A History of Abstract Algebra by Jeremy Gray
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 algebraIt 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)
“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)
Before studying modern languages at Oxford University, MICHAEL IVORY perfected his German by spending time at a Rhineland boarding school. He subsequently taught in Germany and, after qualifying as a landscape architect and urban planner, took many student groups there to learn from the country's considerable achievements in these fields. He has traveled extensively in central and eastern Europe, and has watched with particular interest as the peoples and countries of the former Soviet bloc have adapted to the post-Communist world. Writing a guide to the whole of Germany was the fulfillment of a long-standing ambition. JEREMY GRAY was born of English parents in Louisiana. He began his writing career at news agencies, working at Agence France Presse and Bloomberg in Germany before moving to The Financial Times in Amsterdam. Gray has more than a dozen guidebooks to his credit, including bestselling titles on Amsterdam, Montreal, and Munich, and has contributed travel photography to publications around the globe. Gray now lives in the pulsing heart of Berlin's Mitte district.
| SKU | Unavailable |
| ISBN 13 | 9783319947723 |
| ISBN 10 | 3319947729 |
| Title | A History of Abstract Algebra |
| Author | Jeremy Gray |
| Series | Springer Undergraduate Mathematics Series |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Springer International Publishing AG |
| Year published | 2018-08-16 |
| Number of pages | 415 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |