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Articles 391 - 420 of 2858

Full-Text Articles in Physical Sciences and Mathematics

Blending Mathematics Teaching With Kindness, Kien H. Lim, Anthony Matsuura Feb 2023

Blending Mathematics Teaching With Kindness, Kien H. Lim, Anthony Matsuura

Journal of Humanistic Mathematics

Mathematics can be intellectually demanding, engaging, and fulfilling. Learning mathematical concepts adequately warrants an environment where students can err without penalty, shame, or hurtful consequences. Teaching mathematics efficaciously depends on the trusting relationship between the teacher and the students. We advocate blending mathematics teaching with kindness because it benefits the teacher, the students, and society. Kindness, niceness, caring, and benevolence are interrelated but not synonymous. We outline four progressive levels of kindness: conditional, superficial, optimal, and genuine. Blending mathematics teaching and kindness effectively requires the teacher to decenter from their own perspectives and adopt the student’s perspective as the student …

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Figure-Ground Perception: A Poem Proof, Richard Delaware Feb 2023

Figure-Ground Perception: A Poem Proof, Richard Delaware

Journal of Humanistic Mathematics

This is a proof, in poetic form, of a bit of real analysis, more specifically involving the topology of accumulation points, that exploits the human optical phenomenon of figure-ground perception. Sometimes it is not a change in content, but a snap shift in point of view that yields a proof.

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The Mathematics Of The Harp: Modeling The Classical Instrument And Designing Futuristic Ones, Cristina Carr, Daniel Chioffi, Maya Glenn, Stefan O. Nita, Vlad N. Nita, Bogdan G. Nita Feb 2023

The Mathematics Of The Harp: Modeling The Classical Instrument And Designing Futuristic Ones, Cristina Carr, Daniel Chioffi, Maya Glenn, Stefan O. Nita, Vlad N. Nita, Bogdan G. Nita

Journal of Humanistic Mathematics

We analyze and model the neck of the classical harp based on the length of the strings, their tension and density. We then use the results to design new and innovative harp shapes by adjusting the parameters of the model.

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Using Bloom's Taxonomy For Math Outreach Within And Outside The Classroom, Manmohan Kaur Feb 2023

Using Bloom's Taxonomy For Math Outreach Within And Outside The Classroom, Manmohan Kaur

Journal of Humanistic Mathematics

Not everyone is a great artist, but we don’t often hear, “I dislike art.” Most people are able to appreciate visual arts, music and sports, without necessarily excelling in it themselves. On the other hand, the phrase “I dislike math” is widely prevalent. This is especially ironic in our current society, where mathematics affects our day-to-day activities in essential ways such as e-commerce and e-mail. This paper describes the opportunity to popularize mathematics by focusing on its fun and creative aspects, and illustrates this opportunity through a brief discussion of interdisciplinary topics that expose the beauty, elegance and value of …

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Lessons From Human Experience: Teaching A Humanities Course Made Me A Better Math Teacher, Erin Griesenauer Feb 2023

Lessons From Human Experience: Teaching A Humanities Course Made Me A Better Math Teacher, Erin Griesenauer

Journal of Humanistic Mathematics

As a professor at a Liberal Arts college, I recently taught a General Education course called Human Experience. Far from my normal experiences in the mathematics classroom, in Human Experience I was tasked with teaching topics from the humanities, including art, philosophy, history, and political science. Teaching this course was challenging, but it was also transformative. Teaching a course so far from my background gave me the opportunity to experiment with different pedagogical techniques and to reflect on how I set up my math classes. I learned many lessons that I have brought back to my math classes—lessons that have …

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The Nothing That Really Matters, Szilárd Svitek Feb 2023

The Nothing That Really Matters, Szilárd Svitek

Journal of Humanistic Mathematics

Zero has (a) special role(s) in mathematics. In the current century, we take negative numbers and zero for granted, but we should also be aware that their acceptance and their emergence in mathematics, and their ubiquity today, have not come to happen as rapidly as, for example, that of natural numbers. Students can quickly become confused by the question: is zero a natural number? The answer is simple: a matter of definition. The history of zero and that of negative numbers are closely linked. It was in the calculations of debts that the negative numbers first appeared, where the state …

