Mathematics in Computing: An Accessible Guide to Historical, Foundational and Application Contexts 2/e

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.

從最早的計算示例到現代社會無處不在的數位設備，數學在計算機領域的應用一直是建構我們世界的技術基礎。

這本寫作清晰且啟發性的教科書/參考書提供了一個簡明的入門指南，介紹了計算機科學家使用的關鍵數學概念和技巧。從數論到軟體工程，書中涵蓋了各種主題，展示了看似抽象的概念背後的實際計算應用。書中還討論了Alan Turing和Robert Floyd等重要人物的工作，突顯了理論如何受到歷史發展的影響。

本書特點和主題：非常適合自學，提供了許多教學特色，如章節開頭的關鍵主題、章節介紹和總結、復習問題和詞彙表；將我們目前的知識狀態置於早期文明（如古巴比倫人、埃及人和希臘人）的貢獻背景下；探討了數學的基礎構建塊，包括集合、關係和函數；介紹了邏輯、形式方法和軟體工程的基礎；解釋了數論的基礎及其在密碼學中的應用；描述了編碼理論、語言理論和圖論的基礎；討論了可計算性和可決定性的概念；簡要介紹了微積分、概率和統計、矩陣、複數和四元數。

這本引人入勝且易於理解的書將吸引希望瞭解計算機科學中使用的數學的計算機科學專業學生，以及對於他們的學科如何應用於計算機科學領域感到好奇的數學家。這本書還將引起有動機的一般讀者的興趣。

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.

Dr. Gerard O'Regan是一位CMMI軟體流程改善顧問，他的研究興趣包括軟體品質和軟體流程改善、軟體品質的數學方法以及計算機歷史。他是Springer出版社的作品《World of Computing: A Primer Companion for the Digital Age》、《Concise Guide to Formal Methods》、《Concise Guide to Software Engineering》、《Guide to Discrete Mathematics》和《Introduction to the History of Computing》的作者。