Physical Sciences and Mathematics | Open Access Articles

What Makes A Theory Of Infinitesimals Useful? A View By Klein And Fraenkel, Vladimir Kanovei, Karin Katz, Mikhail Katz, Thomas Mormann Jan 2018

What Makes A Theory Of Infinitesimals Useful? A View By Klein And Fraenkel, Vladimir Kanovei, Karin Katz, Mikhail Katz, Thomas Mormann

Journal of Humanistic Mathematics

Felix Klein and Abraham Fraenkel each formulated a criterion for a theory of infinitesimals to be successful, in terms of the feasibility of implementation of the Mean Value Theorem. We explore the evolution of the idea over the past century, and the role of Abraham Robinson's framework therein.

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Mathematical Arguments In Favor Of Risk In Andy Weir's The Martian, Sarah C. Cobb, Jeff B. Hood Jan 2018

Mathematical Arguments In Favor Of Risk In Andy Weir's The Martian, Sarah C. Cobb, Jeff B. Hood

Journal of Humanistic Mathematics

In Andy Weir’s novel The Martian, the characters encounter high-stakes, life-or-death situations, in which they must make choices based on their assessment of risk and likely outcomes. They have different reactions to risky situations, based on their approaches to assessing risk and their perspectives on the stakes involved. In this paper, we examine the ways that characters in The Martian intuitively assess risk and compare them to mathematical analysis of the situations in the book.

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Predicting The Next Us President By Simulating The Electoral College, Boyan Kostadinov Jan 2018

Predicting The Next Us President By Simulating The Electoral College, Boyan Kostadinov

Journal of Humanistic Mathematics

We develop a simulation model for predicting the outcome of the US Presidential election based on simulating the distribution of the Electoral College. The simulation model has two parts: (a) estimating the probabilities for a given candidate to win each state and DC, based on state polls, and (b) estimating the probability that a given candidate will win at least 270 electoral votes, and thus win the White House. All simulations are coded using the high-level, open-source programming language R. One of the goals of this paper is to promote computational thinking in any STEM field by illustrating how probabilistic …

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Mathematics, Writing, And Rhetoric: Deep Thinking In First-Year Learning Communities, Christine Von Renesse, Jennifer Digrazia Jan 2018

Mathematics, Writing, And Rhetoric: Deep Thinking In First-Year Learning Communities, Christine Von Renesse, Jennifer Digrazia

Journal of Humanistic Mathematics

Through the process of combining two seemingly unlikely bedfellows, mathematics and composition, two instructors explain how rhetoric connects the art of writing and the art of doing mathematics in an inquiry-based learning community. Combining these two courses in a learning community enables students and instructors to practice the deep thinking valued by each instructor and by a traditional liberal arts education while challenging both our and our students’ individual, disciplinary, and rhetorical conventions and beliefs. Using student writing from our course, our assignments from mathematics and composition, and survey evaluation results, we demonstrate how engaging in inquiry-based education provides unconventional …

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Ways Of Relating To The Mathematics Of The Past, Michael N. Fried Jan 2018

Ways Of Relating To The Mathematics Of The Past, Michael N. Fried

Journal of Humanistic Mathematics

Historians of mathematics, by definition, look at mathematics of the past. But mathematicians, too, often look at mathematics of the past; mathematicians of the past themselves often looked very closely at mathematics of their own past. Is their relationship to the past the same as that of the historians? Is every view of the past an historical view? Indeed, is every historical view historical in the same way? Or is it possible that there are different kinds of relationships to the mathematics of the past? This paper will suggest that there are in fact a variety of such relationships. It …

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Communicating Mathematics Across Time, Mark Huber, Gizem Karaali Jan 2018