Guide to discrete mathematics : an accessible introduction to the history, theory, logic and applications /
Gerard O'Regan
- 2nd Edition.
- Switzerland : Springer, c2021.
- xxi, 452 pages : color illustrations ; 24 cm.
Includes index
1. Mathematics in Civilization -- 2. Sets, Relations and Functions -- 3. Number Theory -- 4. Mathematical Induction and Recursion -- 5. Sequences, Series and Permutations and Combinations -- 6. Algebra -- 7. Automata Theory -- 8. Matrix Theory -- 9. Graph Theory -- 10. Cryptography -- 11. Coding Theory -- 12. Language Theory and Semantics -- 13. Computability and Decidability -- 14. A Short History of Logic -- 15. Propositional and Predicate Logic -- 16. Advanced Topics in Logic -- 17. The Nature of Theorem Proving -- 18. Software Engineering Mathematics -- 19. Software Reliability and dependability -- 20. Formal Methods -- 21. Z Formal Specification Language -- 22. Statistics -- 23. Probability Theory -- 24. Operations Research -- 25. Basic Financial Mathematics.
This book provides an introduction to the building blocks of discrete mathematics, including sets, relations and functions; describes the basics of number theory, the techniques of induction and recursion, and the applications of mathematical sequences, series, permutations, and combinations; presents the essentials of algebra; explains the fundamentals of automata theory, matrices, graph theory, cryptography, coding theory, language theory, and the concepts of computability and decidability; reviews the history of logic, discussing propositional and predicate logic, as well as advanced topics such as the nature of theorem proving; examines the field of software engineering, including software reliability and dependability and describes formal methods; investigates probability and statistics and presents an overview of operations research and financial mathematics.