437 karma · joined June 22, 2016
I mention this because I think that the whole idea of political "invention of tradition," while it has lost currency because it seems to reflect poorly on anti-colonial nationalist movements, is far more interesting than that of "random people making up stories for gain."
so it's not that the basics are intellectually difficult as much as practically difficult (unfamiliar, disorienting) for many students. many "transition" books talk about the difficulty in adjusting from talent being redefined from perfectionist "plug and chug" (APs, SATs) to reasoning and creativity.
btw, i'm impressed that you could master college-level proofs at 10. i have a kid about that age who is pretty good at logical reasoning, but i'm not sure what topic (at that level) he could do a rigorous proof about; maybe numbers, as in landau? can you say more about the materials you used?
to me, memorization means to recall the important parts of something accurately and precisely so that they can be used fluently. that is not to say textually (rote memorization). i do not think it is enough to say "well, that's what learning is" because i doubt most people learn most things to that level.
however, i made my comment because i think i disagree that spaced repetition has no place in learning. i think that if you dig around in the Polar guy's earlier comments, you'll find threads where folks like michael nielsen are talking about using spaced repetition tools for much more than purely textual memorization of theorems - basically, cycles of repetition and (re)synthesis. so i don't feel it's right to completely shut him down about card decks. you may disagree, of course.
but false in the sense that doing math requires fluency - in applying a small amount of technique up to lower division math, and in applying a large number of definitions/results after that. in areas like abstract algebra, failing to memorize will kill you. it is as disfluent as writing text in a foreign language without having memorized the working vocabulary and grammar; even if you can eventually recall, derive or look up what you need, it's just not practical to work like that. (and i say this as someone who prefers to mentally index information rather than memorizing...)
but as madhadron says, you can't read/write proofs of upper division or graduate level math without the "foundations" material, which includes naive set theory.
do you need any of that to do engineering math? well, there are a couple of standard quotes, relating to the fact that the technique taught is brittle, in weird and subtle ways. the claim is that understanding the proofs tells you what the limits of applicability are.
"[F]or more than 40 years I have claimed that if whether an airplane would fly or not depended on whether some function that arose in its design was Lebesgue but not Riemann integrable, then I would not fly in it." - richard hamming, "mathematics on a distant planet"
"It is customary to begin courses in mathematical engineering by explaining that the lecturer would never trust his life to an aeroplane whose behaviour depended on properties of the Lebesgue integral. It might, perhaps, be just as foolhardy to fly in an aeroplane designed by an engineer who believed that cookbook application of the Laplace transform revealed all that was to be known about its stability." - tom korner, fourier analysis
on most ships, the air search radars are on masts or platforms well above where any people work while underway. but on US AEGIS ships (CG 47, DDG 51), the pilothouse is located above the phased array panels. however, all of the arrays are on the outside of the blocky superstructure, pointing AWAY from the pilothouse. (there was a quote in that message about not leaning over the rails when standing on the bridge wings!)
the navantia design and derivatives (including the Nansens) did not take up this idea. presumably because they're smaller and needed the stability, but i'm just guessing there.
it's actually consistent with the NHST paradigm to treat any given result with skepticism; the degree of skepticism depends on many things, some of which are statistical and some of which are domain-specific. but skepticism is not the same as assuming invalidity. imperfect experiments are still (expensive) evidence for something.
imo, what you should reject entirely are media reports (usually based on somebody's PR team) that try to tell you to do anything based on one study or the work of a single lab.
i've recently taken upper-division/graduate courses in math, stats, EE and CS at three different US universities. 100% of the courses used piazza, because professors and TAs don't want to pollute their inboxes with questions and most questions end up being answered by students. it's not great, but it supports latex math (!) and its discussion features are much better than canvas (which tends to be the default, officially-blessed system these days).
membership in courses (and hence institutions) is usually managed by the instructors based on university email. "social network" features are pretty basic (based on courses, institutions, and contacts) but definitely exist.
i imagine the main draw for employers is that it's a nearly universal pool (for certain majors) of opted-in university leads with relatively reliable major/institution/coursework data for filtering.
"raid" might not be the best word choice, but given that students "have to" sign up to get course help and will probably manage to click on the opt-in careers button at some point, i can kind of see how people can see this pivot as skeevy.
imagine a house with small children (who are not good at personal hygiene) as a tiny cruise ship which you can never fully disembark, and then when the cooking/cleaning staff (parents) get sick, things get really ugly.
it's generally easier to clean the hard surfaces in your house (with harsh stuff like bleach wipes) than to clean the soft surfaces. that's presumably why she focuses on the laundry infection vector.
even at stanford, perhaps. i was astonished to see that a stanford junior is the listed instructor for EE 364A (a PhD level course in convex optimization, aka CS 334).
that's why i think there's an interesting story lurking here. there were probably a small number of technocratic players involved (maybe even one) who were able to specify how the chain should work.
this instance appears to involve longer-range links and SDRs (in this case, the ettus USRPs).