Groups: A Path to Geometry

ISBN-13: 9780521347938 / Angielski / Miękka / 1987 / 256 str.

R. P. Burn

Opis

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 Mobius 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.

Recenzje

'… 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

Spis treści

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.