Math

So I have pretty much always been a math geek.  That is the short version of this entry.

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I remember CAM(e)L, which I think stood for California Mathematics L*mumble* (League, maybe?) which was a totally optional after-school thing that was sort of mini math tests -- research tells me there were six over the course of a school year, but there were of course practice tests, possibly taken from previous years' real tests -- and I loved them.

I remember the Math Team, an after-school program that went to matches in the area and, er, took math tests, basically, as a competition between schools.  I don't remember details, but it was a combination of different sorts of math, and anyone who got a perfect score in that competition got an extra prize, which was generally math-related.  I managed it once -- not entirely legitimately, because there was a geometry problem that I couldn't figure out so I just eyeballed it and said "eh it looks approximately as long as x" and put that down as the answer and, despite the fact that drawings were generally not to scale (and so eyeballing was not reliable), that was correct.  I got a calculus textbook of my very own.  I loved it.

I remember doing ARML, the American Regional Mathematics League; we trained at Stanford on weekends, and then went to UNLV for the tournament.  It was more varied than the math team stuff, having individual components and group components and also relay components (where each person had a different problem, and the answer to the second person's problem depended on the answer from the first person's problem, and the answer to the third person's problem depended on the answer from the second person's problem, and so on, and if anyone in the chain couldn't finish or screwed up their calculations then no one got points).  I remember there were a lot of Asian males on our team, which didn't seem surprising.  I also remember being amused that the Las Vegas airport had slot machines in it, and none of us were legally old enough to gamble.

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In one of my math classes, the teacher -- a completely kick-ass woman who was a strict and rather formidable teacher but very awesome, especially when  it came to encouraging students (and girls in particular) in math -- told us about a summer program, PROMYS, that was a six-week summer camp in Boston entirely for math.

I, of course, begged my parents to let me go.  Which they did.

The six weeks were devoted to number theory; returning students could take additional seminars in other areas of mathematics, such as combinatorics or abstract algebra.

I remember learning about other number bases, and actually fully comprehending for the first time the base-10 number system we use.  I mean, I knew how to do base 10; you learn early, with blocks and such as physical representation of ones and tens and hundreds, and you know that ten ones make ten and ten tens make a hundred, and you know that if you subtract 75 from 93 you borrow a 1 from the second column to give you 13 in the first column that you can subtract 5 from, and I could do math but I didn't really understand it.  And then you get base 2 and base 8 and base 16, and suddenly the written representation "10" gets divorced from the number ten, because 10 in base 8 is eight, and ten in base 8 is 12, and it's no longer ones and tens and hundreds but ones (really the base number to the 0th power, but that's always one) and base and base-squared and base-cubed.  So 325 in base ten is five ones plus two tens plus three ten-squareds.  And it sounds dorky as a thing to get excited about but I loved it.

I remember writing out proofs of things like "a x 0 = 0 for any value of a" or "a x 1 = a for any value of a", things which are generally presented as basic axioms except that we were using more basic, more fundamental truths to prove them.  And I loved it.

I remember the joke about the horse with an infinite number of legs, done in proof form: A horse has four legs, which is an even number.  But a horse has two forelegs (four-legs) and two hind legs, making ten legs, which is an odd number of legs for a horse to have.  And the only "number" that is both even and odd is infinity.  Therefore, a horse has an infinite number of legs.

I remember the sky at night -- a sort of murky red haze, like living on another planet -- and I remember the thunderstorms and the rains.  Here, where I grew up and live now, we don't ever get summer rain, and the rain we get is icy cold and unpleasant.  There, summer rain was warm and delightful, and I remember going outside (I was using a manual wheelchair at that time, which wouldn't be damaged by getting wet) and spinning in circles and laughing because it felt so good.

I remember the Fourth of July, and the naive assumption that we could get a decent spot without camping out for three days prior.  Fireworks in Boston are a tad bit more crowded than they are here, and we ended up basically on the sidewalk of a city street, with the music from the Boston Pops orchestra piped in through loudspeakers, and we could only see the highest fireworks above the buildings around us.

