Mathematics Commons^™

An Absence Of Elephants In The Room: Religion, Philosophy, And Negative Numbers In Albert Girard’S A New Discovery In Algebra, Ethan Wilmes

Lawrence University Honors Projects

In early seventeenth-century Europe, the lines separating theology, science, and humanism were thin; what the modern reader understands as three distinct spheres of knowledge considerably overlapped with one another. Scientific discoveries and innovations coming from new technologies and foreign lands were laden with implications about theology and the human condition. While bland to all but the most fringe historians of mathematics today, the discovery of negative numbers led to a passionate and occasionally fierce epistemological debate throughout Europe. Falling outside of traditional mathematical knowledge, negative numbers found themselves in a sort of existential limbo; however useful they proved themselves to …

Bbt Side Mold Assy, Bill Hemphill

STEM Guitar Project’s BBT Acoustic Kit

This electronic document file set covers the design and fabrication information of the ETSU Guitar Building Project’s BBT (OM-sized) Side Mold Assy for use with the STEM Guitar Project’s standard acoustic guitar kit. The extended 'as built' data set contains an overview file and companion video, the 'parent' CADD drawing, CADD data for laser etching and cutting a drill &/or layout template, CADD drawings in AutoCAD .DWG and .DXF R12 formats of the centerline tool paths for creating the mold assembly pieces on an AXYZ CNC router, and support documentation for CAM applications including router bit specifications, feeds, speed, multi-pass …

Data Ethics: An Investigation Of Data, Algorithms, And Practice, Gabrialla S. Cockerell

Honors Projects

This paper encompasses an examination of defective data collection, algorithms, and practices that continue to be cycled through society under the illusion that all information is processed uniformly, and technological innovation consistently parallels societal betterment. However, vulnerable communities, typically the impoverished and racially discriminated, get ensnared in these harmful cycles due to their disadvantages. Their hindrances are reflected in their information due to the interconnectedness of data, such as race being highly correlated to wealth, education, and location. However, their information continues to be analyzed with the same measures as populations who are not significantly affected by racial bias. Not …

The Mathematical Foundation Of The Musical Scales And Overtones, Michaela Dubose-Schmitt

Theses and Dissertations

This thesis addresses the question of mathematical involvement in music, a topic long discussed going all the way back to Plato. It details the mathematical construction of the three main tuning systems (Pythagorean, just intonation, and equal temperament), the methods by which they were built and the mathematics that drives them through the lens of a historical perspective. It also briefly touches on the philosophical aspects of the tuning systems and whether their differences affect listeners. It further details the invention of the Fourier Series and their relation to the sound wave to explain the concept of overtones within the …

Sheltered Math Curriculum For Middle School English Learners, Jasmine Ercink

Dissertations, Theses, and Projects

Language barriers have shown a need for differentiation and sheltered instruction in the classroom for English Learners (ELs) to be successful in the United States public school system. This project proposes a mathematics curriculum using SIOP so that both groups of students in the middle school level can increase their proficiency in the mathematics content area as well as experience opportunities for academic and social language development. The purpose of this report is to describe the processes, methods, data, and intent of the mathematics curriculum for these learners. The curriculum acts as an effective intervention to fill gaps in both …

Visions Of Science: An Art Historical Exploration Of Medieval Scientific Manuscripts, Olivia Brock

Undergraduate Honors Capstone Projects

The late 16th century saw a new movement in the world of science to push scientific ideas and practice out of academia and into the hands of the layman. No longer were scholars the sole proprietors of science –everyday laborers, craftsman, and artists now had practical scientific principles at their fingertips that they could incorporate into their professions. This new spread of science was facilitated in several ways, including the publication of books incorporating detailed, explanatory images, new utilitarian instruments, and public lectures. Though science was disseminated through a variety of means, I have been particularly interested in the ways …

John Horton Conway: The Man And His Knot Theory, Dillon Ketron

Electronic Theses and Dissertations

John Horton Conway was a British mathematician in the twentieth century. He made notable achievements in fields such as algebra, number theory, and knot theory. He was a renowned professor at Cambridge University and later Princeton. His contributions to algebra include his discovery of the Conway group, a group in twenty-four dimensions, and the Conway Constellation. He contributed to number theory with his development of the surreal numbers. His Game of Life earned him long-lasting fame. He contributed to knot theory with his developments of the Conway polynomial, Conway sphere, and Conway notation.

