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Mathematics Commons™

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2021

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Articles 841 - 870 of 1314

Full-Text Articles in Mathematics

“You Will Remain Unwavering In Your Determination To Succeed No Matter How Long It Takes”: A Mathematico-Emotional Analysis Of A Guide To Higher Learning, Kathleen M. Clark, Oksana M. Rubis Jan 2021

“You Will Remain Unwavering In Your Determination To Succeed No Matter How Long It Takes”: A Mathematico-Emotional Analysis Of A Guide To Higher Learning, Kathleen M. Clark, Oksana M. Rubis

Journal of Humanistic Mathematics

In this article we present an analysis of the multi-fold artist’s book, A Guide to Higher Learning (Chen, 2009). In our analysis, we propose different perspectives from which to view the mathematical and philosophical aspects found within the book. We explore aspects of “higher learning” by analyzing the complex mathematical equations and textual elements that readers meet in the book. Chen challenges the reader with: “This is a test. You will not be given any assistance or instructions on how to proceed. You will not be told when to begin or when to stop” (Chen, 2009). Thus, in our exploration …

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Aligning Political Options And Aggregated Personal Opinions On The Issues, Kris H. Green Jan 2021

Aligning Political Options And Aggregated Personal Opinions On The Issues, Kris H. Green

Journal of Humanistic Mathematics

Much work has been done in studying how to aggregate voter opinions to decide a fair election. These models presuppose that each voter has a solid understanding of their choices and can express that opinion in the election process. We discuss why this is not always the case. Further, we explore some of the issues that arise when considering the multidimensional nature of both voter preference, with respect to the slate of issues in an election, and the platforms of the various candidates, with respect to the same slate of issues. In light of the complications we encounter and with …

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How I First Heard About Calculus, Bradley J. Lucier Jan 2021

How I First Heard About Calculus, Bradley J. Lucier

Journal of Humanistic Mathematics

An attempt to motivate a class of engineering students leads to insights both personal and pedagogical.

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Computational Thinking In Mathematics And Computer Science: What Programming Does To Your Head, Al Cuoco, E. Paul Goldenberg Jan 2021

Computational Thinking In Mathematics And Computer Science: What Programming Does To Your Head, Al Cuoco, E. Paul Goldenberg

Journal of Humanistic Mathematics

How you think about a phenomenon certainly influences how you create a program to model it. The main point of this essay is that the influence goes both ways: creating programs influences how you think. The programs we are talking about are not just the ones we write for a computer. Programs can be implemented on a computer or with physical devices or in your mind. The implementation can bring your ideas to life. Often, though, the implementation and the ideas develop in tandem, each acting as a mirror on the other. We describe an example of how programming and …

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Teaching From The Unknown, Jon Jacobsen Jan 2021

Teaching From The Unknown, Jon Jacobsen

Journal of Humanistic Mathematics

The goal of teaching is to transform our students' understanding, much as the goal of acting is to transform the audience's reality. In this article we use the context of mathematics to explore connections between teaching and acting and how such connections can help our students learn not only mathematics, but about the nature of mathematics.

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Using Mathematical Equations To Communicate And Think About Karma, Kien H. Lim, Christopher Yakes Jan 2021

Using Mathematical Equations To Communicate And Think About Karma, Kien H. Lim, Christopher Yakes

Journal of Humanistic Mathematics

Two equations are presented in this article to communicate a particular understanding of karma. The first equation relates future experiences to past and present actions. Although the equation uses variables and mathematical symbols such as the integral sign and summation symbol, it reads more like a literal translation of an English sentence. Based on the key idea in the first equation, a second equation is then created to highlight the viability of using math to communicate concepts that are not readily quantifiable. Analyzing such equations can stimulate thinking, enhance understanding of spiritual concepts, raise issues, and uncover tensions between our …

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Real-World Modelling To Increase Mathematical Creativity, Robert Weinhandl, Zsolt Lavicza Jan 2021

Real-World Modelling To Increase Mathematical Creativity, Robert Weinhandl, Zsolt Lavicza