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The Use And Development Of Mathematics Within Creative Literature, Toby S C Peres Feb 2023

The Use And Development Of Mathematics Within Creative Literature, Toby S C Peres

Journal of Humanistic Mathematics

This paper presents a study on the extent to which creative literature been used as a vessel to carry forward the development of mathematical thought. The role of mathematics as a driving force for literature is highlighted, and while many examples exist that clearly show an attempt to disperse mathematical ideas, with Lewis Carroll, OuLiPo and ancient poetry considered, the argument that the sole purpose of the writings was for the sake of mathematical development is not clear-cut.

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The Genesis Of A Theorem, Osvaldo Marrero Feb 2023

The Genesis Of A Theorem, Osvaldo Marrero

Journal of Humanistic Mathematics

We present the story of a theorem's conception and birth. The tale begins with the circumstances in which the idea sprouted; then is the question's origin; next comes the preliminary investigation, which led to the conjecture and the proof; finally, we state the theorem. Our discussion is accessible to anyone who knows mathematical induction. Therefore, this material can be used for instruction in a variety of courses. In particular, this story may be used in undergraduate courses as an example of how mathematicians do research. As a bonus, the proof by induction is not of the simplest kind, because it …

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Where Do Babies Come From?, Marcio Luis Ferreira Nascimento Feb 2023

Where Do Babies Come From?, Marcio Luis Ferreira Nascimento

Journal of Humanistic Mathematics

According to European folklore, popularized by a fairy tale, storks are responsible for bringing babies to new parents. This probably came from observation in certain European countries, such as Norway, Netherlands or Germany, that storks nesting on the roofs of households were believed to bring good luck, as the possibility of new births. People love stories, but correlation simply means that there is a relationship between two factors that tells nothing about the direction of said relationship, if any. Another possibility is simple coincidence. Let us say that it’s possible that one factor causes another. It’s also possible that the …

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Teaching Mathematics After Covid: A Conversation Not A Discussion, Wendy Ann Forbes, Joyce Mgombelo Feb 2023

Teaching Mathematics After Covid: A Conversation Not A Discussion, Wendy Ann Forbes, Joyce Mgombelo

Journal of Humanistic Mathematics

Inspired by Brent Davis' conceptualization of listening and conversation in his book Teaching Mathematics: Toward a Sound Alternative, we propose how we as a mathematics education community may move forward by continuing in the conversation that emerged from COVID. We encourage all involved to listen rather than assume a discussion-oriented stance. Using an enactivist lens, we look at the pandemic learning space, give an overview of the education conversation that emerged in Ontario, and offer a way to rethink Mathematics Education within the frame of a conversation. We believe that if mathematics education is to engage learners in a meaningful …

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Human-Machine Collaboration In The Teaching Of Proof, Gila Hanna, Brendan P. Larvor, Xiaoheng (Kitty) Yan Feb 2023

Human-Machine Collaboration In The Teaching Of Proof, Gila Hanna, Brendan P. Larvor, Xiaoheng (Kitty) Yan

Journal of Humanistic Mathematics

This paper argues that interactive theorem provers (ITPs) could play an important role in fostering students’ appreciation and understanding of proof and of mathematics in general. It shows that the ITP Lean has three features that mitigate existing difficulties in teaching and learning mathematical proof. One is that it requires students to identify a proof strategy at the start. The second is that it gives students instant feedback while allowing them to explore with maximum autonomy. The third is that elementary formal logic finds a natural place in the activity of creating proofs. The challenge in using Lean is that …

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A Classification Of Musical Scales Using Binary Sequences, Thomas Hillen Feb 2023

