Elementary Geometry of Algebraic Curves
An Undergraduate Introduction

This is a genuine introduction to plane algebraic curves from a geometric viewpoint.

C. G. Gibson (Author)

9780521646413, Cambridge University Press

Paperback, published 26 November 1998

268 pages, 75 b/w illus. 12 tables
23.6 x 15.7 x 2 cm, 0.489 kg

"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

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.

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.

Subject Areas: Geometry [PBM]