Mathematics in Computing
An Accessible Guide to Historical, Foundational and Application Contexts
Authors: O'Regan, Gerard
Free Preview Provides a broad review of the applications of mathematics to computing, including software engineering, coding theory, cryptography and software reliability
 Emphasizes the application of mathematics to computing, rather than mathematics for its own sake, covering both discrete and continuous mathematics
 Discusses the application of mathematical techniques to increase confidence in program correctness
 Fully revised and updated new edition
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 About this Textbook

This illuminating textbook provides a concise review of the core concepts in mathematics essential to computer scientists. Emphasis is placed on the practical computing applications enabled by seemingly abstract mathematical ideas, presented within their historical context. The text spans a broad selection of key topics, ranging from the use of finite field theory to correct code and the role of number theory in cryptography, to the value of graph theory when modelling networks and the importance of formal methods for safety critical systems.
This fully updated new edition has been expanded with a more comprehensive treatment of algorithms, logic, automata theory, model checking, software reliability and dependability, algebra, sequences and series, and mathematical induction.
Topics and features: includes numerous pedagogical features, such as chapteropening key topics, chapter introductions and summaries, review questions, and a glossary; describes the historical contributions of such prominent figures as Leibniz, Babbage, Boole, and von Neumann; introduces the fundamental mathematical concepts of sets, relations and functions, along with the basics of number theory, algebra, algorithms, and matrices; explores arithmetic and geometric sequences and series, mathematical induction and recursion, graph theory, computability and decidability, and automata theory; reviews the core issues of coding theory, language theory, software engineering, and software reliability, as well as formal methods and model checking; covers key topics on logic, from ancient Greek contributions to modern applications in AI, and discusses the nature of mathematical proof and theorem proving; presents a short introduction to probability and statistics, complex numbers and quaternions, and calculus.This engaging and easytounderstand book will appeal to students of computer science wishing for an overview of the mathematics used in computing, and to mathematicians curious about how their subject is applied in the field of computer science. The book will also capture the interest of the motivated general reader.  About the authors

Dr. Gerard O'Regan is a CMMI software process improvement consultant with research interests including software quality and software process improvement, mathematical approaches to software quality, and the history of computing. He is the author of such Springer titles as World of Computing: A Primer Companion for the Digital Age, Concise Guide to Formal Methods, Concise Guide to Software Engineering, Guide to Discrete Mathematics, and Introduction to the History of Computing.
 Table of contents (28 chapters)


What Is a Computer?
Pages 111

Foundations of Computing
Pages 1329

Overview of Mathematics in Computing
Pages 3160

Introduction to Algorithms
Pages 6175

Number Theory
Pages 7798

Table of contents (28 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Mathematics in Computing
 Book Subtitle
 An Accessible Guide to Historical, Foundational and Application Contexts
 Authors

 Gerard O'Regan
 Series Title
 Undergraduate Topics in Computer Science
 Copyright
 2020
 Publisher
 Springer International Publishing
 Copyright Holder
 Springer Nature Switzerland AG
 eBook ISBN
 9783030342098
 DOI
 10.1007/9783030342098
 Softcover ISBN
 9783030342081
 Series ISSN
 18637310
 Edition Number
 2
 Number of Pages
 XXVI, 458
 Number of Illustrations
 133 b/w illustrations, 73 illustrations in colour
 Topics