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Abstract algebra. / Ronald Solomon.

By: Contributor(s): Material type: TextTextPublisher number: Brijwasi Book Distributors | H-87,Lalita Park, Laxmi Nagar, New Delhi-110092Publication details: Providence, R.I. : American Mathematical Society , [2009?]Description: xii, 227 pages : illustrations ; 24 cmISBN:
  • 9780821852101
Genre/Form: DDC classification:
  • 512.02 SOL
Contents:
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.
Summary: 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.
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Item type Current library Call number Status Barcode
Books Books SNU LIBRARY 512.02 SOL (Browse shelf(Opens below)) Available 25305
Books Books SNU LIBRARY 512.02 SOL (Browse shelf(Opens below)) Available 25306
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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.

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.

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