Groups
A Path to Geometry
- Author: R. P. Burn
- Date Published: September 1987
- availability: Available
- format: Paperback
- isbn: 9780521347938
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Following the same successful approach as Dr. Burn's previous book on number theory, this text consists of a carefully constructed sequence of questions that will enable the reader, through participation, to study 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 relationships to 3-dimensional isometries are covered, and the climax of the book is a study of the 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
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×Product details
- Date Published: September 1987
- format: Paperback
- isbn: 9780521347938
- length: 256 pages
- dimensions: 229 x 151 x 19 mm
- weight: 0.349kg
- availability: 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.
Related Books
related journals
also by this author
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