A Classification Of Musical Scales Using Binary Sequences, Thomas Hillen

Journal of Humanistic Mathematics

Every beginning music student has gone through the four main musical scales: major, natural minor, harmonic minor, and melodic minor. And some might wonder, why those four and not five, or six, or just three? Here we show that a mathematical classification can be used to identify these scales as representatives of certain scale families. Moreover, the classification reveals another scale family, which is much less known: the harmonic major scale. We find that each scale family contains exactly seven scales, which include the modes (dorian, phrygian,...) and other scales such as the Romanian, …

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The Merchant And The Mathematician: Commerce And Accounting, Graziano Gentili, Luisa Simonutti, Daniele C. Struppa Feb 2023

The Merchant And The Mathematician: Commerce And Accounting, Graziano Gentili, Luisa Simonutti, Daniele C. Struppa

Journal of Humanistic Mathematics

In this article we describe the invention of double-entry bookkeeping (or partita doppiaas it was called in Italian), as a fertile intersection between mathematics and early commerce. We focus our attention on this seemingly simple technique that requires only minimal mathematical expertise, but whose discovery is clearly the result of a mathematical way of thinking, in order to make a conceptual point about the role of mathematics as the humus from which disciplines as different as operations research, computer science, and data science have evolved.

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The Roles Of Mathematical Metaphors And Gestures In The Understanding Of Abstract Mathematical Concepts, Omid Khatin-Zadeh, Zahra Eskandari, Danyal Farsani Feb 2023

The Roles Of Mathematical Metaphors And Gestures In The Understanding Of Abstract Mathematical Concepts, Omid Khatin-Zadeh, Zahra Eskandari, Danyal Farsani

Journal of Humanistic Mathematics

When a new mathematical idea is presented to students in terms of abstract mathematical symbols, they may have difficulty to grasp it. This difficulty arises because abstract mathematical symbols do not directly refer to concretely perceivable objects. But, when the same content is presented in the form of a graph or a gesture that depicts that graph, it is often much easier to grasp. The process of solving a complex mathematical problem can also be facilitated with the use of a graphical representation. Transforming a mathematical problem or concept into a graphical representation is a common problem solving strategy, and …

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From A Doodle To A Theorem: A Case Study In Mathematical Discovery, Juan FernáNdez GonzáLez, Dirk Schlimm Feb 2023

From A Doodle To A Theorem: A Case Study In Mathematical Discovery, Juan FernáNdez GonzáLez, Dirk Schlimm

Journal of Humanistic Mathematics

We present some aspects of the genesis of a geometric construction, which can be carried out with compass and straightedge, from the original idea to the published version (Fernández González 2016). The Midpoint Path Construction makes it possible to multiply the length of a line segment by a rational number between 0 and 1 by constructing only midpoints and a straight line. In the form of an interview, we explore the context and narrative behind the discovery, with first-hand insights by its author. Finally, we discuss some general aspects of this case study in the context of philosophy of mathematical …

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Where Does Mathematics Come From? Really, Where?, Mark Huber, Gizem Karaali Feb 2023

Where Does Mathematics Come From? Really, Where?, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

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Front Matter Feb 2023

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

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Introducing Systems Via Laplace Transforms, Ollie Nanyes Jan 2023

Introducing Systems Via Laplace Transforms, Ollie Nanyes

CODEE Journal

The purpose of this note is to show how to move from Laplace Transforms to a brief introduction to two dimensional systems of linear differential equations with only basic matrix algebra.

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The Sensitivity Of A Laplacian Family Of Ranking Methods, Claire S. Chang Jan 2023

The Sensitivity Of A Laplacian Family Of Ranking Methods, Claire S. Chang

HMC Senior Theses

Ranking from pairwise comparisons is a particularly rich subset of ranking problems. In this work, we focus on a family of ranking methods for pairwise comparisons which encompasses the well-known Massey, Colley, and Markov methods. We will accomplish two objectives to deepen our understanding of this family. First, we will consider its network diffusion interpretation. Second, we will analyze its sensitivity by studying the "maximal upset" where the direction of an arc between the highest and lowest ranked alternatives is flipped. Through these analyses, we will build intuition to answer the question "What are the characteristics of robust ranking methods?" …

