Week 1 : Prime Factorisation in Polynomial Rings, Gauss’s TheoremWeek 2 : Algebraic ExtensionsWeek 3 : Group ActionsWeek 4 : Galois ExtensionsWeek 5 : Finite Fields, Cyclic Groups, Roots of Unity, Cyclotomic FieldsWeek 6 : Splitting Fields, Algebraic ClosureWeek 7 : Normal and Separable ExtensionsWeek 8 : Norms and TraceWeek 9 : Fundamental Theorem on SymmetricWeek 10 : Proof of the Fundamental Theorem Polynomial, of AlgebraWeek 11 : Orbits of the action of Galois groupWeek 12 : Inverse Galois Problem

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