When you do get face to face time with students, don't teach a large group.
Everything you want to teach is already online.
The only goal of meeting students is talking to them individually or in small groups to:
  • understand what they feel
  • transmit your passion for the subject
and letting them do the same amongst themselves.
If you talk to a large group, you will only reach / understand a very small percentage of the group, so your time is wasted.
It is better to deeply understand what 25% of the students feel and adapt the course material, than to talk to everyone at once, and have only 5% understand anything.
Divergence by Ciro Santilli 37 Updated 2025-07-16
Takes a vector field as input and produces a scalar field.
Mnemonic: it gives out the amount of fluid that is going in or out of a given volume per unit of time.
Therefore, if you take a cubic volume:
  • the input has to be the 6 flows across each face, therefore 3 derivatives
  • the output is the variation of the quantity of fluid, and therefore a scalar
Set function by Ciro Santilli 37 Updated 2025-07-16
This section is about functions that operates on arbitrary sets.
MOOCs are a bad idea. We don't want to simply map the pre-computer classroom to the Internet. The Internet allows, and requires, fundamentally new ways to do things. More like Stack Overflow/Wikipedia. More like OurBigBook.com.
Ciro Santilli believes that there is a close link between the ability to create disruptive technology, and the desire to find bugs/exploits in systems.
Both of them destabilize society and enterprises.
Some examples:
And yes, this sometimes leads into a fine line between legality and illegality:
Control theory by Ciro Santilli 37 Updated 2025-07-16
This basically adds one more ingredient to partial differential equations: a function that we can select.
And then the question becomes: if this function has such and such limitation, can we make the solution of the differential equation have such and such property?
It's quite fun from a mathematics point of view!
Control theory also takes into consideration possible discretization of the domain, which allows using numerical methods to solve partial differential equations, as well as digital, rather than analogue control methods.

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