The discrete Fourier series is a valuable tool developed and used by mathematicians and engineers alike. One of the most prominent applications is signal processing. Usually, it is important that the signals be transmitted fast, for example, when transmitting images over large distances such as between the moon and the earth or when generating…

An examination problem and solution gives rise to the question of whether there actually exists a theorem concerning the minimal period of the sum of certain periodic functions. The author discusses such a theorem and uses the situation to support mathematical education as opposed to the teaching of mathematics. (MN)

In this pedagogical article, I explore a unified approach in obtaining the derivatives of functions and their inverses by adopting a guided self-discovery approach. I begin by finding the derivative of the exponential functions and the derivative of their inverses, the logarithmic functions. I extend this approach to generate formulae for the…

The authors draw together a variety of facts concerning a nonlinear differential equation and compare the exact solution with approximate solutions. Then they provide an expository introduction to the elliptic sine function suitable for presentation in undergraduate courses on differential equations. (MNS)

An old way to determine asymptotes for curves described in polar coordinates is presented. Practice in solving trigonometric equations, in differentiation, and in calculating limits is involved. (MNS)

Some concrete examples of the use of historical materials in developing certain topics from precalculus and calculus are presented. Ideas which can be introduced with a reformulated curriculum are discussed in five areas: algorithms, combinatorics, logarithms, trigonometry, and mathematical models. (MNS)

Discusses solutions to the problem of maximizing the range of a projectile. Presents three references that solve the problem with and without the use of calculus. Offers a fourth solution suitable for introductory physics courses that relies more on trigonometry and the geometry of the problem. (MDH)

This quantitative-qualitative study seeks to determine the effectiveness of TIMS (Thomasian Interactive Multimedia Software) in teaching the introductory topics in Trigonometry. The acceptability of the software to the student respondents was established using the content, design, interface, and effectiveness of the media used as the evaluation…

The instructional strategy described was used to incorporate both the computer and the hand calculator into trigonometry courses at an Ohio community college. The computer was used to generate different problem sets for individual students and, at the same time, solution sets for the instructor. The students were required to use calculators to…

Among teachers of mathematics throughout the world there has recently been manifested a notable increase of interest in all educational work. This interest is due in part to the present general agitation in every educational line, in part to the influence of such related departments as physics, in part to the increased demands of industry, and in…

This article, which is organized around a single, well-known algorithm for root extraction, presents a way of incorporating dynamical systems into the teaching of mathematics. Included are sample exercises using complex numbers and the computer where students have the opportunity to do some analysis on this algorithm. (KR)

Brief articles are included on exploring mathematical patterns, with two computer programs listed for finding happy numbers; a simple periodic function in trigonometry; and comments on humorous student errors. (MNS)