Gray, Jeremy 1947
Overview
Works:  104 works in 562 publications in 7 languages and 15,191 library holdings 

Genres:  History Biography Conference papers and proceedings Encyclopedias Criticism, interpretation, etc 
Roles:  Author, Editor, Other, Author of introduction, Compiler, Commentator, Host, Contributor 
Publication Timeline
.
Most widely held works about
Jeremy Gray
 The "old tub," the J.J. Gray : the first 100 yrs. of Cambridge firefighting by David L Thornton( Book )
Most widely held works by
Jeremy Gray
Plato's ghost : the modernist transformation of mathematics by
Jeremy Gray(
)
18 editions published in 2008 in English and held by 2,137 WorldCat member libraries worldwide
Plato's Ghost examines the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. from publisher description
18 editions published in 2008 in English and held by 2,137 WorldCat member libraries worldwide
Plato's Ghost examines the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. from publisher description
Henri Poincaré : a scientific biography by
Jeremy Gray(
)
22 editions published between 2011 and 2013 in English and Undetermined and held by 1,618 WorldCat member libraries worldwide
"Henri Poincaré (18541912) was not just one of the most inventive, versatile, and productive mathematicians of all timehe was also a leading physicist who almost won a Nobel Prize for physics and a prominent philosopher of science whose fresh and surprising essays are still in print a century later. The first indepth and comprehensive look at his many accomplishments, Henri Poincaré explores all the fields that Poincaré touched, the debates sparked by his original investigations, and how his discoveries still contribute to society today. Math historian Jeremy Gray shows that Poincaré's influence was wideranging and permanent. His novel interpretation of nonEuclidean geometry challenged contemporary ideas about space, stirred heated discussion, and led to flourishing research. His work in topology began the modern study of the subject, recently highlighted by the successful resolution of the famous Poincaré conjecture. And Poincaré's reformulation of celestial mechanics and discovery of chaotic motion started the modern theory of dynamical systems. In physics, his insights on the Lorentz group preceded Einstein's, and he was the first to indicate that space and time might be fundamentally atomic. Poincaré the public intellectual did not shy away from scientific controversy, and he defended mathematics against the attacks of logicians such as Bertrand Russell, opposed the views of Catholic apologists, and served as an expert witness in probability for the notorious Dreyfus case that polarized France. Richly informed by letters and documents, Henri Poincaré demonstrates how one man's work revolutionized math, science, and the greater world"
22 editions published between 2011 and 2013 in English and Undetermined and held by 1,618 WorldCat member libraries worldwide
"Henri Poincaré (18541912) was not just one of the most inventive, versatile, and productive mathematicians of all timehe was also a leading physicist who almost won a Nobel Prize for physics and a prominent philosopher of science whose fresh and surprising essays are still in print a century later. The first indepth and comprehensive look at his many accomplishments, Henri Poincaré explores all the fields that Poincaré touched, the debates sparked by his original investigations, and how his discoveries still contribute to society today. Math historian Jeremy Gray shows that Poincaré's influence was wideranging and permanent. His novel interpretation of nonEuclidean geometry challenged contemporary ideas about space, stirred heated discussion, and led to flourishing research. His work in topology began the modern study of the subject, recently highlighted by the successful resolution of the famous Poincaré conjecture. And Poincaré's reformulation of celestial mechanics and discovery of chaotic motion started the modern theory of dynamical systems. In physics, his insights on the Lorentz group preceded Einstein's, and he was the first to indicate that space and time might be fundamentally atomic. Poincaré the public intellectual did not shy away from scientific controversy, and he defended mathematics against the attacks of logicians such as Bertrand Russell, opposed the views of Catholic apologists, and served as an expert witness in probability for the notorious Dreyfus case that polarized France. Richly informed by letters and documents, Henri Poincaré demonstrates how one man's work revolutionized math, science, and the greater world"
The architecture of modern mathematics : essays in history and philosophy by
Jeremy Gray(
)
18 editions published between 2006 and 2009 in English and held by 1,527 WorldCat member libraries worldwide
