Mathematical logic Books

Book SynopsisThis undergraduate textbook promotes an active transition to higher mathematics. Problem solving is the heart and soul of this book: each problem is carefully chosen to demonstrate, elucidate, or extend a concept. More than 300 exercises engage the reader in extensive arguments and creative approaches, while exploring connections between fundamental mathematical topics.Divided into four parts, this book begins with a playful exploration of the building blocks of mathematics, such as definitions, axioms, and proofs. A study of the fundamental concepts of logic, sets, and functions follows, before focus turns to methods of proof. Having covered the core of a transition course, the author goes on to present a selection of advanced topics that offer opportunities for extension or further study. Throughout, appendices touch on historical perspectives, current trends, and open questions, showing mathematics as a vibrant and dynamic human enterprise.This second edition has been reorganized to better reflect the layout and curriculum of standard transition courses. It also features recent developments and improved appendices. An Invitation to Abstract Mathematics is ideal for those seeking a challenging and engaging transition to advanced mathematics, and will appeal to both undergraduates majoring in mathematics, as well as non-math majors interested in exploring higher-level concepts.From reviews of the first edition:Bajnok’s new book truly invites students to enjoy the beauty, power, and challenge of abstract mathematics. … The book can be used as a text for traditional transition or structure courses … but since Bajnok invites all students, not just mathematics majors, to enjoy the subject, he assumes very little background knowledge. Jill Dietz, MAA ReviewsThe style of writing is careful, but joyously enthusiastic…. The author’s clear attitude is that mathematics consists of problem solving, and that writing a proof falls into this category. Students of mathematics are, therefore, engaged in problem solving, and should be given problems to solve, rather than problems to imitate. The author attributes this approach to his Hungarian background … and encourages students to embrace the challenge in the same way an athlete engages in vigorous practice. John Perry, zbMATHTable of ContentsPreface to Instructors.- Preface to Students.- Acknowledgments.- I What's Mathematics.- 1 Let's Play a Game!.- 2 What's the Name of the Game?.- 3 How to Make a Statement.- 4 What's True in Mathematics?.- A Ten Famous Conjectures.-B Ten Famous Theorems.- II The Foundations of Mathematics.- 5 Let's Be Logical!.- 6 Setting Examples.- 7 Quantifier Mechanics.- 8 Let's Be Functional!.- C The Foundations of Set Theory.- III How to Prove It.- 9 Universal Proofs.- 10 The Domino Theory.- 11 More Domino Games.- 12 Existential Proofs.- D Ten Famous Problems.- IV Advanced Math for Beginners.- 13 Mathematical Structures.- 14 Working in the Fields (and Other Structures).- 15 Group Work.- 16 Good Relations.- 17 Order, Please!.- 18 Now That's the Limit!.- 19 Sizing It Up.- 20 Infinite Delights.- 21 Number Systems Systematically.- 22 Games Are Valuable!.- E Graphic Content.- F All Games Considered.- G A Top Forty List of Math Theorems.

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Book SynopsisThis undergraduate textbook promotes an active transition to higher mathematics. Problem solving is the heart and soul of this book: each problem is carefully chosen to demonstrate, elucidate, or extend a concept. More than 300 exercises engage the reader in extensive arguments and creative approaches, while exploring connections between fundamental mathematical topics.Divided into four parts, this book begins with a playful exploration of the building blocks of mathematics, such as definitions, axioms, and proofs. A study of the fundamental concepts of logic, sets, and functions follows, before focus turns to methods of proof. Having covered the core of a transition course, the author goes on to present a selection of advanced topics that offer opportunities for extension or further study. Throughout, appendices touch on historical perspectives, current trends, and open questions, showing mathematics as a vibrant and dynamic human enterprise.This second edition has been reorganized to better reflect the layout and curriculum of standard transition courses. It also features recent developments and improved appendices. An Invitation to Abstract Mathematics is ideal for those seeking a challenging and engaging transition to advanced mathematics, and will appeal to both undergraduates majoring in mathematics, as well as non-math majors interested in exploring higher-level concepts.From reviews of the first edition:Bajnok’s new book truly invites students to enjoy the beauty, power, and challenge of abstract mathematics. … The book can be used as a text for traditional transition or structure courses … but since Bajnok invites all students, not just mathematics majors, to enjoy the subject, he assumes very little background knowledge. Jill Dietz, MAA ReviewsThe style of writing is careful, but joyously enthusiastic…. The author’s clear attitude is that mathematics consists of problem solving, and that writing a proof falls into this category. Students of mathematics are, therefore, engaged in problem solving, and should be given problems to solve, rather than problems to imitate. The author attributes this approach to his Hungarian background … and encourages students to embrace the challenge in the same way an athlete engages in vigorous practice. John Perry, zbMATHTable of ContentsPreface to Instructors.- Preface to Students.- Acknowledgments.- I What's Mathematics.- 1 Let's Play a Game!.- 2 What's the Name of the Game?.- 3 How to Make a Statement.- 4 What's True in Mathematics?.- A Ten Famous Conjectures.-B Ten Famous Theorems.- II The Foundations of Mathematics.- 5 Let's Be Logical!.- 6 Setting Examples.- 7 Quantifier Mechanics.- 8 Let's Be Functional!.- C The Foundations of Set Theory.- III How to Prove It.- 9 Universal Proofs.- 10 The Domino Theory.- 11 More Domino Games.- 12 Existential Proofs.- D Ten Famous Problems.- IV Advanced Math for Beginners.- 13 Mathematical Structures.- 14 Working in the Fields (and Other Structures).- 15 Group Work.- 16 Good Relations.- 17 Order, Please!.- 18 Now That's the Limit!.- 19 Sizing It Up.- 20 Infinite Delights.- 21 Number Systems Systematically.- 22 Games Are Valuable!.- E Graphic Content.- F All Games Considered.- G A Top Forty List of Math Theorems.

