Mathematics Commons^™

Optimal Monohedral Tilings Of Hyperbolic Surfaces, Leonardo Digiosia, Jahangir Habib, Jack Hirsch, Lea Kenigsberg, Kevin Li, Dylanger Pittman, Jackson Petty, Christopher Xue, Weitao Zhu

Rose-Hulman Undergraduate Mathematics Journal

The hexagon is the least-perimeter tile in the Euclidean plane for any given area. On hyperbolic surfaces, this "isoperimetric" problem differs for every given area, as solutions do not scale. Cox conjectured that a regular k-gonal tile with 120-degree angles is isoperimetric. For area π/3, the regular heptagon has 120-degree angles and therefore tiles many hyperbolic surfaces. For other areas, we show the existence of many tiles but provide no conjectured optima. On closed hyperbolic surfaces, we verify via a reduction argument using cutting and pasting transformations and convex hulls that the regular 7-gon is the optimal n-gonal tile of …

The Determining Number And Cost Of 2-Distinguishing Of Select Kneser Graphs, James E. Garrison

Rose-Hulman Undergraduate Mathematics Journal

A graph $G$ is said to be \emph{d-distinguishable} if there exists a not-necessarily proper coloring with $d$ colors such that only the trivial automorphism preserves the color classes. For a 2-distinguishing labeling, the \emph{ cost of $2$-distinguishing}, denoted $\rho(G),$ is defined as the minimum size of a color class over all $2$-distinguishing colorings of $G$. Our work also utilizes \emph{determining sets} of $G, $ sets of vertices $S \subseteq G$ such that every automorphism of $G$ is uniquely determined by its action on $S.$ The \emph{determining number} of a graph is the size of a smallest determining set. We investigate …

Generations Of Reason: A Family’S Search For Meaning In Post-Newtonian England (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Reviewed Title: Generations of Reason: A Family's Search for Meaning in Post-Newtonian England by Joan L. Richards. New Haven, CT: Yale University Press, 2021. 456 pp. ISBN: 9780300255492.

Pricing Multi-Asset Contingent Claims In A Multi-Dimensional Binomial Market, Jarek Kedra, Assaf Libman, Victoria Steblovskaya

Journal of Stochastic Analysis

No abstract provided.

Translation Of: Sur Des Familles Remarquables D’Hypersurfaces Isoparamétriques Dans Les Espaces Sphériques, Mathematische Zeitschrift 45, 335–367 (1939), By Élie Cartan., Thomas E. Cecil

Mathematics Department Faculty Scholarship

This is an English translation of the article "Sur des familles remarquables d’hypersurfaces isoparamétriques dans les espaces sphériques," which was originally published in Mathematische Zeitschrift 45, 335–367 (1939), by Élie Cartan.

A note from Thomas E. Cecil, translator: This is an unofficial translation of the original paper which was written in French. All references should be made to the original paper.

Mathematics Subject Classification Numbers: 53B25, 53C40, 53C42

Iterated Jump Graphs, Fran Herr, Legrand Jones Ii

Rose-Hulman Undergraduate Mathematics Journal

The jump graph J(G) of a simple graph G has vertices which represent edges in G where two vertices in J(G) are adjacent if and only if the corresponding edges in G do not share an endpoint. In this paper, we examine sequences of graphs generated by iterating the jump graph operation and characterize the behavior of this sequence for all initial graphs. We build on work by Chartrand et al. who showed that a handful of jump graph sequences terminate and two sequences converge. We extend these results by showing that there are no non-trivial repeating sequences of jump …

The Chromatic Index Of Ring Graphs, Lilian Shaffer

Rose-Hulman Undergraduate Mathematics Journal

The goal of graph edge coloring is to color a graph G with as few colors as possible such that each edge receives a color and that adjacent edges, that is, different edges incident to a common vertex, receive different colors. The chromatic index, denoted χ′(G), is the minimum number of colors required for such a coloring to be possible. There are two important lower bounds for χ′(G) on every graph: maximum degree, denoted ∆(G), and density, denoted ω(G). Combining these two lower bounds, we know that every graph’s chromatic index must be at least ∆(G) or …

Richard Whately's Revitalization Of Syllogistic Logic, Calvin Jongsma

Faculty Work Comprehensive List

This is an expanded version of the first chapter Richard Whately’s Revitalization of Syllogistic Logic in Aristotle’s Syllogism and the Creation of Modern Logic edited by Lukas M. Verburgt and Matteo Cosci (Bloomsbury, 2023). Drawing upon the author’s 1982 Ph. D. dissertation (https://digitalcollections.dordt.edu/faculty_work/230/ ) and more current scholarship, this essay traces the critical historical background to Whately’s work in more detail than could be done in the published version.

The Malliavin-Stein Method For Normal Random Walks With Dependent Increments, Ian Flint, Nicolas Privault, Giovanni Luca Torrisi

Journal of Stochastic Analysis

No abstract provided.

