This chapter motivates the role and importance of mathematical foundations of computer science by discussing a number of prominent examples of system failures and by illustrating how mathematical modelling tools and techniques can support the design of computing systems that are more dependable and trustworthy. The examples presented are the historic Clayton Tunnel railway accident, the USS Scorpion submarine accident, the Therac 25 radiotherapy malfunctions, the London Ambulance Service automated dispatch service failures, the Intel Pentium bug, the Ariane 5 accident and the man-in-the-middle attack to the Needham-Schroeder authentication protocol. The chapter also provides working definitions for the concepts of system, model, abstraction, notation, specification, implementation and verification; and it discusses their place in design and modelling.
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