O'Regan G. Mathematical Foundations of Software Engineering: A Practical Guide to Essentials

Springer, 2023. — 538. — (Texts in Computer Science). — ISBN 978-3-031-26211-1.The objective of this book is to give the reader a flavour of the mathematical foundations of software engineering. The rich applications of mathematics to software engineering includes its applications to error detection and correcting codes with finite field theory; the field of cryptography which uses the results of number theory; the modelling of telecommunication networks with graph theory; the application of discrete mathematics and proof techniques to the software correctness field (especially safety critical systems using formal methods and model checking); the application of financial mathematics to the banking and insurance fields; and the application of calculus and vectors to 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.Fundamentals of Software Engineering.
Software Engineering Mathematics.
Mathematical Prerequisites for Software Engineers.
Introduction to Algorithms.
Algebra.
Mathematical Induction and Recursion.
Graph Theory.
Sequences, Series, and Permutations and Combinations.
A Short History of Logic.
Propositional and Predicate Logic.
Advanced Topics in Logic.
Language Theory and Semantics.
Automata Theory.
Computability and Decidability.
Software Reliability and Dependability.
Overview of Formal Methods.
Z Formal Specification Language.
Model Checking.
The Nature of Theorem Proving.
Cryptography.
Coding Theory.
Introduction to Statistics.
Introduction to Probability Theory.
Introduction to Data Science.
Calculus I.
Calculus II.
Matrix Theory.
Complex Numbers and Quaternions.
Vectors.
Basic Financial Mathematics.
Introduction to Operations Research.
Mathematical Software for Software Engineers.