When a two-dimensional (2D) traveling salesman problem (TSP) is presented on a computer screen, human subjects can produce near-optimal tours in linear time. In this study we tested human performance on a real and virtual floor, as well as in a three-dimensional (3D) virtual space. Human performance on the real floor is as good as that on a…

Nonroutine function tasks are more challenging than most typical high school mathematics tasks. Nonroutine tasks encourage students to expand their thinking about functions and their approaches to problem solving. As a result, they gain greater appreciation for the power of multiple representations and a richer understanding of functions. This…

This bibliography presents a series of studies that focus on the topic of networks and on the manner in which they have been considered in the literature. Each section of the bibliography provides a working set of references for one of the five major areas of research in which network analysis has been used. The first section deals primarily with…

Some applications of mathematics to bicycle gearing, speedometers, and bicycle braking are discussed. A method of calculating bicycle speed is developed. (MP)

Nine examples of this principle show what a powerful tool it is. Several map coloring theorems are proven and some exercises are listed. (MP)

Part I reviews the mathematical definition of function, and then presents some practical uses of functions in such areas as substitution in a formula, equation solving, and curve fitting. Part II gives examples of functions that can be used to describe some real life situations. (RP)

An actual application of linear graphs is described. (MM)

Four different types of problems from graph theory are presented and discussed. (MK)

As part of their teacher training course, graduate students visited several industries to find what mathematics was in use. (MM)

A discussion of the relation between traffic density, speed and flow, used as an illustration of the ideas of functions and mathematical models. (MM)

The various roles and uses of mathematics in developing global awareness in students are considered. Mathematics as a unifier of human experience and problem solving with a global emphasis are discussed with many illustrative examples. (MNS)

There are many problems that can be translated into the language of graph theory. Such a problem, discussed in this article is to show that in any group of two or more people, there are at least two people who have the same number of acquaintances in the group. (PK)