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Conics and Cubics: A Concrete Introduction to Algebraic Curves

Conics and Cubics: A Concrete Introduction to Algebraic Curves
Catalogue Information
Field name Details
Dewey Class 516.352
Title Conics and Cubics ([EBook]) : A Concrete Introduction to Algebraic Curves / by Robert Bix.
Author Bix, Robert. , 1953-
Other name(s) SpringerLink (Online service)
Publication New York, NY : Springer , 1998.
Physical Details X, 292 pages : online resource.
Series Undergraduate texts in mathematics 0172-6056
ISBN 9781475729757
Summary Note 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.:
Contents note I Intersections of Curves -- II Conics -- III Cubics -- IV Intersection Properties -- References.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
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