According to its defintions, in mathematics and computer science an algorithm is a set of rules for solving a problem in a finite number of steps as for finding the greatest common divisor. In other words, an algorithm is an effective method to get an initial state or an initial input, to compute that value (or values) through a step-by-step procedure to obtain a finite number of well defined states and, finally, to produce an output and terminating to get a final ending state.
From a mathematician’s point of view, an algorithm is a specific and logical procedure that has to be followed in order to solve a given math problem. An example of a very basic algorithm is multiplying two 5 digit numbers – try to do it yourself by hand, using a pencil, a piece of paper and the specific algorithm.