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Subhashis Banerjee wrote:Copyright (C) 1997-2003, Subhashis Banerjee and S. Arun-Kumar. All Rights Reserved. These notes may be used in an academic course with the prior consent of the authors.

Notes Summary:

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.

While writing down algorithms, it is important to choose an underlying model of computation, i.e., to choose appropriate primitives to describe an algorithm. This choice determines the kind of computations that can be carried out in the model.

With each of these models of computing, the rules for specifying a solution (algorithms) are different, and the precision of the solution also differs. Thus, in our study of algorithms and programs, it becomes important to first choose a reasonable model of computation. In these notes we will describe our choice of computational models which are widely used in modern computing using digital computers.

Once a computational model in available, and we can specify an algorithm (or a program) to solve a given problem, we have to ensure that the algorithm is correct. We would also wish that our algorithms are efficient. Correctness and efficiency of algorithm design are central issues in this course. In these notes, we will endeavour to develop methodologies for the design of correct algorithms.