It could have been better, but it could have been a lot worse. While 11th hour studying isn't the best of ideas, it's better than no studying. If I passed, or even did halfway decent, my last minute studying between 10:00 PM and 1:00 AM last night can certainly be given almost 100% of the credit.
After a mad dash to Bahen after having mistakenly thought the test was being done in the lecture room in Lash Miller, I sat down with the thing, and opened it up. Unwinding. Cool. Generally good at that. I get it. I like recursion. It makes me happy, much like lambdas and regular expressions. My mood was dampered however when I realized that it was going to contain a sum. Expletive! I don't actually know how to convert summation notation into a geometric series or whatever it's supposed to be represented as. I encountered that problem while studying last night, but couldn't figure out what the steps involved were. I suppose I ought to have looked into it more, because it came back to bite me. I couldn't fully unwind. Which was a shame, because had I known what it was, I could have easily proven it.
I said I'd let the closed form I should have found be equal to z, and outlined a proof of z step by step. Hopefully that will be mostly sufficient. It has to be. That's what I had.
The second problem went a lot better. There's something immensely satisfying about finally learning material that one is being tested on, during the test itself. I finally truly understand why we set n-hat to be 2^ceil(log(n)). I found myself struggling to define n-hat in my proof, and then I figured I'd just throw in a 2^ceil(log(n)) since that's what I'd seen before. Then I thought about it. I looked at it. And I finally got it. It comes out to the next highest power of 2 after n. I probably should have known that already. Confession: I don't know a lot of stuff that I should know. Especially about log.
I realize that I don't paint an especially glowing picture of myself. I am most certainly far from the ideal CSC236 student. Frankly, I don't know how I'm not failing. Luck has been kind to me. But I can't rely on luck forever. And so, I have a plan, which has conveniently started with starting this SLOG; something I've been meaning to do since being reminded that it was a thing I was supposed to be doing. And then I'll be ready for Term Test 3 when it rolls around!
What's that? Oh, there is no Term Test 3?
...
Damn.
Term test 3 is the final. I think your method is probably reasonably effective: lectures are meant to be watched rather than jotted down.
ReplyDeleteAnd I gather that the grading TA was appreciative of "let z be the closed form I'm going to prove..." So much better than trying to prove an incorrect closed form.