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Elementary Geometry of Algebraic Curves

Elementary Geometry of Algebraic Curves
An Undergraduate Introduction

$184.00 (X)

  • Date Published: January 1999
  • availability: Available
  • format: Hardback
  • isbn: 9780521641401

$ 184.00 (X)
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About the Authors
  • Here is an introduction to plane algebraic curves from a geometric viewpoint, designed as a first text for undergraduates in mathematics, or for postgraduate and research workers in the engineering and physical sciences. The book is well illustrated and contains several hundred worked examples and exercises. From the familiar lines and conics of elementary geometry the reader proceeds to general curves in the real affine plane, with excursions to more general fields to illustrate applications, such as number theory. By adding points at infinity the affine plane is extended to the projective plane, yielding a natural setting for curves and providing a flood of illumination into the underlying geometry. A minimal amount of algebra leads to the famous theorem of Bezout, while the ideas of linear systems are used to discuss the classical group structure on the cubic.

    • Based on a popular course given for many years
    • Has applications in engineering and robotics
    • Very well illustrated
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    Reviews & endorsements

    "This book amply fulfills the promise of its title...far less forbidding than the vast majority of more ambitious textbooks...the author clearly motivates the study of projective curves by showing that several affine problems are more easily studied via the projective setting...a good abstract introduction for mathematicians." Theory of Computation

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    Product details

    • Date Published: January 1999
    • format: Hardback
    • isbn: 9780521641401
    • length: 268 pages
    • dimensions: 236 x 156 x 20 mm
    • weight: 0.49kg
    • contains: 75 b/w illus. 12 tables
    • availability: Available
  • Table of Contents

    List of illustrations
    List of tables
    Preface
    1. Real algebraic curves
    2. General ground fields
    3. Polynomial algebra
    4. Affine equivalence
    5. Affine conics
    6. Singularities of affine curves
    7. Tangents to affine curves
    8. Rational affine curves
    9. Projective algebraic curves
    10. Singularities of projective curves
    11. Projective equivalence
    12. Projective tangents
    13. Flexes
    14. Intersections of projective curves
    15. Projective cubics
    16. Linear systems
    17. The group structure on a cubic
    18. Rational projective curves
    Index.

  • Author

    C. G. Gibson, University of Liverpool
    Chris Gibson received an honours degree in Mathematics from St Andrews University in 1963, and later the degrees of Drs Math and Dr Math from the University of Amsterdam, returning to England in 1967 to begin his 35 year mathematics career at the University of Liverpool. His interests turned towards the geometric areas, and he was a founder member of the Liverpool Singularities Group until his retirement in 2002 as Reader in Pure Mathematics, with over 60 published papers in that area. In 1974 he co-authored the significant 'Topological Stability of Smooth Mappings' (published by Springer Verlag) presenting the first detailed proof of Thom's Topological Stability Theorem. In addition to purely theoretical work in singularity theory, he jointly applied singular methods to specific questions about caustics arising in the physical sciences. His later interests lay largely in the applications to theoretical kinematics, and to problems arising in theoretical robotics. This interest gave rise to a substantial collaboration with Professor K. H. Hunt in the Universities of Monash and Melbourne, and produced a formal classification of screw systems. At the teaching level his major contribution was to pioneer the re-introduction of undergraduate geometry teaching. The practical experience of many years of undergraduate teaching was distilled into three undergraduate texts published by Cambridge University Press, now widely adopted internationally for undergraduate (and graduate) teaching.

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