历史与综述

An edited version is given of the text of G\"odel's unpublished manuscript of the notes for a course in basic logic he delivered at the University of Notre Dame in 1939. G\"odel's notes deal with what is today considered as important…

We discuss the practical problems arising when constructing any (new or old) scales on slide rules, i.e. realizing the theory in the practice. This might help anyone in planning and realizing (mainly the magnitude and labeling of) new…

We give a thoroughful explanation of the general properties of different, general scales, corresponding to different (all possible) mathematical functions f(x), we mention and analyse many examples. These observations and statements might…

We discuss the general theory of realizing two-variable fuctions on slide rules (based on our paper 1977) and offer some new scales for practical use.

This article investigates the attitude toward mathematics among the students enrolled in the Foundation Year Programme at Nazarbayev University. The study is conducted quantitatively and an inventory developed by Tapia and Marsh II is…

This article reviews the so-called "axioms" of origami (paper folding), which are elementary single-fold operations to achieve incidences between points and lines in a sheet of paper. The geometry of reflections is applied, and exhaustive…

Four integer parametrizations for the bi-orthogonal monoclinic Diophantine parallelepiped are given.

First, we give a formula for the foci of an ellipse, $E_0$, as a function of the coefficients of an equation of $E_0$(see Theorem <ref>T2</ref>). To prove Theorem <ref>T2</ref>, we use two interesting formulas proven in <cite>B</cite> and…

The nineteenth century was an important period for both Oxford mathematics and algebra in general. While there is extensive documentation of mathematical research in Oxford at this time, the same cannot be said of the teaching. The content…

In this article, a new method for characterizing nontransitive dice is de- scribed. This new method is then used to describe the "Nontransitive Identities" (NI) that are possible for 3 dice with 3, 4 and 5 sides each as well as for 5 dice…

A popular curve shown in introductory maths textbooks, seems like a circle. But it is actually a different curve. This paper discusses some elementary approaches to identify the geometric object, including novel technological means by using…

The aim of this paper is to generalize Apollonius' problem. The problem is to construct a circle that is tangent to three given circles in a plane. We find the maximum possible number of solution circles in the case of more than the three…

This essay traces the history of three interconnected strands. Firstly, changes in the concept of number, secondly, the study of the qualities of number, which evolved into number theory, and thirdly, the nature of mathematics itself, from…

James Earl Baumgartner (March 23, 1943 - December 28, 2011) came of age mathematically during the emergence of forcing as a fundamental technique of set theory, and his seminal research changed the way set theory is done. He made…

We discuss some problems with the indefinite integral notation and the way of teaching of integrals in Calculus. Based on the discussion, and in order to avoid mistakes, we propose another notation for indefinite integrals.

We describe how to construct a dodecahedron, tetrahedron, cube, and octahedron out of pvc pipes using standard fittings.

Our goal is to present, in what we believe is the most efficient way possible, a construction of four mutually tangent circles.

In this article we describe the life and work of Wolf Barth who died on 30th December 2016. Wolf Barth's contributions to algebraic variety span a wide range of subjects. His achievements range from what is now called the Barth-Lefschetz…

This article, dedicated, with admiration to Reuben Hersh, for his forthcoming 90th birthday, argues that mathematics today is not yet a science, but that it is high time that it should become one.

The Boolean function implicit in the famous Dayenu song, sung at the Passover meal, is expressed in full conjunctive normal form, and it is proved that if there are n miracles the number of truth-vectors satisfying it is $2^n -(n+1)$.