Journal of Humanistic MathematicsCopyright (c) 2014 Claremont Colleges All rights reserved.
http://scholarship.claremont.edu/jhm
Recent documents in Journal of Humanistic Mathematicsen-usWed, 23 Jul 2014 15:28:36 PDT3600Workshop 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-SundströmMortal Taste
http://scholarship.claremont.edu/jhm/vol4/iss1/15
http://scholarship.claremont.edu/jhm/vol4/iss1/15Fri, 31 Jan 2014 10:18:50 PST
In this lighthearted piece of mathematical fiction, the heroine/detective is a mathematician who traps her villain with a mathematician's insight, subtlety, and rigor.
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Robert HaasArnold diffusion
http://scholarship.claremont.edu/jhm/vol4/iss1/14
http://scholarship.claremont.edu/jhm/vol4/iss1/14Fri, 31 Jan 2014 10:18:48 PST
Poem about Arnold diffusion
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Florin DiacuPoeme pour Galois
http://scholarship.claremont.edu/jhm/vol4/iss1/13
http://scholarship.claremont.edu/jhm/vol4/iss1/13Fri, 31 Jan 2014 10:18:47 PSTMara G. LandersArs Mathematica
http://scholarship.claremont.edu/jhm/vol4/iss1/12
http://scholarship.claremont.edu/jhm/vol4/iss1/12Fri, 31 Jan 2014 10:18:46 PSTStan RaatzGame Theory Meets the Humanities and Both Win OR Book Review: Game Theory and the Humanities: Bridging Two Worlds, by Steven J. Brams
http://scholarship.claremont.edu/jhm/vol4/iss1/11
http://scholarship.claremont.edu/jhm/vol4/iss1/11Fri, 31 Jan 2014 10:18:45 PST
This review discusses Brams' wide-ranging book Game Theory and the Humanities and gives some basic examples of the methodology and style, including how the Theory of Moves contributes to understanding such games.
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Karl-Dieter CrismanPromoting Active Studying: The Study Challenge
http://scholarship.claremont.edu/jhm/vol4/iss1/10
http://scholarship.claremont.edu/jhm/vol4/iss1/10Fri, 31 Jan 2014 10:18:43 PST
We explore using a “Study Challenge” to help students become active studiers in mathematics courses. We describe how a Study Challenge works and how we implemented it in calculus and differential equations courses. We discuss qualitative reactions from students who accepted the Study Challenge, which suggest that this might be a useful tool for students’ to add to their examination preparation toolbox. Finally, we offer some suggestions for implementing a Study Challenge within the mathematics classroom.
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Christopher K. Storm et al.PowerPoint Unveils Coordinate Confusion
http://scholarship.claremont.edu/jhm/vol4/iss1/9
http://scholarship.claremont.edu/jhm/vol4/iss1/9Fri, 31 Jan 2014 10:18:42 PST
After six months of working in aerospace, I was tasked to brief, via PowerPoint in teleconference, important customers on the resolution of a seven-month problem that had its roots in coordinate confusion. This article gives my preparation techniques for this PowerPoint presentation and lessons learned from observing other presentations. For people interested in the bare essentials and as an easy guide for students, I’ve included an outlined checklist at the end of this article.
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Jeana MastrangeliWhat is So Negative About Negative Exponents?
http://scholarship.claremont.edu/jhm/vol4/iss1/8
http://scholarship.claremont.edu/jhm/vol4/iss1/8Fri, 31 Jan 2014 10:18:40 PST
While teaching college-level mathematics (from College Algebra to Calculus to Abstract Algebra), I have observed that students are often uncomfortable using negative exponents in calculations. I believe the fault partially lies in the manner in which negative exponents are taught in Algebra 1 or Algebra 2 courses, especially in rigid instructions always to write answers using only positive exponents. After reviewing a sample of algebra texts used in the United States over the last two centuries, it appears that while attitudes toward negative exponents have varied from author to author over time, the current trend is to declare explicitly that an expression is not simplified if it contains negative exponents. I believe that this negative attitude toward negative exponents is at least somewhat to blame for students of Calculus and higher mathematics being less able to solve problems that require conversion between positive and negative exponents, as their algebraic instruction has only taught them to convert negative exponents to positive.
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Geoffrey D. DietzBenjamin Banneker's Original Handwritten Document: Observations and Study of the Cicada
http://scholarship.claremont.edu/jhm/vol4/iss1/7
http://scholarship.claremont.edu/jhm/vol4/iss1/7Fri, 31 Jan 2014 10:18:39 PST
Benjamin Banneker, farmer, mathematician, astronomer, and scientist, is known for his mathematical puzzles, ephemeris calculations, almanacs, his wooden clock, land surveying work, and famous letter on human rights. However, as a naturalist, his scientific and systematic observations of the cicadas are less known. In this paper we publicize Banneker’s naturalistic study of the seventeen-year periodic cycle of the cicada and make available the original handwritten document of his observations. We also introduce the audience of this journal to an intriguing natural problem involving prime numbers.
