Ciro Santilli @cirosantilli 37

Synthesizes MIDI input. vmpk + aconnect + Advanced Linux Sound Architecture hello world: askubuntu.com/questions/34391/virtual-midi-piano-keyboard-setup/1298026#1298026

Supports only very basic effects it seems: chorus effect and reverberation. The main way to add instruments to it is via SoundFont files.

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.

Besides the understandable Wikipedia definition, Video "Simple Groups - Abstract Algebra by Socratica (2018)" gives an understandable one:

We don't really know how to make up larger groups from smaller simple groups, which would complete the classification of finite groups:

In particular, this is hard because you can't just take the direct product of groups to retrieve the original group: Section "Relationship between the quotient group and direct products".

In the classification of finite simple groups, groups of Lie type are a set of infinite families of simple lie groups. These are the other infinite families besides te cyclic groups and alternating groups.

A decent list at: en.wikipedia.org/wiki/List_of_finite_simple_groups, en.wikipedia.org/wiki/Group_of_Lie_type is just too unclear. The groups of Lie type can be subdivided into:

The first in this family discovered were a subset of the Chevalley groups $A_n(q)$ by Galois: $PSL(2,p)$, so it might be a good first one to try and understand what it looks like.

TODO understand intuitively why they are called of Lie type. Their names $A_n$, $B_n$ seem to correspond to the members of the classification of simple Lie groups which are also named like that.

But they are of course related to Lie groups, and as suggested at Video "Yang-Mills 1 by David Metzler (2011)" part 2, the continuity actually simplifies things.

Combination of electromagnetism and general relativity. Unlike combining quantum mechanics and general relativity, this combination was easier.

TODO any experiments of interest at all?

This one is a little confusing: the upper case looks exactly like a letter P, but as the name suggests, it actually corresponds to the letter R. The letter P corresponds to pi instead.

So simple!! You can either:

A handle cancels out a Möbius strip, so adding one of each does not lead to a new object.

You can glue a Mobius strip into a single hole in dimension larger than 3! And it gives you a Klein bottle!

Intuitively speaking, they can be sees as the smooth surfaces in N-dimensional space (called an embedding), such that deforming them is allowed. 4-dimensions is enough to embed cover all the cases: 3 is not enough because of the Klein bottle and family.

If your kids are about to starve, fine, do it.

But otherwise, Ciro Santilli will not, ever, spend his time drilling programmer competition problems to join a company, life is too short for that.

Life is too short for that. Companies must either notice that you can make amazing open source software projects or contributions, and hire you for that, or they must fuck off.

Companies must either notice that you can make amazing projects or contributions, and hire you for that, or they must fuck off.

Bibliography:

Linear map of two variables.

More formally, given 3 vector spaces X, Y, Z over a single field, a bilinear map is a function from:that is linear on the first two arguments from X and Y, i.e.:Note that the definition only makes sense if all three vector spaces are over the same field, because linearity can mix up each of them.

The most important example by far is the dot product from ${\mathbb{R}}^n\times {\mathbb{R}}^n\to \mathbb{R}$, which is more specifically also a symmetric bilinear form.

Made by a single dude. As SsethTzeentach puts it, this is the greatest autism project ever made.