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  3. Elementary Geometry of Algebraic Curves
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    • Publisher:
      Cambridge University Press
      Publication date:
      05 June 2012
      26 November 1998
      ISBN:
      9781139173285
      9780521641401
      9780521646413
      DOI:
      https://doi.org/10.1017/CBO9781139173285
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.49kg, 268 Pages
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.489kg, 268 Pages
      • Subjects:
      Mathematics, Geometry and Topology
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    Subjects:
    Mathematics, Geometry and Topology
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    Book description

    This is a genuine 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 contains several hundred worked examples and exercises, making it suitable for adoption as a course text. From the 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, whilst the ideas of linear systems are used to discuss the classical group structure on the cubic.

    Reviews

    "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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