历史与综述
This is an extended introduction to discrete valuation rings and Dedekind domains. Some natural generalizations of Dedekind domains are also (briefly) discussed including "almost Dedekind domains", Pr\"ufer domains, Krull domains, and…
George Boros and Victor Moll's masterpiece "Irresistible Integrals" does well to include a suitably-titled appendix, "The Revolutionary WZ Method," which gives a brief overview of the celebrated Wilf--Zeilberger method of definite…
The problem of the longest head run was introduced and solved by Abraham de Moivre in the second edition of his book Doctrine of Chances (de Moivre, 1738). The closed-form solution as a finite sum involving binomial coefficients was…
Hodge duality is a central concept of 20th century algebraic and analytic geometry and plays a non-negligible role also in recent mathematical physics. At first sight one might expect that its origins lie in the 1930s when its name-giving…
To give a parametrization of the Diophantine equation $A^{3}+B^{3}=C^{3}+D^{3}$ in terms of integral binary quadratic forms in a constructive way.
Douglas Walton's multitudinous contributions to the study of argumentation seldom, if ever, directly engage with argumentation in mathematics. Nonetheless, several of the innovations with which he is most closely associated lend themselves…
The paper tells about the main features and events of the ergodic seminar organized and headed by V.~A.~Rokhlin at the Leningrad State University. The seminar was active in {\rm1960--1970.\}
I offer a revisionist interpretation of Galileo's role in the history of science. My overarching thesis is that Galileo lacked technical ability in mathematics, and that this can be seen as directly explaining numerous aspects of his life's…
We show how we found substitution rules for a quasiperiodic tiling with local rotational symmetry and inflation factor 1 + sqrt(3). The base tiles are a square, a rhomb with an acute angle of 30 degrees, and equilateral triangles that are…
Abstract axiomatic formulation of mathematical structures are extensively used to describe our physical world. We take here the reverse way. By making basic assumptions as starting point, we reconstruct some features of both geometry and…
Studying Mathematics requires a synthesis of skills from a multitude of academic disciplines; logical reasoning being chief among them. This paper explores mathematical logical preparedness of students entering first year university…
Robust preparation of future secondary mathematics teachers requires attention to the acquisition of mathematical knowledge for teaching. Many future teachers learn mathematics content primarily through mathematics major courses that are…
While students may find spline interpolation quite digestible, based on their familiarity with continuity of a function and its derivatives, some of its inherent value may be missed when students only see it applied to standard data…
We introduce a kind of converse of Pompeiu's theorem. Fix an equilateral triangle $\triangle A_0B_0C_0$, then for any triangle $\triangle ABC$ there is a unique point $P$ inside the circumcircle $\Gamma_0$ of $\triangle A_0B_0C_0$ such that…
Based on Plato's Timaeus, we present some reflections on music, cosmology and mathematics and their mutual influence.The article is dedicated to the composer Walter Zimmermann. The final version of this article will appear in the volume…
We present a detailed proof of the prime number theorem suitable for a typical undergraduate- or graduate-level complex analysis course. Our presentation is particularly useful for any instructor who seeks to use the prime number theorem…
We present a simple but efficient concept for the realization of blended teaching of mathematics and its applications in theoretical mechanics that was conceived, tested and implemented at the University of Trento, Italy, during the…
C.S. Seshadri passed away in July 2020. The first part of this article contains some reminiscences from the early 1980s, when as a graduate student in the Tata Institute of Fundamental Research (TIFR), Mumbai, I had the good fortune to…
About Conway's surreal numbers: A letter to a friend (written in French). In memoriam John Horton Conway.
This is a brief historical note about famous Legendre's criterium for convergent of continued fraction expansion. The paper is written in Russian.