Never in Abelian Years...

Today was the first day of class. For my degree I need eight units in an outside minor, so the plan right now is to do it in the Math department. I know right? Never in a billion years did I think I would take a graduate level math course as a computer science major. But wouldn't you know it, being a computer graphicist requires a decent math background, especially in linear algebra, so I'm taking the advanced matrix computation course. Flying Spaghetti Monster help me. Actually it doesn't seem like it will be too bad... yet.

The course met this morning, but afterward I decided to sit in on differential manifolds. A 2-manifold is a two-dimensional surface that can be embedded in three (or I suppose higher) dimensions, such that the local region around any point on the surface resembles a disk. A 1-manifold is a curve. This is of possible relevance because we often represent an object with its surface boundary in computer graphics, rather than as a volumetric solid.

During the introductory lecture for differential manifolds the professor mentioned that he's had engineers take the course and one even found the course to be so enlightening about what math can be/is, that he switched to the math department. The professor also mentioned that this was an introductory level graduate course. So I thought to myself ok, maybe I can learn something here. Keep in mind I don't have a strong math background. But as soon as he started doing some algebras and defining some vocabulary, like what a "ring" is, I knew I was out of my element. He said that (R, +) is an abelian group. I heard this and I was like what... "a billion groups"? Then he said, if you don't know what abelian means yet, then this course is not for you. And so I proceeded to doodle.