Algebra/Chapter 10/Symmetric Polynomials

Introduction

In Algebra, a polynomial in several variables is called a symmetric polynomial if it remains invariant under any permutation of its variables.

Symmetric polynomials were initially studied in the context of solutions of polynomial equations in a single variable, since the coefficients of the polynomial are symmetric polynomials in its roots.
Over time, symmetric polynomials gained a status of their own, and they appear in various branches of mathematics, mainly in combinatorics.

Chapters

1. Monomial Ordering
2. Permutations and Symmetry
3. Elementary Symmetric Polynomials
4. Fundamental Theorem of Symmetric Polynomials