Mathematics of Discrete Structures for Computer Science

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Mathematics is essential in computer science, with some viewing computers as embodiments of mathematical systems. Whether designing digital circuits, computer programs, or programming languages, mathematics is crucial for reasoning about design aspects such as correctness and robustness. This book provides foundational mathematics for computer science courses, presenting a unique approach. Instead of defining mathematical concepts by their properties first, the author begins with methods for calculating results from operators and subsequently proves their properties. After justifying this approach, the author delves into 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 vital for effective learning. It is designed for both undergraduate and graduate students, focusing on areas frequently applied in computer science, while also being suitable for mathematics and engineering students.