Starting off

Introductions first: I’m a third-year graduate student in Applied Physics and Aerospace Engineering. I originally envisioned becoming a Teaching Fellow to help out in a physics class, a plan which persisted right up to the pairing meeting, when I first realized that physics was not an option this year and that I was in the “math” group. Interesting…

I remember not being terribly fond of math in high school or middle school. Algebra, geometry and statistics were all merged into a three-year integrated sequence in our high school (Plymouth Canton School District, quite nearby), and they were pretty easy, though how interesting they were was largely a function of the teacher’s charisma. I got lucky – in a three year sequence I got two good teachers. Precalculus was a dud, both because it was impossible to believe I would ever need most of that stuff (oh, how wrong…), and because the teacher couldn’t control a class so it was mainly a social hour. AP Calculus in my senior year was one of the first times I remember going “whoa” and really getting my hair blown back with something I wasn’t expecting.

Think back to that time; put yourself in those shoes. You’re pretty good with manipulating this ‘x’ character, you’ve got a handle on things like sines and cosines, though they seem to be taught all out of proportion to your opinion of the relative importance of triangles in the world, and if you had to you could muster some proofs of whether two triangles are congruent or merely similar based on a few axioms. Not bad.

Now we’re going to do two fundamentally new and different things. First, we’re going to take the old, and boring, formula slope = rise /run, and we’re going to give it a twist – if we go slowly enough, and keep track of exactly where our delta-x’s are, the same method of rise / run that worked for straight lines will work for curves. Meaning, even though it makes no sense to think of the slope of a curve (wait…curves have different slopes! they change! that’s not allowed!) if we’re careful and walk the line between not thinking about it and thinking too much, the math will work out and give us…something different. Something that we don’t yet fully understand, that doesn’t fit into our intuitive grasp of things. The slope of y=x^2 is 2x, because it’s variable and changes everywhere, but can still be described. This dovetailed nicely with taking algebra based physics my senior year, by the way. You could just tell that the mathematics of continuous change would eventually come in handy in physics where things are always moving. Second, we learned to add up an infinite number of infinitesimal pieces. I don’t think I realized it at the time, but this one is just as crucial as the other one, though there was no similar “eureka” moment to the formal definition of the derivative.

So, here I am, ambivalent about math for math’s sake, but as an engineer and a physicist, I use math all the time for real things. I probably know more math than 99% of the population, but it’s not like it’s my favorite thing to talk about at parties. The math only ever gets interesting when it describes something physical, something real.

What does all this mean? Why start a blog about my position for the next year with a post describing my mixed feelings about it? Because that’s what makes me exactly right for this job, ultimately. These kids are me writ small. For as long as I can bring something real to the table, something to convince them that someone, somewhere who is not teaching or taking freshman algebra or senior statistics still does stuff that will blow their hair back, I may get their attention. So let’s begin.