We find the smallest field containing the number 1 when using the usual addition and multiplication of real numbers.
We show that the integers modulo any prime forms an integral domain under addition and multiplication modulo p.
We show, step-by-step, that the set of all 2 x 2 matrices with real entries forms a ring under addition and multiplication.
We show that every cyclic group is isomorphic to either the set of integers or the set of integers mod some integer under addition.
I take some time away from doing algebra to look at an upcoming video game, New World, and discuss its potential.