历史与综述
Data scientists are not mathematicians, but they make heavy use of mathematics in their daily work. While mathematicians can study a mathematical object which is inaccessible to our five senses, data scientists must deal with real-world…
This survey paper is an expanded version of an invited keynote at the ThEdu'22 workshop, August 2022, in Haifa (Israel). After a short introduction on the developments of CAS, DGS and other useful technologies, we show implications in…
In this note, we propose simple summations for primes, which involve two finite nested sums and Bernoulli numbers. The summations can also be expressed in terms of Bernoulli polynomials.
Data science for social justice (DS4SJ) is data-scientific work that supports the liberation of oppressed and marginalized people. By nature, this work lies at the intersection of technical scholarship and activist practice. We discuss this…
This is an exposition of the contributions of L\'aszl\'o Lov\'asz to mathematics and computer science written on the occasion of the bestowal of the Abel Prize~2021 to him. Our survey, of course, cannot be exhaustive. We sketch remarkable…
In the history of infinitesimal calculus, we trace innovation from Leibniz to Cauchy and reaction from Berkeley to Mansion and beyond. We explore 19th century infinitesimal lores, including the approaches of Simeon-Denis Poisson,…
`Terquem's problem' is a name given in the twentieth century to the problem of enumerating certain integer sequences whose entries alternate in parity. In particular, this problem asks for the count of strictly increasing length $m$…
We assess the situation of our elementary Linear Algebra classes in the US holistically and through personal history recollections. Possible remedies for our elementary Linear Algebra's teaching problems are discussed and a change from…
These are the third 50 issues of This Week's Finds of Mathematical Physics, from April 9, 1997 to June 18, 2000. These issues discuss quantum gravity, topological quantum field theory, n-categories and other topics in mathematics and…
Practical research was conducted to cultivate students' mathematical computation ability using literature analysis, theoretical practice, and statistical analysis methods. The research involved 171 ninth-grade students from the author's…
In this paper, we draw diagrams of yinyang, wuxing and bagua as the McKay quivers of the groups of order 2, of order $5$ and of order $2^3$.
While proof is a central component of postsecondary mathematical study, proof construction has historically posed significant difficulties for students who intend to earn mathematics degrees at the undergraduate level. This work is…
Sophisticated computation methods were developed 4000 years ago in Mesopotamia in the context of scribal schools. The basics of the computation can be detected in clay tablets written by young students educated in these scribal schools. At…
Aesop's famous fable The Ant and the Grasshopper emphasizes the choice that living beings have to make between survival (the Ant) and reproduction (the Grasshopper). Apis Mellifera colonies face the same dilemma : must they rather collect…
We present a configuration called a magic permutohedron that shows the placement of the numbers of $\{1, 2, 3, \dots, 24\}$ in the vertices of the permutohedra so that the sum of numbers on each square side is 50 and the sum of the numbers…
In this note, we briefly analyse the works on the extractions of amicable pairs in some medieval Arabic literature. In this note, we briefly analyse the works Ibn Sina (c.980-1037), al-Baghdadi (c.980-1037) and al-Kashi (d. c. 1429) on the…
We present a new model of a non-Euclidean plane, in which angles in a triangle sum up to $\pi$. It is a subspace of the Cartesian plane over the field of hyperreal numbers $\mathbb{R}^*$. The model enables one to represent the negation of…
As a Physicist and a Chemist , we have had the opportunity to teach Algebra in our engineering school in Aix-en-Provence. The article deals with the interactions made between Physics, Chemistry and Algebra.
Some children may be intellectually gifted, and yet experience behavioral and academic difficulties. We examined 82 twice exceptional children (2eADHD), having an excellent General Ability Index (GAI) derived from the Wechsler Intelligence…
This article introduces a pedagogical method for {\it solving combinatorial problems} that frequently involve structures that are unfamiliar or less familiar. Indeed, an indirect method has been proposed in order to evade any possible…