By Francis Borceux
This is a unified remedy of some of the algebraic methods to geometric areas. The examine of algebraic curves within the complicated projective airplane is the ordinary hyperlink among linear geometry at an undergraduate point and algebraic geometry at a graduate point, and it's also a massive subject in geometric functions, resembling 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 is often the most well-liked approach of dealing with geometrical difficulties. Linear algebra offers a good software for learning all of the 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, desire those notions not just in genuine or advanced circumstances, but in addition in additional normal settings, like in areas developed on finite fields. and naturally, why now not additionally flip our awareness to geometric figures of upper levels? in addition to all of the linear elements of geometry of their so much normal surroundings, this booklet additionally describes precious algebraic instruments for learning curves of arbitrary measure and investigates effects as complicated because the Bezout theorem, the Cramer paradox, topological workforce of a cubic, rational curves etc.
Hence the booklet is of curiosity for all those that need to educate or research 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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Extra resources for An Algebraic Approach to Geometry: Geometric Trilogy II