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Groups

Groups
A Path to Geometry

£45.99

textbook
  • Date Published: September 1987
  • availability: Available
  • format: Paperback
  • isbn: 9780521347938

£ 45.99
Paperback

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About the Authors
  • This book follows the same successful approach as Dr Burn's previous book on number theory. It consists of a carefully constructed sequence of questions which will enable the reader, through his or her own participation, to generate all the group theory covered by a conventional first university course. An introduction to vector spaces, leading to the study of linear groups, and an introduction to complex numbers, leading to the study of Möbius transformations and stereographic projection, are also included. Quaternions and their relationship to three-dimensional isometries are covered, and the climax of the book is a study of crystallographic groups, with a complete analysis of these groups in two dimensions.

    Reviews & endorsements

    'There is much here of value both for students and for those who are seeking a refresher course in modern group theory.' The Times Higher Education Supplement

    '… the author is encouraging throughout and patiently leads his audience to an understanding of the interplay between group theory and the classical geometry of two and three dimensions … the author is a knowledgeable and considerate guide.' Mathematical Gazette

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    Product details

    • Date Published: September 1987
    • format: Paperback
    • isbn: 9780521347938
    • length: 256 pages
    • dimensions: 228 x 151 x 17 mm
    • weight: 0.31kg
    • availability: Available
  • Table of Contents

    Preface
    Acknowledgements
    1. Functions
    2. Permutations of a finite set
    3. Groups of permutations of R and C
    4. The Möbius group
    5. The regular solids
    6. Abstract groups
    7. Inversions of the Möbius plane and stereographic projection
    8. Equivalence relations
    9. Cosets
    10. Direct product
    11. Fields and vector spaces
    12. Linear transformations
    13. The general linear group GL(2, F)
    14. The vector space V3 (F)
    15. Eigenvectors and eigenvalues
    16. Homomorphisms
    17. Conjugacy
    18. Linear fractional groups
    19. Quaternions and rotations
    20. Affine groups
    21. Orthogonal groups
    22. Discrete groups fixing a line
    23. Wallpaper groups
    Bibliography
    Index.

  • Author

    R. P. Burn

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