Diskret matematik

This book constitutes the refereed proceedings of the 17th International Joint Conference on Theoretical Computer Science-Frontier of Algorithmic Wisdom (IJTCS-FAW 2023), consisting of the 17th International Conference on Frontier of Algorithmic Wisdom (FAW) and the 4th International Joint Conference on Theoretical Computer Science (IJTCS), held in Macau, China, during August 14¿18, 2023.FAW started as the Frontiers of Algorithmic Workshop in 2007 at Lanzhou, China, and was held annually from 2007 to 2021 and published archival proceedings. IJTCS, the International joint theoretical Computer Science Conference, started in 2020, aimed to bring in presentations covering active topics in selected tracks in theoretical computer science. To accommodate the diversified new research directions in theoretical computer science, FAW and IJTCS joined their forces together to organize an event for information exchange of new findings and work of enduring value in the field. The 21 full papers included in this book were carefully reviewed and selected from 34 submissions. They were organized in topical sections as follows: algorithmic game theory; algorithms and data structures; combinatorial optimization; and computational economics.

This book not only presents an essential material to understand fuzzy metric fixed point theory but also enables the readers to appreciate the recent advancements made in this direction. It contains seven chapters on different topics in fuzzy metric fixed point theory.

Nachdem der Autor sich in seinen Abschlussarbeiten mit Themen der Analysis befasst hatte, arbeitete er danach beruflich ausschließlich im Bereich der diskreten Mathematik: forschend im Bereich der Spezifikation und Testgenerierung für kommunizierende diskrete Systeme und lehrend in den Bereichen Petri-Netze, Logik und Theoretischer Informatik. Das bewog ihn letztlich, eine breit angelegte Übersicht über wichtige Bereiche der diskreten Mathematik zu verfassen. Es sollte ein Lehrbuch werden, wie er es sich im Studium gewünscht hätte - und hier liegt es vor. Gegenstand des Buches sind Grundlagenfächer wie Mengen, Relationen, Funktionen, Logik und Algebra, sowie diskrete Anwendungen wie Zahlen, Anzahlen, Graphen und diskrete Wahrscheinlichkeit. Damit werden etliche Grundvorlesungen für Studierende der Mathematik bzw. Informatik abgedeckt. Reizvoll sind die gelegentlich eingeflochten Hinweise auf die Grenzen des formal-mathematischen Vorgehens. Anhand von etwa 250 Übungsaufgaben werden die Leser animiert, das Gelesene aktiv umzusetzen und ihre eigenen Lösungen mit den online einsehbaren Beispiellösungen zu vergleichen. So wird das Buch zu einem wertvollen Begleiter in den ersten Semestern des Mathematik- und Informatikstudiums. Die komplett überarbeitete 2. Auflage enthält zusätzliche Definitionen und ist noch klarer strukturiert.

This book provides an elementary introduction, complete with detailed proofs, to the celebrated tilings of the plane discovered by Sir Roger Penrose in the '70s. Quasi-periodic tilings of the plane, of which Penrose tilings are the most famous example, started as recreational mathematics and soon attracted the interest of scientists for their possible application in the description of quasi-crystals. The purpose of this survey, illustrated with more than 200 figures, is to introduce the curious reader to this beautiful topic and be a reference for some proofs that are not easy to find in the literature. The volume covers many aspects of Penrose tilings, including the study, from the point of view of Connes' Noncommutative Geometry, of the space parameterizing these tilings.

"This largely self-contained text introduces discrete probability and its applications, at a level suitable for beginning graduate students in mathematics, computer science, statistics and engineering. Each chapter includes exercises and pointers to the wider literature, covering a wide spectrum of essential techniques and key examples"--

Intelligent Fractal-Based Image Analysis: Application in Pattern Recognition and Machine Vision provides insights into the current strengths and weaknesses of different applications as well as research findings on fractal graphics in engineering and science applications. The book aims to improve the exchange of ideas and coherence between various core computing methods and highlights the relevance of related application areas for advanced as well as novice-user application. The book presents core concepts, methodological aspects, and advanced feature opportunities, focusing on major, real-time applications in engineering and health science. It will appeal to researchers, data scientists, industry professionals, and graduate students. Fractals are infinite, complex patterns used in modeling physical and dynamic systems. Fractal theory research has increased across different fields of applications including engineering science, health science, and social science. Recent literature shows the vital role fractals play in digital image analysis, specifically in biomedical image processing. Fractal graphics is an interdisciplinary field that deals with how computers can be used to gain high-level understanding from digital images. Integrating artificial intelligence with fractal characteristics has resulted in new interdisciplinary research in the fields of pattern recognition and image processing analysis.

