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2021

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Articles 361 - 390 of 1314

Full-Text Articles in Mathematics

The Power Of A Double Take: Doubling Back To Show Growth In A Pandemic, Lawrence M. Lesser Jul 2021

The Power Of A Double Take: Doubling Back To Show Growth In A Pandemic, Lawrence M. Lesser

Journal of Humanistic Mathematics

The COVID-19 pandemic inspired reflections on the importance and challenges of teaching exponential growth, such as doubling, to varied audiences.

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Can We Science The Poop, Too?, Nat Banting Jul 2021

Can We Science The Poop, Too?, Nat Banting

Journal of Humanistic Mathematics

This article describes how an innocuous question from a primary schooler taught me to pay attention to the dynamic meaning making activities of children—particularly, those of my young daughter. Through this lens, I examine how the verb-based world of children might compel us to think differently about the largely nominalized project of schooling and, more specifically, about the craft of teaching mathematics.

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Math Girl Solves The Pattern, Zoe H. Austin, Jennifer K.M. Austin Jul 2021

Math Girl Solves The Pattern, Zoe H. Austin, Jennifer K.M. Austin

Journal of Humanistic Mathematics

During COVID-19 isolation, Dr. Jennifer Austin and her seven-year-old daughter Zoe co-authored the short story Math Girl Solves the Pattern. Here we meet the superheroine Math Girl and her nemesis Minus Girl. Math Girl is observant, curious, and creative. Houses, balls, and sailboats are disappearing! The mystery must be solved. Persevering Math Girl saves the day.

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Assessment, Evaluation, And Grading: A Reflection On My Radicalization, Priscilla Bremser Jul 2021

Assessment, Evaluation, And Grading: A Reflection On My Radicalization, Priscilla Bremser

Journal of Humanistic Mathematics

The COVID-19 pandemic forced instructors to adapt their assessment practices. For this author, that adaptation led to a reconsideration of evaluation systems, given the ways in which such systems can interfere with learning and perpetuate inequities. The author describes resulting changes in her grading of student work and evaluation of faculty colleagues.

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Crocheting Mathematics Through Covid-19, Beyza C. Aslan Jul 2021

Crocheting Mathematics Through Covid-19, Beyza C. Aslan

Journal of Humanistic Mathematics

As it is often said, something good often comes out of most bad situations. The time I spent during COVID-19, at home and isolated with my two children, brought out one secret passion in me: crocheting. Not only did it help me pass the time in a sane and productive way, but also it gave me a new goal in life. It connected my math side with my artistic side. It gave me a new perspective to look at math, and helped me help others see math in a positive way.

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Work-Life Imbalance In The Time Of Covid-19, Rachel Epstein, Caroline Haddad, Emek Kose, Melissa Sutherland Jul 2021

Work-Life Imbalance In The Time Of Covid-19, Rachel Epstein, Caroline Haddad, Emek Kose, Melissa Sutherland

Journal of Humanistic Mathematics

Four women mathematicians at various stages of their careers at public liberal arts institutions share their struggles and challenges in their professional and personal lives during the pandemic.

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My Year Of Memory And Mathematics, Richard Delaware Jul 2021

My Year Of Memory And Mathematics, Richard Delaware

Journal of Humanistic Mathematics

I relive one stream of my state of mind over the pandemic year of 2020.

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Arithmetics, Interrupted, Matilde Lalín Jul 2021

Arithmetics, Interrupted, Matilde Lalín

Journal of Humanistic Mathematics

I share some of my adventures in mathematical research and homeschooling in the time of COVID-19.

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Making Art In Math Class During The Pandemic, Larson Fairbairn, Kameelah Jackson, Ksenija Simic-Muller Jul 2021

Making Art In Math Class During The Pandemic, Larson Fairbairn, Kameelah Jackson, Ksenija Simic-Muller

Journal of Humanistic Mathematics

For many of us, the pandemic has changed how we teach and how we support students. This manuscript highlights creativity as a way to support for student mathematical and emotional well-being. It describes the positive impact that creative assignments in a mathematics content course for preservice K-8 teachers had on students during the early days of the pandemic. The story is told by the instructor and two former students in the course.

