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Physical Sciences and Mathematics Commons™
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Articles 1 - 7 of 7
Full-Text Articles in Physical Sciences and Mathematics
Harmonics In The Library, Charles Coppin
Harmonics In The Library, Charles Coppin
Journal of Humanistic Mathematics
Students of traditional calculus courses can discover significant mathematics original to themselves, especially if these courses are taught in a way that allows shafts of mathematical light to shine through. We tell a story of such an incident in the form of a dialogue between two fictional students. Our students, on their own, discover (or rediscover) a well-known problem based on the harmonic series. We believe opportunities for such discoveries are greater if students have had some experience with inquiry-based learning prior to entering a traditional course. More broadly, we aim to demonstrate what can occur when students feel no …
A Math Therapy Exercise, Gary Stogsdill
A Math Therapy Exercise, Gary Stogsdill
Journal of Humanistic Mathematics
Math anxiety prevents many liberal arts undergraduates from appreciating mathematics and realizing their potential in math courses and math-related endeavors. The author describes his development and use of a "math therapy exercise" that enables students to move beyond the paralyzing grip of math anxiety and cultivate a more positive relationship with mathematics.
Rock Art Tallies: Mathematics On Stone In Western North America, James V. Rauff
Rock Art Tallies: Mathematics On Stone In Western North America, James V. Rauff
Journal of Humanistic Mathematics
Western North America abounds with rock art sites. From Alberta to New Mexico and from Minnesota to California one can find the enigmatic rock paintings and rock carvings left by the pre-Columbian inhabitants. The images left behind on the rocks of the American plains and deserts are those of humanoids and animals, arrows and spears, and a variety of geometric shapes and abstract designs. Also included, in great numbers, are sequences of repeated shapes and marks that scholars have termed "tallies." The tallies are presumed to be an ancient accounting of something or some things. This article examines rock art …
Some Contributions To The Sociology Of Numbers, Robert Dawson
Some Contributions To The Sociology Of Numbers, Robert Dawson
Journal of Humanistic Mathematics
Those who work with numbers eventually realize that they all have different personalities (the word "numbers" can of course be replaced by any number of other nouns here.) Here is one view of the issue.
How To Cook Up A Math Poem In N Easy Steps, Caleb Emmons
How To Cook Up A Math Poem In N Easy Steps, Caleb Emmons
Journal of Humanistic Mathematics
A mathematical poem attempts to distill a mathematical concept and present it in a literary or visually compelling way. This paper presents an outline of my own personal method of composing such poetry. The outline is elucidated via an extended meditation on the composition of one particular poem.
On Contemplation In Mathematics, Frank Lucas Wolcott
On Contemplation In Mathematics, Frank Lucas Wolcott
Journal of Humanistic Mathematics
In a section about research, we make the case that intentional, structured reflection on the mathematical research process, by mathematical researchers themselves, would result in better mathematicians doing better mathematics. As supporting evidence, we describe the Flavors and Seasons project. In a section about teaching, we describe the contemplative education movement and share personal experiences using meditation in the math classroom. We conclude with an explicit proposal for elucidating the experiential context of mathematics, in both research and teaching environments.
Teaching The Complex Numbers: What History And Philosophy Of Mathematics Suggest, Emily R. Grosholz
Teaching The Complex Numbers: What History And Philosophy Of Mathematics Suggest, Emily R. Grosholz
Journal of Humanistic Mathematics
The narrative about the nineteenth century favored by many philosophers of mathematics strongly influenced by either logic or algebra, is that geometric intuition led real and complex analysis astray until Cauchy and Kronecker in one sense and Dedekind in another guided mathematicians out of the labyrinth through the arithmetization of analysis. Yet the use of geometry in most cases in nineteenth century mathematics was not misleading and was often key to important developments. Thus the geometrization of complex numbers was essential to their acceptance and to the development of complex analysis; geometry provided the canonical examples that led to the …