Foundations of Galols Theory

THE GALOIS theory of equations is simultaneously the source of modern abstract algebra and one of the most concrete applications of abstract algebra. For the problem of solving equations becomes familiar at a very early stage of a school course in mathematics; and the question, answered in the negative by Galois, whether all polynomial equations with integer coefficients can be solved by processes involving only the ordinary operations of arithmetic together with the extraction of n`b roots must seem a natural and unavoidable one to anyone well versed in school algebra.