Ah, the conic sections! Everyone knows (beware of statements that begin with the phrase Everyone knows . . . !) that these beauties, discovered so long ago by the ancient Greeks, are ubiquitous throughout mathematics. They show up in geometry and...
We use a single example to explain: *the Likelihood Principle *Bayesian statistics, and *why classical statistics cannot be used to compare hypotheses. Table of Contents: INTRODUCTION THE SLATER SCHOOL THE LIKELIHOOD A BAYESIAN ANALYSIS A NON-BAYESIAN...
A computer program that produces realistic pictures of opaque objects was implemented in the Lisp language. This type of program is called a hidden line remover. I explain what a hidden line remover does, how features of Lisp made it easier to develop,...
Solving systems of equations has applications in a multitude of disciplines. Once such application is in civil engineering. Although humor has been added to the scenario below, problems similar to this one are encountered by civil engineers on a daily...
Many people first see the application of probability in childhood. Games involving rolling dice, tossing a coin, or spinning an arrow are often a child's first introduction to chance. Much work has already been done for classic games such as Monopoly...
We discuss the introduction, student discovery, and teaching of a system of differential equations that model a circuit. In an engineering mathematics course we provide sufficient physics conceptual framework and differential equations background to...
An iterated-function dynamical system is a continuous map F from a metricspace X to itself. The sequence of iterates of F starting at x, {Fn(x)}, is theorbit of x. There are a number of competing definitions for chaos [Martelli et al. 1998]. Devaney...
What is the best strategy in the bidding game on The Price Is Right? over the last twenty-four years, the television game show The Price Is Right has begun with the announcer asking four contestants to come on down to Contestants' Row. At that point, a...
Early in our mathematical modeling course, Penelope Smith, the student co-author, fulfilled her library research assignment by investigating existing models of fire evacuation. Although there were a few studies of evacuating adults from public...
This article is about one big idea: "The rate at which the distance between us and a given star changes-it increases or decreases over time." This relationship is a powerful tool in detecting a planet orbiting the star and also in determining orbital...
Coin-tossing is generally viewed as the quintessential example of a random process. We focus on some counterintuitive aspects of sequences that cointossing produces. Equally-likely sequences of heads and tails of a specified length are not all equally...
Many problems that the world faces today, such as hunger, pollution, resource scarcity, poverty and violence, are related to rapid population growth. Hence it is essential that students be aware of population-related issues and concepts.
Klackers is a game in which players roll dice and then flip down tiles numbered 1 through 9 depending on the sum of the dice. The object of the game is to flip down as many tiles as possible in order to achieve the minimum score (scoring is described...
Mathematical models from mechanics offer a number of advantages: they are usually easy to interpret in physical terms, their analysis often does not require formidable mathematics, and-when couched in terms of sports- they have wide appeal.
The St. Basil Cake In the Greek Orthodox tradition, New Year's Day is also the Feast Day of St. Basil (329-379), who was known for his generosity and support of philanthropic projects (Saint Basil Academy [2005]; see Trinity Communications [2006] for a...
To Begin Our Session Have a question? Looking for an old friend? Need a reference for a paper? A popular and often effective form of information acquisition is submitting queries to Google.com. In fact, in the past second (on average) more than 3,000...
The finite-dimensional variational inequality is a mathematical formulation not widely taught in undergraduate or graduate mathematics curricula that has found application in many important areas, particularly in optimization and equilibrium problems....
Contents 1. Setting the Scene 2. Situation 1: Designing a New Facility 3. Situation 2: Modeling the Gate System 4. Situation 3: Shutting Down the Old Facility 5. Situation 4: Meeting Demand References Sample Solution Notes for the Instructor...
Introduction On June 17, 1972 five men broke into the headquarters of the Democratic National Committee at the Watergate, an office-apartment-hotel complex on the banks of the Potomac in Washington, DC. Investigating the botched burglary, Bob Woodward...