Computational Algebraic Geometry

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Computational Algebraic Geometry

By Hal Schenck

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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).

Subject: Mathematics & Statistics -> Post-Calculus -> Topology

Computational Algebraic Geometry
1st edition
Publisher: Cambridge University Press 9/29/03
Imprint: Cambridge University Press
Language: English

ISBN 10: 0511075669
ISBN 13: 9780511075667
Print ISBN: 9780521829649

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