This edition now offers a thorough development of the embedding of Latin squares and combinatorial designs. It also presents some pure mathematical ideas, including connections between universal algebra and graph designs.
The authors focus on several basic designs, including Steiner triple systems, Latin squares, and finite projective and affine planes. They produce these designs using flexible constructions and then add interesting properties that may be required, such as resolvability, embeddings, and orthogonality. The authors also construct more complicated structures, such as Steiner quadruple systems.
By providing both classical and state-of-the-art construction techniques, this book enables students to produce many other types of designs.
The book presents several existing, yet still interesting and instructive, examples of modular forms. Two chapters develop useful properties of the Bernoulli numbers and illustrate arithmetic progressions, proving the theorems of van der Waerden, Roth, and Szemeredi. The book also explains applications of the theory to three problems that lie outside of number theory in the areas of cryptanalysis, microwave radiation, and diamond cutting. The text is complemented by the inclusion of over one hundred exercises to test the reader's understanding.
New to the Second Edition
Reorganization of all chapters More complete and involved treatment of Galois theory A study of binary quadratic forms and a comparison of the ideal and form class groups More comprehensive section on Pollard’s cubic factoring algorithm More detailed explanations of proofs, with less reliance on exercises, to provide a sound understanding of challenging material
The book includes mini-biographies of notable mathematicians, convenient cross-referencing, a comprehensive index, and numerous exercises. The appendices present an overview of all the concepts used in the main text, an overview of sequences and series, the Greek alphabet with English transliteration, and a table of Latin phrases and their English equivalents.
Suitable for a one-semester course, this accessible, self-contained text offers broad, in-depth coverage of numerous applications. Readers are lead at a measured pace through the topics to enable a clear understanding of the pinnacles of algebraic number theory.
The book begins by tracing the development of cryptology from that of an arcane practice used, for example, to conceal alchemic recipes, to the modern scientific method that is studied and employed today. The remainder of the book explores the modern aspects and applications of cryptography, covering symmetric- and public-key cryptography, cryptographic protocols, key management, message authentication, e-mail and Internet security, and advanced applications such as wireless security, smart cards, biometrics, and quantum cryptography. The author also includes non-cryptographic security issues and a chapter devoted to information theory and coding. Nearly 200 diagrams, examples, figures, and tables along with abundant references and exercises complement the discussion.
Written by leading authority and best-selling author on the subject Richard A. Mollin, Codes: The Guide to Secrecy from Ancient to Modern Times is the essential reference for anyone interested in this exciting and fascinating field, from novice to veteran practitioner.
With numerous examples throughout, the text begins with coverage of algebraic number theory, binary quadratic forms, Diophantine approximation, arithmetic functions, p-adic analysis, Dirichlet characters, density, and primes in arithmetic progression. It then applies these tools to Diophantine equations, before developing elliptic curves and modular forms. The text also presents an overview of Fermat’s Last Theorem (FLT) and numerous consequences of the ABC conjecture, including Thue–Siegel–Roth theorem, Hall’s conjecture, the Erdös–Mollin-–Walsh conjecture, and the Granville–Langevin Conjecture. In the appendix, the author reviews sieve methods, such as Eratothesenes’, Selberg’s, Linnik’s, and Bombieri’s sieves. He also discusses recent results on gaps between primes and the use of sieves in factoring.
By focusing on salient techniques in number theory, this textbook provides the most up-to-date and comprehensive material for a second course in this field. It prepares students for future study at the graduate level.
New to the Second Edition
• Removal of all advanced material to be even more accessible in scope
• New fundamental material, including partition theory, generating functions, and combinatorial number theory
• Expanded coverage of random number generation, Diophantine analysis, and additive number theory
• More applications to cryptography, primality testing, and factoring
• An appendix on the recently discovered unconditional deterministic polynomial-time algorithm for primality testing
Taking a truly elementary approach to number theory, this text supplies the essential material for a first course on the subject. Placed in highlighted boxes to reduce distraction from the main text, nearly 70 biographies focus on major contributors to the field. The presentation of over 1,300 entries in the index maximizes cross-referencing so students can find data with ease.
