Computational Algebraic Geometry (London Mathematical Society Student Texts Book 58) 1st Edition by Hal Schenck (PDF)

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).

User’s Reviews

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

⭐Very useful text for me. It’s nice to have a brief summary of some of the longer passages from Hartshorne, emphasizing the intuition from varieties and their coordinate rings. I would definitely buy this book if you have an advisor in algebraic geometry who wants you to learn Hartshorne II and III on your own.

⭐I will not say this book is an introduction but that its a confusion remover for a serious student of algebraic geometry. This book I consider a part of the much needed revolution happening in algebraic geometry which means that if you browse or spend time reading a book you must learn something. Excellent coverage of a fascinating subject. Enjoy!

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