Gordon J. Pace

Mathematics plays a key role in computer science, some researchers would consider computers as nothing but the physical embodiment of mathematical systems. And whether you are designing a digital circuit, a computer program or a new programming language, you need mathematics to be able to reason about the design -- its correctness, robustness and dependability. This book covers the foundational mathematics necessary for courses in computer science. The common approach to presenting mathematical concepts and operators is to define them in terms of properties they satisfy, and then based on these definitions develop ways of computing the result of applying the operators and prove them correct. This book is mainly written for computer science students, so here the author takes a different approach: he starts by defining ways of calculating the results of applying the operators and then proves that they satisfy various properties. After justifying his underlying approach the author offers detailed chapters covering propositional logic, predicate calculus, sets, relations, discrete structures, structured types, numbers, and reasoning about programs. The book contains chapter and section summaries, detailed proofs and many end-of-section exercises -- key to the learning process. The book is suitable for undergraduate and graduate students, and although the treatment focuses on areas with frequent applications in computer science, the book is also suitable for students of mathematics and engineering.

Mathematics of Discrete Structures for Computer Science

Brian Davis

Adam Wyner

This book constitutes the refereed proceedings of the 5th International Workshop on Controlled Natural Language, CNL 2016, held in Aberdeen, UK, in July 2016. The 11 full papers presented were carefully reviewed and selected from 15 submissions. The topics range from natural languages which are controlled, to controlled languages with a natural language flavour; and from more theoretical results to interfaces, reasoning engines and real-life applications of CNLs.

Gordon J. Pace

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