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Computer. Automation --- 511 --- Number theory --- 511 Number theory --- Nombres algébriques, Théorie des

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Topological groups. Lie groups --- Nombres algébriques, Théorie des --- Lie, Groupes de

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Group theory --- 512 --- Algebra --- Chevalley groups. --- Representations of groups. --- Modules (Algebra) --- Modules (Algebra). --- 512 Algebra --- Groupes algébriques linéaires --- Groupes algébriques linéaires --- Représentations de groupes

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Group theory --- Borel subgroups. --- Group schemes (Mathematics) --- Linear algebraic groups. --- Group schemes (Mathematics). --- Groupes algébriques linéaires --- Geometrie algebrique --- Schemas de groupes

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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.

Algebraic geometry --- Ordered algebraic structures --- Curves, Algebraic. --- Courbes algébriques --- Courbes algébriques --- Geometry. --- Algebraic geometry. --- Numerical analysis. --- Algebraic Geometry. --- Numerical Analysis. --- Mathematical analysis --- Geometry --- Mathematics --- Euclid's Elements --- Geometrie algebrique --- Courbes planes --- Courbes algebriques --- Coniques