Journal of Humanistic MathematicsCopyright (c) 2014 Claremont Colleges All rights reserved.
http://scholarship.claremont.edu/jhm
Recent documents in Journal of Humanistic Mathematicsen-usTue, 26 Aug 2014 03:12:59 PDT3600A Job Ad OR Mathematics in Context at Pitzer College
http://scholarship.claremont.edu/jhm/vol4/iss2/19
http://scholarship.claremont.edu/jhm/vol4/iss2/19Sun, 27 Jul 2014 19:57:45 PDTJudith V. GrabinerJHM Contents Word Puzzle
http://scholarship.claremont.edu/jhm/vol4/iss2/18
http://scholarship.claremont.edu/jhm/vol4/iss2/18Sun, 27 Jul 2014 19:57:44 PDT
This is a word-search puzzle based on the contents page of the previous (Volume 4 Issue 1-January 2014) issue of the Journal of Humanistic Mathematics.
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Robert HaasThe Physicist's Basement
http://scholarship.claremont.edu/jhm/vol4/iss2/17
http://scholarship.claremont.edu/jhm/vol4/iss2/17Sun, 27 Jul 2014 19:57:43 PDTNora CulikThe Math of Achilles
http://scholarship.claremont.edu/jhm/vol4/iss2/16
http://scholarship.claremont.edu/jhm/vol4/iss2/16Sun, 27 Jul 2014 19:57:42 PDTGeoffrey A. LandisJeffery's Equation
http://scholarship.claremont.edu/jhm/vol4/iss2/15
http://scholarship.claremont.edu/jhm/vol4/iss2/15Sun, 27 Jul 2014 19:57:41 PDTSandra J. SteinComputational Compulsions
http://scholarship.claremont.edu/jhm/vol4/iss2/14
http://scholarship.claremont.edu/jhm/vol4/iss2/14Sun, 27 Jul 2014 19:57:41 PDTMartin CohenThe Discipline of History and the “Modern Consensus in the Historiography of Mathematics”
http://scholarship.claremont.edu/jhm/vol4/iss2/13
http://scholarship.claremont.edu/jhm/vol4/iss2/13Sun, 27 Jul 2014 19:57:39 PDT
Teachers and students of mathematics often view history of mathematics as just mathematics as they know it, but in another form. This view is based on a misunderstanding of the nature of history of mathematics and the kind of knowledge it attempts to acquire. Unfortunately, it can also lead to a deep sense of disappointment with the history of mathematics itself, and, ultimately, a misunderstanding of the historical nature of mathematics. This kind of misunderstanding and the disappointment following from it--both raised to the level of resentment--run through the paper "A Critique of the Modern Consensus in the Historiography of Mathematics." My review of that paper, sent to me blind, became a response to it. In particular, this essay attempts to clarify the nature of the historical discipline and to show that author of the Critique ends up, in effect, wanting and not wanting history at the same time.
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Michael N. FriedA Critique of the Modern Consensus in the Historiography of Mathematics
http://scholarship.claremont.edu/jhm/vol4/iss2/12
http://scholarship.claremont.edu/jhm/vol4/iss2/12Sun, 27 Jul 2014 19:57:38 PDT
The history of mathematics is nowadays practiced primarily by professional historians rather than mathematicians, as was the norm a few decades ago. There is a strong consensus among these historians that the old-fashioned style of history is “obsolete,” and that “the gains in historical understanding are incomparably greater” in the more “historically sensitive” works of today. I maintain that this self-congratulatory attitude is ill-founded, and that the alleged superiority of modern historiographical standards ultimately rests on a dubious redefinition of the purpose of history rather than intrinsic merit.
