Studying for Tutorial 1

This came up on the Wednesday night before our first tutorial quiz (I’m in the Thursday night section). I was mildly worried about it although (for me anyway) it wound up being much easier than I anticipated. I usually find that if I overworry, I overprepare, and that makes me do better, though, so I’m not so unhappy about overworrying because everything goes better than expected. This is the one benefit to being a giant ball of nerves.

Anyway, because I was such a ball of nerves I got a friend to quiz me with induction proofs that he’d yoinked off the internet so that I hadn’t seen them before. The proofs were of varying difficulty. One of them was the standard sum-type sort: 

which is easy enough once you get the trick of splitting the summation into terms that can be induction-hypothesised (from base case to n) and extra terms (the n+1th term). Then it’s straightforward algebra to combine the two into something that looks like the induction hypothesis but with a quick change of variable n -> n+1.

The other was one that looked like:

which we saw later in I think the third week or so, and here you’re supposed to use the fact that the relation LessThan is transitive (so for A < B, and B < C, you know certainly that A < C) and a term-by-term comparison to show the B < C part. Then you’re essentially done. 

Anyway, the rest is less a discussion about the proofs themselves and more about my ridiculous anxiety issues, which I really wish would just go away!

I got both proofs okay, but they took wayyy longer than they should have and I had to tell my friend to actually go away while I was doing them because he was hovering over my shoulder watching me struggle. The most difficult thing about the proofs wasn’t the proofs, it was having to complete them with someone tracking your every move and waiting for the next line, with that feeling of ‘will they tell me the second I go after the red herring or will they just watch me sit there and flounder’ looming over your head. I don’t know about others but I really, really, really don’t do good math in these circumstances. In fact, my mind tends to blank, and every single thing I know, even though I know I know it, somehow can no longer be accessed in my head.

Unfortunately it’s not always the case that you get to choose the sit-down test (where nobody is watching you make dumb mistakes on your scratch paper) over the oral test (where everybody can judge you and what you’re doing with that chalk/whiteboard marker in real time). Unfortunately, the latter is exactly what you have to do in graduate school or academia. Awesome, right? right??! ಠ_ಠ

Probably, a good part of the battle is being able to keep one’s head while under fire, but for me, there is a separate component that is really math-and-science specific - the stress of being examined is also combined with the fear of not doing well. I feel sometimes like I have to do better just to prove to people that I deserve to be here at all.

So this is something I really need to get past, and it’s part of the reason I’m back in school. My confidence is pretty shot and maybe some might think it’s a little sad and Pavlov’d that I rely on getting A+’s as my cue to feel good about myself, but at the same time I find it very nice to have clear-cut hurdles and hoops to jump over and through.