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Using Computational Fluid Dynamics And Optical Sensor Technology To Scale Cell Culture Platforms, Mandar Makwana Jan 2023

Using Computational Fluid Dynamics And Optical Sensor Technology To Scale Cell Culture Platforms, Mandar Makwana

KGI Theses and Dissertations

Different cell culture vessels ranging from micro scale to laboratory scale to commercial scale play critical role in upstream process development for biologics manufacturing. Based on the mode of operation, cell culture vessels have different hydrodynamic environments, making it challenging to scale. Integrated approaches using computational tools supported by experimental studies can overcome these challenges. Computational Fluid Dynamics (CFD) is one such tool that can simulate hydrodynamics within the cell culture vessels and can provide insights at macro and micro-scale. Accuracy of a CFD model significantly depends on the fluid model and assumptions. Traditionally, simple two-equation fluid models were developed …

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Modeling Self-Diffusiophoretic Janus Particles In Fluid, Kausik Das Jan 2023

Modeling Self-Diffusiophoretic Janus Particles In Fluid, Kausik Das

HMC Senior Theses

We explore spherical Janus particles in which a chemical reaction occurs on one face, depleting a substrate in the suspending fluid, while no reaction occurs on the other face. The steady state concentration field is governed by Laplace’s equation with mixed boundary conditions. We use the collocation method to obtain numerical solutions to the equation in spherical coordinates. The asymmetry of the reaction gives rise to a slip velocity that causes the particle to move spontaneously in the fluid through a process known as self-diffusiophoresis. Using the Lorentz reciprocal theorem, we obtain the swimming velocity of the particle. We extend …

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Multilayer Network Model Of Gender Bias And Homophily In Hierarchical Structures, Emerson Mcmullen Jan 2023

Multilayer Network Model Of Gender Bias And Homophily In Hierarchical Structures, Emerson Mcmullen

HMC Senior Theses

Although women have made progress in entering positions in academia and
industry, they are still underrepresented at the highest levels of leadership.
Two factors that may contribute to this leaky pipeline are gender bias,
the tendency to treat individuals differently based on the person’s gender
identity, and homophily, the tendency of people to want to be around those
who are similar to themselves. Here, we present a multilayer network model
of gender representation in professional hierarchies that incorporates these
two factors. This model builds on previous work by Clifton et al. (2019), but
the multilayer network framework allows us to …

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A Visual Tour Of Dynamical Systems On Color Space, Jonathan Maltsman Jan 2023

A Visual Tour Of Dynamical Systems On Color Space, Jonathan Maltsman

HMC Senior Theses

We can think of a pixel as a particle in three dimensional space, where its x, y and z coordinates correspond to its level of red, green, and blue, respectively. Just as a particle’s motion is guided by physical rules like gravity, we can construct rules to guide a pixel’s motion through color space. We can develop striking visuals by applying these rules, called dynamical systems, onto images using animation engines. This project explores a number of these systems while exposing the underlying algebraic structure of color space. We also build and demonstrate a Visual DJ circuit board for …

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Explorations In Well-Rounded Lattices, Tanis Nielsen Jan 2023

Explorations In Well-Rounded Lattices, Tanis Nielsen

HMC Senior Theses

Lattices are discrete subgroups of Euclidean spaces. Analogously to vector spaces, they can be described as spans of collections of linearly independent vectors, but with integer (instead of real) coefficients. Lattices have many fascinating geometric properties and numerous applications, and lattice theory is a rich and active field of theoretical work. In this thesis, we present an introduction to the theory of Euclidean lattices, along with an overview of some major unsolved problems, such as sphere packing. We then describe several more specialized topics, including prior work on well-rounded ideal lattices and some preliminary results on the study of planar …

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An Inquiry Into Lorentzian Polynomials, Tomás Aguilar-Fraga Jan 2023

