A Logical Approach to Discrete Math

1. Front Matter

   Pages N2-xvi

   PDF

2. Using Mathematics

   • David Gries, Fred B. Schneider

   Pages 1-6

3. Textual Substitution, Equality, and Assignment

   • David Gries, Fred B. Schneider

   Pages 7-23

4. Boolean Expressions

   • David Gries, Fred B. Schneider

   Pages 25-40

5. Propositional Calculus

   • David Gries, Fred B. Schneider

   Pages 41-68

6. Relaxing the Proof Style

   • David Gries, Fred B. Schneider

   Pages 69-81

7. Applications of Propositional Calculus

   • David Gries, Fred B. Schneider

   Pages 83-108

8. Hilbert-style Proofs

   • David Gries, Fred B. Schneider

   Pages 109-123

9. Formal Logic

   • David Gries, Fred B. Schneider

   Pages 125-137

10. Quantification

    • David Gries, Fred B. Schneider

    Pages 139-156

11. Predicate Calculus

    • David Gries, Fred B. Schneider

    Pages 157-177

12. Predicates and Programming

    • David Gries, Fred B. Schneider

    Pages 179-194

13. A Theory of Sets

    • David Gries, Fred B. Schneider

    Pages 195-215

14. Mathematical Induction

    • David Gries, Fred B. Schneider

    Pages 217-250

15. A Theory of Sequences

    • David Gries, Fred B. Schneider

    Pages 251-264

16. Relations and Functions

    • David Gries, Fred B. Schneider

    Pages 265-302

17. A Theory of Integers

    • David Gries, Fred B. Schneider

    Pages 303-336

18. Combinatorial Analysis

    • David Gries, Fred B. Schneider

    Pages 337-362

19. Recurrence Relations

    • David Gries, Fred B. Schneider

    Pages 363-385

20. Modern Algebra

    • David Gries, Fred B. Schneider

    Pages 387-421

This text attempts to change the way we teach logic to beginning students. Instead of teaching logic as a subject in isolation, we regard it as a basic tool and show how to use it. We strive to give students a skill in the propo­ sitional and predicate calculi and then to exercise that skill thoroughly in applications that arise in computer science and discrete mathematics. We are not logicians, but programming methodologists, and this text reflects that perspective. We are among the first generation of scientists who are more interested in using logic than in studying it. With this text, we hope to empower further generations of computer scientists and math­ ematicians to become serious users of logic. Logic is the glue Logic is the glue that binds together methods of reasoning, in all domains. The traditional proof methods -for example, proof by assumption, con­ tradiction, mutual implication, and induction- have their basis in formal logic. Thus, whether proofs are to be presented formally or informally, a study of logic can provide understanding.

• Fortran
• algebra
• calculus
• computer
• computer science
• discrete math
• formal logic
• logic
• programming

"This is a rather extraordinary book, and deserves to be read by everyone involved in computer science and - perhaps more importantly - software engineering. I recommend it highly... If the book is taken seriously, the rigor that it unfolds and the clarity of its concepts could have a significant impact on the way in which software is conceived and developed." - Peter G. Neumann

• Department of Computer Science, Cornell University, Ithaca, USA

  David Gries, Fred B. Schneider

Policies and ethics