Basic Algebraic Structures

Course content

Binary operations. Groups, subgroups, cyclic groups. Isomorphisms and homomorphisms. Finite permutation groups. Cosets, normal subgroups, quotient groups. Rings and subrings. Ideals and quotient rings. Ring isomorphisms. Integral domains and fields. The fields of real numbers and complex numbers. Polynomials over a ring. Divisibility and greatest common divisors. Factorization in the ring of polynomials over field. Zeroes of a polynomial.