Geometry (Universitext) 2003rd Edition by Michele Audin (PDF)

Description

Geometry, this very ancient field of study of mathematics, frequently remains too little familiar to students. Michle Audin, professor at the University of Strasbourg, has written a book allowing them to remedy this situation and, starting from linear algebra, extend their knowledge of affine, Euclidean and projective geometry, conic sections and quadrics, curves and surfaces. It includes many nice theorems like the nine-point circle, Feuerbach’s theorem, and so on. Everything is presented clearly and rigourously. Each property is proved, examples and exercises illustrate the course content perfectly. Precise hints for most of the exercises are provided at the end of the book. This very comprehensive text is addressed to students at upper undergraduate and Master’s level to discover geometry and deepen their knowledge and understanding.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is a wonderful book. The treatment of affine spaces (as a set of points on which a vector space acts in a certain way) is gratifying, deepens one’s understanding, and helps to organize a potentially sprawling set of results/phenomena. In the Euclidean plane, the author uses linear rotations to carefully develop the theory of directed angles of rays, and especially of LINES. The latter are an indispensable tool for simplifying proofs (and filling in gaps that almost invariably arise when we try to get by with just Euclidean angles of rays, which lack the kind of additivity we require for smooth-running, complete proofs). The projective plane is treated, with its stunning and eye-opening theory of conics (“curvey” lines based on a theory of STRAIGHT lines — wow!).Audin’s treatment of these subjects is “rigorous” (i.e. complete and correct by modern standards). The reader is assumed to have some experience with linear algebra, so the intended audience comprises people with beyond-average college-level training in mathematics.

⭐Un libro con un contenido propicio para lo que buscaba, el lenguaje se entiende claramente y no deja espacio a dudas

⭐

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