Università Roma Tre

1) Introduction to the concept of infinity in mathematics: three greek theorems (irrationality of square root of two; convergence of the geometric series; infinity of prime numbers).
2 ) The infinite in the modern era according to Peano, Cantor, Dedekind & Co. (axiomatic of the numerical set: natural, rational, real and complex numbers).
3 ) The lesson of Cauchy: limits and mathematical rigor in the calculation .
4 ) What is a function? (A brief digression).
5 ) Infinite and infinitesimal (overview on the fundamentals of differential and integral calculus )

Rudin, W. : Principi di analisi matematica, Milano 1991
Giusti, E. : Piccola storia del calcolo infinitesimale dall’antichità al Novecento, Ist. Editoriali e Poligrafici, 2007.
Morris Kline: Mathematical Thought from Ancient to Modern Times ( 3 Volumes). Oxford University Press, USA | 1972-09-29
Dedekind, Richard, Essays on the Theory of Numbers. Open Court Publishing Company, Chicago, 1901.