Physical Sciences and Mathematics Commons^™

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.

Inquiry Based Learning From The Learner’S Point Of View: A Teacher Candidate’S Success Story, Caroline Johnson Caswell, Derek J. Labrie

Journal of Humanistic Mathematics

The goal of this paper is to review current research on Inquiry Based Learning (IBL) and shed some light, from a student's perspective, on the challenges and rewards of this pedagogy. The first part of the article provides an extensive review of the literature on IBL. The second part focuses on one student's experiences in an IBL classroom.

In particular, a graduate secondary mathematics student reflects upon his experiences in a college mathematics class where the instructor implemented an Inquiry Based Learning model. His experience is validated by current research on IBL educational methodology which structures the classroom environment for …

Does Content Matter In An Introduction-To-Proof Course?, Milos Savic

Journal of Humanistic Mathematics

Introduction-to-proof courses are becoming more prevalent in mathematics departments as more recognize the need to support students while they transition from courses focused on computation (such as calculus) to proof-intensive courses (such as real analysis). In such introduction courses, there are some common proving techniques to teach (induction, contradiction, and contraposition to name a few), but the content varies from institution to institution. This note adds to the discussion on content in such courses by analyzing two prior studies, one using a coding scheme designed to illuminate step-by-step justifications in a proof, and the other focused on interviews with course …

On Commensurability And Symmetry, David Pierce

Journal of Humanistic Mathematics

Commensurability and symmetry have diverged from a common Greek origin. We review the history of this divergence. In mathematics, symmetry is now a kind of measure that is different from size, though analogous to it. Size being given by numbers, the concept of numbers and their equality comes into play. For Euclid, two magnitudes were symmetric when they had a common measure; also, numbers were magnitudes, commonly represented as bounded straight lines, for which equality was congruence. When Billingsley translated Euclid into English in the sixteenth century, he used the word "commensurable" for Euclid's symmetric magnitudes; but the word had …

Paul's Dilemma: Is This A Polyhedron?, Bethany Noblitt, Shelly Harkness

Journal of Humanistic Mathematics

Teachers play the believing game when they honor students’ mathematical thinking, even when it means they must suspend their own mathematical thinking momentarily. The study reported here tells the story of what happened in a university mathematics classroom when one student did not think that a particular figure satisfied the definition of a polyhedron and the instructor chose to play the believing game. The result was a very rich discussion, where both students and the authors grappled with their own mathematical understanding. One author served as the instructor of the course and the other author was an observer, taking field …

The Biblical Value Of Pi In Light Of Traditional Judaism, Morris Engelson

Journal of Humanistic Mathematics

There are numerous attempts at a solution to the puzzle as to why the Biblical value of pi, as demonstrated by the measurements of King Solomon's pool, is exactly 3 and not a better approximation. This article shows that virtually all such published solutions are deficient because volume-based factors are ignored. Issues respecting the volume of this pool are explained, and some possible solutions of the puzzle are presented.

Perchance To Dream: Art, Mathematics, And Shakespeare, Randall E. Cone

Journal of Humanistic Mathematics

Visual representation of textual works has often aided in the understanding of sophisticated concepts. In the Digital Age this is particularly true, given the advent of natural language processing, the ubiquity of general programming languages, and the maturation of digital visualization. In this article, we eschew the traditional disciplinary boundaries to view and analyze Shakespeare’s works in various ways. Our point of departure is Hamlet, where we first examine the play as a unity — both graphically and analytically. We then focus on Act III, Scene 1, where we analyze one of the most famous passages in English Literature: …

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

Infinitely Many Stability Switches In A Problem With Sublinear Oscillatory Boundary Conditions, Alfonso Castro, Rosa Pardo

All HMC Faculty Publications and Research

We consider the elliptic equation −u+u = 0 with nonlinear boundary condition ∂u ∂n = λu + g(λ, x, u), where g(λ,x,s) s → 0, as |s|→∞ and g is oscillatory. We provide sufficient conditions on g for the existence of unbounded sequences of stable solutions, unstable solutions, and turning points, even in the absence of resonant solutions.

