Modern Algebra

This is a first course is Abstract Algebra. It aims to introduce students to the algebraic structures of rings and groups, and to present a range of examples to facilitate the understanding of the abstract theory so that students have a good grasp of the fundamental concepts in abstract algebra. This course will provide a good foundation for further study in advanced algebra topics and in areas where abstract algebra has applications. The topics covered in this course are: Rings and subrings, integral domains and fields, ring isomorphism and homomorphism, rings of polynomials, divisibility in polynomial rings over a field, factorization of polynomials over a field, ideals and quotient rings of commutative rings with identity, First Isomorphism Theorem. Groups and subgroups, cyclic groups, permutations, symmetric group on n letters, cosets, Lagrange's Theorem, quotient groups, group isomorphism and homomorphism, Fundamental Homomorphism Theorems.