Abstract

In this thesis, we describe the historical shift from the classical to the modern definition of probability. We present the key ideas and insights in that process, from the first definition of Bernoulli, to Kolmogorov’s modern foundations discussing some of the limitations of the old approach and the efforts of many mathematicians to achieve a satisfactory definition of probability. For our study, we’ve looked, as much as possible, at original sources and provided detailed proofs of some important results that the authors have written in an abbreviated style.

We then use this historical results to investigate the conceptualization of probability proposed and fostered by undergraduate and graduate probability textbooks through their theoretical discourse and proposed exercises. Our findings show that, despite textbooks give an axiomatic definition of probability, the main aspects of the modern approach are overshadowed by other content. Undergraduate books may be stimulating the development of classical probability with many exercises using proportional reasoning while graduate books concentrate the exercises on other mathematical contents such as measure and set theory without necessarily proposing a reflection on the modern conceptualization of probability.