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Janet E. Barber et al.Improving Equity and Education: Why and How
http://scholarship.claremont.edu/jhm/vol4/iss1/6
http://scholarship.claremont.edu/jhm/vol4/iss1/6Fri, 31 Jan 2014 10:18:37 PST
Progress is possible. When I graduated from college, only $5\%$ of the new U.S. doctorates in mathematics went to women; now it is about $30\%$. There is of course room (and need) for more progress. This paper begins with an account of my research about women and black mathematicians. The latter group claimed that racial equality can be achieved only when better elementary school mathematics education is available to all children in this country. That motivated me to lead a seven-year, grant-supported program to work with elementary school teachers and children in nine New Jersey districts, including Newark, Paterson, and Passaic. I share some disturbing, startling stories about this time as well as some stories of remarkable success. Recent admonitions to ``raise standards for all'' motivate a personal story about my mentally retarded brother; he and I needed and were given very different types of education. I then offer nine reasons for promoting mathematics education for all, three things good teachers need, and a few more suggestions for improving equity and education. The paper includes photographs and references to important books.
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Patricia Clark KenschaftAn Introduction to Fourier Analysis with Applications to Music
http://scholarship.claremont.edu/jhm/vol4/iss1/5
http://scholarship.claremont.edu/jhm/vol4/iss1/5Fri, 31 Jan 2014 10:18:36 PST
In our modern world, we are often faced with problems in which a traditionally analog signal is discretized to enable computer analysis. A fundamental tool used by mathematicians, engineers, and scientists in this context is the discrete Fourier transform (DFT), which allows us to analyze individual frequency components of digital signals. In this paper we develop the discrete Fourier transform from basic calculus, providing the reader with the setup to understand how the DFT can be used to analyze a musical signal for chord structure. By investigating the DFT alongside an application in music processing, we gain an appreciation for the mathematics utilized in digital signal processing.
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Nathan Lenssen et al.Liberal Arts Inspired Mathematics: A Report OR How to bring cultural and humanistic aspects of mathematics to the classroom as effective teaching and learning tools
http://scholarship.claremont.edu/jhm/vol4/iss1/4
http://scholarship.claremont.edu/jhm/vol4/iss1/4Fri, 31 Jan 2014 10:18:35 PST
This is the report of a project on ways of teaching university-level mathematics in a humanistic way. The main part of the project recounted here involved a journey to the United States during the fall term of 2012 to visit several liberal arts colleges in order to study and discuss mathematics teaching. Several themes that came up during my conversations at these colleges are discussed in the text: the invisibility of mathematics in everyday life, the role of calculus in American mathematics curricula, the "is algebra necessary?'' discussion, teaching mathematics as a language, the transfer problem in learning, and the relationship between humanistic mathematics and mathematics as taught in liberal arts contexts.
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Anders K H BengtssonGalileo and Aristotle's Wheel
http://scholarship.claremont.edu/jhm/vol4/iss1/3
http://scholarship.claremont.edu/jhm/vol4/iss1/3Fri, 31 Jan 2014 10:18:34 PST
At the beginning of his last major work, Galileo tackles an old paradox, Aristotle's Wheel, in order to produce a model of the continuum that explains (at least to him) how line segments of different length could be put into a one-to-one correspondence. His argument seems like a playful digression. However, it is precisely this type of a one-to-one correspondence that he needs to support his work on free fall. In this article, we investigate how Galileo's model for the wheel paradox informs his work on free fall. We also examine some of the reasons his results on free fall---results that were grounded in his notion of the continuum---were not readily accepted in his time.
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Olympia NicodemiFront Matter
http://scholarship.claremont.edu/jhm/vol4/iss1/2
http://scholarship.claremont.edu/jhm/vol4/iss1/2Fri, 31 Jan 2014 10:18:32 PSTTurn! Turn! Turn!
http://scholarship.claremont.edu/jhm/vol4/iss1/1
http://scholarship.claremont.edu/jhm/vol4/iss1/1Fri, 31 Jan 2014 10:18:30 PSTMark Huber et al.Computer Maths: Curiosity, Art, Story! The First International Conference on Creative Mathematical Sciences Communication
http://scholarship.claremont.edu/jhm/vol3/iss2/16
http://scholarship.claremont.edu/jhm/vol3/iss2/16Wed, 31 Jul 2013 12:01:42 PDT
This is an invitation to the First International Conference on Creative Mathematical Sciences Communication, Computer Maths: Curiosity, Art, Story!.
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Frances RosamondGrandma Got STEM turns 100 posts old!
http://scholarship.claremont.edu/jhm/vol3/iss2/15
http://scholarship.claremont.edu/jhm/vol3/iss2/15Wed, 31 Jul 2013 12:01:41 PDT
The Grandma Got STEM blog celebrates the contributions of senior women to Science, Technology, Engineering and Mathematics. This announcement discusses the origins of the blog and describes the submission process for the ongoing project.
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Rachel LevyThe Taste of Mathematics: Caroline Herschel at 31
http://scholarship.claremont.edu/jhm/vol3/iss2/14
http://scholarship.claremont.edu/jhm/vol3/iss2/14Wed, 31 Jul 2013 12:01:39 PDT
The poem brings to life how Caroline Herschel (1750-1848) learned mathematics from her brother William as they began to work as professional astronomers.
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Laura LongEquation
http://scholarship.claremont.edu/jhm/vol3/iss2/13
http://scholarship.claremont.edu/jhm/vol3/iss2/13Wed, 31 Jul 2013 12:01:38 PDTNilanjan De