The school year is moving swiftly for me. We’re already a third of the way through Fall Quarter, and I thought I would give an update on my previous blog post titled “Math Anxiety”.
I’m taking two math classes this term, Calculus 4 and Number Theory. The former, I was not especially worried about. I like Calculus, and feel reasonably comfortable in it. This particular course is all about Calculus in three dimensions, taking derivatives with respect to some vector pointing in an arbitrary direction, gradients, that sort of thing. But Number Theory, that’s a whole new realm.
Number Theory is my first “proofs-based” math class. If you’re a math major, you know what I’m talking about, and you’re already nodding with some sympathy. For anyone else, suffice it to say this is a different area of mathematics than I’ve ever tried before, with its own weird symbology and nomenclature, much more abstract than previous math courses. My first week was rough. The homework was making no sense, the textbook read like no math text I’d ever seen before, it provided a relative dearth of example problems worked out, and the back of the book provides almost no answers to any of the problems at the end of each section. Panic! I emailed the prof about my worries, and all he could say was words to the effect of “Yep. Up till now, you’ve been doing using math as a customer. Now you’re working as an active participant. It’s a hell of a transition.” Great. Not exactly reassuring. Nor did it offer much in the way of steps I could take to get out of trouble.
I briefly considered dropping the class. But… well, I have to take the class eventually. And everyone I talked to told me this prof was the absolute best person in the department to take it from. And I’m told the upper-division classes look way more like Number Theory and less like Calculus. Much more theoretical, abstract. So, I girded my loins and soldiered on. I bought the solutions manual for the textbook (almost as useless as the text itself) and a general book on proof writing (meh). I got very active on the online forum for the class, answering what very few questions I could, and asking more of my own. I became diligent about making it to the prof’s office hours, where he would do sample problems for the small group that showed up. And things got a little better. The homework made a little more sense, even if it was still a big effort. Often, I would write down a problem and then I’d have to stall for ten or fifteen minutes to let my brain percolate before I had a clue where to start. Which meant homework was taking me forever to complete. And I seemed to average about one problem per sheet of paper. Regardless, it was progress. Over time, I was able to answer more of the questions posted to the class’s online forum.
This week, I had the first (of two) midterms in both classes! I was especially nervous about the Number Theory test; my knowledge of the material still felt a little shaky and I was worried about the pressure of having to crank out answers quickly, without time for intervening breaks to make tea. Test day came, and it was rocky. For the first time in a long while, I had at least one problem that caused me to seize up completely. Deer-in-the-headlights, total panic, no clue where to even start, nothing seemed to make sense. Skip it and move on. Another problem I thought I understood, but the final answer wouldn’t check, despite how hard I looked for a mistake in my work. Sigh. Skip it and move on. I finally finished the rest of the test and circled back to the skipped problems. After minutes of flop sweat, I found my stupid mistake on the one problem; transposed digits in one line of an equation threw everything off. I fixed that, and it checked correctly. Whew! Then I went back to the proof that stumped me. After wrestling with it for a while, inspiration struck me and I saw a path forward. A few minutes of grinding and I nailed the proof. A quick glance over the paper and then I turned it in and ran away in a cold sweat.
Today we got the test back. The prof admitted that the test ran much longer than he intended, so on everyone’s test he dropped the one problem they did the worst on. Thanks to that bit of grace, I am happy to say I nailed the only 100% in the entire class (of ~40 people)! My relief is so profound, I hardly know how to express it. Suddenly, I’ve moved from wondering if I can pass this class to wondering if I can pull an A in it.
Not quite so dramatic, but the Calc 4 midterm was today, and I think I did well on it. Should get that one back next Monday.