1 - Algorithms and Computers

Summary

Introduction

Discussing algorithms before computers emphasizes the point that algorithms are valuable mathematical constructs in themselves and exist even in the absence of computers. An algorithm is a list of instructions for the completion of a task. The best examples of algorithms in everyday life are cooking recipes, which specify how a list of ingredients are to be manipulated to produce a desired result. For example, consider the somewhat trivial recipe for cooking a three-minute egg. The recipe (or algorithm) for such a task exemplifies the need to take nothing for granted in the list of instructions.

Algorithm Three-Minute Egg

Put water in a pan.

Turn on the heat.

When the water boils, flip over the egg timer.

When the timer has run out, turn off the heat.

Pour some cold water in the pan to cool the water.

Remove egg.

Although this algorithm may appear trivial to most readers, detailed examination further emphasizes (or belabors) how clear and unambiguous an algorithm must be. First, the receiver of these instructions, call it the actor, must recognize all of the jargon of food preparation: water, pan, egg, egg timer, boil, and so forth. The actor must recognize constructions: “put ____ in ____”; “when ____, do ____.” Some parts of these instructions are unnecessary: “to cool the water.” If the actor is an adult who understands English, this may be a fine algorithm. To continue to belabor the point, the actor can only do what the instructions say.