Cox, David A.
Overview
Works:  66 works in 362 publications in 5 languages and 7,644 library holdings 

Genres:  History Conference papers and proceedings 
Roles:  Author, Editor, 958, htt, Other, Actor 
Classifications:  QA564, 516.35 
Publication Timeline
.
Most widely held works by
David A Cox
Ideals, varieties, and algorithms : an introduction to computational algebraic geometry and commutative algebra by
David A Cox(
Book
)
79 editions published between 1991 and 2015 in 4 languages and held by 1,978 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
79 editions published between 1991 and 2015 in 4 languages and held by 1,978 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
Primes of the form x² + ny² : Fermat, class field theory, and complex multiplication by
David A Cox(
)
34 editions published between 1989 and 2014 in English and held by 1,518 WorldCat member libraries worldwide
"Written in a unique and accessible style for readers of varied mathematical backgrounds, the Second Edition of Primes of the Form p = x2+ ny2 details the history behind how Pierre de Fermat's work ultimately gave birth to quadratic reciprocity and the genus theory of quadratic forms. The book also illustrates how results of Euler and Gauss can be fully understood only in the context of class field theory, and in addition, explores a selection of the magnificent formulas of complex multiplication. Primes of the Form p = x2 + ny2, Second Edition focuses on addressing the question of when a prime p is of the form x2 + ny2, which serves as the basis for further discussion of various mathematical topics. This updated edition has several new notable features, including: A wellmotivated introduction to the classical formulation of class field theory ; Illustrations of explicit numerical examples to demonstrate the power of basic theorems in various situations ; An elementary treatment of quadratic forms and genus theory ; Simultaneous treatment of elementary and advanced aspects of number theory ; New coverage of the Shimura reciprocity law and a selection of recent work in an updated bibliography. Primes of the Form p = x2 + ny2, Second Edition is both a useful reference for number theory theorists and an excellent text for undergraduate and graduatelevel courses in number and Galois theory."Publisher's website
34 editions published between 1989 and 2014 in English and held by 1,518 WorldCat member libraries worldwide
"Written in a unique and accessible style for readers of varied mathematical backgrounds, the Second Edition of Primes of the Form p = x2+ ny2 details the history behind how Pierre de Fermat's work ultimately gave birth to quadratic reciprocity and the genus theory of quadratic forms. The book also illustrates how results of Euler and Gauss can be fully understood only in the context of class field theory, and in addition, explores a selection of the magnificent formulas of complex multiplication. Primes of the Form p = x2 + ny2, Second Edition focuses on addressing the question of when a prime p is of the form x2 + ny2, which serves as the basis for further discussion of various mathematical topics. This updated edition has several new notable features, including: A wellmotivated introduction to the classical formulation of class field theory ; Illustrations of explicit numerical examples to demonstrate the power of basic theorems in various situations ; An elementary treatment of quadratic forms and genus theory ; Simultaneous treatment of elementary and advanced aspects of number theory ; New coverage of the Shimura reciprocity law and a selection of recent work in an updated bibliography. Primes of the Form p = x2 + ny2, Second Edition is both a useful reference for number theory theorists and an excellent text for undergraduate and graduatelevel courses in number and Galois theory."Publisher's website
Using algebraic geometry by
David A Cox(
Book
)
51 editions published between 1998 and 2014 in 4 languages and held by 1,433 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
51 editions published between 1998 and 2014 in 4 languages and held by 1,433 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
Galois theory by
David A Cox(
)
32 editions published between 2004 and 2012 in 3 languages and held by 1,200 WorldCat member libraries worldwide
"Galois Theory covers classic applications of the theory, such as solvability by radicals, geometric constructions, and finite fields. The book also delves into more novel topics, including Abel's theory of Abelian equations, the problem of expressing real roots by real radicals (the casus irreducibilis), and the Galois theory of origami." "With Mathematical and Historical Notes that clarify the ideas and their history in detail, Galois Theory brings one of the most colorful and influential theories in algebra to life for professional algebraists and students alike."Jacket
32 editions published between 2004 and 2012 in 3 languages and held by 1,200 WorldCat member libraries worldwide
"Galois Theory covers classic applications of the theory, such as solvability by radicals, geometric constructions, and finite fields. The book also delves into more novel topics, including Abel's theory of Abelian equations, the problem of expressing real roots by real radicals (the casus irreducibilis), and the Galois theory of origami." "With Mathematical and Historical Notes that clarify the ideas and their history in detail, Galois Theory brings one of the most colorful and influential theories in algebra to life for professional algebraists and students alike."Jacket
Mirror symmetry and algebraic geometry by
David A Cox(
Book
)
18 editions published between 1999 and 2014 in English and held by 443 WorldCat member libraries worldwide
