CONICS AND CUBICS.: A CONCRETE INTRODUCTION TO ALGEBRAIC CURVES - Rilegato

Bix, Robert

Rilegato

ISBN 10: 0387984011 ISBN 13: 9780387984018

Casa editrice: Springer Verlag, 1998

Riassunto

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 any two curves without common factors. The book is a text for a one-semester course. The course can serve both as the one undergraduate geometry course taken by mathematics majors in general and as a sequel to college geometry for prospective or current teachers of secondary school mathematics. The only prerequisite is first-year calculus.

Su questo libro

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

Dettagli dell'edizione

• Editore: Springer Verlag
• Data di pubblicazione: 1998
• Lingua: Inglese
• ISBN 10: 0387984011
• ISBN 13: 9780387984018
• Rilegatura: Copertina rigida
• Numero edizione: 1
• Numero di pagine: 299
• Contatto del produttore: non disponibile
• Persona responsabile: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Germania