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Articles 1 - 30 of 45
Full-Text Articles in Arts and Humanities
Musical Actions Of Dihedral Groups, Alissa S. Crans, Thomas M. Fiore, Ramon Satyendra
Musical Actions Of Dihedral Groups, Alissa S. Crans, Thomas M. Fiore, Ramon Satyendra
Alissa Crans
The sequence of pitches which form a musical melody can be transposed or inverted. Since the 1970s, music theorists have modeled musical transposition and inversion in terms of an action of the dihedral group of order 24. More recently music theorists have found an intriguing second way that the dihedral group of order 24 acts on the set of major and minor chords. We illustrate both geometrically and algebraically how these two actions are {\it dual}. Both actions and their duality have been used to analyze works of music as diverse as Hindemith and the Beatles.
Newton’S Third Law In Karmic Warfare, Kazmier Maślanka
Newton’S Third Law In Karmic Warfare, Kazmier Maślanka
The STEAM Journal
A work entitled "Newton's Third Law in Karmic Warfare" is a mathematical visual poem which is a perfect example of a technique, that I call The Paradigm Poem. This piece makes a direct connection with the concept of karma and Newton’s Third Law of motion. I will introduce the concept of “The Mathematical Paradigm Poem” to illuminate an example of how metaphor is used in mathematical visual poetry. I will also discuss much of the process in making this aesthetic expression.
Alan Turing: The Man Behind The Machine, Christopher D. Goff
Alan Turing: The Man Behind The Machine, Christopher D. Goff
College of the Pacific Faculty Presentations
No abstract provided.
Faith Connections In The Math Classroom, Valorie L. Zonnefeld, Ryan G. Zonnefeld
Faith Connections In The Math Classroom, Valorie L. Zonnefeld, Ryan G. Zonnefeld
Faculty Work Comprehensive List
Looking for ways to make faith connections in your math classroom? The Zonnefelds present a framework, developed in collaboration with local teachers, that synthesizes faith connections, the TfT framework, and Common Core standards.
Musical Sound: A Mathematical Approach To Timbre, Timothy Weiss (Class Of 2016)
Musical Sound: A Mathematical Approach To Timbre, Timothy Weiss (Class Of 2016)
Writing Across the Curriculum
What is the mathematical reasoning behind the ear’s ability to distinguish two completely different musical sounds? In answering this question, one must call to mind a fundamental term with regards to music: timbre.
The Fourth Movement Of György Ligeti's Piano Concerto: Investigating The Musical-Mathematical Connection, Cynthia L. Wong
The Fourth Movement Of György Ligeti's Piano Concerto: Investigating The Musical-Mathematical Connection, Cynthia L. Wong
Dissertations, Theses, and Capstone Projects
This interdisciplinary study explores musical-mathematical analogies in the fourth movement of Ligeti’s Piano Concerto. Its aim is to connect musical analysis with the piece’s mathematical inspiration. For this purpose, the dissertation is divided into two sections. Part I (Chapters 1-2) provides musical and mathematical context, including an explanation of ideas related to Ligeti’s mathematical inspiration. Part II (Chapters 3-5) delves into an analysis of the rhythm, form, melody / motive, and harmony. Appendix A is a reduced score of the entire movement, labeled according to my analysis.
Teaching Differential Equations Through A Modeling First Approach, Brian Winkel
Teaching Differential Equations Through A Modeling First Approach, Brian Winkel
Journal of Humanistic Mathematics
No abstract provided.
Menger Sponge, E Laura Golberg
Menger Sponge, E Laura Golberg
Journal of Humanistic Mathematics
No abstract provided.
Quantitative Literacy, Thomas L. Moore
Quantitative Literacy, Thomas L. Moore
Journal of Humanistic Mathematics
No abstract provided.
The Greatest Integer Function, Alanna Rae
The Greatest Integer Function, Alanna Rae
Journal of Humanistic Mathematics
No abstract provided.
Book Review: A New Index For Predicting Catastrophes: Poems By Madhur Anand, Joanne Growney
Book Review: A New Index For Predicting Catastrophes: Poems By Madhur Anand, Joanne Growney
Journal of Humanistic Mathematics
This review explores Madhur Anand’s recent poetry collection from several points of view. One involves consideration of mathematical concepts and imagery in her poems. A second viewpoint takes into consideration Anand’s own field – she is a professor of environmental science with a focus on ecology. A third view considers the poems as art objects – words building pictures that offer to readers both insights and pleasures.
