what I've seen of khan academy is pretty cursory as far as the math goes (about enough to get through an introductory course, usually), and that seems intentional. There are definitely a few gaping holes in the curriculum, such as no wronskian in diff eqs. And nobody really learns a mathematical concept until they've been confronted with something significant they couldn't do with it immediately, yet conquered it.
Teaching advanced math, on the other hand, is really hard to do when you're interacting with a person because there are so many pitfalls and if you hit even a single one you can't usually continue until you've tracked it down. Khan Academy has material on all sorts of non-math stuff, like economics and other sciences, and they seem to be gearing the math stuff more towards a younger audience, not an older one, which is probably more important anyways to be honest. smart move, mr.Khan, smart move.
if i work for facebook and i want to figure out something about my users, isn't it safe to say N = All since the data im accessing is all user data from fb?
it's easy to go wrong with big data, and although the article glossed over some fairly important things (assuming the people who work on these datasets are much dumber than they are in reality), they're right on about idea that the scope and scale of what big data promises may be too grandiose for it's capabilities
Whilst, in the example you provide, it might be the case that "N = all", the cautionary tale offered in the article is that you always need to make sure you are asking the right question, and it is pretty easy to confuse yourself.
So you said "if i work for facebook and i want to figure out something about my users", and for whatever you were doing, looking at your existing user base might be the right thing to do. Perhaps, though, you actually want to know something about all your potential users, not just the users you happen to have right now. Whether or not your current user base offers a good model for your potential user base would then be a pretty important question, and one that almost certainly isn't answered by "big data".
I think that, as with most of statistics, the key point is "think about your problem", and that focusing on a set of solutions rather than the problems themselves can get in the way of that.
Even if you have the full population in question and thereby avoid sampling issues, you still have a lot of pitfalls. For example if you just start correlating every variable against every other one and picking out ones that hit some test of statistical significances as "findings", you run into a range of familiar problems generally grouped under the pejorative term "data dredging".
At first I thought so too. But it's actually easy to come up with cases where N != all. As a radical example, Facebook preserves the accounts of dead users.
YC didn't invent startups, and everyone should be able to do something they actually want to do all day at least once. And for their benefit it should be in their 20s.
The distinction between 'observational' and 'historical' is a matter of political and social convenience.
Consider carbon dating. Since it's been observed, we should assume it's observational. carbon dating indicates that dinosaurs existed hundreds of millions of years ago instead of mere thousands. but that's historical and therefore this is a contradiction, so we can't assume the distinction.
the only logical conclusion is that we have a false premise.
Minor nit pick here, but carbon dating is not used to date fossils and rocks because C14 has a half-life of only ~5k years. With such a short half-life, the C14 all decays away to trace levels in only a few tens of thousands of years.
Other radioactive isotopes with much longer half-lives are more appropriate for geologic dating. The U-Pb system is really good for most geologic applications.
I think that's an uninformed metaphor because it assumes both math is totally foreign and should be able to be read by anyone. if you write code for a server that handles HTTP requests you wouldn't explain the guts of HTTP in your comments, you'd just assume if the reader wants to know more they'll figure it out themselves.
I think sometimes mathematical definitions, especially advanced ones that rely on simpler definitions, are too complicated/long to recant every time you use them, which you have to. If I want to prove something relating or relying on uniform continuity I don't want to state the definition every time both because its repetitive and because definitions often use the same notation, so I don't want my uniform continuity deltas and epsilons getting confused with my normal continuity epsilons and deltas. Try proving advanced things about field extensions and galois theory using induction like that and you may actually run out of symbols.
That being said it is hard to read real math writing/research which can be both dense and obtuse even if you're used to it. Maybe that's why you need a PhD to consider entering the field.
It merely assumes that his co-workers, who did not fluently speak mathematical notation, should somehow learn a foreign language to keep up. I find the idea of being obtuse toward a co-worker who does not speak the same language someone I would have reservations about working with, myself.
I went to highschool with this guy at CRLS and after going there you know your miranda rights as well as exactly whats legal and whats not. they make sure of that, and that he'll stand up for them. weather the FBI cares or not is beyond our hands reach at this point
check out the animation