Conics And Cubics
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Author | : Robert Bix |
Publisher | : Springer Science & Business Media |
Total Pages | : 300 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 1475729758 |
Algebraic curves are the graphs of polynomial equations in two vari 3 ables, such as y3 + 5xy2 = x + 2xy. By focusing on curves of degree at most 3-lines, conics, and cubics-this book aims to fill the gap between the familiar subject of analytic geometry and the general study of alge braic curves. This text is designed for a one-semester class that serves both as a a geometry course for mathematics majors in general and as a sequel to college geometry for teachers of secondary school mathe matics. The only prerequisite is first-year calculus. On the one hand, this book can serve as a text for an undergraduate geometry course for all mathematics majors. Algebraic geometry unites algebra, geometry, topology, and analysis, and it is one of the most exciting areas of modem mathematics. Unfortunately, the subject is not easily accessible, and most introductory courses require a prohibitive amount of mathematical machinery. We avoid this problem by focusing on curves of degree at most 3. This keeps the results tangible and the proofs natural. It lets us emphasize the power of two fundamental ideas, homogeneous coordinates and intersection multiplicities.
Author | : Robert Bix |
Publisher | : Springer |
Total Pages | : 0 |
Release | : 2008-11-01 |
Genre | : Mathematics |
ISBN | : 9780387511986 |
Conics and Cubics offers an accessible and well illustrated introduction to algebraic curves. 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 subject area is described by means of concrete and accessible examples. The book is a text for a one-semester course.
Author | : Henry Seely White |
Publisher | : |
Total Pages | : 16 |
Release | : 1906 |
Genre | : Curves, Cubic |
ISBN | : |
Author | : Séverine Fiedler - Le Touzé |
Publisher | : CRC Press |
Total Pages | : 226 |
Release | : 2018-12-07 |
Genre | : Mathematics |
ISBN | : 0429838255 |
Pencils of Cubics and Algebraic Curves in the Real Projective Plane thoroughly examines the combinatorial configurations of n generic points in RP2. Especially how it is the data describing the mutual position of each point with respect to lines and conics passing through others. The first section in this book answers questions such as, can one count the combinatorial configurations up to the action of the symmetric group? How are they pairwise connected via almost generic configurations? These questions are addressed using rational cubics and pencils of cubics for n = 6 and 7. The book’s second section deals with configurations of eight points in the convex position. Both the combinatorial configurations and combinatorial pencils are classified up to the action of the dihedral group D8. Finally, the third section contains plentiful applications and results around Hilbert’s sixteenth problem. The author meticulously wrote this book based upon years of research devoted to the topic. The book is particularly useful for researchers and graduate students interested in topology, algebraic geometry and combinatorics. Features: Examines how the shape of pencils depends on the corresponding configurations of points Includes topology of real algebraic curves Contains numerous applications and results around Hilbert’s sixteenth problem About the Author: Séverine Fiedler-le Touzé has published several papers on this topic and has been invited to present at many conferences. She holds a Ph.D. from University Rennes1 and was a post-doc at the Mathematical Sciences Research Institute in Berkeley, California.
Author | : Peter Rogers Sherman |
Publisher | : |
Total Pages | : 50 |
Release | : 1949 |
Genre | : Conic sections |
ISBN | : |
Author | : Henry Seely White |
Publisher | : |
Total Pages | : 24 |
Release | : 1900 |
Genre | : Curves, Cubic |
ISBN | : |
Author | : Louis Antoine Victor De Cleene |
Publisher | : |
Total Pages | : 28 |
Release | : 1927 |
Genre | : Conic sections |
ISBN | : |
Author | : Charles Clayton Grove |
Publisher | : |
Total Pages | : 60 |
Release | : 1907 |
Genre | : Collineation |
ISBN | : |
Author | : Herman Walter Lautenbach |
Publisher | : |
Total Pages | : 188 |
Release | : 1940 |
Genre | : Mathematics |
ISBN | : |
Author | : Miles Reid |
Publisher | : Cambridge University Press |
Total Pages | : 144 |
Release | : 1988-12-15 |
Genre | : Mathematics |
ISBN | : 9780521356626 |
Algebraic geometry is, essentially, the study of the solution of equations and occupies a central position in pure mathematics. This short and readable introduction to algebraic geometry will be ideal for all undergraduate mathematicians coming to the subject for the first time. With the minimum of prerequisites, Dr Reid introduces the reader to the basic concepts of algebraic geometry including: plane conics, cubics and the group law, affine and projective varieties, and non-singularity and dimension. He is at pains to stress the connections the subject has with commutative algebra as well as its relation to topology, differential geometry, and number theory. The book arises from an undergraduate course given at the University of Warwick and contains numerous examples and exercises illustrating the theory.