The course aims to present an overview of the milestones of the development of Mathematics from the Middle Ages to today, mainly through contributions of notable scholars. Another further aim is to underline the development of some relevant notions of modern Mathematics.
KNOWLEDGE AND UNDERSTANDING
At the end of the course the student must demonstrate his/her knowledge and understanding of the topics treated in the course.
APPLYING KNOWLEDGE AND UNDERSTANDING
At the end of the course the student must be capable of applying his/her knowledge of the topics treated in the course, demonstrating his/her ability to link them together.
MAKING JUDGEMENTS
At the end of the course the student must have developed a critical attitude by reading and analysing the texts treated in the course.
COMMUNICATION SKILLS
At the end of the course the student must be able to speak appropriately about the topics treated in the course, with language skills and confident exposure.
LEARNING SKILLS
At the end of the course the student must be capable, on the basis of his/her knowledge and his/her ability to analyse and link the topics, of consulting the works of mathematicians or further texts.

Basic notions of algebra, geometry, and mathematical analysis

Interventions aimed at consolidating the prerequisites are planned during the lectures. Active participation in the lectures is strongly recommended.

Overview of the historical development of Mathematics.
Hints on ancient Mathematics (Babylonian, Egyptian, Greek).
Historical journey on the European Mathematics from the Middle Ages to the beginning of the XIX century, focussing three aspects: history of peoples and nations, evolution of mathematical ideas, biographies.

Brundu M., Ritessere i saperi - Laboratorio di matematica, Quaderni didattici - Dipartimento di Matematica e Geoscienze 59 (2012)

Boyer, C. B., Storia della matematica. Mondadori, Milano (1968)

Complement text:
Kline, M., Storia del pensiero matematico, II. Dal Settecento a oggi, Einaudi, Torino (1972)

1. Synthetic framework of the historical development of Mathematics.
2. Overview on ancient Mathematics and Greek Mathematics.
3. Arabic roots and development of Mathematics in the Middle Ages (Fibonacci, Oresme, the Merton rule)
4. The Renaissance (Regiomontano, Pacioli, the war of third degree equations from Tartaglia to Bombelli)
5. Between the sixteenth and seventeenth centuries: towards modern Mathematics (Algebra, trigonometry, logarithms and astronomy: Viète, Napier, Galileo and Kepler)
6. The early seventeenth century: the time of Descartes and Fermat (the “indivisibili” of Cavalieri and the moment of “geniuses”)
7. The middle of the seventeenth century: advances of modernity (infinite sums and new geometry: Torricelli, Desargues and Pascal)
8. From the seventeenth to the eighteenth century: the time of Newton and Leibnitz (infinitesimal calculus arises)
9. The eighteenth century: from the Bernoulli's to Euler (the complexity of modern Mathematics)
10. Late eighteenth century in France (the progress of d'Alembert, Lagrange, Laplace, Legendre)
11. The Golden age of Mathematics: the time of Gauss (new areas of modern Mathematics)
12. The Golden age of Mathematics: the two young geniuses (fruitful legacies of Abel and Galois)

Lectures with teacher-student dialogue, in-depth studies and use of digital technologies.

Some lessons materials will be available on the Moodle platform.

These materials complement but do not replace the study of the textbooks.

The exam consists of a written test about the topics treated in the course and of a half-hour tutorial about a subject agreed with the teacher.