Conics and Cubics

A Concrete Introduction to Algebraic Curves
2. Auflage Softcover version of original hardcover Auflage 2006
ISBN: 978-1-4419-2178-9
Verlag: Springer

Buch, Englisch, 347 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 540 g

Reihe: Undergraduate Texts in Mathematics

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.

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

Bix, Robert

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Elementare Geometrie: Allgemeines
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

Intersections of Curves.- Conics.- Cubics.- Parametrizing Curves.