Mathematics Commons^™

They Say She Was Good -- For A Woman: Poetry And Musings, Joanne Growney

Journal of Humanistic Mathematics

These pages contain ideas and verses that consider the roles of women in mathematics. Details of the life of Amalie “Emmy” Noether inspired a poem and the poem, in turn, led to the poet’s growth and awareness of her self and her voice.

A Mathematician Reads Plutarch: Plato's Criticism Of Geometers Of His Time, John B. Little

Journal of Humanistic Mathematics

This essay describes the author's recent encounter with two well-known passages in Plutarch that touch on a crucial episode in the history of the Greek mathematics of the fourth century BCE involving various approaches to the problem of the duplication of the cube. One theme will be the way key sources for understanding the history of our subject sometimes come from texts that have much wider cultural contexts and resonances. Sensitivity to the history, to the mathematics, and to the language is necessary to tease out the meaning of such texts. However, in the past, historians of mathematics often interpreted …

Mathematics In The Mind's Eye: Michael Schultheis Paints Poetic And Conceptual Geometries, Patricia Grieve Watkinson

Journal of Humanistic Mathematics

Michael Schultheis is an established artist and a formally-educated mathematician. In his practice the two disciplines are inextricably linked. His large-scale lyrical paintings at first glance seem to focus on the effects of light and atmospheres, representing cloudscapes or waterscapes in resonant color. Yet moving through these mists are decidedly mathematical references --- drawn geometric shapes and hand-written equations. These are employed by Schultheis to represent the physical world or to express feelings (or both). For example, he may examine the structure of a pine cone or reflect on human relationships or do both at the same time. The resulting …

On French Pudding And A German Mathematician, Amy Shoemaker

Journal of Humanistic Mathematics

At the turn of the 19^th century, mathematics developed the rigor that is now considered essential to the field. Mathematicians began going back and proving theorems and statements that had been taken to be true on face value, ensuring the underpinnings of mathematics were solid. This era of mathematics was characterized not only by setting foundations, but also by pushing the boundaries of new ideas. In 1830, Bolzano found an example of a function that was nowhere differentiable, despite being continuous. Thirty years later, Cellerier and Riemann each discovered another example of such a pathological function. The first everywhere …

Multifaceted Mathematicians, Juan M. Sepulcre

Journal of Humanistic Mathematics

This report attempts to provide an overview of some of the mathematicians who have combined their mathematical knowledge with other academic and non-academic specialities. The various examples given, many of them included in the well-known MacTutor History of Mathematics archive, corroborate the fact that although the idea of the typical polymath has receded with the passage of time, until the end of the Renaissance, most well-known mathematicians were also well-versed in a number of different sciences such as philosophy, astronomy, and physics. We also highlight other, less common combinations of knowledge, in famous mathematicians who were experts in other disciplines …

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 …

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.

Rethinking The Numerate Citizen: Quantitative Literacy And Public Issues – Discussion, Kira H. Hamman

Numeracy

I dispute Erickson's claim in Numeracy 9(2), Article 4 (2016), that quantitative literacy is neither necessary nor appropriate for informed citizenship, and explore his suggestion that Hardwig's notion of epistemic dependence is more suited to the task.

Quantitative Literacy In The Affective Domain: Computational Geology Students’ Reactions To Devlin’S The Math Instinct, Victor J. Ricchezza, H. L. Vacher

Numeracy

Building on suggestions from alumni from a recent interview project, students in Computational Geology at the University of South Florida were tasked with reading a popular non-fiction book on mathematics and writing about the book and their feelings about math. The book, The Math Instinct by Keith Devlin, was chosen because we believed it would give the students something interesting to write about and not because we had any expectations in particular about what it might reveal about or do for their math anxiety. The nature of the responses received from the students led to the performance of a post-hoc …

Figures And First Years: An Analysis Of Calculus Students' Use Of Figures In Technical Reports, Nathan J. Antonacci, Michael Rogers, Thomas J. Pfaff, Jason G. Hamilton

Numeracy

This three-year study focused on first-year Calculus I students and their abilities to incorporate figures in technical reports. In each year, these calculus students wrote a technical report as part of the Polar Bear Module, an educational unit developed for use in partner courses in biology, computer science, mathematics, and physics as part of the Multidisciplinary Sustainability Education (MSE) project at Ithaca College. In the first year of the project, students received basic technical report guidelines. In year two, the report guidelines changed to include explicit language on how to incorporate figures. In year three, a grading rubric was added …

Conflict-Free Vertex Coloring Of Planar Graphs, Shawn Seymour

Scholarly Horizons: University of Minnesota, Morris Undergraduate Journal

The conflict-free coloring problem is a variation of the vertex coloring problem, a classical NP-hard optimization problem. The conflict-free coloring problem aims to color a possibly proper subset of vertices such that there is a unique color within the closed neighborhood (a vertex and its neighbors) of every vertex. This paper presents recent findings and heuristics to solve the conflict-free coloring problem on both general graphs and planar graphs.

Artin L-Functions Of Small Conductor, John W. Jones, David P. Roberts

Mathematics Publications

We study the problem of finding the Artin L-functions with the smallest conductor for a given Galois type. We adapt standard analytic techniques to our novel situation of fixed Galois type and obtain much improved lower bounds on the smallest conductor. For small Galois types we use complete tables of number fields to determine the actual smallest conductor.

Dynamically Distinguishing Polynomials, Andrew Bridy, Derek Garton

Mathematics and Statistics Faculty Publications and Presentations

A polynomial with integer coefficients yields a family of dynamical systems indexed by primes as follows: For any prime p, reduce its coefficients mod p and consider its action on the field FpFp. We say a subset of Z[x]Z[x] is dynamically distinguishable mod p if the associated mod pdynamical systems are pairwise non-isomorphic. For any k,M∈Z>1k,M∈Z>1, we prove that there are infinitely many sets of integers MM of size M such that {xk+m∣m∈M}{xk+m∣m∈M} is dynamically distinguishable mod p for most p (in the sense of natural density). Our proof uses the Galois theory of dynatomic polynomials largely developed …

Using Well-Known Probability Density Functions To Evaluate Certain Integrals In Calculus, Stacy Pitman, Andreas Lazari

Georgia Journal of Science

A major source of anxiety for engineering and science majors who must take calculus is the topic of integration. The techniques of integration necessary for solving practical problems in the sciences are lengthy and complex. In this paper, we are introducing a method that minimizes the algebra as well as the number of computations for certain types of integrals. It is important to note that we are not suggesting that the conventional methods for teaching techniques of integration be replaced with the innovation we are proposing. Rather, the new approach we suggest is to be presented only after the traditional …

Modeling The Influence Of El Niño On Parasite Transmission In Sand Crab Populations And Seabird Abundance Along The Californian Coast, Aboubacar Dio Seck

Theses and Dissertations

Pacific mole crabs (Emerita analoga) are one of the most important and abundant

invertebrates in sandy beach environments. Consequently, they are a common food source

for seabirds and sea otters. Since the mole crab serves as the primary intermediate host for

acanthocephalan parasites, they have been linked to a number of mortality events. It is

currently estimated that 13-16% of deaths in the threatened California sea otter population

have been caused by infection. In addition, unusually high loads of acanthocephalan

parasites have been linked to episodic deaths of thousands of surf scoters. Studies suggest

that acanthocephalan development and transmission may …