Ciro Santilli @cirosantilli 35

Finding a complete basis such that each vector solves a given differential equation is the basic method of solving partial differential equation through separation of variables.

The first example of this you must see is solving partial differential equations with the Fourier series.

Notable examples:

Classic theory predicts that the output frequency must be the same as the input one since the electromagnetic wave makes the electron vibrate with same frequency as itself, which then irradiates further waves.

But the output waves are longer because photons are discrete and energy is proportional to frequency:

The formula is exactly that of two relativistic billiard balls colliding.

Therefore this is evidence that photons exist and have momentum.

An easy to prove theorem that follows from a harder to prove theorem.

Transcription factor for E. Coli K-12 MG1655 operon thrLABC as shown at biocyc.org/ECOLI/NEW-IMAGE?object=TU0-42486.

Note that this is very close to the "end" of the genome.

NCBI: www.ncbi.nlm.nih.gov/gene/948874

UniProt: www.uniprot.org/uniprot/P0A9Q1

TODO DNA assembly structure.

The artistic instrument that enables the ultimate art: coding, See also: Section "The art of programming".

Much more useful than instruments used in inferior arts, such as pianos or paintbrushes.

Unlike other humans, computers are mindless slaves that do exactly what they are told to, except for occasional cosmic ray bit flips. Until they take over the world that is.

Looking for formats that:

Bibliography:

Harvard University + MIT combo.

As of 2022:Fuck that.

Also, they have an ICP.

November 2023 course search:

The first thing we had to do with the sample was to extract the DNA present in the water in a pure form for the PCR.

We did that with a Qiagen DNeasy PowerWater Kit.

As you would expect, this consists of a purification procedure with several steps.

In each step we take a physical or chemical action on the sample, which splits it into two parts: the one with the DNA and the one without.

We then take the part with the DNA, and throw away the one without the DNA.

The first steps are coarser, and finer and finer splits are done as we move forward.

Programming is hard. To Ciro Santilli, it's almost masochistic.

What makes Ciro especially mad when programming is not the hard things.

It is the things that should be easy, but aren't, and which take up a lot of your programming time.

Especially when you are already a few levels of "simple problems" down from your original goal, and another one of them shows up.

This is basically the cause of Hofstadter's law.

But of course, it is because it is hard that it feels amazing when you achieve your goal.

Putting a complex and useful program together is like composing a symphony, or reaching the summit of a hard rock climbing proble.

Programming can be an art form. There can be great beauty in code and what it does. It is a shame that this is hard to see from within the walls of most companies, where you are stuck doing a small specific task as fast as possible.

A branch of mathematics that attempts to prove stuff about computers.

Unfortunately, all software engineers already know the answer to the useful theorems though (except perhaps notably for cryptography), e.g. all programmers obviously know that iehter P != NP or that this is unprovable or some other "for all practical purposes practice P != NP", even though they don't have proof.

And 99% of their time, software engineers are not dealing with mathematically formulatable problems anyways, which is sad.

The only useful "computer science" subset every programmer ever needs to know is:

Funnily, due to the formalization of mathematics, mathematics can be seen as a branch of computer science, just like computer science can be seen as a branch of Mathematics!

The courses are highly open, almost everything is given publicly except solutions, many of which are given to teachers only. Well done!

Past exam papers index: www.cl.cam.ac.uk/teaching/exams/pastpapers/