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A Guide to Plane Algebraic Curves
By Keith Kendig
Catalog Code: DOL-46
Print Edition ISBN: 978-0-88385-353-5
Electronic ISBN: 978-1-61444-203-5
208 pp., Hardcover, 2011
List Price: $49.95
Member Price: $39.95
Series: Dolciani Mathematical Expositions
Table of Contents | Excerpt | About the Author | Buy on Amazon | Buy in MAA Bookstore |
This guide is an informal and accessible introduction to plane algebraic curves. It also serves as an entry point to algebraic geometry, which is playing an ever-expanding role in areas ranging from biology and chemistry to robotics and cryptology.
The guide's unifying theme is: Give curves enough living space and beautiful theorems will follow.
By keeping the exposition simple and readily understandable, and by introducing abstract concepts with concrete examples and pictures, the book offers readers a lucid overview of the subject. It can also be used as the text in an undergraduate course on plane algebraic curves, or as a companion to algebraic geometry at the graduate level.
Table of Contents
Preface 1. A Gallery of Algebraic Curves 2. Points at Infinity 3. From Real to Complex 4. Topology of Algebraic curves in P2 (C) 5. Singularities 6. The Big Three: C, K, S. Bibliography. Index.
Excerpt: Preface (X):
...there exist curves--many with very simple defining polynomials--that bend, twist and contort so much that in order to fit in the plane, they must have self-intersections and/or kinks. Such points are rare (accounting for their name “singularities”), but rare or not, questions arise:
What do curves look like around singularities?
Are some singularities easily understood, while others are more complicated?
How is their number and type related to the amount of twisting and contorting of the curve?
For a curve with singularities, what happens to Bézout's theorem?
For a curve with singularities, what happens to that remarkably simple genus formula?
Can you transform a curve with singularities into a curve without singularities?
About the Author
Keith Kendig (Cleveland State University) is the author of two other MAA books: Conics and Sink or Float? Thought Problems in Math and Physics. He serves on the editorial boards of Mathematics Magazine and the Spectrum series of MAA books.