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)

A method for solving inequalities of degree greater than one is described. (MK)

Circuits are described, with discussion on how to help students find the algorithms to solve a variety of problems involving circuits. (MNS)

How set theory, combinatorics, probability, and the study of algorithms can be used in solving two problems is described in detail. Three computer programs are listed. (MNS)

A generalized method of synthetic division where the divisor polynomial may be of any degree equal to or larger than 1, and the dividend polynomial may be of equal or larger degree than the divisor polynomial and a generalization of the familiar remainder theorem, are presented. (Author/MK)

Describes a calculator exercise that can help students develop a better visual and numeric feel for Newton's method. (KHR)

The article presents a general test for divisibility that includes composite numbers and shows that such a test can be used to determine divisibility by several numbers simultaneously. (MK)

An algorithm for multiplying natural numbers is described. The algorithm provides a chance for some unusual drill and might serve as an enrichment topic. (MK)

Described is a simple algorithm that can be used for the input, arithmetic manipulation, and output of large integers in their exact representations. Three BASIC programs are included that apply this method to the problem of multiplication of large integers, computation of factorials, and the generation of palindromic integers. (MNS)

The following ideas are shared: (1) a low-stress subtraction algorithm that eliminates the traditional borrowing process, and (2) an approach to graphing circular functions that looks at the process of modifying simple functions as a series of shifting, sliding, and stretching adjustments, with its biggest advantage viewed as its generality. (MP)

The first section promotes use of student notebooks in mathematics instruction as incentives for pupils to do daily work. Part two looks at a geometric interpretation of the Euclidean algorithm. The final section examines an open box problem that is thought to appear in virtually every elementary calculus book. (MP)

Several subtraction algorithms are analyzed to see if they involve borrowing. The main focus is on an analysis of a procedure called the residue method. The operational arithmetic which underlies the symbolic manipulations is examined and conditions where the method does and does not use borrowing are highlighted. (MP)

An unusual algorithm for approximating square roots is presented and investigated using techniques common in algebra. The material is presented as a tool to interest high school students in the logic behind mathematics. (MP)

A method is presented for determining cube roots on a calculator with square root facility that has a rapid rate of convergence. (MP)

The game of Yahtzee is discussed in terms of the various outcomes of turns in the game and their point values and the probabilities associated with achieving specific combinations of dice values. Several tables and methods of table construction are noted, and several challenge exercises are included. (MP)