Aimed at both students and researchers in philosophy, mathematics and the history of science, this edited volume, authored by leading scholars, highlights foremost developments in both the philosophy and history of modern mathematics.  ;This edited volume, aimed at both students and researchers in philosophy, mathematics and history of science, highlights leading developments in the overlapping areas of philosophy and the history of modern mathematics. It is a coherent, wide ranging account of how a number of topics in the philosophy of mathematics must be reconsidered in the light of the lat
18 editions published between 2006 and 2009 in English and held by 1,527 WorldCat member libraries worldwide
Aimed at both students and researchers in philosophy, mathematics and the history of science, this edited volume, authored by leading scholars, highlights foremost developments in both the philosophy and history of modern mathematics.  ;This edited volume, aimed at both students and researchers in philosophy, mathematics and history of science, highlights leading developments in the overlapping areas of philosophy and the history of modern mathematics. It is a coherent, wide ranging account of how a number of topics in the philosophy of mathematics must be reconsidered in the light of the lat
Worlds out of nothing : a course in the history of geometry in the 19th century by
Jeremy Gray(
)
44 editions published between 2006 and 2011 in English and held by 1,297 WorldCat member libraries worldwide
"Worlds Out of Nothing is the first book to provide a course on the history of geometry in the 19th century. Based on the latest historical research, the book is aimed primarily at undergraduate and graduate students in mathematics but will also appeal to the reader with a general interest in the history of mathematics. Emphasis is placed on understanding the historical significance of the new mathematics: Why was it done? How  if at all  was it appreciated? What new questions did it generate?"Jacket
44 editions published between 2006 and 2011 in English and held by 1,297 WorldCat member libraries worldwide
"Worlds Out of Nothing is the first book to provide a course on the history of geometry in the 19th century. Based on the latest historical research, the book is aimed primarily at undergraduate and graduate students in mathematics but will also appeal to the reader with a general interest in the history of mathematics. Emphasis is placed on understanding the historical significance of the new mathematics: Why was it done? How  if at all  was it appreciated? What new questions did it generate?"Jacket
Linear differential equations and group theory from Riemann to Poincaré by
Jeremy Gray(
Book
)
49 editions published between 1985 and 2008 in English and Japanese and held by 1,114 WorldCat member libraries worldwide
"This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. The central focus is on the convergence of three mathematical topics: the hypergeometric and related linear differential equations, group theory, and nonEuclidean geometry."Jacket
49 editions published between 1985 and 2008 in English and Japanese and held by 1,114 WorldCat member libraries worldwide
"This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. The central focus is on the convergence of three mathematical topics: the hypergeometric and related linear differential equations, group theory, and nonEuclidean geometry."Jacket
The History of mathematics : a reader by
John Fauvel(
Book
)
32 editions published between 1986 and 2010 in English and held by 964 WorldCat member libraries worldwide
32 editions published between 1986 and 2010 in English and held by 964 WorldCat member libraries worldwide
Ideas of space : Euclidean, nonEuclidean, and relativistic by
Jeremy Gray(
Book
)
30 editions published between 1979 and 2017 in English and held by 947 WorldCat member libraries worldwide
30 editions published between 1979 and 2017 in English and held by 947 WorldCat member libraries worldwide
Geometry by
D. A Brannan(
Book
)
41 editions published between 1998 and 2012 in English and held by 732 WorldCat member libraries worldwide
"This is a textbook that demonstrates the excitement and beauty of geometry. The approach is that of Klein in his Erlangen programme: a geometry is a space together with a set of transformations of that space. The authors explore various geometries: affine, projective, inversive, nonEuclidean and spherical. In each case the key results are explained carefully, and the relationships between the geometries are discussed."BOOK JACKET. "This richly illustrated and clearly written text includes full solutions to over 200 problems, and is suitable both for undergraduate courses on geometry and as a resource for self study."Jacket
41 editions published between 1998 and 2012 in English and held by 732 WorldCat member libraries worldwide
