Mathematics Commons^™

Examples Of Mathematics Personified, Amenda N. Chow

Journal of Humanistic Mathematics

Synesthesia is a cognitive condition in which multiply senses are stimulated at once. There are different types of synesthesia. For example, in a documented study [9], a person with synesthesia when considering the number three associates it as a male and a jerk. This association is persistent, always the same and automatic. Presented here are a variety of examples about mathematics in personified form. These examples focus on using personification as a way to better understand and appreciate mathematics.

Math Anxiety And Shame Exemplified On The Reality Show Survivor, James Drimalla, Dru Horne

Journal of Humanistic Mathematics

In an episode of season 45 of the reality show Survivor, three contestants competed in a challenge involving mathematics. In their reflections and responses to the challenge, the contestants discussed feelings of anxiety, fear, and shame. In this article, we describe (a) the challenge, (b) the three contestants’ attempts to complete the challenge and their responses to the challenge, (c) responses to the challenge in the media, and (d) relevant details of our personal experiences and related backgrounds. We then discuss themes of math anxiety, shame, and virtues, and encourage leaders in mathematical spaces to place a higher value on …

Introducing The Linear Poem, Cristian Ramirez Rodriguez

Journal of Humanistic Mathematics

In this article I introduce the linear poem, a poetic form I developed in fall 2023 as a pedagogical tool for high-school students. The linear poem is a poem which represents an integer valued linear function, treating the line numbers as inputs and the linguistic units in a line as outputs. Two examples of linear poems are given as well as the steps taken to produce them. By interpreting poetic forms as integer-valued functions as is done in this article, interdisciplinary pedagogy can be achieved, allowing educators and students to express mathematical ideas such as slope-intercept form in a creative …

A Dualistic Interpretation Of Mathematical Creation Through Art And Argumentation, Sofia Almpani, Petros Stefaneas, Mihir Chakraborty

Journal of Humanistic Mathematics

Creativity, informal reasoning and dynamic exchange of ideas form the pulsating heart of mathematical creation. In this approach, the concept of a mathematical object surpasses conventional boundaries of formal presentation, as they also encompass the intention to prove, significant creative stages within the proving, and the overall experience of prover's journey, which may involve arguments, debates, discovery insights, aesthetic visualizations, and narrative elements. In this paper we present two conceptual frameworks, namely Argumentation-based Proof-Events Calculus (APEC) and Mathematical RUPAs, in order to provide distinct yet interconnected perspectives on informal thinking, knowledge creation, and proving in mathematics. Following the two perspectives, …

On Gödel’S Incompleteness Theorem, David Pierce

Journal of Humanistic Mathematics

Gödel’s Incompleteness Theorem is about the logic of mathematics. It is that a certain mathematical structure is so rich that its theory cannot be completely axiomatized. This means there will always be true statements about the structure that cannot be proved as theorems from previously given axioms. To give meaning to this conclusion, we review some examples of mathematical theorems, and their proofs, in geometry, algebra, and logic; we also give an example of a structure that is so simple (while still being interesting) that its theory can indeed be completely axiomatized. First we look at a couple of popular …

Exploring Commutativity In A Hindi Language Classroom, Kumar Gandharv Mishra

Journal of Humanistic Mathematics

Commutativity is an important concept in mathematics. However, not much emphasis is given to it in the elementary or secondary school curriculum, as there is a lack of interesting noncommutative examples at this level. Since most examples of binary operations provided deal with numbers, commutativity appears trivial. In this article we offer an interesting example of noncommutativity that is familiar to Indian school children from a different context. Students in India study a chapter based on the joining of vowels in Hindi grammar. This process is analogous to producing commutative as well as noncommutative operations. When we bring in mathematical …

Revisiting A 19th Century Vector Algebra Book, Olcay Coskun, Alp Eden, Ersin Karabudak