Journal of Humanistic Mathematics

Modelling could be characterised as one of the core activities in mathematics education. However, when learning and teaching mathematics, mathematical modelling is mostly used to apply and deepen mathematical knowledge and competencies. Our educational study aims to explore how mathematical modelling, using real objects and high-quality mathematical technologies, could be utilised to acquire mathematical knowledge and competencies, and how learners could creatively use their existing knowledge. To discover the potential of mathematical modelling using real objects and high-quality mathematical technologies to acquire mathematical knowledge and competencies, and to stimulate learners' creativity, first, we combined cognitive and creative spirals and mathematical …

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A Heart-Centered Stance: Receptivity To Algebra Teachers’ And Students’ Multidimensional Experiences, Nicole L. Fonger Jan 2021

A Heart-Centered Stance: Receptivity To Algebra Teachers’ And Students’ Multidimensional Experiences, Nicole L. Fonger

Journal of Humanistic Mathematics

The algebra classroom in urban public high schools in the United States is a complex space, ripe with many challenges and opportunities. In this paper I introduce the notion of a heart-centered stance for the teacher and the educator, and a method of engaging in creative expression for reflection and introspection toward individual change in the rich context of the high school algebra classroom. My evolving relationships with two high school algebra teachers, observations of their classrooms, as well as my own self-study and professional growth, are incorporated into this paper as I introduce and exemplify two tenets of a …

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A Holistic Mathematics Curriculum Revision: An Adelphi University Case Study, Salvatore J. Petrilli Jan 2021

A Holistic Mathematics Curriculum Revision: An Adelphi University Case Study, Salvatore J. Petrilli

Journal of Humanistic Mathematics

Join me as I take you on a journey with the faculty of the Department of Mathematics and Computer Science at Adelphi University during our two-year re-envisioning and implementation of our mathematics curriculum. From the beginning this involved a data-driven initiative that naturally led to the revisions. Here I describe in detail the process that our department followed. In closing I end with some recommendations for interesting research directions in the field of mathematics education.

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The Prime Number Theorem As A Capstone In A Complex Analysis Course, Stephan Ramon Garcia Jan 2021

The Prime Number Theorem As A Capstone In A Complex Analysis Course, Stephan Ramon Garcia

Journal of Humanistic Mathematics

We present a detailed proof of the prime number theorem suitable for a typical undergraduate- or graduate-level complex analysis course. Our presentation is particularly useful for any instructor who seeks to use the prime number theorem for a series of capstone lectures, a scaffold for a series of guided exercises, or as a framework for an inquiry-based course. We require almost no knowledge of number theory, for our aim is to make a complete proof of the prime number theorem widely accessible to complex analysis instructors and their students. In particular, we highlight the potential pitfalls and subtleties that may …

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Mathematical Representations In Magazine Advertisements: Have The Messages Changed In A Decade?, Jennifer Hall Jan 2021

Mathematical Representations In Magazine Advertisements: Have The Messages Changed In A Decade?, Jennifer Hall

Journal of Humanistic Mathematics

Although people's ideas about mathematics and mathematicians often develop from their school and home experiences, such ideas also are influenced by interactions with popular media. In this article, I report on findings from a study in which I analyzed magazine advertisements for representations of mathematics and mathematicians. Data collection took place in two phases, approximately a decade apart. In each phase, I reviewed a year’s worth of issues in each of six diverse, popular magazines for mathematical representations in advertisements. The frequency of mathematical advertisements decreased from Phase 1 to Phase 2, but the initial frequency was already extremely low, …

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Peer Motivation: Getting Through Math Together, Jessica Mean, Wes Maciejewski Jan 2021

Peer Motivation: Getting Through Math Together, Jessica Mean, Wes Maciejewski

Journal of Humanistic Mathematics

Students have a complex relationship with mathematics. Some love it, but more often than not, the feelings are less favorable. These feelings can lead to decreased motivation which makes it difficult for students to engage with the subject as the semester progresses. Instructors also have difficulty addressing this waning motivation. In this paper, we claim peers are better able to connect with the students and this can be leveraged to better motivate students. We present an approach to having peers motivate their students. These peer interactions integrated with a mandatory mathematics course might improve students’ motivation.

