Abstract nonsense

I spent hours trying to figure out what my students were trying to prove — I knew the questions, but the answers made little sense.

The problem is that they’re focused on doing computations, and for that they use letters, letters, letters… none of them they introduce before use!

Worse, sometimes they will fix, say $x>0$, then later on consider a function $x\mapsto f(x)$… which means a collision!

Even worse, since they’re just toying with letters, they don’t have issues applying a function defined on reals numbers to a complex number or a high-dimensional matrix…

So my current job is to beat some sense into them and have them define things before use, and define as little as possible. This way, when they’ll have the real, serious test at the end of the year, they won’t have ridiculously low marks just because their proofs don’t look like proofs.

If only they had more computer science to do with me, I could try to push them in front of languages which won’t let them use variables without declarations, won’t let them apply operations if they don’t make sense, and won’t let them reuse the same variable in the scope of another!

But I only have them for a little maple work (sigh… unfortunately, xcas or maxima aren’t an option for them), and they have a very hard time just writing a simple function to loop over an array, so I can hardly make use of a compiler to suffer instead of me : I’ll have to do all the complaining myself.