An Algebraic Approach to Geometry : Geometric Trilogy II

種類:

電子ブック

責任表示:

by Francis Borceux

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2014

著者名:

• Borceux, Francis
• SpringerLink (Online service)

ISBN:

9783319017334 [3319017330]    

注記:

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 figur

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