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ABOUT THE BOOK

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.

TABLE OF CONTENTS

1. Fundamentals of Software Engineering

   • Gerard O’Regan

   Pages 1-26

2. Software Engineering Mathematics

   • Gerard O’Regan

   Pages 27-36

3. Mathematical Prerequisites for Software Engineers

   • Gerard O’Regan

   Pages 37-67

4. Introduction to Algorithms

   • Gerard O’Regan

   Pages 69-84

5. Algebra

   • Gerard O’Regan

   Pages 85-107

6. Mathematical Induction and Recursion

   • Gerard O’Regan

   Pages 109-118

7. Graph Theory

   • Gerard O’Regan

   Pages 119-130

8. Sequences, Series, and Permutations and Combinations

   • Gerard O’Regan

   Pages 131-140

9. A Short History of Logic

   • Gerard O’Regan

   Pages 141-151

10. Propositional and Predicate Logic

    • Gerard O’Regan

    Pages 153-179

11. Advanced Topics in Logic

    • Gerard O’Regan

    Pages 181-195

12. Language Theory and Semantics

    • Gerard O’Regan

    Pages 197-218

13. Automata Theory

    • Gerard O’Regan

    Pages 219-228

14. Computability and Decidability

    • Gerard O’Regan

    Pages 229-239

15. Software Reliability and Dependability

    • Gerard O’Regan

    Pages 241-254

16. Overview of Formal Methods

    • Gerard O’Regan

    Pages 255-276

17. Z Formal Specification Language

    • Gerard O’Regan

    Pages 277-293

18. Model Checking

    • Gerard O’Regan

    Pages 295-304

19. The Nature of Theorem Proving

    • Gerard O’Regan