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.