"This is a textbook that demonstrates the excitement and beauty of geometry. The approach is that of Klein in his Erlangen programme: a geometry is a space together with a set of transformations of that space. The authors explore various geometries: affine, projective, inversive, nonEuclidean and spherical. In each case the key results are explained carefully, and the relationships between the geometries are discussed."BOOK JACKET. "This richly illustrated and clearly written text includes full solutions to over 200 problems, and is suitable both for undergraduate courses on geometry and as a resource for self study."Jacket
The Hilbert challenge by
Jeremy Gray(
Book
)
16 editions published between 2000 and 2004 in 4 languages and held by 696 WorldCat member libraries worldwide
Few problems in mathematics have had the status of those posed by David Hilbert in 1900. Mathematicians have made their reputations by solving some of them like Fermat's last theorem, but several remain unsolved including the Riemann Hypotheses, which has eluded all the great minds of this century. A hundred years later, this book takes a fresh look at the problems, the man who set them, and the reasons for their lasting impact on the mathematics of the twentieth century. In this book, the authors consider what makes this the preeminent collection of problems in mathematics, what they tell us about what drives mathematicians, and the nature of reputation, influence and power in the world of modern mathematics
16 editions published between 2000 and 2004 in 4 languages and held by 696 WorldCat member libraries worldwide
Few problems in mathematics have had the status of those posed by David Hilbert in 1900. Mathematicians have made their reputations by solving some of them like Fermat's last theorem, but several remain unsolved including the Riemann Hypotheses, which has eluded all the great minds of this century. A hundred years later, this book takes a fresh look at the problems, the man who set them, and the reasons for their lasting impact on the mathematics of the twentieth century. In this book, the authors consider what makes this the preeminent collection of problems in mathematics, what they tell us about what drives mathematicians, and the nature of reputation, influence and power in the world of modern mathematics
Hidden harmony  geometric fantasies : the rise of complex function theory by
U Bottazzini(
)
16 editions published between 2013 and 2016 in English and held by 499 WorldCat member libraries worldwide
Hidden Harmony Geometric Fantasies describes the history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subject  Cauchy, Riemann, and Weierstrass  it looks at the contributions of great mathematicians from d'Alembert to Poincaré, and Laplace to Weyl. Select chapters examine the rise and importance of elliptic function theory, differential equations in the complex domain, geometric function theory, and the early years of complex function theory in several variables. Unique emphasis has been placed on the creation of a textbook tradition in complex analysis by considering some seventy textbooks in nine different languages. This book is not a mere sequence of disembodied results and theories, but offers a comprehensive picture of the broad cultural and social context in which the main players lived and worked by paying attention to the rise of mathematical schools and of contrasting national traditions. This work is unrivaled for its breadth and depth, both in the core theory and its implications for other fields of mathematics. It is a major resource for professional mathematicians as well as advanced undergraduate and graduate students and anyone studying complex function theory.
16 editions published between 2013 and 2016 in English and held by 499 WorldCat member libraries worldwide
Hidden Harmony Geometric Fantasies describes the history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subject  Cauchy, Riemann, and Weierstrass  it looks at the contributions of great mathematicians from d'Alembert to Poincaré, and Laplace to Weyl. Select chapters examine the rise and importance of elliptic function theory, differential equations in the complex domain, geometric function theory, and the early years of complex function theory in several variables. Unique emphasis has been placed on the creation of a textbook tradition in complex analysis by considering some seventy textbooks in nine different languages. This book is not a mere sequence of disembodied results and theories, but offers a comprehensive picture of the broad cultural and social context in which the main players lived and worked by paying attention to the rise of mathematical schools and of contrasting national traditions. This work is unrivaled for its breadth and depth, both in the core theory and its implications for other fields of mathematics. It is a major resource for professional mathematicians as well as advanced undergraduate and graduate students and anyone studying complex function theory.
