Related papers: Guido Castelnuovo e l'insegnamento della matematic…
This study examines the potential of using math-themed postage stamps in mathematics lessons as a tool to engage students and integrate the subject with history, art, and culture. Since the first mathematical stamps appeared in the early…
I offer a revisionist interpretation of Galileo's role in the history of science. My overarching thesis is that Galileo lacked technical ability in mathematics, and that this can be seen as directly explaining numerous aspects of his life's…
This book is divided into two parts. In the first part we give an elementary introduction to computational physics consisting of 21 simulations which originated from a formal course of lectures and laboratory simulations delivered since…
Lectures notes (in italian) of some arguments of classical analysis, with exercises. A particular emphasis to functional analysis and elementary operator algebra theory is given, by means of exercises and examples.
The aim of this paper is to start a systematic investigation of the arithmetic degree of projective schemes as introduced by D. Bayer and D. Mumford. One main theme concerns itself with the behaviour of this arithmetic degree under…
This article describes the implementation in the software package NumGfun of classical algorithms that operate on solutions of linear differential equations or recurrence relations with polynomial coefficients, including what seems to be…
We will outline our ideas for teaching in the core mathematics disciplines. They are based on our own experience in teaching at a number of universities in the USA, as well as in Europe. While some of the core ideas stay and have stayed…
Lecture Notes for the Erice Summer School 2005 Computer Simulations in Condensed Matter: from Materials to Chemical Biology. Perspectives in celebration of the 65th Birthday of Mike Klein organized by Kurt Binder, Giovanni Ciccotti and…
Scientific research involves mathematical modelling in the context of an interactive balance between theory, experiment and computation. However, computational methods and tools are still far from being appropriately integrated in the high…
Multilayered artificial neural networks are becoming a pervasive tool in a host of application fields. At the heart of this deep learning revolution are familiar concepts from applied and computational mathematics; notably, in calculus,…
To contrast the phenomenon of false positives in the diagnoses of dyscalculia in Italy, among 3rd grade children, a 3-year project (2011-2014), built upon a collaboration between psychologists and mathematics educators, was carried out.…
The reform of the upper secondary school in Italy has recently introduced physics in the curricula of professional schools, in realities where it was previously absent. Many teachers, often with a temporary position, are obliged to teaching…
This paper investigates supervised fine-tuning of large language models (LLMs) to improve their pedagogical alignment in computing education, addressing concerns that LLMs may hinder learning outcomes. The project utilised a proprietary…
This paper was written as part of a book entitled: "Questions of Modern Cosmology - Galileo's Legacy" which is a celebrative book dedicated to Galileo Galilei. The book is published in 2009, the International Year of Astronomy, since it is…
Deep learning has deeply changed the paradigms of many research fields. At the heart of chemical and physical sciences is the accurate ab initio calculation of many-body wavefunction, which has become one of the most notable examples to…
Computation is a central aspect of modern science and engineering work, and yet, computational instruction has yet to fully pervade university STEM curricula. In physics, we have begun to integrate computation into our courses in a variety…
In this article we give a modern interpretation of Kummer's ideal numbers and show how they developed from Jacobi's work on cyclotomy, in particular the methods for studying "Jacobi sums" which he presented in his lectures on number theory…
This is a report of a course on modern physics designed and taught to undergraduate science and engineering students in the Spring of 2013. The course, meant for freshmen, attempts to integrate statistical mechanics into non-classical…
In October 1604, when SN1604, the last naked-eye visible supernova in our Galaxy, exploded, Galileo Galilei was the professor of mathematics and astronomy at the University of Padua, teaching the mechanics of planets. He was therefore the…
Large-enrollment university courses face persistent challenges in providing timely and scalable instructional support. While generative AI holds promise, its effective use depends on reliability and pedagogical alignment. We present a…