Computational algebraic geometry
- 作者: Schenck, Hal.
- 出版: Cambridge, UK ;New York : Cambridge University Press 2003.
- 稽核項: 1 online resource (xiv, 193 pages) :illustrations.
- 叢書名: London Mathematical Society student texts ;58
- 標題: Informatique , Algebraische Geometrie , Electronic books. , Géométrie algébrique Informatique -- Congrès. , Algebraïsche meetkunde. , Algoritmen. , Geometry, Algebraic , GeometryAlgebraic. , Data processing. , Data processing , Geometry, Algebraic Data processing. , MATHEMATICS Geometry -- Algebraic. , MATHEMATICS , Dataprocessing. , Conference papers and proceedings. , Géométrie algébrique , Geometry, Algebraic Data processing -- Congresses.
- ISBN: 0521536502 , 9780521536509
- 試查全文@TNUA:
- 附註: Includes bibliographical references (pages 183-187) and index. Basics of commutative algebra -- Projective space and graded objects -- Free resolutions and regular sequences -- Gröbner bases and the Buchberger algorithm -- Combinatorics, topology and the Stanley-Reisner ring -- Functors: localization, Hom and tensor -- Geometry of points and the Hilbert function -- Snake Lemma, derived functors, Tor and Ext -- Curves, sheaves, and cohomology -- Projective dimension, Cohen-Macaulay modules, upper bound theorem -- Abstract algebra primer -- Complex analysis primer.
- 摘要: Investigates interplay between algebra and geometry. Covers: homological algebra, algebraic combinatorics and algebraic topology, and algebraic geometry.
- 電子資源: https://dbs.tnua.edu.tw/login?url=https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=125147
- 系統號: 005314033
- 資料類型: 電子書
- 讀者標籤: 需登入
- 引用網址: 複製連結
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).
來源: Google Book
來源: Google Book
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