Discrete Structures and Their Interactions highlights the connections among various discrete structures, including graphs, directed graphs, hypergraphs, partial orders, finite topologies, and simplicial complexes. It also explores their relationships to classical areas of mathematics, such as linear and multilinear algebra, analysis, probability, logic, and topology.
The text introduces a number of discrete structures, such as hypergraphs, finite topologies, preorders, simplicial complexes, and order ideals of monomials, that most graduate students in combinatorics, and even some researchers in the field, seldom experience. The author explains how these structures have important applications in many areas inside and outside of combinatorics. He also discusses how to recognize valuable research connections through the structures.
Intended for graduate and upper-level undergraduate students in mathematics who have taken an initial course in discrete mathematics or graph theory, this book shows how discrete structures offer new insights into the classical fields of mathematics. It illustrates how to use discrete structures to represent the salient features and discover the underlying combinatorial principles of seemingly unrelated areas of mathematics.
Interesting examples highlight the interdisciplinary nature of this area
Pearls of Discrete Mathematics presents methods for solving counting problems and other types of problems that involve discrete structures. Through intriguing examples, problems, theorems, and proofs, the book illustrates the relationship of these structures to algebra, geometry, number theory, and combinatorics.
Each chapter begins with a mathematical teaser to engage readers and includes a particularly surprising, stunning, elegant, or unusual result. The author covers the upward extension of Pascal’s triangle, a recurrence relation for powers of Fibonacci numbers, ways to make change for a million dollars, integer triangles, the period of Alcuin’s sequence, and Rook and Queen paths and the equivalent Nim and Wythoff’s Nim games. He also examines the probability of a perfect bridge hand, random tournaments, a Fibonacci-like sequence of composite numbers, Shannon’s theorems of information theory, higher-dimensional tic-tac-toe, animal achievement and avoidance games, and an algorithm for solving Sudoku puzzles and polycube packing problems. Exercises ranging from easy to challenging are found in each chapter while hints and solutions are provided in an appendix.
With over twenty-five years of teaching experience, the author takes an organic approach that explores concrete problems, introduces theory, and adds generalizations as needed. He delivers an absorbing treatment of the basic principles of discrete mathematics.
The superior explanations, broad coverage, and abundance of illustrations and exercises that positioned this as the premier graph theory text remain, but are now augmented by a broad range of improvements. Nearly 200 pages have been added for this edition, including nine new sections and hundreds of new exercises, mostly non-routine.
What else is new?
New chapters on measurement and analytic graph theory
Supplementary exercises in each chapter - ideal for reinforcing, reviewing, and testing.
Solutions and hints, often illustrated with figures, to selected exercises - nearly 50 pages worth
Reorganization and extensive revisions in more than half of the existing chapters for smoother flow of the exposition
Foreshadowing - the first three chapters now preview a number of concepts, mostly via the exercises, to pique the interest of reader
Gross and Yellen take a comprehensive approach to graph theory that integrates careful exposition of classical developments with emerging methods, models, and practical needs. Their unparalleled treatment provides a text ideal for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology.
The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics.
Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook.
A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.
Most available cryptology books primarily focus on either mathematics or history. Breaking this mold, Secret History: The Story of Cryptology gives a thorough yet accessible treatment of both the mathematics and history of cryptology. Requiring minimal mathematical prerequisites, the book presents the mathematics in sufficient detail and weaves the history throughout the chapters. In addition to the fascinating historical and political sides of cryptology, the author—a former Scholar-in-Residence at the U.S. National Security Agency (NSA) Center for Cryptologic History—includes interesting instances of codes and ciphers in crime, literature, music, and art.
Following a mainly chronological development of concepts, the book focuses on classical cryptology in the first part. It covers Greek and Viking cryptography, the Vigenère cipher, the one-time pad, transposition ciphers, Jefferson’s cipher wheel, the Playfair cipher, ADFGX, matrix encryption, World War II cipher systems (including a detailed examination of Enigma), and many other classical methods introduced before World War II.