Journal of Humanistic Mathematics

Hidden gems of mathematics can be recovered when one digs into what might seem an obscure text. In 1882, military officer Vidinli Hüseyin Tevfik Pasha published a book on vector algebra titled Linear Algebra. In this article we revisit the second edition of this book, emphasizing the special multiplication that we call the ’v-product’. This product has both geometric and algebraic characteristics. We attempt to clarify its relationship with complex and quaternion multiplication both geometrically and algebraically. The resulting algebra is called the Vidinli algebra. This algebra admits a Lie algebra structure that gives rise to Heisenberg algebra. We introduce …

Memes As An Effective Approach To Increase Public Engagement With Mathematical Concepts, Juan M. Romero, Carlos Trenado

Journal of Humanistic Mathematics

A meme is a graphical concept or cultural item that is disseminated via the Internet, often through social media platforms. Memes serve as a mechanism for replicating cultural traits by incorporating aspects of cultural mutation and evolution. The potential of memes in learning and education has been emphasized in several recent studies. The present article examines the impact of memes in increasing public engagement with mathematics and mathematical concepts. By focusing on memes that exhibit specific attributes—such as emotional facial expressions of recognizable human characters and dialogues emphasizing the usefulness or beauty of a mathematical concept—we observe a significant increase …

Evaluating Methods Used To Quantify Racial Segregation, Sarah Cannon, Zarina Dhillon

Journal of Humanistic Mathematics

Racial segregation has long been a problem in communities across the United States. One approach to help understand such an important issue is to attempt to describe it quantitatively. Many metrics have been developed, all with various strengths and weaknesses, but none fully capture the nuances of this complicated issue. This work provides an overview of four of the mathematical approaches that have been developed to study segregation, explains how they function using small examples, and compares and contrasts their effectiveness in various situations. We then focus on segregation in Los Angeles (LA) County, including a detailed exploration of the …

Graphical Timetables As A Real-Life Example Of Different Representations Of Functions, Olav G. Imenes

Journal of Humanistic Mathematics

This paper examines 203 pre-service teachers' reactions and learning when they were introduced to a real-life situation in which it is natural to publish officially both graphs and tables of a given function: the situation of operating a railway. I found that almost all the pre-service teachers managed the easiest tasks, like calculating speeds, distances, and time for train represented by graphs. However, the more complicated tasks, which required interpretations of the graphs and tables, such as planning for a delayed train, finding which trains were locals, freight trains etc., were more difficult for them to grasp. There were few …

A Practical Rule Of Divisibility By 7 In Uqlīdisī’S Kitāb Al-Fuṣūl Fī Al-Ḥisāb Al-Hindī, Müjdat Takıcak, Mertkan Şimşek

Journal of Humanistic Mathematics

There are many known examples of divisibility rules in modern mathematics. However, some of these rules are far from being practical, such as the current divisibility rule by 7. A far more useful method can be found in the work of the tenth-century Islamic mathematician Abū al-Ḥasan al-Uqlīdisī (d. 980), who proposed a divisibility rule for 7 in his treatise Kitāb al-Fuṣūl fī al-Ḥisāb al-Hindī. Compared to modern techniques, Uqlīdisī’s rule is both simpler and more practical. This article (re)introduces this rule, and provides an exposition of the mathematical reasoning that underpins it.

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

What Can Mathematics Do For Us?, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

Bayes In The Brain: A Review Of Everything Is Predictable: How Bayesian Statistics Explain Our World, (2024) By Tom Chivers., Michael T. Catalano

Numeracy

Tom Chivers’ Everything is Predictable: How Bayesian Statistics Explain Our World, is an interesting and wide-ranging narrative on Bayesian thinking, its history, and its applicability to both our everyday lives and the pursuit of scientific truth. Although appropriate for the non-expert, afficionados and teachers of quantitative literacy should find the plethora of examples, links to psychology as it applies to how people reason about probabilities, and even Chivers’ philosophical musings informative and thought-provoking.

