HISTORY OF MATHEMATICS
Academic year and teacher
If you can't find the course description that you're looking for in the above list,
please see the following instructions >>
- Versione italiana
- Academic year
- 2022/2023
- Teacher
- ALESSANDRA FIOCCA
- Credits
- 6
- Didactic period
- Primo Semestre
- SSD
- MAT/04
Training objectives
- The lectures will present the main results of the various parts of mathematics in order to explain their historical developments.
The course aims to provide students with tools to design and develop mathematical teaching methodologies starting from the main theoretical frameworks used in the history of mathematics.
At the end of the course the student is able to develop basic historical and bibliographical research on the main areas of mathematical sciences. Prerequisites
- Basic knowledge of Euclidean geometry, elementary algebra, Cartesian geometry, calculus.
Course programme
- 1. Arithmetics : Ancient numeration systems. Pythagorean arithmetic. Indian and Arabic arithmetics and their transmission in the West. Number theory. (8 hours)
2. Geometry: From Egypt to Thales. Euclid and the Elements. Archimedes, Apollonius, Diophantus, Ptolemy and Pappus. Greek Geometry’s return during the Renaissance. (10 hours)
3. Algebra: Arabic algebra. Italian algebraists of the sixteenth century. Cartesian algebra. General insolubility of the equations of degree greater than four. Modern algebra. (10 hours)
4. Applications of algebra to geometry: Viète, Descartes, Newton, Euler. Algebraic geometry. (10 hours)
5. Mathematical analysis: The invention of the differential calculus: Leibniz and Newton. Euler and analytical treatises. Analytical functions. Cauchy’s criticism. Foundations of analysis. Pathological functions and divergent series. Functional analysis. (10 hours) Didactic methods
- Lectures and practices, with the support of data bases, films and materials available in the Net.
Learning assessment procedures
- The oral examination is based on the discussion of two topics developed during the course, one of which is the student choose.
Both topics contribute equally to the final score. To pass the exam the student must obtain a minimum score of 18 out of 30. Reference texts
- C. B. Boyer, History of mathematics. Various editions in English.
M. Giaquinta, La forma delle cose, voll. 2, Roma, Edizioni i Storia e Letteratura, 2014.
E. Giusti, Piccola storia del calcolo infinitesimale, dall'antichità al Novecento, 2007.
