An Apology to My Math Teachers

At this point in my academic career, I feel I owe an apology to every math (and a few physics teachers) I have ever had. At some point in every math class (any my optics classes in college) that I said, either to myself or to the teacher directly, "I will never need this once I finish this class."

Pride goeth before the fall, right?

To date, this is the list of things that I can remember saying I'll never need, and have subsequently found that yes, you do need these things. In fact, most of them are my bread and butter these days:

1) Algebra: solving systems of equations for multiple variables, factoring, expanding and finding roots.

3) Geometry: Mostly the reasoning skills, and some stuff about angles. Learning to use a compass has come in oddly handy.

2) Trigonometry: pretty much everything I can think of. I yell at my own students to learn the unit circle, "All Seniors Take Calculus" comes in handy all the time, and I can't remember the last thing I did that didn't have a trig function somewhere. Also useful for fitting furniture in a car.

3) Calculus: Um, everything. How to do integrals by hand, partial fractions method, complete the square method and integration by parts, all of which I said "I'll get computer to do this", I now do by hand, because the computers don't do it correctly. Calculus in general I'm using a whole lot more than I ever thought I would.

4) Differential Equations: if I had known I'd be dealing with them so much, I would have paid a lot closer attention. They are everywhere, and I have to relearn a lot of stuff from scratch because I seem to have purposely forgotten it all.

5) Optics: I swore the day I finished my first optics class that I would never ever ever use this stuff. It was stupid, useless and boring. Yeah, about that...

If anyone in school is reading this, take it from me. You will end up using this stuff. One way or another it will all come back to haunt you, especially if you tell it you'll never need it.

To any teacher who finds this, please accept this, my own personal apology, for not believing that this stuff was important. Doesn't matter if you taught me or not. To the great collective of teachers past, present and future, I was young and stupid and so are the kids you teach. They just figure out you were right too late to tell you so. Thanks for teaching them anyway.