Mefi, thanks for that article, it illustrates the point I tried to make that when I had a crap teacher one year, I had to battle the next year to understand new work, and the problem got exponentially greater every year.

De nada, Spike—and thanks for you-know-what. ;) (It’s possible that I’m reaching here, but I don’t think so.)

I had two disturbing encounters with Unisa about 25 years ago, one with the Statistics department and the other with the Mathematics department. Needless to say, those episodes are quite pointed and relevant in the context of this thread. The first involved an assignment where the inversion of square matrices was required as part of the solution. The marked and returned assignment bore the red-penned comment, “I don’t understand but you seem to know what you are doing.” I had used a matrix inversion method (the

adjoint-determinant method, if you must know) which is particularly efficient for 2×2 and 3×3 matrices—so much so that with a bit of practice, one can do the inversions in one’s head. Clearly, whoever had marked the assignment wasn’t anywhere near the top of their game. (At the end of the year, I visited the department head and showed him this mini-fiasco. To his credit, he expressed appropriate alarm once I’d shown him the evidence.)

The second bonce-bumping was with the department head of Mathematics. At the end of an aced assignment, he’d written a challenge for me to see what I could come up with regarding a specific theorem of

kernels, image spaces and projections for vector manifolds. With the next assignment, I sent a rigorous, separately enveloped, proof of my own devising for the theorem in question, specifically addressed to him. His response? Basically, that I had “a tendency to overcomplicate things,” followed by what was no less—and certainly no more—than an exercise in hand-waving and (admittedly educated) intuition about the theorem—precisely the approach that mathematics abjures. To be fair, such educated intuition is a remarkably fruitful source, but it should be obvious that passing this practice off as a valid source of subject advancement to a student kinda subtracts from the purpose of attending the courses in the first place: Learn the rules first; you can always work around them later, but to do so, you have to know them well.

'Luthon64