Conics and Cubics
A Concrete Introduction to Algebraic Curves
Seiten
1998
Springer-Verlag New York Inc.
978-0-387-98401-8 (ISBN)
Springer-Verlag New York Inc.
978-0-387-98401-8 (ISBN)
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This text is an introduction to algebraic curves. By focusing on curves of maximum three degrees, the results remain tangible and the proofs transparent. Theorems follow naturally from high school algebra and two key ideas, homogeneous co-ordinates and intersection multiplicities.
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.
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.
Intersections of Curves: Intersections at the origin. Homogeneous Coordinates. Intersections in Homogeneous Coordinates. Lines and Tangents; Conics: Conics and Integrations. Pascal's Theorem. Envelopes; Cubics: Flexes and Singular Points. Addition on Cubics. Complex Numbers. Bezout's Theorem. Hessians; Intersection Properties: Independence and Intersections. Spanning and Homogeneous Coordinates. Determining Cubics.
| Reihe/Serie | Undergraduate Texts in Mathematics |
|---|---|
| Zusatzinfo | 148 illus. |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 611 g |
| Einbandart | gebunden |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 0-387-98401-1 / 0387984011 |
| ISBN-13 | 978-0-387-98401-8 / 9780387984018 |
| Zustand | Neuware |
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