期刊全称 | A History of Abstract Algebra | 期刊简称 | From Algebraic Equat | 影响因子2023 | Jeremy Gray | 视频video | | 发行地址 | 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 | 学科分类 | Springer Undergraduate Mathematics Series | 图书封面 |  | 影响因子 | .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, th | Pindex | Textbook 2018 |
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