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.