Carl Friedrich Gauss : titan of science by
G. Waldo Dunnington(
Book
)
14 editions published between 2004 and 2005 in English and held by 499 WorldCat member libraries worldwide
"This biography of Gauss, by far the most comprehensive in English, is the work of a professor of German, G. Waldo Dunnington, who devoted most of his scholarly career to studying the life of Germany's greatest mathematician. The author was inspired to pursue this project at the age of twelve when he learned from his teacher in Missouri that no full biography of Gauss existed at the time. His teacher was Gauss's great granddaughter, Minna Waldeck Gauss." "Long outofprint and almost impossible to find on the used book market, this valuable piece of scholarship is being reissued in an augmented form with introductory remarks, an expanded and updated bibliography, and a commentary on Gauss's mathematical diary, by the eminent British mathematical historian, Jeremy Gray. Also included are personal reminiscences about Dunnington himself, by FritzEgbert Dohse, who not only knew Dunnington but also had an interesting connection to Gauss: his greatgrandfather, Christian Heinrich Hesemann, was the sculptor whose bust of Gauss is widely known and is pictured in the book."Jacket
14 editions published between 2004 and 2005 in English and held by 499 WorldCat member libraries worldwide
"This biography of Gauss, by far the most comprehensive in English, is the work of a professor of German, G. Waldo Dunnington, who devoted most of his scholarly career to studying the life of Germany's greatest mathematician. The author was inspired to pursue this project at the age of twelve when he learned from his teacher in Missouri that no full biography of Gauss existed at the time. His teacher was Gauss's great granddaughter, Minna Waldeck Gauss." "Long outofprint and almost impossible to find on the used book market, this valuable piece of scholarship is being reissued in an augmented form with introductory remarks, an expanded and updated bibliography, and a commentary on Gauss's mathematical diary, by the eminent British mathematical historian, Jeremy Gray. Also included are personal reminiscences about Dunnington himself, by FritzEgbert Dohse, who not only knew Dunnington but also had an interesting connection to Gauss: his greatgrandfather, Christian Heinrich Hesemann, was the sculptor whose bust of Gauss is widely known and is pictured in the book."Jacket
János Bolyai, nonEuclidean geometry, and the nature of space by
Jeremy Gray(
Book
)
9 editions published between 2004 and 2006 in English and held by 480 WorldCat member libraries worldwide
"Janos Bolyai (18021860) was a mathematician who changed our fundamental ideas about space. As a teenager he started to explore a set of nettlesome geometrical problems, including Euclid's parallel postulate, and in 1832 he published a brilliant twentyfourpage paper that shook the foundations of the twothousandyearold tradition of Euclidean geometry. Bolyai's "Appendix" (published as just that  an appendix to a much longer mathematical work by his father) set up a series of mathematical problems whose solutions would blossom into the new field of nonEuclidean geometry, providing essential intellectual background for ideas as varied as the theory of relativity and the work of Marcel Duchamp. In this short book, Jeremy Gray explains Bolyai's ideas and the historical context in which they emerged, were debated, and were eventually recognized as a central achievement in the Western intellectual tradition. Intended for nonspecialists, the book includes facsimiles of Bolyai's original paper and the 1891 English translation by G. B. Halsted, both reproduced from copies in the Burndy Library at MIT."BOOK JACKET
9 editions published between 2004 and 2006 in English and held by 480 WorldCat member libraries worldwide
"Janos Bolyai (18021860) was a mathematician who changed our fundamental ideas about space. As a teenager he started to explore a set of nettlesome geometrical problems, including Euclid's parallel postulate, and in 1832 he published a brilliant twentyfourpage paper that shook the foundations of the twothousandyearold tradition of Euclidean geometry. Bolyai's "Appendix" (published as just that  an appendix to a much longer mathematical work by his father) set up a series of mathematical problems whose solutions would blossom into the new field of nonEuclidean geometry, providing essential intellectual background for ideas as varied as the theory of relativity and the work of Marcel Duchamp. In this short book, Jeremy Gray explains Bolyai's ideas and the historical context in which they emerged, were debated, and were eventually recognized as a central achievement in the Western intellectual tradition. Intended for nonspecialists, the book includes facsimiles of Bolyai's original paper and the 1891 English translation by G. B. Halsted, both reproduced from copies in the Burndy Library at MIT."BOOK JACKET
Mathematical conversations : selections from the mathematical intelligencer by
Robin J Wilson(
Book
)
14 editions published between 1999 and 2001 in English and held by 453 WorldCat member libraries worldwide
This volume contains approximately fifty articles that were published in "The Mathematical Intelligencer" during its first eighteen years. The selection exhibits the wide variety of attractive articles that have appeared over the years, ranging from general interest articles of a historical nature to lucid expositions of important current discoveries. The articles are introduced by the editors
14 editions published between 1999 and 2001 in English and held by 453 WorldCat member libraries worldwide