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Book SynopsisSuguru is a logic puzzle with simple rules and challenging solutions. The task consists of a rectangular or square grid divided into regions.The rules of Suguru are simple, each region must be filled with each of the digits from 1 to the number of cells in the region. Cells with the same digits must not be orthogonality or diagonally adjacent.This Logic Puzzles book is packed with the following features:- 500 Suguru (12x12) Puzzles from Easy to Hard.- Answers to every puzzle are provided.- Each puzzle is guaranteed to have only one solution. Includes free bonus puzzles you can download book (Tons of Sudoku Puzzles for Adults & Seniors)  Includes free bonus puzzles you can download book (Word Search With Hidden Message: 102 Puzzles for Adults and Seniors)  We hope you enjoy this book, which would also make a great gift for any puzzle lover.

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Book Synopsis ? Great gift for family, friends or work colleagues This Logic Puzzles book is packed with the following features:? 1000 Medium Binary Puzzle (12x12).? Each puzzle is guaranteed to have only one solution. ? Includes free bonus puzzles you can download book (Logic Puzzles & Brain Games for Adults) ? Answers to every puzzle are provided at the back of the book.? Six puzzles per page (8.5 x 11 inches).Playing Binary Puzzle is not just a fun way to pass the time, due to its logical elements it has been found as a proven method of exercising and stimulating portions of your brain, training it even, if you will and just like training any other muscle regularly you can expect to see an improvement in cognitive functions. Some studies go as far as indicating regular puzzles can even help reduce the risk of Alzheimer''s and other health problems in later life.Completing Binary Puzzle regularly helps the brain process both problem solving and improves logical thought process with the use of deductive reasoning, which can also be applied to approaching real life challenges in a different manner.????? The Giant Book of Binary Puzzle offers hours of entertainment for adults of all ages, from young adults to seniors ?????We hope this will be an entertaining and uplifting mental workout, enjoy The Giant Book of Binary Puzzle.

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Book Synopsis? Great gift for family, friends or work colleaguesPlaying logic puzzle is not just a fun way to pass the time, due to its logical elements it has been found as a proven method of exercising and stimulating portions of your brain, training it even if you will and just like training any other muscle regularly you can expect to see an improvement in cognitive functions. Some studies go as far as indicating regular puzzles can even help reduce the risk of Alzheimer''s and other health problems in later life.This Logic Puzzles book is packed with the following features:? 1000  Medium Suguru (12x12) puzzles.? Answers to every puzzle are provided.? Each puzzle is guaranteed to have only one solution.? Six puzzles per page (8.5 x 11 inches).??? Includes free bonus puzzles you can download book (Logic Puzzles & Brain Games for Adults) ???♥♥♥ The Giant Book of Suguru offers hours of entertainment for adults of all ages, from young adults to seniors ♥♥♥

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Book SynopsisThe book provides a fundamental exploration of cloud security, addressing the growing risks associated with modern cloud environments. It combines foundational theory with hands-on applications, equipping readers with the knowledge and tools needed to secure cloud platforms. Topics include cloud attack vectors, defence mechanisms, implementation challenges, and real-world case studies of major cloud service providers. Practical exercises and end-of-chapter questions reinforce key concepts, making this an essential resource. Designed for undergraduate and postgraduate students in computer science and cybersecurity, this book serves as a vital guide to securing cloud infrastructures and ensuring data integrity in a rapidly evolving technological landscape. Covers cloud security concepts, attack types, and defense mechanisms Includes cloud security tools, real-world case studies, and hands-on projects Discusses risk mitigation techniques and security best practices for cloud environments Examines real-world obstacles and solutions in cloud security adoption Analyses major cloud service providers and their security models

