Computational Algebraic Geometry (London Mathematical Society Student Texts)
Publisher: Cambridge University Press
Published: October 6, 2003
Language: eng
Format: Paperback
Number of pages: 208
ISBN-13: 9780521536509
Subjects: Algebra; Algebraic geometry; Science/Mathematics; Geometry - General; Mathematics; Geometry - Algebraic; Mathematics / Applied; Congresses; Data processing; Geometry, Algebraic
First sentence: Somewhere early in our mathematical career we encountered the equation and learned that the set of points in the plane satisfying this equation (the zero locus of f) is a parabola.
Description: The interplay between algebra and geometry is a beautiful (and fun!) area of mathematical investigation. Advances in computing and algorithms make it possible to tackle many classical problems in a down-to-earth and concrete fashion. This opens wonderful new vistas and allows us to pose, study and solve problems that were previously out of reach. Suitable for graduate students, the objective of this 2003 book is to bring advanced algebra to life with lots of examples. The first chapters provide an introduction to commutative algebra and connections to geometry. The rest of the book focuses on three active areas of contemporary algebra: Homological Algebra (the snake lemma, long exact sequence inhomology, functors and derived functors (Tor and Ext), and double complexes); Algebraic Combinatorics and Algebraic Topology (simplicial complexes and simplicial homology, Stanley-Reisner rings, upper bound theorem and polytopes); and Algebraic Geometry (points and curves in projective space, Riemann-Roch, Cech cohomology, regularity).