Ciro Santilli @cirosantilli 37

The proper precise definition of mathematics can be found at: Section "Formalization of mathematics".

The most beautiful things in mathematics are described at: Section "The beauty of mathematics".

When it exists, which is not for all matrices, only invertible matrix, the inverse is denoted:

As usual, it is useful to think about how a bilinear form looks like in terms of vectors and matrices.

Unlike a linear form, which was a vector, because it has two inputs, the bilinear form is represented by a matrix $M$ which encodes the value for each possible pair of basis vectors.

In terms of that matrix, the form $B(x,y)$ is then given by:

The following aspects of Maxwell's equations make no sense without special relativity:

When charged particle though experiment are seen from the point of view of special relativity, it becomes clear that magnetism is just a direct side effect of charges being viewed in special relativity. One is philosophically reminded of how spin is the consequence of quantum mechanics + special relativity.

Bibliography:

Experiments that involve sequencing bulk DNA found in a sample to determine what species are present, as opposed to sequencing just a single specific specimen. Examples of samples that are often used:

One related application which most people would not consider metagenomics, is that of finding circulating tumor DNA in blood to detect tumors.

TODO examples:

Zephyr support: docs.zephyrproject.org/2.7.0/boards/arm/bbc_microbit/doc/index.html

Bluetooth support: not enough RAM for it, though in principle its chip/transceiver could support it! microbit-micropython.readthedocs.io/en/v1.0.1/ble.html

Supported editors: microbit.org/code/

MicroPython web editor and compiler: python.microbit.org/v/2

Everything in this section is tested on the Micro Bit v1 from Micro Bit v1 unless otherwise noted.

Bibliography:

Nobel Prize of Mathematics.

The Nobel Prize of mathematics!

That 15,000 canadian dollar prize though, what a joke! That's what you get when an impoverished scientist, and not a rich industrialist, creates a prize!

Microwave only found applications into the 1940s and 1950s, much later than radio, because good enough sources were harder to develop.

One notable development was the cavity magnetron in 1940, which was the basis for the original radar systems of World War II.

This is notably what the United States emerged to be after World War II. But it was likely what Nazi Germany also was, and many other superpowers.

Ciro Santilli feels that much more relevant would be to also include academia as in "military-industrial-academic" complex, the Wikipedia page actually mentions precedents to this idea.

The addition of congress/politicians is also relevant.

But hey, the name wouldn't sound so slick with three parts.

It is basically in this context that American science and technology flourished after World War II, including notably the development of quantum electrodynamics, Richard Feynman being a prototypical example, having previously worked on the Manhattan Project.

Many hits appear to happen on the same days, and per-day data does exist: archive.org/details/widecrawl but apparently cannot be publicly downloaded unfortunately. But maybe there's another way? TODO select candidates.

The "greatest common divisor" of two integers $x$ and $y$, denoted $\text{gdc}(x,y)$ is the largest natural number that divides both of the integers.

For example, $\text{gdc}(8,12)$ is 4, because: