历史与综述
This is the second volume of a textbook for a two-semester course in mathematical analysis. This second volume is about analysis of multi-variable functions. The topics covered include Euclidean spaces, convergence of sequences, open sets…
This is the first volume of a textbook for a two-semester course in mathematical analysis. This first volume is about analysis of functions of a single variable. The topics covered include completeness axiom, Archimedean property,…
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…
In this paper, I revisit Frege's theory of sense and reference in the constructive setting of the meaning explanations of type theory, extending and sharpening a program--value analysis of sense and reference proposed by Martin-L\"of…
It is often claimed that the theory of function levels proposed by Frege in Grundgesetze der Arithmetik anticipates the hierarchy of types that underlies Church's simple theory of types. This claim roughly states that Frege presupposes a…
In his Foundations of a General Theory of Manifolds, Georg Cantor praised Bernard Bolzano as a clear defender of actual infinity who had the courage to work with infinite numbers. At the same time, he sharply criticized the way Bolzano…
It is shown that each sequence giving the number of times a given day of the month falls on a certain day of the week for $400$ successive years of the Gregorian cycle can be composed of various pieces of various length of one of 4…
In his 1685 paper "Observationes cyclometricae" published in Acta Eruditorum, Adam Adamandy Kocha\'nski presented an approximate ruler-and-compass construction for rectification of the circle. It is not generally known that the first part…
This paper collects open problems that were presented at the ``Hausdorff Geometry of Polynomials" workshop held on July 10-14, 2023 in Sofia, Bulgaria.
The Hummer Principle was born from the mind of Bob Hummer in 1946, which consists of performing card shuffles with an even number of cards while leaving some properties of the deck intact. In this document, we will present a generalization…
We are interested in the learning of 6 to 7 years old children in implementations of a situation of reproduction of figure by folding presented in the first part of this article. In the second part we expose our problem as well as our…
This is a sequel to the author's "Truth and Knowledge", College Publications, 2022, and contains some problems and results in connection with a possible representation for Yablo like structures.
Jigsaw puzzles are typically labeled with their finished area and number of pieces. With this information, is it possible to estimate the area required to lay each piece flat before assembly? We derive a simple formula based on…
Invented by Kurt Hensel at the very end of 19th century on the model of power series in one indeterminate, the $p$-adic numbers have not only become an indispensable tool of contemporary arithmetic, but a research topic per se. In this…
This short note is a comment on a historical aspect of a famous formula dating from the 18th century.
We developed a pilot course focused on mathematical modeling within the tertiary education framework, with a distinct emphasis on sustainability and sustainable development. While an applicable textbook exists for this liberal arts course,…
In this paper, we shall study the stellar work of Norwegian mathematician Selberg and Hungarian mathematician Erd\H{o}s in providing an Elementary proof of the well-known \textit{Prime Number Theorem}. In addition to introducing ourselves…
In this article we present a remarkable concyclicity of four centroids related to the orthocenters of the triangles $ABC,$ $BPC,$ $CPA,$ and $PAB$ of a quadrangle $ABCP$. Furthermore, we establish a result about orthologic triangles…
This paper aims to study the graph radii and diameters induced by the $k$-dimensional versions of the well-known six international chess pieces on every finite $\{n \times n \times \dots \times n\} \subseteq \mathbb{Z}^k$ lattice since they…
We discuss here the geometry of frieze patterns, and add a few words about Greek vases, molecular symmetry, and 2D crystallography. The work is written primarily for school students.