Mathematics in Computing: An Accessible Guide to Historical, Foundational and Application Contexts - Paperback

by Gerard O'Regan (Author)

From the earliest examples of computation to the digital devices that are ubiquitous in modern society, the application of mathematics to computing has underpinned the technology that has built our world.

This clearly written and enlightening textbook/reference provides a concise, introductory guide to the key mathematical concepts and techniques used by computer scientists. Spanning a wide range of topics - from number theory to software engineering - the book demonstrates the practical computing applications behind seemingly abstract ideas. The work of important figures such as Alan Turing and Robert Floyd are also discussed, highlighting how the theory has been informed by historical developments.

Topics and features: ideal for self-study, offering many pedagogical features such as chapter-opening key topics, chapter introductions and summaries, review questions, and a glossary; places our current state of knowledge within the context of the contributions made by early civilizations, such as the ancient Babylonians, Egyptians and Greeks; examines the building blocks of mathematics, including sets, relations and functions; presents an introduction to logic, formal methods and software engineering; explains the fundamentals of number theory, and its application in cryptography; describes the basics of coding theory, language theory, and graph theory; discusses the concept of computability and decideability; includes concise coverage of calculus, probability and statistics, matrices, complex numbers and quaternions.

This engaging and easy-to-understand 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.

Back Jacket

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.

Topics and features:

• Includes numerous pedagogical features, such as chapter-opening 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 easy-to-understand 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.

Author Biography

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.