An Inquiry Into Lorentzian Polynomials, Tomás Aguilar-Fraga

HMC Senior Theses

In combinatorics, it is often desirable to show that a sequence is unimodal. One method of establishing this is by proving the stronger yet easier-to-prove condition of being log-concave, or even ultra-log-concave. In 2019, Petter Brändén and June Huh introduced the concept of Lorentzian polynomials, an exciting new tool which can help show that ultra-log-concavity holds in specific cases. My thesis investigates these Lorentzian polynomials, asking in which situations they are broadly useful. It covers topics such as matroid theory, discrete convexity, and Mason’s conjecture, a long-standing open problem in matroid theory. In addition, we discuss interesting applications to known …

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Discrete Analogues Of The Poincaré-Hopf Theorem, Kate Perkins Jan 2023

Discrete Analogues Of The Poincaré-Hopf Theorem, Kate Perkins

HMC Senior Theses

My thesis unpacks the relationship between two discrete formulations of the Poincaré-Hopf index theorem. Chapter 1 introduces necessary definitions. Chapter 2 describes the discrete analogs and their differences. Chapter 3 contains a proof that one analog implies the other and chapter 4 contains a proof that the Poincaré-Hopf theorem implies the discrete analogs. Finally, chapter 5 presents still open questions and further research directions.

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Long Increasing Subsequences, Hannah Friedman Jan 2023

Long Increasing Subsequences, Hannah Friedman

HMC Senior Theses

In my thesis, I investigate long increasing subsequences of permutations from two angles. Motivated by studying interpretations of the longest increasing subsequence statistic across different representations of permutations, we investigate the relationship between reduced words for permutations and their RSK tableaux in Chapter 3. In Chapter 4, we use permutations with long increasing subsequences to construct a basis for the space of ��-local functions.

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The Green Revolution In California: The Real Costs And Benefits Of Changing Electricity Production, Joseph James Hoffman Jan 2023

The Green Revolution In California: The Real Costs And Benefits Of Changing Electricity Production, Joseph James Hoffman

CGU Theses & Dissertations

In recent years democratic societies have added concern for the environment to the perennial problems of inequality, economic growth, and law and order. What is often called the Green Revolution has focused on the effect of industrial growth on the health of the individuals living in that society and on the effects on climate. In the United States, the State that was the first to see this problem and the first to make changes to deal with it, was California, where geographical factors ensured that the effects of industrial change on the air were much more severe than anywhere else …

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Graph-Based Acoustic Clustering And Classification, Justin Youngho Sunu Jan 2023

Graph-Based Acoustic Clustering And Classification, Justin Youngho Sunu

CGU Theses & Dissertations

The rapid growth of audio data collection in various domains necessitates advanced techniquesfor efficient analysis and classification. This dissertation proposes new approaches for categorizing acoustic data, using both unsupervised and semi-supervised learning methods. Starting with raw audio, we preprocess the signal to segment it into time windows, each of which we consider as an independent data point. We use the short-time Fourier transform to describe the signal in a given time window as a set of Fourier coefficients. We interpret the resulting frequency signature as a high-dimensional feature description of each data point. We then develop a graph-based approach for …

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A New Credit Scoring Model To Reduce Potential Predatory Lending: A Design Science Approach, Anna Zakowska Jan 2023

A New Credit Scoring Model To Reduce Potential Predatory Lending: A Design Science Approach, Anna Zakowska

CGU Theses & Dissertations

This research examines the potential impact of implementing a novel credit scoring model that integrates attributes beyond the traditional FICO model. It aims to address issues related to predatory lending and the financial exclusion affecting individuals often categorized as 'credit invisible,' 'credit unscorable,' 'unbanked,' and 'underbanked.' These individuals typically face difficulties in establishing or repairing a credit history, which poses a challenge for financial institutions in accurately evaluating their creditworthiness. This gap in the credit assessment process often opens doors to unfair lending practices. To tackle this problem, a systematically designed, built, tested, and evaluated innovative credit scoring model was …

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