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Mathematics of discrete structures for computer science

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Gordon J. Pace

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Mathematics is essential in computer science, with some viewing computers as embodiments of mathematical systems. Designing digital circuits, computer programs, or programming languages requires mathematical reasoning to ensure correctness, robustness, and dependability. This book addresses the foundational mathematics needed for computer science courses. Unlike the common method of defining mathematical concepts by their properties, the author adopts a unique approach: he begins with methods for calculating results from operators and subsequently proves that these methods satisfy various properties. After justifying this approach, the author presents detailed chapters on propositional logic, predicate calculus, sets, relations, discrete structures, structured types, numbers, and program reasoning. The book includes chapter and section summaries, comprehensive proofs, and numerous end-of-section exercises, which are crucial for effective learning. It is suitable for both undergraduate and graduate students, focusing on areas frequently applied in computer science while also being beneficial for students in mathematics and engineering.