University studies in computing require the ability to pass from a concrete problem to an abstract representation, reason with the abstract structure, and return with useful solutions to the specific situation. The tools for developing these skills are in part qualitative – concepts such as set, relation, function, and structures such as trees and well-founded orders. They are also in part quantitative – notably elementary combinatorics and finite probability. Recurring in all of these are instruments of proof, both purely logical ones (such as proof by contradiction) and mathematical (the various forms of induction). Features: • Explains the basic mathematical tools required by students as they set out in their studies of Computer or Information Science • Explores the interplay between qualitative thinking and calculation • Teaches the material as a language for thinking, as much as knowledge to be acquired • Uses an intuitive approach with a focus on examples for all...

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