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Book SynopsisMany physical, chemical, biomedical, and technical processes can be described by partial differential equations or dynamical systems. In spite of increasing computational capacities, many problems are of such high complexity that they are solvable only with severe simplifications, and the design of efficient numerical schemes remains a central research challenge. This book presents a tutorial introduction to recent developments in mathematical methods for model reduction and approximation of complex systems.Model Reduction and Approximation: Theory and Algorithms: contains three parts that cover (I) sampling-based methods, such as the reduced basis method and proper orthogonal decomposition, (II) approximation of high-dimensional problems by low-rank tensor techniques, and (III) system-theoretic methods, such as balanced truncation, interpolatory methods, and the Loewner framework is tutorial in nature, giving an accessible introduction to state-of-the-art model reduction and approximation methods; and covers a wide range of methods drawn from typically distinct communities (sampling based, tensor based, system-theoretic). Table of Contents Preface Part I: Sampling-Based Methods Chapter 1: POD for Linear-Quadratic Optimal Control Chapter 2: A Tutorial on RB-Methods Chapter 3: The Theoretical Foundation of Reduced Basis Methods Part II: Tensor-Based Methods Chapter 4: Low-Rank Methods for High-Dimensional Approximation Chapter 5: Model Reduction for High-Dimensional Parametric Problems by Tensor Techniques Part III: System-Theoretic Methods Chapter 6: Model Order Reduction Based on Systems Building Chapter 7: Interpolatory Model Reduction Chapter 8: The Loewner Framework for Model Reduction Chapter 9: Comparison of Methods for PMOR Index.

