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

Presents recently developed generalizations to the sieve of Eratosthenes, showing the principles underlying these improvements, which increase its efficiency without changing too much of its simplicity. Offers several possibilities to propose good investigations for students to explore, find patterns, and make generalizations. (JRH)

Suggests that algorithms, both traditional and student-invented, are proper objects of study not only as tools for computation, but also for understanding the nature of the operations of arithmetic. (Author/NB)

Describes a lesson on long division using chip trading which follows that algorithm for long division. (MKR)

Examines the relation between the sequence of approximations to the square root of a number and the harmonic, geometric, and arithmetic means using the TI-85 graphing calculator. (MKR)

Reviews the historical use of each of the three algorithms used for subtraction in the United States: (1) the equal additions; (2) the decomposition; and (3) the Austrian method. Discusses the modification to the decomposition algorithm and gives a brief overview of the current status of subtraction algorithms. Contains 12 references. (Author/ASK)

The mathematics associated with division is discussed, working from a theorem for the real division algorithm. Real-world, geometric, and algebraic approaches are discussed, as are related topics. (MNS)

A technique for doing long division without the usual estimation difficulty is presented. It uses multiples of 2 combined with a recording technique. (MNS)

Discusses an algorithm that converts a fraction in simplest form into a terminating decimal and allows students to explore the efficacy and conceptual bases of a mathematical algorithm. (ASK)

Presents a method for solving linear equations involving the use of inverses instead of memorizing rules. (MKR)

Presents an algorithm to compute the critical path in a graph representing a project evaluation research task. Once the algorithm is executed, the last matrix obtained permits the visualization of some important information which leads to the determination of the weight of the critical path. (Author/MM)

Two difficulties that students have in computing with fractions are idenfitied. Then a procedure is described, stressing the identity element, that resolves these difficulties and increases students' understanding and retention. (MNS)

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)

Discusses an algorithm from Vedic mathematics that has similarities to FOIL and the standard algorithm for multiplication. (Author/NB)

This learning activity develops algorithms to ensure that the process of selecting materials is well defined and sound. These procedures require the use of many databases to provide the designer with information such as physical, mechanical, and chemical properties of the materials under consideration. A design brief, student quiz, and five…