Generating functions for the columns in Pascal's triangle are constructed through algebraic and geometric interpretations. (JT)

The use of a synthetic division microcomputer program in searching for the zeros in polynomial functions is described. A program listing and outputs are included. (MNS)

Programs are listed for integer powers and fractional powers, with discussion of how to use them in instruction. (MNS)

An activity with non-Euclidean geometry, a worksheet with a device based on geometric principles, and a diagram presenting a geometric view of the geometric series are each briefly presented. (MNS)

Two models are presented that can be understood by students who have completed second-year algebra, as well as by calculus students. The predator-prey population model and the arms race model are included, with a computer program given for each. (MNS)

Factorials are discussed, with note of the enormous size on n! even for modest values of n. A recreational problem to determine the number of zeros at the end of numbers such as 10,000! is given, with a computer program. (MNS)

Ways are suggested in which economists and applied mathematicians construct and use models to study the economy. Several models are developed, each accompanied by a BASIC computer program to test its assumptions. (DT)

Examples, exercises, and solutions involving compound growth are contributed that emphasize the areas of lending, borrowing, and investing. It is felt these areas present a wealth of opportunities for mathematical modeling, the development of algorithms, and practical applications, and can be fully explored throughout typical secondary…

The use of exercises that students can perform independently of any calculating aids and in a reasonably brief space of time is promoted, so that pupils can concentrate on the processes involved and any relationships of interest. Some examples are presented with the goal of increasing learning promoted. (MP)

Problems involving multicolored cubes are discussed with examples of Instant Insanity and Rubik's Cube cited. Sections cover defining chameleonic cubes, producing such a cube, and extending understanding to multidimensional cubes. One theorem proved is that for each positive integer, every cube of that size is chameleonic. (MP)

Teachers are encouraged to have pupils examine the symmetry of crystals when instruction is given on three-dimensional geometry and polyhedra. Crystals are noted to provide students with three-dimensional applications of transformational geometry, and the pupils also learn mineral identification. Suppliers of mineral models and specimens are…

A problem that is seen to allow room for student discovery and exploration is detailed. A discussion starts with an examination of the generation of a general equation for the sum of a set of consecutive integers, and leads to an exploration of more complex sums. (MP)

Three ideas are presented: (1) using a detective story format in problem-solving activities; (2) the mathematics of modern trademarks which express a variety of mathematical ideas; and (3) an approach to the proof of the mean-value theorem that examines the problem geometrically. (MP)

Requiring college mathematics students to write papers as an integral component of a standard mathematics course is promoted. (MP)