The second part of the book examines modern cryptology. The author looks at the work of Claude Shannon and the origin and current status of the NSA, including some of its Suite B algorithms such as elliptic curve cryptography and the Advanced Encryption Standard. He also details the controversy that surrounded the Data Encryption Standard and the early years of public key cryptography. The book not only provides the how-to of the Diffie-Hellman key exchange and RSA algorithm, but also covers many attacks on the latter. Additionally, it discusses Elgamal, digital signatures, PGP, and stream ciphers and explores future directions such as quantum cryptography and DNA computing.
With numerous real-world examples and extensive references, this book skillfully balances the historical aspects of cryptology with its mathematical details. It provides readers with a sound foundation in this dynamic field.
Please visit Dr. Bauer's website, which provides access to exercise sets: http://depts.ycp.edu/~cbauer/
The Handbook of Applied Cryptography provides a treatment that is multifunctional:
It serves as an introduction to the more practical aspects of both conventional and public-key cryptography
It is a valuable source of the latest techniques and algorithms for the serious practitioner
It provides an integrated treatment of the field, while still presenting each major topic as a self-contained unit
It provides a mathematical treatment to accompany practical discussions
It contains enough abstraction to be a valuable reference for theoreticians while containing enough detail to actually allow implementation of the algorithms discussed
Now in its third printing, this is the definitive cryptography reference that the novice as well as experienced developers, designers, researchers, engineers, computer scientists, and mathematicians alike will use.
New to the Second Edition
Separate chapters on Schur complements, additional types of canonical forms, tensors, matrix polynomials, matrix equations, special types of matrices, generalized inverses, matrices over finite fields, invariant subspaces, representations of quivers, and spectral sets New chapters on combinatorial matrix theory topics, such as tournaments, the minimum rank problem, and spectral graph theory, as well as numerical linear algebra topics, including algorithms for structured matrix computations, stability of structured matrix computations, and nonlinear eigenvalue problems More chapters on applications of linear algebra, including epidemiology and quantum error correction New chapter on using the free and open source software system Sage for linear algebra Additional sections in the chapters on sign pattern matrices and applications to geometry Conjectures and open problems in most chapters on advanced topics
Highly praised as a valuable resource for anyone who uses linear algebra, the first edition covered virtually all aspects of linear algebra and its applications. This edition continues to encompass the fundamentals of linear algebra, combinatorial and numerical linear algebra, and applications of linear algebra to various disciplines while also covering up-to-date software packages for linear algebra computations.
Newly enlarged, updated second edition of a valuable, widely used text presents algorithms for shortest paths, maximum flows, dynamic programming and backtracking. Also discussed are binary trees, heuristic and near optimums, matrix multiplication, and NP-complete problems. New to this edition: Chapter 9 shows how to mix known algorithms and create new ones, while Chapter 10 presents the "Chop-Sticks" algorithm, used to obtain all minimum cuts in an undirected network without applying traditional maximum flow techniques. This algorithm has led to the new mathematical specialty of network algebra. The text assumes no background in linear programming or advanced data structure, and most of the material is suitable for undergraduates. 153 black-and-white illus. 23 tables. Exercises, with answers at the ends of chapters.
Written by well-known scholars in the field, CombinatorialReasoning: An Introduction to the Art ofCounting introduces combinatorics alongside moderntechniques, showcases the interdisciplinary aspects of the topic,and illustrates how to problem solve with a multitude of exercisesthroughout. The authors' approach is very reader-friendly andavoids the "scholarly tone" found in many books on this topic.
The authors introduce the core principles of modern cryptography, with an emphasis on formal definitions, clear assumptions, and rigorous proofs of security. The book begins by focusing on private-key cryptography, including an extensive treatment of private-key encryption, message authentication codes, and hash functions. The authors also present design principles for widely used stream ciphers and block ciphers including RC4, DES, and AES, plus provide provable constructions of stream ciphers and block ciphers from lower-level primitives. The second half of the book covers public-key cryptography, beginning with a self-contained introduction to the number theory needed to understand the RSA, Diffie-Hellman, and El Gamal cryptosystems (and others), followed by a thorough treatment of several standardized public-key encryption and digital signature schemes.
