Available for the first time in published form, Groups and Geometry contains the Oxford Mathematical Institute notes for undergraduates and first-year postgraduates, although guided by the Oxford syllabus much other material is also included. Symmetry is visable in all parts of mathematics, and in many other areas, and geometrical symmetry is the most visible of all. For this reason, groups and geometry are such close neighbours. Also included are a number of exercises that will be invaluable to any reader wishing to gain a fuller understanding of this area of mathematics.
Rezensionen / Stimmen
'develops a comprehensive group-theoretic approach to affine, projective and inversive geometry ... It ends with a fascinating chapter on the group theory behind the Rubik cube.'
Ian Stewart, New Scientist 'Both parts contain a number of exercises that will be invaluable to any reader wishing to gain a fuller understanding of this area of mathematics.'
Extrait de L'Enseignement Mathematique, T. 40 1994 The book can be recommended warmly for any interested reader. "Monatshefte fur Mathematik No.3 1996. delightful book ... The group theory is directed towards group actions, but all the basic material is there. * Mathematika, 41 (1994) *
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Illustrationen
Maße
Höhe: 234 mm
Breite: 156 mm
Dicke: 15 mm
Gewicht
ISBN-13
978-0-19-853451-8 (9780198534518)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
1. A survey of some group theory ; 2. A menagerie of groups ; 3. Actions of groups ; 4. A garden of G-spaces ; 5. Transitivity and orbits ; 6. The classification of transitive G-spaces ; 7. G-morphisms ; 8. Group actions in group theory ; 9. Actions count ; 10. Geometry: an introduction ; 11. The axiomatisation of geometry ; 12. Affine geometry ; 13. Projective geometry ; 14. Euclidean geometry ; 15. Finite groups of isometries ; 16. Complex numbers and quaternions ; 17. Inversive geometry ; 18. Topological considerations ; 19. The groups theory of Rubik's magic cube ; Index
