Conics And Cubics
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Conics And Cubics
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Author : Robert Bix
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-07-24
Conics And Cubics written by Robert Bix and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-24 with Mathematics categories.
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.
Conics And Cubics
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Author : Robert Bix
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Conics And Cubics written by Robert Bix and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
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.
Conics And Cubics
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Author : Robert Bix
language : en
Publisher: Springer
Release Date : 2008-11-01
Conics And Cubics written by Robert Bix and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-01 with Mathematics categories.
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.
Geometry Of Curves
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Author : J.W. Rutter
language : en
Publisher: CRC Press
Release Date : 2000-02-23
Geometry Of Curves written by J.W. Rutter and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-02-23 with Mathematics categories.
Interest in the study of geometry is currently enjoying a resurgence-understandably so, as the study of curves was once the playground of some very great mathematicians. However, many of the subject's more exciting aspects require a somewhat advanced mathematics background. For the "fun stuff" to be accessible, we need to offer students an introduction with modest prerequisites, one that stimulates their interest and focuses on problem solving. Integrating parametric, algebraic, and projective curves into a single text, Geometry of Curves offers students a unique approach that provides a mathematical structure for solving problems, not just a catalog of theorems. The author begins with the basics, then takes students on a fascinating journey from conics, higher algebraic and transcendental curves, through the properties of parametric curves, the classification of limaçons, envelopes, and finally to projective curves, their relationship to algebraic curves, and their application to asymptotes and boundedness. The uniqueness of this treatment lies in its integration of the different types of curves, its use of analytic methods, and its generous number of examples, exercises, and illustrations. The result is a practical text, almost entirely self-contained, that not only imparts a deeper understanding of the theory, but inspires a heightened appreciation of geometry and interest in more advanced studies.
On Cubic Transformations
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Author : Casey
language : en
Publisher:
Release Date : 1880
On Cubic Transformations written by Casey and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1880 with categories.
A Treatise On The Higher Plane Curves
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Author : George Salmon
language : en
Publisher: BoD – Books on Demand
Release Date : 2023-10-04
A Treatise On The Higher Plane Curves written by George Salmon and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-04 with Fiction categories.
Reprint of the original, first published in 1873.
A Treatise On The Higher Plane Curves Intended As A Sequel To
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Author : George Salmon
language : en
Publisher:
Release Date : 1873
A Treatise On The Higher Plane Curves Intended As A Sequel To written by George Salmon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1873 with categories.
Pencils Of Cubics And Algebraic Curves In The Real Projective Plane
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Author : Séverine Fiedler - Le Touzé
language : en
Publisher: CRC Press
Release Date : 2018-12-07
Pencils Of Cubics And Algebraic Curves In The Real Projective Plane written by Séverine Fiedler - Le Touzé and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-07 with Mathematics categories.
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.
A Collection Of Examples And Problems On Conics
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Author : Ralph Augustus Roberts
language : en
Publisher:
Release Date : 1882
A Collection Of Examples And Problems On Conics written by Ralph Augustus Roberts and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1882 with Conic sections categories.
American Journal Of Mathematics
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Author :
language : en
Publisher:
Release Date : 1897
American Journal Of Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1897 with Electronic journals categories.
The American Journal of Mathematics publishes research papers and articles of broad appeal covering the major areas of contemporary mathematics.