Theory of Equations English 2013

In Mathematics, the theory of equations comprises a major part of traditional algebra. Topics range from polynomials, algebraic equations, separation of roots, including Sturm's theorem, approximation of roots, and the application of matrices and determinants, to the solving of equations. From the point of view of abstract algebra, the material in the theory of equations is divided between symmetric function theory, field theory, Galois theory, and computational considerations, including numerical analysis. The subject matter of the book is divided into 9 chapters. Chapter 1, “General Properties of Equations”, describes the equations of higher degrees and investigates similar relations which hold in the case of equations of the nth degree. Some elementary properties of equations have been studied. Chapter 2, “Relations between the Roots and Coefficients of a Polynomial Equation of the nth Degree”, explains how to establish the relations between roots and coefficients of a polynomial equation of the nth degree. Chapter 3 deals with the symmetric as well as asymmetric functions of the roots. Chapter 4 explains the methods of transformation of equations.