This engaging text presents the fundamental mathematics and modelling techniques for computing systems in a novel and light-hearted way, which can be easily followed by students at the very beginning of their university education. Key concepts are taught through a large collection of challenging yet fun mathematical games and logical puzzles that require no prior knowledge about computers. The text begins with intuition and examples as a basis from which precise concepts are then developed; demonstrating how, by working within the confines of a precise structured method, the occurrence of errors in the system can be drastically reduced.
Features: demonstrates how game theory provides a paradigm for an intuitive understanding of the nature of computation; contains more than 400 exercises throughout the text, with detailed solutions to half of these presented at the end of the book, together with numerous theorems, definitions and examples; describes a modelling approach based on state transition systems.
Provides an elementary introduction to the mathematics and modelling of computing systems
Introduction.- Part I: Mathematics for Computer Science.- Propositional Logic.- Sets.- Boolean Algebras and Circuits.- Predicate Logic.- Proof Strategies.- Functions.- Relations.- Inductive and Recursive Definitions.- Proofs by Induction.- Games and Strategies.- Part II: Modelling Computing Systems.- Modelling Processes.- Distinguishing Between Processes.- Logical Properties of Processes.- Concurrent Processes.- Temporal Properties.
Reviewing concepts of games and strategies, this book provides a paradigm for understanding computation, explaining the mathematics and modeling of computing systems through exercises and examples. Discusses standard topics, games and winning strategies.