Read: up to the start of Section 3.3.1.
Turn in: 3.24, 3.27, 3.33, 3.36, 3.37, 3.39
- Use Theorem 3.26 when you work on 3.27 (even though you are not being asked to prove 3.26). To do this, you need to determine just one particular root of the given polynomial (by “solving for $x$”), and then you can apply 3.26.
- In problems 3.36 and 3.37, you are asked to prove the subsets $G$ and $U$ of $\mathbb{H}$ are groups. The first thing to address is why $G$ and $U$ are closed under multiplication from $\mathbb{H}$. You should also address why multiplication is associative with respect to $G$ and $U$, but you won’t really need to prove anything because multiplication is already known to be associative with respect to the larger set $\mathbb{H}$ (and you can just state that).
Extra practice: 3.25, 3.26, 3.28, 3.34, 3.38
