On June 2, 1987, the Los Angeles Lakers and the Boston Celtics met in Los Angeles for the first game of the 1987 National Basketball Association championship series, with the Lakers heavily favored to win the series. The posted odds in advance in...
Many health insurance policies carry a deductible. It is the amount below which the insurance company has no responsibility. Only claims above this deductible amount will be compensated by the insurance company. There are two general types of...
Recently Michael RRed criticized the calculus curriculum for teaching how to differentiate functions of the form f (z)g() without providing any real applications [Reed 19871. Without endorsing Reed's sentiment, we present an everyday application of...
We discuss a class of linear programming minimization models known as cutting stock, trim loss, or bin packing models. Specifically, we compare the results of applying two such models to the problem: Given certain stock lengths, how should the stocks...
We construct a three-dimensional unsteady-state mass transport model to predict the behavior of dopamine levels in the brain. The model is based on the principles of molecular diffusion, first-order decay, and instantaneous point-source input. We...
With inexpensive, fast, and reliable scanning devices and computers, it is now standard practice to append a check digit to product identification numbers, to detect errors and forgery. Various schemes for determining the checkdigit have been devised;...
Assume that energy (sound, light, heat, or radiation) is radiating uniformly in all directions from a point source, with a detector of a known size and shape at a given distance away. We are interested in determining how much of the energy emitted...
Racquetball, volleyball, squash, and badminton are games in which one player (or team) serves, points are won only when serving, and the winner of a rally serves the next one. Generally, winning a point enhances the probability of winning the next...
The Mathematical Modeling (MA363) class in the fall of 1990 was populated by 10 mathematics and computer science majors and 11 students from engineering or physics. All of them, being juniors or seniors, had studied three semesters of calculus and one...
I would like to take you back to December 17,1903, near the town of Kitty Hawk, North Carolina, where two brothers from Dayton, Ohio, W11bu and Orville Wright, are about to try to do something that has never been done before: fly a heavier-than-air...
In late 1990, the New York Times carried a story concerning traffic flow, which was not the usual bad news of gridlock and stationary fast-trackers; rather, it concerned an anticipated problem that never developed. City officials had decided to close...
The major news in mathematics in 1991 was the spread of research and applications involving wavelets. Other announced results involved determining the kissing number for spheres, extending the period of random-number generators, and new facts about the...
Property and casualty insurance companies need to establish appropriate reserves to cover the liabilities they incur in underwriting insurance policies. These reserves can be categorized as premium reserves, loss reserves, and expense reserves. They...
Readers with children (or readers who were themselves once children) may be farnilar with the simple board game of Chutes and Ladders. Introduced by Milton Bradley in 1943, it has been played by at least three generations. (It is based on an older game...
This article began as a comparative review of Macintosh programs for producing publication-quality graphics, inspired by one for IBM-style personal computers [Roman 19911. It has evolved into a discussion of three distinctly different graphing...
In the casino game blackjack or 21, mathematically determined best plays have been calculated by various mathematicians and gambling experts. These optimal playing strategies all assume that the casino pays even money on bets (excluding when the player...
Mathematical research in 1992 revealed a surprising connection between a newly discovered means of checking proofs and the intrinsic difficulty of certain optimization problems. A problem dating to 1910 was finally solved, revealing that there are an...
In his book The Blind Watchmaker, Richard Dawkins [1986al argues for the feasibility of evolution using a simple stochastic process. We analyze the running time of this process, and show that it takes O(n1ogn) steps to evolve a string of length n. This...
Recycling is difficult for local governments because it is a multidimensional problem. Not only are there biological, environmental, political, and perhaps even moral problems, but there are also several economic problems associated with recycling....
The problem of computing rotations in three-dimensional Euclidean space has been widely studied. It arises in many areas of mathematics and computer science, including graphics, robotics, animation, and simulation [Pique 19901. A 3 x 3 rotation matrix...