Existence Of Solutions To A Semilinear Elliptic Boundary Value Problem With Augmented Morse Index Bigger Than Two, Alfonso Castro, Ivan Ventura

All HMC Faculty Publications and Research

Building on the construction of least energy sign-changing solutions to variational semilinear elliptic boundary value problems introduced in [A. Castro, J. Cossio and J.M. Neuberger, Sign changing solutions for a superlinear Dirichlet problem, Rocky Mountain J. Math. 27 (1997), 1041--1053], we prove the existence of a solution with augmented Morse index at least three when a sublevel of the corresponding action functional has nontrivial topology. We provide examples where the set of least energy sign changing solutions is disconnected, hence has nontrivial topology.

Pd-Catalyzed Conversion Of Aryl Iodides To Sulfonyl Fluorides Using So2 Surrogate Dabso And Selectfluor, Nicholas Ball, Ariana L. Tribby, Ismerai Rodríguez, Shamira Shariffudin

Pomona Faculty Publications and Research

A one-pot Pd-catalyzed conversion of aryl iodide to aryl sulfonyl fluorides using DABSO and Selectfluor has been developed generating aryl sulfonyl fluorides in good to excellent yields. The reaction results in the generation of electronically and sterically diverse sulfonyl fluorides. Additionally, sulfonyl fluorides can be converted to aryl sulfonamides and sulfonic esters using Cs₂CO₃ under mild conditions.

Ichme-5: Fifth International Conference On The History Of Mathematics Education, Jenneke Krüger

Journal of Humanistic Mathematics

No abstract provided.

Ladies' Night, Robert Dawson

Journal of Humanistic Mathematics

"Lady" Jane is an expert at her racket. The Joint Statistical Meetings are in Vegas, and she reckons it's payday. But she's taking on the professionals.

The University Of Montana Department Of Mathematics Post-Apocalyptic Working Seminar, Kenan A. Ince

Journal of Humanistic Mathematics

No abstract provided.

16, Dan Mcquillan

Journal of Humanistic Mathematics

This 15 word poem suggests that the reader count the words of the poem. Since every line has half as many words as the previous line, and since the poem urges the reader to keep counting forever, one imagines a total of 16 words.

The Geometry Of Morning, Greg Huteson

Journal of Humanistic Mathematics

No abstract provided.

Book Review: Realizing Reason: A Narrative Of Truth And Knowing By Danielle Macbeth, Emily R. Grosholz

Journal of Humanistic Mathematics

This review examines Danielle Macbeth’s novel and compelling account of the formal languages of mathematics, from Euclid’s geometrical diagrams to the algebraic equations of Descartes and the differential equations of Newton and Leibniz, to the much more abstract language of Galois, Bolzano and Riemann. She argues that the practice of those 19^th century mathematicians, reasoning deductively from abstract concepts like ‘group’ and ‘manifold’, inspired the philosophical logician Gottlob Frege, whose Begriffsschrift captures the procedures of those who reasoned in concepts. However, his way of formalizing mathematical reasoning was obscured by the success of Bertrand Russell and Alfred North Whitehead’s …

Solving Equations: A Make-Work Project For Math Teachers And Students, Egan J. Chernoff

Journal of Humanistic Mathematics

The purpose of this article is to share a particular view that I have towards solving equations in the school mathematics classroom. Specifically, I contend that solving equations in the math classroom is a make-work project for math teachers and students. For example, math teachers take a predetermined value that makes a statement true, and then proceed to make it harder and harder and harder for their students to determine the value that makes the statement true. However, math teachers do so with the explicit purpose of teaching their students how to reveal the solution that they themselves have concealed. …

Does Society Need Imo Medalists?, Man Keung Siu

Journal of Humanistic Mathematics

With a title that sounds provocative but with no intention to embarrass the organizers and participants of the event of IMO (International Mathematical Olympiad) this article should be seen as the sharing of some thoughts on this activity, or more generally on mathematical competitions, by a teacher of mathematics who had once helped in the coaching of the first Hong Kong Team to take part in the 29^th IMO held in Canberra in 1988 and in the coordination work of the 35^th IMO held in Hong Kong in 1994. The author tries to look at the issue in …

Basketball, Algebra, And Probabilities, Gunhan Caglayan

Journal of Humanistic Mathematics

This article is an attempt to illustrate some humanistic aspects of mathematics in context, in particular, sports and scoring (basketball). The intriguing and dynamic illustrations demonstrate innovative and creative ways of integrating basketball snapshots into the pedagogy of a high school or college-level mathematics-in-context course. I have used this activity with several mathematics education students in a mathematics-in-context class as they worked in groups of five. I include here a presentation and a discussion of their explorations and analyses.

