Other Mathematics Commons^™

Analysis, Constructions And Diagrams In Classical Geometry, Marco Panza

MPP Published Research

Greek ancient and early modern geometry necessarily uses diagrams. Among other things, these enter geometrical analysis. The paper distinguishes two sorts of geometrical analysis and shows that in one of them, dubbed “intra-confgurational” analysis, some diagrams necessarily enter as outcomes of a purely material gesture, namely not as result of a codifed constructive procedure, but as result of a free-hand drawing.

Structure, Neutrostructure, And Antistructure In Science, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In any science, a classical Theorem, defined on a given space, is a statement that is 100% true (i.e. true for all elements of the space). To prove that a classical theorem is false, it is sufficient to get a single counter-example where the statement is false. Therefore, the classical sciences do not leave room for partial truth of a theorem (or a statement). But, in our world and in our everyday life, we have many more examples of statements that are only partially true, than statements that are totally true. The NeutroTheorem and AntiTheorem are generalizations and alternatives of …

Ethnomathematics: Art, Culture, And Social Justice, John R. Jungck

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Fifteenth International Photovideoanthology On Paradoxism, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Paradoxism is an international movement in science and culture, founded by Florentin Smarandache in 1980s, based on excessive use of antitheses, oxymoron, contradictions, and paradoxes. During three decades (1980-2020) hundreds of authors from tenth of countries around the globe contributed papers to 15 international paradoxist anthologies.

In 1995, the author extended the paradoxism to a new branch of philosophy called neutrosophy, that gave birth to many scientific branches, such as: neutrosophic logic, neutrosophic set, neutrosophic probability and statistics, neutrosophic algebraic structures and so on with multiple applications in engineering, computer science, administrative work, medical research etc.

“May your imagination blossom …

Neutrosophic In Latin America, Advances And Perspectives (Neutrosofía En Latinoamérica, Avances Y Perspectivas), Maykel Leyva-Vazquez, Jesus Estupinan, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophy has given way to its own research method by constituting a unified field of logic for a transdisciplinary study that crosses the borders between the sciences. This paper analyzes the impact of neutrosophic theory in Latin America, its main drivers and the state of the research. The increase in publications since the creation of the Latin American Association of Neutrosophic Sciences is noteworthy. The most approached areas are found in the interrelation of the social sciences and neutrosophy, presenting outstanding results in these areas of research. The most outstanding university and institutions are the Autonomous Regional University of the …

Across The Atlantic: Service-Learning In Spain And Morocco, Lauren Ward

Purdue Journal of Service-Learning and International Engagement

Purdue provides many activities in service-learning each year, and though they are varied experiences, many of the same lessons can be learned. I had the opportunity to participate in two service-learning study abroad trips while at Purdue- the first to Spain and Morocco, and the second to Haiti. While on these trips, I was involved in projects that seemed very different. In Morocco, my group taught high school students about the history of mathematics during the Islamic Golden Age and how mathematics is utilized in Purdue research. In Haiti, I worked with my teammates to teach water sanitation and storage …

Fluids In Music: The Mathematics Of Pan’S Flutes, Bogdan Nita, Sajan Ramanathan

Department of Mathematics Faculty Scholarship and Creative Works

We discuss the mathematics behind the Pan’s flute. We analyze how the sound is created, the relationship between the notes that the pipes produce, their frequencies and the length of the pipes. We find an equation which models the curve that appears at the bottom of any Pan’s flute due to the different pipe lengths.

Mathematics Versus Statistics, Mindy B. Capaldi

Journal of Humanistic Mathematics

Mathematics and statistics are both important and useful subjects, but the former has maintained prominence in the American education system. On the other hand, statistics is more prevalent in daily life and is an increasingly marketable subject to know. This article gives a personal history of one mathematician’s bumpy road to learning and teaching statistics. Additionally, arguments for how and why to include statistics in the K-12 and college curricula are provided.