I remember getting a flare-up of FOP in my right shoulder right around "midterms", leaving me unable to write and thus unable to take the test.  That frustrated me more than the flare-up itself.

I remember the flight home, where I got upgraded randomly to first class, but I was so sleep deprived from the camp that I slept through most of the flight, leaving sticky drool on my face and shirt.

I woke up in time to eat the chocolate chip cookie, though.

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One of the required classes in high school was physics, but the physics teacher at the time was, shall we say, undesirable.  He thought that women had no place in science; he thought that physics was something that no high school student would actually be interested in, and only ever took because they had to; and so on.  At least, that was his reputation, and it didn't sound fun.

But there was a way out.

This being a university town, we had an agreement with the local university: high school students could have the option of taking college classes (for credit!) as long as those classes weren't offered by the high school.  So one could not, for example, take first-year French at the university, because the high school offered that, but fifth-year French was not offered by the high school so could be taken by advanced French students.

More relevantly to this anecdote, one could not take ordinary physics, even if one did not like the attitudes of the only teacher available, but one could take calculus-based physics.

This required taking (and passing) calculus in one's junior year, which in turn required a summer of independent study, because the standard progression of math classes called for calculus in senior year at the earliest, and so in order to take calculus as a junior, one had to jump ahead.

So I did that.

There were several AP calculus classes offered at the high school.  This is partly because there are two AP calculus exams: calculus AB, which covers a set amount of material, and calculus BC, which covers that amount of material plus some extra, and therefore goes at a faster pace.  The class I was in -- calculus BC, taught by the awesome math teacher who introduced me to PROMYS, whom I still consider one of my favorite teachers -- was hard and fast-paced, and the school offered a calculus AB class in the same period that students could drop to if they were having trouble.  As a result, the class size dwindled over the academic year.

I loved it.  (Are we sensing a theme?)

I even remember one time when the teacher asked if anyone knew the answer to a problem, and my hand shot up -- I was so very much a Hermione, except that the Harry Potter books hadn't been written yet and so there was no such comparison to be made -- and she made a comment along the lines of yes, I know you know the answer; you may as well stop putting your hand up every time, and I'll call on you if no one else knows it.  Because, well, yes, I did always know the answer.  Because I loved math.

Now, taking calculus early was primarily for the purpose of taking the calculus-based physics.  (Which was a four-quarter series, so I took the first quarter over the summer, and kind of floundered at first because it was a university course and I was in high school and not used to that level of rigor; I flunked the first exam, though I am still a little resentful that the make-up exam offered didn't allow for partial credit, because one of the questions I had right until one of the last steps where I left off a square root sign, so it was mostly right but never mind that.  I pulled my grade up to a B, and got A's for the other three quarters.)

But it also allowed for taking post-calculus math at the university.  Linear algebra, differential equations, and vector analysis.  I had no explicit reason to take those, except that it was more math, more stuff to learn.

I remember one of these classes, where the instructor would write the top three scores (without names, just numbers) on the board, as well as some other information.  And there was one exam, dealing with matrices, that I found pretty straightforward: do A in X situation, do B in Y situation, just plug and play.  I got the exam back with a 98, and a smileyface, and I was pleased.

And then he went to the board to write the top three scores.

98.  78.  78.

I had literally scored far higher than anyone in the class.  And I was in high school, and young for my grade.

I practically floated out of the classroom that day.

(I also remember overhearing one student asking the professor in a worried voice whether the 98 would seriously affect the curve.  And I just floated, though I was also glad there weren't names attached, because I probably would have gotten beaten up for the grade I got.)

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So yeah.  I loved math.

And then I went to college, and during orientation I approached one of the math faculty and basically said "I've taken calculus and these other classes, what do you recommend I take next?"  And he said "Nothing," because of course AP classes and university classes meant I had fulfilled the math requirement, "and don't come after my job."  Which left me a little baffled, because I'd assumed that a math person would go "oh yay someone excited about math" rather than "stay away from me", but hey, at least I didn't have to take any classes from him.

But college is another chapter, and I'm not quite done with high school yet.