## 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.

Type logic is the logic directly associated to types. It turns out that one can go quite far with regards to proving statements with Haskell. I show how to do that, and even how to prove statements in classical logic with Haskell.

## 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.

## Testing in Python for Scientific Computing

I would like to explain how I carry out testing when I write code for scientific computing. It's partly using techniques that are common to the general philosophy of testing, and partly techniques that are specific to scientific computing.

## Implementation of Norvig's spell checker in Haskell

Another Haskell version of Peter Norvig's spelling corrector, illustrating list monads, type classes and polymorphic programming.

The Reader and Writer monad are well known, but I would like to present their comonadic counterpart.