This course is about computing. The notion of computing is much more fundamental than the notion of a computer, because computing can be done even without one.
In fact, we have been computing ever since we entered primary school, mainly using pencil and paper. Since then, we have been adding, subtracting, multiplying, dividing, computing lengths, areas, volumes and many many other things. In all these computations we follow some definite, unambiguous set of rules. This course is about studying these rules for a variety of problems and writing them down explicitly. When we explicitly write down the rules (or instructions) for solving a given computing problem, we call it an algorithm. Thus algorithms are primarily vehicles for communication; for specifying solutions to computational problems, unambiguously, so that others (or even computers) can understand the solutions. When an algorithm is written according to a particular syntax of a language which can be interpreted by a digital computer, we call it a program. This last step is necessary when we wish to carry out our computations using a computer.