Ebook: Modelling Computing Systems: Mathematics for Computer Science

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.

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We have all experienced delays and frustrations as a result of the notorious ‘computer glitch.’ However, the more dependent we become on computational systems in our daily lives, the more we must ensure that they are safe, reliable and user-friendly.

This engaging textbook 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.

Topics and features:

• Introduces important concepts from discrete mathematics as the basis of computational thinking, presented in a stimulating and motivating style
• 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 an approach to the modelling of computing systems based on state transition systems, exploring the languages and techniques for expressing and reasoning about systems specifications and concurrent implementations

This clearly written and classroom-tested textbook/reference is essential reading for first-year undergraduate modules on discrete mathematics and systems modelling.

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We have all experienced delays and frustrations as a result of the notorious ‘computer glitch.’ However, the more dependent we become on computational systems in our daily lives, the more we must ensure that they are safe, reliable and user-friendly.

This engaging textbook 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.

Topics and features:

• Introduces important concepts from discrete mathematics as the basis of computational thinking, presented in a stimulating and motivating style
• 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 an approach to the modelling of computing systems based on state transition systems, exploring the languages and techniques for expressing and reasoning about systems specifications and concurrent implementations

This clearly written and classroom-tested textbook/reference is essential reading for first-year undergraduate modules on discrete mathematics and systems modelling.

Content:
Front Matter....Pages I-XVI
Front Matter....Pages 15-15
Propositional Logic....Pages 17-55
Sets....Pages 57-86
Boolean Algebras and Circuits....Pages 87-108
Predicate Logic....Pages 109-129
Proof Strategies....Pages 131-154
Functions....Pages 155-178
Relations....Pages 179-199
Inductive and Recursive Definitions....Pages 201-222
Proofs by Induction....Pages 223-250
Games and Strategies....Pages 251-275
Front Matter....Pages 277-277
Modelling Processes....Pages 279-307
Distinguishing Between Processes....Pages 309-332
Logical Properties of Processes....Pages 333-356
Concurrent Processes....Pages 357-379
Temporal Properties....Pages 381-403
Introduction....Pages 1-14
Back Matter....Pages 405-500

---

We have all experienced delays and frustrations as a result of the notorious ‘computer glitch.’ However, the more dependent we become on computational systems in our daily lives, the more we must ensure that they are safe, reliable and user-friendly.

This engaging textbook 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.

Topics and features:

• Introduces important concepts from discrete mathematics as the basis of computational thinking, presented in a stimulating and motivating style
• 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 an approach to the modelling of computing systems based on state transition systems, exploring the languages and techniques for expressing and reasoning about systems specifications and concurrent implementations

This clearly written and classroom-tested textbook/reference is essential reading for first-year undergraduate modules on discrete mathematics and systems modelling.

Content:
Front Matter....Pages I-XVI
Front Matter....Pages 15-15
Propositional Logic....Pages 17-55
Sets....Pages 57-86
Boolean Algebras and Circuits....Pages 87-108
Predicate Logic....Pages 109-129
Proof Strategies....Pages 131-154
Functions....Pages 155-178
Relations....Pages 179-199
Inductive and Recursive Definitions....Pages 201-222
Proofs by Induction....Pages 223-250
Games and Strategies....Pages 251-275
Front Matter....Pages 277-277
Modelling Processes....Pages 279-307
Distinguishing Between Processes....Pages 309-332
Logical Properties of Processes....Pages 333-356
Concurrent Processes....Pages 357-379
Temporal Properties....Pages 381-403
Introduction....Pages 1-14
Back Matter....Pages 405-500
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