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Leonardo Da Vinci In Raphael's School Of Athens, Frode Sirnes Larsen Jul 2021

Leonardo Da Vinci In Raphael's School Of Athens, Frode Sirnes Larsen

Journal of Humanistic Mathematics

At the center of the School of Athens, Raphael painted Plato with a face similar to that of Leonardo da Vinci. In this article I argue that the likeness was intentional, and that Raphael’s fresco contains a set of references to the book De Divina Proportione, to which Leonardo contributed with drawings of polyhedrons. De Divina Proportione was written by Leonardo’s friend and teacher of mathematics, Luca Pacioli, and contains arguments for raising the status of the art of painting, similar to the arguments found in Leonardo’s Paragone. Pacioli and Leonardo thought painting should be regarded as …

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The Math Games Seminar: A Mathematical Learning Community, Anthony Delegge, Ellen Ziliak Jul 2021

The Math Games Seminar: A Mathematical Learning Community, Anthony Delegge, Ellen Ziliak

Journal of Humanistic Mathematics

Learning communities can be an effective means of engaging university students across disciplines. Games have always been a source of both enjoyment and interesting mathematics. Based on our own interest in games, and the deep, strategic discussions we found ourselves having with students when we played games with them, we decided to design a learning community around the mathematics of games. We hoped in particular that such a community could be a great pathway to introducing mathematical thinking to students not majoring in mathematics, and that they would gain a greater appreciation for our field. In this paper, we describe …

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Markov Chains For Computer Music Generation, Ilana Shapiro, Mark Huber Jul 2021

Markov Chains For Computer Music Generation, Ilana Shapiro, Mark Huber

Journal of Humanistic Mathematics

Random generation of music goes back at least to the 1700s with the introduction of Musical Dice Games. More recently, Markov chain models have been used as a way of extracting information from a piece of music and generating new music. We explain this approach and give Python code for using it to first draw out a model of the music and then create new music with that model.

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An Interdisciplinary Rendezvous Between Mathematics And Literature: Reflections On Beauty As A Perspective In Comparative Disciplinary Didactics And A Thematic Approach To Interdisciplinary Work In Upper Secondary School, Uffe Thomas Jankvist, Helle Rørbech, Jesper Bremholm Jul 2021

An Interdisciplinary Rendezvous Between Mathematics And Literature: Reflections On Beauty As A Perspective In Comparative Disciplinary Didactics And A Thematic Approach To Interdisciplinary Work In Upper Secondary School, Uffe Thomas Jankvist, Helle Rørbech, Jesper Bremholm

Journal of Humanistic Mathematics

In this paper we propose a thematic focus on aesthetics in the context of an interdisciplinary collaboration between mathematics and literature (Language Arts) as a way to further students’ reflections on and deeper understanding of what characterizes the two subjects. Furthermore, we argue that approaching aesthetics through the perspective of literacy can potentially strengthen students’ understanding of ways of thinking particular to specific (academic) disciplines; ways of thinking that are otherwise often hidden when teaching focuses on more pragmatic aspects. G. H. Hardy’s A Mathematician’s Apology from 1940 serves as the recurring illustrative example in our discussions of the pedagogical …

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Mathematics Heritage Project: An Exploration Empowering Students' Mathematical Identities, Siddhi Desai, Brianna Kurtz, Farshid Safi Jul 2021

Mathematics Heritage Project: An Exploration Empowering Students' Mathematical Identities, Siddhi Desai, Brianna Kurtz, Farshid Safi

Journal of Humanistic Mathematics

The International Study Group on Ethnomathematics (ISGEm) supports incorporating cultural diversity of mathematical practices to promote the teaching and learning of school mathematics. Through The Mathematics Heritage Project, students at a middle school in the southeastern United States developed unique creations to connect with the mathematics connected to their identities and self-identified cultural group. Upon reflection, students reported an increased awareness of the relevance of mathematics in their lives and a sense of ownership that is both meaningful and modern.

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Logic And Biology: The Correspondence Between Alfred Tarski And Joseph H. Woodger, Paolo Mancosu Jul 2021

Logic And Biology: The Correspondence Between Alfred Tarski And Joseph H. Woodger, Paolo Mancosu

Journal of Humanistic Mathematics

This article makes available some early letters chronicling the relationship between the biologist Joseph H. Woodger and the logician Alfred Tarski. Using twenty-five unpublished letters from Tarski to Woodger preserved in the Woodger Papers at University College, London, I reconstruct their relationship for the period 1935-1950. The scientific aspects of the correspondence concern, among other things, Tarski’s reports on the work he is doing, his interests, and his --- sometimes critical but always well-meaning --- reactions to Woodger’s attempts at axiomatizing and formalizing biology using the system of Principia Mathematica. Perhaps the most interesting letter from a philosophical point …

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Mathematics And Magic Realism: A Study Of "The Raven Legend", Veselin Jungic Jul 2021

Mathematics And Magic Realism: A Study Of "The Raven Legend", Veselin Jungic

Journal of Humanistic Mathematics

This article demonstrates that “The Raven Legend”, a Haida myth transcribed by Franz Boas in 1888, is full of (ethno)mathematical concepts that Haida society used to make sense of the natural, real world. Calculus can be used to model several segments of the story since the narrative relied heavily on ideas that a mathematician would identify as the concepts of infinity and mathematical limits.

