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Undergraduate Texts in Mathematics Ser.: Ideals, Varieties, and Algorithms : An Introduction to Computational Algebraic Geometry and Commutative Algebra by Donal O'Shea, David A. Cox and John Little (2008, Hardcover)

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About this product

Product Identifiers

PublisherSpringer
ISBN-100387356509
ISBN-139780387356501
eBay Product ID (ePID)56984718

Product Key Features

Number of PagesXv, 553 Pages
LanguageEnglish
Publication NameIdeals, Varieties, and Algorithms : An Introduction to Computational Algebraic Geometry and Commutative Algebra
Publication Year2008
SubjectAlgebra / Abstract, Algebra / General, Logic, Geometry / Algebraic
FeaturesRevised
TypeTextbook
Subject AreaMathematics
AuthorDonal O'shea, David A. Cox, John Little
SeriesUndergraduate Texts in Mathematics Ser.
FormatHardcover

Dimensions

Item Height0.5 in
Item Weight75.5 Oz
Item Length9.3 in
Item Width6.1 in

Additional Product Features

Edition Number3
Intended AudienceScholarly & Professional
LCCN2006-930875
ReviewsFrom the reviews of the third edition: "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 a excellent guide to introduce further undergraduates in the algorithmic aspect of commutative algebra and algebraic geometry." (Peter Schenzel, Zentralblatt MATH, Vol. 1118 (20), 2007), From the reviews of the third edition: "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 a excellent guide to introduce further undergraduates in the algorithmic aspect of commutative algebra and algebraic geometry." (Peter Schenzel, Zentralblatt MATH, Vol. 1118 (20), 2007), From the reviews of the third edition:"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 a excellent guide to introduce further undergraduates in the algorithmic aspect of commutative algebra and algebraic geometry." (Peter Schenzel, Zentralblatt MATH, Vol. 1118 (20), 2007)
Dewey Edition20
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal516.3/5
Table Of ContentPreface to the First Edition.- Preface to the Second Edition.- Preface to the Third Edition.- Geometry, Algebra, and Algorithms.- Groebner Bases.- Elimination Theory.- The Algebra-Geometry Dictionary.- Polynomial and Rational Functions on a Variety.- Robotics and Automatic Geometric Theorem Proving.- Invariant Theory of Finite Groups.- Projective Algebraic Geometry.- The Dimension of a Variety.- Appendix A. Some Concepts from Algebra.- Appendix B. Pseudocode.- Appendix C. Computer Algebra Systems.- Appendix D. Independent Projects.- References.- Index.
Edition DescriptionRevised edition
SynopsisThis book details the heart and soul of modern commutative and algebraic geometry. It covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory., Algebraic Geometry is the study of systems of polynomial equations in one or more variables, asking such questions as: Does the system have finitely many solutions, and if so how can one find them? And if there are infinitely many solutions, how can they be described and manipulated? The solutions of a system of polynomial equations form a geometric object called a variety; the corresponding algebraic object is an ideal. There is a close relationship between ideals and varieties which reveals the intimate link between algebra and geometry. Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. The algorithms to answer questions such as those posed above are an important part of algebraic geometry. Although the algorithmic roots of algebraic geometry are old, it is only in the last forty years that computational methods have regained their earlier prominence. New algorithms, coupled with the power of fast computers, have led to both theoretical advances and interesting applications, for example in robotics and in geometric theorem proving. In addition to enhancing the text of the second edition, with over 200 pages reflecting changes to enhance clarity and correctness, this third edition of Ideals, Varieties and Algorithms includes: A significantly updated section on Maple in Appendix C; Updated information on AXIOM, CoCoA, Macaulay 2, Magma, Mathematica and SINGULAR; A shorter proof of the Extension Theorem presented in Section 6 of Chapter 3. From the 2nd Edition: "I consider the book to be wonderful. ... The expositionis 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, This book details the heart and soul of modern commutative and algebraic geometry. It covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. In addition to enhancing the text of the second edition, with over 200 pages reflecting changes to enhance clarity and correctness, this third edition of Ideals, Varieties and Algorithms includes: a significantly updated section on Maple; updated information on AXIOM, CoCoA, Macaulay 2, Magma, Mathematica and SINGULAR; and presents a shorter proof of the Extension Theorem., Algebraic Geometry is the study of systems of polynomial equations in one or more variables, asking such questions as: Does the system have finitely many solutions, and if so how can one find them? And if there are infinitely many solutions, how can they be described and manipulated? The solutions of a system of polynomial equations form a geometric object called a variety; the corresponding algebraic object is an ideal. There is a close relationship between ideals and varieties which reveals the intimate link between algebra and geometry. Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. The algorithms to answer questions such as those posed above are an important part of algebraic geometry. Although the algorithmic roots of algebraic geometry are old, it is only in the last forty years that computational methods have regained their earlier prominence. New algorithms, coupled with the power of fast computers, have led to both theoretical advances and interesting applications, for example in robotics and in geometric theorem proving. In addition to enhancing the text of the second edition, with over 200 pages reflecting changes to enhance clarity and correctness, this third edition of Ideals, Varieties and Algorithms includes: A significantly updated section on Maple in Appendix C; Updated information on AXIOM, CoCoA, Macaulay 2, Magma, Mathematica and SINGULAR; A shorter proof of the Extension Theorem presented in Section 6 of Chapter 3. From the 2nd Edition: "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 MonthlyP>
LC Classification NumberQA564-609QA251.3QA8
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