Introduction to Abstract Algebra (MATH412)

Groups, subgroups, cyclic groups, homomorphisms and isomorphisms, permutations and Cayley's Theorem, cosets and Lagrange's Theorem, quotient groups and the isomorphism theorems, Sylow's Theorem; Rings and fields, ideals and quotient rings, integral domains, prime and maximal ideals, the field of quotients, properties of integers; rings of polynomials, polynomials over C, R and Q, basic ideas of field extensions.

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