Why do we want to study algorithm design? There are of course many reasons, and our motivation for learning something is very much dependent on our own circumstances. There are without doubt important professional reasons for being interested in algorithm design. Algorithms are the foundations of all computing. We think of a computer as being a piece of hardware, a hard drive, memory chips, processors, and so on. However, the essential component, the thing that, if missing, would render modern technology impossible, is algorithms.

The theoretical foundation of algorithms, in the form of the Turing machine, was established several decades before digital logic circuits could actually implement such a machine. The Turing machine is essentially a mathematical model that, using a predefined set of rules, translates a set of inputs into a set of outputs...