr Burn's previous book on number theory. It consists of a carefully constructed sequence of questions which will enable the reader, through his or her own participation, to generate all the group theory covered by a conventional first university course. An introduction to vector spaces, leading to the study of linear groups, and an introduction to complex numbers, leading to the study of Möbius transformations and stereographic projection, are also included. Quaternions and their relationship to three-dimensional isometries are covered, and the climax of the book is a study of crystallographic groups, with a complete analysis of these groups in two dimensions.

Preface
Acknowledgements
1. Functions
2. Permutations of a finite set
3. Groups of permutations of R and C
4. The Möbius group
5. The regular solids
6. Abstract groups
7. Inversions of the Möbius plane and stereographic projection
8. Equivalence relations
9. Cosets
10. Direct product
11. Fields and vector spaces
12. Linear transformations
13. The general linear group GL(2, F)
14. The vector space V3 (F)
15. Eigenvectors and eigenvalues
16. Homomorphisms
17. Conjugacy
18. Linear fractional groups
19. Quaternions and rotations
20. Affine groups
21. Orthogonal groups
22. Discrete groups fixing a line
23. Wallpaper groups
Bibliography
Index.

Subject Areas: Groups & group theory [PBG]