The production of goods by a country depends on the capital available for investment and the number of workers in the labor force. Let Q be the production output, K the capital, and L the labor force; then Q is a function of K and L: Q = f (KL,) . In...
Brad Mann has done an excellent job of explaining various card-shuffling results. That of Bayer and Diaconis is particularly noteworthy because of the wide public recognition it has received [19921. It is not often that mathematicians can prove...
Mathematical discoveries in 1993 included a new polyhedron that will fill space only aperiodically, an algorithm for envy-free fair division of resources, a breakthrough in the combinatorial designs known as Latin rectangles, and yet another new...
College football is a favorite American spectator sport, so a differential equations project involving football is almost guaranteed to generate student interest. It's especially popular here at the University of Nebraska-Lincoln, where Husker football...
How many times do you have to shuffle a deck of cards in order to mix them reasonably well? The answer is about seven times for a deck of 52 cards, according to Persi Diaconis. This somewhat surprising result made the New York Times a few years ago...
Around the world, hundreds of different kinds of mancala games have been observed [Deshayes et al. 1976; Murray 1978; Russ 19841, with some dating back to the Empire Age of ancient Egypt. Their common features involve cupshaped depressions called pits...
Many students are introduced to mathematical modeling through the max/min problems of one-variable calculus. However, a major component of modeling-relating the resolution of the mathematical problem to the original real-world problem-may receive...
In this expository article, we discuss the rankderangement problem, which asks for the number of permutations of a deck of cards such that each card is replaced by a card of a different rank. This combinatorial problem arises in computing the...
This article presents a combinatorial game-theoretic analysis of Konane, an ancient Hawaiian stone-jumping game. Combinatorial game theory [Berlekamp et al. 19821 applies particularly well to Konane because the first player unable to move loses and...
What is the best strategy in the bidding game on The Rice Is Right? Over the last twenty-four years, the television game show The Price Is RighV1 has begun with the announcer asking four contestants2 to come on down to Contestants' ROW.^ At that point,...
College catalogs, not the most edifying reading available on most campuses, do occasionally reflect trends that signal real events. One cannot help but notice these days that many departments that formerly bore the succinct title Mathematics are now...
Albert W. Tucker's note (on the preceding page), which is published here for the first time, was the first written description of what has come to be known as the prisoner's dilemma. The example in that note, with its accompanying story, has played a...
The question of how a group of individuals should choose from among a set of alternatives has drawn the attention of social philosophers throughout history. Major strides have been made in the analysis of social choice within the last thirty years,...
SOVIET DISCOVERY ROCKS MATHEMATICAL WORLD Last November, sensational headlines appeared widely in the news amid reports of a startling discovery by a previously unheralded Russian mathematician, L.G. Khachian. The reports predicted that the discovery...
For the first ten years of their existence, computers were used exclusively t o execute numerical calculations. In fact, the primary motive for the construction of the first electric digital computers was the need for a tool that would quickly and...
Everyone knows that a picture is worth a thousand words. In our algebra, trigonometry, and calculus courses, we acknowledge this by using graphs in our study of functions. But in courses in three-dimensional analytic geometry and multivariable...
First courses in abstract or modern applied algebra are concerned with the investigation of mathematical structures, such as groups and rings, along with certain fundamental properties they, or their associated substructures, possess. Following this...
The term algorithm it self is derived from the name of a ninth century Persian author, Abu Jafar Mohammed ibn Musa a1 Khowarizmi, who wrote a book in which he formulated rules for performing the four basic arithmetic operations of addition,...
A computing system can, in general, be discussed from two points of view: its hardware and its software. In this context, hardware refers first and foremost to the machinery that is used to enter and to store information in the system, to process data...
What accounts for these differences betweeen real and complex differentiable functions? First, when z and f ( z ) are complex, the difference quotient (1) involves subtraction and division of complex rather than real numbers. (We discuss these...