Mathematics Commons^™

Teaching Differential Equations Through A Modeling First Approach, Brian Winkel

Journal of Humanistic Mathematics

No abstract provided.

Menger Sponge, E Laura Golberg

Journal of Humanistic Mathematics

No abstract provided.

Quantitative Literacy, Thomas L. Moore

Journal of Humanistic Mathematics

No abstract provided.

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

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

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

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

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

Journal of Humanistic Mathematics

No abstract provided.

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

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

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 …

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

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.

Model Behavior: The Mathematics Behind Three-Dimensional Modeling And Animation, Kathryn Duff, Vivian Cyrus

Celebration of Student Scholarship Poster Sessions Archive

No abstract provided.

Mathematics And Origami; Unfolding Mathematical "Impossibilities", Dustin Tyler Adams

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

Celebration of Student Scholarship Poster Sessions Archive

No abstract provided.

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

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 …

Volume 08, Meghan Enzinna, Casey Dawn Gailey, Raven Collins, Chiara Enriquez, Amelia Mcconnell, Alexander Morton, Emma Beckett, Leah G. Parr, Briana Adhikusuma, Taylor Embrey, Rowan Davis, Danielle Sisson, Bianca Cherry, Melissa Cacho, Chloe Woodward, Catherine Rollins, Carson Reeher, Landon Cooper, Haley Vasquez, Marlisha Stewart, Eric Whitehead, Sabrina Walker, James Bates

Incite: The Journal of Undergraduate Scholarship

Introduction from Interim Dean Dr. Jennifer Apperson

Indigenous Peoples and the Modern Era by Meghan Enzinna

"Who Says": How Selena Gomez and the Scene Attempt to Subvert the Popular Standards of Beauty by Casey Dawn Gailey

Art by Raven Collins

Meltdown on Social Media: Amy's Baking Company Meets Kitchen Nightmares by Nathena Haddrill

Art by Chiara Enriquez

Design by Amelia Mcconnell

Worth More Than a Thousand Words: A Visual Rhetorical Discussion of Virtual Reality by Examining "Clouds Over Sidra" by Alexander Morton

Design by Emma Beckett

The Sonata: An Analysis of Piano Sonata No. 14 in C Minor, K. …

On Emmy Noether And Her Algebraic Works, Deborah Radford

All Student Theses and Dissertations

In the early 1900s a rising star in the mathematics world was emerging. I will discuss her life as a female mathematician and the struggles she faced being a rebel in her time. I will also take an in depth look at some of her contributions to the mathematics and science community . Her work in algebra and more specifically, ring theory, are said to be foundations for much of the work done since then. Her developments in abstract algebra helped to unify topology, geometry, logic and linear algebra. Also, Noether's theorem is a widely used theorem in physics along …

History Of Mathematics From The Islamic World, Asamah Abdallah

All Student Theses and Dissertations

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 …

Off The Lip Conference - Transdisciplinary Approaches To Cognitive Innovation. Conference Proceedings, Sue Denham, Michael Punt, Edith Doove, Martha Blassnigg, Raluca Briazu, Kathryn Francis, Agi Haynes, Guy Edmonds, Adam Benjamin, Matthew Emmett, Iris Garrelfs, Christopher B. Germann, Joanna Griffin, Diane Humphrey, Bryanna Lucyk, Christie Purchase, Rachel Sansone, Emily Baxter, Amy Ione, Frank Loesche, Abigail Jackson, Alexis Kirke, Eduardo Miranda, Luke Rendell, Simon Ingram, Yutaka Nakamura, Gi Taek Ryoo, Eugenia Stamboliev, Michael Straeubig, Chun-Wei Hsu, Pinar Oztop, Mihaela Taranu, Sundar Sarukkai, James Sweeting, Minami Hirayama

Off the Lip Conference - Transdisciplinary Approaches to Cognitive Innovation

The promise of cognitive innovation as a collaborative project in the sciences, arts and humanities is that we can approach creativity as a bootstrapping cognitive process in which the energies that shape the poem are necessarily indistinguishable from those that shape the poet. For the purposes of this conference the exploration of the idea of cognitive innovation concerns an understanding of creativity that is not exclusively concerned with conscious human thought and action but also as intrinsic to our cognitive development. As a consequence, we see the possibility for cognitive innovation to provide a theoretical and practical platform from which …

Pythagoras Plays His Lyre, Sarah Glaz

Journal of Humanistic Mathematics

A poem about the Pythagoreans' beliefs and way of life.

Dramathizing Functions: Building Connections Between Mathematics And Arts, Gunhan Caglayan

Journal of Humanistic Mathematics

This article focuses on connections between mathematics and performance arts (drama). More specifically we offer an exposition of a segment of college algebra mathematics (an introduction to functions), with an approach primarily emphasizing the aesthetic aspects of mathematical learning, teaching, and performing.

A Meeting Of Minds: An Alternate Humor For Teaching Mathematics To Non-Stem Majors, Paul H. Grawe

Journal of Humanistic Mathematics

John Allen Paulos argued essentially for three forms of humor dear to mathematics: Incongruity, Gotcha, and Word Play. Unfortunately, these three are often combative forms and easily drive non-STEM majors out of mathematics and statistics.

William Dunham in The Mathematical Universe shows how a fine mathematician can use humor to draw non-specialists in. Central to Dunham’s success is his use of Sympathetic Pain humor, which creates softer synthetic Reconciler, Consoler, or Bridgebuilder humor styles.

What If?: Mathematics, Creative Writing, And Play, Emily Clader

Journal of Humanistic Mathematics

Mathematics can inform creative writing by suggesting structures for it to follow, as well as by providing the imaginative impetus for common rules to be broken. In a workshop co-taught by the author, a class of sixth-grade students explored this interplay as they produced fractal-inspired poetry and geometry-inspired fiction. This article describes the form and results of the workshop in the context of a broader discussion of the influence of mathematics upon literature.

The Role Of Sequence In The Experience Of Mathematical Beauty, Leslie Dietiker

Journal of Humanistic Mathematics

In this article, I analyze the aesthetic dimensions of a sequence of mathematical events found in an unusual first grade lesson in order to demonstrate how sequencing may affect an individual’s experience of mathematical beauty. By approaching aesthetic as a sense or felt quality of an experience in context (Sinclair, 2001, 2011), this analysis explains how sequence can affect the way mathematical objects or actions are experienced by an individual. Thus, rather than questioning whether or in what ways a set of mathematical objects are beautiful or not, this paper addresses under what conditions is the mathematics in play beautiful. …

A Beautiful Proof By Induction, Lars-Daniel Öhman

Journal of Humanistic Mathematics

The purpose of this note is to present an example of a proof by induction that in the opinion of the present author has great aesthetic value. The proof in question is Thomassen's proof that planar graphs are 5-choosable. I give a self-contained presentation of this result and its proof, and a personal account of why I think this proof is beautiful.

A secondary purpose is to more widely publicize this gem, and hopefully make it part of a standard set of examples for examining characteristics of proofs by induction.

Alan Turing: The Man Behind The Machine, Christopher D. Goff

College of the Pacific Faculty Presentations

No abstract provided.