历史与综述

The theory uses methods and language of linear algebra to study nonlinear spaces. These techniques can be used particularly to describe analytic geometry of non-linear elliptic, hyperbolic, De Sitter and Anti de Sitter spaces. The main…

The regular hendecagon is the polygon with the smallest number of sides that cannot be constructed by single-fold operations of origami on a square sheet of paper. This article shows its construction by using an operation that requires two…

In this book, there are five chapters: Systems of Linear Equations, Vector Spaces, Homogeneous Systems, Characteristic Equation of Matrix, and Matrix Dot Product. It has also exercises at the end of each chapter above to let students…

In this book, there are five chapters: The Laplace Transform, Systems of Homogeneous Linear Differential Equations (HLDE), Methods of First and Higher Orders Differential Equations, Extended Methods of First and Higher Orders Differential…

We discuss a couple of examples of Markov chains. This note is written primarily for school students; it is based on a lecture given by the first author at a Math Circle at NAS (www.assagames.com/nas).

The aim of this article has been to put together various aspects of the personality of the Italian mathematician Francesco Severi: the mathematical, the political, the institutional, academic and philosophical one. We tried in particular to…

This paper provides a new mathematical axiom system for classical harmony, which is a prescriptive rule system for composing music, introduced in the second half of the 18th century. The clearest model of classical harmony is given by the…

This article is an abridged and commented translation into Spanish of the 1815 memoir where Gauss introduced the quadrature rules now associated with his name. Gauss' work does not resemble at all the stardard text-book treatment of…

We obtain a construction of the total spherical perspective with ruler, compass, and nail. This is a generalization of the spherical perspective of Barre and Flocon to a 360 degree field of view. Since the 1960s, several generalizations of…

Eighteenth century Japan was a time of isolation and peace, where education and the arts blossomed. Originally posted before 1749 by an unknown author, the sangaku (mathematical tablet) that became known as the Gion Shrine problem, has…

This is a biographical sketch and tribute to Abraham Robinson (1918-1974) on the 95th anniversary of his birth with a short discussion of the place of nonstandard analysis in the present-day mathematics.

There has been some interest recently in determining the longest distance one can sail for on the earth without hitting land, as well as in the converse problem of determining the longest distance one could drive for on the earth without…

As Weyl was interested in infinitesimal analysis and for some years embraced Brouwer's intuitionism, which he continued to see as an ideal even after he had convinced himself that it is a practical necessity for science to go beyond…

We generalize Tennenbaum's geometric proof of the irrationality of sqrt(2) to sqrt(n) for n = 3, 5, 6 and 10. Modified version published in Mathematics Magazine \textbf{85} (2012), no. 2, 110--114.

We investigate under which conditions a rectangular table can be placed with all four feet touching a continuous ground by turning it on the spot.

We refute the so-called one-line proof of the infinitude of primes in [1].

This is a historical introduction to the theory of Stirling numbers of the second kind S(n,k) from the point of view of analysis. We tell the story of their birth in the book of James Stirling (1730) and show how they mature in the works of…

This paper addresses some of the experiences encountered and some of the strategies utilized while using flipped classroom pedagogy in an undergraduate Single Variable Calculus (SVC) course in a Confucian Heritage Culture (CHC) environment.…

A significant amount of research has considered mathematical proofs, the students who learn them, and the instructors that teach them, from a variety of perspectives. This paper considers this topic from four main perspectives: students'…

We present here two classes of infinite series and the associated continued fractions involving $\pi$ and Catalan's constant $G$ based on the work of Euler and Ramanujan. A few sundry continued fractions are also given.