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In How Many Days Will He Meet His Wife?, Dipak Jadhav Jan 2021

In How Many Days Will He Meet His Wife?, Dipak Jadhav

Journal of Humanistic Mathematics

In how many days will he meet his wife? This is a question asked at the end of each of two problems embedded in the verses of the last chapter of the Vyavahāra-gaṇita (‘Mathematics of Transaction’) of Rājāditya of 12th century. He infuses elegance in those two problems by choosing the charming idea of a husband’s meeting with his wife after their quarrel. This paper not only presents the algorithms offered by Rājāditya to solve them on their own terms as well as on modern terms and discusses the historicity of the categories of those two problems but also …

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Raise The (Proportion) Bar!, Michael Waters Jan 2021

Raise The (Proportion) Bar!, Michael Waters

Journal of Humanistic Mathematics

This article, drawing mainly on references to teacher preparation textbooks, proposes proportion bars as a somewhat novel graphical approach to solving simple (direct) proportion problems and to illustrate the advantages of such an approach, which include accessibility with materials at early grade levels, allowance of students to better develop number sense and estimation, facilitation of setting up proportions, allowance for conceptual understanding and motivation of the procedure for solving direct proportions, assistance with part-to-part and part-to whole comparisons, and drawing of connections among mathematical topics. The emphasis is on teaching with understanding, rather than procedural knowledge.

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“It’S All For The Best”: Optimization In The History Of Science, Judith V. Grabiner Jan 2021

“It’S All For The Best”: Optimization In The History Of Science, Judith V. Grabiner

Journal of Humanistic Mathematics

Many problems, from optics to economics, can be solved mathematically by finding the highest, the quickest, the shortest—the best of something. This has been true from antiquity to the present. Why did we start looking for such explanations, and how and why did we conclude that we could productively do so? In this article we explore these questions and tell a story about the history of optimization. Scientific examples we use to illustrate our story include problems from ancient optics, and more modern questions in optics and classical mechanics, drawing on ideas from Newton’s and Leibniz’s calculus and from the …

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Humanistic Stem: From Concept To Course, Debra T. Bourdeau, Beverly L. Wood Jan 2021

Humanistic Stem: From Concept To Course, Debra T. Bourdeau, Beverly L. Wood

Journal of Humanistic Mathematics

Blending perspectives from the humanities and STEM fosters the creativity of all students. The culturally implicit dichotomy between the two meta-disciplines can be overcome with carefully designed courses and programs intent on doing so. The why and how of doing so through an online course is described with qualitative evidence of the success. Future plans for a full slate of such course and a virtual community are discussed.

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Ahab's Arithmetic: The Mathematics Of Moby-Dick, Sarah B. Hart Jan 2021

Ahab's Arithmetic: The Mathematics Of Moby-Dick, Sarah B. Hart

Journal of Humanistic Mathematics

In this article we explore mathematical allusions in Herman Melville’s novel Moby-Dick. We argue that both the quantity and sophistication of these allusions are evidence for Melville’s high level of mathematical knowledge and ability. We discuss some of the most compelling mathematical imagery, as well as giving background on the several mathematicians and mathematics books mentioned in the novel. We also include some biographical details supporting the assertion that Melville had an unusually good mathematical education.

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You Can Always Count On Word Problems, Mark Huber, Gizem Karaali Jan 2021

You Can Always Count On Word Problems, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

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Front Matter Jan 2021

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

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Essays On Behavioral Industrial Organization And Welfare., Priyanka Kothari Dr. Jan 2021

Essays On Behavioral Industrial Organization And Welfare., Priyanka Kothari Dr.

Doctoral Theses

Many traits of economic agents are well studied and understood by psychologists that are yet to be captured by economic theory. This thesis, in the field of behavioral economics, is yet another attempt at unifying the different approaches of the two well-established disciplines - we ask what does economics predict of the behavior of economic agents ... once the psychology behind their decisions is accounted for. In a nutshell, this thesis is about the implications of choice-making among available alternatives.We begin with the idea that an economic agent only derives satisfaction from what he consumes without worrying at all (let …

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In Silicoidentification Of Toxins And Their Effect Onhost Pathways: Feature Extraction, Classificationand Pathway Prediction., Rishika Sen Dr. Jan 2021

In Silicoidentification Of Toxins And Their Effect Onhost Pathways: Feature Extraction, Classificationand Pathway Prediction., Rishika Sen Dr.

