Discrete Mathematics Using a Computer

1. Front Matter

   Pages i-xviii

   PDF

2. Introduction to Haskell

   • Cordelia Hall, John O’Donnell

   Pages 1-33

3. Propositional Logic

   • Cordelia Hall, John O’Donnell

   Pages 35-87

4. Predicate Logic

   • Cordelia Hall, John O’Donnell

   Pages 89-109

5. Set Theory

   • Cordelia Hall, John O’Donnell

   Pages 111-127

6. Recursion

   • Cordelia Hall, John O’Donnell

   Pages 129-145

7. Inductively Defined Sets

   • Cordelia Hall, John O’Donnell

   Pages 147-162

8. Induction

   • Cordelia Hall, John O’Donnell

   Pages 163-184

9. Relations

   • Cordelia Hall, John O’Donnell

   Pages 185-227

10. Functions

    • Cordelia Hall, John O’Donnell

    Pages 229-271

11. Discrete Mathematics in Circuit Design

    • Cordelia Hall, John O’Donnell

    Pages 273-293

12. Back Matter

    Pages 295-339

    PDF

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.

• Computer
• Correctness proofs
• Discrete Mathematics
• Formal Methods
• Functional Programming
• Induction
• Mathematical Logic
• Mechanized logic
• Recursion
• Sets, relations, functions
• mathematics
• algorithm analysis and problem complexity

• Department of Computing Science, University of Glasgow, Glasgow, UK

  Cordelia Hall, John O’Donnell

Policies and ethics