Wednesday, January 20, 2010

Yes, you will need to know this in your life

There's no such thing as a useless field of math.

As someone that loves mathematics enough to get an undergraduate degree in it, I am often frustrated by a world of people that are oddly math-illiterate and strangely, shamelessly proud of this! I don't have statistics on hand, but I wonder how connected this math illiteracy is to the current financial and banking crisis, where part of the problem was people took out loans they couldn't understand.

Part of this seems to be the weird belief there are two jobs out there: math track jobs and non-math track jobs. In reality, everyone benefits from math and it opens doors to new careers. Here's a solid expectation for American education: it's a failure if every kid can't speak a second language or at least do calculus.

I expect this kind of attitude from smartassed kids that wonder what it means to their lives, and politicians, but it's a little surprising at times to hear from math teachers too! I grew up at the start of the era of "New Math" instruction, and one thing that we learned was matrix mathematics, a key tool of linear algebra and linear transformations which involves a rectangular array of numbers, each of which are called "elements." This is occasionally pointed to as the
epitome of useless experimentalism on the part of educational psychologists.

I'm gobsmacked to hear this from educators because this is actually a skill I use in my life!

Here's just one area where you may need to know matrix modelling in your life: electronics. One of my hobbies is electronics. Nothing beats a lazy afternoon tinkering on a breadboard with a multimeter and logic probe in hand!

In circuit design, determining resistance to current comes from figuring out either the sum of resistor component values (expressed in Ohms, not to be confused with Watts, a unit of power) as in series circuits (those arranged in a straight line) or in the case of parallel resistors, where the current splits between the impedance elements and flows on the path of least resistance.

Since many circuits use various kinds of resistance elements, figuring out total equivalent resistance can get pretty hairy, because voltage is a relative factor. It can be different at various points along a circuit.

Enter matrix models! A simple way to determine it at various points in a circuit is to create two 2 x 2 matrix models, one with input voltage, input current, output voltage and output current as elements, and another matrix model with four elements: impedance, admittance, and two dimensionless qualities.

Did you get all that? Okay, even if the vocab is a little intimidating, there's no reason to be nervous about them since how they work is relatively simple: all you have to do is multiply the two matrixes together! This is one example where math is the universal language. Even if you don't know your impedance from your admittance, you can actually still figure out how it works if you know the process!

In fact, come to think of it, in a hobby as entertaining as electronics, math is everywhere! When working with alternating current, some trigonometry is necessary, for instance, because you're handling a sine wave, as current strength changes and switches many times per second, so a single value just can't be given.