Galois Theory without abstract algebra (1108.4593v1)

Abstract: Galois theory is developed using elementary polynomial and group algebra. The method follows closely the original prescription of Galois, and has the benefit of making the theory accessible to a wide audience. The theory is illustrated by a solution in radicals of lower degree polynomials, and the standard result of the insolubility in radicals of the general quintic and above. This is augmented by the presentation of a general solution in radicals for all polynomials when such exist, and illustrated with specific cases. A method for computing the Galois group and establishing whether a radical solution exists is also presented.