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Articles 841 - 870 of 26863
Full-Text Articles in Mathematics
(A,B,C) Tilings With Prescribed Symmetry Groups From Regular Triangle Or Hexagon Tiling, Mark D. Tomenes, Ma. Louise Antonette N. De Las Penas
(A,B,C) Tilings With Prescribed Symmetry Groups From Regular Triangle Or Hexagon Tiling, Mark D. Tomenes, Ma. Louise Antonette N. De Las Penas
Mathematics Faculty Publications
A tiling T of the Euclidean plane (E2) is a countable collection of closed topological disks called tiles T = {Ti : i ∈ N} that is a covering (Ui Ti = E2) as well as a packing (Int(Ti) ∩ Int(Tj) = ∅ if i ̸= j, Int(T) denotes the interior of tile T). One of the problems of interest in discrete geometry is the classification of tilings based on transitivity properties of their vertices, edges and tiles. This talk presents a family of tilings whose vertices, edges and tiles have exactly a, b and c orbits, respectively, under the …
Congruences For Quotients Of Klein Forms, Jeffery Opoku
Congruences For Quotients Of Klein Forms, Jeffery Opoku
Theses and Dissertations
This dissertation investigates the arithmetic properties of some modular forms and eta quotients, focusing on the divisibility properties and congruence relations satisfied by these. The first part examines quotients of the Rogers-Ramanujan and Rogers-Selberg functions, defined by \[ f(\tau) = q^{r} (q^5; q^5)^{a_0} (q, q^4; q^5)^{a_1} (q^2, q^3; q^5)^{a_2}= \sum_{n=r}^{\infty} P_{a_0,a_1,a_2}(n-r) q^n, \] and \[ g(\tau) = q^{s} (q^7; q^7)^{a_0} (q, q^6; q^7)^{a_1} (q^2, q^5; q^7)^{a_2} (q^3, q^4; q^7)^{a_3}= \sum_{n=s}^{\infty} P_{a_0,a_1,a_2,a_3}(n-s) q^n, \] respectively. We establish conditions on the exponents \(a_0, a_1, a_2, a_3\) and residue classes \(r\) and $s$ modulo $p$ such that \(P_{a_0, a_1, a_2}(pn - r) \equiv …
Twisted Equivariant Matrix Factorizations, Jan-Luca Spellmann
Twisted Equivariant Matrix Factorizations, Jan-Luca Spellmann
All Graduate Theses and Dissertations, Fall 2023 to Present
We introduce and study categories of twisted equivariant matrix factorizations MFαG(R, w), which are categories of matrix factorizations of a potential w over the local ring R = C[x1, . . . , xn] together with an action by a finite group G that is twisted via a 2-cocycle α. These categories provide rich examples of Z/2Z-differentially graded categories in the context of non-commutative geometry and come up naturally in the study of boundary conditions of 3d Rozansky–Witten theories. We prove that under certain assumptions on (R, w …
Certified Computation Of Julia Sets Via Numerical Methods, Hannah Kaufman
Certified Computation Of Julia Sets Via Numerical Methods, Hannah Kaufman
All Theses
The chaotic and fractal nature of Julia sets makes them difficult to graph. This research aims to provide graphical approximations of Julia sets with known and guaranteed levels of accuracy. We implement three methods to approximate Julia sets with c values chosen from the main cardioid of the Mandelbrot set. Each method utilizes different properties of these Julia sets. The exclusion method makes use of the fact that a Julia set of this type is topologically a circle. Attracting and repelling fixed points are used to find a region on the interior of the Julia set and a region on …
On The Garoufalidis-Kashaev State-Integral Invariant, Amelia Palmer Dusenbury
On The Garoufalidis-Kashaev State-Integral Invariant, Amelia Palmer Dusenbury
Boise State University Theses and Dissertations
This thesis explores a construction of the family of topological invariants for certain oriented 3-manifolds based on the state-integral approach developed by Andersen, Garoufalidis, and Kashaev in the Archimedean setting. Starting from an ideal triangulation of a 3-manifold equipped with angle data, variables are assigned to the faces and tetrahedra, taking values in a so-called 'Gaussian group'. The invariant is defined by integrating a distribution defined from the combinatorics of the triangulation and a special function over a product of the Gaussian group. The special function is a quantum dilogarithm, whose valuable feature, the pentagon relation, ensures the resulting integral …
Analysis Of Popular Songs In The Us Market, Michael Myers
Analysis Of Popular Songs In The Us Market, Michael Myers
Theses, Dissertations and Culminating Projects
In today’s digitally driven music landscape, understanding what drive’s a song’s popularity requires insight not only into its acoustic and lyrical content, but also into patterns of listener engagement across platforms. This thesis explores the predictive and descriptive dimensions of song popularity by applying supervised and unsupervised machine learning models to a multi-source dataset integrating audio features, sentiment analysis, and temporal consumption behavior. Drawing from a novel, multi-platform dataset that includes Billboard Hot 100 rankings, Spotify acoustic features and popularity scores, streaming, airplay, and sales metrics as reported on Luminate’s Music Connect, and lyrics from AZLyrics, the study investigates the …
