2020/2021

2020/2021

DM270

MAT/04 (COMPLEMENTARY MATHEMATICS)

DEPARTMENT OF MATHEMATICS "FELICE CASORATI"

MATHEMATICS

PERCORSO COMUNE

1°

1st semester (01/10/2020 - 20/01/2021)

6

48 lesson hours

Italian

ORAL TEST

ROSSO RICCARDO (titolare) - 6 ECTS

Knowledge of elementary probabilty at the level of an undergraduate student.

The course aims to presenting the historical development of the theory of probability.

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. 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.

Lessons in a class

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.

Oral exam. The student chooses a topic to present among those covered in the course. Other questions are chosen by the teacher, clearly among topics covered in the course