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The Resource A History of Abstract Algebra : From Algebraic Equations to Modern Algebra, by Jeremy Gray, (electronic resource)
A History of Abstract Algebra : From Algebraic Equations to Modern Algebra, by Jeremy Gray, (electronic resource)
Resource Information
The item A History of Abstract Algebra : From Algebraic Equations to Modern Algebra, by Jeremy Gray, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item A History of Abstract Algebra : From Algebraic Equations to Modern Algebra, by Jeremy Gray, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary
 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.
 Language
 eng
 Extent
 XXIV, 415 p. 18 illus.
 Contents

 Introduction
 1 Simple quadratic forms
 2 Fermat’s Last Theorem
 3 Lagrange’s theory of quadratic forms
 4 Gauss’s Disquisitiones Arithmeticae
 5 Cyclotomy
 6 Two of Gauss’s proofs of quadratic reciprocity
 7 Dirichlet’s Lectures
 8 Is the quintic unsolvable?
 9 The unsolvability of the quintic
 10 Galois’s theory
 11 After Galois – Introduction
 12 Revision and first assignment
 13 Jordan’s Traité
 14 Jordan and Klein
 15 What is ‘Galois theory’?
 16 Algebraic number theory: cyclotomy
 17 Dedekind’s first theory of ideals
 18 Dedekind’s later theory of ideals
 19 Quadratic forms and ideals
 20 Kronecker’s algebraic number theory
 21 Revision and second assignment
 22 Algebra at the end of the 19th century
 23 The concept of an abstract field
 24 Ideal theory
 25 Invariant theory
 26 Hilbert’s Zahlbericht
 27 The rise of modern algebra – group theory
 28 Emmy Noether
 29 From Weber to van der Waerden
 30 Revision and final assignment
 A Polynomial equations in the 18th Century
 B Gauss and composition of forms
 C Gauss on quadratic reciprocity
 D From Jordan’s Traité
 E Klein’s Erlanger Programm
 F From Dedekind’s 11th supplement
 G Subgroups of S4 and S5
 H Curves
 I Resultants
 Bibliography
 Index
 Isbn
 9783319947730
 Label
 A History of Abstract Algebra : From Algebraic Equations to Modern Algebra
 Title
 A History of Abstract Algebra
 Title remainder
 From Algebraic Equations to Modern Algebra
 Statement of responsibility
 by Jeremy Gray
 Language
 eng
 Summary
 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.
 http://library.link/vocab/creatorName
 Gray, Jeremy
 Image bit depth
 0
 LC call number
 QA2127
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName
 SpringerLink
 Series statement
 Springer Undergraduate Mathematics Series,
 http://library.link/vocab/subjectName

 Mathematics
 Algebra
 History
 Number theory
 Mathematics
 History of Mathematical Sciences
 Algebra
 Number Theory
 Label
 A History of Abstract Algebra : From Algebraic Equations to Modern Algebra, by Jeremy Gray, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Introduction  1 Simple quadratic forms  2 Fermat’s Last Theorem  3 Lagrange’s theory of quadratic forms  4 Gauss’s Disquisitiones Arithmeticae  5 Cyclotomy  6 Two of Gauss’s proofs of quadratic reciprocity  7 Dirichlet’s Lectures  8 Is the quintic unsolvable?  9 The unsolvability of the quintic  10 Galois’s theory  11 After Galois – Introduction  12 Revision and first assignment  13 Jordan’s Traité  14 Jordan and Klein  15 What is ‘Galois theory’?  16 Algebraic number theory: cyclotomy  17 Dedekind’s first theory of ideals  18 Dedekind’s later theory of ideals  19 Quadratic forms and ideals  20 Kronecker’s algebraic number theory  21 Revision and second assignment  22 Algebra at the end of the 19th century  23 The concept of an abstract field  24 Ideal theory  25 Invariant theory  26 Hilbert’s Zahlbericht  27 The rise of modern algebra – group theory  28 Emmy Noether  29 From Weber to van der Waerden  30 Revision and final assignment  A Polynomial equations in the 18th Century  B Gauss and composition of forms  C Gauss on quadratic reciprocity  D From Jordan’s Traité  E Klein’s Erlanger Programm  F From Dedekind’s 11th supplement  G Subgroups of S4 and S5  H Curves  I Resultants  Bibliography  Index
 Dimensions
 unknown
 Extent
 XXIV, 415 p. 18 illus.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783319947730
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783319947730
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319947730
 Label
 A History of Abstract Algebra : From Algebraic Equations to Modern Algebra, by Jeremy Gray, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Introduction  1 Simple quadratic forms  2 Fermat’s Last Theorem  3 Lagrange’s theory of quadratic forms  4 Gauss’s Disquisitiones Arithmeticae  5 Cyclotomy  6 Two of Gauss’s proofs of quadratic reciprocity  7 Dirichlet’s Lectures  8 Is the quintic unsolvable?  9 The unsolvability of the quintic  10 Galois’s theory  11 After Galois – Introduction  12 Revision and first assignment  13 Jordan’s Traité  14 Jordan and Klein  15 What is ‘Galois theory’?  16 Algebraic number theory: cyclotomy  17 Dedekind’s first theory of ideals  18 Dedekind’s later theory of ideals  19 Quadratic forms and ideals  20 Kronecker’s algebraic number theory  21 Revision and second assignment  22 Algebra at the end of the 19th century  23 The concept of an abstract field  24 Ideal theory  25 Invariant theory  26 Hilbert’s Zahlbericht  27 The rise of modern algebra – group theory  28 Emmy Noether  29 From Weber to van der Waerden  30 Revision and final assignment  A Polynomial equations in the 18th Century  B Gauss and composition of forms  C Gauss on quadratic reciprocity  D From Jordan’s Traité  E Klein’s Erlanger Programm  F From Dedekind’s 11th supplement  G Subgroups of S4 and S5  H Curves  I Resultants  Bibliography  Index
 Dimensions
 unknown
 Extent
 XXIV, 415 p. 18 illus.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783319947730
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783319947730
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319947730
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