On Day 12, we continued to explore the group of permutations of finite sets using S_{3 }as an example, but we also practiced calculations with elements of symmetric groups of higher orders.

In addition to reviewing the concepts of order of an element, inverse, commutativity, we introduced some new concepts:

**Cycles**and their properties**Parity**/ Even and odd permutations

Students practiced switching between different notations used to represent permutations, while also checking our answers by physically moving pieces of paper labeled with numbers 1, 2, and 3.

*Students carried out permutations of pieces of paper
to either find answers or check them.*