历史与综述

This is a short overview of the influence of mathematicians and their ideas on the creative contribution of Mikhailo Lomonosov on the occasion of the tercentenary of his birth.

This is a brief overview of the lives and contributions of S.L. Sobolev and L. Schwartz, the cofounders of distribution theory.

This is a short overview of the origins of distribution theory as well as the life of Sergei Sobolev (1908--1989) and his contribution to the formation of the modern outlook of mathematics.

This is an overview (in french) of the Theory of Species for a general audience. Basic notions are introduced in a non too technical manner, with an explanation of why should one approach the notion of discrete structures in this particular…

This paper gives a condition of the expression of generality in mathematics from the application of L\"owenheim-Skolem theorem to Zermelo's axioms. It gives an example of an "expression problem" from Gauss's Disquisitiones Arithmeticae and…

Game versions of the Monty Hall Problem are discussed. The focus is on the principle of eliminating the dominated strategies, both in the zero-sum and noncooperative formulations.

Let $n$ be a positive integer. Then cyclic group $Z_n$ of order $n$ is the only group of order $n$ iff g.c.d. $(n,\phi(n))=1$, where $\phi$ denotes the Euler-phi function. In this article we have given another proof of this result using the…

We give an overview about well-known basic properties of two classes of q-Fibonacci and q-Lucas polynomials and offer a common generalization.

Gerhard Hochschild's contribution to the development of mathematics in the XX century is succinctly surveyed. We start with a personal and mathematical biography, and then consider with certain detail his contributions to algebraic groups…

We geometrically prove that in a d-dimensional cube with edges of length n, the number of particular d-dimensional tetrahedrons are given by Eulerian numbers. These tetrahedrons tassellate the cube, In this way the sum of the cubes are the…

In this article I will address some questions about a mathematical problem that my friend Patrizio Frederic, a researcher in statistics at the University of Modena, proposed to me. Given some parallel line segments, is there at least one…

C. F. Gauss discovered a beautiful formula for the number of irreducible polynomials of a given degree over a finite field. Assuming just a few elementary facts in field theory and the exclusion-inclusion formula, we show how one see the…

We give an elementary introduction, through illustrative examples but without proofs, to one of the basic consequences of the Langlands programme, namely the law governing the primes modulo which a given irreducible integral polynomial…

In this article (it's only in italian, but I'm translating it) I will try to solve some questions about a mathematical problem that my friend Patrizio Frederic, a researcher in statistics at the University of Modena, proposed to me. Given…

Traditionally, mathematical knowledge is published in printed media such as books or journals. With the advent of the Internet, a new method of publication became available. To date, however, most online mathematical publications do not…

A brief overview on the Centre for Mathematical Sciences India, established in 1977, and its teaching and research programme is given.

This paper concerns the emergence of modern mathematical statistics in France after the First World War. Emile Borel's achievements are presented, and especially his creation of two institutions where mathematical statistics was developed:…

In this paper we have produced different kinds of bimagic squares based on bimagic squares of order 8x8, 16x16, 25x25, 49x49, etc. A different technique is applied to produce bimagic square of order 16x16, 25x25, 49x49, etc. The bimagic…

We survey various classical results on invariants of polynomials, or equivalently, of binary forms, focussing on explicit calculations for invariants of polynomials of degrees 2, 3, 4.

The theory of numbers was supposed to be the less useful branch of mathematics. At the same time, cryptography was thought to be a military or a diplomatic issue. In this note we show how the two concepts are today strictly related and how…