note that this is just part 1 of 4.
(I am assuming you didn't read all four parts, because that material would have to be covered impressively quickly to fit in 20 minutes)
We certainly did changes of basis and arbitrary dimensional rotation in our first lecture. We didn't do quaternions, and in fact never did in the context of these sorts of things.
Of course, we had done basic vectors and matrices in secondary school - we certainly knew how to multiply N dimensional matrices, and were expected to invert 2-D matrices by hand and compute the determinant of 3-D matrices. They were on the final exam.