## Heuristics for Monad Rules

I want to show some simple heuristic calculations which show how monad rules stem from a functor adjunction.

## Heuristic Calculations

Suppose we have some sort of duality product, and some "operators" $A$ and $A^*$.

Adjunctions means that $\langle y , A x \rangle \equiv \langle A^* y , x \rangle$

We assume …

## Where does the entropy come from?

A natural derivation of the entropy from maximum likelihood.

## Foundation of Thermodynamics

The fundamental mathematical ideas behind thermodynamics

## Exponential Families

Some notes on the elementary properties of the exponential families

## Harmonic Divergence in Coq

A proof of the divergence of the harmonic series with the Coq proof assistant.

## Companion Operator

A 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.

## Differential Geometry of Maxwell's Equations

My 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.

## Variational Equation

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.