Geometry Topology

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By Francis Borceux

This is a unified remedy of some of the algebraic ways to geometric areas. The research of algebraic curves within the complicated projective airplane is the common hyperlink among linear geometry at an undergraduate point and algebraic geometry at a graduate point, and it's also a big subject in geometric functions, reminiscent of cryptography.

380 years in the past, the paintings of Fermat and Descartes led us to check geometric difficulties utilizing coordinates and equations. at the present time, this can be the preferred means of dealing with geometrical difficulties. Linear algebra presents an effective 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, desire those notions not just in actual or complicated situations, but in addition in additional basic 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 features of geometry of their so much common environment, this ebook additionally describes invaluable algebraic instruments for learning curves of arbitrary measure and investigates effects as complicated because the Bezout theorem, the Cramer paradox, topological crew of a cubic, rational curves etc.

Hence the booklet 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 do not need to limit themselves to the undergraduate point of geometric figures of measure one or two.

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