Section 8.5

1. I understand the reasoning they used to prove certain properties and classify the groups, but that's merely an artifact of knowing how to apply a theorem. At this point, they're little more than memorized facts and not the concepts they should be (which is necessary for any useful application).

2. Quaternions, as you probably know, have a direct application to rotations in 3D space and avoid the problem known as "gimbal lock" when performing such transformations. They therefore have a direct application to 3D graphics, which I suspected groups would since they are often given geometric interpretations. If I'm not mistaken, quaternions do not entirely "live" in three spatial dimensions--they comprise four--like D_n does not live in two.