/sci/ - Science & Math

fun(ctional) anal(ysis)

>>10321838
You don't have to, but they're just named that to attract normies.
I especially recommend Weapons, it's mostly about data science and shit. Cathy herself was a mathematician with a phd researching at MIT (in algebraic geometry if i remember correctly) and moved out to do data science for a variety of companies. The book is all about how modern data science and ML methods are riddled with issues and social implications, and tons of concrete, explored examples of where those implications are popping up today.
It was especially satisfying as someone who is always looking for more reasons to shit on MLtards.

>>10200092
"the amount of stuff that's leaving the walls of a factory is equal to the amount they're producing inside the factory"
"the amount of water a cell uses and consumes is equal to the amount entering through its membrane"

a surface integral measures how much the vector field is exiting the surface. so if it's tangent to the surface, for example spinning around the surface, the surface integral is 0. if it's pointing out of the surface, the surface integral tells you how much is "leaving" the interior. if it points into the surface, the integral is negative and tells you how much the vectors are entering. if it's mixed, the sign of the surface integral will tell you whether more leaves or enters. this is called the "flux" through the surface.
the divergence theorem says that the amount leaving a surface is equal to the amount produced in the interior (or the amount entering is equal to the amount consumed). this is pretty obvious, since if stuff is leaving then you know it had to come from somewhere inside. but the divergence theorem is a way of stating that properly.
don't think about it too hard.

stoke's theorem is similar, it tells us that the amount that the vector field spins around a surface is equal to the amount of spinning going on inside the surface. very similar to divergence theorem but with a surface integral which measures how "tangent" vectors are and with the curl in the interior.

green's theorem is the 2 dimensional case of stoke's theorem, or of divergence theorem, depending on which form you're looking at. but really, they're all the same thing.

>>9352020
91 :^)

Number theory is for fucking bitches.
Literally meme pop math.
It's a joke that people care so much about PWIME NUMBAHS :D *drools*