Cycle of an element of a group Updated 2025-07-16
Take the element and apply it to itself. Then again. And so on.
In the case of a finite group, you have to eventually reach the identity element again sooner or later, giving you the order of an element of a group.
The continuous analogue for the cycle of a group are the one parameter subgroups. In the continuous case, you sometimes reach identity again and to around infinitely many times (which always happens in the finite case), but sometimes you don't.
A Mathematician's Apology Updated 2025-07-16
With major mathematicians holding ideas such as:it is not surprise that the state of STEM education is so shit as of 2020, especially at the the missing link between basic and advanced! This also implies that the number of people that can appreciate any advanced mathematics research is tiny, and consequently so is the funding.
Exposition, criticism, appreciation, is work for second-rate minds. [...] It is a melancholy experience for a professional mathematician to find himself writing about mathematics. The function of a mathematician is to do something, to prove new theorems, to add to mathematics, and not to talk about what he or other mathematicians have done.
Multidimensional Fourier transform Updated 2025-07-16
Lecture notes:
- www.robots.ox.ac.uk/~az/lectures/ia/lect2.pdf Lecture 2: 2D Fourier transforms and applications by A. Zisserman (2014)
How the 2D FFT works by Mike X Cohen (2017)
Source. Animations showing how the 2D Fourier transform looks like for simple inpuf functions. Fourier inversion theorem Updated 2025-07-16
A set of theorems that prove under different conditions that the Fourier transform has an inverse for a given space, examples:
Laplace transform Updated 2025-07-16
Zermelo-Fraenkel set theory Updated 2025-10-14
One of the first formal proof systems. This is actually understandable!
This is Ciro Santilli-2020 definition of the foundation of mathematics (and the only one he had any patience to study at all).
TODO what are its limitations? Why were other systems created?
Association football Updated 2025-07-16
Football variant Updated 2025-07-16
Calysta Updated 2025-07-16
Sea shanty Updated 2025-07-16
Paco de Lucía Updated 2025-07-16
Watching www.youtube.com/watch?v=-SbZZPX-y9g in 2022, who was one of his inspirations, made Ciro miss his guitar so much... one day, maybe, one day.
Existential quantification Updated 2025-07-16
Universal quantification Updated 2025-07-16
Classification of finite groups Updated 2025-07-16
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.
Feature film Updated 2025-07-16
Television series Updated 2025-07-16
Film director Updated 2025-07-16
Film genre Updated 2025-07-16
Ciro Santilli's film tastes Updated 2025-07-16
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.
There are unlisted articles, also show them or only show them.