Conics and cubics : a concrete introduction to algebraic curves / Robert Bix
Type de document : MonographieCollection : Undergraduate texts in mathematicsLangue : anglais.Pays: Etats Unis.Mention d'édition: 2nd ed.Éditeur : New York : Springer, cop. 2006Description : 1 vol. (VIII-346 p.) : fig. ; 24 cmISBN: 9780387318028; 038731802X.ISSN: 0172-6056.Bibliographie : Bibliogr. p. 340-342. Index.Sujet MSC : 14Hxx, Algebraic geometry - Curves in algebraic geometry51N35, Analytic and descriptive geometry, Questions of classical algebraic geometry
14H45, Curves in algebraic geometry, Special algebraic curves and curves of low genusEn-ligne : Springerlink
| Item type | Current library | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
Monographie
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CMI Salle 1 | 14 BIX (Browse shelf(Opens below)) | Available | 08280-01 |
Bibliogr. p. 340-342. Index
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. (Source : Springer)
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