"Throughout this course, student will explore the algebraic structures of groups, rings, fields, and vector spaces, and develop the skills to apply abstract algebra techniques in solving both mathematical and practical problems. § Group theory: sub groups, cosets, Lagrange's theorem, homomorphisms, normal subgroups and quotient groups, permutation groups, simple groups. § Rings and fields: matrix rings, quaternions, ideals and homomorphisms, quotient rings, polynomial rings, principal ideal rings, Euclidean rings and unique factorization. § Fields and vector spaces: finite-dimensional vector spaces, algebraic field extensions, finite fields."