Penney Ante: Counterintuitive Probabilities in Coin Tossing
Coin-tossing is generally viewed as the quintessential example of a random process. We focus on some counterintuitive...
Optimal Klackers
Klackers is a game in which players roll dice and then flip down tiles numbered 1 through 9 depending on the sum of t...
Finding a Hidden Coin
The St. Basil Cake In the Greek Orthodox tradition, New Year's Day is also the Feast Day of St. Basil (329-379), who...
Googling Markov
To Begin Our Session Have a question? Looking for an old friend? Need a reference for a paper? A popular and often e...
Variational Inequalities: One-Stop Shopping for Optima and Equilibria
The finite-dimensional variational inequality is a mathematical formulation not widely taught in undergraduate or gra...
Water Purification (ILAP)
Contents 1. Setting the Scene 2. Situation 1: Designing a New Facility 3. Situation 2: Modeling the Gate System 4. S...
The Art of Anonymity: Exploring DC-Nets
Introduction On June 17, 1972 five men broke into the headquarters of the Democratic National Committee at the Water...
Pigtail: A Pig Addendum
Introduction to Pig The object of the jeopardy dice game Pig is to be the first player to reach 100 points. Each tur...
Traveling Door to Door with a DNA Computer
Many real-world applications can be modeled with directed networks and posed as a Traveling Sales Problem (TSP). Howe...
A Revolving Door Birthday Problem
The traditional "birthday problem" considers the probability of two or more people in a group of N sharing a birthday...
Math in Any Language
Systems of numeration as quantitative languages fill many interesting pages in the history of mathematics. The most ...
A Bouncing Cube
With the rapid progress of computer technology and applications, we see graphics everywhere. Special effects artists...
Ptolemys Theorem
Ptolemy's Theorem states that if a quadrilateral is cyclic, then the product of the lengths of the diagonals equals ...
Decisive Decades: Celebrating The Closing Century
A glance at the major time periods in the history of mathematics reveals a picture of many dimensions. Inspiring mom...
21 Problems For The Twenty-First Century
The dawning of the twenty-first century provides a rare opportunity for looking ahead, a time of speculating, and a ...
The Modern Geometry of the Triangle Revisited
Members of my senior mathematics course produced the following article. The course was an attempt by the class to ma...
How To Male A Log Table: A Flagrant Exercise In Atavism
Imagine that you're stranded on a desert island and want to make a table of logarithms.Why, for heaven's sakes? That...
Fundamental Theorem of Algebra Part II: The Theorem's Proof, The Theorem's Impact
From the times of the late Renaissance, the theory of equations was characterized in western culture by a high level...
Fundamental Theorem of Algebra Part I: The Theorem Foreshadowed
A far-reaching discovery in the late 1700s was to secure, even more so, the closing century's remarkable standing in...
The Postage Stamp Problem
When Hugh Burkhardt visited Teachers College a few years ago, he began his lecture with the following problem: Imagi...
Reversals of Genetic Fortunes
The last couple of decades have witnessed a thorough mixing of mathematics, computers, and biology. This mixing has ...
Drugs and Blocks
When your doctor prescribes a new drug or treatment (medical or surgical), your hope is that the condition that requ...
Trees, Chains, and Chances
The relatively new field of bioinformatics is undergoing explosive growth. Even before the current impetus provided ...
Partitions: Numbers As More Than The Sums Of Their Parts
Despite the advice of his advisor that he choose a more modest problem to solve for his dissertation, a young gradua...
Mathematics Helps Sort Out Our Genes
One area of intense contemporary activity in applied mathematics is mathematical biology. Advances in the study of m...
It's A Small World
Many people, in one context or another, are familiar with the "small world" phenomenon. You're sitting next to a str...
One Egg or Two? Statistics Helps Shed Light on Paleontology Mystery
One of the goals of paleontology is to connect what we learn through fossil records of extinct animals' biology to t...
Numerical Fulcrums: Providing Leverage for Work with Primes
What might be a numerical fulcrum? Consider the sequence of consecutive
positive integers 1, 2, 3, 4, 5, 6, 7, 8. ...
Taking the Temperature of Mathematical Problems: What Makes Some Hard?
Take a glass of water at room temperature and cool it by a few degrees centigrade. Consider the changes in the water...
A Long Way from Home: Transatlantic Sea Star Migration
For a marine biologist strolling along the eastern coast of South America, finding some sea stars (popularly called ...
Tunnel Vision
In the traditional trigonometry course, no problem is more time-honored than the tunnel problem. What is it? A compe...
Mathematics: A Myriad of Methods (Part 2)
Demonstrative mathematics, dating from the Early Greek Era, has a long and continuing history, and characterizes the...
Reflection
What follows is a direct result of the work I have been doing over the past five years on a National Science Foundat...
That's A Wrap!
In this issue of Consortium, we start a series of Henry's Notes that concern the interaction between a real-world si...
Curves Ahead
The following article was written by several students in my computer graphics class. I have added some diagrams and ...
Mathematics: A Myriad of Methods (Part 1)
A famous problem may have many solutions. The primary goal in any encounter with a challenging problem is that of so...