Conics and Cubics : A Concrete Introduction to Algebraic Curves

Bix, Robert

ISBN 10: 038731802X / ISBN 13: 9780387318028

Published by Springer New York, 2006

About this Item

Pages intact with minimal writing/highlighting. The binding may be loose and creased. Dust jackets/supplements are not included. Stock photo provided. Product includes identifying sticker. Better World Books: Buy Books. Do Good.

Seller Inventory # 15039944-6

Bibliographic Details

• Title: Conics and Cubics : A Concrete Introduction to Algebraic Curves
• Publisher: Springer New York
• Publication Date: 2006
• Language: English
• ISBN 10: 038731802X
• ISBN 13: 9780387318028
• Binding: Hardcover
• Edition: 2nd Edition
• Condition: Good
• Weight: 3.285 pounds

About this title

Synopsis

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.

From the Back Cover

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