3 credits Prerequisites: MTH 253 and MTH 301. The study of algebraic constructs, including groups, rings, and fields. Permutation groups, subgroups, normal subgroups, homomorphisms, quotient groups, fundamental isomorphism theorems. Cayley’s Theorem, Sylow theorems. Commutative rings, integral domains, ideals, prime and maximal ideals, quotient rings, ring homomorphisms. Polynomial rings. Introduction to Galois theory.
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