A Combinatoric Model of the Learning Curve

The specific problem in this project is to predict the large scale connectivity of a certain random network arising in the area of combinatorics. The motivation behind the model is to predict how individuals *learn* when presented with a large network of related *concepts*. We created generating functions to count the large connected *components*. These *components* are the related *concepts* that we referred to previously. The creation of these generating functions enabled us to analyze different graphs to connect the idea of how students understand related concepts to the Percolating Threshold. The model is a dynamical system coming from Percolation Theory. There are potential applications that fall into the areas of machine learning and neuroscience.