Calculus

Calculus isn't technically on the Q. But, it's so foundational to all of mathematics that it seems reasonable to be brushing it up. The theory, I have no trouble with. Those little epsilons and deltas that give Freshman such fits do not bother me in the least. Instead, it's the stuff that the Freshman generally do fine with that I need to bring back.

This isn't a new problem. I recall very well that by the end of Freshman year, I was really struggling with Calculus. I could prove all the theorems, but couldn't get though the homework and exams because I hadn't bothered to memorize the formulas.

Memorization is one of those dirty words in modern education. The rote learning of a simple fact has been downgraded to a task that falls somewhere below intelligence. However, as a Chemistry Professor at Cornell once told me, "a big part of learning is remembering what someone tells you." I've since come to realize that memorization is much more than being able to parrot back a fact. It is that, of course, but it is also the ability to recall that fact in context. That is, it's the ability to realize that said fact is pertinent to the issue at hand. You can only do that when the fact is part of your working knowledge. If your brain has to fish around for it, you won't have it when you need it.

I recall a conversation with my father in the late spring of my Freshman year regarding Calculus. I was expressing my frustration that, despite understanding the concepts, I was getting hammered on the tests.

"Have you memorized the integral formulas?"
"Well, no, not memorized."
"Why not?"
"Ummm."
"Isn't that what the questions call for?"
"Yeah, I guess."
"You might want to give it a try."

I did, but it was so late in the term that I was only able to salvage a C in the course. Yes, really! A "C" in a Freshman math course. Not the stuff most math PhD candidates look back on fondly. That summer, I worked on a farm. That sucked. I decided I needed to figure this academic thing out. I was a 4.0 student for the rest of undergrad. Not because I suddenly got smart, but because I suddenly decided that memorizing stuff wasn't such a bad idea after all.

I still believe that understanding concepts is far better than memorizing facts. But, I also realize that there is some stuff you just have to know, period. So, it's Tuesday. I'm studying Calculus. And, in case you were wondering, ∫cosθ dθ = sin θ (arbitrary constant omitted).