Doctoral Theses

Identification of toxins, which are either proteins or small molecules, from pathogens is of paramount importance due to their crucial role as first-line invaders infiltrating a host, often leading to infection of the host. These toxins can affect specific proteins, like enzymes that catalyze metabolic pathways, affect metabolites that form the basis of metabolic reactions, and prevent the progression of those pathways, or more generally they may affect the regular functioning of other proteins in signaling pathways in the host. In this regard, the thesis addresses the problem of identification of toxins, and the effect of perturbations by toxins on …

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Mathematical Zendo: A Game Of Patterns And Logic, Philip Deorsey, Corey Pooler, Michael Ferrara Jan 2021

Mathematical Zendo: A Game Of Patterns And Logic, Philip Deorsey, Corey Pooler, Michael Ferrara

Journal of Math Circles

Mathematical Zendo is a logic game that actively engages participants in pattern recognition, problem solving, and critical thinking while providing a fun opportunity to explore all manner of mathematical objects. Based upon the popular game of Zendo, created by Looney Labs, Mathematical Zendo centers on a secret rule, chosen by the leader, that must be guessed by teams of players. In each round of the game, teams provide examples of the mathematical object of interest (e.g. functions, numbers, sets) and receive information about whether their guesses do or do not satisfy the secret rule. In this paper, we introduce Mathematical …

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Total Differentiability And Monogenicity For Functions In Algebras Of Order 4, I. Sabadini, Daniele C. Struppa Jan 2021

Total Differentiability And Monogenicity For Functions In Algebras Of Order 4, I. Sabadini, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we discuss some notions of analyticity in associative algebras with unit. We also recall some basic tool in algebraic analysis and we use them to study the properties of analytic functions in two algebras of dimension four that played a relevant role in some work of the Italian school, but that have never been fully investigated.

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Fully-Kinetic Particle-In-Cell Simulations Of Photoelectron Sheath On Uneven Lunar Surface, Jianxun Zhao, Xinpeng Wei, Xiaoming He, Daoru Frank Han, Xiaoping Du Jan 2021

Fully-Kinetic Particle-In-Cell Simulations Of Photoelectron Sheath On Uneven Lunar Surface, Jianxun Zhao, Xinpeng Wei, Xiaoming He, Daoru Frank Han, Xiaoping Du

Mathematics and Statistics Faculty Research & Creative Works

This paper presents a modeling and simulation study of the photoelectron sheath near uneven lunar surface. A fully kinetic 3-D finite-difference (FD) particle-in-cell (PIC) code is utilized to simulate the plasma interaction with local uneven surface terrain on the lunar surface in 2-D photoelectron sheaths. The code is first validated using a 1-D plasma charging and sheath problem by comparing with a semi-analytic solution. Good agreement is obtained. The 2-D FD-PIC simulations present the distributions of electric potential and charged species densities near the uneven lunar surface. It shows that the surface potential is highly influenced by the exposure to …

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Photoelectron Sheath Near The Lunar Surface: Fully Kinetic Modeling And Uncertainty Quantification Analysis, Jianxun Zhao, Xinpeng Wei, Zhangli Hu, Xiaoming He, Daoru Frank Han, Zhen Hu, Xiaoping Du Jan 2021

Photoelectron Sheath Near The Lunar Surface: Fully Kinetic Modeling And Uncertainty Quantification Analysis, Jianxun Zhao, Xinpeng Wei, Zhangli Hu, Xiaoming He, Daoru Frank Han, Zhen Hu, Xiaoping Du

Mathematics and Statistics Faculty Research & Creative Works

This paper presents a modeling and uncertainty quantification (UQ) study of the photoelectron sheath near the lunar surface. A fully kinetic 3-D finite-difference (FD) particle-in-cell (PIC) code is utilized to simulate the plasma interaction near the lunar surface and the resulting photoelectron sheath. For the uncertainty quantification analysis, this FD-PIC code is treated as a black box providing high-fidelity quantities of interest, which are also used to construct efficient reduced-order models to perform UQ analysis. 1-D configuration is chosen to present the analytic sheath solution as well as to demonstrate the procedure and capability of the UQ analysis.

