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

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 general algorithm used in most hand calculators to approximate elementary functions is discussed. Comments on tabular function values and on computer function evaluation are given first; then the CORDIC (Coordinate Rotation Digital Computer) scheme is described. (MNS)

Described are ways that errors of magnitude can be unwittingly caused when using various supercalculator algorithms to solve linear systems of equations that are represented by nearly singular matrices. Precautionary measures for the unwary student are included. (JJK)

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)

How to use the electronic spreadsheet (e.g., VisiCalc) creatively is discussed, with computer printouts for a number of algorithms. (MNS)

Growth functions involved in mathematical models for biological development are discussed using the algebra of polynomials and matrices. (SD)

Provides several algorithms that use extended precision methods to compute large factorials exactly. The programs are written in BASIC and PASCAL. The approach used for computing N considers how large N is, how the built-in limitation on exact integer representation can be bypassed, and how long it takes to compute N. (JN)

The forum is focused on thinking about and with algorithms as a way of unifying all one's mathematical endeavors. The lead article by Maurer presents examples and discussion of this point. Responses, often disagreeing with his views, are by Douglas, Korte, Hilton, Renz, Smorynski, Hammersley, and Halmos. (MNS)

The Euclidean algorithm for finding the greatest common divisor is presented. (MNS)

Presents a theorem and its converse to generate all of the primitive Pythagorean quadruples. Provides a BASIC program generating them. (YP)

Discusses a numerical technique called the method of adjoints, turning a linear two-point boundary value problem into an initial value problem. Described are steps for using the method in linear or nonlinear systems. Applies the technique to solve a simple pendulum problem. Lists 15 references. (YP)

Algorithms are developed and presented for the addition and multiplication of positive rational numbers using only their repeating decimal representation. (MN)