Quantitative Literacy And The Mathematical Association Of America In The 2000’S: Ql Subcommittee Of Cupm , Sigmaa Ql, And Maa Notes #70, Rick Gillman

Numeracy

This Roots and Seeds article is a partial history of the quantitative literacy movement in the Mathematical Association of America in the first decade of the 21st century. It focuses on the inclusion of QL in the MAA Committee on the Undergraduate Program in Mathematics’ CUPM Curriculum Guidelines (2004), the creation of the special interest group for MAA members (SIGMAA QL, 2004), and the work of that body in subsequent years, in particular, the MAA Notes #70, Current Practices in Quantitative Literacy (2006). I discuss some issues that were problematic in the QL movement in the MAA in those years …

Market Research On Student Concert Attendance At Bgsu's College Of Musical Arts, Mary Solomon

Honors Projects

Bowling Green State University boasts a well established College of Musical Arts which holds concerts performed by esteemed faculty, prestigious guest artists, and students. The school hosts these events in Kobacker Hall and Bryan Recital Hall which can accommodate up to 800 and 250 audience members, respectively. However, performances in Kobacker hall only fill one- fourth of the 800 seats, on average. Why is this so? This project aims to investigate the factors that influence students’ decisions to attend concerts at the College of Musical Arts (CMA). By methodology of survey research and statistical analysis, this project will look into …

Taking Notes: Generating Twelve-Tone Music With Mathematics, Nathan Molder

Electronic Theses and Dissertations

There has often been a connection between music and mathematics. The world of musical composition is full of combinations of orderings of different musical notes, each of which has different sound quality, length, and em phasis. One of the more intricate composition styles is twelve-tone music, where twelve unique notes (up to octave isomorphism) must be used before they can be repeated. In this thesis, we aim to show multiple ways in which mathematics can be used directly to compose twelve-tone musical scores.

Asymptotic Quasi-Completeness And Zfc, Mirna Džamonja, Marco Panza

MPP Published Research

The axioms ZFC of first order set theory are one of the best and most widely accepted, if not perfect, foundations used in mathematics. Just as the axioms of first order Peano Arithmetic, ZFC axioms form a recursively enumerable list of axioms, and are, then, subject to Gödel’s Incompleteness Theorems. Hence, if they are assumed to be consistent, they are necessarily incomplete. This can be witnessed by various concrete statements, including the celebrated Continuum Hypothesis CH. The independence results about the infinite cardinals are so abundant that it often appears that ZFC can basically prove very little about such cardinals. …

Was Frege A Logicist For Arithmetic?, Marco Panza

MPP Published Research

The paper argues that Frege’s primary foundational purpose concerning arithmetic was neither that of making natural numbers logical objects, nor that of making arithmetic a part of logic, but rather that of assigning to it an appropriate place in the architectonics of mathematics and knowledge, by immersing it in a theory of numbers of concepts and making truths about natural numbers, and/or knowledge of them transparent to reason without the medium of senses and intuition.

Enthymemathical Proofs And Canonical Proofs In Euclid’S Plane Geometry, Abel Lassalle, Marco Panza

MPP Published Research

Since the application of Postulate I.2 in Euclid’s Elements is not uniform, one could wonder in what way should it be applied in Euclid’s plane geometry. Besides legitimizing questions like this from the perspective of a philosophy of mathematical practice, we sketch a general perspective of conceptual analysis of mathematical texts, which involves an extended notion of mathematical theory as system of authorizations, and an audience-dependent notion of proof.

Don't Ask The Baby To Do Calculus: Thoughts From An Early-Career Math Mama, Caitlin Krul

Journal of Humanistic Mathematics

I very recently became a math mama. In my desperate search for patterns and structure in those first few weeks, my husband told me, "She's only three weeks old; we can't expect her to be doing calculus homework." I suppose he was right. I am working towards tenure and finding a new balance between teaching and family, all while trying to not lose sight of who I am. My personal challenges range from the logistics of being a nursing mother in a shared office to feelings of being seen as less adequate in my job if I present myself as …

Coincidence Of Bargaining Solutions And Rationalizability In Epistemic Games, Todd Stambaugh

Dissertations, Theses, and Capstone Projects

Chapter 1: In 1950, John Nash proposed the Bargaining Problem, for which a solution is a function that assigns to each space of possible utility assignments a single point in the space, in some sense representing the ’fair’ deal for the agents involved. Nash provided a solution of his own, and several others have been presented since then, including a notable solution by Ehud Kalai and Meir Smorodinsky. In chapter 1, a complete account is given for the conditions under which the two solutions will coincide for two player bargaining scenarios.

Chapter 2: In the same year, Nash …

Review Of G. Israel, Meccanicismo. Trionfi E Miserie Della Visione Meccanica Del Mondo, Marco Panza

MPP Published Research

"This is Giorgio's Israel last book, which appeared only a few weeks after his untimely death, in September 2015. For many reasons, it can be considered as his intellectual legacy, since it comes back, in a new and organic way, to many of the research topics to which he devoted his life and his many publications, which include several papers in Historia Mathematica. One of these papers, co-authored with M. Menghini, appeared in vol. 25/4, 1998 and was devoted to Poincaré's and Enriques's opposite views on qualitative analysis, which is a theme also dealt with in this book (pp. 117–122)."

