历史与综述
In this short note we shall give connection between the most perfect "Khajuraho" magic square of order 4x4 discovered in 10th century and the "Lo-Shu" magic square of order 3x3 with the day October 1, 2010, i.e., 01.10.2010. The day has…
A problem that enjoys an enduring popularity asks: "what is the least number of pound weights that can be used on a scale pan to weigh any integral number of pounds from 1 to 40 inclusive, if the weights can be placed in either of the scale…
This paper was published in French under the title \textit{Sur une m\'ethode d'approximation des racines carr\'ees dans l'Inde ant\'erieurement \`a la conqu\^ete d'Alexandre}, in the Bulletin de la S. M. F., volume 7 (1879), p. 98-102. It…
In this short note we have given an equation based on the date 11.09.2001 and presented some magic squares. The magic squares presented are of order 3x3, 4x4, 5x5, 9x9, 16x16 and 25x25. While the magic square of higher order 9x9, 16x16 and…
This note deals with two topics of linear algebra. We give a simple and short proof of the multiplicative property of the determinant and provide a constructive formula for rotations. The derivation of the rotation matrix relies on simple…
The Calculus Concept Readiness (CCR) instrument is based on the broad body of mathematics education research that has revealed major understandings, representational abilities, and reasoning abilities students need to construct in…
In this short note we have produced different kinds of bimagic squares using only the digits 0, 1, 2, 5 and 8. The universal bimagic squares presented are of order 8x8, 9x9, 16x16 and 25x25. In order to bring universal bimagic square of…
In this short note we have produced for the first time in the history different kinds of universal bimagic squares. This we have made using only the digits 0,1 and 2. The universal bimagic squares of order 8x8 and 16x16 are with the digits…
We give a simple geometric proof that $e$ is irrational, using a construction of a nested sequence of closed intervals with intersection $e$. The proof leads to a new measure of irrationality for $e$: if $p$ and $q$ are integers with $q >…
Triggered by a recent interesting New Scientist article on the too frequent incorrect use of probabilistic evidence in courts, I introduce the basic concepts of probabilistic inference with a toy model, and discuss several important issues…
We present the solutions of equations of degrees 3 and 4 using Galois theory and some simple Fourier analysis for finite groups, together with historical comments on these and other solution methods.
The objective of this article is to stimulate discussions in mathematical society about the role of mathematical departments in the life of the community. University community is the center of knowledge and promotes the intellectual…
This is a translation of Euler's 1773 "Variae observationes circa angulos in progressione geometrica progredientes", E561 in the Enestr{\"o}m index. I translated this paper as a result of my study of Euler's work on the infinite product…
The German forces occupying Paris arrested Emile Borel and three other members of the Acad\'emie des Sciences in October 1941 and released them about five weeks later. Why? We examine some relevant German and French archives and other…
One of beautifull mountains in the neighborhood of the Belukha, the tallest summit in the Altai (in Siberia), is called the Delone Peak in the name of Boris Nikolaevich Delone (Delaunay), prominent mathematician. Here we are going to say…
The purpose of this note consists of discrete rational reconstruction which took place during the years 1609-1630 and 1630-1666, ie, the year of the publication of their Astronomia Nova and the year of death of the great German astronomer…
Karl Stein was one of the pillars of the German school of several complex variables. In this article his scientific contributions are outlined in historical perspective.
This paper was presented at the Colloque de Saint-Denis de la Reunion, November 3-7, 1997, and published in the book L'Oc\'ean Indien au carrefour des math\'ematiques arabes, chinoises, europ\'eennes et indiennes (pp. 211-223), Tourn\`es,…
These notes present an approach to obtaining monoid operations which are compatible with a given family of mappings in the sense that the mappings become left translations in the monoid. This can be applied to various situations such as the…
Technologies in mathematical education has been a theme present at CERME from the first edition. The available technologies have evolved a lot during these years. At CERME 5 conference, the conclusions of the technology Working Group…