Mirror symmetry began when theoretical physicists made some astonishing predictions about rational curves on quintic hypersurfaces in fourdimensional projective space. Understanding the mathematics behind these predictions has been a substantial challenge. This book is the first completely comprehensive monograph on mirror symmetry, covering the original observations by the physicists through the most recent progress made to date. Subjects discussed include toric varieties, Hodge theory, K̃hler geometry, moduli of stable maps, CalabiYau manifolds, quantum cohomology, GromovWitten invariants, and the mirror theorem. Features: Numerous examples worked out in detail An appendix on mathematical physics An exposition of the algebraic theory of GromovWitten invariants and quantum cohomology A proof of the mirror theorem for the quintic threefold
18 editions published between 1999 and 2014 in English and held by 443 WorldCat member libraries worldwide
Mirror symmetry began when theoretical physicists made some astonishing predictions about rational curves on quintic hypersurfaces in fourdimensional projective space. Understanding the mathematics behind these predictions has been a substantial challenge. This book is the first completely comprehensive monograph on mirror symmetry, covering the original observations by the physicists through the most recent progress made to date. Subjects discussed include toric varieties, Hodge theory, K̃hler geometry, moduli of stable maps, CalabiYau manifolds, quantum cohomology, GromovWitten invariants, and the mirror theorem. Features: Numerous examples worked out in detail An appendix on mathematical physics An exposition of the algebraic theory of GromovWitten invariants and quantum cohomology A proof of the mirror theorem for the quintic threefold
Applications of computational algebraic geometry : American Mathematical Society short course, January 67, 1997, San Diego,
California by
American mathematical society(
Book
)
20 editions published between 1997 and 2014 in English and held by 377 WorldCat member libraries worldwide
20 editions published between 1997 and 2014 in English and held by 377 WorldCat member libraries worldwide
Toric varieties by
David A Cox(
Book
)
17 editions published between 2011 and 2012 in English and German and held by 292 WorldCat member libraries worldwide
This title covers the standard topics in toric geometry; a novel feature is that each of the first nine chapters contains an introductory section on the necessary background material in algebraic geometry
17 editions published between 2011 and 2012 in English and German and held by 292 WorldCat member libraries worldwide
This title covers the standard topics in toric geometry; a novel feature is that each of the first nine chapters contains an introductory section on the necessary background material in algebraic geometry
A study of singularities on rational curves via Syzygies by
David A Cox(
Book
)
12 editions published between 2012 and 2013 in English and held by 179 WorldCat member libraries worldwide
12 editions published between 2012 and 2013 in English and held by 179 WorldCat member libraries worldwide
Primes of the form x℗ + ny℗ : Fermat, class field theory, and complex multiplication by
David A Cox(
Book
)
7 editions published between 1989 and 2011 in English and held by 31 WorldCat member libraries worldwide
Modern number theory began with the work of Euler and Gauss to understand and extend the many unsolved questions left behind by Fermat. In the course of their investigations, they uncovered new phenomena in need of explanation, which over time led to the discovery of field theory and its intimate connection with complex multiplication. While most texts concentrate on only the elementary or advanced aspects of this story, Primes of the Form x2 + ny2 begins with Fermat and explains how his work ultimately gave birth to quadratic reciprocity and the genus theory of quadratic forms. Further, the bo
7 editions published between 1989 and 2011 in English and held by 31 WorldCat member libraries worldwide
Modern number theory began with the work of Euler and Gauss to understand and extend the many unsolved questions left behind by Fermat. In the course of their investigations, they uncovered new phenomena in need of explanation, which over time led to the discovery of field theory and its intimate connection with complex multiplication. While most texts concentrate on only the elementary or advanced aspects of this story, Primes of the Form x2 + ny2 begins with Fermat and explains how his work ultimately gave birth to quadratic reciprocity and the genus theory of quadratic forms. Further, the bo
Residues and duality for projective algebraic varieties by
Ernst Kunz(
Book
)
5 editions published between 2008 and 2009 in English and held by 20 WorldCat member libraries worldwide
"This book, which grew out of lectures by E. Kunz for students with a background in algebra and algebraic geometry, develops local and global duality theory in the special case of (possibly singular) algebraic varieties over algebraically closed base fields. It describes duality and residue theorems in terms of Kahler differential forms and their residues. The properties of residues are introduced via local cohomology. Special emphasis is given to the relation between residues to classical results of algebraic geometry and their generalizations." "The contribution by A. Dickenstein gives applications of residues and duality to polynomial solutions of constant coefficient partial differential equations and to problems in interpolation and ideal membership, D.A. Cox explains toric residues and relates them to the earlier text." "The book is intended as an introduction to more advanced treatments and further applications of the subject, to which numerous bibliographical hints are given."Jacket
5 editions published between 2008 and 2009 in English and held by 20 WorldCat member libraries worldwide