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Book SynopsisWritten for a wide audience, this is the full story of Hex, inside and out, with all its twists and turns: Hein’s creation, Lindhard’s puzzles, Nash’s proofs, Gale’s Bridg-it, the game of Rex, Shannon’s machines, Bridg-it’s fall, Hex’s resilience, Hex theory, the hunt for winning strategies, and the rise of Hexbots.Trade ReviewClick here to see a review of the book, along with some Hex puzzles set by Oliver Roeder of FiveThirtyEight.“The full story of the game of Hex as told in this ambitious book is in fact two rather distinct stories. On the one hand, there is a deeply human story of how the game of Hex came about and how it has developed over the years; this is a fascinating historical tale full of interesting and often brilliant characters. On the other hand, there is also what is essentially a mathematical story of the game itself; what mathematical theory is involved, what sort of strategies are needed to play the game well, how Hex is similar to or different from games such as chess and Go, and how well computers do playing against expert human Hex players.[. . . ] The story of the birth and early success of Hex has been meticulously researched here and is extremely well told. In particular, the book contains many wonderful old photographs. [. . .] At this point humans still seem to have an advantage over computers on 13 × 13 boards and larger, but as the authors say, ‘The story of Hex continues’” —MathSciNet Mathematical Reviews, American Mathematical Society ". . . this is not a mathematics textbook, and people who are not terribly interested in mathematical proofs and reasoning will still find much of interest here. In addition to discussing some of the mathematics behind the game, for example, the book also addresses at great length the history of Hex [. . .]. In addition to tracing the history of Hex, the authors also include lots of actual puzzles, with solutions, and discuss at length aspects of Hex strategy. Games that are related to Hex, such as Bridg-It and Rex (also known as "reverse Hex"), are also discussed. [. . .] Because of its mathematical content, instructors of courses in subjects like game theory or discrete mathematics might want to flip through it as a potential source of lecture material. People interested in the history of mathematics might find some of the biographical and historical detail here interesting. And of course anybody who enjoys the game of Hex will find much of here interest as well. It’s a fun book." —Mark Hunacek, MAA Reviews“Any well-defined strategy game raises at least two mathematical questions: which player (first or second) wins with best play? and how? Complex games with ad hoc rules (e.g., chess) generally lack symmetry sufficient to fuel mathematical analysis, but many games of elegant simplicity still prove fiendishly hard to crack. Topological principles inspired the creation of Hex by Piet Hein in 1942. Actually a family of games, Hex is played on rhombuses of various sizes paved with hexagonal cells; players alternately take control of cells while aiming to forge a path, however contorted, connecting opposite sides of the rhombus. Famously, while John Nash proved first players win with best play, his non-constructive argument offers no insight into the ideal strategy. Complete computer analysis now handles up to 10 x 10 Hex, but Hein's original 11 x 11 version probably offers complexity sufficient for decades more of vital play. The present volume covers history, variant forms, underlying mathematical ideas, information about exhaustive small-board strategies, and state-of-the-art computer play on full-sized (11 x 11 or 13 x 13) boards. More systematic but less up-to-date, Connections Games by Cameron Browne complements the current volume.” —D. V. Feldman, University of New Hampshire, CHOICE ReviewsClick here to see a review of the book, along with some Hex puzzles set by Oliver Roeder of FiveThirtyEight.". . . this is not a mathematics textbook, and people who are not terribly interested in mathematical proofs and reasoning will still find much of interest here. In addition to discussing some of the mathematics behind the game, for example, the book also addresses at great length the history of Hex[. . .]. In addition to tracing the history of Hex, the authors also include lots of actual puzzles, with solutions, and discuss at length aspects of Hex strategy. Games that are related to Hex, such as Bridg-It and Rex (also known as "reverse Hex"), are also discussed. [. . .] Because of its mathematical content, instructors of courses in subjects like game theory or discrete mathematics might want to flip through it as a potential source of lecture material. People interested in the history of mathematics might find some of the biographical and historical detail here interesting. And of course anybody who enjoys the game of Hex will find much of here interest as well. It’s a fun book."—Mark Hunacek, MAA Reviews“Any well-defined strategy game raises at least two mathematical questions: which player (first or second) wins with best play? and how? Complex games with ad hoc rules (e.g., chess) generally lack symmetry sufficient to fuel mathematical analysis, but many games of elegant simplicity still prove fiendishly hard to crack. Topological principles inspired the creation of Hex by Piet Hein in 1942. Actually a family of games, Hex is played on rhombuses of various sizes paved with hexagonal cells; players alternately take control of cells while aiming to forge a path, however contorted, connecting opposite sides of the rhombus. Famously, while John Nash proved first players win with best play, his non-constructive argument offers no insight into the ideal strategy. Complete computer analysis now handles up to 10 x 10 Hex, but Hein's original 11 x 11 version probably offers complexity sufficient for decades more of vital play. The present volume covers history, variant forms, underlying mathematical ideas, information about exhaustive small-board strategies, and state-of-the-art computer play on full-sized (11 x 11 or 13 x 13) boards. More systematic but less up-to-date, Connections Games by Cameron Browne complements the current volume.”—D. V. Feldman, University of New Hampshire, CHOICE ReviewsTable of Contents1. Birth. 2. Preparing to launch. 3. Polygon in Politiken. 5. The Polygon puzzlist. 6. Rebirth. 7. More games, and machines. 8. Hex goes global. 9 Is Hex easy? 10. Hex theory. 11. Rex theory. 12. The quest for strategies. 13. The rise of the bots. 14. Epilogue, Chronology. Appendices.

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Book SynopsisModel theory is the meta-mathematical study of the concept of mathematical truth. After Afred Tarski coined the term Theory of Models in the early 1950's, it rapidly became one of the central most active branches of mathematical logic. In the last few decades, ideas that originated within model theory have provided powerful tools to solve problems in a variety of areas of classical mathematics, including algebra, combinatorics, geometry, number theory, and Banach space theory and operator theory.The two volumes of Beyond First Order Model Theory present the reader with a fairly comprehensive vista, rich in width and depth, of some of the most active areas of contemporary research in model theory beyond the realm of the classical first-order viewpoint. Each chapter is intended to serve both as an introduction to a current direction in model theory and as a presentation of results that are not available elsewhere. All the articles are written so that they cTable of ContentsI. Real-Valued Structures and Applications. 1. Metastable Convergence and Logical Compactness. 2. Model Theory for Real-Valued Structures. 3. Spectral Gap and Definability. II. Abstract Elementary Classes and Applications. 4. Lf groups, AEC amalgamation, few automorphisms. III. Model Theory and Topology of Spaces of Functions. 5. Cp-Theory for Model Theorists. IV. Constructing Many Models. 6. General Non-Structure Theory. V. Model Theory of Second Order Logic. 7. Model Theory of Second Order Logic.