Algebraic Multigrid Methods For Nonsymmetric And Indefinite Problems: Theory And Applications, Ahsan Ali

Mathematics & Statistics ETDs

Algebraic multigrid (AMG) is a well-established and highly efficient solver for symmetric positive definite (SPD) systems arising from elliptic and parabolic PDEs, while nonsymmetric systems from hyperbolic PDEs remain a significant challenge. This dissertation develops AMG methods and theory for nonsymmetric problems. First, we develop a novel approach combining mode constraints from energy-minimization AMG with local approximations of ideal restriction in $\ell$AIR, resulting in constrained $\ell$AIR (C$\ell$AIR), which demonstrates scalable convergence across advective and diffusive problems. Second, we extend optimal AMG theory by deriving spectral radius estimates for the two-grid error transfer operator using matrix-induced orthogonality, enabling convergence predictions for …

Minimal Error Functions On Irregular Subsets Of The Real Line, Robert Michael Dukes

Mathematics & Statistics ETDs

Chebyshev Polynomials, those that minimize the maximal error on a compact set, are one of the most practical tools for approximating smooth functions. The classical results are on the set [-1, 1]; in this paper, we extend to more complicated subsets of the real line. We demonstrate some classical results and then take the result from [2] on regular Parreau-Widom Sets and extend it to semi-regular sets, defined as sets whose regular part is closed. We introduce the Regularity Coefficient as a series formed by evaluating the Green’s Function at irregular points. This new machinery is applied to the lower …

Derivation Of Adjoint Based Error Estimates For Nonlinear Ordinary Differential Equations With Application To Multistage Sir Models With Demographics, Daniel Alcala

Mathematics & Statistics ETDs

Ordinary Differential Equations (ODEs) are central to the mathematical modeling of various real-world phenomena, from mechanical systems governed by Newton’s laws to epidemic dynamics described by SIR-type ODEs. Since many ODEs do not admit closed-form analytic solutions, we approximate them numerically (e.g., with Euler’s, Runge–Kutta, or other such methods). This raises the key question: How accurate are these numerical solutions? In particular, reliably estimating the error in some quantity of interest (QoI) at time T without having an exact solution is of great scientific interest.

The first main contribution of this thesis is the development and analysis of adjoint-based error …

Toward Simulating 2d Cell Surfaces In A Disk, Myriam Allred

Mathematics & Statistics ETDs

Certain evolution models of cell surfaces (treated in two-dimensions) involve the solution of the Helmholtz equation with jump conditions enforced on an immersed closed curve. This thesis presents a sparse, modal spectral method for solving such Helmholtz problems. The solution is required to be continuous across the curve, but with a jump discontinuity in the normal derivative proportional to the planar curvature. The method relies on classical Fourier-Chebyshev basis functions, with the application of modal Chebyshev integration matrices to achieve sparse, banded approximations of the Helmholtz equation. The method achieves spectral convergence, despite the inherent low regularity of the relevant …

A Data-Driven Approach To Time Series Forecasting And Clustering Of U.S. Regional Drug Overdose Mortality, Koshali Hamy Muthunama Gonnage

Mathematics & Statistics ETDs

The increasing rate of drug overdose deaths in the United States poses a critical public health challenge, particularly due to the surge in synthetic opioids and other high-risk substances. This study presents a data-driven framework that integrates time series forecasting and clustering techniques. Monthly mortality data for five key drug types: cocaine, fentanyl, heroin, methamphetamine, and oxycodone were analyzed using four time series forecasting models: ARIMA, ETS, TBATS, and NNAR. These models were evaluated using standard accuracy metrics RMSE, MAPE, and MAE to assess predictive performance. Signal decomposition approach based on Singular Value Decomposition and subspace modeling was employed to …

The Isoperimetric Inequality For Asymptotically Cat(0) Groups, Edric D. Dabu

Master's Theses

An asymptotically CAT(0) space is one where every ball of radius r is f(r)-CAT(0) for a fixed sublinear function f. An asymptotically CAT(0) group Γ is a group which acts properly and cocompactly by isometries on an asymptotically CAT(0) space X. Fix x0 ∈ X, choose D > 0 such that X = S γ∈Γ �� γ · B �� x0, D 3 ?? , define A = {a ∈ Γ : d(x0, a · x0) ≤ D + 1}, and let R be the set of reduced words in A of length at most 10 that represent the identity in …