The course aims to presenting the historical development of the theory of probability.
Course Prerequisites
Knowledge of elementary probabilty at the level of an undergraduate student.
Teaching Methods
Lessons in a class
Assessment Methods
Oral exam. The oral exams will contain three questions. 1st. A question on a topic selected by the student among those covered in the course. 2nd. A question proposed by the teacher within a chapter of the course, selected by the student. 3rd. A question proposed by the teacher.
Texts
I. Hacking "L'emergenza della probabilità" Il Saggiatore (1975). A. Hald: "History of Probability and Statistics and their applications before 1750" Wiley (2003). A. Hald: "A History of Mathematical Statistics From 1750 to 1930" Wiley (1998). M.C. Galavotti: "Philosophical Introduction to Probability" CSLI (2005). I. Dale: "A History of Inverse Probability. From Thomas Bayes to Karl Pearson" Springer (1999). T.M. Porter: "The rise of statistical thinking 1820-1900" Princeton University Press (1986). S.M. Stigler: " The History of Statistics. The measurement of Uncertainty before 1900". J. von Plato: "Creating modern probability" Cambridge University Press (1998). Notes available on the website of the course.
Contents
Prehistory of probability. Problems in combinatorial analysis related to game of chances. The problem of points from late-medieval manuscript to De Moivre. Early applications of the calculus of probability to mortality tables and life annuities. Jacob bernoulli's "Ars Conjectandi". The Bernoulli-De Moivre theorem. The Saint Petersburg's paradox. The birth of inverse probability: Bayes, Price and Laplace. Error theory. Probsbility in the XIX century. The criticism on the foundations of pobability. The different approaches to probability: frequentist (von Mises), logicist (Keynes), subjective (De Finetti and Ramsey). The axiomatic approach to probability calculus from Bohlmann to Kolmogorov.
