Standard calculus textbooks often include a related rates problem involving light cast onto a straight line by a revolving light source. Mathematical aspects to these problems (both in the solution and in the method by which that solution is obtained) are examined. (JN)

This note presents a simple theorem which explains why the method of undetermined coefficients works in finding a particular solution, both for differential equations and difference equations. (Author)

Given a multiplicative group of nonzero elements with order n, the explicit relationship between the number of cyclic subgroups of order d, which divides n, is used in the proof concerning the cyclic nature of that given multiplicative group. (JJK)

Discusses the teaching of mathematics to engineers in Italy. The four courses (usually taught during the first two years), the role of computers, and related ongoing activities (such as meetings and the suggestion of conducting mathematical research in an engineering environment) are described. (JN)

Learning activities in statistics are described in which data about students in the class are collected and analyzed. (DT)

Presented are solutions to variations of a combinatorics problem from a recent International Mathematics Olympiad. In particular, the matrix algebra solution illustrates an interaction among the undergraduate areas of geometry, combinatorics, linear algebra, and group theory. (JJK)

This column solicits mistakes, fallacies, anomalies, et cetera, that raise interesting mathematical issues and may prove useful to teachers. Included in this issue are yet another proof that zero equals one and a differentiation that yields three equals two. (Author/JJK)

The number theory concepts of perfect, deficient, and abundant numbers are subdivided and then utilized to discuss propositions concerning semiperfect, weird, and integer-perfect numbers. Conjectures about relationships among these latter numbers are suggested as avenues for further investigation. (JJK)

A description is given of a senior seminar in which each student reported on a topic centered around the works of David Hilbert. A brief description of each topic is given as well as a list of references. (MP)

Provides examples to show that parallel coverage of convergence theorems for both series and improper integrals will tend to strengthen each other. Indicates that such coverage should also help students to better understand the concept of asymptote. (JN)

Provides an algorithm for determining the median and quartiles of discrete data sets. Describes the graphical equivalent of the numerical method. (JM)

Discusses the factoring of polynomials and Fibonacci numbers, offering several challenges teachers can give students. For example, they can give students a polynomial containing large numbers and challenge them to factor it. (JN)

Discusses insufficiency of the linear method and some informal practices (or heuristics) used by expositors in trying to alleviate it. Uses the Cantor-Bernstein theorem to illustrate the linear proof, structuring, and the structure proof. Argues that the informal practices considered be consistently applied to the presentation of pivots and…

A computer program is given to simulate the operation of the Galton quincunx, a device to approximate a normal distribution. (MNS)

Clarified is the assertion that the so-called complementary function is indeed the general solution of the homogeneous equation associated with a linear nth-order differential equation. Methods to obtain the particular integral, once the complementary function is determined, are illustrated for both cases of constant and of variable coefficients.…