7.5

1. What was the hardest part of the reading for you?
Well, now I'm kind of embarrassed and confused. When looking at D4 (like in the example on page 200) under function composition, I realized that I am probably crazy, but h*d would have you look at h on the left side of a chart and over to d on the top of the chart. But, according to this, you look at d along the side then to h on the top. Maybe I've been writing my tables wrong, but that is nuts and confusing. The other thing that confused me is how h was congruent to d mod that subset of rotations. What?!? That made no sense to me. It made sense, I suppose, that congruence classes here are ab^-1 in K... but... what? I also hated that they left me confused then changed concepts.

2. Lagrange's Theorem
Um.... what is this malarky? It's more confusing notation and it's a bunch of confusing stuff, and I feel sad and confused.  Pretty much the only thing that I really took out of that section is with these distinct right cosets, where every element of a group belongs to one and only one coset, then of course by adding the number of elements of the right cosets will be the same as the number of elements of a group... But that was pretty much the only thing I took out of that section.