Integrating a more practical perspective without sacrificing rigor, this widely anticipated Second Edition offers improved treatment of:Stream ciphers and block ciphers, including modes of operation and design principles Authenticated encryption and secure communication sessions Hash functions, including hash-function applications and design principles Attacks on poorly implemented cryptography, including attacks on chained-CBC encryption, padding-oracle attacks, and timing attacks The random-oracle model and its application to several standardized, widely used public-key encryption and signature schemes Elliptic-curve cryptography and associated standards such as DSA/ECDSA and DHIES/ECIES
Containing updated exercises and worked examples, Introduction to Modern Cryptography, Second Edition can serve as a textbook for undergraduate- or graduate-level courses in cryptography, a valuable reference for researchers and practitioners, or a general introduction suitable for self-study.
Optional sections designated as "excursion" and "exploration" present interesting sidelights of graph theory and touch upon topics that allow students the opportunity to experiment and use their imaginations. Three appendixes review important facts about sets and logic, equivalence relations and functions, and the methods of proof. The text concludes with solutions or hints for odd-numbered exercises, in addition to references, indexes, and a list of symbols.
Chapters 0–3 cover fundamental operations involving sets and the principle of mathematical induction, and standard combinatorial topics: basic counting principles, permutations, combinations, the inclusion-exclusion principle, generating functions, recurrence relations, and an introduction to the analysis of algorithms. Applications are emphasized wherever possible and more than 200 exercises at the ends of these chapters help students test their grasp of the material.
Chapters 4 and 5 survey graphs and digraphs, including their connectedness properties, applications of graph coloring, and more, with stress on applications to coding and other related problems. Two important problems in network optimization ― the minimal spanning tree problem and the shortest distance problem ― are covered in the last two chapters. A very brief nontechnical exposition of the theory of computational complexity and NP-completeness is outlined in the appendix.
This book will be useful to everyone who has struggled with displaying data in an informative and attractive way. Some basic knowledge of R is necessary (e.g., importing data into R). ggplot2 is a mini-language specifically tailored for producing graphics, and you'll learn everything you need in the book. After reading this book you'll be able to produce graphics customized precisely for your problems, and you'll find it easy to get graphics out of your head and on to the screen or page.
Imhausen shows that from the earliest beginnings, pharaonic civilization used numerical techniques to efficiently control and use their material resources and labor. Even during the Old Kingdom, a variety of metrological systems had already been devised. By the Middle Kingdom, procedures had been established to teach mathematical techniques to scribes in order to make them proficient administrators for their king. Imhausen looks at counterparts to the notation of zero, suggests an explanation for the evolution of unit fractions, and analyzes concepts of arithmetic techniques. She draws connections and comparisons to Mesopotamian mathematics, examines which individuals in Egyptian society held mathematical knowledge, and considers which scribes were trained in mathematical ideas and why.
Of interest to historians of mathematics, mathematicians, Egyptologists, and all those curious about Egyptian culture, Mathematics in Ancient Egypt sheds new light on a civilization's unique mathematical evolution.
Balancing abstract ideas with specific topical coverage, thebook utilizes real world examples with problems ranging from basiccalculations that are designed to develop fundamental concepts tomore challenging exercises that allow for a deeper exploration ofcomplex combinatorial situations. Simple cases are treated firstbefore moving on to general and more advanced cases. Additionalfeatures of the book include:
• Approximately 700 carefully structured problems designedfor readers at multiple levels, many with hints and/or shortanswers
• Numerous examples that illustrate problem solving usingboth combinatorial reasoning and sophisticated algorithmicmethods
• A novel approach to the study of recurrence sequences,which simplifies many proofs and calculations
• Concrete examples and diagrams interspersed throughout tofurther aid comprehension of abstract concepts
• A chapter-by-chapter review to clarify the most crucialconcepts covered
Combinatorial Reasoning: An Introduction to the Art ofCounting is an excellent textbook for upper-undergraduate andbeginning graduate-level courses on introductory combinatorics anddiscrete mathematics.
