Groups and Geometry
About this book
This book, which was originally published in 1985 and has been translated and revised by the author from notes of a course, is an introduction to certain central ideas in group theory and geometry. Professor Lyndon emphasises and exploits the well-known connections between the two subjects and, whilst keeping the presentation at a level that assumes only a basic background in mathematics, leads the reader to the frontiers of current research at the time of publication. The treatment is concrete and combinatorial with a minimal use of analytic geometry. In the interest of the reader's intuition, most of the geometry considered is two-dimensional and there is an emphasis on examples, both in the text and in the problems at the end of each chapter.
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Information
Table of contents
- Cover
- Series Page
- Title
- Copyright
- PREFACE
- CONTENTS
- CHAPTER ONE: SYMMETRIES AND GROUPS
- CHAPTER TWO: ISOMETRIES OF THE EUCLIDEAN PLANE
- CHAPTER THREE: SUBGROUPS OF THE GROUP OF ISOMETRIES OF THE PLANE
- CHAPTER FOUR: DISCONTINUOUS GROUPS OF ISOMETRIES OF THE EUCLIDEAN PLANE: PLANE CRYSTALLOGRAPHIC GROUPS
- CHAPTER FIVE: REGULAR TESSELLATIONS IN HIGHER DIMENSIONS
- CHAPTER SIX: INCIDENCE GEOMETRY OF THE AFFINE PLANE
- CHAPTER SEVEN: PROJECTIVE GEOMETRY
- CHAPTER EIGHT: INVERSIVE GEOMETRY
- CHAPTER NINE: HYPERBOLIC GEOMETRY
- CHAPTER TEN: FUCHSIAN GROUPS
- REFERENCES
- INDEX
