Groups
Groups
$78.99
USDThis 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.
Reviews & endorsements
"What distinguishes this book from all others? Simply, it is not a textbook in the normal sense. The approach of the book is one of development by discovery. There is almost no text as such-the reader being invited to learn about the groups through a sequence of over 800 problems." Times Higher Education Supplement
Product details
September 1987Paperback
9780521347938
256 pages
229 × 151 × 19 mm
0.349kg
Available
Table of Contents
- 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.
