An Algebraic Approach to Geometry: Geometric Trilogy II by Francis Borceux

By Francis Borceux

This is a unified therapy of a few of the algebraic methods to geometric areas. The research of algebraic curves within the complicated projective aircraft is the typical hyperlink among linear geometry at an undergraduate point and algebraic geometry at a graduate point, and it's also an enormous subject in geometric purposes, reminiscent of cryptography.

380 years in the past, the paintings of Fermat and Descartes led us to check geometric difficulties utilizing coordinates and equations. this day, this is often the preferred means of dealing with geometrical difficulties. Linear algebra presents a good software 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 contemporary purposes of arithmetic, like cryptography, want those notions not just in genuine or complicated instances, but additionally in additional normal settings, like in areas developed on finite fields. and naturally, why no longer additionally flip our awareness to geometric figures of upper levels? in addition to all of the linear facets of geometry of their so much common environment, this booklet additionally describes important algebraic instruments for learning curves of arbitrary measure and investigates effects as complex because the Bezout theorem, the Cramer paradox, topological staff of a cubic, rational curves etc.

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

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