New York University 4 credits Math
Introduction to abstract algebraic structures, including groups, rings, and fields. Sets and relations. Congruences and unique factorization of integers. Groups, permutation groups, group actions, homomorphisms and quotient groups, direct products, classification of finitely generated abelian groups, Sylow theorems. Rings, ideals and quotient rings, Euclidean rings, polynomial rings, unique factorization. Prerequisites: Minimum grades of A- in MATH-UA 123 or MATH-UA 133 and MATH-UA 140 or minimum grades of B + in MATH-UA 129 and MATH-UA 148.
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