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Gold, Bonnie – College Mathematics Journal, 2011

Even those with no interest in the philosophy of mathematics take positions on a range of philosophical issues when they teach mathematics. Some of these issues are intimately related to common student confusions. These include the nature of mathematical objects and relations such as real numbers and equality; how we come to conclude a…

Descriptors: Grade 8, Grade 4, Mathematics Education, Teaching Methods

Zitarelli, David E. – College Mathematics Journal, 2005

This is the story of the first American mathematics journal. According to its title page, the journal was "adapted to the present state of learning in America" and "designed to inspire youth with the love of mathematical knowledge, by alluring their attentions to the solutions of pleasant and curious questions".

Descriptors: Mathematics Education, Periodicals, Journal Articles, History

Torrence, Bruce – College Mathematics Journal, 2011

The game "Lights Out" and its mathematical predecessor, the sigma-plus game, has inspired an extensive mathematical literature. In this paper, the original game and a borderless version played on a torus are considered. We define an easy game to be one in which pushing the buttons that are originally lit solves the game. Easy games are classified…

Descriptors: Geometric Concepts, Mathematics Instruction, Teaching Methods, Educational Games

Meyer, Walter – College Mathematics Journal, 2006

David Gale was one of the mathematicians responsible for the modern form of the theory of duality in linear programming and the associated proof of the minimax theorem in the theory of games. He is a member of the National Academy of Sciences and is Professor Emeritus of Mathematics and Operations Research at the University of California at…

Descriptors: Game Theory, Mathematical Applications, Mathematics Education, College Mathematics

Baker, Mark; Beltran, Jane; Buell, Jason; Conrey, Brian; Davis, Tom; Donaldson, Brianna; Detorre-Ozeki, Jeanne; Dibble, Leila; Freeman, Tom; Hammie, Robert; Montgomery, Julie; Pickford, Avery; Wong, Justine – College Mathematics Journal, 2013

Sets in the game "Set" are lines in a certain four-dimensional space. Here we introduce planes into the game, leading to interesting mathematical questions, some of which we solve, and to a wonderful variation on the game "Set," in which every tableau of nine cards must contain at least one configuration for a player to pick up.

Descriptors: Mathematics Instruction, College Mathematics, Mathematical Concepts, Educational Games

Tou, Erik R – College Mathematics Journal, 2013

This project classifies groups of small order using a group's center as the key feature. Groups of a given order "n" are typed based on the order of each group's center. Students are led through a sequence of exercises that combine proof-writing, independent research, and an analysis of specific classes of finite groups…

Descriptors: College Mathematics, Classification, Groups, Mathematical Logic

Kose, Emek; Kunze, Jennifer – College Mathematics Journal, 2013

Students in college-level mathematics classes can build the differential equations of an energy balance model of the Earth's climate themselves, from a basic understanding of the background science. Here we use variable albedo and qualitative analysis to find stable and unstable equilibria of such a model, providing a problem or perhaps a…

Descriptors: College Mathematics, Mathematics Instruction, Equations (Mathematics), Climate

Groetsch, Charles W. – College Mathematics Journal, 2008

How fast does a tank drain? Of course this depends on the shape of the tank and is governed by a physical principle known as Torricelli's law. This note investigates some connections between tank shape and a mathematical function related to the time required for the tank to drain completely. The techniques employed provide some interesting…

Descriptors: Calculus, Mathematics Education, College Mathematics, Mathematical Concepts

Winkel, Brian; Naylor, Michael – College Mathematics Journal, 2010

Biangular coordinates specify a point on the plane by two angles giving the intersection of two rays emanating from two fixed poles. This is a dual of Cartesian coordinates wherein a point on the plane is described by two distances. Biangular coordinates, first written about in 1803 in France, were subsequently studied in Britain at the end of the…

Descriptors: Geometry, College Mathematics, Mathematics Instruction, Geometric Concepts

Barbanel, Julius B.; Brams, Steven J. – College Mathematics Journal, 2011

Barbanel, Brams, and Stromquist (in 2009) asked whether there exists a two-person moving-knife procedure that yields an envy-free, undominated, and equitable division of a pie. We present two procedures: One yields an envy-free, almost undominated, and almost equitable allocation, whereas the second yields an allocation with the two "almost"…

Descriptors: Mathematics Education, Arithmetic, College Mathematics, Mathematics Instruction

Morrison, Kent – College Mathematics Journal, 2010

The original shipping strategy of FedEx was to fly all packages to a hub during the afternoon and evening, sort them there, and then fly them to their destinations overnight for delivery the next day. This leads to interesting mathematical questions: Given a population represented by points in Euclidean space or on a sphere, what is the location…

Descriptors: Census Figures, Population Trends, Mathematics Instruction, Problem Solving

Greer, Meredith L.; Ewing, Holly A.; Cottingham, Kathryn L.; Weathers, Kathleen C. – College Mathematics Journal, 2013

We describe a collaboration between mathematicians and ecologists studying the cyanobacterium "Gloeotrichia echinulata" and its possible role in eutrophication of New England lakes. The mathematics includes compartmental modeling, differential equations, difference equations, and testing models against high-frequency data. The ecology…

Descriptors: College Mathematics, Ecology, Cooperation, Earth Science

Hersh, Reuben – College Mathematics Journal, 2010

"Over-representation" of Jews in the world of mathematics is a common observation, but rarely discussed in print. In response to a new book on the subject by Ioan James, this paper recounts the author's own interaction with Jewish over-representation at universities in the U.S., and also gives information about Hungary and Italy. The…

Descriptors: Mathematics Education, Jews, Foreign Countries, Racial Differences

Chuang, Jer-Chin – College Mathematics Journal, 2009

The "box problem" from introductory calculus seeks to maximize the volume of a tray formed by folding a strictly rectangular sheet from which identical squares have been cut from each corner. In posing such questions, one would like to choose integral side-lengths for the sheet so that the excised squares have rational or integral side-length.…

Descriptors: Calculus, Mathematics Instruction, Mathematical Concepts, Problem Solving

Vis, Timothy; Petersen, Ryan M. – College Mathematics Journal, 2009

A Latin square of order "n" is an "n" x "n" array using n symbols, such that each symbol appears exactly once in each row and column. A set of Latin squares is c ordered pairs of symbols appearing in the cells of the array are distinct. The popular puzzle Sudoku involves Latin squares with n = 9, along with the added condition that each of the 9…

Descriptors: Problem Solving, Mathematics Instruction, College Mathematics, Games