Abstract :

Newton polygons have been an incredibly versatile tool in the study of polynomials. In this talk, first, we shall define the notion of the Newton polygon, and then we shall see some applications of Newton polygons in Algebra and Number Theory like irreducibility of polynomials over rationals, finding the degrees of the irreducible factors of any given polynomial over rationals, computation of the discriminant and an integral basis of an algebraic number field; finding Galois group of a polynomial, etc.​