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Springer Undergraduate Mathematics Series

A History of Abstract Algebra

From Algebraic Equations to Modern Algebra

Authors: Gray, Jeremy

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  • Provides a wide-ranging and up-to-date account on the history of abstract algebra
  • Covers topics from number theory (especially quadratic forms) and Galois theory as far as the origins of the abstract theories of groups, rings and fields
  • Develops the mathematical and the historical skills needed to understand the subject
  • Presents material that is difficult to find elsewhere, including translations of Gauss’s sixth proof of quadratic reciprocity, parts of Jordan’s Traité and Dedekind’s 11th supplement, as well as a summary of Klein’s work on the icosahedron
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eBook 32,12 €
price for Spain (gross)
  • ISBN 978-3-319-94773-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 39,51 €
price for Spain (gross)
  • ISBN 978-3-319-94772-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

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.

About the authors

Jeremy Gray is a leading historian of modern mathematics. He has been awarded the Leon Whiteman Prize of the American Mathematical Society and the Neugebauer Prize of the European Mathematical Society for his work, and is a Fellow of the American Mathematical Society.

Table of contents (30 chapters)

Table of contents (30 chapters)

Buy this book

eBook 32,12 €
price for Spain (gross)
  • ISBN 978-3-319-94773-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 39,51 €
price for Spain (gross)
  • ISBN 978-3-319-94772-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
A History of Abstract Algebra
Book Subtitle
From Algebraic Equations to Modern Algebra
Authors
Series Title
Springer Undergraduate Mathematics Series
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-319-94773-0
DOI
10.1007/978-3-319-94773-0
Softcover ISBN
978-3-319-94772-3
Series ISSN
1615-2085
Edition Number
1
Number of Pages
XXIV, 415
Number of Illustrations
18 b/w illustrations
Topics