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# Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra: 2015 by David A. Cox, Donal O'Shea, John Little (Hardback, 2015)

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## About this product

### Description

- DescriptionThis 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 Grobner 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(TM), Mathematica(R) 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. From the reviews of previous editions: ...The book gives an introduction to Buchberger's algorithm with applications to syzygies, Hilbert polymials, primary decompositions. There is an introduction to classical algebraic geometry with applications to the ideal membership problem, solving polymial equations and elimination theory...The book is well-written...The reviewer is sure that it will be an excellent guide to introduce further undergraduates in the algorithmic aspect of commutative algebra and algebraic geometry. -Peter Schenzel, zbMATH, 2007 I consider the book to be wonderful...The exposition is very clear, there are many helpful pictures and there are a great many instructive exercises, some quite challenging ...offers the heart and soul of modern commutative and algebraic geometry. -The American Mathematical Monthly
- Author BiographyDavid 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.

### Key Features

- Author(s)David A. Cox,Donal O'Shea,John Little
- PublisherBirkhauser Verlag AG
- Date of Publication31/05/2015
- LanguageEnglish
- FormatHardback
- ISBN-103319167200
- ISBN-139783319167206
- SubjectMathematics
- Series TitleUndergraduate Texts in Mathematics

### Publication Data

- Place of PublicationBasel
- Country of PublicationSwitzerland
- ImprintBirkhauser Verlag AG
- Content Note85 black & white illustrations, 10 colour illustrations, biography

### Dimensions

- Weight1255 g
- Width155 mm
- Height235 mm
- Spine37 mm

### Editorial Details

- Edition Statement4th Revised edition

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