Introduction to abstract algebraic structures, including groups, rings, and fields. Sets and relations. Congruences and unique factorization of integers. Groups, permutation groups, homomorphisms and quotient groups. Rings and quotient rings, Euclidean rings, polynomial rings. Fields, finite extensions. | Prerequisites: A grade of C or better in (MA-UY 2114 or MA-UY 2514) and (MA-UY 1044 (formerly 3044) or MA-UY 3054 or MA-UY 3113). Additionally, it is suggested for students to have taken MA-UY 4614 or MA-UY 4644 as a prerequisite. Note: Cannot receive credit for both MA-UY 4044 and MA-UY 4054.