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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Serie: ISTE Consignment
- Sprache: Englisch
Over the past century, advancements in computer science have consistently resulted from extensive mathematical work. Even today, innovations in the digital domain continue to be grounded in a strong mathematical foundation. To succeed in this profession, both today's students and tomorrow’s computer engineers need a solid mathematical background.
The goal of this book series is to offer a solid foundation of the knowledge essential to working in the digital sector. Across three volumes, it explores fundamental principles, digital information, data analysis, and optimization. Whether the reader is pursuing initial training or looking to deepen their expertise, the Mathematics for Digital Science series revisits familiar concepts, helping them refresh and expand their knowledge while also introducing equally essential, newer topics.
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Seitenzahl: 387
Veröffentlichungsjahr: 2025
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Computer Science,Field Director – Jean-Charles Pomerol
Operational Research and Decision,Subject Head – Patrick Siarry
Mathematics for Digital Science 1
Fundamentals
Gérard-Michel CochardMhand Hifi
First published 2025 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the under mentioned address:
ISTE Ltd27-37 St George’s RoadLondon SW19 4EUUK
www.iste.co.uk
John Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USA
www.wiley.com
© ISTE Ltd 2025The rights of Jean-Michel André and Philippe Jonnard to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s), contributor(s) or editor(s) and do not necessarily reflect the views of ISTE Group.
Library of Congress Control Number: 2024946485
British Library Cataloguing-in-Publication DataA CIP record for this book is available from the British LibraryISBN 978-1-78945-194-8
ERC code:PE1 MathematicsPE1_17 Mathematical aspects of computer sciencePE1_20 Control theory, optimisation and operational research
Preface
The term digital relates to information and communication sciences and technologies, covering areas such as computing, digital electronics and telecommunications. Advances in these fields, in terms of discoveries, developments and applications, have grown exponentially over the last 50 years. Such progress has profoundly transformed human activities, making the transition to "all digital" a significant issue not only economically, but also politically. Concurrently, professions related to digital technology are constantly evolving. It is noteworthy that these technological advances are based on a substantial mathematical foundation. Thus, any engineer or researcher aiming to drive innovation must possess a strong knowledge of mathematics.
Many students opt for computer science-related courses early on without first acquiring the essential mathematical foundations they might need in the future. While they can certainly excel as technicians, they may not be as well prepared to become effective engineers or researchers.
It should be recognized that computer science cannot be conceived without a solid mathematical basis. Advances in digital technologies have been closely linked to the support of mathematics. The pioneers of computing were above all mathematicians: Alan Turing, Claude Shannon, John Von Neumann and even Charles Babbage, who is nicknamed the grandfather of computing. They could never have designed computers without their mathematical expertise. Other historical figures such as Euclid, who formulated the first algorithm in history, George Boole, father of binary algebra, Ada Lovelace, pioneer in the creation of the first computer programs, Grace Hopper, to whom the first language compiler is attributed, and Margaret Hamilton, a key figure in software engineering, were also mathematicians. Today, areas such as artificial intelligence, managing large datasets, and information security are at the heart of computer science research. Once again, it is evident that without a solid mathematical foundation, it is difficult to innovate in these areas.
The digital mathematics courses offered aim to meet the need for fundamental mathematical knowledge essential for mastering and advancing digital technologies. While the book primarily targets university and engineering school students, it also serves as a resource for working IT professionals seeking to enhance their mathematical skills as part of continuing education in their respective field.
The three-volume work compiles the lessons taught to numerous generations of students in the first two university cycles, specifically in Bachelor's/Master's degrees in Computer Science or in Computer Methods Applied to Business Management. The first – and present – volume covers the essential mathematical foundations for approaching digital technologies and is described below, while the second volume focuses on digital information, and the third volume is devoted to data analysis and optimization.
Chapter 1 of the present (first) volume presents the fundamental concepts of logic and establishes the foundations of deductive reasoning.
Chapter 2 covers the fundamentals of sets and binary relations, while Chapter 3 focuses on combinatorial analysis.
Chapter 4 covers the definition and properties of the structure of Boolean algebra, as well as the manipulation of Boolean functions. Subsequently, Chapter 5 addresses the theoretical aspects of electronic circuits and their practical implementation for the manufacture of electronic modules.
Chapter 6 revisits arithmetic concepts that were once foundational in mathematics education in primary and secondary schools, now highlighting their profound relevance in the field of information security. Chapters 7 and 8 explore data protection and confidentiality, addressing error detection and correction codes, as well as encryption systems.
The last three chapters, namely 9, 10 and 11, focus on data processing and the predictions that can be derived from it. They re-examine the fundamental notions of probability and statistics, crucial for data analysis. More specifically, the final chapter illustrates how chance can be exploited to conduct experiments through simulations.
To achieve the goal of mastering the application of mathematical results, demonstrations are presented whenever they are accessible to the reader, who is assumed to be familiar with basic knowledge. In some cases, the validity of the results is trusted, while pointing out that detailed demonstrations can be found in more advanced works.
For each chapter, numerous examples are provided to illustrate the presented concepts. Generally, these examples are elaborated in detail to ensure better understanding on the part of the reader.
Finally, for each addressed theme, the choice is made to present them exhaustively, starting from the initial definitions and hypotheses. These basic notions will certainly be familiar to many readers. The intention behind such an approach is to spare those with knowledge gaps the need to look up these concepts in other literature.
October 2024
