Mathematical Foundations of Software Engineering

This textbook presents an introduction to the mathematical foundations of software engineering. It presents the rich applications of mathematics in areas such as error-correcting codes, cryptography, the safety and security critical fields, the banking and insurance fields, as well as traditional engineering applications.

Topics and features:

• Addresses core mathematics for critical thinking and problem solving
• Discusses propositional and predicate logic and various proof techniques to demonstrate the correctness of a logical argument.
• Examines number theory and its applications to cryptography
• Considers the underlying mathematics of error-correcting codes
• Discusses graph theory and its applications to modelling networks
• Reviews tools to support software engineering mathematics, including automated and interactive theorem provers and model checking
• Discusses financial software engineering, including simple and compound interest, probability and statistics, and operations research
• Discusses software reliability and dependability and explains formal methods used to derive a program from its specification
• Discusses calculus, matrices, vectors, complex numbers, and quaternions, as well as applications to graphics and robotics
• Includes key learning topics, summaries, and review questions in each chapter, together with a useful glossary

This practical and easy-to-follow textbook/reference is ideal for computer science students seeking to learn how mathematics can assist them in building high-quality and reliable software on time and on budget. The text also serves as an excellent self-study primer for software engineers, quality professionals, and software managers.

1. Fundamentals of Software Engineering. - 2. Software Engineering Mathematics. - 3. Mathematical Prerequisites. - 4. Introduction to Algorithms. - 5. - Algebra. - 6. Mathematical Induction and Recursion. - 7. Graph Theory. - 8. Sequences, Series and Permutations and Combinations. - 9. A Short History of Logic. - 10. Propositional and Predicate Logic. - 11. Advanced Topics in Logic. - 12. Language Theory and Semantics. - 13. Automata Theory. - 14. Computability and Decidability. - 15. Software Reliability and Dependability.