Stop And Smell The Fractals: An Exploration Into Math, Poetry, And Everything In Between, Caroline Jennings

English Undergraduate Honors Theses

Stop and Smell The Fractals is a collection of poetry written during my time at The University of Arkansas. These poems highlight the connections between mathematics and poetry, focusing particularly on their emergence in everyday life.

Unknowable Truths: The Incompleteness Theorems And The Rise Of Modernism, Caroline Tvardy

Honors Scholars Collaborative Projects

This thesis evaluates the function of the current history of mathematics methodologies and explores ways in which historiographical methodologies could be successfully implemented in the field. Traditional approaches to the history of mathematics often lack either an accurate portrayal of the social and cultural influences of the time, or they lack an effective usage of mathematics discussed. This paper applies a holistic methodology in a case study of Kurt Gödel’s influential work in logic during the Interwar period and the parallel rise of intellectual modernism. In doing so, the proofs for Gödel’s Completeness and Incompleteness theorems will be discussed as …

Volume 13, Payton Davenport, Audrey Lemons, Jacob Shope, Haley Smith, Cassandra Poole, Rachel Cannon, Rachel Boch, Suzanne Stetson

Incite: The Journal of Undergraduate Scholarship

Introduction Dr. Roger A. Byrne, Dean

From the Editor Dr. Larissa “Kat” Tracy

From the Designers Rachel English, Rachel Hanson

The Effect of Compliment Type on the Estimated Value of the Compliment by Payton Davenport, Audrey Lemons, and Jacob Shope

The Imperial Japanese Military: A New Identity in the Twentieth Century, 1853–1922 by Haley Smith

Longwood University’s campus: Human-cultivated Soil has Higher Microbial Diversity than Soil Collected from Wild Sites by Cassandra Poole

Reminiscent Modernism: Poetry Magazine’s Modernist Nostalgia for the Past by Rachel Cannon

Challenges Faced by Healthcare Workers During the COVID-19 Pandemic: A Preliminary Study of Age and …

Semantic Completeness Of Intuitionistic Predicate Logic In A Fully Constructive Meta-Theory, Ian Ray

Masters Theses & Specialist Projects

A constructive proof of the semantic completeness of intuitionistic predicate logic is explored using set-generated complete Heyting Algebra. We work in a constructive set theory that avoids impredicative axioms; for this reason the result is not only intuitionistic but fully constructive. We provide background that makes the thesis accessible to the uninitiated.

Poster Session, Emma Beeler, Maddison Caldwell, Mackenzie Paul, Shirli Salihaj, Sara Lynn Sligh, Stephen Trest

Mississippi Undergraduate Honors Conference

Video provided is of MacKenzie Paul's presentation.

Abstracts

Humanities

Emma Beeler, Mississippi University for Women

Adultery and Fidelity in the Lais of Marie de France

Using both literary and historical analysis, I will examine contrasting depictions of adultery and fidelity within the lais written by 12th-century poet Marie de France. A lai is a type of narrative poem, ranging in length from 118 to 1184 lines. Many of Marie de France’s lais follow the literary trope known as courtly love; however, the reader is encouraged to sympathize with different characters depending on the lai. In some lais, the reader …

Special Issue Call For Papers: Mathematics And Society, Carrie Diaz Eaton, Rachel Roca, Nancy Rodriguez, Tian An Wong

Journal of Humanistic Mathematics

The Journal of Humanistic Mathematics (http://scholarship.claremont.edu/jhm/) is pleased to announce a call for papers for a special issue on Mathematics and Society. Please send your initial proposal submissions via email to the guest editors by August 15, 2022. Initial submission of complete manuscripts is due December 15, 2022. The issue is currently scheduled to appear in July 2023.

