The only book of its kind written specifically for undergraduates which explains the links between these two important mathematical groups. The authors explain these links by recourse to symmetry, a study of groups providing a good means of measuring geometrical symmetry.
Available for the first time in published form, Groups and Geometry presents the Oxford Mathematical Institute notes for undergraduates and first year postgraduates. The content is guided by the Oxford syllabus but includes much more material than is included on the syllabus. This book is about the measurement of symmetry: covering groups and geometry with the symbiotic relationship between the two more than justifying the union. A number of exercises are included in this sylish text to help the reader gain a full understanding of this branch of mathematics.
'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) *
Table of Contents
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
Groups and Geometry by Peter M. Neumann
Peter M. Neumann
Used - Very Good
Oxford University Press
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