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Book SynopsisOriginally published in 1995 Time and Logic examines understanding and application of temporal logic, presented in computational terms. The emphasis in the book is on presenting a broad range of approaches to computational applications. The techniques used will also be applicable in many cases to formalisms beyond temporal logic alone, and it is hoped that adaptation to many different logics of program will be facilitated. Throughout, the authors have kept implementation-orientated solutions in mind. The book begins with an introduction to the basic ideas of temporal logic. Successive chapters examine particular aspects of the temporal theoretical computing domain, relating their applications to familiar areas of research, such as stochastic process theory, automata theory, established proof systems, model checking, relational logic and classical predicate logic. This is an essential addition to the library of all theoretical computer scientists. It is an authoritative work wTable of ContentsPreface 1. Temporal Logic of Programs: Standard Approach 2. Effective Temporal Logics of Programs 3. On the Relation of Programs and Computations to Models of Temporal Logic 4. Branching Time and Partial Order in Temporal Logics 5. Temporal Logic in Stochastic Environment 6. Relational Proof Systems for Applied Temporal Logics 7. An Analysis of Structure of Time in the First Order Predicate Calculus Index

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Book SynopsisOriginally published in 1995 Time and Logic examines understanding and application of temporal logic, presented in computational terms. The emphasis in the book is on presenting a broad range of approaches to computational applications. The techniques used will also be applicable in many cases to formalisms beyond temporal logic alone, and it is hoped that adaptation to many different logics of program will be facilitated. Throughout, the authors have kept implementation-orientated solutions in mind. The book begins with an introduction to the basic ideas of temporal logic. Successive chapters examine particular aspects of the temporal theoretical computing domain, relating their applications to familiar areas of research, such as stochastic process theory, automata theory, established proof systems, model checking, relational logic and classical predicate logic. This is an essential addition to the library of all theoretical computer scientists. It is an authoritative work which will meet the needs both of those familiar with the field and newcomers to it. Table of ContentsPreface 1. Temporal Logic of Programs: Standard Approach 2. Effective Temporal Logics of Programs 3. On the Relation of Programs and Computations to Models of Temporal Logic 4. Branching Time and Partial Order in Temporal Logics 5. Temporal Logic in Stochastic Environment 6. Relational Proof Systems for Applied Temporal Logics 7. An Analysis of Structure of Time in the First Order Predicate Calculus Index

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Book SynopsisCryptography, the science of encoding and decoding information, allows people to do online banking, online trading, and make online purchases, without worrying that their personal information is being compromised. The dramatic increase of information transmitted electronically has led to an increased reliance on cryptography. This book discusses the theories and concepts behind modern cryptography and demonstrates how to develop and implement cryptographic algorithms using C++ programming language.Written for programmers and engineers, Practical Cryptography explains how you can use cryptography to maintain the privacy of computer data. It describes dozens of cryptography algorithms, gives practical advice on how to implement them into cryptographic software, and shows how they can be used to solve security problems. Covering the latest developments in practical cryptographic techniques, this book shows you how to build security into your computer applications, networks, and storage. Suitable for undergraduate and postgraduate students in cryptography, network security, and other security-related courses, this book will also help anyone involved in computer and network security who wants to learn the nuts and bolts of practical cryptography.Table of ContentsBasics of Security and Cryptography. Classical Cryptographic Algorithms. Rotor Machine. Block Cipher. Data Encryption Standard. Advanced Encryption Standard. Asymmetric Key Algorithms. The RSA Algorithm. Elliptic Curve Cryptography. Message Digest Algorithm 5. Secure Hash Algorithm. Fundamentals of Identity-Based Cryptography. Symmetric Key Encryption Acceleration on Heterogeneous Many-Core Architectures. Methods and Algorithms for Fast Hashing in Data Streaming.

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Book SynopsisDrawing on the authorsâ use of the Hadamard-related theory in several successful engineering projects, Theory and Applications of Higher-Dimensional Hadamard Matrices, Second Edition explores the applications and dimensions of Hadamard matrices. This edition contains a new section on the applications of higher-dimensional Hadamard matrices to the areas of telecommunications and information security.The first part of the book presents fast algorithms, updated constructions, existence results, and generalized forms for Walsh and Hadamard matrices. The second section smoothly transitions from two-dimensional cases to three-, four-, and six-dimensional Walsh and Hadamard matrices and transforms. In the third part, the authors discuss how the n-dimensional Hadamard matrices of order 2 are applied to feed-forward networking, stream ciphers, bent functions, and error correcting codes. They also cover the Boolean approach of Hadamard matrices. The final part provides examples of applications of Hadamard-related ideas to the design and analysis of one-dimensional sequences and two-dimensional arrays.The theory and ideas of Hadamard matrices can be used in many areas of communications and information security. Through the research problems found in this book, readers can further explore the fascinating issues and applications of the theory of higher-dimensional Hadamard matrices.Table of Contents2-Dimensional Cases. Lower-Dimensional Cases. General Higher-Dimensional Cases. Applications to Signal Design and Analysis. Index.