As the sophistication of cyber-attacks increases, understanding how to defend critical infrastructure systems-energy production, water, gas, and other vital systems-becomes more important, and heavily mandated. Industrial Network Security, Third Edition arms you with the knowledge you need to understand the vulnerabilities of these distributed supervisory and control systems. Author Eric Knapp examines the unique protocols and applications that are the foundation of Industrial Control Systems (ICS) and provides clear guidelines for their protection. This comprehensive reference gives you thorough understanding of the challenges facing critical infrastructures, new guidelines and security measures for infrastructure protection, knowledge of new and evolving security tools, and pointers on SCADA protocols and security implementation.

This book constitutes the refereed proceedings of the 18th International Symposium on Algorithms and Data Structures, WADS 2023, held during July 31-August 2, 2023. The 47 regular papers, presented in this book, were carefully reviewed and selected from a total of 92 submissions. They present original research on the theory, design and application of algorithms and data structures.

This book is designed to meet the requirement of undergraduate and postgraduate students pursuing computer science, information technology, mathematical science, and physical science course. No formal prerequisites are needed to understand the text matter except a very reasonable background in college algebra. The text contains in-depth coverage of all major topics proposed by professional institutions and universities for a discrete mathematics course. It emphasizes on problem-solving techniques, pattern recognition, conjecturing, induction, applications of varying nature, proof technique, algorithmic development, algorithm correctness, and numeric computations. A sufficient amount of theory is included for those who enjoy the beauty in development of the subject and a wealth of applications as well as for those who enjoy the power of problem-solving techniques.Biographical sketches of nearly 25 mathematicians and computer scientists who have played a significant role in the development of the field are threaded into the text to provide a human dimension and attach a human face to major discoveries. Each section of the book contains a generous selection of carefully tailored examples to classify and illuminate various concepts and facts. Theorems are backbone of mathematics. Consequently, this book contains the various proof techniques, explained and illustrated in details. Most of the concepts, definitions, and theorems in the book are illustrated with appropriate examples. Proofs shed additional light on the topic and enable students to sharpen thin problem-solving skills. Each chapter ends with a summary of important vocabulary, formulae, properties developed in the chapter, and list of selected references for further exploration and enrichment.

This volume collects papers based on talks given at the conference "e;Geometrias'19: Polyhedra and Beyond"e;, held in the Faculty of Sciences of the University of Porto between September 5-7, 2019 in Portugal. These papers explore the conference's theme from an interdisciplinary standpoint, all the while emphasizing the relevance of polyhedral geometry in contemporary academic research and professional practice. They also investigate how this topic connects to mathematics, art, architecture, computer science, and the science of representation. Polyhedra and Beyond will help inspire scholars, researchers, professionals, and students of any of these disciplines to develop a more thorough understanding of polyhedra.

The theory developed for  4-additive codes is the starting point for much generalization about codes over mixed alphabets. They have opened a new, emergent area of research.  The techniques used for  4-linear codes are being generalized and applied to more general codes.  By example, these codes have contributed to the classification of many nonlinear codes. Moreover, they can be considered as the starting point of many different generalizations given over mixed alphabets, thereby representing a useful area of research.  Since 2010, more than 30 papers have been published about the codes considered in the book, which includes important classes of binary codes (1-perfect, Hadamard, etc.) that are not linear in general. For example, much recent research has shown the application of the techniques described for the family of cyclic  4-linear codes.   Topics and Features:Examines everything from the basic definitions to very advanced results                             Provides numerous examples, succinctly and comprehensively gathering and using the relevant information                                                                                                         Includes examples using commands from a new Magma package, developed mostly by the same authors                                                                                                          Proposes algorithms, for instance to describe coding and decoding strategiesThis unique volume will be eminently suitable for researchers working on coding theory over rings, especially over mixed alphabets. Experts will find commands and algorithms that will be useful in the generalization to codes over mixed alphabets. Additionally, by outlining the basic theory of codes over mixed alphabets and providing numerous examples, the book will be useful to researchers wanting to be introduced to the topic.The authors are all affiliated with the Dept. of Information and Communications Engineering at the Universitat Autonoma de Barcelona, Spain. Joaquim Borges and Cristina Fernandez-Cordoba are Associate Professors, Jaume Pujol is a now retired Associate Professor, Josep Rifa is Professor Emeritus, and Merce Villanueva is Associate Professor.

