历史与综述

Starting from the concept that knowledge comes as element of mediation between the convergent thinking, founded on experience, and the divergent thinking, placed in the perceptive, intuitive, creative dimension, in this paper we want to…

This note is a brief survey of some results of the recent collaboration of neurobiologists and mathematicians dedicated to stimulus reconstruction from neuronal spiking activity. This collaboration, in particular, led to the consideration…

In the paper different kinds of proof of a given statement are discussed. Detailed descriptions of direct and indirect methods of proof are given. Logical models illustrate the essence of specific types of indirect proofs. Direct proofs of…

We discuss the following folklore problem. On a bookshelf, there are $N$ tomes of the Encyclopedia in random order. Each hour, a librarian takes a tome which stands not on its place, and puts it in its place. Show that the process will…

One aim of this note is to give an overview of some developments in the area of Dirichlet forms. A second aim is to review the new book "Semi-{D}irichlet forms and {M}arkov processes" by Yoichi Oshima. The book appeared last year, but first…

In the year 2000, Ahmed proposed a family of integrals in the American Mathematical Monthly which invoked a considerable response then. Here I would like to present another solution to this family of integrals. I propose to call this as…

The aim of this short note is to show how can be derived from the properties of fundamental interpolation polynomials some nice identities.

In this paper, we show that an equilateral triangle cannot be dissected into finitely many smaller equilateral triangles, no two of which share two vertices. We do this without the use of Electrical Networks.

This is a book review for Zhan's Matrix Theory (AMS, GSM 147, 2013).

We are interested in the "Journal de Math\'ematiques Pures et Appliqu\'ees" (JMPA) over the period 1917-1937. From the end of 1921, two mathematicians worked to its publication, Henri Villat as editor in chief and Robert Montessus Ballore…

The article shows the pioneering role of the British scientist, Professor G.W.Scott Blair, in the creation of the application of fractional modelling in rheology. Discussion of his results is presented. His approach is highly recognized by…

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…

Among perhaps many things common to Kuratowski's Theorem in graph theory, Reidemeister's Theorem in topology, and Cook's Theorem in theoretical computer science is this: all belong to the phenomenon of simultaneous discovery in mathematics.…

In this paper we investigate the evolution of the concept of area in Peano's works, taking into account the main role played by Grassmann's geometric-vector calculus and Peano's theory on derivative of measures. Geometric (1887) and…

Theorem. There are general position points A, B, C, P on the projective plane. Let A_P be the intersection point of lines AP and BC. Analogously define B_P and C_P. Take any points A_1, B_1, C_1 on AP, BP, CP, respectively. Let W_C be the…

We present a resolution of the celebrated "Surprise Exam Paradox". We argue that if the surprise exam story is analyzed using the exact same meaning of the notion of "surprise" as is dictated by the story itself, then no paradox arises.

In 2001-2002, I happened to have proposed a new definite integral in the American Mthematical Monthly (AMM),which later came to be known in my name (Ahmed). In the meantime, this integral has been mentioned in mathematical encyclopedias and…

This study investigated the use of concept maps on advancing students conceptual understanding of the Euler Circuit concept. The participants were students at the college of Humanities and Social Sciences with a background in Art. A…

This paper, based in part on joint work with Stanis{\l}aw Domoradzki, concerns Lucjan Emil B\"ottcher (1872-1937)-- a little-known Polish mathematician active in Lw\'ow. I outline B\"ottcher's scholarly path, focusing on his studies in…

This article concerns the life and work of Lucjan Emil B\"ottcher (1872-1937), a Polish mathematician. Besides biographical and bibliographical information, it contains a survey of his mathematical achievements in the theory of iteration…