Groups: A Path to Geometry

by R. P. Burn

Overview

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.

Product Details

ISBN-13:	9780521347938
Publisher:	Cambridge University Press
Publication date:	09/03/1987
Series:	Path to Geometry
Edition description:	New Edition
Pages:	256
Product dimensions:	5.94(w) x 9.02(h) x 0.75(d)

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.

Editorial Reviews

"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

From the Publisher