Describes a number sequence made by counting the occurrence of each digit from 9 to 0, catenating this count with the digit, and joining these numeric strings to form a new term. Presents a computer-aided proof and an analytic proof of the sequence; compares these two methods of proof. (YP)

Describes a five-step graphing method for various trigonometric periodic functions. Emphases is on teaching constants and functions. (YP)

Discusses a calculation method to approximate pi. Describes how to get an approximation to the circumscribed and inscribed perimeters of regular polygons of n sides. Presents the computer program and result of the approximation. (YP)

The problem of finding all topological spaces is considered. Two characterizations are presented whose proofs involve only elementary notions and techniques. The problem is appropriate for students in a beginning topology course after they have been presented with the Embedding Lemma. (DC)

Provides an overview of a course, "Applied Linear Algebra," for teaching the concepts and the physical and geometric interpretations of some linear algebra topics. Describes the philosophy of the course, the computer project assignments, and student feedback. Major topics of the course are listed. (YP)

Provided are examples from many domains of mathematics that illustrate the Fubini Principle in its discrete version: the value of a summation over a rectangular array is independent of the order of summation. Included are: counting using partitions as in proof by pictures, combinatorial arguments, indirect counting as in the inclusion-exclusion…

The discrete mathematics topics of trees and computational complexity are implemented in a simple reliability program which illustrates the process advantages of the PASCAL programing language. The discussion focuses on the impact that reliability research can provide in assessment of the risks found in complex technological ventures. (Author/JJK)

Described are ways that specific concepts from abstract algebra can be programed using the software package features of the Ada Programming Language, which is the primary language of the Department of Defense. Included are typical programs with their respective outputs. (JJK)

Discussed are the geometric patterns formed when two geometric patterns are superimposed. General moire fringes, circular and line gratings, physical applications, and projects for students are described. (CW)

This paper presents an assessment tool which can be used during the first weeks of calculus to measure students' visual thinking skills. We have developed and applied this instrument in classes for the last three years, tabulating results and interviewing students on a regular basis. We discuss our findings and provide hints to using the…

In 1750, the Swiss mathematician Gabriel Cramer published a well-written algebra book entitled "Introduction a l'Analyse des Lignes Courbes Algebriques." In the appendix to this book, Cramer gave, without proof, the rule named after him for solving a linear system of equations using determinants (Kosinki, 2001). Since then several derivations of…

The mathematical reasons that we cannot divide by zero are not easy for most students to understand; in fact, even those students who have more than just a basic understanding of algebraic concepts still have difficulty. This is most problematic for college students who are prospective teachers since they need to develop a deep understanding of…

Simple examples are really encouraging in the understanding of rearrangements of infinite series, since many texts and teachers provide only existence theorems. In the absence of examples, an existence theorem is just a statement and lends little confidence to understanding. Iterated sums of double series seem to have a similar spirit of…

This paper compliments two recent articles by the author in this journal concerning solving the forced harmonic oscillator equation when the forcing is periodic. The idea is to replace the forcing function by its Fourier series and solve the differential equation term-by-term. Herein the convergence of such series solutions is investigated when…

What people mean by randomness should be taken into account when teaching statistical inference. This experiment explored subjective beliefs about randomness and probability through two successive tasks. Subjects were asked to categorize 16 familiar items: 8 real items from everyday life experiences, and 8 stochastic items involving a repeatable…