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Seeing Mathematics In The World, Mark Huber, Gizem Karaali Jul 2021

Seeing Mathematics In The World, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

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Front Matter Jul 2021

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

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Group Actions On Hyperspaces, Manpreet Singh Jul 2021

Group Actions On Hyperspaces, Manpreet Singh

Math Theses

In this thesis, we will look at the structure of two spaces associated with a topological space X, C(X) and P(X). Furthermore, from the group action of a topological group G on X, we get the induced group action of G on C(X) and P(X). We will also look at few properties for actions of G on a compact Hausdorff space X: proximality, strong proximality and extreme proximality followed by the main result to give parallel characterizations of proximality and extreme proximality.

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Essays On Collective Contests And Bargaining., Dhritiman Gupta Dr. Jul 2021

Essays On Collective Contests And Bargaining., Dhritiman Gupta Dr.

Doctoral Theses

This thesis consists of three theoretical essays in Microeconomics. The first two essays analyze the properties of a particular class of prize sharing rules groups may employ in a situation of a collective contest with another group, over a private good. The third essay studies a situation of multi-lateral bargaining, where a buyer wants to successfully bargain with multiple sellers, who own an input each, so that he can implement a grand project. The main focus of the thesis is to theorize about and generate hypotheses of the situations summarized above. In the first chapter, we consider a situation of …

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Dealing With Classification Irregularities In Real-World Scenarios., Payel Sadhukhan Dr. Jul 2021

Dealing With Classification Irregularities In Real-World Scenarios., Payel Sadhukhan Dr.

Doctoral Theses

Data processing by the human sensory system comes naturally. This processing, commonly denoted as pattern recognition and analysis are carried out spontaneously by humans. In day to day life, in most cases, decision making by humans come without any conscious effort. From the middle of the past century, humans have shown interest to render their abstraction capabilities (pattern recognition and analysis) to the machine. The abstraction capability of the machine is ’machine intelligence’ or ’machine learning’ [87].The primary goal of machine learning methods is to extract some meaningful information from the ’data’. Data refers to the information or attributes that …

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An Introduction To Generalized Entropy And Some Quantum Applications, Paul Bracken Jul 2021

An Introduction To Generalized Entropy And Some Quantum Applications, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

The concept of generalized entropy is introduced and some of its properties are studied. Irreversible time evolution can be generated by a non-Hermitian superoperator on the states of the system. The case when irreversibility comes about from embedding the system in a thermal reservoir is looked at. The time evolution is found compatible both with equilibrium thermodynamics and entropy production near the final state. Some examples are presented as well as a longer introduction as to how this might play a role in the black hole information loss paradox.

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Non-Archimedean Models Of Morphogenesis, Wilson A. Zuniga-Galindo Jul 2021

Non-Archimedean Models Of Morphogenesis, Wilson A. Zuniga-Galindo

School of Mathematical & Statistical Sciences Faculty Publications

We study a p-adic reaction-diffusion system and the associated Turing patterns. We establish an instability criteria and show that the Turing patterns are not classical patterns consisting of alternating domains. Instead of this, a Turing pattern consists of several domains (clusters), each of them supporting a different pattern but with the same parameter values. This type of patterns are typically produced by reaction-diffusion equations on large networks.

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Amplification Of Hidden Periodic Motions In 3d Videos, Thomas Boccuto, Seraiah Kutai, Kristen Mosley, Samuel Kirk Jul 2021

Amplification Of Hidden Periodic Motions In 3d Videos, Thomas Boccuto, Seraiah Kutai, Kristen Mosley, Samuel Kirk

Mathematics Summer Fellows

Ordinary videos capture a surprising amount of hidden, visually imperceptible information. For instance, videos of peoples' faces may capture color changes in the skin and artery motion from heartbeats, while videos of mechanical systems can capture subtle vibrations indicating imminent failure. Algorithms can extract and exaggerate these signals for visualization on top of the original videos. In particular, Eulerian magnification algorithms sidestep the need to track hidden motions directly and instead devise multiscale bandpass filters to amplify signals in local spatial regions. In this work, we extend these techniques beyond color videos to geometric video data captured by 3D depth …

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Riemann-Hilbert Problems For Nonlocal Reverse-Time Nonlinear Second-Order And Fourth-Order Akns Systems Of Multiple Components And Exact Soliton Solutions, Alle Adjiri Jul 2021

Riemann-Hilbert Problems For Nonlocal Reverse-Time Nonlinear Second-Order And Fourth-Order Akns Systems Of Multiple Components And Exact Soliton Solutions, Alle Adjiri

