Reproduce it in class.

Twenty or more years ago the word "algorithm" was unknown to most educated people; indeed, it was scarcely necessary. The rapid rise of computer science, which has the study of algorithms as its focal point has changed all that; the word is now essential. There are some other words that almost, but not quite, capture the concept that is needed: procedure, recipe, process, routine, method. Like these things an algorithm is a set of rules or directions (instructions) for getting a specific output from a specific input. The distinguishing feature of an algorithm is that all vagueness must be eliminat­ed; the rules must describe operations that are so simple and well-defined that they can be executed by a machine. Furthermore, an algorithm must always terminate after a finite number of steps.

A computer program is the statement of an algorithm in some well-defined language, although the algorithm itself is a mental concept that exists inde­pendently of any representation. Anyone who has prepared a computer pro­gram will appreciate the fact that an algorithm must be very precisely defined, with attention to detail that is unusual in comparison with other things people do. Programs for numerical problems were written as early as 1800 B.C. when Babylonian mathematicians gave rules for solving many types of equations. The rules were as step-by-step procedures applied systematically to particular numerical examples. The word "algorithm" itself originated in the Middle East, although at a much later time. Curiously enough it comes from the Latin version of the last name of the Persian scholar Abu Jafar Mohammed ibn Musa al-Khowaresmi (Algorithmi) whose textbook on arithmetic (c. 825 A.D.) employed for the first time Hindu positional decimal notation and gave birth to algebra as an independent branch of maths. It was translated into Latin in the 12^th century and had a great influence for many centuries on the develop­ment of computing procedures. The name of the textbook's author became associated with computations in general and used as a term "algorithm".

Originally algorithms were concerned solely with numerical calculations; Euclid's algorithm for finding the greatest common divisor of two numbers – is the best illustration. There are many properties of Euclid's powerful algorithm which has become a basic tool in modem algebra and number the­ory. Nowadays the concept of an algorithm is one of the most fundamental notions not only in maths but in science and engineering. Experience with computers has shown that the data manipulated by programs can represent virtually anything. In all branches of maths the task to prove the solvability or unsolvability of any problem requires a precise algorithm. In computer science the emphasis has now shifted to the study of various structures by which information can be represented and to the branching or decision-making aspects of algorithms, which allow them to fall on one or another sequence of operations depending on the state of affairs at the time. It is precisely these features of algorithms that sometimes make algorithmic models more suitable than traditional math models for the representation and organization of knowledge.

Although numerical algorithms certainly have many interesting features, there are non-numerical ones and, in fact, algorithms in cybernetics deal primarily with manipulation of symbols that need not represent numbers. Algorithm-designing is both pure and applied branches of cybernetics. Current algorithms are becoming more and more refined and sophisticated. Algorithms for searching information stored in a computer's memory, such as sequential search, binary search, Tree search, etc., may illustrate several important points about algorithms in general: an algorithm must be stated precisely and it is not an easy task to do that as one may think. When one tries to solve a problem by computer, the first algorithm that comes to mind can usually be greatly improved. Data structures such as optimum-binary-search tree are important tools for the construction of efficient algorithms. When one starts to investigate how fast an algorithm is or when one attempts to find the best possible algorithm for a specific application, interesting issues arise and one often finds that such questions have subtle answers. Even the "best possible" algorithm can sometimes be improved if we change the ground rules. Since computers "think" differently from people, methods that work well for the human mind are not necessarily the most efficient when they are transferred to a machine.