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Geometry

2nd Edition

$76.99 (X)

  • Date Published: February 2012
  • availability: In stock
  • format: Paperback
  • isbn: 9781107647831
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About the Authors
  • This richly illustrated and clearly written undergraduate textbook captures the excitement and beauty of geometry. The approach is that of Klein in his Erlangen programme: a geometry is a space together with a set of transformations of the space. The authors explore various geometries: affine, projective, inversive, hyperbolic and elliptic. In each case they carefully explain the key results and discuss the relationships between the geometries. New features in this second edition include concise end-of-chapter summaries to aid student revision, a list of further reading and a list of special symbols. The authors have also revised many of the end-of-chapter exercises to make them more challenging and to include some interesting new results. Full solutions to the 200 problems are included in the text, while complete solutions to all of the end-of-chapter exercises are available in a new Instructors' Manual, which can be downloaded from www.cambridge.org/9781107647831.

    • Students respond to the authors' modern, easy-to-read writing style
    • Assumes basic knowledge of group theory and linear algebra but a rapid review of both topics is given in appendices
    • Historical notes, teaching comments and diagrams feature in the margins
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    Reviews & endorsements

    'This is a textbook that demonstrates the excitement and beauty of geometry … richly illustrated and clearly written.' L'Enseignement Mathématique

    '… this is a remarkable and nicely written introduction to classical geometry.' Zentralblatt MATH

    '… could form the basis of courses in geometry for mathematics undergraduates. It will also appeal to the general mathematical reader.' John Stone, The Times Higher Education Supplement

    'It conveys the beauty and excitement of the subject, avoiding the dryness of many geometry texts.' J. I. Hall, Mathematical Association of America

    'To my mind, this is the best introductory book ever written on introductory university geometry … readers are introduced to the notions of Euclidean congruence, affine congruence, projective congruence and certain versions of non-Euclidean geometry (hyperbolic, spherical and inversive). Not only are students introduced to a wide range of algebraic methods, but they will encounter a most pleasing combination of process and product.' P. N. Ruane, MAA Focus

    '… an excellent and precisely written textbook that should be studied in depth by all would-be mathematicians.' Hans Sachs, American Mathematical Society

    See more reviews

    Customer reviews

    03rd Mar 2015 by MichaelM

    A perfect book. Richly illustrated and clearly written. The authors explore various geometries.

    Review was not posted due to profanity

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    Product details

    • Edition: 2nd Edition
    • Date Published: February 2012
    • format: Paperback
    • isbn: 9781107647831
    • length: 602 pages
    • dimensions: 245 x 190 x 25 mm
    • weight: 1.28kg
    • contains: 750 b/w illus. 200 exercises
    • availability: In stock
  • Table of Contents

    Preface
    Introduction: geometry and geometries
    1. Conics
    2. Affine geometry
    3. Projective geometry: lines
    4. Projective geometry: conics
    5. Inversive geometry
    6. Hyperbolic geometry: the disc model
    7. Elliptic geometry: the spherical model
    8. The Kleinian view of geometry
    Special symbols
    Further reading
    Appendix 1. A primer of group theory
    Appendix 2. A primer of vectors and vector spaces
    Appendix 3. Solutions to the problems
    Index.

  • Resources for

    Geometry

    David A. Brannan, Matthew F. Esplen, Jeremy J. Gray

    General Resources

    Welcome to the resources site

    Here you will find free-of-charge online materials to accompany this book. The range of materials we provide across our academic and higher education titles are an integral part of the book package whether you are a student, instructor, researcher or professional.

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    These resources are provided free of charge by Cambridge University Press with permission of the author of the corresponding work, but are subject to copyright. You are permitted to view, print and download these resources for your own personal use only, provided any copyright lines on the resources are not removed or altered in any way. Any other use, including but not limited to distribution of the resources in modified form, or via electronic or other media, is strictly prohibited unless you have permission from the author of the corresponding work and provided you give appropriate acknowledgement of the source.

    If you are having problems accessing these resources please email lecturers@cambridge.org

  • Instructors have used or reviewed this title for the following courses

    • Affine and Projective Geometry
    • College Geometry
    • Euclidean Geometry
    • Geometry I
    • Modern Geometries
    • Modern Geometry
    • Topics in Geometry
  • Authors

    David A. Brannan, The Open University, Milton Keynes
    David A. Brannan is Emeritus Professor in the Department of Mathematics and Computing at The Open University, Milton Keynes.

    Matthew F. Esplen, The Open University, Milton Keynes
    Matthew F. Esplen is a Lecturer in the Department of Mathematics and Statistics at The Open University, Milton Keynes.

    Jeremy J. Gray, The Open University, Milton Keynes
    Jeremy J. Gray is a Professor of the History of Mathematics at The Open University, Milton Keynes and Honorary Professor at the University of Warwick.

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