Related papers: How to fairly share a watermelon
During the last decade we have witnessed an impressive development in so-called interpreted languages and computational environments such as Maple, Mathematica, IDL, Matlab etc. Problems which until recently were typically solved on…
Geometry constitutes a core set of intuitions present in all humans, regardless of their language or schooling [1]. Could brain's built in machinery for processing geometric information take part in uncertainty representation? For decades…
This paper addresses the idea of the applicability of mathematics, using, as a case study, a construction and software package that partition the unit sphere into regions of equal area. The paper assesses the applicability of this…
Information geometry is a study of statistical manifolds, that is, spaces of probability distributions from a geometric perspective. Its classical information-theoretic applications relate to statistical concepts such as Fisher information,…
This paper is one of a series in which elementary-education practice is analyzed by comparison with the history of mathematics, mathematical structure, modern practice, and (occasionally) cognitive neuroscience. The primary concerns are:…
In this paper we propose a very specific educational challenge that teachers can use to motivate ambitious and enthusiastic mathematics students who have mastered basic trigonometry and trig functions. The objective is to lead students to a…
[Taken from the "README" in the book] My goal with this book is to provide some kind of bridge for mathematics between the high-school-level and college-level for physics students. From my perspective, our job as physicists is to observe…
A close look at students' written work on examinations offers a wealth of information about their performance, their knowledge of the subject, their strengths, weaknesses and misconceptions, and their overall level of mathematical skills…
Computation, the use of a computer to solve, simulate, or visualize a physical problem, has revolutionized how physics research is done. Computation is used widely to model systems, to simulate experiments, and to analyze data. Yet, in most…
This paper wants to show how practical geometry, created to give a concrete help to people involved in trade, in land-surveying and even in astronomy, underwent a transformation that underlined its didactical value and turned it first into…
We investigate the dynamics of how graduate students coordinate their mathematics and physics knowledge within the context of solving a homework problem for a plasma physics survey course. Students were asked to obtain the complex…
Group Theory has become an invaluable tool in the physics community. Despite numerous introductory books, the subject remains challenging for beginners. Mathematica has emerged as a popular tool for research and education, offering various…
Starting from Greg Moore's description about Physical Mathematics, a framework is proposed in order to understand it, based on Gilles Ch\^atelet's philosophy. It will be argued that Ch\^atelet's ideas of inverting, splitting, augmenting and…
In this short survey article, we showcase a number of non-trivial geometric problems that have recently been resolved by marrying methods from functional calculus and real-variable harmonic analysis. We give a brief description of these…
Here we show how reversible computation processes, like Margolus diffusion, can be envisioned as physical turning operations on a 2-dimensional rigid surface that is cut by a regular pattern of intersecting circles. We then briefly explore…
I survey recent progress on a classic and challenging problem in social choice: the fair division of indivisible items. I discuss how a computational perspective has provided interesting insights into and understanding of how to divide…
Geometrical aspects of quantum computing are reviewed elementarily for non-experts and/or graduate students who are interested in both Geometry and Quantum Computation. In the first half we show how to treat Grassmann manifolds which are…
Much of the research done by modern physicists would be impossible without the use of computation. And yet, while computation is a crucial tool of practicing physicists, physics curricula do not generally reflect its importance and utility.…
Classic cake-cutting algorithms enable people with different preferences to divide among them a heterogeneous resource (``cake''), such that the resulting division is fair according to each agent's individual preferences. However, these…
Interval calculus is a relatively new branch of mathematics. Initially understood as a set of tools to assess the quality of numerical calculations (rigorous control of rounding errors), it became a discipline in its own rights today.…