Bayesian Updating Visualization
This python module is a demonstration of Bayes' rule. Choose some points to define a polynomial prior distribution for the bias of a coin. Flip the coin any number of times, record the results, and you'll see how the distribution changes with each flip.
Tarski's Theorem & The Fixed Point Lemma
Tarski's undefinability theorem is a result that's been almost completely eclipsed by Gödel's first incompleteness theorem in the canon of mathematical logic. This is unfortunate, because although Tarski's result is weaker, it provides a friendlier introduction to Gödel numbering and diagonalization. Assuming some experience with first-order logic, it only takes a few pages to develop. You can see my exposition here.
The fixed-point lemma is a result that's used to to construct Gödel sentences. One nice way to understand the proof is through a puzzle presented by Raymond Smullyan in one of his recreational math books. I've written up this article which presents the puzzle and solution, then turns it into a rigorous formal argument.
Understanding Jordan Normal Form
This article develops the JNF in what I think is a less efficient but more intuitive way. It emphasizes the eventual kernel, eventual image, and the idea of an orbit.
Interactive z-Table and t-Table
I wrote an interactive visual version of the z-table and t-table in javascript to use in the statistics classes I teach. Click and drag the red dots on the horizontal axis to pick your favourite interval.
Category Theory Notes
A few years ago I ran an informal summer course introducing graduate students in computer science to category theory. I made a set of notes complete with exercises, and now they're just sitting in a desk. I started TeXing these, but that project is currently on hold. The Barr & Wells book Category Theory for Computing Science is now freely available, and I highly recommend it.
If you happen to be seeking some online category theory literature, you might want to take a look at this section of Alexander Kurz's webpage.
Thesis
My master's thesis was concerned with coalgebraic modal logic. The idea is to realize a certain class of structures as the class of coalgebras for an endofunctor, and from that functor extract an adequate and expressive modal logic for reasoning about said structures, along with a complete system of inference. In my thesis I do this explicitly for deterministic Kripe machines. The ultimate goal is to find a uniform way of doing this for as many classes of coalgebraic structures as possible. A few of the most influential people involved in this program are Jan Rutten, Alexander Kurz, and Dirk Pattinson.
Older Papers
On the existence of regular approximations is a paper I co-authored with Kai Salomaa and presented at DCFS 2006. In the paper we define an asymptotic measure of how close a given formal language is to being a regular language, and explore properties of this measure.