A History of Abstract Algebra
From Algebraic Equations to Modern Algebra
Format:Paperback
Publisher:Springer International Publishing AG
Published:16th Aug '18
Should be back in stock very soon
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.
“This volume is well written and nicely complements other works on the history of algebra. It can be recommended to all mathematicians and students of mathematics who want to understand how algebra turned into the rather abstract field it is today.” (C. Baxa, Monatshefte für Mathematik, Vol. 201 (4), August, 2023)
“The book under review is an excellent contribution to the history of abstract algebra and the beginnings of algebraic number theory. I recommend it to everyone interested in the history of mathematics.” (Franz Lemmermeyer, zbMATH 1411.01005, 2019)
“This is a nice book to have around; it reflects careful scholarship and is filled with interesting material. … there is much tolike about this book. It is quite detailed, contains a lot of information, is meticulously researched, and has an extensive bibliography. Anyone interested in the history of mathematics, or abstract algebra, will want to make the acquaintance of this book.” (Mark Hunacek, MAA Reviews, June 24, 2019)
ISBN: 9783319947723
Dimensions: unknown
Weight: unknown
415 pages
1st ed. 2018