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We detail the rules and mathematical structure of Al-Jabar, a game invented by the authors based on intuitive concepts of color-mixing and ideas from abstract algebra. Game-play consists of manipulating colored game pieces; we discuss how these colored pieces form a group structure and how this structure, along with an operation used to combine the pieces, is used to create a game of strategy. We also consider extensions of the game rules to other group structures. Note: While this is an article for general readership originally published online by Gathering for Gardner in honor of Martin Gardners birthday (Oct. 2011), Al-Jabar has been played in university abstract algebra courses as a teaching tool, as well as by game enthusiasts, since its release. Moreover, the algebraic game structure described has sparked further work by other mathematicians and game designers. Thus, we submit this article to the ArXiV as a resource for educators as well as those interested in mathematical games.
We use the data of tenured and tenure-track faculty at ten public and private math departments of various tiered rankings in the United States, as a case study to demonstrate the statistical and mathematical relationships among several variables, e.g
We introduce and analyze several variations of Penneys game aimed to find a more equitable game.
These lecture notes attempt a mathematical treatment of game theory akin to mathematical physics. A game instance is defined as a sequence of states of an underlying system. This viewpoint unifies classical mathematical models for 2-person and, in pa
In this note, we present a compatibility test based on John Nashs game-theoretic notion of equilibrium strategy. The test must be taken separately by both partners, making it difficult for either partner alone to control the outcome. The mathematics
Mathematicians have traditionally been a select group of academics that produce high-impact ideas allowing substantial results in several fields of science. Throughout the past 35 years, undergraduates enrolling in mathematics or statistics have repr