This abstract algebra course examines the fundamental properties of basic algebraic structures, especially rings and groups, through concrete examples. Topics discussed mainly cover: sets, groups, permutation groups, cyclic groups, Lagrange’s Theorem, subgroups, normal subgroups, quotient groups, direct product of groups, homomorphism and isomorphism of groups, group actions, the Sylow theorems, ring theory, ideals and quotient rings, Euclidean domains, principle ideal domains, unique factorization domains, and polynomial rings. This course will also covers a basic introduction to topics in fields including extension fields, splitting fields if time permits.

MATH 2160 Linear Algebra