Mathematical modeling of human memory

The mathematical study of human memory is still an open challenge. Cognitive psychology and neuroscience have given a big contribution to understand how the human memory is structured and works. Cognitive psychologists developed experimental paradigms, conceived quantitative measures of performance in memory tasks for both healthy people and patients with memory disorders, but in terms of mathematical modeling human memory there is still a lot to do. There are many ways to mathematically model human memory, for example, by using mathematical analysis, linear algebra, statistics, and artificial neural networks. The aim of this study is to provide the reader with a description of some prominent models, involving mathematical analysis and linear algebra, designed to describe how memory works by predicting the results of psychological experiments. We have ordered the models from a chronological point of view and, for each model, we have emphasized what are, in our opinion, the strong and weak points. We are aware that this study covers just a part of human memory modeling as well as that we have made a personal selection, which is arguable. Nevertheless, our hope is to help scientists to modeling human memory and its diseases.