Can Addressing Language Skills For Fifth Grade Ells In A Multiplication Curriculum Help Address The Achievement Gap In Math? A Multiplication Workbook For Big Kids, Michelle Douglas

Master's Projects and Capstones

Currently, the state of California has 1,332,405 students from grades k-12 who speak a language other than English at home (Caledfacts, 2016). When I started my first year teaching fifth grade with 95% of my students being English language learners (ELLs), I was surprised to see an achievement gap of two to three years in my student’s reading and math skills. I found that my student’s developmental language and math skills contributed to a lack of engagement during math time. Upon further research, I found that these three factors play a role in the wide achievement gaps between ELLs and …

Disciple, Jessica K. Sklar

Journal of Humanistic Mathematics

This is a love poem for mathematics.

Some Thoughts On The Epicurean Critique Of Mathematics, Michael Aristidou

Journal of Humanistic Mathematics

In this paper, we give a comprehensive summary of the discussion on the Epicurean critique of mathematics and in particular of Euclid's geometry. We examine the methodological critique of the Epicureans on mathematics and we assess whether a 'mathematical atomism' was proposed, and its implications. Finally, we examine the Epicurean philosophical stance on mathematics and evaluate whether it was on target or not.

Revolution In Ideology: Crafting A Holistic Scientific Dialectic, Nathan Neill

Dialogue & Nexus

Ideology drives scientific research far more than is acknowledged. Since science itself is conducted by individuals, each scientist has a biased conception of themselves and their surroundings relative to the rest of the universe, even if it is never explicated. This sense of relation to the greater universe is what defines the ideology of the individual. It is this sense of relation and self that creates the individual, who goes on to investigate the natural world by the scientific method. In this paper I will examine extant scientific ideology, particularly in Western science, and propose changes that could be helpful.

Six Septembers: Mathematics For The Humanist, Patrick Juola, Stephen Ramsay

Zea E-Books Collection

Scholars of all stripes are turning their attention to materials that represent enormous opportunities for the future of humanistic inquiry. The purpose of this book is to impart the concepts that underlie the mathematics they are likely to encounter and to unfold the notation in a way that removes that particular barrier completely. This book is a primer for developing the skills to enable humanist scholars to address complicated technical material with confidence. This book, to put it plainly, is concerned with the things that the author of a technical article knows, but isn’t saying. Like any field, mathematics operates …

On Benacerraf’S Dilemma, Again, Marco Panza

MPP Published Research

In spite of its enormous influence, Benacerraf’s dilemma admits no standard unanimously accepted formulation. This mainly depends on Benacerraf’s having originally presented it in a quite colloquial way, by avoiding any compact, somehow codified, but purportedly comprehensive formulation (Benacerraf 1973 cf. p. 29).

Some Comments On Multiple Discovery In Mathematics, Robin W. Whitty

Journal of Humanistic Mathematics

Among perhaps many things common to Kuratowski's Theorem in graph theory, Reidemeister's Theorem in topology, and Cook's Theorem in theoretical computer science is this: all belong to the phenomenon of simultaneous discovery in mathematics. We are interested to know whether this phenomenon, and its close cousin repeated discovery, give rise to meaningful questions regarding causes, trends, categories, etc. With this in view we unearth many more examples, find some tenuous connections and draw some tentative conclusions.

Platonismes, Marco Panza

MPP Published Research

Selon la vulgata philosophique, le platonisme concernant un certain domaine de recherche est la thèse affirmant que ce domaine concerne des objets qui lui sont propres, dont l’existence est indépendante de l’activité cognitive humaine. Souvent, dans la même vulgata on parle aussi de platonisme pour se référer à une thèse un peu différente, d’après laquelle ce qu’on dit concernant ce domaine est vrai ou faux indépendamment de toute justification ou réfutation que l’on puisse apporter. Naturellement, si parmi les énoncées ayant trait à ce demain, il y en a qu’on peut prendre comme particulièrement surs du fait d’en avoir une …

The Greatest Integer Function, Alanna Rae

Journal of Humanistic Mathematics

No abstract provided.

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 …

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 …

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. …