USF Tampa Graduate Theses and Dissertations

We first investigate the solvability of an integrable nonlinear nonlocal reverse-time six-component fourth-order AKNS system generated from a reduced coupled AKNS hierarchy under a reverse-time reduction. Riemann-Hilbert problems will be formulated by using the associated matrix spectral problems, and exact soliton solutions will be derived from the reflectionless case corresponding to an identity jump matrix. Secondly, we present the inverse scattering transform for solving a class of eight-component AKNS integrable equations obtained by a specific reduction associated with a block matrix spectral problem. The inverse scattering transform based on Riemann-Hilbert problems is presented along with a jump matrix taken to …

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Essays In Behavioral Social Choice Theory., Sarvesh Bandhu Dr. Jul 2021

Essays In Behavioral Social Choice Theory., Sarvesh Bandhu Dr.

Doctoral Theses

This thesis comprises four essays on social choice theory. The first three essays/chapters consider models where voters follow “non-standard” rules for decision making. The last chapter considers the binary social choice model and analyzes the consequences of a new axiom. The first chapter introduces a new axiom for manipulability when voters incur a cost if they misreport their true preference ordering. The second chapter considers the random voting model with strategic voters where standard stochastic dominance strategy-proofness is replaced by strategy-proofness under two lexicographic criteria. The third chapter also considers the random voting model but from a non-strategic perspective. It …

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Near-Optimal Learning Of Tree-Structured Distributions By Chow-Liu, Arnab Bhattacharyya, Sutanu Gayen, Eric Price, N. V. Vinodchandran Jul 2021

Near-Optimal Learning Of Tree-Structured Distributions By Chow-Liu, Arnab Bhattacharyya, Sutanu Gayen, Eric Price, N. V. Vinodchandran

Department of Mathematics: Faculty Publications

We provide finite sample guarantees for the classical Chow-Liu algorithm (IEEE Trans. Inform. Theory, 1968) to learn a tree-structured graphical model of a distribution. For a distribution P on Σn and a tree T on n nodes, we say T is an ε-approximate tree for P if there is a T-structured distribution Q such that D(P || Q) is at most ε more than the best possible tree-structured distribution for P. We show that if P itself is tree-structured, then the Chow-Liu algorithm with the plug-in estimator for mutual information with eO (|Σ| …

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Algorithms Related To Triangle Groups, Bao The Pham Jul 2021

Algorithms Related To Triangle Groups, Bao The Pham

LSU Doctoral Dissertations

Given a finite index subgroup of $\PSL_2(\Z)$, one can talk about the different properties of this subgroup. These properties have been studied extensively in an attempt to classify these subgroups. Tim Hsu created an algorithm to determine whether a subgroup is a congruence subgroup by using permutations \cite{hsu}. Lang, Lim, and Tan also created an algorithm to determine if a subgroup is a congruence subgroup by using Farey Symbols \cite{llt}. Sebbar classified torsion-free congruence subgroups of genus 0 \cite{sebbar}. Pauli and Cummins computed and tabulated all congruence subgroups of genus less than 24 \cite{ps}. However, there are still some problems …

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Towards The Homotopy Type Of The Morse Complex, Connor Donovan Jul 2021

Towards The Homotopy Type Of The Morse Complex, Connor Donovan

Mathematics Summer Fellows

Mathematicians have long been interested in studying the properties of simplicial complexes. In 1998, Robin Forman developed gradient vector fields as a tool to study these complexes. Having gradient vector fields to study these simplicial complexes, in 2005, Chari and Joswig discovered the Morse complex, a complex consisting of all gradient vector fields on a fixed complex. Although the Morse complex has been studied since 2005, there is little information regarding its homotopy type for different simplicial complexes. Pursuing our curiosity of the topic, we extend a result by Ayala et. al., stating that the pure Morse complex of a …

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Positive Solutions For The Fractional Schrödinger Equations With Logarithmic And Critical Non-Linearities, Haining Fan, Zhaosheng Feng, Xingjie Yan Jul 2021

Positive Solutions For The Fractional Schrödinger Equations With Logarithmic And Critical Non-Linearities, Haining Fan, Zhaosheng Feng, Xingjie Yan

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we study a class of fractional Schrödinger equations involving logarithmic and critical non-linearities on an unbounded domain, and show that such an equation with positive or sign-changing weight potentials admits at least one positive ground state solution and the associated energy is positive (or negative). By applying the Nehari manifold method and Ljusternik–Schnirelmann category, we investigate how the weight potential affects the multiplicity of positive solutions, and obtain the relationship between the number of positive solutions and the category of some sets related to the weight potential.

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