Mathematics
This paper describes an approach to generating looping animations using the modular flow and elliptic functions. The modular flow is a flow on lattices with many periodic orbits, and elliptic functions are meromorphic, doubly-periodic…
If you only take one thing away from this document I would like it tobe this: Creating accessible documents requires authors have a working understanding of accessibility, and write with accessibility in mind.
This is a lecture on the theory of formal power series developed entirely without any analytic machinery. Combining ideas from various authors we are able to prove Newton's binomial theorem, Jacobi's triple product, the Rogers--Ramanujan…
Drawing on the Data and Predictions strand of the Indicazioni Nazionali per il curricolo 2012, this study proposes a problem based instructional approach to the teaching of probability. More specifically, the study adopts a design based…
This note provides an introduction to selected topics in algebraic graph theory, including strongly regular graphs, Steiner systems, and automorphism groups. We describe constructions and properties of notable graphs such as the Petersen…
We give a method for constructing an interactive art piece which illustrates two different definitions of the braid groups, along with their faithful action on the free group. The box also demonstrates how all motions of points in the plane…
We present, in detail and with a modern rigor, the two title proofs. The Weak Jordan Theorem (WJT) states that the complement of any topological circuit in the plane is disconnected.
This essay develops a parallel between the Fundamental Theorem of Galois Theory and the Stone--Weierstrass theorem: both can be viewed as assertions that tie the distinguishing power of a class of objects to their expressive power. We…
We give an exposition of the Newton-Leibniz calculus. We begin by defining the integral as a limit of Riemann sums, verify the integrals of the standard catalog of functions by direct manipulation, prove the substitution lemmas as theorems…
Access to quality education remains a global challenge, particularly in crisis-affected regions. This study examines the decline in students' mathematical proficiency and proposes an innovative Moodle-based testing system that incorporates…
This text summarizes and expands the content of a general audience talk given in 2018 at the University of Mainz. Motivated by recent developments in dependent type theory and infinity category theory, it presents a history of ideas around…
In the winter semester of 1890--1891 Adolf Hurwitz delivered a lecture course at the Albertina University in K\"onigsberg entitled -Theorie der algebraischen Gleichungen-. These lectures contain a particularly clear presentation of the…
I was interested in the work of Solomon Marcus in Mathematical Linguistics as a high-school student. Later, I had the opportunity to discuss with him about many topics. He was a polymath. We wrote a paper together, and I refereed an…
Preliminary version of a book on univariate real analysis, with 14 chapters and 2 appendices. 1. Real numbers; 2. Limits of real sequences; 3. Series; 4. Limits of real functions. 5. Elementary functions; 6. Continuous functions; 7.…
The {\em Four-dimensional Light Orchestra} or {\em 4DLO} was an interactive sculpture at the National Museum of Mathematics (MoMath) from November 20, 2025 through January 2026, illustrating various sub-symmetries of the 24-cell with…
This study examines the effectiveness of a structured instructional approach to decomposition and recomposition of large numbers in six primary school classes (three Year 4 and three Year 5, N = 120) using a quasi - experimental design with…
Even if it has been less than a decade and a half since Tian introduced his concept of evolution algebras to represent algebraically non-Mendelian rules in Genetics, their study is becoming increasingly widespread mainly due to their…
These personal reminiscences of the great Russian mathematician Sergey K. Godunov (1929-2023) arose from a request by his daughter, Ekaterina, to contribute a piece to a book she is writing about her father's life. I was honoured to accept…
Probabilities is the English translation of the book Probabilit\'es Tome 1 and Tome 2. The mathematic content is authored by Prof. Jean-Yves Ouvrard. The English version has been done by his eldest son Dr. Xavier Ouvrard. In this first…
Existing knowledge management tools either preserve prose but lose structural relationships, or capture relationships but restrict edge semantics to fixed vocabularies. We introduce Astrolabe, a content-addressable hypergraph for semantic…