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- DescriptionThis is a unified treatment of the various algebraic approaches to geometric spaces. The study of algebraic curves in the complex projective plane is the natural link between linear geometry at an undergraduate level and algebraic geometry at a graduate level, and it is also an important topic in geometric applications, such as cryptography. 380 years ago, the work of Fermat and Descartes led us to study geometric problems using coordinates and equations. Today, this is the most popular way of handling geometrical problems. Linear algebra provides an efficient tool for studying all the first degree (lines, planes) and second degree (ellipses, hyperboloids) geometric figures, in the affine, the Euclidean, the Hermitian and the projective contexts. But recent applications of mathematics, like cryptography, need these tions t only in real or complex cases, but also in more general settings, like in spaces constructed on finite fields. And of course, why t also turn our attention to geometric figures of higher degrees? Besides all the linear aspects of geometry in their most general setting, this book also describes useful algebraic tools for studying curves of arbitrary degree and investigates results as advanced as the Bezout theorem, the Cramer paradox, topological group of a cubic, rational curves etc. Hence the book is of interest for all those who have to teach or study linear geometry: affine, Euclidean, Hermitian, projective; it is also of great interest to those who do t want to restrict themselves to the undergraduate level of geometric figures of degree one or two.
- Author BiographyFrancis Borceux is Professor of mathematics at the University of Louvain since many years. He has developed research in algebra and essentially taught geometry, number theory and algebra courses and he has been dean of the Faculty of Sciences of his University and chairman of the Mathematical Committee of the Belgian National Scientific Research Foundation.
- Author(s)Francis Borceux
- PublisherSpringer International Publishing AG
- Date of Publication08/11/2013
- Place of PublicationCham
- Country of PublicationSwitzerland
- ImprintSpringer International Publishing AG
- Content Note117 black & white illustrations, biography
- Weight830 g
- Width156 mm
- Height234 mm
- Spine25 mm
- Format DetailsLaminated cover
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