One of the most difficult things for me to do when I am learning is to make the conceptual leap from one idea to the next. Often, I’m not confused about how to do a problem. Rather, I’m stuck on an idea that preceded it which I am not fully on board with.

A common thread I see between many young students who don’t seem to “get” mathematics is that they aren’t told to look at the way they are taught mathematics as only that: a way. Unfortunately, the impression that is made on them is that mathematics is a strict set of rules that cannot be broken and must be followed every moment.

I find it incredibly disappointing that so many people in the general public seem to regard people who use mathematics in their profession as “number-crunchers”. Each time I hear someone say it, I die a little on the inside (even though I know they mean it in a good way). It’s as if the only notion of mathematics that these people have is that one does arithmetic. In my mind, it’s like saying that all a photographer does is take photographs or that a businessperson only makes calls all day for deals. It’s a narrow-minded view of any of those disciplines, and it gets a lot of it wrong.

If you’ve ever taken a physics class on waves, the first type of mathematical wave you learn is the one due to what is called simple harmonic motion. The idea is pretty simple, so I’ll go through a rough derivation here.