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Conics and Cubics offers an accessible and well illustrated introduction to algebraic curves. 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 subject area is described by means of concrete and accessible examples. The book is a text for a one-semester course.
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Dalla quarta di copertina
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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Conics and Cubics: A Concrete Introduction to Algebraic Curves (Undergraduate Texts in Mathematics)
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Hardcover. Condizione: Fine. 2nd Edition. Viii, 346 Pp. Second Edition, First Printing, 2006. Fine, But Very Faint Waviness To Page Block (No Signs Of Damp Staining, However). Codice articolo 056940
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Conics and Cubics: A Concrete Introduction to Algebraic Curves (Undergraduate Texts in Mathematics)
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Springer (edition 2nd), 2006
ISBN 10: 038731802X
ISBN 13: 9780387318028
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