Symmetry and polynomials: Polynomials with several variables, symmetric polynomials; their use for solving algebraic equations with one variable.

Symmetry and relations: Symmetric and skew-symmetric relations, types of relations, their properties and applications.

Symmetry and groups: Alternating groups, their usage. Link to geometry.

Symmetry and matrices: Symmetric matrices, their link to systems of linear equations and quadratic forms.

Symmetry and graphs: Symmetric graphs, symmetrization of a graph.

This optinal subject covers the following topics: symmetry and polynomials, symmetry and relations, symmetry and groups, symmetry and matrices, symmetry and graphs.