Mathematics of Discrete Structures for Computer Science

Springer Science & Business Media
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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.
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About the author

Gordon J. Pace is an associate professor in the Department of Computer Science of the University of Malta. He has an M.Sc. and a D.Phil. from Oxford, where he was a Rhodes Scholar. He has considerable experience teaching courses on the topic of his book to undergraduates in Computer Science, Mathematics and Engineering. His research interests include formal methods for software and hardware, runtime verification and formal analysis of contracts.
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Additional Information

Springer Science & Business Media
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Published on
Sep 13, 2012
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Computers / Computer Science
Computers / Data Processing
Computers / Information Technology
Mathematics / Discrete Mathematics
Mathematics / History & Philosophy
Mathematics / Logic
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Content Protection
This content is DRM protected.
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An understanding of discrete mathematics is essential for students of computer science wishing to improve their programming competence.

Fundamentals of Discrete Math for Computer Science provides an engaging and motivational introduction to traditional topics in discrete mathematics, in a manner specifically designed to appeal to computer science students. The text empowers students to think critically, to be effective problem solvers, to integrate theory and practice, and to recognize the importance of abstraction. Clearly structured and interactive in nature, the book presents detailed walkthroughs of several algorithms, stimulating a conversation with the reader through informal commentary and provocative questions.

Topics and features: highly accessible and easy to read, introducing concepts in discrete mathematics without requiring a university-level background in mathematics; ideally structured for classroom-use and self-study, with modular chapters following ACM curriculum recommendations; describes mathematical processes in an algorithmic manner, often including a walk-through demonstrating how the algorithm performs the desired task as expected; contains examples and exercises throughout the text, and highlights the most important concepts in each section; selects examples that demonstrate a practical use for the concept in question.

This easy-to-understand and fun-to-read textbook is ideal for an introductory discrete mathematics course for computer science students at the beginning of their studies. The book assumes no prior mathematical knowledge, and discusses concepts in programming as needed, allowing it to be used in a mathematics course taken concurrently with a student’s first programming course.

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