This volume contains approximately fifty articles that were published in "The Mathematical Intelligencer" during its first eighteen years. The selection exhibits the wide variety of attractive articles that have appeared over the years, ranging from general interest articles of a historical nature to lucid expositions of important current discoveries. The articles are introduced by the editors
The geometrical work of Girard Desargues by
Gérard Desargues(
Book
)
17 editions published in 1987 in English and Hungarian and held by 371 WorldCat member libraries worldwide
Our main purpose in this book is to present an English translation of Desargues' Rough Draft of an Essay on the results of taking plane sections of a cone (1639), the pamphlet with which the modem study of projective geometry began. Despite its acknowledged importance in the history of mathematics, the work has never been translated before in its entirety, although short extracts have appeared in several source books. The problems of making Desargues' work accessible to modem mathematicians and historians of mathematics have led us to provide a fairly elaborate introduction, and to include translations of other relevant works. The translation ofthe Rough Draft on Conics (as we shall call it) thus appears in Chapter VI, the five preceding chapters forming an introduction and the three following ones giving translations of other works by Desargues. Chapter I briefly reviews parts of ancient geometrical works available to Desargues which seem to be relevant to his own work, namely theorems in Euclid's Elements, the first four books of Apollonius' Conics and some remarks by Pappus in his Collection. These Hellenistic works belong to the 'high' mathematical tradition whose development has been the main theme of all histories of mathematics. It is from these works that Desargues took the theorems whose theory he was to reformulate in the Rough Draft on Conics
17 editions published in 1987 in English and Hungarian and held by 371 WorldCat member libraries worldwide
Our main purpose in this book is to present an English translation of Desargues' Rough Draft of an Essay on the results of taking plane sections of a cone (1639), the pamphlet with which the modem study of projective geometry began. Despite its acknowledged importance in the history of mathematics, the work has never been translated before in its entirety, although short extracts have appeared in several source books. The problems of making Desargues' work accessible to modem mathematicians and historians of mathematics have led us to provide a fairly elaborate introduction, and to include translations of other relevant works. The translation ofthe Rough Draft on Conics (as we shall call it) thus appears in Chapter VI, the five preceding chapters forming an introduction and the three following ones giving translations of other works by Desargues. Chapter I briefly reviews parts of ancient geometrical works available to Desargues which seem to be relevant to his own work, namely theorems in Euclid's Elements, the first four books of Apollonius' Conics and some remarks by Pappus in his Collection. These Hellenistic works belong to the 'high' mathematical tradition whose development has been the main theme of all histories of mathematics. It is from these works that Desargues took the theorems whose theory he was to reformulate in the Rough Draft on Conics
The real and the complex : a history of analysis in the 19th century by
Jeremy Gray(
)
14 editions published in 2015 in English and held by 298 WorldCat member libraries worldwide
" ... contains a history of real and complex analysis in the nineteenth century, from the work of Lagrange and Fourier to the origins of set theory and the modern foundations of analysis. It studies the works of many contributors including Gauss, Cauchy, Riemann, and Weierstrass. This book is unique owing to the treatment of real and complex analysis as overlapping, interrelated subjects, in keeping with how they were seen at the time. It is suitable as a course in the history of mathematics for students who have studied an introductory course in analysis, and will enrich any course in undergraduate real or complex analysis."Back cover
14 editions published in 2015 in English and held by 298 WorldCat member libraries worldwide
" ... contains a history of real and complex analysis in the nineteenth century, from the work of Lagrange and Fourier to the origins of set theory and the modern foundations of analysis. It studies the works of many contributors including Gauss, Cauchy, Riemann, and Weierstrass. This book is unique owing to the treatment of real and complex analysis as overlapping, interrelated subjects, in keeping with how they were seen at the time. It is suitable as a course in the history of mathematics for students who have studied an introductory course in analysis, and will enrich any course in undergraduate real or complex analysis."Back cover
Episodes in the history of modern algebra (18001950)(
Book
)
13 editions published in 2007 in English and held by 290 WorldCat member libraries worldwide
