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Unformatted text preview: Fall 2009 MAT 322: ALGEBRA WITH GALOIS THEORY PROBLEM SET #1 Week #1: September 21st - September 27th. Topics : Fundamental theorem of algebra, roots of unity, cubic equations, Cardans formula, unsolvability of the quintic, Newtons approximation method, geometric construction problems, ruler and compass, Gauss theorem on regular polygons, Fermat primes, groups, subgroups, multiplication tables, orders, generators, cyclic groups, C n , D n , V 4 , S n , Q 8 , homomorphisms, cosets, Lagrange, normal subgroups. Read : GT [5-18] Problems due Friday, September 25th, at 4:00 pm in Martin Luus mailbox: Problem 1 : Let G be a group. Prove the generalized associative law: Given n elements a 1 ,...,a n G , all ways of bracketing this ordered sequence to give it a value by calculating a succession of binary products yield the same value, denoted a 1 a n . How many ways can this be done?...
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