Author | Bix, Robert. author |
---|---|

Title | Conics and Cubics [electronic resource] : A Concrete Introduction to Algebraic Curves / by Robert Bix |

Imprint | New York, NY : Springer New York : Imprint: Springer, 1998 |

Connect to | http://dx.doi.org/10.1007/978-1-4757-2975-7 |

Descript | X, 292 p. online resource |

SUMMARY

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

CONTENT

I Intersections of Curves -- II Conics -- III Cubics -- IV Intersection Properties -- References

Mathematics
Algebraic geometry
Numerical analysis
Geometry
Mathematics
Geometry
Algebraic Geometry
Numerical Analysis