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Book SynopsisAlgorithms and Theory of Computation Handbook, Second Edition: Special Topics and Techniques provides an up-to-date compendium of fundamental computer science topics and techniques. It also illustrates how the topics and techniques come together to deliver efficient solutions to important practical problems.Along with updating and revising many of the existing chapters, this second edition contains more than 15 new chapters. This edition now covers self-stabilizing and pricing algorithms as well as the theories of privacy and anonymity, databases, computational games, and communication networks. It also discusses computational topology, natural language processing, and grid computing and explores applications in intensity-modulated radiation therapy, voting, DNA research, systems biology, and financial derivatives.This best-selling handbook continues to help computer professionals and engineers findTable of ContentsPreface, Editors, Contributors, 1 Computational Geometry I, 2 Computational Geometry II, 3 Computational Topology, 4 Robot Algorithms, 5 Vision and Image Processing Algorithms, 6 Graph Drawing Algorithms, 7 Algorithmics in Intensity-Modulated Radiation Therapy, 8 VLSI Layout Algorithms, 9 Cryptographic Foundations, 10 Encryption Schemes, 11 Cryptanalysis, 12 Crypto Topics and Applications I, 13 Crypto Topics and Applications II, 14 Secure Multiparty Computation, 15 Voting Schemes, 16 Auction Protocols, 17 Pseudorandom Sequences and Stream Ciphers, 18 Theory of Privacy and Anonymity, 19 Database Theory: Query Languages, 20 Scheduling Algorithms, 21 Computational Game Theory: An Introduction, 22 Artificial Intelligence Search Algorithms, 23 Algorithmic Aspects of Natural Language Processing, 24 Algorithmic Techniques for Regular Networks of Processors, 25 Parallel Algorithms, 26 Self-Stabilizing Algorithms, 27 Theory of Communication Networks, 28 Network Algorithmics, 29 Algorithmic Issues in Grid Computing, 30 Uncheatable Grid Computing, 31 DNA Computing: A Research Snapshot, 32 Computational Systems Biology, 33 Pricing Algorithms for Financial Derivatives, Index

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Book SynopsisA How-to Guide for Implementing Algorithms and ProtocolsAddressing real-world implementation issues, Understanding and Applying Cryptography and Data Security emphasizes cryptographic algorithm and protocol implementation in hardware, software, and embedded systems. Derived from the authorâs teaching notes and research publications, the text is designed for electrical engineering and computer science courses.Provides the Foundation for Constructing Cryptographic ProtocolsThe first several chapters present various types of symmetric-key cryptographic algorithms. These chapters examine basic substitution ciphers, cryptanalysis, the Data Encryption Standard (DES), and the Advanced Encryption Standard (AES). Subsequent chapters on public-key cryptographic algorithms cover the underlying mathematics behind the computation of inverses, the use of fast exponentiation techniques, tradeoffs between public- and symmetric-key algorithms, and the minimum key lengths necessary to maintain acceptable levels of security. The final chapters present the components needed for the creation of cryptographic protocols and investigate different security services and their impact on the construction of cryptographic protocols.Offers Implementation Comparisons By examining tradeoffs between code size, hardware logic resource requirements, memory usage, speed and throughput, power consumption, and more, this textbook provides students with a feel for what they may encounter in actual job situations.A solutions manual is available to qualified instructors with course adoptions.Trade ReviewThis book is a good technical reference for someone who wishes to implement (or install) a security system based on existing techniques … a good complementary book for a technical course to students who already know about the theory of cryptography but need to learn the technical details in order to implement existing protocols in new hardware.—Jeremy Barbay, University of Chile, in SIGACT NEWS, December 2011This book is a good technical reference for someone who wishes to implement (or install) a security system based on existing techniques … a good complementary book for a technical course to students who already know about the theory of cryptography but need to learn the technical details in order to implement existing protocols in new hardware.—Jeremy Barbay, University of Chile, in SIGACT NEWS, December 2011Table of ContentsIntroduction. Symmetric-Key Cryptography. Symmetric-Key Cryptography: Substitution Ciphers. Symmetric-Key Cryptography: Stream Ciphers. Symmetric-Key Cryptography: Block Ciphers. Public-Key Cryptography. Public-Key Cryptography: RSA. Public-Key Cryptography: Discrete Logarithms. Public-Key Cryptography: Elliptic Curves. Cryptographic Components. Cryptographic Protocols. References. Index.

