A set of theorems that prove under different conditions that the Fourier transform has an inverse for a given space, examples:
As shown in Video "Simple Groups - Abstract Algebra by Socratica (2018)", this can be split up into two steps:This split is sometimes called the "Jordan-Hölder program" in reference to the authors of the jordan-Holder Theorem.
Good lists to start playing with:
History: math.stackexchange.com/questions/1587387/historical-notes-on-the-jordan-h%C3%B6lder-program
It is generally believed that no such classification is possible in general beyond the simple groups.
Ciro Santilli has already watched all the best films in history, and as a result any of those new movies that is full of clichés and has no innovative aspect at all (99.99999% of all modern movies) makes Ciro want to puke and to start Googling TV Tropes to classify as many clichés as possible.
Good movies are those that teach you mechanisms of the real world. Willing suspension of disbelief must be maintained at all costs.
Love is not an interesting aspect of the world. You solve your love life at university, Tinder or Tango.
The actually interesting aspects of the world are:
The Sliding scale of idealism vs. cynicism must be close to Cynicism max at all times. Movies with pure good and pure bad are shit.
How LEDs work by VirtualBrain
. Source. 2021. Good 3d schematics clearly explaining part of the LED electronic package.Exams as a prerequisite for a degree are useless. Exams as part of a degree must be abolished. And degrees must be abolished. Ultimately the only metrics that really matter are money and fame. See also: motivation.
The only thing exams should matter for is as a screening tool to select people with specific abilities that you care about as an employer or principal investigator. If:then exams are useless for your purposes. then might as well just go by interviews (basically what all employers do already, though not PIs). Degrees are too course grained to mean anything to anybody. Employers and PIs likely only care about very few specific subjects.
- you have no idea about what the content of specific exams are (and you don't because they are all ad-hoc university secrets)
- or don't have a way to machine learn what grades correlate with your desired performance (you don't because where's the data?)
Once the question of an exam has been formulated, the usefulness of the problem is already been completely destroyed, because formulating the problem that matters is the most important part of things. And any problem with an answer, is useless to put effort into: give answers.
Furthermore, preventing people from searching for answers while answering an exam, AKA preventing "cheating", also makes absolutely no sense. In the real world, we want people to find answers as quickly as possible! We should be teaching people how to "cheat"! What we should teach them instead is what a fucking license is, and what you have to do to comply with it.
And if you must absolutely have exams, they must be open to anyone who wants to applies. Then people have to pay to take the exam, with subsidies for "official course takers", who are spending 100x more anyways due to not living with their parents.
And those exams must be applied by professional test application companies to ensure no cheating and to factor out the anti-cheat work, while still making the tests available to people anywhere.
A quote from Richard Feynman present in the book Surely You're Joking, Mr. Feynman chapter O Americano, Outra Vez!:
The only metric that matters is "to feel that you've satisfied youre curiosity". When one studies for that, it can take a lot more time to actually learn everything, because it is sometimes not as clear when you should stop. But it is the only way to go deeper.
The bane of multicellularity.
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