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)

Shortcuts to use when performing operations with the calculator are given. Algorithms discussed include reciprocals, powers, parentheses, infinite series, and synthetic division. (MP)

Solutions to difficult equations are illustrated with numerical techniques that can be used easily on calculators. Flowcharts and programs for computers and calculators are included. (MP)

Topics covered include alternate methods for finding LCM and GCF, imaginative word problems, and a primes-breakdown method of factoring quadratics. (MP)

The algorithms for finding cube roots is approached by slicing a cube. (SD)

Variations on a card trick are noted, with a formula for generalizing them. Another trick which can be proved with algebraic principles is then presented. (MNS)

Activities are described in which number patterns in two-digit multiplication exercises are investigated. (DT)

Suggestions are given for having students write or modify computer programs for listing prime positive integers and continued fractions, to help them discover mathematical concepts. Sample programs are included. (MNS)

Described is a learning activity that requires students to write a manual to explain how to apply procedures and algorithms used in mathematics. A list of possible precalculus and calculus topics that can be used in this activity is included. (KR)