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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Serie: ISTE Invoiced
- 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: 292
Veröffentlichungsjahr: 2025
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Computer Science, Field Directors –Jean-Charles Pomerol
Operational Research and Decision, Subject Head –Patrick Siarry
Mathematics for Digital Science 3
Data Analysis and Optimization
Gérard-Michel Cochard
Mhand 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, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, 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 2025
The rights of Gérard-Michel Cochard and Mhand Hifi 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: 2025935043
British Library Cataloguing-in-Publication DataA CIP record for this book is available from the British LibraryISBN 978-1-78945-196-2
ERC code:PE1 Mathematics PE1_17 Mathematical aspects of computer science PE1_20 Control theory, optimisation and operational research
Preface
The term “digital” relates to information and communication sciences and technologies, including computing, digital electronics and telecommunications. Over the past 50 years, advancements in these fields, through discoveries, developments and applications, have grown at an exponential rate. Such progress has profoundly transformed human activities, making the transition to an “all digital” world a significant economic and political issue. At the same time, professions related to digital technology are continuously evolving. It is noteworthy that these technological advancements are grounded in a substantial mathematical foundation. Consequently, any engineer or researcher aiming to drive innovation must possess extensive 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 may excel as technicians, they might not be as well-prepared to become effective engineers or researchers.
It should be recognized that computer science cannot be fully understood without a solid mathematical foundation. Advances in digital technologies have been closely linked to mathematical support. The pioneers of computing were primarily mathematicians: Alan Turing, Claude Shannon, John von Neumann and Charles Babbage, often referred to as 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, George Boole, the father of binary algebra, Ada Lovelace, a pioneer in the creation of the first computer programs, Grace Hopper, who developed the first language compiler, 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 central to computer science research. Once again, it is evident that without a robust mathematical foundation, innovation in these areas would be challenging.
The digital mathematics courses offered are designed to provide the fundamental mathematical knowledge essential for mastering and advancing digital technologies. While the book primarily targets university and engineering students, it also serves as a resource for IT professionals looking to enhance their mathematical skills as part of their ongoing professional development in the field.
The three-volume series compiles lessons taught to multiple generations of students in the first two university cycles, specifically within bachelor’s and master’s programs in Computer Science or in Computer Methods Applied to Business Management. The first volume covers the essential mathematical foundations necessary for understanding digital technologies. The second volume focuses on digital information. The third – and current – volume is dedicated to data analysis and optimization, as detailed below.
For data analysis, Chapter 1 revisits the fundamentals of descriptive statistics, linear regression and linear correlation, as covered in Volume 1.
In Chapter 2, these concepts are extended to multi-dimensional arrays, which are graphically represented as point clouds in n-dimensional space. Analyzing these point clouds forms the basis for principal component analysis and factor analysis.
Chapter 3 focuses on automatic classification through partitioning methods, highlighting the k-means algorithm, as well as hierarchical classification using aggregation strategies such as Ward’s method.
Chapter 4 provides a detailed examination of linear programming techniques, which aim to identify an optimal solution among numerous variable combinations that must satisfy a set of linear constraints.
Chapter 5 introduces graph theory in its basic form, covering fundamental definitions and properties, before progressing to more advanced concepts such as connectedness and extremal spanning trees.
Chapter 6 focuses on the classic problem of finding a path with minimum or maximum length in a graph, using various algorithms.
Chapter 7 presents several graph-based traffic problems that involve optimizing a function, including the maximum flow problem, the minimum cost transportation problem and the assignment problem.
Finally, Chapter 8 examines scheduling problems related to project planning and shop floor scheduling, using the flow-shop and job-shop as examples.
To achieve the goal of mastering the application of mathematical results, proofs are presented whenever they are accessible to the reader, who is assumed to have a basic knowledge of the subject. In some cases, the validity of the results is accepted without detailed proofs, with references to more advanced works where such demonstrations can be found.
Each chapter includes numerous examples illustrating the concepts presented. These examples are generally elaborated in detail to enhance the reader’s understanding.
Finally, each topic is presented in detail, starting with the foundational definitions and hypotheses. While many readers may already be familiar with these basic concepts, this thorough approach is designed to help those with potential knowledge gaps, minimizing the need to consult additional sources.
May 2025
1Linear Modeling for Two-Dimensional Data
CONCEPTS COVERED IN THIS CHAPTER. –
This brief chapter serves as a reminder of the concepts presented in detail in Volume 1. It primarily provides an overview of basic statistical analysis tools, particularly linear regression and correlation for two-dimensional data.
References: [SAP 11].
