@Will. Fair. I see in the first line of the FAQ that this is for "research level math questions". I wouldn't have asked my question here if I'd read that first. Thank you for the pointer.

...I was not asking anyone to be a slave. Maybe answers would have been too system-idiosyncratic and closing the question was the reasonable thing to do. But I don't think my question was a priori unreasonable. I may be reading some of these responses wrong, but they give me the feeling that academic elitism is alive and well here.

Thanks to those providing constructive feedback. I have to admit I'm bothered by some of the responses though. I suppose there's no substitute for knowing set theory, but we go ahead and learn to count. I suppose there's no substitute for knowing how the internal combustion engine works, but we go ahead and drive cars. Sure, knowing numerical analysis would improve my programming greatly, but I was inquiring about a few basic rules-of-thumb that would improve it marginally. I provided a couple examples that, for me, helped serve that end. I thought others might have some as well...

So maybe I should ask this specifically for, say, R over on the StackOverflow board?

@Sridhar. It's not a dot product. It's element-wise multiplication.

@Henry: e.g., in R, even though x^2 and x*x return the same, length-n vector, the former is computationally more burdensome.

@Robert. VERY useful. I must get Maple (or Mathematica). Thx!