A few examples are discussed of situations where some solution to writing a computer program for an algorithmic problem is immediately evident, but the best solution is some distance away. (MP)

This investigation concerns the repeated application of the rule "take the sum of the squares of the digits." (MP)

A test for divisibility by any prime number is discussed and its proof is given. (MP)

Comparisons are made between the errors obtained when approximating the integral with the midpoint rule, the trapezoidal rule, and Simpson's rule. (MP)

The problem of rounded numbers used in computations on digital computers is discussed and examples showing the effect of round-off errors are given. (DT)

Two algorithms are developed for finding the square roots of numbers. One is based on the rule that x square is the sum of the first x odd numbers; the other is algebraic. (MP)

The method described here converts a given problem in a base other than ten to a related problem in base ten, solves the related problem in base ten, and converts the answer back to the original base. Limitations are discussed. (MP)

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

Algorithms are developed and presented for the addition and multiplication of positive rational numbers using only their repeating decimal representation. (MN)

Several algorithms for solving initial value differential equation problems using the definitions of derivative and integral and a computer are discussed. (MN)