## Where does the entropy come from?

A natural derivation of the entropy from maximum likelihood.

Read moreA natural derivation of the entropy from maximum likelihood.

Read moreThe fundamental mathematical ideas behind thermodynamics

Read moreSome notes on the elementary properties of the exponential families

Read moreA proof of the divergence of the harmonic series with the Coq proof assistant.

Read moreA companion matrix is a matrix with a prescribed characteristic polynomial. I would like to show them from a broader perspective: companion matrices are the matrix version of a shift operator.

Read moreMy goal is to derive Maxwell's equations of electromagnetism with almost no effort at all.
As often in mathematics, things look simpler when there is *less* structure.
Here, as in mechanics, we do not assume any prior metric, so the geometry of the space at hand is very simple.

The variational equation is a fundamental tool in engineering.
It is the description of the sensitivity with respect to the initial conditions.
A remarkable fact, often presented only in \(\mathbf{R}^n\), is that this is in fact the solution of *another* differential equation, sometimes called *the variational equation*.
I would like to show that this is valid in general manifolds.

A little JavaScript application to demonstrate two ideas:

Equivariance

Modified vector field