By Francis Borceux

This is a unified remedy of some of the algebraic techniques to geometric areas. The examine of algebraic curves within the complicated projective aircraft is the normal hyperlink among linear geometry at an undergraduate point and algebraic geometry at a graduate point, and it's also a massive 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 present day, this can be the preferred approach of dealing with geometrical difficulties. Linear algebra offers an effective instrument 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 functions of arithmetic, like cryptography, desire those notions not just in genuine or complicated circumstances, but in addition in additional common settings, like in areas developed on finite fields. and naturally, why no longer additionally flip our realization to geometric figures of upper levels? along with all of the linear points of geometry of their such a lot basic environment, this ebook additionally describes helpful 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 publication is of curiosity for all those that need to educate or examine linear geometry: affine, Euclidean, Hermitian, projective; it's also of significant curiosity to those that don't need to limit themselves to the undergraduate point of geometric figures of measure one or two.

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Extra info for An Algebraic Approach to Geometry: Geometric Trilogy II

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