By Francis Borceux

This is a unified remedy of some of the algebraic techniques to geometric areas. The learn of algebraic curves within the advanced projective airplane is the usual hyperlink among linear geometry at an undergraduate point and algebraic geometry at a graduate point, and it's also an enormous subject in geometric functions, reminiscent of cryptography.

380 years in the past, the paintings of Fermat and Descartes led us to review geometric difficulties utilizing coordinates and equations. this present day, this can be the preferred manner of dealing with geometrical difficulties. Linear algebra presents a good device for learning the entire first measure (lines, planes) and moment measure (ellipses, hyperboloids) geometric figures, within the affine, the Euclidean, the Hermitian and the projective contexts. yet fresh purposes of arithmetic, like cryptography, want those notions not just in genuine or complicated situations, but in addition in additional normal settings, like in areas developed on finite fields. and naturally, why no longer additionally flip our recognition to geometric figures of upper levels? in addition to all of the linear points of geometry of their such a lot common environment, this e-book additionally describes priceless algebraic instruments for learning curves of arbitrary measure and investigates effects as complicated because the Bezout theorem, the Cramer paradox, topological staff of a cubic, rational curves etc.

Hence the booklet is of curiosity for all those that need to train or research linear geometry: affine, Euclidean, Hermitian, projective; it's also of significant curiosity to people who don't need to limit themselves to the undergraduate point of geometric figures of measure one or two.