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

3319947729 rar 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 Gausss theory of numbers and Galoiss 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, Fermats 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 Galoiss approach to the solution of equations. The book also describes the relationshipbetween Kummers ideal numbers and Dedekinds ideals, and discusses why Dedekind felt his solution to the divisor problem was better than Kummers. Read more