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 
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|u
856 40 |3EBSCOhost|u