The present book is based on the curriculum of undergraduate and postgraduate courses of universities in India and abroad. Every effort is made to present the various topics in the theory of graphs in a logical manner with adequate historical background and include suitable figures to illustrate concepts and results ideally. The formidable exercises, neither easy nor straightforward, are bold faced and highlighted. The theory portion of each chapter is studied thoroughly as it helps solve many of the problems with comparative ease. Selected material from this book is used for a semester course on graph theory, while the entire book serves for a whole session course.

Digital Technology in Public Health and Rehabilitation Care: COVID Era provides an in-depth examination on how digital technology has impacted public health and rehabilitation during the COVID-19 pandemic. The book showcases the range of digital technology applications utilized in healthcare, including the use of mobile phones, computers, wearable and non-wearable technologies, sensors, 3D printers, robotics, Artificial Intelligence (AI), internet technologies, websites and apps, virtual and augmented realities, and computer games. With a wealth of case studies and insights, this book is an essential resource on the impact of digital technology on public health and rehabilitation services in the COVID-19 era. The COVID-19 pandemic had a major impact on the rehabilitation services available to those in need, particularly for older adults, people with physical and cognitive impairments, children with autism and ADHD, and individuals with physical and mental health disorders. In response to these challenges, the book focuses on the potential for advanced digital technologies to revolutionize public health and rehabilitation services, highlighting the need for researchers and healthcare professionals to work together to promote digital-based interventions.

De nombreux systèmes physiques, mécaniques, financiers et économiques peuvent être décrits par des modèles mathématiques qui visent à optimiser des fonctions, trouver des équilibres et effectuer des arbitrages. Souvent, la convexité des ensembles et des fonctions ainsi que les conditions de monotonie sur les systèmes d'inéquations qui régissent ces systèmes se présentent naturellement dans les modèles. C'est dans cet esprit que nous avons conçu ce livre en mettant l'accent sur une approche géométrique qui privilégie l'intuition par rapport à une approche plus analytique. Les démonstrations des résultats classiques ont été revues dans cette optique et simplifiées. De nombreux exemples d'applications sont étudiés et des exercices sont proposés.Ce livre s'adresse aux étudiants en master de mathématiques appliquées, ainsi qu'aux doctorants, chercheurs et ingénieurs souhaitant comprendre les fondements de l'analyse convexe et de la théorie des inéquations variationnelles monotones.

A Simple Approach of Limit of A FunctionThis is an Easy to understand Review and self-teaching Practice workbook on Limit of Functions. It consist of lots of examples on Limit theorem, Continuity of Function, Trigonometric limits and limits involving infinity. The book will also enhance your knowledge in mathematics. Learn more and Increase your math skills on... Limit Theorem Continuity of a Function Trigonometric Limit Limits involving infinity Worked Examples ranging from Simple to ComplexImprove your math skills by grabbing a copy

This book collects together original research and survey articles highlighting the fertile interdisciplinary applications of convex lattice polytopes in modern mathematics. Covering a diverse range of topics, including algebraic geometry, mirror symmetry, symplectic geometry, discrete geometry, and algebraic combinatorics, the common theme is the study of lattice polytopes. These fascinating combinatorial objects are a cornerstone of toric geometry and continue to find rich and unforeseen applications throughout mathematics. The workshop Interactions with Lattice Polytopes assembled many top researchers at the Otto-von-Guericke-Universitat Magdeburg in 2017 to discuss the role of lattice polytopes in their work, and many of their presented results are collected in this book. Intended to be accessible, these articles are suitable for researchers and graduate students interested in learning about some of the wide-ranging interactions of lattice polytopes in pure mathematics.

Discrete Mathematics: A Gateway to the Mathematical Garden is an introduction to finite and discrete mathematics. This book includes all the important and foundational mathematics to support the student learning finite mathematics for the first time: logic, set theory, number theory, proofs, combinatorics, and graph theory. The exposition helps the student-reader learn to think logically and reasonably about mathematical structures. Discussions of cryptology, computer science, machine-readable codes, and operations research are used to give the student a sense of how the mathematics is applied. Throughout the book, examples illustrate the material and provide insight into the mathematical theory. The book is essentially self-contained. There are very few prerequistes aside from some mathematical maturity and familiarity with algebra. Problems to help the student master the concepts are included at the end of each section. Each chapter concludes with a set of supplementary problems and a set of sample test questions.Discrete Mathematics: A Gateway to the Mathematical Garden, Chuck Garner, paperback, color, first edition, 7.44in by 9.68 in, 217 pages, ISBN 978-1-312-71237-9, copyright 2023 Charles R. Garner Jr.