The Battle Against Malaria: A Teachable Moment, Randy K. Schwartz

Journal of Humanistic Mathematics

Malaria has been humanity’s worst public health problem throughout recorded history. Mathematical methods are needed to understand which factors are relevant to the disease and to develop counter-measures against it. This article and the accompanying exercises provide examples of those methods for use in lower- or upper-level courses dealing with probability, statistics, or population modeling. These can be used to illustrate such concepts as correlation, causation, conditional probability, and independence. The article explains how the apparent link between sickle cell trait and resistance to malaria was first verified in Uganda using the chi-squared probability distribution. It goes on to explain …

The Hidden Symmetries Of The Multiplication Table, Zoheir Barka

Journal of Humanistic Mathematics

In this article we explore some of the symmetries that hide in the distribution of numbers in the multiplication table of positive integers when viewed through modulo k arithmetic as we vary k.

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.

Moneyball For Creative Writers: A Statistical Strategy For Publishing Your Work, Jon Wesick

Journal of Humanistic Mathematics

Writers face a challenge getting their poems and stories published. Rather than following the traditional strategy I model creative writing submission as a statistical process and explore the use of numerical metrics to maximize publications.

Franz And Georg: Cantor's Mathematics Of The Infinite In The Work Of Kafka, Kevin P. Knudson

Journal of Humanistic Mathematics

The infinite plays a significant role in many of Franz Kafka's stories. In this note we show that a version of the middle-thirds Cantor set construction appears in Kafka's Great Wall of China. His description of the Wall's construction mirrors an iterated system of functions whose limit set is the Cantor set; we present the relevant mathematical details and a close reading of the text of the story to illustrate this metaphor.

The Graduate Student Blues, Marion D. Cohen

Journal of Humanistic Mathematics

This is a memoir about my rather unconventional path to a mathematics Ph.D. There were difficulties, due partly to university politics, partly to my youth and immaturity, and partly to the thesis material itself – it was, in the words of some of my fellow students, “not what’s being done now”. I had written the thesis entirely on my own, without help from my Master’s thesis advisor or any other professor at my school. This is not the usual procedure of course. Nobody in my department could understand the thesis or was willing to vouch for it. There followed three …

Every Minute Of Your Life Has Been Interesting, Susan D'Agostino

Journal of Humanistic Mathematics

In this short paper, we prove that every minute of your life has been interesting. We also provide four exercises intended to solidify understanding of this result, including one exercise related to the torturously boring family road trip you took as a child.

From Pythagoreans And Weierstrassians To True Infinitesimal Calculus, Mikhail Katz, Luie Polev

Journal of Humanistic Mathematics

In teaching infinitesimal calculus we sought to present basic concepts like continuity and convergence by comparing and contrasting various definitions, rather than presenting “the definition” to the students as a monolithic absolute. We hope that our experiences could be useful to other instructors wishing to follow this method of instruction. A poll run at the conclusion of the course indicates that students tend to favor infinitesimal definitions over epsilon-delta ones.

Badiou’S Logics: Math, Metaphor, And (Almost) Everything, Vladimir Tasic

Journal of Humanistic Mathematics

Mathematics plays a central role in the philosophical system of Alain Badiou. The aim of this essay is to situate this appeal to mathematics in the broader context of his work, including its literary and political elements.

Utilizing Social Network Analysis To Study Communities Of Women In Conflict Zones, James R. Gatewood, Candice R. Price

Journal of Humanistic Mathematics

This article proposes to study the plight of women in conflict zones through the lens of social network analysis. We endorse the novel idea of building a social network within troubled regions to assist in understanding the structure of women's communities and identifying key individuals and groups that will help rebuild and empower the lives of women. Our main argument is that we can better understand the complexity of a society with quantitative measures using a network analysis approach. Given the foundation of this paper, one can develop a model that will represent the connections between women in these communities. …