Blackbody Thermodynamics

Blackbody radiation as an application of the foundation of thermodynamics

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.