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MARC 21

Conics and Cubics: A Concrete Introduction to Algebraic Curves
Tag	Description
020	$a9781475729757
082	$a516.352
099	$aOnline Resource: Springer
100	$aBix, Robert.$d1953-
245	$aConics and Cubics$h[EBook]$bA Concrete Introduction to Algebraic Curves$cby Robert Bix.
260	$aNew York, NY$bSpringer$c1998.
300	$aX, 292 pages$bonline resource.
336	$atext
338	$aonline resource
440	$aUndergraduate Texts in Mathematics,$x0172-6056
505	$aI Intersections of Curves -- II Conics -- III Cubics -- IV Intersection Properties -- References.
520	$aConics 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.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
710	$aSpringerLink (Online service)
830	$aUndergraduate Texts in Mathematics,
856	$uhttp://dx.doi.org/10.1007/978-1-4757-2975-7