Before primitive man had grasped the concept of number, the written word or even speech, he was able to count. This was important for keeping track of food supplies, sending messages, trading between villages and even keeping track of how many animals were in their herd. Counting was done in various ways, but in all cases, the underlying principle…

Investigating the relationship between fractions and their equivalent decimal representations helps clarify to students that both representations stand for a single (rational) number on the number line. Since students are taught to perform computations with fractions and also to compute with decimals, performing these computations side-by-side…

If the point of suspension of a multiple pendulum is suitably oscillated then the pendulum can remain in motion in an upside-down position. Since such pendulums can model flexible materials, this inverted motion is sometimes referred to as an 'Indian rope trick'. Despite the complexity of the governing differential equations, this rope trick can…

The telescoping sum constitutes a powerful technique for summing series. In this note, this technique is illustrated by a series of problems starting off with some simple ones in arithmetic, then some in trigonometry, famous families of numbers, Apery-like formulas, and finally ending with a class of problems that are solved by computer.

Hidden Markov models (HMMs) are widely used in bioinformatics, speech recognition and many other areas. This note presents HMMs via the framework of classical Markov chain models. A simple example is given to illustrate the model. An estimation method for the transition probabilities of the hidden states is also discussed.

In this note the well-known Lagrange identity is extended to matrices. The resulting generalized Lagrange identity is used to give characterizations of symmetry, commutativity of projectors and normality.

The mean and variance of the number of turning points in random permutations of two kinds of distinct elements are evaluated. These results are applied to a Wald-Wolfowitz run test.

Research indicates that children do not typically understand the connection between counting and cardinality for several months after learning to count, yet parents speak to 3-year-olds as though they already understood the significance of counting. The present research was designed to investigate mothers' awareness of the discrepancy between…

The self-weighted mean ("WS')--in which each value is weighted by itself--is presented in several contexts and illustrated. It is incorporated in a set of more familiar means. Intuitions concerning "WS" are explored.

This article defines the generalized mean and shows how it relates to such statistics as the arithmetic, geometric and harmonic means.

This article describes the most compact 100c% interval for a probability density for 0

Descriptors: Probability, Computation, Mathematical Concepts, Statistics