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Elementary Geometry of Algebraic Curves

An Undergraduate Introduction

By: C. G. Gibson, Christopher G. Gibson, Gibson C. G.

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Hardcover | 25 January 1999

At a Glance

Hardcover
268 Pages

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22.86 x 15.24 x 1.91

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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.

Industry 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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Non-Fiction Mathematics Geometry Algebraic Geometry Differential & Riemannian Geometry Topology

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Paperback

Published: 25th January 1999

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List of illustrations
List of tables
Preface
Real algebraic curves
General ground fields
Polynomial algebra
Affine equivalence
Affine conics
Singularities of affine curves
Tangents to affine curves
Rational affine curves
Projective algebraic curves
Singularities of projective curves
Projective equivalence
Projective tangents
Flexes
Intersections of projective curves
Projective cubics
Linear systems
The group structure on a cubic
Rational projective curves
Index
Table of Contents provided by Publisher. All Rights Reserved.

Elementary Geometry of Algebraic Curves

An Undergraduate Introduction

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

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