Algebra, as a subdiscipline of mathematics, arguably has a history going back some 4000 years to ancient Mesopotamia. The history, however, of what is recognized today as high school algebra is much shorter, extending back to the sixteenth century, while the history of what practicing mathematicians call "modern algebra" is even shorter still. The present volume provides a glimpse into the complicated and often convoluted history of this latter conception of algebra by juxtaposing twelve episodes in the evolution of modern algebra from the early nineteenthcentury work of Charles Babbage on functional equations to Alexandre Grothendieck's midtwentiethcentury metaphor of a "rising sea" in his categorical approach to algebraic geometry. In addition to considering the technical development of various aspects of algebraic thought, the historians of modern algebra whose work is united in this volume explore such themes as the changing aims and organization of the subject as well as the often complex lines of mathematical communication within and across national boundaries. Among the specific algebraic ideas considered are the concept of divisibility and the introduction of noncommutative algebras into the study of number theory and the emergence of algebraic geometry in the twentieth century. The resulting volume is essential reading for anyone interested in the history of modern mathematics in general and modern algebra in particular. It will be of particular interest to mathematicians and historians of mathematics. Copublished with the London Mathematical Society beginning with Volume 4. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners
13 editions published in 2007 in English and held by 290 WorldCat member libraries worldwide
Algebra, as a subdiscipline of mathematics, arguably has a history going back some 4000 years to ancient Mesopotamia. The history, however, of what is recognized today as high school algebra is much shorter, extending back to the sixteenth century, while the history of what practicing mathematicians call "modern algebra" is even shorter still. The present volume provides a glimpse into the complicated and often convoluted history of this latter conception of algebra by juxtaposing twelve episodes in the evolution of modern algebra from the early nineteenthcentury work of Charles Babbage on functional equations to Alexandre Grothendieck's midtwentiethcentury metaphor of a "rising sea" in his categorical approach to algebraic geometry. In addition to considering the technical development of various aspects of algebraic thought, the historians of modern algebra whose work is united in this volume explore such themes as the changing aims and organization of the subject as well as the often complex lines of mathematical communication within and across national boundaries. Among the specific algebraic ideas considered are the concept of divisibility and the introduction of noncommutative algebras into the study of number theory and the emergence of algebraic geometry in the twentieth century. The resulting volume is essential reading for anyone interested in the history of modern mathematics in general and modern algebra in particular. It will be of particular interest to mathematicians and historians of mathematics. Copublished with the London Mathematical Society beginning with Volume 4. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners
NonEuclidean geometry in the theory of automorphic functions by
Jacques Hadamard(
Book
)
10 editions published in 1999 in English and Russian and held by 284 WorldCat member libraries worldwide
"This unique exposition by Hadamard offers a fascinating and intuitive introduction to the subject of automorphic functions and illuminates its connection to differential equations, a connection not often found in other texts."Jacket
10 editions published in 1999 in English and Russian and held by 284 WorldCat member libraries worldwide
"This unique exposition by Hadamard offers a fascinating and intuitive introduction to the subject of automorphic functions and illuminates its connection to differential equations, a connection not often found in other texts."Jacket
The symbolic universe : geometry and physics 18901930(
Book
)
14 editions published between 1999 and 2005 in English and held by 268 WorldCat member libraries worldwide
14 editions published between 1999 and 2005 in English and held by 268 WorldCat member libraries worldwide
L'Europe mathématique : histoires, mythes, identités = Mathematical Europe : history, myth, identity(
Book
)
10 editions published in 1996 in 3 languages and held by 134 WorldCat member libraries worldwide
10 editions published in 1996 in 3 languages and held by 134 WorldCat member libraries worldwide
A History of Abstract Algebra : From Algebraic Equations to Modern Algebra by
Jeremy Gray(
)
6 editions published in 2018 in English and held by 126 WorldCat member libraries worldwide
This textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and eighteenth centuries, and exploring the impact of ideas on the development of the subject. Beginning with Gauss's theory of numbers and Galois's ideas, the book progresses to Dedekind and Kronecker, Jordan and Klein, Steinitz, Hilbert, and Emmy Noether. Approaching mathematical topics from a historical perspective, the author explores quadratic forms, quadratic reciprocity, Fermat's Last Theorem, cyclotomy, quintic equations, Galois theory, commutative rings, abstract fields, ideal theory, invariant theory, and group theory. Readers will learn what Galois accomplished, how difficult the proofs of his theorems were, and how important Camille Jordan and Felix Klein were in the eventual acceptance of Galois's approach to the solution of equations. The book also describes the relationship between Kummer's ideal numbers and Dedekind's ideals, and discusses why Dedekind felt his solution to the divisor problem was better than Kummer's. Designed for a course in the history of modern algebra, this book is aimed at undergraduate students with an introductory background in algebra but will also appeal to researchers with a general interest in the topic. With exercises at the end of each chapter and appendices providing material difficult to find elsewhere, this book is selfcontained and therefore suitable for selfstudy.
