Reid, Miles (Miles A.)
Overview
Works:  37 works in 240 publications in 4 languages and 5,791 library holdings 

Genres:  Personal narratives‡vBritish Textbooks Conference papers and proceedings 
Roles:  Author, Translator, Editor, Other, tra 
Publication Timeline
.
Most widely held works by
Miles Reid
Undergraduate algebraic geometry by
Miles Reid(
Book
)
56 editions published between 1988 and 2009 in 3 languages and held by 847 WorldCat member libraries worldwide
Leerboek voor studenten
56 editions published between 1988 and 2009 in 3 languages and held by 847 WorldCat member libraries worldwide
Leerboek voor studenten
Geometry and topology by
Miles Reid(
Book
)
14 editions published between 2005 and 2012 in English and held by 465 WorldCat member libraries worldwide
"Geometry provides a whole range of views on the universe, serving as the inspiration, technical toolkit and ultimate goal for many branches of mathematics and physics. The book introduces the ideas of geometry, and includes a generous supply of simple explanations and examples. The treatment emphasises coordinate systems and the coordinate changes that generate symmetries. The book is based on many years' teaching experience, and is thoroughly class tested. There are copious illustrations, and each chapter ends with a wide supply of exercises. Further teaching material is available for teachers via the web, including assignable problem sheets with solutions"Jacket
14 editions published between 2005 and 2012 in English and held by 465 WorldCat member libraries worldwide
"Geometry provides a whole range of views on the universe, serving as the inspiration, technical toolkit and ultimate goal for many branches of mathematics and physics. The book introduces the ideas of geometry, and includes a generous supply of simple explanations and examples. The treatment emphasises coordinate systems and the coordinate changes that generate symmetries. The book is based on many years' teaching experience, and is thoroughly class tested. There are copious illustrations, and each chapter ends with a wide supply of exercises. Further teaching material is available for teachers via the web, including assignable problem sheets with solutions"Jacket
Undergraduate commutative algebra by
Miles Reid(
Book
)
25 editions published between 1995 and 2004 in English and Japanese and held by 465 WorldCat member libraries worldwide
Commutative algebra is at the crossroads of algebra, number theory and algebraic geometry. This textbook is affordable and clearly illustrated, and is intended for advanced undergraduate or beginning graduate students with some previous experience of rings and fields. Alongside standard algebraic notions such as generators of modules and the ascending chain condition, the book develops in detail the geometric view of a commutative ring as the ring of functions on a space. The starting point is the Nullstellensatz, which provides a close link between the geometry of a variety V and the algebra of its coordinate ring A=k[V]; however, many of the geometric ideas arising from varieties apply also to fairly general rings. The final chapter relates the material of the book to more advanced topics in commutative algebra and algebraic geometry. It includes an account of some famous 'pathological' examples of Akizuki and Nagata, and a brief but thoughtprovoking essay on the changing position of abstract algebra in today's world. (A cura dell'editore)
25 editions published between 1995 and 2004 in English and Japanese and held by 465 WorldCat member libraries worldwide
Commutative algebra is at the crossroads of algebra, number theory and algebraic geometry. This textbook is affordable and clearly illustrated, and is intended for advanced undergraduate or beginning graduate students with some previous experience of rings and fields. Alongside standard algebraic notions such as generators of modules and the ascending chain condition, the book develops in detail the geometric view of a commutative ring as the ring of functions on a space. The starting point is the Nullstellensatz, which provides a close link between the geometry of a variety V and the algebra of its coordinate ring A=k[V]; however, many of the geometric ideas arising from varieties apply also to fairly general rings. The final chapter relates the material of the book to more advanced topics in commutative algebra and algebraic geometry. It includes an account of some famous 'pathological' examples of Akizuki and Nagata, and a brief but thoughtprovoking essay on the changing position of abstract algebra in today's world. (A cura dell'editore)
Number theory and algebraic geometry : to Peter SwinnertonDyer on his 75th birthday by
Miles Reid(
Book
)
19 editions published between 2003 and 2004 in English and held by 264 WorldCat member libraries worldwide
