Ideals, Varieties, and Algorithms

书名：Ideals, Varieties, and AlgorithmsAnIntroductiontoComputationalAlgebraicGeometryandCommutativeAlgebra
作者：DavidA.Cox/JohnLittle/DonalO'Shea
译者：
ISBN：9783319167206
出版社：Springer
出版时间：2015-4-30
格式：epub/mobi/azw3/pdf
页数：646
豆瓣评分：

书籍简介：

This text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects. The first four chapters form the core of the book. A comprehensive chart in the Preface illustrates a variety of ways to proceed with the material once these chapters are covered. In addition to the fundamentals of algebraic geometry—the elimination theorem, the extension theorem, the closure theorem and the Nullstellensatz—this new edition incorporates several substantial changes, all of which are listed in the Preface. The largest revision incorporates a new Chapter (ten), which presents some of the essentials of progress made over the last decades in computing Gröbner bases. The book also includes current computer algebra material in Appendix C and updated independent projects (Appendix D). The book may serve as a first or second course in undergraduate abstract algebra and with some supplementation perhaps, for beginning graduate level courses in algebraic geometry or computational algebra. Prerequisites for the reader include linear algebra and a proof-oriented course.It is assumed that the reader has access to a computer algebra system. Appendix C describes features of Maple™, Mathematica® and Sage, as well as other systems that are most relevant to the text. Pseudocode is used in the text; Appendix B carefully describes the pseudocode used.

作者简介：

David A. Cox is currently Professor of Mathematics at Amherst College. John Little is currently Professor of Mathematics at College of the Holy Cross. Donal O'Shea is currently President and Professor of Mathematics at New College of Florida.

书友短评：

@ Renko 还不错 有很多具体的例子 证明清楚 @ Renko 还不错 有很多具体的例子 证明清楚

Preface
Notation for Sets and Functions
1. Geometry, Algebra, and Algorithms
2. Groebner Bases
3. Elimination Theory
4.The Algebra-Geometry Dictionary
5. Polynomial and Rational Functions on a Variety
6. Robotics and Automatic Geometric Theorem Proving
7. Invariant Theory of Finite Groups
8. Projective Algebraic Geometry
9. The Dimension of a Variety
10. Additional Groebner Basis Algorithms
Appendix A. Some Concepts from Algebra
Appendix B. Pseudocode
Appendix C. Computer Algebra Systems
Appendix D. Independent Projects
References
Index
· · · · · ·

　　Undergraduate Texts in Mathematics(共140册)，这套丛书还有《Topics in the Theory of Numbers》《From Fermat to Minkowski》《Introduction to Linear Algebra》《An Introduction to Wavelets Through Linear Algebra》《Computing the Continuous Discretely》等。

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