Study On Galois's Theory Of The Algebraic Equation

The map of Lagrange's algebraic equation theory is to transform the solution of the given equation into a series of auxiliary equations which are constructed by the relationship of any two resolutions,in order to decompose substitutions setS_n by solving these auxiliary equations.However,it is the key problem that how to ensure these equations,such as binomial equation,are“solvable”.Based on the Lagrange's map,Galois introduced a new concept of "group of equation",then proved auxiliary equations are solvable if and only if the corresponding subgroups are normal subgroups from the structure of the group,i.e.the relation between the group of an equation in field K and the subgroups.In this way,Galois solved the key problem completely,and established Galois theory of the algebraic equation.Thus Galois completely solved the problem of solving algebraic equations.This paper is from the original and the researching files.Based on the Lagrange's mapand,and the Research method of "Why Mathematics" proposed by Professor Qu Anjing in the Changiing the Paradigm:Research on History of Mathematics in China,we wish research these problems as follows:1.What is Lagrange's problem?2.What's the problem with Galois?Why he introduce the new concept“the group of equation”?3.How to solve the Lagrange's problem and establish the Galois theory of the algebraic equation?4.How Galois applied the theory?...