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Book SynopsisThe Most Progressive and Complete Guide to DDO-Based Ciphers Developers have long recognized that ciphers based on Permutation Networks (PNs) and Controlled Substitution-Permutation Networks (CSPNs) allow for the implementation of a variety of Data Driven Operations (DDOs). These DDOs can provide fast encryption without incurring excessive hardware costs in modern telecommunication networks. However, until now, with a few exceptions, most DDO-based ciphers have been poorly represented in available literature and have continued to remain known to only a small number of encryption experts. In Data-Driven Block Ciphers for Fast Telecommunication Systems, Nikolai Moldovyan and Alexander Moldovyan, major innovators and holders of several dozen international patents in encryption technology, provide the background and detail the applications needed to investigate new properties of PNs especially relevant to the improvement of modern wireless systems.Furthermore, they propoTable of ContentsConventional Block Cipher Designs. Data-Driven Permutations. Controlled Substitution-Permutation Networks. General Designs of Data-Driven Ciphers. Block Ciphers Based on Data-Dependent Operations.

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Book SynopsisAll current methods of secure communication such as public-key cryptography can eventually be broken by faster computing. At the interface of physics and computer science lies a powerful solution for secure communications: quantum cryptography. Because eavesdropping changes the physical nature of the information, users in a quantum exchange can easily detect eavesdroppers. This allows for totally secure random key distribution, a central requirement for use of the one-time pad. Since the one-time pad is theoretically proven to be undecipherable, quantum cryptography is the key to perfect secrecy. Quantum Communications and Cryptography is the first comprehensive review of the past, present, and potential developments in this dynamic field. Leading expert contributors from around the world discuss the scientific foundations, experimental and theoretical developments, and cutting-edge technical and engineering advances in quantum communications and cryptography. The book deTable of ContentsQuantum Cryptography. Quantum Communications with Optical Fibers. Advanced Quantum Communications Experiments with Entangled Photons. The DARPA Quantum Network. Experimental Cryptography Using Continuous Polarization States. Quantum Logic Using Linear Optics. Practical Quantum Cryptography: Secrecy Capacity and Privacy Amplification. Quantum State Sharing. Free-Space Quantum Cryptography. Noise-Immune Quantum Key Distribution. Index.

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Book SynopsisFrom the Rosetta Stone to public-key cryptography, the art and science of cryptology has been used to unlock the vivid history of ancient cultures, to turn the tide of warfare, and to thwart potential hackers from attacking computer systems. Codes: The Guide to Secrecy from Ancient to Modern Times explores the depth and breadth of the field, remaining accessible to the uninitiated while retaining enough rigor for the seasoned cryptologist.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 authTable of ContentsFrom the Riddles of Ancient Egypt to Cryptography in the Renaissance-3,500 Years in the Making. From Sixteenth-Century Cryptography to the New Millennium-The Last 500 Years. Symmetric-Key Cryptography. Public-Key Cryptography. Cryptographic Protocols. Key Management. Message Authentication. Electronic Mail and Internet Security. Applications and the Future. Non-Cryptographic Security Issues. Information Theory and Coding. Appendix A: Mathematical Facts. Appendix B: Pseudo-Random Number Generation. Appendix C: Factoring Large Integers. Appendix D: Technical and Advanced Details. Appendix E: Probability Theory. Appendix F: Recognizing Primes. Appendix G: Exercises. Bibliography. List of Symbols. Index.

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Book SynopsisThe huge number and broad range of the existing and potential applications of fuzzy logic have precipitated a veritable avalanche of books published on the subject. Most, however, focus on particular areas of application. Many do no more than scratch the surface of the theory that holds the power and promise of fuzzy logic.Fuzzy Automata and Languages: Theory and Applications offers the first in-depth treatment of the theory and mathematics of fuzzy automata and fuzzy languages. After introducing background material, the authors study max-min machines and max-product machines, developing their respective algebras and exploring properties such as equivalences, homomorphisms, irreducibility, and minimality. The focus then turns to fuzzy context-free grammars and languages, with special attention to trees, fuzzy dendrolanguage generating systems, and normal forms. A treatment of algebraic fuzzy automata theory follows, along with additional results on fuzzy languages, minimizationTable of ContentsIntroduction. Max-Min Automata. Fuzzy Machines, Languages, and Grammars. Fuzzy Languages and Grammars. Probabilistic Automata and Grammars. Algebraic Fuzzy Automata Theory. More on Fuzzy Languages. Minimization of Fuzzy Automata. L-Fuzzy Automata, Grammars, and Languages. Applications. References. Index. List of symbols.

