History of mathematics

Course objectives

General goals acquiring general knowledge of the main stages of the historical developement of mathematics from the time of the Greeks to the beginning of the seveteenth century. Specific goals Knowledge and comprehension: at the end of the course the students who will pass the exam will get the basic knowledges and the methodological tools suitable for further studies in the history of mathematics. Apply Knowledge and comprehension: at the end of the course the students who will pass the exam will be able to understand some of the most significant excerpts taken from the writings of Euclide, Archimede, Cavalieri, Torricelli, Descartes, Fermat, Newton e Leibniz (in italian translation) and they will be able to compare the methods employed by their authors with those of contemporary mathematics. They will also appreciate the educational value of an historical approach to mathematics and to apply it to the elaboration of educational modules for school teaching. Critical skills and judgment: the student will get the basic knowledge necessary for appreciating the historical developement of the elementary concepts and techniques of geometry and analysis and for analysing the analogies and the relationships between the topics treated in this course and those treated in the courses of Calcolo I, Analisi Matematica I and Geometria I. Communication skills: ability to explain the content of the course in the oral part of the exam and to summarize the acquired knowledge in the written part. Learning skills: the acquired knowledge will allow an individual study or a study of a course taught at "Laurea Magistrale", concerning more advanced topics in the history of mathematics.

Channel 1
ENRICO ROGORA Lecturers' profile

Program - Frequency - Exams

Course program
Pre ellenic mathematics. Greek mathematics: the theory of proportions and the method of exhaustion of Eudoxus, the Elements of Euclid and their axiomatic approach, Archimedes' and Apollonio's contributions to geometry. One topic among the following: Galileo and its disciples: the necessity to treat motion mathematically; the works of Bonaventura Cavalieri and Evangelista Torricelli. The birth of analytic geometry: the work of Descartes and Fermat. The birth of differential calculus: the work of Leibniz and Newton. Mathematics in Rome between Risorgimento and the second world war
Prerequisites
This course requires a knowledge of the main topics of Calcolo I, Analisi Matematica I, Geometria I and Fisica I. This knowledge is necessary.
Books
Teacher's notes available on line Excerpts in italian of original works, available on line.
Teaching mode
Traditional lessons, reading and discussion of excerpts of original writings in italian translation.
Frequency
In presence
Exam mode
The final exam intends to evaluate the learning process of a student with a written exam (consisting of a brief essay on a topic chosen by the teacher) and in an oral exam (consisting of a discussion on the topics of the program and on one or more original excerpts chosen from those analyzed during the lectures). The written part will last about two hours. To pass the exam the minimum grade is 18/30, for which the student must show a sufficient knowledge of the topics and to understand the general historical background within which to frame the developement of mathematics. He must also show to be able to comment on the original excerpts analysed during the lectures in italian translation. In order to get the top grade, 30/30 with honor, the student must show an excellent knowledge of all the topics of the course, to be able to comment on the original excerpts analysed during the lectures in italian translation and to be able to connect all of this in a coherent logical way.
Bibliography
M. Giaquinta, La forma delle cose, Edizioni di Storia e Letteratura, Roma 2010
Lesson mode
Traditional lessons, reading and discussion of excerpts of original writings in italian translation.
  • Lesson code1051921
  • Academic year2024/2025
  • CourseMathematics
  • CurriculumStoria, didattica e fondamenti
  • Year3rd year
  • Semester2nd semester
  • SSDMAT/04
  • CFU6
  • Subject areaFormazione Teorica