6 editions published in 2018 in English and held by 126 WorldCat member libraries worldwide
This textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and eighteenth centuries, and exploring the impact of ideas on the development of the subject. Beginning with Gauss's theory of numbers and Galois's ideas, the book progresses to Dedekind and Kronecker, Jordan and Klein, Steinitz, Hilbert, and Emmy Noether. Approaching mathematical topics from a historical perspective, the author explores quadratic forms, quadratic reciprocity, Fermat's Last Theorem, cyclotomy, quintic equations, Galois theory, commutative rings, abstract fields, ideal theory, invariant theory, and group theory. Readers will learn what Galois accomplished, how difficult the proofs of his theorems were, and how important Camille Jordan and Felix Klein were in the eventual acceptance of Galois's approach to the solution of equations. The book also describes the relationship between Kummer's ideal numbers and Dedekind's ideals, and discusses why Dedekind felt his solution to the divisor problem was better than Kummer's. Designed for a course in the history of modern algebra, this book is aimed at undergraduate students with an introductory background in algebra but will also appeal to researchers with a general interest in the topic. With exercises at the end of each chapter and appendices providing material difficult to find elsewhere, this book is selfcontained and therefore suitable for selfstudy.
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Related Identities
 Poincaré, Henri 18541912 Author
 Ferreirós Domínguez, José Editor
 Fauvel, John Other Author Editor
 Open University Producer
 Esplen, Matthew F. Other Contributor
 Brannan, D. A. Author
 Hilbert, David 18621943 Bibliographic antecedent Honoree
 Dunnington, G. Waldo (Guy Waldo) 1906 Author
 Bottazzini, U. (Umberto) Author
 Dohse, FritzEgbert Author of introduction
Useful Links
Associated Subjects
Aesthetics, Modern Algebra Algebra, Abstract Automorphic functions Bolyai, János, Chaotic behavior in systems Conics, Spherical Desargues, Gérard, Differential equations Differential equations, Linear Europe Fire extinction France Functional analysis Functions of complex variables Functions of real variables Gauss, Carl Friedrich, Geometry Geometry, NonEuclidean Germany Group theory Hilbert, David, History Influence (Literary, artistic, etc.) Mathematical analysis Mathematical physics Mathematicians Mathematics MathematicsPhilosophy New York (State)Cambridge New York (State)Washington County Number theory Perspective Poincaré, Henri, Scientists Space and time Space and timeMathematical models Threebody problem
Covers
Alternative Names
Gray, J.
Gray, J. J.
Gray, J. J. 1947
Gray, J. J. (Jeremy J.), 1947
Gray, Jeremy
Gray, Jeremy 1947
Gray, Jeremy J.
Gray, Jeremy J. 1947
Gray, Jeremy John
Jeremy Gray Brits wiskundige
Jeremy Gray englischer Mathematikhistoriker
Jeremy Gray matemàtic britànic
Jeremy Gray matematician britanic
Jeremy Gray matemático británico
Jeremy Gray mathématicien britannique
جرمی گری
グレイ, J. J.
グレイ, ジェレミー・J.
Languages