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...
Abstract Crop rotation is an important component of organic farming because it can help to maintain healthy soil and provide weed and pest control without the use of synthetic fertilizers or pesticides. Dickinson College has a certified organic farm...
Abstract This paper is motivated by the essays of N.N. Taleb [2001; 2007; 2008] on randomness in the real world. In particular, we are interested in the "rare" event, one residing in the tail of some distribution. We begin with Taleb's mythical...
Introduction This article is about randomness, in particular about random binary strings, and, even more particularly, about the use of randomness in cryptography. • What do we mean by the word "random," • why do we need randomness, and • are there...
Introduction Digital signatures are all around us (though barely noticeable by the average person), especially in electronic (digital) financial transactions. Like its paper-and-pen ancestor, a signature has as its purposes guaranteeing the integrity...
Abstract Rankings play an important role in sports, as well as in the evaluation of proposals and the operation of search engines. How are such rankings obtained? We outline several linear algebra approaches used in sports ranking methods and then...
In the Interdisciplinary Contest in Mathematics (ICM) and Mathematical Contest in Modeling (MCM), a team provides a one-page executive summary as the first page of their submission. Despite the guidance in the paragraph below (from the MCM/ICM Contest...
Abstract The Kansas Republican Party uses an apportionment method of its own invention to apportion delegates to candidates in its presidential caucus. This method includes a threshold that eliminates candidates (and their votes) who receive less than...
Introduction Applied mathematics and science have made substantial progress in modeling methodologies that have resulted in the advancement of knowledge and improvement of solutions to important problems. Until the mid- 20th century,...
Introduction So what is a "change point"? Formally, a change point is a point at which the statistical properties of a model change. But what does that actually mean? Suppose that we are trying to fit a linear model to the data shown in Figure 1a,...
Introduction The Game of the Goose (hereafter simply "Goose") is an early modern board game, existing as early as 1463 [Seville 2019]. Goose is a race game similar to Chutes and Ladders, with landing on some positions sending a player forward or...
Introduction In Isaac Newton's theory, gravity is a force between masses. You are probably familiar with the equation, F = Gm1m2/r2, where F is the force, G is the gravitational constant,m1 andm2 are masses, and r is the distance between the masses....
Introduction The U.S. Social Security Administration offers and administers retirement income to workers who have paid Social Security taxes on their working income generally for at least 10 years. A worker has the option of deciding when to retire and...
Abstract We detail two different mathematical solution techniques for a system of first-order differential equations used to model the diffusion of a drug in a transdermal drug delivery system. We include derivation of the mathematical model from first...
Introduction Woodlawn, Chicago In Fall 2019, my wife and I undertook a residency to learn the stark realities of life faced by disadvantaged black communities, living in an apartment in theWoodlawn neighborhood on Chicago's South side. Woodlawn is a...
By the time students begin their post-secondary education, most have been preconditioned to expect a structured environment full of objectively-right and -wrong answers when they cross the threshold of a mathematics classroom. They have come to expect...
Context and Motivation Magic: The Gathering® is a collectible card game created in 1993, and iswidely regarded as the first trading card game ever produced. To this day,it remains wildly popular, with millions of players and billions of cardsprinted....