Related papers: MadeinMath. A Math Exhibition out of Many Threads
The motivation of this paper is to construct the theory of vector calculus of multivariate arithmetical functions. We prove analogues of integral theorems and Poincare's lemma.
This purely recreational paper is about one of the most colorful characters of the Italian Renaissance, Girolamo Cardano, and the discovery of two basic ingredients of quantum theory, probability and complex numbers. The paper is dedicated…
We consider tiling rectangles of size 4m x 4n by T-shaped tetrominoes. Each tile is assigned a weight that depends on its orientation and position on the lattice. For a particular choice of the weights, the generating function of tilings is…
Interpretability is essential for deploying deep learning models in symbolic music analysis, yet most research emphasizes model performance over explanation. To address this, we introduce MUSE-Explainer, a new method that helps reveal how…
Introductory lectures notes on cosmology, aimed at master students in physics and based on a course held at Milano University (in Italian).
We introduce invariant rings for forms (homogeneous polynomials) and for d points on the projective space, from the point of view of representation theory. We discuss several examples, addressing some computational issues. We introduce the…
We present correspondences induced by some classical mappings between measures on an interval and measures on the unit circle. More precisely, we link their sequences of orthogonal polynomial and their recursion coefficients. We also deduce…
Mathematics as an area of study occupies an important place in higher education. Due in part to its utility in other disciplines as well as its role in student learning, institutions of higher education (IHEs) often have large numbers of…
We extend Langdon Winner's idea that artifacts have politics into the realm of mathematics. To do so, we first provide a list of examples showing the existence of mathematical artifacts that have politics. In the second step, we provide an…
Physics education researchers have argued that authentic physics education includes computation as part of a physics student's training, and many parties have made efforts towards this goal. However, most research on this teaching modality…
Italian master's thesis in Computer Science. It is an overview of the standard tecniques developed in the field of Proof Theory, ending with some results in the new field of Deep Inference, plus an original contribution trying to relate…
We consider a wide range of matrix models and study them using the Monte Carlo technique in the large $N$ limit. The results we obtain agree with exact analytic expressions and recent numerical bootstrap methods for models with one and two…
The paper contains a short review of techniques examining regional wealth inequalities based on recently published research work but is also presenting unpublished features. The data pertains to Italy (IT), over the period 2007-2011: the…
At the School I gave three lectures on neutrino masses and mixings. Much of the material covered in my first two lectures is written down in a review on the subject that I published not long ago with F. Feruglio \cite{rev}. Here, I make a…
This paper discusses region wealth size distributions, through their member cities aggregated tax income. As an illustration, the official data of the Italian Ministry of Economics and Finance has been considered, for all Italian…
Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…
The following paper is a variation on a theme of Gianfranco Cimmino on some integral representation formulas for the solution of a linear equations system. Cimmino was probably motivated for giving a representation formula suitable not only…
Vertigan has shown that if $M$ is a binary matroid, then $|T_M(-\iota,\iota)|$, the modulus of the Tutte polynomial of $M$ as evaluated in $(-\iota, \iota)$, can be expressed in terms of the bicycle dimension of $M$. In this paper, we…
The growing disconnection of the majority of population from mathematics is becoming a phenomenon that is increasingly difficult to ignore. This paper attempts to point to deeper roots of this cultural and social phenomenon. It concentrates…
Mnay models situated in the current research landscape of modelling and simulating social processes have roots in physics. This is visible in the name of specialties as Econophysics or Sociophysics. This chapter describes the history of…