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Viktor BlåsjöNine Mathematical Ways of Watching a Baseball Game
http://scholarship.claremont.edu/jhm/vol4/iss2/11
http://scholarship.claremont.edu/jhm/vol4/iss2/11Sun, 27 Jul 2014 19:57:37 PDT
Whatever its other flaws or merits as a game, baseball gives us plenty of time to think. (How else to spend the 2 hours, 50 minutes when nothing in particular is happening?) In the long gaps between pitches, my own thoughts veer towards mathematics. Are statistics really changing the game? Can any sense emerge from baseball's symmetries and odd patterns? Is it now a sport of science, or as ever one of superstition? And the aesthetic question that arises from all of this:\ In a human pursuit like baseball, can mathematical perspectives ever help us to create meaning?
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Ben OrlinHow Do I Love Thee? Let Me Count the Ways for Syllabic Variation in Certain Poetic Forms
http://scholarship.claremont.edu/jhm/vol4/iss2/10
http://scholarship.claremont.edu/jhm/vol4/iss2/10Sun, 27 Jul 2014 19:57:36 PDT
The Dekaaz poetic form, similar to haiku with its constrained syllable counts per line, invites a connection between poetry and mathematics. Determining the number of possible Dekaaz variations leads to some interesting counting observations. We discuss two different ways to count the number of possible Dekaaz variations, one using a binary framework and the other approaching the count as an occupancy problem. The counting methods described are generalized to also count variations of other poetic forms with syllable counts specified, including haiku. We include Dekaaz examples and suggest a method that can be used to randomly generate a Dekaaz variation.
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Mike PinterFields in Math and Farming
http://scholarship.claremont.edu/jhm/vol4/iss2/9
http://scholarship.claremont.edu/jhm/vol4/iss2/9Sun, 27 Jul 2014 19:57:35 PDT
A young woman’s search for a a contemplative, insightful experience leads her from farming to mathematics.
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Susan D'AgostinoBeing Reasonable: Using Brainteasers to Develop Reasoning Ability in Humanistic Mathematics Courses
http://scholarship.claremont.edu/jhm/vol4/iss2/8
http://scholarship.claremont.edu/jhm/vol4/iss2/8Sun, 27 Jul 2014 19:57:34 PDT
Developing reasoning ability is often cited as one of the principal justifications of a mathematics requirement for liberal arts undergraduates. Humanistic math courses have become recognized as a paradigm for liberal arts mathematics, but such courses may not provide the opportunity to develop reasoning ability. The author describes his procedure for using brainteasers to promote reasoning in a humanistic math course for liberal arts undergraduates.
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Gary StogsdillJoining ``the mathematician's delirium to the poet's logic'': Mathematical Literature and Literary Mathematics
http://scholarship.claremont.edu/jhm/vol4/iss2/7
http://scholarship.claremont.edu/jhm/vol4/iss2/7Sun, 27 Jul 2014 19:57:33 PDT
This paper describes our team-taught interdisciplinary mathematics and literature course, Mathematical Literature and Literary Mathematics, which invites students to consider Raymond Queneau's challenge: "Why shouldn't one demand a certain effort on the reader's part? Everything is always explained to him. He must eventually tire of being treated with such contempt.'' We study works by Berge, Borges, Calvino, Perec, Queneau, Robbe-Grillet and Stoppard, among others. From a literary critical perspective, the course highlights the play of language rather than the primacy of meaning. We choose texts where mathematical concepts are subjects or structuring elements of the literature, and ideally both. Overall, the course has been enjoyable and productive for both students and its professors so far: the students learn; we learn, both from each other and from the students; and a good time is had by all.
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Rita Capezzi et al.A Subjective Comparison Between a Historical and a Contemporary Textbook on Geometry
http://scholarship.claremont.edu/jhm/vol4/iss2/6
http://scholarship.claremont.edu/jhm/vol4/iss2/6Sun, 27 Jul 2014 19:57:32 PDT
In order to investigate how a 19^{th} century mathematical textbook (in contrast to a contemporary one) would be experienced by a novice reader, we embarked on the following project: In the summer of 2013, a student with no previous training in college-level mathematics (the first author) set out to learn projective geometry from Pasch's 1882 textbook Lectures on Modern Geometry. Afterwards, he studied the same material from Coxeter's 1994 popular undergraduate textbook Projective Geometry. We report here some of his experiences and impressions contextualizing them along the way.
