Relevance and Difficulty of Teaching Stochastics, the Science of Randomness

SUMMARY

The science stochastics has unique characteristics. It is based completely on mathematics and hence exhibits the rigour of demonstration being inherent to mathematics; but it is founded on a model of randomness, representing a quantity the greatest philosophers have failed to define satisfactorily. The great significance of stochastics arises from its role in modelling nature and systems which is of almost unlimited applicability. There are two major difficulties with stochastics. (1) Selection and verification of stochastical models as well as proper understanding of stochastical concepts are far more difficult than for deterministic models and concepts. (2) Stochastics is far from being a unified and commonly acknowledged science. Each field of traditional sciences creates its own stochastical branch, thus preventing a unification.