The oddest thing happened in calculus class yesterday… we started covering some territory that was actually familiar from my first time in calculus class, Lo Those Many Years Ago [fall of 1985]. Summations.
It’s like a combination of shorthand and a secret code. You get the initial number, the final number, and the function you perform on each number in the series. Then you add them up. You can look at the notes I took in class and see right when I perked up. Two pages of notes on L’Hôpital’s Rule? I did more erasing and rewriting than writing because I couldn’t keep my eyes open. (It starts to remind me of the joke that Lawrence Block told about the writer who took a bunch of LSD and was inspired to write a brilliant novel; when he woke the next morning he found that he’d written it all on the same line on the piece of paper.) Then, Section 5.1: Integrals, and bam! Clear notes, precise diagrams, lucid commentary. You can tell by my writing that I was getting what was going on.
The class feels split into two camps; the first, the high school super-geniuses who already know all this material and show up whenever they feel like it. A couple of days ago one student spent the whole lecture with her laptop open and playing Bubble Blast. AND she had the correct response every time the professor asked for feedback. (Today she used her laptop to do her online homework in class.) But to their credit, most of the HSSGes are friendly and willing to explain concepts and share their notes with the second camp — the strugglers. We’re trying, we’re showing up every day, we’re going to study sessions, we’re calling each other for help. Some of us get sick a lot. One of us (not I!) is dropping out of college altogether. Some of us will make it and some of us won’t. Our motto is, “I’ll try to do better on the next section.”
Anyway, summations were something I did before. Yesterday I was walking with my professor after class and told her, “I remember doing trig, exponential growth, summations, and integrals. But I don’t think I ever saw a derivative back then.”
“That’s weird,” she said.
On the other hand, since I sold back that textbook and my notebooks from Math 151 seem lost to time, it could also be a faulty memory. I don’t know why I wouldn’t remember doing derivatives, but it’s highly probably that was what I was supposed to be learning while I was personally going backwards in the book trying to understand the concepts of e and i.
Anyway, I have a bunch of homework to start on tonight, and a quiz tomorrow on antiderivatives. I have to be careful on the homework; on Sunday night I spent about 20 minutes on a single problem in the homework set, only to discover too late that I had written down “3 + x” as the denominator instead of “2 + x”. For what it’s worth, I suspect the answer to my own problem was correct, but the online grader is unforgiving.
I need to get good…. the next exam is the Tuesday after Thanksgiving, and I need to do very well. It’s time to register for next semester, and all I’m planning to take is Calculus II.