Groups and geometry
著者
書誌事項
Groups and geometry
Oxford University Press, 1994
- : hbk
- : pbk
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注記
Includes index
内容説明・目次
- 巻冊次
-
: pbk ISBN 9780198534518
内容説明
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.
目次
- 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
- 巻冊次
-
: hbk ISBN 9780198534525
内容説明
"Groups and Geometry" contains the Oxford Mathematical Institute notes for undergraduates and first-year postgraduates. The content, although guided by the Oxford syllabus, covers other material, some introductory and some that, because of limited time, had to be excluded from or curtailed in the syllabus. This book is about the measurement of symmetry, which is what groups are for. Symmetry is visable in all parts of mathematics and in many other areas, and geometrical symmetry is the most visable of all. For this reason, groups and geometry are close neighbours. The first half of the book (chapters 1-9) covers groups and the second half (chapters 10-18) covers geometry, with the symbiotic relationship between the two more than justifying the union. Both parts contain a number of exercises that should be helpful to the reader wishing to gain a fuller understanding of this area of mathematics.
目次
- A survey of some group theory
- a menagerie of groups
- actions of groups
- a garden of G-spaces
- transitivity and orbits
- the classification of transitive G-spaces
- G-morphisms
- group actions in group theory
- actions count
- geometry - an introduction
- the axiomatization of geometry
- affine geometry
- projective geometry
- Euclidean geometry
- finite groups of isometries
- complex numbers and quaternions
- inversive geometry
- topological considerations
- the group theory of Rubik's magic cube.
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