Ronald Solomon. creator Ronald Solomon. text Algebra.-Algebra, Abstract.-Universelle Algebra. xxu Providence, R.I : American Mathematical Society , [2009?] monographic eng

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xii, 227 pages : illustrations ; 24 cm. Takes a novel approach to the standard introductory material on groups, rings, and fields. This title offers a semi-historical journey through the early decades of the subject as it emerged in the revolutionary work of Euler, Lagrange, Gauss, and Galois. It focuses on the central problem of studying the solutions of polynomial equations. Geometry -- What is congruence? -- Some two-dimensional geometry -- Symmetry -- Polynomials -- The root of it all -- The renaissance of algebra -- Complex numbers -- Symmetric polynomials and the fundamental theorem of algebra -- Permutations and Lagrange's theorem -- Orbits and Cauchy's formula -- Hamilton's quaternions (optional) -- Numbers -- Back to Euclid -- Euclid's lemma for polynomials -- Fermat and the rebirth of number theory -- Lagrange's theorem revisited -- Rings and squares -- More rings and more squares -- Fermat's last theorem (for polynomials) -- Still more Fermat's last theorem (optional) -- The grand synthesis -- Constructible polygons and the method of Mr. Gauss -- Cyclotomic fields and linear algebra -- A Lagrange theorem for fields and nonconstructibility -- Galois fields and the fundamental theorem of algebra revisited -- Galois' theory of equations -- The Galois correspondence -- Constructible numbers and solvable equations. / Ronald Solomon. 512.02 SOL 9780821852101 Brijwasi Book Distributors H-87,Lalita Park, Laxmi Nagar, New Delhi-110092 180705 20180705144143.0