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Undergraduate Texts in Mathematics

Conics and Cubics

A Concrete Introduction to Algebraic Curves

Authors: Bix, Robert

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  • ISBN 978-0-387-39273-8
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Hardcover $74.99
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Softcover $59.99
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  • ISBN 978-1-4419-2178-9
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About this Textbook

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

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)


Table of contents (4 chapters)

Table of contents (4 chapters)

Buy this book

eBook $44.99
price for USA in USD (gross)
  • ISBN 978-0-387-39273-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $74.99
price for USA in USD
  • ISBN 978-0-387-31802-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $59.99
price for USA in USD
  • ISBN 978-1-4419-2178-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Conics and Cubics
Book Subtitle
A Concrete Introduction to Algebraic Curves
Authors
Series Title
Undergraduate Texts in Mathematics
Copyright
2006
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-39273-8
DOI
10.1007/0-387-39273-4
Hardcover ISBN
978-0-387-31802-8
Softcover ISBN
978-1-4419-2178-9
Series ISSN
0172-6056
Edition Number
2
Number of Pages
VIII, 347
Topics