# Guide to Discrete Mathematics

## An Accessible Introduction to the History, Theory, Logic and Applications

Gerard O'Regan

ISBN | 9783319445601 |

Publication Date | September 2016 |

Formats | Hardcover Ebook |

Publisher | Springer |

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Gerard O'Regan

ISBN | 9783319445601 |

Publication Date | September 2016 |

Formats | Hardcover Ebook |

Publisher | Springer |

This stimulating textbook presents a broad and accessible guide to the fundamentals of discrete mathematics, highlighting how the techniques may be applied to various exciting areas in computing. The text is designed to motivate and inspire the reader, encouraging further study in this important skill.

Features: 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; examines the field of software engineering, describing formal methods; investigates probability and statistics.

Sets, Relations and Functions

Number Theory

Mathematical Induction and Recursion

Sequences, Series and Permutations and Combinations

Algebra

Automata Theory

Matrix Theory

Graph Theory

Cryptography

Coding Theory

Language Theory and Semantics

Computability and Decidability

A Short History of Logic

Propositional and Predicate Logic

Advanced Topics in Logic

Software Engineering Mathematics

Formal Methods

Z Formal Specification Language

Probability, Statistics and Applications.

“This book is … an encyclopedic overview of topics of and related to discrete mathematics in the broad sense, including many topics from computer science and software engineering. … Each chapter has a summary and a list of review question which help the reader to recapitulate the contents … . for each topic the reader is able to grasp the specific flavor and can move forward to more specific and advanced literature.” (Dieter Riebesehl, zbMATH 1358.68004, 2017)