Wednesday 29 April 2020

Morse Theory a Must Know for the PyCrypto

Morse Theory is the theory made up by Marston Morse from Maine, an American mathematician known for his work on "calculus of variations in the large".

The Morse-Palais Lemma is named after him and Richard Palais.

Eisenstein and Irreducibility

Gotthold Eisenstein gives his name to Eisenstein's criterion, a famous theorem on the irreducibility of polynomials with coefficients in Z to polynomial products over Q (the rationals being a larger "field" than the integers). German mathematician Theodor Schรถnemann was in fact the first to publish it.

Tuesday 21 April 2020

Fisher Information (Info about a PopPar in an RV X)

At some point a statistician will come head-to-head with the Fisher information, which measures the "information" about a population parameter contained in an observable random variable X. 

It is the expected value of the observed information (sounds a bit like "maximum likelihood", right?).

Formally it is what statisticians call the "variance of the score".  

The notion of "score" is something quite peculiar and distinctive to this branch of mathematics and is also known as the "informant". It is the rate of change of the log likelihood function of the population parameter, with respect to the parameter.

It is named after British polymath, Sir Ronald Aylmer Fisher, FRS.