Thursday, July 19, 2018

Understanding Math vs Understanding Math


One of the things hard about engineering — electrical engineering, in particular — is that you can’t really visualize what’s important. Sure, you can see a resistor and an LED in your hands, but the real stuff that we care about — electron flow, space charge, and all that — is totally abstract. If you just tinker, you might avoid a lot of the inherent math (or maths for our UK friends), but if you decide to get serious, you’ll quickly find yourself in a numerical quicksand. The problem is, there’s mechanically understanding math, and intuitively understanding math. We recently came across a simple site that tries to help with the latter that deserves a look.

If you don’t know what we mean by that, consider a simple example. You can teach a kid that 5×3 is 15. But, hopefully, a teacher at some point in your academic career pointed out to you what the meaning of it was. That if you had five packages of three items, you have 15 items total. Or that if you have a room that is five feet on one side and three feet on the other, the square footage is 15 square feet.

That’s an easy example. But as you get higher into math it is more common to just use a result and not really understand the why of it.  For example, you’ve probably heard of convolution and you know it has applications in digital signal processing among other areas. But could you explain it to a 9th grader? Using a combination of animations and graphics, the author takes you through not only what convolution does, but how you arrived at it and some applications. There aren’t many topics on the site, but the detail on each that is there is great. There are topics on algebra, calculus, complex numbers, and a great pair of articles on the Fourier transform. There is even an article on a different way to think about multiplication that lets you factor things graphically!

We love sites that make math more understandable. We enjoyed solving equations with colors, for example. And we couldn’t stop watching the visual representation of the creation of square waves with harmonically-related sine waves which effectively demonstrates the Fourier transform.
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