历史与综述
There have been several modifications of how basic calculus has been taught, but very few of these modifications have considered the computational tools available at our disposal. Here, we present a few tools that are easy to develop and…
This article solves the Hume's problem of induction using a probabilistic approach. From the probabilistic perspective, the core task of induction is to estimate the probability of an event and judge the accuracy of the estimation.…
The Ratio Test and the Root Test for absolute convergence/divergence of series of numbers $\sum_{n=0}^{\infty}a_n$ are frequently discussed and proved independently in Calculus courses. The Root Test is stronger (verifies convergence for…
We present some similarities between Leibnizian and Robinsonian calculi, and address some objections raised by historians. The comparison with NSA facilitates our appreciation of some Leibnizian procedures that may otherwise seem obscure.…
Combination locks are widely used to secure bicycles. We consider a combination lock consisting of adjacent rotating dials with the first nonnegative integers printed on each of them. Assuming that we know the correct combination and we…
Ce texte, \'ecrit pour la Gazette de la Soci\'et\'e math\'ematique de France, \'evoque les fonctions de type positif et leur histoire avant 1950 ; on y pr\'esente notamment des extraits de lettres \'ecrites par Roger Godement, qui leur…
It is a classical fact in Euclidean geometry that the regular polygon maximizes area amongst polygons of the same perimeter and number of sides, and the analogue of this in non-Euclidean geometries has long been a folklore result. In this…
We discuss two proof evaluation activities meant to promote the acquisition of learning behaviors of professional mathematics within an introductory undergraduate proof-writing course. These learning behaviors include the ability to read…
Pulli Kolam is an ancient mathematical artform that is still practiced today in south India by over a quarter million people. "Pulli" in the Tamil language means dots. A specific type of pulli kolam is "sikku" kolam where a series of dots…
Recent economic developments of countries like Japan, Korea, and Singapore, as a result of improvement in the quality of their education, show that having a high-quality education may lead to economic growth. In this article, using some…
Kepler's thinking is highly original and the inspiration for discovering his famous third law is based on his rather curious geometric approach in his Harmonices mundi for explaining consonances. In this article we try to use a modern…
Lights Out is a single-player electronic handheld game from the 1990s that features a 5 by 5 grid of light-up buttons. The game begins with some lights on and others off. The goal is to turn off all lights but pressing a button changes its…
This paper carries out a scientific study of the effects of strike on Nigerian Universities. A mathematical model is formulated to examine the behavior of Nigerian University System when Public Universities are on strike. The results show…
In 2016 Vladimir Voevodsky sent the author an email message where he explained his conception of mathematical structure using a historical example borrowed from the \emph{Commentary to the First Book of Euclid's Elements} by Proclus; this…
The following magic trick is at the center of this paper. While the audience writes the first ten terms of a Fibonacci-like sequence (the sequence following the same recursion as the Fibonacci sequence), the magician calculates the sum of…
In this article we would like to consider some approaches to non-integer integro-differentiations and its implementation in computer algebra system Wolfram Mathematics.
Whilst Paul de Casteljau is now famous for his fundamental algorithm of curve and surface approximation, little is known about his other findings. This article offers an insight into his results in geometry, algebra and number theory.…
This paper presents an updated biography of Samgamagr\=ama M\=adhava incorporating viewpoints expounded by scholars in the recent past and collecting together in one place more details about his works culled from recent researches into his…
Effective and timely feedback in educational assessments is essential but labor-intensive, especially for complex tasks. Recent developments in automated feedback systems, ranging from deterministic response grading to the evaluation of…
We investigate fractal structures in African and African diasporic music, building on hypotheses of choreographer Reggie Wilson and research on fractals in African material culture by Ron Eglash.