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Conics and Cubics: A Concrete Introduction to Algebraic Curves (Undergraduate Texts in Mathematics) - Softcover
Inhaltsangabe
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, homogeneous 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. The course can serve either as the one undergraduate geometry course taken by mathematics majors in general or as a sequel to college geometry for prospective or current teachers of secondary school mathematics. The only prerequisite is first-year calculus.
The new edition additionally discusses the use of power series to parametrize curves and analyze intersection multiplicities and envelopes.
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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
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Conics and Cubics: A Concrete Introduction to Algebraic Curves (Undergraduate Texts in Mathematics)
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Conics and Cubics: A Concrete Introduction to Algebraic Curves
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Paperback. Zustand: Brand New. 2nd ed. edition. 352 pages. 9.00x6.00x0.81 inches. In Stock. Artikel-Nr. x-1441921788
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Conics and Cubics
Verlag:
Springer New York, Springer US Nov 2010, 2010
ISBN 10: 1441921788
ISBN 13: 9781441921789
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Taschenbuch
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Taschenbuch. Zustand: Neu. Neuware -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, homogeneous 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. The course can serve either as the one undergraduate geometry course taken by mathematics majors in general or as a sequel to college geometry for prospective or current teachers of secondary school mathematics. The only prerequisite is first-year calculus.The new edition additionally discusses the use of power series to parametrize curves and analyze intersection multiplicities and envelopes.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 356 pp. Englisch. Artikel-Nr. 9781441921789
Anzahl: 2 verfügbar
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Conics and Cubics : A Concrete Introduction to Algebraic Curves
Verlag:
Springer New York, Springer US, 2010
ISBN 10: 1441921788
ISBN 13: 9781441921789
Neu
Taschenbuch
Anbieter: AHA-BUCH GmbH, Einbeck, Deutschland
Verkäuferbewertung 5 von 5 Sternen
Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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, homogeneous 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. The course can serve either as the one undergraduate geometry course taken by mathematics majors in general or as a sequel to college geometry for prospective or current teachers of secondary school mathematics. The only prerequisite is first-year calculus.The new edition additionally discusses the use of power series to parametrize curves and analyze intersection multiplicities and envelopes. Artikel-Nr. 9781441921789
Anzahl: 1 verfügbar