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19,904 full-text articles. Page 10 of 624.

How I First Heard About Calculus, Bradley J. Lucier 2021 Purdue University (emeritus)

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.


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

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 ...


Teaching From The Unknown, Jon Jacobsen 2021 Harvey Mudd College

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.


Using Mathematical Equations To Communicate And Think About Karma, Kien H. Lim, Christopher Yakes 2021 University of Texas at El Paso

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 ...


Real-World Modelling To Increase Mathematical Creativity, Robert Weinhandl, Zsolt Lavicza 2021 Johannes Kepler University, Linz

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 ...


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

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 ...


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

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.


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

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 ...


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

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 ...


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

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.


In How Many Days Will He Meet His Wife?, Dipak Jadhav 2021 Govt. Boys Higher Secondary School, Anjad Distt. Barwani (M. P.) India

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 ...


Raise The (Proportion) Bar!, Michael Waters 2021 Northern Kentucky University

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.


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

“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 question 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 ...


Humanistic Stem: From Concept To Course, Debra T. Bourdeau, Beverly L. Wood 2021 WW/Humanities & Communication

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.


Ahab's Arithmetic: The Mathematics Of Moby-Dick, Sarah B. Hart 2021 Birkbeck College, University of London

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.


You Can Always Count On Word Problems, Mark Huber, Gizem Karaali 2021 Claremont McKenna College

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

Journal of Humanistic Mathematics

No abstract provided.


Front Matter, 2021 Claremont Colleges

Front Matter

Journal of Humanistic Mathematics

No abstract provided.


Mathematical Zendo: A Game Of Patterns And Logic, Philip DeOrsey, Corey Pooler, Michael Ferrara 2021 Westfield State University

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 ...


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

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.


Maximum Number Of Almost Similar Triangles In The Plane, József Balogh, Felix Christian Clemen, Bernard Lidicky 2021 University of Illinois at Urbana-Champaign

Maximum Number Of Almost Similar Triangles In The Plane, József Balogh, Felix Christian Clemen, Bernard Lidicky

Mathematics Publications

A triangle T′ is ε-similar to another triangle T if their angles pairwise differ by at most ε. Given a triangle T, ε>0 and n∈N, Bárány and Füredi asked to determine the maximum number of triangles h(n,T,ε) being ε-similar to T in a planar point set of size n. We show that for almost all triangles T there exists ε=ε(T)>0 such that h(n,T,ε)=n3/24(1+o(1)). Exploring connections to hypergraph Turán problems, we use flag algebras and stability techniques for the proof.


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