This book equips the student with essential intellectual tools that are needed from the very beginning of university studies in computing. These consist of abilities and skills - to pass from a concrete problem to an abstract representation, reason with the abstract structure coherently and usefully, and return with booty to the specific situation. The most basic and useful concepts needed come from the worlds of sets (with also their employment as relations and functions), structures (notably trees and graphs), and combinatorics (alias principles of counting, with their application in the world of probability). Recurring in all these are two kinds of instrument of proof -- logical (notably inference by suppositions, reductio ad absurdum, and proof by cases), and mathematical (notably induction on the positive integers and on well-founded structures). From this book the student can assimilate the basics of these worlds and set out on the paths of computing with understanding and a platform for further study as needed.
David Makinson is currently Visiting Professor at London School of Economics (LSE). Previous affiliations include the Department of Computer Science at King's College London, UNESCO in Paris, and the American University of Beirut in Lebanon. He is well known for his early research in modal and deontic logics, and more recently in the logic of belief change (as one of the founders of the AGM paradigm) and nonmonotonic reasoning.