Peter SwinnertonDyer's mathematical career encompasses more than 60 years' work of amazing creativity. This volume, dedicated to him on the occasion of his 75th birthday, provides contemporary insight into several subjects in which his influence has been notable. The contributions come from leading researchers in analytic and arithmetic number theory, and algebraic geometry. Topics treated include rational points on algebraic varieties, the Hasse principle, ShafarevichTate groups of elliptic curves and motives, Zagier's conjectures, descent and zerocycles, Diophantine approximation, and Abelian and Fano varieties
19 editions published between 2003 and 2004 in English and held by 264 WorldCat member libraries worldwide
Peter SwinnertonDyer's mathematical career encompasses more than 60 years' work of amazing creativity. This volume, dedicated to him on the occasion of his 75th birthday, provides contemporary insight into several subjects in which his influence has been notable. The contributions come from leading researchers in analytic and arithmetic number theory, and algebraic geometry. Topics treated include rational points on algebraic varieties, the Hasse principle, ShafarevichTate groups of elliptic curves and motives, Zagier's conjectures, descent and zerocycles, Diophantine approximation, and Abelian and Fano varieties
Explicit birational geometry of 3folds by
Alessio Corti(
Book
)
14 editions published in 2000 in English and held by 263 WorldCat member libraries worldwide
One of the main achievements of algebraic geometry over the past twenty years is the work of Mori and others extending minimal models and the EnriquesKodaira classification to 3 folds. This integrated suite of papers centers around applications of Mori theory to birational geometry. Four of the papers (those by Pukhlikov, Fletcher, Corti, and the long joint paper by Corti, Pukhlikov and Reid) work out in detail the theory of birational rigidity of Fano 3folds. These contributions work for the first time with a representative class of Fano varieties, 3 fold hypersurfaces in weighted projective space, and they include an attractive introductory treatment with a wealth of detailed computation of special cases
14 editions published in 2000 in English and held by 263 WorldCat member libraries worldwide
One of the main achievements of algebraic geometry over the past twenty years is the work of Mori and others extending minimal models and the EnriquesKodaira classification to 3 folds. This integrated suite of papers centers around applications of Mori theory to birational geometry. Four of the papers (those by Pukhlikov, Fletcher, Corti, and the long joint paper by Corti, Pukhlikov and Reid) work out in detail the theory of birational rigidity of Fano 3folds. These contributions work for the first time with a representative class of Fano varieties, 3 fold hypersurfaces in weighted projective space, and they include an attractive introductory treatment with a wealth of detailed computation of special cases
Basic algebraic geometry by
I. R Shafarevich(
Book
)
20 editions published between 1994 and 2016 in English and held by 111 WorldCat member libraries worldwide
Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevich's book is a must.'' The second volume is in two parts: Book II is a gentle cultural introduction to scheme theory, with the first aim of putting abstract algebraic varieties on a firm foundation; a second aim is to introduce Hilbert schemes and moduli spaces, that serve as parameter spaces for other geometric constructions. Book III discusses complex manifolds and their relation with algebraic varieties, Kähler geometry and Hodge theory. The final section raises an important problem in uniformising higher dimensional varieties that has been widely studied as the ``Shafarevich conjecture''. The style of Basic Algebraic Geometry 2 and its minimal prerequisites make it to a large extent independent of Basic Algebraic Geometry 1, and accessible to beginning graduate students in mathematics and in theoretical physics
20 editions published between 1994 and 2016 in English and held by 111 WorldCat member libraries worldwide
Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevich's book is a must.'' The second volume is in two parts: Book II is a gentle cultural introduction to scheme theory, with the first aim of putting abstract algebraic varieties on a firm foundation; a second aim is to introduce Hilbert schemes and moduli spaces, that serve as parameter spaces for other geometric constructions. Book III discusses complex manifolds and their relation with algebraic varieties, Kähler geometry and Hodge theory. The final section raises an important problem in uniformising higher dimensional varieties that has been widely studied as the ``Shafarevich conjecture''. The style of Basic Algebraic Geometry 2 and its minimal prerequisites make it to a large extent independent of Basic Algebraic Geometry 1, and accessible to beginning graduate students in mathematics and in theoretical physics
Algebra I : basic notions of algebra by
I. R Shafarevich(
Book
)
8 editions published between 1990 and 2014 in English and held by 68 WorldCat member libraries worldwide
