Sunday, December 05, 2004

Tales from Linear Algebra

Before I begin, I must say that I apologize for the unsatisfying nature of my previous post. I realize it would leave readers wondering many things. Does Kyle get his computer science assignment done? Does he manage to prepare for linear algebra, at least enough to pass the exam? Will he get his HL2 fix?

Alas, dear readers, these were questions that I myself was grappling with on that fateful night. I hope I will be able to resolve at least a couple of these pressing issues here.

First off, let me say that I did indeed complete my final computer science assignment. Sort of. I ended up handing in two version of the program. The first version worked, but the second version was all commented out and broken up into files with all the proper data hiding and stuff done. It was the data hiding that got me. Try as I might, I absolutely could not make it call a function from a class that was addressed by a pointer. I tried every combination of symbols possible. I tried:

class->function
class::function
&class::function
&class->function
class.function
&class.function
*class.function
*class->function
*class::function

Then, I started doubling up:

&class->.function
&class->&function
*class::*function
class::.function
(*)&class->::function
((&)(&class))::->.function
etc...

Nothing worked. So hopefully, they will see that it is mostly done properly, and it is all commented out, not to mention the fact that I did include a working version, and give me a relatively good mark.

Now on to the second part of the story. I mentioned in my last part that I was "woefully unprepared" for the linear algebra exam. Now, not two days later, I believe that statement to be incorrect. During the past two days, I went through all my lecture notes, the entire course supplement (all 156 pages of it), the handout on "diagonalization" (which admittedly I still don't quite understand, and quite a bit of the textbook. In doing this, I generated 16 new pages of notes; most of which are solutions to problems in the supplement. It's true, what my old mathematics mentor used to say: "Mathematics is not a spectator sport". Indeed, blithely copying what the prof writes on the chalkboard does not teach you math (as seen in the 14.5/40 I got on my last term test). But now, I have done problems (hopefully correctly; I haven't managed to find any solution sets anywhere), and I feel that I almost fully understand what has been taught in the course. Regrettably, I am still unable to visualize higher-dimensional space, which is a skill that would come in enormously handy for some concepts in linear algebra. Three dimensions is sometimes just not enough.

It is somewhat interesting, though: I always have considered myself somewhat of a mathematician. I distinctly remember being the only person in any of my high school math classes that actually "liked" math. Not only that, but I always wrote all the math contests, and for most of my high school career I would sacrifice my entire Tuesday night in order to go to London to take a special math class (taught by the aforementioned math mentor). The peak of my mathematical career was when I wrote the Fermat contest in grade 11, recieving a score of 134/150. Only 26 people in all of Canada got a higher score than that.

But I digress. The point I was attempting to make was this: although I consider myself a mathematician, I prefer mathematics that is grounded in the real world, and not things that are logically sound but are merely abstract creations that have nothing to do with the physical world. However, the only part of linear algebra I understand is the physically grounded "diagonalization". All the abstract stuff about "bases", "rank", "vector spaces", etc., I understand perfectly (okay, not perfectly, but close enough). I suppose this situation will have to be rectified. Not tonight though; I'll do it tomorrow. The last thing I want to do during the exam season is to fuck up my sleep cycle.

As for Half-Life 2, it turns out that I was very close to finishing it, and in fact beat it in about 15 minutes yesterday. So that fulfilled my desire to play it, at least for a while. Most of the time I allocate for breaks is spent on watching Stargate SG-1. I honestly don't know why I never watched this show until now. It is, by far, the best show ever created.

To come full circle, I guess this post is a bit unsatisfying as well. It leaves you wondering. Will Kyle pass his exam? Will he have time enough to study for the other exams that he does well on them? Will he get to the end of season 2 of Stargate before tomorrow?

But rest assured, my friends. These questions, and more, will be answered in time.

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