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 : 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.
Triangles And Quadrilaterals Inscribed To A Cubic And Circumscribed To A Conic
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Author : Henry Seely White
language : en
Publisher:
Release Date : 1906
Triangles And Quadrilaterals Inscribed To A Cubic And Circumscribed To A Conic written by Henry Seely White and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1906 with Curves, Cubic 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.
Plane Cubics And Irrational Covariant Cubics
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Author : Henry Seely White
language : en
Publisher:
Release Date : 1900
Plane Cubics And Irrational Covariant Cubics written by Henry Seely White and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1900 with Curves, Cubic categories.
A Scrapbook Of Complex Curve Theory
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Author : Charles Herbert Clemens
language : en
Publisher: American Mathematical Soc.
Release Date : 2002-12-10
A Scrapbook Of Complex Curve Theory written by Charles Herbert Clemens and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-12-10 with Mathematics categories.
This fine book by Herb Clemens quickly became a favorite of many algebraic geometers when it was first published in 1980. It has been popular with novices and experts ever since. It is written as a book of ``impressions'' of a journey through the theory of complex algebraic curves. Many topics of compelling beauty occur along the way. A cursory glance at the subjects visited reveals a wonderfully eclectic selection, from conics and cubics to theta functions, Jacobians, and questions of moduli. By the end of the book, the theme of theta functions becomes clear, culminating in the Schottky problem. The author's intent was to motivate further study and to stimulate mathematical activity. The attentive reader will learn much about complex algebraic curves and the tools used to study them. The book can be especially useful to anyone preparing a course on the topic of complex curves or anyone interested in supplementing his/her reading.
The Syzygetic Pencil Of Cubics With A New Geometrical Development Of Its Hesse Group G216
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Author : Charles Clayton Grove
language : en
Publisher:
Release Date : 1907
The Syzygetic Pencil Of Cubics With A New Geometrical Development Of Its Hesse Group G216 written by Charles Clayton Grove and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1907 with Collineation categories.
Conics
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Author : Keith Kendig
language : en
Publisher: Cambridge University Press
Release Date : 2005-08-11
Conics written by Keith Kendig and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-11 with Mathematics categories.
This book engages the reader in a journey of discovery among three characters: philosopher, teacher and student.
Undergraduate Algebraic Geometry
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Author : Miles Reid
language : en
Publisher:
Release Date : 1988
Undergraduate Algebraic Geometry written by Miles Reid and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
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.
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.