Mathematics

A method of obtaining the number pi is considered, which derives pi from the number of elastic collisions between two blocks and a wall.

This paper aims to develop the mathematical representation of a surface generated by elliptical arcs joining the sides of a regular polygon to a point lying vertically upward on the central axis of the polygon. The volume of the corresponding solid has also been determined.

The article deals with the problems of information and communication technologies (ICT) development in teaching mathematics of engineering specialities students in the United States. In the article the nature of trends of convergence of information system in higher technical education and other tendencies in the USA are characterized. The main historical stages of development of the theory and methods of ICT use in teaching mathematics of engineering specialities students in the United States are defined. The study of historical sources has been allowed to emphasize six stages, at each stage it is analyzed the use of ICT for teaching mathematics, it is shown the contradictions and the main features of the use of ICT in teaching mathematics of engineering specialities students.

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 to improving our understanding of mathematical arguments. I concentrate on two such innovations: dialogue types (§1) and argumentation schemes (§2). I argue that both devices are much more applicable to mathematical reasoning than may be commonly supposed.

This paper presents a brief account of the important milestones in the historical development of the theory of differential equations. The paper begins with a discussion on the date of birth of differential equations and then touches upon Newton's approach to differential equations. Then the development of the various methods for solving the first order differential equations and the second order linear differential equations are discussed. The paper concludes with a brief mention of the series solutions of differential equations and the qualitative study of differential equations.

The purpose of the present work is to provide short and supple teaching notes for a 30 hours introductory course on elementary \textit{Enumerative Algebraic Combinatorics}. We fully adopt the \textit{Rota way} (see, e.g. \cite{KY}). The themes are organized into a suitable sequence that allows us to derive any result from the preceding ones by elementary processes. Definitions of \textit{combinatorial coefficients} are just by their \textit{combinatorial meaning}. The derivation techniques of formulae/results are founded upon constructions and two general and elementary principles/methods: - The \textit{bad element} method (for \textit{recursive} formulae). As the reader should recognize, the bad element method might be regarded as a combinatorial companion of the idea of \textit{conditional probability}. - The \textit{overcounting} principle (for \textit{close form} formulae). Therefore, \textit{no computation} is required in \textit{proofs}: \textit{computation formulae are byproducts of combinatorial constructions}. We tried to provide a self-contained presentation: the only prerequisite is standard high school mathematics. We limited ourselves to the \textit{combinatorial point of view}: we invite the reader to draw the (obvious) \textit{probabilistic interpretations}.

This article analyses geometric constructions by origami when up to n simultaneous folds may be done at each step. It shows that any arbitrary angle can be m -sected if the largest prime factor of m is p≤n+2 . Also, the regular m -gon can be constructed if the largest prime factor of ϕ(m) is q≤n+2 , where ϕ is Euler's totient function.

This paper develops a unified voice-leading model for the genus of mystic and Wozzeck chords. These voice-leading regions are constructed by perturbing symmetric partitions of the octave, and new Neo-Riemannian transformations between nearly symmetric hexachords are defined. The behaviors of these transformations are shown within visual representations of the voice-leading regions for the mystic-Wozzeck genus.

We are asking: why are the dynamics and control of Covid-19 most interesting for mathematicians and why are mathematicians urgently needed for controlling the pandemic? First we present our comments in a Bottom-up approach, i.e., following the events from their beginning as they evolved through time. They happened differently in different countries, and the main objective of the first part is to compare these evolutions in a few selected countries with each other. The second part of the article is not "country-oriented" but "problem-oriented". From a given problem we go Top-down to its solutions and their applications in concrete situations. We have organized this part by the mathematical methods that play a role in their solution. We give an overview of the main branches of mathematics that play a role and sketch the most frequent applications, emphasising mathematical pattern analysis in laboratory work and statistical-mathematical models in judging the quality of tests; demographic methods in the collection of data; different ways to model the evolution of the pandemic mathematically; and clinical epidemiology in attempts to develop a vaccine.

This text (in Spanish) hopes to offer the reader a starting point to deliver good talks on mathematical topics.