In preparation for an open class on computer programming, I collected a few ideas that I would like to mention. Here is the current draft (v2017.12.30).
I start every course with a sort of philosophical introduction. It is usually about asking `What is the most important idea of …?’, and by trying to answer the question, I can give an overview of the whole course. Today I started a computing-focused discrete math course, so the question was:
What is the most fundamental idea of digital computation?
The holonomy algorithm is the main method used in SgpDec for computational tools of the Krohn-Rhodes theory. The details of the algorithm might not be the easiest to grasp, but the underlying ideas are quite simple. Here is a short description of the general ideas used in the holonomy decomposition.
The whole course content, tutorial notes, assignments can be found on GitHub.