Revisiting the fundamental structures and concepts of mathematical analysis from a historical and critical point of view, also in light of the specific learning objectives of upper secondary school. Knowing how to design learning units on central themes for mathematical analysis in the context of a school course.
teacher profile teaching materials
The birth of calculus: Newton and Leibniz. The development of calculus: the Bernoullis, de l'Hôpital, Euler, and Lagrange.
The father of mathematical analysis: Cauchy. Weierstrass. The Riemann integral. The axiomatization of the real numbers: Cantor and Dedekind.
The Lebesgue integral. The qualitative study of differential equations: Poincaré. Functional analysis: Hilbert, Banach, and von Neumann.
E. Giusti Piccola storia del calcolo infinitesimale dall'antichità al Novecento
Programme
History of infinitesimal calculus. The Greeks and the calculation of areas and volumes. Cavalieri's indivisibles. Descartes, Fermat.The birth of calculus: Newton and Leibniz. The development of calculus: the Bernoullis, de l'Hôpital, Euler, and Lagrange.
The father of mathematical analysis: Cauchy. Weierstrass. The Riemann integral. The axiomatization of the real numbers: Cantor and Dedekind.
The Lebesgue integral. The qualitative study of differential equations: Poincaré. Functional analysis: Hilbert, Banach, and von Neumann.
Core Documentation
E. Giusti, Analisi Matematica 1E. Giusti Piccola storia del calcolo infinitesimale dall'antichità al Novecento
Type of delivery of the course
5 hours of frontal teaching a week live remote lesson and recording of the lesson itself.Attendance
not compulsoryType of evaluation
written test with exercise and subsequent oral test