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Conics and Cubics : A Concrete Introduction to Algebraic Curves /

By: Bix, Robert [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Undergraduate Texts in Mathematics: Publisher: New York, NY : Springer New York, 2006.Edition: Second Edition.Description: VIII, 347 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9780387392738.Subject(s): Mathematics | Algebraic geometry | Numerical analysis | Geometry | Mathematics | Algebraic Geometry | Geometry | Numerical AnalysisDDC classification: 516.35 Online resources: Click here to access online
Contents:
Intersections of Curves -- Conics -- Cubics -- Parametrizing Curves.
In: Springer eBooksSummary: 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.
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Item type Current location Call number Status Date due Barcode Item holds
E books E books PK Kelkar Library, IIT Kanpur
Available EBK7787
Total holds: 0

Intersections of Curves -- Conics -- Cubics -- Parametrizing Curves.

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.

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