Modern cryptology has been described as the science of the integrity of information, covering all aspects like confidentiality, authenticity and non-repudiation and also including the protocols required for achieving these aims. In both theory and practice it requires notions and constructions from three major disciplines: computer science, electronic engineering and mathematics. Within mathematics, group theory, the theory of finite fields, and elementary number theory as well as some topics not normally covered in courses in algebra, such as the theory of Boolean functions and Shannon theory, are involved.Although essentially self-contained, a degree of mathematical maturity on the part of the reader is assumed, corresponding to his or her background in computer science or engineering. Algebra for Cryptologists is a textbook for an introductory course in cryptography or an upper undergraduate course in algebra, or for self-study in preparation for postgraduate study in cryptology.
This highly versatile text provides mathematical background used in a wide variety of disciplines, including mathematics and mathematics education, computer science, biology, chemistry, engineering, communications, and business.
Some of the major features and strengths of this textbook
More than 1,600 exercises, ranging from elementary to challenging, are included with hints/answers to all odd-numbered exercises.
Descriptions of proof techniques are accessible and lively.
Students benefit from the historical discussions throughout the textbook.
"Seamless R and C++ integration with Rcpp" is simply a wonderful book. For anyone who uses C/C++ and R, it is an indispensable resource. The writing is outstanding. A huge bonus is the section on applications. This section covers the matrix packages Armadillo and Eigen and the GNU Scientific Library as well as RInside which enables you to use R inside C++. These applications are what most of us need to know to really do scientific programming with R and C++. I love this book. -- Robert McCulloch, University of Chicago Booth School of Business
Rcpp is now considered an essential package for anybody doing serious computational research using R. Dirk's book is an excellent companion and takes the reader from a gentle introduction to more advanced applications via numerous examples and efficiency enhancing gems. The book is packed with all you might have ever wanted to know about Rcpp, its cousins (RcppArmadillo, RcppEigen .etc.), modules, package development and sugar. Overall, this book is a must-have on your shelf. -- Sanjog Misra, UCLA Anderson School of Management
The Rcpp package represents a major leap forward for scientific computations with R. With very few lines of C++ code, one has R's data structures readily at hand for further computations in C++. Hence, high-level numerical programming can be made in C++ almost as easily as in R, but often with a substantial speed gain. Dirk is a crucial person in these developments, and his book takes the reader from the first fragile steps on to using the full Rcpp machinery. A very recommended book! -- Søren Højsgaard, Department of Mathematical Sciences, Aalborg University, Denmark
"Seamless R and C ++ Integration with Rcpp" provides the first comprehensive introduction to Rcpp. Rcpp has become the most widely-used language extension for R, and is deployed by over one-hundred different CRAN and BioConductor packages. Rcpp permits users to pass scalars, vectors, matrices, list or entire R objects back and forth between R and C++ with ease. This brings the depth of the R analysis framework together with the power, speed, and efficiency of C++.
Dirk Eddelbuettel has been a contributor to CRAN for over a decade and maintains around twenty packages. He is the Debian/Ubuntu maintainer for R and other quantitative software, edits the CRAN Task Views for Finance and High-Performance Computing, is a co-founder of the annual R/Finance conference, and an editor of the Journal of Statistical Software. He holds a Ph.D. in Mathematical Economics from EHESS (Paris), and works in Chicago as a Senior Quantitative Analyst.
The second edition adds a discussion of vector auto-regressive, structural vector auto-regressive, and structural vector error-correction models. To analyze the interactions between the investigated variables, further impulse response function and forecast error variance decompositions are introduced as well as forecasting. The author explains how these model types relate to each other.
The introductory chapter presents an overview of the foundations of the subject, consisting of topics such as logic, set theory, relations, functions, algebraic structures, and graphs. The subsequent chapters provide detailed coverage of each of these topics as well as major areas of discrete mathematics such as combinatorics, lattices and Boolean algebras. Major applications such as computer models and computation, coding theory, cryptography and databases are dealt with in the final chapters of the book. In addition to this, a new chapter on matrices is included in this edition of the book, which forms a part of MCA course curriculum.
