Like many mathematics teachers, the authors often find that students who struggle with a difficult concept may be assisted by the use of a well-chosen graph or other visual representation. While one should not rely solely on such tools, they can suggest possible theorems which then might be proved with the proper rigor. Even when a picture…

A generally-educated individual should have some insight into how decisions are made in the very wide range of fields that employ statistical and probabilistic reasoning. Also, students of introductory probability and statistics are often best motivated by specific applications rather than by theory and mathematical development, because most…

The number Pi has a rich and colorful history. The origin of Pi dates back to when Greek mathematicians realized that the ratio of the circumference to the diameter is the same for all circles. One is most familiar with many of its applications to geometry, analysis, probability, and number theory. This paper demonstrates several examples of how…

This brief investigation exemplifies such considerations by relating concepts from number theory, set theory, probability, logic, and calculus. Satisfying the call for students to acquire skills in estimation, the following technique allows one to "immediately estimate" whether or not a number is prime. (MM)

Presents several theoretical solutions to a geometry problem involving circles and probability. Includes simulation procedures to estimate the solutions. (MKR)

Decribes a variation on Bingo that provides a non-routine probability investigation through which students develop concepts of chance. (Author/CCM)

The rapid rate of expansion of the disciplines of biotechnology, genomics, and bioinformatics emphasizes the increased interdependency between computer science and biology, with mathematics serving as the bridge between these disciplines. This paper demonstrates this inter-relationship within the context of a computational model for a biological…

Advantages and disadvantages of common ways to justify the answer to a probability problem are discussed. One explanation appears superior to the others because it is easy to understand, mathematically rigorous, generalizes to a broader class of problems, and avoids the deficiencies of the other explanations. (MNS)

Determines the theoretical probability that a regular polygon will cross a crack when dropped onto floorboards. By following two special cases, a pattern emerges that enables students to consider the general case. (ASK)

Explains a non-standard definition of an ellipse familiar to astronomers and workers in celestial mechanics but which is not usually given in undergraduate text books on mathematics. (MM)

As part of a discussion on Monte Carlo methods, which outlines how to use probability expectations to approximate the value of a definite integral. The purpose of this paper is to elaborate on this technique and then to show several examples using visual basic as a programming tool. It is an interesting method because it combines two branches of…

One way in which a computer simulation can convince students of the validity of formulas for the density and distributive functions of the sum of two variables is described. Four computer program listings are included. (MNS)

An exercise simulating the tossing of N dice is described. Calculation of expected gain and extension to a two-person game are each discussed. (MNS)

Three computer programs are listed for finding binomial probabilities. Other applications and variations are discussed. (MNS)

Presents an example from probability and statistics that ties together several topics including the mean and variance of a discrete random variable, the binomial distribution and its particular mean and variance, the sum of independent random variables, the mean and variance of the sum, and the central limit theorem. Uses Excel to illustrate these…