Overview

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.

Full Product Details

Author:   R. P. Burn
Publisher:   Cambridge University Press
Imprint:   Cambridge University Press (Virtual Publishing)
ISBN:  

9781139163590

ISBN 10:   1139163590
Publication Date:   05 June 2012
Audience:   College/higher education ,  College/higher education ,  Professional and scholarly ,  Tertiary & Higher Education ,  Undergraduate
Format:   Undefined
Publisher's Status:   Active
Availability:   In stock  
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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.

Reviews

'There is much here of value both for students and for those who are seeking a refresher course in modern group theory.' Times Higher Education Supplement '... 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

'There is much here of value both for students and for those who are seeking a refresher course in modern group theory.' The Times Higher Education Supplement '… 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

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