Abstract We present a review of the binomial option pricing model introduced by Cox et al. [1979]. The material is suitable for an upper-level undergraduate course in finance, mathematical finance, or mathematics. and can be covered in two to three...
Introduction Where should you study? For a minimum of distractions, you should study in the library. But where in the library? I once worked at a college whose science library had a mezzanine floor with a row of study desks beneath and parallel to a...
Background In deciding where to live, people face the financial decision of whether to buy or rent. We analyze this question for a family considering houses in the $80,000 range. Based on the author's location in Texas, such a price would buy a...
In Rublein [2015], we considered the stability of long boats with a square cross section. Here we study a long solid boat of uniform weight density whose cross section has an isosceles triangular shape. We are interested in geometric configurations in...
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...