Introduction: Software for Calculus The choice of software for teaching calculus depends on several objectives and constraints, including: • availability; • instructor experience; • graphics, symbolic, and numerical capabilities; • and steepness of the...
Modeling is equally important in social science as it is in physical science. Introduction We recently heard a colleague explain why mathematics and modeling are so important for interdisciplinary problem solving. The elegance of his comment struck us...
Introduction On the whole, standard card solitaire games notoriously resist the calculation of their winning probabilities. Yan et al. [2005] have said, in referring to what is commonly known as Klondike solitaire, "It is one of the embarrassments of...
Traditional actuarial functions in the world of insurance include pricing of an insurance product (life, health, or car insurance, pension etc.) and reserving for future benefit payouts to an existing policy-that is, estimating how much of the past...
Introduction I have often advocated that a mission of mathematicians is to help people to "see, seek, and speak" mathematics [Campbell 2002]. Doing so can be a matter of pointing out features in nature (e.g., Fibonacci sequence in sunflowers) or...
Statistics is running the risk of appearing irrelevant to today's undergraduate students. Today's undergraduate students are familiar with data science projects, and they judge statistics against what they have seen. Statistics, especially at the...
Introduction In a recentGuest Editorial [Gordon 2013], I presented the case for changing the focus of existing college algebra / precalculus courses to make mathematicalmodeling the central and organizing theme. Doing so would • make the courses far...
Abstract We examine a novel variation of the classic cylindrical can optimization problem encountered in almost every first-semester calculus course: to minimize the cost of the material used to make the can, which amounts to minimizing the surface...
Abstract We investigate the optimal amount of liquid to place in a container, such as a soda can or cup of coffee, so that the angle at which the container will tip over is as large as possible. Classic investigations assume that the water is static...
Introduction Have you seen the party trick where a soft drink can balances on its edge? The bottom edge of a standard aluminum 12-ounce beverage can has a fairly wide bevel on which the can will balance when partially full. We model the geometry of the...
Prelude and Vademecum This article is an amplification with illustrations of a write-up of my talk at the University Mathematics Teaching Conference at Sheffield Hallam University, 7 September 1999 [Singmaster 2000]. That talk was based on earlier...
Abstract We cite broad support for using modeling in mathematics coursework in undergraduate studies and address the possibilities for doing so in the undergraduate differential equations course. We describe one current support community, SIMIODE,that...
Abstract: This activity gives students a chance to build a differential or difference equation model similar to standard textbook mixing problems.The activity uses tangible objects ("fish") and a student-designed restocking and fishing plan for a lake....
Introduction So what is modern about Modern Algebra anyhow? It is an old subject, to be sure, and calling it "modern" in the sense of "recent" is a misnomer. The first conception of an abstract group-a set of elements whose natures were completely...
Abstract We modify the Massey rating method so as to rate and rank the players in the Professional Golf Association (PGA) Tour based on their individual performance. We then compare the accuracy of the Massey rankings with the accuracy of the Official...
Abstract Devil Facial Tumor Disease (DFTD) is a transmissible parasitic cancer that, since the first reported case in 1996, has caused Tasmanian devil populations to decline dramatically. Several strategies such as selective culling and isolation have...
Abstract We use a computer model to analyze and compare a variety of strategic paradigms in the game of Monopoly®, with an emphasis on strategies that can be implemented by humans. The strategies that we consider can be divided into two categories:...
Introduction We often model temperature change as an exponential process: According to Newton's law of cooling, the object temperature approaches the ambient temperature (e.g., room temperature) exponentially. But Newton's law of cooling is only a...
Introduction and Warmup On a cool autumn day in October, 1980, a marginally-talented high school freshman got his first big lesson on scoring a cross-country race. In his races to date, the freshman runner (whom we'll call "Pokey") had always finished...
Abstract The Treaty of Lisbon, the latest treaty governing law-making in the European Union (EU), went fully into effect in 2014. Since then, the United Kingdom (UK) has petitioned to leave the European Union, based on a 2016 referendum in the UK (that...