This 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 notions not only in real or complex
cases, but also in more general settings, like in spaces
constructed on finite fields. And of course, why not 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 not want to restrict
themselves to the undergraduate level of geometric figures of
degree one or two.
General
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!