Conics and Cubics

A Concrete Introduction to Algebraic Curves

By: Robert Bix

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Hardcover | 24 July 2006 | Edition Number 2

At a Glance

Hardcover
356 Pages

Edition Type
Revised

Dimensions(cm)
16.6 x 28.3 x 3.1

Hardcover

$129.00

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Conics and Cubics is an accessible introduction to algebraic curves. Its focus on curves of degree at most three keeps results tangible and proofs transparent. Theorems follow naturally from high school algebra and two key ideas, homogeneous coordinates and intersection multiplicities.

By classifying irreducible cubics over the real numbers and proving that their points form Abelian groups, the book gives readers easy access to the study of elliptic curves. It includes a simple proof of Bezout's Theorem on the number of intersections of two curves.

The book is a text for a one-semester course. The course can serve either as the one undergraduate geometry course taken by mathematics majors in general or as a sequel to college geometry for prospective or current teachers of secondary school mathematics. The only prerequisite is first-year calculus.

The new edition additionally discusses the use of power series to parametrize curves and analyze intersection multiplicities and envelopes.

Industry Reviews

"...This book therefore belongs to the admirable tradition of laying the foundations of a difficult and potentially abstract subject by means of concrete and accessible examples. ... Two major strengths of the book are its historical perspective, in the form of informative introductions to the chapters which give the main developments in non-technical language, and its exercises, which are numerous and interesting." Peter Giblin for MathSciNet

From the reviews of the second edition:

"Algebraic geometry is a hard subject. ... But could it, or at least some of it, be presented, at the undergraduate level? This book attempts to do that. ... At the beginning of each of the four chapters, the author provides a synopsis of the historical development of the subject. And within each section many exercises are provided for further discussion and illumination. ... And the author manages to keep things concrete. So, the end result is a book which is accessible ... ." (Donald L. Vestal, MathDL - online, October, 2006)

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Preface	p. vii
Intersections of Curves	p. 1
Introduction and History	p. 1
Intersections at the Origin	p. 4
Homogeneous Coordinates	p. 17
Intersections in Homogeneous Coordinates	p. 31
Lines and Tangents	p. 50
Conics	p. 69
Introduction and History	p. 69
Conics and Intersections	p. 73
Pascal's Theorem	p. 92
Envelopes of Conics	p. 110
Cubics	p. 127
Introduction and History	p. 127
Flexes and Singular Points	p. 134
Addition on Cubics	p. 153
Complex Numbers	p. 175
Bezout's Theorem	p. 195
Hessians	p. 211
Determining Cubics	p. 229
Parametrizing Curves	p. 245
Introduction and History	p. 245
Parametrizations at the Origin	p. 249
Parametrizations of General Form	p. 276
Envelopes of Curves	p. 304
References	p. 340
Index	p. 343
Table of Contents provided by Ingram. All Rights Reserved.

Conics and Cubics

A Concrete Introduction to Algebraic Curves

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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Paperback

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