From the reviews: "This is one of the few mathematical books, the reviewer has read from cover to cover ... The main merit is that nearly on every page you will find some unexpected insights..." Zentralblatt für Mathematik und Ihre Grenzgebiete, 1991 "...which I read like a novel and undoubtedly will become a classic. ... A merit of the book under review is that it contains several important articles from journals which are not all so easily accessible. ... Furthermore, at the end of the book, there are some Notes by the author which are indispensible for the necessary historical background information. ... This valuable book should be on the shelf of every algebraist and algebraic geometer." Nieuw Archief voor Wiskunde, 1992 "... There are few proofs in full, but there is an exhilarating combination of sureness of foot and lightness of touch in the exposition ... which transports the reader effortlessly across the whole spectrum of algebra.... The challenge to Ezekiel, "Can these bones live?" is, all too often, the reaction of students when introduced to the bare bones of the concepts and constructs of modern algebra. Shafarevich's book  which reads as comfortably as an extended essay  breathes life into the skeleton and will be of interest to many classes of readers..." The Mathematical Gazette, 1991 "... According to the preface, the book is addressed to "students of mathematics in the first years of an undergraduate course, or theoretical physicists or mathematicians from outside algebra wanting to get an impression of the spirit of algebra and its place in mathematics." I think that this promise is fully justified. The beginner, the experts and also the interested scientist who had contact with algebraic notions  all will read this exceptional book with great pleasure and benefit." Zeitschrift für Kristallographie, 1991
8 editions published between 1990 and 2014 in English and held by 68 WorldCat member libraries worldwide
From the reviews: "This is one of the few mathematical books, the reviewer has read from cover to cover ... The main merit is that nearly on every page you will find some unexpected insights..." Zentralblatt für Mathematik und Ihre Grenzgebiete, 1991 "...which I read like a novel and undoubtedly will become a classic. ... A merit of the book under review is that it contains several important articles from journals which are not all so easily accessible. ... Furthermore, at the end of the book, there are some Notes by the author which are indispensible for the necessary historical background information. ... This valuable book should be on the shelf of every algebraist and algebraic geometer." Nieuw Archief voor Wiskunde, 1992 "... There are few proofs in full, but there is an exhilarating combination of sureness of foot and lightness of touch in the exposition ... which transports the reader effortlessly across the whole spectrum of algebra.... The challenge to Ezekiel, "Can these bones live?" is, all too often, the reaction of students when introduced to the bare bones of the concepts and constructs of modern algebra. Shafarevich's book  which reads as comfortably as an extended essay  breathes life into the skeleton and will be of interest to many classes of readers..." The Mathematical Gazette, 1991 "... According to the preface, the book is addressed to "students of mathematics in the first years of an undergraduate course, or theoretical physicists or mathematicians from outside algebra wanting to get an impression of the spirit of algebra and its place in mathematics." I think that this promise is fully justified. The beginner, the experts and also the interested scientist who had contact with algebraic notions  all will read this exceptional book with great pleasure and benefit." Zeitschrift für Kristallographie, 1991
Basic algebraic geometry by
I. R Shafarevich(
Book
)
11 editions published between 1997 and 2013 in English and held by 60 WorldCat member libraries worldwide
Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, "For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevichs book is a must." The third edition, in addition to some minor corrections, now offers a new treatment of the RiemannRoch theorem for curves, including a proof from first principles. Shafarevich's book is an attractive and accessible introduction to algebraic geometry, suitable for beginning students and nonspecialists, and the new edition is set to remain a popular introduction to the field
11 editions published between 1997 and 2013 in English and held by 60 WorldCat member libraries worldwide
Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, "For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevichs book is a must." The third edition, in addition to some minor corrections, now offers a new treatment of the RiemannRoch theorem for curves, including a proof from first principles. Shafarevich's book is an attractive and accessible introduction to algebraic geometry, suitable for beginning students and nonspecialists, and the new edition is set to remain a popular introduction to the field
