Overview
- Attractive subject area described by means of concrete and accessible examples
- A large amount of illustrations
Part of the book series: Undergraduate Texts in Mathematics (UTM)
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Table of contents (4 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
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)
Authors and Affiliations
Bibliographic Information
Book Title: Conics and Cubics
Book Subtitle: A Concrete Introduction to Algebraic Curves
Authors: Robert Bix
Series Title: Undergraduate Texts in Mathematics
DOI: https://doi.org/10.1007/0-387-39273-4
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag New York 2006
Hardcover ISBN: 978-0-387-31802-8Published: 24 July 2006
Softcover ISBN: 978-1-4419-2178-9Published: 25 November 2010
eBook ISBN: 978-0-387-39273-8Published: 22 November 2006
Series ISSN: 0172-6056
Series E-ISSN: 2197-5604
Edition Number: 2
Number of Pages: VIII, 347
Topics: Algebraic Geometry, Geometry, Numerical Analysis