This volume constitutes the proceedings of the 9th International Conference on Variable Neighborhood Search, ICVNS 2023, held in Abu Dhabi, United Arab Emirates, in October 2022.The 11 full papers presented in this volume were carefully reviewed and selected from 29 submissions. The papers describe recent advances in methods and applications of variable neighborhood search.

The ever-growing applications and richness of approaches to the Riordan group is captured in this comprehensive monograph, authored by those who are among the founders and foremost world experts in this field. The concept of a Riordan array has played a unifying role in enumerative combinatorics over the last three decades. The Riordan arrays and Riordan group is a new growth point in mathematics that is both being influenced by, and continuing its contributions to, other fields such as Lie groups, elliptic curves, orthogonal polynomials, spline functions, networks, sequences and series, Beal conjecture, Riemann hypothesis, to name several. In recent years the Riordan group has made links to quantum field theory and has become a useful tool for computer science and computational chemistry. We can look forward to discovering further applications to unexpected areas of research. Providing a baseline and springboard to further developments and study, this book may also serve asa text for anyone interested in discrete mathematics, including combinatorics, number theory, matrix theory, graph theory, and algebra.

This book constitutes the proceedings of the 18th International Workshop on Algorithms and Models for the Web Graph, WAW 2023, held in Toronto, Canada, in May 23¿26, 2023.The 12 Papers presented in this volume were carefully reviewed and selected from 21 submissions. The aim of the workshop was understanding of graphs that arise from the Web and various user activities on the Web, and stimulate the development of high-performance algorithms and applications that exploit these graphs.

Anders als viele denken, heißt ¿Kombinatorik können¿ nicht, irgendwelche Formeln geschickt anwenden zu können. Es heißt vielmehr, die klaren, konstruktiven und oft originellen Ideen hinter diesen Formeln zu durchschauen und im Idealfall selbst zu entdecken. Kombinatorik ist die Theorie des intelligenten Zählens. Sie ist die Kunst, die Mächtigkeiten von Mengen zu bestimmen, ohne diese mühevoll abzählen zu müssen. Es gibt keinen Grund, darunter nur endliche Mengen zu verstehen. Daher widmet sich das letzte Kapitel dieses Buchs der Entdeckung des Unendlichen. In ¿Hilberts Hotel¿ und mit ¿Cantors Diagonalen¿ verliert das Unendliche alles Rätselhafte, das so gern hineingeheimnisst wird. Wie vieles (nicht alles) in der Mathematik ist Kombinatorik zuallererst ein spannendes Denkabenteuer. Haben Sie Spaß an Mathematik? Oder hatten Sie den einmal, und er ist Ihnen irgendwann abhandengekommen? Dann ist dieses Buch genau für Sie geschrieben worden. Besondere Vorkenntnisse sind nicht erforderlich. Das nötige Vorwissen haben Sie bereits.

Dieses Lehrbuch bietet eine kompakte Einführung in die Grundlagen der Graphentheorie und die Methoden der Netzwerkanalyse. Zahlreiche praktische Beispiele und Übungsaufgaben mit Lösungsvorschlägen helfen Leser:innen dabei, die theoretischen Konzepte besser zu verstehen und anzuwenden. Dabei werden unterschiedliche Technologien und Programmiersprachen verwendet, um ein breites Spektrum an Anwendungen abzudecken. Darüber hinaus beleuchten spezielle Kapitel die Methodik mit Blick auf die Planung und Durchführung eigener Netzwerkanalyseprojekte sowie ethische und datenschutzrechtliche Aspekte. So liefert das Buch nicht nur einen theoretischen Überblick, sondern auch praktische Tipps und Anleitungen für die Untersuchung eigener netzwerkanalytischer Fragestellungen. Dieses Buch eignet sich nicht nur als Nachschlagewerk für Studierende und Dozierende vielfältiger Fachdisziplinen mit curricularem Bezug zum Thema, sondern auch als Ergänzung des Repertoires von Praktiker:innen im Bereich Data Science mit Interesse an der Untersuchung von Netzwerken. Ob als theoretischer Einstieg oder als praktischer Ratgeber - dieses Buch leistet einen Beitrag für die Untersuchung und Analyse von Netzwerken und bietet eine Grundlage für weiterführende Studien und Projekte.

