O'Shea, Donal
Overview
Works:  19 works in 251 publications in 10 languages and 5,526 library holdings 

Genres:  History 
Roles:  Author, Translator, Editor, Other 
Classifications:  QA564, 516.35 
Publication Timeline
.
Most widely held works by
Donal O'Shea
Ideals, varieties, and algorithms : an introduction to computational algebraic geometry and commutative algebra by
David A Cox(
Book
)
105 editions published between 1991 and 2015 in 3 languages and held by 2,253 WorldCat member libraries worldwide
"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. This book bases its discussion of algorithms on a generalization of the division algorithm for polynomials in one variable that was only discovered in the 1960s. Although the algorithmic roots of algebraic geometry are old, the computational aspects were neglected earlier in this century. This has changed in recent years, and new algorithms, coupled with the power of fast computers, have led to some interesting applications  for example, in robotics and in geometric theorem proving."BOOK JACKET
105 editions published between 1991 and 2015 in 3 languages and held by 2,253 WorldCat member libraries worldwide
"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. This book bases its discussion of algorithms on a generalization of the division algorithm for polynomials in one variable that was only discovered in the 1960s. Although the algorithmic roots of algebraic geometry are old, the computational aspects were neglected earlier in this century. This has changed in recent years, and new algorithms, coupled with the power of fast computers, have led to some interesting applications  for example, in robotics and in geometric theorem proving."BOOK JACKET
Using algebraic geometry by
David A Cox(
Book
)
46 editions published between 1997 and 2013 in 4 languages and held by 1,432 WorldCat member libraries worldwide
"This book illustrates the many uses of algebraic geometry, highlighting some of the more recent applications of Grobner bases and resultants. In order to do this, the authors provide an introduction to some algebraic objects and techniques which are more advanced than one typically encounters in a first course, but nonetheless of great utility." "The book is written for nonspecialists and for readers with a diverse range of backgrounds. It assumes knowledge of the material covered in a standard undergraduate course in abstract algebra, and it would help to have some previous exposure to Grobner bases. The book does not assume the reader is familiar with more advanced concepts such as modules."Jacket
46 editions published between 1997 and 2013 in 4 languages and held by 1,432 WorldCat member libraries worldwide
"This book illustrates the many uses of algebraic geometry, highlighting some of the more recent applications of Grobner bases and resultants. In order to do this, the authors provide an introduction to some algebraic objects and techniques which are more advanced than one typically encounters in a first course, but nonetheless of great utility." "The book is written for nonspecialists and for readers with a diverse range of backgrounds. It assumes knowledge of the material covered in a standard undergraduate course in abstract algebra, and it would help to have some previous exposure to Grobner bases. The book does not assume the reader is familiar with more advanced concepts such as modules."Jacket
The Poincaré conjecture : in search of the shape of the universe by
Donal O'Shea(
Book
)
45 editions published between 2007 and 2014 in 9 languages and held by 1,275 WorldCat member libraries worldwide
Conceived in 1904, the Poincaré conjecture, a puzzle that speaks to the possible shape of the universe and lies at the heart of modern topology and geometry, has resisted attempts by generations of mathematicians to prove or to disprove it. Despite a milliondollar prize for a solution, Russian mathematician Grigory Perelman, posted his solution on the Internet instead of publishing it in a peerreviewed journal. This book "tells the story of the fascinating personalities, institutions, and scholarship behind the centuries of mathematics that have led to Perelman's dramatic proof." The author also chronicles dramatic events at the 2006 International Congress of Mathematicians in Madrid, where Perelman was awarded a Fields Medal for his solution, which he declined
45 editions published between 2007 and 2014 in 9 languages and held by 1,275 WorldCat member libraries worldwide
Conceived in 1904, the Poincaré conjecture, a puzzle that speaks to the possible shape of the universe and lies at the heart of modern topology and geometry, has resisted attempts by generations of mathematicians to prove or to disprove it. Despite a milliondollar prize for a solution, Russian mathematician Grigory Perelman, posted his solution on the Internet instead of publishing it in a peerreviewed journal. This book "tells the story of the fascinating personalities, institutions, and scholarship behind the centuries of mathematics that have led to Perelman's dramatic proof." The author also chronicles dramatic events at the 2006 International Congress of Mathematicians in Madrid, where Perelman was awarded a Fields Medal for his solution, which he declined
Programming for mathematicians by
R Seroul(
Book
)
6 editions published in 2000 in English and held by 264 WorldCat member libraries worldwide
"The aim of this book is to teach mathematics students how to program using their knowledge of mathematics. For this they require only to know how to construct a proof. The entire book's emphasis is on "how to think" when programming. Three methods for constructing an algorithm or a program are used: a) manipulation and enrichment of existing code; b) use of recurrent sequences; c) deferral of code writing, in order to deal with one difficulty at a time. Many theorems are mathematically proved and programmed. The last chapter explains how a compiler works and shows how to compile "by hand" little (but not trivial  even recursive) programs. The book is intended for anyone who thinks mathematically and wants to program and play with mathematics."Jacket
6 editions published in 2000 in English and held by 264 WorldCat member libraries worldwide
