A History of Abstract Algebra: From Algebraic Equations to Modern Algebra (Springer Undergraduate Mathematics Series)

Gray, Jeremy

ISBN 10: 3319947729 / ISBN 13: 9783319947723

Published by Springer, 2018

About this Item

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Seller Inventory # ria9783319947723_new

Bibliographic Details

• Title: A History of Abstract Algebra: From Algebraic Equations to Modern Algebra (Springer Undergraduate Mathematics Series)
• Publisher: Springer
• Publication Date: 2018
• Language: English
• ISBN 10: 3319947729
• ISBN 13: 9783319947723
• Binding: Soft cover
• Condition: New

About this title

Synopsis

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 relationshipbetween 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 Author

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.