Ciro Santilli @cirosantilli 37

Unlike over non-commutative rings, polynomials do look like proper polynomials over commutative ring.

In particular, Hilbert's tenth problem is about polynomials over the integers, which is a commutative ring, and therefore brings mindshare to this definition.

In this section we collect results about algebraic equations over more "exotic" fields

Generates numpy/fft_plot.svg, the plot of $2\sin (t)+\cos (4t)$ with 25 points and its DFT.

The output was also uploaded to: commons.wikimedia.org/wiki/File:DFT_2sin(t)_%2B_sin(4t).svg and added to en.wikipedia.org/w/index.php?title=Discrete_Fourier_transform&oldid=1176616763 only to be later removed of course: Deletionism on Wikipedia.

A hard problem ha been found for it, and it was called the "antihydra":

The good:

The bad: everything else. Closed source learning materials + a university-like selection program. Such a waste of efforts that could benefit way more people with more open resources.

meta.mathoverflow.net/questions/4889/request-to-keep-an-eye-out-for-promys-admissions-problems asking to remove PROMYS problems from MathOverflow. And it seems to have been mostly accepted. Newbs. Any maths problem should be allowed to be askeable online. There are no fundamentally new problems, copyright takedown is just silly.

Staring from a triangle wave, this explains why we always get the same musical notes:See also: solving partial differential equations with the Fourier series.

TODO: do higher overtones decay faster in time than the base ones?