# Discrete Mathematics Using a Computer

• Cordelia Hall
• John O’Donnell
Textbook

1. Front Matter
Pages i-xviii
2. Cordelia Hall, John O’Donnell
Pages 1-33
3. Cordelia Hall, John O’Donnell
Pages 35-87
4. Cordelia Hall, John O’Donnell
Pages 89-109
5. Cordelia Hall, John O’Donnell
Pages 111-127
6. Cordelia Hall, John O’Donnell
Pages 129-145
7. Cordelia Hall, John O’Donnell
Pages 147-162
8. Cordelia Hall, John O’Donnell
Pages 163-184
9. Cordelia Hall, John O’Donnell
Pages 185-227
10. Cordelia Hall, John O’Donnell
Pages 229-271
11. Cordelia Hall, John O’Donnell
Pages 273-293
12. Back Matter
Pages 295-339

### Introduction

Several areas of mathematics find application throughout computer science, and all students of computer science need a practical working understanding of them. These core subjects are centred on logic, sets, recursion, induction, relations and functions. The material is often called discrete mathematics, to distinguish it from the traditional topics of continuous mathematics such as integration and differential equations. The central theme of this book is the connection between computing and discrete mathematics. This connection is useful in both directions: • Mathematics is used in many branches of computer science, in applica­ tions including program specification, datastructures,design and analysis of algorithms, database systems, hardware design, reasoning about the correctness of implementations, and much more; • Computers can help to make the mathematics easier to learn and use, by making mathematical terms executable, making abstract concepts more concrete, and through the use of software tools such as proof checkers. These connections are emphasised throughout the book. Software tools (see Appendix A) enable the computer to serve as a calculator, but instead of just doing arithmetic and trigonometric functions, it will be used to calculate with sets, relations, functions, predicates and inferences. There are also special software tools, for example a proof checker for logical proofs using natural deduction.

### Keywords

Computer Correctness proofs Discrete Mathematics Formal Methods Functional Programming Induction Mathematical Logic Mechanized logic Recursion Sets, relations, functions mathematics

#### Authors and affiliations

• Cordelia Hall
• 1
• John O’Donnell
• 1
1. 1.Department of Computing ScienceUniversity of GlasgowGlasgowUK

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4471-3657-6
• Copyright Information Springer-Verlag London 2000
• Publisher Name Springer, London
• eBook Packages
• Print ISBN 978-1-85233-089-7
• Online ISBN 978-1-4471-3657-6
• Buy this book on publisher's site