山西大同大学图书馆书目检索系统

Online Public Access Catalogue

题名/责任者:

An algebraic approach to geometry / Francis Borceux.

出版发行项:

北京 : 世界图书出版公司, 2017.

ISBN:

9787519220754

载体形态项:

xvii, 430 p. : ill. ; 23 cm.

变异题名:

几何的代数方法

丛编说明:

Geometric trilogy = 几何三部曲

个人责任者:

Borceux, Francis, 1948-

丛编个人名称:

Borceux, Francis, 1948- Geometric trilogy ; 2.

论题主题:

Geometry, Algebraic.

论题主题:

Mathematics.

中图法分类号:

O187

一般附注:

Cover title.

书目附注:

Includes bibliographical references (p. 423-424) and index.

内容附注:

1.The Birth of Analytic Geometry -- 2.Affine Geometry -- 3.More on Real Affine Spaces -- 4.Euclidean Geometry -- 5.Hermitian Spaces -- 6.Projective Geometry -- 7.Algebraic Curves -- Appendices:?A.Polynomials Over a Field -- B.Polynomials in Several Variables -- C.Homogenous Polynomials -- D.Resultants -- E.Symmetric Polynomials -- F.Complex Numbers -- G.Quadratic Forms -- H.Dual Spaces.

摘要附注:

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

原版附注:

Reprint. Originally published: Switzerland : Springer, c2014. 9783319017327.

原版附注:

Reprint. Originally published: New York : Springer, 2014. 9783319017327.

豆瓣简介：