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

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)

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)

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)

A program for drawing a line segment is developed. (MNS)

An efficient division algorithm is developed, using a computer program, to convert any positive fraction to its decimal representation. The computer program listing is included. (MNS)

This article develops an algorithm to find all solutions to the problem, making all sums of a hexagram's nine lines the same. It shows how to exploit the geometric structure of the hexagram and its group of automorphisms. (YP)

The rule of 78 is used by banks and loan companies to compute the amounts due when installment loans are paid early. Describes an unexpected case of negative amortization when the rule is applied. Presents an actual problem and discusses the case. (YP)

Presents the algorithm to approximate square roots as reproduced from the 1579 edition of an algebra book by Rafael Bombelli. The sequence of activities illustrates that the process of understanding an original source of mathematics, first at the algorithmic level and then with respect to its mathematical validity in modern terms, can be an…

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)

Presents an example using a computer to illustrate concepts graphically in an introductory course on differential equations. Discusses the algorithms of the computer program displaying the solutions to an equation and the inclination field of the equation. (YP)