Rutgers University 3 credits Mathematical Sciences
Groups: subgroups; homomorphisms; cyclic groups; Lagrange's theorem; quotient groups; symmetric, alternating, and dihedral groups; direct products and sums; free groups; free abelian groups; finitely generated abelian groups; and Sylow theorems. Rings: homomorphisms, integral domains, fields, ideals, prime and maximal ideals, Chinese remainder theorem, factorization in commutative rings, UFD, PID, Euclidean rings, rings of quotients, localization, local rings, polynomial rings, Gauss's lemma, and Eisenstein criterion.
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