Diskret matematik

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.

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 constitutes the refereed proceedings of the 31st Annual International Cryptology Conference, CRYPTO 2011, held in Santa Barbara, CA, USA in August 2011. The 42 revised full papers presented were carefully reviewed and selected from 230 submissions. The volume also contains the abstract of one invited talk. The papers are organized in topical sections on randomness and its use; computer-assisted cryptographic proofs; outsourcing and delegatin computation; symmetric cryptanalysis and constructions; secure computation: leakage and side channels; quantum cryptography; lattices and knapsacks; public-key encryption; symmetric schemes; signatures; obilvious transfer and secret sharing; and multivariate and coding-based schemes.

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.

This book constitutes the refereed proceedings of the 34th International Workshop on Combinatorial Algorithms, IWOCA 2023, held in Tainan, Taiwan, during June 7¿10, 2023. The 33 full papers included in this book were carefully reviewed and selected from 86 submissions. They were organized in topical sections as follows: algorithms and data structures; algorithmic and combinatorical aspects of cryptography and information security; algorithmic game theory and complexity of games; approximation algorithms; complexity theory; combinatorics and graph theory; combinatorial generation, enumeration and counting; combinatorial optimization; combinatorics of words; computational biology; computational geometry; decompositions and combinatorial designs; distributed and network algorithms; experimental combinatorics; fine-grained complexity; graph algorithms and modelling with graphs; graph drawing and graph labelling; network theoryand temporal graphs; quantum computing and algorithms for quantum computers; online algorithms; parameterized and exact algorithms; probabilistic and randomized algorithms; and streaming algorithms.

Professor Stephen A. Cook is a pioneer of the theory of computational complexity. His work on NP-completeness and the P vs. NP problem remains a central focus of this field. Cook won the 1982 Turing Award for "his advancement of our understanding of the complexity of computation in a significant and profound way." This volume includes a selection of seminal papers embodying the work that led to this award, exemplifying Cook's synthesis of ideas and techniques from logic and the theory of computation including NP-completeness, proof complexity, bounded arithmetic, and parallel and space-bounded computation. These papers are accompanied by contributed articles by leading researchers in these areas, which convey to a general reader the importance of Cook's ideas and their enduring impact on the research community. The book also contains biographical material, Cook's Turing Award lecture, and an interview. Together these provide a portrait of Cook as a recognized leader and innovator in mathematics and computer science, as well as a gentle mentor and colleague.

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.

This book constitutes the refereed proceedings of the 24th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2023, held in Madison, WI, USA, during June 21¿23, 2023.The 33 full papers presented were carefully reviewed and selected from 119 submissions. IPCO is under the auspices of the Mathematical Optimization Society, and it is an important forum for presenting present recent developments in theory, computation, and applications. The scope of IPCO is viewed in a broad sense, to include algorithmic and structural results in integer programming and combinatorial optimization as well as revealing computational studies and novel applications of discrete optimization to practical problems.

This book constitutes the refereed proceedings of the 14th International Conference on Combinatorics on Words, WORDS 2023, held in Umeå, Sweden, during June 12¿16, 2023.The 19 contributed papers presented in this book were carefully reviewed and selected from 28 submissions. In addition, the volume also contains 3 invited papers. WORDS is the main conference series devoted to combinatorics on words. This area is connected to several topics from computer science and mathematics, including string algorithms, automated proofs, discrete dynamics, number theory and, of course, classical combinatorics

This book constitutes the refereed proceedings of the 30th International Colloquium on Structural Information and Communication Complexity, SIROCCO 2023, held in Alcalá de Henares, Spain, during June 6¿9, 2023.The 26 full papers presented in this book were carefully reviewed and selected from 48 submissions. SIROCCO is devoted to the study of the interplay between structural knowledge, communication, and computing in decentralized systems of multiple communicating entities. Special emphasis is given to innovative approaches leading to better understanding of the relationship between computing and communication. This is the 30th edition of SIROCCO, and 3 of the 26 papers in this book are devoted to celebrating this fact, plus an additional paper about a recent trend to study special models of computation.

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.

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.

This book serves as an introduction to linear algebra for undergraduate students in data science, statistics, computer science, economics, and engineering. The book presents all the essentials in rigorous (proof-based) manner, describes the intuition behind the results, while discussing some applications to data science along the way.The book comes with two parts, one on vectors, the other on matrices. The former consists of four chapters: vector algebra, linear independence and linear subspaces, orthonormal bases and the Gram-Schmidt process, linear functions. The latter comes with eight chapters: matrices and matrix operations, invertible matrices and matrix inversion, projections and regression, determinants, eigensystems and diagonalizability, symmetric matrices, singular value decomposition, and stochastic matrices. The book ends with the solution of exercises which appear throughout its twelve chapters.

"e;The appearance of Grunbaum's book Convex Polytopes in 1967 was a moment of grace to geometers and combinatorialists. The special spirit of the book is very much alive even in those chapters where the book's immense influence made them quickly obsolete. Some other chapters promise beautiful unexplored land for future research. The appearance of the new edition is going to be another moment of grace. Kaibel, Klee and Ziegler were able to update the convex polytope saga in a clear, accurate, lively, and inspired way."e; (Gil Kalai, The Hebrew University of Jerusalem) "e;The original book of Grnbaum has provided the central reference for work in this active area of mathematics for the past 35 years...I first consulted this book as a graduate student in 1967; yet, even today, I am surprised again and again by what I find there. It is an amazingly complete reference for work on this subject up to that time and continues to be a major influence on research to this day."e; (Louis J. Billera, Cornell University) "e;The original edition of Convex Polytopes inspired a whole generation of grateful workers in polytope theory. Without it, it is doubtful whether many of the subsequent advances in the subject would have been made. The many seeds it sowed have since grown into healthy trees, with vigorous branches and luxuriant foliage. It is good to see it in print once again."e; (Peter McMullen, University College London)

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 focuses on the dynamic complexity of neural, genetic networks, and reaction diffusion systems. The author shows that all robust attractors can be realized in dynamics of such systems. In particular, a positive solution of the Ruelle-Takens hypothesis for on chaos existence for large class of reaction-diffusion systems is given. The book considers viability problems for such systems - viability under extreme random perturbations - and discusses an interesting hypothesis of M. Gromov and A. Carbone on biological evolution. There appears a connection with the Kolmogorov complexity theory. As applications, transcription-factors-microRNA networks are considered, patterning in biology, a new approach to estimate the computational power of neural and genetic networks, social and economical networks, and a connection with the hard combinatorial problems.

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.

CoPart 3 is a dual complement to Visual Category Theory Brick by Brick Part 3. It covers adjoint functors, diagram shapes and categories, cones and cocones, limits and colimits, pullbacks, pushouts.

This book constitutes the proceedings of the 17th International Conference and Workshops on Algorithms and Computation, WALCOM 2023, which took place in Hsinchu, Taiwan, in March 2023.The 30 full papers presented together with 2 invited papers were carefully reviewed and selected from 75 submissions. They cover topics such as: computational geometry; string algorithm; optimization; graph algorithm; approximation algorithm; and parameterized complexity.