An Exploration Of The Structure Of The Linear Algebraic Model Of Color, Isaac Martin
An Exploration Of The Structure Of The Linear Algebraic Model Of Color, Isaac Martin
University Honors Theses
This thesis surveys the mathematical grounding of linear algebraic models of color. It aims to build from the ground up the framework by which additive color is broadly understood in the digital age. Primarily building on the work of Jozef Cohen, Eric Dubois, David H. Krantz, and Günter Wyszecki, it aims to chart the construction of a model of color that underpins most modern understandings of color. While the construction is certainly established in colorimetric circles, the construction is, in the thesis author's opinion, either obtuse or non-rigorous. Ideally, this thesis serves to make the construction accessible to an audience …
Studies In Number Theory: Reciprocity Laws And Fundamental Domains, C. Xavier Parent
Studies In Number Theory: Reciprocity Laws And Fundamental Domains, C. Xavier Parent
All Graduate Theses and Dissertations, Fall 2023 to Present
This thesis consists of two sections. The first section is an introductory survey of number theory discussing the reciprocity laws with a focus on accessibility. Number Theory has always been a fundamental area of mathematical study, with Gauss calling it “the queen of mathematics”. The reciprocity laws are a classical set of results from number theory which have driven number theory for quite a long time. Unfortunately, these results, while important, have always been very inaccessible to undergraduate students, making it hard to start studying the field. This survey attempts to help bridge that gap, giving a resource for novices …
Multiple Monochromatic Subgraphs In Edge-Colored Graphs, Emma Felicity Jent
Multiple Monochromatic Subgraphs In Edge-Colored Graphs, Emma Felicity Jent
Dissertations
Ramsey theory, though a relatively young branch of mathematics, has captivated the attention of graph theorists, combinatorialists, and theoretical computer scientists alike through its raw beauty, versatility, and powerful applications. Before it emerged as a branch of mathematics, the central idea of Ramsey theory appeared in the form of three lemmas in three separate papers by three different mathematicians working on three distinct areas of research. The first such lemma was published by David Hilbert in 1892, followed by the second lemma published by Issai Schur in 1916. However, Frank Ramsey’s renowned lemma, published in 1930, compelled mathematicians to establish …
Optimal Quantization For Nonuniform Discrete Distributions, Russel Cabasag, Samir Huq, Eric Mendoza, Mrinal Kanti Roychowdhury
Optimal Quantization For Nonuniform Discrete Distributions, Russel Cabasag, Samir Huq, Eric Mendoza, Mrinal Kanti Roychowdhury
School of Mathematical & Statistical Sciences Faculty Publications
This paper explores the process of optimal quantization for several types of discrete probability distributions. Quantization is a technique used to approximate a complex distribution with a smaller set of representative points, which is important in fields such as data compression and signal processing. We begin by examining two specific nonuniform distributions over a finite set of values and identify the best representative points for different levels of approximation. We then extend our analysis to two infinite discrete distributions: one supported on the reciprocals of natural numbers and another on the natural numbers themselves. For these distributions, we compute the …
Interlace: A Journal Of Mathematics And Fiber Arts, Carolyn Yackel, Sarah-Marie Belcastro
Interlace: A Journal Of Mathematics And Fiber Arts, Carolyn Yackel, Sarah-Marie Belcastro
Journal of Humanistic Mathematics
Interlace: A journal of mathematics and fiber arts is a peer-reviewed, open-access completely free journal devoted to publishing high-quality original research at the intersection of mathematics and fiber arts. The journal is now accepting submissions.
Sudoku Grids, David Sheskin
Sudoku Grids, David Sheskin
Journal of Humanistic Mathematics
Ten images depicting numerical grids of the mathematical logic puzzle Sudoku are presented. The digit values in each puzzle are represented on either domino tiles, postage stamps, mah-jong tiles, or playing cards.
The Unending Constant, Christopher Banyas
The Unending Constant, Christopher Banyas
Journal of Humanistic Mathematics
No abstract provided.
Totality Fractal, Heather L. Cook
Totality Fractal, Heather L. Cook
Journal of Humanistic Mathematics
This fractal was inspired by the Total Solar Eclipse on April 8, 2024. Here, the sun and the moon are represented when in totality.
