MARC 主機 00000cam 2200505Ki 4500
001 865554668
003 OCoLC
005 20140206010242.0
006 m o d
007 cr cnu|unuuu||
008 131218s2014 sz a ob 001 0 eng d
020 9783319017334 (electronic bk.)
020 3319017330 (electronic bk.)
024 7 10.1007/978-3-319-01733-4
035 (OCoLC)865554668
040 GW5XE|beng|erda|epn|cGW5XE|dN$T
050 4 QA564
082 04 516.35|223
100 1 Borceux, Francis,|d1948-,|eauthor
245 13 An algebraic approach to geometry /|cFrancis Borceux
264 1 Cham :|bSpringer,|c2014
300 1 online resource (xvii, 430 pages) :|billustrations
336 text|btxt|2rdacontent
337 computer|bc|2rdamedia
338 online resource|bcr|2rdacarrier
490 0 Geometric Trilogy ;|vII
504 Includes bibliographical references and index
505 0 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
520 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
588 Description based on online resource; title from PDF title
page (SpringerLink, viewed November 11, 2013)
650 0 Geometry, Algebraic
650 7 MATHEMATICS / Geometry / General|2bisacsh
650 14 Mathematics
650 24 Geometry
650 24 Projective Geometry
655 4 Electronic books
856 40 |3SpringerLink|uhttp://dx.doi.org/10.1007/978-3-319-01733-
4
856 40 |3EBSCOhost|uhttp://search.ebscohost.com/
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