Journal For Mathematics And The Arts Call For Papers: Special Issue On The Mathematics Of Fiber Arts, Carolyn Yackel, Sarah-Marie Belcastro

Journal of Humanistic Mathematics

The Journal for Mathematics and the Arts (https://www.tandfonline.com/journals/tmaa20) a peer-reviewed journal that focuses on connections between mathematics and the arts, is pleased to announce a call for papers for a special issue on Mathematics of Fiber Arts. Please send your queries via email to the guest editors. Initial submission of complete manuscripts is due August 1, 2022. The issue is currently scheduled to appear in Fall 2023.

A Non-Euclidean Story Or: How To Persist When Your Geometry Doesn’T, Rami Luisto

Journal of Humanistic Mathematics

Too little mathematics has been written in prose. Thus we prove here, via a fantasy novellette, that a locally L-bilipschitz mapping f : X → Y between uniformly Ahlfors q-regular, complete and locally compact path-metric spaces X and Y is an L-bilipschitz map when Y is simply connected. The motivation for such a result arises from studying the asymptotic values of BLD-mappings with an empty branch set.

As far as the author is aware, the result is new, even though it would not be hard for specialists in the field to prove. The proof is essentially a modest extension of …

So Long My Friend, Bryan Mcnair

Journal of Humanistic Mathematics

No abstract provided.

Heuristic Or Stochastic?, E Laura Golberg

Journal of Humanistic Mathematics

This is a poem about laying odds on the outcome of weddings.

The Solipsist’S First Paper, Sabrina Sixta

Journal of Humanistic Mathematics

The angst of a graduate student who has not yet written a paper, but really wants to.

Wrong Way, Joseph Chaney

Journal of Humanistic Mathematics

No abstract provided.

What's So Great About Non-Orientable Manifolds?, Michael Mccormick

Journal of Humanistic Mathematics

No abstract provided.

Poetry In The Glade: Bridges 2021 Fib Collection

Journal of Humanistic Mathematics

A Fibonacci poem follows the Fibonacci sequence to any length in its count of syllables per line, or words per line, or lines per stanza, or any other countable thing connected with the poem. A Fib is a special case of Fibonacci poem, a poem of 6 lines whose syllable line count follows the first 6 numbers of the Fibonacci sequence: 1; 1; 2; 3; 5; 8. The present collection of Fibs arose out of the Bridges poetry community in response to the Bridges organization’s efforts to make the Bridges 2021 conference more interactive.

Mathematics For The Masses: Door-To-Door Missionaries Of Math And Twelve-Step Recovery Programs, Daniel S. Helman

Journal of Humanistic Mathematics

Conversion of strangers, or proselytizing, is a feature of a range of groups for religious, organizational and other aims. In twelve-step recovery programs, such as Alcoholics Anonymous, belief in a higher power is a requirement for working the steps to recovery. People are encouraged to find a higher power of their own understanding. This paper presents a model for using mathematics as a higher power, and shows how recovery works with mathematics in that role instead of a more traditional higher power such as God. A contemplative definition of math is given along with a description of a three-categoried epistemology: …

An Urgent Plea For More Graduate Programs In Statistics Education, David Eli Drew, Sam Behseta, Cherie L. Ichinose

Journal of Humanistic Mathematics

Lately, much has been written about the importance of amplifying statistics-related content in the K-12 curricula. This can be viewed in parallel or as an addendum to the existing mathematics curricula in the United States. Nevertheless, a key component of this debate is the lack of robust and cutting-edge academic programs in statistics education. In this piece, we emphasize the urgent need for investing in creating strong statistics education programs, which would significantly contribute to nurturing quantitative literacy as well as preparing a more informed citizenry in the 21^st century.

