ABEL’S THEOREM IN PROBLEMS AND SOLUTIONS
In high school algebraic equations in one unknown of first and second degree are studied in detail. One learns that for solving these equations there exist general formulae expressing their roots in terms of the coefficients by means of arithmetic operations and of radicals. But very few students know whether similar formulae do exist for solving algebraic equations of higher order. In fact, such formulae also exist for equations of the third and fourth degree. We shall illustrate the methods for solving these equations in the introduction. Nevertheless, if one considers the generic equation in one unknown of degree higher than four one finds that it is not solvable by radicals: there exist no formulae expressing the roots of these equations in terms of their coefficients by means of arithmetic operations and of radicals. This is exactly the statement of the Abel theorem.
Đây là một cuốn sách về Đại số rất hay và cần thiết cho những ai muốn tìm hiểu thêm về các chuyên ngành Đại số ở các Trường Đại Học Sư Phạm, Khoa Học hay những học viên cao học và nghiên cứu sinh các ngành Toán Đại số. Sau đây là mục lục: