History of Mathematics 1
A.Y. 2025/2026
Learning objectives
Analysis of some fundamental moments in the path of history of mathematics.
Expected learning outcomes
Students will acquire adequate methods, both technical and critical, that will enable them to get more familiar with some fundamental masterpieces of the history of mathematics.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Lesson period
Second semester
Course syllabus
The prehistory of probability
Combinatorial problems relevant to gambling.
The problem of points from the late middle-age to De Moivre.
Early applications of probability to determine annuities upon lives.
Jacob Bernoulli's Ars Conjectandi. The Bernoulli-De Moivre theorem.
Abraham De Moivre's The Doctrine of Chances.
Saint Petersburg paradox.
The birth of inverse probability: Bayes, Price, and Laplace.
The theory of errors.
The criticism of the foundations of probability.
The points of view on probability: frequency theory (von Mises), logical theory (Keynes), subjectivism (De Finetti and Ramsey).
The axiomatic approach to probability from Bohlmann to Kolmogorov.
Combinatorial problems relevant to gambling.
The problem of points from the late middle-age to De Moivre.
Early applications of probability to determine annuities upon lives.
Jacob Bernoulli's Ars Conjectandi. The Bernoulli-De Moivre theorem.
Abraham De Moivre's The Doctrine of Chances.
Saint Petersburg paradox.
The birth of inverse probability: Bayes, Price, and Laplace.
The theory of errors.
The criticism of the foundations of probability.
The points of view on probability: frequency theory (von Mises), logical theory (Keynes), subjectivism (De Finetti and Ramsey).
The axiomatic approach to probability from Bohlmann to Kolmogorov.
Prerequisites for admission
A knowledge of basic probability theory
Learning outcomes
The course aims to present the historical development of the mathematical theory of probability
Learning outcomes
The course aims to present the historical development of the mathematical theory of probability
Teaching methods
Lessons in a class
Teaching Resources
Notes available on the website of the course
Assessment methods and Criteria
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.
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.
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 6
Lessons: 42 hours