Life Of A Working Ramsey Theorist: Conversation With Thomas C. Brown, Kyle Singh, Veselin Jungic, Jun Bo Mei

Journal of Humanistic Mathematics

This interview, conducted in November 2020, explores the fascinating life and work of Ramsey theorist Thomas Craig Brown. We hope, through our conversation with Dr. Brown, to show that mathematics is not a discipline that is only concerned with numbers, but that it is, in a fundamental way, also about people and connections.

Decisions, Decisions: How Should The Votes Be Counted?, Michael J. Caulfield

Journal of Humanistic Mathematics

It is a simple matter for the members of a group to decide among two options. When there are three or more options among which to choose, the situation is much more complicated. This is precisely what faces the electorate each time there are more than two candidates running for a single office. And while there is debate over which voting method should be used, there is wide agreement over the method that should not be used: plurality, the most common approach taken in the United States. This article presents a simple classroom activity which provides students the opportunity to …

A Cognitive View Of "Pandemic Meditation" (A Mathematical Visual Poem), Kazmier Maslanka

Journal of Humanistic Mathematics

Mathematical visual poetry is a poetic genre whereby metaphorical expressions are created using mathematical structures. Within the structure, the poetics are understood by the cross-mapping of numerous conceptual domains including visual, lexical, and mathematical. Here I focus on one particular mathematical visual poetic structure: what I call a Similar Triangles Poem or Proportional Poem. To illustrate the ideas discussed, I present "Pandemic Meditations," a mathematical visual poem; in particular I discuss how this mathematical poem uses the mechanisms of poetic metaphor in the context of the embodied mind. The intent of this paper is not to explain "Pandemic Meditation," …

Twisting The Cube: Art-Inspired Mathematical Explorations, Lingguo Bu

Journal of Humanistic Mathematics

A cube can be twisted in a playful manner for visual and algebraic insights. The twisting process and the resulting ruled surfaces can be demonstrated using 3D modeling tools (e.g., GeoGebra® and Autodesk Fusion 360®) or elastic cords on a 3D-printable scaffold. The twisted cube is aesthetically appealing, posing interesting questions that are worthwhile at multiple levels. Algebraically, the volume of the twisted cube is shown to be two-thirds of the reference cube. The twisted faces are parts of hyperbolic paraboloids, whose implicit and parametric equations can be established from diverse perspectives in support of further dynamic explorations and discussions …

Alice’S Adventures In Wonderland: Carroll’S Symbolic Attack On Mathematical Symbolism, Firdous Ahmad Mala

Journal of Humanistic Mathematics

In 2009, a literature scholar, Melanie Bayley, proposed that Lewis Carroll's famous books about Alice visiting the magical and illogical Wonderland were attempts to mock and critique the modern mathematics of the day. In this short paper, I aim to support Bayley's thesis and expound upon Carroll's artful use of symbolism to attack excessive use of symbolism in mathematics.

Accidental World Teacher, Richard Delaware

Journal of Humanistic Mathematics

When the College Algebra and Calculus I video courses I created were posted on my university’s YouTube channel in 2009, I suddenly began to receive dozens of heartfelt emails from students around the world thanking me. Here I tell the story of the creation of those videos and sample the effect they seem to have had over the last decade, as I accidentally became a teacher available to the entire planet.

The Problem Of Words: Learning To Teach Mathematics When Numbers And Languages Mix, Gladys Krause

Journal of Humanistic Mathematics

In this piece I propose a perspective shift, from a simplified view of mathematics story problems to a more academically rigorous perspective that integrates mathematical proficiency and language practices crucial for educating bilingual students. The data presented in this article provide a window into what preparing bilingual pre-service teachers to teach mathematics might involve. I discuss issues that arise in the context of preparing Spanish-English bilingual pre-service teachers in a way that can inform their practice in linguistically and culturally diverse classrooms.