linear algebra

Continuing the theme of "classes I should have taken five years ago," there was definitely a moment when I thought, "Hey, I've been sort of doing linear algebra for years now!  Tell me again why I didn't take this class five years ago?"

On the other hand, I really, really appreciate the course.  It might be an illusion, but I felt like I could glimpse a little bit more of the reasons why someone bothered to invent linear algebra in the first place: ("Boy, it's annoying to keep writing those variables over and over.  Maybe I can write the coefficients down as shorthand.    Hey, they have cool properties when you write them in a table form.  In fact, let me figure out how the properties of equations can translate over into manipulating the rows of coefficients.... so much less painful than doing it the old way!"  Except that this takes place over multiple years and looks far messier than the neatly presented classroom lectures.)

I have no idea if this little story is at all what the original creators were thinking, but in any case some variation on this idea was true for my own research project.  Matrices ended up being far less painful than solving the original equations, and enabled insights that probably wouldn't have  been possible if I was still slogging through things the old way.  So mostly I just ended up really appreciating how elegant all the rules for matrix math were... and the fact that I didn't have to personally discover any or all of it.  There is a time and place for discovery, and a time and place to appreciate that someone else has already done the work.  This would be a case for the latter.

Or in short, despite not quite having digested all the concepts in a fast summer course, I have seen enough to conclude that linear algebra is pretty.