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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)

Creator
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 self-contained and therefore suitable for self-study.--
Language
eng
Work
Publication
Extent
1 online resource (XXIV, 415 pages)
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
Link
http://ezproxy.eui.eu/login?url=http://dx.doi.org/10.1007/978-3-319-94773-0
Instance
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
Creator
Subject
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 self-contained and therefore suitable for self-study.--
Member of
Assigning source
Provided by publisher
http://library.link/vocab/creatorName
Gray, Jeremy
Image bit depth
0
Literary form
non fiction
Nature of contents
dictionaries
Series statement
  • Springer eBooks.
  • Springer eBooks
  • Springer Undergraduate Mathematics Series,
http://library.link/vocab/subjectName
  • Algebra
  • History
  • Mathematics
  • Number theory
Label
A History of Abstract Algebra : From Algebraic Equations to Modern Algebra, by Jeremy Gray, (electronic resource)
Link
http://ezproxy.eui.eu/login?url=http://dx.doi.org/10.1007/978-3-319-94773-0
Instantiates
Publication
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
Control code
978-3-319-94773-0
Dimensions
unknown
Extent
1 online resource (XXIV, 415 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319947730
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
18 illustrations
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1048608394
Label
A History of Abstract Algebra : From Algebraic Equations to Modern Algebra, by Jeremy Gray, (electronic resource)
Link
http://ezproxy.eui.eu/login?url=http://dx.doi.org/10.1007/978-3-319-94773-0
Publication
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
Control code
978-3-319-94773-0
Dimensions
unknown
Extent
1 online resource (XXIV, 415 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319947730
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
18 illustrations
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1048608394

Subject

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