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)

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)

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)

A traveling salesman problem is used to illustrate the key idea in a general proof of a reduction technique. It is reduced to a problem in propositional calculus. (MNS)

This article provides three examples from elementary calculus concerning the use of the long ago popular method of parametric differentiation as an alternative form of solution. Included are a partial fraction decomposition, an indefinite integral solution, and an integration by parts. (JJK)

This paper is a report on experimental courses in calculus and linear algebra which have been given for the past three years at Swarthmore College. Computing is used to represent the ideas and concepts of calculus and linear algebra and to facilitate their analysis and exploration. APL is used as the notation. (MN)

The overwhelming tendency of textbooks to ignore the midpoint-rectangle method of approximating a definite integral is noted. Examples are given, with stress on the accuracy of the method. (MNS)

Graphic displays of elliptic, parabolic, and hyperbolic surfaces can be generated by computers. (SD)

When students were given calculus instruction based on the nonstandard defintion of limit, achievement was comparable to that of a control group using regular text materials. Attitudes of teachers regarding the use of the nonstandard approach are reported. (SD)

A general method is given for determining an efficient problem-solving process for a given type problem. An application of the method is then described in an experiment involving teaching indefinite integration. (MP)

A college course is described in which mathematics was taught through the perspective of historical development. Readings for the course and synopses of lectures are included. (DT)

Some of the implications and advantages of an instructional approach using results from the calculus of finite differences and finite sums, both for motivation and as tools leading to applications, are discussed. (MP)