Groups and Geometry

Häftad, Engelska, 1994

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Beskrivning

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.

Produktinformation

Utgivningsdatum:1994-02-03
Mått:156 x 232 x 15 mm
Vikt:428 g
Format:Häftad
Språk:Engelska
Antal sidor:264
Förlag:OUP OXFORD
ISBN:9780198534518

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Recensioner i media

'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

Innehållsförteckning

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