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A Path to Geometry

$74.99 (X)

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

$ 74.99 (X)

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About the Authors
  • Following the same successful approach as Dr. Burn's previous book on number theory, this text consists of a carefully constructed sequence of questions that will enable the reader, through participation, to study 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 relationships to 3-dimensional isometries are covered, and the climax of the book is a study of the crystallographic groups, with a complete analysis of these groups in two dimensions.

    Reviews & endorsements

    "What distinguishes this book from all others? Simply, it is not a textbook in the normal sense. The approach of the book is one of development by discovery. There is almost no text as such-the reader being invited to learn about the groups through a sequence of over 800 problems." Times Higher Education Supplement

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    Product details

    • Date Published: September 1987
    • format: Paperback
    • isbn: 9780521347938
    • length: 256 pages
    • dimensions: 229 x 151 x 19 mm
    • weight: 0.349kg
    • availability: Available
  • Table of Contents

    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

  • Author

    R. P. Burn

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