历史与综述
How do we move a robot efficiently from one position to another? To answer this question, we need to understand its configuration space, a 'map' where we can find every possible position of the robot. Unfortunately, these maps are very…
The article is dedicated to thye memory of a distinguished mathematician Professor Misha Shubin
By combining theoretical and computational techniques from geometry, calculus, group theory, and Galois theory, we prove the nonexistence of a closed-form algebraic solution to a Japanese geometry problem first stated in the early…
This paper discusses our experiences and challenges in teaching advanced undergraduate Real Analysis classes for Mathematics Education students at the University of PGRI (Persatuan Guru Republik Indonesia, Indonesian Teachers Association)…
We give a probabilistic proof of the orbit-counting lemma.
The "Millennium Prize Problems" have a place in the history of mathematics. Here we tell some little-known anecdotes from the perspective of the planner of that project. These stories are far from their end; more likely they are just at…
Krull's Fundamentalsatz, the generalisation of the main theorem of elementary number theory to integral domains, is the starting point of Lorenzen's career in mathematics. This article traces a conceptual history of Lorenzen's successive…
We invoke the Law of Sines to prove Morley's Trisector Theorem. Though the sinusoidal function appears, the proof is safe for the trigonometrically distanced.
The usual modelling of the syllogisms of the Organon by a calculus of classes does not include relations. Aristotle may however have envisioned them in the first two books as the category of relatives, where he allowed them to compose with…
There are $n$ bags with coins that look the same. Each bag has an infinite number of coins and all coins in the same bag weigh the same amount. Coins in different bags weigh 1, 2, 3, and so on to $n$ grams exactly. There is a unique label…
Voronoi mosaics inspired by the seed points placed on the Archimedes Spirals are reported. Voronoi entropy was calculated for these patterns. Equidistant and non-equidistant patterns are treated. Voronoi mosaics built from cells of equal…
In its December 2019 edition, the \textit{Notices of the American Mathematical Society} published an essay critical of the use of diversity statements in academic hiring. The publication of this essay prompted many responses, including…
We identified three most challenging points related to diverse, equitable, and inclusive (DEI) issues. First, the majority of our students entering the College lack the math skills essential to success in Calculus, as basic as College…
Two centuries ago, Sophie Germain began to work on her grand plan to prove the theorem of Fermat, the famous conjecture that $x^n + y^n = z^n$ is impossible for nonzero integral values of $x$, $y$, and $z$, when $n > 2$. At that time, this…
We introduce and analyze several variations of Penney's game aimed to find a more equitable game.
The K\=aty\=ayana \'Sulvasutra has been much less studied or discussed from a modern perspective, even though the first English translation of two adhy\=ayas (chapters) from it, by Thibaut, appeared as far back as 1882. Part of the reason…
Notes from a course at the ATM Workshop on Schubert Varieties, held at The Institute of Mathematical Sciences, Chennai, in November 2017. Various expansions of Schur functions, the Lindstr\"om-Gessel-Viennot lemma, semistandard Young…
We present a manuscript of Paul Lorenzen that provides a proof of consistency for elementary number theory as an application of the construction of the free countably complete pseudocomplemented semilattice over a preordered set. This…
The online homework system WeBWorK has been successfully used at several hundred colleges and universities. Despite its popularity, the WeBWorK system does not provide detailed metrics of student performance to instructors. In this article,…
A magic SET square is a 3 by 3 table of SET cards such that each row, column, diagonal, and anti-diagonal is a set. We allow the following transformations of the square: shuffling features, shuffling values within the features, rotations…