# Mathematics of Discrete Structures for Computer Science

• Gordon J. Pace
Book

1. Front Matter
Pages I-XVI
2. Gordon J. Pace
Pages 1-8
3. Gordon J. Pace
Pages 9-56
4. Gordon J. Pace
Pages 57-77
5. Gordon J. Pace
Pages 79-110
6. Gordon J. Pace
Pages 111-140
7. Gordon J. Pace
Pages 141-155
8. Gordon J. Pace
Pages 157-174
9. Gordon J. Pace
Pages 175-210
10. Gordon J. Pace
Pages 211-255
11. Gordon J. Pace
Pages 257-285
12. Back Matter
Pages 287-293

### Introduction

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.

### Keywords

discrete mathematics discrete structures mathematical logic predicate calculus propositional logic relations sets

#### Authors and affiliations

• Gordon J. Pace
• 1
1. 1.Department of Computer Science, Faculty of InformationUniversity of MaltaMsidaMalta

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-642-29840-0
• Copyright Information Springer-Verlag Berlin Heidelberg 2012
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages Computer Science
• Print ISBN 978-3-642-29839-4
• Online ISBN 978-3-642-29840-0