[maps]

How about stop trying to take shortcuts and have an actual rigorous progression? It sure would help out on problems of statistical errors in scientific literature, Sure not everyone might be able to pass these classes, but that is kind of the point. Why do we want to just pass through students with weak to no understanding? Ah yes tuition fees.

[alexhutcheson]

Most students don't need the full rigorous understanding that a multi-semester deep dive into probability theory and statistics would provide. It would be nice to know, but there is a significant opportunity cost, since they could be spending that time diving deeper on their primary subject area.

[swiley]

Having an argument for why rather than just being handed a formula helps me. I don’t see why people think this would make it harder.

[chongli]

Because the “why” of statistics has many turtles before you get to the bottom. Measure theory, topology, real analysis, abstract algebra. You need to learn a lot of math before you get a complete picture of the theoretical underpinnings of modern probability theory, which forms the foundation of all of statistics.

Most people just want to calculate a P value or a 95% confidence interval for the mean of whatever they’re researching. They’re not interested in how it all works.

[adrianN]

You need a bit of analysis, but I'm pretty sure that you can understand p-values for normal distributions of a single variable without abstract algebra or topology. Understanding simple cases from first-ish principles makes it much easier to swallow handwavy explanations for complicated stuff.

[soVeryTired]

You can't understand the why of the normal distribution without Fourier analysis though - which is pretty heavy going for anyone who's not hardcore science or engineering.

[adrianN]

Can't you introduce the normal distribution as the limit of the binomial distribution? I think you can prove the central limit theorem without using terribly advanced math.

[chongli]

That's only the most limited version of the theorem which has since been renamed the de Moivre-Laplace theorem [1]. The rabbit hole goes much deeper when you talk about the most general form which works for any set of independent and identically distributed random variables, not just binomial random variables.

[1] https://en.wikipedia.org/wiki/De_Moivre–Laplace_theorem

[swiley]

Fourier analysis is not that bad. Most kids in the calculus class at the university I went to had the basics of that explained to them.

[madhadron]

I'll bite. Why do you need Fourier analysis to understand the normal distribution?

[soVeryTired]

The only proof of the central limit theorem I know of relies on it. Iterated convolutions tend toward a Gaussian. Essentially you take the Fourier transform of any nice probability distribution, do a Taylor expansion, and Bob's your uncle.

Another child poster pointed out that in special cases (like the limiting case of the binomial distribution) you can get away with other arguments. And you can certainly 'prove' it via simulation. So maybe you don't need the full generality of Fourier analysis in the end.

[mikorym]

This dichotomy seems almost insurmountable today.

1) Mathematics majors should be taught how to prove. 2) Engineering/Applied Math majors should be taught to use.

Fortunately or unfortunately they take the same classes. Personally, I think the obvious solution would have been to just take whichever classes you want to and to get "a degree" once you fill some sort of criterion. But the CAs and actuarial scientists, uhm basically everyone, don't want that human resources headache to actually read through someone's CV patiently and ask a few patient questions.

[commandlinefan]

Well, why not both, really? We’re talking about four years of education - is it really that hard to learn proofs and applications with four years to spend looking at it?

[mikorym]

I don't think the current system is abysmal or anything like that—I don't think I am that vociferous or opinionated—but what I do think is that in your first and second year it is likely that you don't know yet whether you want to go the "applied" route or the "abstract" route.

So you might drop out of either of the two by year two and so you don't have the full four years. [1]

[1] In South Africe, a bachelor's degree is three years. I don't know whether this is a good or bad idea, but that is how it works. Your fourth year is called "honours" and is a separate degree.

[soVeryTired]

Sounds a bit like arguing that in order to use a programming language you should be able to build one. Not incorrect, but not very practical either.