Solitons : differential equations, symmetries, and infinite dimensional algebras by
T Miwa(
Book
)
7 editions published between 2000 and 2011 in English and held by 40 WorldCat member libraries worldwide
"The goal of this book is to investigate the high degree of symmetry that lies hidden in integrable systems. To that end, differential equations arising from classical mechanics, such as the KdV equation and the KP equations, are used here by the authors to introduce the notion of an infinite dimensional transformation group acting on spaces of integrable systems. The work of M. Sato on the algebraic structure of completely integrable systems is discussed, together with developments of these ideas in the work of M. Kashiwara." "This book should be accessible to anyone with a knowledge of differential and integral calculus and elementary complex analysis, and it will be a valuable resource to the novice and expert alike."Jacket
7 editions published between 2000 and 2011 in English and held by 40 WorldCat member libraries worldwide
"The goal of this book is to investigate the high degree of symmetry that lies hidden in integrable systems. To that end, differential equations arising from classical mechanics, such as the KdV equation and the KP equations, are used here by the authors to introduce the notion of an infinite dimensional transformation group acting on spaces of integrable systems. The work of M. Sato on the algebraic structure of completely integrable systems is discussed, together with developments of these ideas in the work of M. Kashiwara." "This book should be accessible to anyone with a knowledge of differential and integral calculus and elementary complex analysis, and it will be a valuable resource to the novice and expert alike."Jacket
Commutative ring theory by
Hideyuki Matsumura(
Book
)
12 editions published between 1985 and 2006 in English and Undetermined and held by 34 WorldCat member libraries worldwide
In addition to being an interesting and profound subject in its own right, commutative ring theory is important as a foundation for algebraic geometry and complex analytical geometry. Matsumura covers the basic material, including dimension theory, depth, CohenMacaulay rings, Gorenstein rings, Krull rings and valuation rings. More advanced topics such as Ratliff's theorems on chains of prime ideals are also explored. The work is essentially selfcontained, the only prerequisite being a sound knowledge of modern algebra, yet the reader is taken to the frontiers of the subject. Exercises are provided at the end of each section and solutions or hints to some of them are given at the end of the book
12 editions published between 1985 and 2006 in English and Undetermined and held by 34 WorldCat member libraries worldwide
In addition to being an interesting and profound subject in its own right, commutative ring theory is important as a foundation for algebraic geometry and complex analytical geometry. Matsumura covers the basic material, including dimension theory, depth, CohenMacaulay rings, Gorenstein rings, Krull rings and valuation rings. More advanced topics such as Ratliff's theorems on chains of prime ideals are also explored. The work is essentially selfcontained, the only prerequisite being a sound knowledge of modern algebra, yet the reader is taken to the frontiers of the subject. Exercises are provided at the end of each section and solutions or hints to some of them are given at the end of the book
Geometries and groups by
V. V Nikulin(
Book
)
7 editions published between 1987 and 1994 in English and held by 18 WorldCat member libraries worldwide
This is a quite exceptional book, a lively and approachable treatment of an important field of mathematics given in a masterly style. Assuming only a school background, the authors develop locally Euclidean geometries, going as far as the modular space of structures on the torus, treated in terms of Lobachevsky's nonEuclidean geometry. Each section is carefully motivated by discussion of the physical and general scientific implications of the mathematical argument, and its place in the history of mathematics and philosophy. The book is expected to find a place alongside classics such as Hilbert and CohnVossen's "Geometry and the imagination" and Weyl's "Symmetry."
7 editions published between 1987 and 1994 in English and held by 18 WorldCat member libraries worldwide
This is a quite exceptional book, a lively and approachable treatment of an important field of mathematics given in a masterly style. Assuming only a school background, the authors develop locally Euclidean geometries, going as far as the modular space of structures on the torus, treated in terms of Lobachevsky's nonEuclidean geometry. Each section is carefully motivated by discussion of the physical and general scientific implications of the mathematical argument, and its place in the history of mathematics and philosophy. The book is expected to find a place alongside classics such as Hilbert and CohnVossen's "Geometry and the imagination" and Weyl's "Symmetry."
