Common Wisdom, Logarithmic Differentiation, and Compound Interest
Recently Michael RRed criticized the calculus curriculum for teaching how to differentiate functions of the form f (z...
Waste Minirnization via Cutting Stock Models
We discuss a class of linear programming minimization models known as cutting stock, trim loss, or bin packing models...
Distribution of Dopamine in the Brain
We construct a three-dimensional unsteady-state mass transport model to predict the behavior of dopamine levels in th...
Error Detecting Schemes Using Dihedral Groups
With inexpensive, fast, and reliable scanning devices and computers, it is now standard practice to append a check di...
Spherical Geometry in Medical Imaging
Assume that energy (sound, light, heat, or radiation) is radiating uniformly in all directions from a point source, w...
Racquetball as a Stochastic Process
Racquetball, volleyball, squash, and badminton are games in which one player (or team) serves, points are won only wh...
Commentary on Spherical Geometry in Medical Imaging
In Moore and Moore [19901, we gave exercises (Exercises 1, 7, and 8) that ask the reader to find the dihedral angle f...
Finding Best Approximate Circle
The Mathematical Modeling (MA363) class in the fall of 1990 was populated by 10 mathematics and computer science majo...
The Wright Stuff
I would like to take you back to December 17,1903, near the town of Kitty Hawk, North Carolina, where two brothers fr...
Braess's Paradox: A Puzzler from Applied Network Analysis
In late 1990, the New York Times carried a story concerning traffic flow, which was not the usual bad news of gridloc...
Mathematical Develovments in 1991
The major news in mathematics in 1991 was the spread of research and applications involving wavelets. Other announced...
Estimating Unreported Losses
Property and casualty insurance companies need to establish appropriate reserves to cover the liabilities they incur ...
Some Transcendental Results Concerning Air Resistance
When a projectile is shot or a ball is thrown, the simplest mathematical model ignores air resistance and obtains the...
Bertrand's Paradox
A chord is a straight line whose endpoints are any two points on a circle. What is the probability that a chord of a ...
The Dimensions of Window Glass for a Trapezoidal Opening
Recently, I received a request from a local window manufacturer for help in determining the dimensions of a window to...
Aggregate Demand and Supply-side Economics
Since the publication of the first edition of Samuelson's Principles text in 1948, introductory treatments of the sho...
The Power of Incumbency
We are interested in modeling the length of tenure in office of a legislator. Once he or she is initially elected, th...
The Zip Code Bar Code
I was recently asked by a chemist to figure out the scheme used to create the bar code for the extended zip code on b...
Equilibrium Populations in Singles Bars
Singles bars are generally regarded as places where people go to meet other people. But alas, not every person one me...
Simpson's Rule for Double Integrals
In a previous paper and UMAP module, this author developed an extension of the trapezoid rule to evaluate double inte...
The Role of Mathematics in Atonal Music
The study of atonal music might seem far removed from mathematics, but in fact a close bond exists. Moreover, a good ...
Secret Encryption with Public Keys
For centuries people have wished to communicate with one another while keeping their communications secret from outsi...
Absorbing Markov Chains and the Number of Games in a World Series
A process whose stages are governed by the initial state the process was found in is known as a Markov process. The s...
The Growth of Administrative Problems
Many administrators experience the feeling that the amount of paperwork they need to deal with increases substantiall...
An Application of Matrices to Space Shuttle Technology
Shuttle's Robot Arm Snares Errant Satellite [Wilford 1984al; Robot Arm Knocks Troublesome Ice Off Space Shuttle [Wilf...
Editorial Process of a Bimonthly: A Case Study
We analyze the editorial processing of manuscripts for a bimonthly professional journal. Our goal is to determine the...
Fire and Ice: The Effect of Latitude and Season on Solar Collection
Recently, my student Steven Beck brought me a problem which was on the one hand highly practical, and on the other ha...
Strategy for Hiring a Secretary
An employer is seeking a new secretary. Under a rather rigid hiring procedure, the employer is allowed to interview n...
Accelerated Life Testing
Producers and consumers of products are interested in knowing how long items will function before failure. Producers ...
Practitioner's Commentary : Emergency Evacuation
The first thing I must do is make clear that I am not an emergency evacuation practitioner, but rather a researcher w...
Evacuating an Elementary School Building
Early in our mathematical modeling course, Penelope Smith, the student co-author, fulfilled her library research assi...
The Highway Slope Problem
One of the most widely used sources of problems for a mathematical modeling course is the series of modules prepared ...
The Minor Means
The Office of Publications of Local College makes the following statement: Although our College is large, its individ...
A Statistical Model for Describing the Response of Diabetic Patients to Insulin
In this paper we develop a model for the response of a diabetic patient to medical therapy. The main tools for the mo...
Modelling River Flow
From early experiences of dropping sticks into a river and watching their passage downstream, or later it becomes evi...
The Surgical Correction of Astigmatism
Following corneal transplants and cataract surgery patients are often left with considerable astigmatism. There are a...