Placement tests are rapidly joining the ranks of high-stakes testing and college freshmen are required to take mathematics placement exams to determine their first mathematics course upon entering college. Unfortunately, these exams tend to place students in a lower-level or remedial course. As a result, additional expenses are incurred, degree…

Nonstandard Analysis gives an alternative approach to teaching elementary calculus. This paper hopes to communicate to the reader the ideas of this recent development in mathematics and its implications in teaching undergraduate students. The development of the approach is first briefly traced. Then a method of constructing on ordered field…

Linear ciphers, substitution ciphers, public-key cryptosystems, and trapdoor knapsacks are each discussed. (MNS)

The behavior of certain functions in advanced calculus is discussed, with the mathematics explained. (MNS)

An exhibit at the San Francisco Exploratorium is used to discuss problem solving and illustrate optimization. The solution is discussed in detail. (MNS)

How current calculus textbooks consider the relationship between the tangent line and the derivative are discussed, with three theorems presented. (MNS)

An extension of the integration by parts formula, useful in the classroom for products of three functions, is illustrated with several examples. (MNS)

An interesting graphical interpretation of complex roots is presented, since it is probably unfamiliar to many mathematics teachers. (MNS)

The results of investigations into finite geometries, prompted by questions raised in a course for secondary school mathematics teachers, are presented. The discussion of points, lines, and incidences led to consideration of graphs of second-degree equations in finite projective planes. (MNS)

The behavior of some functions near the point of origin is discussed. Each function oscillates, and as x approaches 0, the oscillations become increasingly more rapid; their behavior near the origin improves with increasing values of n. Examples for a calculus class to consider are given. (MNS)

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)

The purpose of this phenomenological study was to talk to students about their experiences taking introductory statistics. The author met with eleven students individually for four interviews throughout the semester, followed by a member-checking focus group during the last week of classes. One of the most salient themes to emerge was the…

A simple model for how traffic moves around a closed loop of road is introduced. The consequent analysis of the model can be used as an application of techniques taught at first year undergraduate level, and as a motivator to encourage students to think critically about model formulation and interpretation.

Computer simulation provides an effective vehicle for teaching many concepts, especially in probability and statistics. Described is a simulation for the applicability of the t distribution to the estimation of a population mean when the standard deviation of the population is unknown. (MNS)

A model for teaching college remedial mathematics is presented, with information on the background, the development of the model, and the model itself, as well as a discussion of how the model is used. (MNS)