THE RECOVERY OF COMPREHENSIBLE MATHEMATICS

The main objective is to get over the gap that exists between mathematics and common people, especially grown up people. Apart mathematical details, the problem lies in a good choice of notices (curiosity) and nice problems (play). Some historical notes about great mathematicians are presented and discussed, with explicit reference to the cases when the boundary between Nobel prize and mathematics was broken. Favourable fields are probability and operations research. Since probability tends to an excess of theory, operations research seemed to be a good choice. The Fields Medal, a kind of Nobel prize for Mathematics, was also considered, since in 2018 it was achieved by the Italian mathematician Figalli, former student of Scuola Normale Superiore di Pisa. He started from an important field in the frame of Operations Research, namely Optimal Transport. This sector allows to summarize a very nice procedure for its solution, non at all obvious to be trasferred to the computer. Since mathematics is forgotten in the course of life, except for those few parts of current use, to bring the adult back into the interest of mathematics, topics related to everyday life should be presented. Operations research, and especially network optimization, provide significant but pleasing problems

The Singular Points Binomial Method for pricing American path-dependent options

We introduce a new numerical approach, called the \u201csingular points method\u201d, for pricing American path-dependent options. This method, which is based on a continuous representation of the price at each node of the binomial tree, allows us to obtain very precise upper and lower bounds for the discrete binomial price. Moreover, the method provides a priori estimates of the difference between the upper and lower bounds. The algorithm is convergent and provides efficient estimates of the continuous price value. We apply the method to the case of Asian and lookback American options

SCENARI IPOTETICI PER L\u2019ANALISI DEL CONTENUTO PEDAGOGICO DELL\u2019INSEGNAMENTO DELLA MATEMATICA IN DOCENTI DELLA SCUOLA PRIMARIA

A survey was conducted on mathematical knowledge for teaching of nine teachers in service in the basic school with the aim of providing some guidance for the vocational training of teachers, so that it is more aligned with the teaching and disciplinary knowledge and experience of teachers. Similarly, it was intended to provide greater incentive for a reflection on the teaching / learning of math by the teachers involved in the survey

The Hahn decomposition theorem for fuzzy measures and applications

We deal with measures on Δ-l-semigroups, in particular on MV-algebras. Examples of such measures are T∞-valuations on clans of fuzzy sets. We first provide the Hahn decomposition theorem for measures on Δ-l-semigroups. This is then used to obtain a representation theorem for such measures, which itself is a basic tool in the proof of Liapounoff type theorems

The Hahn decomposition theorem for fuzzy measures and applications

We deal with measures on \u394-l-semigroups, in particular on MV-algebras. Examples of such measures are T 1e-valuations on clans of fuzzy sets. We first provide the Hahn decomposition theorem for measures on \u394-l-semigroups. This is then used to obtain a representation theorem for such measures, which itself is a basic tool in the proof of Liapounoff type theorems

Interactive tools to support Linear Algebra students: GeoUniud

GeoUniud \ue8 una piattaforma intuitiva integrata attraverso tutor interattivi. Permette agli studenti di indagare su specifiche attivit\ue0 selezionando i loro input iniziali e risolvendo gradualmente un problema. In ogni fase viene fornito un insieme di feedback immediato. In questo articolo verranno descritti solo alcuni strumenti sulle applicazioni lineari e gli autovettori per migliorare il sense-making degli studenti in un ambiente di geometria dinamica nella prospettiva della teoria della mediazione semiotica