Another week (and a day) in the life of Hoxie.
GRE Prep is coming along well! This week, I refreshed my linear algebra and differential equations (diffeq). Unlike some of the multivariate calculus topics, I’ve been using both matrices and diffeq fairly frequently for the last couple of years, so it was more remembering the formulas and tricks than learning new concepts. That said, a couple of quick thoughts on the two subjects:
- I took an advanced linear algebra course that built from the foundations of vector spaces up to matrix manipulation and linear transformations. It was my first real pure mathematics course aside from calculus, so I had never been exposed to things like spaces or closure before. I got a lot out of the course (I still love saying “Gershgorin disk theorem” when I want to sound unnecessary fancy), but after taking a year of real analysis and just hanging around the math department for a couple of years, everything I studied this week made a lot more sense. (Even the phrase “linear algebra” made more sense this time around. See, there are algebras, right, and they’re linear! Get it?)
- I remember when Professor Devaney told us on the first day of diffeq that, until very recently, most diffeq classes covered tedious, specialized tricks for solving special instances of certain differential equations, since most of them don’t have exact solutions. However, we would be using computers to study the general behavior of differential equations and gaining a lot more insight as we did it. And we did. I remember teaching people diffeq when I was in Arizona and being amazed at how much I remember a year later and how useful graphical techniques were when building models.
The Mathematics GRE seems to focus on tedious, specialized tricks for solving special instances of certain different equations. I didn’t draw a single picture while doing any of the problems. No finding equilibrium points, no nullclines or phase portrait diagrams , just checking to see if certain conditions were met so that I could use some random formula to come up with an integrating factor to make things magically work. It felt a little bit empty.
I also reviewed my set theory, probability/combinatorics, finally kinda figured out what sinh() and cosh() are, and noticed that we seem to have learned a lot of what my review book calls “point-set topology” in my real analysis class. I started teaching myself abstract algebra, a topic I’ve never formally seen, and was actually doing pretty well with it until I stopped to do review problems instead. The strategy for the next twoweeks is just to do tons of review problems, with emphasis on calculus, diffeq, and linear algebra. I will be a calculus ninja in two weeks.
So yeah, it was a busy week in the world of GRE prep.
In other news, I found a visible feature in Snow Leopard that I actually might use! I never minimize windows because there’s no way to retrieve them from the dock using the keyboard only (that I’ve found, anyway, and I’ve looked.) I’ve always used Apple+h to hide the windows, or moved them to another Space. I still don’t think there’s a way to retrieve minimized windows using only the keyboard, but now minimized windows appear in Expose! Smaller versions of the minimized windows appear at the bottom of the screen, something that didn’t used to happen. Working on a small laptop screen, I use Expose all the time to navigate windows, so this could actually be useful.
And finally, the grad school applications are coming along about as quickly as I thought they would. I’m done with the “getting organized” phase, filled in most of my personal information on applications, and have done a fair amount of writing. Rather than waffling among apps, I decided to just pick a target school and finish it. This weekend, I finished drafts of all required essays and statements for my target, so after some more editing and submitting my recommenders’ contact information, I should be done with that one! One almost down, six to go…