历史与综述

In version v1 (under a different title) I was trying to give a new proof of Wedderburn's Little Theorem (WLT), stating that a finite dision ring is commutative, but I failed. So I had to withdraw the paper (version v2). Firstly I became…

Ellipsoids possess several beautiful properties associated with classical potential theory. Some of them are well known, and some have been forgotten. In this article we hope to bring a few of the "lost" pieces of classical mathematics back…

For students and their lecturers and instructors interested in the natural problem of a possible generalization of l'Hopital's rule for functions depending on two or more variables, we offer our approach. For instructors, we discuss the…

A sentence from Carl Boyer's A History of Mathematics can be interpreted so that the full brothers Nicolaus II (02/06/1695 - 07/31/1726) and Daniel Bernoulli (02/08/1700 - 03/17/1782) are the authors of the St. Petersburg paradox. The…

Much effort and research has been invested into understanding and bridging the gaps which many students experience in terms of contents and expectations as they begin university studies with a heavy component of mathematics, typically in…

The present note generalizes a well-known formula for pi/2 named after the English mathematician John Wallis. The two new formulas for infinite products containing the natural numbers and their roots express them using the Euler-Mascheroni…

This overview article gives an elementary approach to continuous q-Hermite polynomials. We stress their relation to Fibonacci, Lucas and Chebyshev polynomials and to some q-analogues of these polynomials.

The introduction of the quadratic Hencky strain energy based on the logarithmic strain tensor log V is a milestone in the development of nonlinear elasticity theory in the first half of the 20th century. Since the original manuscripts are…

This is an English translation of Reidemeister's book "Einf\"uhrung in die kombinatorische Topologie" from 1932, the first monograph on combinatorial group theory and topology, with some added comments by the translator and Warren Dicks.

We analyze the main arguments that attempt to explain why there is no point in changing the envelope. Most people confuse estimation and calculation, conditional and unconditional probabilities, random and non-random variables, modelling…

Magic squares have been an enthralling topic in mathematics for centuries. They are formed by filling in all the cells of a square matrix with the numbers starting from one so that the sum of all rows, columns, and diagonals is the same.…

Biography and publications list for Donald Arthur Preece, who died on 6 January 2014, who made many contributions in statistics (experimental design) and in combinatorics.

This essay, an excerpt of the author's Ph.D. in Philosophy of mathematics (2012) thought of as being a companion to recent discoveries of new explicit Cartan geometry curvatures, analyzes how Gauss, after having devised the isometrically…

We give a purely mathematical interpretation and construction of sculptures rendered by one of the authors, known herein as Fels sculptures. We also show that the mathematical framework underlying Ferguson's sculpture, {\it The Ariadne…

This article introduces, informally, the substance and the spirit of Grothendieck's theory of the Picard scheme, highlighting its elegant simplicity, natural generality, and ingenious originality against the larger historical record.

We survey the reasons for the ongoing boycott of the publisher Elsevier. We examine Elsevier's pricing and bundling policies, restrictions on dissemination by authors, and lapses in ethics and peer review, and we conclude with thoughts…

We investigate the journal impact factor, focusing on the applied mathematics category. We discuss impact factor manipulation and demonstrate that the impact factor gives an inaccurate view of journal quality, which is poorly correlated…

The calculations of the Tibetan calendar are described, using modern mathematical notations instead of the traditional methods.

We provide an analytical closed-form solution of the exponential equation $a^x+a^{-x}=x$ for a specific value $a$, discuss the number of roots in general case, and provide bounds on the roots.

For any particularly interesting theorem one proof is never enough. Instead, the first proof sets the challenge to find a more elegant method that illuminates subtle features of the math, is simpler to understand, or even avoids using…