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Conics and Cubics

A Concrete Introduction to Algebraic Curves

  • Robert Bix

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Pages 69-126
  3. Pages 127-244
  4. Pages 245-339
  5. Back Matter
    Pages 340-347

About this book

Introduction

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: homogenous 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 on algebraic curves for junior-senior mathematics majors. The only prerequisite is first-year calculus.

The new edition introduces the deeper study of curves through parametrization by power series. Two uses of parametrizations are presented: counting multiple intersections of curves and proving the duality of curves and their envelopes.

About the first edition:

"The book...belongs in the admirable tradition of laying the foundations of a difficult and potentially abstract subject by means of concrete and accessible examples."

- Peter Giblin, MathSciNet

Keywords

Area Grad algebra algebraic curve calculus geometry mathematics proof theorem

Authors and affiliations

  • Robert Bix
    • 1
  1. 1.Department of MathematicsThe University of Michigan-FlintFlint

Bibliographic information

  • DOI https://doi.org/10.1007/0-387-39273-4
  • Copyright Information Springer Science+Business Media, LLC 2006
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-31802-8
  • Online ISBN 978-0-387-39273-8
  • Series Print ISSN 0172-6056
  • Buy this book on publisher's site