Aho, Hopcroft, UllmanのData Structures and Algorithm の１章にこうあるよ。
日本語訳の本もでてるとおもうが。

Algorithms
Once we have a suitable mathematical model for our problem, we can attempt to find
a solution in terms of that model. Our initial goal is to find a solution in the form of an
algorithm, which is a finite sequence of instructions, each of which has a clear meaning
and can be performed with a finite amount of effort in a finite length of time. An integer
assignment statement such as x := y + z is an example of an instruction that can be
executed in a finite amount of effort. In an algorithm instructions can be executed any
number of times, provided the instructions themselves indicate the repetition. However,
we require that, no matter what the input values may be, an algorithm terminate after
executing a finite number of instructions. Thus, a program is an algorithm as long as
it never enters an infinite loop on any input.