Cover image for Elementary geometry of algebraic curves : an undergraduate introduction
Title:
Elementary geometry of algebraic curves : an undergraduate introduction
Author:
Gibson, Christopher G., 1940-
Publication Information:
Cambridge ; New York : Cambridge University Press, [1998]

©1998
Physical Description:
xvi, 250 pages : illustrations ; 24 cm
General Note:
Includes index.
Language:
English
Subject Term:
ISBN:
9780521641401

9780521646413
Format :
Book

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QA565 .G5 1998 Adult Non-Fiction Central Closed Stacks
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Summary

Summary

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.


Reviews 1

Choice Review

Though algebraic geometry arguably counts as both the most classical and the most modern branch of mathematics, the undergraduate curriculum sadly neglects it. Indeed, the subject's double nature may lie at the root of the trouble: if presenting its modern aspect to undergraduates seems too daunting, taking an old-fashioned approach seems too regressive. Aside from Miles Reid's excellent Undergraduate Algebraic Geometry (CH, Dec'89), Gibson's has essentially no competition. Comparing Gibson's book to Reid's, one finds Gibson more classical, less algebraic, more elementary, more richly illustrated, and better supplied with examples and exercises. Where Reid also looks at surfaces, Gibson sticks to curves only, as per his title. The group law on cubics forms a high point of both books, but Reid gets there after an eighth of the pages Gibson takes. In the final analysis, the books complement one another and will appeal to different students, depending on their learning styles. Recommended for college libraries. Undergraduates and up. D. V. Feldman University of New Hampshire


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