Rediscovering The Artistic Side Of Mathematics, Bogdan G. Nita, Ashwin Vaidya

LASER Journal

Welcome to the inaugural issue of the LASER, a journal devoted to the problems at the interface of math and art. The terms ’math’ and ’art’ are to be broadly construed to encompass all quantitative sciences and forms of art. The journal’s name, acronym for Linking Art and Science through Education and Research, suggests our interest in the theory, practice and pedagogy of this interdisciplinary subject.

Outer Independent Double Italian Domination Of Some Graph Products, Rouhollah Jalaei, Doost Ali Mojdeh

Theory and Applications of Graphs

An outer independent double Italian dominating function on a graph $G$ is a function $f:V(G)\rightarrow\{0,1,2,3\}$ for which each vertex $x\in V(G)$ with $\color{red}{f(x)\in \{0,1\}}$ then $\sum_{y\in N[x]}f(y)\geqslant 3$ and vertices assigned $0$ under $f$ are independent. The outer independent double Italian domination number $\gamma_{oidI}(G)$ is the minimum weight of an outer independent double Italian dominating function of graph $G$. In this work, we present some contributions to the study of outer independent double Italian domination of three graph products. We characterize the Cartesian product, lexicographic product and direct product of custom graphs in terms of this parameter. We also provide …

Current Scenario Of Solar Energy Applications In Bangladesh: Techno-Economic Perspective, Policy Implementation, And Possibility Of The Integration Of Artificial Intelligence, Monirul Islam Miskat, Protap Sarker, Hemal Chowdhury, Tamal Chowdhury, Md Salman Rahman, Nazia Hossain, Piyal Chowdhury, Sadiq M. Sait

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Bangladesh is blessed with abundant solar resources. Solar power is considered the most desirable energy source to mitigate the high energy demand of this densely populated country. Although various articles deal with solar energy applications in Bangladesh, no detailed review can be found in the literature. Therefore, in this study, we report on the current scenario of renewable energy in Bangladesh and the most significant potential of solar energy’s contribution among multiple renewable energy resources in mitigating energy demand. One main objective of this analysis was to outline the overall view of solar energy applications in Bangladesh to date, as …

Between Heaven And Earth! A Poem-Collage Pair About Hypatia Of Alexandria, Sarah Glaz, Mark Sanders

Journal of Humanistic Mathematics

The poem-collage pair presented here is a work of collaboration between the mathematician and poet, Sarah Glaz, and the collage and ceramic artist, Mark Sanders. The piece is part of their larger joint poem-collage project involving the history of mathematics. Included as background is a brief discussion on the history and mathematics involved, and a reflection on several landmark locations and some of the relevant imagery appearing in the poem and the collage.

Astor Place Barber, Audrey Nasar

Journal of Humanistic Mathematics

"Astor Place Barber" is a short story about a math professor and a barber. It plays with the logical concept of a paradox via the Barber's Paradox, which, made famous by Bertrand Russell, tells the story of a barber who both shaves himself and does not shave himself.

The Babelogic Of Mathematics, Vijay Fafat

Journal of Humanistic Mathematics

How would the Bible written about a Mathematical God start, describing the Creation of Mathematics and Logic? How would Rigveda's "Nasadiya sukta" read if it were describing the Void before mathematics was "born"? Here is an attempt at a partial answer, one which takes the original Genesis chapter and the Nasadiya sukta and makes suitable changes to create a fairly consistent, if somewhat anachronistic narrative (with the slight mixing up of Bertrand Russell and Lobachevsky / Bolyai attributable to "Babelogic"), along with a new ending to the Beginning...

Unsolved Haiku, Scott W. Williams

Journal of Humanistic Mathematics

This poem describes the still unsolved 1937 conjecture of Lloyd Collatz: Do repeated applications of the algorithm described yield the number 1?

Locked In Functions: A Short Poem For Robert Langlands, Virgilio A. Rivas

Journal of Humanistic Mathematics

This short poem is inspired by Robert Langlands, recipient of the 2018 Abel Prize. The poem tries to sum up in poetic language, as brief but substantial as it can be, the philosophical and rhetorical connotation of his contributions to mathematics, from automorphic forms to number theory, and the famous Langlands programme, among others. Also partly inspired by Edward Frenkel's tribute to Langlands, the book Love and Mathematics, the poem seeks to capture the philosophical beauty of mathematics that privileges the importance of 'functions' over 'passions', consistent with Langlands' purely mathematical side.

Mathematics, Kim Regnier Jongerius

Journal of Humanistic Mathematics

Inspired by the song "Memories" from the musical Cats, this work describes some of the frustrations and joys inherent in mathematical work.

Wartime Logic, Tony Bedenikovic

Journal of Humanistic Mathematics

No abstract provided.

Self-Reference And Diagonalisation, Joël A. Doat

Journal of Humanistic Mathematics

This poem is an exercise on self-reference and diagonalisation in mathematics featuring Turing’s proof of the undecidability of the halting problem, Cantor’s cardinality argument, the Burali-Forti paradox, and Epimenides' liar paradox.