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...
The topic of tank calibration provides an ideal setting for introducing important ideas in computational mathematics. The basic problem is to mark a dipstick so that a volume of fluid in the tank can be read from the dipstick markings. A broad range of...
When one of the authors (Campbell) was a graduate student at Cornell in the late 1960s, he never ceased to be amazed at how graduate mathematics courses were scheduled. At the start of each term, all 80 or so graduate students and all 30 or so faculty...
This paper began as a class assignment for Prof. James Sandefur's Discrete Dynamical Systems course at Georgetown University in Spring 1993. In an effort to encourage critical thinking and creativity among the students, Prof. Sandefur divided the class...
A frequent problem that college students face is that of scheduling their courses. Part of the problem stems from required courses being offered at conflicting times. To rectify the problem, Spelman students rearrange their schedules by taking a course...