I often have occasion to wish that more programmers and software engineers knew about things like probability densities...I rarely wish more programmers knew more calculus.
Does anyone else notice the contradiction here? This is a perfect illustration of my point: a "probability density" is a function whose integral gives you the probability. In fact, not only is the very definition of the object logically dependent on calculus, but understanding why the object exists requires knowledge of measure theory (specifically the Radon-Nikodym theorem).
...which, come to think of it, is not surprising given that measure theory is required to define "probability" in the first place!
Yes, mathematical education is extremely screwed up. But the usual complaints and controversies don't even begin to get to the real issue, which is that people can go through education in mathematics without appreciating the power of abstraction or understanding the need for the ideas in their head to form a coherent logical structure.
Ironically (in view of the parent comment), the solution is probably to teach computer programming! I don't know anything about programming myself, but my impression is that this is exactly the kind of thing one needs to "get" in order to be a good programmer.
I meant that at, perhaps, a more basic level. Taboo "calculus".
If you ask a programmer for an "estimate" (most often, of the time a given task will take) everyone thinks it natural to give you a single number.
That's what I did along with everybody else. It came as a shock to me the first time I stumbled across the idea of expressing estimates with degrees of confidence: that is, my 50% confidence estimate should be such that half of the time I'd be early and half of the time I'd be late. (To many a programmer, the notion of finishing ea...
This guy says that the problem is that high-school math education is structured to prepare people to learn calculus in their freshman year of college. But only a small minority of students ever takes calculus, and an even smaller minority ever uses it. And not many people ever make much use of pre-calc subjects like algebra, trig, or analytic geometry.
Instead, high-school math should be structured to prepare people to learn statistics. Probability and basic statistics, he argues, are not only more generally useful than calculus, they are also more fun.
I have to agree with him. What do the people here think?