Notice bibliographique
- Notice
Type(s) de contenu et mode(s) de consultation : Texte noté : électronique
Auteur(s) : Borceux, Francis
Titre(s) : An Algebraic Approach to Geometry [Texte électronique] : Geometric Trilogy II / by Francis Borceux
Publication : Cham : Springer International Publishing : Springer e-books : Imprint: Springer, 2014
Description matérielle : 1 online resource
Note(s) : This is a unified treatment of the various algebraic approaches to geometric spaces.
The study of algebraic curves in the complex projective plane is the natural link
between linear geometry at an undergraduate level and algebraic geometry at a graduate
level, and it is also an important topic in geometric applications, such as cryptography.
380 years ago, the work of Fermat and Descartes led us to study geometric problems
using coordinates and equations. Today, this is the most popular way of handling geometrical
problems. Linear algebra provides an efficient tool for studying all the first degree
(lines, planes, ...) and second degree (ellipses, hyperboloids, ...) geometric figures,
in the affine, the Euclidean, the Hermitian and the projective contexts. But recent
applications of mathematics, like cryptography, need these notions not only in real
or complex cases, but also in more general settings, like in spaces constructed on
finite fields. And of course, why not also turn our attention to geometric figures
of higher degrees? Besides all the linear aspects of geometry in their most general
setting, this book also describes useful algebraic tools for studying curves of arbitrary
degree and investigates results as advanced as the Bezout theorem, the Cramer paradox,
topological group of a cubic, rational curves etc. Hence the book is of interest for
all those who have to teach or study linear geometry: affine, Euclidean, Hermitian,
projective; it is also of great interest to those who do not want to restrict themselves
to the undergraduate level of geometric figures of degree one or two
Sujet(s) : Mathématiques
Indice(s) Dewey :
516 (23e éd.) = Géométrie
Identifiants, prix et caractéristiques : ISBN 9783319017334
Identifiant de la notice : ark:/12148/cb446747519
Notice n° :
FRBNF44674751
(notice reprise d'un réservoir extérieur)