A History of Abstract Algebra

From Algebraic Equations to Modern Algebra

Nonfiction, Science & Nature, Mathematics, Algebra, History
Cover of the book A History of Abstract Algebra by Jeremy Gray, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Jeremy Gray ISBN: 9783319947730
Publisher: Springer International Publishing Publication: August 7, 2018
Imprint: Springer Language: English
Author: Jeremy Gray
ISBN: 9783319947730
Publisher: Springer International Publishing
Publication: August 7, 2018
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book Purification of Peptides in High-Complexity Arrays by Jeremy Gray
Cover of the book Information Search, Integration, and Personlization by Jeremy Gray
Cover of the book Shared Services and Outsourcing: A Contemporary Outlook by Jeremy Gray
Cover of the book Medicine, Knowledge and Venereal Diseases in England, 1886-1916 by Jeremy Gray
Cover of the book Software Failure Investigation by Jeremy Gray
Cover of the book Cooperative Interactions in Lattices of Atomic Dipoles by Jeremy Gray
Cover of the book Designing Pilot Projects as Boundary Objects by Jeremy Gray
Cover of the book Scientific Computing by Jeremy Gray
Cover of the book Ecological and Evolutionary Modelling by Jeremy Gray
Cover of the book Metabolic Control by Jeremy Gray
Cover of the book Rabi N. Bhattacharya by Jeremy Gray
Cover of the book Safe Zone by Jeremy Gray
Cover of the book Clinical Pharmacology: Current Topics and Case Studies by Jeremy Gray
Cover of the book Information and Communication Technologies in Education, Research, and Industrial Applications by Jeremy Gray
Cover of the book Application of Surrogate-based Global Optimization to Aerodynamic Design by Jeremy Gray
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy