Groups and Geometry

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Overview


This volume presents the Oxford Mathematical Institute notes for the enormously successful advanced undergraduate and first-year graduate student course on groups and geometry. The book's content closely follows the Oxford syllabus but covers a great deal more material than did the course itself. The book is divided into two parts: the first covers the fundamentals of groups, and the second covers geometry and its symbiotic relationship with groups. Both parts contain a number of useful examples and exercises. This book will be welcomed by student and teacher alike as a lucidly written text on an important topic.
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Product Details

  • ISBN-13: 9780198534518
  • Publisher: Oxford University Press, USA
  • Publication date: 3/28/1994
  • Series: Oxford Science Publications
  • Pages: 264
  • Product dimensions: 6.13 (w) x 9.13 (h) x 0.63 (d)

Meet the Author

The Queen's College, Oxford

Lady Margaret Hall, Oxford

Jesus College, Oxford

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Table of Contents

1 A survey of some group theory 1
2 A menagerie of groups 17
3 Actions of groups 30
4 A garden of G-spaces 38
5 Transitivity and orbits 50
6 The classification of transitive G-spaces 61
7 G-morphisms 74
8 Group actions in group theory 83
9 Actions count 100
10 Geometry: an introduction 108
11 The axiomatisation of geometry 116
12 Affine geometry 127
13 Projective geometry 148
14 Euclidean geometry 159
15 Finite groups of isometries 172
16 Complex numbers and quaternions 188
17 Inversive geometry 210
18 Topological considerations 229
19 The group theory of Rubik's magic cube 242
Index 249
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