历史与综述
This is a survey of characterizations and relationships between some properties of lattices, particularly the modular, Arguesian, linear, and distributive properties, but also some other related properties. The survey emphasizes finite and…
Order and symmetry are main structural principles in mathematics. We give five examples where on the face of it order is not apparent, but deeper investigations reveal that they are governed by order structures. These examples are finite…
We provide an historical overview of how advances in technology influenced high school and university mathematical competitions in the United States and at the International Mathematical Olympiad. While students are not allowed the usage of…
We describe a system of plane algebraic curves defined over \Z, attached naturally to the exponential function. On of these is a remarkable curve of degree 6 that has genus equal to 1. As the sectic curve has rational points, it is an…
An age-old controversy in mathematics concerns the necessity and the possibility of constructive proofs. The controversy has been rekindled by recent advances which demonstrate the feasibility of a fully constructive mathematics. This…
Leibniz's mathematical texts are a perfect example of a type of historical document that is extremely difficult to deal with in the context of an editorial enterprise: the draft. The tables in Leibniz's mathematical manuscripts are a…
People typically consider only European mathematics as orthodox, often intentionally or unintentionally overlooking the existence of mathematics from non-European societies. Inspired by Maria Ascher's two well-known papers on sand drawings…
In order to help students learn how to write mathematical proofs, we adapt the Coq proof assistant into an educational tool we call Waterproof. Like with other interactive theorem provers, students write out their proofs inside the software…
A convenient framework for dealing with asymptotic limit problems of probabilistic nature is provided. These problems include questions such as finding the asymptotic proportion of terms of a sequence falling inside a given interval, or the…
Patrick Moss (1947--2024) had two distinct lives as a mathematician. The first was as a ring theorist in the late 1970s, in which he worked with Ginn and Lenagan as a student. After a long career as an inspirational mathematics teacher,…
A camel can carry one banana at a time on its back. It is on a diet and therefore can only have one banana at a time in its stomach. As soon as it has eaten a banana it walks a mile and then it needs a new banana (in order to be able to…
A camel can carry $B$ bananas on its back. It can have $2$ bananas at a time in its stomach. For each mile the camel walks, the amount of bananas in its stomach decreases $1$. As soon as the amount of bananas in the camel's stomach is at…
The exposition in Euclid's Elements contains an obvious gap (seemingly unnoticed by most commentators): he often compares not just angles, but *groups* of angles, and at the same time he avoids summing angles (and considering angles greater…
The problem `Exploring Mount Neverest' by Henry Ernest Dudeney is solved. Dudeney formulated the problem in the beginning of the 20th century and gave a non-optimal solution (without estimating the non-optimality).
The field of ethnomathematics holds significance in the pursuit of comprehending how students can grasp, express, manipulate, and ultimately apply mathematical concepts. However, ethnomathematics is also considered a complex concept in…
We present results and ideas on flexibility and its teaching for university mathematicians based on research and our experience in professional development programs. We believe this could provide food for thought for instructors of calculus…
In 1738, the King of Naples and future King of Spain, Carlos III, commissioned the Spanish military engineer Roque Joaqu\'in de Alcubierre to begin the excavations of the ruins of the ancient Roman city of Pompeii and its surroundings,…
The goal of this expository paper is to present the basics of geometric control theory suitable for advanced undergraduate or beginning graduate students with a solid background in advanced calculus and ordinary differential equations.
We report the results of our NSF-funded project in which we alpha- and beta- tested a survey comprising all aspects of the ethical practice standards from two disciplines with relevance to mathematics, the American Statistical Association…
Ivan Niven's succinct proof that pi is irrational is easy to verify, but it begins with a magical formula that appears to come out of nowhere, and whose origin remains mysterious even after one goes through the proof. The goal of this…