Math and Me

[…] I will end my first year with straight A’s, which makes me very happy. I almost didn’t get an A in math, but then Mr. Carlo told me to stop asking ‘why?’ all the time and just follow the formulas. So, I did. Now, I get perfect scores on all my tests. I just wish I knew what the formulas did. I honestly have no idea.

The quote is from The Perks of Being a Wallflower, by Stephen Chbosky (what? did you think CS students read nothing but The Hitch Hiker’s Guide to the Galaxy?). Now, it’s not quite the same with math and me, but it nevertheless struck a chord. Fact is, when the results from the math exam came out last Tuesday, I actually had an A+, to nobody’s surprise except mine. Generally, the results were quite good. In our core group, I know of four more A’s and B’s. Only 40% of those taking the exam failed. The usual expectation, as I mentioned earlier, is that 50 to 70% will fail. I haven’t heard from everybody yet, but even two of us who were worried about failing passed, albeit just barely.

Now that grade made me think back to last summer, after I had decided I wanted to go back to school and study CS. I was confident about my programming abilities after a few months of teaching myself Java. But at some point I got seriously worried about math. You see, even though UAS doesn’t emphasize math nearly as much as UHH (which after all was one reason for my decision to study at the former), I was clear to me that I would need at least a passing grade in what still amounted to high school level math. And it had been 26 years since I had last done math at school, and that had ended with my handing in an empty sheet in the final examination (and in the honour’s course to boot).

A strange end to a school career in which I had always enjoyed math, to the degree of being no. 1 in my class (not a very good class, to be sure) for seven years straight. For most of the time, I was a math natural. I never needed being explained a problem, I never needed any formulas. Somehow I just saw the solution right away, particularly in geometry, and whenever a particular problem could be solved either arithmetically or geometrically, I picked the latter, because it was so obvious to me. So I never studied for math.

That got me into bad trouble in the senior grades with analysis and stochastics, because these were things that defied my imagination. With some luck I could picture the derivative of a function, but the second derivative was beyond me. For the first half year I carried on in the same old style, somehow muddling through and ending up with an A- in my mid-term certificate, while my co-students simply learned the formulas by rote without, for the most part, giving them any thought. And that meant that most of them passed the course by more or less blindly applying the formulas, while I passed from near top to dead bottom of the class before the end of the year because in seven years I had simply never learned to just follow the formulas (which brings us back to the Wallflower quote). To be fair, all this came at a very bad time for me personally too, with my parents divorcing and me moving out from home as a result, so school really was low on my list of priorities for a while. That I got my high school diploma at all is only thanks to a strange quirk in the back then Bavarian high school grading system which lumped together the last half year’s grade with the final examination grade in honour’s courses (only), and a kind math teacher who generously gave me an E, rather than the straight F I certainly deserved, just for attending his course. So I got an E in the final math exam as well, in spite of the empty sheet, and got my Abitur (diploma) with a C+ average (actually it was just a tad shy of B-). As the principal kindly pointed out to me, this was much better than I deserved.

So I went to study history, one of the subjects in I had still managed to keep up my good grades, and, more to the point, one without a numerus clausus. (To be completely honest, I didn’t give the decision any serious kind of thought. After my 15 months of alternative civilian service in an overcrowded refugee camp I just wanted to use my brains again for a change. It had to be university; the subject hardly mattered.)

With that as a background, you may imagine I had reason to be worried, 26 years later, at the perspective of having to pass in math to be able to study CS. So, much as I enjoyed programming in my spare time, I decided I had better prepare, seriously, for math. I got myself a couple of really thick textbooks in the “math for CS students” line and applied myself to self-study. And a good thing too, because most of the things I found in the books I had either long forgotten or never known. The good thing is that in the quarter of a century since I had been at school I had wasted a lot of time on things that led nowhere (like a Habilitation in history), but I had learned some other things that were valuable now, like work discipline, acquiring new things from books really quick, and a dogged determination to solve problems rather than run from them. So I worked through the books whenever I found time, sometimes hating it, but sometimes, to my surprise, having fun. In math, after all, things are often quite simply either right or wrong, and if right, then often even kind of elegant, quite unlike in academics, where you can debate everything to death and it always remains somewhat murky.

When the term started in September with the math preparation course (a quick catching-up program before the actual lectures), I felt I had spent my time well. I worked through the interactive video tutorials before the course even began, I religiously attended the course too (which had the added advantage of learning to know the people who eventually formed our study group), and when the math lectures actually started I felt comfortable with things like propositional logic or relations that had been all Greek to me just half a year earlier. In fact, for a while there I thought the math course would be really easy. As I related several times before, it wasn’t, not after the first couple of weeks, for reasons well known. But I truly believe that without my determined preparation I would had a much harder time even passing. At the very least, the psychological momentum was in my favour. And while there were still moments when I felt completely stupid–for instance when nobody except me seemed to have problems with the Gauss algorithm for solving equation systems, something high school students in Hamburg apparently have to practice ad nauseam while I can’t recall I ever had before–they were rare. Of course, math was still the major effort in this first term. By my estimate I spent about 60% of my study time outside lectures for this single course out of five.

Seeing that A+ in the computer system was, truly, a great reward for all that effort. Did I overdo it? Most certainly. After all, all I really needed was a passing grade. It is universally understood that math is the lock before the door that leads to the halls of studying computer science. Once you have entered, nobody ever will be interested in your math grade again.

But then I think that on a deep personal level when I made sure I got not just a passing grade, but a very good grade in math this time, my true aim was to overcome my earlier failure, to find a way back to the boy who had always been fascinated by math. Unlike Charlie (the hero of Wallflower) I didn’t stop asking questions, not by a long way (our math professor can attest to that!). But this time I did study and follow the formulas, to make sure I knew how to solve a problem even if I did not (completely) understand it. In the end, I believe I did math not for the key to studying computer science, but for myself.

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