历史与综述
The M\=anava \'Sulvas\=utra, while less sophisticated than the other \'sulvas\=utras, is seen to contain some mathematical ideas and constructions not found in the other \'sulvas\=utras. Here we discuss some of these constructions and…
We argue that Robinson's hyperreals have just as much claim to applicability as the garden variety reals. In a recent text, Easwaran and Towsner (ET) analyze the applicability of mathematical techniques in the sciences, and introduce a…
We find an interesting relationship between the golden ratio, the Moebius function, the Euler totient function and the natural logarithm - central players in the theory of numbers. A number of identities involving the golden ratio and its…
There are compelling reasons to shift our pedagogy toward evidence-based active learning methods that substantially improve student success, and now plenty of resources to aid in that shift. These include the recent CBMS Statement on Active…
The Rascal Triangle was introduced by three middle school students in 2010, and in this paper we describe number triangles that are generalizations of the Rascal Triangle and show that these Generalized Rascal Triangles are characterized by…
This is a theoretical and computational strategy exploration of the visually attractive game IQ-Link. Not all games which are visually appealing are worthy of your time as a puzzlist. This analysis gives a would-be addict some idea of what…
In a delightful article that recently appeared in Mathematics Magazine, David and Lori Mccune analyze the board game "Count Your Chickens!", recommended to children three and up. Alas, they use the advanced theory of Markov chains, that…
This article discusses the process of creating, implementing and experiencing Flipped Learning in a Multivariable Calculus course for second year engineering students. We describe the construction of the teaching material, consisting of…
Those of us who teach Mathematics for Liberal Arts (MLA) courses often underestimate the mathematical abilities of the students enrolled in our courses. Despite the fact that many of these students suffer from math anxiety and will admit to…
Current concerns about reproducibility in many research communities can be traced back to a high value placed on empirical reproducibility of the physical details of scientific experiments and observations. For example, the detailed…
We provide a proof of Wilson's Theorem and Wolstenholme's Theorem based on a direct approach by Lagrange requiring only basic properties of the primes and the Binomial theorem. The goal is to show how similar the two theorems are by…
This is an expanded version of my review of Nina Engelhardt's book "Modernism, Fiction and Mathematics", Edinburgh University Press 2018. A considerably shortened version will appear in the Notices of the AMS.
In 1941 a mechanical problem about a rod in a moving train (there is a initial position such that rod does not touch the floor while train is moving) was published by R.Courant and H.Robbins in their popular book "What is mathematics?" and…
We present an interactive game which challenges a single player to match 3-dimensional polytopes to their planar nets. It is open source, and it runs in standard web browsers
We present details of logically simplest integral sufficient for deducing the Stirling asymptotic formula for n!. It is the Newton integral, defined as the difference of values of any primitive at the endpoints of the integration interval.…
In order to implement a STEAM approach including the use of technology, namely the use of interactive mathematics software GeoGebra, in mathematics classes, in the lusophone space, the materials presented here were conceived, to be…
Math placement is a crucial step between admission and full engagement with the university for students in STEM majors. Students' placement experiences influence not only their mathematical entry point on their degree pathway, but their…
To be successful, junior faculty must properly manage their time in the face of expanding responsibilities. One such responsibility is supervising undergraduate research projects. Student research projects (either single or multi-student)…
We present statistical evidence for the importance of the "mystic chord" in Scriabin's Piano Sonata No. 5, Op. 53, from a computational and mathematical counterpoint perspective. More specifically, we compute the effect sizes and $\chi^{2}$…
A counterpoint theory for the whole continuum of the octave is obtained from Mazzola's model via extended counterpoint symmetries, and some of its properties are discussed.