Conics and Cubics: A Concrete Introduction to Algebraic Curves (Undergraduate Texts in Mathematics) - Hardcover

Buch 20 von 170: Undergraduate Texts in Mathematics

Bix, Robert

 
9780387318028: Conics and Cubics: A Concrete Introduction to Algebraic Curves (Undergraduate Texts in Mathematics)
Hardcover
ISBN 10: 038731802X ISBN 13: 9780387318028
Verlag: Springer, 2006

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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Von der hinteren Coverseite

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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Verlag
Springer
Erscheinungsdatum
2006
Sprache
Englisch
ISBN 10 
038731802X
ISBN 13 
9780387318028
Einband
Gebundene Ausgabe
Auflage
2
Anzahl der Seiten
355
Kontakt zum Hersteller
ProductSafety@springernature.com
ProductSafety@springernature.com

Poststr. 9
Darmstadt
64293
Deutschland

Weitere beliebte Ausgaben desselben Titels

9781441921789: Conics and Cubics: A Concrete Introduction to Algebraic Curves (Undergraduate Texts in Mathematics)

Vorgestellte Ausgabe

ISBN 10:  1441921788 ISBN 13:  9781441921789
Verlag: Springer, 2010
Softcover