Ideals, Varieties, and Algorithms

An Introduction to Computational Algebraic Geometry and Commutative Algebra

Nonfiction, Science & Nature, Mathematics, Geometry, Algebra
Cover of the book Ideals, Varieties, and Algorithms by David A. Cox, John Little, Donal O'Shea, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: David A. Cox, John Little, Donal O'Shea ISBN: 9783319167213
Publisher: Springer International Publishing Publication: April 30, 2015
Imprint: Springer Language: English
Author: David A. Cox, John Little, Donal O'Shea
ISBN: 9783319167213
Publisher: Springer International Publishing
Publication: April 30, 2015
Imprint: Springer
Language: English

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.

Readers who are teaching from Ideals, Varieties, and Algorithms, or are studying the book on their own, may obtain a copy of the solutions manual by sending an email to [email protected].

From the reviews of previous editions:

 “…The book gives an introduction to Buchberger’s algorithm with applications to syzygies, Hilbert polynomials, primary decompositions. There is an introduction to classical algebraic geometry with applications to the ideal membership problem, solving polynomial 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

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

Readers who are teaching from Ideals, Varieties, and Algorithms, or are studying the book on their own, may obtain a copy of the solutions manual by sending an email to [email protected].

From the reviews of previous editions:

 “…The book gives an introduction to Buchberger’s algorithm with applications to syzygies, Hilbert polynomials, primary decompositions. There is an introduction to classical algebraic geometry with applications to the ideal membership problem, solving polynomial 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

More books from Springer International Publishing

Cover of the book Ethnocentric Political Theory by David A. Cox, John Little, Donal O'Shea
Cover of the book Computer Performance Engineering by David A. Cox, John Little, Donal O'Shea
Cover of the book Leadership Performance and Rhetoric by David A. Cox, John Little, Donal O'Shea
Cover of the book Immune Infertility by David A. Cox, John Little, Donal O'Shea
Cover of the book Human Reliability, Error, and Human Factors in Power Generation by David A. Cox, John Little, Donal O'Shea
Cover of the book Beyond the Turnout Paradox by David A. Cox, John Little, Donal O'Shea
Cover of the book Public Sector Reform in Ireland by David A. Cox, John Little, Donal O'Shea
Cover of the book Influenza Pathogenesis and Control - Volume I by David A. Cox, John Little, Donal O'Shea
Cover of the book Introduction to Parallel Computing by David A. Cox, John Little, Donal O'Shea
Cover of the book Management of Atopic Dermatitis by David A. Cox, John Little, Donal O'Shea
Cover of the book Roboethics by David A. Cox, John Little, Donal O'Shea
Cover of the book Ethics in Medicine by David A. Cox, John Little, Donal O'Shea
Cover of the book Pedagogies of Educational Transitions by David A. Cox, John Little, Donal O'Shea
Cover of the book Balanced Phono-Amps by David A. Cox, John Little, Donal O'Shea
Cover of the book Sustainability in Manufacturing Enterprises by David A. Cox, John Little, Donal O'Shea
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy