Journal of Humanistic MathematicsCopyright (c) 2015 Claremont Colleges All rights reserved.
http://scholarship.claremont.edu/jhm
Recent documents in Journal of Humanistic Mathematicsen-usTue, 21 Apr 2015 22:50:51 PDT3600Special Issue Call for Papers: The Nature and Experience of Mathematical Beauty
http://scholarship.claremont.edu/jhm/vol5/iss1/22
http://scholarship.claremont.edu/jhm/vol5/iss1/22Fri, 30 Jan 2015 21:40:34 PSTManya Raman-SundströmThe Cantor Trilogy
http://scholarship.claremont.edu/jhm/vol5/iss1/21
http://scholarship.claremont.edu/jhm/vol5/iss1/21Fri, 30 Jan 2015 21:40:33 PST
The Cantor trilogy is a mathematical dystopia featuring JHM as an important part of that world... at least to humans.
]]>
Harun ŠiljakMy Finite Field
http://scholarship.claremont.edu/jhm/vol5/iss1/20
http://scholarship.claremont.edu/jhm/vol5/iss1/20Fri, 30 Jan 2015 21:40:32 PST
A love poem written in the language of mathematics.
]]>
Matthew SchroederPrisoner's Dilemma
http://scholarship.claremont.edu/jhm/vol5/iss1/19
http://scholarship.claremont.edu/jhm/vol5/iss1/19Fri, 30 Jan 2015 21:40:31 PSTRaymond N. GreenwellCompleteness
http://scholarship.claremont.edu/jhm/vol5/iss1/18
http://scholarship.claremont.edu/jhm/vol5/iss1/18Fri, 30 Jan 2015 21:40:30 PSTLaura Eleanor HollowayIntermediate Values
http://scholarship.claremont.edu/jhm/vol5/iss1/17
http://scholarship.claremont.edu/jhm/vol5/iss1/17Fri, 30 Jan 2015 21:40:29 PSTPhilip HolmesBook Review: Love and Math: The Heart of Hidden Reality by Edward Frenkel
http://scholarship.claremont.edu/jhm/vol5/iss1/16
http://scholarship.claremont.edu/jhm/vol5/iss1/16Fri, 30 Jan 2015 21:40:28 PST
This review traces Edward Frenkel’s attempt to convey the excitement of mathematical research to a popular audience. In his expositions and explanations of his own research program, he shows how processes of mathematical discovery depend on the juxtaposition of various iconic and symbolic modes of representation as disparate fields of research are brought together in the service of problem solving. And he shows how crucial the encouragement of various older mathematicians was to his own development, as they guided his choice of problems, and served as inspiration.
]]>
Emily R. GrosholzTeaching Mathematics with Mathematical Software
http://scholarship.claremont.edu/jhm/vol5/iss1/15
http://scholarship.claremont.edu/jhm/vol5/iss1/15Fri, 30 Jan 2015 21:40:26 PST
The history of contemporary mathematical education is the history of a struggle against computers and IT. As a result specially selected simplified math problems are used while teaching. Just as it was a hundred years ago, contemporary students are forced to memorize a lot of rules and theorems in order to solve math problems. But we know that today they can get the same results using simple computer calculations. Information technologies can (and in this paper we argue that they should) change the traditional methods of solving mathematical problems. Here we share some simple problems that helped engineering students learn the basics of mathematics and computer science and even enjoy the learning process. In particular we point out that the ability to visualize solutions is very important in most contexts, and modern mathematical software packages offer users convenient and simple tools of visualization and even animation. Including them on our pedagogical team, we can significantly increase our students' understanding of the basic concepts and theorems of mathematics.
]]>
Valery F. Ochkov et al.Abscissas and Ordinates
http://scholarship.claremont.edu/jhm/vol5/iss1/14
http://scholarship.claremont.edu/jhm/vol5/iss1/14Fri, 30 Jan 2015 21:40:25 PST
In the manner of Apollonius of Perga, but hardly any modern book, we investigate conic sections as such. We thus discover why Apollonius calls a conic section a parabola, an hyperbola, or an ellipse; and we discover the meanings of the terms abscissa and ordinate. In an education that is liberating and not simply indoctrinating, the student of mathematics will learn these things.
]]>
David PierceOn Mathematics and Culture: Insights from an International School
http://scholarship.claremont.edu/jhm/vol5/iss1/13
http://scholarship.claremont.edu/jhm/vol5/iss1/13Fri, 30 Jan 2015 21:40:23 PST
We explore the factors that influence the relationship between mathematics and culture in the international school context. First, we share some thoughts about international schools in general and the international mathematics curriculum implemented at the middle grades level at our school in particular. Second, we present some interesting snapshots from our culturally-diverse mathematics classrooms.
]]>
M. Sencer Corlu et al.The Disciplinarity of Mathematical Practice
http://scholarship.claremont.edu/jhm/vol5/iss1/12
http://scholarship.claremont.edu/jhm/vol5/iss1/12Fri, 30 Jan 2015 21:40:22 PST
Despite an extensive literature on the nature and origins of mathematical truth, few if any studies exist of the everyday practices through which the adequacy of mathematical argumentation is cultivated and assessed. The work of a novice prover afforded insight into these practices and, in particular, into the disciplined character of discovering and proving mathematical theorems.
]]>
Eric LivingstonHow Can Mathematics Students Learn to Play?
http://scholarship.claremont.edu/jhm/vol5/iss1/11
http://scholarship.claremont.edu/jhm/vol5/iss1/11Fri, 30 Jan 2015 21:40:21 PST
When we teach mathematics, we strive to teach students to think like mathematicians. In this paper we discuss one particular mathematical habit of mind that students do not naturally display. More specifically our study of voting patterns in data collected from classroom voting questions indicates that the undergraduate students who were in the classes using these questions did not understand the significance of counterexamples to statements, or lacked the ability to construct them, or both. Searching for counterexamples to disprove statements is a natural habit of mind for professional mathematicians. In this paper we give examples, and make some recommendations. We believe that if our students get used to routinely seeking out counterexamples, as they play with various mathematical ideas, they may also end up enjoying their mathematical experiences more.
]]>
Christopher K. Storm et al.The Case of the Missing Speedometer: The First Day of Calculus
http://scholarship.claremont.edu/jhm/vol5/iss1/10
http://scholarship.claremont.edu/jhm/vol5/iss1/10Fri, 30 Jan 2015 21:40:20 PST
This article describes the way I've been teaching the first day of Calc I, my single-variable Calculus class. By the end of the hour students have (A) dictated difference quotients for me to write on the board, (B) dictated one example of the limit of difference-quotients definition of derivative of a function at a point, and (C) calculated a few derivatives. The more rigorous definitions of function, of operations on functions, and of limits can wait until later. This approach has been very successful, and students have said they "get it this time around."
]]>
Marion D. CohenThe Schilling Kinematic Models at the Smithsonian
http://scholarship.claremont.edu/jhm/vol5/iss1/9
http://scholarship.claremont.edu/jhm/vol5/iss1/9Fri, 30 Jan 2015 21:40:18 PST
The kinematic models manufactured by the German firm of Martin Schilling were used in the late 19^{th} and early 20^{th} centuries to depict mathematical curves. The Smithsonian Institution owns twelve Schilling models. As a volunteer researcher in mathematics at the Smithsonian National Museum of American History, the author has chosen a few of her favorite models as an introduction to this interesting set of kinematic models.
]]>
Amy Shell-Gellasch DrThe Symbolic and Mathematical Influence of Diophantus's Arithmetica
http://scholarship.claremont.edu/jhm/vol5/iss1/8
http://scholarship.claremont.edu/jhm/vol5/iss1/8Fri, 30 Jan 2015 21:40:17 PST
Though it was written in Greek in a center of ancient Greek learning, Diophantus's Arithmetica is a curious synthesis of Greek, Egyptian, and Mesopotamian mathematics. It was not only one of the first purely number-theoretic and algebraic texts, but the first to use the blend of rhetorical and symbolic exposition known as syncopated mathematics. The text was influential in the development of Arabic algebra and European number theory and notation, and its development of the theory of indeterminate, or Diophantine, equations inspired modern work in both abstract algebra and computer science. We present, in this article, a selection of problems from the Arithmetica, which have been rewritten for ease of reading, and consider Diophantus's advancements in mathematics and mathematical notation in the context of ancient Greek mathematics. In particular, we examine Diophantus's use of syncopated mathematics, most notably his use of generic solutions that present an algorithm for solving an entire class of equations through the application of that algorithm to a single representational example, and how these techniques suggest a more extensive use of concrete examples when approaching modern mathematics.
]]>
Cyrus HettleRecreational Mathematics – Only For Fun?
http://scholarship.claremont.edu/jhm/vol5/iss1/7
http://scholarship.claremont.edu/jhm/vol5/iss1/7Fri, 30 Jan 2015 21:40:16 PST
In this paper, I explore recreational mathematics from two perspectives. I first study how the concept appears in educational policy documents such as standards, syllabi, and curricula from a selection of countries to see if and in what way recreational mathematics can play a part in school mathematics. I find that recreational mathematics can be a central part, as in the case of India, but also completely invisible, as in the standards from USA. In the second part of the report, I take an educational historical approach. I observe that throughout history, recreational mathematics has been an important tool for learning mathematics. Recreational mathematics is then both a way of bringing pleasure and a tool for learning mathematics. Can it also be a tool for social empowerment?
