Stochasticity x Determinism in elementary math

Most of the problems I'm having in studying theoretical topics nowadays stem from the fact that I've had null measure content of Statistics as a math student. I've seen interesting topics as Analysis, and Differential Geometry in undergrad, and useful stuff like Linear Algebra and Computational Linea Algebra in the masters course, but absolutely no Probability and Inference.

Nothing related to Data (not the android) at all. And this is mostly my fault. I knew before the Masters Course I wouldn't be pursuing a PhD in Math, and I knew my Math teachers wouldn't deal with topics I would most likely need in the near future (the one I'm living now).

I'm chasing the lost time, with books in Bayesian Data Analysis and Inference, but I although most of the times I understand what I read, I never seem to grok it. I will, certainly, in time, but time is a commodity a grad student doesn't have - I need Statistics now. As well as Biology, Ecology, Evolutionary Biology, and (why not?) a little Computer Science. So it's fair to say I'm chasing the lost time, and losing.

Prior to leaving I've seen the creation of a new undergrad course, Applied Math, in my former University; it started with concentrations in Finances, Mathematical Biology and Scientific Computing, and it soon became obvious to the faculty that some basic knowledge in Probability and Inference were a must, so it's been introduced as obligatory courses for all concentrations. My former advisor there told me he thought it was overkill at first but soon (in the first year or so) realized how suitable it was.

This is why I think it's a terrific idea (definitely worth spreading) this nice Arthur Benjamin fella presented on this talk on TED.



Obviously I don't think you should rip out everything related to Calculus (I like it, after all :) ). If you are really to grok Probability, you need a strong base in Calculus (from integrals, to maximizing Likelihood functions). But a change in paradigm is definitely well deserved. Our modern western societies are still studying according to old rules. Rules that fit well to the time and reality where they were idealized, but probably are just outdated now. We are a new society on overdrive, with a new (still changing) set of moral rules, new problems and challenges, new perspectives, new age limits. Why stick with the 19th century education philosophies? At least let's realize it's about time to discuss if it's worth changing it. See also another TED talk on this subject.

This all also brings an old question I've always had: is it a good thing that education curricula should be centralized? It's good to know beforehand what people must (might? should?) have learned looking at their curriculum. I'ts useful for the teacher/professor to know what to expect the student to know, and this also applies to the student. I've been bitten before, when the pre-requisites for a course weren't clear. I also have first hand experience of how good and dynamic an improvised class can be, when given by a motivated (and skilled) professor. OTOH, I also have firsthand experience in improvised classes that sucked.

Which is the lesser evil?