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.
Author(s): C. G. Gibson
Edition: 1
Publisher: Cambridge University Press
Year: 1998
Language: English
Pages: 268
cover......Page 1
Elementary Geometry of Algebraic Curves: an Undergraduate Introduction......Page 4
Contents......Page 8
List of Illustrations......Page 11
Preface......Page 14
1 Real Algebraic Curves......Page 18
2 General Ground Fields......Page 37
3 Polynomial Algebra......Page 50
4 Affine Equivalence......Page 64
5 Affine Conics......Page 77
6 Singularities of Affine Curves......Page 88
7 Tangents to Affine Curves......Page 102
8 Rational Affine Curves......Page 112
9 Projective Algebraic Curves......Page 125
10 Singularities of Projective Curves......Page 142
11 Projective Equivalence......Page 154
12 Projective Tangents......Page 165
13 Flexes......Page 179
14 Intersections of Projective Curves......Page 190
15 Projective Cubics......Page 207
16 Linear Systems......Page 218
17 The Group Strueture on a euhie......Page 234
18 Rational Projective Curves......Page 251
Index......Page 264
