Sebastian Sundblom: Symmetric Polynomials

Abstract.

The theory of symmetric polynomials is one that has applications in several branches of mathematics, and in this paper we will begin to see what a symmetric polynomial means and how they are built by first looking at the monomial, elementary and power sum symmetric polynomials before moving onto proving Newton’s identities and the fundamental theorem of symmetric polynomials. We will also look at the transformation matrix from the elementary symmetric polynomials to the power sum symmetric polynomials and vice versa.