Fuzzy Logic In Health Care Settings: Moral Math For Value-Laden Choices, Sarah Voss
Fuzzy Logic In Health Care Settings: Moral Math For Value-Laden Choices, Sarah Voss
Journal of Humanistic Mathematics
This essay is intended as an example of “moral math”, i.e., ideas culled from mathematics which can positively impact social behavior. Specifically, it combines fuzzy logic with the ethical decisions which hospital staff and others are sometimes forced to make about health care (e.g., euthanasia issues following Hurricane Katrina). The assumption is that such decisions involve value-laden choices which lend themselves to “fuzzy” or “smart” protocols. The article discusses the history of fuzzy logic – what it is, how it is used, and how it might be even better-used as a support basis for making difficult choices …
Al-Khwarizmı And The Hermeneutic Circle: Reflections On A Trip To Samarkand, Asuman G. Aksoy
Al-Khwarizmı And The Hermeneutic Circle: Reflections On A Trip To Samarkand, Asuman G. Aksoy
Journal of Humanistic Mathematics
In this paper we discuss al-Khwarzmi's life and aspects of his work and suggest a possible hermeneutic avenue into his contribution to mathematics.
Combinatorics Of The Sonnet, Terry S. Griggs
Combinatorics Of The Sonnet, Terry S. Griggs
Journal of Humanistic Mathematics
Using a definition of a sonnet, the number of basic rhyming schemes is enumerated. This is then used to discuss the 86 sonnets which appear in John Clare's The Rural Muse.
Connections, Mark Huber, Gizem Karaali
Connections, Mark Huber, Gizem Karaali
Journal of Humanistic Mathematics
No abstract provided.
The Philosophy Of Mathematics, Erin Wilding-Martin
The Philosophy Of Mathematics, Erin Wilding-Martin
Erin Wilding-Martin
The philosophy of mathematics considers what is behind the math that we do. What is mathematics? Is it some cosmic truth we discover, or is it created by humans? Do mathematical objects such as numbers and functions really exist, or are they just symbols we have invented? Two of the great debates in the history of mathematical philosophy center around ontology and epistemology. Where did mathematics come from? How do we know that it is true? Where did mathematics come from? Is it discovered or created? Ontological questions are concerned with the nature and status of mathematical objects. Some people …
Critical Thinking Skills And Academic Maturity: Emerging Results From A Five-Year Quality Enhancement Plan (Qep) Study, Ian N. Toppin, Shadreck Chitsonga
Critical Thinking Skills And Academic Maturity: Emerging Results From A Five-Year Quality Enhancement Plan (Qep) Study, Ian N. Toppin, Shadreck Chitsonga
Journal of Inquiry and Action in Education
The QEP that was implemented in this study focused on enhancing students’ critical thinking skills. A pretest/ posttest approach was used to assess students’ critical thinking progress in freshman level core English and Math courses. An intervention was performed involving intensive instruction and assignments relating to a set of reasoning strategies such as: analytical, analogical, inductive, deductive, and comparative reasoning, among others. When students performed well on assignments by applying the reasoning strategies, it was assumed that critical thinking occurred. However, pre/ posttest results in these classes were often disappointing, and seemed at times to suggest that freshmen are not …
The Remedy That's Killing: Cuny, Laguardia, And The Fight For Better Math Policy, Rachel A. Oppenheimer
The Remedy That's Killing: Cuny, Laguardia, And The Fight For Better Math Policy, Rachel A. Oppenheimer
Dissertations, Theses, and Capstone Projects
Nationwide, there is a crisis in math learning and math achievement at all levels of education. Upwards of 80% of students who enter the City University of New York’s community colleges from New York City’s Department of Education high schools fail to meet college level math proficiencies and as a result, are funneled into the system’s remedial math system. Once placed into pre-college remedial arithmetic, pre-algebra, and elementary algebra courses, students fail at alarming rates and research indicates that students’ failure in remedial math has negative ripple effects on their persistence and degree completion. CUNY is not alone in facing …
Primality Proving Based On Eisenstein Integers, Miaoqing Jia
Primality Proving Based On Eisenstein Integers, Miaoqing Jia
Honors Theses
According to the Berrizbeitia theorem, a highly efficient method for certifying the primality of an integer N ≡ 1 (mod 3) can be created based on pseudocubes in the ordinary integers Z. In 2010, Williams and Wooding moved this method into the Eisenstein integers Z[ω] and defined a new term, Eisenstein pseudocubes. By using a precomputed table of Eisenstein pseudocubes, they created a new algorithm in this context to prove primality of integers N ≡ 1 (mod 3) in a shorter period of time. We will look at the Eisenstein pseudocubes and analyze how this new algorithm works with the …
Reading Between The Lines: Verifying Mathematical Language, Tristan Johnson
Reading Between The Lines: Verifying Mathematical Language, Tristan Johnson
Honors Theses
A great deal of work has been done on automatically generating automated proofs of formal statements. However, these systems tend to focus on logic-oriented statements and tactics as well as generating proofs in formal language. This project examines proofs written in natural language under a more general scope of mathematics. Furthermore, rather than attempting to generate natural language proofs for the purpose of solving problems, we automatically verify human-written proofs in natural language. To accomplish this, elements of discourse parsing, semantic interpretation, and application of an automated theorem prover are implemented.
