# Section 5.2: Analysis

## Congruence Class Arithmetic

This section is remarkably similar to Section 2.2. It deals with the developments of rings in $F[x]$ and arithmetic of congruence classes in $F[x]$. The notation for these types of rings is different from what has previously been encountered: $F[x](p(x))$ where F is a field and $p(x)$ a non constant polynomial in $F[x]$.

The ideas behind this section are relatively straightforward given that rings in $\mathbb{Z}$ have already been studied. However arithmetic in this form may be more difficult. At least right now I fail to see how the ring $\mathbb{Z}_2 [x] / (x^2+x+1)$ is composed of the elements $\{ 0,\ 1,\ [x],\ [x+1]\}$.