A few examples are discussed of situations where some solution to writing a computer program for an algorithmic problem is immediately evident, but the best solution is some distance away. (MP)

The calculator is used to solve certain formidable equations, which arise naturally and which may be difficult or impossible to solve by standard methods, by a method of successive approximations. (MP)

A possible method of derivation of prescriptions for solving problems, found in Babylonian cuneiform texts, is presented. It is a kind of "geometric algebra" based mainly on one figure and the manipulation of or within various areas and segments. (MNS)

Mathematical models that are used to solve facility location problems are presented. All involve minimizing some distance function. (MNS)

Algorithms to determine the optimal locations of emergency service centers in a given city are presented, with theorems and proofs. (MNS)

The problem of finding cube roots when limited to a calculator with only square root capability is discussed. An algorithm is demonstrated and explained which should always produce a good approximation within a few iterations. (MP)

One difficulty that mathematically naive subjects encounter in solving arithmetic word problems involves the limitation on short term memory (STM) capacity. It is hypothesized that naive subjects, not having access to formal problem solving strategies, may find visualization useful in reducing strain on STM. Two experiments are reported. The…

Three teaching ideas are presented: how to present changes between scientific notation and decimal form that eliminate some student confusion; an analysis of an incorrect algebra equation that produced a correct answer; and aspects of a standard calculus problem dealing with minimum and maximum values. (MP)

When problems defy solution, mathematicians can settle for "almost." This branch of mathematics (called computational complexity) encompasses both the number of parts involved in a problem and the intricacy of their interrelatedness. Current research in this area is discussed, considering various computer applications involved. (JN)

A procedure for constructing a magic cube is presented, with related teaching activities appropriate for students familiar or unfamiliar with the algorithm covered. (MP)

This document contains two units that examine integral transforms and series expansions. In the first module, the user is expected to learn how to use the unified method presented to obtain Laplace transforms, Fourier transforms, complex Fourier series, real Fourier series, and half-range sine series for given piecewise continuous functions. In…

A method for teaching students to solve complex algebraic equations is described. The method, which relies on sequentially reducing the complexity of the problem has been successfully used with secondary students and in remedial college courses. (SD)

An unusual alternative starting point for instruction in a beginning calculus course that focuses on Fixed Point Iteration (FPI) is presented. (MP)

The role of the computer in coordinating the activities surrounding five modes of mathematics instruction is discussed. The modes are: computer-assisted instruction, computer-managed instruction, computer-based simulations, algorithmic exercise solving, and computer-aided problem solving. (MP)

Provides a short list of integral triples for the design of problems employing unit fractions (so solutions will be positive integers). Also presents an algorithm whereby both primary and imprimitive sets of triples can be easily obtained and shows how to extend the algorithm to solve three-variate unit fraction equations. (JN)