The Evolution Of Cryptology, Gwendolyn Rae Souza
The Evolution Of Cryptology, Gwendolyn Rae Souza
Electronic Theses, Projects, and Dissertations
We live in an age when our most private information is becoming exceedingly difficult to keep private. Cryptology allows for the creation of encryptive barriers that protect this information. Though the information is protected, it is not entirely inaccessible. A recipient may be able to access the information by decoding the message. This possible threat has encouraged cryptologists to evolve and complicate their encrypting methods so that future information can remain safe and become more difficult to decode. There are various methods of encryption that demonstrate how cryptology continues to evolve through time. These methods revolve around different areas of …
Nonlinear Harmonic Modes Of Steel Strings On An Electric Guitar, Joel Wenrich
Nonlinear Harmonic Modes Of Steel Strings On An Electric Guitar, Joel Wenrich
Senior Theses
Steel strings used on electric and acoustic guitars are non-ideal oscillators that can produce imperfect intonation. According to theory, this intonation should be a function of the bending stiffness of the string, which is related to the dimensions of length and thickness of the string. To test this theory, solid steel strings of three different linear densities were analyzed using an oscilloscope and a Fast Fourier Transform function. We found that strings exhibited more drastic nonlinear harmonic behavior as their effective length was shortened and as linear density increased.
Exploring Argumentation, Objectivity, And Bias: The Case Of Mathematical Infinity, Ami Mamolo
Exploring Argumentation, Objectivity, And Bias: The Case Of Mathematical Infinity, Ami Mamolo
OSSA Conference Archive
This paper presents an overview of several years of my research into individuals’ reasoning, argumentation, and bias when addressing problems, scenarios, and symbols related to mathematical infinity. There is a long history of debate around what constitutes “objective truth” in the realm of mathematical infinity, dating back to ancient Greece (e.g., Dubinsky et al., 2005). Modes of argumentation, hindrances, and intuitions have been largely consistent over the years and across levels of expertise (e.g., Brown et al., 2010; Fischbein et al., 1979, Tsamir, 1999). This presentation examines the interrelated complexities of notions of objectivity, bias, and argumentation as manifested in …
Model Behavior: The Mathematics Behind Three-Dimensional Modeling And Animation, Kathryn Duff, Vivian Cyrus
Model Behavior: The Mathematics Behind Three-Dimensional Modeling And Animation, Kathryn Duff, Vivian Cyrus
Celebration of Student Scholarship Poster Sessions Archive
No abstract provided.
Undergraduate Research Fellowships: A Strategic Investment To Reduce Women Underrepresentation In The Mathematical Sciences, Janie L. Knell, Wilson Gonzalez-Espada
Undergraduate Research Fellowships: A Strategic Investment To Reduce Women Underrepresentation In The Mathematical Sciences, Janie L. Knell, Wilson Gonzalez-Espada
Celebration of Student Scholarship Poster Sessions Archive
No abstract provided.
Mathematics And Origami; Unfolding Mathematical "Impossibilities", Dustin Tyler Adams
Mathematics And Origami; Unfolding Mathematical "Impossibilities", Dustin Tyler Adams
Celebration of Student Scholarship Poster Sessions Archive
No abstract provided.
Applications Of The Sierpiński Triangle To Musical Composition, Samuel C. Dent
Applications Of The Sierpiński Triangle To Musical Composition, Samuel C. Dent
Honors Theses
The present paper builds on the idea of composing music via fractals, specifically the Sierpiński Triangle and the Sierpiński Pedal Triangle. The resulting methods are intended to produce not just a series of random notes, but a series that we think pleases the ear. One method utilizes the iterative process of generating the Sierpiński Triangle and Sierpiński Pedal Triangle via matrix operations by applying this process to a geometric configuration of note names. This technique designs the largest components of the musical work first, then creates subsequent layers where each layer adds more detail.
Drawing Numbers And Listening To Patterns, Loren Zo Haynes
Drawing Numbers And Listening To Patterns, Loren Zo Haynes
Honors College Theses
The triangular numbers is a series of number that add the natural numbers. Parabolic shapes emerge when this series is placed on a lattice, or imposed with a limited number of columns that causes the sequence to continue on the next row when it has reached the kth column. We examine these patterns and construct proofs that explain their behavior. We build off of this to see what happens to the patterns when there is not a limited number of columns, and we formulate the graphs as musical patterns on a staff, using each column as a line or space …
History Of Mathematics From The Islamic World, Asamah Abdallah
History Of Mathematics From The Islamic World, Asamah Abdallah
All Student Theses
Learning the history of mathematics is crucial to fully understanding the world of mathematics today. This paper will explore the history of mathematics from the Islamic world. It will focus on the contributions of well-recognized mathematicians including, Al-Khwarizmi, Al-Khayyam, Uqlidisi, Kushyar ibn Labban, and Abu Kamil. It will also concentrate on the contributions that the Islamic world had on algebra, beginning with Al-Khwarizmi and his contribution to the developmental of algebraic equations, and Khayyam and his contribution to the geometrization of algebra. This paper will also discuss the ways in which the Muslims applied the mathematics they learned into their …