3.1, due on 1/21

1. The first example in this half of the reading was a little confusing not in concept just in utility.  I have no idea why or where you would need the Cartesian product of these two rings but whatever.

2.  Theorem 3.1 seemed very straightforward but I'm still not sure of its utility.  Subrings made sense and seem like they should be useful.  So did subfields.  Theorem 3.2 will be useful in proving something is a subring and the proof was trivial.