"The aim of this book is to teach mathematics students how to program using their knowledge of mathematics. For this they require only to know how to construct a proof. The entire book's emphasis is on "how to think" when programming. Three methods for constructing an algorithm or a program are used: a) manipulation and enrichment of existing code; b) use of recurrent sequences; c) deferral of code writing, in order to deal with one difficulty at a time. Many theorems are mathematically proved and programmed. The last chapter explains how a compiler works and shows how to compile "by hand" little (but not trivial  even recursive) programs. The book is intended for anyone who thinks mathematically and wants to program and play with mathematics."Jacket
An exposition of catastrophe theory and its applications to phase transitions by
Donal O'Shea(
Book
)
1 edition published in 1977 in English and held by 166 WorldCat member libraries worldwide
1 edition published in 1977 in English and held by 166 WorldCat member libraries worldwide
Ideals, Varieties, and Algorithms : an Introduction to Computational Algebraic Geometry and Commutative Algebra by
David Cox(
)
6 editions published in 2007 in English and Undetermined and held by 36 WorldCat member libraries worldwide
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 Monthly
6 editions published in 2007 in English and Undetermined and held by 36 WorldCat member libraries worldwide
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 Monthly
Gastrointestinal endocrine tumours(
Book
)
5 editions published in 1996 in English and held by 29 WorldCat member libraries worldwide
5 editions published in 1996 in English and held by 29 WorldCat member libraries worldwide
Gurebuna kitei to daisū tayōtai nyūmon : idearu, tayōtai, arugorizumu by
David A Cox(
Book
)
10 editions published between 2000 and 2012 in Japanese and held by 10 WorldCat member libraries worldwide
10 editions published between 2000 and 2012 in Japanese and held by 10 WorldCat member libraries worldwide
An introduction to dynamical systems and mathematical modelling by
Donal O'Shea(
Book
)
1 edition published in 1992 in English and held by 9 WorldCat member libraries worldwide
1 edition published in 1992 in English and held by 9 WorldCat member libraries worldwide
Gurebunā kitei : daisū kika to kakan daisū ni okeru Gurebunā kitei no yūkōsei by
David A Cox(
Book
)
4 editions published in 2000 in Japanese and held by 6 WorldCat member libraries worldwide
4 editions published in 2000 in Japanese and held by 6 WorldCat member libraries worldwide
Gastrointestinal endocrine tumours(
Book
)
2 editions published in 1996 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1996 in English and held by 3 WorldCat member libraries worldwide
Ideals, Varieties, and Algorithms by
David A Cox(
Book
)
1 edition published in 2007 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 2007 in English and held by 3 WorldCat member libraries worldwide
Using Algebraic Geometry by
David A Cox(
)
2 editions published between 1998 and 2005 in English and held by 3 WorldCat member libraries worldwide
2 editions published between 1998 and 2005 in English and held by 3 WorldCat member libraries worldwide
On [mu]equivalent families of singularities by
Donal Bartholomew O'Shea(
Book
)
2 editions published between 1980 and 1982 in English and held by 2 WorldCat member libraries worldwide
2 editions published between 1980 and 1982 in English and held by 2 WorldCat member libraries worldwide
Idealy, mnogoobraziâ i algoritmy : vvedenie v vyčislitel'nye aspekty algebraičeskoj geometrii i kommutativnoj algebry by
David A Cox(
Book
)
2 editions published in 2000 in Russian and held by 2 WorldCat member libraries worldwide
2 editions published in 2000 in Russian and held by 2 WorldCat member libraries worldwide
Gastrointestinal endocrine tumours(
)
1 edition published in 1997 in English and held by 1 WorldCat member library worldwide
1 edition published in 1997 in English and held by 1 WorldCat member library worldwide
La congettura di Poincaré : da Euclide a Perelman, la storia di uno dei più affascinanti enigmi del millennio by
Donal O'Shea(
Book
)
1 edition published in 2014 in Italian and held by 1 WorldCat member library worldwide
1 edition published in 2014 in Italian and held by 1 WorldCat member library worldwide
Departmental manual of elementary surveying by
D. B O'Shea(
Book
)
1 edition published in 1940 in English and held by 1 WorldCat member library worldwide
1 edition published in 1940 in English and held by 1 WorldCat member library worldwide
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Audience Level
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Related Identities
 Little, John B. Other Author
 Cox, David A. Author
 Poincaré, Henri 18541912
 Perelman, Grigori 1966
 Cox, David Author
 Seroul, Raymond Author
 RandonFurling, Julien Translator
 Bloom, Stephen Robert Editor
 SpringerLink (Online service)
 北村, 知徳
Useful Links
Associated Subjects
Algebra AlgebraData processing Algebraic topology Algorithms Carcinoid Catastrophes (Mathematics) Commutative algebra Commutative algebraData processing Commutative rings Computer programming Computer science Computer scienceMathematics Computer software Differential topology Endocrine glandsTumors Geometry, Algebraic Geometry, AlgebraicData processing International Congress of Mathematicians Logic, Symbolic and mathematical Mathematical models Mathematicians Mathematics MathematicsAwards MathematicsData processing Nigeria Perelman, Grigori, Phase diagrams Phase transformations (Statistical physics) Poincaré, Henri, Poincaré conjecture Programming (Mathematics) Shape theory (Topology) Singularities (Mathematics) Surveying System analysis Threemanifolds (Topology) Topology ZollingerEllison syndrome
Covers
Alternative Names
Donal O'Shea Canadees wiskundige
Donal O'Shea Canadian mathematician
Donal O'Shea canadisk matematiker
Donal O'Shea kanadensisk matematiker
Donal O'Shea kanadischUSamerikanischer Mathematiker
Donal O'Shea kanadisk matematikar
Donal O'Shea kanadisk matematiker
Donal O'Shea matematico canadese
O’Shea, D. (Donal)
O'Shea, D.
O'Shea, D. 1952
O'Shea, D. B.
O'Shea, D. (Donal)
O'Shea, Donal B.
O'Shea, Donal Bartholomew 1952
O'Shea, Donald B.
O'Ši, D.
א'ושי, דונל
오셔, 도널
オシー, D
オシア, ドナル
Languages