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Douglas Roland Campbell et al.Religion and Language as Cultural Carriers and Barriers in Mathematics Education--Revisited
http://scholarship.claremont.edu/jhm/vol4/iss2/5
http://scholarship.claremont.edu/jhm/vol4/iss2/5Sun, 27 Jul 2014 19:57:31 PDT
Here we revisit a paper which examined two theses regarding the roles of religion and language of instruction in mathematics education. The first thesis states that if values of mathematics education are incompatible with the value system of the mother culture, then mathematics will be ``appended'' to the culture as a ``technology'' rather than assimilated as a ``mode of thinking''. The second thesis states that as soon as mathematics is applied in problems and situations, the language of instruction and learning becomes a cultural carrier in terms of behaviors, social relations, habits, and values. In the original paper, the first thesis was examined in the context of Islamic-Arab culture, while the second thesis was developed in the context of Lebanon. Here the original paper is first presented in its complete form, with some minor modifications. Next I offer some reflections on the relevance of these two theses today.
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Murad E. JurdakLoxodromic Spirals in M. C. Escher's Sphere Surface
http://scholarship.claremont.edu/jhm/vol4/iss2/4
http://scholarship.claremont.edu/jhm/vol4/iss2/4Sun, 27 Jul 2014 19:57:30 PDT
Loxodromic spirals are the analogues in spherical geometry of logarithmic spirals on the plane. M.C. Escher's 1958 woodcut Sphere Surface is an image of black and white fish arranged along eight spiral paths on the surface of a sphere. By connecting the plane and spherical models of the complex numbers, we show that Sphere Surface is the conformal image on the sphere of a tessellation of fish on the plane, and that the spirals running through the fish are indeed loxodromic spirals to a high degree of accuracy.
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James Marcotte et al.Some Effects of the Human Genome Project on the Erdős Collaboration Graph
http://scholarship.claremont.edu/jhm/vol4/iss2/3
http://scholarship.claremont.edu/jhm/vol4/iss2/3Sun, 27 Jul 2014 19:57:29 PDT
The Human Genome Project introduced large-scale collaborations involving dozens to hundreds of scientists into biology. It also created a pressing need to solve discrete mathematics problems involving tens of thousands of elements. In this paper, we use minimal path lengths in the Erdős Collaboration Graph between prominent individual researchers as a measure of the distance between disciplines, and we show that the Human Genome Project brought laboratory biology as a whole closer to mathematics. We also define a novel graph reduction method and a metric that emphasizes the robustness of collaborative connections between researchers; these can facilitate the analysis of both within- and between-community connectivity in collaboration graphs.
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Chris FieldsMathematical Perspectives
http://scholarship.claremont.edu/jhm/vol4/iss2/2
http://scholarship.claremont.edu/jhm/vol4/iss2/2Sun, 27 Jul 2014 19:57:27 PDTMark Huber et al.Front Matter
http://scholarship.claremont.edu/jhm/vol4/iss2/1
http://scholarship.claremont.edu/jhm/vol4/iss2/1Sun, 27 Jul 2014 19:57:26 PDTWorkshop on Beauty and Explanation in Mathematics
http://scholarship.claremont.edu/jhm/vol4/iss1/16
http://scholarship.claremont.edu/jhm/vol4/iss1/16Fri, 31 Jan 2014 10:18:51 PST
On March 10-12, 2014, Umeå University in Sweden will host a workshop on mathematical beauty and explanation. The goal of this workshop is explore the question of whether beauty and explanation are related in mathematics. The workshop will bring together top researchers from fields such as mathematics, philosophy, and mathematics education for which this topic is relevant. Many of these researchers have till now worked within their own discipline boundaries on related topics, but have not met or worked with each other. We hope the workshop not only develops the programs of these established researchers, but also sparks interest in young researchers and encourages others to contribute to this specific question, or other related questions about the nature of mathematics. Registration is currently open, and will remain so until the capacity, of around 30 participants, is filled.
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Manya Raman-Sundström