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This Chapter presents a brief introduction to the study of algorithms, which are described from first-principles as formal sets of directions which describe how to perform a task. The goal is to demonstrate that algorithms are fundamental tools in Computer Science, but, on the other hand, no more complicated than a set of driving directions or cookery instructions.
A running example, namely the task of exponentiation (or powering) of one number by another, is used throughout; similar arithmetic is used within cryptographic schemes studied in later Chapters. By analysing how different algorithms for exponentiation behave, the Chapter shows we can compare them fairly against each other. Ultimately, this means we can select the most efficient algorithm for a given task.
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