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,...
More Than a Process Two days after stepping into my role as Executive Director of COMAP, I found myself in a classroom at Pui Kiu College in Hong Kong, sitting with five secondary school modeling teams and their advisors. These students had recently...
A number of basic measurements are used in describing populations and populated communities. Among these are population density, abundance of particular species, distribution of species, population size, and population age structures. Ecologists call a...
When two water (or other solvent) volumes are separated by a semi-permeable membrane, water will flow from the side of low solute concentration to the side of high solute concentration. This is known as osmosis. The flow of solvent across the membrane...
Cars, trucks, motorcycles, and buses emit significant quantities of carbon monoxide (CO), hydrocarbons (HC), nitrogen oxides (NOx), and fine particles (PM). These chemical compounds play dominant roles in air pollution problems. In the densely...
This remark highlights the remarkable resemblance of Fourier series to Ptolemy representation of the motion of a planet. We may say that Ptolemy anticipated Fourier analysis some sixteen centuries ago [Zebrowski 2000]. Perhaps Lagrangewas the first to...
Contents 1. Setting the Scene 2. Background 3. Mission 3.1 Track Facts 3.2 Tire Performance 4. Requirements References Sample Solution Notes for the Instructor Acknowledgment About the Authors
This article describes a coordinate transformation problem that arose while I was working in the summer of 1978 a t Raytheon on the computer software for an airtraffic control radar system for West Germany. The key to solving the problem was a 3x3...
Telemetry is the process of gathering data from an isolated location and sending it to a central location where it can be analyzed. We first outline how a telemetry system might work and then use a Fourier sine series to solve a mathematical problem...
The four major parts of a V-6 or V-8 engine are the block, the intake manifold, an3 the two heads, as shown in Figure 1. Various other items get bolted t o these, such as the carburetor, pan, exhaust manifolds, rods, pistons, crankshaft, and the...
This is the second paper in a series on the conic sections. The series is intended to be a dazzling potpourri of realworld applications and examples. The conic sections should nwer be called the chronic sections.
Diane Carswell is reluctant to learn about auto mechanics for the purpose of repairing her own vehicle, but she wants to know enough about cars to ask the right questions, to ensure that her vehicle will be serviced properly.
This is the third papr in a series on the conic sections. This series contains 'real-world applications of these beautiful and fascinating curves. May we all become conicsseurs.
The manner in which Pythagoras calculated the height of Hercules is indeed naive by today's standards, but the model he used was straight-forward. After the model is presented, it may be criticized and revised in accordance with contemporary knowledge....
The birthday paradox is well known and appears in many popular books on mathematics. In the form in which it is most commonly stated, it says that if 23 (or more) randomly chosen guests attend a party, then the probability of two of them sharing the...
This paper surveys the landscape of courses outside the track leading to calculus, describes an offering of a Finite Mathematics course that featured environmental modeling, discusses what such a course requires from an instructor and from students,...
Putting messages or data into coded form usually calls to mind the cloak and dagger world of spies and secret communications. But there are reasons besides secrecy for using codes. Sometimes the technology we choose to use forces coding upon us. Morse...