The graph of this function is analyzed by using calculus methods and the computer. The graph in most texts is shown to be misleading. (MP)

Discussed is the problem of finding the volume common to two intersecting right circular cylinders. (MP)

Comparisons are made between the errors obtained when approximating the integral with the midpoint rule, the trapezoidal rule, and Simpson's rule. (MP)

It is advocated that introductory calculus texts should present topics in a manner that is understandable to students without necessarily sacrificing rigour. Illustrative examples are given of a conversational approach to problem solving. (Author/MN)

Ten recent results in pure mathematics are described, covering the continuum hypothesis, Diophantine equations, simple groups, resolution of singularities, Weil conjectures, Lie groups, Poincare conjecture, exotic spheres, differential equations, and the index theorem. Proofs are omitted, but references are provided. (DT)

A simple geometric construction giving acceptable approximations to the locations of twelve points for placing frets on a guitar is described both geometrically and analytically. (DT)

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)

About half of the half-million students taking the introductory college calculus course each year fail. Some ways to change the course and the way it is taught were discussed at a conference attended by 25 persons. (MNS)

Misconceptions which students have about the convergence of an alternating series are identified, and counterexamples are provided for each of the misconceptions. (DT)

Properties of solids generated by the rotation of some of the well-known solids about given axes are discussed. (DT)

Examples are given of difficulties that students have in determining extrema of real-valued functions of real variables. (DT)

An example is given of an application of calculus to biology in which a straightforward mechanical approach leads to a difficult situation, but the theory of beginning calculus leads quickly to a solution. (Author/DT)

Three modes of instruction were compared: regular classroom instruction, self-paced, and self-paced plus tutor. Results showed that in an introductory basic concepts of mathematics course, the two self-pacing methods were superior to the regular instruction, while in a calculus course the results were not as clear-cut. (DT)

This study compared a traditionally-taught calculus course with a self-paced one. Based on performance on a common final examination, students in the self-paced course did substantially better than those in the traditional course. (DT)

Many colleges and universities use a mathematics placement process to guide students to the appropriate entry-level mathematics course. The mathematics placement process presented here was developed over a four year period to make placement recommendations to Calculus I, Precalculus, and College Algebra. Placement recommendations are based on the…