Elementary Geometry of Algebraic Curves

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.

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.