Euclidean Vision (A Poem), Joseph Chaney
Euclidean Vision (A Poem), Joseph Chaney
Journal of Humanistic Mathematics
"Euclidean Vision" is a short poem that evaluates geometry from a humanistic perspective, focusing partly on its pleasures. Geometry gives us the pleasing assurance of certainty. It does this through the radical abstraction of space and form, which makes possible a completeness of mathematical vision based on axioms. It's this purity that guarantees a knowledge that "can go on forever." In the end, the poem points to the wonderful freedom that geometry and other mathematical disciplines give us in the midst of difficult and confusing lives. In its beauty and universality, geometry stands as an eternal aspect of the human …
Dream Series, Jim Wolper
Dream Series, Jim Wolper
Journal of Humanistic Mathematics
Dream Series converge to numbers we cannot analyze. They exist, like dreams, but resist attempts to put them into order.
Solving For..., Jan B. Shafer
Solving For..., Jan B. Shafer
Journal of Humanistic Mathematics
This poem is about an appreciation of mathematics and its relationships to people and nature.
When I Was One-In-Twenty, Daniel Kowalczyk
When I Was One-In-Twenty, Daniel Kowalczyk
Journal of Humanistic Mathematics
A poem by A.E. Housman inspired the engineer John R. Pierce to feel awe in the technological progress of telecommunications. Tangentially, Housman also evoked a strong emotion in me when making use of statistical p-values.
Found Poem By Abraham De Moivre, Richard Delaware
Found Poem By Abraham De Moivre, Richard Delaware
Journal of Humanistic Mathematics
No abstract provided.
Mathiverse - A Potpourri Of Mathematical Stanzas, Vijay Fafat
Mathiverse - A Potpourri Of Mathematical Stanzas, Vijay Fafat
Journal of Humanistic Mathematics
A collection of very short verses, mathematical in nature.
Book Review: Zero's Whisper By Tom Petsinis, Sarah Glaz
Book Review: Zero's Whisper By Tom Petsinis, Sarah Glaz
Journal of Humanistic Mathematics
Tom Petsinis is an internationally acclaimed Australian novelist, playwright, and poet. He also holds a Ph.D. degree in mathematics and works as a mathematical adviser at Deakin University, Melbourne. Zero’s Whisper, Petsinis’ tenth poetry collection, offers a rich blend of the literary and the mathematical. The collection, comprising of over one hundred fourteen-line poems, is divided into nine sections, each of which considers a different aspect of a world steeped in mathematics and poetry. This review aims to provide a taste of the poetry and the themes included in the book. To discover all its hidden delights, one needs to …
Compare Problems: Complexity In Content And Language, Gladys Krause
Compare Problems: Complexity In Content And Language, Gladys Krause
Journal of Humanistic Mathematics
When learning to teach mathematics in elementary school, pre-service teachers (PSTs) spend considerable time studying word problems. Here I present a resource I have created for my mathematics methods course in order to engage PSTs in learning about these problems and to support them in identifying these problem types.
Let’S Teach More Accurate And Inclusive History! The Case Of Islamic Contributions To Mathematics And Science, Nuh Aydin
Journal of Humanistic Mathematics
Schools commonly teach a history of mathematics and science that is Eurocentric. This selective version of the history of science, called Classical Narrative by some, is rooted in colonial times and mindset, and has reinforced certain negative opinions about other cultures. It ignores or downplays contributions to mathematics and sciences from non-western civilizations, and falsely attributes many scientific discoveries to European scholars. Medieval Islamic Civilization, which had strong connections to Renaissance Europe, serves as a clear example of how this narrative is distorted. Based on research on primary sources since the middle of the 20th century, we now know that …
From Shudu [Sudoku 數獨] To Dushu [Learning Of Mathematics 讀數]?, Man Keung Siu
From Shudu [Sudoku 數獨] To Dushu [Learning Of Mathematics 讀數]?, Man Keung Siu
Journal of Humanistic Mathematics
The puzzle game Sudoku has been popular for over two decades, and even at one time became a craze for the public. This paper will briefly describe what the game is, a little bit of its history, and how to play it, but will leave the details to the many published books about the game. Some interesting and difficult mathematical problems relevant to the game will be highlighted, again leaving the detailed discussion to specific books published on this issue. The main point the paper tries to focus on is a discussion on the cognitive and the psychological aspects of …
The Fake Mathematical Mindsets Of Preservice Teachers, Carmen M. Latterell
The Fake Mathematical Mindsets Of Preservice Teachers, Carmen M. Latterell
Journal of Humanistic Mathematics
Many students have a fixed mindset, as do some teachers. Recently I accidentally discovered that most of the preservice elementary teachers in my class were faking their mindset and pretending that they had a growth mindset. This raises a variety of questions, such as, will this follow a fake it until you make it track?
Small Number And The Old Game, Veselin Jungic
Small Number And The Old Game, Veselin Jungic
Journal of Humanistic Mathematics
Through a conversation between Small Number and his Auntie, this article describes the Throwing Game, a Haida tradition recorded by John Swanton in 1905. Several mathematical concepts that may be associated to the game are mentioned.
Examples Of Mathematics Personified, Amenda N. Chow
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
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
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
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, …