The book is replete with features which enable the building of a firm foundation of the underlying principles of the subject and also provide adequate scope for testing the comprehension acquired by the students. Each chapter contains numerous worked-out examples within the main discussion as well as several chapter-end Supplementary Examples for revision. The Self-Test and Exercises at the end of each chapter provide large numbers of objective type questions and problems respectively. Answers to objective type questions and hints to exercises are also provided. All these pedagogic features, together with thorough coverage of the subject matter, make this book a readable text for beginners as well as advanced learners of the subject.
Facilitating effective and active learning, each chapter contains a mixture of discovery activities, expository text, in-class exercises, and homework problems.
Elementary exercises at the end of each expository section prompt students to review the material Try This! sections encourage students to construct fundamental components of the concepts, theorems, and proofs discussed. Sets of discovery problems and illustrative examples reinforce learning. Bonus sections can be used for take-home exams, projects, or further study Instructor Notes sections offer suggestions on how to use the material in each chapter
Discrete Mathematics with Ducks offers students a diverse introduction to the field and a solid foundation for further study in discrete mathematics and complies with SIGCSE guidelines. The book shows how combinatorics and graph theory are used in both computer science and mathematics.
Concepts are presented in a readable and accessible manner, and applications are stressed throughout so the reader never loses sight of the powerful tools graph theory provides to solve real-world problems. Such diverse areas as job assignment, delivery truck routing, location of emergency or service facilities, network reliability, zoo design, exam scheduling, error-correcting codes, facility layout, and the critical path method are covered.
The first part of the book presents the syntax and semantics of access control logic, basic access control concepts, and an introduction to confidentiality and integrity policies. The second section covers access control in networks, delegation, protocols, and the use of cryptography. In the third section, the authors focus on hardware and virtual machines. The final part discusses confidentiality, integrity, and role-based access control.
Taking a logical, rigorous approach to access control, this book shows how logic is a useful tool for analyzing security designs and spelling out the conditions upon which access control decisions depend. It is designed for computer engineers and computer scientists who are responsible for designing, implementing, and verifying secure computer and information systems.
The four-part treatment begins with a section on counting and listing that covers basic counting, functions, decision trees, and sieving methods. The following section addresses fundamental concepts in graph theory and a sampler of graph topics. The third part examines a variety of applications relevant to computer science and mathematics, including induction and recursion, sorting theory, and rooted plane trees. The final section, on generating functions, offers students a powerful tool for studying counting problems. Numerous exercises appear throughout the text, along with notes and references. The text concludes with solutions to odd-numbered exercises and to all appendix exercises.
Just as with the first three editions, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible to the talented and hardworking undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings, Eulerian and Hamiltonian cycles, and planar graphs.
New to this edition are the Quick Check exercises at the end of each section. In all, the new edition contains about 240 new exercises. Extra examples were added to some sections where readers asked for them.
The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, the theory of designs, enumeration under group action, generating functions of labeled and unlabeled structures and algorithms and complexity.
The book encourages students to learn more combinatorics, provides them with a not only useful but also enjoyable and engaging reading.
The Solution Manual is available upon request for all instructors who adopt this book as a course text. Please send your request to firstname.lastname@example.org.
The previous edition of this textbook has been adopted at various schools including UCLA, MIT, University of Michigan, and Swarthmore College. It was also translated into Korean.
New to the Fifth Edition
New or expanded coverage of graph minors, perfect graphs, chromatic polynomials, nowhere-zero flows, flows in networks, degree sequences, toughness, list colorings, and list edge colorings New examples, figures, and applications to illustrate concepts and theorems Expanded historical discussions of well-known mathematicians and problems More than 300 new exercises, along with hints and solutions to odd-numbered exercises at the back of the book Reorganization of sections into subsections to make the material easier to read Bolded definitions of terms, making them easier to locate
Despite a field that has evolved over the years, this student-friendly, classroom-tested text remains the consummate introduction to graph theory. It explores the subject’s fascinating history and presents a host of interesting problems and diverse applications.