]]>
Lovisa SumpterImproving Project Success in an Online Mathematics Course
http://scholarship.claremont.edu/jhm/vol5/iss1/6
http://scholarship.claremont.edu/jhm/vol5/iss1/6Fri, 30 Jan 2015 21:40:15 PST
With more mathematics courses migrating to online environments, it is important to know whether these courses are comparable to their face-to-face counterparts. To that end, in two different years, I taught an online and a face-to-face section of the same finite mathematics course. After analyzing the data regarding differences in the two sections for the first year, I incorporated changes intended to improve the consistency of project success between the two sections as well as the overall success of the class projects in the online section. My main tool was mimicking the interaction of group members and providing immediate instructor feedback in the early stages of project completion. Happily, I saw an increase in the success of the class projects in the online section.
]]>
David ShoenthalLove Games: A Game-Theory Approach To Compatibility
http://scholarship.claremont.edu/jhm/vol5/iss1/5
http://scholarship.claremont.edu/jhm/vol5/iss1/5Fri, 30 Jan 2015 21:40:13 PST
In this note, we present a compatibility test with a rigorous mathematical foundation in game theory. The test must be taken separately by both partners, making it difficult for either partner alone to control the outcome. To introduce basic notions of game theory we investigate a scene from the film "A Beautiful Mind" based on John Nash's life and Nobel-prize-winning theorem. We recall this result and reveal the mathematics behind our test. Readers may customize and modify the test for more accurate results or to evaluate interpersonal relationships in other settings, not only romantic. Finally, we apply Dyson's and Press's "zero-determinant payoff strategies'' to this setting and explore the existence of such strategies and the corresponding implications for relationship dynamics.
]]>
Kerstin Bever et al.Perspective: of Time and Eternity
http://scholarship.claremont.edu/jhm/vol5/iss1/4
http://scholarship.claremont.edu/jhm/vol5/iss1/4Fri, 30 Jan 2015 21:40:12 PST
This paper considers geometric perspective in relation to devotional requirements in Italian religious painting from about 1250 to about 1450. The content of the altarpiece consisted in antithetical elements---the graphic exposition of Christian dogmatics, and a dramatis personae increasingly to be identified in empathetic terms. The one-point perspective system that was invented towards the end of that period, then, presented an opportunity and a difficulty. It enabled the creation of a naturalistic space, aiding empathetic identification with psychologically plausible individuals in the pictured world. On the other hand, whilst superficially the space marked out by the geometry of the vanishing point coincided with that of Christian hierarchy, it threw dogmatics into crisis, as it set picture space against picture plane. In addition to a humanistic imperative, the method was driven by a mathematical one, consideration of which allows us to see it as the last stage in a process of simplification of the conditioning geometry governing representation within the altarpiece. The paper shows that, despite first impressions, the earlier mathematical perspective systems were systematic. It demonstrates that, as there was a stand-off between dogma and empathy, there was one between iconic stability and mobile perspective in the earlier perspective methods, and one between static viewpoint and imaginative mobility in the invention. From within these antitheses came the necessity for very devious negotiations of the timeless and the historical---all compromising one another in one way or another---and, after the invention of the one-point system, the proposition of an expanded mental life both in those depicted and in those observing.
]]>
James G. LawsonOn the Persistence and Attrition of Women in Mathematics
http://scholarship.claremont.edu/jhm/vol5/iss1/3
http://scholarship.claremont.edu/jhm/vol5/iss1/3Fri, 30 Jan 2015 21:40:11 PST
The purpose of this study was to investigate what motivates women to choose mathematics as an undergraduate major and to further explore what shapes their future career goals, paying particular attention to their undergraduate experiences and their perceptions of the role of gender in these decisions. A series of semi-structured, individual interviews were conducted with twelve undergraduate women mathematics majors who were attending either a large public university or a small liberal arts college. This study found that strong mathematical identities and enjoyment of mathematics heavily influenced their decisions to major in mathematics. At the career selection stage, these women desired careers that are service-oriented, social in nature, and involved mathematical applications. For those planning to become teachers, the desire to help others predominantly influenced their career decision. Many of the non-teaching majors were unaware of mathematical careers other than teaching that satisfied these career qualities. Implications of these results with respect to women’s participation in mathematics are discussed.
]]>
Katrina Piatek-Jimenez