I Served Serial Joe a Slushie

Three down, none to go.

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As M can attest, I have been a miserable bastard this past month or so. I don't think I have ever been more stressed in my life than I was the days leading up to my exams. The main problem, I think, (as with most stressful situations) is lack of information. You don't know what type of questions will be asked, what sections of the book/subject they will be asked from, how many questions there will be, etc, etc.

Some of my six examiners were nice enough to give me sample questions, but that wasn't the case for everyone. And so the stress begins. Taking a class is one thing - you've been studying the material with the help of an "experienced" instructor, and by the time exams roll around, you know sort of what they expect and what they want. Here, you (re)learn the material on your own, then go in blind.

A great example of this was the part of my category theory final which dealt with enriched category theory. As I didn't know much about this subject before, I spent a lot of time studying it. Now, the material I was supposed to learn came from chapters 1-5 of a book. Chapter 1 is sort of an introduction to stuff I already sort of knew, so I spent most of time learning the more complicated concepts in chapters 2, 3, 4, 5. Of course, the exam arrives, and all of the questions dealt with stuff from chapter 1 or the first page of chapter 2. I could hardly believe my eyes when I saw the exam. It reminded me of the final exam in measure theory at Waterloo - does anyone else from there remember - we study for weeks about abstract measure theory, and then all of the questions were specific things in R^n which had little to nothing to do with the stuff we learned. Crazy.

Of course, none of this was helped by my lackadaisacal approach to studying. If it's not a week before the exam, I simply can not force myself to study for very long. Of course, then I start freaking out because I haven't studied enough; I try to study more, get frustrated, and the cycle continues.

The absolute worse part of this is (believe it or not) when I try to get really interested in the material. Sounds counter-intuitive, right? Not exactly. One of the main things I love in math is trying to understand why a particular concept was defined in a certain way, and to try and explore alternatives. It goes along with why I like category theory so much - it formalizes being able to deconstruct mathematical objects and their relationships, and so provides a framework for this kind of thinking.

Of course, this is the absolutely worst thing to do when studying. The examiners don't want to read about other theories and ideas, they want to hear about the standard, accepted theories and how they relate and work together. Now, this is not to say one shouldn't learn the standard theories and what not - after all, if they've been around for long enough, they're probably valuable for something. In the end, I am (sort of, grudgingly) grateful that I now know a bit more about standard things in mathematics. The difficulty has been not being able to work the way I want to to be able to pass these exams. Any time one is forced to do things a certain way, it makes life difficult.

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As for the exams themselves, I'm pretty sure I passed at least two of the three (analysis, and category theory). The topology was a bit shaky, but I think (I hope) I demonstrated enough to be able to pass. We'll see how the results come this week.

And once that it is all cleared up - freedom! Two years of (more or less) freedom to start doing research again. What a beautiful thought.