Ciro Santilli @cirosantilli 35

Like a heat equation but for functions without time dependence, space-only.

TODO confirm: does the solution of the heat equation always converge to the solution of the Laplace equation as time tends to infinity?

In one dimension, the Laplace equation is boring as it is just a straight line since the second derivative must be 0. That also matches our intuition of the limit solution of the heat equation.

Uniqueness: Uniqueness theorem for Poisson's equation.

Invertible matrices. Or if you think a bit more generally, an invertible linear map.

When the field $F$ is not given, it defaults to the real numbers.

Non-invertible are excluded "because" otherwise it would not form a group (every element must have an inverse). This is therefore the largest possible group under matrix multiplication, other matrix multiplication groups being subgroups of it.

TODO motivation. Motivation. Motivation. Motivation. The definitin with quotient group is easy to understand.

Our notation: $D_n$, called "dihedral group of degree n", means the dihedral group of the regular polygon with $n$ sides, and therefore has order $2n$ (all rotations + flips), called the "dihedral group of order 2n".

Free borrow on the Internet Archive: archive.org/details/inwardboundofmat0000pais/page/88/mode/2up

The book unfortunately does not cover the history of quantum mechanics very, the author specifically says that this will not be covered, the focus is more on particles/forces. But there are still some mentions.

Basically a GUI music editor where you can specifically see and export classical music notation instead of tablature-style notation.

Best open source one found so far as of 2020: MuseScore.

Allele means "other" in Greek.

Ciro Santilli defines a "business film" as a film about business, enterprises or entrepreneurship. Political thrillers are closed related as well.

This is one of his favorite film genres!

Some lists:

by The New Republic

Ciro Santilli really loved his documentary called Can't get you out of my head by Adam Curtis (2021), and then proceeded to basically watch all of this films.

A convenient notation for the elements of $GF(n)$ of prime order is to use integers, e.g. for $GF(7)$ we could write:which makes it clear what is the additive inverse of each element, although sometimes a notation starting from 0 is also used:

For fields of prime order, regular modular arithmetic works as the field operation.

For non-prime order, we see that modular arithmetic does not work because the divisors have no inverse. E.g. at order 6, 2 and 3 have no inverse, e.g. for 2:we see that things wrap around perfecly, and 1 is never reached.

For non-prime prime power orders however, we can find a way, see finite field of non-prime order.

The neutron temperature example is crucial: you just can't give the cross section of a target alone, the energy of the incoming beam also matters.