"This book, which grew out of lectures by E. Kunz for students with a background in algebra and algebraic geometry, develops local and global duality theory in the special case of (possibly singular) algebraic varieties over algebraically closed base fields. It describes duality and residue theorems in terms of Kahler differential forms and their residues. The properties of residues are introduced via local cohomology. Special emphasis is given to the relation between residues to classical results of algebraic geometry and their generalizations." "The contribution by A. Dickenstein gives applications of residues and duality to polynomial solutions of constant coefficient partial differential equations and to problems in interpolation and ideal membership, D.A. Cox explains toric residues and relates them to the earlier text." "The book is intended as an introduction to more advanced treatments and further applications of the subject, to which numerous bibliographical hints are given."Jacket
Galois Theory by
David A Cox(
)
1 edition published in 2012 in English and held by 20 WorldCat member libraries worldwide
1 edition published in 2012 in English and held by 20 WorldCat member libraries worldwide
Primes of the form x p2 s + ny p2 s : Fermat, class field theory, and complex multiplication by
David A Cox(
Book
)
1 edition published in 1989 in English and held by 16 WorldCat member libraries worldwide
1 edition published in 1989 in English and held by 16 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
Primes of the form xp2s + nyp2s : Fermat, class field theory, and complex multiplication by
David A Cox(
)
2 editions published between 1989 and 2013 in English and held by 10 WorldCat member libraries worldwide
From Fermat to Gauss  Class field theory  Complex multiplication  Additional topics
2 editions published between 1989 and 2013 in English and held by 10 WorldCat member libraries worldwide
From Fermat to Gauss  Class field theory  Complex multiplication  Additional topics
Ideals, Varieties, and Algorithms : an Introduction to Computational Algebraic Geometry and Commutative Algebra by
David Cox(
)
2 editions published in 2007 in English and held by 9 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
2 editions published in 2007 in English and held by 9 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
A guide to Canadian policies on arms control, disarmament, defence and conflict resolution by
Jane Boulden(
Book
)
1 edition published in 1986 in English and held by 9 WorldCat member libraries worldwide
1 edition published in 1986 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
)
5 editions published between 2000 and 2012 in Japanese and held by 7 WorldCat member libraries worldwide
5 editions published between 2000 and 2012 in Japanese and held by 7 WorldCat member libraries worldwide
The beginnings and evolution of algebra by
Izabella Grigorʹevna Bašmakova(
Book
)
2 editions published in 2000 in English and held by 6 WorldCat member libraries worldwide
The elements of algebra were known to the ancient Mesopotamians at least 4000 years ago. Today algebra stands as one of the cornerstones of modern mathematics. How then did the subject evolve? How did its constituent ideas and concepts arise, and how have they changed over the years? These are the questions that the authors address in this work. The authors challenge the existing view that the development of algebra was driven by the investigation of determinate equations and in particular their solution by radicals. In short they claim that the study of indeterminate equations was no less important.From publisher's description
2 editions published in 2000 in English and held by 6 WorldCat member libraries worldwide
The elements of algebra were known to the ancient Mesopotamians at least 4000 years ago. Today algebra stands as one of the cornerstones of modern mathematics. How then did the subject evolve? How did its constituent ideas and concepts arise, and how have they changed over the years? These are the questions that the authors address in this work. The authors challenge the existing view that the development of algebra was driven by the investigation of determinate equations and in particular their solution by radicals. In short they claim that the study of indeterminate equations was no less important.From publisher's description
Ideals, Varieties, and Algorithms by
DAVID A COX(
Book
)
3 editions published between 1997 and 2016 in English and held by 6 WorldCat member libraries worldwide
3 editions published between 1997 and 2016 in English and held by 6 WorldCat member libraries worldwide
Primes of the form x2 ̊ny2 by
David A Cox(
Book
)
3 editions published between 1989 and 2013 in English and held by 6 WorldCat member libraries worldwide
3 editions published between 1989 and 2013 in English and held by 6 WorldCat member libraries worldwide
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Related Identities
 Little, John B. Author
 O'Shea, Donal
 Katz, Sheldon 1956 Contributor
 Sturmfels, Bernd 1962 Other Editor
 Manocha, Dinesh N.
 Schenck, Henry K. 1963
 Polini, Claudia 1966
 Kustin, Andrew R. 1953
 Ulrich, Bernd 1954
 American Mathematical Society Other Editor
Useful Links
Associated Subjects
Algebra AlgebraData processing Algebraic fields Algebraic varieties Algorithms Arms control CalabiYau manifolds Canada Class field theory Combinatorial analysis Commutative algebra Commutative algebraData processing Commutative rings Computer software Congruences and residues Disarmament Equations, Theory of Forms, Quadratic Galois theory Geometry Geometry, Algebraic Geometry, AlgebraicData processing Geometry, Projective Gröbner bases Logic, Symbolic and mathematical Mathematical physics Mathematics Military policy Military readiness Mirror symmetry Multiplication, Complex Nuclear disarmament Numbers, Prime Number theory Polynomials Scientists Singularities (Mathematics) Toric varieties United States
Covers
Alternative Names
Cox, D. 1948
Cox D. A.
Cox D. A. 1948
Cox David
Cox David 1948....
Cox, David A.
Cox, David Archibald 1948
Cox, David (David A.)
Cox, David fl.1989
Cox, David mathématicien
David A. Cox Amerikaans wiskundige
David A. Cox matemàtic estatunidenc
David A. Cox matematico statunitense
David A. Cox mathématicien américain
David A. Cox USamerikanischer Mathematiker
David Archibald Cox
Koks, D.
Дэвид А. Кокс
Кокс Д.
Кокс, Д. (Дэвид А.)
Кокс Дэвид
دايفيد أ. كوكس رياضياتي أمريكي
دیوید ای. کاکس ریاضیدان آمریکایی
コックス, D
Languages