Last on the list by
Miles Reid(
Book
)
6 editions published between 1974 and 1975 in 3 languages and held by 14 WorldCat member libraries worldwide
6 editions published between 1974 and 1975 in 3 languages and held by 14 WorldCat member libraries worldwide
Basic algebraic geometry by
I. R Shafarevich(
Book
)
3 editions published in 1994 in English and Undetermined and held by 8 WorldCat member libraries worldwide
3 editions published in 1994 in English and Undetermined and held by 8 WorldCat member libraries worldwide
The complete intersection of two or more quadrics by
Miles Reid(
)
5 editions published in 1972 in English and Undetermined and held by 5 WorldCat member libraries worldwide
5 editions published in 1972 in English and Undetermined and held by 5 WorldCat member libraries worldwide
The harp of Salem; a collection of historical poems from the scriptures ... by
Miles Reid(
Book
)
1 edition published in 1827 in English and held by 5 WorldCat member libraries worldwide
1 edition published in 1827 in English and held by 5 WorldCat member libraries worldwide
Using the Am9511 arithmetic processing unit with the Motorola M6800 microprocessor by
Miles Reid(
Book
)
4 editions published in 1979 in English and held by 4 WorldCat member libraries worldwide
4 editions published in 1979 in English and held by 4 WorldCat member libraries worldwide
Review of bovine brucellosis and tuberculosis traceback methods in South Australian abattoirs.(
Book
)
1 edition published in 1983 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 1983 in English and held by 4 WorldCat member libraries worldwide
A temperature controller in the 6000 series by C. E Cox(
Book
)
2 editions published in 1981 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1981 in English and held by 3 WorldCat member libraries worldwide
New Trends in Algebraic Geometry by
Klaus Hulek(
)
2 editions published in 1999 in English and held by 0 WorldCat member libraries worldwide
Seventeen articles from the most outstanding contemporary topics in algebraic geometry
2 editions published in 1999 in English and held by 0 WorldCat member libraries worldwide
Seventeen articles from the most outstanding contemporary topics in algebraic geometry
The harp of Salem : a collection of historical poems, from the Scriptures : together with some reflective pieces by
Miles Reid(
)
2 editions published in 1827 in English and held by 0 WorldCat member libraries worldwide
2 editions published in 1827 in English and held by 0 WorldCat member libraries worldwide
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Related Identities
 Corti, Alessio 1965 Author Editor
 Skorobogatov, Alexei 1961 Editor
 SwinnertonDyer, H. P. F. Honoree Dedicatee
 Shafarevich, I. R. (Igorʹ Rostislavovich) 19232017 Author Editor
 Szendrői, Balázs Editor
 Kostrikin, Alekseĭ Ivanovich Editor
 Miwa, Tetsuji Author
 Date, Etsuro
 Matsumura, Hideyuki (1930 ...). Author
 Hulek, K. Author Editor
Useful Links
Associated Subjects
Algebra Algebraic varieties Brucellosis in cattle Commutative algebra Commutative rings Europe Evolution equations, Nonlinear Geometry Geometry, Algebraic Greece Group theory Homology theory Kortewegde Vries equation Ktheory Mathematics Military campaigns Number theory Physics Quadrics Reid, Miles Religious poetry Rings (Algebra) Solitons SolitonsMathematics South Australia Surfaces, Algebraic Temperature control Threefolds (Algebraic geometry) Topological groups Topology Tuberculosis in cattle World War (19391945)
Alternative Names
Miles Reid britischer Mathematiker
Miles Reid Brits wiskundige
Miles Reid Mathematician researching Algebraic Geometry
Miles Reid mathématicien britannique
Reid, M
Reid, M. 1948
Reid, M. A.
Reid, M. A. 1948
Reid, M. A. (Miles A.)
Reid, M. A. (Miles A.), 1948
Reid, Miles
Reid, Miles A.
Reid, Miles A. 1948...
Reid, Miles (Miles A.)
Rid, M.
Рид, М
Рид, М. (Майлз)
マイルス・リード
リード, M.
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