The book's three sections look at foundations, multiagent networks, and networks as systems. The authors give an overview of important ideas from graph theory, followed by a detailed account of the agreement protocol and its various extensions, including the behavior of the protocol over undirected, directed, switching, and random networks. They cover topics such as formation control, coverage, distributed estimation, social networks, and games over networks. And they explore intriguing aspects of viewing networks as systems, by making these networks amenable to control-theoretic analysis and automatic synthesis, by monitoring their dynamic evolution, and by examining higher-order interaction models in terms of simplicial complexes and their applications.
The book will interest graduate students working in systems and control, as well as in computer science and robotics. It will be a standard reference for researchers seeking a self-contained account of system-theoretic aspects of multiagent networks and their wide-ranging applications.
This book has been adopted as a textbook at the following universities:
University of Stuttgart, Germany
Royal Institute of Technology, Sweden
Johannes Kepler University, Austria
Georgia Tech, USA
University of Washington, USA
Ohio University, USA
A manual of selected solutions is available for sale to students; see sidebar. A complete solution manual is available free to instructors who have adopted the book as a required text.
The lively and accessible text requires only minimal scientific background. Designed for senior college or beginning graduate-level students, it assumes only elementary calculus and basic probability theory for the first part, and ordinary differential equations and continuous probability for the second section. All problems require students to study and create models, encouraging their active participation rather than a mechanical approach.
Beyond the classroom, this volume will prove interesting and rewarding to anyone concerned with the development of mathematical models or the application of modeling to problem solving in a wide array of applications.
Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Chapter 3 contains an extended treatment of the principle of inclusion and exclusion which is indispensable to the enumeration of permutations with restricted position given in Chapters 7 and 8. Chapter 4 examines the enumeration of permutations in cyclic representation and Chapter 5 surveys the theory of distributions. Chapter 6 considers partitions, compositions, and the enumeration of trees and linear graphs.
Each chapter includes a lengthy problem section, intended to develop the text and to aid the reader. These problems assume a certain amount of mathematical maturity. Equations, theorems, sections, examples, and problems are numbered consecutively in each chapter and are referred to by these numbers in other chapters.
This book features a unique combination of comprehensive coverage of logic with a solid exposition of the most important fields of discrete mathematics, presenting material that has been tested and refined by the authors in university courses taught over more than a decade.
The chapters on logic - propositional and first-order - provide a robust toolkit for logical reasoning, emphasizing the conceptual understanding of the language and the semantics of classical logic as well as practical applications through the easy to understand and use deductive systems of Semantic Tableaux and Resolution. The chapters on set theory, number theory, combinatorics and graph theory combine the necessary minimum of theory with numerous examples and selected applications. Written in a clear and reader-friendly style, each section ends with an extensive set of exercises, most of them provided with complete solutions which are available in the accompanying solutions manual.
Key Features:Suitable for a variety of courses for students in both Mathematics and Computer Science.Extensive, in-depth coverage of classical logic, combined with a solid exposition of a selection of the most important fields of discrete mathematicsConcise, clear and uncluttered presentation with numerous examples.Covers some applications including cryptographic systems, discrete probability and network algorithms.
Logic and Discrete Mathematics: A Concise Introduction is aimed mainly at undergraduate courses for students in mathematics and computer science, but the book will also be a valuable resource for graduate modules and for self-study.
Key features of Number Theory: Structures, Examples, and Problems:
* A rigorous exposition starts with the natural numbers and the basics.
* Important concepts are presented with an example, which may also emphasize an application. The exposition moves systematically and intuitively to uncover deeper properties.
* Topics include divisibility, unique factorization, modular arithmetic and the Chinese Remainder Theorem, Diophantine equations, quadratic residues, binomial coefficients, Fermat and Mersenne primes and other special numbers, and special sequences. Sections on mathematical induction and the pigeonhole principle, as well as a discussion of other number systems are covered.
* Unique exercises reinforce and motivate the reader, with selected solutions to some of the problems.
* Glossary, bibliography, and comprehensive index round out the text.
Written by distinguished research mathematicians and renowned teachers, this text is a clear, accessible introduction to the subject and a source of fascinating problems and puzzles, from advanced high school students to undergraduates, their instructors, and general readers at all levels.