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Introduction To Statistics In The Psychological Sciences, Linda R. Cote, Rupa Gordon, Chrislyn E. Randell, Judy Schmitt, Helena Marvin Jan 2021

Introduction To Statistics In The Psychological Sciences, Linda R. Cote, Rupa Gordon, Chrislyn E. Randell, Judy Schmitt, Helena Marvin

Open Educational Resources Collection

Introduction to Statistics in the Psychological Sciences provides an accessible introduction to the fundamentals of statistics, and hypothesis testing as need for psychology students. The textbook introduces the fundamentals of statistics, an introduction to hypothesis testing, and t Tests. Related samples, independent samples, analysis of variance, correlations, linear regressions and chi-squares are all covered along with expanded appendices with z, t, F correlation, and a Chi-Square table. The text includes key terms and exercises with answers to odd-numbered exercises.

Psychology students often find statistics courses to be different from their other psychology classes. There are some distinct differences, especially involving …

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Lattice-Ordered Pregroups Are Semi-Distributive, Nikolaos Galatos, Peter Jipsen, Michael Kinyon, Adam Přenosil Jan 2021

Lattice-Ordered Pregroups Are Semi-Distributive, Nikolaos Galatos, Peter Jipsen, Michael Kinyon, Adam Přenosil

Mathematics, Physics, and Computer Science Faculty Articles and Research

We prove that the lattice reduct of every lattice-ordered pregroup is semidistributive. This is a consequence of a certain weak form of the distributive law which holds in lattice-ordered pregroups.

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Huygens' Principle For The Generalized Dirac Operator In Curved Spacetime, Karen Yagdjian Jan 2021

Huygens' Principle For The Generalized Dirac Operator In Curved Spacetime, Karen Yagdjian

School of Mathematical & Statistical Sciences Faculty Publications

In this article we give sufficient conditions for the generalized Dirac operator to obey the incomplete Huygens principle, as well as necessary and sufficient conditions to obey the Huygens principle by the Dirac operator in the curved spacetime of the Friedmann-Lemaître-Robertson-Walker models of cosmology.

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A Gentle Introduction To Inequalities: A Casebook From The Fullerton Mathematical Circle, Adam Glesser, Matt Rathbun, Bogdan Suceavă Jan 2021

A Gentle Introduction To Inequalities: A Casebook From The Fullerton Mathematical Circle, Adam Glesser, Matt Rathbun, Bogdan Suceavă

Journal of Math Circles

Run for nearly a decade, the Fullerton Mathematical Circle at California State University, Fullerton prepares middle and high school students for mathematical research by exposing them to difficult problems whose solutions require only age-appropriate techniques and background. This work highlights one of the avenues of study, namely inequalities. We cover Engel's lemma, the Cauchy--Schwartz inequality, and the AM-GM inequality, as well as providing a wealth of problems where these results can be applied. Full solutions or hints, several written by Math Circle students, are given for all of the problems, as well as some commentary on how or when to …

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Arithmetic Properties Of Septic Partition Functions, Timothy Huber, Mayra Huerta, Nathaniel Mayes Jan 2021

Arithmetic Properties Of Septic Partition Functions, Timothy Huber, Mayra Huerta, Nathaniel Mayes

School of Mathematical & Statistical Sciences Faculty Publications

Congruences and related identities are derived for a set of colored and weighted partition functions whose generating functions generate the graded algebra of integer weight modular forms of level seven. The work determines a general strategy for identifying and proving identities and associated congruences for modular forms on the principal congruence subgroup of level 7. Ramanujan's partition congruence modulo 7 serves as a prototype for the process used to prove new congruences for modular forms of level 7.

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