There are two schools of thought about whether it’s fair to take the piss out of the things that students write in exams and homework. I belong to the correct school of thought, which states that as long as the perpetrators remain strictly anonymous, this kind of thing can’t do any harm and may occasionally, by exposing tempting errors, do a wee bit of good. I also feel that in these days when our teaching — whoops, our enhancement of the student experience — is supposed to be student-centred, research-linked (or was that “linkaged”?), constructively-aligned, vertically-integrated and generally pegged down by clumsily constructed compound adjectives, we need all the relief we can get.

In this spirit, I propose the establishment of a new journal. Undergraduate Advances in Mathematics will exist to disseminate the very best in student-led mathematical thought. To qualify for publication, a contribution must not merely possess original daftness: it must also have immediate and significant consequences for the rest of the discipline. So, mere algebraic blunders aren’t acceptable, but the Law of Universal Linearity, if it weren’t so well established already, certainly would be.

To illustrate what I mean, here’s a recent contribution from a student on a classical mechanics course, which demonstrates how to get from classical to quantised variables in a single quantum leap. The problem concerns a particle accelerating from rest under the influence of a force $F$. The reasoning proceeds thus.

The kinetic energy is equal to the work done, so

$\dfrac{1}{2}mv^2 = \textrm{Work done} = \displaystyle\int F$.

But we also know that

$mv = \textrm{Impulse} = \displaystyle\int F$.

So far, so usual: neither the lack of vector notation nor the failure to specify a variable of integration is unusual. It was the next blithe statement that impressed me:

Therefore $\dfrac{1}{2}mv^2 = mv$ and so $v = 0$ or $v = 2$.

(The student then proceeded to work through the rest of the question on the basis that $v = 2$, independent of $F$ or any other element of the problem. I can’t remember why s/he discarded the other root, which would have offered a still more powerful simplification, but it rarely falls to the originator of an idea to be its perfector too.)

More examples will be posted, I fear, as they are received.