These are the proceedings of Eurocrypt 2010, the 29th in the series of Eu- pean conferences on the Theory and Application of Cryptographic Techniques. The conference was sponsored by the International Association for Cryptologic Research and held on the French Riviera, May 30¿June 3, 2010. A total of 191 papers were received of which 188 were retained as valid submissions. These were each assigned to at least three Program Committee members and a total of 606 review reports were produced. The printed record of the reviews and extensive online discussions that followed would be almost as voluminous as these proceedings. In the end 35 submissions were accepted with twosubmissionpairsbeingmergedtogive33paperspresentedattheconference. The ?nal papers in these proceedings were not subject to a second review before publication and the authors are responsible for their contents. The ProgramCommittee, listed on the next page, deservesparticular thanks for all their hard work, their outstanding expertise, and their constant c- mitment to all aspects of the evaluation process. These thanks are of course extended to the very many external reviewers who took the time to help out during the evaluation process.It was also a greatpleasure to honor and welcome Moti Yung who gave the 2010 IACR Distinguished Lecture.

The congruences of a lattice form the congruence lattice. Over the last several decades, the study of congruence lattices has established itself as a large and important field with a great number of interesting and deep results, as well as many open problems. Written by one of the leading experts in lattice theory, this text provides a self-contained introduction to congruences of finite lattices and presents the major results of the last 90 years. It features the author¿s signature ¿Proof-by-Picture¿ method, which is used to convey the ideas behind formal proofs in a visual, more intuitive manner. Key features include:an insightful discussion of techniques to construct "nice" finite lattices with given congruence lattices and "nice" congruence-preserving extensionscomplete proofs, an extensive bibliography and index, and over 180 illustrationsadditional chapters covering new results of the lastseven years, increasing the size of this edition to 430 pages, 360 statements, and 262 referencesThis text is appropriate for a one-semester graduate course in lattice theory, and it will also serve as a valuable reference for researchers studying lattices. Reviews of previous editions:¿[This] monograph¿is an exceptional work in lattice theory, like all the contributions by this author. The way this book is written makes it extremely interesting for the specialists in the field but also for the students in lattice theory. ¿ Cosmin Pelea, Studia Universitatis Babes-Bolyai Mathematica LII (1), 2007 "The book is self-contained, with many detailed proofs presented that can be followed step-by-step. I believe that this book is a much-needed tool for any mathematician wishing a gentle introduction to the field of congruences representations of finite lattices, with emphasis on the more 'geometric' aspects." ¿ Mathematical Reviews

This book is a compilation of all basic topics on functions of Several Variables and is primarily meant for undergraduate and post graduate students.

This book is motivated by the fascinating interrelations between ergodic theory and number theory (as established since the 1950s). It examines several generalizations and extensions of classical continued fractions, including generalized Lehner, simple, and Hirzebruch-Jung continued fractions.

This textbook aims to point out the most important principles of data analysis from the mathematical point of view. Specifically, it selected these questions for exploring: Which are the principles necessary to understand the implications of an application, and which are necessary to understand the conditions for the success of methods used? Theory is presented only to the degree necessary to apply it properly, striving for the balance between excessive complexity and oversimplification. Its primary focus is on principles crucial for application success. Topics and features:Focuses on approaches supported by mathematical arguments, rather than sole computing experiencesInvestigates conditions under which numerical algorithms used in data science operate, and what performance can be expected from themConsiders key data science problems: problem formulation including optimality measure; learning and generalization in relationships to training set size and number of free parameters; and convergence of numerical algorithmsExamines original mathematical disciplines (statistics, numerical mathematics, system theory) as they are specifically relevant to a given problemAddresses the trade-off between model size and volume of data available for its identification and its consequences for model parametrizationInvestigates the mathematical principles involves with natural language processing and computer visionKeeps subject coverage intentionally compact, focusing on key issues of each topic to encourage full comprehension of the entire bookAlthough this core textbook aims directly at students of computer science and/or data science, it will be of real appeal, too, to researchers in the field who want to gain a proper understanding of the mathematical foundations ¿beyond¿ the sole computing experience.