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Book SynopsisFor propositional logic it can be decided whether a formula has a deduction from a finite set of other formulaas. This volume begins with a method to decide this for the quantified formulas of those fragments of arithmetic which express the properties of order-plus-successor and of order-plus-addition (Pressburger arithmetic). It makes use of an algorithm eliminating quantifiers which, in turn, is also applied to obtain consistency proofs for these fragments.Table of Contents1. Consistency, Decidability, Completeness for the Arithmetic of Order with Successor 2. Consistency, Decidability, Completeness for the Arithmetic of Addition and Order 3. Antinomies, Pseudomenos, and Their Analysis 4. Undefinability and Incompleteness, General Theory 5.Elementary and Primitive Recursive Functions 6. Recursive Relations and Recursive Functions 7. The Arithmitization of Syntax 8. Consequences of Arithmetization 9. Axioms for Arithmetic 10. Peano Arithmetic PA and Its Expansion PR 11. Unprovability of Consistency

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Book SynopsisThis volume is a combinatorial study of derivations and deductions. The author''s approach is syntactical and builds from Gentzen''s basic ideas into logical rules and a calculus of deductive situations. The book concludes with the algorithms producing the results of Gentzen''s midsequent theorem and Herbrand''s theorem for prenex formulas.In this volume, logic starts from the observation that in everyday arguments, as brought forward by say a lawyer, statements are transformed linguistically, connecting them in formal ways irrespective of their contents. Understanding such arguments as deductive situations, or sequents in the technical terminology, the transformations between them can be expressed as logical rules. The book concludes with the algorithms producing the results of Gentzen''s midsequent theorem and Herbrand''s theorem for prenex formulas.Table of Contents1. Sequent Calculi for Positive Logic 2. Cuts 3. Continuous Cut Elimination 4. Sequent Calculis for Minimal and Intuitionistic Logic 5. Classes of Algebras Associated to a Calculus 6. Calculii of Formulas 7. Sequent Calculii for Quantifier Logic 8. Semantical Consequence Operations and Modus Ponens Calculi 9. Selected Topics in Sequential Quantifier Logic

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Book SynopsisThe first thing you will find out about this book is that it is fun to read. It is meant for the browser, as well as for the student and for the specialist wanting to know about the area. The footnotes give an historical background to the text, in addition to providing deeper applications of the concept that is being cited. This allows the browser to look more deeply into the history or to pursue a given sideline. Those who are only marginally interested in the area will be able to read the text, pick up information easily, and be entertained at the same time by the historical and philosophical digressions. It is rich in structure and motivation in its concentration upon quadratic orders.This is not a book that is primarily about tables, although there are 80 pages of appendices that contain extensive tabular material (class numbers of real and complex quadratic fields up to 104; class group structures; fundamental units of real quadratic fields; and more!). This book is primarTable of ContentsList of Symbols Preface Introduction Background from Algebraic Number Theory Quadratic Fields: Integers and Units The Arithmetic of Ideals in Quadratic Fields The Class Group and Class Number Reduced Ideals Quadratic Orders Powerful Numbers: An Application of Real Quadratics Continued Fractions Applied to Quadratic Fields Continued Fractions and Real Quadratics: The Infrastructure The Continued Fraction Analogue for Complex Quadratics Diophantine Equations and Class Numbers Class Numbers and Complex Quadratics Real Quadratics and Diophantine Equations Reduced Ideals and Diophantine Equations Class Numbers and Real Quadratics Halfway to a Solution Prime-Producing Polynomials Complex Prime-Producers Real Prime-Producers Density of Primes Class Numbers: Criteria and Bounds Factoring Rabinowitsch Class Number One Criteria Class Number Bounds via the Divisor Function The GRH: Relevance of the Riemann Hypothesis Ambiguous Ideals Ambiguous Cycles in Real Orders: The Palindromic Index Exponent Two Influence of the Infrastructure Quadratic Residue Covers Consecutive Powers Algorithms Computation of the Class Number of a Real Quadratic Field Cryptology Implications of Computational Mathematics for the Philosophy of Mathematics Appendix A: Tables Table A1: This is a list of all positive fundamental radicands with class number h? = 1 and period length l , of the simple continued fraction expansion of the principal class, less then 24. Table A8 is known to be unconditionally complete whereas Table A1 is complete with one GRH-ruled out exception, as are Tables A2-A4, A6-A7 and A9 Table A2: This is a subset of Table A1 with D ? 1 (mod 8) Table A3: h? = 2 for fundamental radicands D > 0 with l ? 24 Table A4: This is a list of all fundamental radicands of ERD-type with class groups of exponent 2, broken down into three parts depending on congruence modulo 4 of the radicand Table A5: This three-part table is an illustration of a computer run done for the proof of Theorem 6.2.2

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