Introduction Polychlorinated biphenyls (PCBs) are human-made organic chemicals. Exposure to PCBs can have adverse health effects on humans and other animals; they have been shown to cause cancer in animals (and hence are probable human carcinogens) and...
Introduction Barges are an integral component of the freight transportation system. The capacity of a barge is 60 times that of a semi-trailer truck; and in tonnage per mile, barges are 9 times as fuel efficient, saving shippers and consumers over $7...
Introduction The world is facing a wide range of ecological challenges, including species extinction and the climate crisis. The mathematical concept of a bifurcation point underlies many of these phenomena (see Wikipedia [2022]) and hence is an...
Introduction In undergraduate mathematics classes, counting is often taught by presenting formulas for students to memorize so they can solve a standard set of problems. We provide an alternative to this approach in the form of an activity that is...
Abstract Partial differential equations were developed in the 18th century to model physical systems. Their inception has led to the continued development of a beautiful mathematical theory with an ever-increasing range of applications. In 1890,...
Introduction World Vision World Vision World Vision (WV) is a Christian relief and development organization working with children, families, and communities worldwide to tackle the causes of poverty and injustice; every child deserves to live life to...
Solomon Garfunkel’s delightful reflection on the 40th anniversary of COMAP [2022] reminded us that our book, How to Model It: Problem Solving for the Computer Age [Starfield, Smith, and Bleloch 1990], has passed its 30th anniversary and is still going...
Abstract We offer a simple model of pitching and batting choices of Major League Baseball players and use game theory to investigate strategies for when a runner is on second base. We find that while a runner on second base can affect the outcome of...
Introduction Linear algebra includes finding eigenvalue solutions to eigenequations, which have applications in many fields, including quantum mechanics. We describe the core role in quantum mechanics of eigenstates, which involve both eigenvalues and...
Lyme disease is the most common vector-borne disease in the United States. It is caused by bacteria Borrelia burgdorferi and transmitted to humans by blacklegged ticks. The transmission is a complex process that involves several different non-human...
We propose a new method for music composition in the style of Johann Sebastian Bach, using geometrical transformations of the plane. The method consists of analyzing a classical opus, identifying the motif, and mapping the occurrences of this motif and...
Model Reality Check We present a differential equation that models the process of evaporation from a free-water surface, based on the principle of conservation of mass and Dalton’s evaporation law. We collected experimental data to verify the accuracy...
Introduction The general public, students in public school mathematics classes, future teachers, and even mathematics majors are typically not aware that many mathematics researchers have done and are still doing research about applying mathematics to...
Introduction The Football Association Challenge Cup, more commonly known as the FA Cup, is an annual knockout tournament in men’s English professional football. (It is now known officially as The Emirates FA Cup after its current sponsor. There is also...
Abstract We describe how we used contextual teaching and learning principles to build a graph theory project for mathematics courses at the U.S. Air Force Academy. We leveraged an Air Force targeting scenario to make the mathematics relevant to our...
Abstract Within the tertiary education framework, we developed a pilot course focused on mathematical modeling, placing a distinct emphasis on sustainability and sustainable development. While an applicable textbook exists for this liberal arts course,...
Abstract We present a case study in which differential equations are applied to a real-world problem: protecting water pipes from freezing under extreme winter weather conditions. The primary objective is to estimate the minimum ambient temperature in...
Abstract As gerrymandering has become a powerful tool to create and maintain power in an increasingly polarized U.S. political landscape, the courts have wrestled with ways to definitively identify gerrymandering. We describe the efficiency gap, a...
Septaria In Septaria, there are only seven numbers, six of which are classified as digits. The numbers 1, 2, and 3 correspond to the digits of the left hand and the numbers 4, 5, and 6 correspond to the digits of the right hand. The divine or sacred...
Introduction Introduction Many colleges and universities have a first-year seminar program, serving as a crucial bridge for new students entering higher education. These seminars introduce the rigors of college-level work through writing assignments,...